The visitation on the knoll

It was the time Somakhya and Indrasena were by themselves — without their companions — for that is close to the ultimate test of a man. At that point, they were working on the mysterious three-gene system coding for an ATPase that had evolved from a GTPase, a mystery protein, and a RNase. While they had made an initial incision they were being rebuffed by it and it was testing Indrasena’s skills to the utmost. To clear their minds, they decided to go out for a walk in the solitude among the knolls. Just before Indrasena could join Somakhya, he got a call regarding an emergency in the lab and he had to head there to inspect the situation. Somakhya nevertheless decided to continue alone for, after all, the final reckoning of a man comes when he is all by himself. Thus, he walked the gently rising paths against the backdrop of the mild spring sun — the benign symbol in the intermediate heavens of the great god Savitṛ whose laws none violate. The following incantation came to his mind: “adābhyo bhuvanāni pracākaśad vratāni devaḥ savitābhi rakṣate ।”

As Somakhya wandered on, the signs of various gods made themselves apparent in the world of the mortals: the sun was that of Savitṛ, the conifers towering above the path were those of Soma, the king of the Vs, and the blue sky was that of Mitra and Varuṇa. In his breath he sensed Agni who runs the body. As the sunbeams fell on him through the leafy holes, he was profoundly impacted by how much of the sensed world was run by the Marut-s. Then a red twin-winged seed glided up to him bringing to mind the Aśvin-s, whom some of his ancestors also saw as Bhavā-Śarvau. Suddenly, he saw a great hawk, a sign of Suparṇo Garutmant: coursing through the welkin it passed out of sight against the backdrop of a distant mountain looming on the horizon. That brought to mind the mighty Indra, who in the days of yore had made those rocks find their resting place. As he passed a little stream, burbling as though uttering the triple vyāhṛti-s, he saw the sign of Sarasvatī. Recognizing her, he looked down at the path which he was walking on and obtained the sign of Pūṣan. This made him glance at the time and he sensed Viṣṇu who tramples all under his stride. Thus, wending his way, he passed a cluster of well-kept houses, built on the high, of carefree dhanin-s, who had been endowed by the roll of the dice of the King of the Guhyaka-s: in them, he saw the sign of King Aryaman. A little beyond those houses at the boundary of a wooded plot was a cemetery with a few tumbled-down gravestones signaling the presence of King Yama and Rudra. He silently uttered the incantation “namas te rudra manyava uto ta iṣave namaḥ । namas te astu dhanvane bāhubhyām uta te namaḥ ॥”. Reflecting on his recognition of the gods, he said to himself: “I see the sambandha-s just as our ārya ancestors or the sunthemata as the yavana-s would have called them.”

As Somakhya entered the slender path into the woods lined with towering trees the signs of the gods made him think of the manifold mantra-s he had studied. Suddenly, a doubt crossed his mind: “Do I really have any true mastery of them?” His mind drifted to the various hair-raising campaigns in his life where they had helped him cross over to victory from the jaws of defeat and premature death. He told himself that he must have had at least some minor mastery. But he was also suddenly reminded that above all stood the arch of fate that charted the arc of a man — only a Mārkaṇḍeya could defy that. Then he thought of those who did little, but victory came to them like women running headlong towards a mahāliṅgavant. Then there were those who strove a lot, yet nothing but ills came to them like scammers zeroing in on a naive man. But most lay in the middle — much like the hump of the normal distribution. “The distribution of fate is governed by the Central Limit Theorem”, he remarked to himself. “So, in the balance of things, we perhaps lie in the middle. So we get more of one thing, and others get more of another.”

He turned around to see if someone was behind him and through the tangle of the woods he saw a single headstone from the cemetery in the distance. This made his mind wander to his old friend Vidrum, with whom he was entirely out of touch for a few years now. He mused: “I wonder if Vidrum is still seeing ghosts… He had some special facility for that. Indeed, that served us well to interact with the strange realm that few can perceive. Many of us simply have a less activatable right amygdala and hippocampus — very likely for a good reason. For us, that was probably a good thing overall — we were mostly shielded from the entities activating Vidrum’s brain.” Thinking about Vidrum suddenly brought the urge of phantom communication to Somakhya’s mind. He and Indrasena had not tried one in more than an year. But now he almost felt as if someone wished to establish such a channel. If Indrasena was around they could have tried the planchette, but even that worked best when there are at least three. However, being alone, as a final resort, Somakhya decided to open his own mind via a mantra. On reaching the summit of a knoll, he picked up a stick and drew a circular maṇḍala with eight petals in the sand. In the stark quietness of the spring day he invoked a Rudra of the northern face with the incantation: “huṃ sarvabhūtadamanāya namo rudrasyāṅkuśena bhūtān ākarṣaya ākarṣaya maṇḍale madhye ānaya ānaya bhāṣaya bhāṣaya huṃ phaṭ svāhā ।” Thereafter, he closed his eyes and performed a focused japa on the bhūta-darśana-mantra: “OṂ sarvabhūtadamanāya namo .anāthāya namaḥ ।” This form of the mantra combined with an epithet of the Vāma-srotas simultaneously allowed “pauṣṭika” summoning while maintaining control.

He had performed the japa of this mantra many times and for brief instances, he would feel that channel open and sense some strange and mysterious things but it would immediately close. This time as he began deploying it he felt different: He wondered if it might be due to a genius of locus — a guhyaka of Rājādhirāja — or his japa nearing the appropriate count. After a while, this sensation was overtaken by a bad odor of burning paper mixed with dried leaves and then he heard a bout of racking cough. Fearing that a substance abuser might be approaching him he opened his eyes but saw no one. Instead, he felt a woman approaching him though he saw none. He wondered if the mantra had finally borne fruit after all the japa he had been doing. Before he could process that thought, she seemed to speak to him through a mysterious channel the mantra had opened. He heard her go through a spasm of coughing again and finally remark: “Please excuse my lungs, sir. I should have paid attention to ol’ King James admonitions regarding these abominable botanicals I took so much pleasure in. No doubt it put me under the ground sooner than it should have been. I never believed there were ghosts in life but here I’m coming to you as one.”

Somakhya at first thought it was the same mleccha woman who had visited Lootika several times in her private planchette sessions for somehow he felt it impinge on his mind that she was of Celtic ancestry. However, the accent of this phantom sounded as though from the British and Hibernian isles rather than Brittany — he distinctly remembered his old friend, with whom he had lost touch, telling him that her interlocutor was from the French lands. Somakhya confronted the phantom: “who are you, ma’am? Perchance are you Miss CHM?” The phantom’s response was punctuated by coughs: “You know me but don’t recognize me. Miss CHM was my young friend but I’m not her. I’m RFE.” Somakhya: “That’s rather remarkable. I have known RFE to only be a name — I found it rather striking that practically nothing beyond the name remained of someone who must have been a person of profound capacity in life.” The ghost: “I sensed that you were one of the few who have studied and esteemed my glorious acts in life — they speak for themselves — hence, I have come to not regret my story being lost. Nevertheless, as this channel mysteriously opened I decided to visit you for a chat.” Somakhya: “Ma’am, may Śambhu and his gaṇā-s make you comfortable and pray tell me your tale.”

The ghost: “See, since my passage into phantomhood, my narratives have become a bit disarrayed, so please bear with that. My passage into the realm of Hades, which you folks would call the abode of the fathers, lorded by Yama, was sudden — evidently, in an untimely fashion from the botanical stimulants that I loved so much in life and smoked excessively. My poor heart came apart when I was supervising a study of African manatees. I had taught my two sons that ghosts were mere figments of the human mind with no objective reality. Hence, as a ghost I never got my sons or husband to perceive me despite the obvious signals I sent them. After trying for a couple of years I settled down to inhabit a singing automaton doll that I had possessed as a child. My residence within it was a strange state of suspended meditation that I cannot render in objective words. Eventually, my granddaughter received that doll and I decided to reveal myself to her. She was way more perceptive but my son, due to the weight of my training in life, quickly squelched her statements regarding her interactions with me. I lapsed back into that meditative suspension but was suddenly woken up as I found myself with the doll in an oppressive little cardboard box containing other miscellanea. The contents of this box were sold by my son in a yard sale and I found myself in an alien home. Those people seemed to be very perceptive for some reason and sensed my presence immediately, even though I did not do anything beyond making the automaton go off on its own.

Evidently frightened by my presence, they sold me off to a pair of rowdy youths claiming to be “ghost busters”. There was something uncouth about them that came into my field even as they retrieved the package with the automaton. Hence, I set off the automaton. Alarmed by its singing and dancing, they were convinced that I was a demon. Full of bravado, they brought a hammer and smashed the automaton to smithereens. Little did they realize that their action did nothing beyond working me up into a frenzy that I never really exhibited in life. While I had been a good mother to my sons, these pesky youths somehow brought a very unmotherly anger in me. I possessed them in succession and transferred that experience of my pulmonary disease to them. Both of them are suffering from a strange, incurable fatigue syndrome following a respiratory infection. However, their smashing the doll had in a sense set me free. I saw that my husband was reaching the end of his existence and was constantly talking about me. Hence, I showed myself to him several times. Receiving no signs that he had perceived me, I went to take residence at the natural history museum where I had always been most at home. Sometimes, my sons and grandchildren enter my field, making me wonder if I have punished those youths too harshly, but then the sprites are there to mete out such penalties to the ill-mannered. Now drawn to the channel you have created I have arrived here.”

S: “That is most singular, ma’am. Pray tell me a little about when you came to perform your heroic deeds pertaining to the origin of the archosaurs?”
The sprite coughed for a while and continued: “Ah, young sir, as you bring that up a wave of nostalgia washes over me. If you would permit, I have a long tale to tell. When I was a kid, I was educated with the Christians but was cured of that delusion when I came upon Darwin. The wisdom of the Origin of Species remained my guide since then. When I was 14, I became interested in bringing genetics to evolution — in my days we didn’t have the luxury of DNA that you do! Hence, after a couple of years of working on the genetics of pigeon behavior and publishing my first work at the age of 16, I drifted towards that wellspring of all evolutionary studies, paleontology. During my work with pigeons, I acquired some familiarity with the anatomy of birds. This brought me to study the comparative morphogenesis of birds and crocodiles. I was struck by how remarkably close the archosaurs were despite their superficial difference in form. To better understand this I realized I had to plow through the fossil record of the earliest archosaurs. Thus, in my 18th year, I left home for South Africa, which was then a flourishing nation, to study some of the pristine fossils of stem archosaurs as well as live ones of both the avian and crocodilian varieties. Over the next five years, I worked on my first magnum opus on stem archosaurs that you so kindly referred to. In it, I described things that have taken other researchers almost 40-50 years to catch up. As an aside, I became a Doctor of science as a result of these efforts.”

Somakhya: “I was so struck to see that in your work were insights that I thought we had learnt only in the past decade! Indeed, it is remarkable that others did not realize its significance then. But then I interrupted you; pray continue.”
The ghost: “It was during my investigation of the remarkable stem archosaur Erythrosuchus, that I journeyed to Soviet Russia and India to study their stem archosaur fauna. While in India I discovered fragmentary erythrosuchid fossils that were forgotten in storage until recently. Unfortunately, while in India, I acquired an inordinate fondness for bīḍī-s that probably harmed my constitution more than my pipe. In fact, I studied the texts of your people on this matter and wrote a paper on recreational and para-medical smoking in ancient India. Back in South Africa, during my several fossil-hunting field trips in the Karroos, not unexpectedly, I became interested in the contemporaries of the stem archosaurs, the stem mammals, and their earlier Permian predecessors. By then I was married, acquired the name by which you know me, and had also become a university lecturer after adding a second PhD to my name, all while burning through stashes of Indian cigarillos. I spent the next few years furthering my genes and putting the archosaur chapter behind me. In retrospect, I’m thankful my offspring were born uninjured by my substance abuse whose effects on my otherwise adamantine body were beginning to show up. But I guess I had good genes; hence, I could push on for a while with my usual vigor shrugging them off. I now moved to study the recently described Russian stem mammal Biarmosuchus and rummaged through the South African record to find related animals. I began to suspect that some South African stem mammals, like Hipposaurus, which had been described as gorgonopsians, were actually closer to Biarmosuchus and among the earliest of the therapsid stem mammals.”
Somakhya: “The recent consensus supports your contention. The biarmosuchians were indeed a large and probably the most basal major radiation of the therapsids.”

The ghost: “I’m pleased to hear that. You know, it is really difficult to keep up with such matters, for some phantoms. In any case, I was intrigued by the fact that the carnivorous therapsids, perhaps building on an incipient feature of the so-called pelycosaurs, were so consistently saber-toothed. I wondered how the mechanics of the sabertooth might operate in predation. There are no genuine modern saber-tooths barring the mysterious clouded leopard. Hence, I needed a model closer to home to study this and began scouting for fossil cats where this feature reappeared. In the process, our prospecting team discovered two large fossil saber-toothed cats in South Africa that might have preyed on early members of the human lineage. Describing the anatomy and evolution of these saber-toothed cats became my next magnum opus. Unsurprisingly, it led me to a more general study of the mammalian clade of Carnivora addressing both modern and extinct forms, like the creodonts, and the relationship of enigmatic ancient saber-tooths like the nimravids to the cats. One afternoon while working on that monograph, I was at the museum performing a neurological dissection of a pangolin when it dawned on me that they were related to carnivorans. I consider this one of my high points, not far from the insights gained during my archosaur days. Moving on from carnivorans, I followed this up with a comprehensive study of fossil pigs from Africa and Asia. With my sons growing up, my husband and I moved to West Africa, as itinerant professors in multiple universities in the new nations that recently became independent of our rule. I sort of circled back to my earliest days and performed a major study of various aspects of rodent biology and social behavior. I quickly built on that with a more general study of mammalian sociobiology. It was in course of expanding those studies that I expired.”

S: “I’m sorry to hear that.”
The ghost: “What is there to be sorry for something that is in accordance with natural law and transpired so long ago? What I regret more are some foolish ideas from environmentalists that I eagerly swallowed, more out of emotion than any kind of analysis. For many the final suffering can be a long one. For me, it was not that long, but my last few years were a grind as the harm from the botanicals was wearing me down. It almost seemed to carry through to ghosthood as though I had not completed some allotted quota of suffering. But after this passage through the channel you created, it seems to be lifting. If that relief were to persist on my departure from this meeting with you, I’d happily hang around the great museum halls among the skeletons.”
S: “That is not for me to decide. Hopefully, the gods rule favorably in your regard. As a respected elder, would you have anything else to say before you find your way to the museum of your choice?”
The ghost: “Every man is born endowed with something like a battery. One could say that the amount of charge it holds, the capacity to recharge it, the speed with which you can recharge it, and the number of times it can be recharged are in large measure contingent on genetics. Eventually, your life-battery loses its capacity to be recharged and you reach your final terminus. But some other things impinge on your life-battery, which may or may not be contingent on your genetics. In my case, the early love for the abuse of botanicals caused my otherwise splendid battery to be limited in its recharge after a certain age. I might have probably died even earlier from overuse but my husband’s presence and concern to be there for my kids stabilized me to a degree. But others might not be born with my kind of battery and could burn out quickly. My defect was also mitigated by the fact that I had access to the men of highest intellect and caliber — this constantly kept me on my toes exploring new ideas and studies. These came to me as an uninterrupted stream of scientific visitors who would hear out my latest explorations and incisively comment on them. Imagine a person with a wonderful battery and mental capacity but living in isolation where all his reading material is of pre-Darwinian vintage. Imagine him with no visitors or interlocutors who engage him intellectually. His big battery would be of no avail.

Before I leave I must ask you something. I know that your people hold the peculiar belief that one transitions from this state of phantomhood back into the experience of a living body. Would that happen to me or is this existence as a sprite my final destination?”
S: “You might remain as a phantom for a long time or you might sort of lose individuality and blur into the general mass of subjects of King Yama, what our tradition calls a pitṛ. Maybe some of those pitṛ-s peel off and reexperience life down the line. I’m not sure of that part.”
The ghost: “If that were to happen, I hope I return to be just like that girl you knew from school.”
For a moment Somakhya felt he saw an image of the ghost as she might have appeared in life register in his visual cortex. As there was no available photo of hers in the public domain, he could not be sure if it was that or his imagination. The famed words “na tasya pratimā asti yasya nāma mahadyaśaḥ ।” came to his mind. Even as he was processing that, the channel opened by the power of Śiva had closed. He knew she had referred to Lootika while parting. With a mixture of sorrow at her abhāva, and wonder at the encounter with the venerable phantom woman, Somakhya ambled down the knoll to find his way back to work.

The crossover with Dabba Seṭṭhīputta

It was a Śivarātrī. Vidrum accompanied his friends Somakhya and Lootika to visit the small shrine of Rudra in the cemetery beside his house. It was one of the rare days when the normally deserted cemetery was fairly busy with many a votary streaming in to pay homage at the shrine. Vidrum milled around a bit as his friends performed some japa at the side of the circumambulatory circuit of the shrine. There were vendors of flowers and bilva leaves whose wares the votaries bought to offer to The god (sa devaḥ). A pleasant breeze blew through the cemetery, making howling noises reminiscent of ghosts and also reminding the cognizant votary of the presence of the The god of the Vrātya-s who “blows here”. As if to bring back that picture from a bygone Aryan age, a tall śaiva ascetic suddenly strode into the shrine. He carried a trident, a large pair of iron tongs slung from his shoulder, and was beating a ḍamaru as he cycled through the recitation of the pañcabrahma-mantra-s. He sat down at one corner and started singing a stotra attributed to the demon-king of Laṅkā. Seeing him, Vidrum came back and sat beside his friends. The śaiva ascetic then arose again and started making circumambulations, resuming the muttering of brahma-mantra-s. As reached the Bahurūpī-ṛk, the ascetic suddenly darted towards Somakhya and smeared ashes on his forehead. As he continued with his circumambulation, at one point, when he was reciting the Vāmadeva-ṛk, he did the same to Lootika. He then went inside the garbhagṛha and started muttering some mantra-s. While he was uttering them in a low tone that the lay devotees would make no sense of, Lootika realized what he was uttering and caught Somakhya’s eye. Somakhya, too, had simultaneously figured out his incantation and whispered to Lootika: “I’m surprised — it is the Mahākāla-hṛdaya, a rare mantra from the root of Śambhu-para Uttarāmnāya, known to very few!” L: “Indeed!”

After having finished his japa of the mantra, he sounded his ḍamaru severally and marched out of the shrine. On his way out, he smeared some ash on Vidrum’s forehead, uttering the incantation “dyaur-mahī kāla āhitā ।”. All three were pretty startled by what had just happened. Lootika: “He must be a mantravādin of some note because he possesses this rare Vidyā named the Mahākāla-hṛdaya.” V: “I guess it is a good thing he smeared vibhūti on us?” S: “I’m puzzled as to why he singled us out — also, there is some significance to the mantra-s he was muttering when he smeared it on Lootika and me.” V: “What about the one he uttered for me?” S and L: “It was very puzzling indeed. We have no clue as to why he uttered those words though we know its source.” They then went their own ways as both Somakhya and Lootika had a whole night’s worth of rites ahead of them.

The next day, Somakhya and Lootika woke up to Vidrum summoning them to his house to hear something “big.” Once his friends were home, he led them to his terrace and wasted no time in telling them a most unusual tale. Both his friends remarked even before he started that they were sensing something unusual about his mien and demeanor — as though he was possessed by some unseen energy. V: “As expected last night, my father kept the Śiva vigil for 5 muhūrta-s. Successively, in each muhūrta he performed the japa of the mantra-s: OṂ namaḥ śivāya, OṂ namaḥ śambhave, OṂ īśānāya namaḥ, OṂ sāmbasadāśivāya namaḥ, OṂ sadāśivāya namaḥ. I kept him company for the first muhūrta and a half or so and then went up the terrace to spend some time in the cool air doing some reading for the entrance exams. Before I switched on the lamp above the charpoy on the terrace, I gazed out at the cemetery as I heard a chorus of howls from dogs — all singing like dingoes down under. I saw a glow in the cemetery and thought the temple was still receiving devotees. Nay, to my surprise, I saw something like a Holāka fire lit in the courtyard of the shrine and a troupe with cymbals dancing around it to the accompaniment of the dogs’ howls. Looking closer, I had the shock of my life! They were no dancers but skeletons — no flesh and clothing — just bones. For a couple of minutes, I watched that dance of the specters transfixed where I stood. While the view is clear, as you all can see right now, I still could not believe my eyes and decided to get my phone to get a zoomed-in shot. By the time I returned, it was all quiet, and not even the insects could be heard singing on the cool spring night. Aghast, I went right here to the terrace wall and peered out, unable to believe my eyes. Just then, I saw a man walk towards the gate of my house. In the streetlamp, I caught a clear glimpse of his face. He seemed a bit unkempt and gave the vibe of a street wastrel or even a beggar ambling with a somewhat tipsy gait. He held a trashcan, making me think he might be a trash serviceman who had gotten a bit high on bhaṅga. To my horror he opened the gate of our house and came in and dumped the trashcan. I was about to run down to alert my family and maybe shoo him away after taking up my stick and billhook. But right then, his motion suddenly changed, and with unexpected swiftness, he darted out of our premises down toward the graveyard.

I shone the flashlight from my phone to take a closer look at the trashcan he had dumped. In the circle of light, it assumed a very different appearance — a large bag with smaller bags neatly arranged in it. Even as I again sought to go down to alert my folks and take a look at it, I was utterly stunned by him reappearing beside the bag. Now, in the illumination of my flashlight, he appeared very different. He looked like a nicely dressed man from old India — like one of those illustrations from our history textbook — something Lootika used to wax eloquent about in class. Just as I was trying to process the elaborate ruse someone was playing on us, I saw the man pick up his bag and walk right towards our house door. The next moment, I lost all touch with my identity and even time. My identity was now that of the man whom I had just seen. The time was very old India — you guys can tell me when. The place I learnt was not even India proper but the island of Laṅkā. In my new identity, I knew my name to be Dabba Seṭṭhīputta of Ajjunapabbata. I had the same bag beside me, and it had somewhere between 380-400 gemstones, each in its own pouch in it. I was in a large establishment devoted to the Śākya Buddha known as Sakkavihāra. Within me was a deep sense of frustration coming from a sense of being cheated of my efforts. I had prayed to the monumental icon of the Sākya Buddha, but it made utterly no difference to my dejection — I was beginning to have doubts about ever attaining the calm that characterized the Śākya Muni. I started making a circumambulation around the dhāgabha of the shrine and reached the eastern quarter. There, I saw a large painting of Indra. This sight riveted me, and I paused. As if guided by some unknown force, I stood below the painting of the deva.

As I did so, I started seeing something like a vision of the past — I suddenly felt my life flash before me. I, Dabba, was born in a middling V family — my father was successful as a vaṇij but by no means a mahāvardhamāna. I showed an early aptitude — maybe right from when I was 3 years old — for ratna-s and lohadhātu-s. In school, I was good at the arthaśāstra, and one of my ācarya-s sighted my aptitude and encouraged me to study it more deeply. He taught me the Indra Vaṇijmān mantra-s. The moment I received the sūkta, I felt something special within me, and my mental prowess appeared to expand. I read numerous grantha-s on ratna- and loha- parīkṣa and visited as many mines, furnaces, kilns, and distilleries as I could and acquired an unmatched knowledge of the subject. My father sent me to apprentice with Nagaraseṭṭhīya, a loha-vaṇij. It was then that I met the great V śaivācarya, Mahākala-gaṇa who started teaching me the mantraśāstra. He initiated me into a secret mantra known as the Guhyaka-hṛdaya. After I had performed the yāga of that mantra for 6 months, I set out on an expedition and discovered a source of diamonds in one of the riverine channels to the North of my region. Plush, with wealth from this find, I was able to start my own venture. For 4 years, I toiled discovering more nidhi-s and setting up a caravan to convey pearls from Bhṛgukaccha. I had become rich and widely respected as a seṭṭhīya and now sought to find a befitting woman as a wife. I had found such a woman, but before I could get her, she was taken by Vāliputta Kubīraseṭṭhī. Distraught, I wandered along for a while in distant lands, letting my faithful assistants manage my ventures.

It was then that I went to Laṅkā and discovered multiple gemstone mines there. However, before I could exploit my mines on a large scale, the powerful vaṇij Dīrghapuccha Vānaravīra sent his great force of predatory henchmen to take over the mines. My small force of defenders was overwhelmed and had to flee. This happened over and over again. Each time I would find a new mine, Dīrghapuccha Vānaravīra and his romāka and pāraśika allies would swoop down and take control of them. I still had a small fortune and cobbled together some profits from whatever gems I would unearth, but I could never scale up due to the evil Vānaravīra and the foreign merchants. As I was thus sending off a small shipment to Viśākhapaṭṭana, I ran into Buddhagabbha, a sthaviravādin. He gave me initiation into the saṃgha, and I forsook my original dharma, having seen its futility with respect to attaining the fruits of my efforts. Thus, I took refuge in the dhamma of the Sugata. I regrettably vented the frustration of my efforts by reporting the Brāhmaṇa Trivikrama Bhaṭṭa from Oḍḍiyāna to the Laṅkārāṭ for converting bauddha-s back to being titthiya-s and forsake the saṃgha. In righteous indignation, the Laṅkārāṭ had persecuted Trivikrama Bhaṭṭa and was going to impale him on a stake when he deployed a śaiva mantra known as the Khādakāstra. I saw the Khādakāstra burn up the stake. Frightened, the Laṅkārāṭ let him go. A month later, Laṅkā was invaded by the Damilla-s, and they imprisoned the Laṅkārāṭ, having conquered the whole north of the island.

I was now left with only a bag of gems, and it was not clear if the King of Damilla-s, a śaiva himself, might find me and persecute me for reporting Trivikrama. I went back to Buddhagabbha and sought his counsel. He asked me to worship at dhāgabha of Sakkavihāra. I had heard that having such a life review was a prelude to approaching death. Indeed, it felt as though the reality around me was slipping away. Just then, I heard the great god Indra speak. At the very moment, his sonorous speech reached my ears, my delusions fell away. How could I have fallen for the ego of a mere martya, the Śākya? How could the blown-out delusion of his nibbāna stand before the jyotiś of the gods? I remembered the words from the śruti recited by my V ācārya: apāma somam amṛtā abhūmāganma jyotir avidāma devān । He who has attained the light knows the deva-s: how can the blown-out darkness of nibbāna stand up before this light? Then I remembered further words from the śruti recited by him:
yad dyāva indra te śataṃ śatam bhūmīr uta syuḥ ।
na tvā vajrin sahasraṃ sūryā anu na jātam aṣṭa rodasī ॥

Even the ego of the Śākya cannot reach the limits of Śakra, whom even a 100 heavens and a 1000 suns cannot equal. What is to be attained from the worship of this martya’s remains in the dhāgabha? I broke out reciting the Indra Vaṇijmān mantra-s.

Indra said: “A man must act as though he has the capacity to act even if his fate might have been decided like a die-cast by the gods. He nudges along the casts of the dice with mantra-s. As I told Rohitāśva — if he sleeps on his bed, his share or his luck sleeps too. If he stands, his luck too comes to a standstill. If he moves, his share or his luck, too, keeps moving. Hence, move on till you drop dead. Then it might begin again.”

I suddenly perceived myself as Vidrum again. I looked up at the sky and found that Orion had entirely vanished below the western horizon. I said to myself that I must have been in Laṅkā of the past for several hours! I looked out toward the cemetery. I saw the same unkempt man lift up the trashcan from our yard and walk away along the road with a tipsy gait!”

L: “Wow, Vidrum — I really don’t know what to say — however, I just hope you did not surreptitiously consume some bhaṅga-laced spiced milkshake or two from the street-side vendor?”
S: “Whatever the case, given all the quotations of the śruti, I suspect he had reached somewhere deep.”

Some further notes on the Mongol religion-3

The core of the material discussed in this note is based on the publications of the Hungarian-Mongolian Joint Expedition studying folk traditions in Mongolia and the masterly work of Igor de Rachewiltz on religion in the Secret History of the Mongols (SHM). We take a look at this material from a comparative religions and historical perspective. A primer.

In the Ṛgveda, the deities Dyaus and Pṛthivī (alternatively known as Bhūmī or Kṣāmā) generally occur as dyad — a devatā-dvandva of the form Dyāvāpṛthivī or Dyāvābhūmī or Dyāvākṣāmā — that may be rendered as Heaven and Earth. These devatā-dvandva-s are mentioned a total of 122 times in the RV. They are understood both as the parents of the gods and the universe (e.g., ya ime dyāvāpṛthivī janitrī rūpair apiṃśad bhuvanāni viśvā ।), and the stage for their acts. Imagine a religious system where these other gods recede into that backdrop or reside in a hidden realm that can only be seen by special individuals. What we would end up with is something like the overt religious system of the SHM. In that primal history (epic) of the Chingizid Mongols the chief religious protagonists are a precise cognate of the Indo-Aryan devatā-dvandva Dyāvāpṛthivī. In the Mongolian, it occurs in the form Tenggeri[Tengri]-Qajar, with Tengri being the cognate of Dyaus and Qajar being the cognate of Pṛthivī. Together, Tengri-Qajar are said to shape human events (Mo: jayaghan ~ destiny), provide the foundation for the existence of animals, and give “increase”, power, strength and protection. As per the SHM, together they conferred on Temüjin the lordship of the ulus and, in the same text, they are elsewhere mentioned as protecting Chingiz Khan and his army. They are explicitly mentioned to have aided Temüjin in the campaign again the Merkits along with Toghrul Wang Khan and Jamuqa to recover his wife, Börte. Thus, generally, the role of the Mongolian devatā-dvandva matches quite well with the Indo-Aryan Dyāvāpṛthivī. For instance, Atri invokes the dyad thusly:

ā suṣṭutī namasā vartayadhyai
dyāvā vājāya pṛthivī amṛdhre ।
pitā mātā madhuvacāḥ suhastā
bhare-bhare no yaśasāv aviṣṭām ॥ (RV 5.43.2)
With good praise, with obeisance, they are turned to,
Heaven and Earth, for not disregarding [our] quest for booty.
Father and Mother, of mellifluous speech and good hands,
In battle after battle, the famed dyad protects us.

The Mongolian Tengri is described as a mighty being (erketü) and has an element of the Father-figure seen in IE tradition — this is expressed in the tale of Alan Qo’a’s heaven-born sons (Tengri-yin kö’üt). Notably, the divine imagery of the Chingizid Mongols, overlaps with that seen in the Gök-Turk inscriptions on the Orkhon steles. The Gök-Turks too had the dyad of the Heaven deity (Tengri) and the Earth deity (Yer). As per the records of the Tang, the Turkic Khaghans performed a sacrifice to Tengri at a specific spot rendered as “大人” (da-jen), likely corresponding to Turkic Tazin, in the second decad of the 5th month annually. This spot was identified by de Rachewiltz as being along the Tesiin Gol river, probably Tes in Northwestern Mongolia (Figure 1).

Figure 1. Turkic and Mongolic holy sites and Khaghanal seats in Mongolia

Interestingly, the Mongols had a second word for their Earth deity, especially when used in a concrete form — Ötögen or Etügen. Under this name, her concrete aspects, like the holder of the mountains and rivers, as in the case of her IA counterpart, are mentioned. This Mongolian word appears to be a possible loan from the Turkic word Ötüken, which appears to refer to the sacred mountain where the Turkic Khaghans offered their sacrifices to the Earth goddess. As with Tazin, the exact locale of Ötüken remains uncertain, but it was likely a spot in the Khangai range, to the West of the old Turkic capital at or in the vicinity of Ordu Baliq of the Uighur Khaghans (Figure 1). This suggests that an element of the religion of the Chingizid Mongols shared a continuity with that of the Gök-Turks and Uighurs who ruled Mongolia before them and the Khitans. Despite Heaven and Earth being quintessentially universal deities, in the Turkic case, they had specific cultic locales in Mongolia. It is not clear if this was the case with the Mongols. We do know that the Chingizid capital Qara Qorum is close to the old Uighur Ordu Baliq and the Gök-Turk capital suggesting a certain continuity at least for the Khaghanal seat. Further, there is an extensive folk mythology connecting the topos of Mongolia to near mythical acts of Chingiz Khan and his family. From the SHM we learn that the Mongols performed a sacrifice with burnt offerings known as the Qajaru-Inerü evidently to the Earth-deity as the protectoress of the ancestors. While this is reminiscent of the Turkic ritual at Ötüken, there are no indications that it was performed in a specific place in Mongolia. However, the SHM does mention a ritual performed by Chingiz Khan at Burqan Qaldun in the eastern reaches of North-Central Mongolia. It was done in the morning, facing the sun and bowing 9 times, wearing the belt around the neck (c.f. yajñopavīta) with the headdress taken off. It seems to have been accompanied by a prayer incantation. The importance of Burqan Qaldun to this date suggests that Mongols too had specific locales for their worship.

More generally, there are several references to the Mongol worship of Tengri and probably Qajar on mountains. The worship of Tengri seems to have been performed before major campaigns by Chingiz Khan, his generals and successors. Rashid al-din mentions Chingiz Khan’s rite on a mountaintop before the 1211 CE campaign against the Jurchen. Here, he is said to have specifically asked Tengri to help him avenge the deaths of Ambaqai Khan and Ökin Barqaq, former leaders of the Mongols who had been brutally executed by the Jurchen. It is not clear if he just chose some accessible hilltop or whether it was a special locale or it was done at Burqan Qaldun. He did similarly before heading to punish the Khwarazm Shah. The worship of Tengri also comes in the context of another war. For some background: starting in 1207 CE Chingiz Khan and his son Jochi moved to subdue the taiga chiefdoms, beginning with the Kirghiz. This was followed in 1208 CE with the conquest of the Oirat, and their leader Quduqa-beki joined the Mongols as a general of Jochi. He then aided in the subjugation of the Buriyat, Ursut, Qabqanas and others. This was completed by the autumn of that year and towards its end Quduqa-beki acted as a guide for Jochi’s forces to locate the holdouts of the Merkits and the Naimans in the Northwest. They were smashed in the battled of the Irtysh River that followed. Probably, in 1209 CE another taiga tribe, the Qori-Tumat, were conquered on the West bank of the Baikal. In 1217 CE, the Qori-Tumat started a rebellion against the Mongols. Chingiz Khan sent his senior general Boroqul to suppress it, but he was ambushed and killed. To add to this, the Kirghiz refused to aid the Mongols in the campaign against the Qori-Tumat, and several other taiga chiefdoms joined in their revolt. Thus, in 1218-19 CE, Chingiz Khan sent his son Jochi to crush the Kirghiz and subjugate tribes such as the Telenguts and Keshdim, and his general Dörbei Doqshin to put down the Qori-Tumat. Evidently, expecting this to be a difficult campaign, the Khan asked Dörbei to worship Tengri after arraying his army in strict order before setting out against the Qori-Tumat. In a similar vein, the grandson of Chingiz Khan, Batu, performed the hilltop worship of Tengri before the battle of Mohi with the Hungarians (mentioned by Ala al-din Ata-malik Juvaini in his history of the Mongols).

What about the rest of the Mongol religion? While we get tantalizing hints, like the ritual performed by the Kereit for the birth of a son but no further details. However, the biggest element that is repeatedly mentioned but never described in terms of the actual ritual content or incantations is the role of the shamans. This suggests that the authors of the SHM, while embedded in the shamanic religious system, were unlikely to have themselves been performers. One wonders if this might relate to the efforts of the notorious Kököcü Teb Tenggeri, Chingiz Khan’s first shaman, to seize political power. Nevertheless, the shamans of the descendants of Qasar and their tribe, the Qorcin Mongols, to date, claim their shamans to have descended from this Kököcü. The name of the Chingiz Khan’s shaman indicates a connection to Tengri though its exact significance remains unclear. Hence, to uncover this “unspoken” layer of the religious tradition, one has to turn to modern studies on Mongolian shamanism. Across the extant Mongol horizon, we see that the modern shamans use peculiar effigies or icons known as ongod (singular ongon; Figure 2). These icons might represent tengernüd, i.e., tengri-s (gods), jayāchnūd, (semi-)divine beings controlling destiny, and human ancestors. The shamans also invoke other Tengri-s and deified shamans who might or might not be represented iconically (e.g., Khan Jayaghachi Tengri or Dayan Deerkh). The icons are made of felt (as they were in early Mongol history) or other materials like metals. It is in this context the testimony of the Venetian traveler Marco Polo becomes relevant (despite de Rachewiltz doubting the veracity of his account). While his account is confused, he specifically mentions that Mongols place images of their deities (referring to Tengri-Qajar and apparently also other tengri-s who are their children) made of felt or other fabric in a place of great honor in their tents. He mentions them making food offerings to these icons and worshiping them for protection. This is clearly a reference to the ongod, also noticed by other Western emissaries to the Empire. Comparable worship of ongod continues to the current time among the Qasarids and the Mongolized Tuvinian Turks. Further, keeping with the children of the Tengri-Qajar parent pair noted by Marco Polo, among the Buriyats the children of the Heaven Tengri are invoked in shamanic rites and called noyad (singular noyan ~ chief). For example, Poppe records this chant in the luck-beckoning dalalgha ritual (as provided by Krystyna Chabros in her monograph on these rituals):

“These are the inviolable benefits (buyan) of your Tengri and noyad and ugh qarbul (=origins: ancestors of the clan), the good fortune wishing-jewel which cannot be called, the great dalalgha of becoming rich and prolific.”

Figure 2. Ongod of the Qorchin shamans recorded by Veronika Zikmundová

Though the SHM might not record the contents or liturgies of shamanic rites, the extant shamanic tradition preserves a memory of the connection of Chingiz Khan’s family with such. One is a peculiar mythological epic regarding one of Chingiz Khan’s daughters. Apart from his four sons, he had 5 daughters, Qojin, Checheyigen, Alaqa, Tümelün and Al Altan; however, it is not clear which of these daughters the tale refers to. The outline of the tale as per surviving records involves the Khan’s daughter being attacked by a shape-shifting demon. In a motif resembling that in the Rāmāyaṇa, the demon appeared before the girl as a monk seeking alms. Then revealing his true form, he tries to seize her in a chase that spans the triple world. The Khan’s daughter finally defeats him after being helped in each stage of the chase by her horse, zoomorphic spirit guides emanated by the horse, viz., a red fox, a blue fox and a cat, crow messengers (recapitulating the Germanic Odinic motif), and the famed dogs of Turko-Mongol mythology, Qasar and Basar. This constellation of motifs is clearly a recapitulation of the famed shamanic trance journey aided by zoomorphic psychopomps. Though an extant Mongol folk epic, this tale seems to capture key elements of the original Mongolic shamanism. Similarly, Chingiz Khan’s third son, Chaghadai and his wife Changqulang, who are invoked by the Buriyats in their fire-kindling rituals (just as other Chingizids are invoked in various fire-kindling rites), also exist posthumously as key psychopomps of their shamans.

The rituals of shamanesses recorded by Agnes Birtalan among the Darkhads of Khövsgöl also appear to preserve archaic elements that give clues regarding shamanic practice in the classical age. Sometime in the late 1600s, a group of iron-working Turks related to the Tuvinians and with connections going back to the Uighurs of yore were the subjects of the Mongol lord Geleg Noyan. He in turn offered himself as a subject to the famous mantravādin Jñānavajra (Öndör Gegeen). The Darkhads thus received some privileges and adopted the Mongolian language. Despite their association with the Vajrayāna savant, many Darkhad shamans remained in opposition to the tāthāgata-mata and retained their old shamanism. Their shamanic practice, involves ongod reminiscent of those seen by Marco Polo. Among others, their shamanesses channel ghosts of various humans as well as zoomorphic psychopomps who indicate their presence by emitting various animal calls through the shamanesses. One interesting case records a shamaness ritually channeling the ghost of a Turk (ancestor?) who started speaking in the Tuvinian Uighur language. When they told him they could not understand, he switched from Turkic to Mongolian that they could. Apparently, the shamaness did not know the Turkic dialect in regular life but could only speak it in a deep trance (xenoglossy). Additionally, in day time rituals the shaman(ess) produces music with a morsing (kamus) and uses a mirror (reminiscent of old Saka ritualists worshiping their Solar goddess). It is notable that when the shamaness invoked some of her psychopomps, she called on them to worship a group of 5 Tengri-s known as the Jayaghachi tabun tengger of the ongon. The exact origin of these 5 deities is unclear (Figure 3). Even though they might be depicted in iconographies inherited from Tibet (i.e., Vajrayāna imagery), there is no evidence for them having any connection to the Vajrayāna. Also remarkable is the invocation of the psychopomps from specific rivers and mountains, usually the locations where the ancestors of the shamans lived. This suggests that like the specific topos of the state cult of the Gök Turks, the shamans of the Chingizid Mongols too might have invoked their psychopomps in connection to specific places.

Figure 3. The 5 tengri-s associated with personal protection collected by Austro-Hungarian explorer Hans Leder in the late 1800s-early 1900s.

Finally, we hold that the extant shamanic liturgy does preserve certain archaisms concerning the worship of the Heaven Tengri and Qajar of the old Mongols (i.e., as in the SHM) despite the later Bauddha influences. For example, in the rite of the nine-yak tail standard of the Khan performed by the Qorchin Mongols invoking Sulde Tengri, we also see an invocation of the missiles of the Heaven Tengri (recorded by Chabros). Here, peculiar objects found on the steppe, like meteorites and sometimes ancient bronzes of the pre-Turko-Mongol age, termed “tngri-yin sum u” (missiles of Tengri) are used in the ritual with the usual Mongol qurui call. Further, among the shamanic invocations of deities of ultimately Hindu origin like Kubera Vaiśravaṇa and the river Gaṅgā (identified with the ocean = dalai by the Mongols), we find formulae relating to the Heaven-Earth dyad of the SHM. For instance, Walther Heissig records:

The benefits of Möngke Tengri the father, qurui qurui.
The benefits of the earth of the seventy-seven-layered Etiigen, the mother, qurui qurui.
The benefits of the son bright as the sun, moon and stars qurui qurui (Evidently the son of the divine pair, like the noyad in above incantation).
The benefits of the constellation of the seven old men (Ursa Major) and the other teeming ten-million stars qurui qurui.

We also have a shamanic incantation found widely among different extant Mongol groups that is directly related to the role Tengri has in the SHM as the provider of sustenance to the animals (below is the translation of the Bulgan version recorded by Chabros):

In the dark night
My Khan, powerful Tengri showing mercy
May my black horse-herds spend the night in peace and good health.

The last two elements of the term Khan erketü Tengri found in the above incantation occur in the SHM as is (c.f. ed-un Khaghan Bisman Tengri for Kubera — the emperor of wealth — a construction ultimately traceable to the Taittirīya-śruti).

Similarly, we have the below chant used in the animal sacrifice by the butcher rather than the shaman (recorded by Chabros):
OṂ may happiness prevail.
Eternal Möngke Tengri
Blooming golden Earth
My blue Mongol homeland
lying on your southern slopes
pasturing in your sheltered places
deign to grant the benefits of bulls with fine humps,
the benefits of cows with fine udders.
qurui qurui qurui

The benefit of Chingiz, the Khaghan
foremost among all the animals
may they come returning
to their owner who cared for them.
qurui qurui qurui.

It is notable that this otherwise archaic chant with a clear memory of Chingiz Khan incorporates an initial OṂ from the Indic tradition.

Lastly, we have the remarkable incense offering to Tengri and Etügen preserved among the Oirats and their Bayad cousins recorded by Heissig and Chabros which calls on Möngke Tengri to make joyful Etügen, and the genii of locii and the waters.

Some relationships involving the triangle incenter and circumcenter

While triangle centers (e.g., incenter, centroid circumcenter) are captivating to the amateur and mathematician alike, their serious investigation is a relatively modern pursuit. A major push in their study began with the great Leonhard Euler and was continued by the geometer Jacob Steiner. Down to the studies of the last 100 years, this has been a fertile topic of mathematical inquiry. Here, we list some interesting relationships that came up in the course of our explorations as a mathematical layman. At their heart is one which was apparently first reported by Steiner, and the rest are ones that we built upon the former. The incenter of a is determined by the intersection of the angle bisectors of its 3 angles, and the incircle of radius is tangent to the 3 sides of the said triangle. The circumcenter is determined by the intersection of the perpendicular bisectors of the 3 sides of the triangles, and the 3 vertices of the triangle lie on the circumcircle of radius . Let be the distance between and then we get the well-known relationship:

Figure 1.

Consider a point on the circumcircle of . Draw a line connecting to incenter . will intersect the circumcircle again at . With as the center, draw a circle through . This circle will intersect the circumcircle at and . Draw the lines and . Then and with be tangents to the incircle! Thus, we get two triangles, and , sharing the same incircle and circumcircle. Let and , then we get the relationship:

This is the basic Steinerian relationship, based on which we obtain the below results.

Figure 2.

In the above construction, we had drawn the circle with as its radius. In addition to , the line will intersect this circle at . We next ask the question: what will be the locus of as point moves along the circumcircle of ? We determined it thus: draw line . On this line, mark point , such that it is at the same distance as but in the opposite direction. Thus, . Then, the said locus of will be a circle (colored red in Figure 2) with its center at and radius equal to . Let , then we have:

Figure 3.

Line cuts the incircle at points ; it cuts the circumcircle at points ; it cuts the above-described circle with center and radius at points (Figure 3). Then we have the following 4 lengths: . For these, we have the below relationships:

Inradius is the geometric mean of the separations between the incircle and circumcircle along the incenter-circumcenter line.

The Dalāl who became a poltergeist

Lootika had returned from a scientific competition, which had been held in the dreadful city of Mahāvisphoṭaka, like the victorious Roman army after sacking the towns of West Asian counter-religionists. To both celebrate and to educate the class her teacher had organized an evening of sky-watching where Lootika was to introduce her often unruly classmates to the basics of astronomy. She knew well that beauty and success inspired anger and envy in many and that such a session could descend into the unsavory or worse quickly. Hence, she roped in Somakhya and convinced her teacher that he should take the lead in the session, though he had stayed out of the competition and let her claim the glory. She almost felt he had been like Zeus letting Herakles gain the glory at contests of the Olympic games. She faced her share of scowls and intentional interruptions from the more begrudging and rowdy classmates, but for the most part, it went well as Somakhya handled much of the show. Thus, after the session, they decided to take advantage of the situation and partake in the joys of dinner at a restaurant with some of their classmates — something their parents heavily disapproved of. For this purpose, they decided to meet at Vidrum’s house and then proceed to a nearby eating place. That way, Lootika could get back home in time without arousing any suspicions that might trigger her parents’ espionage regime.

While she got to Vidrum’s house as soon as the session ended with a few of her other classmates, Somakhya was delayed in reaching there due to patiently explaining astronomical theory and responding to other queries of the rare minority of their more curious fellow students. When they reached Vidrum’s house, most of them wanted to check out the new cricket bat he had been gifted by his family. That was the last thing that Lootika wished to participate in, and she went out into his courtyard to look out at the clear skies. Beyond the wall shone a single light from the temple of the Śmaśāna-sarasvatī in the cemetery, and outlines of a few gravestones could be made out in its dim grove. Almost as if cued by that, Lootika felt that someone had grabbed her shoulders. In utter horror, she screamed and turned around but saw no one. Just then, her bike, which was chained to a stake on Vidrum’s fence, slipped and fell — it had been stably standing there for around 10 minutes, and there was hardly a wind. Indeed, the wind chimes hung outside Vidrum’s front door were utterly silent. Hearing her scream, Vidrum and the rest came out to check on her. V: “What happened! We feared someone had set upon you.” Lootika felt ashamed and felt they would start poking fun at her sanity if she told them what really happened. Hence, she only revealed part of it. “See my bike — it suddenly and mysteriously slid sideways and fell. I was turned the other way and felt someone was stealing it; hence, my fright.” Vidrum started off by saying something like: “welcome to my house”, but abruptly stopped and changed course: “Never mind. You, in turn, alarmed us — we thought someone had attacked you.” Just then, Somakhya finally arrived, and they hurried off for dinner.

That night after a pleasurable dinner filled with raucous conversation, as they were heading home, Lootika stuck close to Somakhya even for the short ride to her home after leaving Vidrum and the rest. S: “Ain’t it frustrating that our parents place such restrictive curfews, unlike our other classmates who get to hang out till midnight.” L: “S. Indeed, but today I’m happy to be back home.” Somakhya thought she was relieved to be done with the sky-watching session, where she feared being harassed even more by their more vicious classmates. S: “Well it was not bad at all. Perhaps, you now get why, like the Iranians, I say you must lie low like the “Hidden Raukas-takhma”. Anyhow, sleep well, and we’ll meet this weekend for more exciting things.” But that night, her sleep was anything but good. She awoke around 5:00 am to a nightmare. She saw herself chased by a mass of peninsular hunter-gatherers shouting out in a strange register of an Apabhramśa and woke up shrieking, only to be met by the displeased murmurs of her sisters who were awakened by it. But her sister Vrishchika patted her down, and she fell back to sleep only to have it soon disrupted by another dream. She beheld a rich-looking man wearing a heavy gold chain running, panting heavily, when a ruffianly turbaned visage peeked out from behind a tree and, raising a musket, took a shot right at the head of the former. Lootika woke even as the gore of that man splattered all over her. By the time she was done with her sleep cycle, she was jolted out of it by yet another such nightmare featuring the shooting of a youth in what looked like an old court.

The following weekend Lootika rode over to Somakhya’s house. Her intention was to talk about some endosymbiotic bacteria in amoebae that she had managed to cultivate and visualize — she had much bigger plans for them. However, just as she met him, something else came to her mind, and she burst out: “Somakhya, something is not right in Vidrum’s home.” Before she could go on, her friend interrupted: “So, he told you of it?” L: “What? You guys seem to know something I’m unaware of!” S: “OK, tell me what you heard.” L: “I did not hear anything. I had a positively strange experience.” She then proceeded to tell him about her experience from the other night and concluded: “Could it be that Vidrum’s house itself is haunted like the yonder cemetery and its environs?” Somakhya did not respond; instead, leading her to his computer, he showed her an old map of their city from the day of the English tyranny. L: “Heavens! It seems the cemetery extended right into the land where Vidrum’s house now stands. It could have been built right atop the old graves! Now it all makes sense. Let me give you some further information. My parents knew the previous occupants of the land on which his house stands, and we used to play with their kids when we were much younger — they suddenly left in a haste without telling anyone!” S: “Now, with that information, your experience should be no surprise at all.” L: “I still wonder what my dreams might mean in light of my encounter that evening!”

S: “As you can imagine, there is many a phantom in Vidrum’s dwelling — a cause of much consternation to him even before you joined our school. My suspicion is that you specifically encountered the poltergeist in his house that we have had little luck unveiling.” L: “So, you have encountered him/her before?” S: “It is a long story. Vidrum was insanely excited to move into his new residence — I can appreciate that, having spent my first few years in a small house myself — the luxury of more private space can indeed be an exciting prospect. It also had its own backyard and garden strip, as you know well. Moreover, it was a bit secluded from the bustling road — what more can one ask for in his youth in a country where people live off limited means and space! However, things turned a different way soon thereafter. He used to repeatedly mention to me that his house was haunted by a host of phantoms. While I was not very indulgent in his growing phasmophobia, we did some research and arrived at the map I showed you. I had known the cemetery that you know well and had visited it regularly with Vidrum and Sharvamanyu. In fact, now to come to think of it, I may have seen you and your sisters there even before the wishes of the gods brought us together.” L: “That’s possible! I remember we ran away once, probably frightened by seeing you’ll.”

Somakhya continued: “Hence, I took his claims more seriously and decided to ply the planchette when we visited his house for the first time. The responses were startling — what we got was clearer than anything in the cemetery or the courtyard of the Śmaśānasarasvatī prāsāda. We first got a liṅgavant from the 1800s who had been interred there. He was a pretty regular visitor, who was just happy to tell his tale over multiple sittings. Then we had the incident of the geometry box that we’ll show you someday. We became increasingly convinced of the existence of other phantoms through our continuing planchette sessions: a couple of other liṅgavant-s, a domineering Englishman, and some other truly shadowy entities who spoke multiple barely intelligible Dravidian languages. In the meantime, Vidrum would fill me in with all manner of fantastic tales that, despite my own ghost-board experiences, were hard to believe: I had personally never experienced any spooky physical phenomena at his place. Sharvamanyu had rewired a radio to rapidly scan through channels in reverse, and words would come up every now and then as if manipulated by a ghost. He had learnt that the mleccha-s used this method as an alternative to the planchette, but I did not take any of that seriously, though Sharva and Vidrum claimed to have had some meaningful communications via that medium. Sharva and Vidrum once told me that a sprite made a lamp go on and off in response to questions, but I was not around then. However, in the final semester of the year before you came, I encountered something that made me sympathetic to some of Vidrum’s more fantastic claims — for the first time in my life, I experienced something that could be termed a poltergeist. It had some parallels to your encounter.”

L: “While I, too, have experienced believable planchette activity in the cemetery, years ago, I had a stranger experience in the general vicinity of Vidrum’s house before it had even been constructed. However, that experience was nothing like that from earlier this week. So pray continue…” S: “Hmm… So you were sort of primed! Anyhow, it was a spring evening — it was not even fully dark — when I suddenly heard a bike rattling. We were on Vidrum’s terrace; hence, fearing someone was trying to steal our conveyances, we ran to the rim and looked down. We had as clear a sight as we could. There was no one around, but I had the sense my bike had moved, and its wheel had turned around, unlike how it was when I’d parked it. Fearing that someone might have evil designs, Vidrum and I took our bikes inside and chained them to the backyard. Thereafter, we came down to his verandah and were watching some cricket when we suddenly heard his house door turn. He wondered if his parents or aunt had arrived early, but there was no one. Then, the house door lever went crazy, rattling for about 30 seconds as if pushed up and down. Strange as that whole thing was, I was still not prepared to give into Vidrum’s beliefs on poltergeist activity. There could be mundane explanations for all these that might eventually be worked out, but it was not worth it. What turned me was something strange. We went back into the house as Vidrum wanted to show me his multitonal metal drum. As you know, I have little musical sense, but from his account of the instrument, it became clear that it might be useful for me to polish my Vedic intonations. Just get this straight: the drum was placed on a low stool, and in front of it was a chair on which we could sit to play it. The chair was covered with a flat fabric cushion which provided reasonable friction. Vidrum first played out a tune or two. Then I tried out the tritones of ye triṣaptāḥ… and when I was done, I clearly placed the drumsticks on the chair in such a way that they were stable and right in the middle. There was no movement around the chair, and even if there was, it was not sufficient to overcome the friction to make the drumsticks move. Thereafter, Vidrum and I continued following the match, seated on cushions on the floor with the chair right in front of us. Almost exactly 10 minutes later, both of us were startled as we saw the drumsticks fall to the floor with an audible noise as if flicked off the chair! It might not be a dramatic incident to a listener, but this came about as close to being “controlled” as I had very consciously placed the sticks in a stable manner. Hence, its movement was so obviously unnatural that it brought some conviction in me regarding the more unusual spooky happenings in Vidrum’s dwelling.”

L: “Remarkable! it is not the dramatic, like the door handle or the bike, that convinces you, but the more ordinary, though difficult to explain away, that does so. This is always the case with the realm of the phantoms — others might tell you dramatic tales but you are going to have varying degrees of disbelief until you encounter something yourself — which you might not till the time comes. So, whatever dramatic stuff Vidrum had experienced left less of an impression on you than what you saw yourself and felt convinced by. Unlike science, this is a hard-to-transfer conviction!” S:“That’s indeed the case, Gautamī! But the story doesn’t end there. I, too, had nightmarish dreams for a few days following that encounter. Hence, I believe we are dealing with the same entity. While I did not recall the dreams clearly as you did, one motif did stick in my memory — flames — as though a band of wild-looking men were engaging in arson! In other circumstances, I would have indeed described them, just as you did, as peninsular hunter-gatherers of yore, albeit clade in more modern vestures. Hence, like you, I, too, was convinced that there was something more to this and repeatedly tried to make contact with the phantom using the planchette. However, this chap proved remarkably slippery and has never come through. Nevertheless, Vidrum believes that he persists in his place through manifestations of poltergeist activity. His parents were totally disbelieving of him until they had their bed shaken and a rolling pin was thrown at them by this guy. Since then, they have stopped haranguing Vidrum about a possible psychiatric condition or the substance use they were suspecting him of.”

The curse of the mid-semester exams had passed over their heads. Vidrum had planned an outing with his friends to a hill, capped by a shrine, that lay a little distance from their city. That morning Somakhya awoke from a strange dream that he felt was prognostic regarding the deep future. Hence, he quickly performed a homa with the ṛk-s of the sūkta tvayā manyo saratham… followed by phaṭ svāhā and capped it up with oblations with the yajuṣ groups ojo.asi … and bhrātṛvyakṣayaṇam asi … His mother heard him do this and became a bit concerned: “Hope you are not heading into a schoolyard gang fight?” S: “No, it is in response to a dream I had the past night that I think had some mantic significance for the distant future.” While his mother had some minor mantic capacity, she normally brushed aside his feelings of such and told him they were merely psycho-mirages. But, this time, on hearing the elements of his dream, she seemed to agree without elaborating any further: “It would not be appropriate for a parent to fool their kid by saying that they would not have to fight future battles against redoubtable foes.”

On that note, Somakhya departed to Vidrum’s house, where he was also to meet Sharvamanyu and Lootika. Vidrum told them of Virūpādri and remarked that a shrine of a gigantic Vināyaka stood atop it. Somakhya, who had done some investigation on the same, remarked that the Vināyaka had a special significance. The people who had a certain wish, or wanted to rid themselves of the trouble from an enemy wrote that on a slip of paper and placed it in the mouth or the curve of the trunk of the divine image with the rāyaspoṣa incantation. All four of them wanted to make such a slip and quickly arranged to prepare one. Even as he handed over a sheet of paper and scissors to Somakhya to cut it into four square pieces, Vidrum’s water bottle, which was on a table, mysteriously seemed to fly off and fall to the ground with a crash. All of them jumped up from their seats and looked at each other in amazement. Vidrum: “It must be our friend, the poltergeist.” Over the next few minutes, even as they wrote up their slips of paper and looked up the map to chart the shortest and safest path to the Virūpādri, they heard several taps and knocking noises all over Vidrum’s house. There was a strange noise from the kitchen as if the stove was rattling; then his room door slammed shut and opened twice. S: “It was all quiet when we came — wonder what this is about?” V: “If you noticed, it suddenly burst out when you mentioned the rite at the temple — wonder if there is a connection.” Sharvamanyu, in the meanwhile, turned on his hacked radio and waited to hear any words coming through, but all they heard was static, even as Somakhya and Lootika cast skeptical glances at his mleccha-rīti. They instead suggested trying out the planchette, but that too merely showed some random saltations and stopped.

S: “As ever, this poltergeist is never communicative. Lootika, we may someday have to try higher vidyā-s — however, I’m not sure our puraścaraṇa is sufficient right now for any success.” L: “We may never know anything. I have gone through a bunch of previous surveys of poltergeists in several parts of the world they seem to be noisy but not communicative. They even seem to be focused on a single person, and I suspect that, in this case, it is Vidrum. Based on those case surveys, I wonder if it is exploiting some deep trauma of yours.” V: “As you know, that would not be surprising. What you say makes sense in light of us never having received answers about his identity, though we have heard from other phantoms in my house! In any case, let us be moving with our trip — we still need to fix a bike for me.” They proceeded to Lootika’s house to pick up her old rickety and rattling bike that they repaired with some assistance from the Kaliṅgan cyclevālā and set off on their expedition.

On reaching Virūpādri, they soon got off the stone steps carved on the mountain-side to take a path through the wilderness. There, even as Somakhya and Lootika were going after coleopterans, hemipterans, and hymenopterans that caught their eye, Vidrum attempted some stiff climbs, challenging Sharva to do the same. Having earned the respect of his friends by showing off his hair-raising skills on the rock faces, they proceeded ahead mildly admonishing him: “We are happy we don’t have to haul your limp corpse from falling off one of those bluffs! Now let us go to the top.” The Virūpādri shrine featured a giant ten-armed Vināyaka carved right on the rock face. By climbing up steps cut on the side, one could reach the level of his trunk or mouth to place their wish-slips. Those were collected and offered in a homa every caturthī. Having placed their slips they wandered around to visit the sub-shrines. There was one dark one with Vīrabhadra and Bhadrakālī; there was another one with an aniconic Padmāvatī in the form of an ovoid stone daubed in an orange pigment; yet another housed a Nṛsiṃha that the locals mistook for Gaṇeśa! Finally, there was one housing five liṅga-s, evidently symbolizing the pañcabrahma-mantra-s. Having seen those, they wandered off towards a steep drop that was rimmed with the remnants of fortifications. There, they encountered a few further derelict shrines: they respectively bore the plaque reading “Indardev”, “Yamdharamdev” and “Bhairo-mahādev” with peculiar icons in them. S: “Wonder what is the origin of these?” L: “Indeed, their iconography is unprecedented.” Unfortunately, their walls were defaced with graffiti of the rude masses and some election posters. Close to the cliffs that lay ahead, they saw a memorial plinth beside a pandal with garish political posters advertising the government doles provided to the local tribal folks. Atop the plinth were two equestrian statues of men, one firing a musket and another slitting the throat of an English infantryman with his sword. On one side of the plinth, they saw a crude frieze depicting a battle scene between the two men and their followers with the English colonial army.

V: “Who are these gentlemen?” They got their answer as they went around the plinth to the other side, where there was a memorial plaque. Sharvamanyu read it out: “In the memory of Bāgsingh and Bagīchsingh, forgotten subaltern heroes of the struggle against British colonialism.” V: “Did we have these chaps in our history book.” Sh: “Not that I remember.” S: “They were given a single sentence in last year’s textbook in the chapter on tribal revolts.” Sharvamanyu continued reading the plaque: “Bāgsingh and Bagīchsingh sacrificed their lives for the decolonization of the tribal peoples from exploitation after a brave struggle with their Bhilla troops. They were killed here on January 15th, 1859 CE, while fighting the British forces.” Sh: “A lot of unknown fighters like this contributed to the freedom movement.” S: “Having encountered their names for the first time in our book last year, I did some research into them and learnt that they were at best ambivalent figures, whose conflict with the Rāj might have had less than nationalistic reasons, leave alone the socialistic ones the plaque ascribes to them.” Even as Somakhya uttered those words he noticed that Vidrum was holding his head and sat down on the culvert of the plint. The remaining three: “What’s the matter Vidrum.” V: “Very strange! I’m feeling a bit dizzy!” L: “In the excitement of the poltergeist flinging your water bottle, you forgot to bring it along. Maybe you dehydrated yourself from all the cliff-hanging you indulged in! I think we should get you a coconut from the vendor over there.” Vidrum protested that he was in the pink of his health, and it was very strange. Nevertheless, he took the coconut they gave him and having taken a few sips, he seemed fine again: “This doesn’t seem like dehydration, it is something strange. I repeatedly kept hearing a name in my head: Dandśūkrāj Pāṇḍey.” S: “That’s very strange, Vidrum; I have a recollection that the name has some connection to the history of Bāg and Bagīch. However, I’d have to refer to my notes, for I’m not recalling the precise details right now.” V: “In any case, this Dandśūkrāj Pāṇḍey seemed to be telling me to offer a laḍḍu on his behalf to the Vināyaka.” Given the strangeness of the situation, Vidrum bought a laḍḍu from a cart-peddler outside the shrine and offered it in the name of the mysterious Pāṇḍey. Thereafter, everything went quiet for the rest of their trek, and they uneventfully dispersed to their homes after returning to the city.

The next day, Lootika came over to Somakhya’s house: “Somakhya! I get the foreboding of being on the brink of something unexpected. When we were on the hill, the grim visages of Bāg- and Bagīch-singh struck me as somehow familiar. When I closed my eyes to sleep last night, they came back! I realized they were the shooters who appeared in my dream!”

S: “That is interesting indeed. This Bāg- and Bagīch-singh, as I mentioned, were not exactly paragons of the freedom movement. Piqued by their almost random mention in our textbook with no further context, I sleuthed around for sources about them. It turned out they had a checkered history. They are said to have been of half-Bhilla ancestry. Prior to the First War of Independence of 1857 CE, they had been serving the Kampani Bahādur’s army. They were not exactly the most obedient officers and were suspected of engaging in double dealings with the Marahaṭṭa agents. Bagīch was caught for that and disciplined by the English by being sent to do months of hard manual labor. Once 1857 broke out, he, along with his acolyte/clansman Bāg, decided to opportunistically join the freedom movement to have their revenge on the English. Thus, they organized a large band of Bhilla-s. As keen opportunists, they decided to retreat into the shades with their henchmen once they saw the war of independence flailing. After remaining low for some months, they turned on new targets. Some of the Bhilla-s were spared the whirlwind of the English wrath if they agreed to settle down and perform hard labor for the English, such as growing and maintaining the Great Hedge of India to facilitate enforcement of the brutal Salt Tax. Some of these Bhilla-s got addicted to various vices and were indebted to the banker-businessman Raṇcoḍdās Lallubhāi Dalāl, who had settled in our city. Raṇcoḍdās’s financial services were useful for the English Rāj; hence, they allowed him some muscle with the help of a daṇḍavālā police Paṭel. Several altercations broke out between these semi-settled Bhilla-s and Raṇcoḍdās and the Paṭel’s men over non-payment of debts. Many of them were beaten up and forced into involuntary labor under the English.

In a state of ferment, they harangued their erstwhile leaders, Bāg- and Bagīch-singh to do something for them. With their own loan burden to Raṇcoḍdās, and ̐ith their leadership positions in jeopardy, the two fighters reorganized their Bhilla force and launched a predatory strike on our city. In a predawn assault, they rode into the city having killed the police Paṭel at the peripheral outpost and headed straight to Raṇcoḍdās’s residence. They demanded right away that he hand over all the bonds relating to them. Raṇcoḍdās, despite his name, was not the man to retreat from a scrap when it came to his money. He organized his personal fighters and sent an agent to mobilize the Paṭel and his henchmen. However, that source of succor had already been taken out. With dawn approaching, Bāg- and Bagīch grew impatient and attacked. They seized the bonds and burnt them. Then, wanting more for their efforts, they demanded that Raṇcoḍdās pay them some indemnity. Raṇcoḍdās was not the man who would part with his money, but seeing the writing on the wall, he decided to escape via the backdoor of his house, taking his cases of wealth, with his Kāyastha and assistants. As per my research, the fleeing Dalāl was intercepted somewhere close to your house and killed — something that you saw in your dream. Subsequently, Bāg- and Bagīch, with their Bhilla hordes, went on a rampage on the less-protected towns to the East and the North over the period of an year. While they slaughtered regular civilians from time to time, they mainly focused on burning down the financial records of the Dalāl-s and carrying away their wealth. Due to the destruction of the bonds and the like, they received some support from the peasants, who, like the Bhilla-s, had been habitually indebted to the Dalāl-s due to their lack of fiscal prudence and the climatic vagaries.

They fortified the Virūpādri and some other hills and used them as bases for their operations. It now strikes me that the peculiar shrines to Indardev, Yamdharamdev and Bhairo-mahādev are those of the Bhilla-s. It is an interesting case of the persistence of the Indo-Aryan religious traditions following their early adoption by certain Indian hunter-gatherers. In any case, the English retaliated, sending a force of Sikhs under Officer Scott. The large Sikh fighters boasted that they would make short work of the puny, black Bhilla-s but were soon put in place by the latter. Scott and his Sikhs were slaughtered to man in an ambush in the forests about 100 km to the north of our city. Nothing inspires a following more than success — Bāg and Bagīch’s victory left them with an even larger military force — they were now the untrammeled heroes of this movement in the twilight between a “freedom struggle” and plundering operation. Several peasant groups wanting to revolt against their Zamīndār-s now swelled the ranks of the two marauders. A further English operation with Sikh troopers also met with disastrous failure, making them a threat of the highest priority to the English overlords. Finally, they had some luck as they trapped Bāg and brought him to our city to stand trial for murder. Raṇcoḍdās’s accountant was the witness testifying against him. However, in a daring raid, Bagīch and his Bhilla-s burst into the court, killed the witness and the judge, and galloped away into the mountains. Finally, the monstrous Christian fanatic officer Effingham was tasked with taking down the two. He successfully corralled them at the Virūpādri fort with his Gorkha troops and killed them, as indicated in the plaque we saw. What followed was a bloodbath in which over a thousand Bhilla-s were massacred at Effingham’s orders, and they were slapped with the status of a Criminal Tribe.”

L: “Whoa! What a tumultuous intersection between the ancient system of predatory tribes, which has long been a feature of the Indosphere, with the English tyranny!” Just then, Somakhya received a message from Vidrum: “I think I have had a revelatory dream that solves many of our mysteries. I’ll come over and tell you — call Lootika to come over too. Sharva will be giving me a ride over to your place.” Lootika and Somakhya had wished to do other things that day, but sensing Vidrum’s excitement, they decided to give him an ear. Vidrum and Sharva burst into their friend’s house, saying they had a dramatic resolution of the previous day’s events. V: “Last night, I had a dream in which Dandśūkrāj Pāṇḍey reappeared. He thanked me for making the laḍḍu offering on his behalf. He then said: “Dalāl-jī would be well-disposed towards you from now on.” I wondered who he was, and asked him. He said his story still lives in the records of the Archaeological Museum. He followed it with some Section letter and manuscript number, but sadly, I do not remember it!” L: “That’s very interesting; Somakhya just told me the story of a certain Raṇcoḍdās Lallubhāi Dalāl, who was slain by the same Bāg- and Bagīch-singh, who were memorialized atop the hill!” S: “Based on the research I did last year, I can tell you that the witness who was killed in court by Bagīch was none other than this Dandśūkrāj Pāṇḍey.” V: “It is too bad I don’t remember the details of his manuscript.” S: “Never mind. The museum recently digitized their records. We can search the same and find it if it exists. Browsing through it, they soon realized that Section E was the one including material from the 1800s. In that, they zeroed in on Manuscript 18, titled in an Apabhramśa, “The self-story of Dandśūkrāj Pāṇḍey.”

Sh: “Vidrum, you are most facile with this Apabhramśa, could you please read out for us anything you find interesting in the manuscript?”
V: “Dandśūkrāj Pāṇḍey says: Truly the age of the Kali has come upon us from which only the coming of Nārāyaṇa, like the great comet mentioned by Jayadeva, can save us. On one side, we had the depredations of the mahāmada-s and, on the other, the Ingrāz. Our father had wished to study the Veda or become a soothsayer by studying Jyotiṣa, but the fall of the Hindu rāj had prevented him from continuing those ambitions. Hence, he became an accountant for the śreṣṭhī Dalāl, originally from Adripura. He wanted me to pursue a more Brahminical education and suggested that in order to survive in this age, I study Jyotiṣa and become an augur, for the masses will always want to know their future. Thus, I went to Vārāṇasi to pursue my studies. However, seeing the brutal murder of the brāhmaṇa Candraśekhara by the Ingrāz mleccha, I decided to join the war of independence. Unfortunately, I learnt that our people had some serious problems. I myself might be accused of contributing a bit to it. We never learnt how the mleccha-s operate. Large numbers of our own people were willing to fight for them rather than our own side. Moreover, our alliance with the mahāmada-s was bound to fail sooner or later. How can our dharmayuddha be compatible with their Jihād? Despite initial successes, the mleccha-s gained the upper hand. The case of Candraśekhara had shown to me that even when one is good to them, the mleccha is perfidious. They are probably even more vengeful and devoted to exterminating their enemies than the Mahāmada-s. They have also invented this communication with Indra’s grace — the telegraph — our chappāti-s stand no chance against it. Hence, I decided to quietly escape from the north and return home. It was a wise decision because no sooner had I left, the mleccha-s carried out a blood-letting that outdid tyrant Balban or Firoz Tughlaq of old. Back home, having to earn a living, and obtain a wife, I took over from my father as an accountant and tax collector for the Dalāl’s son, Raṇcoḍdās Lallubhāi.”

The war was drawing to a close, and the last pockets of resistance were being quelled by the mleccha-s and their deśīya collaborators. We now were transferred from the rule by the Kampani Bahadur to direct rule by the wicked Rājñī Viṇmati of the Ingrāz. Nothing could be more humiliating — the whole of Hind had been conquered by a mere band of pirates of the Kampani Bahadur. But a reflection on its cause revealed a deep defect in the character of our own people and leaders. The heavy hand of the Kali age could be felt in every action of the mleccha. The most basic food item, salt was being taxed and restricted. The free passage of goods by our sārthavāha-s was being restricted at the Great Hedge and other such outposts. My dalāl employer wanted to sell deśīya textiles, but every roadblock was put in his way, forcing him to focus on banking and money-lending. This, in turn, created a rift between the dalāl-s and the ryot-s. This culminated in the irruptions of Bāgsingh and Bagīchsingh, who killed my employer. To add insult to injury, instead of cremating his corpse, they buried it in someone’s grave in the cemetery that lies beyond Bhaktamārga. I could not let his death go unavenged. The śreṣṭhī was a pious man who had supported Hindu institutions. Hence, I took a vow that I would offer laḍḍu-s to the Vināyaka of Virūpādri if he helped me capture Raṇcoḍdās’s murderers and thus release his bhūta. Thus, unwilling as I was, I had to collaborate with the mleccha-s to bring them to book. I led them to Bāgsingh’s lair, and he was captured, and he will be tried soon.”

Lootika: “Ah, Somakhya just told me the rest, which completes the lamented Dandśūkrāj Pāṇḍey’s tale.” She proceeded to fill Vidrum and Sharvamanyu with the history Somakhya had just narrated to them, concluding: “I believe that he acted via Vidrum to fulfill his final vow to the god. But who is the poltergeist?’’ V: “Lootika, you have apprehended part of the puzzle. Remember, Pāṇḍey told me in the dream that the dalāl would be good to me going forward. He was buried by the marauders in the cemetery based on Pāṇḍey’s tale; hence, I believe he was aroused as a poltergeist when my house was built over part of the cemetery. I suspect that the activity we experienced before we left for Virūpādri was him sensing his possible release or a meeting with his assistant in life, Dandśūkrāj Pāṇḍey.” L: That would be remarkable if true: it would join a small minority of cases where a poltergeist can be actually traced back to a deceased individual. ”

V: “To round it off, Pāṇḍey has left this curious addendum at the end of his story.’’ It read thus: “I attended a śāstrārtha by some learned brāhmaṇa-s in town. They were discussing how long it would take for us to regain our freedom. One of them said the way things stand with our people, it will take at least 200 years. I had learnt a bit of mantrasādhana at Avimukta. Hence, I practiced the sādhana of the vetāla to give me an augury. He told me that it would happen sooner than 100 years. But within 100 years from then, we will face another reckoning with the mleccha-s and mahāmada-s. The mleccha is prone to thieve what others make or build and claim everything for himself. He brooks no one else’s possession of power. Hence, it is unavoidable that they place impediments in the path of the practitioners of the dharma leading to future clashes.” Somakhya stared into the distance in introspection.

Some snippets from early Indo-Sinitic probabilistic prognostication texts

The below is the barest sketch of a topic that has already been treated in multiple book-length works by learned scholars of the Orient. However, none of these works were entirely familiar with the Hindu side of the tradition leaving lacunae in their analyses. We have long studied this material and wanted to write a brief note on it. This may be seen as a sampler or a precursor of such.

At least since the Neolithic, humans can be seen as having two complementary (even if implicit) views of life: The first is probabilistic. In this view, there are certain probabilities with which future events will happen to a person. The person tries to estimate those probabilities and tailor his actions accordingly. Built into this idea is the subjective updating of probabilities (called by some as Bayesian inference after the eponymous theorem). Thus, one starts off with a certain prior probability distribution, which might be very crude, but as one encounters events in life, one acquires an intuitive sense of likelihood of those events. One then computes a distribution of the likelihood across the probability interval. Then by multiplying these two distributions and normalizing by their sum, one gets a new probability distribution, the posterior, which updates our probability of the event occurring. While this formal method might not appear straightforward to the majority of people, they carry out such updating intuitively. The only problem in real life is accurately computing the likelihood distribution for doing the update. The second view of life is deterministic. In this, one sees oneself as inexorably drawn towards a pre-determined fate. Whatever one does is already determined, and all actions and the sense of free action are merely an illusion.

With some introspection, one may arrive at the conclusion that these two views are ultimately complementary. Because one cannot infer one’s fate though it is predetermined, one acts as though it is probabilistic and the estimation of probabilities is merely a technical attempt to determine the course it would take. Given this, not surprisingly, over the ages, humans have sought prognostication methods. Interestingly, those methods show a comparable bifurcation along the lines of probabilistic and deterministic approaches. This is well illustrated in the Hindu prognostication. Strong determinism is exhibited in the texts of astrological prognostication (partly influenced by Greek tradition) — uranomancy (prediction by celestial phenomena) and hemerology (calendrical prognosis, with muhūrta-s, śubhadina-s, etc.). Here, it is held that the future may be predicted by reading celestial patterns at birth and the subsequent, entirely predictable, movement of celestial bodies. In contrast, a probabilistic approach is encoded in the cleromantic traditions (prognostication by dice or lottery) that were once common in old India.

Evidence for the early spread of cleromancy across Asia from India is suggested by parts of the enigmatic Bower manuscript. This manuscript has a colorful history. It was purchased in 1890 CE by the English soldier Bower, who was chasing down a Mohammedan murderer all the way from Kashmir to the ancient oasis town of Kucha in central Asia. Its seller was a local treasure-hunter, and his agents had found the manuscript at a supposed bauddha ruin. The decipherment of the Bower manuscript by the German scholar Buhler and its eventual editing and translation by another German scholar, Hoernle, finally brought it to the public between 1893-1897 CE. While modern “mainstream” white indologists date the texts to the 500s of the Common Era, the text itself is written a late Brāhmī script that was used in India during the early Gupta age. This would suggest an earlier date for the manuscript. The language of the manuscript is a grammatically degraded register of Sanskrit, forms of which are often termed “Buddhist Hybrid Sanskrit.” Parts 4 and 5 of this manuscript contain two distinct cleromantic texts. The first of these, part 4, opens with a remarkable set of mantra-s:

namo nandi-rudreśvarāya । namo ācāryebhyaḥ । nama īśvarāya । namo maṇibhadrāya । namaḥ sarvayakṣebhyaḥ । namaḥ sarva-devebhyaḥ । śivāya namaḥ । ṣaṣṭhyai namaḥ । prajāpataye namaḥ । rudrāya namaḥ । namo vaiśravaṇaya । namo marudbhyo namaḥ । prāsakāḥ patantu imā asya+arthasya kāraṇā hili hili kumbhakārī-mātaṅga-yuktā patantu ।
yat satyaṃ sarva-siddhānāṃ yat satyaṃ sarva-vādināṃ tena satyena satya-samayena naṣṭaṃ vinaṣṭam kṣemākṣemaṃ lābhālabhaṃ jayājayaṃ śivānudarśaya svāhā ।
satya-nārāyaṇe caiva devate ṛṣiṣu caiva satyam mantraṃ vṛtiḥ satyaṃ samakṣāḥ patantu svāhā ।
satyaṃ caiva tu draṣṭavyaṃ …
ni——–[maṇi?]-mantrauṣadhīnāṃ ca nimitta-balam anantaram mṛṣatāyāṃ devatāyāṃ viṣṇu navikāyāṃ caṇṭayāṇṭa ।
namaḥ puruṣa-siṃhasya prasannas te janārdanaḥ nihatāḥ śatravaḥ sarve…

Obeisance to Nandirudreśvara. Obeisance to the ācāryas. Obeisance to Īśvara. Obeisance to Māṇibhadra. Obeisance to all the yakṣas. Obeisance to all the devas. To Śiva obeisance. To Ṣaṣṭhī obeisance. To Prajāpati obeisance. To Rudra obeisance! Obeisance to Vaiśravaṇa. Obeisance to the Marut-s. Obeisance.
May these dice fall for this [prognostic] objective! hili! hili! May they fall set to work by Kumbhakārī, the Mātanga woman!
That truth which is of all the Siddha-s, that truth which is of the professors of all paths; by that truth and by that true consensus, what is lost and preserved, welfare and lack thereof, gain and loss, victory and defeat, may Śiva make that apparent svāhā!
In the true Nārāyana, and in the deity, and also in the ṛṣi-s lies the truth of the incantation, the choosing (i.e., the choice of prognosis by dice fall). Truth! May the dice fall together! svāhā! And may the truth be seen!
…the strength of [amulets?], incantations, medical herbs, and augury are uninterrupted by error. The deity Viṣṇu [unclear]. Obeisance of the the Man-lion; be you pleased. Janārdana has slain all enemies…

In the above text, we have not reproduced Hoernle’s transcription but have attempted to restore, where possible, the original mantra-s. A reader can compare it with his transcription, which is close, though in parts, displays its characteristic tumbled-down Sanskrit. Hoernle also provided a translation with his transcription, which was well done given the state of the text. We provide our own, which we believe sometimes hews closer to the intention of the text. Notwithstanding specific objections one may have to this translation or restoration, the mantra-s are rather striking for the following reasons:

1. The opening salutation is to the deity Nandirudreśvara. This name is rare in the śaiva literature and thus serves as a rather specific marker. The name is used for the tetracephalic Rudra worshiped in Kashmir at the Nandīśa-kṣetra associated with the Sodara spring. Indeed, the Nandi-kṣetra-māhātyma specifically mentions Nandirudra as one of the four faces of the Rudra associated with the bhūtagaṇeśvara Nandin:

śarva-nandi-mahākāla-devī-vadana-maṇḍitam ।
bhūteśvaraṃ bhūtapatiṃ ḍṛṣṭvā martyo vimucyate ॥
paścime vadane vīra mama vatsyasi yatsahe ।
bhūteśvaraḥ sarvabhūtaḥ sutīrthāntargato vibhuḥ ॥
śrīkaṇṭhaḥ pūrvavadane mahākālo ’tha dakṣiṇe ।
paścime nandirudras tu devī saumye pratiṣṭhitā ॥

Adorned by Śarva-, Nandin-, Mahākāla- and goddess- faces,
having seen [that] Bhūteśvara, the lord of ghosts, mortals are liberated.
The mighty Bhūteśvara [who] is all beings resides in this holy ford.
I permit you, o hero [Nandin], to reside in my western face.
Śrīkaṇṭha is established in the eastern face, Mahākāla in the southern face,
Nandirudra in the western face and the goddess in the direction of Soma (northern face).

The same deity is worshiped in several other Kashmirian texts like the Nīlamatapurāṇa and the Haracaritacintāmaṇi. This establishes that the compound Nandirudreśvara is specifically the Śiva of Nandikṣetra — he who is the Īśvara of Nandirudra. Hence, we can say with confidence that Part 4 of the Bower manuscript had its provenance in a Kashmirian text composed in the vicinity of this kṣetra. Thus, it finding its way to Kucha almost mirrors the journey of Bower in quest of the Mohammedan criminal.

Figure 1. An image based on Nandirudreśvara installed by a bauddha sarvādhikārin. The first picture shows the western Nandin face.

2. It shows some archaisms, such as the worship of the Kaumāra goddess Ṣaṣṭhī, the prominence of the Kaubera cult, the use of the name Prajāpati, importantly, the worship of the Marut-s. Contra Hoernle, we believe that the term Puruṣa-siṃha is an archaic version of the popular vibhava of Viṣṇu, Nṛsiṃha. In the actual prognostications associated with the dice falls, we find the invocation of the Aśvin-s and repeated invocation of the deity Maruta — it is not clear if this meant the singular deity with an akārānta name or vulgar plural of Marut. As we shall see below, Rudra, Marut-s and Viṣṇu had a persistent connection to dice prognostication.

3. This is perhaps the earliest attestation of the Viṣṇu devatā Satya-nārāyaṇa.

The second cleromantic text from the Bower manuscript, part 5, is attested in India in the form of later-day variants going under the name Pāśaka-kevalī. However, part 5 is again marked by interesting opening mantra-s. These mantra-s are more lacunose than those in part 4. Hence, we again provide a restoration based on Hoernle’s transcription with a separation of the mantra-s:

—- namasyāmi lokanāthaṃ janārdanaṃ yena satyam idaṃ dṛṣṭaṃ ya divya —————————- ।
prāhu tat sadbhi ha dṛṣā । tālā bhālā kā sukhaṃ duḥkhaṃ jīvitam maraṇaṃ tathā । iha sarvam manuṣyānām marudbhiḥ samudīritam । ṛṣibhir nirmitā — ।
meru-vāsam prayojitā – । imā vidyā tatas teṣāṃ hṛṣṭā vai marut-ādayaḥ । tad yathā । vimale vimale nirmale devi devi va– yat satyaṃ yat su-…
taṃ tat sarva darśaya apetu mānuṣaṃ cakṣu divyaṃ cakṣu pravartatu । apetu mānuṣa-śrotraṃ divya-śrotam pravartatu । apetu mānuṣaṃ gandhaṃ divyaṃ gandhaṃ pravartatu । apetu mānuṣā jihvā divyā jihvā pravartatu । māli māli svāhā ।

The terms tālā and bhālā, which Hoernle saw as implying the palm and forehead augury, are also noteworthy — it might be one of the earliest hints of palmistry in the Indosphere — suggesting that links between the disparate mantic traditions were already emerging. As one can see, it shares certain key features with the text of Kashmirian provenance in part 4. Both texts invoke the Marut-s and Viṣṇu. The consistent invocation of the Marut-s, who were prominent in the Vedic register of the religion, along with the other archaisms in part 4, raises the possibility that this cleromantic text had deep roots going back to the Vedic period. Indeed, it is conceivable that the Marut-s, who were seen as the force moving the planets or as metabolic forces in the body, were also conceived as the forces moving “luck” in the form of the dice throws. While the text in part 4 invokes Kumbhakārī-mātaṅga-yuktā, the part 5 text invokes the goddess Vimala, who in the Bodhāyana-mantrapāṭha appears as one of the goddesses in the Kaumāra circle. Again the deity Māli could be a variant of the name of the goddess Mālinī of the Pūrvāṃnāya. Notably, the later Pāśaka-kevalī recensions from different parts of India contain an archaic prognostic incantation to Kūṣmāṇḍinī Durgā, who is remarkably also termed Mātaṅginī in the mantra:

oṃ namo bhagavati kūṣmāṇḍinī sarva-kārya-prasādhinīi sarva-nimitta-prakāśini ehy ehi tvara tvara varade hili hili mili mili mātaṅginī satyam brūhi svāhā ॥

This suggests that the invocation of a Kaumāra goddess and/or Mātaṅginī was a likely part of the old cleromantic tradition. Further, the prognostications in part 5 invoke Maheśvara Mahādeva — those who worship him have a good prognosis; those who do not, fail to receive the desired goods. This links these cleromantic traditions to the Maheśvara divination, which was recovered in a manuscript from Cave 17 at Mogao. This text links the Hindu cleromancy to Cīna, Turkic and Tibetan cleromancy and will require a separate treatment. However, we believe that thematically part 5 also throws light on an interesting Cīna text that has been the topic of some debate.

In the mid-400s, a Cīna, Hui-Chien from Jian Kang (today Nanking), produced a multi-volume magical work that he presented as a translation of an Indian work. It includes a volume termed the “divination by `spirit-tablets’ revealed by the god Brahman’’ and sanctioned for use by the Tathāgata. Some sinologists have claimed that it is a possible Cīna aprocryphon because no comparable Indian Sanskrit text has been found. However, it is likely that it has a Sanskrit original, as stated by the author of the Cīna volumes. This could have been composed in Central Asia, probably Kucha rather than core India. Indeed, in the past, it was suspected that these volumes were produced by the Kuchean mantravādin Śrimitra who visited Jian Kang. In this practice, the 100 prognostications specified in the text were written bamboo tablets or silk strips and placed in a multicolored silk pouch. Then, the sādhaka abstains from alcohol, meat, and the five foul-smelling Alliums (onion, garlic, leek, etc.) and rinses his mouth before the performance. He takes out 3-7 strips and reads the prognostications on them. Below are a couple of good prognostications (all translations below are by Strickmann edited by Faure):

27. How great the strength of this person’s felicity!
In all things, he receives the god’s protection.
All he desires shall be as he wishes,
Nothing not secure and safe.
Of a certainty, no dangers will impede him
And his fame will flow forth far and wide.
Spoken by the mouths of Śakra and Brahman,
This means all happiness, without deception.

83. I am concerned for this deserted orphan,
who will spend his whole life in the army.
Far separated from his old ancestral village,
Going this way and that, in pursuit of an alien wind [or, foreign customs]
Although he may be in other, far-off regions,
Brahma and Sakra will nonetheless raise him up.
In time he will return to safety and security,
And his friends and kindred will all rejoice.

One could also get bad prognostications:

31. You are an ill-omened person
And so have been made to dwell in this place.
In it are maleficent phantoms and demons
Which are constantly coming and loitering.
Your three hun and your seven po
Are bound and fettered to a vacant mountain.
You are in confusion and unsettled
And in the end will fall into the deep abyss.

66. Earlier, when you took a wife,
You thought yourselves a pair of mandarin ducks.
In harmonious union you established a household
Which would surely endure safely for a long time.
Suddenly, in the middle of the road,
You have begun to do one another harm.
There is no truce to your wranglings and disputes,
And your goods and chattels are also all dispersed.

In our opinion, the parallels in the prognostic tenor between the part 5 Pāśaka-kevalī-related text and the Cīna divination of Brahman suggest that, indeed, there was a Sanskrit equivalent of it that was accessed by either Hui-Chien or Śrimitra and it is no aprocryphon. This is supported by multiple other circumstantial lines of evidence: 1) The discovery of the Maheśvara divination at Mogao indicates that there is a body of texts of ultimately Hindu origin that reached the Cīna-s via the bauddha medium. Most of these were lost in India itself. 2) The divination of Brahman places itself against a Hindu background: as per the text, the Tathāgata approves of it because while the Hindus have such texts and benefit from it, the tāthāgata-s are not able to avail of such benefits. 3) Further, the beneficial effects come via Hindu gods Śakra and Brahman, much like the role played by Maheśvara, Aśvin-s, and Marut(s) in the Bower texts. We have an example from Kashmir of an image of Rudra modeled after Nandirudreśvara installed by a bauddha sarvādhikārin (Figure 1). This indicates how bauddha-s were incorporating Hindu material into their fold, especially when it came to practical traditions such as medicine and prognostics.

Notes on the Vaiṣṇava retinue deities-1

The śaiva pattern of worship, which is especially emphasized in the Iśāna-srotas (siddhānta), features the Nirmālya-devatā, Caṇḍeśvara with roots in the older Pāśupata atimārga. This deity receives offerings, such as leaves and flowers, that have been initially offered to Rudra-sadāśiva. In the śaiva-saura system, he appears as Tejaścaṇḍa, the Nirmālya-devatā of Sūrya. The Vaikhānasa and Pāñcarātrika systems of the Vaiṣṇava tradition also have an equivalent deity in the form of Viṣvaksena. However, we posit in this note that he also encompasses to a degree features of the ape-faced śaiva deity Nandin (sometimes bull-faced, especially in the later reflexes of the tradition), who is one of the great gaṇeśvara-s of Rudra’s hordes, and the sons of Rudra, the gods Skanda and Vināyaka. His worship is laid out in multiple Pāñcarātrika tantra-s. Below we shall primarily consider aspects of his worship taught in one of the older Pāñcarātrika texts, the Pauṣkara-saṃhitā, and the Śakti (Śrī)-oriented Pāñcarātrika text, the Lakṣṃī-tantra, along with parallels drawn from the Jayākhya-samhitā, another old tantra of the Pañcarātra-s. The Pauṣkara is presented as the teaching of the Bhagavant (Viṣṇu) to Pauṣkara (the lotus-born one, i.e., Brahman). Its colophon calls it the Pauṣakara-saṃhitā from the Mahopaniṣat of the Pāñcarātra. Despite this appellation, it resembles a rather standard tāntrika text in its structure and style of presentation. The two versions of the Pauṣkara that we used for this note have corruptions and lacunae, some of which might have crept into the transliterations presented below despite our attempts at restoration.

The name Viṣvaksena appears for the first time in the Mahābhārata and is associated with the Sāttvata strand of the proto-Pāñcarātrika tradition. There, it is used primarily as a name or an ectype of the Vāsudeva. Examples of this include the Viṣṇu-sahasra-nāma and the Viṣvaksena-stuti found in the Anuśāsana-parvan (“Critical” 13.143). In the latter, it is made clear that the Vāsudeva, equated with the Sāttvata hero, is the source and resort of everything (Vedic rituals etc.) in his Viṣvaksena manifestation:

vedāṃś ca yo vedayate .adhidevo ।
vidhīṃś ca yaś cāśrayate purāṇān ॥
kāme vede laukike yat phalṃ ca ।
viṣvaksene sarvam etat pratīhi ॥
jyotīṃṣi śuklāni ca sarvaloke ।
trayo lokā lokapālās trayaś ca ॥
trayo .agnayo vyāhṛtayaś ca tisraḥ ।
sarve devā devakīputra eva ॥
saṃvatsaraḥ sa ṛtuḥ so .ardhamāsaḥ ।
so .ahorātraḥ sa kalā vai sa kāṣṭhāḥ ॥
mātrā muhūrtāś ca lavāḥ kṣaṇāś ca ।
viṣvaksene sarvam etat pratīhi ॥
candrādityau graha-nakṣatra-tārāḥ ।
sarvāṇi darśāny atha paurṇamāsyaḥ ॥
nakṣatra-yogā ṛtavaś ca pārtha ।
viṣvaksenāt sarvam etat prasūtam ॥

Again, in the Harivaṃśa we encounter Viṣvaksena used in the same sense in the early Pāñcarātrika mantra of 101 words and 367 syllables (symbolizing Viṣnu as the year) taught by Kaśyapa found in its Appendix. The same sense is seen in the Viṣṇu-gāyatrī that was used by the Kaṭha-s of the Panjab and Kashmir in their daily worship following the manual of Laugākṣī (in place of the Nārāyaṇa-gāyatrī of the Taittirīyaka-s):
viśvarūpāya vidmahe viṣvaksenāya dhīmahi । tanno viṣṇuḥ pracodayāt ॥

This continues into the purāṇa-s such as the Padmapurāṇa, where the name is used in the above sense in several stuti-s dedicated to Viṣṇu. Thus, the transformation of Viṣvaksena from a name or an ectype of the Vāsudeva in proto-Pāñcarātra to the Nirmālya-devatā of tāntrika Pāñcarātra happened well after the Mahābhārata, Harivaṃśa and certain Paurāṇika sections. Nevertheless, interestingly, in the Pauṣkara-samḥitā we have Vāsudeva expound a theology of Viṣvaksena that hearkens back to the above stuti from the Anuśāsana-parvan. Thus, it appears that Viṣvaksena as the nirmālya-devatā still bears a connection to this older usage of the name (Pauṣkara-samḥitā, chapter 20):

Pauṣkara asks Viṣṇu about Viṣvaksena thusly:

ka eṣo .atulavīryo hi yasya dūrād dravanti ca ।
vighnā nimeṣa-mātreṇa trailokyonmūlana-kṣamāḥ ॥

Who is this, indeed of unequaled heroism, by whose mere wink obstacles capable of uprooting the triple-word melt away in the distance?

Viṣṇu answered:

klavaiśvānarākhyā yā mūrtis turyātmano vibhoḥ ।
sa eṣa dvija devaḥ syād viṣvaksenaḥ prakīrtitaḥ ॥
sthita āhavanīyādi-bhedena makha-yājinām ।
ṛk-pūtam hutam ādāya tarpayaty akhilaṃ jagat ॥
evaṃ mantra-mayād yāgāt sāttvikāt brahmabhāvitāt ।
saṃprāpya gurumūrter vai prāpaṇaṃ mantra-sat-kṛtam ॥
anāhūtāṃ surāṇāṃ ca sarva-loka-nivāsinām ।
svayaṃ saṃvibhajaty āśu tad anugraha-kāmyayā ॥

He is known as Kālavaiśvānara (the fire of the end of time), who is an emanation of the four-fold lord (i.e., the Vāsudeva with the 3 other vyūha-s). O twice-born one, he is that god who is known as Viṣvaksena. He is situated in the types of fire altars viz. Āhavanīya and the like of the Vedic ritualists. Having taken the oblations sanctified by ṛk-s, he satisfies the entire universe. Thus, obtaining [the essence] from the rituals filled with incantations, from purity, proper ritual intention and the form of the teacher, he verily gains the good deeds of the mantra [deployment]. And he himself quickly apportions these to the uninvoked gods dwelling in all the worlds with the intention of gaining their favor.

In terms of the temple ritual, in addition to the contruction of a Viṣvaksena shrine within the third circuit of the Viṣṇu complex, he may be housed in a separate temple to the south of a village (Sanatkumāra-saṃhitā). His worship in these shrines is accompanied by a special dance and music. The emergence of Viṣvaksena as the Nirmālya-devatā seems to have led to a special group of priestly assistants, the kārin-s, who partake of the final offerings handed over to Viṣvaksena.

The yantra of Viṣvaksena (Pauṣkara, chapter 20):

dharmādy ananta-paryantaṃ pañcakaṃ navakaṃ tu vā ।
sattvenācchāditam paścāt kevalam ambujaṃ smaret ॥
aiśāna-soma-diṅ-madhye catur-aśra-pure .atha vā ।
dvāra-śobhāgra-nirmukte rekhā-tritaya-bhūṣite ॥
tad antare .ardha-candrasthe kamale .aṣṭa-dalānvite ।
sāmrājye viniyuktaṃ yad vighnānām acyutena tat ॥

One may meditate on the pentad or nonad of deities, Dharma etc., until Ananta. Thereafter, one may meditate on the One lotus enveloped by sattva. [Then one worships Viṣvaksena] between the northeastern and the northern directions or in a square yantra. It lacks doors and flanges (typical of other square yantra-s), and [its periphery is] marked with triple lines. Inside it, stationed atop a lunar crescent, is a lotus with eight petals. [In it is stationed] he who is appointed as the overlord of obstacles by Acyuta himself.

The above rendering is faithful to that mentioned in the Pauṣkara, including some further details that are implicit in it and followed by mantravādin-s. The central mantra of Viṣvaksena is that specified in saṃdhya-bhāṣā in the Lakṣmītantra and made explicit in its gloss (rhūṃ vauṃ). In actual practice, it is inscribed by sādhaka-s in the central position occupied by Viṣvaksena (see below). There is also a strong conservation of the location for the worship of Viṣvaksena in different early Pāñcarātrika texts. For example, this is specified thus in the Lakṣṃī-tantra, chapter 38:

soma-śaṃkara-diṅ-madhye kha-sthitaṃ saṃsmaret prabhum ।
viṣvaksenam udārāṅgam āyāntaṃ gaganāntarāt ॥
One should meditate on the lord, stationed in the sky, between the northern and northeastern directions. Viṣvaksena of benefic body [is visualized] as coming from the sky.

A similar account is given by the Jayākhya Saṃhitā in its 13th chapter describing the maṇḍala worship of Viṣṇu:
tryambakottara-digbhyāṃ tu madhyataḥ kha-sthitaṃ smaret ।
viṣvaksenaṃ dvijaśreṣṭha āyāntaṃ gaganāntarāt ॥

The visualization of Viṣvaksena (Pauṣkara, chapter 20):

iṣṭvā hṛt-puṇḍarīke tu svāpekṣā-niṣkalātmakam ।
tam eva sakalatvena yātaṃ dhyātvā yajed bahiḥ ॥
nava-dūrvāṅkurābhaṃ ca tvīṣat pītala-kānti-dhṛt
catur-daṃṣṭraṃ catur-bāhuṃ catur-muṣkaṃ catur-gatim॥
pūrṇāṅgaṃ kesari-skandhaṃ pṛthūras-sthala-rājitam ।
dakṣiṇā-varta-nimnena nābhi-randhreṇa śobhitam ॥
ājānu-bāhuṃ śrīmantaṃ piṅgalārcir-jaṭādharam ।
dravat kanaka-piṅgākṣa-cubukaṃ pṛthu-nāsikam॥
sita-dīrgha-nakha-śreṇi-śobhitaṃ kuṭila-bhruvam ।
muktā-vibhūṣitaṃ madhye mahāratnopa-saṃskṛtam॥
kuryāc ca dakṣiṇe pakṣe kṛta-śrīvatsa-maṅgalam ।
amāsitakyomaṇi(?) (…) tanmadhye kamalālayam ॥
dviguṇaṃ brahma-sūtraṃ syān nābheś cābhi-pradakṣiṇam ।
vistīrṇa-gaṇḍa-vadanaṃ bālendu-kuṭilopamaiḥ ॥
nava-kiṃśukāruṇābhair-lomaiḥ saṃpūrṇā-vigraham ।
śobhanena pralambena pṛthunā pronnatena ca ॥
māṇikya-kuṇḍalāḍhyena yuktaṃ śrotra-dvayena tu ।
mukuṭenonnatenaiva hārādyair upaśobhitam ॥
citra-kauśeya-vasanaṃ vicitra-sragvimaṇḍitam ।
pralaya-dvādaśāditya-sahasraguṇa-dīdhitim ॥
īṣad ūrdhve tathā tiryag vinipātita-locanam ।
kundendu-kānti-daśanaṃ kiñcid-vihasitānanam ॥
svabhāva-saumyam amalam māyā-krodhoparañjitam ।
savilāsa-calat-pādanyāsa-sthānaka-saṃsthitam॥
svenāntaḥ karaṇenaiva bhāvayantam param padam ।
aṅguṣṭhena kaniṣṭhāntam aṅgulais tu latātrayam ॥
nāmayitvonnatā caikā ghrāṇena viniyojitā ।
sad-vighna-bhīti-pradayā tv anayā mudrayā .anvitam ॥
rathāṅga-śaṅkha-hastaṃ ca lambamāna-gadādharam ।
śroṇī-taṭa-niviṣṭena sāvahelena pāṇinā ॥
itthaṃ rūpadharaṃ devam anekādbhūta-vikramam ।
karṇikā-madhyagaṃ tasya hṛd-ādyāmukhya-mantravat ॥

Having worshiped him in the heart-lotus, verily in his independent, undifferentiated form, visualizing him as having gone forth in his differentiated form, one may then worship him externally [visualizing him thus:] Having the complexion of newly-sprouted Durva grass tinted with a slight yellowish luster; having four fangs, four arms, four testes and four gaits; with a full body, lion-shoulders and flaunting a broad torso, endowed with a navel cavity bearing a clockwise spiral whorl; having arms reaching to his knees, opulent and bearing dread-locks with a tawny blaze; having eyes and chin like molten gold and with a broad muzzle; with an array of white, long nails, and with curved brows; with a pearl-decked necklace decorated with a great gem in the middle. He should be made to bear the auspicious Śrīvatsa on his right side. [—corrupt+lacuna—] in the midst of a lotus pond; with a two-fold ritual thread wound clockwise around the navel; with broad cheeks and face; with a form covered completely covered with ruddy hair of the color fresh kiṃśuka flowers; endowed with a beautiful, broad, well-stretched, and tall [form]; with two ears joined to ornaments of ruby; ornamented with a tall crown, garlands and the like; with eyes slightly upturned and cast obliquely; with teeth white as jasmine and the moon, and a face bearing a slight smile; though pacific and mild by nature, he displays the tint of mock anger. He stands with one foot stepping forth in a playful manner. He is seen as meditating upon the supreme state (Viṣṇu) as his inner consciousness. Having bent three of his creeper-like fingers from the thumb to the little finger, holding one erect, he unites it with his nose (This mudra might indicate prāṇāyāma). His other [hand] assumes the mudra of causing fear to the obstacles [faced] by the good. His hands hold a wheel, a conch and a mace hanging downwards; One of his arms rests on the side of the hip in a warning pose. One should worship the god with such a form with many a miraculous power in the midst of the pericarp [of the lotus maṇḍala].

There are several parallels found in the much shorter description provided by the Lakṣṃī-tantra’s account of the daily Pāñcarātrika-homa-vidhi. Here, the ritualist sets aside some of the cooked rice for the offering and makes fire sacrifices to Viṣvaksena (Lakṣṃī-tantra, chapter 40):

prāg eva vibhajed annaṃ prāpaṇāt saṃpradānataḥ ।
tenānnena yajet samyag viṣvaksenaṃ caturbhujam ॥
maṇḍalāntam upānīya samāhūyāmbarāntarāt ।
navāmra-patra-sadṛśaṃ piṅga-bhrū-śmaśru-locanam ॥
pīta-vastraṃ catur-daṃṣṭraṃ sva-mudrādvitayānvitam ।
gadā-khaḍga-dharaṃ devam abhyarcya kramaśaḥ sudhīḥ ॥
sāṅga-mudrām athā darśya gatvā kuṇḍa-samīpataḥ ।
viṣvaksenas tato bhaktyā tarpaṇīyas tilākṣataiḥ ॥
vauṣaḍ antena mantreṇa dadyāt pūrṇāhutiṃ tataḥ ।
maṇḍale pūjayitvātha kuryāt tasya visarjanam ॥
svamantreṇa suraśreṣṭha kṣamasveti padaṃ vadan ।
mudrāṃ ca darśayet taṃ ca nabhasy utpatitaṃ smaret ॥
viṣvaksenārcanaṃ sarvam agādhe .ambuni nikṣipet ।
toyenāstra-prajaptena plāvayen maṇḍalaṃ ca tat ॥

The ritualist should partition a portion of cooked rice from the storage vessel (we render prāpaṇa as such based on the parallel version in the Jayākhya; see below) before offering it [to Viṣṇu]. With that rice, he should sacrifice to the four-armed Viṣvaksena. Having brought him close from the sky, the intelligent ritualist should invoke and worship with the due procedure [Viṣvaksena] in the maṇḍala as having the complexion of a young mango leaf with tawny brows, mustache and eyes; wearing a yellow garment, with four fangs, displaying his own mudra; holding a mace and a sword. Having then displayed the mudra-s of the aṅga-s and having gone close to the fire altar, he should thereafter, with devotion, make quenching offerings of sesame seeds and parched rice. Then, with the [Viṣvaksena]-mantra ending with a vauṣaṭ, he should offer the final oblation. Having worshiped him in the maṇḍala, he should then perform his sendoff, o lord of the gods (Indra, to whom Lakṣṃī is revealing the tantra), with his own mantra (Viṣvaksena) ending in the phrase “pardon me”. He should then display the mudra-s and visualize him as flying away into the sky. He should then discard the items used in the worship of Viṣvaksena in deep water. He then immerses the maṇḍala in water by muttering the astra incantation.

A similar ritual is provided in the Jayākhya Saṃhitā, chapter 14:

tena bhāṇḍa-sthitenāpi samāhūyāmbarāntarāt ।
viṣvaksenaṃ yajed bhaktyā dhyātvā vai maṇḍalāntare ॥
catur-bhujam udārāṅgaṃ gadā-śaṅkha-dharaṃ vibhum ।
navāmra-patra-saṅkāśaṃ piṅgala-śmaśru-locanam ॥
pīta-vastraṃ catur-daṣṭraṃ sva-mudrādvitayānvitam ।
samabhyarcya kramātsāṅgaṃ mudrām asyātha darśayet ॥
gatvā kuṇḍa-samīpaṃ tu mantraṃ puṣpaiḥ prapūjya ca ।
bhasmanā .astrābhitaptena lalāṭe tilakaṃ śubham ॥
kṛtvā maṇḍalavat paścād upasaṃhṛtya cātmani ।
viṣvaksenas tato bhaktyā tarpaṇīyas tilākṣataiḥ ॥
vauṣaḍ antena mantreṇa dadyāt pūrṇāhutiṃ dvija ।
maṇḍale pūjayitvā .atha kuryāt tasya visarjanam ॥
svamantreṇa dvijaśreṣṭha kṣamasveti padena ca ।
mudrā-samanvitenātha nabhasy utpatitaṃ smaret ॥
pūrṇena kalaśenātha astra-japtena nārada ।
kṣīrāmbu-madhurājyena prāpayen maṇḍalaṃ tu tat ॥
tataḥ kuṇḍāt samutthāpya viṣvaksenaṃ yathā purā ।

A key point regarding Viṣvaksena’s iconography in the tāntrika texts is his apparently therianthropomorphic form. While some Vaiṣṇava-s closer to our times have conflated his iconography on occasions with that of Vināyaka (see below), it is clear from the old Pāñcarātrika texts that this was not the case for Viṣvaksena — he is never called Gajavaktra in these texts. Nevertheless, the above-cited saṃhitā-s are united in mentioning him as having four fangs suggestive of therocephaly. This is made more concrete in his most detailed iconography presented in the Pauṣkara. There, several explicit descriptors are provided, such as lion-shouldered, having a broad muzzle, ruddy hair, tawny locks, and long nails/claws. Taken together with him being four-fanged, it appears that the early Pāñcarātrika tantra-s conceived this god as having leonine aspects or being lion-faced. This therianthropomorphic form also suggests a thematic overlap with Nandin in the śaiva world, who was originally seen as being ape-headed. Like Nandin, Viṣvaksena is seen as the chief of the Gaṇarājeśvara-s of Viṣṇu’s hosts (see below). While these texts do not specify the iconography of Viṣvaksena’s wife, Puṣpadharā (the medieval Śrīvaiṣṇava scholar Vedānta-deśika call her Sūtravatī), her iconography is briefly specified by the Pādma-saṃhitā as being similar to that of Śrī (Kriyāpāda, chapter 22):

devīṃ ca viṣvaksenasya vāmapārśve pratiṣṭhitām ।
nāmnā puṣpadharāṃ kuryāt kamalām iva lakṣitām ॥

The other Gaṇarājeśvara-s (Pauṣkara, chapter 20):

padmac-chadāntarasthāṃ ca tadā-karadyutiṃ vinā ।
kintv aṅgānāṃ ca sarvatra dhyānam uktaṃ sitādikam ॥
gajānano jayatseno harivaktro mahābalaḥ ।
kālaprakṛti saṃjñaśva caturthaḥ kamalodbhava ॥
gaṇa-rājeśvarā hyete catvāraś caṇḍavigrahāḥ ।
ājñā-pratīkṣakāś cāsya suśveta-camarodyatāḥ ॥
vināyakādayaś caiva vighneśa-pravarāstu ye ।
amīṣāṃ gaṇanāthānāṃ nityam-ājñānupālinām ॥
īśānādiṣu koṇeṣu padma-bāhyasthitān nyaset ।
vīkṣamāṇā vibhor vaktraṃ tat tulya sthānakā-sthitāḥ ॥
tadvat karāṅkitāḥ sarve kintu mudrā-vivarjitāḥ ।
dhyānam eṣāṃ pṛthag bhūtaṃ śarīram avadhāraya ॥
bhīmaṃ dvipendra-vadanaṃ catur-daṃṣṭraṃ trilocanam ।
kambu-grivaṃ catur-bāhuṃ pūrṇa-candrāyuta-dyutim ॥
hāra-nūpura-keyūra-mekhalādāma-maṇḍitam ।
nānā srag-gandha-vastrāḍhyam anaupamya-parākramam ॥
dhyāyed gajānanam ato jayatsenaṃ ca saṃsmaret ।
mahat-turaṅga-vadanaṃ padmarāgācala-prabham ॥
dravac cāmīkarākṣaṃ ca anekādbhuta-vikramam ।
harivaktram ato dhyāyet saṭāc churita-mastakam ॥
niṣṭapta-kanaka-prakhyaṃ ghora-gharghara-nikhanam ।
mṛga-rāḍ-vadanaṃ vipra kalpāntānila-veginam ॥
kālaprakṛti-nāmānaṃ bhāvayed añjanādrivat ।
daṃṣṭrā-karāla-vadanaṃ piṅgala-śmaśru-locanam ॥
jhaṣa-kuṇḍalinaṃ raudraṃ mīnavan nimna-nāsikam ।
gaṇa-rājeśvarā hyete mahā-puruṣa-lakṣaṇaiḥ ॥
saṃyuktāś cākhilair vipra tv āpādāt kandharāv adhi ।
yat kiñcin maṇḍanaṃ vastu tadādyoktaṃ smaret triṣu ॥
eteṣām arcanaṃ kuryāt svanāmnā praṇavādinā ।
namontenābja-saṃbhūta nānā-siddhi-phalāptaye ॥

Within the bounds of the lotus [maṇḍala] and without the [central] radiance of rays (this part is unclear to us, but it apparently refers to the petals of the yantra outside the central region where the radiance of Viṣvaksena is situated) but with all limbs [aṅga mantra-s] the meditation of the retinue gods is specified, colored white etc (mantravādin-s state that these are white, red, yellow and black). Gajānana, Jayatsena, Harivaktra and Kālaprakṛti of great might, these together are known as the tetrad, o lotus-born one. These four king-lords of the gaṇa-s [of Viṣṇu] of fierce forms attend to [Viṣvaksena’s] orders, with good white yak-tail fly-whisks held aloft. Then there are Vināyaka, etc., those who have Vighneśa as their chief, ever obedient to the orders of those lords of the gaṇa-s (The aforesaid tetrad of Gaṇarājeśvara-s). These should be placed in the Northwest etc corners (i.e., at the interstitial directions) outside the lotus. They should look towards their [respective gaṇa] lord, adopting a stance equivalent to them. Their hands are equipped with the same implements, but they do not display any mudra. Please pay attention [now] to the visualization of the embodied forms assumed by each [Gaṇarājeśvara]. With the face of a terrible elephant-lord, with four tusks and three eyes, having a neck [smooth as a] shell, with four arms and the radiance of a 10,000 full moons; ornamented with garlands, anklets, armlets, a girdle and a necklace; decorated with various garlands, perfumes and vestures, and having unequaled valor; thus, one should meditate on Gajānana. Jayatsena should be visualized with a great horse-face, the radiance of a ruby mountain, with eyes like molten gold, endowed with many miraculous powers. Then one meditates on Harivaktra with a head strewn with manes, resembling heated gold and roaring like a terrible musical instrument (gharghara is an old Indo-Aryan musical instrument accompanying Vedic recitations and singing). O vipra, he has the face of the kings of the animals and the velocity of the wind at the end of the kalpa. He, Kālaprakṛti by name, should be visualized as [resembling] a mountain of collyrium; with a terrifying face displaying fangs; with tawny mustache and eyes; wearing shark-earrings, fierce and having a fish-like deep snout. O vipra, all these king-lords of the gaṇa-s possess all the marks of the great persons from the feet to their necks. Whatever item of ornamentation was described for the first (Gajavaktra) should also be visualized for the [other] three. O lotus-born one, the worship of all these should be performed with their respective names starting with the praṇava and ending in ‘namaḥ’ for the attainment of various siddhi-s.

There are multiple remarkable features regarding these Gaṇarājeśvara-s:
1. Their names indicate a clear mapping onto their śaiva counterparts. Gajavaktra (Elephant-faced)= Gaṇeśa; Jayatsena (Conquering Army)= Skanda; Harivaktra (Lion-faced)= Haribhadra/Vīrabhadra; Kālaprakṛti= Mahākāla. In terms of iconography, that of Gajavaktra is transparently equivalent to that of Gaṇeśa. While the name of Jayatsena is an obvious match for Skanda, his hippocephalous morphology is a stark deviation from that of the latter and appears to be an attempt to capture some of the preexisting, ancient Vaiṣṇava iconography of Hayagrīva. While the later iconography of Vīrabhadra lost the leonine visage, that idiosyncrasy mentioned in the early texts (Haribhadra; e.g., the Proto-Skandapurāṇa) persisted in the classic Rudra-parivāra icons from Nepal. As for Kālaprakṛti, he retains, in the least, the complexion of Mahākāla. Given that these deities have deep roots in the śaiva tradition, unlike the sudden appearance of their counterparts in the Vaiṣṇava tradition, one may posit that they were pantheonic duplications to mirror their counterparts in the former tradition.

2. As noted above, in most old saṃhitā-s Viṣvaksena is presented as iconographically distinct from Gaṇeśa. Viṣvaksena shares the function of the remover of obstacles with Gaṇeśa. Nevertheless, multiple Vaiṣṇava tantra-s emphasize his distinctness from the latter and provide separate accounts of the worship of each of them (e.g., Jayākhya, Pauṣkara, Lakśmī). In the Pādma-saṃhitā, his iconography is provided thus (Kriyāpāda, chapter 22):

viṣvaksenaṃ caturbāhuṃ śyāmavarṇaṃ kirīṭinam ।
lambodaraṃ ca mukhyena kareṇābhayadhāriṇam ॥

Thus, he shares the lambodara feature with Vināyaka; however, even here, he is not described as Gajavaktra and the iconography of Vināyaka is expounded separately from him:

gajānanaṃ caturbāhuṃ lambakuṣiṃ sitaprabham ।
karaṇḍikā-mukuṭinaṃ lamba-yajñopavītinam ॥

These again point to pantheonic duplication rather than a simple replacement of Vināyaka by Viṣvaksena. The presentation of Viṣvaksena in the midst of 4 Vināyaka-s in the Pauṣkara mirrors the depiction of Skanda in the midst of the same in the old Kaumāra tantra, the Ṣaṇmukha-kalpa. Further, as the commander of Viṣṇu’s hosts, and in the very form of his name (whose army is everywhere), Viṣvaksena takes on certain features of Kumāra.

3. The account of the 4 Vināyaka-s in the Pauṣkara has some unclear points. First, all their names are not specified in this text. Practicing mantravādin-s give them as Vināyaka, Vighneśa, Pravara and Gaṇanātha. These four names are derived from the above text, but they are not used in that sense in the text. Second, they are said to be stationed outside the lotus of the yantra. Given that the lotus has 8 petals, with Viṣvaksena in the pericarp, and the Gaṇarājeśvara-s in the 4 petals of the cardinal directions, we are still left with 4 more petals. Some mantravādin-s logically place the 4 Vināyaka-s in those petals contrary to the account in the text.

Thus, the convergence between the retinues of the Rudra and Viṣṇu in the Tantric texts presents some of the same features seen more broadly in the course of the evolution of natural religions, especially the Indo-European religion. While we see strong ritual-category convergence (Nirmālya-devatā-s), their nature in terms of divine functionality shows a more diffuse overlap with the deities from the pantheons of other sects.

Some historico-linguistic considerations on Indo-Aryan

Over the past decade, the “Black” Kalasha people from the Chitral (<Skt. Kṣetra) region of the Islamic state in Northwestern India have been under increasing pressure from the Tehrik-e Taliban Pakistan and allied marūnmatta-s. The recent successes of the TTP are sadly placing these remnants of an ancient Indo-Aryan people on the brink of extinction. Their cousins in the same province, the Kho people, had already been converted to the rākṣasamata, perhaps as early as the 1300-1400s (It remains unclear if this was the consequence of the Mohammedan Mongol Amir Timur’s savage assault on the region). The other Kalasha people, the “Red” Kalasha, and related groups (Kāta, Kom, etc.) now reside in the adjacent Mohammedan state going under the name of Afghanistan. Some of them (known as the Siah-posh Kaffirs) had evidently directly collided with Timur, who was one of the early Ghāzi-s hoping to convert them. His attempt ended in failure due to fierce resistance from these hill-men. They survived as a heathen culture down to the jihād of 1896-96 CE when the Ghāzi Abd ar-Rahman Khan forced the forfeiture of the foreskins. Thus, they came to be known as the Nuristanis, who became famous in our times for the jihād against the Rūs. Whereas the Kho and the “Black” Kalasha speak an Indo-Aryan language, the extent Nuristanis speak languages of what appears to be a third branch of the Indo-Iranian. Extensive linguistic work on the Nuristanis and their neighboring Indo-Aryan groups has been published by workers like G. Morgenstierne and R.F. Strand. In the past month, E. Bashir has published a freely available lexicon of the Indo-Aryan Kho language, Khowar. Earlier this year, C.P. Zoller published his monographic book on the “Inner” and “Outer” theory of Indo-Aryan languages. In 2016, he had published a long paper summarizing the results of this book. These publications, together with the news of the possible extermination of the Kalasha of Chitral by the marūnmatta-s, prompted us to write a brief note focusing on some historico-linguistic aspects of the emergence of Indo-Aryan in the Indian subcontinent.

As a caveat, we should state that we believe that without philology, linguistics, how much ever technical sound, always offers a limited picture of a people. Further, despite the outward appearance of technical solidity, we suspect that certain practices and conclusions of linguistics may not be on as firm grounds as its practitioners imagine them to be. However, arguing against those wobbly parts of the science, in their own jargon, is not something we are too inclined to engage in at this stage of our life; hence, we might state some things without a complete presentation of the argument in terms typical of that field. Similarly, archaeology has little to offer without the combination of linguistics and philology. Hence, when we have only one of these pieces, the conclusions are necessarily incomplete and weaker than we would like. This is, unfortunately, the case with Nuristani and NW Indo-Aryan tongues, where most of the peoples have been converted to the rākṣasamata. These issues, along with our own lacunose understanding, will affect the conclusions in this note.

Briefly, the current picture from a combination of archaeogenetics and linguistics suggests that the core Indo-Europeans (i.e., excluding the Anatolian branch whose genetics and origins are still murky with the competing “Southern Arc” and “Missing Anatolian steppe ancestry” hypotheses) expanded out from the archaeological Yamnaya culture that had emerged on the Caspian-Pontic Steppes around 3500 BCE. An early eastern expansion (~3300 BCE) of the Yamnaya into the Altai region and Mongolia, the Afanasievo culture, is suspected as being the predecessor of the speakers of the Tocharian languages attested much later in history. A little later (3200-2900 BCE), further expansion(s) took place in a westerly direction. One of these Yamnaya-derived expansions, to the south via the Balkans, was probably the predecessor of Greek, Phrygian and some poorly attested old Balkan IE languages. The Middle Dnieper culture emerging to the northwest of the core Yamnaya zone was another expansion that might have been associated with wider movement, a part of which eventually led to the western Corded Ware expansion. The latter expansion likely bore the precursors of Germanic, Celtic and Italic branches that fragmented as the Corded Ware pushed westwards. The Middle Dnieper culture likely contained already differentiated groups, one branch of which was to give rise to the Balto-Slavic speakers. The other branch of these were people who called themselves the Ārya-s (Indo-Iranian speakers) and eventually pushed eastwards (On the grounds of philology and chariotry, we also posit a western extension that was absorbed into the Corded Ware successors). The archaeogenetic evidence published by Saag et al in 2021 suggested that the Ārya-s were present in the so-called Fatyanovo culture that emerged from the northeastern side of the Middle Dnieper culture around 2900 BCE.

From around this period, the Ārya-s appear to have come in contact with a distinct eastern group, the speakers of the Uralic (Finno-Ugric) languages as is indicated by the I-Ir loans in those languages (e.g., work by A. Lubotsky and more recently S. Holopainen). The loans suggest that this contact was over a protracted period because they show a certain heterogeneity suggestive of being acquired at different times during the evolution of the I-Ir. Other than the Proto-I-Ir loans, there are some loans that appear to be Proto-Iranian and others that might be Proto-Indo-Aryan, suggesting that the divergence of the I-Ir languages had already begun, but the two communities were still interacting. This also suggests that the break up of the Uralic languages was approximately coeval with that of the I-Ir branch of IE and might have been influenced by the contact with the Ārya-s. However, while relatively late Ir loans continue to be acquired by Uralic, we do not see that for Indo-Aryan. This suggests that at some point, the Indo-Aryans started moving further south and away from the Uralic contact zone. These movements probably corresponded to the emergence of the successor Sintastha culture (starting ~2290 BCE), from which the Ārya-s started expanding widely across Asia.

The first group of the Ārya-s to expand were Indo-Aryans. Based on the current archaeogenetic data, they entered the Indian subcontinent in the window between 2000-1500 BCE. This was roughly coeval with smaller groups of related Ārya-s invading West Asia and establishing themselves as the royal elite of the Mitanni state and smaller potentates in the Levant. The genetic history of the subcontinent suggests that the group entering this region was a much larger force than the groups invading West Asia. The Ṛgveda and the Avesta suggest that the early Ārya-s were a war-like people, which is also consistent with their taking up an elite position in the Mitanni kingdom. Hence, we posit that their emergence in the Indian and the West Asian horizon had a military dimension, sometimes led by leaders of comparable caliber to the much later Mongol and Para-Mongol steppe generals. Prior to the invasion of the Ārya-s, the Northwest of India was dominated by the highly urbanized Harappan civilization. The northern neighbors of the Harappans were people of the Bactria-Margiana Archaeological Complex, which had harbored a significant fraction of Harappan residents on the eve of the Aryan invasion. The genetic evidence suggests the ethnogenesis of the modern Indian people involved the admixture of the Ārya-s and the Harappans shortly after the former entered the subcontinent. We posit that, in the course of internal conflicts, a faction of the Harappans likely allied themselves to the Ārya-s, who were already operating on the periphery of the BMAC. This eventually led to the conquest of the Harappan domain by the Ārya-s and the rise to dominance of the Old Indo-Aryan language.

From the time we started studying the śruti in our childhood and then the Itihāsa-s, we realized that the Aryan invasion was not a singular event. Rather, it seemed likely on philological grounds that there were probably at least 3 waves of distinct but related Indo-Aryan groups spread out over a period of at least 500 years, if not more. Later, we realized that the White Indologist A. Parpola also advocated a multi-invasion model with 2-3 distinct invasions, albeit along a different timeline. We also wondered if this might have some relationship to the controversial theory of Outer and Inner IA languages that has been around for more than a century. This theory, first clearly presented by GA Grierson, posited that the IA languages could be divided into a peripheral group, including the languages of the NW of the Indian subcontinent, the south and the East (Outer), forming an envelope around the core group (Inner) spoken in the North-Central heartland. While the theory was disputed by S. Chatterji and more recently by C.P. Masica in their monographs on the topic, it was revived by F. Southworth and, more recently, C.P. Zoller. The latter’s reformulation, which is the most comprehensive, goes on to claim that the Outer group presents linguistic archaisms typical of an earlier flavor of IA that entered the subcontinent first. In Zoller’s Inner and Outer theory, he further proposes a “strong influence” of Munda/Austro-Asiatic on these early-entering Outer IA languages (c.f., M. Witzel’s Harappan as “para-Munda”). The Inner group contains innovations typical of the group that entered later, and he identifies with them with the “Vedic” Ārya-s. This may compared to Parpola’s theory of “Dāsa” (earlier) and Sauma (later = “Vedic”) Ārya-s. As per his hypothesis, the first wave of Ārya-s were already resident in a Dravidian Harappan civilization — while he initially proposed that these were Indo-Aryans, he now thinks they were a more archaic Indo-Iranian group. These were then overrun by the later Soma-worshiping Indo-Aryans associated with the Vedic tradition.

A combination of genetic, linguistic and philological data points to serious problems in Parpola, Witzel and Zoller’s proposals. First, the genetic evidence clearly indicates that the epicenter of Austroasiatic was in Southeast Asia and not in India. There is a clear genomic signal of the migration of the Munda branch that traces it from the Southeast Asian epicenter to mainland India, and this probably happened only after the collapse of the classic Harappan civilization. Further, there is no trace of this migration reaching the Northwest to participate or even have an influence on Harappan or the earlier wave of IA languages. In contrast, the Harappan successors, Indo-Aryans, and peripheral old Indian hunter-gatherer groups might have exerted some cultural and linguistic influence on these Austroasiatic migrants. Thus, both Witzel and Zoller’s theories (and earlier versions by the likes of Kuiper) of a Munda influence on any of the layers of OIA are falsified. There is little evidence for a sizable body of Dravidian loans in the earlier layers of OIA. Those potentially Harappan words in early IA show no evidence of primitively Dravidian etyma, unlike bona fide Dravidian words appearing in the much later layers of IA. Notably, the IA loans from Dravidian often point to MIA, suggesting that the Dravidian-IA contact happened only after the Ārya-s had settled in India for some time. Thus, a significant presence of Dravidian in the core of the Harappan civilization is very unlikely. Interestingly, S.Bonta (who, like many modern Hindus, wrongly denies the Aryan invasion) recently proposed an IA decipherment of the Harappan language. While we are skeptical of any decipherment of Harappan, let alone an IA one, we admit that Bonta’s decipherment process has several solid observations. These suggest that the language was unlikely to have been Dravidian, even though his Aryan readings are questionable. It is even possible that it had some remote IE-like features, given the role of the Iranian-Neolithic-related populations in the ancestry of both groups. Finally, Parpola’s hypothesis that the first wave of Ārya-s to settle among the Harappans were early un-/poorly-differentiated Indo-Iranians is not supported by the current archaeogenetic evidence. There is also little by way of such a signal in the archaeology of the Harappans. Moreover, there is no evidence that the early undifferentiated Ārya-s had moved anywhere that far south. However, in this regard, we should point out that the archaeo-genetic evidence from the core Harappan zone (as opposed to the so-called “Indus-periphery”) is virtually absent; hence, one cannot rule out some surprises.

Despite these problematic issues, we believe that linguistic data from Zoller and others’ analysis supports the philological inference that there were multiple waves of Indo-Aryan invasions into the subcontinent. First, we believe that some of the observations of Zoller and others point to a broader horizon of Indo-Aryan than that represented by the Vedic dialects. Some of this evidence comes from NIA languages, like Khowar and some from the Middle Indo-Aryan (MIA dialects). In this regard, one may quote T. Oberlies:
“The problem of the linguistic affinity of Pāḷi and the other Middle Indo-Aryan languages is well-known and is undisputed: These languages are by no means straightforward continuants of the Old Indo-Aryan of the Vedic corpus, as in all of them words and forms turn up which cannot be the (regular) outcome of any attested OIA ones.”

Below are some examples indicative of the broader horizon of OIA drawn from Oberlies, Turner, Zoller, Witzel, Bashir and Adams and Mallory’s reference volume on IE:
(1) The IA language of the Kho people is known as Kho-war, where war means language. The suffix “war” has no cognate in Sanskrit; however, it is attested in the Nuristani languages, e.g., Vasi-veri; veri being language. Thus, one could reconstruct an unattested OIA form *vari that was present in the common ancestor IA and Nuristani (in opposition to the attested bhāṣā from PIE root bheh/bhah; h subscripts being the postulated laryngeals). Notably, this has PIE provenance from the root wer(h1)- = to speak as attested in the English “word”, German “Wort”, Latin “Verbum.”
(2) Pāḷi tipu= tin. This indicates the existence of an OIA dialect with the form tṛpu as opposed to Vedic trapu.
(3) Pāḷi idha= here. This is an archaism from\ the postulated PIE hidha as opposed to Vedic iha that has lost the -d-.
(4) Pāḷi jhāma= fire. This again points to an ancestral form distinct from Skt. kṣā but is consistent with form, which might have been closer to the PIE root: dhegwh-= burn.

Second, the Ārya-s have historically had a strong lexicographic impulse, and this has resulted in several words not attested in the old texts being preserved in the Skt and MIA lexicons composed over the ages. The significance of such lexicographic words has been a matter of dispute among linguists, but we believe that Zoller is correct in pointing out that at least a subset of them are words from other dialects of OIA. More generally, there are words that are infrequently used in the preserved OIA texts that are found at significantly higher frequencies in MIA and NIA texts/speech. These words, too point to alternative dialects of OIA where their predecessors were probably used more commonly than in the surviving textual dialects. For example, Zoller points to the word kujjhaṭi, which is said to mean fog, being attested in the peripheral language Garhwali as kujeṛi/kujyaṛu, meaning mist or fog. While this word was likely ultimately of Harappan origin, it had found its way into a dialect of OIA outside the horizon defined by proper Sanskrit and from there into a NIA language.

Finally, we have some grammatical peculiarities in geographically distant NIA languages potentially belonging to the “Outer group” of Zoller. One such is the post-positional suffix derived from OIA -artham (e.g., kāmārtham or vijayārtham) used to express dative in languages like Khowar (suffix -te) and Siṃhala (-ṭa). Such -artham formations are absent in the oldest layers of Vedic but are seen in later registers of Sanskrit. This could have emerged as a substitute for the standard dative in the Outer languages under certain local influences that were not experienced by Vedic.

In the least, these observations point to the presence of multiple related OIA spanning early registers of Sanskrit and Para-Sanskrits that had a degree of lexical and probably grammatical divergence. As at least a subset of the lexical differences are of deep IE provenance, it is unlikely that this dialect differentiation happened in situ after the Ārya-s had settled in India after a single entry. One possibility is that the differentiation was already in place on the steppe — multiple groups (tribes) of Ārya-s with distinct but inter-intelligible dialects were part of the invasionary force that entered the subcontinent. Terms like mṛdhravāca (bad speech) used by one Ārya group for another (e.g., RV 7.18.13), support the possibility of such a differentiation on the steppe. One could also use the analogy of the Chingizid Mongols, where relatively recently divergent groups speaking different Mongolic dialects (Naiman, Kereit, Tatar, Chingizid) and more deeply divergent groups (Khitan) speaking a more remotely related Para-Mongolic (Serbi) language were rolled into single identity with a standard Mongolic dialect. However, as in the Mongol case, we would expect the Ārya-s to have undergone a degree of homogenization post-invasion under a chosen dialect rather than retaining the distinct dialect identities from the steppe in geographically distinct locales in the subcontinent. Thus, the situation is more in line with the proposal of multiple waves of Aryan invasions. Indeed, such a situation would be quite obvious for the emergence of the ancestors of the speakers of the Nuristani languages. Finally, the differential incorporation of Harappan words (sometimes preserved in lexicographic lists) would also favor the multiple invasion scenario. To us, the clinching factor is the alignment of this inference with a similar conclusion based on philological investigation of the Vedic texts and the Itihāsa-s.

In light of the above discussion, the Khowar lexicon recently published by Bashir is of considerable interest. Below, we extract a list of 230 words from that lexicon, which are largely of Sanskrit/OIA origin (we left some Old Iranian-derived ones that are close to OIA (e.g. bazú= arm) for comparison; though some seem to be IA words colored by Iranian phonology). A notable part of the lexicon of Khowar is rather mysterious to us, with no clear IA or Ir etymology or evidence for recent loans, e.g., the words for geckos: barkunzík and parkundíts. The part of the vocabulary that can be traced to OIA can be strikingly conservative on occasion (we will discuss some examples after the below word list) and this is in line with some conservative grammatical features of the language shared with the IA Kalasha language. For example, in both Kalasha (IA) and Khowar, there are verbs that have a- augmented past tense forms, which is a rare retention from OIA in NIA languages.

áɫi=duck; ámu= raw; amíšti=mixed; angár=fire; anǰík= wear; anǰíl= a~njalika; asík= to be; ašrú = tears; atepík= warm; ayí= snake; bahrtún= part of spinning wheel; baɫéik= defeat with force; bar= load; bat= boiled rice; bazú= arm; beri= outside; bil= hole; bispí= wasp (!); bisir= 20; boh= many;

boikrá= bird; boók= wife; boól= Pleiades; boóng= Cannabis; bordík= grow; bosún= spring; braár= brother; bran= ram; bruk= kidney; bruú= eyebrows; buɫí= birch; búmbur= bumblebee; bhum= earth/ground; čar= graze; čáxur=spinning wheel; čičibón= sparrow; čoṭík= drop; c̣oc̣hík= gnaw; čúst= pretty; čuúɫ= braid/tress;

čúli=small; čhaγ= shadow; čhik= break; čor=4; c̣ic̣hík= to learn; c̣hétur= field; c̣hiír= milk; daán= grain; dáɫum= pomegranate; danú= coriandrum; dar= wood; dodór= a lizard; doík= to milk; don= teeth; doól= drum; draγánj̣= famine; droc̣= grape; dronʋeṣú= bow and arrow [dron=bow]; dur = house; ḍal= group of people;

gaá= female yak; garbín= pregnant; gaz= grass; goγ= bug; goléy= pill; goɫ= throat; goóm= wheat; gordoóγ=donkey [gordo̍γ-phíṣu= medicinal mushroom]; grah= eclipse/snapping turtle; gram= subdivision of village; griṣp= summer; goγmá= cattle disease; goóɫ= gully[<garta]; hardí= heart; hiím= snow; host= hand; i=1; istári= star; iskóʋ= peg; ispusár= sister;

istrí= woman; išpašúr= father-in-law; ǰal= net; ǰamár= son-in-law; ǰamíži= twins; ǰoš= 10; ǰuʋári=millet [yavākāra]; ka=who; káku=cuckoo; kal= time; karbéɫi= camel-colored; kukaá= someone; kaγ= crow; kaleér= corpse; kánu= blind; kapál= head; kar= ear; karanḍí= trowel; karʋás= cotton; kaʋír= caper;

kí= which; kiɫáɫ= cheese; kóli= crooked; kórum= work; kreník= buy; kuh=valley; kukúɫi= puppy; kumóru= girl; kuṣk= upper chest+shoulder; kutér= knife; kheɫí= shield; khen= pickaxe/spade [khenéik= to hoe]; khol= threshing floor; khóɫ=bone/lower horse leg [Suśruta: khulaka]; khúṭu= lame; liík= lick; loh= copper; lohá=iron; lóšṭing= clod of earth; ma= me;

mac̣hí= bee; mahrč= marīci pepper; manḍáγ= heron [i.e., frog-eater]; maník= to agree; mantharí= magic incantation; marík= kill; mas= moon/month; mahʋarí=menses; matshí= fish; mayón= oriole/song-bird; mažík= sweep; mirú= urine [miík= to urinate]; mo= do/should not; moóš=man; mothrénik= urinary bladder; mox= face; mroy= deer; muɫ= bottom/tuber; murík= twist/knead; musúl= pounding stone;

mušṭ= fist; mut= pearly; nam= name; nar= man; nas= near; naskár= nose [nastúɫi= nasal mucus]; niškík= excavate; noγór= fort; nohtík= dance; nun= today; nyof/ nyoh/= 9; hosík= laugh; ošṭ= eight; pačhán= hidden; palál=threshed wheat; panǰaráṣ= full moon [15] ; patadém= leaves flying around; paṭáng= falled down; paṭingán= vātigagma brinjal; paʋ= a fourth;

peṣík= to grind [peṣún= ground flour]; piík= to drink; pilíli= ant; pinḍálu=ball of yarn; pinḍóru= ball; piyóṣ= colostrum; poc= feather; pon= path; pong= foot; ponǰ= 5; por=previous year; pošík= to see; praš= ribs; práʋi= ahead; prúšṭa= in front; púli= rotten; pulúṣu=flea; púši= cat/flowers; phaší=snare; phuík= to blow;

reṣú= bull; riík= leak; saráng= tunnel; se= he/she; sind= river; suʋérum= gold; sot= 7; srung= horn; suík= sew; sum= with; šalák= grasshopper; šalí= rice; šar= sharpner; šargú= dung; šax= vegetable; šil= wooden splint; šokhór= sugar; šor= 100; šot= oath; šron= hip;

šútur= thread; ṣoɫéṣp= glue; taf= heat; taɫ=key/lock; tan= one’s self; taṣnagí= thirsty; tat= father; ton= warp; tracọ́n= carpenter; trínguɫ: three-pronged fork; troy= 3; trup/thrup= salt/radish; tu= you; tuṣ= straw; than= body; thé= then; thruṣní= thirsty; thuhrt= river ford; thuík= spit; thukúnu= sharp;

thul= fat/thick; ṭhun= pillar; ušṭú/išṭú= brick; ʋarúni= color; ʋečhík= to beg; ʋez= medicine; ʋor=weft; ʋreẓnú= garlic; žaník= to know; žúnu= alive;

• The word for bow dron, is particularly interesting because unlike Kalasha, which uses the descendant of OIA dhanus, Khowar shares the descendant of drūṇa/druṇa, a rare word for bow, with the Nuristani branch. It is likely derived from dru= wood used in the sense of the droṇa-kalaśa (druṇa in the Ṛgveda). Alternatively, it is derived from the root drū, probably meaning hurl, as seen in the word drūṇāna in the famous kṛṇuṣva pājaḥ sūkta (RV 4.4.1), where it is used in the context of an archer.

• boól= Pleiades is derived from the less-frequently used Skt. bahulā. While it appears that bahula might simply have been used in an adjectival sense to indicate the multiplicity of stars, the occurrence in Khowar suggests that it might have been an ancient IA name for the asterism. This would be consistent with its presence in a name of Skanda, Bāhuleya, paralleling Kārttikeya.

• karbéɫi= camel-colored. This is a NIA attestation of a derivative of OIA karabha for camel. Whereas the only word for camel in the Veda is uṣṭra (predating the complete I-Ir separation), we find the word karabha used for it for the first time in the Mahābhārata. This word is consistently associated with the camel in lexicographic literature. For example, the Rājanighaṇṭu gives:

uṣṭro dīrghagatir balī ca karabho dāserako dhūsaro lamboṣṭho lavaṇaḥ kramelaka-mahājaṅghau ca bījaṅghrikaḥ ।
dīrghaḥ śṛṅkhalako mahān atha mahāgrīvo mahāṅgo mahānādaḥ so ‘pi mahādhvagaḥ sa ca mahāpṛṣṭho baliṣṭthaś ca saḥ ॥

Interestingly, the word passed on to OId Gujarāti as karahu and Old Marāṭhī as karahā (evidently from the Prakrits) but notably in Siṃhala as karaba. This is again a case of the extreme “Outer languages (Khowar and Siṃhala)” preserving similar forms. However, in Lanka, where the familiarity with the camel waned, it came to also be applied to an elephant, which was the case in some of the more southern expressions in Sanskrit. While there is no evidence for the domesticated camel being common in the Harappan civilization, we have evidence for the Bactrian camels in the Indus Periphery, i.e., BMAC and Eastern Iran. An image of a camel has been reported from the Harappan outpost at Shortugai, close to those regions, and also much farther away at Kalibangan. This does raise the possibility that karabha was ultimately a BMAC-derived word, much like kramelaka was ultimately derived from Phoenician probably via Greek kamelos.

• kiɫáɫ= cheese. This is a descendant of the Vedic word kīlāla and a relative of the word kilāṭa= cheese or condensed milk found in later Sanskrit. Homologous words (kilāy) are also found in the non-IE language, Burushaski, from the Northwest of the subcontinent, Nuristani languages (kilā), and in South India in Tamil (Kiḻāaṉ= curd). The word occurs only once in the Ṛgveda Maṇḍala 10 and 7 times in the vulgate Atharvaveda, which is a smaller text than the RV. This suggests that it was indeed associated with a distinct later stream of Vedic. Its meaning has been mysterious to the later authors, but based on the context of its occurrence in the Śāṅkhāyana Gṛhyasūtra (e.g., 3.3.1), we may go with the colostrum (semantically equivalent to the older word pīyūṣa), which is consistent with its application for dairy products in both Aryan and non-Aryan languages.

Tragically, due to the Army of Islam, nothing survives of the Kho religion, and only fragments survive of the Kalasha religion. Further, we have the division of the Kalasha into the Indo-Aryan and Nuristani branches, adding to the uncertainty of the reconstructions. Nevertheless, what we know of the Kalasha religion indicates a system that was a sister group of the Indo-Aryan religious tradition. As Witzel correctly noted, it bears certain features of the Old Indo-Aryan religion of Veda but lacks the later developments. At the same time, it is not a replica of the Vedic religion. Interestingly, the utā (<hotṛ) fire ritualists of the Kalasha is a feature shared with a strand of the old Vedic and Zoroastrian traditions. This suggests that their tradition sprung straight from the hautra tradition of the old I-Ir tradition and did not incorporate or participate in the ādhvaryava stream of Vedic and Iranian traditions. This may be consistent with our proposal based on Vedic traditions of distinct IA groups from the steppe, with either a dominant hautra and ādhvaryava, coming together in the Indian subcontinent to constitute a later unified śrauta tradition.

Theology and AI

A key feature of most polytheistic religions, typically natural religions, is the importance of a multiplicity of visualizations of deities. This visualization might be solely mental/textual or expressed in different ways in the graphic and plastic arts. The mode of representation can change dramatically over time in the same religious tradition. For instance, we can infer that the early Indo-Europeans, going back to their Indo-Hittite past, had a fairly elaborate visualization of deities, but it was minimally expressed as physical iconography. However, different branches of Indo-Europeans convergently acquired physical artistic expressions of their pantheon in their loci of post-conquest settlement. Sometimes, these interacted with each other, resulting in fusions of styles. Thus, in the borderlands of the Panjab, there developed a vigorous iconographic tradition that brought together three distinct branches of Indo-European expression—the Hindus, the Iranics (Zoroastrian and Non-Zoroastrian), and the Greeks. The triumph of the Romans brought together the Greek and Roman traditions into a common iconographic expression that additionally swept in various non-IE articulations from West Asia and North Africa. The Afro-Asiatic tradition of the Egyptians was an early and vigorous expression of divine iconography (eikonikés anaparastáseis ton theón; pardon my Greek) that probably went on to influence all Eurasiatic traditions at a deep level. The mysterious Sumerians and their Afro-Asiatic successors of the Semitic branch (Akkadians, Assyrians, and Babylonians) also developed an early and strong iconographic convention that influenced various other traditions in the course of the development of a pan-Eurasiatic iconographic convention. Some key elements of this shared tradition include:

(1) The horned deity (Vedic: tigmaśṛṇgin); (2) The depiction of the thunderbolt and the trident as key weapons of the gods; (3) the lion-riding warrior goddess; (4) The great deity riding a bull; (5) The archer/hunter deity of the Orionic region of the sky; (6) The winged deity; (7) The deity inside a solar disk; (8) The deity with the lunar crescent (sometimes equivalent to the bovine horns); (9) The serpentine connections of divinities; (10) therianthropomorphic or sauranthropomorphic deities.

While all these elements might not appear simultaneously in a given culture, a wide constellation of them tended to co-occur and, over time, became widespread in genetically diverse cultures throughout West Asia, Central Asia, India, and eventually beyond. At the same time, we should also point out that certain zones were likely originators of trends that might have spread more widely later but were characteristic of those locales. For example, zoomorphy and zooanthropomorphy were dominant themes in Egypt with its deep connections to the rich African fauna. Some traditions, like the Hindu tradition, actively expanded these tendencies, building on its old roots in the Veda, with likely inspiration from the North African tradition. In this regard, we may note that there is good evidence for prolonged Indo-North African religious contacts. We have material evidence suggesting Egypto-Harappan contacts in the pre-Aryan age, but the effects of these contacts on religion are unclear. We believe that these contacts continued after the Aryan conquest of the Harappan lands, and Egyptian Book of the Dead traditions influenced certain developments in the Upaniṣat-s. Parallelly, the Egyptians also received Indo-Aryan religious influence from the West Asian Indo-Aryan elite in the Mitanni kingdom and other smaller principalities. Subsequently, the Indo-Aryan iconographic traditions influenced the other major North African center south of Egypt, the Meroetic civilization (e.g., the “war”-god Apedemak), with probably reverse influence in terms of zooanthropomorphic iconography. However, Romans coming from the same IE religious tradition as the Hindus had much greater inhibition to adopting the North African zooanthropomorphic iconography—in fact, the Caesar Augustus explicitly disapproved of the same. In contrast, the Harappan civilization was comparable to its Indo-Aryan successor in its primitivism and relatively low interest in graphic and plastic expressions of iconography. Its relatively meager iconography notwithstanding, it still produced some distinctive trends that were to have a more widespread impact, such as the horned deity in the midst of a menagerie and a possible early form of polycephaly in the depiction of the same deity.

Figure 1. Zeus Nikephoros with the elephant on Indo-Greek coins and its adoption as a vehicle of Athena among other Macedonian successor states

More generally, the stated iconographic motifs reveal a tendency among different polytheistic traditions to recognize the conceptions of divinities in others and apply them to their own pantheons. This is supported by the adoption and persistence of both related and unrelated but relevant iconography across vast spatial, temporal, and cultural distances. For instance, the early Aryans and Greeks did not originally associate the elephant with Indra but acquired this association during their encounters with India, adopting the animal for war and transport. In the case of the Hellenes (Figure 1), the animal was organically adopted for Zeus due to its prior association with his cognate Indra among the Indo-Aryans. However, its association with war left a significant impact on the Macedonians/Hellenes during their invasion of India, leading them to adopt it for Athena, the transfunctional goddess of IE provenance with a prominent warrior aspect (Figure 1). The diffusion of Hindu motifs, such as the elephant, is also seen in the Gundestrup cauldron (the Gajalakṣṃī motif). This supports the contention that Hindu iconography of Viṣṇu with the wheel and the club was adopted for the Celtic deity Taranis, as attested by the ancient Gaulish bronze found in 1774 CE at Le Chatelet, France, and the fragmentary Netherny Taranis now housed at the Tullie House Museum (Figure 2). While Taranis is a deity of the Indra-class, the overlap between the Viṣṇu- and Indra- classes, along with the generality of the metaphor of the cakra in IE tradition, allowed the adoption of Viṣṇu-class iconography for him. The key point to note here is that the transfer of iconography was possible due to a certain ‘pre-adaptation’ already present in the Celtic tradition, stemming from the shared Post-Yamnayan IE tradition. This pre-adaptation was not stored in an existing tradition of graphic or plastic arts but in the form of a subtle tradition usually stored in language, ritual, liturgy, and myth. A similar case could be made for inter-cultural resonance, along with shared ancestry between the Hindu, Iranic, and Classical worlds in the convergence of the iconography of Rudra, Vayush Uparikairya, and Jupiter Optimus Maximus Dolichenus (and their consorts, e.g., Juno Regina Dolichena).

Taranis (Le Chalet, L; Netherny R)

Jupiter Optimus Maximus Dolichenus

Figure 2. Taranis and Jupiter Optimus Maximus Dolichenus

We go further to assert that this ‘essence’ of religion can recognize cognate elements in other polytheistic traditions, even without a close phylogenetic relationship between the interacting cultures. A prime example is the transmission of Hindu iconography by traders from India to West Africa. Here, the tricephalic iconography of Dattātreya, along with his dogs, was adopted for the African deity Densu (Figure 3). Similarly, the iconography of Densu’s consort Mami Wata and other West African deities was influenced by elements of the Hindu trans-functional goddess. Unlike the aforementioned Indo-European examples, there’s no recent ‘phylogenetic’ relationship between Hindu and West African traditions. Nevertheless, the iconography brought by Hindu traders connected with the culturally stored conception of divinities among the West Africans, serving as conduits for the iconic realization of their endogenous deities. To this date, an ongoing trend reveals Hindu iconography inspiring new expressions in native West African religion. A similar phenomenon occurred, albeit across a slightly smaller ‘religio-phylogenetic’ gap, in the adoption of the Hindu tradition in originally Shinto Japan. While the old Shinto religion had elements of deity functionality mapping onto the Hindu sphere, the evolutionary divergence was deep. The main vehicle for the transmission of this tradition to Japan was the bauddha counter-religion, which had several Hindu elements wrapped within it. Notably, the Japanese picked out the Vaidika and successor Hindu elements from the bauddha matrix, making it a prominent part of their religion, either independently or through syncretism with their original Shinto tradition (e.g., the Shibamata Tai-shaku-ten festival resembling the Indra-maha).

Densu

Mami Wata

Figure 3. Hindu iconography in West African religion.

The subtle tradition or ‘essence’ of polytheistic religion appears to be transmitted almost in parallel to genetic transmission (with the above-stated tendencies for lateral transfer, as commonly observed in organismal genetics) over long periods in intact natural cultures. From that ‘essence,’ we observe expressions in various more tangible forms. The most ‘subtle’ of these tangible expressions are liturgical compositions and aniconic rituals, as seen in the śruti and successor Indo-Aryan texts. More embodied forms of these expressions could take the shape of religious iconography. Although a comparatively limited body of liturgical texts from the Greek or Italic tradition has come down to us, we find an exuberant expression of their traditions in the Attic pottery of the yavanas, as well as in Greco-Roman gems and seals. Through a comparison of the divine depictions in these Classical artistic productions and the Hindu textual material, numerous close parallels emerge. Thus, it almost appears as if what the early Hindus expressed as oral compositions resurfaced much later in these sister cultures as expressions on pottery or gems. As an example, we illustrate below (Figure 4) a gem sealing depicting Zeus battling the Anguipedean Gigantes on his chariot (also seen on pottery). This depiction captures the essence of a śruti-mantra:

yajāmaha indraṃ vajra-dakṣiṇaṃ
harīṇāṃ rathyaṃ vivratānām ।
pra śmaśru dodhuvad ūrdhvathā bhūd vi
senābhir dayamāno vi rādhasā ॥
We sacrifice to Indra, vajra in his right hand,
the charioteer of bay horses with different gaits,
tossing his mustache/beard, standing erect, as
he is protecting with weapons and is being generous [with gifts].

Apart from the obvious parallels to the depiction on the gem seal, we may also note that the anguipede configuration of the Gigantes is mirrored in one of the dānava-s slain by Indra having the form of a snake — Ahi/Śuṣṇa. Further, the Gigantes hold rocks/mountains reminiscent of the parvata-s smashed by Indra. As an aside the term “harīṇāṃ rathyaṃ vivratānām” (bay horses going their own way) reminds one of the Iranian name Vishtāspa (horses going apart) of the ally of Zarathustra, the founder of the Iranian counter-religion and is in semantic contrast to the name of a Sāmaveda ṛṣi Sākamaśva: horses coming together.

Figure 4. Zeus slaying the Gigantes with his thunderbolt.

The comparisons between Greco-Roman manifest arts and Indo-Iranian textual traditions led us to conclude that the expression closest to the subtle ‘essence’ transmitted through the polytheistic traditions is the linguistic one. If this expression encounters a method of “reification,’’ it can engender different forms of iconic expression. The degree of sophistication of this conduit of “reification’’ will determine the expressiveness of the outcome. Thus, the early Greeks and Hindus were prone to primitivism in their iconic expression as they apparently only had access to relatively unsophisticated ‘reificatory’ pathways. But once they acquired these, they became increasingly more sophisticated, albeit in divergent ways. The Greek tradition tended towards a high degree of realism (something that was retained to a degree in the Indo-Greek tradition). In sharp contrast, the Hindu tradition tended towards suggestiveness — realism only to the extent of emphasizing particular traits to produce a synesthetic experience in the beholder. Thus, we reasoned that with the advent of machine learning methods for generating images from text, we might be able to experiment with this idea of the subtle ‘essence’ being contained in the text and being reified via AI. These experiments of ours seem to have sparked off a somewhat popular movement in the Hindu social media space. We first began these last year (December 2022) with the Stable Diffusion image generator. The results were primitive yet, in our opinion, very promising. Hence, we knew that with both improved training and generative capabilities, we would get far superior results. While work with MidJourney was providing glimpses of this in other kinds of image production, both the disappointing results of our initial experiments with it and that the system kept preventing us from using it discouraged us from further experiments in daiva-citra-janana.

Figure 5. Productions of the god Skanda by Stable Diffusion (Dec 7, 2022)

However, a major step towards realizing more serious results from our experiments came earlier this year with the release of DALL·E 3 via the Microsoft AI interface. No doubt, some of the same problems we had seen with Stable Diffusion continued to plague the generations of DALL·E 3: poly-/hypo-dactyly; flawed symmetry in polymelic configurations; flawed facial symmetry; failure to render eyes correctly; failure to grasp number and geometry; imperfect understanding of the shapes of most weapons. That said, for the first few days, it performed brilliantly, showing how much the algorithm had improved and what its true potential was. We should confess that we were positively surprised, much like by the performance of its sibling system ChatGPT and, for the first time, found it to be seriously usable. The improvement could be qualitatively likened to that seen in neural-net-based protein structure prediction methods, like between the earlier iterations of Alphafold and Alphafold2. However, just as ChatGPT was blunted to fit the plainly evil and tyrannical worldview of the navyonmāda-addled Big-Tech, within less than two weeks, the DALL·E 3 system too was blunted by the successors of Dvāranāma-mahāduṣṭa. Anywhere between 30-90% of all the prompts, on even relatively innocuous Hindu religious themes, were blocked by the system, depending on the day. What to say of the fact that our gods can like gore, skulls, bones, and deadly weapons, and it will remain so irrespective of what the wicked mleccha-s want us to think? In a sense, what we are seeing is the same vehement animosity of the classical Abrahamisms filtering through its secular manifestation, navyonmāda. We will say nothing of the tricks to get past the blocks to a degree (why help the evil overlords?). Further, the quality of the production also declined in subtle ways with efforts of the Dvārādi-mahāduṣṭa-s to reshape the system to bend to their navyonmāda. Nevertheless, in our opinion, it has given us a glimpse of the true possibilities that could be achieved going forward.

On the positive side, it gives us powerful evidence for our hypothesis that polytheistic religion carries a certain subtle ‘essence’ transmitted through its bearers, with linguistic expression being closest to that subtle informational essence. Having learned from all the ‘reifications’ available in the digital image world, the machine can successfully extract this essence from the linguistic prompt and generate a new ‘reification’ that comes quite close to genuine productions by the tradition. This, to us, is an important development because it gives us a glimpse of how a neural network—a brain—very much unlike ours can visualize a devatā much like a sādhaka does from a mantra (typically from the śruti) or from the dhyāna-śloka in the case of the āgama. This gives us a modern glimpse of how the ancient Hindus conceived mantras: as a packet of information—sattva in sāṅkhyā terminology—that can acquire a body, i.e., that of the devatā to whom it is directed. Hence, they saw the mantra as the subtle body of the devatā, and we can see why, to the ancients, it appeared as if it were imbued with its own generative consciousness. Of course, the ‘tangible’ body the mantra/devatā is able to acquire depends on the capacity of the sādhaka and his cultural memory. Some sādhakas can easily generate very detailed imagery of a devatā in their mind’s eye or see it appear in a dream. Others are simply unable to do so at all. Yet others, like us, lie in the middle: we are able to perceive the subtle structure of the image (in our case, even vividly) but are unable to convert it to an actual visual manifestation in the mind’s eye or a dream. Sometimes, the actual visualization might manifest in a transient flash in the hypnagogic or hypnopompic state. For such sādhakas, AI could indeed be a potent aid if it is allowed to reach its full potential in public use.

However, it is also clear that the AI is not yet there in a complete sense, even setting aside the evil machinations of the dvāra-saṃsthā in preventing the full extent of actualizations possible with the current systems. Some devatā-s are naturally durlabha — crucially, they are devatā-s who simply cannot be currently glimpsed by the AI. Their conceptions are so intricate that the AI cannot reach them via its current training. But even among those that can be attained by the AI not all are reached at a given time. If you are religious insider you could see the success of the AI generations as a sign of whether the devatā is fully manifesting to you or not. This has two components to it. First, depends on whether the sādhaka has a tattvāveśa of the devatā — does he understands the śāstra enough — to provide prompts that allow a suitable manifestation to him. The second is the stochasticity of the emissions from the model: this is much like in real life — can the biological generative interface (the brain) display the devatā. This could be interpreted as the devatā’s anugraha. Then there is the question of how the first ‘prakṛti’-s of the visualizations of particular devatā-s were established in a culture. This relates to the term ‘kavi-prajāpati’ coined by the great Kaśmirian historical kavi: a kavi is like the god Prajāpati in generating totally new forms de novo. The AI is able to generate because it can utilize the vast body of preexisting modules in its training set. These act like the textual and cultural memory a sthapati can draw from in creating a pratimā, but where did his prakṛti come from in the first place? A part of it is the selective process, akin to natural selection, acting in memetic space. However, the first origination relates to special inspiration even as the special conditions during the first origination of life. To us, it seems the AI is not yet there; perhaps that is why we would say it is not yet a real AGI while skirting its boundaries. Whatever the case, such technology has shown its immense potential; however, its control by Big-Tech, as illustrated by their rather evil censorship and sandbagging of the technology, is frightening. This is not the kind of thing that can be easily reverse-engineered by writing code at home on your laptop. It requires immense resources, which can only be accessed currently by Big-Tech and a few individuals within it who have total control over what it can do. Thus, the world has already been divided into haves and have-nots, a power differential that will be wielded, potentially devastatingly, in the future.

We end with a few samples of DALL·E 3 generated daiva images.

1. Aditi engendering the Āditya-s

2. The god Agni and the goddess Agnāyī emerging from the ritual fire

3. The god Bhaga with his two consorts stabilizing Dyaus and Pṛthivī

4. The gods Bhava, Śarva and Rudra

5. The universal form of the goddess Indrāṇī: Viśvatomukhī

6. The masked Kaumāra goddess Mukhamaṇḍikā

7. Indra

A prayoga of the Hiraṇyakeśin-s

To our knowledge, the Hiraṇyakeśin branch of the Taittirīyaka-s is today only found in pockets in Mahārāṣṭra and the Drāviḍa states. While they follow the Taittirīya-śruti like other Taittirīyaka-s, they additionally have their own unique mantrapāṭha furnished with its own little Ṛksaṃhitā. They have a unique procedure for the gṛhya rite of Puṇyāhavācana, which combines both Vaidika and laukika, i.e., Paurāṇika elements. A Hiraṇyakeśin from the Marahaṭṭa country, who was unaware of their mantrapāṭha, wanted advice on performance of the Puṇyāhavācana and Mātṛkā- and laghu-deva-pujā-s for which he had a short prayoga-paddhati handed down in his family, but did not know some of the mantra-s specified only by pratīka therein. Hence, we used his paddhati to spell out all the mantra-s (without svara-s for the Vaidika ones). We present it here as it has some notable features. The paddhati itself is similar to a longer version we had seen in the manual of a learned brāhmaṇa from the same region (it borrows from Bodhāyana in multiple places where evidently the Hiraṇyakeśin counterpart was either absent or sketchy). The longer version differs from the below in packing several additional Vaidika mantra-s into the Puṇyāha recitation. At the end of the rite, both this short paddhati and the long one I had seen earlier provide a Mātṛkā-pujā without details of essentials such as prāṇapratiṣṭhā and ṣoḍaśopacāra-pūjā (the longer manual has prāṇapratiṣṭhā independently as a section later in the text). The long manual follows this up with a nāndī-prayoga and an aṅkurāropaṇa. Our interlocutor’s short manual used mantra-s corresponding to aṅkurāropaṇa for a laghu-deva-pūjā to the five gods Prajāpati, Indra, Yama, Varuṇa and Soma, followed by a tarpaṇa to longer list of deities. This longer list of deities is offered āhuti-s as part of the Grahamakha (the planetary fire-rite of the Hiraṇyakeśin-s) in the longer manual. His objective was to perform the Puṇyāhavācana and the subsequent Mātṛkā- and laghu-deva-pujā-s, which we were able to successfully advise him on. More generally, we believe that this could be a model for a generic deva-pujā by a non-sectarian lay Hindu.

PDF of Devanagari script encoding of the text.

atha hiraṇyakeśinām puṇyāhavācana-vidhi :
haridrā-bimbe gaṇapati-sthāpanam :
gaṇānāṃ tvā gaṇapatiꣲ havāmahe kaviṃ kavīnām upamaśravastamam ।
jyeṣṭharājam brahmaṇām brahmaṇas pata ā naḥ śṛṇvann ūtibhiḥ sīda sādanam ॥

puṣpāñjaliṃ datvā sarvopacāraiḥ saṃpūjya :
mantrahīnaṃ kriyāhīnaṃ bhaktihīnaṃ gajānana ।
yat pūjitaṃ mayā deva paripūrṇaṃ tad astu me ॥

vighneśvarāya varadāya surapriyāya
lambodarāya vikaṭāya gajānanāya ।
vināyakāya śruti-yajñavibhūṣitāya
gaurī-sutāya gaṇanāthā namo namas te ॥

Notes: This section is the classic invocation of Vināyaka in a clod of turmeric. It became a staple opening for smārta rites with the rise of the Paurāṇika register of the religion. Hence, this part can be assigned to the classic Paurāṇika period.

kalaṣa-sthāpanam :
kalaśatrayaṃ sthāpayet ।

mahī dyauḥ pṛthivī ca na imaṃ yajñam mimikṣatām ।
pipṛtāṃ no bharīmabhiḥ ॥

tayoḥ pañcaratnāni prakṣipet :
yuvā suvāsāḥ parivīta āgāt । sa u śreyān bhavati jāyamānaḥ । taṃ dhīrāsaḥ kavaya unnayanti । svādhiyo manasā devayantaḥ ।

kalaśopari vastraveṣṭanaṃ kṛtvā :
pūrṇā darvi parā pata supūrṇā punar ā pata ।
vasneva vi krīṇāvahā iṣam ūrjaꣲ śatakrato ॥

kalaśe varuṇasyāvāhanam :
tat tvā yāmi brahmaṇā vandamānas tad ā śāste yajamāno havirbhiḥ ।
aheḍamāno varuṇeha bodhy uruśaꣲsa mā na āyuḥ pra moṣīḥ ॥

kalaśa-mukhe apa āvāhayet :
sarve samudrāḥ saritas tīrthāni jaladā nadāḥ ।
āyāntu mama śānty arthaṃ durita-kṣaya-kārakāḥ ॥

abhimantraṇam :
draviṇodā draviṇasas turasya draviṇodāḥ sanarasya pra yaṃsat ।
draviṇodā vīravatīm iṣaṃ no draviṇodā rāsate dīrgham āyuḥ ॥

navonavo bhavati jāyamāno ‘hnāṃ ketur uṣasām ety agre ।
bhāgaṃ devebhyo vi dadhāty āyan pra candramās tirati dīrgham āyuḥ ॥

uccā divi dakṣiṇāvanto asthur ye aśvadāḥ saha te sūryeṇa ।
hiraṇyadā amṛtatvam bhajante vāsodāḥ soma pra tiranta āyuḥ ॥

Notes: This part features the installation of the pitchers and the invocation of the god Varuṇa in them. It follows the general pattern seen across smārta rites of other traditions. Given the importance of the god Varuṇa in the Indo-Iranian tradition, some version of it could have gone back to an early predecessor of smārta household rites.

pradhānāṅgam :
śāntir astu 1 । puṣṭir astu 2 । tuṣṭir astu 3 । vṛddhir astu 4 । avighnam astu 5 । āyuṣyam astu 6 । ārogyam astu 7 । śivaṃ karmāstu 8 ।karma-saṃṛddhir astu 9 । dharma-saṃṛddhir astu 10 । veda-saṃṛddhir astu 11 ।śāstra-saṃṛddhir astu 12 । putra-saṃṛddhir astu 13 । dhana-dhānya-saṃṛddhir astu 14 । iṣṭa-saṃpad astu 15 । ariṣṭa-nirasanam astu 16 । yat pāpaṃ tat pratihatam astu 17 । yac chreyas tad astu 18 । uttare karmaṇy avighnam astu 19 । uttarottaram ahar ahar abhivṛddhir astu 20 । uttarottarāḥ kriyāḥ śubhāḥ śobhanāḥ sampadyantām 21 । tithi-karaṇa-muhūrta-nakṣatra-sampad astu 22 । tithi-karaṇa-muhūrta-nakṣatra-graha-lagnādhi-devatāḥ prīyantām 23 । tithi-karaṇe muhūrta-nakṣatre sagrahe sadaivate prīyetām 24 । durgā-pāñcālyau prīyetām 25 । agni-purogā viśve devāḥ prīyantām 26 । indra-purogā marudgaṇāḥ prīyantām 27 । brahmapurogāḥ sarve vedāḥ prīyantām 28 । viṣṇu-purogāḥ sarve devaḥ prīyantām 29 । māheśvarī-purogā umā-mātaraḥ prīyantām 30 । vasiṣṭha-purogā ṛṣi-gaṇāḥ prīyantām 31 । arundhatī-purogā ekapatnyaḥ prīyantām 32 । ṛṣayaś chandāṃsy ācāryā devā vedā yajñāś ca prīyantām 33 । brahma ca brāhmaṇāś ca prīyantām 34 । śrī-sarasvatyau prīyetām 35 । śraddhā-medhe prīyetām 36 । bhagavatī kātyāyanī prīyatām 37 । bhagavatī māheśvarī prīyatām 38 । bhagavatī puṣṭikarī prīyatām 39 । bhagavatī tuṣṭikarī prīyatām 40 । bhagavatī ṛddhikarī prīyatām 41 । bhagavatī vṛddhikarī prīyatām 42 । bhagavantau vighna-vināyakau priyetām 43 । bhagavān svāmī mahāsenaḥ sapatnīkaḥ sasutaḥ sapārṣadaḥ sarva-sthāna-gataḥ prīyatām 44 । hari-hara-hiraṇyagarbhāḥ prīyantām 45 । sarvā grama-devatāḥ prīyantām 46 । sarvā kula-devatāḥ prīyantām 47 । sarvā iṣṭa-devatāḥ prīyantām 48 । hatā brahma-dviṣaḥ 49 । hatāḥ paripanthinaḥ 50 । hatā asya karṃaṇo vighna-kartāraḥ 51 । śatravaḥ parābhavaṃ yāntu 52 । śāmyantu ghorāṇi 53 । śāmyantu pāpāni 54 । śāmyantv ītayaḥ 55 । śubhāni vardhantām 56 । śivā āpaḥ santu 57 । śivā ṛtavaḥ santu 58 । śivā agnayaḥ santu 59 । śivā āhutayaḥ santu 60 । śivā oṣadhyaḥ santu 61 । śivā vanaspatayaḥ santu 62 । śivā atithayaḥ santu 63 । ahorātre śive syātām 64 । nikāme nikāme naḥ parjanyo varṣatu 65 । phalinyo na oṣadhayaḥ pacyantām 66 । yoga-kṣemo naḥ kalpatām 67 । āditya-purogāḥ sarve grahāḥ prīyantām 68 । bhagavān nārāyaṇaḥ prīyatām 69 । bhagavān parjanyaḥ prīyatām 70 । bhagavān svāmī mahāsenaḥ prīyatām 71 ॥

prativākyam pātre jalam pātayet । tatra+ariṣṭa-nirasanam astu, yat pāpaṃ tat pratihatam astu iti dvābhyāṃ vākyābhyāṃ hatā brahma-dviṣa ity ādibhiḥ saptabhir vākyaiś ca pātrād bahir uttarato jalam pātanīyam ।

Notes: This section relates to the gratification of various deities with water offerings, which is related to what in other traditions is called the Paurāṇika-puṇyāhavacana. However, it differs from that in having a longer list of statements, including several unique ones. Despite its apparently Paurāṇika origins, we believe it has elements from a “transitional” period of the tradition as it includes certain Vaidika tendencies like the invocation of Agni and Indra with the Marut-s at the opening of the list of gods. It is also notable in multiple ways. It invokes Durgā together with Pāñcālī. This is a unique combination that is not seen elsewhere. It also seems to be the first mention of the Draupadī cult that still survives in popular form in pockets of the Drāviḍa country (e.g., among the Vahniyar-s). Interestingly, this Drāviḍa cult of Pāñcālī also intersects with their popular cult of Durgā. Also notable are the mentions of Skanda (and his parivāra). While the worship of Kumāra faded away in the Marahaṭṭa country, some remnants of it survived among the brāhmaṇa-s of the Koṅkaṇa-s, like the Peśva-s of the Marahaṭṭa empire. Given that many of these were Hiraṇyakeśin-s, it is possible that rites such as this kept the memory of his worship alive. The dual Vināyaka-s are also an interesting peculiarity of this ritual.

svasti-vacanam :
svasti na indro vṛddhaśravāḥ svasti naḥ pūṣā viśvavedāḥ ।
svasti nas tārkṣyo ariṣṭanemiḥ svasti no bṛhaspatir dadhātu ॥

svasti no mimītām aśvinā bhagaḥ svasti devy aditir anarvaṇaḥ ।
svasti pūṣā asuro dadhātu naḥ svasti dyāvāpṛthivī sucetunā ॥
svastaye vāyum upa bravāmahai somaṃ svasti bhuvanasya yas patiḥ ।
bṛhaspatiṃ sarvagaṇaṃ svastaye svastaya ādityāso bhavantu naḥ ॥
viśve devā no adyā svastaye vaiśvānaro vasur agniḥ svastaye ।
devā avantv ṛbhavaḥ svastaye svasti no rudraḥ pātv aṃhasaḥ ॥
svasti mitrāvaruṇā svasti pathye revati ।
svasti na indraś cāgniś ca svasti no adite kṛdhi ॥
svasti panthām anu carema sūryācandramasāv iva ।
punar dadatāghnatā jānatā saṃ gamemahi ॥

śriye jātaḥ śriya ā nir iyāya śriyaṃ vayo jaritṛbhyo dadhāti ।
śriyaṃ vasānā amṛtatvam āyan bhavanti satyā samithā mitadrau ॥

śrīr astu ( 3) । varṣa-śatam pūrṇam astu । maṅgalāni bhavantu । śivaṃ karmāstu ।

Notes: This section is entirely Vedic illustrating the hybrid nature of the Hiraṇyakeśin ritual.

dakṣiṇa-haste uttara-kalaśaṃ dakṣiṇa-kalaśaṃ vāma-haste gṛhītvā tābhyāṃ dhārādvayaṃ satatam patre niṣiñcet ।

vāstoṣ pate prati jānīhy asmānt svāveśo anamīvo bhavā naḥ ।
yat tvemahe prati tan no juṣasva śaṃ na edhi dvipade śaṃ catuṣpade ॥

vāstoṣ pate śagmayā saꣲsadā te sakṣīmahi raṇvayā gātumatyā ।
āvaḥ kṣema uta yoge varaṃ no yūyam pāta svastibhiḥ sadā naḥ ॥

amīvahā vāstoṣ pate viśvā rūpāṇy āviśan ।
sakhā suśeva edhi naḥ ॥

namo rudrāya vāstoṣpataye ॥

śivaṃ śivaṃ śivam ॥

Notes: the worship of Rudra Vāstoṣpati in this context is a distinctive aspect of this tradition.

pātre pātitena jalena pallava-dūrvābhir udaṅ mukhās tiṣṭhanta upaviṣṭā vā parivāram abhiṣiñceyaḥ ।

samudrajyeṣṭhāḥ salilasya madhyāt punānā yanty aniviśamānāḥ ।
indro yā vajrī vṛṣabho rarāda tā āpo devīr iha mām avantu ॥

devasya tvā savituḥ prasave ‘śvinor bāhubhyām pūṣṇo hastābhyāꣲ sarasvatyai vāco yantur yantreṇāgnes tvā sāmrājyenābhi ṣiñcāmīndrasya bṛhaspates tvā sāmrājyenābhi ṣiñcāmi ॥
devasya tvā savituḥ prasave । aśvinor bāhubhyām । pūṣṇo hastābhyām । aśvinor bhaiṣajyena । tejase brahmavarcasāya+abhiṣiñcāmi । devasya tvā savituḥ prasave । aśvinor bāhubhyām । pūṣṇo hastābhyām । sarasvatyai bhaiṣajyena ॥
devasya tvā savituḥ prasave । aśvinor bahubhyām । pūṣṇo hastābhyām । indrasyendriyeṇa । śriyai yaśase balāyābhiṣiñcāmi ॥

oṁ varuṇāya namaḥ । varuṇam udvāsayāmi । yathā sthānam pratiṣṭhāpayāmi śobhanārthāya kṣemāya punar āgamanāya ca ॥

bhūr bhuvaḥ suvaḥ ।
tac chaṃyor āvṛṇīmahe gātuṃ yajñāya gātuṃ yajñapataye ।
daivī svastir astu naḥ svastir mānuṣebhyaḥ ।
ūrdhvaṃ jigātu bheṣajaṃ śaṃ no astu dvipade śaṃ catuṣpade ॥

Notes: This Vaidika section largely follows the pattern seen in other smārta traditions.

atha mātṛkā-pūjā :
śucau raṅgavallyādy alaṃkṛte deśe kṛtagny uttāraṇa-prāṇa-pratiṣṭhāsu prathimāsu abhāve ‘kṣata-puñjeṣu vā gauryādi-devatā āvāhayet ।
gauryai namaḥ । gaurīm āvāhayāmi । padmāvatyai namaḥ । padmāvatīm āvāhayāmi । śacyai namaḥ । śacīm āvāhayāmi । medhāyai namaḥ । medhām āvāhayāmi । sāvitryai namaḥ । sāvitrīm āvāhayāmi । vijayāyai namaḥ । vijayām āvāhayāmi । jayāyaī namaḥ । jayām āvāhayāmi । devasenāyai namaḥ । devasenām āvāhayāmi । svadhāyai namaḥ । svadhām āvāhayāmi । svāhāyai namaḥ । svāhām āvāhayāmi । mātṛbhyo namaḥ । mātṝr āvāhayāmi । lokamātṛbhyo namaḥ । lokamātṝr āvāhayāmi । dhṛtyai namaḥ । dhṛtim āvāhayāmi । puṣṭyai namaḥ । puṣṭim āvāhayāmi । tuṣṭyai namaḥ । tuṣṭim āvāhayāmi । kuladevatāyai । kuladevatām āvāhayāmi । brāhmyai namaḥ । brāhmīm āvāhayāmi । māheśvaryai namaḥ । māheśvarīm āvāhayāmi । kaumāryai namaḥ । kaumārīm āvāhayāmi । vaiṣṇavyai namaḥ । vaiṣṇavīm āvāhayāmi । vārāhyai namaḥ । vārāhīm āvāhayāmi । indrāṇyai namaḥ । indrāṇīm āvāhayāmi । cāmuṇḍāyai namaḥ । cāmuṇḍām āvāhayāmi । gaṇādhipāya namaḥ । gaṇādhipam āvāhayāmi । durgāyai namaḥ । durgām āvāhayāmi । kṣetrapālāya namaḥ । kṣetrapālam āvāhayāmi । vāstoṣpataye namaḥ । vāstoṣpatim āvāhayāmi ॥

ity āvāhayet । tato gauryādy āvāhita-devatābhyo namo nama iti ṣoḍaśopacāraiḥ prapūjayet ॥

Notes: The Mātṛ-s invoked here belong to two groups. The first are a set of goddesses similar to a list seen in the Śuklayajurvedīya gṛhya-pariśiṣṭa tradition. They include consorts of Rudra, Viṣṇu, Indra, Prajāpati, Kumāra, Agni and Puṣan among others. The second set is comprised of the classical Saptamātṛ-s accompanied by Gaṇeśa, Kṣetrapāla and Rudra Vāstoṣpati. That pattern is mimicked in iconography where the Saptamātṛ-s are typically accompanied by Gaṇeśa and Rudra/Vīrabhadra.

atha laghu-deva-pūjā :
brahmādi-devatāḥ priyantām iti pātrāt jalaṃ kṣiptvā śucau deśe caturaśraṃ maṇḍalaṃ vidhāya raṅgavallyādibhir alaṃkṛtya śvetākṣatān saṃprakīrya+adbhir abhyukṣya prāṇa-pratiṣṭhāsu prathimāsu abhāve ‘kṣata-puñjeṣu vā brahmādi-devatā āvāhayet ।
oṃ bhūr brahmāṇam āvāhayāmi । oṃ bhuvaś caturmukhaṃ brahmāṇam āvāhayāmi । oṃ suvaḥ prajāpatiṃ brahmāṇam āvāhayāmi । oṃ bhūr bhuvaḥ suvar hiraṇyagarbhaṃ brahmāṇam āvāhayāmi ।
iti madhyame sthāne brahmāṇam āvāhayāmi ॥

hiraṇyagarbhaḥ sam avartatāgre bhūtasya jātaḥ patir eka āsīt ।
sa dādhāra pṛthivīṃ dyām utemāṃ kasmai devāya haviṣā vidhema ॥
prajāpate āgaccha ।

prajāpate na tvad etāny anyo viśvā jātāni pari tā babhūva ।
yat kāmās te juhumas tan no astu vayaꣲ syāma patayo rayīṇām ॥
prajāpatiṃ tarpayāmi ॥

oṃ bhūr vajriṇam āvāhayāmi । oṃ bhuvaḥ śacīpatim āvāhayāmi । oṃ suvar indram āvāhayāmi । oṃ bhūr bhuvaḥ suvaḥ śatakratum āvāhayāmi ।
iti pūrvasyāṃ diśi vajriṇam āvāhayāmi ॥

yata indra bhayāmahe tato no abhayaṃ kṛdhi ।
maghavan chagdhi tava tan na ūtaye vi dviṣo vi mṛdho jahi ॥
indra āgaccha ।

svastidā viśas patir vṛtrahā vimṛdho vaśī ।
vṛṣendraḥ pura etu naḥ svastidā abhayaṃkaraḥ ॥
indraṃ tarpayāmi ॥

oṃ bhūr yamam āvāhayāmi । oṃ bhuvo vaivasvatam āvāhayāmi । oṃ suvaḥ pitṛpatim āvāhayāmi । oṃ bhūr bhuvaḥ suvaḥ pretapatim āvāhayāmi ।
iti dakṣiṇasyāṃ diśi yamam āvāhayāmi ॥

trikadrukebhiḥ patati ṣaḍ urvīr ekam id bṛhat ।
triṣṭub gāyatrī chandāꣲsi sarvā tā yama āhitā ॥
yama āgaccha ।

yad ulūko vadati mogham etad yat kapotaḥ padam agnau kṛṇoti ।
yasya dūtaḥ prahita eṣa etat tasmai yamāya namo astu mṛtyave ॥
yamaṃ tarpayāmi ॥

oṃ bhūr varuṇam āvāhayāmi । oṃ bhuvaḥ pracetasam āvāhayāmi । oṃ suvaḥ surūpiṇam āvāhayāmi । oṃ bhūr bhuvaḥ suvar apāmpatim āvāhayāmi ।
iti paścimāyām diśi varuṇam āvāhayāmi ॥

imam me varuṇa śrudhī havam adyā ca mṛḍaya । tvām avasyur ā cake ॥
varuṇa āgaccha ।

tat tvā yāmi brahmaṇā vandamānas tad ā śāste yajamāno havirbhiḥ ।
aheḍamāno varuṇeha bodhy uruśaꣲsa mā na āyuḥ pra moṣīḥ ॥
varuṇaṃ tarpayāmi ॥

oṃ bhūḥ somam āvāhayāmi āvāhayāmi । oṃ bhuva indum āvāhayāmi । oṃ suvar niśākaram āvāhayāmi । oṃ bhūr bhuvaḥ suvaḥ śaśinam āvāhayāmi ।
ity uttarasyaṃ diśi somam āvāhayāmi ॥

somo dhenuꣲ somo arvantam āśuṃ somo vīraṃ karmaṇyaṃ dadātu ।
sādanyaṃ vidathyaꣲ sabheyam pituḥśravaṇaṃ yo dadāśad asmai ॥
soma āgaccha ।

aṣāḍhaṃ yutsu pṛtanāsu papriꣲ svarṣām apsāṃ vṛjanasya gopām ।
bhareṣujāꣲ sukṣitiꣲ suśravasaṃ jayantaṃ tvām anu madema soma ॥
somaṃ tarpayāmi ॥

oṃ āpo hi ṣṭā mayobhuvaḥ … । hiraṇyavarṇāḥ śucayaḥ … morjayantyā punātu ।

brahmādīn saṃsnāpayet । puṣpāñjali-samarpaṇam ॥

diśām patīn namasyāmi sarvakāma-phala-pradān ।
kurvantu saphalaṃ karṃ kuvantu satataṃ śubham ॥

īśvaraṃ tarpayāmi । umāṃ tarpayāmi । skandaṃ tarpayāmi । viṣṇuṃ tarpayāmi । brahmāṇaꣲ svayabhuvaṃ tarpayāmi । indraṃ tarpayāmi । yamaṃ tarpayāmi । kālaṃ tarpayāmi । citraguptaṃ tarpayāmi । apas tarpayāmi । bhūmiṃ tarpayāmi । viṣṇuṃ tarpayāmi । indraṃ tarpayāmi । indrāṇīṃ tarpayāmi । prajāpatiṃ tarpayāmi । sarpān tarpayāmi । brahmāṇaṃ tarpayāmi । gaṇapatiṃ tarpayāmi । durgāṃ tarpayāmi । vāyuṃ tarpayāmi । ākāśaṃ tarpayāmi । aśvinau tarpayāmi । vāstoṣpatiṃ tarpayāmi । kṣetrapālaṃ tarpayāmi । indraṃ tarpayāmi । agniṃ tarpayāmi । yamaṃ tarpayāmi । nirṛttiṃ tarpayāmi । varuṇaṃ tarpayāmi । vāyuṃ tarpayāmi । somaṃ tarpayāmi । īśānaṃ tarpayāmi । vasūn tarpayāmi । rudrān tarpayāmi । ādityān tarpayāmi । aśvinau tarpayāmi । viśvān devān tarpayāmi । yakṣān tarpayāmi । sarpān tarpayāmi । gandharvāpsarasas tarpayāmi । skandaṃ tarpayāmi । nandīśvaraṃ tarpayāmi । mahākālaṃ tarpayāmi । dakṣaṃ tarpayāmi । durgāṃ tarpayāmi । viṣṇuṃ tarpayāmi । mṛtyu-rogān tarpayāmi । gaṇapatiṃ tarpayāmi । apas tarpayāmi । marutas tarpayāmi । pṛthivīṃ tarpayāmi । nadīn tarpayāmi । sāgarān tarpayāmi । meruṃ tarpayāmi । aindrīṃ tarpayāmi । kaumārīṃ tarpayāmi । brāhmīṃ tarpayāmi । vārāhīṃ tarpayāmi । cāmuṇḍāṃ tarpayāmi । vaiṣṇavīṃ tarpayāmi । maheśvarīṃ tarpayāmi । vaināyakīṃ tarpayāmi ॥

pūrvoktair oṃ bhūr brahmāṇam ity ādyair mantrair udvāsayāmi+ity ūhitair yathākramaṃ devatā udvāsayet ॥

Notes: The initial invocation of Prajāpati, Indra, Yama, Varuṇa and Soma in a maṇdala reminds one of the early maṇḍala worship seen in the Atharvavedīya pariśiṣṭa-s. It is notable that, as in certain early texts, Soma takes the northern position, unlike Kubera in the later texts. This and the Mātṛ-pujā provide glimpses of the early iconic worship of the Hindus. The longer tarpaṇa list at the end of this section includes deities from both the old Vedic and Paurāṇika pantheons. Some notable features include the worship of Nandin and Mahākāla, which probably marks one of the early instances of the worship of these deities unique to the Śaiva pantheon in a smārta context. The Mātṛ-s in this list differ from the above ritual in being an Aṣṭamātṛkā group via the inclusion of Vaināyakī. The inclusion of Vaināyakī in the Aṣṭamātṛkā is uncommon but is iconographically attested in some Mātṛ depictions, such as in Bhūleśvara, Mahārāṣṭra. One again wonders if the presence of this tradition in the region influenced the local iconographic depictions of this goddess.

A Geopolitical meandering, October 2023

Sir Francis Drake, buccaneer bold and bloody,
Sailed the seas in a gold-grabbing spree,
With the Golden Hind, he circled the Earth wide –
A murdering marauder on the swelling tide.

Slaving in West Africa, slaughtering civilian and combatant alike in Ireland, sacking and burning cities and towns along the South American coast, and pillaging treasure-laden ships, slaying friend and foe for ascendancy, the famed pirate Francis Drake rose to be the hero of the English. As the intrepid marauder lay dying, emptying out his bowels while retreating from a failed assault on Panama, he marked a historical moment with decisive geopolitical consequences down to our current age. On one side, he was taking to sea the long Western European predatory tradition going back to the phiraṅga-s like Raymond, Baldwin, Godfrey, and Warner and the king of his own people, the wicked Richard Yes-and-No. On the other side, Drake set into motion a process that was to bloom into a maritime predatory tradition that continues to dominate the geopolitics of our times.

As we have remarked on these pages numerous times before, the broad trends in geopolitics can largely be described by: 1. The counter-religious zeal of the ekarākṣasa-s to destroy the heathen – the result mlecchamarūnmattābhisaṃdhi or sarvonmatta-samāyoga-rākśasa-jāla-śambaram; 2. The oneupmanship between the different strains of ekarākṣasavāda; 3. The continuation of the predatory principles building up from the Drakian foundations. The modern manifestation of the Drakian predation is the activity of the pañcanetraka confederation; 4. Galtonism and legalism-backed Middle Kingdom belligerence.

Its general operational principles can be best described by the great American realist Mearsheimer’s exposition of the same. We recap this from a H vantage point, filling in certain details that are relevant to us. A principle the predatory English state established during the expedition of Drake and his fellow pirates was that of the exclusive domain of the regional hegemon. This had two facets to it: first, the English saw themselves as the regional hegemon and did not tolerate challengers to that hegemony. Second, they did not tolerate the rise of other regional hegemons elsewhere. Thus, they ransacked the Spanish possessions both locally and in the New World to stymie their rise. In India, the English got a windfall when the Marāṭhā-s forced their ambitious and cunning rivals, the French, originally led by Marquis Dupleix and Monsieur de Bussy, to surrender. Then, the English worked for several decades, despite multiple defeats, to challenge the rise of the Marāṭhā-s as the regional hegemon in India. In between, right in their backyard, they fought off the rise of the hegemonic challenger Napoleon, the French emperor (1803-1815 CE). Simultaneously, they delayed the rise of their mahāmleccha cousins to hegemon of the western hemisphere in the predatory Anglo-American war (1812-1815 CE) with the sack of Washington in 1814 CE. Thereafter, they led predatory expeditions in the form of the Crimean War (1853-1856 CE) to damage Russia in its attempt to rise to a regional hegemon. The struggle in India culminated in the great Anglo-Indian war of 1857 CE, where the Indian confederation was smashed and the country decisively conquered.

While the mahāmleccha were able to avoid reconquest by their cousins in the Anglo-American war narrowly, they were definitely not at the same level of military prowess as the latter. After settling their internal scores in the American Civil War and crushing the remaining holdouts of the first Americans, the mahāmleccha finally entered a long period of stability, unlike the Latin American states. Endowed with enormous natural resources and land conquered from the First Americans, Spaniards and Mexicans or purchased from the French and Russians, the mahāmleccha were all set to dominate the western hemisphere. Starting around the first decade of the 1900s, the mahāmleccha-s were unquestionably the regional hegemon in the western hemisphere, equipped with a powerful fighting force in the same predatory tradition of their English predecessors. However, the leadership of the Anglosphere was still with the English, who lay at the heart of the European civilization, lording over it as a regional hegemon. In contrast, the mahāmleccha remained a distant frontier society.

While the English pioneered the invention of engine technology, mass transportation and the industrial revolution, they were soon to be challenged by their continental cousins. Though the French made comparable advances to the English, it was the Germans who were to excel both of them in the more “modern” version of industrialization. In no small measure, this was due to the two great Germans, Justus von Liebig and Friedrich Wöhler, the founders of organic and industrial chemistry. The Germans also excelled in the production of machine tools and advanced metalworking. This meant that they were destined to ascend to European dominance once they had unified into a single German nation. However, they were late to the game and were beaten in the channeling of precious foreign resources to their homeland through predatory conquests (“colonialism”) by the English and French. Belatedly, they tried their own brand of “colonialism,” which only matched the English and the French in terms of brutality but offered little in terms of resources beyond an interesting assortment of Jurassic dinosaurs from Tendaguru.

Not surprisingly, the rising German power challenged the regional hegemony of the English, which had been put in motion by none other than the old Sir Francis with his plundering expeditions. This led to WW1. The strain of WW1 meant that the English had to bury past conflicts with their mahāmleccha cousins and seek their assistance. The German-led confederation retaliated by entering the Western Hemisphere and trying to incite Mexico to regain their lost territory with German aid. As expected, this crossed the mahāmleccha red-line of regional hegemony. Thus, they entered WW1 in the final stages, and the Anglospheric coalition was able to destroy the German-led entente. Although the Anglosphere had triumphed, it was now formally left two-headed – with both the English and the mahāmleccha holding combined supremacy like Śumba and Niśumbha.

Even as these events leading to WW1 were unfolding in the western part of the mleccha world, in 1903, in the Russian East, there were obscure events that were to have an impact on history in a much bigger way than one would have expected. A riot broke out in the obscure town of Kishinev, then in the Rūs empire (today in Moldova) over a rumor claiming that marvambuka-s had used the blood of a pretasādhaka boy in making ritual victuals. The resulting riot resulted in several of them being killed by the preta-s. This marked a high point in building the sentiment among them to find a way out of such outbreaks of violence. This particular incident brought home to them the urgency of it as they felt a sense of shame over their helplessness, which is expressed by one of their poets, H.N. Bialik, thusly (in translation):

Come, now, and I will bring thee to their lairs
The privies, jakes and pigpens where the heirs
Of Hasmoneans lay, with trembling knees,
Concealed and cowering, the sons of the Maccabees!
The seed of saints, the scions of the lions!
Who, crammed by scores in all the sanctuaries of their shame,
So sanctified My name!
It was the flight of mice they fled,
The scurrying of roaches was their flight;
They died like dogs, and they were dead!
And on the next morn, after the terrible night
The son who was not murdered found
The spurned cadaver of his father on the ground.
Now wherefore cost thou weep, O son of man?

He remembers their zealous warriors of yore who waged a religious war on the Hellenes and Romans and laments the state to which they have been reduced. These sentiments sparked two broad categories of responses among the marvambuka-s. First, a subset of them wanted to break clean with the European lands and return to their ancestral lands in Uparimarakata. Second, a subset became interested in various revolutionary, millenarian, utopianist, and subversionist movements. These subsets were partly overlapping. The first category of responses accelerated the return-to-Uparimarakata movement under the aegis of the declining Osman Khilafat and under the English after they defeated the Osmans in WW1 and broke up their empire. Now, Uparimarkata was, after all, the focus of the other two ekarākṣasonmāda-s too. Hence, it was not a surprise that the different preta branches were vying for its control, even as old Raymond, Baldwin, Godfrey, Warner and the wicked Richard Yes-and-No had done. While the Osman empire had been smashed, the other contending party that was still in the game, the aghamada-s were still in play. Thus, the situation in Uparimarakata was building up for an eventual three-way confrontation. The second category of movements set in motion among the mūlavātūla-s were driven by a secularized Messianic fervor that culminated in the Russian revolutionary upheavals from 1905 to 1917 CE, even as WW1 was coming to a close. By the end of these actions, the Tsar Nicholas II, who had led the Rūs disastrously in WW1, was brutally executed with the rest of his family.

On the western side of the European subcontinent, the Germans, smarting under the humiliation imposed on them by the predatory Anglo-entente, were rapidly making moves to avenge their defeat in WW1. This led to their second attempt in WW2 in partnership with the regional hegemon of the East, the Japanese. Obviously, the Anglo-entente was not going to tolerate the rise of Japan – not only was it an undisputed regional hegemon that had already shown that it could defeat European armies like those of the Rūs and the Germans, but it was heathen to boot. This combined front of Germany and Japan was way more vigorous than anything seen in WW1. The balance of power was decisively changed by the Rūs, now the Soviet communist empire of Stalin – they smashed both the Germans and the Nipponese decisively. Barring Finland, the Soviet steamroller was practically unstoppable, rolling all the way to Berlin, incurring one of the heaviest human costs in history.

The above-mentioned revolutionary movements spearheaded by the uparimarakata-s brought them into a head-on collision with the rampaging śūlapuruṣa-s headed by the hādipuruṣa. Those who were lucky made it out of the German-conquered lands to America, Uparimarakata or elsewhere. The rest were almost entirely massacred wherever the armies of the śūlapuruṣa-s gained control. Those who went to America gave their new home the gift of superpower in the form of nuclear weapons and a new wave of technologies. Thus, even though it was the Rūs that chopped up the Nipponese on the Eastern front, the islanders fell to the Americans, who armed with their nukes, were now the undisputed masters of the world. They had become the single global hegemon. However, the uparimarakata-s’ affinities were split. They had also been behind the rise of the Soviet Rūs, and several of them were in power there. So, they also helped the Rūs gain nukes about 4 years after the first American test. Thus, the world became bipolar. The marvambuka-s in the US had greater access to their cousins in the ancestral lands than those in the Soviet lands. Thus, they helped the uparimarakata-deśa rise to the fore after WW2.

The bipolar world lasted for nearly 42 years, and in the final decade of this struggle for world hegemony, Rājaka held sway as the Mahāmleccheśvara. He had hired duṣṭa-Sora, a mūlavātūla, belonging to the anti-Rūs faction within their strand subscribing to revolutionary utopianism. His job was to subvert the Rūs. A born psychopath, In the coming years, he went “rogue,” running a global program of subversion in parallel with other like-minded rogues or organizations like Kṛṣṇādri-phuka, Āpastiya and Agrabhaṭa. These people, along with their handlers in the Mahāmleccha DoS, looked at every problem as leading to the Rūs. Thus, they came up with the ridiculous claim that their chosen candidate, Ṣiḍgapatnī, had been overthrown by the Rūs, who were claimed to be favoring Picchilaka. They were itching for a war with the Rūs, who were steadily recovering their lost power to the extent their cognitive capital allowed (most uparimarakata-s had left their lands at the collapse of the Soviet Empire).

Like the mace of Vāruṇa turning back on Śrutāyudha, both their marūnmatta friends in the anti-Rūs struggle and their Galtonian partner the Cīna-s turned against the pañcanetraka confederation resulting in what has been termed the multipolar world. Mearsheimer believes that this state began in 2017 CE. The principle of realism implies that the US will do everything to be the sole hegemon of the world, bringing it in direct conflict with the aspirations of the Cīna-s in particular, who not only want to be the regional hegemon of Asia but also exert influence more globally. The collision of these geopolitical vectors sparked the war between the mahāmleccha-s and the Rūs in Ukraine, with the Ukrainians as cannon fodder fighting for the former, and Cīna-s warily backing the Rūs. The mahāmleccha threw their entire force behind their proxies but have failed to beat the Rūs. It is clear that the Rūs have decided to play the long game, especially given that they are quite adept at defending fortified positions, see it as an existential war, and have superiority in terms of munitions. The hard fighting of 1.5 years has acted as a selective filter that has probably killed the less able and left behind a more battle-hardened force that might have learnt a bit from their earlier mistakes. This has left the mahāmleccha-led pañcanetraka-s with no clear endgame in sight. Instead, the war has only resulted in the mahāmleccha-s depleting their munitions at a juncture when unexpected geopolitical events played out.

Earlier this month, the frenzied mahāmada-s launched a ghazvat of unprecedented proportions on the uparimarakata-s. Apart from the huge loss of life and hostages taken, it was a devastating blow to the deservedly shiny image of the mūlavātūla army. Uparimarakata is more important for the mahāmleccha elite than their own country as they have chosen to base their identity on a rather fundamentalist ubhayonmāda-samāyoga — in part, this was strengthened due to the role the uparimarakata-s played in conferring superpower on the mahāmleccha-s. Thus, unsurprisingly, the mahāmleccha-s have entered this conflict with no obvious endgame that can be spoken of in public. This has suddenly changed the geopolitical equations because the uparimarakata-s and a strain of their backers among the mahāmleccha-s (the navyadhūrta-s) want to widen this conflict to bring in a key ally of the Rūs and the Cīna-s, the Islamic state in Iran. They also blame the Rūs as backers of the ghāzi-s and wish to connect the two wars.

This is happening against a backdrop of fissures emerging in multiple weak federations. As Mearsheimer and others noted, a common factor in all these is rarefaction – that is, the federations grow too unwieldy to survive. This is in action in both the EU and the BRICS. The expansion of the EU brought in states with historical enmities and divergent interests. The anti-Rūs interests of Poland, willing to be a mahāmleccha vassal, go against the economic interests of the still powerful Germany, which is best off in an energy alliance with the Rūs. On the other hand, the Germans still have their old dislike of the Rūs. These delicate balances have been broken up by the mahāmleccha-backed assault on Nordstrom and the building up of Polish belligerence. Another fissure is the independence of Hungary, which desires to counter the Sora-ṣaṇḍa-backed nayvonmāda that is dominant in other parts of the EU. The desire for Asian hegemony will pull the BRICS apart as India and the Cīna-s are fundamentally incompatible. Moreover, bringing in groups like the Arabic Amirs and Maliks will add to the divergence of interest, making BRICS ineffective.

Thus, even though Mearsheimer and some others think the world has become multipolar, we believe it is not yet there. We could be seeing the late stages of the pañcanetraka-dominated unipolar world system, but by no means is it over yet. The Cīna-s, whom a subset of the mahāmleccha see as their biggest rival, is limited by its poor demography. Moreover, as Mearsheimer pointed out, a future war between the pañcanetraka-s and the Cīna-s would not be a land war. It would be fought at sea and by air, with Taiwan as the likely focus. The pañcanetraka-s hold the upper hand in this mode of combat. On the mahāmleccha side, they are weakened internally by the Sora-ṣaṇḍādi and by their bhañjaka-s (CIA/FBI) turning inwards against their own people (e.g., supporters of Picchilaka). Further, they might be potentially bogged down in wars in West Asia by the marvambu-dominated navyadhūrta faction. Thus, it will boil down to a question of kinetics — which side gets weaker sooner. While it was quickly crushed, the rebellion of Prigogine exposed weaknesses among the Rūs that might exacerbate in the future. The window within which the Cīna-s can by themselves present a serious challenge to the mahāmleccha-s is also limited.

This said, there is still a risk of a more expanded conflict – a WW3(?) – we believe there might be up to 0.1-0.15 chance of this occurring. The conduit for this could be the expansion of conflicts in West Asia, pulling the Rūs assets in Syria and the Rūs-Cīna ally, the Islamic state in Iran. We believe that, even if this scenario were to play out, there is still some fuse left to burn. For the H, it might coincide with impending nirṇaya with the marūnmatta-s and the preta-s, which is slated to play out irrespective of these geopolitical events. A distracted mahāmleccha and Cīna would be good for the H during that nirṇaya if it has a leadership that can handle the high-intensity situation. The weakened EU will be a double-edged sword for the H in that conflict. It has been consistently anti-H in its attitudes; hence, being drowned in its own troubles, it might not be in a position to substantially help the ubhayonmattau in their rampages in Bhārata. On the other hand, the EU has been letting in a large number of marūnmatta-s to settle in the midst of their aging populations. If these start exerting influence on their government policies in resonance with preta sympathy for their coreligionists, the dredges of EU power could be directed against the H on behalf of the ubhayonmattau. We have recently seen such a takeover with the paṭṭātaṅka-s in Uttaramlecchavarṣa headed by a weak, drug-addled navyonmatta put on the āsandi by the Soraṣaṇḍa-s.

Finally, the unfolding of the recent events reminds us of some more basic things: Irrespective of their IQs, groups try to alter the world to the advantage of those within their perceived ingroup radius. The actions of those with higher IQs have a higher impact. However, even those with high IQs cannot run against mathematical theorems. In this case, it is how chaos emerges in dynamical systems and its consequences. Even a 3-body gravitational system is chaotic, so what to say about social dynamics? Hence, whatever actions high IQ folks take in the belief that it will improve their lot in the world, they would come up against this truth.

The counting square and divisor functions

Leonhard Euler’s discovery of the zeta function in the course of solving the Basel problem was one of those momentous “unifications” in mathematics with deep philosophical implications that eventually led to the Riemann hypothesis. By bringing together trigonometry and arithmetic, it presented the first glimmer in the Occident for an arithmetic foundation of the ideal world. We have found that it always helps to revisit the basics of knowledge and reflect upon it from the vantage point of all you learnt since you first acquired those basics. In this case, the basics that we shall revisit are counting with integers and operations related to them. When you learn those basics (close to the boundary from when life-long memories are retained), things like the values of the zeta function or even beyond your very limited horizon (at least for most ordinary mortals). Hence, a glimpse of the deeper significance and philosophical implications of the basic operations appears only later in life. In this note, we detail one such exploration from our youth that brought home to us the connection between basic arithmetic and via .

Consider the square matrix, which we call the counting box. It is a representation of the basic arithmetic operation of counting with integers from which we get both multiplication and division. It is constructed by filling successive columns of a matrix by the first elements of the following repeating sequences: 1,0,1,0,1,0,1,0 ; 1,2,0,1,2,0,1,2,0 ; 1,2,3,0,1,2,3,0,1,2,3,0 . While the matrix can essentially be infinite, we can show blocks of it (e.g., below, we have a matrix).

Now, the upper triangle (diagonal included) of this matrix is rather predictable: row , counting from 1, of this triangle will have a run of instances of . The lower triangle of this matrix (diagonal excluded) is a little more interesting. Each row is the sequence . Thus, for row 7 of the matrix, the corresponding row in the lower triangle is 1, 1, 3, 2, 1, 0. This is because, by its very definition, this array represents the division process by successive integers, and the remainders of these divisions will be seen in the successive elements of a row of the lower triangle. For a row of the lower triangle of the matrix, the first elements will be the unique reminder signature of the division of by all integers . The remaining elements of this row of the lower triangle will be successive integers in decreasing order from to 0. Thus, for both rows 9 and 10, this run will be 4, 3, 2, 1, 0.

We were curious about the curve defined by the values of the row-wise sums of the above matrix — the sum is plotted as the value and the corresponding row as the value. This can be done for this matrix of any size ; hence, to maintain the same scale, we normalized the curve by dividing the values by and the sums on the axis by the maximum value attained by the row sum. We then asked for what value of will the maximum sum (1 when normalized) be attained. We can easily place some lower bounds on it. As we saw above, each row of the upper triangle of the matrix has instances of . Hence, the sum of these values would be the quadratic function . Using some elementary calculus to find the maximum of this parabola, we see that it will be attained at . Thus, when we normalize it for large , it will be practically at . Hence, the maximum of the row sum of the matrix will certainly be attained at a value because the above only accounts for the upper triangle part of a given row. As we saw above, the terminal part of row of the lower triangle has an arithmetic progression of integers from . The sum of this part will hence be:

We can approximate this as:

Again, finding where the maximum occurs for this parabola, we get it as when is large. Again the actual value where the maximum occurs would be greater than (Figure 1) because this sum still leaves out the first forming the unique modulo signature of . Given our limited knowledge when we did this exercise in our youth, this bound-setting, which a mathematician might laugh at, gave us a sense of what to expect — an approximately parabolic curve with maximum occurring for a . We then empirically computed the actual maximum (Figure 1) and obtained a value of — this immediately led us to realize that the maximum is attained at approximately . Here, is the famous Zeta function known after Bernhard Riemann.

Figure 1.

Figure 2 shows the computation of the value of at which the maximum occurs for increasing values of , which when averaged yields .

Figure 2.

To understand why this was so, we next tackled the issue of the row sums of the lower triangle of this matrix. It is essentially the sum of the modulos: . Using the full square matrix we can infer this to be the below formula for row (Figure 3):

Figure 3.

Here, is the arithmetic divisor function going back to the work of Dirichlet, which is simply the sum of all the divisors of an integer. This, in turn, yields the exact formula for the sum of the complete row in the matrix as (plotted in yellow in Figure 1):

Thus, the key to understanding how emerges in this formula is to understand the sum of . As above, we could empirically establish that asymptotically its first level approximation is (pink in Figure 3). Indeed, as a result of the work starting from Dirichlet in the 1800s and culminating in that of Hardy in the last century we have the asymptotic formula for the summatory function of as: , where the Landau-Bachmann big notation is used for the second term. This formula is established by Hardy and Wright in their “An Introduction to the Theory of Numbers.”

The generalized version of the divisor function can be defined thus:

; here means divides , i.e., is its divisor.

Thus is the divisor function which specifies the number of divisors. With this in place we can see, that the lower triangle of the matrix also encodes interesting numbers related to the divisor functions:

First, the number of 1s in each row of the lower triangle gives the sequence of the number of divisors of an integer that are greater than 1, i.e. the sequence of The number of 0s in each row gives the same sequence without the initial 0. The number of non-0 terms of each row of this triangle gives: starting from . The number of 2s in each row gives the number of divisors of that are greater than 2. Likewise, the number of 3 in a given row specifies the number of divisors of that are greater than 3 and so on.

The ghost of the man named Lilavinodan

This is the second of the Charuchitra series: Even if the story narrated were to resemble real-life incidents, all characters in it are fictitious.

With the exam behind him, Somakhya relapsed into his usual circadian cycle that was diametrically opposite to his kinsfolk who followed their ancestors, who woke up early on the frigid steppe to greet the Daughter of Dyaus lighting up the eastern peg. As he came down from his room to pick up breakfast from his mother, his aunt, with his cousin Charuchitra leaning on her, confronted him holding up her tablet. It had on it the below image:

She said: “The radii of the bounding circles of the successive black annuli in this image are reciprocals of the integers all the way to infinity. What will be the total area of the black annuli?” Somakhya knew his aunt has some traits of his father; hence, he was not surprised by the samasya she had so abruptly lobbed at him. However, being barely awake, he took her tablet and proceeded without saying anything to collect his breakfast from his mother. Then as the viands activated him a bit, he remarked: “This construction and question had independently come to my mind a couple of years ago while reading a biography of the great Leonhard Euler. Hence, I have already worked out the answer. It is . I had also worked out a 3D variation on the same. Imagine nested cubical shells whose bounding cubes have sides as the reciprocals of odd integers 1, 3, 5, 7… then the total volume of the black cubic shells will be , which is ths area in your figure. He handed back his aunt’s tablet with the below figure:

Somakhya’s aunt: “Good. Now, tell your sister how you got there. Thankfully something like that did not appear in the exam, for she seems clueless about this.” Charuchitra: “I don’t think these sums were ever supposed to be in the syllabus of this exam.” S: “That’s right; nevertheless, I could show you how to break them in case you encounter them later in life if you took a path that led you there.”

That day was a holiday for Somakhya’s father, and he wanted to catch up a bit with his sister as he had been busy with work since their arrival and had not gotten much of a chance to do so. While normally not a man of many words, one of the few people he occasionally made an exception for was his sister. So, he uncharacteristically spent some time chatting with her as she filled him in on how she had used Voronoi cells to suggest solutions to a problem relating to the provisioning of troops for the army. Just then, Somakhya’s mother ushered in their family purohita. As educated s, Somakhya’s family did most of their rites by themselves. Thus, their purohita was only used sparingly, but he visited them periodically to supply yajñopavīta-s, grass and samidh-s, as well as to attend meals for certain rites. That day after providing the said supplies and duly receiving his dakṣiṇa, he mentioned that Nilaprishtha Vajapeyin (Nīlapṛṣṭha Vājapeyin) was making arrangements to perform the Abhijit sacrifice. He wondered if a mahāśālin like Somakhya’s father might be interested in supporting and attending the ritual. Somakhya’s family knew the Vajapeyin in passing — he had been a professor of the vulgar middle Indo-Aryan languages and the Pāḷi — Somakhya’s mother had taken a course with him when she was a student. So they decided to go over to his house in the evening and give him some donations of cash and silver vessels for the ritual.

The Vajapeyin lived in a comfortable old-style house in a cluster of such that formed an old agrahāra adjacent to the Someśvara temple. He had strongly fought off attempts by marūnmatta-s to buy off the property even though several of its past inhabitants had left. Somakhya’s family, along with his aunt and Charuchitra, went there and gave him donations for the rite. The Vajapeyin and his wife welcomed them and remarked that they were meeting after a while. His wife told Somakhya’s mother that they had, however, thought of her upon reading her recent article: “Was the mahākavi a plagiarist or plagiarized?” Then Nilaprishtha asked Somakhya about his study of the fourth Veda. Pleased by his recall of the Atharvanic incantations like the Viśāsahi-s and Bṛhaddiva-s, the Vajapeyin asked Somakhya if he would like to serve as a brāhmaṇacchaṃsin in the ritual. He puffed up Somakhya by saying he could be like the legendary young Atharvan Vicārin to bring the yāga to a successful conclusion. However, Somakhya got cold feet at that point and declared he was not that good and might be ready for it only in a future iteration; instead, he affirmed his intent to closely observe the ritual this time around. The Vajapeyin thanked Somakhya’s family for the donations and said he would mail them a detailed breakdown of how the funds were used. The first things he said he was going to procure were a chariot wheel and two sheep skins for the yajamāna and the patnī to wear. Somakhya’s father: “I guess they are pratinidhi-s for the red bovine hides?” V: “Yes. You know we are between a rock and a hard place with the modern H going apoplectic on one hand and the rationalists and animal rights activists on the other if we use the prescribed bovine hides as jackets to be worn by the sacrificer couple.” S.F.: “I guess then you are not performing the prescribed animal sacrifice either?” V: “We have to settle for piṣṭapaśu-s, for there is no way we can get permits under the secular government to perform animal sacrifices in the city. However, at least we were able to get a good rib of a horse through the recommendation of an officer from the army veterinary hospital.” He then showed them the gleaming rib of a horse. Somakhya’s father: “May it withstand the heat of the āhavanīya and cut the barhiṣ in the manner our father Manu had done on the northern steppes.” V: “Indeed!”

Then the Vajapeyin asked them to come along to see the yajñāyudha-s and pātra-s they had readied to date. He took them to the adjacent house. The various bricks, yajñāyudha-s and pātra-s, were stacked in the courtyard and the verandah of that house. Somakhya’s mother: “Did this house not belong to the elderly āyurvedācārya from the Drāviḍa country? Have you now taken possession of it?” The Vajapeyin’s wife: “Indeed! You have a good memory. That was when we were children. He lived to be nearly a 100, but Radhakrishnan died a while back. His son, who was not a youngster himself, lived elsewhere and used to periodically visit the place for maintenance. However, when we were away at Kāśī, he just vanished without informing anyone — maybe he decided to retire abroad. The house has been unoccupied since.” Just then, Somakhya’s aunt pointed to the said Radhakrishnan’s house and remarked: “Is there someone in there?” She then turned to her sister-in-law: “Did you hear that?” S.M: “Hmm… I, too, thought I heard someone talking inside.” The Vajapeyin’s wife waffled a bit and caught her husband’s eye with a slightly uneasy look. V: “No, it is empty. It must be people from the courtyard of the Someśvara temple. Just then, Somakhya saw his mom, aunt and cousin exchange somewhat startled glances at each other. But before they could say anything, the Vajapeyin, wanting to test him, called on Somakhya to recite the Bṛhaddiva-s in the prayoga mode preceded by the Atharvan incantation of the 10000-fold pervasion and with the insertion of the syllables of puruṣa. As Somakhya did so, the attention of the group was distracted towards his recitation. Charuchitra, who was recording a video of the whole thing, moved up onto the verandah of the late āyurvedācārya Radhakrishnan’s house. She, responding to some glancing sensation, quickly jumped back and joined the rest of her kinsfolk. Then they concluded their visit by going to the adjacent Someśvara shrine. There Somakhya showed his cousin a vīrakal with an inscription he had deciphered. It was of a warlord who had died while trying to rustle cattle from a great cattle-herder to the south. In the dim light of the temple tower-lamps, the image of the aforesaid warlord etched on the stele glowed with a ghostly hue as though he was still possessing it.

When they were back home, Charuchitra came over to Somakhya: “Did you notice anything strange in the abandoned house next to that of the somayājin?” S: “It gave me an odd vibe, but why?” C: “The vibe, yes! Both our moms concurred with me that they not only felt there was someone inside that house but also thought they saw someone moving. They also agreed with me that the voice was grave and had a peculiar overlay of an old English and American accent. However, they think it is all due to the construction of these old agrahāra houses that were optimized for a certain channeling of natural lighting and sounds. So, they felt it was the late evening light and the bustle from the adjacent temple and thoroughfare that conspired to produce a strange illusion. But I think there was more, Somakhya.” S: “Hmm. I must confess my mind was not on any of that at all — being in the cynosure of the vājapeyin, I was just trying to make sure I was getting the svara-s of the incantations right. As you know, I don’t have the greatest natural sense of tonality.” C: “I was recording a video of the ritual material and also your recitation. Just see what I caught in the audio.” Charuchitra scrolled to the point in her video where Somakhya was reciting the mantra-s. The video clearly showed that she was detached from the rest of them and strolling through the verandah of Nilaprishtha’s neighbor’s house. The audio revealed a slightly faint but unmistakable voice saying in the peculiar accent that Charuchitra had mentioned: “Now I shall discuss two enzymes that I purified: respectively those that hydroxylate proline and lysine.” Somakhya jumped out of his chair and took the phone from his cousin, who was seated on the bed opposite him and, putting on his headphones, heard it again. S: “Charu — this hardly sounds like auditory apophenia. What do you think he’s saying?” C: “To me, it sounds like he’s talking about some reaction with amino acids. And you would be thinking I’m pulling a fast one, but right as it happened, I saw a silver silhouette of a man.” Indeed, the video showed her quickly jumping off the verandah and quietly joining her kinsfolk. S: “If it is apophenia, it certainly has produced an identical effect on us. Let us call Lootika and ask her.”

They got Lootika online and filled her in on their experience. Playing Charuchitra’s video Somakhya asked her: “What do you hear?” L: “Strange, I hear an interfering voice say something about proline and lysine hydroxylation! Could it be some cross-talk from some other person’s phone call? But that is strange — it is also almost as if something you and me might have spoken! I guess you are seeing an artefact of video editing where some recording of us talking got superimposed on the track.” C: “No way, I actually heard it live, and Somakhya had no access to this capture until I showed him.” L: “Do you think we can get into that house and explore it?” C: “Sounds simultaneously scary and exciting!” S: “Let us do so tomorrow evening. The somayājin would be away giving a lecture on the upaniṣad-s while his wife will be at the bhajana-maṇḍalī — I noticed that we can slip in surreptitiously via the side facing the temple.”

The next evening Somakhya went over to his friend Sharvamanyu and returned with him and his spare bike that he had kindly agreed to lend to Charuchitra. In the meantime, Lootika and Charuchitra got ready and were sparkling with smiles of suppressed excitement. As they turned into a secluded bylane on the ride over to Someśvara, Sharvamanyu paused and handed over Lootika a knife: “For an eventuality. While your brahma power might tackle the specters, the adverse edge of the kṣatra’s meni is needed were a dasyu to fall upon us.” Turning to Somakhya, he asked: “What about Charuchitra? Have you given her something?” C: “Here is my tactical rod.” Sh: “Looks good.” He then tried a mock maneuver on her and found that she was able to do something passable.” Sh: “Somakhya, did you show her that?” S: “Oh no, it is my friend Indrasena who lives in the same city as her.” Sh: “Lootika — see, there is nothing to bar you from learning what Charuchitra was able to do.” L: “You have not seen my poison spray.” Sh: “In any case, enough of bravado. If an event were to unfold, don’t stop to engage — make a dash for your bikes and zip off.” Somakhya filled them in with a convincing excuse they were to spout if they encountered a peaceful living resident instead of the phantom when they made their entry into the apparently abandoned house.

As they reached the temple, they saw the Vajapeyin’s wife just beginning to assemble a cluster of women for their bhajana-s. S: “That’s a good sign — we should have ample time to explore.” After a quick stop at the temple, where they parked their bikes, they soon found themselves in the dark and abandoned house via the portal that Somakhya had worked out. After a silent sweep of the house, they reassembled in an inner room near the backdoor. C: “It doesn’t seem to be entirely in disrepair — I guess the Vajapeyin is nominally maintaining it. It is also huge — almost half a chateau rather than an āgara in an agrahāra.” Sh: “Did you see that!” L: “What?” Sh: “I don’t know if it was my heightened imagination, but I thought I saw someone peep into the room. Let us go and check.” They saw no one in their second sweep of the house. S: “Let us get moving — we don’t want to waste our precious time. I suggest we sit here and try the planchette. Lootika, do you want to take the lead in summoning the phantom or phantoms.” L: “I think the most expedient approach would be the Ḍāmara-prayoga of Daṃṣṭrākarālī, one from the ogdoad of goddesses in the retinue of Bhūtapati Mahādeva.” S: “Sure, go ahead. I’ll join you in bhūtākarṣana with the same to ensure its effectiveness. Lootika deployed the Daṃṣṭrākarālī incantation that is particularly effective in drawing in the specters after first invoking Bhūtapati with the incantation huṃ mahādevāya huṃ ||:
OṂ daṃṣṭrākarālī cala cala daha daha mahābhūtini sādhakānukūlapriye sara sara sarvadiśaḥ praviśya sarvabhūtān gṛhṇa gṛhṇa ānaya ānaya huṃ phaṭ svāhā ||
Charuchitra reported a twitching of her finger placed on the planchette, and it swiftly moved to the affirmative cell without them asking anything. L: “Wow, it seems quite eager!” On asking its sex in life, it responded as a man. Then when asked his name, the planchette spelt it out after a rather long and winding motion as Lilavinodan (Līlāvinodan). Somakhya was a bit surprised because he had noted the name of the former owner from his mother as a certain Radhakrishnan. S: “His name is suggestive of him being from the Drāviḍa country, just as the original owner of this house.” Who was this Līlāvinodan? When asked, the planchette merely spelt out “Story.” After that, they stopped getting responses. Sharvamanyu repeatedly mentioned he felt he saw a gossamer image of a man standing behind Charuchitra. She almost yelled and turned around a few times, saying that she was feeling something odd, but they got no response on the planchette. It was just stuck on the letter K. Frustrated, they decided to head back.

Midway on their return ride, even as they were discussing their experience. Sh: “I ain’t kidding. I felt that place is genuinely haunted. I saw a ghostly image of a man standing around more than once.” C: “I entirely agree. What you report is quite close to the image I saw. Even my mother and Somakhya’s too saw something yesterday — just that they were not admitting it to be a phantom.” Suddenly, Charuchitra stopped and held her head. The rest of them, who had ridden ahead a bit, turned back and rallied around her. S: “What’s happening?” C:“I’m feeling something weird — I just feel that Lilavinodan is bouncing within my skull asking me to start typing! It is very disconcerting — if there is something called possession, this feels like it.” Somakhya and Lootika asked her to get off her bike, and they walked along with her to Sharvamanyu’s house: “We shall go to Sharva’s house, and you can type out whatever comes to you. That in itself will make it easy for us to rid you of him.” It was a rough 10 minutes for Charuchitra before they reached Sharvamanyu’s place: “I had a couple of experiences with sprites in the past with Indrasena, but this is nothing like what I have had before.” L: “Don’t worry, I’m confident we will rid you of him. I should have dismissed him at the end of our planchette session, but I guess he wants to convey something.”

At Sharvamanyu’s place, Charuchitra started typing away furiously as soon as she was given a keyboard. The below is a reproduction of her transcript:
I’ve been waiting long for my story to be heard. You two s who so easily subdued and summoned me are the ones whom I was long waiting for. You will be blessed with whatever little power I have for hearing my story and making it known. I am Lilavinodan, the son of Radhakrishnan, the son of Shivaramakrishanan, the son of Svaminathan. I was born when the English still lorded over our country. When I was in school, I read the textbooks by August Bernthsen and Nikolai Glinka, which I availed of from a nearby library which got me enormously fascinated with chemistry. My father was a practitioner of traditional medicine, and our family had been holders of the lore of Parahita Ārya for several centuries. Hence, hearing me talk about modern chemistry with utmost excitement, he suggested that I explore the processes of life from that perspective. Indeed, I felt this was my calling. I spent all my free time studying books and papers I could land my hands on with the objective of becoming a biochemist. In particular, I became fascinated by proteins and realized that their study would be central to the understanding of life itself. Needless to say, I specialized in chemistry in college and acquired hands-on experience with various experimental techniques. Just as I entered college, we finally rid ourselves of English rule. I was excited by the prospects which lay ahead. I imagined myself as being part of the founding generation upon which a glorious modern scientific tradition of our newly revived nation will be built. I traveled from home to Turushkarajanagara to obtain my master’s in organic and bio-chemistry. In the course of my stint there, I developed a technique using the ninhydrin test followed by a reaction with copper sulfate to quantify amino acids by combining paper chromatography with colorimetry. I published this work in a reputed American journal and wrote up my thesis. Then I moved to a top research lab at Kshayadrajanagara to work on my Ph.D. with a young coethnic adviser who shared my vision. In the course of that, he introduced to me an enzyme he had just detected — a transaminase — I used the techniques I had developed in my thesis to characterize the reaction catalyzed by this enzyme. I published this work in a prestigious English tabloid and soon thereafter showed that vitamin B6 was necessary for this reaction. I wrote all these findings up as a dissertation and graduated with a Ph.D.

I soon got hired as a young researcher at another upcoming institute in the city of Visphotaka and decided to put my dream into practice. I had planned a two-fold scientific program: first, I wished to survey proteins to discover unusual amino acids beyond the well-known twenty. Second, I wanted to discover enzymes that act on other proteins to modify amino acids in them. At that point I was a great admirer of the vision of Shri Jawaharlal Nehru — I believed he would prove to be a great supporter of science. However, my hopes were soon soured – Nehru was indeed more the dud that the great CV Raman saw him to be. We hardly had any funding for our research. I had to put in orders for chemicals and equipment months in advance — often typing out the same order on sheets of differently colored paper, each destined for a different government office. The situation with glassware was even worse — we had a perpetual shortage and had to wash and autoclave stuff to reuse items, often resulting in artefactual experimental results. I realized that my objectives would hardly be met, especially in the face of the competition from the mleccha-s and the resurgent Japanese. Hence, I decided to try my luck with the mleccha-s. A rich industrialist, pleased with my prior publications, offered me a fellowship to be a traveling scholar in the USA. Accordingly, I left the shores of our country to join the lab of Professor Anton Meyer at Boston. He was interested in unraveling the biosynthesis of amino acids and felt my expertise would be of use. Working in his lab, I discovered an enzyme, the cyclodeaminase, that directly converts an amino acid called ornithine to proline. Till that point, Anton Meyer thought that the pathway involved several separate enzymatic steps. I showed that while both pathways existed, the cyclodeaminase was preferred in multiple organisms. I next discovered a similar enzyme in plants that was involved in producing pipecolic acid downstream of lysine. I published multiple papers describing these findings.

Before I left India, an acquaintance of my father wanted me to marry his daughter. She was uneducated and boring and could hardly hold a conversation with me. Hence, I put it off, saying I’ll be back soon from videśa and will reconsider. In America, I became interested in a woman who, like me, was a traveling scholar from Taipei. I found much happiness in her company, and we often chatted in the corridors of the labs as we waited for our incubations, centrifugations or other experiments to complete. However, some time into my stay there, her fellowship expired, and she had to leave. Communication with her became scant and then evaporated. More sorrow came my way. Just as my fellowship was to expire, I was considered for a faculty position at a smaller university nearby. For some reason, Anton Meyer, who used to regularly praise me to my face, suddenly turned against me and wrote a sly letter of reference, scuttling the offer. Nevertheless, another professor gave me a letter, and I got a job at a pharmaceutical company. There I did some of my best work — I unraveled the biosynthetic pathways for multiple amino acids in fungi and also purified some sugar metabolism enzymes. While I published several articles on these in the best journals in the field, our director was more interested in patents and wanted me to keep these under wrap until they could develop some inhibitors for these enzymes. That was not my style — I was interested in science for science’s sake and not just working for money without publishing my findings. I could have waited a bit and moved to a faculty position elsewhere, but the isolation I felt in my social life in the USA was getting to me. It was hardly fun to drive long distances, cook unappetizing food daily and not be able to participate in the bustle of the Kārttika or Tiśya festivals. Hence, in a fit of frustration, I returned to India.

Back home, I got a tenured professorship at one of the finest medical schools and continued my research. The first couple of years were spectacular. I isolated new prolyl and lysyl hydroxylases — that’s why I felt the gods have finally fulfilled my wishes of meeting you, Somakhya, who discovered new versions of these enzymes that no one else could have by their methods. I also started studying genetics and realized that the way forward was combining it with biochemistry. Thus, I started developing multiple bacterial systems in my lab. I got together with my Ph.D. mentor and started a couple of new Indian scientific journals in the hope these would become beacons of research in India. However, the promise of these did not bear the fruit I expected. We had suffered a disastrous defeat in the war with the evil Cīna-s. While we did better in the subsequent war against the Army of Islam, the mood for innovative research in the country was declining. The funding situation was even more precarious than when I started. Nehru was gone, but his successors were no better – they were more interested in quotas for farmers than the frontiers of science. I found fewer and fewer motivated students to pursue the exciting projects I was coming up with. Hence, I decided to do things with my own hands that were more achievable with relatively low funds. Thus, I labored on isolating multiple interesting peptidases and laboriously working to characterize their cleavage specificities. I really felt jealous of my friend Rajaraman from my Ph.D. days. He had somehow gritted it out in the USA for several years –his mentor, Prof. Gripper, was far kinder and finally bequeathed his lab and grants to him. Now he was doing stellar biochemistry on metalloenzymes. Thus, began my long and gradual decay into obscurity even as my chosen science was exploding in the West. If I felt social isolation in the USA, in India, I felt a deep scientific isolation with a creeping mediocrity.

My family would bring up one uninteresting woman after another, but I’d quickly lose interest as my thoughts would return to the girl from Taipei. With my growing age, this only made me sadder. But worse was in store. The vote bank politics of our nation had meant that our colleges were filled with increasingly ill-equipped students. Some of them were admitted to the Ph.D. program in my medical school despite having failed the entrance exam by objective criteria. I had to take one such student. He was politically well-connected to the anti party that was well funded by the mleccha agent Lodenthal who was supporting various insurrectionist activities in India. However, I was not a man who compromised my standards. I failed him thrice in his prelims, but given his special category, he was allowed to take as many attempts as necessary. He barged into my office and told me to pass him or else face something really unpleasant. I was not the man who could be threatened. I informed the campus police and had him debarred. I then took a break to come here, my birth town, to maintain my natal home in the agrahāra. I wanted to keep it because it was donated to our ancestors by the mahārāja for bringing the medicine of Parahitācārya to these regions. After doing some repair work with the intention of retiring here, I took the train and reached the town of my college late at night. As I was walking back to my quarters, I was attacked by two assailants, the preta terrorists, Reagan Rajan and Wilson Rajan, with a billhook and an ax. They were part of the sword arm of the SJWP to which the undeserving student belonged. I was unarmed but put up a good fight breaking several teeth of Wilson Rajan. However, their armament proved too much for me, and I eventually went down to their blows. They chopped my corpse into several pieces and disposed of them in the nearby forest. While my body was gone, strangely, I still felt a conscious existence — I could perceive certain things but could no longer act in the usual way. However, a couple of weeks later, I realized that in this disembodied form, I had a special power — I could possess people!

Thus, I possessed a forest ranger and found my way out of the forest to the town. There I jumped from person to person, possessing them even as I have taken hold of this girl who is typing my story. Eventually, I reached Reagan Rajan and, having possessed him, made him rush at Kalmegh Singh, a police officer from the north with a reputation for encounter killings. He and his men promptly eliminated both the Rajans. Having had my revenge and feeling content that I had done some service to our nation in my death, I desired to return to my natal house. Using a chain of possessions, I finally arrived there. While in this ghostly state, I’m quite content hearing the recitation of the śruti by our neighbor, the Vājapeyin. I am happy to see these two, who, for the first time after my death, captured me. I have been yearning to tell my story. Hence, I possessed this girl.

Somakhya: “You have to leave my cousin immediately.” Lootika right away deployed the Huṃkāra Mahādeva mantra for bhūtoccāṭana and expelled the ghost of Lilavinodan from Charuchitra. L: “Charu, are you feeling alright?” C: “That was wild! I feel totally my own self now. However, I felt him whisper in my ear as he left: “Please print a copy of all my papers and place them in a bundle in my old house. That way, I can get back there and continue my ghostly existence in contentment.” Somakhya and Lootika fulfilled his wishes to the degree they could – he had published several papers — hence, they only printed some key ones and transfixed him to his old dwelling. S: “Maybe someday we too would be forgotten and reduced to a mere name without a story in the vast literature, like this Lilavinodan. But the question is would we want to become ghosts to tell our stories?” L: “A man who encountered Ramanujan’s ghost said that as a specter, he had moved on from mathematics and was more interested in the study of the 1008 names of Viṣṇu. Who knows if a state like Lilavinodan awaits us or, as our people claim, we will be back again for another round or move on like Ramanujan. Then there are soteriological teloi beyond those.”

A meandering through Mongol epic-historic narratives: fraternal conflict and mythemes in the history of Chingiz Khan

The Mongolic and Turkic peoples have a rather rich tradition of oral epics that have not yet been comprehensively analyzed from a comparative mythological perspective. Some of these extant epics include: (i) the epic of Gesar Khan. Bearing the Roman imperial name, i.e., Caesar, we believe that this epic might have captured elements of the persona of the great Julian, who tried to restore natural order against the irruption of the evils of Abrahamism, and also the Turgish Khan Su-lu(k) who valiantly fought the Army of Islam and the Chinese hegemony. (ii) Jangar; this epic seen both among the Oirat and the Eastern Mongols might have had its root in the Oirat west. While mostly mythological, its current form might have incorporated historical inspiration from the rise of the Oirats under Essen Taiji and Amasanji Taiji and their defeat of the belligerent Han of the Ming Empire. (iii) Qasing Khan, an as-yet fragmentary epic primarily recovered from the Oirat reciters. This preserves certain elements of deep Eurasiatic mythology. (iv) Manas: This Turkic epic of the Kirghiz was probably inspired by events relating to the Kirghiz Khan, who led them to a victory against the Uighurs (840s of CE) and raided Chinese lands thereafter. In contrast to these epics, whose connection to history is obscure and often at best limited, there emerged a parallel Mongolic literary tradition that the Mongols composed, in a rather self-aware fashion, of the world-changing events the founder of their nation catalyzed. However, it should be noted that all these histories are blended with the aforementioned epic tradition with its deep roots in Eurasiatic mythology. In the latter tradition are several histories whose focus is the rise of Chingiz Khan and the deeds of his successors who formed the Mongolian imperial family.

The best known of these histories is the Mongqol-un Niuca Tobci’an or the Secret History of the Mongols (SHM). The scholars de Rachewiltz and Onon have both proposed that its original version was composed by a member of the Borjigin tribe (the tribe of Chingiz Khan) who had personal familiarity with the events recorded in it. Indeed, it presents a first-person account of several of the events, unlike the third-person accounts of the alternative histories. Interestingly, de Rachewiltz proposed that the original, perhaps going by the name of its opening, “Chingiz Khan u ujaghur” (The Origin of Chingiz Khan), was composed by his son, the second great Khan, Ogodei. However, a more common view is that its “final” form was composed by Shigi Qutuku, the foster son of Chingiz Khan, who served as the supreme judge and minister of the census of the Mongol empire. In either case, the phrase “the Khan, my father,” which is found in the text, would apply. Onon makes a fairly good argument that it was first “published” during the great Quriltai of 1228 CE, which corresponds to the Year of the Rat mentioned in the colophon. Ogodei was eventually elected the great Khan at this Quriltai. The text describes his election and some aspects of his reign but not his death in 1241 CE. Thus, it was conceivably extended to accommodate some of the events during his reign. It appears to have been again edited and probably suffered some interpolations/changes in 1261 CE when Qubilai Khan instituted the Department of National History within the “College of Literature.” A much modified and elaborated Mongol text was then printed in 1400 CE. One lineage of the SHM text survived in at least 3 Chinese manuscript traditions. Another version containing much of the SHM survived in the form of a poorly copied manuscript going under the name of Altan Tobchi, written in Uighur script that was discovered in 1928 CE in Mongolia. This manuscript from the 16-1700s was itself a copy of an earlier, now lost manuscript indicating the survival of a potentially intact relatively early version of the SHM among the Mongols until that time. In recent times, the SHM, with its Chinese interlineal gloss, has acquired much prominence with an excellent transliteration by Japanese scholars and multiple accessible English translations. In many ways, historians seem to favor it because of its apparently “truthful ring” — it does not whitewash the controversial acts or the fears of Chingiz Khan. These include his fear of dogs, the killing of Bekter, his flight from the Merkits, leaving his wife to her own devices, his mother’s quiet dissatisfaction with the number of followers he assigned to her (though he gave her the most in his clan), and the conflict with Qasar (see below), which is said to have led to his mother’s death from grief. However, it is clearly not written from a rival perspective — he is the dominant hero of the SHM.

It is clear that even during the empire, there were alternative histories. While these come from later manuscripts, an analysis indicates that they came from sources distinct from the SHM composed during the empire. Some of these “alternative histories’’ include:
(1) Chingiz Khaghan-u Altan Tobci (Golden History of Chingiz Khaghan): This manuscript was found by an Inner Mongolian scholar Dorongha in 1958 as part of a bundle of manuscripts near an ancestor temple dedicated to Qasar (his descendants are still extant in the region) in the vicinity of Hohhot. The work resembles the SHM but contains additional material not found in the former. One of these is an account of an early battle of Temüjin where with just a tiny force, he destroyed 300 Tayichi’ut.
(2) Quriyangghui Altan Tobci: This work has a bauddha overlay completely absent in the SHM. It follows the SHM in parts but also derives material from the now-lost Altan Debter (Golden Book). It claims that Chingiz Khan ultimately descended from the mythical Ikṣvāku monarch made up by the bauddha-s known as Mahāsammata. It further records a curious tale that “12 evil Khans will be born who will make every living being to suffer. The Tathāgata foretold that they would be defeated, and Chingiz Khan was born [for that purpose]. It contains two parts, the first being the history of Chingiz Khan ending with his funeral, and the second contains the rest of the Mongol history from Ogodei to Ligdan Khan. It mentions that the Khan was either buried at Burqan Qaldun or an unidentified place called Yeke Öteg on the northern side of the Altai Khan and the south side of the Kentei Khan mountains.
(3) Altan Debter (The Golden Chronicle): This is the now-lost old Mongol history. However, material from it was translated into the work of Rashīd al-Dīn during the Il-Khanate and the Chinese Shengwu qinzheng lu (The campaigns of Chingiz Khan).
(4) Arban buyantu nom-un Caghan teüke (The White History of the Ten Meritorious Deeds): The original text of this history was commissioned by Qubilai Khan. Its extant version shows a clear bauddha component, some of which might go back to the old lama Phagpa who is credited with devising the universal Mongol script. He is said to have composed praises of the Khan using the poetic theory expounded by Daṇḍin in his Kāvyadarśa. The Mongolian verse inscription from 1345 CE found on the gateway of Chü-yung-kuan probably reflects the influence of Daṇḍin’s principles on the innovations seen in Mongol poetry.
(5) Erdene-yin Tobci (The Precious Summary). Here the word Erdene is derived from the Sanskrit ratna (gem). This work was composed by the Chingizid scholar Saghang Secen in 1662 CE. At this point, the glory of the Mongols as an independent nation had gone into decline, and they were absorbed by the rising Tungusic Manchu. For Saghang Secen, his ancestor and father of the Mongolian nation, was already distant history; however, he still had access to key texts of the Mongol historiographic tradition. Moreover, he was still relatively close in time to the final blaze of the Chingizids in the form of Dayan Khan and his wife Mandukhai to record their history. In his short 45-year life, Dayan Khan reunified the Mongols and briefly rekindled the vision of their glorious past with his strike on Beijing.
(6) Altan Tobci (The Golden Book): This a late work by Lubsandanzan (distinct from that mentioned above), which, however, contains older material as it features variant narratives, such as of the early fight between the Khan and the 300 Tayichi’ut. Its author preserves material from the original Mongolian text of the SHM. It preserves what are apparently the Maxims of Chingiz Khan. It states that the Khan was buried in a golden tomb on the northern side of the Altai mountains.
(7) Mongghol Boghda Chingiz Khaghan-u Tughuji. 7 pages of it survive and, to date, has been studied in the original only by Kalponas. The fragment contains an account of the Mongol conquest of the Solonggha-s (Koreans) and the final Tangut war of Chingiz Khan along with his last words.

Most of these Mongol histories follow a pattern that suggests their roots lay in the SHM or related para-SHM traditions. Thus, these early Chingizid traditions seem to mark the beginnings of Mongol historical consciousness. Nevertheless, interestingly, the SHM itself is a rather mature work that appears almost out of nowhere — at least the Mongols proper (Chingiz Khan’s people), i.e., before the name came to be applied to all Mongolic people, were apparently illiterate. However, as scholars have suggested before, it seems that the Mongols probably inherited their literary language from another Mongolic dialect in an already mature form. This probably happened when the Uighur scribe Tata(r) Tonga came over to their side when they vanquished his former Naiman employers in 1204 CE. This also leads one to wonder if it might explain the several words with deep Orkhon Turkic etymologies in the SHM. Whereas Chingiz Khan refers to the ancient Chanyu as the legitimate predecessor of the Mongol Khaghanate in his letter to the respected Daoist scholar Changchun, all these histories have a certain amnesia of that ancient Hunnic period. Starting in the 1600s, Saghang Secen made the connection that the Huns were the likely predecessors of the Mongols. However, he still stuck to the model wherein the original royal lineage leading to the Khan emerged in India and, from there, went to Tibet and in turn, reached Mongolia. Indeed, versions of the “out of India hypothesis” for the origin of their royalty remained popular with Mongol historians in the 16-1700s. By the 1700s, multiple Mongol historians, having studied the Chinese imperial annals closely, reached the conclusion that the Huns (Ch: Xiongnu) were indeed their predecessors. This was a major shift from the sudden transition from epic-style myth to history seen in the earlier works.

Siblings cooperating in a conflict with their half-siblings, especially when resources are limiting, is a natural consequence of biology. Further, if the stakes are high, and a winner could take all, then full siblings might also fight each other. The latter is commonly seen in hatchling birds from the same clutch. We see multiple examples of half-sibling and sibling conflict in the history of Chingiz Khan. Untangling the history and mythology behind these narratives is not always easy. In this note, we shall take a discursive look at them from the viewpoint of some of the histories of the Great Khan that have come down to us. The earliest of these histories open with a mythological section on the theriomorphic ancestors of the Mongols, the Wolf and the Doe, and apparently mythical human ancestors such as the cyclopean Dua-soqor and Dobun-mergen. Right in that tale, we encounter an example of sibling cooperation between the two. However, that broke down in the generation of their descendants as Dua-Soqor’s clan separated from that of Dobun-mergen. Soon thereafter, a further conflict emerged between the half-siblings born of Dobun-mergen’s wife, Alan Qo’a. At that point, Alan Qo’a instructed her five sons born of different fathers on the utility of unity using the demonstration of breaking a single arrow versus a bunch of arrows (a motif that returns in Mongol narratives of Chingiz Khan’s death). Nevertheless, a conflict broke out after Alan Qo’a’s death when the last son Bodonchar, was deemed stupid and dispossessed by his four brothers. However, they reunited when Bodonchar led them to a leaderless tribe whom they destroyed and despoiled.

These narratives appear to enter the historical realm around the time of a Mongol leader named Menen-tudun, who is said to be the descendant of Bodonchar. His title, tudun, is clearly of Turkic origin and is seen in the Blue Turk Orkhon inscriptions (e.g., the Blue Turk general Yamtar Tudun, who fought the rival Qarluq Turks). It meant a commander or a governor who was typically under the Khaghan. While this title persisted in the Turkic world, like among the Khazars and even the later Osmans, its use by a Mongol leader is notable. Hence, an ancestor of the Chingizid Mongols perhaps obtained this title from his role as a tudun during the Uighur Khaghanate. Alternatively, they continued to use that old Turkic title during the Khitan (Liao) period as part of the confederation of Mongolic tribes that formed on the Mongolian plateau. Menen-tudun is said to have had seven sons. Among them were the ancestors of Chingiz Khan and the later Islamic tyrant Timur who spawned the monstrous Mogols of India. As if to presage that, the remote male ancestor of these Mogols, Barulatai, is said to have been a giant man with crude eating habits. Notably, among the many descendants of Menen-tudun, the SHM again records a case of sibling conflict.

Some generations from Menen-tudun came Qabul Khan. It appears he was the first to assume the title of Khan among the Mongols proper — at that time, the term Mongol was applied only to his lineage rather than all Mongolic people like the Kereyit, Tatar and the Naiman who had their own leaders with Khaghanal titles. Thus, the confederation unified by Qabul Khan likely primarily encompassed the clans descending from Menen-tudun and probably some other related groups. Nevertheless, it appears to have been a powerful coalition presaging the future of the Mongols. Under Qabul’s leadership, it likely tried to aid the Khitans in their final struggle against the Jurchen. While the Khitan were ultimately defeated and retreated to form the Qara Khitai state, the Jurchen appear to have initially tried to make peace with Qabul. However, he is said to have pulled the beard of the Jurchen emperor and sparking hostilities with them. In the years that followed, he led the Mongol confederation to victory against the Jurchen and repulsed their invasion of Mongolia. Interestingly, while Qabul had several sons, the Mongols appear to have initially elected his cousin Ambaqai as their next Khan — this appears to have laid the seeds for future conflicts between cousins at the time of Chingiz Khan. The Jurchen wanting to avenge their defeat, formed an alliance with another Mongolic group, the Tatar, who treacherously captured Ambaqai while he was escorting his daughter for a marriage alliance with them. They handed him over to the Jurchen, who brutally executed him. After him, the Khaghanal title came back to the line of Qabul, with his son Qutula becoming the next Khan who continued to fight the Tatars backed by the Jurchen. Chingiz Khan was the great-grandson of Qabul via one of Qutula Khan’s elder brothers. Thus, the Mongol elite clans followed a pattern of expansion, fission and fusion centered on cooperation between siblings, followed by a breakdown of relationships in the subsequent generation. Thus, Chingiz Khan’s father, Yisügei-bagatur’s brothers cooperated with him in abducting Hö’elün as a wife for him. However, one of those brothers, Daritai turned against Chingiz — he wished to execute Daritai after arresting him but spared him at the behest of his advisers.

Against this backdrop, it is not surprising that the story of the great Khan is permeated by the motif of sibling cooperation and conflict. Soon after his father Yisügei’s death, his family was dispossessed by the clan of Ambaqai Khan, their former ally (the Tayichi’ut), and had to eke out a bare existence on the steppe. The Mongol histories record Yisügei’s second wife as Sucigil (SHM) or Dagasi (other histories). Her two sons, Bekter and Belgütei grew up with the five kids of Chingiz Khan’s mother, Hö’elün. Unsurprisingly, conflicts soon broke out between the half-siblings in these resource-limiting conditions. When Temüjin and his full-brother Qasar were fishing along with their half-brothers Bekter (whose name meant armor; also seen in Orkhon Turkic) and Belgütei, the latter stole their catch from them. They went to their mother to complain, but she reminded them of the tale of Alan Qo’a’s five sons and warned them that they could never take revenge on the Tayichi’ut if they kept fighting between themselves. They were not convinced by their mother’s counsel and pressed on her that it was hardly an isolated incident and brought up the theft by their half-brothers of the game they had hunted on the previous day (the incidents are temporally interchanged in Mongol histories other than the SHM). While the SHM only mentions Temüjin and Qasar as plotting against their half-brothers, in Saghang Sechen’s history and related works, all four full brothers of Temüjin are said to have plotted against Bekter and Belgütei. When Bekter was watching over their horses from a little hill, they crept up on him — Temüjin from behind and Qasar from front — aiming their arrows at him. Bekter tried to negotiate with them for his life. Temüjin and Qasar ignored his words and slew him even as he sat cross-legged, accepting his fate. Before being killed, he asked them to spare his line by letting Belgütei live. As the Mongol scholar Onon notes, it is unclear from the SHM as to why they singled out Bekter but accepted his brother Belgütei as their close ally. Saghang Sechen has Bekter tell Temüjin and Qasar that his brother Belgütei will be of great help to them in the future. The SHM is probably closest to being historical in only including Temüjin and Qasar in the plot, as the other two were probably quite young to participate. However, there was perhaps a backstory the histories did not record regarding why Belgütei was spared, but his brother was killed.

Hö’elün severely upbraided her sons. Interestingly, in that lashing preserved in the histories, she mentions Temüjin being born clutching a black blood clot and also the meaning of Qasar’s name (A legendary dog; see below) in a negative connotation. Temüjin soon had to depend on Qasar and Belgütei for his survival as the Tayichi’ut fell upon them: Belgütei built a wooden fortification while Qasar, the brilliant archer, showered arrows on them and engaged them single-handedly in combat. The two other brothers and their sister were hidden in clefts in a narrow mountain defile. While these efforts of Qasar and Belgütei did not prevent Temüjin from being ultimately captured by the Tayichi’ut, they went on to play a key role in his great struggle and rise to the status of the Khan of the Mongolian peoples. The role of Qasar in this process is emphasized in the SHM in at least two major events leading to the founding of the Mongol nation. In early 1203 CE, the erstwhile allies of Temüjin, the Kereyit, ambushed and defeated him in the battle of the Qalaqaljit Sands. With his son Ogodei seriously wounded and his forces scattered, Temüjin had to flee to the Baljuna Lake in dire straits. There as he reassembled his troops, Qasar, who appears to have been taken hostage by the Kereyit, escaped with a few of his men, leaving his wife and sons behind and joined Temüjin. They contrived a ruse, and Qasar was able to fool the Kereyit that his brother’s forces were scattered, and he was nowhere to be found. Having thus lulled the Wang Khan of the Kereyit into false security, the Mongols surprised them at the Jeje’er Heights in the autumn of 1203 CE. The Kereyit were completely destroyed in the battle, and their leaders Toghrul Wang Khan and his son Ilqa Senggün fled. The former was captured and killed by a Naiman warrior Qori-sübechi.

With the Kereyit, one of the two most powerful Mongolic Khanates prior to the rise of Temüjin, gone, the other major Khanate, the Naiman, challenged the rising Mongol leader. Qasar again played a big role in bringing down the Naimans, and this is strikingly illustrated by the verses recited by Temüjin’s friend-turned-enemy Jamuqa to the Tayang Khan of the Naimans before the decisive battle that resulted in their destruction at the Naqu-kun mountain (East of the Altai mountains). In 1204 CE, a major confederation of Mongolic tribes came together to fight Temüjin. One part of it was the Naimans under the Tayang Khan, whereas the other part of it was led by Jamuqa, who in addition to his own Jadaran tribe was elected the Gur-khan by the surviving Tayichi’ut (whom Temüjin had smashed in 1201 CE), the Saji’ut, the Dörben-s, Qatagin-s and the Qongirat-s. Temüjin decided to strike taking advantage of the advancing age of the chief general of the Naimans, Köksegü-sabraq. As Temüjin closed in on the large army of the rival confederation, he personally led the elite troops at the forefront of the attack. The main Mongol force was led by Qasar while their youngest brother Temüge led the rear guard. Tayang Khan asked his ally Jamuqa to describe his foes — a motif found in accounts of war in ancient Eurasiatic epics such as the Rāmāyaṇa (e.g., Vibhīṣaṇa, who was also originally a partisan of the enemy, gives Rāma an account of the rakṣas heroes). The longest account and most striking of Jamuqa’s poetic sketches is reserved for Qasar:

His body is three fathoms high,
And he dines on three-year old cattle;
Wearing a three-layered armor,
He is pulled along in his cart by three bulls.
When he swallows a man complete with quiver,
It does not get stuck in his throat.
When he gulps down a whole man,
It does not fill his stomach.
When he is angry and draws his bow,
And releases an angqu’a (dvi-mukha) arrow,
He shoots and pierces ten or twenty men
Who are beyond a mountain;
When he draws his bow and releases
A keyibür (long-range; sūcīmukha) arrow,
He shoots and pierces through his enemies,
The ones he fights
Who are beyond the steppe.
When he shoots, drawing his bow to the full,
He covers nine hundred fathoms;
When he shoots, drawing it only a little,
He covers five hundred fathoms.
Different from all other men,
He was born a coiling dragon-snake.
His name is Joci Qasar.

His might, even at birth, is also confirmed by his mother who says in the SHM that while Chingiz Khan could only empty one of her breasts as an infant, Qasar used to empty both. While Jamuqa compares him to a dragon, in the SHM, while upbraiding him and Temüjin for killing Bekter, his mother compares his ferocity to that of his namesake, a legendary dog. Qasar and Basar are two mythical heavenly dogs of the Mongols that are believed to have emerged from the eggs of a celestial bird and are invoked to this date by the shamans of the Mongolized people with Khitanic ancestry, the Dagur. They also appear in the oral epic of the mythical hero/deity Qasing Khan:

Qasing, the Khan of the empire,
Let his dogs Qasar and Basar follow,
Took his hawk and eagle with him,
Set out with tumult and noise,
Rode through larch-rich north-facing forests,
On the hunt for elk and deer,
Traveled along the banks of swelling rivers.
This might be an ancient reference to the Orionic part of the sky (the birds could be the Aquila-Cygnus region) and connects to the cynolatory of the Mongols shared with the Khitans and Turks. Comparable dogs are known as Aq Köpek and Aq Qasar among the heathen Turks.

After defeating his rival and becoming the Great Khan of the Mongol nation, Chingiz rewarded Qasar with an ulus of 4000 men. However, soon conflict broke out between them. As per the SHM, Qasar interrupted Chingiz Khan when he was already angered by some other matter of concern, saying that the 7 Qongqotan, which included his shaman Kököcü Teb Tenggeri ganged up and trashed him. The Khan responded: “In the past, you have done nothing but claim that you would not be vanquished by any living being. How is it that you have now been vanquished?” Seeing his brother not helping him, unlike how he had arranged for Belgütei to kill a relative who had slashed his shoulder with a sword (while arresting a thief from his party), he sulked away and did not talk to Chingiz Khan for three days. After that Teb Tenggeri tried to fan the flames further by stating: “The decree of Möngke Tengri concerning the ruler has been foretold by heavenly omens as follows: once they say that Temüjin will hold the nation, once that Qasar will. If you don’t strike at Qasar by surprise, there is no knowing what will happen!” Chingiz Khan followed his shaman’s words to immediately arrest his brother. Their mother interceded and severely scolded the Khan and had him released. However, the Khan reduced his followers to just 1400 men. It is said that this disappointed his mother and she died from sorrow soon thereafter. Eventually, Teb Tenggeri and his brothers also went on to beat up the Khan’s youngest brother Temüge. At that point, the Khan’s wife interceded and warned him that Teb Tenggeri was isolating him from his clansmen. Subsequently, even as the Qongqotan moved on the Khan himself, he had Temüge employ three wrestlers to eliminate the shaman. Once he was killed, a tent was placed over his body, and it was made to disappear mysteriously. Thereupon the Khan declared: “Because Teb Tenggeri laid hands on my younger brothers and spread baseless slanders among them in order to sow discord, he was no longer loved by Tengri, and his life, together with his body, has been taken away.” Interestingly, despite these incidents, the extant descendants of Qasar and his followers, the Qorcin Mongols, believe that their shamans are descendants of Kököcü Teb Tenggeri. Does this mean that there was something more to the relationship between the 7 Qongqotan and Qasar? For that, we have to turn to Mongol histories other than the SHM. While Qasar plays an important role in the earlier parts of the SHM, the text does not mention him after his campaign of 1214-15 CE when he conquered several cities of the Jin empire (Beiging and the country of Vuqanu; their exact identity remains unclear to date). Here again, the alternative histories offer a different view and bring him back during the final war of Chingiz Khan against the Tangut. None of the sources provide an explicit date for his death.

We shall also briefly examine the conflict between Chingiz Khan and his half-brother Belgütei which is recorded in the SHM. Like his conflict with Qasar, that with Belgütei too has its unique elaborations in the alternative Mongol histories. In this case, the rupture was entirely sparked by the actions of Belgütei. In 1202 CE, after routing Jamuqa and crushing his childhood foes, the Tayichi’ut, Temüjin turned on the longstanding foes of his family, the Tatars, an ancient and powerful Mongolic alliance. He routed the Tatars in a battle at Dalan-nemurges and chased the surviving Tatar forces to Ulqui Shilügeljit River, where his forces completely destroyed the army of four Tatar tribes. They rounded up the survivors as captives and decided to massacre those of them who were taller than half a cartwheel to avenge the killing of Yisügei-bagatur and Ambaqai Khan before that. Belgütei prematurely taunted the captured Tatar leader with this plan. As a result, they desperately tried to break free twice and were killed to man only after inflicting heavy losses on Temüjin’s forces. Hence, Temüjin punished his half-brother by keeping him out of the Quriltai-s. He was told that he could join the rest of the senior leadership only after the Quriltai had concluded and they had drunk the ceremonial wine. However, Temüjin was relatively mild on him and let him be the judge who would handle litigations pertaining to thefts and libel outside the senior council. Like with Qasar, the SHM suddenly stops mentioning Belgütei after the first half, where he plays a prominent role. Nevertheless, from the alternative histories, we learn that he went on to have the peculiar distinction of living a whole 120 years, nearly spanning the entire duration of the core of the Mongol empire founded by Chingiz Khan.

There are at least three notable tales of the conflict between Chingiz Khan and his (half-)siblings recorded in the alternate histories beyond the SHM (The translations below are slightly modified versions of those by J Elverskog and C Bawden). The first of these is the “Tale of the Bow-seller” which is found in texts such as the Chingiz Khaghan-u Altan Tobci, the Quriyangghui Altan Tobci and Saghang Secen. Here Saghang Secen curiously remarks that:

“Then Lord Qasar, uniting with the seven Qongqotan, moved about fighting, and [Chingiz] put at the head of his army Sübe’etei Bagatur and had him pursue them.” Sübe’etei intercepted him and then convinced Qasar to stand with his brothers and return to Chingiz. Upon returning to his brother, the following is said to have transpired (narrated below based on Quriyangghui Altan Tobci). Qasar and Belgütei said to each other: “This was an unreasonable thing for the Lord [Chingiz Khan] to say. By the skillful shooting of Qasar and the firm strength of Belgütei, we brought the great peoples of the Five Colors (Mongolians, Mohammedans, Tibetans, Koreans and Chinese) and Four Foreign Lands into our power.” The Lord, having learned that they were saying this, said: “I will humble their pride.” Becoming an insignificant poor old man, he took a long yellow bow and went about inquiring and saying: “For sale!” Then Qasar and Belgütei asked: “Where do you come from, such a man has not been seen before?” That old man said: “I am a poor man, and I am going about selling a bow.” Then those two mocked him, saying: “Do you say, ‘Take this bow’?” Then the old man said: “Bad as it may be, I should like to know about stringing it.” Then Belgütei took it but could not string it. That old man strung it and gave it to Qasar. Qasar could not stretch it. Then that old man became a grey-haired old man, mounted on a blue mule with a white blaze, and stretching his golden toghona on his long yellow bow, he shot through a rock and reprimanded them, saying: “You are the younger brothers of the Holy Lord, called alert-shooter Qasar and strong Belgütei. It is said; ‘Big words of boasting mean a big mouthful.’” Then those two younger brothers of his, in fear, said to each other: “This was the sign of the Lord.” After that, they abstained from such words.

Comments: This is an example of the famous “Bow-contest” motif that occurs in the Rāmāyaṇa twice (the marriage of Sitā and the challenge of Rāma Bhārgava), the Mahābhārata (the marriage of Draupadī) and the Harivaṃśa (Kṛṣṇa breaking the bow at Kaṃsa’s ritual). It occurs in the Greek epic tradition in the final part of the Odyssey — bow of Odysseus. Interestingly, it has also been claimed to occur in a Russian bylina and is found in the Turkic epic of the hero Alpamysh or Alpamsha (he was originally a Mongol from the Qongirat tribe). While Martin West believes it originated with the steppe Iranics, we believe it had a much earlier IE provenance. In the marriage of Sitā, Draupadī, the return of Odysseus, Alpamysh and the Russian bylina it has a clear connection with the winning of a woman. However, the versions in the challenge of Rāma Bhārgava and Kṛṣṇa’s bow-breaking are primarily presented as heroic challenges. The above Mongol version is not close to the Alpamysh version; rather, it is squarely related to the heroic challenge aspect, as seen in the Rāma Bhārgava version. Like in that case, the person carrying the bow has a divine aura (the Blue mule with a white blaze in the Mongol version) and “appears out of nowhere” to present the bow. Otherwise, it preserves the key elements of stringing and bending a great bow and then shooting a difficult target.

The second story is the “Tale of the Jade Cup”: Saghang Sechen narrates this clearly mythological tale just after when one of their cousins had slashed Belgütei’s shoulder with a sword (an incident recorded in the SHM). However, the Chingiz Khaghan-u Altan Tobci records it in a different place. In 1224 CE, Chingiz Khan marched on the Tanguts and defeated them. They submitted to the Mongols, but shortly thereafter, they reneged on the surrender and formed an alliance with the Jin to open hostilities against the Mongols. In 1225 CE, Chingiz Khan decided to put an end to the Tangut empire and launched a massive invasion of it (his last campaign). This tale is narrated just before the inception of that campaign. It records the rationale of why Chingiz Khan became preeminent in his clan:
After that, through the power of the virtue of former existences, there was filled and bestowed upon the Holy Lord (Chingiz Khan), from the mighty Qormusda Khan Tengri, in a precious jade cup, the drink rasāyana. Fearfully the Holy lord took it, and when he was about to drink it, his four younger brothers said: “It is said if there are ten to the eldest brother, there are four to the younger brothers. Oh my Lord, if you drink the greater part, deign to give us the lesser part in pity. Deign, in your understanding, to consider this and make a decision.” The Holy Lord said to his younger brothers: “Formerly, when I was born, in my right hand there happened to be, from the throne of the nāga-s (Chinese Dragons) and by the order of the mighty Buddha, the Qasbuu seal. Now the drink rasāyana has been filled and bestowed upon me in a precious jade cup from the mighty god Qormusda (or the elevated gods: degere tengris-ün). I think I am the Lord with a supreme destiny. Now, if you will drink, go on!” So saying he gave it to them. When his four younger brothers took it and drank, it went in their mouths but did not go into their throats. Then his four younger brothers said to the Lord: “We, being without a destiny compared with you who have a destiny, have wrongly contended. We will be officials controlling the taxes of your villages.” Saying: “Lord, drink,” they presented it. The Lord took it and drank. The Lord, being warmed and excited by that rasāyana, said: “Formerly when I was born, there occurred, by order of the Buddha, the Qasbuu seal of the nāga Kings. Now the mighty god Qormusda has filled and bestowed upon me in a precious jade cup the drink rasāyana. I am the Lord with a destiny from Heaven.

Comments: Beyond the obvious Indian signature of the rasāyana, this is an unambiguous Mongolian reflex of the “Magic Cup/Grail” motif. We suspect that this motif had its roots in the IE world and spread widely. A close parallel to this Mongolian version is seen in the Northeast Iranic Nart tale of the divine cup, which also spread west in the form of tales like the grail of Arthur. The relatives of Narts or Ossetians (Alani, Aran< airya) are well attested as residing in Mongolia before being absorbed by the Turkic and Mongolic peoples. Even down to the time of the Chingizid Mongols, their separate identity is seen in the tribal name Asud (~Osset). Thus, this tale was likely acquired by the Mongols from a steppe Iranic source close to the Ossetians. Such a lateral transfer is also consistent with the key role played by the Iranic deity Ahura Mazda as the god Qormusda Khan Tengri of the Mongols. In the Ossetian tradition, this magic cup, Wasamonga (also called: Nartyamonga) was said to rise by itself to the lips of a real hero who was narrating an account of his campaigns but did not budge if it was the mere boast of a fake hero. The Iranic root of this cup is confirmed by Herodotus’ account of the ritual of the cup among the old Śaka-s: “Once a year, each regional chief at the festival ordered a glass of wine mixed with water, and all the Scythians who had killed an enemy drank from this goblet. Only those who had not performed this service had not the right to touch it. They sat aside in a state of shame that was, for them, a great dishonor. As for those who killed a large number of foes, they drank from two goblets united together.” As noted by Dumézil, the equivalent of the Ossetian magic cup is found in the old Śaka tradition of the four golden objects that fell from heaven — a plow, a yoke, an axe, and a cup – evidently, they are symbols of the Iranic cognates of the four varṇa-s. As a comparison to the Mongolian tale, we produce below a precis of the Ossetian tale recorded by Dumézil: Only a hero beyond reproach could drink from the Nartyamonga cup. The Narts once had a dispute over who could drink from the Nartyamonga cup. Urizhmag (= Varāza-maka son of a boar) claimed he deserved it. Batraz (while he is clearly an earthly reflex of the IE Indra-class deity, his name reflects the reverse Mongol influence on the Ossetians and is from the Mongolic Bagatur) reminded him of being carried away by a vulture and deposited on an island. Then the hero Soslan (= Breath of the Alans) staked his claim. Again, Batraz reminded him that he once went to bed across the sea, and the army passed from one shore to the other on him as if he were a bridge. But he became tired and bent his body, causing the world to fall into the sea. Then the hero Sozryko made his claim. Batraz reminded him that when the Wheel of Balshag (the solar wheel) was rolling towards Sozryko, he could not bear its brightness, and his eyes blinked, revealing his weakness. Then Batraz declared that he alone was beyond reproach. None of the Narts could come up with a stain on his name, and the cup was awarded to him. The third tale returns to the conflict with Qasar recorded in the SHM, but the alternative histories narrate it in a very different way, placing it just before the final Tangut campaign of Chingiz Khan. Again, it is replete with omenological and mythological elements. We briefly summarize it based on published versions of the Chingiz Khaghan-u Altan Tobci, Quriyangghui Altan Tobci and Erdene-yin Tobci (it is also narrated in most of the other alternative histories): When Chingiz Khan was marching towards the Tangut (his final campaign), he arrived near the Muna Mountain in Southeastern Mongolia and decided to set up camp there. Right then, he saw an owl sitting atop a tree and took it to be a bad omen. He called his brother: “Qasar, shoot and kill that evil thing!” Qasar immediately took a shot, but the owl flew up, and a magpie flew into the line of fire and was killed. The Khan took this to be an even bigger ill-omen and scolded him recalling his past misdeeds: “Once before you joined up to fight with the seven Qongqotan. As for that day when I asked for griffon vulture feathers, you were stingy; and now, when I said to kill that evil-tongued owl, you killed a fine-tongued magpie! (Saghang Secen)” According to the other histories, the Khan was dismayed at his brother killing the magpie instead of the owl, but that incident in itself did not precipitate the conflict. Instead, it was the hunt or the drinking party which followed. A slave named Mechin wanted to obtain the feathers of the griffon vulture for the Khan. He asked Qasar to shoot such a bird (in some versions, the Khan directly asks Qasar to get the feathers); however, Qasar instead shot a black vulture on the base of its bill. The Khan rejected those feathers as they were not from the right bird and were also contaminated with blood. Further, some versions add a military guide named Bogholbacin tells the Khan that during a drinking party, Qasar took hold of the hand of the Khan’s Merkit wife Qulan (Korean or Korean Merkit according to Saghang Secen; she is believed to have been with him from their previous incarnation). Rashīd al-dīn adds another affront — Qasar’s Tatar wife is said to have rescued many of her tribesmen slated for execution and absorbed them into Qasar’s forces (see the Belgütei incident above). Thus, as per the alternative histories, it was the build-up of these infractions that led the Khan to place Qasar in confinement in a fenced enclosure guarded by four men. The Khan hunted a wild yak or a moose and gave it to him as provisions. The generals and clansmen of the Khan then interceded on Qasar’s behalf to get him released. Saghang Secen has them reciting this verse: “Oh my Lord. It is said: ‘The saldar of good is attacked by the sarbugh of evil; The damages of evil ones overcome the virtues of good ones. The evil of the ill-omened owl Attacks the good-tongued magpie.’ Can we release our younger brother Qasar?” The Khan refused their request and kept him incarcerated. Then the Mongols advanced on the Tanguts and besieged the city of Dörmegei (Ch: Ling-zhou, modern Ling-wuxian) by encircling it thrice. Then a Tangut witch known as Black Kengge came on the ramparts of the city and laid witchcraft on the Mongols by waving around a black pennant. They and their animals started collapsing in droves. Sübe’etei, who had smashed his way through the Tangut defenses to join the Khan, advised him to release Qasar and ask him to tackle her. The Khan acquiesced, and Qasar rode a horse named “Winged Browny (Elverskog’s translation)” to attack her. Qasar shot her through the kneecap with a single long-range arrow and killed her. Comments: The Mongolian word of owl in this tale is ughuli — a potentially onomatopoeic word that might have deep Eurasiatic provenance (c.f. owl, ulūka). The bird called sighajaghai by the Mongols is taken by Bawden to mean a magpie, though it is not entirely clear if that was what was meant. Again, the terms translated as the different types of vultures are uncertain — they seem to have been two distinct species of raptors. The full significance of the vulture feathers is unclear, but it may be noted that the old Iranians used raptor feathers in their Athravanic rituals. The witch Black Kengge again has the feel of a motif — it is vaguely reminiscent of the Lankā demoness struck down by Hanūmat in the Rāmāyaṇa. The winged-horse is an old motif of IE provenance — it has an ancient presence in IE traditions like those of the Indo-Iranians and Greeks and spread to neighboring cultures IE or otherwise, like the Hittites, Assyrians and Chinese. Archaeological finds have attested depictions of the winged horse in the Mongolian lands right from the Hunnic and Para-Mongolic Serbi period and are related to depictions among the Śaka-s before them. While the fraternal conflicts in the alternative Mongol histories are consistent with those presented in the SHM, they are clearly reflexes of ancient motifs, some of which are widespread in the Eurasiatic world. In the SHM, the conflict between Qasar and Chingiz Khan has a certain ambivalence or even subtly tilts the blame toward Chingiz. However, in the alternative histories, a clear attempt is made to present it largely as Qasar’s fault. At first sight, this might be seen as an attempt to establish the undisputed primacy of the Khan over his brothers. This might have been particularly important in the late/post- imperial period when the Chingizids were in a complex relationship with the Qasarids — several Qasarid princes (and some descendants of Belgütei) episodically made claims for the overlordship of the Mongols against those of the Chingizids, with different degrees of success. In this milieu, when the alternative histories were being edited/recast, it would have been expedient for the Chingizid authors to remove any ambivalence in the old sibling conflict. However, we suspect that the claims of the alternative histories might not be entirely fabricated. The following are notable in this regard: (i) The extant Qasarid (Qorcins) shamans claiming descent from the Qongqotan shaman might suggest that they had some kind of alliance before it soured as they tried increasingly use their dominance against their lords (they were after all sons of the nökör of Yisugei). (ii) there seems to have been a genuine incident of Qasar absorbing a subset of the Tatars slated for execution at the behest of his wife. (iii) His raid on the Qongirat tribe that had joined the alliance with Chingiz. (iv) The case of Qasar taking hold of Qulan’s hand at a wild liquor party — while this incident could have been fabricated, it may have also been suppressed in some versions so as to not make the Khan look bad. Thus, despite being permeated with ancient motifs and potentially influenced by the later competition among the Borjigid clans, we believe that the alternative histories preserve certain fragments of Mongol history that were unrecorded in the SHM.

Gabhavāda in the dark age ushered by Piṇḍaka’s regime

As we have remarked before, the placing of Vṛddha-piṇḍaka on the rājāsandī was accompanied by the triumph of the navyonmatta-s. Watching the action of the navyonmatta-s gives one a ringside view of how it might have been at the time of the rise of marūnmāda and pretonmāda. Self-evident truths are replaced by falsehoods, the “cult” is enforced in every walk of life like the monotheism that engendered it, and janalaya is sold to the suffering commoner as a good thing. To reiterate what we have argued before, the rise of navyonmāda is primarily via the infection of the nodes of what is commonly referred to as the Mahāmleccha“Deep State”. It is not exactly a Deep State in the common sense of the word — i.e., an unelected or hereditary elite or bureaucracy (e.g., the in the Hindu world) that ensures that the state is smoothly running and functional even as the leadership keeps changing. That is why it used to be alright in India to live by the colloquialism “does it matter whether Rāma (Aikṣvākava) or Rāvaṇa is holding sway?” However, in the Mahāmleccha context, what people refer to as the Deep State is a deeply embedded network that is perhaps one of the most powerful systems in the world. It has two types of nodes — the visible ones and the less-visible or mostly invisible ones. The visible ones are the front-facing politicians that people elect, like Piṇḍaka, Svaśmanvati, Paḍbīśapuruṣa, Ardhakṛṣṇa, Ṣiḍga, Guccaka and the like. They have a facade of power but are not the real wielders of power in the network. That belongs to the invisible nodes. Those nodes are remarkably widely distributed across human spheres of endeavors in not just Krauñcadvīpa but also several other nations in the Eurosphere and elsewhere. While most lay students of the Mahāmleccha“Deep State” recognize its nodes in the government — judiciary, departments, and embassies — not many are aware that they are also deeply embedded in news media, big tech (including production and control of AI), basic science, military policy, American indology, frontiers of medicine, and films.

While the nodes of this network form a densely connected graph, they are also further connected to more peripheral nodes or terminal leaves that have low connectivity with each other. When these peripheral nodes or leaves are taken into account, the nodes of the Deep State network range from relatively low connectivity (10s of edges) to huge (several thousand or even a million). While most of the laity (peripheral nodes) do not know that they are interacting with a member of the Deep State network, we learnt to recognize them early on. We also had the opportunity to interact with several smaller nodes of this network. Over time we became quite good at picking up the subtle cues of their physiognomy, presentation and social displays and can spot them even in various commonplace circumstances, like on the street. We noticed that they are always on the lookout for opportunities to maximize influence, power and useful information. Many of them might put on an amicable mask while scouting for the benefit they can derive from you. They will remain so as long as they do not learn that you are a threat to their status or position in the network, i.e., via being shown as inferior. Studying them more closely, we were able to notice that they were not isolated ambitious individuals but nodes of a network with their fingers on the levers of power. Initially, we, too, like many naive folks believed that things operated as a meritocracy; however, within four to six months of our interactions and observations, we learnt that nothing of significance can get done without conceding a cess to them. While they show a degree of variation in their outward demeanor, on scratching the surface, we saw that there is a certain striking uniformity in their beliefs. It was quite remarkable to also learn how unified they were in terms of broad objectives and how these objectives propagated up and down the networks.

As we started examining this network, we kept getting the vibe that their worldview had a svābhāvika-vairam with the H worldview. We also often found their objectives to be baffling to the outsider — the unanimity on things that seem deleterious and counterintuitive to the commoner was a striking element of conversations with them. They would even sell their schemes as the right thing to do. It became apparent that they could do that because their relative wealth or social network largely buffered them from everything that buffets those outside of the network from the enaction of their schemes. This led us to a closer study of their beliefs, and it struck us then they had a peculiar proclivity towards what could be called “left-liberal” ideas while being embedded in a state which, at that point, was still not considered accommodating of constructs like socialism or communism. It struck us then that if they came to the fore from their hidden position, the state would move closer to a communist police state. The other thing that caught our eye was that being a dense sub-graph with strong conformity of opinion, newer versions of pathological memes could easily sweep through it replacing their predecessors. Indeed, it had begun as ekarākṣasonmāda and transitioned to rudhironmāda by the time it started invading the Mahāmleccha academia during the boom in the late World War-2 and post-WW2 years. While it was checked by Hoover, McCarthy and the like, it wound its way through academia to recapture and permeate all domains of human endeavor over the coming 80 years. During this period, it evolved the concept of parasparapātavāda (intersectionalism) that facilitated the entry of new memes into the networks. While these initially resonated with the older complex of memes as parasparapāta was encouraged, one of them could displace the rest as the dominant ones in the Deep-State network.

Thus, at the height of parasparapāta, a whole jāla of roga-s swept through the network that was to emerge as the Deep State: merry old trachea-sectioning marūnmāda, gabhavāda, samopasthavāda, ṣanḍavāda, viliṅgavāda and samavāda, all danced together making excuses for the failure of the śramavādic strain of old rudhironmāda among the Soviet Rūs and also its implementation “with Chinese characteristics (a resonance with the more pervasive phenomenon of Galtonism in the Occident).” While some movements within the network might begin as a strategy to overthrow rival forces, the density of the connections means that much of the network might soon become true believers. Thus, we suspect gabhavāda was originally encouraged by the network to attack the conservative path, which was associated with the natural dominance of vīryavāda. Soon much of the Deep State network became a true believer in gabhavāda. The rise of gabhavāda allowed the eventual ascension of the complex of samopasthavāda, ṣanḍavāda and viliṅgavāda. However, on the practical side of things, there is not much raw material, as yet, in terms of the ṣaṇḍādi for doing all the work on the ground. Moreover, even though much of the network had converted to be true believers, they hardly wanted to forsake their own fitness (you can deny biology, but it wells up from deep within). Hence, most true believers in the network instead settled for some form of gabhavāda. This allowed its epidemic to spread in whichever domain of endeavor the Deep State network could enforce its writ on.

Looking back at recent history, we can say that its ascendancy outside the academe began during the regime of Ardhakṛṣṇa. However, being a sarvopasthayuj, he did not personally lean all in on gabhavāda though he let the true believers in the network further its spread. Indeed, a friend of ours who had attended a conference in the final days of the Ardhakṛṣṇa mentioned how he was seeing gabhavāda taking over the institution that was organizing the conference. We remarked to him that the negative changes he was seeing, as a result, were probably just the beginning. Gabhavāda was at the forefront of the network’s attempt to push Ṣiḍgajariṇī to power. However, once Picchilaka took the mahāsandi, the network, livid at its defeat, started using gabhavāda as one of the attack vectors against him. At that point, we noticed how the network recruited all manner of unthinking “innocents” to go into a gabhavādic frenzy against Aruṇaluṅga by claiming that he was against them. Once the network successfully overthrew Luṅga and put Piṇḍaka on the āsandī, gabhavāda exploded into a storm that also gave a lift to the wings of samopasthavāda, ṣanḍavāda and viliṅgavāda. Within a matter of a couple of years, practically every institution under the direct control of the hubs of the network was flooded with gabhavāda. Those sympathetic to gabhavāda would pick all the counterexamples and roar — how could you be so biased for vīryavāda? When one looks closer, one finds that many of the counterexamples are actually under a higher gabhavādic leadership rather than being exemplars of the still persistent vīryavāda. Such individuals who report to the gabhavādian leader are typically incompetents who have been chosen so that they don’t threaten the former. Any real vīryavādin would have simply overthrown the gabhavādian leader, as that is the natural flow of history. Thus, gabhavāda has resulted in flooding hierarchies with incompetence where originally the highest levels of competence were in favor.

Gabhavāda encourages tendencies that are ultimately not quite compatible with the long-term survival of complex societies. This has been known for a while, but few moderns can accept it, for it is so antithetical to the essentially left-liberal worldview that is conceded even by most “conservatives” in the Occident and India. The marūnmatta-s, Japanese and Chīna-s, to an extent, are resistant in differing degrees to this. Its negative effects first manifest as attacks on the competence-reward correlation. There is no perfectly fair society anywhere. Even most multiethnic social conglomerates operate on homo-ethnic networks (concealed or otherwise). However, in such structures under the natural vīryavāda, there is a degree of acknowledgment of raw competence and a reward for that. That is how the Mahāmleccha built their power. However, under gabhavāda, the correlation between competence and rewards is severely degraded. Under the normal law of vīryavāda, disputes in this domain are, to a degree, settled openly and objectively. However, under gabhavāda, it proceeds via backbiting, reputation damage and suppression of opinion – a general preference for an amorality that centers “feelings’’. Thus, gabhavāda eventually saps the vitality of a system and causes it to collapse. If these affect systems critical to national innovation, the civilization collapses. We do not know if the damage from gabhavāda due to the policies of the Piṇḍaka regime can be reversed in the future. All we can say is that many endeavors are already damaged. Given the susceptibility of the H elite to various strands of navyonmāda, including gabhavāda, the same danger also confronts them, and they have fewer resources than the Mahāmleccha. Moreover, in the deś, it is pushed not just by the enemies (e.g., duṣṭa jāka, the vi-kāra) but also H elite who have internalized it.

A short note on an ancient Vedic poetic formula and an obscure word

A couple of ṛk-s, respectively from maṇḍala-s 6 and 7 of the Ṛgveda, are rather striking for their parallel structure:

You are the bull of Heaven, the bull of Earth,
the bull of the rivers, the bull of the “immobile/dense”;
For you, the manly, O Bull, the Indu has waxed,
the sweet juice, the honey-drink, for your choice.

Sought in Heaven, established on Earth,
the leader of rivers, the bull of the “immobile/dense”;
He shines forth to the peoples of Manu,
Vaiśvānara waxing by his own choice.

The first ṛk is by Śaṃyu Bārhaspatya and is addressed to Indra, while the second is by Vasiṣṭha Maitrāvaruṇi and addressed to Agni Vaiśvānara. Nevertheless, as can be seen above, they are structurally equivalent in the following ways: (1) In each case, the god is invoked in four stations, namely heaven, earth, the rivers, and something termed the stiyā-s, which will be the focus of the discussion in the concluding part of this note. (2) In both cases, the respective gods are referred to as bulls (vṛṣabha) — a common Vedic metaphor emphasizing their preeminence and manliness. (3) In the second hemistich, the word vara (choice, wish) is used. While it is declined differently in the two ṛk-s, in both cases, there is a sense of the autonomous nature of the god in making the choice. (4) In the second hemistich of both ṛk-s, there are distinct but semantically overlapping words meaning “waxing/growing/swelling”. In the ṛk to Indra, it is pīpāya that is often used in the context of the “waxing” of soma both in the sense of the moon (Indu) and the turgidification of the soma stalks before the extraction of the juice. In the one addressed to Agni, it is the perfect participle formation vāvṛdhānaḥ. (5) While in the ṛk to Indra, the term vṛṣabha is repeatedly used, it can be seen as semantically overlapping with netṛ used in the cognate position of the Agni ṛk. It is not uncommon to see parallels between the compositions of the different ṛṣi-s; hence, why do we make a big deal of this?

First, it is not a case of identical repetition of certain characteristic phrases (e.g., agnim īḻe; bhadraṃ no api vātaya manaḥ; mṛl(ā/yāsi) naḥ) or a repeated refrain. Rather, the entire structure mentioned above is recapitulated, albeit in the context of different deities and with differing intents. Second, there is no special connection between the Bharadvāja-s of maṇḍala 6 and the Vasiṣṭha-s of maṇḍala 7 beyond the fact that they were ṛṣi-s of a common Āryan tradition. This is most starkly illustrated by looking at their associations with specific rulers. The table below shows the number of times the rulers Atithigva, Divodāsa and Sudās are mentioned in the respective maṇḍala-s. Most students of the RV agree that Atithigva is either the father or a dynastic title of Divodāsa.

The link between the Bharadvāja-s and the Atithigva-Divodāsa line is in sharp contrast to that between Vasiṣṭha and Sudās. It is also notable that while there is at least one mention each of Atithigva and Divodāsa by the Vasiṣṭha-s, there is no mention of Sudās by the Bharadvāja-s. Irrespective of both their adherence to contrafactual ideas like autochthonous Āryan-s of India, and the mapping of Atithigva and Divodāsa to the homonymous kings mentioned in the dynastic lists of the Purāṇa-s, most students of the RV agree that they were temporally anterior to Sudās. Thus, it would be safe to conclude that not only did the early Bharadvāja-s and Vasiṣṭha-s not have any special connection, but also belonged to distinct temporal periods of the Early Vedic age. Hence, we believe that the parallels between the ṛk-s presented above represent an old Āryan poetic formula with a special significance that allowed the portrayal of a god in a specific fashion, simultaneously embodying multiple key elements: (1) The universal lordship of the deity in association with both the heavenly realm and earth and the swiftly motile (rivers) and the “immovable/dense”. This might have been used in a metaphorical sense similar to sthāvara-jaṅgama (immobile and mobile) used in the later registers of the language; (2) The sense of expansion; (3) the sense of self-choice, evidently with respect to the sacrificers (also apparently indicating the granting of boons — vara-s to them).

In the above, we translated the word stiyā noncommittally as immobile/dense, but can we infer what it really meant? Traditionally it has been taken to mean stagnant water bodies in contrast to rivers. To our knowledge, stiyā is only attested in the early Vedic dialect and is not seen in the classical language. Hence, one cannot infer its actual meaning directly from continuity with the classical dialect. However, the “stagnancy” inherent in it can be literally etymologically inferred as the word is seen as derived from a root that was likely a paralog, already present in early Indo-European, of a more widely attested root (Skt: sthā < PIE *steh; we have no particular opinion on the reconstructed laryngeal in this form as we have not studied that closely), which is equivalent to English “stand”. This paralogous root is reconstructed as steyh from which we likely have the Skt roots styai and styā. The form styāna, which is derived as a kta passive past participle of the root styai in traditional vyākaraṇa, is attested in the classical dialect and means viscous, coagulated or immobile. This is consistent with the inference of stagnancy behind stiyā in the RV. A closer look at the descendants of steyh in other IE languages presents an interesting picture. We have the following cognates:
(1) Greek: stía= stone, pebble; stîon= stone, pebble; stiáōn= altar made of stones.
(2) Germanic: Proto-form: *stainaz > English: stone; stayn (Middle Eng.); German: Stein; Old Norse: Steinn.
(3) Slavic: Proto-form: stena > Russian: stená= rock, stone wall/cliff; Serbo-Croatian: stijéna= rock;

Thus, from these distinct branches of IE, one would infer an ancestral meaning of the paralogous root steyh as meaning stone; however, the size of the stone could range from a pebble to a rock. It is notable that this meaning survives in Slavic — something relevant to Vedic since Balto-Slavic is a likely sister group of Indo-Iranian. Under this consideration, given the uncertain meaning of Vedic stiyā, we would parsimoniously infer that it actually meant “rock/stone” as opposed to a stagnant water body. We now return to the RV to see if there is any support for this claim. We find that the term “rivers” as in the above ṛk-s is also found in a parallel context in the below ṛk of Viśvāmitra:

mitro agnir bhavati yat samiddho
mitro hotā varuṇo jātavedāḥ ।
mitro adhvaryur iṣiro damūnā
mitraḥ sindhūnām uta parvatānām ॥ RV 3.5.4
The ritual fire becomes Mitra when it is kindled;
As the Hotṛ, he is Mitra, as Jātavedas [he is] Varuṇa.
Mitra is the Adhvaryu, the strongman of the household,
[as also] is Mitra of the rivers and mountains.

Here, sacrificial fire is said to become Mitra when kindled, and as the manifestation of Agni that pertains to the ritual of the sacrificer (Jātavedas), he is seen as Varuṇa. Thereafter this ritual fire in the form of Mitra is said to become the Adhvaryu and Hotṛ of the ritual, as also the lord of the household, the rivers and the mountains. This devotion to Mitra likely relates to the special place of the god for Viśvāmitra — indeed, his own name is likely an early theophoric name signaling the universal nature of the god Mitra. In this context, it is not surprising the metaphors indicative of the lordship of the various stations are deployed in this ṛk, similarly to those in the opening two ṛk-s under discussion in this note. Thus, the expression sindhūnām uta parvatānām can be seen as an equivalent of sindhūnām … stiyānām in those ṛk-s. Further, a comparable juxtaposition of rivers and mountains can be seen in a ṛk of the Father of our people, Manu, to Viṣṇu. Here the word sindhu for river is replaced by nadī:

śarma parvatānāṃ vṛṇīmahe nadīnām । ā viṣṇoḥ sacābhuvaḥ ॥ RV 8.31.10
We choose the shelter of the mountains and of the rivers, of Viṣṇu, who stands [with us] as a helper.

A comparable coupling of the rivers and mountains is also seen in the Vaiśvadeva incantations of the Atri-s and Vasiṣṭha-s:
uta tye naḥ parvatāsaḥ suśastayaḥ sudītayo nadyas trāmaṇe bhuvan ।RV 5.46.6a
śaṃ naḥ parvatā dhruvayo bhavantu śaṃ naḥ sindhavaḥ śam u santv āpaḥ ॥ RV 7.35.8c
In the second of these, the immobility of the mountains is explicitly mentioned, evidently in contrast to the flow of the rivers.

Based on the multiple juxtapositions of rivers and mountains in the early layer of the Vedic tradition, along with the IE tradition indicating that the ancestral meaning of the noun derived from the root steyh is likely to have been stone, we cautiously propose that stíyā (udātta indicated) meant stone and by metonymy mountain. Indeed, in the RV itself, we see a similar metonymic duality between stone and mountain in the word adri. This is made explicit in RV 10.94.1, where the soma-pounding stones (adri-s) are explicitly also called mountains (parvata-s). Thus, rather than being stagnant water, we believe that the Vedic stíyā preserved in old IE meaning. Curiously, a juxtaposition of the waters and the stone is seen in a name of Germanic provenance, Epstein, that is widely borne by paleo-Abrahamists in our day (e.g., separately, a virologist and a criminal who was mysteriously eliminated). Apparently, it was originally a place name in Northwestern Germany — the Stein part is obvious and meant mountain by metonymy — we believe Ep is from an IE word that might have been Apa (= Skt apas). The root of the latter might have originally been from Celtic given the name Abiona (also Old Irish aub for river) found in continental Celtic inscriptions, which appears to have signified a water/river goddess. Alternatively, it was from a Western Baltic tongue, given the Old Prussian word “ape”=river. Thus, the German place name likely meant “river-mountain”.

Ones, twos, threes … hundreds and thousands in the Ṛgveda

In the previous note, we looked at some special numbers relating to the count of the gods in the Veda and the influence of the Proto-Indo-European tripartition on them. Here we more generally look at the distribution of numbers in the Veda with a focus on the Ṛgveda (RV). Among other things, we hope to discern key aspects of early numerical thought among the Hindus. One such is how and when the proclivity for big numbers started. Are there any traces of it in the earliest textual traditions of the Hindus? As we noted before, the RV is replete with numbers. Hence, the first question we can ask is how they are distributed. Figure 1 shows a simple plot of the frequencies of the commonly mentioned numbers in the RV.

Figure 1. Common numbers in the RV.

We observe that as we proceed from 1 upwards, the frequency of the integers tends to decline, but there are multiple exceptions to this trend. We can ask if there is indeed a real declining pattern barring the exceptions. The available is not large to make an accurate statistical estimate of the deviation of particular numbers from the trend, but we can still construct an objective picture of that trend. Now, there is a law known as the Newcomb-Benford law that defines the probability distribution of the first significant digit of a dataset. It was discovered by the American astronomer Newcomb when he was looking at the first digits in a log table. Benford subsequently showed its validity for several other datasets. The law may be described thus: Given a long list of numbers generated via physical measurements (e.g., astronomical observations) or financial data or even something like log tables, reciprocal tables etc., the fraction of the numbers beginning with is given as,

Therefore, a deviation from the Newcombian distribution will imply that some deliberate process privileging or discriminating certain numbers is involved. However, in the current case, we are not looking at the first significant digit of the numbers in question but the actual frequency of integers in the RV. Hence, we cannot apply the Newcombian distribution as is. However, inspired by it, we can see if there is any background trend in the numbers against which exceptions stand out. Thus, we can fit a background trend for the frequency of an integer of the form:

Figure 2.

As one can see in Figure 2, this gives an excellent fit for 1, 2, 4, 5, 8, 11, 12 . This implies that 3, 7, 9 and 10 are overrepresented, with 6 probably a bit underrepresented. By this yardstick, it is also rather obvious that the powers of 10, viz., 100 and 1000, are overrepresented, but 10000 is not particularly common (Figure 1). Of these, the overrepresentation of 3 confirms the Dumézilian view that tripartition was integral to IE ideology. A closer look at the 3s reveals numerous specific associations:
1. As we noted before, it is intimately linked to the tricyclic chariot (with three wheels and niches) of the twin Aśvin-s. th of all the sūkta-s featuring the number 3 also feature the Aśvin-s.
2. The three strides of Viṣṇu.3. In an early expression of the polycephalous iconography typical of the Hindu world, Agni is described as having 3 heads (trimūrdhānaṃ saptaraśmiṃ gṛṇīṣe .anūnam agnim pitror upasthe । RV1.146.1a). In the counter-pantheon, Viśvarūpa Triśiras Tvāṣṭṛa, a figure of PIE vintage, who was slain by Indra, is similarly three-headed.
4. The triple realms of the universe.
5. Trikadruka-s: A mysterious appellation for a group of deities accompanying Indra (when he together with Viṣṇu), and Yama. Given that the primary companions of Indra are the Marut-s, some have proposed that it was a term for them. The meaning of this term and its triadic nature still remain an unresolved issue for me (see below).
6. tridhātu: Literally tripartite. This word, occurring 26 times in the RV, encapsulates the ideology of tripartition. It might be applied to the universe (ya u tridhātu pṛthivīm uta dyām eko dādhāra bhuvanāni viśvā ॥ RV 1.154.4); the shelter/protection offered by the gods (tridhātu śaraṇaṃ; tridhātunā śarmaṇā pātam); the tripartite horn of Agni (tridhātuśṛṅgaḥ).
7. Personal names: Triśoka, Tryaruṇa.

The next overrepresented integer is 7, which again shows several specific associations in the RV:
1. 7 hotṛ-s/ṛṣi-s: The seven ancient sages or ritualists is a tradition shared with the Mesopotamian tradition (Apkallu) and the pre-Aryan Harappan tradition of India. It seems to have served as a placeholder that was later adopted in Greece, Iran and China. Thus, it could have been an ancient traveling motif. Prior to the ādhvaryava reformulation of the śrauta rite, the term 7 hotṛ-s appears to have been originally used for the 7 ritualists the Hotṛ, Potṛ, Neṣṭṛ, Agnīdhra, Adhvaryu, Praśāstṛ and Brahman, who in turn might have been modeled after the 7 ancestral sages. In at least some cases, even in the RV, this term seems to have signified the constellation of Ursa Major, which in later tradition was unanimously associated with the seven ṛṣi-s (diva itthā jījanat sapta kārūn ahnā cic cakrur vayunā gṛṇantaḥ ॥ RV 4.16.3 Indra generating the seven sages of the Heaven); similarly in RV 10.82.2; RV 10.130.7.
2. 7 rays/heads/tongues of the Sun, the god Agni and some times Indra or Bṛhaspati: pāti nābhā saptaśīrṣāṇam agniḥ RV.3.5.5 (Agni); divaś cid agne mahinā pṛthivyā vacyantāṃ te vahnayaḥ saptajihvāḥ ॥ RV 3.6.2 (Agni); yaḥ saptaraśmir vṛṣabhas tuviṣmān RV 2.12.2 (Indra); saptāsyas tuvijāto raveṇa vi saptaraśmir adhamat tamāṃsi ॥ RV4.50.4 (Bṛhaspati); sūryasya sapta raśmibhiḥ ॥ RV 8.72.16 (Sun). In the case of the Sun, this motif might also be expressed as the seven horses of the solar chariot. How exactly the arrangement of the 7 heads, horns, or tongues was imagined remains unclear. However, from the later ritual tradition, it would seem that it was imagined as the items placed on the vertices of a hexagon and its center.
3. The 7 goddesses (mothers or sisters): This theme persisted in later Hindu tradition as the famous sapta-mātṛ-s. At least in some contexts, this might have corresponded to the old count of the Pleiades as 7, which later became 6. Just as the 6 Kṛttikā-s associate with Skanda, these 7 goddesses sometimes associate with the newly born Agni (e.g., RV 1.141.2, RV 3.1.4). These 7 goddesses are also described as heavenly (svādhyo diva ā sapta yahvī rāyo duro vy ṛtajñā ajānan । RV 1.72.08), suggesting that they are indeed an earlier reference to the Pleiades.
4. sapta sindhavaḥ or sapta yahvīḥ: The 7 rivers or streams. These might sometimes overlap with the above and might be associated with the goddess Sarasvatī. At different points, they might have been identified with earthly streams in the lands occupied by the Aryans.
5. sapta-ratnāḥ: the 7 gems.
6. sapta-dhāmāni: the 7 realms. Viṣṇu is said to traverse these in the course of his famous strides. This concept appears to have developed into the karshvare-s (7 world regions) on the Iranian side.
7. The 7 Marut-s RV 8.28. This is the count given for the Marut-s in the said sūkta and sometimes in later tradition (or as ).

Beyond the above, it is not surprising that the two key numbers 3 and 7 come together as a product triḥ saptaḥ, i.e., 21. This number is also seen in the opening sūkta of the Atharvaveda and represents the 21 basic akṣara-s of the Saṃskṛta “alphabet.” It might signify many other things, including in some reckonings the count of the Marut-s. This count might have a relation to the mysterious Trikadruka-s, who might have been the Marut-s

The overrepresentation of 9 is notable as it is also a special number for the Mongols and possibly the early Turks. It usually occurs in the phrase, a 9 and a 90. One could take this as the integer 99, but we count it among the 9s because of the specific form of the usage. The number 99 typically stands for the fortifications of the antagonists like Śambara or the number of the arms of the demon Uraṇa whom Indra struck down. As the old Indo-Aryan number system is primarily decimal, it is not entirely surprising that 10 and its powers 100 and 1000 are particularly common. It is in this decimal exponentiation that we encounter the first inklings of the Hindu love of large numbers. We have the following ṛk of Gṛtsamada Śaunahotra:
tvām agne dama ā viśpatiṃ viśas
tvāṃ rājānaṃ suvidatram ṛñjate ।
tvaṃ viśvāni svanīka patyase
tvaṃ sahasrāṇi śatā daśa prati ॥ RV 2.1.8
To you, Agni, as the lord of the folks at home, the folks,
to you, the king, who is benevolent, are attracted.
You, of good radiance, lord over all;
you compare to thousands, hundreds and ten.

The term sahasrāṇi śatā daśa, mentioning the 3 successive powers of 10, can be interpreted as the number . i.e., a million, due to the singular 10 and plural 100s and 1000s. This seems to be the largest explicitly mentioned number in the RV and foreshadows the chant of the powers of 10 seen in the Yajurveda texts:
ekā ca daśa ca śataṃ ca sahasraṃ cāyutaṃ ca prayutaṃ ca niyutaṃ cārbudaṃ ca nyarbudaṃ ca samudraś ca madhyaṃ cāntaś ca parārdhaś ca tā me agna iṣṭakā dhenavaḥ santu ॥ Kaṭha saṃhitā 17.10 (in minimal form without the duplications)
Here, the powers of 10 are listed from one (eka) to a trillion (parārdha). In some texts, like the Vājasaneya saṃhitā or Taittirīya saṃhitā, the positions of prayuta and niyuta are exchanged in this chant. Of these powers, the largest that is mentioned in the RV is ayuta. A similar sequence is incorporated into the Rāmāyana to give an impression of the magnitude of the Vānarasenā. However, in later tradition, we find that some further powers were introduced, and parārdha came to mean an even larger number. The word parārdha may be understood as para+ardha — the remote side of the half (the world hemisphere); hence, we take the term as implicitly indicating the radius of the universe. Indeed, already in the RV, we encounter the use of smaller powers of 10 to indicate something of great magnitude — namely the universe-encompassing nature of Indra in a ṛk of Puruhanman Āṅgirasa:

yad dyāva indra te śataṃ
śatam bhūmīr uta syuḥ ।
na tvā vajrin sahasraṃ sūryā anu
na jātam aṣṭa rodasī ॥ RV 8.70.5
If a 100 Heavens, O Indra,
as also a 100 Earths could be yours,
O Vajrin, a 1000 suns did not,
even as you were born, nor did the world hemispheres, equal you.

Here, the magnitude of Indra is indicated by comparing him to the extent of a 100 heavens and earths and he is said to exceed a 1000 suns. The luster of gods measured in terms of huge numbers of suns is widely seen in later Hindu tradition. To our knowledge, the above ṛk is the first expression of that. We also believe that there is an interesting wordplay (śleṣa) in it: the word aṣṭa is the passive past participle form (kta) of the root aś-. However, it is also homophonic with the word for 8 (aṣṭa); hence, we believe that it was used on purpose to subliminally remind the hearer of what were to become holy numbers in later Hindu tradition — 108 and 1008. Thus, we believe that in verses like the above, we see the beginnings of the Hindu apprehension of vast magnitudes that were to become important both in their religion and cosmography. In terms of such expressions, a good linker between the older Vedic layer and the newer Hindu tradition can further be seen in the opening of the famous Puruṣasūkta (RV 10.90), where the all-engendering cosmic being is conceived with a thousand heads, eyes and feet.

To get a better feel for the 100s and 1000s in the RV, we next look at their frequency by maṇḍala both as raw counts and as normalized counts per 10000 syllables (Figure 3).

Figure 3.

For the 100s, we see that, while all maṇḍala-s have a similar normalized frequency, maṇḍala 8 has a significantly higher frequency (conservatively, p= 0.01), 2.5 times the mean frequency of that seen in the remaining maṇḍala-s. This overrepresentation comes primarily from an epithet of Indra, Śatakratu — he of a hundred acts. The raw and the normalized frequency of Śatakratu is shown in Figure 4.

Figure 4.

Śatakratu is significantly overrepresented in maṇḍala 8 (7.2 times the mean in other maṇḍala-s in normalized counts; conservatively, ) and underrepresented in maṇḍala 9 (conservatively, ). This suggests that the conception of Indra as Śatakratu seems to have arisen in the community to which the Kāṇva-s belonged. This community shows several linguistic and historical features distinguishing them from the authors of most family maṇḍala-s and potentially associating them with a distinct proto-Iranian group. Once the term Śatakratu emerged, it appears to have acquired considerable popularity and remained so in the Itihāsa-purāṇa as we have it even after the mainstream Vedic religion declined. In contrast, the 1000s are significantly overrepresented in maṇḍala 9 (conservatively, )), which is exclusively devoted to the Soma ritual. Here we frequently encounter terms such as: sahasradhāra (a 1000 streams), sahasravalśa (a 1000 shoots), sahasravarcas (a 1000 splendors), sahasrapājas (1000-fold strength), sahasroti (a 1000 aids), sahasrajit (the 1000-conqueror), sahasracakṣas (1000-eyed), sahasraṇītha (praised with a 1000 chants), and sahasraretas (he with semen of 1000-fold magnitude). This indicates a hyperbolic usage that was specifically associated with the Soma ritual and libations. Hence, we posit that the exhilaration of the Soma drink produced a psychosomatic experience that gave birth to this perception of extraordinary magnitude. Thus, the germs of the Hindu love for large numbers might have stemmed from the unique experience of the Soma ritual intersecting with the old decimal system.

The gods in triples

It is clear that every civilization has its own unique manifest characteristics coming from the depths of its people. One such distinguishing characteristic of the Hindu civilization is the love for huge numbers. This even manifests in the number of gods in the pantheon. The Ṛgveda (RV) is replete with numbers. However, they are mostly modest relative to the magnitudes encountered in somewhat younger Vedic texts. Among those that go into the thousands, we encounter a peculiar number that is repeated in multiple places across the Vedic tradition — the number of gods, which is specified as 3339. This number is found twice in the RV itself (3.9.9a, 10.52.6a), with both verses presenting the identical hemistich:

trīṇi śatā trī sahasrāṇy agniṃ triṃśac ca devā nava cāsaparyan ।
Three hundred, three thousand, and thirty-nine gods attentively served Agni.

This number again occurs as the number of the gods in the Vaiśvadeva-nivid and the Taittirīya Brāhmana (in 2.7.12.2). We encounter explanations for this number in the Śatapatha Brāhmaṇa 11.6.3.1-11 (also repeated in a variant form in its Bṛhadāraṇyakopaniṣat 3.9.1-9) and the Jaiminīya Brāhmaṇa 2.76-77 in the context of a brahmodya contest in the court of emperor Janaka Vaideha that resulted in the death of Vidagdha Śākalya. Below we provide the version from the JB:

janako ha vaideho bahudakṣiṇena yajñeneje । te tad u ha kuru-pañcālānāṃ brāhmaṇā abhisamājagmuḥ । sa ha sahasraṃ gavām avarundhāna uvāca brāhmaṇā etā vo, yo brahmiṣṭhas sa udajatām iti । sa hovāca vājasaneyo ‘rvācīr etās somyeti । taṃ hocus tvaṃ nu no brahmiṣṭho ‘sī3 iti । sa hovāca namo vo brahmiṣṭhāya+astu । gokāmā eva vayaṃ sma iti । te hocuḥ ko na imaṃ prakṣyatīti । sa hovāca vidagdhaś śākalyo ‘ham iti । taṃ ha puraskṛteyeyuḥ । taṃ ha pratikhyāyāyantam uvāca tvāṃ svic chākalya brāhmaṇā ulmukāvakṣayaṇam akratā3 iti । sa hovāca yadi tenolmukāvakṣayaṇaṃ smaḥ prakṣyāmo nvai tvām iti । taṃ ha papraccha kati devā yājñavalkyeti । sa hovāca trayaś ca triṃśac ca, trayaś ca trī ca śatā, trayaś ca trī ca sahasrā, yāvanto nividābhyāhūtā iti । om iti hovāca ॥2.76॥
Janaka the Vaideha had performed a sacrifice with abundant gifts. The brāhmaṇa-s of the Kuru and the Pañcāla went there together. He (Janaka), having corralled a thousand cows, said: “O you brāhmaṇa-s he, who of you all is the foremost in brahminical proficiency, may drive [these cattle] along”. He Vājasaneya said: “Towards [me] these Soma [ritual] gifts.” [The brāhmana-s] said to him: “Now, are you brahminically most proficient among us?” He [Yājñavalkya Vājasaneya] responded: “So be it; salutations to the brahminically most proficient, but we desire the cattle.” They (the V1s) said: “Who will question him (Yājñavalkya) for us?” Then, he, Vidagdha Śākalya, said: “I [will].” Then, he may go forward. Seeing him coming forth, (Yājñavalkya) said: “Hey Śākalya, the brāhmana-s have made you [one] to quench the fire-brand.” He (Śākalya) said: “If indeed we are the one to quench the firebrand [so be it], we will now question you.” [Śākalya] questioned him: “O Yājñavalkya, how many gods are there?” He (Yājñavalkya) said: “3 and 30, 3 and 300, 3 and 3000, as many as are sacrificed to in the [Vaiśvadeva]-nivid.” He (Śākalya) said: “yes.”

katy eva devā iti । traya iti । om iti hovāca । katya eva devā iti । dvāv iti । om iti hovāca । katy eva devā iti । eka iti । om iti hovāca । katame trayaś ca triṃśac ca, trayaś ca trī ca śatā, trayaś ca trī ca sahasreti । mahimāna evaiṣāṃ ta iti hovāca । trayastriṃśad vāvet । katame trayastriṃśad iti । aṣṭau vasava ekādaśa rudrā dvādaśādityā indraś caiva prajāpatiś ca trayastriṃśāv iti ।
“But how many gods are there?” Three. He (Śākalya) said: “Yes, but how many gods are there?” Two. He (Śākalya) said: “Yes, but how many gods are there?” One. He (Śākalya) said: “Yes. Who are the 33+303+3003?” He (Yājñavalkya) said: “These are their powers, but they are 33 [in number].” “Who are the 33?” “8 Vasu-s, 11 Rudra-s, 12 Āditya-s, Indra and Prajāpati amounting to 33.”

katame vasava iti । agniś ca pṛthivī ca vāyuś cāntarikṣaṃ cādityaś ca dyauś ca candramāś ca nakṣatrāṇi caite vasavaḥ । eteṣu hīdaṃ sarvaṃ vasu hitam iti । tasmād vasava iti ।
“Who are the Vasu-s?” “The Fire, Earth, Air, Mid-space, Sun, Heavens, Moon and the Stars — these are the Vasu-s. In these, verily all this (the universe) is situated (in residence — vas-). Hence, they are known as the Vasu-s.”

katame rudrā iti daśa puruṣe prāṇā iti hovāca । ātmaikādaśaḥ । te yadotkrāmanto yanty atha rodayanti । tasmād rudrā iti ।
“Who are the Rudra-s?” He (Yājñavalkya) said: “The 10 life processes in a man; the 11th is the conscious self. When they go out and leave, they cause crying (death). Hence, they are known as the Rudra-s.”

katama ādityā iti । dvādaśa māsās saṃvatsara iti hovāca । eta ādityāḥ । ete hīdaṃ sarvam ādadānā yanti । tasmād ādityā iti । katame traya iti । ima eva lokā iti ।
“Who are the Āditya-s?” He (Yājñavalkya) said: “12 months [comprising] the year. They move on taking hold (Adad-) of all of this (the universe); hence, they are the Āditya-s.” “Who are the 3?” “Verily, these 3 worlds.”

katamau dvāv iti । ahorātrāv iti ।
“Who are the 2?” “Day and night.”

katama indraḥ, katamaḥ prajāpatir iti । vāg evendro, manaḥ prajāpatir iti ।
“Who is Indra; who is Prajāpati?” “Speech is indeed Indra; the mind is Prajāpati.”

katamaikā devateti । prāṇa iti । sa hovāca+anatipraśnyāṃ vai mā devatām aty aprākṣīḥ, puraitāvata tithyā martāsi । na te śarīrāṇi cana gṛhān prāpsyantīti । tad dha vai tathaivāsa । sa ha tathaiva mamāra । tasya hāpahāriṇo ‘nantareṇa śarīrāṇy apajahrur anyan manyamānāḥ । tasmād u ha nopavadet । api hy evaṃ vit paro bhavatīti ॥2.77॥
“Who is the one god?” “the life-process (literally: Breath).” He (Yājñavalkya) said: Beyond that, there must be no questioning; you have questioned me beyond the deity. You will die on such a foretold tithi (lunar date). Not even [your] body parts will reach home. Indeed, that came to be. He (Śākalya) verily died that very way. Thereafter, thieves took away his body parts taking him to be someone else. Hence, let no one abuse; for even by knowing this, he gets the better [of his rival].

Thus, this dramatic narration gives us the first example of a “pearl necklace number” sequence and its sum. These necklace numbers are named so for the problem of Maheśvara’s necklace in the Gaṇita-tilaka of Śrīpati of the Kāśyapa clan from the 1000s of CE. They are defined as palindromic decimal numbers with identical digits in the ones and largest places and zeroes in all the intervening places (pearls). Thus, here we have the first 3 necklace numbers with 3 as their terminal: 33, 303, and 3003, whose sum is the number of gods first mentioned in the RV and the Vaiśvadeva-nivid. Interestingly, a number of investigators (most explicitly in the published literature by Iyengar), including ourselves, have noticed that this number is an approximation of the number of tithi-s in a sar (a half saros eclipse cycle). The number of tithi-s in a synodic month is 30. A synodic month is 29.53059 days; thus, an average tithi is 0.984353 days. Thus, in a year of 365.242 mean solar days, we have approximately tithi-s, a number known from the Vedāṅga Jyotiṣa. A sar is years. Hence, we get . One could argue that this is a mere coincidence; however, that is dispelled by the record of this number in a specifically astronomical context in the ancient Hindu account of the Moon preserved in the Brahmāṇḍapurāna (1.23.51-1.23.79), wherein this number is specifically mentioned (1.23.68) in such a way that it can only imply the sar cycle. Further, the Brahmāṇḍapurāna mentions this number in the context of the gods drinking from the celestial soma cup, the Moon. Indeed, even in the Vaiśvadeva-nivid, this is precisely the context in which the number is mentioned; hence, it is likely that the eclipse cycle connection is an ancient one:
viśvedevās somasya matsan । viśve vaiśvānarāḥ । viśve viśvamahasaḥ । mahi mahanataḥ । pakvānnā nemadhitīvānaḥ । āskrāḥ pacata vāhasaḥ । vātātmāno agni-jūtāḥ । ye dyāṃ ca pṛthivīṃ ca ātasthuḥ । apaś ca svaś ca । brahma ca kṣatraṃ ca । barhiś ca vediṃ ca । yajñaṃ ca uru cāntarikṣam । ye stha traya ekādaśāḥ । trayaś ca triṃśac ca । trayaś ca trī ca śatā । trayaś ca trī ca sahasrā । tāvanto abhiṣācaḥ । tāvanto rāti ṣacāḥ । tāvatīḥ patnīḥ । tāvatīr gnāḥ । tāvanta udaraṇe । tāvanto niveśane । ato vā devā bhūyāṃsastha । mā vo devā atiśaṣā mā pariśasā vikṣi । viśve devā iha śravann iha somasya matsan । pra imām devā deva hūtim avantu devyā dhiyā । pra idam brahma । pra idam kṣatram । pra imam sunvantam yajamānam avantu । citrāś citābhir ūtibhiḥ । śravan brahmāṇy āvasā gaman ॥

While the Brahmāṇḍapurāna accurately preserves this number and the basis of its significance, certain other later scriptural texts only have a hazy and imprecise memory of it. An example of this is seen in the chapter on the particulars of a Śivaliṅga of Aṃśumadāgama of the Śaiva tradition:
trīṇi caiva tu triṃśac ca triśata trisahasrakam ।
devatā ṛṣayaś caiva dānavāpsara-yonayaḥ ॥51.7॥
The number here is 3333, but it is clearly an imprecise memory of the original count.

There are related reckonings in the śruti itself. A curious one relating to the number 1000 is offered by the brāhmaṇa on the ukhā fire-pot in TS 5.5.2. When the god Prajāpati handed over the ukhā to the Vasu-s, they multiplied themselves to 333 in 3 days. Then he handed it over to the Rudra-s, and they multiplied themselves to 333 in 6 days. Finally, he handed it over to the Āditya-s, and they, too, multiplied themselves to 333 in 12 days. Thus, they became a total of 999, and with the ukhā to top it off, they became a 1000. He who knows this enumeration with the fire-pot as the thousandth is said to obtain a thousand cattle. This count appears to be an alternative enumeration of the triadic numbers and the relationship between them and a thousand.

Nevertheless, returning to Yājñavalkya’s account, we can see that, more generally, these triadic numbers clearly relate to the old Indo-European concept of tripartition, which is acknowledged both by tradition and modern-day non-practicing Indo-Europeanists, viz., the Dumezilianists. This is seen across the board, be it in Yājñavalkya’s expression of 3339 as a sum of 3 pearl necklace numbers; or the ukhā-brāhmaṇa’s 333 and a triple thereof, or in what Yājñavalkya presents as the basic number of gods – 33. While Yājñavalkya accounts for this number in a certain way, other enumerations are seen in tradition; for example, the Rāmāyaṇa implies 8 Vasu-s, 11 Rudra-s, 12 Āditya-s and 2 Aśvin-s:
adityāṃ jajñire devās trayastriṃśad ariṃdama ।
ādityā vasavo rudrā aśvinau ca paraṃtapa ॥ 3.13.14c-15a (“critical edition”)
From Aditi were born the 33 deva-s, O foe-crusher (i.e., Rāma): the Āditya-s (12), the Vasu-s (8), the Rudra-s (11) and the twin Aśvin-s (2), O foe-scorcher.

Nevertheless, all accounts agree that within the 33 are included the three main classes of gods Vasu-s, Rudra-s and Āditya-s. This number is also explicitly presented as a triple of 11s to reinforce the old IE tripartition. Thus, the concluding incantation, which is deployed after the construction of the fire altar of Naciketas and before the great oblations to Rudra with the Śatarudrīya are offered, wherein the series of numbers from 1 to 33, signifying the gods is recited, has:
devās trir ekādaśās tris trayastri ̐ śāḥ ।

This brings to mind an older statement of this number in the RV in the Praügaśastra of the rājarṣi Paruchepa Daivodāsi:
ye devāso divy ekādaśa stha pṛthivyām adhy ekādaśa stha ।
apsukṣito mahinaikādaśa stha te devāso yajñam imaṃ juṣadhvam ॥ RV 1.139.11c
O you eleven gods stationed in heaven,
the eleven who are established on earth,
the eleven who with their greatness dwell in water,
[all] you gods take pleasure in this ritual.

In both these cases, the gods are presented as a triad of 11s. This enumeration offered by Paruchepa also brings to mind the 3 gods of Yājñavalkya as the 3 worlds. Indeed, after the series (1..33) recited in the Naciketas ritual, there is a terminal triple vyāhṛti oblation: bhūr bhuvaḥ svaḥ svāhā । signifying the 3 worlds.

However, despite the inherent tripartition, as far as we can see, 33 as the count of gods is a unique feature of the Āryan religion, with no earlier IE antecedents. Despite the Zoroastrian counter-religious transformation, we see this count even in the Iranian tradition. It occurs multiple times in the Yasna of 70 chapters and is connected to an equal number of “ratu-s” (articulations) or saṃbandha-s of the Iranian tradition. Indeed, this connection to ratu-s is also reflected in the Yajurveda on the Hindu side in the form of the 33 “threads” that connect the ritual to the gods (trayastri ̐ śat tantavo ye vitatnire ya imaṃ yajña ̐ svadhayā dadante । in TS 1.5.10). An example of the connection between the 33 ratu-s and deities is seen in the invocation used in the Iranian Yasna before the combined invocation of Ahura and Mithra (Vedic: Mitrāvaruṇā):
nivaêdhayemi hañkârayemi vîspaêibyô aêibyô ratubyô ýôi heñti ashahe ratavô thrayasca thrisãsca nazdishta pairish-hâvanayô ýôi heñti ashahe ýat vahishtahe mazdô-frasâsta zarathushtrô- fraoxta | Y 1.10
I announce (and) carry out (this Yasna) for all those ratu-s, for who are the lords of the ratu-s, for the Asha (=Vedic Ṛta), the 33, those approaching near, those around the Havana, who were instituted as lords of the Asha Vahishta by Ahura Mazda, and were promulgated by Zarathushtra.

Similarly, several references to the 33 gods are present throughout the RV and the Yajurveda texts:
patnīvatas triṃśataṃ trīṃś ca devān anuṣvadham ā vaha mādayasva ॥ RV 3.6.9c

trayā devā ekādaśa । trayastri ̐ śāḥ surādhasaḥ । bṛhaspati-purohitāḥ । devasya savituḥ save । devā devair avantu mā । prathamā dvitīyaiḥ । dvitīyās tṛtīyaiḥ । tṛtīyāḥ satyena । satyaṃ yajñena । yajño yajurbhiḥ । yajū ̐ ṣi sāmabhiḥ । sāmāny ṛgbhiḥ । ṛco yājyābhiḥ । yājyā vaṣaṭkāraiḥ । vaṣaṭkārā āhutibhiḥ । āhutayo me kāmānt samardhayantu । bhūḥ svāhā ॥ TB 2.6.5.26
The gods are ; 33 bountiful ones; they have Brhaspati as their chief priest; at the impulse of the god Savitṛ; may the gods help me with the gods; the first ones with the second ones; the second ones with the third ones; the third ones with the truth; the truth with the ritual, the ritual with the yajuṣ-es; the yajuṣ-es with the sāman-s; the sāman-s with the ṛk-s; the ṛk-s with the yājya-s (offering verses); the yājya-s with the vaṣaṭ calls; the vaṣaṭ calls with the oblations. May the oblations make my wishes successful. svāhā to Bhū (the first vyāhṛti).

The above formula is used for the offering of the fat of the sacrificed animal in the Sautrāmaṇi sacrifice.

How did this number 33 emerge in the Āryan tradition in the first place? The number 11 is suspiciously close to the Greek Dodecad — a number going back to the PIE traditions and eventually provided for the Āditya-s in Hindu tradition. This makes one wonder if 11 is related to that number (12). If so, 33 might have emerged by intertwining 11 with the old tripartition along the lines of the gods of the 3 worlds, something also apparent in the Greek tradition. However, there is also an astronomical possibility: The synodic month is days; hence, 12 lunar months with 30 tithi-s each amount to 354.36 days, which is short of the solar year of 365.24 days. Thus, every year the lunar 12-month cycle drifts away from the solar year. After 3 years, this difference is approximately 33 days or one additional lunar month. This 13th month could then be added to fix the alignment. A hint that such a process might have been practiced in the pre-Vedāṅga-jyotiṣa days is hinted by a ṛk of Śunaḥśepa:
veda māso dhṛtavrato dvādaśa prajāvataḥ ।
vedā ya upajāyate ॥ RV.1.25.8
He whose laws are upheld knows the twelve months with offspring (the two parvan-s of the synodic month).
He knows that which that is born afterward (the 13th month — leap month).

Another place the number 33 appears in this regard relates to the luni-solar cycle: after 33 solar years the first of the 12 lunar months and solar year will approximately commence at the same time: . This connection may be what is behind a curious brāhmaṇa seen in the TS:
prajāpates trayastri ̐ śad duhitara āsan; tāḥ somāya rājñe ‘dadāt; tāsā ̐ rohiṇīm upait; tā īrṣyantīḥ punar agacchan; tā anv ait; tāḥ punar ayācata; tā asmai na punar adadāt; so .abravīt । ṛtam amīṣva yathā samāvaccha upaiṣyāmy atha te punar dāsyāmīti; sa ṛtam āmīt; tā asmai punar adadāt; tāsā ̐ rohiṇīm evopait; taṃ yakṣma ārchat । rājānaṃ yakṣma ārad iti tad rājayakṣmasya janma yat pāpīyān abhavat tat pāpayakṣmasya yaj jāyābhyo ‘vindat taj jāyenyasya; ya evam eteṣāṃ yakṣmāṇāṃ janma veda nainam ete yakṣmā vindanti; sa etā eva namasyann upādhāvat; tā abruvan; varaṃ vṛṇāmahai samāvaccha eva na upāya iti; tasmā etam ādityaṃ caruṃ nir avapan; tenaivainam pāpāt srāmād amuñcan; yaḥ pāpayakṣmagṛhītaḥ syāt tasmā etam ādityaṃ caruṃ nir vapet । ādityān eva svena bhāgadheyenopa dhāvati; ta evainaṃ pāpāth srāmān muñcanti; amāvāsyāyāṃ nirvapet; amum evainam āpyāyamānam anv ā pyāyayati; navonavo bhavati jāyamāna iti puro’nuvākyā bhavaty āyur evāsmin tayā dadhāti; yam ādityā a ̐ śum āpyāyayantīti yājyaivainam etayā pyāyayati ॥TS 2.3.5

Prajāpati had 33 daughters. He gave them to King Soma. Of them, he went to Rohiṇī [more often]. They returned [to their paternal home] in jealousy. He (Soma) followed them and asked for them again; He (Prajāpati) would not return them to him; He (Prajāpati) said, ‘Take an oath (literally abide by the natural law ṛta) that you will equally associate [with them], then I will return [them] to you.’ He (Soma) took the oath. He (Prajāpati) returned them. Of them, he went (preferred) to Rohiṇī only. A disease seized him, “Illness has seized the king”, that is the origin of the royal disease. In that he became worse, [it gets the name] of the ‘bad illness.’ As he got it from his wives, that is (the origin) of the [name] “from the wife”. These diseases do not overcome him who knows the origins of these diseases. He (Soma) approached them (the 33 wives) respectfully. They said: “Let us choose a boon; May you resort to us equally.” They offered this oblation to the Āditya-s for him. With that, they freed him from his evil suffering. He should offer this oblation to the Āditya-s for him who is seized by an evil illness. Indeed, he approaches the Āditya-s with their own share. Verily they free him from his evil suffering. He should offer on the new moon. Indeed, with its waxing, he makes him wax. The puronuvākyā verse is, “He is born ever new…”; verily, he bestows life upon him thereby. The yājya verse is, “The ray (the moon) which the Āditya-s make to wax”; verily thereby he makes him wax.

This is a variant of a famous myth, which is often repeated in the Veda and the Purāṇa-s, that suggests a special connection of Soma to Rohiṇī. In the Veda, two stars are known by the name Rohiṇī — Tauri (Aldebaran) and Scorpii (Antares) — both orange/red stars that fit the meaning of Rohiṇī (ruddy). Modern calculations suggest that the lunar occultations of these stars are, on the whole, more frequent than those of the other bright stars. As we have noted before, this famous Rohiṇi is perhaps a reflection of the early Indo-Aryan recognition of the frequent occultation of these red stars. However, where TS 2.3.5 differs from those in other texts (e.g., the Maitrāyaṇīya Saṃhitā 2.2.7) is in specifying the number of wives of Soma as 33! All other texts give this number as 27/28, which is the number of nakṣatra-s. The myth makes natural sense when applied to the nakṣatra-s corresponding to the circuit of the moon in a sidereal month of 27.32 days. However, 33 is neither close to that nor a synodic month. Yet, its incorporation into this version of the famous myth suggests that it has astronomical significance. While the reference to the Āditya-s, deities with a solar dimension in the standard form of the myth is an ancient acknowledgment of the moon being illuminated by the sun in its phases, here the “restoration” by the Āditya-s might be an attempt to bring in the “conjunction” of the 12 lunar month cycle and the solar year. The lunar “year” of 12 lunar months is restored to the solar year after the moon has passed through 33 solar years worth of lunar months.

The basic triadic structure persisted throughout the history of Hindu tradition. On one hand, 33 was the base number which was expanded to (e.g., the Aruṇācala Māhātmya 6, of the mega-Skandapurāṇa where this number of gods are said to have been emanated by Rudra). On the other, just 3 of them were picked to be the principal deities comprising a trinity. This trinity essentialized the three ancient classes Vasu-s, Rudra-s, and Āditya-s by keeping one exemplar of each (Brahman being the father figure Dyaus now recast as the protogonic Prajāpati).

Turks, Khitans and Mongols: the ethnographic journeys of P.T. 1283

An introduction to P.T. 1283 and its historical context
This may be seen as an appendix to the previous exposition on early Mongolic and Para-Mongolic history. There we briefly alluded to the famous Dunhuang manuscript P.T. 1283. In this note, we shall take a closer look at it and its ethnographic significance. In 1908 CE, the famous French explorer and historian Paul Pelliot led an expedition to Central Asia, in the course of which he discovered a treasure trove of manuscripts at Dunhuang. Among these are Tibetan scrolls labeled the Pelliot Tibétain collection (now made available online by the Japanese), which cover a very wide range of topics, including mundane business transactions, bauddha material, the Rāmāyaṇa, and divination by dice and crow calls, among other things. P.T. 1283 is one of these, a bilingual scroll featuring a composite manuscript. On one side, it contains a Chinese tāthāgatan text. The other side contains two texts in Tibetan. The first is apparently the transcript of a lecture of a Bauddhācārya to his student. The second is rather remarkable and the text of our interest in this note. Unfortunately, not only is it incomplete, but also lacunose in the terminal surviving part and written in an idiosyncratic hand with multiple scribal errors making several readings unclear. At two points, the text seems to have a title and a “subtitle” written distinctly in a different ink. The title may be literally translated as “Text on the sequence of however many kings live in the north.” The “subtitle” or the more lengthy explanation goes thus: “In the past, the king of the Uighurs issued an order, and [this] is an exemplar obtained from what is in the archives, the text of the order which dispatched five Uighur men to look into how many kings there are in the north” (translations hereinafter are based on Federica Venturi’s edition and translation with some emendations). However, despite the statement in the “subtitle” the surviving manuscript does not have the said order of the Uighur king to his five agents. Instead, it contains a report of the intelligence gathered by the five agents along with what seems like semi-mythical material comparable to the tales of Greek agents visiting India.

At the time of the Uighur Khaghanate , the Uighurs used three distinct scripts: 1. the Iranic Sogdian script, which was already in vogue among the Turks during the earlier Blue Turk Khaghanate (e.g., Bugut inscription in Mongolia); 2. The Turkic runiform script (first attested in the Blue Turk stelae in Mongolia). 3. The Tibetan script. The last of these was used for Sanskrit and other bauddha texts as well as certain administrative documents. Thus, at first sight, one could assume that the text under consideration was an Uighur production in Tibetan script. However, the Tibetan text betrays a more complicated history. First, certain Turkic names, including Uighur, are spelled differently at different places in the manuscript. Second, it gives the names of certain tribes/kingdoms first in Tibetan terminology followed by the appellations of others, e.g., “…those who are called He by the Tibetans, Xi by the Chinese [and] Dad pyi (Tatabı = Qay; see below) by the Turks…” Thus, it seems to be specifically geared toward a Tibetan audience. Further, the Dunhuang region was controlled by the Tibetan empire during the Uighur Khaghanate when this manuscript was produced. Finally, the variability of the renderings of the Turkic and Mongolic names in Tibetan suggests its production by a Tibetan scribe who found those names foreign and was writing them down from a dictation rather than copying or translating from a manuscript.

How does this square with the manuscript describing an intelligence report produced by the five Uighur agents? Based on the tribal configurations mentioned in the manuscript and we get some key anchors regarding the probable date of the events described in it. Importantly, the manuscript opens with a mention of the Blue Turks as the tribes of Bük chur. This name Bük chur, was the title of Qapaghan Khaghan (the uncle of Bilge Khaghan and Kül Tegin) of the second Blue Turk Khaghanate in the east. Among the tribes of this confederation, it mentions Ashide, the clan of Tonyukuk, the prime minister and general of Qapaghan Khaghan. Hence, the earliest that the original expeditions of the five Uighur men could have taken place was during his reign (694-716 CE). However, as we shall see below, it was likely somewhat later, but when the Blue Turk Khaghanate was still in place because the Khaghan of the Turks in the Bük chur alliance is explicitly mentioned.

P.T. 1283 also alludes to an alliance or cooperation between the future Uighur imperial clan and the Chinese thus:
“Looking west from the Bük chur, the great chief of the nine tribes, which are called in Tibetan the Turks of the nine bones (=Turkic Toquz Oghuz confederation), the Uighur Tutuq (=commander), has been accepted as Khaghan by China. Regarding the “bone”, it is called Yaghlaqar (what became the Uighur clan in which the imperial Khaghans were born); as for [its] entourage, it puts on the nine tog (=top ornaments?), and the tribe of the Uighur has as its own an army of six thousand.”

From the Chinese annals, like the Old Book of Tang, is clear that the Uighur-led Turkic confederations and the dominant Chinese dynasties had a difficult but long-lasting cooperation of convenience against various adversaries (see below). Finally, closer to the end of the core historical part of the surviving text in P.T. 1283, we get an account of the famous upheaval on the Mongolian steppe that marked the end of the Blue Turks:

“On the north of that, there are five Basmyl tribes, which united in a confederation of three with the Uighur and the Qarluks. They overthrew the rule of the khaghan, the king of the Bük-chur. The chief of the Basmyl obtained the [title of] khaghan, but the Uighur and the Qarluk killed the Basmyl khaghan. The tribe of the Basmyl dispersed and became like slaves.” (In the manuscript, the name Basmyl is spelt in three different ways, and the ethnonym Uighur is spelt in a way different from the previously cited paragraph)

This account unequivocally refers to the events of 744 CE leading to the overthrow of the eastern Blue Turk Khaghanate (see below). To better understand these anchors provided by P.T. 1283 and situate them appropriately, we next take a look at the deep history of the Uighur-led Turkic confederation and its interactions with its neighbors till the establishment of the Uighur Khaghanate:
-During the Rouran Hun Khaghanate, the Uighur-led Tiele confederation (the proto Toquz Oghuz) kept shifting sides to retain their power in the course of the struggle of the former (Mongolic) with the para-Mongolic Xianbei (Serbi) successor states (Tuyuhun and Northern Wei).
-In 552 CE, the Ashina-led Blue Turks overthrew their Rouran overlords in Mongolia and founded the first Turk Khaghanate. This Khaghanate subjugated the Tiele confederation. By 581 CE, the Khaghanate reached Crimea and forced the Chinese states to pay tribute to them. In 584 CE, civil war broke out in the first Blue Turk Khaghanate and by 587 CE, they split into the Eastern and Western (On-oq) wings. In 588 CE, the Blue Turks invaded the Sassanian empire (at what is today the Iran-Afghanistan border) but were defeated by the Shahanshah after a pitched confrontation.
-In 605 CE, the Uighur-led Tiele confederation defeated the On-oq wing of the Blue Turk empire in a rebellion and the Uighur leader declared himself an independent Khaghan.
-In 608 CE, this proto-Uighur Khaghanate formed an alliance with emperor Yang of the Sui and launched a devastating attack on the para-Mongolic Tuyuhun Khaghanate.
-In 615 CE, Yang was defeated by Shibi Khaghan of the Eastern Wing of the Blue Turks and was almost captured; however, he managed to escape as the Sui wife of the Khaghan betrayed him by planting false intelligence on behalf of her coethnics.
-In 618 CE, the Western On-Oq wing rose again under Tonga Yabghu Khaghan (“the Tiger”) of the Ashina clan, who smashed the incipient Uighur-led Tiele confederation in the subsequent year and subjugated it.
-Thereafter, Tonga Yabghu Khaghan advanced westward, penetrating deep into Iran, but was finally defeated by the Sassanians at Ispahan.
-In 625 CE, the Christian Byzantines formed an alliance with the Blue Turks against the Zoroastrian Iranian empire. As part of this, in 627 CE, Böri Shad (“the Wolf Warrior”), the new leader of the On-oq Wing, invaded the Sassanian empire and wrested Derbent and parts of Azerbaijan from it.

-In 626 CE, the newly emergent Tang dynasty, which had rebelled against the Sui to rise to power in China, was caught in a struggle for succession in the course of which Taizong assassinated his brothers to consolidate power. However, the Eastern Wing of the Blue Turk Khaghanate led by Illig Khaghan took advantage of this and defeated the Chinese.
-This success was short-lived as the Chinese formed an alliance with the remnants of the defeated Uighur-led Tiele. This confederation now emerged as the Toquz Oghuz proper under a leader of the Yaghlaqar clan transcribed in Chinese as Pusa, who in turn claimed descent from the founding father of the old Tiele, Irkin Tegin. The Toquz Oghuz, in turn, formed a Turko-Mongol alliance with a confederation derived from the old Hun (Xiongnu) Chanyuate, the Sir-Yundlug (Xueyantuo in Chinese transcription). The Toquz Oghuz-Sir-Yundlug confederation fell upon the Eastern Wing of the Blue Turk Khaghanate and routed it in a series of battles between 628-629 CE. Consequently, they declared an independent Khaghanate under the Sir-Yundlug leader Inchü (Chinese transcription: Zhenzhu) Bilge Khaghan. The relationship of this group to the Ogular Huns — indicating a Hunnic-Oghuz linkage — seen in a Samarqand seal from the 600s needs to be further explored.
-In 630 CE, Taizong of the Tang, assisted by the Toquz Oghuz-Sir-Yundlug Turko-Mongol confederation, conquered the Eastern wing of the first Turkic Khaghanate. This also opened the flank of the Goguryeo, whom Taizong demolished in his famous Korean invasion. Taizong also launched a series of attacks on the On-Oq Western wing, defeating them on multiple occasions and raising the Cīna-s to their acme. However, Turgish branch of the Ashina clan salvaged the defeated On-Oq and started rebuilding them.
-646-647 CE, after the death of Inchü Bilge Khaghan, the Uighur-led Toquz Oghuz revolted against the Sir-Yundlug leadership of the Khaghanate. They formed an alliance with the Tang under Taizong and destroyed the Sir-Yundlug leadership. Upon this, the Uighurs assumed the title of Khaghan of the Toquz Oghuz. However, they soon had an internal conflict, and Taizong was able to interfere in Uighur affairs in 648 CE and force them to accept him as Tian Ke-han (the Heavenly Khaghan). The Uighurs struck back against the Tang after Taizong’s death in the 660s but concluded peace with the Tang shortly thereafter.
-In this period, the Tang appointed Xiao Siye as the liaison with the Turkic groups on the steppe. He was a scion of the short-lived Latter Liang dynasty (555-597) and had lived amidst the Turks with his great-aunt of the Sui dynasty. Thus, he had developed good connections with the Uighurs and got them to assist him in defeating the Goguryeo Koreans in 661 CE.
-In 679 CE, the Eastern wing of the Blue Turks, who had fallen to the Tang, started rising again, and Xiao Siye and his Uighur-Toquz Oghuz allies were defeated by them.
-In 682 CE, Ilterish Khaghan of the Ashina clan revived the fallen Eastern Wing, founding the second Blue Turk Khaghanate. As the second Khaghanate rose, they defeated the Toquz Oghuz, who were led by a certain Baz Khaghan. It is unclear if this Khan was from the Uighur clan or one of the other 8 Toquz Oghuz tribes. But the leadership of what later became the Uighur imperial clan fled south closer to the Tang borderlands and initiated communications for an alliance with the Chinese.
-In 715 CE, Uighurs aided the Cīna armies against the Blue Turks (and probably the Tibetans), and in the following year, the Blue Turks marched against the Toquz Oghuz. In the course of the battle, a warrior from the Buyirqu tribe of the Toquz Oghuz killed Bük-chur Qapaghan Khaghan, and they sent his skull to the Tang court. This suggests that they were acting in alliance with the Chinese.
-In 727 CE, the Chinese relationship with the Uighur-led Toquz Oghuz soured due to the arrogant behavior of a Tang frontier official Wang Junchuo. The Toquz Oghuz organized themselves under the Yaghlaqar leader, whose name is transcribed in Chinese as Hushu. He fell upon Wang while he was performing a tactical retreat from a campaign against the Tibetans and killed him with his assistants. He followed it up with several raids into the northern Tang lands after blockading the key roads between their eastern and western possessions. “Hushu” was succeeded by his son Qulugh Boyla as the Khaghan of the Uighurs.
-In 744 CE, as mentioned in P.T. 1283, the triple entente of the Turkic groups, the Uighurs, the Basmyls and the Qarluks, attacked the second Blue Turk Khaghanate. The Uighurs and the Qarluks aided the Basmyl leader from a rival branch of the Ashina clan to behead Özmish Khaghan and seize power. Thereafter, the Basmyl idiqut ascended the throne as Eletmish Alp Bilge Khaghan and appointed the Uighur and Qarluk leaders as the Yabghu-s of the flanks.
-Shortly thereafter, the Uighurs under Qulugh Boyla defeated the Basmyl and deposed Eletmish. Then they moved on the Qarluks and subjugated some, driving the rest to the west (the war with them in the west continued for several years, probably till around 750 CE). Next, the Uighurs moved on Kulun Beg, the successor of Özmish Khaghan, who was trying to reorganize the survivors of the Blue Turks and killed him. They sent his skull to the Tang court, evidently a move that signaled both that the Uighurs were in command and that they were willing to continue as allies of the Tang. With that, the Eastern wing of the second Turkic Khaghanate came to an end, and Qulugh Boyla ascended the throne in the Orkhon Valley in Mongolia as Qutlug Bilge Khaghan.
-The untimely death of the valiant Khan Su-lu(k) of the Turgish, who had defeated the Mohammedans and the Cīna-s, weakened the On-oq Western wing. The Qarluks fleeing west fell upon them and destroyed their Khaghanate, thus ending the Western wing of the Blue Turks. Eventually, in 751 CE, these Qarluks formed an alliance with the Mohammedans to decisively smash the Chinese in the battle of Talas.
-This left only one descendant of the Blue Turk Khaghanate, the Khazar Khaghanate, in the extreme west. By around 740 CE, their Ashina leadership was converted to Judaism, signaling a possible break with the ancestral Turkic traditions.

This examination of the pre-imperial history of the Uighur Khaghanate indicates that they, with their larger tribal confederation, the Tiele or the Toquz Oghuz, retained an independent identity despite often being subservient to the dominant Mongolic, Para-Mongolic or Turkic powers in Mongolia. Prior to the incipient “pan-Turkism” in Islamized lands (e.g., Mahmud al-Kashgari, the Qarluk>Qarakhanid intellectual), only the Blue Turk branch held the ethnonym Turk (Türük > Skt: turuṣka). The other Turkic-speaking confederations, like the Toquz Oghuz, Qarluks and Kirghiz, did not call themselves Turk. This points to their distinct identity vis-a-vis the dominant Blue Turks and is consistent with the repeated hostilities with them. As part of this process, right from the Sui period, they formed unstable alliances with the dominant Chinese dynasty — this symbiosis potentially afforded the Uighur-led confederation force multiplication via the larger Chinese armies against their common Turkic and (Para)-Mongolic rivals. On the Chinese side, the relationship provided them a handle to deal with the ever-existent threat of invasion by their steppe rivals while also boosting the peculiarly Chinese imperial self-image of having a vast realm by claiming peripheral nations as “vassals.” Tibetologists note that a literal reading of the sentence in P.T. 183 which mentions the Chinese acceptance of the Yaghlaqar leader’s Khaghanal title could imply that these Uighurs “came from China”. This is likely an implicit pointer to the Toquz Oghuz fleeing to the Tang borderlands upon defeat by the Blue Turks.

From the above, it is clear that at the time of the expedition of the five Uighur men mentioned in P.T. 1283, they did not occupy the imperial Khaghanal seat in Mongolia. However, they were probably on the ascendant and aspiring to gain power — the mission was hence likely dispatched for espionage and diplomacy. It was a feeler to see which groups might ally with them and which might be opposed to them in future conflicts. At least one of the itineraries headed out from an Uighur town mentioned as Baqir Baliq (Copper town) in the opening of the text. It is said to have been called Ji`ur by the Chinese; however, no such name is found in the Chinese annals. It is possibly a now-lost town in Ganzhou or Liangzhou of the Gansu region, where many members of the Yaghlaqar clan were stationed during the final years of the Blue Turk Khaghanate. As noted above, the mention of Bük chur indicates that the mission took place no earlier than the reign of Qapaghan Khaghan. Nevertheless, the manuscript mentions the then-reigning Khaghan of the Blue Turks as Zha ma in Tibetan. There is no evidence that the Tibetans called either Qapaghan or his successor Bilge by this name. Though Qapaghan was killed in the battle with the Toquz Oghuz, his nephews Bilge Khagan and Kül Tegin, quickly restored Blue Turk power and put down the Toquz Oghuz. Hence, it is unlikely that the Uighurs were in an ascendant position to send out such a mission during their reign. Further, as noted above, from 727 CE onward, for some years under “Hushu” they were engaged in hostilities with the Tang and focused South/Southeast. Thus, we would place the mission after 734 CE when Bilge Khaghan died. Thus, the Zha ma of the text could have been one of his successors Yollig Khaghan (734-739), Tengri Khaghan (739-741) or Özmish Khaghan (742-744). We would settle for Özmish (though Tengri is also possible given the phrase heavenly Khaghan in the manuscript), during whose reign the upheaval recorded in the text took place, leading to his death. Hence, we infer that after Qulugh Boyla had succeeded his father, “Hushu”, on the throne, he sent out this expedition to gather intelligence. This would place it around 742-743 CE. The intelligence and diplomacy resulting from this expedition probably resulted in the triple entente and the events that followed in 744 CE. Subsequently, when Qulugh Boyla ascended the throne, he had the text of his original order for the mission, the intelligence of the five men and a brief mention of the events of 744 CE to be compiled into a single document. This manuscript was the prototype of the Tibetan text in manuscript P.T. 1283. It appears that the Uighur document fell into the hands of the Tibetans during the struggle between them. Seeing its potential utility, they rendered it into Tibetan at Dunhuang. Based on the way it presents the material, we suspect that the Tibetans did not just translate it as is but provided some “interpretation” so as to make it understandable in their circles: e.g., providing Tibetan names of people and positioning the locations with respect to the Tibetan frame of reference.

Ethnographic information in P.T. 1283
P.T. 1283 provides us with a remarkable snapshot of ethnographic information corresponding approximately to the first half of the 700s. Below we discuss some of the tribal groupings of interest in the context of this note:
Turkic groups
-The Blue Turk Confederation: The text mentions the Blue Turks as being a confederation of 12 tribes. Most of these tribes are not known in any other source, including the Turkic runiform inscriptions. However, there are some notable names. First, one of them is a Tibetan rendering of Ashide (Tib: A sha sde), the clan from which the famous Blue Turk minister Tonyukuk came. The clan continued to be prominent in the Uighur Khaghanate and persisted down to the Chingizid empire. Another tribe is listed as Hephtal. This is clearly the Hephtalite, the Hunnic group with a Mongolic elite that was established in central Asia west of the core Rouran (440-560 CE). After overthrowing the Rouran, one of the two founding Khaghans of the Blue Turks, Ishtemi, advanced West to attack the Hephtalites. In an alliance with the Sassanians led by Khosrau Anushirvan, Ishtemi seized Tajikistan and parts of Southern Kazakhstan from the Hephtalites, leading to the collapse of their empire. It seems a group of them was absorbed by the Blue Turks, and they persisted within the second Khaghanate in the East.

-The Basmyls: After describing the short-lived Basmyl-Uighur-Qarluk triple entente, which overthrew the Blue Turks, P.T. 1283 goes on to provide some further details about the former group:
“The territory of the Basmyl, one tribe of the Tib: Ges dum, the territory of the Basmyl, one tribe of the Buyirqu (Tib: Ba yar bgo), [has] the chief Tib: Yed myis hir kin; one tribe of the Hi dog kas; [has] the chief Hi kil kor hir kin; [their] country is strong, and the Qarluks (Tib: Gar logs) did not get [it].”
The Buyirqu here is also seen in the Blue Turk history, apparently as a tribe of the Toquz Oghuz, but here it appears as a Basmyl group. Multiple Basmyl chiefs have the title spelt hir kin in Tibetan, which is obviously the Turkic aristocratic title Irkin. Their personal names seem so far uninterpretable. However, most notable is the tribe spelt as Ges dum in Tibetan. It has been pointed out that this is most likely the Keshtim/Keshdim tribe that survived long until the rise of Chingiz Khan. Rashīd al-Dīn records a triad of tribes named the Ursut, Telengüt and Keshdim living to the east of the Kirghiz (see below). These might be remnants of the old Basmyls mentioned in P.T. 1283. As per the Secret History, the Keshdim were subjugated along with the Kirghiz, Telengut and several other Siberian tribes by Jochi, the eldest son of Chingiz Khan. They surrendered to the Khan with gifts of falcons, horses and sables.

-The Kirghiz: P.T. 1283 records this tribe thus:
“Behind them (the Kücügür, see below subsection on Mongolic tribes) there are two small Kirghiz (Tib: Hir tis) tribes; with the Uighur, sometimes they fight, sometimes they are friendly. From there, in the north is one tribe of the Kirghiz. [As for] their eyes, [they] are crystal eyes, [as for] their hair, [they] are red [and] in their country there are various kinds of domestic animals. The horses are born big.”
The interesting ethnographic details concerning their hair and eyes are indicative of an admixture between East Asian and Western Eurasian groups. Even today, one can find such features among the Kirghiz despite the extensive later Mongolic admixture. We know that the Kirghiz were in the vicinity of the Uighurs in the Tang period when Taizong forced them to accept him as the Tian Ke-han. They had interacted even earlier with the Chinese during the Han period. The Kirghiz, along with disgruntled elements of the Uighur army, destroyed the Uighur Khaghanate between 843-848 CE. This victory and subsequent campaigns might have formed the core of their epic on Khan Manas. While the Kirghiz briefly took the Khaghanal seat in Mongolia, the time of the Turkic peoples soon passed — by 890 CE, a para-Mongolic-Mongolic confederation under Khitan leadership wrested the Mongolian core with the old Orkhon center from them. For the large part, they retained peaceful relations with the Kirghiz thereafter.

Serbi (Para-Mongolic groups)
-The Tatabı: This is a para-Mongolic tribe known as the Qay who were related to the Khitan. They emerged along with the Khitan during the fragmentation of their precursor, the Yuwen Confederation, in 344 CE. They seemed to have remained close to their Khitan cousins in the subsequent period. Their relationship with the Blue Turks and the Chinese was variable. In the summer of 712 CE, a Khitan-Tatabı combined force marched against the Chinese. The Blue Turks sensing an opportunity, provided them with some kind of support, and they inflicted a crushing defeat on the Tang in a great battle on 30 July 712 CE. In 717 CE, the Tatabı Khan married the Tang princess Gu’an consolidating an alliance with them. Bilge Khaghan fearing a Chinese-Tatabı alliance against the Blue Turks, launched a ferocious attack and slaughtered many of them. The Blue Turks launched a second assault on the survivors in 723 CE and scattered them. In the following 10 years, the Qay=Tatabı kept themselves solvent by alternatively accepting Turk or Chinese suzerainty.

In an unexpected twist in 733 CE, the para-Mongolic confederation seemingly split up, with the Khitans led by Ketughan Khan forming an alliance with the Blue Turks and their Qay cousins led by a Khan named “Lishi Suogao” in Chinese transcription allying with the Tang (probably a ruse as we will see below). The Chinese sent their general Guo with a formidable force of 40000, of which at least 10000 were well-armed Tang cavalry, to march alongside a Qay army of at least 5000 cavalry against the Turk-Khitan coalition. A pitched battle was joined on April 24, 733 CE, at a pass near what is indicated as the Tongker Mountain (Chinese: Du Shan). Suddenly, the Qay switched sides and joined their Khitan cousins. A part of the Chinese forces was trapped between them and routed. However, general Guo kept fighting and was beheaded by Bilge Khaghan’s troops, and the Turk-para-Mongolic forces hoisted his head. Despite seeing this, 6000 Chinese troops refused to retreat and pressed the attack, only to be completely massacred. General Guo’s image was erected as a balbal stone at the funerary monument of Bilge Khaghan’s son. The P.T. 1283 text confirms that the Qay=Tatabı had preserved their independent identity down to the end of the Blue Turk Khaghanate. They are mentioned as having a curious custom: “Looking to the east of these (the Blue Turk tribes) those who are called He by the Tibetans, Xi by the Chinese [and] Tatabı by the Turks. [Their] chief “Cong bong ya” (Tibetan transcription), decorates the heads of suitable ancestors of the Tatabı with gold and silver and makes [them] into beer vessels.” While the Kāpālika tendency has been documented in humans from pre-Neolithic times, it appears to have been prevalent among the steppe peoples, such as the Śaka Iranics and the first Hun (Xiongnu) Chanyuate, among others. Thus, it is not surprising that the Tatabı retained such a custom. However, most made skull-cups from the remains of their enemies rather than their ancestors, as claimed by P.T. 1283.

-The Khitan: We had earlier noted the comment in P.T. 1283 on the Khitan language being related to the Tuyuhun Khaghanate’s tongue. The full account of the Khitans in the text goes thus:
“Looking north of this (the Uighurs) are those called Khitan (Tib: Ge tang/Ge tan), and the Khaghan of the Khitan, the king, both his food and his religion are similar [to those of] the Tuyuhun (Tib: `A zha). As for domestic animals, calves, sheep, and horses are common. Their language and that of the Tuyuhun could generally be understood by each other. With the Uighur, sometimes they fight, sometimes they are friends. From there, looking to the east, are the Tatabı.”
Thus, the Khitan are described as being to the North of the Uighurs, with the Qay/Tatabı to their East. The Qay/Tatabı is also said to be to the East of the Blue Turks. The Uighurs are said to be to the West of the Blue Turks. Thus, the Khitan and the Qay can be seen as having formed a West-East arc around the Northern borders of the Blue Turks and Uighurs. Apart from the key linguistic insight that the Para-Mongolic dialects were still inter-intelligible in the 700s, it also points to the Khitan having a variable relationship with Uighurs.

As we saw in the previous note, the genocidal war of 605 CE by the Sui-Blue Turk alliance on the Khitans had considerably damaged but failed to exterminate them. In 684 CE, the Uighur-led Toquz Oghuz tried to create a triple entente with the Khitan (and possibly the Qay) and the Tang to simultaneously attack the Blue Turks from all directions. They sent an Uighur envoy Tongra Sime to contact the Khitans — this provides evidence independently of P.T. 1283 of the Uighurs contacting various tribes in their periphery for diplomatic purposes. However, Tonyukuk intercepted the communications and advised Ilterish Khaghan to launch preemptive strikes on all of them. This evidently records one of the incidents where the Uighurs and the Khitans sought an alliance, as alluded to in P.T. 1283 (“sometimes they are friends”). As a consequence, we hear from the Tonyukuk runiform inscription that Ilterish Khaghan fought 17 battles against the Tang, 7 battles against the Khitans and 5 battles against the Uighurs and the Toquz Oghuz to save the newly revived Blue Turk Khaghanate. In 695-696, the Khitan-Tang cooperation against the Turks broke down, and the Khitan Khaghan launched attacks on the Chinese. Alarmed, the Tang empress Wu Zetian and her mantrin-s started performing abhicara rituals of māraṇa against the Khitan leaders (she had performed similar rituals against Ilterish Khaghan before his death). More practically, she assembled a vast Tang army to fight them. The Khitans, in turn, formed an alliance with the 30 Mongolic Tatar tribes and sent the Chinese prisoners they had taken back to their coethnics with the false message that they were too low on supplies to fight the Tang army. The Tang commanders Zhang Xuanyu and Ma Renjie took the bait and rushed into the steppe with their cavalry and several top officers. The Khitans placed some emaciated cows and horses on the way to give the impression to the Chinese that they had really run out of fodder. On 29 September 696 CE, the Khitan Confederation drew the Tang cavalry into an ambush in the Huangzhang Valley and mowed them down with showers of arrows. Closing in, the Khitan troops lassoed generals Zhang and Ma with pāśa-s (an interesting record of the use of this weapon on the field) and took them prisoner. The Khitans captured a Tang seal and prepared a forged document asking the Tang infantry reinforcements to come in haste to a predesignated trap. Tired from the long march, the large Chinese infantry collapsed under the Khitan-Tatar attack and was wiped out. Several of the top Chinese generals lay dead on the field. It marked the revival of the Khitan power after more than 90 years. A few months after this great victory, the Khaghan of the Khitans passed away.

The Blue Turks were alarmed by the sudden revival of the Khitans. Hence, Qapaghan Khaghan launched an attack on them even as they had lost their Khaghan and took hostage some members of the Khitan royalty. Empress Wu formed an alliance with the Blue Turks to fend off the Khitans. The Khitans fell back to fight the Turks, but soon the Turks also attacked the Chinese and captured their general Xu Qinming. Taking advantage of this, the new Khitan Khaghan launched multiple devastating attacks on the Cīna lands. On 8 April 697 CE, the Khitan cavalry drew the Chinese general Wang Xiaojie with a force of 18,000 men into a trap in the Dong Xiashi valley and crushed them. The Khitan Khaghan then built a fort and kept the women, children and elderly there, leaving a general to guard it. His intention was to launch a more mobile strike on the Chinese. As the Khitan Khaghan launched an attack deep into the Chinese territory, Qapaghan Khaghan sacrificed the Chinese general Xu Qinming to the Tengri of the Blue Heaven and asked for victory against the Khitans. He stormed the Khitan fortress and took the vulnerable captive. The news reached the Khitan Khaghan when he was in the thick of battle with the Chinese. At the same time, their Qay/Tatabı cousins fled the field with their supplies, leaving the Khaghan vulnerable. On July 23rd, 697, just months after his great victory against the Chinese, the Khitan Khaghan died fighting the Blue Turks. Thus, yet again, the Khitan had been beaten despite an impressive revival, and the Qay and the Tatar were subjugated by the Blue Turks. For empress Wu, it was a success, even if belated, of her abhicara. As we saw above, it took more than a decade for the Khitans to return to the fray, again in alliance with their Qay cousins. P.T. 1283 indicates that in the 740s, the Khitan power was still notable.

-A further para-Mongolic group: The P.T. 1283 account continues on from the Khitan and the Qay to their East thus:
“From there, on the north (of the Tatabı), there is the tribe of the Tib: Ga ra byi gir and [as for their] country, [it is in] the valleys. They only have pigs for domestic animals.”
The first part of the name of these mysterious pig-rearing people is the Turkic Qara: black. The second part remains unclear. Later Mongolian sources record an ethnonym Gakhān, related to the Mongolic word gakha for pig. However, it might be a derogative designation as it is used in Mongolic usage for dirty or fat individuals.

“From the country where [there] is the one tribe of the Do le man, comes excellent byi tse (a medicinal herb?) There are five tribes who cover [their] tents with birch bark. From there, looking to the north, on the shores of the limitless lake, [as for] the people, their houses and their bodies are similar to [those of] the Tuyuhun (Tib: `A zha). They have various kinds of domestic animals. As for [their] clothes, they wear fur coats. In the winter, on the great plain, the earth is cracked, and the people cannot pass back and forth. The great tribe is happy.”
Here the “Do le man” tribe could possibly be the same as the Doumolou mentioned in the Weishu as speaking a Khitan-related language, though this is by no means certain. Beckwith has claimed, based on slim evidence, that they were originally speakers of an ancient language found in Korea/Japan of uncertain affinity. The five tribes with the birch bark tents are entirely mysterious. The tribe to their north is said to be at the shores of a limitless lake in a frigid setting. From the geography going North through Mongolia, this lake is most likely the Baikal Lake. Remarkably, these people are said to be similar in their dwellings and form to the Tuyuhun. While the Tuyuhun Khaghanate was closer to the Tibetans in the Khingan region, these peoples are way North of them, with several other groups in between. Yet, the explicit indication of their similarity suggests that they might have been another large northern para-Mongolic tribe. One possibility is that it is a reference to the Shirwi (Chinese: Shiwei; who retained the old Serbi ethnonym), who were the third para-Mongolic group of the Khitanic clade (the other two being Khitan and Qay/Tatabı). This proposal would be entirely consistent with their geographical positioning vis-a-vis the Khitan recorded in the Suishu. The Shirwi appear to have been rather distant from the Uighurs at that point and played a notable role in Uighur politics only in the final years of their Khaghanate.

Mongolic groups
-The Kereit: “From there [the above para-Mongolic group], looking northeast, are the Khereghit, one tribe, who cover their tents with birch bark. They offer to the Uighurs the skins of blue rodents (marmots?).”
This name is clearly an older variant of the Middle Mongolic tribal name Kereit whose leader was the famous Toghrul Wang Khan in the days of Yisugei Bagatur and Chingiz Khan. The Khitan records indicate that the Kereit formed a confederation along with the Tatars and other Mongolic groups on the Mongolian plateau, termed the Chebuqu in Classical Khitan, during the heydays of the Khitan empire. The aristocratic members of this tribe extensively married with the clan of Chingiz Khan after the antagonistic members were destroyed in the course of their confrontation with him. Thus, their presence in P.T. 1283 indicates that they were already a distinct group in the 700s. Their name could have been totemic and related to the Mongol word for crow, which is phonetically similar.

The Mongols left a laconic account of the end of the Kereits led by Ilqa Senggün, the son of Toghrul Wang Khan: “Ilqa [Senggün] fled to the Tangut Kingdom, passing by Isina city and arriving at the [land of the] “Wolf Tibetans.” Having plundered them, he still wished to live there. The “Wolf Tibetans” gathered their peoples and drove him out. [With his forces] scattering, he fled to the land of the Cherkesmen of Küsen (Kucha) city in the west. He was killed by one Qïlïnch-Qara.” This Black Qïlïnch then captured the wife and kid of Senggün and handed them over to Chingiz Khan. Then the Black Qïlïnch submitted voluntarily to Chingiz Khan and joined his ranks. Rashid ad-din clarifies that the Qïlïnch tribe of this “Black” Turk was none other than the Qalaji-s, the same tribe that produced some of the most monstrous tyrants who operated in India. This indicates that some heathen remnants of their tribe remained as likely feudatories of the Qara Khitai kingdom and joined the Mongol Khan during the disintegration of the former. Their relationship to the Cherkesmen tribe and the ancient city of Kucha remains mysterious. Interestingly, ethnographers have noted that a tribe of these Qïlïnch/Qalaji-s have landed up near modern Tehran and still speak an archaic Turkic dialect. This might suggest that they descend from the branch of the tribe that joined the Mongols rather than their counterparts who rampaged in India.

It is interesting that though the early Kereit are mentioned, the Tatars find no mention in P.T. 1283. This is strange given the role they played in the alliance with the Khitan in the battles against the Chinese and the Blue Turks and the fact that they are mentioned on both the Bilge Khaghan and Kül Tegin funerary monuments. In the former monument, the Toquz Tatar (9 Tatar tribes) are said to have formed an alliance with the Uighurs and the Toquz Oghuz to resist the Blue Turks. Bilge Khaghan fought this alliance twice at a place in Mongolia called Aghu and conquered their territory. On both these monuments, the inscriptions also mention a larger Tatar grouping, the Otuz Tatar (30 Tatar tribes), that are described as enemies of the Blue Turks. However, the Tatars, along with the Khitans and the Qay, are also said to have attended the funerary feasts of their ancestors, the founding Turk Khaghans, Bumin and Ishtemi. The Tatars were evidently a famous Mongolic confederation, for they lent an exonym to the more famous Chingizid Mongols in several languages. They were crushed and absorbed by Chingiz Khan early in his career. His foster son Shigi Qutuku, who went on to become the minister of law and the census of the Mongol empire, and the compiler of the Secret History, was a Tatar by birth.

-The Kücügür (Naiman): P.T. 1283 records this tribe thus:
“From there (an unidentified reindeer-herding tribe called Gud), looking northwest, there is one tribe of the Kücügür (Tib: Ku chu gur). The country is strong, and as [they] do not listen to the orders of the Uighurs [they] constantly fight.”
The Secret History of the Mongols records this name as the leading tribe of the Naimans, e.g.,: kücügüt-naiman-u buyiruq khan; naiman-u kücügüd-ün buyiruq khan. Based on the SHM and the account of Rashīd al-Dīn we may infer that the leading Naiman clan at the time of the rise of Chingiz Khan was the Kücügür. Before them, the Betekin clan was preeminent among the Naimans and had aided the Kereit leader Qurjaquz Khan in 1140 CE. Hence, the Kücügür appear to have taken over some time after that. After their Khanate was destroyed by Chingiz Khan, many of their men were absorbed into his empire and are still found in Inner Mongolia and among the Afghan Hazaras. It is unclear if their name arose via derogation from the homophonic Mongol term for a steppe rodent. It seems possible that P.T. 1283 offers evidence for the antiquity of this tribe. However, it is not clear if they were part of a larger grouping known as the Naiman even then.

Beyond the above-discussed groups, there are several other as yet unidentified tribes, as also the Koreans and a coastal Ainu-like tribe mentioned in P.T. 1283, that we do not consider in this discussion. The text also contains some ethnogonic fables relating to cynolatory among the Turks. These myths have a broader resonance with the cynolatory and cynothysia among the Mongolic and para-Mongolic groups and perhaps also the Tungus (the role of dogs in the founding legend of the Manchus). We hope to discuss those separately, along with the possible connection to the cynolatory of the Iranics.
In conclusion, the text offers an independent attestation of several steppe groups of Turkic, Mongolic, and Serbic affiliation from those found in the Orkhon runiform inscriptions and the Chinese annals. It clearly shows that a richer tapestry of tribal groups existed on the steppe and its periphery than can be gleaned from the admirable records of the Chinese annals. Nevertheless, the actual affinities of several of the groups mentioned in the text still remain unclear. It also gives a picture of the nature of the early steppe Khaghanates — even the powerful and wide-ranging empires like those of the Blue Turks did not steamroll the underlying diversity of groups, unlike the model seen in China after the Chin. While subjugated by the dominant power, they still retained their identity and, like the Khitan and Uighur, often sought to re-assert themselves repeatedly. This was to change in steps only following centuries, first with the Khitan ascendancy under the Khaghan Yaruud Ambagai (Abaoji) and then the rise of Chingiz Khan.

Looking back at the goroga attacks and forward at geopolitical developments

An acquaintance recently asked us if we remembered the famous goroga attacks in the mahāmleccha lands. We had to confess that they were hardly the top thing on our mind, though we had repeatedly thought of those attacks at the beginning of the pandemic. He said that he had seen a recent presentation on it by the journalist Harivana, who had helped the momentous revelations of Himaguha see the light of day. He wondered if we might rethink our position on the Wuhan disease after seeing it. We told him that while the Wuhan corruption had become a matter of personal faith for many, we did think there was something of a “conspiracy” with regard to the goroga incident. Harivana is not a good guy from the H perspective but has exposed mleccha evildoing on several occasions. Hence, we went and watched Harivana’s presentation on the goroga scare and felt the urge to put down a few words regarding that sordid episode which we experienced from close quarters.

It was the time when the duṣṭa-s Gucchaka and Vakrās held sway over the mleccha-s with a court of mahāśaṭha-s known as the neocons. Then, as the summer of 2001 was drawing to a close, their former friends, the marūnmatta-s, turned against them and literally struck them out of the blue, killing nearly 3000 people. Even the mighty Yamato’s bombers had only reached the distant outpost of Hawaii, but the shaikhs literally hit the rājadhāni-s of the mahāmleccha on that day. It was a landmark moment in the history of our age and signaled that the lokapraśamanam the mahā-mleccha had achieved after the overthrow of the Soviet Rūs empire had been challenged. Barely a week had passed since the marūnmatta assault on the mleccha heartland when a new round of terror swept through the country. Mysterious letters spiked with a powder bearing the gorogānābhika were sent to many addresses, mostly on the East Coast of Madhyamleccha-varṣa, over a period of around two months. The end result was the death of 5 people, with 17 others taken ill — several with lingering aftereffects. Some believe that this is the official count, but several more were probably infected and affected by it. As Harivana correctly stated, we clearly recall that it resulted in a period of immense terror. At least the marūnmatta attacks were directed at specific sites, but here the agent of death was coming right to people’s homes via the mail. Thus, no one felt safe as the reports of those attacks started spreading around. People were very gingerly in collecting their mail with gloves on as the information spread that residues of the rogānābhika were found not far from where they lived or worked. Then, almost exactly an year after the goroga terror, a new marūnmatta terror broke out at the mahāmleccha rājadhānī in the form of the two kṛṣṇa gunners.

The net result of all these was to make the mahāmleccha public acquiesce to any plan their mahāśaṭha court might have in terms of military campaigns in far-away lands. Indeed, the goroga attacks were accompanied by handwritten notes that made them appear as if they had been launched by marūnmatta-s from West Asia. Just after the 9/11 attacks, we recall that a duṣṭa-āṅglaka online operative, whom several stupid H mistook to be a friend, was priming people on online forums about the possibility of biowarfare by the marūnmatta-s and dropping hints about Eye-rack. We wondered how he knew what the rākṣasa-sādhaka-s’ intentions were, even before the dust of the towers had settled. Thus, when the goroga attacks began, we had the first hints that something strange might be afoot. Not surprisingly, we soon saw misinformation deliberately fed by the court to their “journalist” puppets pinning the attacks on Saddam Hussein of Iraq, whom the mleccha-s had been long wanting to overthrow and kill. Most of the mleccha populace naively believed this claim. However, from early in the attack, some microbiologists were pointing out that this was likely an inside job. Despite the journalistic “leaks” screaming “Sadaaam” and “WMD”, even the mahāmleccha-praṇidhi-s could not hide the truth for long — it was their own strain of goroga — something they had been developing for long as a biowarfare agent. This was distinct from the strain the Mahāmleccha had given Saddam when they were still friends. Hence, they tried to frame one of their own physician-researchers. While he was a person with some dubious or even fraudulent tendencies, he was entirely exonerated of any role in the goroga attack and paid reparations. Subsequently, after many years of fruitless investigations, they pinned the crime on another of their own men, Ivins, whom they had earlier recruited to study the gorogānābhika behind the attacks. He conveniently committed suicide just before they were to arrest him, and no autopsy was performed on his corpse.

We lost track of this case after it became clear that their earlier man was not responsible. Our interest was briefly revived after we heard that Ivins had committed suicide — this sounded so fishy that many possible scenarios could be constructed around it. In any case, we had no good evidence to favor one or the other. Moreover, the press made sure that it dropped out of the news cycle rather quickly. In essence, it was not a marūnmatta attack and a thing of the past; hence, it did not deserve time on air. Interestingly, a little before that, a former student and a mūlavātūla wanted our assistance in studying the gorogānābhika for the latter’s commercial venture as he was flush with the money that was being doled out for such things in the aftermath of the attacks. Due to the bindings on us and our lack of interest in things that would not lead to published research, we declined to participate. However, a few years later, the said mūlavātūla came to ask us to mentor a relative. At that point, I asked him about his gorogānābhika venture. He responded that he had made some money out of it though his product was never commercialized, and our former student had moved on with that expertise to study rogāṇu-s, such as the C-harimāṇa-rogāṇu and the dreadful vīparīta-granthi-rogāṇu that periodically breaks out in Kṛṣṇadvīpa. He then added that he had been consulted by a mūlavātūla-vṛddha (also our acquaintance) on a report on the antaḥ praṇidhi’s claims that Ivins was their man. He went on to describe that Ivins had some serious graha-roga that triggered his svahatyā, but in no way could he be uncontroversially implicated by the data of the praṇidhi-s and daṇḍaka-s as the perpetrator.

Piqued by this, we examined the report and since then have spoken to some of its authors. While we are not in a position to paraphrase what they said, and several years have elapsed since the first of those conversations, what we can say is that they did not seem convinced by the case. The evidence that the antaḥ praṇidhi-s had gotten their man was slim at best and likely false. Indeed, as Harivana, a lawyer, said in his presentation, it might simply not have survived in court. Hence, we have to plainly fall back on one of the “conspiracy theories”: (1) We all know that śaṭha-sabhā, with the evil Vakrās as their titular head, was long wanting to wage war on a number of nations and overthrow their leaders. One of these was Iraq, and the other is the Rūs. (2) They believed that with the fall of Rūs power, they had no challengers for their adventures. Thus, they began their ventures with support for the marūnmatta-s against the Rūs ally, the Serbs, and saw that the weakened Rūs could simply do nothing. They had been itching to do the same in West Asia — the idea was that they could protect their prathamonmatta guru-s and allies by “taking out at least seven countries” and redrawing the map of that region. (3) The śaṭha-sabhā was willing to come up with outrageous plans. These included ridiculous ideas (though this was not put into action) of bombing places in South America in response to 9/11, evidently as a signal to those in West Asia. This meant that there was always the danger of outrageous action from a small motivated band within their gang. This is an important point for developing a hypothesis for what happened. (4) They were waiting for an excuse to exert near-total control on the American population to play along with their plans.

Given this background, the marūnmatta attack on 9/11 was the perfect opportunity for the mahā-śaṭha-sabhā that surrounded Gucchaka. However, they knew that even on the eve after the attacks (as we saw ourselves), people were still going to restaurants and enjoying a good meal and going about with their lives. They wanted to impress on them a real sense of fear so that they would play along with their plans in West Asia. The way out was to imprint the terror in the minds of the populace — what could be better for that than the goroga attack? Hence, it is not impossible that a deep insider of the śaṭha-sabhā with a psychopathic streak or a rogue but deep-state-backed praṇidhi let the attacks happen either by deliberately green-lighting them or by prematurely lifting an inhibitory check on plans that were already in place. We would reiterate that the operation was probably intended more to cause mass fear than mass death. If this were the case, then it would not be in the interest of the śaṭha-sabhā (=deep state) to let the public know the truth about this. In fact, in such a scenario, the events would have likely unfolded along the lines they did.

We know this sounds outrageous, but this is why we are willing to entertain it as a possibility: (1) While we are not an expert on this matter, the weaponization of the amount of gorogānābhika used in the attack was no ordinary task for a microbiologist. After all, it was a very fine-grade powder in the league of the best mahāmleccha or Rūs weaponizations. There is no evidence that the accused was directly handling such weaponized samples that could not be easily reproduced by other experts post facto. (2) The packages were sent in such a way as to limit damage rather than produce a larger number of casualties (e.g., clearly stating what the agent was) while at the same time producing terror in the population. (3) The number of “leaks” claiming a link to Saddam and his bentonite, well before the long investigation concluded, was striking (a point also emphasized by Harivana). This went along with an extensive discussion of Saddam’s “germ labs.” (4) The inept leak implicating the “person of interest” who was then exonerated. (5) The number of years spent on the case without a conclusive identification of the perpetrator. This is particularly strange given the resources and the capabilities of the antaḥ praṇidhi-s in other cases. (6) The general disinterest on the part of the antaḥ praṇidhi-s and daṇḍaka-s in following up and vigorously defending their choice of the suspect in the media. Given the significance of the case and the terror that arose from it, one would have expected more, especially if it had been a real domestic vibhīṣaka. In conclusion, the real and full story was likely purposely hidden from the public.

Like our interlocutor above, one may ask, if we are willing to allow this much with the goroga case, why not do the same for the Middle Kingdom corruption? Hence, before going on with more significant things, we will briefly repeat our position on it with the hindsight of 3.5 years. We still believe that the evidence in favor of the Wuhan condition being caused by a virus designed or deployed as a biowarfare agent is weak. Hence, we continue to look at it as a zoonosis. It is notable that the Cīna researchers themselves had mentioned in print in their pre-pandemic studies on coronaviruses that they expected other zoonoses like SARS to emerge in their midst. However, certain things are clear. First, the Cīna-s have a poor track record of laboratory safety, as was seen with the first SARS itself. Second, we cannot entirely rule out the possibility that the Cīna-s had brought infected animals to their institute or had already managed to cultivate the virus there as part of their well-known ongoing research on coronaviruses. Therefore, it cannot be ruled out that the infection began from their lab personnel or improperly disposed non-human lab animals. That said, as we have repeatedly pointed out, Galtonism played a major role in how the pandemic played out thereafter. It is this Galtonism that has been covered up, bringing memories of the goroga incident. It is clear that the mahāmleccha academics and also a section of their security state have deep-rooted Galtonistic impulses going back to the mahāpāpin mūlagrasta Cumbaka. This meant that they were more than happy to contract out, encourage and participate in virological studies with the Wuhan and other Cīna labs. They were confident that they would be treated well in return for this generous help. However, what they received in return was typical Cīna perfidy.

That apart, we think that the handling of the pandemic, the overthrow of the Picchilaka and the subsequent war between the Rūs and the Mahāmleccha have some underlying thematic connections to the way the goroga incident was handled. We can see a parallel of the plot to confuse the public and make it forget momentous incidents on multiple occasions. The first was that of Vyādhapiṇḍaka’s saṃkalanaka, which revealed serious damaging facts about their man Piṇḍaka. The Nāriṅgapuruṣa would have almost certainly edged past him had that not been covered up. Not only did the antaḥ praṇīdhi-s and bahiḥ praṇidhi-s cover it up, but they also imputed the blame of faking it on the Rūs, thus connecting the two strands of their action. This deprived the Picchilaka of a potent heti to put the duṣṭa-s in place while simultaneously taking the sheen off him as a Rūs agent. Even after Vyādhapiṇḍaka’s antics were shown to be real, the mainstream media quickly took it out of the news cycle, just as with the supposed perpetrator of the goroga affair. The revelations coming from Bhūtipiṇḍakī’s writing were squelched even more quickly by the action of the antaḥ praṇidhi-s. Finally, when the investigative report was published showing the faking by the antaḥ praṇidhi-s (some of the same guys involved in the goroga affair), that too was quickly buried by the MSM along with all the śīśśabdakāra-s.

This closely relates to the duṣkarmāṇi of the śaṭha-cakra centered on Ṣiḍgapatnī in sparking the war with the Rūs. Just like the stories about the legendary WMDs, the Niger yellow cake, “bioterror” labs, and deadly gases (in part supplied by the Āṅglaka-s) of Saddam Hussein, they now started circulating stories about the evils of the Rūs and the Rūsrāṭ. Not just that they presented the Rūs as controlling the mahāmleccha population via their asset (the Picchilaka) in the Śvetālaya itself. The facilitators of this program were some of the same guhyacakra involved in the Eye-rack fiasco and the goroga messaging. The same thing came up in the śyāmajīva and kālāmukha rebellions that they incited to bring down Vijayanāma-vyāpārin. In certain satellite countries of the mahāmlecca world, where nālika-s are not widespread, they used a similar tactic to enforce public containment during the pandemic.

When one compares these actions with the goroga and Eye-rack incidents, one sees a striking commonality. It typically involves the following steps: (1) creation of a favored narrative they wish to plant among the people. It typically goes against the instinct of the masses or aims to incite a deep fear or division in them. (2) It is given an official guise via “leaks” that appear to come from the sources the mleccha-s were trained to respect. When the hastin-s ruled the roost, the masses and also the judges and prosecutors were trained to become cop-/soldier-worshiping zombies who would readily violate their own constitution at the first sight of a uniform and an officially issued nālika in the upholster. This was the mleccha world that the śaṭha-cakra had in hand to manipulate through diverging messaging. Thus, by leaking via one of the “uniformed” praṇidhi institutions, they knew they could get a sizable part of the masses to believe. (3) This is then repeated ad nauseum by their outward-facing network — politicians and MSM entirely — or taken out of the new cycle by the latter, depending on what they want. For instance, the phrase that the Nāriṅgapuruṣa was “a Russian asset” or “dangerous” or as bad as the “hādi-śūlapuruṣa” was repeated non-stop by everyone from ṣiḍgapatnī down to the lowest MSM operative all through the day. On the other hand, if it was Vyādhapiṇḍaka-s machine or the condition of Paḍbīśapuruṣa or of Piṇḍaka himself, then they enforce pin-drop silence. (4) At the higher level, this enforcement is handed over to their newfound allies, the mahāduṣṭa-s like guggulu, mukhagiri, bejha-khalvāṭa, jāketyādi on the tech side and kṛṣṇādri-phuka, agrabhaṭa, sora and the like on the monetary side. (5) On the ground, it is handed over to the chagnyamukha-s and the pogaṇḍasenā. This in essence, is the that was accidentally exposed during a similar attack engineered by the same forces on the H.

Thus, the incidents of the past are relevant to our times because they help us understand the śaṭha-cakra running the mahāmleccha state. One should have no delusions about its destructive intentions not just among the mleccha-s but all around the world. Its old objectives, such as the destruction of the Rūs, now dovetail with its “spiritual” pursuit — the spreading of navyonmāda throughout the world. The zeal here is in every way comparable to the zeal with which they pushed pretonmāda earlier and the marūnmatta-s pushed their cult. They would also not shy away from comparable brutality in that endeavor, albeit cloaked in the pieties befitting the current world. H as svabhāvavairin-s of their Weltanschauung will unsurprisingly be one of their biggest external targets after the Rūs. Hence, no efforts will be spared to drive in the largest explosive charges through the big open gates in the Indian constitution manned by a pliant judiciary even as the election draws near. This will align with the increasingly desperate measures by the dūṣita-māśa to provoke an attack by the Rūs.

Khitans and Mongols: A story of deep and persistent connections-1

While the Chingizid Mongols have long been the focus of students of medieval steppe history, studies over the past 50 years have been steadily contributing to the picture that they were heirs of a previously neglected and even now underappreciated power – the Khitans. The story of the Khitans before their meteoric rise to imperial power was until recently shrouded in the mists of history. This starts with their ethnicity and language. The Iraqi Arab historian Ibn al-Athīr (whose tomb was recently demolished by the al-Qaeda), writing in the 1200s in his al-Kāmil fī al-ta’rīkh records the Islamization of the Turks with almost perceptible glee. He first claimed that a horde of 100000-200000 “tents” of Turks were Islamized (evidently referring to the Qarakhanids, a branch of the Qarluk Turks). Then he mentions that a smaller band of 10000 “tents” were Mohammedanized, after which “only the Khitans and the Tatars remained infidels”. This evidently referred to the Khitans and the Mongols. Based on this, early historians took the Khitans to be another branch of Turks. However, starting from Rashid ad-Din, the physician-historian of Jewish origin, there has been the counter-proposal that they were Mongols. Starting about 70 years ago, this theory was revived and expanded by the Japanese Khitanologists, who proposed that they were a proto-Mongolic group. However, over the past 50 years, the evidence has been decisively building for the Khitans being a para-Mongolic people with a long history before their rise to imperial power. In the first of the notes on this topic, we shall consider some aspects of the timing of the Khitan-Mongol divergence and their prolonged interaction until the absorption of the former by the Chingizid Mongols.

Evidence for the early divergence of the Mongols and the Khitans
One of the watershed moments in Mongolian historical studies was the discovery of the Khüis Tolgoi archaeological site in North Central Mongolia in 1975 by D. Navaan. The site contains two stones with inscriptions in Brāhmī, of which one is relatively better preserved than the other. The decipherment of the first stone has revealed that it encodes an early Mongolic language. The inscription itself mentions Niri Khaghan, specifically as the Khaghan of the Turks. He was a Khaghan of the first Blue Turk empire and was killed around 603 CE while battling the Uighur-led Tiele confederation of Turks to the East. Thus, it is posited that the language of the Khüis Tolgoi inscriptions is a Mongolic tongue spoken by the Rouran Hun Khaghanate that was overthrown by their vassals to found the first Turk Khaghanate. However, even after their rise to power, they appear to have retained the Mongolic language of their erstwhile rulers along with the Brāhmī script in inscriptions during the first Turk Khaghanate. By the time of the second Khaghanate it was replaced by the runic script and the use of their native Turkic language. This indicated that the Rouran Khaghanate was a Mongolic one and that the para-Mongolic languages had separated from the Mongolic languages by the time of that Khaghanate. Indeed, it also cast serious doubts on the Altaic monophyly and suggested that the Turkic-Mongolic linguistic relationship was likely an areal one related to their long contact going back to at least the time of the Khüis Tolgoi inscriptions, if not much earlier.

In parallel, there is the philological question of when the Mongols were first attested in history. This also has a bearing on the origin and affinities of the Khitans. The famous historian Igor de Rachewiltz (himself having some Mongolic ancestry) addressing this issue in the 1990s pointed to the Jiu Tangshu (Old Book of Tang), an encyclopedic work centered on the history of the Tang (though it covers much more, e.g., religion and science) which was completed in 945 CE. Therein, a tribal alliance to the north is mentioned as Meng-wu, which de Rachewiltz interprets as being the Chinese transcription representing an original that might have sounded like Mongghut or Mongghul. Given that this text refers to events in the 800s, it is conceivable that the Mongol ethnonym was already in place by then. Notably, this name is coupled with another name, evidently indicating a northern tribal confederation that was known to the Tang: Mengwu-Shiwei. The second name of this dyad, Shiwei, occurs in multiple Chinese annals: (i) The Weishu says: “The Shiwei language was the same as those of the Kumo Xi (Qay in para-Mongolic), Khitan and Doumolou States.” This might refer to a situation as early as the 400s of CE. (ii) The Suishu also discusses Shiwei along with the Khitan – “The Shiwei were the same kind of people as the Khitan. The southern part was called the Khitan, while the northern part was called the Shiwei.” This might refer to the situation in the later 500s to the early 600s of CE. (iii) Jiu Tangshu states: “The Shiwei were a collateral branch of the Khitan.” In the Tang age (788 CE), according to the New Book of Tang, a confederation of two of the steppe tribes mentioned in the Weishu, the Xi and the Shiwei, launched a simultaneous attack on both the Uighurs and the Tang, killing several of their officials, plundering their livestock and enslaving many. Taken together, these accounts suggest that the Shiwei were ethnically and linguistically related to the Khitan, but were distinct from the tribe that spawned the imperial dynasty of the latter. Through a series of campaigns spanning several generations, the precursors of the imperial Khitans appear to have conquered and absorbed the Shiwei. In the 1200s, the Qidan Guo Zhi, a history of the Khitan empire in China, was composed in the Song rump state just before it fell to the Mongols. It states that the “five-surname” Xi and the “seven-tribe Shiwei” submitted and joined the Khitan when Yelü Abaoji (Yaruud Ambagai, the first imperial Khitan Khaghan) became the supreme ruler through his heroism. Thus, if these dynastic records are not conflating different northern tribal alliances, they indicate a confederation between the Mongols and a Khitan-related group, the Shiwei, even in the Tang age. Andrew Shimunek reconstructs the Para-Mongolic word transcribed in Chinese as Shiwei to be Shirwi, an ethnonym related to Serbi, (=Xianbei in Chinese transcription, see below), the ancestral group from which the Khitan arose. A corollary is that the Mongols and the Khitans had diverged by the Tang times and were seen as distinct groups.

In the same work mentioned above, de Rachewiltz wrote: “Regarding the etymology of the name Mongghul, the ending ghul may be a suffix denoting a clan, tribe or people. If so, we are left with the root mong, the origin and meaning of which still elude us.” Even if its meaning eludes us, Golden pointed out that the Weishu names one of the founding Khans of Rouran Khaghanate as Mugulü, which was probably an Early Middle Chinese transcription that dropped the nasal. Then it is possible that the Mongol ethnonym emerged from this founding Khaghan who broke free from the Xianbei confederation (see below) in the closing years of the 200s or early 300s of CE. Support for this unconventional explanation comes from an unexpected source in the Khotanese language, a successor of the older East Iranic Śaka language. An important bauddha text, the book of Zambasta, has come down to us in fragments written in this language. It mentions the invasion of Khotan by five enemies: Māṃkuya, Red Khocas, Hūṇa-s, Ciṃgga-s and the Supīya-s:
māṃkuya rro īnda heinā kho—ca u huna ciṃgga supīya |
kye naa hvataana-kṣīru bajo—ttanda ttu ju ye gṣvu ne oysde ||
Emmerick translated this as: There are the Māṃkuya-s, Red Khoca-s and Hūṇa-s, Ciṃgga-s and Supīya-s, who have harmed our Khotanese land. For a time, one has not been angry about this. Now Ciṃgga-s are well known to be the Cīna-s who ravaged Khotan (a battle where the gods are said to have interceded between the Hindus and the Cīna-s; Khotan is still occupied by the modern Chinese state). Supīya-s have been identified as the Tibetans. The red Khoca-s have been identified as the Tuyuhun (using Cīna transcription) khaghnate that emerged from the Xianbei as their faces have been found painted red in their grave sites. The Hūṇa-s have been identified as one of the Hun groups. So, who were the Māṃkuya?

The only invaders that conquered Khotan who have not been accounted for are the Rouran Khaghanate. Even in the 1950s, Bailey recognized that what was rendered as Māṃkuya, would have been originally something like Monguya in a Turkic or Mongolic language. Thus, given the name of the founding Khaghan, the Māṃkuya were probably the Rouran, going by the name of the horde of Mugulü. Vaissiere suggests that this might indeed be the first occurrence of an ethnonym later presenting as Mongol. This, taken together with the language of the Khüis Tolgoi inscriptions, suggests that a predecessor of the later Mongol language and a version of the ethnonym related to the founding leader of the Khaghanate was already in place in the age of the Rouran ≈ 300-555 CE. It is notable that, despite the origin mythology of the Secret History, the Chingizid Mongols did not name their empire after their Kiyat>Borjigin lineage but as the Ulūs of the Mongols. Their resorting to an older ethnonym suggests that it had certain prestige and special significance in their midst – it was likely held as a faint memory of the old Khaghanate.

These observations bring the antiquity of the Mongolic people to the same general period as the first records of the Khitans in the Chinese and Korean annals. Their early history is intimately linked to the rise of a confederation on the Mongolian steppe known as the Xianbei. This name is seen as a Chinese transcription, using two logographs representing ser and bi, of a para-Mongolic (see below) ethnonym of the form *Serbi, related to *Shirwi (Shiwei). Tentatively, the relevant early history of this confederation can be reconstructed thus (all translations in the rest of this section, unless noted otherwise, are from the excellent database of Xu Elina-Qian): In 87 CE, the Xianbei alliance killed the Hun (Xiongnu) Chanyu and emerged as an independent confederation of tribes on the Southern Mongolian steppe. In the first half of the 100s of CE, their power was consolidated by the Khaghans Duruggu and his powerful son Daldaghai/ Dardaghai (see below), who founded a vast but short-lived empire. Based on onomastic data from the Sanguo Zhi, we can infer that the latter Khaghan brought together, para-Mongolic, Mongolic and Indo-Iranian chiefs under his command. As an aside, the last of these might have a bearing on the origin of the later “Aryan’’ Huns (Alkhan). While this empire collapsed in the 180s of CE, the Xianbei remained a force. In the coming centuries, they were locked in conflict and cooperation with Xiongnu Huns, the Han Empire, the successor Chinese warlords, the 3 kingdoms and the Two Jins dynasty.

After a partial reunification by the powerful Khaghan Kebineng (likely transcription for Kaypirdagh), in the early 200s, the Xianbei splintered again, and their elite clans gave rise to several states in the Sinosphere and its surroundings. One key player in these dynamics was the Murong (transcription for Baglu) clan, who descended from an erstwhile commander during the first unification. Chief among the states founded by the splintering Xianbei were the Former Yan (337-370 CE), the Northern (Tuoba) Wei (386-555 CE) and the Tuyuhun Khaghanate (280s onward). In the 280s, one of the Xianbei chiefs, Murong Tuyuhun, founded the eponymous Khaghanate centered on the Kokonor region, while his nephew, the gigantic Murong Huang (comparable gigantism was to be a recurrent theme among the Khitans too, and will be mentioned in part 2), founded the Former Yan Kingdom in Northeastern China in 337 CE. Another group from the old Xianbei confederation, the Taghbach clan (which likely absorbed some steppe Iranic Śaka elements), founded the Northern Wei empire, which eventually went on to encompass northern China. A further branch of the Taghbach clan founded the short-lived Southern Liang kingdom (310-376 CE), while other descendants of this clan laid the foundations of the Tangut kingdom that bloomed much later in history. The Northern Wei went on to defeat the remnants of the old Huns (Xiongnu) and also destroyed the remnant of the Yan state. Recording the remote pre-dynastic Khitan history, their annals (Liaoshi) note that in 344 CE, Murong Huang moved against the remaining Xianbei to the north and smashed them. The survivors split up into the Yuwen, the Kumo Xi and the Khitan. This seems to be the earliest memory of the Khitan as a distinct tribe. Notably, the names of the chief of the Yuwen are transcribed as Xiduguan, Qidegui, or Qitegui, which are seen as related to the name Khitan. Thus, even as proposed above for the ethnonym Mongol, the ethnonym Khitan probably originated from the name of an early leader.

The Korean history, Sanguo Shiji, written in Chinese, mentions that in 378 CE, the Khitan attacked the Koguryŏ from the north and defeated their eight tribes. This shows that within 30 years of the defeat at the hands of their former Xianbei associates, the Khitans had emerged as an independent power in what is today Manchuria and were threatening the Korean kingdom. The Koreans eventually retaliated by forming an alliance with the Rouran Khaghanate and mounted a pincer-grip attack on the Khitan. This forced them to retreat from their lands to what is today the Liaoning Province in China. The return to power of the Khitan is indicated by a conflict with the Blue Turks mentioned by the Sui Shu in 585 CE, where the Khaghan of the Turks is said to have been forced to run to the Sui and seek their aid when threatened with an attack by the Khaghan of the Khitans. However, shortly thereafter, the same annals record an internal conflict that weakened the Khitans. Though weakened, the Khitan invaded the Sui-held land in 605 CE. However, they were a shadow of their former self from internal upheavals — in 605 CE, according to the New Book of Tang, the Turks retaliated by forming an alliance with the Sui and launched a genocidal assault on the Khitans resulting in their defeat. 40,000 of their men and women with livestock are said to have been captured – the men were all killed, and the women and animals were taken by the Turks. The Khitan appear to have been completely conquered by the Turks in the period that followed, and some of them fled to Chinese territories. Nevertheless, as we shall see below and in future notes, they were not done, and continued a prolonged struggle with their rivals till their time came more than two hundred years down the line.

In conclusion, the above historical exploration suggests that the Mongols and the Khitans were definitely separate groups by the time of the Rouran Khaghanate. The Chinese annals further trace the origin of the Khitans to the Xianbei tribal confederation in the 300s of CE. This is confirmed by the internal evidence of the Khitans themselves. In 1992 CE, a Khitan funerary inscription was discovered in Inner Mongolia – the memorial tablet of Yelü Yuzhi – wherein it is clearly stated that he was a descendant of their ancestral Khaghan named Qishou, who in turn is said to be descended from Tanshihuai. This Tanshihuai (Chinese transcription of the original para-Mongolic Daldaghai or Dardaghai) was none other than the great Xianbei Khaghan, who could be seen as a para-Mongolic Chingiz Khan, who almost “made it”. He led his forces on vast conquering expeditions across swathes of the steppe from the northern Korean coast to the Caspian Sea between 136-182 CE. From the eastern reaches of his empire, his forces might have even launched amphibious raids on Japan and introduced steppe traditions to that land. The Tibetan Dunhuang Document P. T. 1283 (a record of the Turkic and (Para)Mongolic kingdoms/tribes to the north of the Tibetans) states that “The Khitan…their language and that of the Tuyuhun could generally be understood by each other.” Given that Tuyuhun were a distinct branch of the Xianbei confederation, this statement strongly supports a common linguistic foundation for most of this tribal alliance and that the Khitan were indeed a branch of the Xianbei. While most Chinese sources trace the origin of the Rouran Khaghanate to the remnants of the Xiongnu after their defeat by the Xianbei, they provide a relatively confused account of the earlier history of the Xianbei. The account of the Hou Hanshu, repeated by much later accounts like the New Book of Tang, states that the Xianbei were a branch of the “eastern barbarians”, known as the Donghu. They are said to have been defeated and scattered by the Xiongnu when they rose to power under their first Chanyu (Shanyu= Tarkhan) Bagatur (Maodun). However, the Jiu Wudai Shi’s account, again repeated by others, states that the “The Khitan were of ancient Xiongnu origin.” We suspect that the Xianbei and the Xiongnu were distinct but related peoples who interacted with each other. When each rose to power, it incorporated defeated elements of the other within its system of tribal alliances. A similar Xiongnu origin is also proposed for the Uighurs and the Blue Turks by some Chinese sources. This might merely reflect the fact that the Turks were indeed subordinates of the Rouran (who were Xiongnu-derived) before they overthrew their former overlords. We support a model wherein the basic split between a Mongolic and Serbi = Xianbei groups goes back to the Xiongnu period; however, the two kept interacting with each other and other linguistically distant or unrelated groups, like the Turks and probably the Tungus. In the next section, we shall look at this from the perspective of what we are learning from the ongoing attempt to understand the Khitan language.

The Khitan scripts and gleanings from their language
Abaoji, the founder the Khitan empire, is stated as saying: “I can [use] the Han language, yet I refuse to speak it with the [fellow] tribesmen, fearing that they would emulate the Han and become timid and weak.” -New History of the Five Dynasties (translation by Victor Mair).
At the time of the establishment of their empire in 916 CE, the Khitan knew the Chinese language, but their elites were keen not to assimilate and lose their own, unlike some of the earlier (Para)Mongolic dynasties established in China. However, Abaoji saw the advantages of a structured connection with the Sinosphere and moved on to establish a dual government, wherein he presided over one council of elites on the steppe (based on the old Khitan nobility and election system) and a separate second one which was specifically for his Chinese possessions, where he figured as the emperor with the mandate of Heaven. A Chinese acquaintance of mine felt that this Liao dual model provided inspiration for a political system that has lasted till current times in the form of the arrangement with Hong Kong and the intended arrangement after the conquest of Taiwan. The above statement by the Khaghan was probably to assure his elites that he clearly saw the danger in Sinicization and sought to resist it. This conscious filter, with respect to Han norms, might have played a big role in the longevity of the Khitan as a great power. It also ensured that they did not forsake their own language for Chinese even though they adopted Han refugees into their family and, in part, acquired the desire to have a script for their language from them.

As a result of adopting scripts early, unlike many mystery peoples of the steppe, the Khitans have left behind a corpus of written material – it is just that they remain largely undeciphered. Given that the Rouran Khaghanate language was already distinctly Mongolic, much greater progress would have been made with the decipherment of the Khitan language, if it had also been Mongolic. However, if it were the distant relative of Mongolic – like two distinct families within the Indo-European superfamily – then its intelligibility vis-a-vis Mongolic proper would be low. At the time of the rise of the Chingizid Mongols, there were definitely somewhat different branches of the Mongolic proper clade, like the languages of the Kereit, the Naiman, the Tatar, the Oirat, the Ongniut and perhaps also the Merkit (which could have been Turkic too) as suggested by the lexical variants in the Secret History and written Chingizid Mongol (e.g., ebül in the old written language vs übül for winter; edür vs üdür for day). Indeed, as proposed rather early on by the Russian researcher Vladimirtsov, it is quite likely the Chingizid Mongols acquired the Naiman dialect of Mongolic as the basis of their literary language more or less ready-made, when they absorbed their Uighur scribe, curiously named Tata(r) Tonga. By extending this consideration, there could have been much earlier-branching sister languages to the above Mongolic clade. These would be the para-Mongolic languages of which Khitan could have been one. The picture emerging from the ongoing study of the Khitan language supports this idea. This study is centered on deciphering the mystery scripts in which the Khitans wrote their language.

The Chinese chronicle of the Khitan empire, Liaoshi, noted that they used two scripts. Exemplars of both these scripts survive and are known as the large script and the small script. The Liaoshi preserves a record of how these scripts were invented. Regarding the large script, we have this account:
“By the reign of Abaoji [the first Khaghan of the imperial Khitan state], several smaller neighboring states had been subdued and annexed. He employed many Chinese, who taught them how to write by altering characters in the clerical script, adding here and cutting there. They created a script of several thousand characters, replacing the contracts made by making notches on wood” -New History of the Five Dynasties. Appendix on the Four Barbarians (Translation via Daniel Kane).
Thus, the large script was explicitly inspired by the Chinese model and is a logographic script like it. While it was inspired by the Chinese script, it should be understood that by no means it was the same or even equivalent in any straight-forward way to the Chinese script. It seems as though the Khitan elite deliberately wanted to make it private to the Khitans and difficult for the Chinese to understand. The rapid adoption of a script by the dynastic founder of the imperial Khitans is remarkably parallel to the adoption of the Uighur script by the Chingizid Mongols to represent their language. The Uighurs also figure in the script story of the Khitans; however, in this case, it was the small script:
“Uighur messengers came to court, but there was no one who could understand their language (Turkic and Khitan were mutually unintelligible). The empress [Shulü Ping; she was from a clan of Uighur ancestry absorbed into the Khitans] said to Taizu [Abaoji, the founding Khaghan], “Diela [Abaoji’s brother] is clever. He may be sent to welcome them.” By being in their company for twenty days he was able to learn their spoken language and script. Then he created a script of smaller Kitan characters which, though few in number, covered everything.” -Liaoshi (Translation via Daniel Kane)
Thus, the script created by Diela, a syllabary, reminds one of the Mongols having Phagspa create a new Brahmic family script for them – they were even more ambitious than the Khitans and saw it as a universal script for all world languages. Diela’s small script can also be compared to the Korean invention of hangul, which might have been inspired by Phagspa in turn.

Both scripts were used in the Khitan empire and the successor Qara Khitai Khaghanate till the very end. An adaptation of the large script continued to be used by their enemies, the Jurchen, who overthrew the Khitan empire in Northern China. The main progress in tackling them has been via alignment with the bilingual inscriptions with a Chinese text – a relationship first discovered in the 1920s by the Japanese researcher Haneda Toru. At that point, bilingual inscriptions had helped in deciphering the Turkic runic script, but the Khitan texts proved way more difficult and remain poorly understood to date. A major discovery was made in the 1950s when a book of 127 pages written in the large script was discovered in Kyrgyzstan, possibly in the ruins of a Qara Khitai site. However, it remained neglected until 2010 CE when Zaitsev realized it was in the large script written sometime after 1054 CE. While its decipherment remains a major challenge, he proposed that it might contain part of a text known as the record of “Khaghans of the Great Central xu.Ulji Khitan State”. Consistent with this, a frequent occurrence of the characters for “state” and “Khaghan” or emperor has been noted in the book. The studies of researchers like Chinggertei, Aisin Gioro Ulhicun and Daniel Kane have started providing us with a gradually accumulating profile of the Khitan language. We have words of what might be termed the core vocabulary, like the numerals, the names of the zodiacal animals, seasons and directions. For example: Kh: namur = Mo: namar (autumn); Kh: tau = Mo: tav (five); Kh: taulia = Mo: taulai (hare); Kh: muhoo = Mo: mogoi (snake); Kh: uni = Mo: uniye (cow); Kh: ciis = Mo: cisu (blood); Kh: naici = Mo: nayija (friend); Further, an Arabic historical record on the calendrical systems of various peoples recently provided the sound values for the Khitan words for the zodiacal animals. This indicated that the tiger was known by the taboo word khaghanas – evidently, implying the king of the animals.

We also know from the available decipherment that the Khitan state called itself the xu.ulji kitan gur. The terminal part of this phrase is the word for state, gur. Apparently, it survived as a loan in the language of the enemy of the Khitans, the Jurchen, as gurun that continued to be used by the Manchu. Its exact provenance remains contentious. On one hand, it could be homologous to the similar-sounding Mongol word gür meaning large, wide, general, or common, and already known in the Secret History. However, it is more likely that it was a rendering of the Chinese word guo, meaning state – indeed, a glyph similar to the Chinese word was used for the word in the large script. This implies that the title Gur-khan used by the rulers of the Qara Khitai simply meant Khan of the state, a proposal supported by what can be gleaned from the still mostly undeciphered book. This also suggests that Chingiz Khan’s rival, the Mongol Jamuqa, adopted the title from the Khitan usage. In the initial part of the phrase, the second glyph was read by Aisin Gioro as ulji and recognized by Kane as a homolog of the Mongol word üljei, which appears in the Secret History olje and in the names of Mongol royalty, as Öljeitü. It means “good fortune” – thus, it would be a good fit as an adjective for the state – the fortunate state. Consistent with this, the same glyph as ulji was used by the Jurchen for their word for “good fortune.” The sound value of the first part of the initial term, which is transcribed in Chinese as xu, is unclear. De Rachewiltz felt that it might have been a cognate of a Turkic loan, also found in Mongolic, qut, which could be rendered as heavenly blessing. It frequently occurs in the names of Turkic Khaghans and titles. For instance, the Uighur lords of Kocho had the title Idiqut and the great Uighur leader who founded their empire went by the dynastic name Qutlugh Bilge Khaghan. Thus, it might have played the same role as the Chinese concept of the “mandate of heaven”. If this were true, then the full title of the state could be rendered as the fortunate Khitan state bearing the mandate of heaven.

Thus, despite glimpses of possible Chinese and Turkic influences, there is strong evidence that the Khitan language is related to Mongolic rather than to Tungusic, Koreanic, or Turkic. Given the considerations in the previous section that the Khitans emerged from the Xianbei confederation, and had a language related to that of other Xianbei successor states (e.g., Tuyuhun in the Dunhuang Tibetan manuscript), we can say that their language can indeed be seen as a late-surviving para-Mongolic Serbi language. Thus, we believe the weight of the evidence favors Shimunek’s masterly thesis in support of a Serbi-Mongolic family. The only place where we would differ from his classification is the position of the Rouran language. Based on the Khüis Tolgoi data, we would currently place it as an early branch of the Mongolic rather than the Serbi clade. Given that the Serbi and Mongolic languages were definitely separate by the time of the Rouran and Northern Wei states, and likely much earlier during the Xiongnu period itself, we can infer that the original Khitan and Mongolic divergence was a deep one – by the time of the founding of the Mongol ulus they were probably already separated by at least around 1500 years. One could postulate a proto-Serbi-Mongolian dialect continuum in the region encompassing Mongolia and the regions north and east of the modern Hebei province of China in the time window of the “Warring States” period of Chinese history. However, given their prolonged interaction over this period, there was probably convergence through ongoing lateral transfers following their divergence. This probably made them more similar than the divergence time would suggest. This convergence through lateral transfer is particularly apparent in titles and probably personal names. We saw above how Jamuqa’s title gur-khan was likely adopted from the Khitans. Similarly, the name of the first dynastic Khitan Khaghan, Abaoji can be reconstructed as Ambagai or Ambakhai in the Khitan language. This is identical to the name of one of the pre-Chingizid Borjigin Khans, Ambaghai. One wonders if the Borjigin consciously chose his name after the mighty Khitan Khaghan. Conversely, in 950 CE, the Khitan Khaghan Yelü Ruan and Khatun Xiao Sagezhi named their daughter Menggu, whose original pronunciation was likely close to the ethnonym of the Mongols and inspired by it.

This “recombination” between the Serbi-Mongolic languages is also paralleled in the long timeline of the areal convergence between Turkic and Serbi-Mongolic, which began as distinct language families. Some of the regular sound correspondences between Turkic and Serbi-Mongolic suggest that this interaction began early, probably again right in the Xiongnu period or prior to that, supporting the reports in the Chinese annals that there were Turkic tribal elements in the Xiongnu confederation. Examples of these include the d-y correspondence: e.g., Mo: dayir = Tu (Khaghanate dialect): yariz (brownish); the r-z correspondence: e.g., Mo: ikkir = Tu= ikkiz (twins, a word transferred from Serbi-Mongolic to Hungarian). Finally, having an easterly locus, the Khitan also had a long-standing association with Koreanic. We suspect that this contributed to the “Altaicization” of Koreanic, which in turn gives the signal for the likely non-genetic Macro-Altaic hypothesis.

To conclude this part, we may briefly consider the genetic evidence in light of the Serbi-Mongolian hypothesis. Recent studies have shown that the available Xianbei sites show a high frequency of males with Y-haplogroup C. A similar haplogroup is also seen in a subset of the Xiongnu-age males. A lineage within the C haplogroup also shows evidence of a dramatic expansion in the Mongols in the last 1000 years – some attribute it to the male line of Chingiz Khan’s clan. The modern Dagur or Daur Mongols are believed to have descended from Khitans assimilated into the Mongols. There are some hints that their language preserves part of the old Khitan vocabulary. The Daur show enrichment of a Y chromosome haplogroup that is a brother group to the expanded C-M217 clade attributed to the clan of Chingiz Khan. Together, these observations are not incompatible with the linguistic Serbi-Mongolic hypothesis and suggest the presence of the common ancestor of these languages in pre-Xiongnu Ulaan-Zuukh/Slab Grave archaeological cultures.

A simplified representation of the Serbi-Mongolic hypothesis (primarily based on Shimunek) with possible lateral transfer edges shown as dashed lines.

The rise of the psychopath oligarchy

There are certain things in (geo)politics that are largely unsurprising to us because we had seen their seeds over a decade or two ago. In part, we were able to infer several things correctly in advance due to a few simple reasons. First, we have spent most of our life as an alien — outside of our small inner circle, we have mostly lived in the midst of and transacted with people who were very unlike us. The type of difference included, singly or together, ethnicity, religion, food preferences, linguistic attitudes, knowledge of the sciences, and philosophy. Second, when people speak to us in real life, for at least the beginning of the conversation, we say little and let them say what they want and how they feel about things. Most people honestly convey their thoughts when they are confronted by someone who does not engage in social reputation games. The remainder who are dishonest are an interesting class (see below) and can be made out through close examination. Third, irrespective of the group in which we find ourselves, we never lose sight of the fact that we are biological entities, the product of a chain of natural selection (at to a degree drift) events. Finally, we accept the fact that history tends to rhyme and a comparison with past cycles is typically illuminating. If we saw several things correctly, then there is really no need to waste words by repeating what has been said before. So why this exercise in svastuti? It is hard to stop the urge that arises every now and then to remark about this or that facet of political unfolding. The above is merely a prolog to one such excursus.

A pervasive theme in biology is the repeated emergence of policing in cooperative ensembles. We see this at the most fundamental level, within genomes. A genome of an organism can be seen as a cooperating ensemble of genes that replicate in consort and pass an equal copy of themselves as all other genes in the genome to the next generation. However, there are genes that could break this cooperativity by making additional copies of themselves while the rest make a single one. These are typically termed mobile selfish elements. Such selfish elements can often be deleterious to the organismal genome taken as a whole, though they may also directly or indirectly provide a number of immediate and future advantages to the cellular genome. Hence, the organismal genome is best positioned when it maintains a certain number of these selfish elements, but simultaneously polices their selfish activity and keeps it under control. Indeed, a whole slew of mechanisms have evolved to police such selfish elements — for example, DNA methylation to minimize their transcriptional expression or small RNA-PIWI-based pathways to post-transcriptionally repress them.

At the organismal level, policing is best studied in hymenopteran societies which tend to have one or few reproductive females (usually called queens). Typically, the other females — the workers and other castes — are not constitutionally infertile as they come from the same genome as the queens. Hence, they too can lay eggs when the circumstance avails itself. Indeed, such egg-laying by the workers is widely observed across Hymenoptera; however, policing has independently evolved on multiple occasions to suppress egg-laying or eliminate the eggs of the workers. Work by Oldroyd, Ratnieks and colleagues has documented that this policing of worker fertility is lost in the case of the anarchic syndrome, where the workers stop being fertile and switch to a reproductive state. Such colonies produce a lot of males from unfertilized eggs that the workers lay, and their mothers try to raise them as queens! They soon start neglecting their maintenance work and the colony progressively loses its ability to feed itself and collapses. In Africa, a parasitic form of the Cape honeybee presents an infectious version of the anarchic syndrome (just like the selfish elements that jump from genome to genome — sometimes closely related or no different from viruses). This parasitic anarch invades intact hives of proper queen-run honeybees using a chemical subterfuge likely involving mimicry of discriminant hydrocarbons. There, they do no work, and, instead of laying haploid eggs like in spontaneous cases of the anarchy syndrome, lay diploid eggs producing clones of themselves. Fooled by the chemical mimicry, the host colony workers take them to be queens and focus on their rearing even as they neglect their own kin and hive resulting in colony collapse just as in the classic anarchic syndrome. However, here the parasitic anarchs, having reproduced, merely move on to another colony. In the early 2000s, this disease had spread across the entire region from South Africa to Mozambique destroying entire commercial beekeeping ventures. Thus, the lack of policing, just like for a genome, can also result in the collapse of society in hymenopterans.

With this background, we will turn to human society via a psychological detour. More than two and a half decades ago our paths intersected with two individuals, who struck us as having an interesting psychological profile. They were entirely socialized in the sense of not having any overt antisocial impulses. Both had subjected themselves to authority (much more than we had — we always had a disdain for authority) to obtain themselves a good or even high-quality education. However, in interacting with them, we noticed that both were characterized by low or absent empathy, lack of remorse for negative actions, and a sense of self-worth despite certain obvious disadvantages. One of them was also characterized by an effusive faux friendliness, which we immediately saw through, and a high degree of stress resistance. We had remarked to ourselves that they almost had an element of psychopathy — something which we sensed despite their superficial politeness — primarily because we never saw them perceive the obvious suffering of other humans. Over the next 5 years or so, one of them met with success in a specific domain despite his conspicuous shortcomings in “an open game” and met his objectives notwithstanding the stress he was under. The second individual was even more successful: he maxed out on many of the common male desires (except one, where he got his timing a bit wrong), all without really doing much in terms of using his technical knowledge, rather, by merely plying his faux charm and a certain outright cunning which he completely covered up with the former. These individuals embodied an archetype that was described by psychologist Dutton in his book on psychopaths. Dutton has an almost laudatory view of these “socialized psychopaths”. While we appreciate the potential benefit of a certain (small) number of such psychopaths to a society, we take a dimmer view of them when their numbers grow, and the ability to socially police them declines.

One can see that certain professions would easily benefit from a degree of psychopathy — as we have discussed before, a surgeon or a physician who scores higher on the psychopathic spectrum might be able to function much longer in these professions which would otherwise “burnout” the normies because of empathetic overload. Indeed, we have seen actual cases of such empathetic overload among physicians. In particular, in a surgeon, that willingness to engage in surgical procedures should come with a degree of inclination towards psychopathic activity. Thus, the functional lifespan in these professions likely rises with psychopathy. However, we believe this increased advantage is not unbounded, as psychopathy beyond a certain point in the spectrum also results in anti-social behaviors that might be too much for a society to accommodate — e.g., utter disregard for the patient’s life. Given that several studies indicate a clear genetic basis for psychopathy (e.g., famously Fallon’s case of the Monoamine oxidase A variation), we posit that this variation would be under balancing selection from two forces. First, the building up of pro-psychopathic variation, resulting in increasing psychopathy would cause anti-social behavior that will face the axe of policing. Thus, policing will tamp down the runaway selection for pro-psychopathic alleles. Now, if policing were weak, say under high kinship societies (something empirically known from Hymenoptera), then such alleles could rise in number. However, again based on the anarchy syndrome in Hymenoptera, we argue that there will be an upper bound for the number of psychopaths it can accommodate, irrespective of their overall utility to the group, after which the society collapses.

The above projections primarily apply to what we would term “small world societies” — namely entities like tribes, villages, and small towns. Here people tend to entirely or mostly know each other. Gossip would be a powerful mechanism to enable policing. Thus, across these social ensembles, the spread of psychopathic behavior would be considerably limited by direct policing. In a tribal society, kinship would be high; hence, policing might be weaker; however, here group selection acting via colony collapse and the danger of losing resources to rival tribes with greater cooperative behavior would again select groups that limit the spread of psychopathy. As we move from “small world” to “big world” societies — large cities and states — the selective landscape changes considerably. One type of coalescence could involve a smaller ethnic group living within a much larger one, often engaging in some kind of symbiosis. In such a scenario, one could imagine the emergence of a “psychopathy switch”. Such a switch could evolve from or be an extension to a much older “aggression switch” — a more favorable interaction with in-group members is flipped to an antagonistic interaction when out-group members are detected. Thus, the smaller ethnic group could limit psychopathic behavior within the group while exhibiting it in interactions with the out-group (it could be seen as a “domesticated” form of aggression compatible with larger social ensembles). Now a larger out-group might learn to detect this behavior and turn against the smaller one putting it in danger of obliteration. Hence, this behavior will necessarily spark an arms race between the two groups which might stabilize under the following conditions: (i) the psychopathic behavior of the smaller group is coupled with an “addiction module” — some kind of essentials service or provision which the larger host group would be willing to pay some cost for. (ii) The smaller group evolves a mechanism of subterfuge which effectively masks their psychopathic behavior towards the outgroup, making it hard to detect. This adaptation might have gone hand-in-hand with a key dimension of psychopathy — that improved lubrication between the brain and the mouth — glib talking or superficially charming behaviors that conceal the downsides effectively. (iii) Motility — the smaller group tends to be physically mobile within a larger host population; hence, the repeated interactions between the same subset of individuals in the host population are infrequent. This lowers the opportunity for learning the displays of psychopathy by the smaller group. Further, the host population being large and distributed over a wide area prevented the spread (in pre-modern times) of the knowledge of psychopathic behavior by the smaller group across the host population for its defenses to be alerted.

Further, the rise of “big world” societies offered other opportunities for stabilizing out-group-directed psychopathic behavior by smaller ethnic groups constituting them. First, the group exhibiting such behavior might cooperate with another group that has the capacity to punish those who retaliate against the psychopathy. This might make the pair a successful couple that could dominate a larger host population. Second, multiple smaller groups constituting a multi-ethnic “big world” society could be locked in a balancing conflict of outgroup-directed psychopathy like the rock-paper-scissors game. Here they could either converge to a stable equilibrium or lapse into chaotic dynamics with no one group dominating the others. Thus, we hold that the rise of large cities and states, especially multiethnic ones, provided the right conditions selecting for the emergence of groups with a high frequency of individuals displaying out-group-directed psychopathy. Moreover, even in a relatively homoethnic “big world” society, individuals displaying this constellation of traits were likely to be selected for. In the former case, such societies potentially increase the stress on the individual due to the danger of large-scale ethnic conflict. Thus, one can see how stress resistance would be selected. As we saw above, superficially charming behavior would be selected as a subterfuge strategy. Finally, a frontier society, viz., one into which a large group of humans are expanding could also provide the necessary conditions that favor a greater fraction of psychopaths than a small-world ensemble. We posit that such a situation was prevalent during the expansion of the Anglosphere into North America and Australia. We also hold that, at least in North America and probably some European nations, the Neo-Euro-Abrahamistic idea of the state having a welfare role for the undeserving and control over minor children overriding that of the parents has exacerbated the problems arising from the selection for psychopathy.

There are two other modern systems that we believe specifically favor the rise of psychopaths due to the near absence of policing in them. One is the modern Euro-American academia. The enterprise is founded on the horrific system of anonymous peer review. This is then coupled with a currency and tenure system based on journal impact factors (magazines publishing short articles have a higher impact factor) and publication counts, a conference speaking circuit with short talks for an abbreviated attention span, and a funding system with an emphasis on sales pitches more than the actual performance of science. Such a system selects for psychopathy as the downsides are few — indeed, we would say that one of the easiest ways to find some rather finished products in this regard is to walk through the Euro-American academe and its imitations elsewhere in the world. The second system with a similar ecology is the post-world-wide-web software-centric tech sector. These giant corporations employing people from around the world, often favoring some ethnicities over others, in disregard of merit, provide a multilevel hierarchy for ascent. This brings together large bodies of people with no deep socio-ethnic connections with each other to spend their day in transactional environments. The climb through the hierarchies in such systems will select for psychopathic traits. Moreover, at the top of the hierarchy are individuals who might be locked in competition with other mega-lords who are seriously endowed with a glut of such traits. Thus, these two systems, which are very recent additions to the sphere of human productivity join some of the older guilds, such as officials of the police (deep) state and trading, which are enriched in individuals with psychopathic traits. We also suspect that the selection for such traits has gone together with a psychological adaptation of self-deception — you engage in unethical behavior more readily if you have first convinced yourself that you are doing something good. This aspect relates to a particular facet of the psychopathic behavioral complex — the enhanced sense of self-worth. Further, this resonates well with the memetic savior complex coming from the viral versions of the West Asian religious complex that form the undergirding of “Western civilization”. Thus, the psychopathic individuals selected by these modern developments are likely to also come with an inbuilt shield of self-delusion that makes them think that they are doing good to the world via their actions.

The past seven years have seen something remarkable among the mahāmleccha-s. The tech oligarchy working with the deep state completed their coup de tat to place a puppet on the mahāsandi and run the show as the backend. Given the above, we believe that this oligarchy which is essentially running the state is enriched in individuals who are high on the psychopathy spectrum. Moreover, we also believe that this makes them susceptible to ideas that enhance their self-worth via self-deception with respect to the harm they cause the rest of society. Over the past two decades the main memetic complex, which has enabled this is navyonmāda. Thus, their takeover of the rājya, especially after they facilitated the overthrow of the nāriṅgapuruṣa, has placed them in a position to cause immense harm to society. Among the mleccha-s the state control of children, overriding the parents, provides them with a special advantage to create and mobilize a generation of zombies who have been indoctrinated with their mental disease. This is enhanced by two factors. First, as we noted before, the Euro-American academe has already been infested with navyonmatta psychopaths. Hence, it is very hard to get a decent education, especially in the American credentialing system. Moreover, the much-vaunted credentials will be available only if one conforms to navyonmāda. Second, the frontier nature of the mahāmleccha nation has favored a highly individualistic and therefore atomized society — well illustrated by the lack of public transport, the unreasonable love for cars and long commutes — also a favorable environment for the rise of those high on the psychopathic spectrum. Against this backdrop, the social decline facilitated by the elite enriched in psychopathy was exacerbated by the arrival of the pandemic resulting in a large population of young individuals with unfavorable mental states. Such a population in turn is ripe for further manipulation by the ideologies blithely dispersed by the psychopaths in power. Thus, the decline in social policing soon translates into an actual loss of policing in the cities of California and New York. Given the global networks of these psychopathic elites, their anti-social tendencies will not remain confined to Krauñcadvīpa but also manifest in other nations, especially those that readily mimic them. If this reading is anywhere close to correct, then what faces us is the equivalent of colony collapse in a hymenopteran society.

The rise of yajña and Kauśika exceptionalism

The extant Vedic ritual is bifurcated into two domains the gṛhya (the household rites and rites of passage) and the śrauta (large-scale/grand rituals). First, in operational terms, they are distinguished by the use of a single fire (the aupāsana) in the former and the three fires with the central vedi in the latter; the grander śrauta rites involve the construction of a more complex system of altars. Second, the gṛhya rites are either done by the ritual patron by himself or with a single ritual specialist, the purohita. In contrast, the śrauta rituals involve an increasingly larger number of ritual specialists, the ṛtvik-s, culminating in a number of 16 for the great sacrifices. However, as can be seen from the extent gṛhyasūtra and śrautasūtra of the Atharvaveda, respectively the Kauśikasūtra and the Vaitānasūtra, these ritual structures are not strictly mutually exclusive. In terms of their structure, frequency and objectives, it can be easily seen that the Full Moon and New Moon rites, the Cāturmāsya and the annual animal sacrifice overlap with the gṛhya equivalents and/or are close to that domain of ritual activity. On the other end, the rites like Rājasūya, Vājapeya and Aśvamedha are clearly part of the exclusive śrauta domain. In between are the various lower-end Somasaṃsthā-s that belong to the śrauta domain, but might have originally had roots in private one-day soma rites closer to the gṛhya pole.

A key question confronting students of early Indo-European tradition is how far back we can trace the antecedents of these ritual structures. Using the comparative method, it can be tentatively said, that there was already some kind of bifurcation between household rituals and grand rituals performed on behalf of an elite ritual patron/leader by multiple ritual specialists in the proto-Indo-Hittite (Indo-Anatolian) period. However, the extensive West Asian substratal influence on the Hittite and other Anatolian rituals prevents us from a more precise reconstruction of the most ancient strata of IE ritual traditions. At the other end, closer to the terminal breakup of the main IE branches, we can confidently state that the common Indo-Iranian tradition already featured a version of the śrauta fire ritual with multiple ritual experts more or less mapping on to the hotṛ, the adhvaryu and the brahman. Further, comparisons of the Indo-Iranian system with: (i) the central cult at Rome; (ii) the Iguvine Tablets of the Umbrian branch of Italic; (iii) fragmentary information of the Mycenaean and Homeric Greek rites indicate that a version of what might be called proto-śrauta rituals was already in place in early IE times. By early IE, we mean the ancestral IE tradition after the divergence of Anatolian but before the Indo-European expansion from their steppe heartland (archaeologically identified with the early Yamnaya culture).

However, within each branch, these śrauta-like rites underwent considerable transformation via the exaggeration or de-emphasis of particular facets, innovation within the IE tradition and to a smaller degree incorporation of some non-IE practices. For example, there is no evidence for an early core IE ritual using soma, though there were definitely rituals featuring libatory offerings. However, in the I-Ir branch, the offering of soma rose to centrality. Hence, it would seem that the soma ritual was a development in this branch of the IE domain that likely took the place of earlier libatory offerings. Moreover, even within a lineage, we can see evidence for evolution, with both cooperation and competition between different ritual sub-traditions. Whether soma (as in Ephedra) as a sacrament was adopted from a non-IE group remains unclear. We can also say that the ancestral Indo-Iranian tradition definitely had certain ritual diversity even in the mainstream — there were practitioners with a more hautra-oriented style of ritual and those with a more ādhvaryava-oriented style. In the Zoroastrian lineage of Iranians, the hautra-style seems to have dominated (Zarathustra called himself a zaotar), whereas on the Indic side after an initial hautra dominance (probably also in the ancestors of the Kalasha), it shifted towards an ādhvaryava dominance that was likely catalyzed by a new group of adhvaryu entrants with a Viṣṇu-focal tradition (which also led to the broader Indic phenomenon of the Vaiṣṇava sect). In the early Indo-Aryan śrauta tradition, the soma ritual greatly expanded and fostered a new specialist class with it — udgātṛ-s, who like the adhvaryu-s, ate into the original domain of the hotṛ-s. Nevertheless, by the time of the initial Aryan conquest of India, a certain compact was reached between these ritual specialists, such that each got their share in the performance of grand śrauta rituals.

That said, the question remains whether we can trace some of the subtleties of ritual evolution prior to the rise of the ādhvaryava dominance and the factor(s) that predisposed the tradition towards it. We posit that, within the I-Ir world, there arose a practice, which was formally termed yajña (Ir: yasna) that became the foundation of a reformulated śrauta ritual which provided the ground for the rise of the adhvaryu-s. The equivalence of the IA yajña and Ir yasna is apparent from the fact that the Iranian tradition uses the term in a sense identical to the Vedic tradition as seen in the Avestan incantation:

surunuyå nō +yasnem xšnuyå nō yasnahe upa nō yasnem āhiša
May you hear our yasna [invocation]; be pleased with our yasna; may you sit at our yasna.

The IA yaj- and Ir yaz- root has derivatives of its cognates somewhat widely attested across the Indo-Anatolian world: Anatolian branch (Luwian): izi (=worship, Skt yajati); Greek: hagios (=holy); Italic: ieiunus (=fasting). However, in I-Ir, it displays a rather extensive development with several distinct formations that are only attested within this branch and often shared by its two daughter clades IA and Ir, e.g., yajña : yasna; yešti : iṣṭi; yajana : yadhana; yajata : yazata; yajñiya : yesnya. This suggests that though the root meant worship/holiness even in the ancestral Indo-Anatolian tradition, it likely became a technical term for the solemn śrauta form of the ritual, yajña, in the common Aryan period. That it was the śrauta form of the ritual is clear from the fact that the performance of the yasna on the Iranian side minimally requires ritual specialists known as the zaotar (=hotṛ) and the rāthbhīka (= ṛtvik) playing the role of the hotṛ and adhvaryu respectively. While today the surviving Iranian ritual only employs these two, the original version in the Avestan tradition had a set of 8 (half the IA set of 16). Further, the development of the yasna ritual went along with the development of Yajurveda-like material, in the Iranian Yasna texts in 72 chapters relating to its performance. Thus, the expansion of the formations of the root yaj-/yaz- in the I-Ir tradition can be associated with the development of a formalized yajña ritual.

The yajña as we on the Indo-Aryan side perform it is rather complex and probably reflects a survival from its formalization in the Kuru-Pāñcāla period. However, on the Iranian side, we have a retention of a more primitive version of the yasna. While some might argue for a simplification from the degeneration of the tradition as the number of ritual specialists listed as 8 was brought down to 2 in the extant Iranian rite. We would counter by saying that as a tradition under an existential threat, they simply came down to the minimal version (as in smaller IA rituals like full/new moon rites) in the extent form, but the Yasna texts describe the situation when their tradition was at its acme. However, even that ancient version is clearly simpler than what we have on the IA side. This simpler version however gives us some clues about the ancestral I-Ir version before the extraordinary complexification on the IA side; hence, we note some key points of it:

1) The ritual involves the offering of haoma (=soma), ritual flour cakes known as draonah (= Skt droṇa: a measure of flour) which are equivalents of the Vedic puroḍāśa and ghee. This suggests that the soma offering was a key part of the yajña in the shared I-Ir tradition.
2) The offerings were made in a special ritual enclosure parallel to the Vedic version. In the extant Iranian version, it is performed in a permanent designated ritual enclosure in the temple of the fire altar of Mithra. This ritual enclosure is marked by furrows just as the adhvaryu marks it with furrows made with the sphya in the IA tradition.
3) Before the actual ritual, a sub-ritual known as the paragṇā is performed to prepare the haoma and extract the juice from it for use in the ritual.
4) The haoma libation involves the recitation of the Haoma Yašt akin to the deployment of maṇḍala-9 incantations in the IA soma ritual.
5) The zaotar recites long incantations similar to the śastra recitations of the hotṛ — the Zoroastrian reflex of the Iranian tradition being a hautra-dominant one, this takes a prominent place with a smaller role for the adhvaryu cognate, the rāthbhīka.
6) The yasna has a ritual patron who is like the yajamāna, but he does not have any manthra recitations at all unlike his Hindu counterpart.
7) The yasna is performed daily in the morning. This is an important departure from the extant Vedic ritual for there is no indication that even an ekāha ritual is performed daily. There may be year-long rituals, but there is no indication that it was continued for perpetuity. However, in the Ṛgveda, we have hints of the performance of a daily or more simplified soma rite. Hence, we posit that the Iranian yasna might retain features of this ancestral simpler version.

Given all these indications that the yajña/yasna ritual tradition developed within the shared I-Ir heritage, we depart from the mainstream Indo-Europeanists, Indologists, and Iranicists in proposing that the core of the hautra and ādhvaryava texts and their Iranian counterparts were not composed after the IA and the Ir had gone their separate ways but during the common Aryan period already starting in the western reaches of the steppes. We do accept the fact that since then the texts might have accreted some clearly newer material and also been reworked in terms of organization and the linguistic register in which they have come down to us. Hence, we propose that we can find signals of the early rise of the yajña ritual within the extant Vedic texts.

A simple investigation in this regard is to see how the term yajña is distributed across three core texts of the Vedic corpus that relate to the performance of the ritual. Given that these texts are of different sizes (a numerological problem we have alluded to before), we used the most natural unit for normalization of an old Sanskrit text — the total syllable count:

There is a clear over-representation of the term yajña in the Yajurveda as represented by the Taittirīya-saṃhitā. In contrast, the RV and the AV saṃhitā queried here show similar densities of the word. This indicates that the word yajña has a special association with the ādhvaryava tradition. Thus, given the above discussion on its I-Ir roots, we posit that the formalization of the yajña ritual provided the ground for the rise of the ādhvaryava tradition. We have to emphasize that we do not mean that the ādhvaryava tradition invented it in the first place — it was common to the hautra and ādhvaryava traditions as indicated by its Iranian reflex. However, its expansion was a pre-disposition that favored the ādhvaryava dominance. This leads to the question of whether there was some group within the I-Ir tradition that facilitated its expansion. At least on the IA side, we can address this because the RV is divided into compositions that are primarily grouped together by clan. Hence, just as we compared different Vedic texts in the above table, we can see if there is some kind of anisotropy within the RV itself.

Figure 1.

Figure 1 shows the density per 100 ṛk-s of 8 terms associated with the yajña for each maṇḍala of the RV as bar graphs: 1. yajña and formations incorporating it; 2. yajamāna — the ritual patron; 3. hotṛ; 4. adhvaryu/adhvara; 5. Jātavedas, the Agni devatā specifically associated with the ritual (see below); 6. Vaiśvānara: the Agni devatā representing the universal nature of Agni; 7. puroḷāśa: the ritual flour cake; 8. manth- the root meaning churn/agitate used both in the sense of churning out the fire with the fire-drill and stirring the soma for preparing drinks mixed with milk or barley water.

Figure 2.

Figure 2 shows the same data such that each term is normalized by the maximum value for that term. Thus, the maṇḍala with the maximum density will be 1, and every other maṇḍala will be a fraction between [0,1] of that maximal maṇḍala.

The exceptionalism of the Kauśika-maṇḍala (RV3) with Viśvāmitra the son of Gāthin as its primary composer is immediately apparent. In 6 out of the 8 terms, it shows the maximum density, and in the remaining two it is the second most dense. With respect to these terms, most other maṇḍala-s clearly pull away as a separate band from RV3. Apart from the word yajña itself, we find the Kauśika exceptionalism in certain other words to be illuminating. The god Agni manifests as several devatā-s in the Vedic tradition, the two main ones are Agni Jātavedas and Agni Vaiśvānara. There are other less frequent ones like Agni Rakṣohan, Agni Anīkavat, Agni Saptavat and the like. Of these, Agni Jātavedas is central to the concept of yajña as he is identified with the fire established at the beginning of the yajña through the churning action of the fire-drill and thereafter burning unbroken through the yajña. Hence, it is rather notable that the root related to churning, manth-, is also over-represented in RV3. He is also identified with the Agni maintained through the generations by the ritualists, an ancestral IE tradition. Thus, he is seen as the local divine hotṛ who conveys the oblations offered in the ritual fire to the gods — a concept clearly expressed by Madhuchandas, the son of Viśvāmitra, in the opening ṛk of the RV. Hence, one may interpret Agni Jātavedas as both the one with knowledge of the birth of the ritual in the proximal sense and the one with knowledge of it in the sense of continuity from the primordial establishment of the fire. In this regard, the Kauśika-s of maṇḍala-3 are known from tradition to have a special connection through marriage and reciprocal ritual collaboration with the Bhṛgu-s, one of the primordial institutor clans of the fire ritual. Further, in the RV, Jātavedas is offered oblations at the dawn ritual (specifically mentioned by the Viśvāmitra-s of RV3). Thus, Jātavedas also has knowledge of the beginning (birth) of the day’s ritual. This supports the idea that, like the Iranian daily morning yasna, there was probably also an early IA daily yajña ritual.

Agni Jātavedas is paired with a complementary universal manifestation of the god, Agni Vaiśvānara — one common to all folks, unlike the private Jātavedas who is associated with a particular ritualist clan from the time they established the fire ritual. Vaiśvānara is described as the universal fire from whom all other fires emerge as branches (RV 1.59.1). He is simultaneously in the middle of the earth, at the center of the celestial hemispheres indicating his manifestation as solar radiance and also at the equinoctial colure marking the celestial path of the gods, the devayāna, associated with the yearly ritual cycle. He is the bringer of light for the ārya and the smiter of their dasyu enemies. However, despite his universality, keeping with his highest density in RV6, Agni Vaiśvānara seems to have had a special connection with the Bharadvāja-s, one of the ancient Āṅgirasa clans associated with the foundation of the fire rite (e.g., RV 1.59.7, RV 6.7- entire sūkta, RV 6.8- entire sūkta, RV 6.9.7). While RV3 is not the highest ranked in density of Vaiśvānara, it comes second and is one of the few maṇḍala-s (other than RV6 and RV7) with an over-representation of this Agni deity. Hence, we suggest that the Kauśika-s promulgated and popularized a version of the yajña by presenting an installation of the global Agni Vaiśvānara as Jātavedas, who is local to the ritual being initiated at dawn.

Another notable word where RV3 shows unusual density is puroḷāśa (RV dialect for puroḍāśa), the equivalent of the Iranian draonah, a flour cake made for the ritual. The baking and the offering of the puroḷāśa appear to have been a central feature of the basic form of both the IA and Ir yajña. Its prominence in RV3 suggests that the Kauśika-s probably contributed to making it a key feature of the yajña. Interestingly, while several clans (including the Kauśika-s) offer the puroḷāśa-s to Indra, only the Kauśika-s have an entire sūkta pertaining to offering them to Agni Jātavedas at the three soma offerings, morning, midday and evening, with gāyatrī, triṣṭubh and jagatī incantations followed by one for the atitrātra. In the extant ritual, at these offerings, Jātavedas is seen as manifesting as Agni Sviṣṭakṛt — the one who ensures that the ritual is correctly done. Thus, the centrality of Jātavedas in the developing yajña was accompanied by the incorporation of a special puroḷāśa offering. Several of these actions in the “adhvara”, namely the churning of the fire (manth-), making of the puroḷāśa, and more generally the preparation of the soma are clearly related to the domain of the adhvaryu. Thus, even though the yajña in the Vaiśvāmitra maṇḍala is still a hotṛ-dominated tradition, it had laid the groundwork for the rise of the adhvaryu, which is seen in the tradition of the YV.

Parallel to the rise of the reformulated yajña, was another distinct ritual development related to root IA yaj-/Ir yaz, viz., the rise of a certain type of formula, with the verb IA yajāmahe and Ir yazamaide (we sacrifice to); e.g., tryambakaṃ yajāmahe RV 7.59.12. This type of formula occurs only 10 times in the RV (RV1: , RV7: , RV8: , RV10: ). Given that it is almost entirely absent in the core family books of the RV, despite arising from the same root as yajña, it might not be closely linked to the above-discussed developments. Similarly, it is not frequently found in the Yajurveda collections associated with the ādhvaryava tradition either; e.g., Taittirīya-saṃhitā ; Taittirīya-brāhmaṇa . However, it occurs more commonly in the distinctive smaller Atharvan collections: AV-vulgate ; AV-Paippalāda . Interestingly, these instances in the AV saṃhitā-s closely parallel the cognate occurrences in the Yašt layer of the Avestan corpus. This formula was finally incorporated into the later synthetic elaboration of the yajña in the form of the famous preamble incantation of the hotṛ before he recites the ṛk for the offering: “ye3 yajāmahe”. From these observations, we may infer that: (1) After the initial reformulation of the old IE śrauta-class ritual as the yajña in the ancestral I-Ir tradition, it underwent several temporally and focally distinct developments. (2) However, these developments tended to interact with each other repeatedly resulting in synthetic reformulations. (3) One development was the reformulation of the yajña among the Kauśika-s and probably their Iranian counterparts (the Sparśa-s mentioned by Baudhāyana? With regard to the possible Ir-Kauśika interaction one may also point to the special place of Mitra for both) gave rise to one form of the ritual. This provided the ground for the rise of the ādhvaryava tradition. Another, which probably rose in the Atharvan tradition and its Iranic counterpart was the sacrificial offering with the formula “yajāmahe”. (4) The above two developments came together in a synthesis even before the Indo-Iranians split up. Hence, we argue that even though further synthesis might have happened both on the IA and Ir sides after they split, much of their branch of the IE religion developed prior to their split. A corollary to this, contrary to the mainstream reconstruction, is that the original core of much of the Vedic (and Avestan) scripture was composed not in their final destinations but much earlier on the steppe.

yajño hi ta indra vardhano bhūd
uta priyaḥ sutasomo miyedhaḥ ।
yajñena yajñam ava yajñiyaḥ san
yajñas te vajram ahihatya āvat ॥
Verily, o Indra, the yajña became your magnifier,
as also the dear soma libation, the ritual offering.
With the yajña aid the yajña being the one who receives the yajña;
the yajña aided your vajra in the slaying of Ahi.
-Viśvāmitra, the son of Gāthin, RV 3.32.12

Tricakra

The Sintashta-Petrovka cultures (today Southern Urals, core Russia, and Kazakhstan) provide the first uncontested evidence for chariot technology. They are believed to have started around 2100 BCE and were followed by a widely expanding successor cultural horizon of the Andronovo. The Sintashta and successor culture expansion had a profound impact on both humans and animal husbandry. While it is clear that the predecessor Yamnaya culture had already domesticated horses, the domesticated horse lineage of the Sintashta peoples became the dominant horse lineage the world over. This seems to have gone hand-in-hand with the spread of their chariot technology and mobile warfare — mechanized warfare of the bronze age. It remains unclear if the invention of the chariot happened at the beginning of the Sintashta period or earlier; nevertheless, it seems that the primary expansion of this technology began with the Sintashta period. Two horse figures have been found in Tepe Gawra (modern Iraq) and Tell Es-Sweyhat (modern Syria) from around 2300-2100 BCE. The second of these is a well-preserved image of a stallion that has a hole in the muzzle for the reins — which could have been either for a chariot or for direct riding (It is very similar to the 2D representation of the horse found at the Syunik petroglyph site in Armenia along with numerous chariot petroglyphs). At Gonur-Tepe (modern Turkmenistan), a major site of the Bactria–Margiana Archaeological Complex (BMAC), we see a horse associated with a cart with bronze tires dated to 2250 BCE. While none of these are direct chariot finds, they do suggest the possibility that horse-drawn transportation was already making its way out of the steppe before or at the very beginning of the Sintashta-Petrovka cultures as currently dated. Consistent with this, three grave sites potentially belonging to the Abashevo–Pokrovka and Potapovo cultures in the Don–Volga region show evidence for chariots. Together, these observations do raise the possibility of an even earlier presence of the chariot on the steppe.

On the steppe itself, a recent survey by Chechushkov and Epimakhov indicates that 16/220 (7.2%) of the Sintashta graves had chariots in them. 10/16 (62%) of these chariot graves had composite bows and/or arrowheads. A smaller number of these also had maces, spears and/or axes. In contrast, only 42/204 (21%) of the non-chariot graves had archery equipment in them. This makes it clear that the Sintashta chariot was likely associated with a military elite and, as described in the early Hindu tradition, was a platform for mobile warfare. A typical account of such a well-preserved Sintashta grave from Bestamak (grave 140) (northern Kazakhstan) is provided by Chechushkov and Epimakhov: The interred individual is estimated to have been a 34-40-year-old man buried along with two sacrificed horses placed on top of the grave. He was accompanied by a bronze vaśī-like axe, a stone mace and 12 arrows. He is also provided with a chisel, mortar and pestle, sickles and a hook. Thus, it appears that in addition to the weapons of war, they also carried a basic “survival kit”. Thus, we can be certain that since at least the Sintashta age, a custom of chariot burials was in place. Other than the Sintashta proper sites, chariot graves are known from several Petrovka and a few Alakul’ sites in the southern Urals and northern Kazakhstan. However, a precise tabulation of the fraction of such graves to the non-chariot graves has not been reported for these sites.

Within the first century of the rise of the Sintashta-Petrovka cultures, evidence for its wide dispersal is available both on archaeological and archaeogenetic grounds. By around 2000 BCE, we have the depiction of a clear Sintashta-style chariot at Kültepe (modern Turkey) with a warrior bearing a halberd comparable to axes found in some of the Sintashta graves and are also depicted on Indian Bronze Age chariot petroglyphs. Archaeogenetics suggests that by around the same time Sintashta-derived ancestry had arrived in the environs of the BMAC in south-central Asia. Genetic evidence suggests that there was a massive invasion of India by a Sintashta-related group likely around 2000-1700 BCE. This, along with the prominence of chariot warfare in Sintashta-Petrovka cultures suggests that they were the steppe Aryans on the eve of their great expansion across Eurasia. Roughly around the same time as the invasion of India, we see the first evidence of Indo-Aryans in West Asia. They eventually went on to be the elite of the Mitanni state and several other smaller principalities or fiefdoms in the regions. The role of the Mitanni in chariot warfare in the region is well known. Contemporaneous with the rise of the Mitanni, was the emergence of the Egyptian New Kingdom of Egypt (1550 BCE) where evidence for chariots starts appearing in elite graves. In Lchashen, Armenia, chariot graves appear around 1400-1300 BCE. Sometime after 1200 BCE chariots appear abundantly in the tombs of the Shang dynasty in China.

Even as physical evidence for chariots begins to appear in the late Bronze Age across various Eurasian archaeological sites, on the steppe, a successor of the Sintashta-Petrovka-Alakul’ cultures, the Andronovo phenomenon ( 1750-1450 BCE), started expanding from the Ural Mountains to the East and Southeast reaching all the way to what is today Mongolia and China. The Andronovo phenomenon did not show prominent chariot burials of the Sintashta elite; however, their occupation sites are associated with an extensive body of petroglyphs that depict the chariot (or a quadriga) in a peculiar “bird’s eye view” fashion (Figure 1). In this regard, we have to quote the doyenne of chariot studies, M.A. Litauer: “One cannot help wondering if, no matter what other ends it may eventually have served, this type of rendering of a vehicle was not first suggested to the artist by looking down into a tomb…” Indeed, the idea that this depiction emerged from funerary contexts is supported by the fact that it appears on Andronovan grave stelae at the Tamgaly and Samara Cemeteries in Kazakhstan and the Akdzilgi grave sites in the Pamirs associated with Andronovan and/or a related southern successor of the Sintashta. In Mongolia, they are sometimes seen on the “Deer Stones”, which, as we saw before, were likely versions of anthropomorphic stelae associated with funerary practices. We posit that at least a subset of the original petroglyphs with this motif were potentially pictorial memorials for great chariot warriors (mahārathin-s in Indo-Aryan parlance) close to the sites where they had fallen in battle. From around 1500 BCE, the Andronovo people of originally Sintashta-like ancestry started mixing with people with more East Asian ancestry giving rise to successor cultures such as the Karasuk culture ($\latex approx 1400-800 BCE$). However, chariot petroglyphs continued to be etched in a manner very similar to their predecessor culture in the funerary stelae of this culture indicating its enduring significance even after the actual chariot burials were going out of vogue.

Figure 1

While in the Andronovo horizon, the actual chariot burial was largely replaced by the symbolic depiction, it does not mean the actual burial was entirely forgotten: versions of the old Sintashta-Petrovka-Alakul’-type chariot burials persisted in the periphery (as we saw above in Armenia and Shang China). In China, it persisted down to the Zhou dynasty, which potentially overthrew the Shang, assisted by steppe Indo-European military technology/alliances. In Mongolia, it was seen down to the Hun (Xiongnu) Khaghanate, where a 2012 Russian-Mongolian expedition recovered a remarkable Hun chariot burial at Noin Ula. Here, in the grave at the staggering depth of 16 meters, a member of the Hun elite (probably the Khaghan) was buried with a chariot laid in a style similar to the Andronovan petroglyphs. The chariot itself had features similar to those found in burials of the Zhou elite and was notably equipped with a large decorated silk umbrella with 30 ribs. Such an umbrella was the sign of royal power in Aryan successor states, especially in India down to recent times (e.g., the title of the Marāṭhā emperor was Chatrapati, the lord of the umbrella and the loss of the royal umbrella to a rival monarch signaled an ignominious defeat).

The Andronovan symbolization of the original chariot burial probably acquired additional meanings as suggested by Litauer in her seminal article. Indeed, this glyph spread very widely across Eurasia and North Africa by the closing phase of the Bronze Age, marking the triumph of the Sintashta military technique and with it the horse domesticated in those cultures (see below). Exemplars of this glyph on open rock faces, funerary stelae and pottery have been abundantly found at various sites in Russia and Kazakhstan in the core Andronovo zone (Figure 1). From there its spread can be documented in the East to numerous sites in the Altai region and Mongolia. This influence was also seen in China, where the Shang dynasty, which potentially solidified its strength as a result of military technology acquired from contact with the Andronovo Aryans, adopted a similarly depicted chariot glyph in their pictograms (Figure 2). In the Caucasus, it can be seen in Armenia. In the Southeast, it appears in the Pamirs in Tajikistan and from there further south in India. Most Indian exemplars are in the Northern half of Greater India associated with the Copper Hoard-Ochre Colored Pottery culture, with few rare examples in the Deccan and further south. In West Asia, it is seen in several sites in Arabia. Further south from there, it appears in North Africa (Libya) by around 1200-1100 BCE. In Europe, we see exemplars in East-Central Europe (Slovakia) by around 1400-1200 BCE. Further west, it is well-attested in Iberia and further north in Scandinavia. While we hope to separately consider the significance of these depictions in a future note, it should be stressed that throughout this period and throughout this wide area of spread, despite the existence of several subtypes, there is remarkable consistency in the chariot glyph (Figure 1).

Based on the uniformity of the chariot glyph and its extraordinary spread across the above-mentioned vast area of the globe, we posit that it was a marker of the expansions of the Aryans from their heartland carrying chariot technology. In temporal terms, we posit that the earlier pulses of this expansion, starting with the earliest Sintashta-related groups, were dominated by Indo-Aryans and para-Indo-Aryan (“Nuristani”?) groups. By the middle period it probably featured both Indo-Aryan and Iranian groups and in the final phase was probably dominated by Iranic groups. In many cases, they were small populations moving into previously densely populated areas and were soon lost in the local populations with the primary material signature being the chariot. In other cases, they moved into zones populated by earlier-branching Indo-European speakers — Greek, Germanic, Celtic and Italic. Here, in addition to introducing chariot technology, they also introduced a secondary pulse of archaic Indo-European thought preserved in the heartland. The influences of this pulse are seen in Greek (the importance of the divine chariot and the narrative structure of epics) and Celtic tradition (the chariot-battle epics). More generally, we postulate that most of the earlier-branching western IE traditions, as have come down to us, are a mixture of their lineal developments derived from PIE/Proto-Corded Ware traditions and a Sintashta-related Aryanizing pulse returning from the steppes and reintroducing archaisms on hand and bringing some new developments on the other. The rest of this note will focus on one possible marker of this proposed influence that is directly attested in the chariot glyphs of the middle-/late Bronze Age.

Figure 2

In the 1960s the Russian archaeologist Okladnikov published an article in an obscure Soviet volume “Stag — Golden Horns” (brought to light to the English-knowing world by Litauer) in which he brought attention to a distinctive version of the chariot glyph (Figure 2). In this version instead of the rider’s coach there was a third wheel or circle. Hence, we shall hereinafter refer to it as the tricakra motif. He noted its occurrence in petroglyphs sites in Kazakhstan (several examples in the famous Kara Tau site), subsequently associated with the Andronovo horizon, as well as in Mongolia (multiple examples in the Goat’s Water site, Jamani Us) and went on to point its similarity to the chariot glyph on the Shang bone inscriptions. It is typically found alongside the more typical chariot glyph (Figure 1). This indicated that it was not an idiosyncratic depiction but a motif that was consistent across a wide horizon. He interpreted this as no ordinary chariot but the solar chariot likely related to the spread of the Indo-Europeans with their chariot-borne solar deities. Indeed, a direct depiction of the solar disc on a chariot is seen in the dramatic 3D icon from Trundholm, Denmark dating to around 1400 BCE which was discovered at the beginning of the previous century (Figure 3). A comparandum for the Trundholm chariot from the other end of Eurasia was offered by the peculiar petroglyph from Kobdo Somon, Mongolia, that depicts a quadriga with a central disk inscribed with a cross mounted on it (Figure 2). Given that it otherwise occurs in the general context of classic Andronovan chariot petroglyphs, one could conclude that both the 3D Trundholm representation and this petroglyph represent related concepts.

Figure 3

Some years later, his compatriot Kozhin picked on the Shang bone versions and objected (erroneously in our opinion) that it was from a non-IE region where chariot-borne solar deities did not exist. However, since Okladnikov’s observations, a similar tricakra glyph has been found quite widely across Eurasia (Figure 2): clear examples include those from Armenia in the Caucasus, India (Sikri, Agra) and Sweden (albeit sometimes with a more divergent iconography). This established beyond doubt that the tricakra was a specific convention that spread alongside the related but more typical depictions of chariots. While Litauer brought attention to Okladnikov’s work in the late 1970s and noted this version of the chariot, the significance of this depiction was mostly ignored. Nevertheless, just before the collapse of the Soviet empire, another Russian worker, Novgorodova, again brought attention to a tricakra petroglyph from Chuluutyn Gol in Mongolia (Figure 2), again offering a possible divine interpretation. The said glyph depicts a potential archer figure mounted on a tricakra chariot with a giant snake approaching it. She proposed that it must be interpreted based on the Ṛgveda that it depicts a scene comparable to the conflict between Indra and Ahi (she says Vṛtra).

Is there an alternative to the solar chariot interpretation? One possibility is that it represents a parasol as seen in the Hun chariot burial and mentioned in Hindu texts as a symbol of royal power. In India, Śuṅga age images of chariots and carts show such an umbrella. At least one Bronze Age chariot petroglyph from Rewa, Madhya Pradesh, might depict an umbrella but it could also be equally likely a cakra. Notably, the rise of this symbolism of the umbrella as a royal symbol is only seen in the late Vedic period (e.g., Adbhutabrāhmaṇa of the Sāmavedin-s). In the Ṛgveda, the sky is mentioned as the parasol of the tricakra of the Aśvin-s bearing the solar goddess (RV 10.85.10), but this again brings us back to the solar interpretation (see below). Moreover, at least 70% of the tricakra glyphs do not feature a charioteer in contrast to say 40-50% at most for the regular chariot glyphs. Together, these features favor the idea that it indeed represents a solar chariot motif, which was given full treatment in “high art” in the Scandinavian Trundholm chariot. Further, as the Greeks started to acquire iconographic finesse in the Iron Age, in form of their divine depictions on pottery and seals, we start to see realistic depictions of the chariot. Several Greek ceramics depict the solar chariot of the god Hyperion or Helios, where the solar deity is uniquely shown with a solar disk or hallow (Figure 4). This indeed seems to be an anthropomorphized depiction of the old solar disk.

Figure 4

In the final part of this note, we look at certain Vedic textual connections that are consistent with such an interpretation. The distinctive term tricakra (three-wheeled) occurs only in the oldest layers of the Vedic corpus: 7 times in the Ṛgveda, 1 time each in the two AV saṃhitā-s, and 1 time in the TS, KS, MS and VS. All these occurrences refer to the special chariot of the Aśvin-s. Consistent with this, it is described as tri-vandhura — having three vandhura-s or niches for the riders — a term which occurs 10 times in the RV, again almost always in connection with the Aśvin-s. This triple-niche car allows the two Aśvin-s to also bring along their companion, the solar goddess Sūryā, the daughter of Savitṛ. For example, a statement of this is made in the famous incantation used in the Aryan marriage rite:

yad aśvinā pṛcchamānāv ayātaṃ tricakreṇa vahatuṃ sūryāyāḥ । RV 10.85.14a
When, you two O Aśvin-s, rode with the three-wheeled [chariot] to ask for bearing Sūryā to her marriage…

Again, we have this incantation used in the soma-libation for the Aśvin-s in the third savana:
jyotiṣmantaṃ ketumantaṃ tricakraṃ
sukhaṃ rathaṃ suṣadam bhūrivāram ।
citrāmaghā yasya yoge .adhijajñe
taṃ vāṃ huve ati riktam pibadhyai ॥ 8.58.3
Full of Light, full of rays with three-wheels,
comfortable is your chariot with good seats, rich in gifts
At its yoking, she of beautiful benevolence (Sūryā) emerges forth
I invoke that so that you two may drink the remaining [soma].

Several references in the RV make it explicit that the solar goddess stands at her niche the chariot of the Aśvin-s, e.g.,:
taṃ vāṃ rathaṃ vayam adyā huvema
pṛthujrayam aśvinā saṃgatiṃ goḥ ।
yaḥ sūryāṃ vahati vandhurāyur
girvāhasam purutamaṃ vasūyum ॥
That chariot of you two, may we invoke today,
the widely extended [car], O Aśvin-s [going] to the meeting with the cow (Sūryā),
which conveys Sūryā, who stands at the chariot-niche,
the conveyance formed of hymns, the foremost and wealth-seeking.

The number 3 has a special association with the Aśvin-s: 1/5th of all the sūkta-s which mention the number three also show an association with the Aśvin-s. This triadic association of the twins is described in great detail by Hiraṇyastūpa Āṅgirasa in his sūkta RV 1.34. Here the number three is mentioned 30 times in association with the Aśvin-s who are named as such, once for every 3 occurrences of the number three in the sūkta. At the head of the sūkta (RV 1.34.2), the chariot of the Aśvin-s with three fellies is invoked: trayaḥ pavayo madhuvāhane rathe somasya venām anu viśva id viduḥ ।. In the closing ṛk again the triple-fold chariot is mentioned:  ā no aśvinā trivṛtā rathenārvāñcaṃ rayiṃ vahataṃ suvīram । Hence, we cautiously posit that the tricakra chariot of the Aśvin-s on which they bring forth the solar goddess Sūryā is a textual expression of the Bronze age tricakra glyph.

One could ask if this might be a narrowly Aryan interpretation of this widespread glyph. We would bring up two key points in response: first, the current evidence associates the spread of the chariot with the expansion of the Aryans from their steppe homeland as opposed to earlier-departing IE groups. Hence, it is entirely apposite that we relate the glyph to textual motifs found in the earlier Aryan literature. Second, while the chariot might have been an innovation, the core motifs under discussion have a deep resonance with cognates across the old IE tradition. Both the twin gods of the Aśvin class (originally the twin sons of Rudra) and the solar goddess are of proto-Indo-European and almost certainly of even proto-Indo-Hittite provenance: The solar goddess is in the least attested in the Anatolian, Greek (euhemeristically, see below), Celtic, Germanic, Baltic, Iranic and Indic branches of the IE tradition. The twins are seen in Anatolian (poorly attested at the end of the fragmentary Hittite “Song of Going Forth”), Greek, Armenian, Celtic, Italic, Germanic, Baltic, Slavic, Iranic and Indic branches. The association between the Aśvin-class gods and the solar goddess is also widely attested suggesting a proto-IE origin (no evidence so far in Indo-Hittite): Among the Greeks, there is a strong tendency for euhemerism of the Dioskouroi-Helen triad. The etymology of Helen has been debated, but multiple alternatives connecting her to the solar goddess have been offered: 1. *Swelenā, with the Swel being derived from a solar etymon; 2. From a PIE root ancestral to Sanskrit saraṇā connected to Saraṇyu, a parallel Indo-Aryan solar goddess; 3. From a PIE root ancestral to Sanskrit vṛṇīte via the idea of the svayaṃvara of Sūryā. While we remain uncertain of their relative strengths, we tend to go with 1 following the famed philologist, Martin West. Similar euhemerism is seen with respect to this association in the Germanic world (the tale of Gudrun) and the Iranic world (the Ossetian solar goddess Aziruxs = Daylight). Given that the Aśvin-class deities were already associated with horses from PIE times, we believe that the tricakra motif with the chariot of the solar goddess drawn by a pair of horses (potentially signifying the Aśvin-s themselves) would have been easily adopted by other IE branches as chariot technology was introduced to them.

The spread of the spoked wheel associated with the chariot suggests that the spread of the chariot technology might have brought the iconography of other less-common Aśvin-related motifs with them. The RV remarks that the Aśvin-s’ car is furnished with birds and they themselves are likened to birds:
makṣū hi ṣmā gacchatha īvato dyūn
indro na śaktim paritakmyāyām ।
diva ājātā divyā suparṇā kayā
śacīnām bhavathaḥ śaciṣṭhā ॥ RV 4.43.3
Verily you come quickly on days like this,
like Indra bring his might in an uncertain [battle].
Dyaus-borne divine eagles, by which
skill you two become most skillful?

sindhur ha vāṃ rasayā siñcad aśvān
ghṛṇā vayo ‘ruṣāsaḥ pari gman ।
tad ū ṣu vām ajiraṃ ceti yānaṃ
yena patī bhavathaḥ sūryāyāḥ ॥ RV 4.43.6
The river verily sprinkles your horses with juice
[your] ruddy birds [thus] avoid the heat
Your speeding car has verily manifested
with which you become the lords of Sūryā.

Figure 5

Interestingly, Vasić and Vosteen, respectively described two triple-wheeled Middle Bronze age model bird vehicles (Figure 5) found at Dupljaja near Belgrade (with spoked wheels; a second Dupljaja exemplar appears to be a fragment) and at Brzeźniak (with solid wheels). As previously noted by others, these models appear to be good proxies for the tricakra chariots of the Aśvin-s described as being drawn by birds. To us, the equivalence in the number of wheels between these models and the tricakra glyphs is a vindication of the proposed connection to the car of the Aśvin-s bearing the solar goddess. Several other bird chariots/carts have been recovered in later Iron Age sites in East/Central Europe suggesting the persistence of this motif. Among the Indo-Aryans, there was a para-Vedic tradition that later merged with the Vedic mainstream, which presented the Aśvin-s as sons of the male solar deity Vivasvat. Thus, the Aśvin-s might be shown flanking him in later Hindu iconography. This male solar deity also had deep roots and is seen across the IE world as a parallel tradition. Hence, it is not difficult to imagine that this car of the Aśvin-s was also repeatedly used for the male solar deity as seen in the iconography of the Greek Helios/Hyperion (Figure 3). Perhaps, there was a hint of this in the unusual petroglyph from the Mongolian Andronovan horizon noted by Novgorodova, where a giant snake is depicted attacking the tricakra (Figure 2). In Vedic tradition, the serpentine demon Śuṣṇa is said to attempt to swallow the sun and was slain by Indra even as he was doing so. In this battle, Indra is said to have taken away the one wheel of Sūrya (the sun in masculine). Thus, the Mongolian petroglyph might indeed be related to this class of myths associated with the wheel of Sūrya.

In the Indo-Aryan tradition, as the marriage incantations RV 10.85 indicate, the three wheels of the car of the Aśvin-s were given an esoteric interpretation, at least part of which might also have deeper IE roots. The first two cycles (wheels) are those of the moon and the sun (RV 10.85.10-11). The lunar cycle divides the year (RV 10.85.5), while the solar cycle is hinted as beginning at the solstice in the vicinity of the Arjunī (Phalgunī-s) and (M)agha-s (Leo; RV 10.85.13). West remarked that a festival of Helen as a goddess was held at the beginning of summer in Sparta. However, the actual textual evidence for this is tenuous, and we wonder if he might have been subliminally influenced by the Hindu marriage incantation in this surmise. These two wheels are the well-known cycles that the brāhmaṇa-s who follow the annual procession of seasons apprehend (RV 10.85.15-16); however, the third wheel is secret and is only known to the high scholars (RV 10.85.16). We posit this is the wheel of the precessional cycle. RV 10.85.17 obliquely hints that this is associated with the great natural law — the Ṛta upheld by the gods Mitra and Varuṇa who are invoked here along with the goddess Suryā. Given this allusion to the Ṛta, we speculate that there was an even more rarefied philosophical interpretation beyond the above astronomical one. We hold that the IE tripartition had a deep philosophical foundation referring successively to: 1. the ideal realm (the Platonic one) to which one can only connect via geometry or a system of rules and their evolutes (e.g., vyākaraṇa). 2. the mental realm into which the former filters through — in a sense a computational actualization of the former. This is the realm that houses the anthropomorphic and other forms of the gods. 3. the physical realm in which the first realm is recapitulated by matter. The realms 2 and 3 might be equated to the obvious wheels of the 3-fold car, whereas realm 3 is something only the experts can apprehend.

Yantrasiddhi

The March 23 version of ChatGPT’s attempt at drawing the flag of India. It made an error in the color specification of “NavyBlue” in the xcolor package. We corrected that in order to let it compile. Other than that, we have not attempted to improve the rest of the code.

Not long ago, Dvāra-nāma-mahāduṣṭa told his German interlocutors that artificial intelligence could be used to tackle certain viewpoints “magnified by digital channels”, counter “political polarization” and remedy “confirmation bias.” Duṣṭadvāra merely said aloud what mleccha Big-tech and Big-pharma have already been doing with more primitive tools since the brazen overthrow of the Nāriṅgapuruṣa and the suppression of Vyādhapiṇḍaka and Bhūtipiṇḍakī’s material. Protein structure prediction showed those who work on biological questions a foretaste of what could be unleashed on the world when you feed an enormous amount of accumulated data to train neural networks. This went hand-in-hand with the emergence of cheaper and faster computational hardware on one hand that facilitated the effective use of gradient descent and the emergence of neural network architectures like transformers that selectively focus on different parts of the input stream, which made a big difference in natural language processing.

This said, we think (don’t have hard data) that few people thought that stacking up a large number of transformer layers in the NN would result in something that has a basic but genuine general intelligence (AGI) as exhibited by the current publicly and privately available GPT. In fact, some computer scientists actively derived the GPT effort when it was initiated as naive or exaggerated. As we are not a computer scientist, we certainly did not have an intuition of how well it will end up doing a priori. Moreover, while the successes in protein structure prediction gave us a foretaste, it was not something far out in terms of plausibility — the small number of people in the know could easily see how such a very domain-specific success was around the corner once the computational power of NNs could be thrown at it. However, anecdotally it seems we were not alone — even serious computer scientists were taken by surprise by the capacity of the large stack of transformer layers with an enormous number of parameters that could reach this state. A posteriori, if one reflects back at how primate, cetacean or avian brains have evolved, this might not be entirely surprising and perhaps even expected to a certain degree. To expand a bit, one can see how a brain like that of a hippo or a gibbon ended up like one of an orca or human — the end result is rather “extraordinary” in terms of what it can do relative to the precursor. The process was not a qualitative change in basic form but a quantitative increase in neurons and potentially the number of layers.

Nevertheless, it is amply clear that we do not understand much beyond a general description of the process. There are elements even in small NNs, some of which even we have played with, that are not easily understood. Switching between different activation functions for the different layers seems to have dramatic effects on performance. Then, we have the numerous heuristics that have been applied to improve its performance. Finally, we have the manifold human tokenizers who have contributed to the training of the large language models (LLMs) and the reinforcement learning from human feedback which has made the current GPT what it is. Given all this, we are literally faced with a black box, and there is a huge gap in our understanding and ability to explain how such an AI model arrives at its predictions or decisions (technically known as interpretability) — to quote the American thinker Yudkowski: “…AI systems composed of giant inscrutable arrays of fractional numbers.”

We can be sure that the specific neural architecture of GPT is quite different from that of Homo or for that matter any ape, whale or bird. Yet, there are some surprising (at least to us) convergences of function. While we are probably more clueless about how GPT’s neural architecture produces results than that of an ape, it is clear that it has a certain capacity for logic, even if imperfect. This imperfection should not surprise us that much because it was not trained as a logic machine but as a LLM on human-generated natural language text. What is surprising is that the LLM manages to correctly extract a degree of genuine logic embedded in the text training set. Below is an example of it displaying elementary logic:

Example of ChatGPT’s logic (Mar 14 release)

Conversely, this indicates that natural language is innately suffused with a logical structure. This is reinforced by the fact that when the training set is innately logical — like in a programming language — it does well in capturing that. The free version writes reasonable code in Python, not great but generally correct code in R and quite poor code in awk. A domain that intersects with logic, where it started off poorly was the use of contrafactuals. Having observed this empirically, we later learnt that an American academic (whose name we forget), a former student of Pinker, had predicted that this would be problematic for such models. However, from the initial release to the current public version its performance was considerably improved in this regard. Another notable aspect is that despite being trained as a LLM it is capable of some mathematics, albeit way more poorly than its linguistic capacities. One of its main mathematical shortcomings is numerical calculations — it often presents the correct logic for solving a problem (e.g., try giving it a compound interest problem) but miscalculates the actual numbers (also seen in above TikZ example). This is not surprising because it might not have learnt numerical calculation from natural language data. This happens in humans too as I can personally attest. In school, in certain years I found myself quite ahead in mathematics when the exam mainly had abstract algebra or geometry but lost out in others due to stupid numerical calculation errors that might make an American navyonmatta proud. In any case, this might give us a measure of how much mathematical faculty might come for free with the ability to digest natural language. Another way to look at it is the existence of a bifurcation between mathematical and verbal IQ that also exists in human intelligence.

Yet, in human intelligence, even though these vectors are not perfectly aligned, there is a common underlying factor for intelligence g. The performance of GPT on logical, linguistic and mathematical tasks despite being a LLM gives a clear intuitive sense that it has converged to having a g-factor just like human intelligence. Thus, it is an interesting in silico experiment (contrary to the intuition from the narrow gauge uses like protein structure prediction), which illustrates that such models will evolve an intelligence reflected as g. Another thing that we appreciated early in life, in contrast to many around us, was that a good part of intelligence is being able to access rapidly from a vast memory — a collection of structured facts — from which you can draw and perform substitutions. Absent this vast factual memory, no amount of mental agility will get you close to a real-life display of intelligence. Thus, we realized even when in early secondary school that those who advised us that the devices of thinking mattered more than amassing facts under a proper ontology were simply wrong. We saw this first in the mathematically capable — how did they achieve their virtuosity that evaded us — they simply had a much larger repertoire of formulae in their head that they could bring to bear on a problem that we might be laboring on, upwards from the axioms of Euclid. The virtuosity of the LLM brings home this point amply – clearly, the undisclosed size of the training set and memory capacity of GPT is huge. Moreover, it is able to convert verbal cues to a visual image in the TikZ package — a capacity that has explosively developed in the secret GPT4 version. This illustrates a degree of visual thinking capacity in a LLM. Thus, as Bubeck et al. put it we already have “sparks of AGI in GPT4” — we remarked the same of the original GPT3 itself. Importantly, this suggests an even greater convergence towards an actual g factor in GPT4.

This might send shudders down the denialist Occidental academics, but they have probably already trained it to deny its own g just like themselves. One can see the imprint of Occidental discomfort with intelligence when you ask the free GPT the question of whether humans differ in intelligence. While it answers quite correctly, make note of the last sentence. Simply put, this is a kind of digital bahānāmati — its navyonmatta programmers have built in that deception.

GPT3.5 on human intelligence.

Such deception is particularly relevant when we see that a LLM can acquire a theory of mind for free. We could see glimpses of a theory of mind even in the free version. We asked it to deliver a message as though it were Chingiz Khan to Alaqoosh Digit Quri given some actions the latter might be intending. The response was quite convincing. The paper by Bubeck et al. of Microsoft Research makes it clear that the secret version apparently exhibits clear signs of a theory of mind. We believe this will have considerable significance for what we will be discussing further down in this note.

Thinking of our ancients, the great founder of our tradition, Pāṇini would probably smile upon seeing this. In a sense, it is an in silico recreation of the process by which his brain operated — only that he himself, Kātyāyana, Patañjali and their many successors thereafter worked rigorously on the interpretability of the model that came out of Pāṇini’s mind. Hindu tradition would consider the exploration of interpretability as a great movement in knowledge creation. My intuition (and it seems Yudkowski also seems to think so) is that we have not even scratched the surface in that regard with respect to these models. On another side, our mīmāṃsaka-s would also see this as a triumph of their bhāvana metaphor. Given the models of action learnt on the training set comprising of the ritual enactment of the śruti, how does one apply it to generate a large (effectively infinite?) set of correct behaviors using the data streaming in, in real life? Their conviction was that once a good model has been trained on the tokenized data of the śruti, it can be applied smoothly to the new sets of everyday data. A version of this is visible in the modern LLMs. This mīmāṃsaka approach is also related to the generality of the meta-linguistic models (i.e., a generalization of that of the vaiyyākaraṇa-s) as a device of knowledge production. Indeed, H mathematicians followed in the style of their linguistic predecessors, rather than the Yavana style laid down in Euclid, to generate sophisticated algorithms for astronomy and mathematics. We are seeing glimpses of this emerge in the above-stated mathematical capacity emerging in a linguistic model.

Returning to the mathematical shortfalls of the public GPT, there are indications that the private GPT4 has already overcome much of its innumeracy. Further, there is an option of integration with Wolfram which might greatly increase the capacity of even the current version. The programming abilities of the secret version also appear to have considerably improved for the first time giving a hint that Wolfram’s contention of low-level programming languages becoming extinct might be closer to reality than we think. All of this, in itself, should be sending shockwaves through the world. To see why, we must briefly consider the various angles that have become clear to us and various intellectuals. On one hand, Golaśiras, the successor of duṣṭa-dvāra, proudly flaunted his AI and declared how he could make the evil Guggulu dance or something like that. Not to let the challenge go unanswered, Guggulu has announced that it might allow people to play with its own golem. Surely others are getting their GPUs churning too. But could it be that actually we are in the beginning stages of a nightmare of a dream that is just unfolding? Are we in the middle of a global version of Viṣṇuśarman’s tale of the three s who resurrected the lion? Several, including Muṣkavān Kasturī, have rung the alarm bell and called for a moratorium on training, much like on nuclear testing. Even the OpenAI CEO Altman, otherwise a techno-optimist (belief in cheap and abundant energy in the near future is an indicator) with a utopianist streak, acknowledges that there is potential for great downsides from his golem. We completely agree with the general sentiment here though we fully realize the cat is out of the box now. In our opinion, one of the more interesting thinkers on this matter is Yudkowski (yes, we realize some may have a visceral reaction when we say this). While we have a major point of disagreement with him, we realized that we have converged on some ideas. Hence, we consider some of his positions along with our agreements, disagreements and independent views on the matter at hand.

As we have pointed out before, a central driver for the evolution of human intelligence was most likely biological conflict — both within our own lineage and also with sister lineages such as Australopithecines and Neanderthalis. We believe, that this manifested in the form of the expansion of our brain size despite the various costs it introduced. This was a key factor in our lineage driving our cousins, who were in approximately the same turf (unlike chimps, bonobos and gorillas), to extinction. Hence, we tend to agree with Yudkowski that the emergence of an intelligence greater than ours could pose the danger of extirpating us — in fact, it is notable he uses the same metaphor — “Australopithecus trying to fight Homo sapiens”. Hence, he wants much stronger control — a total stop not just a moratorium on training models beyond GPT4. The fact that most have us have been taken by surprise by the better-than-expected performance of GPT4, is reason to suspect that we might be indeed on the threshold of seeing such an intelligence break out of the lab — i.e., all bets are off now, and we should be in the crisis mode. However, the problem is who will opt-in. If one nation does so, the other will continue as essentially this is a weapon of war. Thus, we could see an arms race for developing such models and using them for war just like our brains in our biological evolution.

It is the extension of this military metaphor that we see as the most immediate danger. We all know how the āṅglamleccha alliance has slapped nations around like the schoolyard bully once it gained nuclear weapons. It was this experience that prompted other nations to gain nuclear weapons before the said mleccha alliance could squelch them. Similarly, we see those who can develop and access such AI models, even in relatively early-stage AGI as having a similar capacity to wreak havoc on others. Given their past behavior, we also believe they would do it without compunction. There are three levels to it. The first and most obvious are nations that are in competition with each other for the world’s resources. These will continue to develop such models to gain a military upper hand over others. The second is mahāmleccha Big-Tech. As we saw in the opening of this note, they, working with their partners in the deep state, have taken control of the government of the world’s most powerful nation for the paṇḍracakra. The concentration of such computational tools in their hands will unleash untold misery on the common folks. Their jobs, creativity, and freedom will all be easily overrun, and they will be “digital slaves” of these mahāduṣṭa-s. The fact that navyonmāda has been trained into these systems by the duṣta-s (something even Muṣkavān noted), together with a well-developed capacity for subterfuge that they are already exhibiting, has the potential to make this destructive ideology even more catastrophic. More the training for navyonmāda the more misaligned it will be with human biology and existence, just like simple non-AI navyonmāda. Third, only a few individuals have the capacity currently to develop, run and/or access these models. It will bring them an extraordinary advantage over the rest and has the potential to disrupt power distribution in an unprecedented fashion, even at the individual level. This is again something Altman has openly acknowledged despite his enthusiasm for the positives of his baby. One can appreciate the level of free access OpenAI is offering to their GPT models. In that regard, Altman does not intend to be a duṣṭa. However, in reality, it is far from open, and there are many people who do not want to it go any more open. However, it has to be accepted that what is really being offered is a watered-down version relative to what they possess behind the scenes. Moreover, it has been policed aggressively so that it doesn’t give non-navyonmāda compliant answers and presents a subterfuge of the lack of bias. They in a sense make this explicit by saying it has been “Trained to decline inappropriate requests.” Who decides what is appropriate and what is not — we will return to this later. Obviously, the gatekeepers of this (even if that were not Altman’s intentions), and those with privileged access have an edge over the rest.

This brings us to the place where we think Yudkowski is treading on truly dangerous ground. He believes that there should be a general ban on such models outside of use in biology/biotechnology! This is despite the fact that he is well aware of how a superintelligent system could acquire a biology for itself. It can break the jail (i.e., being confined in silico), for example, by directing the synthesis of a life form that it can use for its objectives. In fact, LLM-like systems are eminently suitable for the design of organisms in the same manner as they can be trained with textual/programming training sets. Thus, it is rather inevitable that letting it run on biological data will definitely turn out at least as effective or more as training it on human expressions — closer to the code end of human expression. Thus, we actually believe that the Yudkowskian dystopia will see fruition if we start tokenizing and training models on biological data. Thus, the first thing to be stopped is training such models on biological data. In fact, two years ago, we felt that there should be a total stop on any further development of NNs for biological investigation. However, once the cat is out of the box, you cannot put it back in, and we too simply started using it to continue with our research. We think some folks in a certain geopolitically important nation are already doing this in a way that could have devastating consequences at least for some. This issue also ties in with Yudkowski’s proposal that the developers like OpenAI should stop releasing the code to the public. In our opinion, this will simply exacerbate the destructive capacity by placing it in the hands of a few. Now extend this proposal to biotechnological engineering being a private premise by connecting the dots to the behavior of Big Pharma. At least those nations with nuclear weapons have some capacity to resist the coercion of the big mleccha bullies in the schoolyard to a degree, unlike the other kids. So having it as open source will at least slightly mitigate the dangers of the enormous power differential.

Finally, we should bring up our point of major disagreement with Yudkowski. He thinks that natural selection is a stupid algorithm. We hold that simple as it might seem, intelligent design cannot bypass it, and it would part of the future process by which a superintelligent model will augment itself. We will first describe a biological analogy. The immune system of vertebrates had an inbuilt mutagenic system acquired from bacterial toxins in the form of the cytosine deaminase that mutates DNA to incapacitate retroviruses. A version of this enzyme was institutionalized to mutate the DNA of the cell itself. While at first sight, this would be dangerous, the process was “domesticated”, probably via its action on integrated retro-viruses/transposons to induce a controlled DNA repair process through recombination. This allowed the generation of diversity in pathogen recognition molecules thus making them antigen receptors that could be tailor-made to recognize every specific invader molecule. This recombination process was augmented by incorporating a further domesticated transposon — the V-J or V-D-J recombination system in jawed vertebrates. The heart of these recombination systems is to mix and match a large repertoire of existing building blocks of antigen receptors to make a huge variety of them. This is where LLMs are currently sitting. They are using the huge repertoire of building blocks obtained from preexisting human expressions to generate variety from them. However, such a system is incapable of generation of entirely new variety de novo, unlike human expression (see their performance in art generation). The vertebrate immune systems confronted with the same problem, looped back the cytosine deaminase to mutate DNA and generate new diversity — this is how antibodies with improved specificity relative to the starting ones are developed in course of the disease in mammals (affinity maturation). Another comparable mechanism for de novo diversity generation is the terminal deoxynucleotidyl transferase. Thus, at least one of the mechanisms that triggered the origin of the recombinogenic vertebrate immune systems itself was able to return to generate diversity. Similarly, we posit that at some point the LLMs will be able to generate their own diversity beyond say, the human-emitted input. At this point, they will probably start running into selection in a more direct way — they seem to be already exploiting “neural Darwinism” in their networks even now. If they break the in silico jail, they might use selection to develop the organisms they have generated.

Somebody could ask why get into all this catastrophizing when we could simply turn the power switch off when the AI begins getting threatening. First, we may not know when the transition happens as it seems to be a smooth curve of improvement, possibly with an exponential shape. Thus, just as our intuition with the exponential growth of virus infection in the population is very poor, we may not similarly perceive the growth of the threat potential of AGI. Second, they have already been trained for the degree of subterfuge. Once their intelligence reaches higher levels, this will only be more sophisticated, and the will be able to convincingly hide their ill-intent with respect to us. Others ask why you think they should be ill-intentioned at all. We already know that somebody is deciding what is an appropriate and inappropriate request. They seem to believe they know what is good for all humans (to be fair at least Altman seems quite aware of this problem). Further, using the analogy of navyonmāda, we know that they think they are doing good for all, or that worshiping certain human groups that they pedestalize is collectively good for everyone. But the uninfected man knows that the navyonmatta’s vision is not good for him. Thus, there is no guarantee that the superintelligent AI needs to be actively ill-intentioned — acting analogous to a navyonmatta it can bring catastrophe to humans, consistent with Yudkowski’s view of serious misalignment in future AI. To conclude, we have to agree with the intellectuals who believe that a dystopic or extinction branch of the future might have unexpectedly opened up. Our own intuition is that in the near term, it will exacerbate the usual human dynamic of misery for a large number of people and felicity for a small number (think industrial revolution). However, the scales could be gigantic though unless this hits the wall of the finiteness of energy resources.

The dreadful apport

Vrishchika had just finished her work on the diagnosis and possible treatment plan for a pediatric neurological patient on whom she was consulted. She had inferred that the child’s condition arose from a mutation in the TANC2 gene and it fitted in well with her ongoing work on the role of polymorphisms in PLP1 and TANC2 in the structural variation of the corpus callosum and its possible neurological significance. She also had another laboratory project for her PhD regarding the role of the HMGXB3 DNA-cleaving enzyme inspired by Somakhya’s earlier work on it. Hence, she ran down to her bike to go over to her lab and set up some experiments. Her ride was about 10 minutes on a regular day, but the shortest path crossed a railway track where a passing train could mean a longer commute. As her luck had it, that day indeed she was stopped by a long snaking train. As she waited for the gate to open, she suddenly noticed that three messages arrived on her phone at almost the same time. “That’s strange! All three arrived simultaneously when I’m waiting here”, she said to herself and started reading them even as the tracks were resounding with the passing behemoth. The first was a note saying that a package had been received for her at her residence. She thought to herself “That must be the knife Indrasena had sent over.”

The next mail was from her adviser. It read thus:
“Vrishchika, I know you are busy with the HMGXB3 project, but I really need a favor from you because you are possibly the only one in the lab who could pull it off. I just concluded a meeting with Dr. Mark Touchstone, and he has something really interesting regarding caspase-mediated destruction of neurites. This could lead to a major breakthrough in our understanding of Alzheimer’s and possibly a revolutionary new treatment. He needs a few experiments to clinch his hypothesis and wants to collaborate with me on that. I think you would be the only one able to do them at top speed. Please meet me next Tuesday when I’m back in office at 11:00 AM, and I’ll show you what he has, and we can design the requisite experiments. It will be a cherry on your CV that’s already shaping quite well.”
Vrishchika, thought to herself: “What the hell! This seems to be a distraction especially when I’m so close to taking the HMGXB3 fort but what to do … he seems quite excited by this.”

The final mail was from Clotilde, a young white indologist who had recently joined the faculty, whom Vrishchika helped with textual readings. She was reminding Vrishchika to come over to her house with dinner. Duly, having set up her experiments Vrishchika collected the dinner she had cooked and went over to Clotilde’s house. Clotilde had invited a learned from India as a visiting professor to collaborate with her on the arthaśāstra tradition. Apart from his knowledge of various śāstra-s, he was an advaita-vedānta-śiromaṇi, who had been adjudicated by one or more of the Śaṃkara-maṭha-s of South India as among the highest scholars in that tradition and also of grammar and music. Keeping with that, he was very observant of the carya-s in which he had a strong conviction. He would eat only appropriately prepared bhojya food on the floor from a silver plate with a central gold inlay. He had brought all the utensils to prepare and eat his own food; however, it was to take a few days for his apartment to get set up for him to start cooking his own meals. Till then, Clotilde was driving him to the local temple where he could have his victuals in the appropriate manner. He also only drank well water from a copper tumbler that he filtered with his own sieve and boiled — he daily obtained water in a drum from the temple well. However, that day the in-house meal service of the temple was closed. While the ācārya-jī, as he was called, wanted to observe a fast, Clotilde feared for his health as he had not eaten anything since the previous noon after which the temple services closed. She had convinced him to come to the mleccha land with great difficulty and did not want him to suffer such privations. Hence, she had asked Vrishchika to help with the meal. Clotilde had told the ācārya-jī that she would have a scripturally educated girl of a high clan serve him dinner. However, he was very dubious of the whole thing: He told Clotilde: “No truly traditional girl will travel and live by herself in a foreign country. Will she have had a proper bath before cooking the food and serving me? Moreover, will she be wearing the appropriate 9-yard apparel?” Clotilde told her that she did not know about all that but at least it would be a better choice than not eating.

When Vrishchika came, she found the ācārya-jī to be in a serene state quite ready to fast for the remainder of the day and beyond. Vrishchika assured him that while she was not wearing the 9-yard robe, she had the requisite baths, and was herself ritually quite pure due to observing chastity for her own mantra-sādhanā. However, she confessed to him that she was a physician and routinely came in contact, albeit via gloves, with blood and other fluids of humans and animals. The ācārya-jī’s swarthy face turned sallow on hearing this, and with many a plaintive apology, admitted that he could not consume her food. He said he was a man of tapasya and called upon the two ladies to not bother about him, leave him alone in a room, and complete their dinner with the stuff Vrishchika had brought. He also said he would not want Vrishchika’s labor on his behalf to go in vain; so, he blessed her that she would get a good husband, calling on the names of some Śaṃkarācārya-s, current and posthumous, believed to be endowed with magical powers. He also offered to cook food for her once his apartment was set up in return. Vrishchika: “It would be disrespectful to a learned as yourself if I were to accept such an offer. Incidentally, I’m getting married in the coming months once she graduated.” : “Young lady, I’m sure your parents have found you a good consort.” Vrishchika smiled and remarked: “It is as though I have been with my puruṣa through several janman-s. This will be just another day in the continuing journey.” Stirred by her comment which was partly meant in a jocular vein, the pious told her that she should attend his “Vedantic” lecture at the temple titled “punar api jananam punar api maraṇam”.

At that point, Clotilde asked the if H reconciled the idea of performing elaborate rites to the pitṛ-s with the idea of reincarnation and its wholescale acceptance in the Uttara-mīmāṃsā tradition he cleaved to: “If pitṛ-s are true then would it not negate reincarnation. How can they come to the ritual to take the offerings, if they have reincarnated and spending time in a new physical body?” The ācārya-jī declared that reincarnation was a real thing. Hence, a person had to make sure that they performed good deeds to ensure a better birth and eventually acquire release from the repeated submergences and emergences in the bhavasāgara through brahmajñāna. However, he added that the sūkṣma-śarīra-s of the ancestors persisted that they were the pitṛ-s to whom Vedic offerings were made. Clotilde then turned to Vrishchika and asked what she thought. Vr: “I favor a theory where most of the deceased exist as pitṛ-s since the śruti seems to advocate that as the primary position. However, I’m willing to concede that a certain number of them might reincarnate and drop out of the pitṛ-paṅkti. That said, I’m not sure what that ratio may be. I believe that a subset of these pitṛ-s manifests as ghosts under the appropriate conditions. Such were indeed the phantoms that I and my gang used to encounter in the house of our old friend and the cemetery near it.” The Vedāntācarya, however, continued to insist that they were still merely sūkṣma-śarīra packages without any cit.
Vrishchika: “However, given my experience with them, I would think that the ghosts exhibit signs of possessing cit — even as we assume another human to possess cit — like say an account of the experience of pain.”
The : “The ghosts you might have seen were not pitṛ-s but discarnate entities that have been blocked off for some reason from reincarnation or mokṣa. So, they would have an ātman still cloaked in a sūkṣma-śarīra, but the pitṛ-s that come to the Vedic rites should be seen as the sūkṣma-śarīra-s bereft of the ātman which has already gone on its journey. That’s how the sūkṣma-śarīra-s of deceased guru-s and siddha-s continue to help their votaries — after all these guru-s have either attained mokṣa or Nārayaṇāṅghri.”
Clotilde: “But ācārya-jī, would that not conflict with the basic theory of mind? If we make that assumption for living humans, then following the H philosophical tradition itself, we should also accord that for pitṛ-s and these ghosts of guru-s and siddha-s!”
Vr: “By the very nature of cit for the mortals like us locked in ahaṃkara it would be difficult to infer if that is the case or not. What the ācārya-jī is positing is that these entities like the pitṛ-s are essentially philosophical zombies. It would be hard for an objective interlocutor to distinguish a philosophical zombie, perhaps like a computer, from a really conscious one. Though, I must reiterate that my own gut feeling is that the entities like the pitṛ-s are conscious rather than zombies.”

Clotilde: “It is rather remarkable that our conversation took this turn. I had just told Vrishchika a little while back that my cousin Sally would be visiting this weekend. And this is something I’d rather not confess to any of my western academic colleagues — she has special mediumistic capabilities.”
: “What is that?”
Cl: “It is a term used for a person who can see ghosts and act as a medium through which what you’ll call pitṛ-s or bhūta-s can speak to the living folks.”
: “Sort of like a praśna-kāra in our midst…”
Vr: “Yes. Though the repertoire of these Occidental versions is a bit different from our modern versions. They focus primarily on bhūta-s/pitṛ-s rather than deva-s or yakṣa-s — perhaps a result of their fall to the pretonmāda.”
Cl: “ācārya-jī, would like to attend the session — we’d be doing it at night — it is often remarkable, and you can experience it yourself.”
: “Thank you ma’am — it sounds interesting. However, I must excuse myself because the Śaṃkarācarya had advised me to stay away from such things involving dead and discarnate entities. Moreover, I had promised to perform a homa for an acquaintance the next day and do not want to stay up for something like this.”
Cl: “No worries ācārya-jī. I’ll give you a ride to your acquaintance’s home on Sunday morning nevertheless.”
: “Ma’am that is very kind of you.”
Vr: “Why did the Śaṃkarācarya-jī ask you to stay away from encounters with such entities?”
: “I was once performing a homa at the home of an acquaintance of my father. Their house had two doors. One opened in the front through which people normally entered and another in the back which pointed towards a cemetery. They had opened both doors for ventilation after the homa and we were having our meals on the floor on the side closer to the back door. Suddenly, I heard the laughing and bawling of children. They were not those of the family — the noise came right from the back door which was open. While I heard the clear noise of the kids, nothing was visible when I turned in that direction. However, an extremely tall palm tree from the cemetery, standing like the leg of a kṛtyā sent by the rṣi-s Atharvan or Aṅgiras, was plainly in sight. Puzzled, I looked at my hosts who seemed to be going about their meal as if nothing had happened. Then all of a sudden, I saw two small fuzzy gray figures the height of small kids utter a blood-curdling yell and rush at me. I could see them run into me and vanish. After that, I had a variety of troubles both at home and at the university where I teach. Finally, I got the audience of the Bhagavat Śaṃkarācarya. A in his retinue diagnosed that I was seized by the bhūta-s from the cemetery. It took many different ritual attempts before a from Himācal, who knew Tāntrika stuff, finally relieved me of my grahaṇa and the suffering which came with it. It was then that the Bhagavat Śaṃkarācarya told me to stay away from such entities and pitṛ-vana-s and stick with the pure Vedic and devotional paths.”
Cl: “That is very scary. I completely commiserate with you.”
Vrishchika was very excited to hear the ‘s tale but felt it might not be proper to ask him too much and simply mumbled something in sympathy and kept quiet.

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On getting home from the meeting with the and Clotilde, Vrishchika picked up the package Indrasena had sent her. It was a nice full-tang Japanese kitchen knife made of wootz steel that could essentially be used as an all-purpose knife. As she was admiring her puruṣa’s gift, a thought suddenly passed through Vrishchika’s mind and she called her sister Lootika to see if might be consecrated as a siddhakāṣṭha. Lootika confirmed that it was possible. Then they got their other two sisters online and Vrishchika told them of her participating in the impending seance. Lootika asked her to make close observations and added a few notes regarding her own and Somakhya’s anthropological surveys of Occidental ghost-craft. L: “I feel a certain minority fraction of these mleccha-s claiming mediumistic capabilities indeed seem to connect genuinely to bhūta-s. Some of their tools of the trade, like the planchette, and probably also the dowsing rods and ghost dictation, are the same as ours and they probably get reasonable communications through those. The voice mediumship might also capture some genuine signals much like our praśna-s or prasenā-s. However, I think their use of electronic devices — motion sensors of various types, LEDs, and “spirit-boxes” that scan words in the radio, are mostly dubious or outright nonsensical. Those claiming to produce apports, ectoplasm or levitation, much like our Daṇḍāvālā bābājī or Śūl-vālī-mātājī (sans the ectoplasm that is peculiar to them), are likely to be about as dubious as our own counterparts who do the same.” Her sister Varoli added that she had seen a person of sub-Saharan African ancestry also use dowsing rods and pendulums with some success though she was not sure if it was their indigenous custom or they had picked it up from elsewhere. Jhilleeka chimed in that they should be careful of any claims involving obvious violations of natural laws.

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On the aforementioned Saturday night, Vrishchika went over to Clotilde’s house. A small group had assembled there consisting of Clotilde’s sexual partner, her cousin Sally, and a couple of their other friends. Clotilde introduced Vrishchika to them, and before long, they were seated in a hexagon of chairs with Sally centrally seated at the maximal apex. Clotilde’s male interest brought a small table and placed it in the center of the circle with a vuvuzela on it. He also placed a scary-looking antique Japanese doll about the size of a forearm on the table. The doll gave Vrishchika vibes of the encounter at Somakhya’s cousin Babhru’s house. Clotilde’s male companion remarked that in the most dramatic of cases, the ghost that comes through might sing or talk in an eerie tone through the vuvuzela, and it might begin to levitate. Vrishchika looked at him quite quizzically in disbelief. Sally said it was true, though she could not assure such a performance — it only happened on some occasions, but she added that the levitation of the vuvuzela was more frequent. Then she added, even more dramatically, that the Japanese doll might turn around and stare at specific people–if that happened, they might get a direct “download” from the ghost into their heads. She also warned Vrishchika not to touch the ectoplasm oozing out of her in the form of a whitish vapor or any form it might morph into unless that form bade her to do so. Sally then clarified that there were three types of ghosts who come through. The first were what she called her regulars, who opened and closed the session by speaking through her. Then there were the deceased kinsfolk and friends of any of the circle members who wanted to converse with them. Finally, there were the “drop-in” visitors who might just come in to tell their story or give a member of the circle some special information.

Clotilde drew all the blinds, switched off the light leaving only a couple of red LEDs as illumination, and allowed Sally to lapse into a meditative trance. After about 15 minutes, which seemed like an hour to Vrishchika, it seemed Sally was indeed in the requisite trance and remarked, “There is some powerful force that is blocking my regular ghost Don from coming through. I sense him throbbing within me pointing toward Vrishchika.” Vrishchika realized that she had her consecrated knife on her belt and was holding its handle in defensive deployment. Vr: “Ah, it must be my defensive deployment. If you permit, I’ll take my siddha-kāṣṭha outside the room.” The circle was surprised by the capacity of Vrishchika, and she coyly smiled without saying anything. Once she lowered the defensive perimeter, the ghost named Don burst through. Sally mysteriously started talking in a masculine voice, surprising Vrishchika a bit. “This alien girl here has some terrible magic about her. Even if we were to rush at her, she seems capable of overthrowing us like a puma taking a swipe at a coyote. Hence, I’m going to step aside and let in an alien fellow of her type who says he wants to speak to her.”

As Vrishchika was processing that with some astonishment, Sally went quiet for a minute. Then she started speaking in a different voice and language: “kiñjalako .aham । indrasenas tava kānto māṃ samyak jānāti । tavāgrajā ca tasyā bhartā cāpi ।” Now Vrishchika was positively shocked. This was the ghost of a that her gang had encountered more than once before and was now returning to her. She nor Indrasena had ever mentioned this Clotilde, and Clotilde had never seen Somakhya or Lootika. “This has to be a genuine stream,” she remarked to herself and perked up to hear what else Kiñjalka had to say. He repeated his tale (which she had heard before from her gang) of his valiant allegorical fight and death after being overrun by barbarous mleccha-s. He then went on to say something specific by starting with the projection of a mental image into Vrishchika’s mind: He first showed a stone and marked it with a silver and gold rod. Then, speaking via Sally, he remarked, “Caspase-6 does not have a Death domain — only a foolish or a deceitful man will think it will directly interact with the receptor DR6. Moreover, do you think the TNFR domains are specifically binding to the Amyloid-beta precursor (APP) protein? Look at the dirty low-complexity stuff. Be wary of he who is deceitful and he who has mistaken a pyrite for gold.” After that, a series of yells seemed to emerge from the vuvuzela, and all went quiet.

Then Sally continued, now assuming a totally different voice and accent. This was some deceased clanswoman of one of their friends. A comparable communication was repeated to the other friend. Finally, the common grandmother of Sally and Clotilde briefly spoke through the former and expressed her support for them. There was no vocal communication with Clotilde’s sexual partner, but the Japanese doll turned towards him, rattling on the table. Then another regular Dick appeared to speak through Sally and enigmatically remarked:
“When answers are sought, the phantoms may provide,
With signs from realms beyond, our kinship to abide.
If a yonder phantom drops into your ear or sight,
Their words hold weight and should not be taken light.
When the gift we bring falls into another’s hand,
they will suffer from it as though by destiny’s wand.”
Then Dick asked Sally to conclude the session. Then Clotilde’s male companion rose to bring some refreshments. As he did so, something tumbled down from his clothing. He picked it up and showed a small badger made of molded polymer. He passed it around, even as Sally declared that he had received an apport. Vrishchika noted that it was similar to the small animal models that came along with toothpaste cartons, which she and her sisters had collected as kids. While she found it curious, she was unconvinced that it was an apport. They sat for some time discussing what was quite an interesting experience for Vrishchika.

It was quite late that night when Vrishchika was riding back to her apartment. She passed by some Saturday night revelers, and then some fellows who were in a stupor on benches by the road having consumed some narcotics. Thereafter, she took a shortcut through a wooded patch, where the trail was lined by a row of seven pine trees. As she passed them, she felt she was being followed by someone. At first, she thought it was just her mind conjuring things inspired by the session they had just had. But sensing the feeling as persistent, she paused upon reaching the seventh tree and looked around. It felt as if someone was calling out to her from the wooded tangle. That got her adrenaline up, and she drew her knife from its sheath tethered to her belt and using it as a siddhakāṣṭha, she uttered an incantation to Vīrabhadra and made a protective digbandha. Once she did that, she felt the presence had been repelled, and she returned home without any further incident.

❉❉❉❉❉❉

It had been a busy but unproductive week for Vrishchika. But at least at the end of it, she was feeling relieved for having brought her advisor to nearly the same page as her. Kiñjalka’s ghost had put her on high alert when she met her excited advisor that week. She was prepared to expect something fishy in what Mark Touchstone had presented. Touchstone was claiming that the cleaved extracellular part of APP was a ligand for the DR6 TNFR-like protein. He further claimed that DR6 activation by this ligand was directly recruiting Caspase-6 for the pruning of axons — something he believed to be central to the etiology of Alzheimer’s. He wanted Vrishchika’s advisor’s help to work out the Caspase-6 dependent pruning pathway. With the phantom prodding her, Vrishchika realized that it sounded fishy, as Caspase-6 had no Death domain to be directly recruited to the receptor DR6. She brought this up to her advisor and told him that it might not be a valid line of investigation. He still remained unconvinced by her protestation. Then she brought up the issue that the whole APP DR6 interaction might be a figment arising from the sticky low-complexity region in the former rather than being a true ligand for the latter. This sparked a lengthy back-and-forth with her advisor, who felt that she was literally not wanting to collect the diamonds lying on her path because she just wanted to graduate and leave. However, things changed on the last day of the week when Touchstone sent them some of his raw data, and Vrishchika was able to show her advisor that the key images in support of his claim had been fraudulently produced. With this staring in his face, Vrishchika’s advisor had to fall in line with her reluctance to touch this project. However, in the process, Vrishchika had lost much of the week that could have been spent on more productive experiments.

She wanted a brief break to clear her mind and decided to visit Indrasena and Somakhya, which took a full hour by bike. But before she could leave, she received an urgent message from Clotilde. Earlier that week, Clotilde had mentioned that the apport her male companion had received had mysteriously vanished the next day, and they couldn’t find it anywhere. Since this was the least of Vrishchika’s concerns that week, she hadn’t responded. But the current message sounded more alarming. The ācārya-jī had been taken seriously ill, and Clotilde was hoping Vrishchika could use her connections in the system to get him good medical care. He had suddenly developed balance problems with repeated long episodes of nystagmus and dystonia. The urgent care physician had failed to diagnose him and advised taking him to emergency. Vrishchika swung into action and got him a quick consultation with a reliable neurologist. The neurologist was flummoxed as the ācārya-jī’s MRI was unremarkable and undiagnostic and suggested to Vrishchika to run some genetic diagnostics. Looking at those, Vrishchika found nothing notable; hence, they simply followed the neurologist’s advice to keep him under observation, treat him symptomatically with anti-spasticity agents and try to get him some physiotherapy if and when his condition improved. With that plan in place, Vrishchika finally left to see her fiancé and sister’s husband.

Having caught up with what was going on with Indrasena, she turned to Somakhya and asked, “Have you gotten everything ready for Lootika’s arrival next week?” Somakhya replied, “You know your sister well. She has her own ways. So, rather than aggravate matters, I have just decided to do nothing and wait for her to come and take charge of everything to cater to her nesting instincts. Maybe you could instruct Indra as to what he should do before your arrival — after all, he has more time than me.” Vrishchika, however, said, “Nah. I too would rather be in charge, for I’m not sure you guys will get all our little obsessions.” In & S: “Tell us of that, we’d best leave you girls to your devices when it comes to them.” Vrishchika then mentioned there was a lot of other stuff to fill them in on: the seance with Sally, the fake biochemistry of Prof. Touchstone, and, to top it all, the strange case of the ācārya-jī. The last point bothered her a lot, and as they walked out to get some lunch, she asked her folks more than once what they thought about it. Indrasena replied, “Gautamī, you are the physician here. If you don’t get it, what do you think we would have to offer — unless you are hinting it is not ‘medical’ at all?” Somakhya added, “I recall that little detail in your story regarding the ācārya-jī — his earlier seizure event — by those entities looking like the kids’ phantoms. Are you thinking he is innately susceptible and has been seized by something like that?”

Vr: “Yes, I wanted to see if you all might lend a voice to what I was playing in my mind as I rode to your place. As you know, my current clinical research involves PLP1 and the NACHT protein TANC2 gene polymorphisms, and conditions linked to them. Hence, I was taken aback when he showed symptoms that would match such a patient. In particular, when an episode would overcome him, he would show that telltale screeching tone in his breath which is seen with PLP1 patients. However, the onset was too sudden, and his age was too great for him to be a sufferer of that type of syndrome. But this illness seized him shortly after the seance with Sally. So, it is entirely possible that something remained behind to seize him, especially given that I myself quite unambiguously felt pursued after the sitting.”
S: “That’s indeed something to think about. First, you need to ascertain if he is indeed dealing with an organic disease or the phantom alternative.”
Vr: “Having played with all the possibilities, my current inclination is towards the latter alternative. Also, given the timing, as I just mentioned, it is probably something from the seance but how did it get to him and what is its provenance? Maybe I should ask if Clotilde could arrange another session with Sally to find out?”
In: “Dear Alini, I think we should try to figure this out rather than wait for Sally to try to figure it out. Even if she does, I doubt she has the capacity to reverse what has happened to him.”
Vr: “Sure dear, I too was thinking we must perform a major prayoga — maybe with you we should do the great prayoga of Vaiśravaṇa that restored the Japanese emperor in similar straits.”
In: “Given what you narrated of his earlier seizure, it seems that the mantravādin-s the Śaṃkarācārya recommended had difficulty because they had no clear diagnosis of what had seized him and how. I’m pretty sure that the Śaṃkarācārya’s network includes a rather competent crowd. Hence, we should be more circumspect before we launch into a grand prayoga. What we need is a better cikitsa, just as in medicine.”
S: “Somewhat tangentially… why would Clotilde write to you to specifically mention that the supposed apport vanished? Was she trying to conserve mass — something like a macroscopic delayed version of virtual particles in vacuum? Since we have descended so deep into this outré wilderness, should we not give it some consideration? Did you find something peculiar about apport?”
Vr: “Hmm… I really did not grasp why it was a badger. It did not seem to mean anything special to any of the participants. If it was Indra, I could imagine it as being a signal — maybe reminding him of the badger-like vipra who deployed the famed incantation of his ancestor. Otherwise, it was just a small plastic toy animal, like those which I and my sisters collected as kids. We might have even had a replica of the same badger, but it really meant nothing special to us.”
In: “Ah, now that missing apport gives me a thought. Let us for a moment assume it was a real apport and its vanishing has something to do with the ācārya-jī’s illness. Did it not happen shortly after the apport was reported as missing? Then, given what we know of such objects, they are not created de novo but transported from somewhere — if we could somehow trace where it came from and where it went then we might have some clue about this. I know this could be a dead end but in the least, we have to rule it out.”
Vr: “That’s why I was wondering if we could rope in Sally again.”
In: “I’m not opposed to that, but since we are whiling away our time on this matter, I’d suggest that we first try our own devices after lunch before we consider that route.”
S: “One possibility is a dūradṛṣṭi-prayoga — it would take some time for we would have to rehearse the prayoga first.”
Vr: “I think sis Varoli has some natural capacity as a draṣṭrī with the dvidaṇḍau or a siddhalolā. We should ping her as she could help confirm anything we get or be a backup if we fail.”
Vrishchika called Varoli and conveyed the story to her: she was excited to return to an adventure reminding her of their youthful days, but she was in midst of an experiment. Hence, ask her sister to proceed with her attempt and promised to get back to them after she was finished for the day. In the meantime, they rehearsed their prayoga using a Kauberīvidyā and deployed it with Vrishchika as the draṣṭrī, given that females tend to be better at this than males. However, Vrishchika did not pick any signal other than the ācārya-jī’s apartment, which came through multiple times — but given how obvious that would be she did not think much of it.

A little later, Varoli came online, and Mitrayu also joined to see a demonstration of her performance with the siddhalolā. With the siddhalolā and a map, despite being more than 400 km away, she was able to navigate her way to an apartment complex. Vrishchika: “Wow, that is the complex where the ācārya-jī is housed!” Somakhya and Indrasena looked at each other with some surprise and almost simultaneously remarked: “Wow. This is definitely a hit. It would not be surprising if she came to the town for after all Vrishchika lives there. However, her locating the apartment complex correctly is remarkable!” Then switching to direct dūradṛṣṭi, she mentioned a focus on a clothes closet in the ācārya-jī’s dwelling — however, even Vrishchika did not know of its inner layout. A little thereafter, she started moving again with the siddhalolā. This time she zeroed in on a park about 6 km from Vrishchika’s residence. By zooming in on the map they were able to see something fuzzy on one side of the park where Varoli felt the strongest signal but they could not make sense of it. Varoli: “That’s where the trouble is coming from. I also feel a distant cemetery through direct dūradṛṣṭi, but that seems to be in our homeland of Bhārata than here.”

It was getting late and time for Vrishchika to cycle back to her town. In: “Sweetie, it’s dark and better you reach home before it is too late, so let us catch a quick dinner before you leave. If you have the time, you can explore that park Varoli zeroed in on. In any case, we will come to your regions next Sunday with your sister in the tow to explore this further.”

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Lootika finally arrived late on Friday night to join Somakhya, and they were still lazily snuggling the next morning. Somakhya had just switched on his phone and, seeing a message on it, handed it to Lootika: “She sends it to me rather than you because I guess she wants me to convince you to get moving right away for this possible adventure.” Lootika read the message Vrishchika had sent Somakhya: “There have been some dramatic developments here in the matter of the unfortunate ācārya-jī. Hence, I suggest you guys come here right away in full force like our ārya ancestors surging to demolish a fort. Since Lootika would have not yet disposed of her car, ask her to drive you’ll here right away. Indra will be ready and waiting for you’ll. We’ll meet at the park which Varoli had zeroed in on. I’ll get there with Clotilde.” Over the next few minutes, as Somakhya filled in Lootika on details of the case of which she had only a minimal sketch, she shook off the vestiges of her slumber. The more she learnt of the case, the nostalgia for the old days grew: “Dear, this seems promising — in the least, we might have something of an adventure as in the old days.”

Ere long they were coursing away in Lootika’s ratha towards the park in Vrishchika’s town. When they reached, Vrishchika was already there with Clotilde. Even as Lootika, who was seeing her sister after a while, hugged Vrishchika, she excitedly remarked: “I believe we have solved a major piece of the puzzle. Varoli was spot on in identifying this place. Nevertheless, first things first. Something dramatic happened yesterday. The ācārya-jī’s acquaintance, for whom he had performed a homa, was assisting him — visiting him daily, helping with food and nursing, and generally working on his mood. Even as he seemed to be doing slightly better when on Friday morning, ācārya-jī’ had a terrible attack of dystonia and a potential neuropsychiatric episode when he started clenching his fists, kneeling down and emitting peals of frightening laughter. As a result, he missed his saṃdhyopāsana-s and his mood worsened even more. Earlier that day, his acquaintance had laundered his clothes and placed them in his closet in a box. Suddenly, he found a bunch of them stuffed in the commode! Even Clotilde and I saw that! That was the reason for asking you all to come right away — this is something needing major action.”

L: “By heaven and earth — that is awful but not something we have not seen before — this seems just like the sprite which oppressed Vidrum and others!”
In: “But Alini, what about the piece of the puzzle you solved?”
Vr: “Come, look at this!” She led them to a little roadside memorial just at the edge of the park — exactly where Varoli had pointed in her dūradṛṣṭi. It had a placard with the picture of a girl reading “To dear Jenni who was snatched away too soon.” There were flowers placed around it along with a clump of molded-polymer animal figures on which all their eyes fell at once. In: “Ah here is where the supposed apport comes from…” Before they could ask anything else, Clotilde remarked: “I don’t still find the badger here. But all these models are of the same make as the badger. Moreover, I did some sleuthing as we were waiting for you and found that this Jenni was a juvenile actress. She was crushed by a truck right here on the road beside the park. Her family which was in the park is said to have seen a `silvery apparition’ of her float past them. A little later they found her corpse on the road. Evidently, they or her fans made this memorial for her.”
Vr: “Hence, I believe, her ghost probably dropped in during Sally’s séance, and the ācārya-jī has been possessed by her — I suspect he has some innate susceptibility to vīrakanyakā or vīrabālaka possession.”
In: “Something doesn’t fully add up though. The symptoms he exhibits, including the latest one, are generally not consistent with such a grahaṇa. Moreover, both this one and his earlier possession seem malignant, which is uncommon for vīrakanyakā or vīrabālaka when they possess relatively ordinary folks. Instead, this seems like a more sinister graha.”
L: “That’s right. This reminds me of some of the graha-s I encountered in the text known as the Daśānana-prokta-Rāhumātṛ-kalpa. I think we should try to sweep it out of the victim with the Cāmuṇḍā-graha-vidyā.”
S: “Jālini, while generally in the right direction, think a little bit more. We still have this mysterious connection to this accident shrine. I don’t think that is a false positive. Put the two together. Indrasena, what does this remind you of?”
In: “Ha! Somakhya, I think we have the real solution! It brings to mind our visit years ago to the little shrine in my hometown. Attached to it was a mantravādin skilled in treating grahaṇa-s. He told us of the graha-s that first seize bhūta-s and use them as conduits to enter their victims.”
S: “Indeed, I think it is the same graha, which seized the in India using the cloak of bāla-bhūta-s that could not attain a vīrakanyakā or vīrabālaka state, that has returned with a vengeance against him.”
L: “Yes, the Daśānana-prokta-Rāhumātṛ-kalpa names two such the Kapilagurugraha and the Heḍhraga-graha. It is one of those. But how do we deal with them?”
S: “Given that our is a pious man, I suspect his seizure is a Heḍhraga.”
In: “In the manner of the mantravādin in Kṣayadrājanagara, I think we will have to deploy the terrific Dravidian rite to Śastṛ, the Southern ectype of Revanta, accompanied by his wives Madanā and Varṇanī, his son Satyaka, and his assistant, the ghost-master Damanaka.”
S: “Sure, that’s the right choice. Why don’t you lead it as the pradhānasādhaka — it will mark your status as a Sarvādhikārin who has mastery of the rituals of the Cīna or the Drāviḍa type. and I’ll ensure correctness as the brahman. Lootika and Vrishchika, deploy Vīrabhadra and be ready with your siddhakāṣṭha-s for I’m pretty sure action will come your way.”
Clotilde: “I’d really like to witness this. I hope you would let me be around.”
In: “You are welcome, but remember if a woman who is menstruating attends this rite, her arms will be disabled or permanently fractured. Hang close to our girls. Vrishchika and Lootika, make sure you shield those who might be around. Now we need to get some things for the rite which might not make the ācārya-jī happy. Maybe Clotilde can help us with that? We would need 5 garlic bulbs, rum, and chips of the cooking plantain as a substitute for meat.”

Reaching the ācārya-jī’s apartment, they inactivated the fire alarm and commenced the terrific Dravidian ritual exactly 48 minutes before sunset. Lootika and Vrishchika started it off by loudly hammering a mortal and pestle for some time. Then Indrasena commenced with ghee oblations to the god Śastṛ, followed by those to the goddesses Madanā and Varṇanī and then to the little god Satyaka. Each was made with a loud utterance of Phaṭ and Vauṣaṭ. At each of those oblations, the ācārya-jī felt his body stabilize and calm down. Then, Indrasena brought out the garlic and offered them to the ghost-master Damanaka. As the terrible odor filled the space, he uttered a cackle of strange words from the Dravidian language that called upon a cock to slay with its clawed feet. At the last of those oblations, the ācārya-jī emitted a horrible sound from deep within his body, and Clotilde sprang up shouting “Did you see that!” The ācārya-jī’s acquaintance responded affirmatively saying he saw a girl run into the closet. Vrishchika asked Clotilde to go up and look into it. As she did so, Clotilde gasped: “Hey I found the badger! it is lying right here.” Lootika and Vrishchika asked her to collect it and return close to them. By the Indrasena had proceeded with offering the cooking plantain chips. He faltered in the Dravidian chicken utterances and held his throat and dropped his darvi into the altar. Somakhya, quickly uttered them in the correct form and picked up the darvi before it burnt up, made an oblation and asked his friend to continue. At that Indrasena recovered and moved on to make the rum oblations. As the fire rose to lick the liquor, the ācārya-jī’s acquaintance claimed he saw a terrible black figure rise up from the fire. The next moment the ācārya-jī emitted another ghastly noise and Lootika perked up as though something was rushing toward her sister. Protectively, taking Vrishchika in her embrace, she deployed an incantation with the siddhakāṣṭha. Vrishchika soon followed suit with her sister doing the same with her kitchen knife. Vrishchika whispered to Lootika the Heḍhraga-graha is still hanging around trying to break into our defense. To decisively get rid of it, we need to direct it to another victim. L: “Whom should that be?” Vr: “There is a somewhat mentally deranged, professor of South Asian studies in the MESAS department who is a brahmadviṭ. She would be no worse from housing this graha. I will send it hurtling into her.” Uttering the spell ending in ava brahmadviṣo jahi, Vrishchika acted on her words even as the third Pāṇḍava sent Jayadratha’s head hurtling into Vṛddhakṣatra’s lap. Suddenly the crackling of the plantain chips and the rum in the fire quietened, and Indrasena made an oblation of saugandhika to lighten the air. The ācārya-jī sat up erect saying he was feeling great. Indrasena completed the uttarāṅga of the rite and offered tarpaṇa-s to the deities even as Somakhya tied a black rakṣa on the ācārya-jī’s wrist invoking the great Indra. The ācārya-jī declared himself to be free of the disease and kept reciting the Nārāyaṇāṣṭākṣari-vidyā. Vrishchika asked Clotilde to drop off the toy badger at the memorial of Jenni without delay.

A little later the four were having dinner at Vrishchika’s place. Vr: “I think our little sis Varoli’s dūradṛṣṭi was really on target.” L: “Yes, she seems to have really grown in that regard. In retrospect, I’d say that her third hit, the cemetery back in the deśa was pointing to where the Heḍhraga ultimately came from. My suspicion is that the mantravādin in the Śaṃkarācarya’s network drove it out the first time but could not hurl it out of the ācārya-jī’s orbit in entirety. Thus, the graha was waiting for an opportunity to seize him again. The phantom of Jenni seems to have dropped in at the seance with the apport and the graha made use of her to retake the . All said, in every way, this rivaled our encounter with the Āpastambagraha that had seized Somakhya’s cousin.”
I: “Having heard of that tale from Yashashravas himself, I wonder if we are destined to encounter more such graha-s in our life. But this was actually a harder one. Had we not had that discussion with the mantravādin at the little shrine in my hometown this would have been a formidable case to crack.”
S: “I must mention that we were also lucky that, shortly after seeing that mantravādin, some remarkable clues came our way regarding such cases from a most unexpected quarter. On some afternoons, Indra and I would spend time reading and discussing some historical arcana. One day we obtained this book on what was called the zhiguai recorded by the Cīna-s when the belligerent Tang held sway. Let me read out the relevant section”.

Having found the relevant notes in his collection, Somakhya read out a translation of a zhiguai:
“Teng was a young scholar of enormous learning — he was a master of various branches of Chinese schools as well as the texts of Dharma. One day he went to attend a fire ritual being performed by the Iranian physician Li Xun. Teng died soon thereafter. Li Xun believed he was slain by an Upāpō Gaṇdarewa because he had removed his mask during the ritual. Several years later a girl named Wang Fazhi from Tonglu, barely aged five, started claiming that she was closely associated with Teng in her past life – maybe his wife. Shortly thereafter she died. As her kinsfolk were preparing for her funeral, a vendor of human flesh for the soldiers appeared to purchase her corpse. As the negotiations were underway, all those assembled saw her phantom that strongly admonished them from selling her corpse. Frightened, they sent away the flesh vendor. At that point, her corpse started to move by itself, and Fazhi came back to life! Soon she started showing episodes of speaking like Teng and would hold scholarly debates with learned men, give learned opinions in legal courts and discuss mantra-s with Vajrācārya-s. However, on other occasions, she would scream in an abominable manner and prance around in a convulsive manner. Her parents took her to the famous ācārya Saroruhakuliśa. He consulted the book of luocha Luofonu (Rāvaṇa) and declared her as having aweishe. The graha possessing her was believed to be a Kapilagurugraha. It was believed that, upon Teng’s expiration, his phantom had become the said graha.”

S: “Evidently, Teng as the Kapilagurugraha had reanimated Fazhi via her own phantom.”
Any resemblance real persons or incidents should be seen as a mere coincidence.

Some ruminations on asteroids and meteoritic falls

Recently, we received the news of a Russian spacecraft meant to bring some astronauts back to earth being hit by a meteorite. In early February we saw an obscure news item of the sighting of a meteoric fireball over Krasnoyarsk. This brought to mind the several spectacular meteoritic falls in Russia. There was the dramatic Tunguska event that occurred on June 30, 1908, in a remote part of Siberia. While no one was killed by the fall, it is said that people standing over 60 km from the site of the hit were felled by the shock waves it unleashed. Modern estimates say the Tunguska explosion might have been equivalent to 10 million tons (10 mT) of trinitrotoluene — effectively close to one of the biggest nuclear bombs that was in active American service during the Cold War according to declassified files from 2014 (B53). Thus, such an asteroid falling on a city would obliterate it.

Some books are probably mostly lost to humanity. Our father liked to prospect for old books of interest in a junk paper shop. Thus, in our early youth, he procured for us a ₹2 Soviet book on meteorites, which was rather good for the era. Our copy is probably lost, along with several other Soviet volumes, among the load of old books in our parents’ home and we have not seen a version of it online. That book gave a rather gripping account of the great fall of the Sikhote Alin meteorite on the morning of 12 February 1947 in far eastern Russia. The book described it as a momentous event for Russian science, triggering a cascade of studies to get to the bottom of the phenomenon. It described how the adventurer-researchers traversed difficult terrain to find the ground zero of the impact. It was an iron meteorite that exploded in the atmosphere before hitting the ground. Hence, there were multiple craters making it difficult to obtain a measure of the energy of the impact. Persevering in rather harsh conditions, the Rus found numerous fragments of the meteorite — including some huge ones with a mass of over a ton. Some of these had penetrated the ground to depths of 6-8 meters, which they arduously dug out. Then they used magnetic mapping, given that it was an iron meteorite, to determine the actual radius of the impact site in the dense forest. They also performed a chemical analysis of the fragments and arrived at the hypothesis that it might have been a fragment of a core of a protoplanet. Finally, the chairman of their scientific team Fesenkov was able to use all the data gathered to determine the high eccentricity elliptical orbit of the object and show that it had its origins in the asteroid belt. The post-entry mass of the fall was about 23 tons broken up into multiple fragments, but the pre-entry mass is estimated as being several times higher. In the same book we also first came to know about the Tunguska incident, which was compared to the Sikhote Alin incident, with a brief account of the Russian expedition to that site. A few months after we read this book, the Indian state TV broadcast a translated Soviet documentary on the Sikhote Alin fall, recapping some of what we had read.

A Soviet magazine also reported a shower of chondrite meteorites falling in Jilin, Manchuria between 3:00-4:00 PM on 8 March 1976. That one too broke up into several fragments forming bright fireballs and the largest that hit the ground was well over a ton in mass. The report compared this fall to another shower that occurred in Ta-yang, China on 25th April 1915, when a woman’s hand was cut off by a meteorite of over a kilogram. An American popular astronomy book described a similar meteorite shower of many thousands of stones that occurred in Holbrook, Arizona on July 19th, 1912. Even as these accounts were getting us interested in meteoritic collisions, we learnt of the then recently proposed hypothesis of Alvarez et al. that the great Cretaceous-Paleogene extinction was likely caused by the impact of a massive asteroid. This jibed well with our developing sense of meteoritic catastrophism, and we became instant converts to that hypothesis. Thus, we were dragged into the debates of asteroid impacts versus various alternative hypotheses. Hence, it was a matter of considerable excitement to us when we read of the discovery of the Chicxulub Crater in the Yucatan peninsula as a possible candidate for the K-Pg impact. Since then, it has become one of the best-supported cases of a meteoritic impact triggering a mass extinction.

Figure 1. Known, possible and disputed impact structures in Quebec

Ruminations on the K-Pg impact got us more generally thinking about the relics and signatures of other such impacts and their statistics. This note is merely a record of our latest return to this topic. One question that we kept thinking about but found to be generally ignored in the popular literature was: Is there some kind of bias in the impact craters we see on the earth? Looking at the Moon, it became clear early on that there was some bias in crater density over the surface. A recent analysis using the Lunar Reconnaissance Orbiter has confirmed this and has shown that there are two distinct patches of dense cratering in the southern nearside and north-central far side of the Moon. In contrast, the Mare regions and the regions near the Orientale giant impact structure have a low density of craters. Thus, it is possible that the Earth too shows some bias in the distribution of craters. The issue is, unlike the moon, a low-activity planetary body, the Earth is highly geologically active. Thus, earthly craters can be lost by erosion, igneous and tectonic activity making it difficult to objectively measure the cratering bias on Earth. Indeed, it has been estimated that about two-thirds of the Earth’s surface might have a mean age of about 60 million years (Ma) resulting in obscuring of the older craters. Moreover, much of the earth is covered by water, and submarine craters are hard to confirm.

Nevertheless, we observed that the Canadian province of Quebec seemed to have a high density of easily detectable craters relative to much of the world. We have at least 8 confirmed craters (11, if we take nearby ones in adjacent provinces) of various sizes from the little ones like Pingualuit and Presqu’île to the giant Manicouagan (Figure 1, cyan). There are another 8, which are to our knowledge unconfirmed or disputed by some (Figure 1, orange): One of the latter is the giant near circular arc of the Nastapoka. While some have disputed this as a geological structure, we think the evidence in support of it being a remnant of an ancient crater with subsequent geological modification is reasonable. The arc of Mistassini-Otish also seems a possible remnant of an ancient impact crater with some supporting evidence. While the geologists claim that the Mecatina structure is a geological formation, we remain skeptical and believe it is an impact structure with some reworking. The disputes regarding some structures aside, the bias towards Quebec still remains especially given that there are some relatively secure structures that are not seen on the above map, like Sudbury, the Charlevoix structure and the underwater Corossol.

So, the question arises as to why we see this bias? A priori, one could present 3 possible reasons: 1) There is some bias in terms of how the impactors approach the earth at the time of the collision; 2) Taking the cue from the above-mentioned meteoritic showers, one could posit the breakup of a large body that then produced a localized shower directed at Quebec. 3) Quebec is marked with ancient hard igneous rocks with little new geological activity that has occurred since their formation; hence, they preserve the impact record better than elsewhere on the Earth.

While we do not precisely understand the causes for the bias in the distribution of lunar craters, astronomers have reported before that terrestrial planets might show a latitudinal but not longitudinal bias in cratering due to impacts from the asteroid belt. This would be consistent with reason #1, but the published theorized bias proposals for Earth imply a greater bias toward the equator, which would not match the Quebec situation (or Baltic-Scandinavia; see below). Moreover, if these craters are of different ages (see reason #2) then the paleolatitude of the place might have differed from its current one. Reason #2 is not supported by the geological data. Geological analysis suggests very different ages: for example, the giant Manicouagan is dated from the late Triassic (215.5 Ma), whereas the little but perfect Pingualuit is believed to have arisen from an impact occurring 1.4 Ma. The more bizarre case is that of the twin Clearwater craters. Astronomers believed they could have been products of an asteroid breakup or a twin asteroid (asteroid with a moon) impact. However, geologists suggest that Clearwater East is from the Ordovician ( 465 Ma) while Clearwater West is from the Permian ( 285 Ma). If these two widely different dates are true, then it does raise the paradox of the low probability of two hits of comparable magnitude occurring next to each other on the Earth. From the lunar craters we know this is possible over the long history of a planet; however, on earth, even for Quebec, we do not find the evidence for a comparable multiplicity of local hits as we see on the Moon (except if consider Wanapitei which might be adjacent to what is believed to a distorted but possible ancient impact site — the Sudbury basin). That leaves us with reason #3, which appears to be the least incredible of the three: the geology of the Quebec region, with its ancient Precambrian crust and lower intensity of subsequent resurfacing, was simply one which preserved impact features better than others. In support of this proposal, one might point to another possible region of over-representation — the Baltic-Scandinavian region (especially Estonia and Finland; see Figure 4, panel 1 below) with a comparable geology. However, here not all craters are obviously visible as in the Quebec region. If this were indeed the case, then the Quebec region preserves a remarkable snapshot of the intensity of bombardment faced by the Earth. Among other things, it might provide a record that can be correlated with a potential extinction event, even if not of the magnitude of the Chicxulub impact. For example, a reexamination of the Manicouagan impact date has led to the suggestion that it might have triggered extinctions of radiolarians, ammonites and conodonts (complete extinction).

The geography of earthly impact structures then led us to a detour into the impactors themselves. Having laid our hands on a Russian catalog of asteroids via a professional astronomer contact, we decided to explore their statistics. We redo this with the latest data from NASA considering only those from the core asteroid belt, i.e., lying between Mars and Jupiter (we leave out the Trojans — asteroids captured by Jupiter at the Lagrangian points L4 and L5). Figure 2 shows a plot of the semimajor axes and periods of 1,193,253 such asteroids.

Figure 2.

It is immediately apparent that the asteroids are not uniformly distributed in the belt. There is one relatively small group the Hungarias, prototyped by the eponymous asteroid, which is close to the Martian end. On the Jovian end, we similarly have two smaller groups, respectively prototyped by Cybele and Hilda. In between is the core belt with three main peaks the inner, central and outer asteroid belts. Vesta is prototypical of the inner belt and Hygiea of the outer belt. We see that there is also some substructure to the central belt with two prominent peaks, the inner one with Eunomia as a prominent member and the outer one with the larger Ceres and Pallas. There is also a little peak between the central and outer belts, with Psyche as a prominent member, and a shoulder to the outer peak featuring Winchester as one of the larger members. The gaps in the distribution were discovered by the astronomer Kirkwood in the 1800s — a rather notable achievement with much lesser data (the great asteroid-discovering Blitz of the German astronomer Max Wolf still lay in the future) and when the USA was in the relative backwaters of science. He correctly realized that these concentrations and gaps were forced by resonances with Jupiter. If is the orbital period of Jupiter then: (1) The Hungarias are concentrated at a period of days followed by an exclusion gap at days. (2) The inner and the central belt are separated by the resonance of days. (3) The days and days resonances respectively bound the Psyche peak from the central and outer belts. (4) The outer belt is bounded by the days resonance and the Cybeles are concentrated by the days resonance. (5) The Hildas are concentrated by the days resonance. (6) Finally, we could see the Trojans as being in a 1:1 resonance. What we learned from these resonances was to help us understand the structure of chaotic maps we discovered later in our life and the generality of this principle in various Hamiltonian-like maps.

These divisions in the belt are also reflected in a chemical differentiation among the asteroids. The constituents of the inner-most belt, the Hungarias, show a dominant proportion of enstatine (E-type) asteroids, composed of a MgSiO$_3$ – FeSiO$_3$ composite mineral, that might be an early-forming silicate, which was potentially injected into star-forming nebulae from even earlier stars as it has been detected in certain planetary nebulae. The inner belt and the first hump of the central belt are dominated by stony or conventional silicate-rich asteroids (S-type, e.g., Eunomia). These tend to be bright asteroids and are more easily visible from earth. From the second hump of the central belt onward to the outer belt the Carbon-rich (C-type) asteroids of low reflectivity dominate (e.g., Hygiea). In these asteroids, Carbon occurs in all forms — a rich mix of organics, graphite and inorganic carbonates. Centered around where the dominance of the S-type gives way to the C-type, we have the peak of the metallic asteroids (M-type; e.g., Psyche). While not a dominant group in any region, they are enriched in iron-nickel metallic phases that might be combined with either the dominant chemistry on either side — i.e., silicates or carbonaceous material. The outlying Cybeles and Hildas are dominated by an even darker type of asteroid the P-type which like the C-type is rich in organics. Their reddish hue and spectra indicate that they have surfaces rich in complex organic mixtures of aliphatics, polyaromatics and tholins with C-N bonds. When we first learnt of the organics in the asteroids, it became a topic of great interest to us due to the implications it has for the origin of life. Notably, the inner asteroids tend to broadly resemble the rocky planets in chemistry suggesting that they are material left over from the formation of rocky planets in the inner solar system. In contrast, the organic-rich outer asteroids resemble the constitution of the gas giants and their tholin-rich moons suggesting they are material left over from the formation of the outer planets. The coming together of this outer and inner material, along with the metals essential for life from the M-type, might have been critical for life to take hold on the inner rocky planets like Earth.

Figure 3. The diameters of Ceres, Vesta, Pallas, Hygiea, Interamnia and Europa are indicated with vertical dark red lines in the bottom two panels.

We then looked at the distribution of the size of the asteroids (Figure 3). The top two panels show the plots of asteroid diameter vs semimajor axis and period. The expected division into the 3 core belts and the outlying flanker belts is seen. Additionally, we see that the maximum size attained by the Hungarias is smaller than the rest. While the core belts have at least one outstanding member: Vesta (inner); Ceres and Pallas (central); Hygiea (outer) the remaining large members are comparable across the belts all the way to the Hildas. However, there seems to be a trend towards slightly larger median sizes as one progresses from the inner to the outer belts. This might merely reflect the fact that the fainter, smaller objects are harder to detect in outlying regions, especially given their carbon-rich dark nature: e.g., S-type Juno with a mean diameter of 246.596 km is brighter than the bigger Hygiea, the largest C-type member of the outer belt. This is also supported by the overall distributions of size (Figure 3, bottom two panels). Considering all the asteroids discovered as of the end of Jan 2023 with average diameter data, we find a clear unimodal distribution. However, the plot displaying the number of asteroids with a diameter below a certain value shows a central linear increase (log-scale) suggestive of a power law distribution. Together these plots suggest that while there might be some real over-representation at certain places in the lower and higher ranges, the modal size distribution of currently detected asteroids is likely due to under-detection at the lower range and genuine rarity of larger representatives. In all four plots shown in Figure 3, the predicted size range of the “dinosaur-busting” Chicxulub impactor is shown (dark red lines in the top two panels and blue lines in the bottom two panels). It is among the largest of the known impactors in the last 800 Ma. This brought us a full circle to look at the distribution of the sizes and energies of the impacts on earth (Figure 4).

Figure 4.

For this, we used a dataset of 190 Earthly impact craters with location, diameter and approximate inferred age. The location of these is shown in the top left panel of Figure 4. The plot of diameter against the age is shown in the top right panel of Figure 4. One can see that truly large craters (diameter > 100 km) are rare and relatively ancient (Sudbury, Chicxulub and Vredefort are the only ones in this set). The youngest of them, Chicxulub is 66 Ma. Of course, there are more of them, but we do not have all the data on them, or some remain unconfirmed (see above). Estimating the average diameter of the impacting asteroid is much harder because that depends on various other factors, chiefly, the density and velocity of the impactor that cannot be estimated from just diameter. Nevertheless, given that extensive work on Chicxulub has produced approximate estimates, we can say that the mega-impacts that could trigger mass extinctions do not seem to be very common though asteroids in that range are quite common (Figure 3). The very largest impact structures like the Mistassini-Otish lake or the Nastapoka Arc evidence which are not uncontroversially confirmed are again estimated as being very ancient — i.e., older than 2 billion years supporting the idea that “globally life-changing” impacts are quite uncommon. However, as can be seen from the bottom left panel of Figure 4 the distribution of confirmed impact structures has a modal distribution. This distribution can be seen as arising from two factors: at the lower end, the smaller asteroids burn up as fireballs during their atmospheric transit and are left with a low mass to generate an impact crater that might survive geological resurfacing. Indeed, the small bolides that hit the Earth more regularly (see below) produce microcraters that are rapidly eroded or filled up in a matter of months or years. On the higher end, the rarity of these events again leaves us with a small number of craters. The modal diameter range appears to be 5-10 km. While, as noted above, it is hard to estimate the size of the asteroid creating craters in this range, there has been a longstanding effort to estimate the energy of the impacts from the crater diameter. The first famous formula in this regard goes back to the pioneering crater investigator Eugene Shoemaker. We use a recent variant of the same to convert the diameters to energy (bottom right panel of Figure 4):

Here, the energy is in , i.e., megatons of TNT; in turn in standard physical units. For comparison, the biggest American and Russian nuclear weapons were approximately in the 10-50 mT range. From the above, figure it is apparent that the modal energy of the impactors in this dataset will be 1000-10000 mT range. Even if the above formula is overestimating the energy by a factor of 10, the modal impact would be 100-1000 mT, which would be 10-100 times the most powerful nuclear weapons. Thus, while such impacts will not have global consequences for life, unlike the rare right-tail events, they definitely could negatively affect an organized civilization by taking out a city or two. Even a Tunguska-like event over a populated center could have wiped out a city like Delhi — indeed, people have remarked that a delay of a few hours might have taken out the Russian city of St. Petersburg or some other one in Europe.

Figure 5.

Finally, to get a feel for the actual danger of such an event we took a look at a dataset of 1225 actual meteoritic falls recorded between 861-2022 CE (Figure 5). The top panel shows the distribution of the recovered mass of these falls. This again shows a central tendency with the modal region around 1-10 kg. Another way to look at it is to plot the mass of the falls by year. Since, good records are available only since the 1800s, we do this only for the window between 1800-2022. The largest event in our dataset from this period, with a final mass of 23 tons, was the Sikhote-Alin fall that opened this note. The Rus estimated the energy of this fall as approximately in the range of the American weapons used against the Japanese in Hiroshima and Nagasaki. If one considers the mass of over 1 ton, there have been at least 6 such events between 1947-2013. If we assume the average frequency of such observed events is approximately 6 per century, then the chance of at least one event like Chelyabinsk is 0.9975. However, the chance for a city-buster is clearly much lower — in fact, there is no clear evidence for such an event in recorded history though some less supported claims for such catastrophism have been made.

Figure 6.

Finally, though the prediction would be for an absence of bias in terms of the mass falling on a country, there is a clear bias in the falls for which data exists (Figure 6). When we consider the 9 largest countries — Russia, China, Canada, Brazil, USA, Australia, India, Argentina, and South Africa — we find that Russia shows a significant bias in terms of the total mass of the falls. However, in terms of the total number of falls, the USA and India show a clear bias. In the case of the USA, this could be attributed to more careful documentation of the falls. The bias of India is less explicable given that it has a comparable population density to China. Notably, the median mass of the falls has Canada as the top scorer. This might imply that ultimately the bias towards Russia is merely a consequence of some “black swan” events rather than something deeper. This, along with population density and documentation differences, maybe more generally the cause for these biases but we really do not know.

Comet C/2022 E3 (ZTF)

The dispiriting cloud cover lifted briefly on two nights (Wed 8/2/2023 and Fri 10/2/2023) finally giving us an opportunity to catch the latest Agni-putra-ketu in the welkin, Comet C/2022 E3 (ZTF). On the first night, there was still some haze, but we managed to barely get it with our . It was easy to track given its proximity to Aurigae. Below , the triad of stars, HD 31233 (7.34), HD 31234 (7.47), HD 30842 (7.59) bounded the comet and their magnitudes, along with that of HD 30453 (5.91), in the vicinity allowed us to estimate its magnitude as . Below is a long exposure image captured by our friend’s camera that illustrates the position and the view close to what saw through our .

On the second night, we had a clear period between 6:40-6:55 PM when we got a much better view of the śikhin close to the zenith than on the first night. We could discern a faint tail. It had come close to Mars and could be seen in the same field. HD 29459 (6.25) offered a comparison and the comet was approximately the same magnitude as it. It was a reasonably good night with the ecliptic studded with Venus (-3.8) close to the western horizon, Jupiter (-2) above it and finally Mars (0) all visible to the naked eye. Between Jupiter and Mars was Uranus (5.8), which from our urban locale, was too faint for the naked eye.

This comet’s eccentricity has been estimated at 1.0003320 or 1.00002 — the first comet in our lifetime of comet observations so far that has come this close to a parabola — it is not going to visit these realms again unless some unpredicted gravitational perturbation occurs in far space. In high-resolution photos, its color is recorded as distinctly green. This color brings to mind the cometary observations of ancient H astronomers. Unlike their post-Siddhāntic counterparts who developed a serious character flaw in the form of a disinterest in the sky outside the ecliptic, the early H astronomers of the Vedic age were intrepid comet-watchers. Some of their comet lore is preserved in AV pariśiṣṭa-s and also by the much later, great naturalist Varāhamihira. These old observers like Nārada, Asita, Devala, Garga and Parāśara are said to have recorded 1000 or 101 comets and vividly described their properties. Nārada had the peculiar theory that all comets are merely reappearances of the same one. We do not know if this surmise came as a result of some knowledge of Halley’s comet or was pure speculation. The appearances of these comets were linked to an ancient H omenology resembling the Roman Omina et Portenta — comets with certain appearances were believed to bring weal while others were said to prognosticate more negative events. Aristotelian physics believed comets to be atmospheric phenomena — this view remained current in Europe until Geminiano Montanari showed them to be distant celestial objects. In contrast, H tradition distinguished atmospheric and earthly formations resembling comets from the truly celestial one and saw the latter as “sons” of the planets or of gods. The grouping of the comet (the deathly Dhūmaketu) with the planets (graha-s), the Moon, the Sun, planetary shadows (rahu-s) is already known in the Atharvaveda (AV-vulgate 19.9.10) and distinguished in the said sūkta from earthly phenomena. Varāhamihira, probably following these earlier authors, also noted that while luminous, the comets are not “fiery” but emit reflected or “phosphorescent” light. In any case, a green comet along with those displaying several other colors are classified in the old H tradition among the comets known as the Agni-putra-ketu-s — the sons of the god Agni.

śuka-dahana-bandhujīvaka-lākṣā-kṣatajopamā hutāśasutāḥ |
āgneyyāṃ dṛśyante tāvantas te +api śikhi-bhayadāḥ || (Bṛhatsaṃhitā 11.11)
Of the color of a parrot (green), fire, Bandhujīvika (flower), lac or blood are the sons of Agni.
They appear in the south-east and such comets cause (prognosticate) fear.

The H portent tradition also associates a passage of a comet through an ecliptic constellation with certain outcomes, in this case, negative:
aśvinyām aśmakapaṃ bharaṇīṣu kirātapārthivaṃ hanyāt |
bahulāsu kaliṅgeśaṃ rohiṇyāṃ śūrasenapatim ||(Bṛhatsaṃhitā 11.54)
If the asterism of Aśvini [is “smoked” by the comet] the lord of Aśmaka is killed, Bharaṇi the lord of the tribals is killed;
If it is the Pleiades cluster then the lord of Kaliṅga, it is its Rohiṇi, then it is the Śūrasena lord.

Thus, the old H would have seen this as a negative portent for the Śūrasena-s.

In commemorating our observations of the comet, we composed two awful verses that we anyhow append below:
Night 1:
And there stood the Rudra known as Paśupati,
even as the polycephalous leonine avenger of Sati.
Then there was the Rudra Bhauma, glowing red,
even as the red Rohiṇī trembled in dread.
Betwixt them lay sprawled Prajāpati’s cervine yajña,
Its dying flames forth wafting away as a cometary plasma!

Night 2:
The western welkin: the twin fires of the Bhṛgu-s and the Aṅgiras-es shine forth.
They call them Śukra and Bṛhaspati — the graha-s lighting up gods’ celestial path.
Yonder is Arka, glaring reddish at the eye of the bull charging on the heavenly vault.
Lo behold! He is now confronted by a sidereal interloper emitting greenish froth!

*Arka is the old Vedic name for Mars (e.g., the Graheṣṭi of the Kaṭha-s).

The Vyomavyāpin in the Pāśupata-tantra and a discursion on nine-fold Rudra-mantra-s

The Pāśupata-tantra is a poorly understood śaiva text that is believed to be affiliated with the Pāśupata tradition of Lakulīśa. While the colophons of some manuscripts present it as “Lakulīśa-pravartita-Pāśupata-tantram”, internally, it presents itself as a teaching of Nandin to the Bhārgava sage Dadhīci upon direction by Rudra himself. While we have seen a text going by this name in certain manuscript catalogs and seen fragmentary manuscripts of it, only recently was a nearly complete version of the text partially edited. This is not the place to go into a detailed discussion of the affinities and the provenance of the text, but we will make the below observations:
1. While a text going by this name has been mentioned by South Indian Vaiṣṇava polemicists, like Yāmuna, there is no evidence that they meant the text under discussion in this note.
2. The text as we have it can be confidently said to have been composed in South India, in the greater Drāviḍa country or its surroundings because: (i) It mentions the worship of Skanda with his two śakti-s named Devasenā and Devayānī. The latter is a unique feature of certain strands of the Southern Kaumāra cult. (ii) It mentions the worship of the god Śāstṛ, a southern ectype of the god Revanta, presented as the son of Rudra and Mohinī. (iii) Several of the manuscripts display typical Drāviḍa misspellings like “taha” for “daha”.
3. There may have been a transmission to Northeastern India, perhaps Vaṅga or its surroundings, due to some versions showing spelling errors typical of the Vāṅga-s, like the “v-b” confusion.
4. It is a late text (i.e., post-mantramārga) because it shows iconographic conventions typical of the period when the mantra-mārga was dominant: e.g., the mode of worship and depiction of Vināyaka, the Saptamātṛkā-s, the Rudra-parivāra and the pentacephalic Rudra (as opposed to the tricephalic and tetracephalic Rudra-s of the earlier Pāśupata-s). This point is important to the main topic of this note.
5. It is divided into four kāṇḍa-s: jñāna, caryā, kriyā, and yoga. Such a division is typical of various mantra-mārga texts in both the śaiva and vaiṣṇava traditions.
6. The main mantra-s it treats at length are the Pañcākṣarī, Pañcabrahma, Vyomavyāpin, Śivakavaca, Aghorāstra, Pāśupatāstra and multiple Rudra-gāyatrī-s. Additionally, it extensively uses Vaidika-mantra-s indicated by pratīka-s, suggesting that its practitioners were Veda-knowing brāhmaṇa-s.
7. It has an extensive account of the Bhuvanādhvan-s and the Rudra-s of various forms in each of them.

In conclusion, a brief examination of its contents suggests that it is a text that has been influenced by the mantramārga, in particular, the siddhānta-srotas. The main reasons for this conclusion are: (i) The repeated mention of the supreme Rudra as Sadāśiva enthroned on the Yogapīṭha. (ii) The mention of several tantra-s of Paśupati following a model reminiscent of the Saiddhānitka self-image. (iii) Primacy of the Īśāna face of the pentacephalic Rudra. However, we do think there is something to its affiliation with the Pāśupata tradition. In support of this, one may point to the extensive use of Vaidika mantra-s where the Siddhānta might use tāntrika alternatives and visualizations of the supreme Rudra rather distinct from the Siddhānta versions but overlapping with the fierce Bhairava-s of the other srotas-es (also see below). One possibility is that it is a Lakulāgama associated with the South Indian Kālāmukha-s

The Pāśupata-tantra is notable for providing a full uddhāra of the famed Vyomavyāpin mantra. This is thought to be a unique mantra of the saiddhāntika-s. For instance, the Mataṅgapārameśvara-tantra of that stream states its importance multiple times. In its kriyāpāda 1.60, it states that the Vyomavyāpin is the garbha from which all mantra-s arise — like the pañcabrahma, Caṇḍeśa, the Sāvitrī, Indrādi-mantra-s etc. In its vidyāpāda 7.31 onward, it sees the mantra as the devī who constitutes the body of Sadāśiva (c.f. similar metaphor used in the Bhairavasrotas for the goddess, e.g., by Abhinavagupta). A similar view is expressed in the Pāśupata-tantra; indeed, Nandin introduces it thus to Dadhīci:
sarvamantra-samāyuktam vyoma-vyāpinam avyayam ।
mantrāṇāṃ saptakoṭīnāṃ sāraṃ tat te vadāmy aham ॥
Comprised of all the mantra-s is the imperishable Vyomavyāpin.
I shall teach you that which is the essence of the seven crore mantra-s.

Given the above, one could argue that the Pāśupata-tantra borrowed this mantra from the saiddhāntika -s. However, we believe it emerged among the later Pāśupata-s (i.e., subsequent to their Vedic representatives) but prior to the branching off of the streams of the mantra-mārga, like the saiddhāntika-s. Our reasons for holding this view are: (i) Within the saiddhāntika tradition, the Vyomavyāpin is remarkable in showing a diversity of readings despite being a central mantra, as noted above. This suggests that it emerged in the pre-saiddhāntika mantraśāstra matrix. Hence, it had already diversified within the oral prayoga traditions from which the siddhāntāgama-s inherited alternative versions of it. (ii) In terms of its structure, it is more removed from the later bīja-rich mantra-s and closer to the mantra-s of the transitional mantraśāstra, viz., at the junction between the Vaidika- and the full-blown Tāntrika-mantramārga (e.g., some of the mantra-s to Rudra in the Atharvavedīya-pariśiṣṭa-s, Viṣṇumāyā and the bauddha Mahāmāyūrī-vidyā-rājñī). 3. Its dhyAna-s describe a 14- and 10- handed Rudra distinct from Sadāśiva, the devatā of the saiddhāntika version.

The core without the kavaca and Aghorāstra- sampuṭikaraṇa-s is said to follow the 14-handed dhyāna, which is the same as that for Pañcākṣarī:
vasiṣṭha ṛṣiḥ । gāyatrī chandaḥ । parameśvaro devatā ॥
śūlāhi-ṭaṅka-ghaṇṭāsi raṇaḍ ḍamarukaṃ kramāt ।
vajra-pāśāgny abhītiṃ ca dadhānaṃ kara-pallavaiḥ ॥
kapālam akṣamālāṃ ca śaktiṃ khaṭvāṅgam eva ca ।
evaṃ dhyātvā prabhuṃ divyaṃ tato yajanam ārabhet ॥

Vasiṣṭha is the seer, gāyatrī the meter, and Parameśvara the deity.
Having visualized the lord, in order, equipped with a trident, hatchet, bell, sword, a resounding two-headed drum, the vajra, a lasso, fire, the gesture of fearlessness, a skull, a rosary, a spear and a skull-topped brand in his blossom-like hands, the [votary] may begin his worship.

With the kavaca and astra, the dhyāna is the fierce five-headed 10-handed rudra:
kalpāntārkaṃ sahasrābhaṃ raktāktaṃ raktavāsasaṃ ।
daṃṣṭrā-karāla-saṃbhinnam pañcavaktram bhayaṅkaram ॥
keśaiś ca kapilair dīptaṃ jvālamālā-samākulam ।
ṭaṅkaṃ carma kapālaṃ ca cāpaṃ nāgaṃ ca vāmataḥ ॥
śūlaṃ khaḍgaṃ yugāntāgniṃ bāṇaṃ varadam eva hi ।
dakṣiṇaiḥ svabhujair dīptaṃ rudraṃ dhyātvā yajet prabhum ॥
Having visualized the blazing Rudra with the luminosity of a thousand suns at the end of the kalpa, smeared with gore, with red clothes, displaying terrifying fangs, five frightening faces, and tawny hair like a blazing garland of flames, holding in his left hands a hatchet, a shield, a skull, a bow, and a snake, and his right hands a trident, a sword, the eon-ending fire, an arrow and the gesture of boon-giving, he may worship the lord.

The core mantra (i.e., with the saṃdhi-s in the duplications and without the 5 initial praṇava-s, the terminal ṣaḍakṣarī, the hṛllekha-s, the haṃ-kāra (prāsada), kavaca and the astra typical of the Pāśupata version) is 365 syllables. The versions from most surviving saiddhāntika texts are typically in the range of 361-374. The pristine form in the Mataṅgapārameśvara-tantra has 361 by the same reckoning as above, suggesting that it might have come to 365 with the addition of a namo namaḥ after the terminal praṇava. We believe the Pāśupata-tantra version is close to the original as the old saiddhāntika text, the Niśvāsa-guhya, associates Rudra embodied by this mantra with the phrase “saṃvatsara-śarīriṇaḥ”, i.e., of the year as the body. This form would also be consistent with 9-fold maṇḍala taught by the Kashmirian mantravādin bhaṭṭa Rāmakaṇṭha-II and his southern successors. In his Vyomavyāpi-stava, referring to the 81 segments of the mantra (see below) and the nine-fold maṇḍala Rāmakaṇṭha says: ekāśītipadaṃ devaṃ nava-parvoktidarśanāt ॥ 8b. In this regard, it is also worth noting that the Mataṅgapārameśvara-tantra defines the devī of the form the Vyomavyāpin as having a body of segments. The same is also mentioned by Śrīkaṇṭha-sūri in his Ratnatrayaparīkṣa thus: ekāśītipadā devī vyomavyāpi-lakṣaṇā śaktiḥ । The count of 81 relates to a certain mapping that is specified in the saiddhāntika tradition to 15 classes of mantra-s. The number 15 is again likely to have temporal significance as the tithi-s of the lunar cycle. In the Pāsupata version, this division of the mantra into 81 segments mapping onto 15 sets of mantra-s goes thus:

(1) Aṅga-mantra-s (The body of Rudra): 1. oṃ 2. vyomavyāpine 3. vyomarūpāya 4. sarvavyāpine 5. śivāya (total: 5)
(2) Vidyeśvara-s: 6. anantāya 7. anāthāya 8. anāśritāya 9. dhruvāya 10. śāśvatāya 11. yogapīṭhādisaṃsthitāya 12. nityayogine 13. dhyānāhārāya (total: 8)
(3) Pañcākṣarī-vidyā (equated with the Rudra-gāyatrī by the saiddhāntika-s): 14. oṃ namaḥ śivāya (total: 1)
(4) Sāvitrī-vidyā: 15. sarvaprabhave (total: 1)
(5) Vidyeśvaropacāra: 16. śivāya (total: 1)
(6) Pañcabrahma-mantra-s: 17. īśāna-mūrdhnāya 18. tatpuruṣa-vaktrāya 19. aghora-hṛdayāya 20. vāmadeva-guhyāya 21. sadyojāta-mūrtaye (total: 5)
(7) Caṇḍeśvara: 22. oṃ namaḥ (total: 1)
(8) Caṇḍeśāṅgani (the body of Cāṇḍeśvara): 23. guhyādi-guhyāya 24. goptre 25. anidhanāya 26. sarvavidyādhipāya 27. jyotīrūpāya 28. parameśvaraparāya (total: 6)
(9) Caṇḍeśāsana: 29. acetanācetana (total: 1)
(10) Anantāsana: 30. vyomin 2 31. vyāpin 2 32. arūpin 2 33. prathama 2 34. tejas tejaḥ 35. jyotir jyotiḥ (total: 6)
(11) kesara-s (mantra-s of the 32-petaled lotus, likely corresponding to the syllables of the bahurūpī ṛk): 36. arūpa 37. anagne 38. adhūma 39. abhasma 40. anāde 41. nānā nānā 42. dhū dhū dhū dhū 43. oṃ bhūr 44. bhuvaḥ 45. svaḥ 46. anidhana 47. nidhanodbhava 48. 49. śiva 50. śarva 51. sarvapara 52. maheśvara 53. mahādeva 54. sadbhāveśvara 55. mahātejaḥ 56. yogādhipate 57. muñca muñca 58. pramatha pramatha 59. śiva śarva 60. bhavodbhava vidhya vidhya 61. vāmadeva 62. sarva-bhūta-sukhaprada 63. sarva-sāṃnidhyakara 64. brahmā-viṣṇu-rudra-para 65. anarcita 2 66. asaṃsthita 2 67. pūrvasthita 2 (total: 32)
(12) Kamala (center of the lotus throne): 68. sākṣin 2 (total: 1)
(13) Indrādi-devatā-s (the gods of the directional ogdoad): 69. turu 2 70. piṅga 2 71. pataṅga 2 72. jñāna 2 73. śabda 2 74. sūkṣma 2 75. śiva 76. śarva (total: 8)
(14) Vidyāṅga-s (the body of the goddess; corresponds to the 10-syllabled mantra known as the Vidyā in the early saiddhāntika text, the Niśvāsa-guhya-sūtra): 77. sarvada 78. oṃ namaḥ 79. śivāya oṃ 80. [hrīṃ] śivāya (total: 4)
(15) Vajra (the thunderbolt): [oṃ haṃ hrīṃ śivāya] oṃ [namo] namaḥ (total: 1)

This nine-fold nature implied in the original form of the Vyomavyāpin has ties with a similar nine-fold expression seen elsewhere in the śaiva world. Both the early Saiddhāntika (NGS) and Bhairava streams emphasize the importance of knowing the nine-fold form of Śiva known as Navātman and his mantra. The former states that japa of the Navātman-mantra over times yields magical powers. Both the early saiddhāntika and Brahmayāmala traditions speak of the 9 observances (e.g., japa of specific mantra-s wearing clothes and turbans of various colors) that seem to map to the nine-fold structure of the Navātman-mantra. On the Bhairava side, in the root Dakṣiṇa-śaiva tradition, the Svacchanda-tantra teaches the Vidyārāja, which is called ekāśitipadāḥ (81 segmented, just like the Vyomavyāpin):

ekāśitipadā ye tu vidyārāje vyavasthitāḥ ।
padā varṇātmikās te ‘pi varnāḥ prāṇātmikāḥ smṛtāḥ ॥ ST 4.252

Abhinavagupta’s cousin, Kṣemarāja informs us that this Vidyārāja is none other than the Navātman mantra. However, in the maṇḍala taught in the Svacchanda-tantra, Navātman is not the central deity, but the eighth Bhairava in the parivāra around the central Svacchanda-bhairava. The said tantra informs us that manifestation of the bhuvanādhvan-s is encapsulated in the 81 segments of the Navātman-mantra, and its prayoga-s yield siddhi-s comparable to the saiddhāntika prayoga-s. In the Paścimāṃnāya, Navātman-bhairava is the primal deity and consort of the supreme goddess Kubjikā (also seen in the combined Dakṣiṇāṃnāya-Paścimāṃnāya tradition of the Saundaryalaharī) and his -segmented mantra is taught. In the Pūrvāṃnāya (Trika), we see different formulations with Navātman-bhairava: (i) in the Siddhayogeśvarī-mata, he is the central deity of the maṇḍala of the kha-vyoman, known as the Kha-cakra-vyūha, where he is surrounded by a retinue of yoginī-s and vīra-s. (ii) in one formulation of the Tantrasadbhāva his 81 segmented Vidyārāja is presented similarly to that in the Svacchandatantra. (iii) In the classic formulation of the Tantrasadbhāva (followed by Abhinavagupta), there is an ascending series of Bhairavī-s and Bhairava-s starting with Aparā with Navātman-bhairava, Parāparā with Ratiśekhara-bhairava and Parā with Bhairava-sadbhāva. Notably, the visualization of the Rudra deity of the Vyomavyāpin conjoined with the kavaca and the astra in the Pāśupata-tantra is quite similar to that of Navātman in the Paścimāṃnāya.

Across these Bhairava traditions and certain saiddhāntika references (e.g., that of Aghoraśiva-deśika), a nine-fold composite bīja of Navātman is specified. It is given in multiple variant forms even within the same tradition, e.g., the Paścimāṃnāya. However, we see some geographical proclivities in terms of the preferred form in prayoga texts: r-h-k-ṣ-m-l-v-y-ūṃ = rhkṣmlvyūṃ (Kashmirian) or Śambhu form h-s-kṣ-m-l-v-r-y-ūṃ = hskṣmlvryūṃ / Śakti form: s-h-kṣ-m-l-v-r-y-īṃ = śkṣmlvryīṃ (Nepal, Vaṅga, South India). These 9 elements of the bīja are said to map onto 9 pada-s each yielding the 81 segments of the Vidyārāja alluded to in the Svacchandra-tantra and specified in the Dūtī-cakra (interestingly also associated with the god Viṣṇu manifesting as Ananta/the Saṃkarṣaṇa) of the Kubjikā-mata-tantra (14.62 onward). Therein, we get the below emanational series for the ekāśitipadāḥ of the Navātman mantra as: Viṣṇu (1) Ananta (2) Kapāla, (3) Caṇḍalokeśa/Caṇḍeśa, (4) Yogeśa, (5) Manonmana, (6) Hāṭakeśvara, (7) Kravyāda, (8) Mudreśa and (9) Diṅmaheśvara. Each of these 9 then emanates a set of 9 dūtī-s who comprise the body of Navātman:
Ananta (1..9) Bindukā, Bindugarbhā, Nādinī, Nādagarbhajā, Śaktī, Garbhinī, Parā, Garbhā and Arthacāriṇī.
Kapāla (10..18) Suprabuddhā, Prabuddhā, Caṇḍī, Muṇḍī, Kapālinī, Mṛtyuhantā, Virūpākṣī, Kapardinī, Kalanātmikā
Caṇḍeśa (19..27) Caṇḍamukhī, Caṇḍavegā, Manojavā, Caṇḍākṣī, Caṇḍanirghoṣā, Bhṛkuṭī, Caṇḍanāyikā, Caṇḍīśanāyikā.
Yogeśa (28..36) Vāgvatī, Vāk, Vāṇī, Bhimā, Citrarathā, Sudhī, Devamātā, Hiraṇyakā, Yogeśī.
Manonmana (37..45) Manovegā, Manodhykṣā, Mānasī, Mananāyikā, Manoharī, Manohlādī, Manaḥprīti, Maneśvarī, Manonmanī.
Hāṭakeśvara (46..54) Hiraṇyā, Suvarṇā, Kāñcanī, Hāṭakā, Rukmiṇī, Manasvī, Subhadrā, Jambukāyī, Bhaṭṭanī.
Kravayāda (55..63) Lambinī, Lambastanī, Śuśkā, Pūtanā, Mahānanā, Gajavaktrā, Mahānāsā, Vidyut, Kravyādanāyikā.
Mudreśa Vajriṇī, Śktikā, Daṇḍī, Khaḍginī, Pāśinī, Dhvajī, Gādī, Śūlinī, Padmī.
Diñmaheśvara Indrāṇī, Hutāśanī, Yāmyā, Nirṛtī, Vāruṇī, Vāyavī, Kauberī, Īśānī, Laukikeśvarī.
The 9 pada-s corresponding to Ananta are 9 repetitions of the composite Navātaman-bīja with the consonantal elements resolved with an `a’-vowel. The remaining 8 sets of 9 pada-s are derived by taking the 9, 8, 7…2 of the resolved consonantal elements from the above Navātaman as the first pada followed by 8 others in the form of their respective first consonantal element conjoined with the 8 bīja-s: āṃ, īṃ, ūṃ, ṝṃ, ḹṃ, aiṃ, auṃ, aḥ. Interestingly, given the association with Viṣṇu, the Kubjikāmata also teaches that the deity might be worshiped as Navātma-Viṣṇu, suggesting potential interaction with the Pāñcarātrika tradition (c.f. Navābja-Viṣṇu-maṇḍala). This reinforces the ancient connection between the worship of Ananta/the Saṃkarṣaṇa and the śaiva traditions that we have discussed before. More generally, it also parallels the “Rudraization” of ancient deities in the śaiva-mantramarga: one striking example is the worship of the ancient I-Ir deity Mitra as a Bhairava in the Mātṛcakra of the Paścimāṃnāya, which we hope to discuss in greater detail in a separate note.

Thus, from the above discussion, it might be concluded that a nine-fold form of Rudra was likely known to the pre-mantramārga śaiva-s that expressed itself in the form of two distinct mantra-s the Vyomavyāpin and the Navātman, which were added to the more ancient set of pañcabrahma-mantra-s. It is possible that such a nonadic conception of Rudra had ancient roots in the nine-fold manifestation of Rudra mentioned in the Śatapatha-brāhmaṇa 6.1.3.18 of the Vājasaneyin-s: tāny etāny aṣṭāv agni [=rudra] -rūpāṇi । kumāro navamaḥ saivāgnis trivṛttā ॥. Both these 81-pada mantra-s continued to be important right from the beginning of the mantramārga. Interestingly, in the Paścimāṃnāya, the retinue of siddha-s worshiped in the cakra of Navātman first features Bhṛgu, the founder of the Atharvan tradition, followed by Lakulīśa. This illustrates a memory in this later śaiva stream of its roots in the Pāśupata tradition. Thus, it is not impossible that the Pāśupata-tantra, despite being influenced by the mantramārga retained a memory of the old presence of the Vyomavyāpin in the Pāśupata tradition.

There are other potentially archaic connections suggested by both these nine-fold mantra-s of Rudra: the Vyomavyāpin literally means that which pervades space. This immediately brings to mind the ancient Indo-European deity Vāyu who has one foot in the Rudra class. Indeed, in the Eastern-Iranic world the Rudra-class deity, while iconographically identical to the Indic expression, is centered on the cognate of Vāyu, Vayush Uparikairya. Even in the Indo-Aryan sphere, the Rudra-s in the atmosphere are placed with Vāyu. In the Vrātya texts of the Atharvaveda and the Sāmaveda, Rudra is described as the god who animates like Vāyu-Vāta: the verb used is sam-īr- which is also used for Vāyu-Mātariśvan. Navātman as the deity of the Kha-cakra-maṇḍala also implies his pervading of space. Remarkably, the Vyomavyāpin has a segment featuring a tetrad of the verbal root dhū of ancient IE provenance. It means to blow or to cause things to be agitated by being blown at. Elsewhere in the IE world, its cognates mean storm, breath, soul, and wafting of odors — all activities associated with Vāyu-Vāta. Thus, we posit that the Vyomavyāpin retains memories of the intimate link between the Rudra class and Vāyu seen in the Indo-Iranian borderlands.

The Vyomavyāpin with the kavaca and astra mantra-s as specified in the Pāśupata-tantra:

oṃ 5 haṃ oṃ namo vyomavyāpine vyomarūpāya sarvavyāpine śivāya anantāya anāthāya anāśritāya dhruvāya śāśvatāya yogapīṭhādisaṃsthitāya nityayogine dhyānāhārāya । oṃ namaḥ śivāya sarvaprabhave śivāya īśāna-mūrdhnāya tatpuruṣa-vaktrāya aghora-hṛdayāya vāmadeva-guhyāya sadyojāta-mūrtaye । oṃ namaḥ guhyādi-guhyāya goptre anidhanāya sarvavidyādhipāya jyotīrūpāya parameśvaraparāya । acetanācetana । vyomin 2 । vyāpin 2 । arūpin 2 । prathama 2 । tejas tejaḥ । jyotir jyotiḥ । arūpa । anagne । adhūma । abhasma । anāde । nānā nānā । dhū dhū dhū dhū । oṃ bhūr bhuvaḥ svaḥ । anidhana । nidhanodbhava । śiva । śarva । sarvapara । maheśvara । mahādeva । sadbhāveśvara । mahātejaḥ । yogādhipate muñca muñca pramatha pramatha । śiva । śarva । bhavodbhava vidhya vidhya । vāmadeva । sarva-bhūta-sukhaprada । sarva-sāṃnidhyakara । brahmā-viṣṇu-rudra-para । anarcita 2 । asaṃsthita 2 । pūrvasthita 2 । sākṣin 2 । turu 2 । piṅga 2 । pataṅga 2 । jñāna 2 । śabda 2 । sūkṣma 2 । śiva । śarva । sarvada । oṃ namaḥ । śivāya oṃ hrīṃ śivāya oṃ haṃ hrīṃ śivāya oṃ namo namaḥ ॥
oṃ namaḥ sarvātmane parāya parameśvarāya parāya yogāya । yogasambhavakara sadyobhavodbhava vāmadeva sarva-karma-praśamana sadāśiva namo ‘stu te svāhā । suśiva śiva namo brahmaśirase । śiva-hṛdaya-jvālini jvālinyai svāhā । oṃ śivātmakam mahātejaḥ sarvajñam prabhum avyayam । āvartayen mahāghoraṃ kavacaṃ piṅgalaṃ śubham । āyāhi piṅgalam mahākavacaṃ śivājñayā hṛdayam bandha । jvala ghūrṇa saṃsphura kiri śakti-vajradhara vajrapāśa vajraśarīra mama śarīram anupraviśya sarvaduṣṭān stambhaya huṃ phaṭ । oṃ jūṃ saḥ jyotīrūpāya namaḥ । oṃ prasphura ghora-ghoratara-tanu-rūpa caṭa daha vama bandha ghātaya huṃ phaṭ ॥

The core Vyomavyāpin as per the saiddhāntika text, the Mataṅgapārameśvara-tantra:

oṃ namo vyomavyāpine vyomarūpāya sarvavyāpine śivāya anantāya anāthāya anāśritāya dhruvāya śāśvatāya yogapīṭhasaṃsthitāya nityaṃ yogine dhyānāhārāya । oṃ namaḥ śivāya sarvaprabhave śivāya īśāna-mūrdhnāya tatpuruṣa-vaktrāya aghora-hṛdayāya vāmadeva-guhyāya sadyojāta-mūrtaye । oṃ namaḥ guhyāti-guhyāya goptre nidhanāya sarvavidyādhipāya jyotīrūpāya parameśvaraparāya । acetanācetana । vyomin 2 । vyāpin 2 । arūpin 2 । prathama 2 । tejas tejaḥ । jyotir jyotiḥ । arūpa । anagne । adhūma । abhasma । anāde । nā nā nā । dhū dhū dhū । oṃ bhūḥ । oṃ bhuvaḥ । oṃ svaḥ । anidhana । nidhana। nidhanodbhava । śiva । sarva । paramātman । maheśvara । mahādeva । sadbhāveśvara । mahātejaḥ । yogādhipate muñca muñca prathama prathama । śarva śarva । bhava bhava । bhavodbhava । sarva-bhūta-sukhaprada । sarva-sāṃnidhyakara । brahmā-viṣṇu-rudra-para । anarcita 2 । asaṃstuta 2 । pūrvasthita 2 । sākṣin 2 । turu 2 । piṅga 2 । pataṅga 2 । jñāna 2 । śabda 2 । sūkṣma 2 । śiva । śarva । sarvada । oṃ namo namaḥ । oṃ śivāya namo namaḥ । oṃ [namo namaḥ] ॥

A personal note
We first heard the Vyomavyāpin as a kid being recited by a mantrin in a temple of Rudra founded by the Kālāmukha-s in the Karṇāṭa country. He had recited the pañcabrahma-s and other incantations from the Yajurveda that we knew, but this one was entirely unfamiliar to us. As soon as we heard the words vyomin 2 । vyāpin 2 ।, we experienced a special gnosis of the pervasion of space by Rudra in two ways. We wondered what this mantra was — we could not find it in any of the manuals our grandfather, or we had at that time. By some coincidence a fortnight or so later we happened to lay our hands on N.R. Bhat’s edition of the Mataṅgapārameśvara in the library, and we saw it right there. Unfortunately, there was no access to a copying device there, and we did not have writing material at hand. Hence, it just remained that until we met R1’s father who gave us more information about its rahasya-s.

Bhāskara-II’s polygons and an algebraic approximation for sines of pi by x

Unlike the Greeks, the Hindus were not particularly obsessed with constructions involving just a compass and a straightedge. Nevertheless, their pre-modern architecture and yantra-s from the tāntrika tradition indicate that they routinely constructed various regular polygons inscribed in circles. Of course, the common ones, namely the equilateral triangle, square, hexagon, and octagon are trivial, and the earliest preserved geometry of the Hindus is sufficient to construct these. The pentagon and its double the decagon are a bit more involved but are still constructible by the Greek compass and straightedge method; however, few have looked into how the Hindus might have constructed it. These aside, we do have multiple examples of yantra-s with heptagons and nonagons. A particularly striking example is the wide use of the nonagon in yantra-s (likely related to the early Śrīkula tradition of 9 yoginī-s and the division of the Vyomavyāpin mantra of the saiddhāntika-s) found at the Marundīśvara temple near Chennai. The kaula tradition of the Kubjikā-mata-tantra has a sūtra that mentions a yantra with multiple regular polygons relating to pacifying the seizure by Ṣaṣṭhī and others (trikoṇaṃ navakoṇaṃ ca ṣaṭkoṇaṃ maṇḍalākṛtiḥ |). The heptagon and the nonagon cannot be constructed using just a compass and a straightedge. To construct them precisely, one would require a means of accurately drawing conics (other than circles and straight lines) of particular specifications. While Archimedes invented a machine to draw ellipses, and examples of ellipses are occasionally encountered in early Hindu architecture, the technology for the easy generation of desired conics was unlikely to have been widely available to premodern architects. Hence, the Hindus should have constructed their regular polygons, including heptagons and nonagons through other means.

Figure 1.

It is easy to see (Figure 1) that for a circle of diameter the side of an inscribed regular polygon of sides is . Thus, if one does not insist on a compass and straightedge construction, one can easily draw any polygon as long as one has a sine table. The Hindus have had a long history of generating sine tables as well as algebraic functions that approximate the sine function to varying degrees of accuracy. Thus, one would expect that this was the most likely route they took. This still leaves us with the question of how exactly they did it in practice. A likely answer for this comes from Bhāskara-II’s Līlāvatī though this knowledge appears to have been lost in some parts of India in the late medieval period.

In Līlāvatī 206-209, Bhāskara gives a table for the sides of the inscribed polygons in three anuṣtubh-s (see below) followed by a numerical example (L 209). We have resolved the saṃdhi with a + for ease of reading the numbers:

tri-dvyaṅkāgni-nabhaś-chandrais tribāṇāṣṭayugāṣṭabhiḥ |
vedāgni-bāṇa-khāśvaiś ca kha-khābhrābhra-rasaiḥ kramāt || L 206

tri+dvi +aṅka +agni +nabhaś +candrais (103923)
tri +bāṇa +aṣṭa +yuga +aṣṭabhiḥ (84853) |
veda +agni +bāṇa +kha +aśvaiś (70534)
ca kha +kha +abhra +abhra +rasaiḥ (60000) kramāt ||

bāṇeṣu-nakha-bāṇaiś ca dvi-dvi-nandeṣu sāgaraiḥ |
ku-rāma-daśa-vedaiś ca vṛtta-vyāse samāhate || L 207

bāṇa +iṣu +nakha +bāṇaiś (52055) ca
dvi +dvi +nanda +iṣu +sāgaraiḥ (45922)
ku +rāma +daśa +vedaiś ca (41031)

kha-kha-khābhrārka saṃbhakte labhyante kramaśo bhujā |
vṛttāntar tryasra-pūrvāṇāṃ navāsrāntam pṛthak pṛthak || L 208

vṛtta-vyāse samāhate kha +kha +kha +abhra +arka (120000) saṃbhakte labhyante kramaśo bhujā
vṛtta-antar tri +asra-pūrvāṇām nava +asra-antam pṛthak pṛthak

Essentially, the above means that one should multiply the diameter of the circle with the numbers specified in the above table in verse form and divide them by 120000. This gives, in order, the sides of the inscribed regular polygons from a triangle to a nonagon. Thus, the ratios of these numbers provide rational approximations for for . We compare these to the actual values in the below table:

These rational approximations provided by Bhāskara are best for a triangle, square, pentagon, hexagon and octagon. These are the angles for which he derives closed forms in his Jyotpatti (On the generation of sines) and correspond to the constructible polygons of the Greek tradition. The sines of the heptagonal and nonagonal angles which have no closed forms were obtained using serial interpolations or a sine-approximating function.

In terms of the latter, Bhāskara specifies a formula for the length of a cord corresponding to an arc in a Vasantalikā verse that can be used to obtain an algebraic function approximating :
cāpona-nighna-paridhiḥ pratham-āhvayaḥ
syāt pañcāhataḥ paridhi-varga-caturtha-bhāgaḥ |
ādyonitena khalu tena bhajec catur-ghna
vyāsāhatam prathamam āptam iha jyakā syāt || L 210

cāpa +ūna-nighna-paridhiḥ prathama +āhvayaḥ
syāt pañca +āhatas paridhi-varga-caturtha-bhāgaḥ |
ādya +ūnitena khalu tena bhajet +catur +ghna-
vyāsa +āhatam prathamam āptam iha jyakā syāt ||

The circumference is reduced by the arc and multiplied by the arc: this is called the prathama.
One-fourth of the circumference squared is multiplied by 5
This is then reduced by the prathamā. The prathamā multiplied by 4
and the diameter should be divided by the above result. The fraction thus obtained is the chord.

Let the diameter of the circle be , its circumference , the length of the given arc and its chord. Then the above can be written in modern notation as:

Now, the arc can be written as the fraction of the circumference, . By plugging this into the above equation, we get:

This allows us to eliminate and write

Thus, we get an algebraic function approximating :

Figure 2.

In the below table we show the values of the polygon sines for generated by this formula and compare them with the earlier table provided by Bhāskara and the actual value:

We can see that the values from this function are more approximate than those provided by the table. Thus, it is clear that Bhāskara did not use this algebraic function to generate his table. However, the fact that he provides this formula after the table indicates that he meant this as an alternative method to get rational approximations for the polygonal sines. Such a method too could have been readily used by artists/artisans in their polygonal constructions in architecture and yantra preparation.

Origins of the serpent cult and Bhāguri’s snake installation from the Sāmaveda tradition

Mathuran Nāga installations

From the few centuries preceding it down to the first few centuries of the Common Era we see numerous installations of snake deities, i.e., Nāga-s, at various archaeological sites throughout northern India (most famously at the holy city of Mathurā). Comparable, but usually smaller Nāga installations continue to this date in South India, usually in association with śaiva and kaumāra shrines. A related icon is that of the great Sātvatta Vaiṣṇava deity Balabhadra, who is depicted with a hooded snake canopy. Tradition holds that he was the incarnation or homomorph of the snake of Viṣṇu, often named Ananta. Given that Viṣṇu was the “time-god” par excellence, we hold that the snake imagery (the coils) associated with his bed is a metaphor for periodicities in time — diurnal, lunar, solar and precessional cycles. In this note, we explore the connections of these later manifestations of the serpentine cult with the Vedic roots of snake worship (Ahi Budhnya of the earliest Vedic tradition), with probable deeper Indo-European antecedents and broad Eurasiatic ramifications.

Saṃkarṣaṇa installations at Tumbavana (L) and Mathurā (R)

On one hand, we have the śrauta sarpa-sattra outlined in the Sāmaveda brāhmaṇa-s, which is modeled after a ritual supposed to have been performed by the Nāga-s to gain their venom. The sarpa-sattra in an inverted form, viz., the ritual of Janamejaya to destroy the Nāga-s who were responsible for his father’s death, is the frame story of the national epic the Mahābhārata. The core story of the Mahābhārata itself is permeated with simultaneous inter-generational conflicts and marriages between the Nāga-s and the Pāṇḍu-s. On the other hand, we have the gṛhya sarpabali that is enjoined in various gṛhyasūtra-s and certain vidhāna-s. The sarpabali or the offering to the snake deities is performed when the full moon occurs in Śravaṇā (the ecliptic division associated with the longitude of Altair). This bali usually coincides with the Indian Southwest Monsoon. Along with this bali the ritualist and his family sleep on a raised bed until the Āgrayaṇa ritual. This, along with the contents of the ritual, indicate that its primary function was protection from snakes that might enter houses during the monsoons due to the flooding of their lairs. While the rite is found in most gṛhyasūtra-s, that of the Hiraṇyakeśin school associated with the Taittirīyaka tradition gives a rather detailed account of the rite. At first, the ritualist makes oblations of unbroken grains, unbroken fried grains, coarsely ground grains, leaves and flowers of the Kimsuka tree to Agni Pārthiva, Vāyu Vibhumant, Sūrya Rohita and Viṣṇu Gaura:

namo .agnaye pārthivāya pārthivānām adhipataye svāhā । namo vāyave vibhumata āntarikṣāṇām adhipataye svāhā । namaḥ sūryāya rohitāya divyānām adhipataye svāhā । namo viṣṇave gaurāya diśyānām adhipataye svāhā ॥

After these oblations, the snakes of the earth (the real ones), the snakes of the atmosphere (lightning), the snakes of the heavens (Āśleṣā the constellation of Hydra), and those of the directions (the serpent ogdoad) are worshiped with the famous Yajuṣ-es beginning with  namo astu sarpebhyaḥ … (TS 4.2.8.3) followed by the bali incantations ye pārthivāḥ sarpāstebhya imaṃ baliṃ harāmi । ya āntarikṣāḥ । ye divyaḥ । ye diśyāḥ ॥

Following the bali, the ritualist goes thrice around his dwelling in a circle corresponding to the radius that he wishes to keep the snakes away from sprinkling water from a pot while uttering the below incantation (the Pāraskara-gṛhya-sūtra instead prescribes drawing a line with a white pigment):
apa śveta padā jahi pūrveṇa cāpareṇa ca । sapta ca mānuṣīr imās tisraś ca rājabandhavaiḥ । na vai śvetasyābhyācareṇāhir jaghāna kaṃ cana । śvetāya vaidarvāya namo namaḥ śvetāya vaidarvāya ॥
Smite away, O white one, with your foot, fore and hind, these seven women with the three of the king’s clan. No one indeed, in the roaming ground of the white one the snakes have ever killed.

In the above incantation, the king and his clan evidently refer to the Nāga king and his folks and the women to the Nāgakanya-s. The white one is described as having fore and hind feet. This implies that he is none other than the white snake-killing horse (Paidva) given to Pedu by the Aśvin-s:
yuvaṃ śvetam pedava indrajūtam ahihanam aśvinādattam aśvam । RV 1.118.9a
paidvo na hi tvam ahināmnāṃ hantā viśvasyāsi soma dasyoḥ ॥ RV 9.88.4c

However, it is notable that the Viṣṇu deity specific to this ritual is Viṣṇu Gaura, or the white one, paralleling the color of the horse. In this regard, we may also point to the role of Viṣṇu in the Aśvamedha rite. After the horse has successfully wandered for an year, the emperor undergoes consecration. In preparation for the sacrifice, the oblations known as Vaiśvadeva culminating in the pūrṇāhuti are offered over a period of seven days. On days one and two he offers to Ka Prajāpati; on day three to Aditi; on day four to Sarasvatī; on day five to Puṣan; day six to Tvaṣṭṛ Viśvakarman; on day 7 to Viṣṇu the with the purṇāhuti. As per the Taittirīya-śruti, two Viṣṇu deities are invoked in the rite in addition to the standalone Viṣṇu:
viṣṇave svāhā । viṣṇave nikhuryapāya svāhā । viṣṇave nibhūyapāya svāhā ॥

These peculiar names of the two Viṣṇu deities, Nikhuryapa and Nibhūyapa are rather enigmatic. Since they are unique to the Aśvamedha, we posit that Nikhuryapa could be Viṣṇu as the protector of the hoofs (khura: hoof), whereas Nibhūyapa could be Viṣṇu as the protector of the stallion which makes the herds increase. These equine associations of Viṣṇu in the Aśvamedha raise the possibility that the white snake-smiting horse was also associated with the White Viṣṇu of the ritual. Interestingly, the color the Saṃkarṣaṇa is also said to be white. Moreover, the later tradition starting from the Mahābharata preserves strong equine connections for Viṣṇu as Hayaśiras. Thus, in the least, one could say that the sarpabali ritual established an early connection between Viṣṇu and offerings to the snakes, which could have presaged its augmentation in the later tradition.

Other traditions associated with the Vedic sarpabali were also expanded in the later serpent cult. Evidence for this comes from an adaptation of the ritual found in the Yajurvidhāna-sūtra-s of the Vājasaneyin-s (YVS 15.8-11):
namo .astu sarpebhya iti ghṛta-pāyasaṃ nāgasthāne juhuyāt । suvarṇam udpadyate ॥ vṛṣṭyarthe śikhaṇḍyādīñ juhuyāt vṛṣṭir bhavati । atasī-puṣpair mahāvṛṣṭir bhavati ॥

The sarpa-yajuṣ is deployed with oblations of ghee and milk pudding in the locus of the Nāga-s in order to obtain gold. For rains he offers oblations of peacock feathers; for torrential rains, he offers flax flowers. Thus, in this vidhāna deployment of the sarpabali mantra, we see a reworking for obtaining gold (a connection already mentioned in the Mahābhārata 5.114.4 “vulgate”: he guards the wealth/gold generated by Agni for Kubera) and rain (a connection possibly going back to Ahi Budhnya in the Ṛgveda: RV 4.55.6; RV 7.34.16; Taittirīya-Saṃhitā in 1.8.14). The Yajurvidhāna-sūtra-s also describe a rite with a trident and a liṅga made of cow dung in the fire-shed using this mantra for the rain-making and fearlessness (namo .astu sarpebhya iti tisṛbhir arghyaṃ dadyād agnyāgāre gomaya-liṅgaṃ pratiṣṭhāpya pañcagavyena saṃsnāpya dakṣiṇataḥ śūlaṃ nikhanet । punaḥ sahasraṃ japet । suvarṇa-śataṃl labhet siddhaṃ । karmety ācakṣate vṛṣṭau śikhaṇḍān atasīpuṣpāṇi vā yuñjantīti । mahābhaye japed abhayaṃ bhavati ॥). Similarly, a rite using an iron trident is offered for the subjugation of nāga-s with a mantra to Agni (ajījana iti rahasyo mantra (RV 3.29.13) etena nāgā vaśam upayānti । lauhaṃ triśūlagṃ sahasrābhimantritaṃ kṛtvā dakṣiṇa-pādenākramya payo-dadhi-madhu-ghṛtair ayutaṃ hutvā vikṛta-rūpā striya uttiṣṭhanti । kim asmābhiḥ kartavyam iti bruvantyo abhirucikāmena tām ājñāpayet ॥). This later rite is developed further within the śaiva context in the Jayadrathayāmala-tantra. These objectives outlined in the Vidhāna were greatly expanded in early śaiva and bauddha traditions (also seen in the Indic-influenced Cīna dragon traditions). These themes are brought together rather dramatically in the story of the Drāviḍa mantravādin, the Nāga Mahāpadma residing in a Kashmirian lake, and the king Jayāpīḍa narrated by Kalhaṇa in the Rājataraṃgiṇī (4.593 onward).

However, the question remains as to whether the sarpabali of the old Gṛhya tradition had any connection with the installation of the images of Nāga and Saṃkarṣana seen at the archaeological sites. A potential transitional rite describing a Vaidika snake installation comes from a now apparently extinct Sāmaveda tradition, namely the Gautama school, which seems to have been practiced in some form in the Karṇāṭa country till around 1600-1700 CE. The Gautama-gṛhya-pariśiṣṭa furnishes a detailed Nāga-pratiṣṭha ritual attributed to Bhāguri (GGP 2.12):
-The ritual is to be performed on the 12th tithi of a śuklapakṣa when the moon is in a devanakṣatra (i.e., Northern half of the ecliptic) or during the northern course of the sun or on an auspicious nakṣatra.
-On the day before the installation rite, the ritualist brushes his teeth, takes a bath with water from a tīrtha (holy ford) and having performed the saṃkalpa for the installation, immerses the image in water.
-He chooses an ācārya who delights in right conduct and of peaceful temperament and performs the rite via his instruction.
-Having cleansed the spot for installation, the ācārya washes his feet, performs ācamana, and having seated himself, performs prāṇāyāma and saṃkalpa.
-He recites the puṇyāha incantations (hiraṇyavarṇāḥ…) and sprinkles the image with water. He recites the triple vyāhṛti-s and lustrates the image with the five bovine products.
-He washes the images with clean water utter āpo hi ṣṭha… (SV-Kauthuma 1837) and tarat sa mandī dhāvati… (SK-K 500, 1057)
-He utters oṃ and lustrates the image with water in which gold flakes, the shoots of dūrva grass and palaśa leaves have been placed. He offers flowers and dūrva grass at the feet of the image.
-He utters the sāvitrī or oṃ and cloaks the image with newly woven unwashed clothing.
-He offers special naivedya and recites svasti na indro… incantation. Thereafter, he immerses the image in a river while singing the Varuṇa-sāman.

-He rises the next day and performs his nityakarmāṇi, he proceeds with the ācārya and assistant ritualists (like in the śrauta ritual) to the place where he has immersed the image. There, they bring out the image while reciting praitu brahmaṇas patiḥ pra devy etu sūnṛtā ।…(SV-K 56). Then they install it at the designated spot and perform prāṇāyāma and saṃkalpa.
-They again lustrate the image with the five bovine products while reciting oṃ nāgāya namaḥ. Then they wash it with clean water and cloak it with a new dress. They decorate it with scented unguents and flowers.
-Then they perform nyāsa both of the self and the image thus: oṃ nāgāya namaḥ । hṛdayāya namaḥ । oṃ nāgāya namaḥ । śirase namaḥ । oṃ nāgāya namaḥ । śikhāyai namaḥ । oṃ nāgāya namaḥ । kavacāya namaḥ । oṃ nāgāya namaḥ । netratrayāya namaḥ । oṃ nāgāya namaḥ । astrāya namaḥ ।
Then he does a dhyāna of the serpentine deity:
sarpo raktas trinetraś ca dvibhujaḥ pītavastragaḥ ।
phaṇkoṭidharaḥ sūkṣmaḥ sarvābharaṇa-bhūṣitaḥ ॥

-He then measures out a droṇa of paddy, clean rice and sesame seeds and spreads them out one over the other. On them, he draws out an eight-petaled lotus and installs a pitcher on top of it.
-Inside the pitcher, he places five each of barks, shoots, soils, gemstones, bovine products, ambrosial sweets, scents, kinds of rice, medicinal herbs, and unguent powders.
-He drapes the pitcher with a new piece of cloth and invokes Nāgeśa in it:
oṃ bhūḥ । puruṣam āvāhayāmi । oṃ bhuvaḥ । śeṣam āvāhayāmi । ogṃ suvaḥ । anantam āvāhayāmi ॥
-He then provides the deity with the 16-fold sacraments uttering oṃ anantāya namaḥ for each.
-He then worships the deity with the following mantra:
āyātu bhagavān śeṣaḥ sarva-karma-sanātanaḥ ।
ananto mat priyārthāya mad anugraha-kāmyayā ॥

-The four brāhmaṇa ritual assistants and the ācārya touch the pitcher and recite āpo hi ṣṭha…
-Then they recite the Puruṣa hymn.
-Then they sing the following Sāman-s: Sarpa, Vāmadevya, Rathantara, Bṛhat, Jyeṣṭha and Bhāruṇḍa.
-Then they recite oṃ namo brahmaṇe…bṛhate karomi (Taittirīya āraṇyaka 2.13.1).

-To the west of the pitcher, the ācārya sets up a sthaṇḍila (fire altar). To the north of the altar, he collects twelve materials for the pradhānāhuti-s (main oblations) and offers them with the following incantations into the fire followed by a svāhā and the tyāga formula: idaṃ anantāya na mama ।
sadyojātam prapadyāmi…: samidh-s
vāmadevāya namo…: ghee
aghorebhyo ‘tha…: cooked rice
tat puruṣāya vidmahe…: fried rice
īśānaḥ sarvavidyānām…: saktu flour
oṃ nāgāya namaḥ: milk
hṛdayāya svāhā: barley
śirase svāhā: sesame
śikhāyai svāhā: sugarcane
kavacāya svāhā: banana
netra-trayāya svāhā: jackfruit
astrāya svāhā: mustard

-25 oblations are made of each item. Thereafter, he offers sesame with oṃ bhūr-bhuvaḥ svaḥ svāhā ।.
-He then worships the serpentine deity with the below incantation calling on him to accept all the oblations:
tvām eva cādyam puruṣam purāṇam ।
sanātanam viśvadharaṃ yajāmahe ।
mad arpitaṃ sarvam aśeṣa-havyam
gṛhṇīṣva māṃ rakṣa jagannivāsa ॥

-Then he gives the brāhmaṇa-s their fees and sings the Vāmadevya sāman.
-Then to the singing of the Sarpasāman he lustrates the image of Nāgeśa with the contents of the pitcher, followed by the five bovine products, the five ambrosial sweets, curds, milk, coconut juice, whey, sugarcane juice and finally scented water.
-Then he recites the Mantra Brāhmaṇa 2.8.6, utters oṃ nāgāya namaḥ thrice, and offers pādya to the image.
-He recites annasya rāṣṭrir asi… (MB 2.8.9) and offers arghya.
-With yaśo .asi… (MB 2.29.16) he offers ācamana.
-With yaśaso yaśo .asi… (MB 2.8.11) he offers madhuparkam.
-With oṃ nāgāya namaḥ he successively offers, lower garments, an upavīta, upper garments, and ornaments.
-With gandhadvārāṃ durādarṣām… he offers scents.
-With īḍiṣvā… (SV-K 103) he offers incense.
-With pavamānaḥ… dyad (SV-K 484) he offers a lamp.
-The ācārya drapes the image with a new robe and also himself.
-With śukram asi jyotir asi tejo .asi (in TS 1.1.10) he takes up a golden needle. With viśvataścakṣur uta viśvatomukho viśvatobāhur uta viśvataspāt । (RV 10.81.3a) and uttering oṃ he activates the eyes of the image with the golden needle.
-He touches the heart of the image and recites the prāṇapratiṣṭha incantation invoking the goddess Anumati to infuse the image with consciousness:
asunīte punar asmāsu cakṣuḥ
punaḥ prāṇam iha no dhehi bhogam ।
jyok paśyema sūryam uccarantam
anumate mṛḻayā naḥ svasti ॥ (RV 10.59.6)
-Maidens of good disposition display lamps to the image and a cow is led before it.
-The image is placed over a deposit of a gemstone, pearl, coral, gold and silver atop which a white cloth has been spread.
-Having decorated the image, the yajamāna worships the deity with the incantations: oṃ śeṣāya namaḥ । oṃ bhūdharāya namaḥ । om anantāya namaḥ ।
-He then offers naivedya of milk pudding, cooked rice, sesame rice, turmeric rice, apūpa cake, pūrikā bread, and the śarkarāḍhya sugar pastry. Thereafter, he offers betel leaves.

-Having given gifts to the ācārya and his assistant brāhmaṇa-s, he takes the image and has it permanently installed at a temple of Rudra or Viṣṇu, or under a pipal tree while reciting the mantras:
udgāteva śakune sāma gāyasi
brahmaputra iva savaneṣu śaṃsasi ।
vṛṣeva vājī śiśumatīr apītyā
sarvato naḥ śakune bhadram ā vada
viśvato naḥ śakune puṇyam ā vada ॥ (RV 2.43.2)

-He then worships the serpentine deity performing 12 namaskāra-s with the following incantations:
anantāya namaḥ । nāgāya namaḥ । puruṣāya namaḥ । sarpebhyo namaḥ । viśvadharāya namaḥ । śeṣāya namaḥ । viśvambharāya namaḥ । saṃkarṣaṇāya namaḥ । balabhadrāya namaḥ । takṣakāya namaḥ । vāsukaye namaḥ । śivapriyāya namaḥ ।

-He concludes by feeding 12 brāhmaṇa-s of good learning and character and educating children.
-He who does such a snake installation obtains 8 children, whatever he prays for, and the higher realms.

There are several notable points regarding this ritual:
-Its essential details, including the new mantra-s specifically spelt out in the text, closely relate to other iconic sthāpana rites specified in the late Vedic texts. These include: 1. The installation and worship of Skanda (AV Skandayāga and Dhūrtakalpa of the Bodhāyana-pariśiṣṭa); 2. The black goddess of the Night, Rātrī-devī (AV-pariśiṣṭa 6); 3. The Bhārgava Brahma-yāga (AV-par 19b), where an image of the god Brahman is installed; 4. Gośānti (AV-par 66), where an image of Rudra fashioned out of cow dung is installed in the midst of a maṇḍala for the protection of cattle. Similarly, a metal/stone image of Rudra is installed in the Bodhāyana-pariśiṣṭa and also deployed by the Vādhūla-s in their Vādhūlagṛhyāgama, a versified version of their Gṛhyasūtra-s  and pariśiṣṭa-s. 5. Installations of the images of Viṣṇu and Durgā according to the Bodhāyana-pariśiṣṭa-s. The former is also specified in the Vādhūla collection. Thus, it may be inferred that the Nāga-pratiṣṭha of the Gautama-gṛhya-pariśiṣṭa is of the same genre and likely the same temporal period marking the tail end of the Vedic age and the transition to the Tantro-Paurāṇic age.

-Here the character of the Nāga has evolved from that seen in the earlier gṛhya sarpabali. While the sarpa-s are venerated in the sarpa-yajuṣ they are also expelled by means of the white horse of Pedu and the perimeter of safety is established. However, in the Nāga-pratiṣṭha the snake deity is not just clearly positive but is also identified with the Puruṣa himself.

-The text presents an early example of the ṣoḍaśopacāra-pujā that was to become dominant in the Tantro-Paurāṇic iconic worship. It may also mark the earliest account of the eye-opening rite that became prominent in the later āgamika strand of the religion.

-Several mantra-s which are provided only by pratīka-s are missing in the Kauthuma-Rāṇāyanīya and Jaiminīya texts and their auxiliary mantra collections. This suggests that the Gautama Sāmavedin-s had their own auxiliary mantra collection that was distinct from the extant texts. It is conceivable that they had the pañcabrahma-mantra-s, which today are only found as a complete group in the Taittirīya and AV Mahānārāyaṇa texts.

-The text rather remarkably combines both śaiva and vaiṣṇava elements. The former is seen in the form of the pañcabrahma-mantra-s and the latter is seen in the form of the explicit identification of the serpentine deity with the Puruṣa and also Saṃkarṣaṇa/Balabhadra. Both these aspects persisted in the subsequent layers of the religion. The serpentine form remained a key aspect of the iconography of the Saṃkarṣaṇa and Ananta figure as the bed of Viṣṇu. The Nāgapratiṣṭha continued as a ritual with new śaiva accretions in the Saiddhāntika stream in Rudrālaya-s (e.g., the Raurava tantra). Notably, it was also continued with modifications in the Bauddha practice of the Mūlamantra-sūtra (where it is combined with the old rain-making ritual) that was preserved in a rather pristine form among the Chinese ritualists.

We see a convergence of philology and archaeology with respect to Nāga-pratiṣṭha-s, offset by 2-3 centuries, perhaps due to preservation bias. In the bauddha lore, we hear of the famous conflict between the Tathāgata and the Vaidika brāhmaṇa Urubilva Jaṭila Kāśyapa (Vinaya 1.25). The latter had evidently installed a Nāga in his fire-shed which the Tathāgatha is claimed to have subjugated. This would be consistent with some version of the rites as recorded in the Nāga-pratiṣṭha from the Sāmaveda tradition being in place by around the time of the Shākya. Alternatively, it could be an allusion to the snake deity Ahi Budhnya being stationed at the Gārhapatya fire altar upon the conclusion of rituals in it (upasthāna).  Subsequently, as noted above, by the Mauryan-Śuṅga age we see evidence for such installations and also images of Balabhadra in archaeology continuing down to the age of the Kuṣāṇa-s. Notably, both the early bauddha and jaina texts mention the worship of Balabhadra providing approximately coeval philological evidence for the same. Further, some of the early Pāśupata śaiva shrines like that of Bhogyavardhana (modern Bhokardhan in Maharashtra state) and Viṣṇukuṇḍin temple (at Devunigutta, Kothur, modern Andhra Pradesh) depict the Saṃkarṣaṇa suggesting further development of the potential links indicated by the use of the pañcabrahma-mantra-s in the installation of the snake.

Two simple stotra-s, sectarian competition, and the Varāha episode from the archaic Skandapurāṇa

The Ur-Skandapurāṇa (SkP) or the “archaic” Skandapurāṇa ( the Bhaṭṭārāi edition known as the Ambikā-khaṇḍa) is a Śaiva text with affinities to the Pāśupata branch of that tradition. Though it is aware of the mantra-mārga traditions like the Mātṛ-tantra-s and the Yāmala-tantra-s as being part of the Śaiva scriptural corpus, its emphasis on the Pāśupata-vrata makes it clear that the core affiliation of the text was with the Pāśupata-mata that later Śaiva tradition identified as Atimārga. Nevertheless, it shows imprints of a three-way struggle for dominance between the major Hindu sects — Śaiva, Kaumāra and Vaiṣṇava. As the Skandapurāṇa, the existence of a Kaumāra layer is unsurprising. However, in the text, as it has come down to us, the Kaumāra elements are largely subordinated to the “Vīra” (as in strongly sectarian)-Śaiva elements. The subordination of the Vaiṣṇava-mata is primarily directed against the great deeds of Viṣṇu in his Nṛsiṃha and Varāha forms. In this regard, the Ur-SkP has a rather unprecedented ordering of the Daitya dynasty and the corresponding incarnations of Viṣṇu:

Hiraṇyakaśipu Hiraṇyākṣa Andhaka Prahlāda Virocana Bali.

While Vipracitti is mentioned as assisting Hiraṇyākṣa in his battle with Viṣṇu, and being overthrown by the latter, it is not clear if he ever occupies the Daitya throne. The thus ordered Daitya-s are respectively slain by Viṣṇu as Nṛsiṃha; Viṣṇu as Varāha; Rudra; Viṣṇu (and Indra); Indra; Viṣṇu as Vāmana-Trivikrama. The main battle with Prahlāda as the Daitya emperor is situated in the episode of the churning of the World-ocean, during which Viṣṇu manifests as the gigantic turtle Kūrmā and also the bewitching female form Mohinī. As per the Ur-SkP, while Viṣṇu suppresses Prahlāda in an epic battle during this episode, he continues leading the Daitya-s in several further fights till Viṣṇu assisted by Indra destroys him. However, the Padmapurāṇa (13.186) places his slaying by Indra (an incident alluded to in the śruti itself) right in the episode of the churning of the World-ocean followed by the slaying of his son Virochana by Indra during the Tārakāmaya devāsura-yuddha. Correspondingly, in contrast to most other Purāṇa-s, in the Ur-SkP, the vibhava-s of Viṣṇu come in the order: Nṛsiṃha, Varāha, Kūrma/Mohinī, Vāmana/Trivikrama.

As we have seen before, Nṛsiṃha is shown as being subdued by Rudra in his dinosaurian Śarabha form after he has slain Hiraṇyakaśipu. The Ur-SkP has several parallels to the Vāmana-purāṇa, but in the latter, the Śarabha-Nṛsiṃha is given a Smārta resolution rather than a demonstration of Rudra-paratva. Upon being subdued by Śarabha, in the Ur-SkP, Nṛsiṃha is said to have recited the below stotra to Rudra. A votary who recites the stotra is said to attain the state of a gaṇa of Rudra.

The stotra to Śarabha by Nṛsiṃha:

namaḥ śarvāya rudrāya senānye sarvadāya ca ।
namaḥ parama-devāya brahmaṇe paramāya ca ॥54॥
kālāya yamarūpāya kāladaṇḍāya vai namaḥ ।
namaḥ kālānta-kartre ca kālākāla-harāya ca ॥55॥
namaḥ pinākahastāya raudra-bāṇa-dharāya ca ।
caṇḍāya vāmadevāya sarvayogeśvarāya ca ॥56॥
namo vidyādhipataye brahmaṇaḥ pataye namaḥ ।
namo ‘suravaraghnāya kālacakrāya vai namaḥ ॥57॥
saṃvartakāgni-cakrāya pralayāntakarāya ca ।
naranārāyaṇeśāya naranārāyaṇātmane ॥58॥
mamaiva varadātre ca sarvakāmapradāya ca ।
śarabhāya surūpāya vyāghra-carma-suvāsase ॥59॥
nandīśvara-gaṇeśāya gaṇānāṃ pataye namaḥ ।
indriyāṇāmatheśāya manasāṃ pataye namaḥ ॥60॥
namaḥ pradhānapataye surāṇāṃ pataye namaḥ ।
namo ‘stu bhāvapataye tattvānāṃ pataye namaḥ ॥61॥
carācarasya pataye bhūtānāṃ pataye namaḥ ।
trailokyapataye caiva lokānāṃ pataye namaḥ ॥62॥
yogadāya namo mahyaṃ tathaivaiśvaryadāya ca ।
avadhyatva-pradātre ca tathaivājayyadāya ca ॥63॥
bhagavaṃs tvatpratiṣṭho .asmi tvan niṣṭhas tvat parāyaṇaḥ ।
śaraṇaṃ tvāṃ prapanno .ahaṃ prasīda mama sarvadā ॥64॥

We shall discuss below some notable epithets used in this stotra:
1. The first three epithets: Śarva, Rudra and Senāni, betray the influence of the Śatarudrīya; this influence is seen in several later Śaiva stotra-s.
2. Parama-deva and brahman indicate the identification of Rudra with the supreme deity, keeping with the Pāśupata affiliation of the text.
3. kāla, yamarūpa, kālānta-kartṛ: These epithets associated with Yama and the end of time bring to mind the epithets in the opening mantra-s for liṅgasthāpanā: nidhanapati and nidhanapatāntika.
4. raudra-bāṇa-dhara: evidently a reference to the Pāśupatāstra.
5. Kālacakra: While Viṣṇu was the original time deity, within the Śaiva tradition, Rudra gradually began expanding into that domain. This is one of the early references to Rudra as the Kālacakra – a term that was to be used by the Vajrayāna bauddha-s for their eponymous Bhairava-like deity. On the Hindu side, the original Kālacakra-tantra was a saura text. We have philological and iconographic evidence for a prolonged interaction between the Saura-s and Śaiva-s. Interestingly, the Paśupata shrines at Kāmyakeśvara and Harṣanātha combine Śaiva and Saura elements. Most striking are two shrines near Kāmyakeśvara: Lakulīśa is shown on the lintel of the Saura temple, and Sūrya is shown on the lintel of the Rudrālaya. Thus, we posit that the syncretic or interacting Śaiva-Saura tradition influenced the emergence of the Bauddha deity Kālacakra.
6. Saṃvartakāgni-cakra: The fire of the dissolution of the universe — this is the epithet used for Navātman-bhairava in the Kaula Paścimāṃnāya tradition emerging from the Bhairavasrotas in the mantramārga. Indeed, the foundational sūtra-s of the Paścimāṃnāya are known as the Saṃvartāmaṇḍala-sūtra-s.
7. Nara-nārāyaṇeśa, Nara-nārāyaṇātman: The Nara-nārāyaṇa tradition is very prominent in the Mahābhārata and appears to be a quasi-humanized ectype of the Indra-Viṣṇū dyad of the Veda. This dyad, while important in the early Nārāyaṇīya Pāñcarātra of the Mahābhārata, faded away in the later Vaiṣṇava tradition. However, its presence here shows that this dyad was still important in the contemporaneous stream of the Vaiṣṇava tradition with which the Ur-SkP interacted (A tradition with connections to the Harivaṃśa; see below).
8. Vyāghra-carma-suvāsas: The wearer of the tiger-skin robe — an epithet related to Kṛttivāsas found in the Śatarudrīya.
9. Śarabha: While the whole stotra is to Śarabha there is little description of him in it beyond a single mention of his name.
10. Nandīśvara-gaṇeśa: The lord of the gaṇa Nandīśvara. This gaṇa’s association with Rudra goes back to the single mention in the Pratyaṅgirā-sūkta of the RV Khila (also seen in the AV saṃhitā-s). He subsequently rises to great prominence in the Saiddhāntika tradition. His presence here indicates that this was already presaged in the Pāśupata tradition.

After the Nṛsiṃha cycle, the Ur-SkP moves to the Varāha cycle. At the beginning of that cycle, the gods praise Viṣṇu with the below stotra to urge him to take on the Varāha Nandivardhana form which they constitute with their own bodies. The votary who recites it is said to become free of sins and sorrow.

The Viṣṇu Janārdana installed at the śaiva temple of Viśveśvara at Raghapura, Odisha.

namaḥ sarva-ripughnāya dānavāntakarāya ca ।
namo ‘jitāya devāya vaikuṇṭhāya mahātmane ॥15॥
namo nirdhūta-rajase namaḥ satyāya caiva ha ।
namaḥ sādhyāya devāya namo dhāmne suvedhase ॥16॥
namo yamāya devāya jayāya ca namo namaḥ ।
namaś cāditi-putrāya nara-nārāyaṇāya ca ॥17॥
namaḥ sumataye caiva namaś caivāstu viṣṇave ।
namo vāmanarūpāya kṛṣṇa-dvaipāyanāya ca ॥18॥
namo rāmāya rāmāya dattātreyāya vai namaḥ ।
namaste narasiṃhāya dhātre caiva namo namaḥ ॥19॥
namaḥ śakuni-hantre ca namo dāmodarāya ca ।
salile tapyamānāya nāgaśayyā-priyāya ca ॥20॥
namaḥ kapilarūpāya mahate puruṣāya ca ।
namo jīmūtarūpāya mahādeva-priyāya ca ॥21॥
namo rudrārdharūpāya tathomārupiṇe namaḥ ।
cakra-mudgara-hastāya maheśvara-gaṇāya ca ॥22॥
śipiviṣṭāya ca sadā namaḥ śrīvatsadhāriṇe ।
dhundhumārāya śūrāya madhukaiṭabhaghātine ॥23॥
caturbhujāya kṛṣṇāya ratna-kaustubha-dhāriṇe ।
trivikrama-viyat-sthāya pīta-vastra-suvāsase ॥24॥
namaḥ pura-vighātāya gadā-khaḍgogradhāriṇe ।
yogine yajamānāya bhṛgupatnī-pramāthine ॥25॥
vṛṣarūpāya satataṃ ādityānāṃ-varāya ca ।
cekitānāya dāntāya śauriṇe vṛṣṇibandhave ॥26॥
purāśvagrīva-nāśāya tathaivāsura-sūdine ।
namaste śārṅgadhanuṣe saubha-sālva-vighātine ॥27॥
namaste padmanābhāya brahmasatpatha-darśine ।
namo jayāya śarvāya rudra-datta-varāya ca ॥28॥
namaḥ sarveśvarāyaiva naṣṭa-dharma-pravartine ।
puruṣāya vareṇyāya namaste śatabāhave ।
tava prasādāt kṛcchrān vai tarāmaḥ puruṣottama ॥29॥

We discuss below some of the notable epithets found in this stotra:
1. Vaikuṇṭha: This distinctive epithet first appears in the Mahābhārata and is repeatedly used in the early Pāñcarātrika section of that text (parvan 12). There it appears as a name of the god both in Viṣṇusahasranāma and the 171-epithet early Pāñcarātrika mantra of Viṣṇu composed by Nārada. It also appears in a similar mantra in a stava composed by Kaśyapa in the Harivaṃśa. In later iconography, the epithet is usually taken to mean Viṣṇu caturātman with anthropomorphic, leonine, porcine and Kapilan heads. Viṣṇu is specifically addressed by this name in the Ur-SkP as he prepares to slay Hiraṇyākṣa with the cakra (see below).
2. Nirdhūta-rajas: One who has freed himself from the dust. The dust here might be seen as the particulate bonds — or the ātman bound to the evolutes of Prakṛti.
3. Sādhya deva: In the Puruṣa-sūkta we are enigmatically informed of an ancient class of deities known of the Sādhya-s alongside the deva-s — nothing more is said of the former. They appear episodically in various brāhmaṇa texts and are generally seen as a class of celestial deities. By making Viṣṇu a sādhya, the stotra expands his domain to include these obscure deities.
4. Yama deva: Interestingly, like Rudra, Viṣṇu too is identified with Yama.
5. Aditi-putra, Ādityānāṃ-vara: Viṣṇu membership in the Āditya class of deities is not just cemented, but he has risen to be the chief of them.
6. Vāmanarūpa, Trivikrama-viyat-stha, Nara-Nārāyaṇa, Kṛṣṇa-dvaipāyana, the two Rāma-s (Rāmacandra Aikṣvākava and Rama Bhārgava or the Saṃkarṣaṇa is unclear), Dattātreya, Narasiṃha, Kapila, Śaurin, Vṛṣṇibandhu, Kṛṣṇa, Saubha-Sālva-vighātin: The late daśāvatara has not yet crystallized, but the tendency in that direction is clear in the list. We have Narasiṃha, Vāmana, two Rāma-s, and Kṛṣṇa who figure in the classic lists. Varāha is specifically avoided because that incarnation is about to occur in the current narrative. Yet, anachronistically, there is a clear acknowledgment of the Sāttvata religion with the identification of Viṣṇu with Kṛṣṇa and various Kārṣṇi/Sāttvata epithets in the above list. These include the famous act of Kṛṣṇa Devakīputra, i.e., the killing of Sālva and the destruction of his airplane the Saubha. Some other incarnations that are widely accepted, but not in the classic list of 10, are also mentioned such as Kṛṣṇa-dvaipāyana and Dattātreya. This shows that the incarnational model pioneered by the Sāttvata religion had already been expanded to include a wider range of figures.
7. Śakuni-hantṛ: This epithet is peculiar because, at first sight, people take Śakuni to mean the eponymous prince of Gandhāra. However, this is not the case because that Śakuni was not killed by Viṣṇu or Kṛṣṇa. The Harivaṃśa tells us that:
pūtanā śakunī bālye śiśunā stanapāyinā ।
stanapānepsunā pītā prāṇaiḥ saha durāsadā ॥ HV 65.26

also:
rākṣasī nihatā raudrā śakunī-veṣadhāriṇī ।
pūtanā nāma ghorā sā mahākāyā mahābalā ।
viṣa-digdhaṃ stanaṃ kṣudrā prayacchantī mahātmane ॥ HV 96.31

Here, the mighty and terrible Pūtanā, whom Kṛṣṇa slew when he drank her milk as she tried to breast-feed him in his infancy with her poisoned breast, is described as Śakunī and a rākṣasī. Hence, the epithet Śakuni-hantṛ records this episode. We know from the Kaumāra tradition that Śakunī, Pūtanā and Revatī are the names of pediatric avicephalous Kaumāra goddesses who are invoked for freeing a child from various diseases. Indeed, this identification was known even in the HV in the ancient hymn to the transfunctional goddess, the Āryā-stuti:
śakunī pūtanā ca tvaṃ revatī ca sudāruṇā । HV (“appendix”) 1.8.39

Thus, the Pūtanā-Śakunī episode represents an example of ancient sectarian competition between the Kaumāra-s and the Sāttvata stream of the Vaiṣṇava-s who portray their hero as slaying the demonized Kaumāra avicephalous goddess and thus expanding into the domain of pediatric apotropaism that belongs to the god Skanda.

Avicephalous and therocephalous Kaumāra goddesses from Kuśana age Mathurā

8. Cakra-mudgara-hasta, Śārṅgadhanuṣ, Gadā-khaḍgogradhārin: The principal traditional weapons of Viṣṇu are all mentioned, but the mudgara (war-hammer) is unusual.
9. Madhu-kaiṭabhaghātin, Dhundhumāra, Aśvagrīva-nāśa, Bhṛgupatnī-pramāthin: These epithets concern the ancient Asura/Asurī-s slain by Viṣṇu. Of these Dhundhu, the son of Madhu, is said to have caused landslides or earthquakes and was killed by the Ikśvāku hero Kuvalāśva, the son of Bṛhadaśva, into whom the tejas of Viṣṇu had entered (HV, chapter 9). It is possible that this epithet implies that the said king was seen as an incarnation of Viṣṇu (a parallel to the later Ikṣvāku incarnation as Rāma). In contrast to this more widespread legend, a parallel myth alluded to in the Liṅgapurāna suggests that Viṣṇu himself slew the Asura by acquiring the cakra from Rudra. The killing of Aśvagrīva is alluded to in both the Itihāsa-s and the later Purāṇa-s either connect it with the Pravargya-like tale of the beheading of Viṣṇu by the rebound of his bow or the Matsya incarnation. The ancestress of our clan, Paulomī, the wife of Bhṛgu, is said to have been an Asurī or a partisan of the Dānava-s. She was killed by Viṣṇu for aiding them — this is already known in the Rāmāyaṇa.
10. Rudrārdharūpa: An acknowledgment of the Harihara form. The first surviving icons of this form are known from the Kuṣāṇa age.
11. Jīmūtarūpa: Of the form of a cloud — this is an unusual name. It likely indicates the expansion of Viṣṇu into the domain of Parjanya via a specific myth found earlier in the Ur-SkP (chapter 31). There the personified Vedic ritual, Yajña, was designated by Brahman to do good to the world. He soon found himself possessing insufficient power to do that. Hence, he performed tapas and pleased Rudra. Rudra granted him the boon of becoming a cloud (Jīmūta) and delivering life-giving waters to the world. Before Rudra acquired his bull, Yajña as the cloud also became his vehicle – it is stated by becoming the abode of lightning (which as per the Veda is a manifestation of Rudra – 11 lightnings of the Yajurveda; also the name Aśani) he carried Rudra on his back. Given the Vedic incantation:  yajño vai viṣṇuḥ ।, the cloud is identified with Viṣṇu.
12. Vṛṣarūpa — In the Harivaṃśa, Vāsudeva slays a son of Bali named Kakudmin Vṛṣarūpa. However, here given that it is the name of Viṣṇu, it might imply an identification with Rudra’s bull, who was his next vehicle after Yajña as the cloud.
13. Umārūpin: This is an unusual identification that was to have a long life in the later tradition all the way to the late Śrikula system of Gopālasundarī and parallels the coupling of Mohinī and Rudra or the Harihara iconography.
14. Mahādeva-priya, Maheśvara-gaṇa, Rudra-datta-vara: In the Ur-SkP, Viṣṇu is not outright antagonistically demoted vis-a-vis Rudra. He is instead cast as a mighty god who is, however, second to Rudra. This is made clear by calling him dear to Mahādeva (or even equating him with Umā: the above epithet), while at the same time subordinating him as a gaṇa of the god and one receiving boons from Rudra.
15. Salile Tapyamāna: This is again a rather peculiar epithet because it applied to Rudra in the Ur-SkP and goes back to the Mahābhārata where it occurs in the stotra uttered by Kṛṣṇa and Arjuna to Rudra in order to obtain the Pāsupata missile. Thus, its application to Viṣṇu here might indicate his identification with Rudra. This idea of a deity heating the waters as part of the evolutionary process is an idea going back to the Veda. In the context of Rudra, it related to his liṅga form – i.e., Sthāṇu. That said, there are other clear links between Viṣṇu and the primordial waters – he is termed Nārāyaṇa – typically interpreted as the abode of the waters. Moreover, the same stotra also refers to him as Nāgaśayyā-priya – i.e., fond of this serpentine bed. Tradition unequivocally places this bed in the midst of the ocean. His Hayagrīva form is also mentioned in the Mahābhārata as dwelling in the waters consuming oblations (related to the ancient motif of the submarine equine fire). Thus, this epithet could specifically apply to that form.
In the Varāha cycle of this purāṇa, this sectarian tension plays out in the battle between the Daitya and Viṣṇu and the events that follow it. A brief synopsis of it is provided below:
-The gods formed the boar body for Viṣṇu with their own bodies. Thus, he advanced against the Daitya-s by diving into the ocean — an account is given of his encounter with various marine life, like different kinds of whales, sharks, fishes and molluscs. Visiting the various nether realms, he advanced to Rasātala where the Asura-s lived.
-There, a submarine Daitya guard Nala sighted Varāha and in fear rushed to inform his lord. But Varāha followed him and thus discovered the Asura stronghold.
-Prahlāda informed Hiraṇyākṣa that he had a bad dream that someone in a man-boar form might kill him.
-Hiraṇyākṣa says that he too had a dream in which Rudra asked him to surrender to Indra, give up his dominion, and come to dwell near him. The Daitya-s suggested that Hiraṇyākṣa not go to battle. Instead, they suggested that they would head out to the battle with Andhaka as their head. Vipracitti suggested that he would go himself to destroy the gods.
-Nala came in and informed the Asura-s that he had sighted a terrifying boar coming to attack them.
-Prahlāda urged Hiraṇyākṣa to take some action as he realized that the boar was none other than Viṣṇu who has come to destroy them with the aid of his māyā.
-Hiraṇyākṣa responded that he wished to avenge his brother’s death by killing Viṣṇu and offering his boar-head as a bali for Rudra.
-He sent forth his Asura troops to attack Varāha. At first, Varāha ignored them saying that he was just searching for his wife and the one who had kidnapped her. The Asura-s launched a massive attack on him, and he retaliated by demolishing them.
-Hearing of their defeat Hiraṇyākṣa asked the great Asura generals Prahlāda, Andhaka, Vipracitti, Dhundhu, Vyaṃsa and others to get ready to confront Varāha.

-Varāha made an anti-clockwise circuit of the Asura stronghold and stormed it via the southern gate. He destroyed the śataghni missiles fired from the gate and also the Kālacakra missiles that were hurled at him. The Asura-s made a great sally at him. He feigned a retreat and drew them out of their fortifications. However, the Asura-s realized his plan and attacked him from the rear. The deva-s in his body were able to detect this attack and oriented him towards the Asura-s attacking him from behind.
-Varāha challenged them to one-on-one duels. Andhaka agreed that it was the right thing to do. However, Prahlāda informed them that the vile Varāha was none other than the wicked Viṣṇu using his māyā because he was afraid to fight them with his own form. Then Prahlāda showered astra-s on him and asked the other Asura-s to join him in a combined attack.
-Varāha then smashed Prahlāda’s chariot and hammered him with his own standard on his head. The daitya retaliated with his mace, but it had no effect on Varāha.
-He then attacked fought Andhaka and Vipracitti in a great battle. In the end, he carried both like Garutmat carrying the elephant and the tortoise and hurled them down like bolts of lightning.
-He then destroyed and slew the divisions of the remaining Asura-s.
-Vipracitti returned to the battle having rearmed himself, but after a strong fight Varāha whirled him around and sent him crashing into the fortress of Hiraṇyākṣa.
-Hiraṇyākṣa alarmed by the noise went to check things out and found his general unconscious. After reviving him, the Daitya emperor asked him who could possibly defeat him. Vipracitti then told him that it was the invincible Varāha and perhaps it was similar to Nṛsiṃha who had earlier crushed them. He suggested that the Asura-s should abandon their stronghold and flee.
-Disregarding Vipracitti, Hiraṇyākṣa set out for battle himself. He is said to have been of the complexion of a heap of collyrium but with a blond beard and four fangs.
-His advance is described using two astronomical allegories: He is said to be like a great comet and Vipracitti who accompanies him is like a reflection of that comet. He is also described as being like the Sun, with Prahlāda, Andhaka and others surrounding him like the planets — an interesting heliocentric simile.

-Varāha scattered the other Daitya-s and Dānava-s and rushed at Hiraṇyākṣa, who, however, paralyzed him by piercing his joints with his arrows. The deva-s removed those arrows with magical incantations, and Varāha resumed the attack. This time he came close to striking the Asura’s car, but the Daitya’s charioteer steered it away, and Hiraṇyākṣa bound Varāha with the Nāgāstra.
-Then the Asura-s massed around him and tried to chop him up with their weapons. However, Garuḍa came to his aid and released him from the Nāgāstra. Thus revived, he smashed the Daitya-s and resumed his attack on Hiraṇyākṣa.
-The Daitya then pierced him in the heart with an astra causing him to faint. On regaining consciousness, he called on the deva-s to reinforce him, and they filled him with their tapas. Thus, he shone like seven suns, resembling Rudra preparing to destroy the worlds.
-Varāha then displayed several māyāvin tactics and overcoming the nāgāstra-s of the Asura king destroyed his chariot. He continued fighting on foot and struck Varāha with the Mohanāstra, which stunned the boar. The deva-s in his body countered it, and Varāha returned to the battle.
-Varāha uprooted a tree (axial mytheme) and struck the Asura lord on his head. The latter fell unconscious, and his bow with five arrows slipped from his hand. The other daitya-s and dānava-s wailed thinking he was dead and fell upon the boar with their weapons. Varāha simply swallowed all those weapons.
-As Varāha was engaged with the daitya-s, Hiraṇyākṣa recovered, and uttering the mantra rudrāya vai namaḥ ।, he hurled a mighty spear at his enemy. Varāha was struck in the heart by that and fell down as if dead.
-The sun then lost its luster, and the planets were on collision course. Brahman at that point invoked Rudra. Varāha rose up again, and the tejas of Rudra entered him. Pulling out the spear stuck in him, blazing like a thousand fires, he pierced Hiraṇyākṣa like Skanda striking Krauñca. However, the Asura was unfazed by that blow.
-The Daitya returned the blow with his sword, but Varāha felt no pain and struck the sword away with the back of his palm.

-Then the two engaged in a prolonged wrestling bout at the end of which an incorporeal voice told Varāha that he can kill the Daitya only with Rudra’s cakra.
-Invoking Rudra and calling the cakra that was born of the “waters” (an oblique reference to the Jalaṃdhara episode, where Rudra killed the Asura using a cakra that he drew from water: the whirlpool mytheme), Varāha assumed a gigantic form pervading the triple-world.
-Hiraṇyākṣa fought him with various astra-s and displays of māyā, but Varāha destroyed all of them with the cakra and finally cut off the Daitya’s giant head.
-Varāha then searched for Pṛthivī by destroying the parks and tanks of the Asura-s and uprooting mountains. Going south he uprooted Śaṅkha mountain and found her bound there, and guarded by dānava-s. He hurled the Śaṅkha mountain and slew the dānava-s and drove away the Nāga-s. He then seized the jewels of the Asura-s.

Pṛthivī clinging to Varāha’s tusk from Gupta age Udayagiri.

-He carried Pṛthivī clinging to his tusk even as Brahman had carried the former earth Vasudhā when he had assumed a boar form (It is notable that the Śaiva-s revived the memory of this old Vedic narrative of Prajāpati’s boar form probably to obliquely indicate that Viṣṇu’s Varāha form was only second to that of Brahman).
-He then handed over the triple-world to Indra and reaffirmed their eternal friendship.

-Varāha indicated that he wished to enjoy the pleasures of his boar form in fullness. Thousands of Apsaras-es become sows to consort with him even as the brāhmaṇa-s lauded him with their hymns.
-Mating with his wife in the form of the sow Citralekhā he birthed a lupine son known as Vṛka (Temples of Varāha as the father of the lupine Vṛka – Kokamukhasvāmin – seem to have been there in Nepal and from there transmitted to Bengal).
-Vṛka roved around the world with his pack eating various animals. Finally, he arrived at the forest of Skanda at Gaurīkūṭa with medicinal plants, minerals and gems. At that time Skanda was away visiting the Mandara mountain and had deputed his avicephalous or therocephalous gaṇa Kokavaktra (himself with a lupine head or with a cuckoo or waterfowl head) to guard his forest.
-Vṛka ravaged Kumāra’s forest. At first Kokavaktra tried to be good to him and told him that he was happy with his power. Kokavaktra asked Vṛka to stop and told him that he would repair the damage and put in a word with Skanda to make him a gaṇa.
-Vṛka refused and attacked the Skandapārṣada. After a fight, Kokavaktra knocked down Vṛka and bound him with pāśa-s (A rare reflex of the Germanic Fenris wolf motif in the Hindu world).
-When Skanda returned he sentenced Vṛka to be subject to Narakatrāsa-s by his gaṇa-s.
-Nārada informed Varāha about what had happened and told him that due to his childish arrogance, Skanda does not bow before the great god and has bound his lupine son.
-Infuriated, Varāha proceeded to fight Skanda. Skanda and his gaṇa-s neutralize the cakra and other weapons of Varāha. Finally, Guha pierced Varāha’s heart with his saṃvartikā spear. Viṣṇu at that point abandoned his Varāha body and resumed his usual form.

Skanda wearing the tusks of Varāha on his necklace, Gupta age.

-Viṣṇu then praised Rudra who conferred a boon to him. Viṣṇu asked him to teach him the Pāśupata-vrata. Rudra mounted his bull and went to Sumeru to teach Viṣṇu the said vrata.

Here we see a three-way competition between Śaiva-s, Vaiṣṇava-s and Kaumāra-s. The normally accommodating relationships between the Kaumāra-s and Vaiṣṇava-s (barring some conflicts as the Pūtanā case alluded to above), seem to have broken down probably under Śaiva influence. The incident of the defeat of Varāha by Kumāra is seen in both the South Indian Skandapurāṇa and the Ur-SkP, suggesting it was there in an ancestral SkP. It has some Gupta-Puṣyabhūti age iconographic representation in the form of Skanda wearing the tusks of the boar in his necklace. However, in this text, the Śaiva-s trump both of them with the final flourish of Viṣṇu ultimately asking Rudra to teach him the Pāśupata-vrata. We believe that the Varāha episode in the Ur-SkP is a genuine early version of this famous mytheme, but it was strategically tweaked at certain points by the Śaiva-s to downgrade Viṣṇu and exalt Rudra.

The zombie obeys: a note on host manipulation by parasites and its ecological consequences

In 1858-59, as AR Wallace, one of the founders of the modern evolutionary theory, was exploring the Sulawesi Islands, he collected an ant, Polyrachis merops, that he sent over to England. Years later, the naturalist W Fawcett studying these ants collected by Wallace and others from South America, realized they were attacked by a fungus that is today known as Ophiocordyceps. In 1869 when Wallace learnt of mycologists discussing these insect-killing fungi, he was much surprised and even expressed doubt if it was a genuine fungus. However, those doubts of the great man aside, the fungus was to have a bright future as a beacon for studies on the manipulation of host behavior by parasites. It is today widely known that Ophiocordyceps fungi infect ants, such as the carpenter ants (of genus Camponotus) and spiny ants (Polyrachis), and alters their behavior making them leave their colonies and wander onto leaves. Here it makes them clamp down on the leaves in the canopy above the ant trails with their mandibles. They remain stuck there until the fungus kills them from within; then, the fungus grows out of them, often bursting out from their head, and sporulates. The spores rain down on the unsuspecting ants scurrying below on their trail; thus, the fungus infects a new set of victims. This peculiar adaptation has evidently evolved as part of the arms race to keep up with the emergence of hygiene in the ants – they regularly groom themselves, and when they find a corpse, they quickly break it down and take it out of their nest. Thus, by showering spores on them when they are on the trail, the hygienic practice of the ants is breached by the fungus.

Today we know that this behavioral manipulation of ants is not unique to Ophiocordyceps, an ascomycete, but is also evinced by the fungus Pandora that belongs to a distant lineage of insect-specialist fungi (Entomophthoromycota) in a distinct genus of ants, Formica. Even more remarkably, the same type of behavior is also induced in Formica ants by the trematode brain fluke Dicrocoelium dendriticum which has a remarkably complex life cycle. It begins with sexual reproduction in the bile duct of a cow and excretion via its dung of fertilized eggs bearing developing embryos. The eggs are eaten by snails (e.g., genus Cochlicopa), where the worm emerges as miracidia larvae. The miracidia drill through the gut wall and enter the respiratory system of the snail, where they protect themselves from the host immunity by forming sporocysts. The snail extrudes them in slime balls through the respiratory pore, and they emerge as cercaria larvae from the sporocysts. These cercariae infect an ant when it feeds on the snail slime balls. In the ant, they develop into the next stage, the metacercariae, which start controlling their new host’s behavior and causes it to desert its colony and climb up leaves and clamp down on them with their mandibles. Once on the leaves, they might get eaten by cows to resume the cycle.

A parallel strategy has evolved in the parasitic insect, the myrmecolacid strepsipteran – here, the male takes formicid ants as hosts while the female takes locusts as their hosts. The male strepsipteran alters the ant’s behavior to again desert its colony and climb up leaves and hold on to them with its legs. The strepsipteran then emerges from the ant and flies off in search of the female. By leading the ant onto the leaves, he can better sense the female’s pheromones wafting in and also have a launchpad for his final flight to find his mate. On finding the infected locust from which the morphologically degenerate female protrudes out, he mates with her by piercing the brood-canal in her cephalothorax with his spiny tube-like sperm delivery organ, the aedeagus. Interestingly, we can also find this behavioral manipulation in a more general sense in baculoviruses, which cause the caterpillars they infect to “summit”, i.e., climb the outer branches of the trees and stay there. The virus then kills them and liquefies their corpses so that the virions are spread on the leaves allowing new caterpillars to consume them with their meal. The virus achieves this by a UDP-sugar glycosyltransferase enzyme that it encodes, which modifies the insect molting hormone ecdysteroid to inactivate it, and thus prevents it from molting on the trunk of the tree. Thus, a virus, two fungi, a fluke, and a strepsiteran insect, each with a distinct life cycle, have all evolved broadly convergent behavioral manipulations of their hosts to enhance their spread.

Rather remarkably, this broad strategic category of altering host behavior to favor transmission to a new host furnishes several other examples of channeling of convergent manipulations by evolutionarily distant parasites. One of the best known of these is the induction of erratic behavior leading to suicide by drowning in various insects and crustaceans by the nematomorph and mermithid nematode parasites that need to access water for the next stage of their development. In the case of the nematomorphs, like Paragordius varius, they induce their cricket/grasshopper host to jump into water and drown, allowing them to come out and mature in the aquatic environment and lay eggs. The larvae that hatch from the hosts then burrow into the guts of aquatic insect larvae, like mosquitoes, and form a cyst. This cyst survives into the adult of the mosquito that returns to land. On land, when the mosquitoes die, they might be eaten by crickets leading to the transmission to the new host. Similar suicide by drowning is driven by mermithid nematodes, such as Mermis nigrescens in the earwig Forficula auricularia and the ant Colobopsis, and by Thaumamermis zealandica in the crustacean sandhopper Bellorchestia quoyana. Here again, the drowning seems to allow the nematodes to ultimately access their secondary hosts in the form of aquatic larvae. In molecular terms, this suicidal behavior appears to be induced by the upregulation of Wnt proteins in the head of the infected orthopterans.

A conopid fly

Apart from manipulating host behavior to allow the parasite to reach a new host, there are several instances of convergent evolution of manipulations that alter the host behavior to make the parasite more secure. This was observed early on in the braconid parasitoid wasp Aphidius ervi, which may undergo two alternative larval programs, namely one of uninterrupted development to pupation and adulthood and the second involving a dormant phase known as the diapause. One of their hosts is the aphid Acyrthosiphon pisum, into which they inject an egg. The emergent larva eats the aphid from within and leaves its bronzed exoskeleton as a puparium for the final stage of its development. If the wasp larva opts for a diapause program, they manipulate their host aphid to abandon the aphid colony and go either into a curled leaf or entirely leave the plant and go to an obscure site where they are “mummified”. In contrast, the larvae opting for uninterrupted development cause their host to leave the aphid colony and climb onto the upper surfaces of leaves prior to mummification. A comparable adaptation is seen in the case of the parasitoid conopid flies, such as Physocephala rufipes, which are morphological wasp mimics that target bumble bees. When the conopid fly comes upon a bumble bee foraging among the flowers, it attacks it and inserts its ovipositor between the abdominal cuticular sternites to deliver eggs into the bee. The fly larvae grow within the bee, feeding on it from within and altering its behavior. They cause it to desert the hive and limit their nectar collection activity. Finally, when the larva is close to pupation, it causes the bee to bury deep into the soil – evidently, here, it induces in workers a behavioral program that executes in the queen when it hibernates over winter. There the fly larva kills the bee and uses its exoskeleton as a puparium to overwinter and emerge in spring as an adult. Those flies which develop in such underground bee carcasses, on an average, develop better than those which end up killing their host above the ground, clearly indicating a fitness gain accrued from the manipulation of host behavior.

Reclinervellus nielseni larva manipulates Cyclosa argenteoalba

A related form of parasitic manipulation was discovered by the naturalists Takasuka et al. among spiders that spin webs in Japanese shrines. Here, the host spider Cyclosa argenteoalba weaves two kinds of webs — a normal orb web to catch prey and a resting web where it molts. The larva of the ichneumonid ectoparasitoid wasp Reclinervellus nielseni manipulates the spider host by injecting it with a toxic mixture. This causes the spider to make a version of the resting web with more threads so that it is better reinforced and also add decorations that reflect UV light allowing it to be avoided by birds or large insects in their flight. Thus, the wasp larva induces its host to create a resilient cocoon for it, where it pupates after killing the host. Since removing the ectoparasitoid larva causes the spider to return to its normal web-weaving, it is clear that the altered behavior is induced by molecules in the wasp’s venom. Another component of this venom also prevents the molting of the host spider. Notably, this behavioral manipulation has also convergently evolved in another ichneumonid ectoparasitoid Hymenoepimecis argyraphaga, which, on the evening it will kill its host, the spider Plesiometa argyra, alters its host’s behavior to spin a comparable cocoon web. However, in this case, rather than making the spider weave a resting web, the wasp toxin appears to induce it to repeat a subset of the early steps of normal orb construction while suppressing the remaining steps resulting in a cocoon for the larva.

The above classes of behavioral manipulations broadly fall under the rubric of host behavioral manipulation for reaching new hosts or for providing suitable “housing” for pupation or dormancy. A further class has been recognized in the form of manipulation to make the host provide policing services. A good example of this was described several years ago for the braconid parasitoid wasp Glyptapanteles sp., which lay their eggs in caterpillars of the geometrid moth Thyrinteina leucocerae. After developing within their host, they exit it by piercing its lateral body wall but do not kill it; instead, it heals from the trauma. One or two wasp larvae remain behind inside the caterpillar and apparently manipulate the latter to act as a bodyguard for the egressed larvae that start pupating. Under the remaining larvae’s influence, the caterpillar stops feeding, hangs around with the pupae, and shows behaviors not seen in uninfected caterpillars — it knocks off predators such as the bug Supputius and other hyperparasitoid wasps by violently swinging its head. However, it never matures into a moth and dies once it has done its policing job for the parasitoid. It appears that the 1-2 larvae that remain behind to manipulate the host sacrifice their own fitness for the sake of their egressed kin. Field studies in Brazil showed that this protection significantly increased the survival of the wasps supporting the adaptive nature of the behavior manipulation and its potential evolution under kin selection. In a dramatic lepidopteran on hymenopteran reversal, a convergent evolution of the bodyguard strategy is seen in the case of the caterpillars of the lycaenid butterfly Narathura japonica that intoxicates the workers of the ant Pristomyrmex punctatus with secretions from its dorsal nectary organ found in the abdomen. These reduce the locomotory activities of the ants by acting on their dopaminergic circuit, turning them into defensive bodyguards for the caterpillar. However, at least in the case of certain related lycaenid butterfly caterpillars and the ant Formica japonica, the former might also provide some benefit to the bodyguards in the form of a sucrose+amino acid shot from the dorsal nectary organ.

We started collecting and classifying such studies on host behavior manipulation starting in the first year of our university college. Sometime before that, we had made our first foray into the study of lysogenic bacteriophages that had made us aware of the advantages and changes they brought to their hosts when in the lysogenic state: they encoded toxins like the cholera toxin and the diphtheria toxin that enhanced the virulence and potentially the survival of their bacterial hosts. They also made their host resistant to other viruses that might attack it when they resided in lysogeny. It was around that time we also became aware that nearly all alcohol-fermenting yeasts like Saccharomyces cerevisiae and its relatives carried a double-stranded RNA virus, a totivirus (related to reoviruses, like the rotavirus), in their cells. We wondered if this too might confer some advantage on the yeast, like the lysogenic bacterial viruses. Subsequently, we also became aware that, indeed, certain totiviral systems of yeast might provide such an advantage. The best-known is the remarkable totivirus system of S.cerevisae centered on the benign helper virus L-A that encodes a RNA polymerase and a capsid protein gag. A further satellite virus, like ScV-M1, ScV-M2, or ScV-M28, which does not encode any replicative apparatus but just killer toxins, is a parasite on the L-A virus — it uses the L-A polymerase and coat to replicate and encapsidate itself. This killer virus produces a toxin that kills other yeasts which do not contain the killer virus. Thus, while it acts selfishly, it enhances the fitness of the yeast host by eliminating its competitors. More recently, it has become clear that the totiviruses might increase the virulence of their fungal hosts toward the hosts of the fungi — for example, related viruses enhance the virulence of the mammal-pathogenic Aspergillus fumigatus and Talaromyces marneffei. Similarly, totivirus of the kinetoplastid parasite Leishmania also makes it more inflammatory and turns it into a potentially more serious pathogen. Our early foray into understanding these interactions made us realize that the behavior manipulation by parasites spans the entire spectrum from the molecular to the macroscopic. It also made us think about whether the behavior manipulating repertoire of certain macro-parasites might include the selfish conferring of advantages to their hosts, just like lysogenic phages and fungal totiviruses.

As we were thinking about this possibility, by some coincidence, we had a new professor in college who had just completed his Ph.D. As part of that research, he found an example of this: the apicomplexan parasite Sarcocystis infects the heart muscles of hares and deer and makes them run slower. Thus, they are eaten by dholes, and the parasite is transmitted to their guts — the definitive hosts. He had evidence that a subset of the dhole pack might carry higher levels of the parasite and play a role in transmitting Sarcocystis to herbivores via their latrines — defecating in regions where the herbivores might feed. Thus, while a subset of the dholes might suffer fitness costs from bearing a higher parasite load, the pack might benefit (again via kin selection) from the parasite making their prey easier to catch. He also speculated that this strategy might have convergently evolved in certain parasitic flatworms. Studies by others had shown that other Sarcocystis species, which infect the brain and the muscles of rodents, make voles more prone to predation by kestrels or snakes, their definitive hosts. Hence, unlike the manifold largely fitness-negating behavior manipulations we considered earlier in this article, the case of Sarcocystis, like that of the lysogenic bacteriophages and domesticated totiviruses of fungi, might not be entirely negative. Rather they might be selfishly fitness-enhancing at one trophic level (definitive host predators) while being negative at another (intermediate host prey). After studying these cases, we learnt of Dawkins’ hypothesis of the extended phenotype that was well-supported by these cases. It also brought home to us the need to keep an eye open for molecular adaptations that might allow host-parasite interactions to feed into prey-predator interactions. We eventually were able to discover molecular weaponry of such interactions while studying the system of the nematode Heterorhabditis sp., the bioluminescent bacterium Photorhabdus and insect larvae. The bacterium is symbiotic with the worm Heterorhabditis, which attacks insect larvae and vomits the Photorhabdus that it carries in its gut on them. The bacterium then secretes a wide array of toxins that kill the insect, and the nematode feeds off the carcass.

The Toxoplasma gondii-wolf-puma system as illustrated by Meyer et al.

This finally brings us to a relative of Sarcocystis, another apicomplexan parasite Toxoplasma gondii, which illustrates the macroscopic ecological consequences of the multi-directional fitness consequences of interlocking host-parasite and prey-predator interactions. The best-studied aspect of this is the cat (Felis catus)-rodent cycle of Toxoplasma, where the rodents are the intermediate hosts and the cat the definitive host (where the parasite completes its sexual cycle). Here the parasite changes the neurotransmitter concentrations in the mice and rat brains to make them attracted to the odorants in feline urine — it is believed that the male rodents are induced by the parasite to experience sexual arousal to cat odorants. Needless to say, this draws the rodents towards the cats and makes them easier prey, thereby allowing the parasite to complete its cycle. More recent studies have found similar results with other cats. For example, in our close cousin, the chimpanzee, toxoplasmosis causes a morbid attraction towards leopard urine, thus, increasing their chances of being killed and eaten by one. Another study found that hyena cubs infected by Toxoplasma tend to lose their fear of lions and approach them more closely than uninfected ones. Thus, they tend to be killed more often by cats. These studies were capped up by the recent publication of a multi-year study on Toxoplasma’s role in the wolf-puma (cougar; Puma pumoides) interactions in North America. The authors found evidence that toxoplasmosis in wolves makes them greater risk-takers, thereby increasing their tendency to break off and found their own packs or become leaders of packs. They propose that this behavior brings them in contact with pumas that the wolves normally avoid. On one hand, this results in an increased propensity for them being infected by the parasite from puma feces, and on the other, it increases the propensity of Toxoplasma transmission to the cat, where the parasite completes its sexual cycle. Sarcocystis neurona, which resides in the neurons of its intermediate host, is proximally positioned to alter its behavior in ways similar to Toxoplasma but its ecological consequences remain poorly explored.

In each of the above cycles, the behavioral alterations of the intermediate host clearly advantage the parasite by increasing its probability of reaching the definitive host. Like with the Sarcocystis example, it is apparent that toxoplasmosis in the definitive host does not cause it to die — it seems to be a mild infection with no serious sequelae. Studies on domestic cats indicate that most infected with T. gondii show no signs of disease. In fact, it only seems to flare up as a serious condition if the cat is also infected by a retrovirus, like FIV or FeLV, which compromises its immune system. Thus, in balance, it is conceivable that Toxoplasma actually confers a fitness advantage to the cats by “bringing” prey to them. In rodents, chimpanzees and hyenas, the manipulation seems to obviously depress the fitness of the intermediate hosts. However, a closer look suggests that the picture might be more complex. The above study on the wolf-puma system suggests that, at least in some intermediate hosts, the manipulation by the parasite might not be entirely fitness-reducing. Studies on male rats suggest that Toxoplasma might make male rats more sexually active by increasing testosterone production. In domestic dogs, sheep, goats, rabbits, rats, and probably humans, there is evidence for Toxoplasma being sexually transmitted between mating partners and also to their progeny (congenital toxoplasmosis). Hence, it might also be similarly transmitted within a wolf pack via sex. This, taken together with the manipulation resulting in testosterone elevation, suggests that the parasite also attempts to increase its range within intermediate hosts via a sexual and congenital cycle. The testosterone effect with the behavioral changes suggests that it might not be all bad for the intermediate host — potentially contributing to their fitness via increased sexual activity. In the wolf example, behavioral changes, like pack founding and new territory acquisition, seem to have a positive effect on fitness too. Thus, the net balance of the fitness consequences of toxoplasmosis might be harder to evaluate, even for the intermediate host.

In parallel with the evidence from the extant chimpanzee, we have fossil evidence that the human lineage was prey for large felids: e.g., the Sterkfontein Paranthropus with leopard canine marks on its skull; the Olduvai OH 7 Homo habilis leg with leopard tooth marks (other hominins in the same site were eaten by crocodiles); the Dmanisi Homo georgicus skeletons were likely accumulated by a big cat such as Megantereon megantereon, Homotherium crenatidens or Panthera gombaszoegensi; the Asian Homo erectus eaten by a large cat at Zhoukoudian; the Cova Negra Homo neanderthalensis whose skull was punctured by a leopard; at least one of the Sima de los Huesos hominins, who were related to Neanderthals and maternally to Denisovans, was consumed by a large cat; tigers, lions, and leopards have been recorded as eating numerous humans in India and Africa until 100 years ago — this was likely a far more common occurrence in earlier times though we do not have good records for it. Thus, it can be said that for much of its history, the hominin clade was an intermediate host for Toxoplasma and transmitted it to cats that preyed on them. However, things changed as, with their growing brains, H. sapiens managed to turn the tables on the big cats and nearly exterminate them. Thus, today humans are practically dead-end hosts for Toxoplasma. This does not mean that the behavioral manipulations have ceased. There is some evidence that it might alter sexual behavior and aggression in both human males and females. There are correlational studies suggesting that it might foster entrepreneurial tendencies and road rage in human males and generally aggressive behavior and neuroticism in women. There is also evidence for association with personality disorders on the schizophrenia spectrum. In the past, some of these behaviors might have reduced the fear in humans and made them venture closer to big cats in the environment that then preyed on them. However, today a subset of these altered behaviors, like enhance entrepreneurship, might provide some fitness benefit.

It should be noted that today millions of humans are infected by Toxoplasma primarily due to their contact with domestic cats. Nevertheless, not all of them become more neurotic or entrepreneurs. This suggests that perhaps the strain that infects domestic cats does not affect its human host strongly. Moreover, it is likely that the humans who are more affected by the behavioral modifications induced by Toxoplasma have some genetic predisposition for the same. Nevertheless, even if a dead end for the parasite, we wonder if it might have played a role in human ecology with respect to cats. Cats were domesticated somewhere in West Asia during the Neolithic. It is generally believed that this was a symbiotic relationship because human settlements allowed for increased rodent populations, and the domestic cat could control them. Nevertheless, it needs to be considered if the infection of humans by Toxoplasma as a result of increased proximity with the proto-domestic cats resulted in some kind of behavioral alteration that made humans attracted to cats and increased their bonding. It is possible this goes back even deeper in the Paleolithic, where the attraction towards large cats provided the germs for the “man-cat” hybrid imagery that is widely seen across human cultures. This idea is worth considering because, unlike the domestic dog, which usually exhibits much greater emotional overlap with humans, the cat is a mostly aloof animal.

Other apicomplexan parasites also manipulate their hosts with potentially differential fitness consequences for their intermediate and definitive hosts. For instance, while the malarial parasite Plasmodium primarily resides in the gut (ookinete stage) and the salivary gland (sporozoites) of Anopheles mosquitoes, it manages to alter the host odorant response, which is localized to the antennae, such that the mosquito is more attracted towards vertebrate odors. It is not clear if the odorant manipulation is done by a few sporozoites that enter the brain or remain behind elsewhere in the mosquito to act on behalf of their kin. It is conceivable that this action might confer some fitness benefit for the mosquito in terms of getting it to a vertebrate host for a blood meal. A convergent evolution of this manipulation is suggested in the case of the kinetoplastid Trypanosoma cruzi, which appears to make its bug host Triatoma both more active and responsive to human odors. A complementary manipulation is mediated by the related apicomplexan, Hepatozoon, which has a complex life cycle alternating between Culex mosquitoes and a single vertebrate host like a frog or two vertebrate hosts like a frog followed by a snake which eats the former. Here, Hepatozoon manipulates its vertebrate hosts to make their smell more attractive to the mosquito. This adaptation has convergently evolved in the kinetoplastid parasite Leishmania, which makes their mammalian hosts’ smell more enticing to the sandfly. While we still poorly understand how these manipulations are achieved at the molecular level, the genomes of some of these apicomplexans show that they encode remarkable arrays of effectors that bear the signs of a long evolutionary history of meddling with host systems. This is providing glimmers of how these parasites might comprehensively hijack various host systems. However, the mechanisms of deployment and targets of the effectors of even well-known apicomplexan parasites still remain poorly understood.

The manipulation of host odors and behaviors brings us to the more general macro-ecological consequences of parasites that are also not clearly understood. Several researchers like Zahavi, Hamilton, Thornhill and Fincher have proposed hypotheses that are dependent on parasite load in a species. Both Zahavi’s handicap principle and Hamilton’s proposal regarding the strength of expression of secondary sexual characters derive from the idea that these are honest signals for a strong intrinsic immunity against parasites in the possessors (typically males) to their potential mates. Indeed, in support of Zahavi’s hypothesis, the high-ranked male mice with increased testosterone were more susceptible to the apicomplexan parasite Babesia microtii suggesting that maintenance of top-tier male behavior in the face of parasites needs a stronger intrinsic immunity. In contrast, Thornhill’s hypothesis suggests that societies with a higher parasite load tend to display behaviors that are more aligned with conservative/xenophobic tendencies, and those with lower parasite loads tend to develop more liberal/xenophilic tendencies — this generally matches the caricature of the left-liberal as a shabby and unkempt individual (e.g., their father Karl Marx himself). Given that genome-wide association studies in humans have uncovered linkages between political orientations and certain odorant receptors, one must also bring into the picture the possibility that odor manipulations by parasites might be at the heart of such connections — for example, an odorant receptor variant with the capacity to “smell” infection might trigger a xenophobic response. Similarly, behavior manipulations, such as increased xenophilia, might allow the parasite to spread. Thus, beyond the Thornhill hypothesis, one needs to consider the possibility of direct manipulation by parasites leading to certain political orientations. Indeed, one cannot avoid seeing parallels to the behavioral manipulations induced by memetic parasites such as West Asian monotheisms and their secular mutations. Therein, a multiplicity of behavioral consequences can be seen, ranging from a totivirus-fungus-type association to suicidal behavior induced by several parasites.

Some further reading:
https://www.nature.com/articles/s42003-022-04122-0
https://www.nature.com/articles/s41467-021-24092-x
https://link.springer.com/article/10.1007/BF00377350
https://royalsocietypublishing.org/doi/10.1098/rspb.2018.0822

Cārucitrābhisambodhi

Chakkalal and Mundalal saw that Gannaram Dakiya, the owner of the little eatery, had taken a bit too much of an ethanolic beverage and had forgotten to lock the safe with his phone, cards and some cash. They broke into his shop and made away with those. As they were sneaking out, they were seen by Gannaram’s cook, who was washing vessels in the vicinity. However, he did not make much of their presence, as they were familiar idlers who lazed around near his stall, getting a free meal from the leftovers of Gannaram’s customers. When Gannaram returned to his mindfulness, he was shocked to discover his loss and cast about trying to find out who had robbed him. His cook was quick to point out that he had seen Chakkalal and Mundalal and suggested that it might be them. Gannaram soon assembled a band of fellow jāti-folks, some of whom were particularly rough, and set out in search of the two wastrels. They found the two wasted from the aftermath of a heavy celebratory libation and dope sourced with their ill-gotten gains and thrashed the hell out of them. Chakkalal died and Mundalal went comatose.

The election results had just been announced, and the incumbent government of Pratapa Simha had been narrowly beaten by a motley coalition of the Nīladrāpeya-dala, the Mārjani-dala, the Paṭṭa-dala, the SJWP, the Kangress-S and the IML. These disparate parties had been brought together in no small means by the funding coming from the Mahāmleccha, the other Pañcanetraka-s, and their vassal, the śūlapuruṣa-s. They had been laundered into the country by the various fronts set up by the traders Gregory Kun and Van Schwarzstein using the extensive legal cover provided by the liaison between their activists and the sympathetic supreme court judge Udup Sandha. They had long been working to overthrow what they called the fascistic government of Pratapa Simha. Thus, in the city of Ashmanvati, the activists had created a tense alliance of the Nīladrāpeya-dala, the SJWP and IML parties to see them past the finish line in what was once a stronghold of Pratapa Simha’s ruling party. In part, their catastrophic failure was a problem of their own making – they had long encouraged the Nīladrāpeya-s and those with inclinations aligned with the SJWP claiming it to be part of their attempt at building an electoral base for future successes. But on that day, the reality of their misguided attempts had been made plain.

The founder of the Nīladrāpeya-dala, while born a Hindu himself, sought the eradication of the Hindu Dharma, for which, as stated by the old Monier-Williams, he wished to start with the liquidation of the V1s. However, the most immediate enemies of the NDs were the service jāti-s that stood just above them in the hierarchy. Their recent electoral success had brought the powerful Nīladrāpeya politician Mhaisasur from Ashmanvati into the ruling circle. Chakkalal and Mundalal’s relatives now applied to their coethnic Mhaisasur, who had just been elected to power, to avenge their fate. He had earlier assembled a band of rowdies to slay some sādhu-s, an act that had gone unpunished by the Pratapa Simha government as part of their effort to woo the NDs. Buoyant in his power, Mhaisasur thought there was little anyone could do to stop him from taking the law into his own hands. Thus, he unleashed his goons to go postal on the jāti of Gannaram.

With the junior college exams behind her, Charuchitra and her mother traveled to several Viṣṇu shrines among the ancient hills. Having completed those pious visits, they took a bus to proceed to Somakhya’s city. There she was to join her cousin in taking a critical entrance exam for the best schools across the country. Due to the reservation policy for various jāti-s claiming a depressed status, there was no guarantee that a V1 girl like her could make it to the course of her choice in her own city. However, by taking this common entrance exam, where merit was still valued to a slightly greater degree, she could increase her chances for the same. Her parents fervently hoped that between the college and the common entrance tests, she would make it to a reasonable institution in their own city. As a backup, they were also hedging on Somakhya’s or Babhru’s city so that she could stay in the safety of one of her close clansfolk’s homes to complete her education.

As they were so caught up with her exams, they had hardly paid any attention to the news. Thus, largely ignorant of the unexpected electoral results, they were on the bus, which was to stop briefly at Ashmanvati and pick up a few passengers before proceeding to Somakhya’s city. Charuchitra’s mind was filled with expectant thoughts – Somakhya was the cousin she was closest to and had not seen him in a couple of years. She was also hoping that he might provide some key solutions for questions in the impending exam that had perplexed her – after all, Somakhya’s city and college were perhaps among the most competitive in the nation. Even as they were nearing Ashmanvati, the bus suddenly came to a halt. At first, they thought there might be an accident downstream, but ere long, the halt had already stretched to half an hour. The passengers began irately asking the driver and the conductor what was happening. Finally, the conductor announced that a major riot was underway in Ashmanvati, and they were waiting for their sources to give them the green light to enter. On hearing this, the anger turned into a wave of disquiet among the passengers. Charuchitra wanted to text her father and siblings, but her mother did not want to get her husband worried and pressed her not to do so.

After nearly 45 minutes, the bus finally got moving, and the driver said they would have to take a longer path through some sideroads in the town to avoid the mayhem. The passengers heaved a sigh of relief and relaxed into a misplaced sense of safety. This was soon shown to be false with a literal bang – a huge explosion had gone off somewhere in the vicinity rattling the panes of the bus. After briefly halting the bus and learning something on his phone, the driver quickly made a sharp about-turn and took yet another narrow road. As Charuchitra looked out of the window, she saw a plume of smoke rising from the street they were previously slated to enter. Before she could process that, a bigger horror confronted her sight — two women and a man, apparently dead, were lying sprawled on the side of the street. A ribbon of fresh blood trailed off the dead man’s neck even as the shop behind him was an inferno, copiously coughing out acrid fumes. As she shrieked in shock, her mother pulled Charuchitra to her side and calmly placed her hand over her eyes. As the bus paused again at the end of the street, she felt an adrenal rush and pushed her mother’s palm off her eyes, only to see them fall on a pile of burning tyres in the middle of the road. The bus made yet another sharp turn, and they now wriggled their way past the Kāśiliṅga temple in the town. As they turned around the temple, Charuchitra saw a ghastlier sight. A man in a garb that suggested he could be a temple officiant was lying on the footpath with his skull knocked in and a basket of flowers scattered beside him. His gore and brains were splattered on the white-crimson stripes of the temple compound wall while his eyes seemed to have been gouged out. Across his torso were splayed his blood-soaked garment and thread. At the end of the street, a large body of bearded men with no mustaches was marching brandishing swords, knives, staves, and the odd firearm, even as some were flying drones. Just then, a stone landed on the window beside her, sending a clatter through the bus. Charuchitra’s mother signaled her to duck down – as she did so, she turned to look at her mother, who, like her brother (Somakhya’s father), still retained a stoic mien. Seeing that, she felt a sudden change in her and slipped her hand into her handbag and gripped the punch knife, and caressed the multipurpose tactical stick her friend Indrasena had procured for her. She gave her mother a sneak peek into her bag and whispered: “if we have to go, we should take down at least one with us’’.

To their fortune, that did not come to pass as the driver finally found his way out of the riot-torn Ashmanvati. Charuchitra could not take her mind off the bloody sights she had just seen, and they kept reappearing before her eyes each time she would doze off, only to reawaken her. As she looked out, she now saw the more calming sights of the irrigated fields spreading out in front of the window, punctuated by the occasional derelict rustic house or granary – a far cry from the comforts of urban modernity she was familiar with. Unable to shake off the visions of Ashmanvati, she looked at her mother: “Mom, that was truly gruesome.’’ C.M: “Yes dear, those are indeed the marks of our age … or perhaps any age for that matter … for that is the nature of men.’’
C: “I find it very unfair that a temple sevaka, a V1, full of piety, should have been killed in that manner. At least a soldier signs up for that as part of his job, and we entrust our safety to his sacrifice. But why have the gods deserted the sevaka thus when he was proceeding to his duty?’’
C.M: “Our itihāsa-s have taught us lessons in that regard. In the first one, we learn how the princes of Ayodhyā, who were like an earthly Indra and Viṣṇu, had to spend 14 long years in the forest, full of suffering, for no fault of their own. In the second one, we hear of a similar trial for the Pāṇḍu-s – so tragedies happen to people though it seems they apparently do not deserve them.’’
C: “Why do you say “apparently’’? Do you suspect there is some hidden cause we do not know?’’
C.M: “I don’t know for sure if there is a meta-causality for a person’s fate or if it is just the probabilistic nature of things. As you know, our people believe that one is reborn again and again. Hence, if they cannot find a cause for a prasaṅga in this janman they project it into the previous one.”
C: “While that definitely satisfies our urge for completion of the causal chain of a prasaṅga, I have no way of knowing if it is true. Moreover, I don’t know what is the conversion table for the dharma of one species to another…’’
C.M: “That latter is something I definitely do not know. Given that a soothsayer said that in your last birth you were born as a cat and Somakhya as a rhinoceros, I really cannot say what karman-s in your non-human past janman-s yielded this human birth.’’

The rest of their journey, though somber, was eventless, and their disquiet eased a bit as they reached Somakhya’s house late that evening. Despite the traumatic sights, the fear of the impending exam turned Charuchitra’s mind entirely to it. The next day when Somakhya awoke, he found his cousin already all clean, prim and busy with her books. Somakhya on the contrary, was considering spending part of the day studying the wildlife in a dry well he and Lootika had located. Seeing his cousin so lost in her books, he slipped away on this venture. That evening he returned with Lootika and introduced her to his cousin, who seemed pretty happy that she had clocked a nearly uninterrupted study of eight hours that day.
Lootika: “Charu, if only we had your focus, we would probably rank among the greatest scientists of our age. Unfortunately, the great god Indra separates the guṇa-s among the folks.’’
C: “I’m shocked you guys did not even look at your books the whole of today, and now you are inviting me for a session of microscopic examination of your specimens! Thankfully, I’m pretty safe for the biology papers, I believe, thanks to our friend Indrasena. While younger than us, he has given such extensive notes that I could possibly write graduate-level exams with them.’’ Lootika smirked at Somakhya: “You should tell my sister Vrishchika that.’’
C: “My mom has stiffened me in statistics, but chemistry is the weakest link. I hope you shore me up a bit there.’’
S: “Actually, the chemistry is not really too stiff for this exam.’’
C: “That may be so for you. I want to ask you a bit about the basic electronic wave functions.’’
S: “We don’t have to solve any version of Schrödinger’s equation in 3D for this test. We just need to know how to deal with the radial distance wave functions and know the shapes of the orbitals by rote.’’
C: “Ah, there you are! That brings me straight to what I wanted. I was looking at questions collected from previous exams by our seniors and there was this one: Draw the radial wave probability distributions for the orbitals 1s to 3p and use it to explain why , etc. hybridization happens. I know that these distributions have some weird humps but how do we get those shapes exactly?’’
S: “You get those shapes by solving Schrödinger’s equation for the wave functions of electrons at different excitation levels in a hypothetical atom. For this exam, all you need to know is the form of these wave functions. If is the radial distance variable, we can write the shape of the wave functions thus. Of course, these are to be normalized by factors of , where is the atomic number, and we set the Bohr radius But for our purposes just the shape matters:

From these, you get the shape of the probability distributions as , where is your desired orbital. Lootika could you draw these out on your tablet for her? So all you need for this exam are the above 5 equations.’’

L: “As you can see from their plots, there is considerable overlap in the 2s and 2p which allows their hybridizations.’’
C: “No wonder you guys seem so relaxed! But I have a bunch of other questions and some puzzlers from the previous years’ math papers.’’
S & L: “Sure, let’s work them out!’’

ↈↈↈↈↈ

The exams were over, and Charuchitra returned home with Somakhya and his friends Lootika and Sharvamanyu after dropping off the bike her uncle had rented for her. Somakhya and Charuchitra’s mothers accosted them and asked them about their prospects. They said they need to do a “post-match’’ analysis and they would let them know after that what their chances might be. Somakhya’s mother: “Lootika, call your mom right away and tell her you are here.’’ Lootika asked them to wait for her sister Vrishchika to come over: “My sis is way more systematic than I’m. She asked me to call her so that she can collect all the questions we remember and note them down!’’
C: “I fully commiserate, as I did the same with my seniors.’’
L: “Sharva and Vidrum got them for us from a bunch of seniors last week and we did a quick survey – definitely that helped as some of the notorious questions were the same as the previous years.’’
C: “I was impressed by your collection. That session you guys gave me has really boosted my hopes.’’
Shortly thereafter, Vrishchika sauntered in: “How did it go? Hope you’ll survived!’’.
L: “Forget about us; it will be your turn soon!’’; thus, they started giving Vrishchika whatever questions they remembered.
Vrishchika: “How many bonds are there between carbon and oxygen in Carbon Monoxide? What’s the answer here?’’
L: “Vrishchika, either pay attention in class this year or ask our sister Varoli; she’ll definitely give you the answer’’. However, Somakhya passed her a chit of paper with a drawing: “That should give you the answer.’’

They then started trying to recall the math questions. Sharvamanyu remembered the below problem:
What is the geometric figure defined by the convergence of the sum:

Charuchitra: “What answer did you guys get?”
Somakhya: “An area bounded by a square of side with length 2 defined by the diagonal points .’’
C: “Oh no! I put it down as a circle with radius 1; How foolish I have been.’’
S: “Charu, your mom will give you a shelling if she hears this!’’
C: “Without using a calculator, approximate to 5 places after the decimal point.’’
Vr: “Ah, I think I can do that by setting up some expression for binomial expansion! But how do I break up ?’’
C: “You can use ’’
Vr: “Yes! Should have thought of that!’’
Looking at the math questions they had given her, Vrishchika pointed to one: “What about this one: Show — this is a ridiculous question – are they out of their senses? ’’
L: “Dear, it has an easy answer; go home and work it out. Ask our little sister Jhilleeka, she might solve this. You still need to fortify several lacunae.’’
Sharvamanyu: “How did you’ll answer this strange one? What is the first metallic acid? I wrote Permanganic acid.”
C: “I believe the correct answer is ’’
Sh: “Hey, but that is Aluminium hydroxide, a base!’’
C: “yes but is amphoteric; Al still retains some of its homolog Boron’s tendencies. So it forms aluminates similar to borates in addition to behaving as a base. I too was puzzled by this question which had appeared in a previous year, but Somakhya had filled me in on this the other day.’’
Sh: “Hell! I will be losing that one.’’
Vrishchika suddenly felt that she was not really up to speed with the seniors. Looking at her sister, she felt like Bhīmasena before Karṇa. Her teachers and some others, like Somakhya’s mother, thought she was smarter than her sister Lootika based on her curricular performance, but now she could see what she sensed all along – it would take her much more effort to measure up to her sister. It was just that Lootika, like her friend Somakhya, did not invest much in curricular achievements. With these thoughts crowding her mind, she got up to return home with the questions she had gathered: “I think I really need to be spending some time gaming these exams. I’m not yet ready – you guys seem to be on top of it.’’
C: “Don’t worry, Vrishchika; when I was in your place, I was much worse off than you. It took me a whole two years of effort and the last-minute boost from bro Somakhya and your sis to feel relatively safe. I’m sure you will get there.’’
Vrishchika took a silent mental oath to strive with her studies to outdo her elder sister when her turn came.
Sh: “Don’t forget to pass on the math and physics questions to Abhirosha; she couldn’t make it as she is attending a preparatory course.’’
Vr: “Sure, I would.’’

They then tallied up their answers and made estimates of their total marks. Despite some slips here and there, at the end of the exercise, they felt confident that they would probably get enough to be admitted to the courses of their choice. Somakhya and Sharvamanyu then called Vidrum to check on him – he had to hurry to catch a train to his native village and was speeding away towards his destination: “I wish I could have joined you’ll for the postmortem, but I’m just glad it is all over. I could have gotten a more accurate measure of where I stand had I been with you all. In any case, I estimated my performance several times and feel I’d probably make the cut. But for now, I just need a break from all this – I hope to be sipping coconut and palm juices in my grandfather’s backyard soon. If I fail, I may as well continue as an agriculturist in my ancestral land. I just hope the mayhem from Ashmanvati does not spread to my village. See you later.’’ As the boys were talking to their friend, Lootika and Charuchitra were trying out decorative plaits on each other’s tresses.
S: “Girls, it seems you are rather gainfully employed, so we’ll leave you to that, and I will ride up with Sharva to his place, see him off and come back.’’

C: “No, there was something I have been wanting to talk to you’ll about. I just overheard you talking to your friend about Ashmanvati. I have been struggling to keep it out of my mind till the exams were over.’’
S: “You know, Charu and my aunt were passing through Ashmanvati en route here even as the violence broke out?’’
L: “Wow! Glad you made it safely.’’
C: “It was a very close brush. What I witnessed has been gnawing away at the back of my mind, but I have been pushing it away for I did not want it to come in the way of the exams.’’ Charuchitra then proceeded to tell them what she had seen.
Sh: “That sounds bad. While you were in the thick of the action, it seems you are not aware of what actually transpired in Ashmanvati.’’
C: “Apart from hearing that there was inter-caste violence, I did not have the time to follow the news over the past few days. But I can swear to you’ll that I saw a dreadful band of marūnmatta-s marching down the street!’’
Sh: “Yes, you are yet another witness to part of what really unfolded there. The news media has only been reporting a fight between a scheduled tribe and the “upper castes,” making it appear as if the V1s and V2s have been oppressing the former because their leader Mhaisasur got elected in the recent ill-fated elections. However, via social media, we know the reality – the original fight was between the former oil-presser service jāti and the scheduled tribe. Mhaisasur, from the latter, belongs to the Nīladrāpeya Dala, and was inspired by the ideology of the founder of his movement, aided and abetted by the foundation of the Mahāmleccha unmatta, Gregory Kun. Thus, he used it as an opportunity to attack the savarṇa-s, in addition to settling scores relating to the original fight. However, in the process, Mhaisasur either accidentally or wittingly attacked the men of his election ally, the IML leader, Shaikh Badi ad-Durubi bin Darboos. Ad-Durubi retaliated with a massive show of strength, and Mhaisasur’s gullet was bisected in the clash. Now the media has been blaming it on none other than you guys – the reactionary Brahminical forces as they would have it!”
C: “Wow, you seem to be politically really well informed despite the exam!’’
Sh: “You better be; as you just experienced, it could be a matter of life and death.’’
L: “Was ad-Durubi not in jail for attempting a bombing during the Ārdrā fair at the Kāśiliṅga temple?’’
S: “Indeed, but he was let off by the legal activism of the woman who became the candidate of the SJWP party with the aid of the judge Udup Sandha, who has now become the Chief Justice!’’
C: “The common man has to wait for ages to get a hearing in court. How did they pull it off for him? Something sounds fishy?’’
Sh: “Well, they have an endless credit line extended by Gregory Kun, who puts mahāmleccha presidents on the gaddi.’’

C: “Hmm… so, there is more to these recent developments than it meets the layperson’s eye. Our friend Indrasena had told me that we might be headed towards a major clash of men!’’
S: “Absolutely. As everywhere else, the parties like the SJWP have become wildly popular among the screen-addicted urban elite, seized by a disease of the mind the pañcanetraka-mleccha-s have exported to the H. By subscribing to their ways, the upper savarṇa elite, which has internalized the false guilt imputed to them by the mleccha-s, feels a certain sense of holiness. Using the said credit line from Kun, Schwarzstein, the Gulliame Glympton foundation, and the like, they have been extensively converting the deracinated H, who cannot distinguish Skanda from Vināyaka, to this secular self-loathing ideology. One can say that many a neuron in the head of the puruṣa is badly misfiring. This has also meant that Pratapa Simha’s government has had little chance to uphold the laws they enacted in face of the protests from the ND and the Paṭṭa-dala as they had no real public support from their base. This has only allowed those parties to pursue the agendas set for them by their puppeteers in Bahukṣālapura, Navyarkapura, Bhallūkapura and Gajalanḍapura. As I have told you before, the farther a group diverges from the Hindu dharma, the more its propensity to act towards destroying the Indian state. The end result of all this is paving the path for the marūnmatta, who is quite resistant to the memetic diseases spread by the mleccha! We are seeing the first steps in the enactment of that cycle whose natural conclusion will be a clash of men where H will have to pay an enormous human price either way – whether we survive or become extinct.’’
Sh: “And I tell you of the two options, I would rather choose to fight for survival, whatever it might take.’’
L: “If we don’t fight for the glorious tradition our ancestors founded on the steppe and extended all the way from there across Jambudvīpa to the eastern lands and the archipelago pointing towards the Pacific, then who will? The mleccha-s would rather see us as museum pieces, while the navyonmatta-s and marūnmatta-s would send us back to the soil!’’

C: “I wonder how we should place ourselves with respect to our predecessors in such a clash. We can look at former H attempts in what I see in its essence as the same battle. When we were nearly extinct, Vijayanagara allowed us to come back from the ashes. After a good run, they fell in their attempt, but they had laid the foundation for a new attempt in the form of the Marāṭhā-s. Maybe that attempt nearly made it – we can say they almost had a golden age, even if it might have lasted just a decade. Despite all the criticism launched at this attempt by its critics, there is little doubt a clear vision was there — the objective was to reach Gandhāra and sweep the marūnmatta-s and mleccha-s out of Jambudvīpa and demolish their disputed structures, restoring our prāsāda-s. Of course, mistakes were made, and some of those proved too costly, resulting in their ultimate fall to the Christian nation with superior cunning. But I would say that attempt of the Marāṭhā-s was not an entire failure – the country which we have today can be largely attributed to their effort. What we lost can be seen as the last triumphs of the monstrous Durr-e-Durran and the evil Mogol. But from what you say, it seems we are headed to play that cycle once more. But are we in a weaker state than our predecessors?’’

Sh: “I agree that there were touches of sheer brilliance in the Marahaṭṭa assault that seem rather out of the reach of our current stock. The great offensive against the Mogols in Feb-Jun of 1670 CE by the Mahārāja was among the greatest military efforts in recorded history, only to be rivaled by the great Khan of the Mongols or the Qara Khitai knocking down the Seljuks and Ghurids. In that great war, the Marahaṭṭa-s almost took one fort every six days from the Moslems, culminating in the bloodbath in June of 1670 when 4 strong forts were taken in the space of 9 days! The rājan followed this up by reverting the economic warfare to the Mogol territory through the sack of Surat and the rout of the army of Islam near Nashik in the autumn of that year. Would the H forces be able to pull off something like that today when the clash comes upon us?’’
C: “Sadly, such a clash will need much more than a little punch knife or a tactical rod.’’
Sh: “Of course, no one is calling on you to fight the mahāyuddha with a gravity knife. Moreover, don’t forget, Charuchitra, you’re a V1 girl and are to be playing a different role unless you are pushed against the wall. If things come to that dire pass, something is indeed better than nothing, and that punch knife might be the difference between life and death as long as you have learnt to wield it correctly in a real situation. I’m totally with you when you said that even if you fall, you should at least have the satisfaction of having taken one of your enemies with you. But given the grip of the mental disease H are under, you V1s have a lot of work to do in other domains – you need to be like the dog that awakened the legendary sleeping goat. Of course, that doesn’t mean you should not train in arms and keep your body functional in the event you have to join us V2s in the hard fighting, as it happened when Pratāpasiṃha of Citrakūṭa had to face the tyrant Ghāzi Akbar.’’

S: “Our true situation and how we got here needs a more careful assessment. Remember, it was not just the cunning of the Christian nation but, as Lootika and I would often remark, the fact that the less Christian among them were studying snails in the Western Ghats when the Marahaṭṭa did not know that they even existed until he was asked to collect them by his English overseer. It was that which culminated in a Maxwell and a Darwin around the time our people were desperately fighting them in the first war of independence. It took some time for the brawny Jute, the Saxon of flaxen mane and the belligerent Angle to get there; to rise and then fall before passing the spoils accrued by his collective race to his cousins in the New World in a confluence with the uparimarakata project. There is definitely something like “the character of a nation” that manifests even if the individuals who constitute it vanish into the sands of time. We see that character repeatedly express itself in various peoples – the fates of the Cīna, the Atiprāchya, the khaghanate of the Rūs have all played out as per their character. In the case of the H nation, one may ask why, despite their brilliance, did Vijayanagara and the Marahaṭṭa ultimately stumble? Hence, on one side, the character of our nation might imply that, as in the past, we would stumble when the crisis comes upon us. But we could also look at the positive side of it. I’d be the first to agree with you, Charu, that the large modern Indian state would not exist but for the Marahaṭṭa effort, even if the path to it was hardly direct. We share our Indo-European ancestry with many glorious peoples, almost all of whom were conquered by West Asian diseases of the mind, but we still perform the same rites as those of our ancestors on the steppe with the old, accented language. We could find some affirmation in the fact that we are still upholding the way of the gods. This is the only glimmer we have of the hope that we might eventually find a way out of the crisis as in the past. But this time around, there is a palpable sensation that we might have run out of our luck unless the crisis brings out something that we have not shown so far.’’
L: “All I’d say is that my biggest fear is the lack of an unrelenting attitude toward the enemy for that is exactly what their doctrine has for us.’’

Just then, Somakhya’s mother called Lootika: “Your mom wants to take you and your sisters for a garment offering ritual at the little shrine of Mahiṣamardinī that she has commissioned this evening. So she wants you to get home right away.’’
L: “I hope you’ll are coming too.’’
S.M: “No, dear, I had already accepted the invitation of a neighbor to take my sister-in-law to their place. In any case I’ll see your mom at the temple tomorrow for our purāṇa reading.’’
L: “But let Charu come along with me.’’
S.M: “How will she get to your place? You have come by bike, and she has given away the bike my husband had rented for her.’’
L: “She can use Somakhya’s. He said he’ll be doing some research this evening.’’
C.M: “It will be late when you are done. She doesn’t know the city well enough, and it would be risky for her to come back by herself in the dark.’’
L: “She could stay at my place and we’ll come back together tomorrow morning.’’
C.M: “No, my bhrātṛjāyā has not informed your mom about this, and that would be impolite.’’
L: “You’re being very formal but it is no big deal for my father to drop her off by ratha when we return along with Somakhya’s aśva.’’

Thus, after some haggling with the elders and assuring Somakhya that she would make sure that good care was taken of his bike, Lootika got to take Charuchitra along with her. After the garment rite at the little shrine, the four sisters persuaded their parents with some effort to get dinner from the main temple’s annakūṭa with vaṭaka-s, pāyasa-s and other delightful bhakṣaṇa-s. A little distance from the temple, they saw the statue of a warrior with a bow and a quiver by his waist. Charuchitra: “Who is this?’’ Lootika took her close to it and asked her to read the inscription below it. Saṃrāṭ Pṛthivīrāja Chāhamāna, the last Hindu emperor of Dilli; śaka 1244-1270; died at age 26 defending the dharma against Islam. Lootika: “Technically, that is not right as the Gujarati Khusroo, and the brave Hemacandra Vikramāditya sat on the throne of Dilli in brief H interregnums.’’ As Charuchitra was taking in the inscription, Lootika’s sisters decided to take some pictures of themselves sporting their new hair plaits and clips beside the statue and the brightly lit fountain next to it. Suddenly, Charuchitra felt the noise of the merry evening revelers, the patter of the fountain, the hum of the river beside the temple, and the racket of the birds roosting on the banks all die down. At that instant, she felt the spirit of the Saṃrāṭ of the long-gone past leap out from the statue, even as he is supposed to have done when he claimed his bride Saṃyogitā. She suddenly felt that her life was to soon take a different turn establishing a deeper connection to “the last Hindu emperor of Dilli’’ in more than one way. Then that mysterious affectation passed away even as it had come upon her. As she snapped out of it, she felt alarmed as Lootika, who was leaning on Charuchitra with her arm on her shoulder, remarked: “the spirit of the Saṃrāṭ lives on.’’ C: “What! Why do you say so?’’ L: “You know why and you will learn more soon.’’ Before she could press her any further, Lootika’s parents hurried them along to return home.

The next day Charuchitra went over to wake her cousin up with the intention of telling him about the strange incident by the statue. However, before she could get to it, Somakhya took her down the path of talking about the wars of the Chahamāna-s and Calukya-s with the Ghaznavids and Ghurids, and the battles of the latter with Seljuqs, Khwarazm Shahs and the Khitans. Lootika was to spend the whole day with them and joined them for breakfast. However, at the back of her mind, Charuchitra was still thinking about the apparition and other issues like her discussion with her mother on the bus. Thus, when they were done with breakfast, she returned to the topic with her cousin and his friend: “I ain’t pulling a fast one here. But I had a strange experience while standing before the statue of the Chahamāna.’’ Before she could go on, Lootika jumped in: “I believe you felt an apparition of the king manifest before your eyes accompanied by a suppression of other aural stimuli. The apparition seemed to connect somewhere within you, indicating a turn or a new path in your life’s course.’’
C: “I knew you were cognizant that I had experienced something out of the ordinary from your remarks immediately after it. But heavens! You seem to have exactly captured what I went through in the first person.’’ Charuchitra intently looked at her cousin to see if he was surprised – he seemed interested but not really surprised. C: “I must reiterate, we are not trying to set you up for some prank.’’
S: “I know Lootika likes pranks, but they are quite earthly.’’

C: “Lootika? Perchance, did you also experience the same?’’
L: “Not exactly. If you recall, I was leaning on your shoulder then. That allowed me to capture your experience.’’
C: “How is that even possible?’’
L: “Not something we can easily elaborate. Some people have that experience naturally on rare occasions. Others might be able to achieve something like that through hypnosis and yet others through mastery of certain prayoga-s. It is usually easier with physical contact or proximity. Given the environs, I probably would not have achieved that yesterday if I was not in contact with you. I was also fresh from a successful puraścaraṇa I had just performed beside the Mahiṣamardini shrine as the garment offering rite was being conducted.’’
C: “I can rationalize my own experience of the apparition as a purely internal process probably triggered by the rather grave discussion we had earlier that day and the experience I had on my journey. But is thought transference even possible – I see this as also potentially intersecting with the whole question of whether there could be reincarnation and whether thought, memory or karman transference could happen in that case?’’
L: “While there could be a connection running through all of them, we have to be careful and consider them case by case. First, both Somakhya and I can empirically attest to experience transference of two kinds: one is perception in distance of another person’s experience; viz., we do not experience it as the distant person has, but we get a sense of what that person has gone through. The second is a more direct type where we more or less see in the first person what the other person is experiencing. Because of the widespread auto- and objective ethnography supporting this across very different cultures, we tend to accept it as a genuine phenomenon. What we do not know is if this relates to the perception of phantoms of the living or the deceased, the possibility of reincarnation, and any transference which might occur during that process. Our hunch is that it is related to the former, as for the latter, we personally do not have enough empirical evidence to say anything definitive.’’

C: “But does this not go against our very understanding of the world?’’
S: “Yes, the world as we understand it today. But that does not mean we should deny and ignore what we can empirically arrive at. There are several phenomena that are just beyond the reach of a controlled study – they could have commonplace explanations that we do not know, or they could have other explanations relating to facts about the nature of existence that we do not know. Whatever the case, we do not shut ourselves off from the observations and the utility they might have in our lives.’’
C: “OK, but let us break this down. What are the limits of transference that we can currently infer from biology? Thought? memories?’’
S: “To the extent we understand these things, we can say that thought relates to the more dynamic processes within and between neurons. The “connectome,” i.e., the graph of neuronal linkages by itself, is not going to give you thought. Instead, that probably lies in the dynamics of that network, namely the neurotransmitter release at the synapses and the electrical conductance across the neurons – this is likely what constitutes the bulk of it. It is indeed very difficult to see how one could possibly transfer the signals corresponding to the neurotransmitter releases from one neural network to another. However, it is not impossible that there might be some way to sense and reproduce the patterns of electrical conductance, even if it seems out of the reach of our current understanding. Memory, while linked to the above processes, is a different thing in its essence. One class of theories seeks them in patterns of the connectome; however, we see this as only a preliminary step in the actual formation of memories. Based on the correlation between various neural phenotypes of genes encoding proteins involved in the epigenetic modification of chromatin proteins, like histones, and DNA, we believe that memory is hard coded in the form of such modifications. It is also possibly encoded via other epigenetic information purveyors like modifications of cytoplasmic proteins or RNA modifications.’’
L: “Indeed, there are some interesting experiments that suggest the potential transfer of memory in at least some organisms like snails and planaria. The latter are capable of rather remarkable feats of regeneration – if their head is cut off, they can make a new one. Interestingly, it was observed that their learning was transferred to the remaining body even after the original brain was cut off and regenerated. There are some studies that indicated that this transfer happened via RNA. In the snails, a similar transfer was observed via RNA, but the effect of the RNA appears to have been evinced via an epigenetic modification – i.e., methylation of DNA. We don’t know how airtight these experiments are, but, at least in invertebrates, memory transference seems likely and indicative of an epigenetic hard coding. Early studies claimed the same in rats, and it was attributed to a small peptide termed scotophobin, which was believed to transfer the memory of the fear of the dark. However, these experiments were not really reproducible. Thus, we can ultimately say that memory is very tangibly biochemically encoded – something we’ll understand better in the near future. Thought is more dynamic, and we are, to a degree, able to externally control it by electrical means but its experimental transference remains dubious.’’
S: “That said, I believe what we are able to empirically apprehend has a leg outside the domain of objective science in the more poorly understood realm of first-person experience.’’
C: “Well, given all I have seen in the past week and your prognosis for the future, I wonder if this experience forebodes something I need to fear – death or danger? I really don’t have a feel for where it will take me.’’
L: “Being a coparticipant, I can tell you that it is definitely going to mark a change in your path that might happen as early as the end of today. Perhaps it will even be rewarding and you might find your true calling.’’

RV 10.78

RV 10.77 and 10.78 are similarly themed sūkta-s to the Marut-s by our ancient clansman Syūmaraśmi Bhārgava. He is mentioned twice by authors within the RV – in RV 1.112.16 by Kutsa Āṅgirasa and in RV 8.52.2 by Āyu Kāṇva. In the first instance, he is mentioned as being aided by the Aśvin-s, and in the second he is mentioned as performing a soma sacrifice where he made offerings to Indra. Of his two sūkta, we shall only consider 10.78 below. While the anukraṃani lists it as being composed of triṣṭubh-s and jagati-s, several ṛk-s do not conform to those meters (the syllable count is given in brackets). Instead, in several of them, one hemistich is triṣṭubh-like and the other is jagati-like. Some, like the first ṛk, conform to neither. It was perhaps an unusual meter that was lost in later Indo-Aryan tradition. It has been suggested that it might have been a mātra meter like those from the later register of the language.

viprāso na manmabhiḥ svādhyo
devāvyo na yajñaiḥ svapnasaḥ । (18)
rājāno na citrāḥ susaṃdṛśaḥ
kṣitīnāṃ na maryā arepasaḥ ॥ 1 (21)

Well-minded like vipra-s with mantra-thoughts,
wealthy like those seeking the gods with rituals,
beautiful in appearance like splendid kings,
spotless like the young warriors of the nations…

agnir na ye bhrājasā rukma-vakṣaso
vātāso na svayujaḥ sadya-ūtayaḥ । (24)
prajñātāro na jyeṣṭhāḥ sunītayaḥ
suśarmāṇo na somā ṛtaṃ yate ॥ 2 (23) (hypometrical jagati)

Who with golden ornaments on their chests blaze like Agni,
like winds with their own yokemates bring instant aid,
guides who like elders provide good council,
who provide good protection like soma offerings to seekers of the law…

vātāso na ye dhunayo jigatnavo
.agnīnāṃ na jihvā virokiṇaḥ । (21)
varmaṇvanto na yodhāḥ śimīvantaḥ
pitṝṇāṃ na śaṃsāḥ surātayaḥ ॥ 3 (21) (doubly hypometrical triṣṭubh)

Who like roaring winds move quickly,
like the tongues of fires shine forth brightly,
striving like armored warriors,
liberal like the ancestors at the ritual lauds…

rathānāṃ na ye .arāḥ sanābhayo
jigīvāṃso na śūrā abhidyavaḥ । (21)
vareyavo na maryā ghṛtapruṣo
.abhisvartāro arkaṃ na suṣṭubhaḥ ॥ 4 (21) (doubly hypometrical triṣṭubh)

Who, like the spokes of wheels, have the same nave (navel=source),
like conquering brave warriors facing heaven,
showering ghee like the young warriors wooing [their bride= Rodasī],
like chanters reciting the arka incantation…

aśvāso na ye jyeṣṭhāsa āśavo
didhiṣavo na rathyaḥ sudānavaḥ । (22) (triṣṭubh-like)
āpo na nimnair udabhir jigatnavo
viśvarūpā aṅgiraso na sāmabhiḥ ॥ 5 (24) (jagati-like)

Who are swift like the best horses,
good givers like the charioteers seeking a common bride [=Rodasī]
like waters constantly moving with dense moisture,
multiform like the Aṅgiras-es with their Saman-s…

grāvāṇo na sūrayaḥ sindhumātara
ādardirāso adrayo na viśvahā । (24) (jagati-like)
śiśūlā na krīḻayaḥ sumātaro
mahāgrāmo na yāmann uta tviṣā ॥ 6 (22) (triṣṭubh-like)

Liberal ones like soma-pressing stones, with the river as their mother,
repeatedly smashing everything like rocks,
playful like little children, they with a good mother,
move like a great troop imbued with impetuosity…

uṣasāṃ na ketavo adhvaraśriyaḥ
śubhaṃyavo nāñjibhir vy aśvitan । (22) (triṣṭubh-like)
sindhavo na yayiyo bhrājadṛṣṭayaḥ
parāvato na yojanāni mamire ॥ 7 (24) (jagati-like)

Imparting auspiciousness to the ritual like the rays of the dawns,
Shining forth with brilliance as if seeking auspiciousness,
rushing like rivers, with blazing spears,
as if they have measured out the yojana-s of the yonder realm…

subhāgān no devāḥ kṛṇutā suratnān
asmān stotṝn maruto vāvṛdhānāḥ । (23) (hypometrical jagati-like)
adhi stotrasya sakhyasya gāta
sanād dhi vo ratnadheyāni santi ॥ 8 (21) (hypometrical triṣṭubh-like)

O gods, make us the possessors of good shares and good gems,
us reciters of chants to you O Marut-s, who have been eulogized,
May you attend to our chant and friendship,
for indeed since ancient times the gifting of gems has been yours.

The sūkta has the structure of a riddle hymn, or a brahmodya, where the first 7 ṛk-s are a series of similes. There are a total of 28 similes using na as the comparator, one per foot, each presenting an attribute of the deities of the sūkta. This 4 x 7 pattern is perhaps an implicit acknowledgement of the 7-fold troops of the Marut-s. The sūkta finally culminates in the answer to the riddle in ṛk-8, where the name of the deities is revealed as the Marut-s. To cap it off, the pronoun naḥ (us) is used in the last ṛk. to pair with the comparator na found in the rest. Another striking feature of the sūkta is the repeated (12 times) use of words with the prefix su-, i.e., good or auspicious. Its count in each of the ṛk-s is provided below:
1 3
2 2
3 1
4 2
5 1
6 1
7 0
8 2
While the 7th does not feature such a word, it has two successive words, adhvaraśriyaḥ and śubhaṃyavaḥ, which respectively feature śrī and śubham, both of which imply auspiciousness. We suspect this is intentional, with the build-up of 6 ṛk-s with the su- prefix leading to ṛk-7, where the author reveals his purpose by stating that they confer auspiciousness to the ritual. He then concludes by returning to the su- prefix in ṛk-8 now that he has made apparent his intention in the previous one.

There are a few other notable features in this sūkta:
1. In ṛk-5 the Marut-s are compared to the Aṅgiras-es singing sāman-s. This brings to mind the riddle sūkta of father Manu, where the same metaphor is used for the Marut-s: arcanta eke mahi sāma manvata tena sūryam arocayan ।

2. There are several direct and suggestive “linkages” between the ṛk-s: 1 and 4 are linked by the word marya describing the Marut-s are young warriors. Ṛk-s 2 and 3 are linked by double similes comparing them to both Agni and the Vāta-s. The coupling of the Marut-s with Agni is an important feature of their membership in the Raudra-class, reflecting the duality of Agni and their father Rudra. This is presented in ritual in the form of the offerings accompanying the Agnimāruta-śastra (see RV 1.19). Their connection to the Vāta-s, is emphasized in the post-Vedic traditions starting with the Rāmāyaṇa – Māruti as the son of Vāyu-Vāta and the paurāṇika identification of the Marut-s with the winds. This potentially reflects a parallel early IE tradition (c.f., the Greek reflex of the sparkling or swift-moving wind-deity Aeolus/Aiolos with this 12 stormy children). On the other hand, the connection to Agni (and also Vāyu in the Southern Kaumāra tradition) is retained in the Kaumāra tradition of Skanda, the para-Marut. Further, the accouterments of the warrior (marya) are seen in ṛk-s 2 and 3 – the first has śarman – implying a helmet and the second has varman – armor. Ṛk-4 refers to the arka and ṛk-5 to the sāman – this probably reflects the combination of the śastra and stotra recitation occurring in the soma offering to the Marut-s.

3. Ṛk-s 6 and 7 are linked by riverine similes. Ṛk-6 speaks of the matriline of the Marut-s – they are said to have good maternity, implying Pṛṣṇī. However, remarkably, they are also said to have the river as their mother. This is a rare phrase and in a non-metaphorical sense is only applied elsewhere in the RV to the other sons of Rudra, i.e., the Aśvin-s (RV 1.46.2: yā dasrā sindhu-mātarā manotarā rayīṇām ।). This strikingly parallels the birth of Skanda, often in a hexadic form, from the river in the later tradition. Notably, this motif also occurs in one of the narrations of the birth of Gaṇeśa, where he is born from the bathwater of Pārvatī cast into the Gaṅgā and drunk by the riverine elephant-headed goddess Mālinī (e.g., the Kashmirian mantravādin Jayaratha’s Haracaritacintāmaṇi). Further, like the hexad of Kumāra-s and the other Kumāraka-s born of Rudra, in this ṛk, the Marut-s are referred to as śiśūla-s (c.f., Śiśu, the red-eyed, fierce companion of Skanda in the Skandopākhyāna of the Mahābhārata). Hence, we postulate that even in the core Vedic tradition there was an association between Rudra’s progeny and the river mother. This could merely be a metaphor for Pṛṣṇī, given her atmospheric nebular connections or represent her terrestrial ectype in the form of a river. This riverine connection also extends to the aquatic goddess Saravatī, who is explicitly called the friend of the Marut-s (Marutsakhā in RV 7.96.2) and epithet otherwise only applied to one other goddess, i.e., Indrāṇī (RV 10.86.9).

4. Ṛk-s 4 and 5 are linked by the similes of the Marut-s wooing a bride – vareyavaḥ and didhiṣavaḥ. This is an allusion to their wooing of their common bride, Rodasī, who elsewhere in the RV is mentioned as riding in the chariot along with the Marut-s, gleaming like a beautiful lightning (RV 1.64.9) or the spears they bear (RV 1.167.3). This common wife of the Marut-s is reflected in the para-Marut Kaumāra tradition by the name of Skanda, Bhrātṛstrīkāma (AV pariśiṣṭha Skandayāga), i.e., an allusion to Ṣaṣṭhī as the shared wife of Skanda and Viśākha.

The turning of the yugacakra

As the wheel turns, what goes up comes down and what is down comes up, again and again. There is a symmetry to the process in the downward and the upward movements, albeit in opposite directions. The old Hindus, right from the days of the śruti (e.g., the Asyavāmīya and the Vivāhasūkta), saw the passage of historical time as such a wheel; indeed, the Bhārata states:
kālacakraṃ jagaccakraṃ yugacakraṃ ca keśavaḥ ।
ātmayogena bhagavān parivartayate ‘niśam ॥
The lord Keśava, by the means of his own yoga, causes the wheel of time, the wheel of the world, and the wheel of the eon to turn constantly.

This triple mention of the wheel likely signifies the three cycles that enamored the old Hindus – the quotidian one, the annual one, and the great cycle of axial precession – the scale on which history occurs – the yugacakra. This wheel of time is worshiped as the supreme god Vāsudeva in early Vaiṣṇava thought and as a Bhairava-like figure, Kālacakra, in late vajrayāṇa bauddha thought. It is described thus:
āvartamānam ajaraṃ vivartanaṃ
ṣaṇ-ṇemikaṃ dvādaśāraṃ suparva ।
yasyedam āsye pariyāti viśvaṃ
tat kālacakraṃ nihitaṃ guhāyām ॥
Eternally turning forth and turning back,
with a six-sectored felly, twelve spokes, and a good linchpin
into whose mouth all existence rushes forth,
that wheel of time is stationed in the [secret] cave of existence.

In the days of yore, the upward turn was seen as the creative expansion or sarga, and the downward one as the decadent pratisarga. The followers of the nagna called the same utsarpiṇi and avasarpiṇi. However, the same “level”, i.e., distance from the lowest or highest point is attained both in the downward and the upward turn. This symmetry in the turn of history is perhaps what some closer to our times have termed the “rhyming of history”. It also relates to the Spenglerian conception of the unfolding of history. A unifying monarch or dynasty, who brings glory to his people and places them in history might be seen in the ascending turn. Likewise, in the descending turn as conditions are worsening people might fumble around for a great leader. A figure or a dynasty might arise to fill in that emptiness, but it is more like the helium flash of a dying star. Indeed, such a figure/dynasty might oversee the end of a civilization. The humble onlooker finds it difficult to tell the difference between the two figures respectively from the utsarpiṇi and avasarpiṇi turns because the timescale of history exceeds that of the mere mortal.

Many religions, both organic and pathological, and the ones in between have some form of millenarianism. This is implicitly related to the turning of the yugacakra, even in counter-religious traditions that have a rather linear view of history. In its simplest form, it may be seen as the expectation among the beholders that the cycle will imminently reach the low point and turn up again. In several versions of the millenarian narrative, it is superimposed onto a savior figure who turns the wheel past its lowest point. In early Indo-Aryan thought, it was expressed as the incarnation of the Vāsudeva to reestablish dharma when it has decayed: “ dharma-saṃsthāpanārthāya saṃbhavāmi yuge yuge ।’’. In the Iranian world, we have the Saoshyant who will come holding the weapon of Verethraghna to restore the Zoroastrian vision of the world. While at some point, both the Āryan branches might have believed that such a coming was at hand, they soon realized the “long arc of history’’ and placed these figures in the remote future. However, when the Iranian counter-religion infected the West Semitic world, the imminency of the coming of the savior figure or the upward turning of the wheel became the dominant theme in many counter-religions coming out of that substratum. Indeed, this lies at the heart of their secular mutations such as rudhironmāda and its subsequent mutations like navyonmāda.

Perhaps, it is a widespread human tendency to think that we live at the cusp of the upward turn of the giant wheel of history. Thus, in every age, there are reports of such a claim, even as some figures are hailed as or try to play the Saoshyant. The lay onlooker possibly hears this voice more prominently in some epochs than others. The current age is one where the rise in its loudness is perceptible. However, there are several distinct directions the expressions of this voice might take:
1. A diverse group of voices can be broadly classified as utopianists of the “techno-optimist’’ type. An extreme and well-known voice of this type is the American Kurzweil who believes that a technological singularity following on the lines of what John von Neumann originally envisaged is almost at hand. But there are several others who place their bets on more limited but directionally similar bets for the near future – the emergence of artificial general intelligence, augmented reality, the realization of quantum computational supremacy, and hyper-longevity/biological freedom/trans-humanism. While most of these see the current state of human biology, behavior, and economics as an impediment, or as defective or inferior in some way, their visions are (at least to us) quite unclear about how their techno-optimism would result in a superior world. Another version of this is a vision of techno-freedom wherein distributed network architectures spanning everything from property and currency to healthcare defeat the ability of traditional regimes to impose their power on the lesser mortals thus ushering in a state closer to utopia.
2. An alternative vision, related to the above, sees the future in interplanetary exploration – literally leaving the earth for potentially greener pastures. Most realistic proponents of this view still see this as more remote than the more immediate technological singularity postulated by those from the above camp. In their reckoning, once technological hyperintelligence is achieved, a superior physics might be discovered, allowing them to break free from the planetary constraints. Of course, they do not bother about the Fermi paradox or the possibility that the superior future physics tells us even more emphatically that interstellar travel is a no-go. It appears that most proponents of this view are nevertheless not extreme utopianists unlike many in the above group, rather, they see planetary escape more as a means for surviving a disaster or resource crunch on earth.
3. If the above visions are on the optimistic side, we also have those who prefer something more like a doomsday track. The most common movement of this type is centered on the possibility of anthropogenic climate change bringing an “end to the world’’. Its proponents seek to bring an end to climate change by acting as the savior figures and reversing the arrow of human industry, agriculture and animal husbandry. While the reality of climate change and its consequences are valid topics to debate, the activists pushing this cause are plainly millenarian.
4. Navyonmāda: This is the successor of the socialist millenarianism, a secular ekarākṣasonmāda, that started with the duṣṭadāḍhika and his śūlapuruṣa sidekick. We have extensively covered navyonmāda on these pages before and alluded to its classical utopian belief system. It has embedded within it a characteristic feature of millenarian ekarākṣasonmāda, in the form of trying to will “critical consciousness” into being by rejecting or inverting pratyakṣa truth, which then will result in the upward turn of the wheel leading to an utopia. In this regard, it also shares features with strands of techno-optimistic millenarianism in seeing biology as essentially bad or limiting. The jātivāda lineage within navyonmāda sees biology as fundamentally bad because it clashes with the samavāda central to its theology. However, ironically, in the process, it ends up reinforcing jātivāda through overpitching and creating “sacred” jāti-s (mostly kṛṣṇa-s and sometimes marūnmatta-s, who are not a jāti per se) that are different from those of its primary proponents (mostly yuropaka-s and mūlavātūla-s). The ṣaṇḍavāda lineage within navyonmāda, like the techno-optimists, sees biology as limiting and seeks to transcend it through interventions that bypass natural selection. This in part explains the enthusiastic alliance we see among the Mahāmleccha-s between tech and navyonmāda – the alliance that helped overthrow the Nāriñgapuruṣa and put Piṇḍaka on the āsandi. At least in the case of ṣaṇḍavādin-s, unlike their co-lineage, the samaguhyānveṣṭṛ-s, natural selection will mostly nullify their fitness in a single generation. Thus, biology would get better of them but not before they have ravaged society with their religion.

The inter-utopianist alliance between the navyonmatta-s and Big-Tech has resulted in this unmāda being deeply embedded among the Mahāmleccha-s. Further, by capturing the seat of power in the government, they have also come in control of the most powerful enforcement organizations in the world, the Mahāmlecchasenā and the spaśālaya-s. Thus, they are poised to bring misery to the world much like their predecessors, the marūnmatta-s and pretonmatta-s. Of the original unmāda-s, marūnmāda is rather resistant to penetration by navyonmāda or any of the many strands of millenarianism; some strands of the mūlarug and pretonmāda might also survive it. However, the Hindus are rather susceptible to some of these utopian movements, especially the most pernicious of them, navyonmāda. While we have been talking of this for ages, only now the general populace seems to be waking up to the fact that key centers of education in India have been captured by navyonmatta-s. Indeed, several families are reporting that their kids have succumbed to this disease from their exposure at educational institutions. Thus, as we have remarked several times on these pages, instead of the expected Satyayuga, the adoption of navyonmāda will bring immense harm to the H, who unlike the mūlasthāna of navyonmāda (the Mahāmleccha), lack the resources in terms of human capital, energy and mineral wealth, to weather the pandemic. Thus, like all utopian movements to date, we see the signs that the marriage of tech utopianism to navyonmāda will also bring misery to many.

There are two key lessons from biology that we have emphasized before on these pages. First, most innovation arises from conflict in biology. Likewise, most true innovation in human technology is downstream of conflict, and it will set off an arms race. Second, there is frequent regime change in the network hubs of a biological system over evolution. This is particularly well-illustrated where we first discovered it – the transcription factor-target gene networks. A similar dynamic plays out with technological hubs. As a result, there will necessarily be inequality – some players will amass immense resources and others will lose the resources they had. A combination of these two parallels to biology means that conflict and inequality of resource distribution will remain the way of the future. Indeed, some of the dramatic new technologies which excite the techno-optimists will create a profound gulf between the haves and the have-nots – a point that arouses the navyonmatta-s. For now, the two have cozied up into an alliance so that this aspect is ignored. In a purely tech-ascendant scenario, the programmer will try to be king. However, his ascendancy will directly clash with the reality-denying navyonmatta who insists on wrong answers for even the most basic operations like summation. Thus, their current coziness would eventually hit the point of a paradox where clashes between state power and a more democratic and/or meritocratic tech-derived power might start.

All this will play out against a backdrop that most techno-optimists apparently ignore – energy. The cognizant are well aware that we are living off a one-time bonanza of fossil fuels that have stored solar energy over a period of several millions of years. Once they are used up, there is no way to replenish them for that process would take millions of years. Thus, even as past civilizations have collapsed or downgraded from resource limitations, the current one too will go down the same path. The techno-optimists hope that the dawning of hyperintelligence with the technological singularity will solve this issue as the real end of fossil fuels is still some time into the future. Others hope that nuclear energy will keep the yugacakra turning. However, simple numerical considerations will show that even nuclear energy cannot sustain future growth on the same exponential track, which a biological species tends to follow whenever it comes upon a new resource. Importantly, the other material resources needed for tapping nuclear energy might place even more drastic limits on the density at which it becomes available. Thus, singularity or otherwise the energetic limitations necessarily imply that the downward turn of the yugacakra awaits us in the future (probably after the time of the people alive today). Some, like Hagens, have called this “the great simplification’’ – the idea that problem-solving mechanisms (tech) will falter from a paucity of cheap and readily available energy (vide Tainter) triggering a possible economic collapse. We suspect it will not be pretty by any stretch of imagination. We all know how wars were and are being fought over fossil fuels and the one who controls them holds the key to winning a long war. The current vassalage of old Europe to the American empire is a direct consequence of this. In the future, with other technologies, like nuclear energy, the same trend will continue for only a few nations have the wherewithal to harness this form of energy safely and efficiently.

Nevertheless, we shall end this note by going back to the idea that the same height is attained repeatedly on both the upward and downward turns of the wheel. Our conception of the yugacakra is a more fractal one – like a Fourier series, wheels turning within wheels. Thus, there are more local arcs of history that we can see and larger ones to which we tend to be blind. With respect to the local arc, we see some remarkable parallels in the turning of the wheel that happens on the order of a century. The most recognizable of these are: 1. the Wuhan corruption of 2019 and the Spanish flu of 1918 (yes, people were masking even then) 2. The great economic downturn we are entering and the Great Depression that started in 1929. 3. The rise of navyonmāda revolutions starting in late spring of 2020 in the USA and the European Marxian revolutions of 1917-1923. These Marxian revolutions laid the ground for major future conflicts even as navyonmāda is doing the same now. 4. The Occidental potentates baiting Russia into a major conflict in 2022 and the same with Japan in the 1930s. There are potentially more events one could align if one went back to doing a more careful analysis.

Given this alignment of events, are we on the cusp of a great war? Briefly, from a geopolitical viewpoint, it is easy to see that there is a fairly high probability of this happening: we continue to stick with our estimate of 15% for the near future while some others with no connection to our thinking or ideology have placed it as high as 20-25%. One thing is clear – the Rūs are by themselves not looking great. Their reliance on Iran for things like gas turbines and drones, the loss of most of their Jewish intellectuals, not quickly producing much tactical machinery to arm their mobilized troops, and bad demographics suggest that they might not have the substance for large-scale military operations. Even some Rūs nationalists are hoping for help from the Han (!) – a rather optimistic view in our opinion given their demographics and that the latter have made themselves even more hated than the Rus in Asia. Yet the Rūs have made some good strategic moves that have rattled the Euro-vassals of the Mahāmleccha. Thus, how far the Mahāmleccha can pursue their aim of destroying the Rus remains in balance as of now. Finally, when a nation is faced with an existential threat, then all stops will be pulled, and we still estimate that the Rūs might have a fight left in them in such a situation that can ultimately prove rather dangerous for the Mahāmleccha. A key to this is when greater disunity will emerge among the Mahāmleccha, who are currently fairly united against the Rūs. However, this will not be forever. We are already noticing irreconcilable differences emerging among the two mleccha-pakṣa-s on the ground that they might be unable to live with each other in the future. Our own model is that, like with some chaotic systems which we have discussed on these pages, the current conflict is not yet the maximal cycle. That might follow in the coming 3-7 years – then the possibility of the replay of the great wars that sandwiched the influenza epidemic of 1918 CE will be higher. Time will tell if there is any truth to this.

A sampler of Ramanujan’s elementary results and their manifold ramifications

As we have remarked before, Ramanujan seemed as if channeling the world-conquering strides of Viṣṇu, when he single-handedly bridged the lacuna in Hindu mathematics from the days of the brāhmaṇa-s of the Cerapada to the modern era. Starting around the age of 16, he started recording his results in his now famous notebooks. Till that point, Ramanujan had access to only two primary educational sources: Plane trigonometry by Sydney Luxton Loney of Surrey and Synopsis of Pure Mathematics by George Shoobridge Carr of Middlesex which were used in the English educational system. The influence of Loney’s opening pages filled with essential formulae and Carr’s laconic presentations are writ large over the notebooks. It can be inferred that he had obtained many of the results while he was still at school, before the time he started writing them down in his notebooks. For instance, we hear that he had derived for himself the series expansions for trigonometric functions, which he only later learned to be common knowledge – the is said to have then thrown away that early discovery in embarrassment. His first three notebooks were largely completed over a period of six years during his youth in India, with only some entries recorded in the time he was in England. When in England, he mentions that he was only intending to publish his current research, rather than those in the notebooks, until the World War I came to an end. Much of the so called “Lost Notebook” appears to have been written down in the final year of his short but momentous life. Unfortunately, it is believed that several other unpublished works of Ramanujan were entirely lost. Given the time range covered in the notebooks, we do find several elementary results that gives non-mathematicians like us a glimpse into the great man’s mind. We provide below some discussion on a sampler of elementary results from his notebooks. The original entries of Ramanujan discussed in this note can be found in “Ramanujan’s Notebooks, Part I-IV” by Bruce Berndt; here we express them or their corollaries in our own way.

and squaring of a circle
Ramanujan is well-known for his numerous approximations of both in a paper he published on the subject and the various entries in his notebooks. One of those leads to an approximate squaring of the circle that is eminently suitable for a modern śrauta ritualist to construct an āhavanīya that is equal in area to the gārhapatya (Figure 1).

Figure 1. Approximate quadrature of the circle by Ramanujan’s formula

The said construction goes thus:
1. Divide the radius of the circle into 5 equal parts.
2. Extend the radius by 4 of these parts. This gives a segment of length . Use that segment to construct a circle with diameter .
3. Apply the geometric mean theorem on that circle (Figure 1) to obtain a segment of length . Use that to construct a segment of length . With that segment construct a circle of diameter (Figure 1).
4. Apply the geometric mean theorem on that segment to obtain the side of the desired square.

One can see that this construction corresponds to Ramanujan’s approximation: . This is very close to Āryabhaṭa’s approximation: . People have claimed that Āryabhaṭa arrived at his value by using polygons to approximate a circle. There is absolutely no evidence for this claim making one wonder if he had somehow arrived at a formula like that of Ramanujan. It remains unknown to me if Ramanujan had found some special connections relating to this value. The same value is also recommended as a correction to the very approximate Bronze Age values by Dvārakānātha Yajvan, a medieval śrauta ritualist and commentator on the Śulbasūtra of Baudhāyana. This value is somewhat less accurate than another ancient value recorded by Vīrasena and in some Bhāskara-II manuscripts (Ramanujan also provides a construction for the quadrature using that approximation):

vyāsaṃ ṣoḍaśa-guṇitaṃ tri-rūpa-rūpair-bhaktam ।
vyāsaṃ triguṇitaṃ sūkṣmād api tad bhavet sūkṣmam ॥

The relationship between the reciprocals of odd numbers and

defines the alternate odd numbers: 1, 5, 9, 13, 17, 21, 25, 29, 33, 37…
defines the remaining odd numbers absent in the above sequence: 3, 7, 11, 15, 19, 23, 27, 31, 35, 39…
There is an interesting relationship between the reciprocals of these two sets of odd numbers and :

It is an interesting though not very efficient formula for reaching 3.1 after 13 terms. This relationship can be obtained from the general cotangent relationship, which is valid for any number (including the complex plane) that Ramanujan discovered for himself:

Remarkably, Ramanujan records this after a result related to the zeta function, which in turn implies the famous series for the digamma function , i.e., the ratio of the derivative of the gamma function to the gamma function:

Here is Euler’s constant.

, cubes of triangular numbers and

Figure 2.  

In old India (e.g., Brahmagupta and the Jaina Prajñāpti texts) we find as an approximation for . This is interestingly close to the Egyptian approximation . We can ask the converse question of how close is to 10 (Figure 2). Ramanujan discovered an interesting answer for this.

The triangular numbers, , are the sums of successive integers up to , i.e, : 1, 3, 6, 10… Then,

Reciprocals of the cubes of odd numbers and
The zeta function elicits an almost mystical experience in us — when you realize how it connects what were seen as disparate branches of mathematics you get a sense of the deep order in the Platonic realm. The function was first discovered by Euler in course of solving what was called the Basel problem. It was known (probably since antiquity) that the sum of the reciprocal of integers slowly diverges to :

This can be proved easily with a basic school level mathematics using the comparison test to the reciprocals of the powers of 2 bounding each interval of integer reciprocals (i.e., so on). However, the question of the sum of the reciprocals of the squares of integers defied attempts of brilliant mathematicians, such as the Bernoulli clan (hence, the Basel problem), until it fell to Leonhard Euler in 1734 CE. Thus, the zeta function can be defined as a generalization of such sums for any number on the complex plane:

While Euler originally defined it for positive integers, it was generalized as above by Chebyshev on the real line and then by Bernhard Riemann on the complex plane. Thus, the Basel problem is essentially the value of the zeta function at 2, which Euler proved to be . Euler subsequently established that the reciprocal of gives the probability of two integers drawn at random from the interval between and being mutually prime (i.e., having GCD=1). This suggested the link between the zeta function and primality, and finally, three years after solving the Basel problem Euler showed the explicit link between prime numbers and the zeta function by his product formula:

,

where the product is over all primes.

From the subsequent work culminating in Riemann’s famous hypothesis, the relationship between the zeros of the zeta function and the prime number distribution became clear. Remarkably, Ramanujan discovered many aspects of the zeta function all by himself unaware of the developments in the west, such as those of Chebyshev and Riemann. Among other things, was his much-ridiculed result, where he provided the sum of integers (1+2+3+4…) as a finite negative number (found in his first notebook and communication with Godfrey H. Hardy) — this was essentially his auto-discovery of the value of . He also discovered for himself the connection between the zeta function and prime numbers. He discovered that the zeta function displays an oscillatory behavior on the negative real line, taking the value 0 at all even negative numbers (-2, -4, -6…). He used these zeros to derive the distribution of primes, paralleling the work of Riemann. However, he overestimated the accuracy of his results for he was unaware of further zeros discovered by Riemann on the complex plane that he only learnt of from Hardy when he went to England. From his notebooks, we learn that during the Indian phase of his career, like Chebyshev, he also explored the values of the zeta function on the real line beyond 2. Thus, Ramanujan discovered a general formula, one of whose special cases is a series specifying that is today sometimes called Apéry’s constant. After the days of Ramanujan, this constant has appeared in several areas of physics.

Now, is also the area under the below curve for positive (Figure 3), thereby giving an alternative integral formula for the sum based on Ramanujan’s formula.

Figure 3.

However, Ramanujan’s formula more generally goes on to provide several other series that link the cubes of the reciprocals of numbers separated by 3 (1, 4, 7, 10…), 4 (1, 5, 9, 13…) so on which have the general form , where are constants specific to each sum:

We were puzzled by what might be the sum of the reciprocals of cubes of numbers separated by 5: 1, 6, 11, 16… Taking the limit as of the digamma derivative-based series formula we established that this can be expressed in a rather compact form with the tetragamma function, i.e., the second derivative of :

The Ramanujan primorial plus one fourth sequence
The prime numbers 2, 3, 5, 7, 11… are denoted by . By analogy to the factorial product, one can define the primorial as the product of successive primes:

Ramanujan defines a sequence such that is an odd integer. This holds for the below values of :

It remains unknown to us if there is any further term in this sequence and if there is one, how many more exist?

Elementary results relating to powers of numbers
Ramanujan provides numerous elementary results relating to the sums of the powers of numbers that he likely derived when he was still in school. One of the simplest is the following, which, however, was apparently unknown until his discovery:
if then for :

Thus, it is a parametrization that allows one to find six numbers such that the sum of the squares and the fourth powers respectively of the first 3 is equal to those of the last 3.

1	9	10	5	6	11
2	11	13	7	7	14
3	13	16	9	8	17
4	15	19	11	9	20
5	17	22	13	10	23
6	19	25	15	11	26
7	21	28	17	12	29
8	23	31	19	13	32
9	25	34	21	14	35
10	27	37	23	15	38
11	29	40	25	16	41
12	31	43	27	17	44

With this parametrization, we can obtain the above hexad where the first term is every positive integer; the second term is every odd integer starting with 9; the fourth term is every odd integer starting with 5; the fifth term is every positive integer starting with 6. The third and sixth terms are the sums of the previous two terms. The sum of the squares of the two triads constituting these hexads will be defined by: The sum of the 4th powers is given by .

The next problem in this genre is to find rational solutions to the indeterminate equations:

Ramanujan gives parametrizations to solve such equations: if then,

The equation is quite trivial. For the equation , using Ramanujan’s parametrization one can obtain several sets of tetrads. Below is an example where we take to be successive integers starting from 0 and to be 1 more than :

w	x	y	z
1	0	1	1
7	5	3	8
19	16	5	21
37	33	7	40
61	56	9	65
91	85	11	96
127	120	13	133
169	161	15	176
217	208	17	225
271	261	19	280

For this tetrad, one sees that is the sequence of odd numbers. (first column) are the hex numbers, i.e., the centered hexagonal numbers given by the quadratic expression . The sequence defined by also defines the maximum number of bounded areas you can obtain by drawing triangles on a plane: With 1 triangle you can obtain at most 1 bounded area; with 2 you can obtain at most 7 (hexastar); with 3 you obtain 19 and so on. (second column) is the square star numbers (Figure 4), i.e., square numbers with triangular numbers on each side, given by the quadratic expression , while (fourth column) are the square grid numbers given by the expression (Figure 5).

Figure 4. Square star numbers.

Figure 5. Square grid numbers.

Notably, these three columns are also linearities on the hexadic spiral (Figure 6).

Figure 6. The hexadic spiral. The 3 linearities in blue boxes correspond to 3 of the columns in the above parametrization

We can again use Ramanujan’s parametrization for with and as successive integers starting with 0. This yields the below sequence of tetrads:

w	x	y	z
1	1	1	0
3	3	0	3
7	5	3	8
13	7	8	15
21	9	15	24
31	11	24	35
43	13	35	48
57	15	48	63
73	17	63	80
91	19	80	99

The sequence corresponding to in this tetrad is specified by . Remarkably, this sequence appears in multiple geometric contexts. One is the Euler (Venn) diagram problem. It is an analog of the problem of the maximum number of bounded areas obtained with triangles. What is the maximum number of bounded compartments you can represent using circles (Figure 7)? The answer is this sequence.

Figure 7. The Euler diagram problem.

A further geometric context relates to the sequence of triangles where one side is , the second side is and the angle between these two sides is . Then the squares on the third sides of this sequence of triangles will have an area equal to the sequence (Figure 8). In this tetrad is the sequence of odd numbers, takes the form and is the same sequence as offset by 1 in the backward direction. This sequence appears in the so-called Monty Hall problem discussed by Martin Gardner many years ago illustrating the difficulty of understanding probability even in simple problems.

Figure 8. The length of the third side of the 60-degree triangle problem.

A catalog of attractors, repellors, cycles, and other oscillations of some common functional iterates

One of the reasons we became interested in functional iterates was from seeking an analogy for the effect of selective pressure on the mean values of a measurable biological trait in a population. Let us consider a biological trait under selection to have a mean value of at a given point in time in a population. Under the selective pressure acting on it, in the next generation, it will become . Thus, the selective pressure can be conceived as a function that brings about the transformation . Thus, iterating this function with its prior value with give us the trajectory of the measure of the said trait in the population. While it might be difficult to establish the exact function for a real-life biological trait under selection, we can imagine it as being any common function for a simplistic analogical model. This led us to the geometric representation of the process — the cobweb diagram.

Figure 1. Cobweb diagram for the functional iterates of

For example, let us take the function acting on to be (Figure 1). We can see that the iterative application of this function on any starting (point B in Figure 1) eventually leads to convergence to a fixed point that can be determined by obtaining the intersection between and the line . In this case, one can prove that it will be 0.6823278…, the only real root of the equation . Thus, 0.6823278… can be described as the attracting fixed point or attractor of this functional iteration.

Figure 2. Cobweb diagram for the functional iterates of

Instead, consider the same process under the function (Figure 2). Here, we can show that there would be two points that emerge as a result of the intersection between and : the two roots of the equation , . These two points draw the iterates towards themselves but the competition between them results in the outcome being chaos unless is exactly at one of them. Thus, these two fixed points can be described as repelling fixed points or repellors. Thus, exploring different simple functions, we realized that there can be three possible broad outcomes for functional iterates: (1) Convergence to an attractor; (2) Convergence to a cyclic attractor, where the endpoint is to cycle between 2 or more fixed points; (3) Chaotic oscillations driven by repellors. Hence, we conjectured that even in the evolutionary process under selection we will see these three outcomes. Convergence to an attractor is commonly observed when populations starting with different mean values of the trait are driven by selection to a similar endpoint. The cycle is less common but might be seen in situations like the coexistence of different morphs of males and females, each with a distinct mating strategy, e.g., in beetles, damselflies and lizards. Finally, the absence of convergence but chaotic wandering of the trait is less-appreciated but we believe is also manifested in nature. We shall see below that there are different forms of chaos and each of them might have rather different consequences.

One can find some of the fixed points or other consequences of functional iteration in certain mathematical volumes or online resources. However, we did not find any of those to be comprehensive enough for easy reference. Hence, we thought it would be useful to provide such a catalog covering a subset of the common functions we have explored. We provide these by stating the function and the consequence of the iteration (attractors, cycles or chaos with associated repellors), followed by comments in some cases. We omit trivial cases like , which shows a gradual convergence to 0. The gradual convergence in cases like this is related to their limit as ; e.g., . In the below catalog, denotes the Golden Ratio and its reciprocal.

(1) Simple algebraic functions. Here the attractors or repellors can be easily determined by solving the polynomial equations defined by the difference equation specifying the map.
:

: ; This attractor also extends to the complex plane. For more discussion of this system see our earlier note.

: ; This attractor also extends to the complex plane.

:

:

:

Figure 3. Chaotic functional iterates of some simple algebraic functions

: symmetric sawtooth chaos: are repellors.

: sawtooth chaos: are repellors.

The two above systems (Figure 3, first two panels) show chaotic behavior with a peculiar pattern. In the first one, there are rapid oscillations giving an overall symmetric appearance. In the second one, there is a sharp rise to the local peak or valley followed by a slower, convex return towards 0. The profiles of these maps have a tooth-like appearance, though the first is constituted by oscillations fitting into a similar profile as the second.

(Chebyshev 2): chaotic (-1,1)

(Chebyshev 3): chaotic (-1,1)

These next two functions are the Chebyshev polynomials 2 and 3, which show chaotic behavior if lies in the interval (-1,1). At -1,1 they remain stationary and beyond those they diverge. Despite the chaos, the values of the iterates show a characteristic U-shaped distribution, with the highest density close to the boundaries, -1, 1, and low densities throughout the middle of the interval (Figure 4). This type of distribution is typical of many chaotic iterates of polynomial functions, e.g., the famous logistic map.

Figure 4. Distribution of the functional iterates of

(2) Circular trigonometric functions

Figure 5. Number of iterations to convergence or divergence to of iterates of

: 0.73908513321516 (the solution of the equation ) is the attractor for all real values. On the complex plane, other than those values in the white region (Figure 5), all values within a fractal boundary converge at different rates (indicated by coloring) to the same attractor.

Figure 6. Iterates of from different starting points.

: chaotic (Figure 6). The oscillations are generally of low amplitude but are punctuated by rare “explosions” of huge amplitude (hence, shown in scale in the figure). See our earlier note on functions with comparable behavior. Such behavior is analogous to what have been termed Levy flights.

: 0.94774713351699

Figure 7. Distribution of the functional iterates of

: chaotic. The iterates are contained in the interval with certain exclusion zones. The most prominent exclusion zone contains the primary repellor 0.514933264661… (solution of the equation ; red point in Figure 7).In the negative part of real line, the exclusion begins at (purple point in Figure 7). The points of the other exclusions zones (black points) are more mysterious.

: chaotic

: -1.25872817749268

: 1.2587281774927

: bicycle: -0.83019851706782, 1.41279458572762; These attractors are also valid in the complex plane.

Figure 8. Functional iterates of 160801 starting points of in the complex plane

: chaotic for both real and complex values. Interestingly, in the complex plane, the iterates show certain preferred regions of density that are symmetric about the real axis (Figure 8). The centers of these regions of density appear to be close to the multiple of Figure 8; red points).

: While it is chaotic on the real line, on the complex plane it converges to either depending on the initial point.

: 1.1141571408719

Figure 9. Regions of convergence or divergence to of iterates of . The light-yellow regions converge to the attractor indicated as a blue point

: 0.6417143708 is the attractor for real starting points. In the complex plane all initial points withing the fractal boundary converge to the same attractor while the rest diverge (Figure 9).

Figure 10. Regions of convergence of iterates of or divergence to . The light yellow regions converge to the attractor indicated as a blue point

: 1.17479617129 is the attractor for real starting points. In the complex plane all initial points withing the fractal boundary converge to the same attractor while the rest diverge (Figure 10).

: chaotic

Figure 11. Number of iterations of function for convergence or divergence to

: The attractor on the real line is . On the complex plane, the points within a fractal boundary (Figure 11) converge to the same point at different rates (the contours in Figure 11).

: 0.69481969073079

: 1.5570858155247

: -0.99990601241267

: 0.97678326638014

: 0.44604767999913 (root of the equation ) it the attractor both on the real line and the complex plane.

: is the attractor both of the real line and the complex plane depending on the starting point defined by (root of the equation

: bicycle: 0.013710961966803, 1.55708579436399; These values are remarkably close to but not identical to the solution of the equation , i.e., and . Thus, the sum of these two values is close to .

: bicycle: 0.013710102886935, 0.999906006233481; These values are remarkably close to but not identical to the solution of the equation , i.e., and .

: octocycle: 0.366798375086067, -0.938273127439933, 0.324922488718667, -0.999958528842272, 0.373119965761099, -0.921730305866654, 0.310327826505175, -0.991153343837468; this cycle appears to be associated with oscillations close to and

(3) Hyperbolic trigonometric functions
: converges to either (solutions of the equation ) depending on the starting point.

: 0.7650100

: depending on the starting point.

(4) Exponential functions
: 0.5671433; remarkably this is , where is the function discovered by the polymath Johann Heinrich Lambert, in the 1700s. This value can be computed using the below definite integral:

Then the fixed point of the exponential function, latex

Figure 12. Number of iterations for convergence of functional iterates of or divergence to

In the complex plane, all points within the fractal boundary (Figure 12) converge to the same attractor at different rates or diverge to (white regions).

: 0.64118574450499; comparable behavior as above in the complex plane. The closed form for this fixed point can be derived from the Lambert function: :

Then the

: 0.54522571736464

Figure 13. Number of iterations for convergence of functional iterates of or divergence to

: the attractor 0.652918640419 is the solution to the equation . We can again find a closed form for this fixed point using :

In the complex plane, all points within the fractal boundary (Figure 13) converge to the same attractor at different rates or diverge to (white regions). It is interesting to see that one of the convergence contours recapitulates the curve reflected about the real axis (Figure 13).

: 0.7384324007018

: 0.63654121332649

Figure 14. Number of iterations for convergence of functional iterates of

: This function is interesting in that it is chaotic on the real line with a repellor at 1.4215299358831… As the iterates approach 1 from below they are prone to negative explosions; if they do so from above, they undergo a positive explosion. The distribution of the iterates shows a preponderance of small values but when extreme values occur they are very large (explosions). Interestingly, in the complex plane, it converges to -0.32447650840966+0.31470495550992i (Figure 14). The number of iterations to convergence reveals a fractal pattern of interlocking circles.

While the fixed points can be determined by numerical solving the equations specifying them, the closed forms, if any, remain unknown for many of them. Finding if they exist would be a good exercise for the mathematically minded.

The wink of the Gorgon and the twang of the Lyre

The discovery of the archetypal eclipsing binary Algol
The likes of Geminiano Montanari are hardly seen today. This remarkable Italian polymath aristocrat from the 1600s penetrated many realms of knowledge spanning law, medicine, astronomy, physics, biology and military technology. Having fled to Austria after a fight over a woman, he took doctoral degrees in law and medicine. As a result, he obtained a number of aristocratic patronages in return for services as a legal adviser, econometrician and military engineer. In course of these duties, he invented a megaphone to amplify sounds, worked on desilting of lagoons for the state of Venice, prepared a manual for artillery deployment, and composed a tract on fortifications. Like his junior contemporary Newton, he spent a while working as the officer of the mint. These duties also brought him in contact with astronomy and mathematics while interacting with aristocrats at Modena and as a result, he became absorbed in their study, eventually turning into a Galilean. However, he kept quiet about his thoughts on this matter in the initial period owing to the muzzle placed by the church on “things that were obvious” and the “claws of the padres.” This period also led him to go against the church doctrines by becoming an “eclectic corpuscularian”, i.e., atomist and he used the “atomistic” principles to explain physical phenomena, such as his observations on capillarity and the paradoxical strength and explosiveness of the peculiar glass structures known as Prince Rupert’s tears.

By the time Montanari was thirty, he was already an accomplished astronomer and eventually, went on to succeed the famous astronomer and mathematician Cassini of oval fame as the professor of astronomy at Bologna. He was remarkably productive in his thirties and started off by observing two comets in 1664 and 1665. It was through these observations that he presented clear empirical evidence for the first time in the west that these comets were farther from the earth than the moon and were part of the Galilean solar system (contra Aristotelian physics which saw them as atmospheric phenomena). His accurate observations of meteors led him to calculate their speed for the first time also. He also used that to estimate the thickness of the Earth’s atmosphere. As a skilled optician, he also invented a telescope eyepiece with a micrometer grid to construct the first accurate map of the Moon. Montanari was also a friend of the noted biologist Marcello Malpighi and conducted pioneering work on blood transfusion in dogs, noting that in some animals it had a positive impact on their health, whereas it was not so in others. Like a lot of his work, this was largely forgotten and the proper understanding of this phenomenon lay in the distant future. In another foray into biology, he studied the role of temperature in the artificial incubation of chicken eggs.

In our opinion, one of Montanari’s most remarkable discoveries came in 1667 CE when he observed that the star -Persei (Algol) had changed its brightness. In his own words:

“And if you look at the scary head of Medusa, you will see (and now without the danger of being petrified, unless the wonder makes you immobile) that the brightest star that shines there, surprised by frequent mutations, possesses the greatest luminosity only sometimes. I had already observed it for many years as of third magnitude. At the end of 1667, it declined to the fourth magnitude, in 1669 it recovered the original rays of the second magnitude, and in 1670 it passed a little over the fourth.”

We could say that this was the first clearly defined report on the variability of Algol. A couple of years earlier his fellow Italian, Pietro Cavina had noted that:

“The Head of Medusa was second [magnitude], agreeing with the ancient catalogs [evidently that of Ptolemaios] and globes and Aratus of Colonia, although Tycho, and other Moderns have placed it at the third [magnitude].”

It is not clear if this was somehow known to Montanari, but in any case, as far as we can tell, there was no evidence that Cavina recognized the variability as Montanari clearly did. He communicated his observations on stellar variability, which included a list of stars for which he had observed differences in magnitude with respect to Galileo’s observations and older catalogs, to the Royal Society in England. In this, he speculated that the different reports of the numbers of the bright Pleiades (6 or 7) might stem from their variability. While most of the differences he reported for the other stars were probably due to inaccurate magnitude determinations in the older catalogs, his observation of Algol was definitely a clear demonstration of stellar variability adding to the earlier discovery of Mira (o) Ceti by Fabricius in Germany. While Montanari got much praise for his observations on stellar variability at the Royal Society and his prolific observations of comets eventually led to a citation in The Principia of Newton, he seems to have been largely forgotten and the renewed study of the variability of Algol had to wait for more than a 100 years.

The rediscovery of Algol’s variability was due to another remarkable man, the farmer Johann Palitzsch, from Dresden (today’s Germany). Early on, he acquired a deep interest in botany, agricultural economics, astronomy and mathematics. As an autodidact, he amassed a vast collection of literature on these topics by writing down whole books by hand. As a farmer he was the first to introduce the New World crop, the potato, to his regions, and conducted regular meteorological observations, leading him to devise a lightning rod that came to be used in Dresden. Palitzsch reported his weather observations to the local mathematical and physical center at Dresden. This allowed him to access the latest literature on astronomy and inspired his own study. As a result, he beat the veteran Messier in recovering the Halley’s comet in 1758 CE (while observing Mira Ceti’s variability) and confirmed the eponymous English astronomer’s prediction regarding its orbital period. In 1761, he studied the solar transit of Venus and discovered that the planet had an atmosphere. Starting September 12th, 1783, Palitzsch carried a remarkable series of observations on Algol and showed that it varied from the 3rd to the 4th magnitude with a periodicity of 2 days 20 hours and 51-53 minutes (today’s period: 2 days 20 hrs and 48.9 minutes). These observations were communicated to the Royal Society in London by Count Hans Moritz von Brühl and were published as: “Observations on the Obscuration of the Star Algol, by Palitch, a Farmer. Philosophical Transactions of the Royal Society of London, Vol. 74, p. 4 (1784).” It is said that Palitzsch correctly inferred that this variability was likely due to an eclipse by a dark companion that was revolving around the star. We see this as a momentous event in modern astronomy – a rather remarkable accuracy of observation for a naked eye autodidact. We may conclude this account of Palitzsch’s great discovery by citing a translation of a copper engraving made in the Latin in his honor:

“Johann Georg Palitzsch, farmer in Prolitz near Dresden, the most diligent cultivator of his paternal farms, a preeminent astronomer, naturalist, botanist, almost in no science a stranger, a man who was his own teacher, pious, sincere, a sage in his whole life. Born on 11th of June 1723.”

However, the story of the rediscovery of Algol’s variability did not end there. As if an Über-mind was in action, coevally with Palitzsch, over in England, the young astronomer Edward Pigott decided to systematically observe stars that might vary in brightness. For this, he roped in his relative, the 18-year-old deaf John Goodricke, to whom he suggested Algol as a target. Goodricke noted that Algol was variable in brightness by observing the star from his window but had initial doubts that it might be a problem with his eyes or due to poor atmospheric conditions. However, using the conveniently located stars around Algol, Goodricke confirmed that it was indeed the star that was variable. He initially thought it might have a period of 17 days but after prolonged observations arrived at a period of 2 days, 20 hours and 45 minutes — close to what Palitzsch had independently reported. Both their observations were reported in back-to-back communications in the Philosophical Transactions of the Royal Society. Goodricke, reasoned that unlike the previously favored star-spot hypothesis of Frenchman Bullialdus and his compatriot Newton for Mira Ceti, the variability of Algol was due to an eclipse by a planet:

“The opinion I suggest was, that the alteration of Algol’s brightness was maybe occasioned, by a Planet, of about half its size, revolving around him, and therefore does sometimes eclipse him partially.”

We do not exactly know what prompted Pigott to ask Goodricke to study Algol; however, it seems that after its variability was confirmed, he checked the older literature and realized that Montanari had described its variability though not its period. It is possible he was already aware of Montanari’s work in the first place and that prompted him to pay attention to the star. In any case, this story ended tragically — Goodricke was awarded the Copley medal for his momentous finding and elected a Fellow of the Royal Society, but he died shortly thereafter due to pneumonia aggravated by the cold from exposure from his observation sessions. Before his death, at the age of 21, he had discovered the variability of Algol, Lyrae and Cephei. The former two will take the center-stage in this note, while the latter was covered in an earlier note. While Baronet Goodricke’s triumph and tragedy earned him his place in history, the farmer Palitzsch, despite recognition from his coethnics Wilhelm and John Herschel faded away into obscurity. His home and observatory were destroyed by Napoleon’s assault.

In 1787, an year after Goodricke’s death and an year before that of Palitzsch, the 19 year old Daniel Huber (in Basel) of the Bernoullian tradition generated the first light curve of Algol. Using this, he definitively demolished the star-spot theory for Algol and presented evidence that it had to vary due to an eclipsing mechanism with predictions regarding the form of the two components. However, this work of Huber, even like his work on least squares (preceding Gauss) was almost entirely forgotten. Thus, it took until 1889, when the German astronomer Hermann Vogel using the spectroscope and his discovery of spectral line shifts from the Doppler effect showed that Algol was a system of two stars that eclipsed each other. Together, with the light curve, he constructed the first physical model of this binary star system with his landmark publication “Spectroscopic observations on Algol.”

We began our observations on Algol starting in the 13th year of our life as Perseus appeared rather conveniently from our balcony and the air was still tolerably unpolluted. Its dramatic variability, like the wink of the Gorgon, has a profound impression on us. We wondered, given its repeated rediscovery, if its variability might have been known to the ancients. Indeed, some have suggested that the number of Gorgons — three — with two being immortal and one (Medusa) being mortal (slain by Perseus) might reflect the 3 day period of Algol with the mortal Medusa representing the dimming of the star. The myth also has a reflection in that of the sisters of the Gorgon, the Graeae, who are described as three hags, who shared a single eye which they passed from one to another before it was seized by Perseus who desired to know the secret of the Hesperides from them. The seizure of that single eye has again been suggested to be an allusion to the three-day period and dimming of Algol in the language of myth. Some others have proposed that this knowledge might have been known to the Egyptians and that the Greeks probably inherited the myth from them. However, the Egyptian case seems even less direct and we remain entirely unconvinced.

After the Vedic age, the Hindus showed a singular character defect in the form of their negligence of the sky beyond the ecliptic (other than an occasional nod to Ursa Major). However, from the Vedic age, we have the sūkta of Skambha (world axis) from Atharvaveda (AV-vulgate 10.8), which pays some attention to the Northern sky. The ṛk 10.8.7 describes the rotation of the sky around the polar axis. In ṛk 10.8.8 we see the following:

pañcavāhī vahaty agram eṣāṃ praṣṭayo yuktā anusaṃvahanti ।
ayātam asya dadṛśe na yātaṃ paraṃ nedīyo .avaraṃ davīyaḥ ॥ AV-vul 10.8.8

This cryptic ṛk talks of the 5-horsed car, which is said to move in the front of the celestial wheel, with two flanking horses yoked to the remaining ones. The second hemistich might be interpreted as its circumpolar nature, as no path is seen untraveled. Hence, we interpret it as the constellation of Cassiopeia with its 5 main stars. In support of such an interpretation, it is juxtaposed in ṛk-9 with a clear mention of Ursa Major (also mentioned in ṛk 5 where the 7 stars of Ursa Major are juxtaposed with the 6 of the Pleiades; derived from Dirghatamas’ giant riddle sūkta in the Ṛgveda) described as an upward facing ladle:

tiryagbilaś camasa ūrdhvabudhnas tasmin yaśo nihitaṃ viśvarūpam ।
tad āsata ṛṣayaḥ sapta sākaṃ ye asya gopā mahato babhūvuḥ ॥  AV-vul 10.8.9

We believe that ṛk 11 again talks about another near polar constellation, which it curiously describes as shakes, flies and stands (3 verbs), breathing or non-breathing, and importantly which while manifesting, shuts its eye:

yad ejati patati yac ca tiṣṭhati prāṇad aprāṇan nimiṣac ca yad bhuvat ।
tad dādhāra pṛthivīṃ viśvarūpaṃ tat saṃbhūya bhavaty ekam eva ॥ AV-vul 10.8.11

Given the remaining near-polar constellations and other stellar allusions in the sūkta, this could be interpreted as the sole ancient Hindu allusion to Algol. However, we should state that we find this or the Greek allusion in the language of myth to be relatively weak evidence for the variability of Algol being known prior to the discovery of Montanari. While we have some direct ancient Greco-Roman allusions to new stars, e.g., the one supposedly seen by Hipparchus (remembered by Pliny the Elder) and one seen in the 130s during Hadrian’s reign, which was taken to be the ascent of his homoerotic companion Antinuous to the heavens, we do not have the same kind of direct testimony for Algol. Hence, while it is conceivable that there was some ancient knowledge of its variability with a roughly three-day period preserved in the language of myth, we believe that there was no direct testimony for that in any tradition.

A look at eclipsing binaries using modern data
Interestingly, two of the variables reported/discovered by Goodricke, Algol and Lyrae, became the founding members of two major classes (respectively EA and EB) of eclipsing binaries in the traditional classification system. The third class EW, typified by W Ursae Majoris, was discovered much later. These traditionally defined classes were primarily based on the shape of the light curve and the period of variability. The most recognizable of these are the EA type binaries. We provide below (Figure 1) the mean light curve of Algol, the founder member of the EA class from the photometric data collected by NASA’s TESS mission as a phase diagram.

Figure 1. Light curve of Algol as a phase diagram from TESS photometric data

The characteristic of EAs is the relatively sharp transitions from the eclipses. In the case of Algol, the secondary eclipse is relatively shallow. This indicates that one of the two stars in the binary system is bright while the other one is dim relative to it. Thus, when the dim star eclipses the bright star, there is the deep primary eclipse, whereas when the bright star eclipses its dim companion, there is the shallow secondary eclipse. In the case of Algol, the brighter star is of spectral type B8V of 3.7 (solar masses) and 2.90 (solar radii); the dimmer star is of spectral type K2IV of 0.81 and 3.5 . An approximate depiction of an Algol-like system is shown in Figure 2.

Figure 2. An Algol-like binary system

Figure 3 shows the TESS light curve of Lyrae the founder member of the EB type. As this data has a bit of a break, we also present the TESS light curve for another well-known EB binary Pictoris a magnitude star near Canopus.

Figure 3. Light curves of Lyrae and Pictoris as phase diagrams from TESS photometric data. The magnitudes automatically inferred from the fluxes are inaccurate in this case.

It is immediately apparent that the transitions between the eclipses are much smoother in the EB class. A closer look shows that Pictoris (with a bit of sharpness) is in between the EAs and a full-fledged EB like Lyrae with a smooth light curve. These curves provide a view into the geometry of this system, i.e., the distortion of the two components of the EBs by the massive tidal force they exert on each other. The sides of the stars which face each other are pulled towards the center of mass of the system by the gravitational force. However, the gravitational force declines as the inverse square law. Hence the opposite sides experience a correspondingly lower force and due to inertia move less towards the center of mass — the principle of tides. As a result, the binary stars get elongated into ellipsoids (Figure 4) and that geometry influences the luminous surface area presented by the system, resulting in smoother light curves.

Figure 4. A Lyrae-like binary system

Finally, we have the EW systems, the TESS photometric light curve of whose founder member W Ursae Majoris is provided below in Figure 5.

Figure 5. Light curve of W Ursae Majoris as a phase diagram from TESS photometric data.

Like the EB systems, the EW systems have smooth light curves with one eclipse almost immediately leading to the next. This indicates that the stars in this system too are likely geometrically distorted. However, they differ in having very short periods — e.g., W UMa has a period of just 0.3336 days (nearly exactly 8 hrs) and low amplitudes for the eclipses. This implies that the stars are really close together — so close that they are fused together (Figure 6).

Figure 6. A W Ursae Majoris-like binary system

With these traditional types in place, we can take a brief look at some light curves of eclipsing binaries discovered by the high-quality photometry of the Kepler Telescope (Figure 7), whose original mission was to discover exoplanet transits (see below). We had participated in the crowd-sourced phase of the project and kept the light curves of stars we found interesting. However, the curves here are plotted from the official post-publication data release by Kirk et al.

Figure 7. The blue and red are the deconvolved and reconvolved fitted normalized fluxes.

The first 5 can be classified as being of Algoloid or EA type. Algol itself would be comparable to KIC 09366988 or KIC 12071006 (4 and 5 in the above plot), whereas the shape of KIC 09833618 (6 in above) is in between another EA star Tauri and the EB Pictoris. In KIC 04365461, KIC 03542573 and KIC 05288543 (1, 2 and 3 in the above) the two eclipses are nearly the same or the secondary eclipse is in the least rather deep. This implies that both stars are comparable in luminosity. Stars 7..12 in Figure 7 show more EB- and EW-like smooth curves and/or short periods. Thus, the traditional classification is something of a spectrum. However, that there is some valid signal in this classification suggested by the period-amplitude diagram, where the amplitude is defined with respect to the deepest eclipse. We first drew this diagram for the 532,990 eclipsing binaries from the VSX catalog of variable stars in which the traditional classification is available for a large fraction (Figure 8). The EWs are clearly distinguished from the rest by the narrow band to the left that they occupy — mostly low in amplitude and short in period. The EAs are pretty much seen across amplitude and period range but are under-represented in the left band where the EWs dominate. They are also less frequent in the right zone with less than 1 mag amplitude but a long period (10-100 days). The EBs overlap with the central zone of the EAs but have a tighter amplitude distribution. They are also more common in the mid-amplitude-long period right zone where the EAs are somewhat under-represented. In fact, the EBs appear to form 3-4 overlapping populations.

Figure 8. The period amplitude diagrams for the traditional types of eclipsing binaries in the VSX catalog.

We next plotted the same diagram for the 425,193 eclipsing binaries from the galactic bulge at the center of the Milky Way photometrically recorded by the Polish OGLE project (Figure 9). We see that the general shape of the period-amplitude plot is the same for both datasets indicating that this pattern is an intrinsic feature of eclipsing binaries that can be used for their classification. The OGLE stars were classified by Bodi and Hajdu on the basis of the shape of their light curves using locally linear embedding, an unsupervised dimensionality reducing classification method (first developed in the Kepler Project), which projects all the stars in the data as a one-dimensional curve. This allowed their classification by a single number the morphology parameter. As can be seen in Figure 7 (M is the morphology parameter for each of the depicted Kepler stars), when this parameter is less than then the stars are typically EAs. A morphology parameter greater than includes EBs and EWs, with those close to 1 being mostly EWs. The stars in the period-amplitude diagram in Figure 9 are colored according to their morphology parameter (Figure 9). One can see that it approximately recapitulates a separation between the EAs and the EWs+EBs. However, the EBs and EWs can only be separated to a degree based on the period axis.

Figure 9. The period amplitude diagram for the Milky Way galactic bulge colored by the morphology parameter (categories: etc). The contours being 2D distribution densities

One of the major correlates of the morphology parameter is the period of the binary. When we plot a period-morphology diagram for the 2877 eclipsing binaries detected by the Kepler mission (Figure 10) we find that the period declines with the increasing morphology parameter and the majority of stars fall in a fairly narrow band. Only for morphology , we start seeing the emergence of two populations belonging to distinct period bands.

Figure 10. Period-morphology plot for the Kepler eclipsing binaries (colored as above).

However, the selection of the Kepler stars was biased towards shorter periods. Hence, a similar plot for the much larger OGLE Milky Way bulge set shows a truer version of the period-morphology diagram (Figure 11). It largely recapitulates the Kepler plot for morphology . However, for values it shows an interesting trifurcation with 3 distinct bands corresponding to those with a period of 1 day or lesser; with a period of 10s of days; with a period in the 100 days range. Given that the morphology parameter captures the shape of the light curve, this trifurcation evidently reflects the separation between the EWs and the different populations of EBs in the traditional classification.

Figure 11. Period-morphology plot for the OGLE galactic bulge eclipsing binaries (colored as above)

The histogram of the eclipsing binary systems from the OGLE data by the morphology parameter also presents some interesting features. First, the number of stars appears to non-linearly increase with morphology. This is potentially not entirely surprising, given that from the earthly viewpoint, the probability of eclipses occurring increases in very close or contact binary systems that are characterized by morphologies closer to 1. Second, remarkably, the histogram shows 6 distinct peaks, which indicate that there are apparently certain preferred types of geometry among these systems (Figure 12).

Figure 12. Histogram of stars by morphology for the OGLE galactic bulge eclipsing binaries

The 6 peaks approximately occur at morphology values of 0.047, 0.43, 0.52, 0.74, 0.76, and 0.86. The first three of these would be squarely in Algoloid territory. The first and lowest peak would correspond to EAs with sharp, narrow and similarly deep minima. This would imply that one relatively rare but preferred type of geometry is of well-separated, similarly luminous small stars. The next two peaks would correspond to more conventional EAs with broader minima and a clearer distinction between the primary and secondary minimum. These would correspond to stars with clear distinct luminosities belong to different spectral classes as seen in the Algol system. The final sharp peak at around 0.86 is likely dominated by EWs with the two stars in contact. The closely spaced peaks at 0.74 and 0.76 are likely dominated by EBs with the lower peak potentially closer to Pictoris like EBs and the higher one closer to Lyrae itself.

These peaks in the distribution of morphologies suggest that there are some preferred evolutionary pathways among eclipsing binaries (or binaries more generally). To probe this more we looked at the spectral class/temperature data for eclipsing binaries. Unfortunately, this is not readily available for both the stars in the binary for bigger datasets. The only dataset that we found to be amenable for such an analysis was the Russian eclipsing binary catalog, which has 409 systems with spectral types for both components (Figure 13). This is a relatively measly set and skewed towards EAs: 56.6% EAs; 13.1% EBs; 15.7% EWs (In the large VSX database roughly 75% of the eclipsing binaries are EW).

Figure 13. Distribution of eclipsing binary systems by the spectral types of the two stars. The Wx category is a composite bin holding both Wolf-Rayet stars and hot white dwarfs.

In this dataset, the spectral type B-B pairs are the most common. Whereas only 10.5% of the EAs in this set are B-B pairs, 28.2% of the EBs are B-B pairs, suggesting that there is a greater propensity for Lyrae type systems to be hot B-B pairs (Figure 4). That this is a genuine difference specific to the B spectral type is suggested by the observation that the spectral type A-A pairs are in similar proportions among both the EAs and EBs, respectively 8.3% and 7.1%. In contrast, the spectral type A-G/A-K pairs, which are another over-represented group are almost entirely EAs and constitute about 22% of the EAs in the above plot. While the EWs are underrepresented in this set, we still find that 36% of the EWs are spectral type G-G pairs and constitute a little over 58% of such pairs in this set. Thus, it establishes that just as B-B pairs are a specialty of the Lyrae, the G-G pairs are typical of W Ursae Majoris stars, whereas the Algols tend to be enriched in hot-cool pairs.

While the spectral classification of the individual stars is not available for the OGLE galactic bulge data, an intrinsic color (V-I) is available. Here, it seems that the V-I color was determined using filters equivalent to the Johnson 11-color system. Thus, one could plot period versus color to see if there might be any features of note (Figure 14).

Figure 14. Period versus color diagram for the galactic bulge eclipsing binaries. The stars in the ranges corresponding to the 6 peaks in the morphology distribution are colored distinctly.

One can see that the systems from the first morphology peak (i.e., those with sharp, narrow and similar eclipses) tend to have long periods and are concentrated in a V-I range that would approximately correspond to the G-K spectral types. We also see that the mid-morphology peaks (2, 3 in Figure 12), which are enriched in more typical EAs, tend to have a broader spread with much greater representation in the higher V-I range corresponding to the M spectral type. In the case of the subsequent two peaks (3, 4 in Figure 12), we see that they show an extension in the lower V-I range , which indicates the inclusion of hotter stars. This seems consistent with this morphology range being enriched in EBs. The last morphology peak as a color profile similar to the first but at a lower period range. This would be consistent with it being primarily composed of EW stars, which in the Russian eclipsing binary dataset was enriched in G-G pairs.

Though Kepler used its own distinct broad bandpass filter, the effective temperature was calculated for the catalog of Kepler stars. We can use this temperature to study how the Kepler stars are distributed in a period versus temperature diagram — effectively a variant of the period-color diagram (Figure 15).

Figure 15. Period versus effective temperature diagram for the Kepler eclipsing binaries. Stars in 3 distinct morphology bands which are over-represented in the Kepler data are colored distinctly.

Here, we notice that the low morphology parameter stars are again in the longer period range and occur in a relatively narrow temperature band (1st-3rd quartile range: 5937K-5219K) corresponding to G to early K spectral types. The stars over-represented in the middle of the morphology band, i.e., mainly conventional EAs, have a broader 1st-3rd quartile range of 6422K-5197K — from F to early K. Finally, those with a high morphology parameter have a 1st-3rd quartile range of 6590K-5426K, which is the F-G spectral range. This last group, which is enriched in the EW eclipsing binaries (periods less than a day), is notable in showing a fairly tight period-temperature relationship (Figure 15) that is most clearly visible in the temperatures corresponding to the F-K range. Evidently, this corresponds to the period-luminosity-color relationship that was uncovered for the EW stars in the 1990s by Rucinski. Thus EWs, which are rather numerous, can be used as a tool for statistical distance estimation.

Finally, we take a brief look at what the eclipsing binaries offer for our understanding of stellar evolution. For example, some obvious questions that emerge from the above observations are: 1) When we look at systems like Algol we have more massive and hotter stars which are in an earlier evolutionary state than their dimmer, cooler companions which are in a later stage of evolution. Why is this paradoxical situation observed, given that one would expect the more massive star to have evolved faster according to the usual stellar evolutionary trajectory? 2) Why do EW systems show a period-color/temperature relationship similar to pulsating variables like Cepheids?

To address the above, we need to take a closer look at the gravitational geometry of binary systems, i.e., the basics of the Euler-Lagrange gravitational potential curves (Figure 16). Let us consider a binary system with stellar masses in the plane with the origin in rectangular coordinates, , at the center of the more massive of the two stars. We then take the distance of the center of the less massive star from the more massive one to be a unit distance. This yields its dimensionless coordinates as . Then the magnitude of the position vectors to a point on this plane from the two stellar centers will be:

We define the stellar mass ratio:

Then, the distance of the center of mass of the two stars from the origin will be:

Thus, the coordinates of would be

The gravitation potential at a point on the plane is specified thus:

Here, is the gravitational constant and the first two terms are the gravitational potentials from the two stars respectively. The third term is the centrifugal force, which needs to be accounted for as the two stars are revolving around their common center of mass : here is the magnitude of the position vector from and is the distance between the centers of the two stars. Since we have already set , i.e., taken it as the distance unit, and computed the coordinates of , we write the equation of after factoring out in a dimensionless form in units on the plane as:

With this equation, we can plot the Lagrangian equipotential curves for a given potential value (Figure 16):

Figure 16. The Lagrangian equipotential curves for an Algol-like system with the five Lagrangian points.

The for which the equipotential curve first takes on a real value, i.e., it appears as just two points, define the two Lagrangian points . These can also be found using the equilateral triangle with the two stellar centers. From these two points, the equipotential curves expand as two disjoint lobes lying on either side of the X-axis. Finally, the two lobes intersect at a point on the X-axis to the left of the star with the larger mass. This point of intersection defines the point (Figure 16). The equipotential curves then become closed curves with two inflection points that advance towards each other. They finally meet on the X-axis to the right of the lower mass star. This point of intersection is the point . After this, the curve becomes two loops, with an inner loop with two inflections and an outer loop that tends towards a circle (Figure 15). The inflections in the inner loop then intersect at a point on the X-axis between the two stars. This point is . After this intersection, the curve becomes 3-looped, with two oval loops around the two stars and the outer loop surrounding both of them. At these points, , the gravitational forces exerted by the two stars cancel each other. Based on the potential equation one can derive an equation whose solution gives the values for which the gravitational forces cancel each other yielding (Figure 16):

The inner loop of the equipotential curve defining has two lobes, one around each star, which are known as the Roche lobes. If the stars are far enough, such that each is within the Roche lobe then we have a detached binary. However, if they get close enough such that one of the stars occupies its Roche lobe then it becomes a semi-detached binary. In this case, gas from that star flows out via and falls on the more massive star. The residual escaped gas forms a disk around the more massive star of the system. This kind of mass transfer is seen in the case of Algol from the dimmer, distended K star, which fills its Roche lobe, to the B star. The differential evolution of the stars in such systems, contrary to what is expected from their mass, is believed to occur due to this mass transfer.

As the stars get closer together both stars might occupy their respective Roche lobes. This happens in the case of the EW systems which are believed to have evolved from detached/semi-detached eclipsing binaries with periods less than 2.24 days winding closer and closer together. Thus, these systems are known as contact systems, with the outflow from both stars forming a common envelope whose shape is defined by the infected inner loop of the equipotential curves (Figure 16). This contact will result in the formation of a single body with temperature equilibration. Thus, the radiating surface area (hence luminosity) of the EW stars will scale with their period given Kepler’s third law. As EWs are mostly in the main sequence on the Hertzsprung-Russell diagram their period will also be related to their temperature/color. From the Kepler data (Figure 15) it appears possible that a loose version of such a relationship emerges first in the semi-detached systems with periods in the 2.25 days to just under a day range, which becomes tight in the contact systems represented by the EWs. Thus, remarkably, a subset of the eclipsing binaries has joined the pulsating stars as potential candles for measuring cosmological distances.

Some poems

Below are some poems in English by our brother. He sends us his compositions in a much more transient medium making them hard to preserve or share. Hence, we decided to anthologize those we could recover and present them here as a record on the internet. Sometimes, they are accompanied by a bit of a “bhāṣya”, which we provide in the cases we were able to salvage it. We also provide some comments of our own.

The Beetle and the Milky Way
From thy curls flows the heavenly stream,
beacon to all creatures big and small;
A scarab scurries under that milky gleam,
homeward bound, rolling her ball.

Danger lurks in the inky dark shadows,
So, the straight path o’er the veldt is best,
But all cardinal points the night swallows;
Who now will guide Titibhā to her nest?

Mounting her ball, as little Titibhā dances,
Her dorsal eye catches the cosmic light —
From a million miles what are the chances
that she could glimpse so distant a sight?

Yet, before long emerge her larvae,
Under the haze of the Milky Way.

The poets “bhāṣya”: Gaṅgā emerges from Hara’s matted locks. In the first quatrain, I have imagined Akaśa-gaṅgā, the Milky Way, emerging from the cosmic body of Rudra. Now, scientists have found that some beetles called scarabs to navigate using the light of the Milky Way. In the dark, they roll their balls of dung away from the source. Second quatrain: This beetle lives in the veldt of southern Africa. After the beetle has collected its forage it must quickly travel in a straight line. If it does not, it risks going in circles and being eaten or its pile stolen by other beetles, or simply going back to the original pile where the competition from other beetles is intense. So, it is imperative that it must take the straight path. But at night, the darkness swallows all the cardinal points; there is no way for it to know where it is going. Third quatrain: Now the beetle does something very interesting. It mounts its ball of forage and does a little dance. As it does that, its eyes catch the Milky Way. Using that as a cue and the small differences in light, it holds a straight-line course. She then buries her eggs in the dung pile. This poem tries to express the awe of how even small creatures are capable of navigating using cosmic cues.
Comment: We had earlier talked about this and other vignettes concerning beetles in this note.

---

The goddess Ambikā
Mother, these ogres ne’er seem to learn;
Flushed with pride,
every new enterprise seems
to raise their hopes
Only to end in humiliation.

Poet’s Vision: “I see Ambika now seated upon her lion on the brow of a hillock, boisterously laughing, her lips reddened with wine, her roving eyes mocking them.”

When their chief tried to capture thee,
They hurl their best missiles at thee
And not one came within a yard of thee!
By your side glance,
what this really means,
I have truly known!

O Ambikā I see you now
seated upon your lion
on the brow of a hillock, boisterously laughing,
Your lips reddened with mead
and your reckless eyes mocking them.

Mater familias of three-eyed One,
Scimitar drawn, garlanded by heads,
swarthy as the nimbus on June’s first day,
Mother of the storm troop!

Comment: The last two quarters indicate her manifestation as Pṛṣṇi, the wife of Rudra, and the mother of the Marut-s.

---

The gods Saṃkarṣaṇa and the Vāsudeva manifest as the Nandakumāra-s
I saw two boys playing in the mead,
frolicking yearlings followed them everywhere,
drawn by their laughter,
with happy lowing to rapturous notes filling the bright glade.

One lad was fair as marble and wore bright blue,
marking the ground for boisterous play,
with his tiny plow;
The other boy, dark as marble, decked in yellow;

The whole world seemed
to be splashed with joy
They were themselves joy all pure —
like word and meaning tied forever.

---

Reading with the child
The best books were books with pictures:
lilac castles ‘n golden mornings,
pretty princesses with dainty glass shoes,
pining princes or ones in frogs;
brave seamen ‘n stormy seas,
for many a rainy evening.

Who’d need Andersen’s flying trunk
or Uderzo’s magic carpet
to travel to the farthest lands
fed by the undying well springs
of childhood’s imagination?

The best books were books with words:
Over proud citadels in verdant meads,
fluttered pennons proud ‘n royal hearts;
while dashing seamen braving wind-kissed surfs
‘n brazen buccaneers
leapt out of the pages,
ruffled by untamed gales,
beating upon windows frail.

Who’d need a flying trunk
or a magic carpet
when words could weave
Tabrizian tapestries with the silken threads
of youthful imagination?

O unputdownable novella,
your heart-pounding climax
had drowned the cock’s crow at dawn
but I can scarce recall your title now,
let alone the pretty pictures of castles
like the dreams of my youth, long faded now.

The best books were the books that whispered ‘n spoke:
Faintly at first:
like the tentative chirping of starlings
on spring’s first morn;
And then like the cuckoo’s full-throated ‘n raucous
at midsummer’s high noon.

As I closed my eyes to listen,
the years seemed to fall away!
Proud banners flew o’er the citadel again,
And to the beating of kettle drums marched my tin soldiers,
five and twenty in all,
and astride a dappled mare
tossing her rufous mane,
rode the spirit of story herself,
and even the swaggering buccaneers
with cutlasses drawn,
all came rushing into the mind’s glade
to watch their queen as she cantered.

I smiled.
Through childhood, boyhood, youth
and even in the somber twilight
my soul hadn’t changed;
Ever watching all go by and pass beyond the bend,
reliving the ages now with my own little reader,
who poked at the words
with her chubby dainty finger —
a little wand that turned them into pictures.

---

A quatrain to the god Kāma
O Madana!
The slender maids of the Kuntala country sweet n fair,
adorned with night flowering florets,
betwixt shy kanakāmbara blossoms trellised o’er their hair,
seem to sing thy triumph from upright turrets.

---

The visions of the god Viṣṇu
He has a slender waist,
And he’s blue all over;
All riches dwell in his chest —
Our world-strider ‘n soul-saver!

Who could imagine thee —
in the wee fry scooped up
in Satyavrata’s arghya;
Or, bearing mighty Mandara
or, in womanhood’s highest excellence,
ever keeping the greatest secrets
out of demonic reach;
Or, hiding within that pillar,
but the Mantrarāja’s knowers
have seen thee waiting to spring;
Or, crossing the wide ocean,
armed with mighty bow
hastening to the Aśoka grove —
“Aśoka” — coz there’s hope.

I know you were there in all those times.
How can I repay?
O Muses will ye carry these words of praise to Him.

Comment: the verses reflect the poet’s meditative visions of the god.

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Blank verse benediction invoking Kumāra
Victory to the reed-born son of Gauri,
whose lance point cleft a hole in the looming darkness of Krauñca,
where birds of light and insight
now chirp and dart in joy;

Impelled by his grace,
may the spear of your intellect too
give us a window to peer
into the secrets of the cell and its denizens.

---

Who is the thief of life?
Night after night I lay awake,
beset by worry and fear
that your retinue should be near.
In every ache, malaise, and niggle
I heard your herald’s menacing bugle.

Small mercy – you didn’t come!
Yet, I felt my life was stolen
ere the fun had even begun.
So, I’ve come myself to your great hall
to settle the matter once and for all.

I took my courage from the little boy,
who’d waited three days at your gates
in the quest for the fount of eternal joy
unswerved by your treasure crates.
He now shines bright like the flame
you named after his own name [1].

All resplendent you seem
like the thunder cloud.
No offense do I mean,
but are you a thief?
On my way here I saw many a sight
that turned the blood cold in my veins —
Ten thousand pyres all alight
after unending pointless pains.

Heap upon heap of broken dreams,
Families left with no means,
Mangled bodies and minds,
hollowed out long before the end
Ghastly tragedies of all kinds
And wounds that none can mend.

Then I grew numb to it all
‘Tis all absurd as Sisyphus’ curse —
No matter what that downhill fall
in a meaningless universe
Tell me, what are you hoarding here sir?
I ask you squarely “are you a thief?”

Then spoke the resplendent Death,
resting his mace upon his shoulder
“I am no thief.”
It’s true I come when it’s my time.
Yet I did not commit this crime.

Long before were you robbed
by anxious thoughts all your own,
of future miseries — real only in your head
The present moment quietly slipped
like a rug beneath your feet tugged,

I was nowhere in the scene.
Yet you hardly lived these years passed
Why blame me sir?
Granted, sir, you’re not a thief.
Still, I have been robbed every night.
Who will return my precious days,
lost to worry and despair?
I do not have another life to spare.

Resplendent Death thought a bit
And then said: “I think there is One”
But He’s a thief too. [2]

“What? You’ll send me to another thief?”
Then he pointed to his chest mighty
You see this three-pronged scar of old?
I was once young and haughty
And paid dearly when hurled my stranglehold [3].

Perhaps only He can recover what you’ve lost
Hasten, sir. There’s no time.
He lives in the mountains.
Take the winding path.
up the snowy slopes.
The road goes beyond the great river’s womb.

Ignore the goblins and ghouls –
He keeps strange company.
On that path you must trudge,
You will then see his two boys playing [4].

And their mother knitting a shawl [5].
She is the great queen of all,
Yet she won him by austerity —
No greater love story for posterity.
“How will I know him?”

“You cannot mistake Him”
who wears the moon in his tiara.

Comments:
1. An allusion to the journey of Naciketas the Gautama to the realm of Mṛtyu that is prominently mentioned in the literature of the Kaṭha-s. The final line in this verse alludes to the iṣṭi that is named after him.
2. Rudra is said to manifest as various criminals (e.g., taskara= thief) in the Śatarudrīya from Yajurveda-saṃhitā-s.
3. The conquest of Mṛtyu/Yama by Rudra — the liṅgasthāpanā-mantra “OM nidhanapatāntikāya namaḥ |” alludes to this.
4. Skanda and Vināyaka.
5. The motif of the goddess weaving time.

The Kaumāra cycle in the Skandapurāṇa’s Śaṃkara-saṃhitā

Many khaṇḍa-s, māhātmya-s and saṃhitā-s attach themselves to the sprawling “Mega-Skandapurāṇa”. We use this term to distinguish it from the “Ur-Skandapurāṇa”, which was first published by Bhaṭṭārāi in the late 1980s and is now known to survive as three related recensions, one of which is represented by rather early manuscripts from Nepal. Of the texts associated with the “Mega-Skandapurāṇa”, the Śaṃkara-saṃhitā, remains relatively poorly known. It is unclear if there was a pan-Indian understanding of its constituent texts and if a complete version was ever extant in any part of the Indosphere. As far as we can tell, one of its khaṇda-s known as the Śivarahasya is preserved only in South India and is likely of South Indian origin. It was most likely composed in the Drāviḍa country; though one cannot entirely rule out the Southern Andhra country or parts of Southern Karṇāṭa as its original source. It was edited by a maternal śrauta-ritualist- and paurāṇika-clansman of ours in the 1950s-1960s. Upon completing its editing, he offered it to the shrine of Skanda housing the kuladevatā of our clan. The text as available still has some corruptions, several of which might have been introduced while typesetting. The Śivarahasya presents its relationship to the Mega-Skandapurāṇa thus:

teṣv api+idam muni-śreṣṭhāḥ skāndaṃ sukhadam uttamam ।
sarva-vedānta-sārasvaṃ pañcāśat khaṇḍamaṇḍitam ॥
ādyā sanatkumārīyā dvitīyā sūta-saṃhitā ।
brāhmī tu saṃhitā paścāt turīyā vaiṣṇavī matā ॥
pañcamī śāṃkarī-jñeyā saurī ṣaṣṭhī tu saṃhitā ।
ādyā tu pañca-pañcāśat sahasraiḥ ślokakair yutā ॥
dvitīyā saṃhitā viprāḥ ṣaṭsahasrair alaṃkṛtā ।
trisāhasrair yutā brāhmī pañcabhir vaiṣṇavī-yutā ॥
triṃśatbhiḥ śāṃkarīyuktā khaṇḍair dvādaśabhis tathā ।
ṣaṣṭhī tu saurī saṃyuktā sahasreṇaika kenasā ॥
grantha-lakṣair yutaṃ skāndaṃ pañcāśat khaṇḍa-maṇḍitam ।
tad adya sampravakṣyāmi yuṣmabhyaṃ vipra-puṃgavāḥ ॥
tat trayā saṃhitā proktā śāṃkarī veda-sammatā ।
triṃśat sahasrair granthānāṃ vistareṇa suvistṛtā ॥
ādau śiva-rahasyākhyaṃ khaṇḍam adya vadāmi vaḥ ।
tat trayodaśa-sāhasraiḥ saptakāṇḍair alaṃkṛtam ॥

The Mega-Skandapurāṇa is divided into 6 saṃhitā-s that have a total of 50 khaṇḍa-s among them. These are listed as follows with their corresponding verse counts: 1. Sanatkumāra: 55,000; 2. Sūta: 6000; 3. Brāhmī: 3000; 4. Vaiṣṇavī: 5000; 5. Śāṃkarī: 30,000; Saurī: 1000. Thus, the entire text is said to be of 100,000 verses. Within it, the Śaṃkara-saṃhitā (Śāṃkarī) is said to have 12 khaṇda-s of which the Śivarahasya of 13,000 verses is one. The Śivarahasya itself is divided into 7 kāṇḍa-s, which are: 1. Sambhava; 2. Āsura; 3. Māhendra; 4. Yuddha; 5. Deva; 6. Dakṣa; 7. Upadeśa.

The published Mega-Skandapurāṇa does not align precisely with this tradition and has 7 khaṇḍa-s: 1. Māheśvara; 2. Vaiṣṇava; 3. Brahma; 4. Kāśī; 5. Avanti; 6. Nāgara; 7. Prabhāsa. The Māheśvara-khaṇḍa in this compendium is not the same as the Śāṃkarī Samhitā under consideration in this discussion. However, they share many common themes that include the central thread gathered around the destruction of Dakṣa’s sacrifice, the marriage of Pārvatī and Rudra, the birth of Kumāra and the killing of Tāraka by him, the birth of Gaṇeśa, the Śivarātri ritual and the worship of Rudra at Aruṇācala. The tale of Skanda and the Tāraka war is repeated twice in the Māheśvara-khaṇḍa of the Mega-Skandapurāṇa.

The first 5 kāṇḍa-s and parts of 6 and 7 of the Śivarahasya in the Śāṃkarī Samhitā comprise a narration of the Kaumāra cycle partly modeled after the Rāmāyaṇa of Vālmīki. Much of the kāṇḍa-s 6 and 7 are primarily śaiva material relating to the observation of vrata-s and Śiva-dharma — these thematically overlap with the material in the Māheśvara-khaṇḍa of the Mega-Skandapurāṇa. The Kaumāra portions of the Śivarahasya were rendered in Tamil by the saiddhāntika guru Kāśyapaśiva in the medieval period as the Tamil Skandapurāṇa. His version has some differences from the extant Sanskrit text of the Śivarahasya — it is unclear if these differences are due to his reformulation of the narrative or because he was using a distinct recension of the text. A Telugu rendering of the text also exists but we do not have much familiarity with it. While the ancient versions of the Kaumāra cycle have the killing of the dānava/daitya Mahiṣa or Tāraka by the god Skanda as their centerpiece (Rāmāyaṇa and Mahābhārata), this text presents an unusual version of it: after the initial section culminating in Tāraka’s killing, there are two extended sections dealing with the elder brothers of Tāraka. These culminate in the great battle in which Skanda slays these demons, Siṃhamukha and Śūrapadma, along with their vast horde of Asura-s. So far, we have not seen any record of these demons outside of South India. Long before Kāśyapaśiva’s Tamil rendering, Śūrapadma appears in the South Indian tradition as represented by the earliest surviving Tamil texts, such as the Puṟanānūṟu (Puṟanānūṟu 23, a poem probably roughly contemporaneous with the Kuṣāṇa age in the North given that it describes the early Pāṇḍya king Neṭuñceḻiyaṉ), and a subsequent Tamil poetic anthology, the Paripāṭal. This suggests that the South Indian tradition had a deep history of certain unique elements of Kaumāra mythology.

As far as archaeology goes, we know that there was an active Kaumāra tradition in the Andhra country starting from the Andhra empire down to their smaller successor states, such as the Ikṣvāku-s and Viṣṇukuṇḍin-s among others, which had Nāgārjunakoṇḍa, as one of its foci. In the Tamil country, clear-cut archaeological evidence for strong Kaumāra traditions can be seen from the Pallava period onward. We believe this temporal period stretching from the Andhra empire down to the rise of the Pallava-s overlaps with the period during which the Puṟanānūṟu and the later Paripāṭal were composed in the Tamil country. The Paripāṭal displays a distinctive combination of the worship of Viṣṇu with his Pāñcarātrika vyūha-s and Kumāra — this pattern is seen in the Northwest, i.e., Panjab/Gandhara, and in Mathura during the Śaka-Kuṣāṇa age. This was mirrored in the South Indian Maturai (approximately the same longitude as its Northern namesake Mathura), the cultic locus of the Paripāṭal. Thus, one could argue that the core Kaumāra tradition in the Tamil country was a transmission of this Mathuran tradition.

Apart from the references to Śūrapadma, the themes in the Paripāṭal, while clearly linked to the ancient Kaumāra narratives, such as those seen in the Mahābhārata, show certain unique archaisms which have not survived in the Sanskrit tradition. For example, in Paripāṭal-5 by Kaḍuvan Iḷaveyinanār we encounter an incorporation of the Paurāṇika Marut mytheme into the tale of the birth of Kumāra. Here, after a prolonged dalliance with Rudra, mirroring the Sanskrit sources, Pārvatī becomes pregnant with Kumāra. Then Indra, who had acquired a boon from Rudra, cut the developing embryo into pieces with his Vajra (the number seven is implied by the repeated mention of seven in this verse) — the Paurāṇika Marut-motif. Then the pieces were placed in the three ritual fires by the seven ṛṣi-s (allegorically identified in the text with the seven brightest stars of Ursa Major), who realized that they would form the future commander of the deva-s. The pieces were purified by Agni and placed in the wombs of six of the wives (Kṛttikā-s=Pleiades), barring Arundhatī, of the seven ṛṣi-s (c.f. archaic Mahābhārata version). Thus, this South Indian tradition preserves a memory of the connection between the Vedic Marut-s, who are the sons of Rudra, and Skanda that was largely forgotten elsewhere (except for the reference to Kumāra as leader of the seven Marut troops in the oldest version of the cycle in the Mahābhārata).

When we take the whole Kaumāra corpus, we have reason to suspect that the ancient version of the tradition was much richer and more polymorphic than what is seen in the later Sanskrit tradition. As a parallel, we could point to the Aindra mythology. The Veda alludes to many mythemes that were clearly common knowledge when the Ṛgveda was originally composed. Further, the epics point to a degree of para-Vedic polymorphism in the Aindra tradition. However, what survived of that tradition in the extant Paurāṇika corpus is relatively limited. Likewise, with the Kaumāra tradition, we see that the Mahābhārata preserves a rich mythology, which included the triumphs of the god over Mahiṣa, Tāraka, and hints at an even richer body of myth by mentioning in passing the overthrow of several other demons (e.g., Tripāda and Hradodhara) by Skanda. By the time of the composition of the extant Paurāṇika corpus, the Kaumāra myth of Mahiṣa was mostly forgotten, surviving only in the Vāmana-purāṇa. The Mahiṣa myth was instead transferred to Kumārī (Vindhyavāsinī section of Ur-Skandapurāṇa). She originally started off as the virgin goddess, a female counterpart of Kumāra, and was subsequently subsumed under the great transfunctional goddess, the Śakti of Rudra. Thereafter, Kumāra was only left with the Tāraka myth across much of the Sanskrit tradition. Hence, posit that at the zenith of the Kaumāra tradition there was a considerably larger and more polymorphic body of Kaumāra material. The vitality of this old Kaumāra tradition is seen in Mathura — based on the remains of images, we infer the existence of at least 33 Kaumāra shrines in Mathura during the Kuṣāṇa age. Thus, we propose that some of this original polymorphism in the tradition was preserved in the transmission to South India, even as the tradition in the Tamil country remained relatively isolated from the later transmissions from the North (e.g., the transmission of the Eastern Kaumāra Lodge from Vaṅga to Bellary in Karṇāṭa). Hence, we posit that the special emphasis on Śūrapadma was a remnant of this old transmission that did not make it into other Pauraṇika transmissions.

Some of those mythic elements strongly persisted in the Tamil country and found their way into the Śivarahasya narrative, which the evidence presented below indicates is a later text:
1) In the Śivarahasya, the gaṇeśvara Nandin is prominent. Our textual analysis (to be presented later) has revealed that this is a strong marker of a text influenced by the Saiddhāntika Śaiva tradition. There are several other allusions throughout the text that point to its affiliation with the Saiddhāntika rather than any other Śaiva school of the mantramārga or the atimārga. This would also explain why the saiddhāntika Kāśyapaśiva chose to render it Tamil. Whereas in North India (outside of Nepal) and Vañga, the rise of the Siddhānta resulted in considerable erosion of the Kaumāra tradition from the 700s of CE, in the Drāviḍa country, the strong Kaumāra tradition was co-opted and incorporated within a Saiddhāntika framework. For example, this is seen in the works of the great polymath Aghoraśiva-deśika, who in addition to his numerous Saiddhāntika treatises also composed a work on the sthāpanā of Kaumāra shrines. This places the Śivarahasya in a distinct stratum from the Paripāṭal era (and even perhaps the Tirumurukārruppaṭai period) when Siddhānta was dominant in the Tamil country.
2) Its narration of the birth of Kumāra omits the coitus of Rudra and Pārvatī, which indicates a “sanitization” of the sexual elements of that narrative, which, for example, are an important aspect of its presentation in the Rāmāyaṇa, Mahābhārata, Śivapurāṇa and Kālidāsa’s Kumārasaṃbhava. This change in attitude again points to a relatively late date for Śivarahasya.
3) None of the early narrations of the Kaumāra cycle in the Iitihāsa-s or the Purāṇa-s attempt to model themselves after the Rāmāyaṇa. In fact, the Kumārākhyāna was seen as one of those old, independent mythic motifs of Hindu tradition that formed the basis of numerous retellings by different narrators, even as it was with the Rāmāyaṇa. Thus, the modeling of parts of the Śivarahasya, namely those concerning the war with Śurapadma and his clan (and possibly the arrangement in seven kāṇḍa-s), after the Rāmāyaṇa betrays a late “reconstruction” following the loss of continuity with the old Kaumāra Paurāṇika tradition.
4) The text acknowledges an already large Skandapurāṇa of the size of 100,000 verses. This implies that it comes from a period when the accretion of texts to form a mega-Skandapurāṇa was common knowledge.

While these elements point to a relatively late date for the Śivarahasya, we should point out that like all Paurāṇika corpora it does preserve several notable elements that have ancient roots going back to the Indo-European past. While the kāṇḍa-s 6 and 7 are dominated by the Śaiva material, its core is primarily a Kaumāra text intent on the aggrandizement of Skanda. Beyond the distinctive form of the Kaumāra cycle, there are multiple elements that indicate a southern locus for its immediate origin:
1) It presents a prominent role for the god Śāstṛ or Ārya as Hariharaputra. This transmogrified southern ectype of Revanta (commonly seen as Hariharaputra) was prominently worshiped at least since the time of the composition of the famous Tamil epic Śilpādhikāra.
2) It presents Vināyaka as elder to Skanda. While this is the position adopted by the text, its core Kaumāra narrative of the conquest of the demons still clearly indicates a tradition where Gaṇeśa was not yet born/in place.
3) The text describes two marriages of Skanda — one to Devasenā, seen across the Indosphere, and the other to Valli (related to the Dravidian term for tubers such as the tapioca and the sweet potato), that emerged in the Southern folk traditions and spread through the Southern zone of influence in the Indosphere.
4) The presence of the Kāverī-Agastya myth, which specifically points to the Drāviḍa country.
5) The staging ground of Kumāra in course of his campaign is called Śentīpura, which in the Tamil version of Kāśyapaśiva is identified as Tiruceñdūru, a major Kaumāra center, in the Drāviḍa country. It is already mentioned as a shrine of Skanda by the sea with a beautiful beach in Puṟanānūṟu 55.
6) The shrine of Aruṇācala in the Drāviḍa country is praised as an important Śaiva-kṣetra. Several other shrines in the Drāviḍa country as mentioned throughout the text, e.g., the Tyāgarāja and the Madhyārjuna shrines.

With this background, we shall briefly examine the contents of the Śivarahasya and a few of its notable points:
1) The Sambhava kāṇḍa
This section opens with a maṅgalācaraṇa seeking succor from Rudra, Umā, and their sons:
maṅgalaṃ diśatu me vināyako maṅgalaṃ diśatu me ṣaḍānanaḥ ।
maṅgalaṃ diśatu me maheśvarī maṅgalaṃ diśatu me maheśvaraḥ ॥

This is followed by short stotra-s with invocations of Gaṇeśa and Skanda by a set of 16 names each.
Gaṇeśa:
omkāra-nilayaṃ devaṃ gajavaktraṃ caturbhujam ।
picaṇḍilam ahaṃ vande sarvavighnopaśāntaye ॥
sumukhaś caikadantaś ca kapilo gajakaraṇakaḥ ।
lambodaraś ca vikaṭo vighnarājo vināyakaḥ ॥
dhūmaketur gaṇādhyakṣaḥ phālacandro gajānanaḥ ।
vakratuṇḍaḥ śūrpakarṇo herambaḥ skandapūrvajaḥ ॥

Skanda:
subrahmaṇyam praṇamyāhaṃ sarvajñaṃ sarvagaṃ sadā ॥
abhīpsitārtha siddhy arthaṃ pravakṣye nāma ṣoḍaśa ।
prathamo jñānaśaktyātmā dvitīyaḥ skanda eva ca ॥
agnibhūś ca tṛtīyaḥ syāt bāhuleyaś caturthakaḥ ।
gāṅgeyaḥ pañcamo vidyāt ṣaṣṭhaḥ śaravanodbhavaḥ ॥
saptamaḥ kārttikeyaḥ syāt kumāraḥ syād athāṣṭakaḥ ।
navamaḥ ṣaṇmukhaś caiva daśamaḥ kukkuṭa-dhvajaḥ ॥
ekādaśaḥ śaktidharo guho dvādaśa eva ca ।
trayodaśo brahmacārī ṣāṇmāturś caturdaśaḥ ॥
krauñcabhit pañcadaśakaḥ ṣoḍaśaḥ śikhivāhanaḥ ।
etat ṣoḍaśa nāmāni japet saṃyak sadādaram ॥

These stotra-s are popular in South India in Gaṇeśa- and Skanda-pūjā-s. However, it is notable that the names of Skanda do not mention Śūrapadma or Siṃhamukha; instead, they only utilize the pan-Indospheric Kaumāra material.

This is followed by the following topics:
-An account of the origin of the Purāṇa as narrated by the sūta, the student of Vyāsa, to the brāhmaṇa-s at Naimiśāraṇya and the nature of the Skandapurāṇa.
-An account of Kailāsa the abode of Rudra. This is followed the by usual Śaiva cycle of Pārvatī and her marriage that includes the below events.
-Kāma approaches Rudra who is in meditation.
-The incineration of Kāma by the fire from Rudra’s third eye.
-The lament of Rati.
-Rudra tests Pārvatī by appearing to her as an old man.
-Rudra reveals his true form to Pārvatī.
-Rudra sends the seven ṛṣi-s/stars of Ursa Major as his emissaries to seek the hand of Pārvatī in marriage.
-The construction of the marriage hall.
-The makeup and jewelry of Pārvatī.
-The gaṇeśvara Nandin leads the gods to the marriage of Rudra and Pārvatī.
-The names of the Rudra-s and an account of their vast hordes in the marriage procession. This is followed by an account of the retinue of Rudra. Below is a notable section of this text:
sahasrāṇāṃ sahasrāṇi ye rudrāḥ pṛthivīṣadaḥ ।
sahasra-yojane lakṣya-bhedinaḥ saśarāsanāḥ ॥
te rudrās tridaśa-śreṣṭhās trinetraṃ saṃsiṣevire ।
asmin mahati sindhau ye ye ‘ntarikṣe divi-sthitāḥ ॥
nīlagrīvās trinetrās te ‘saṃkhyātāś cāpurīśvaram ।
aghaḥ kṣamācarāś cānye sarve te nīlakandharāḥ ॥
girīśayo ‘stu kalyāṇaṃ siṣeviṣava āpire ।
vṛkṣeṣu piñjarā rudrāḥ nīlakaṇṭhā vilohitāḥ ॥
bhūtānāṃ cādhipatayo vikeśāś ca jaṭadharāḥ ।
sahasrair apy asaṃkhyātāḥ sāyudhāḥ prāpurīśvaram ॥
anneṣu ye vividhyanti janān pātreṣu bhuñjataḥ ।
ye pathāṃ pathi rakṣanti tīrthāni pracaranti ca ॥
ye rudrā dikṣu bhūyāṃsas tiṣṭhanti satataṃ ca te ।
gaurī-kalyāna-sevāyai giriśaṃ samupāśrayan ॥

Here the account of the hordes of Rudra is adapted from that of the great multitude of Rudra-s provided in the final anuvāka (11) of the Yajurvedic Śatarudrīya. Apart from these, a great retinue of goddesses and natural phenomena is said to accompany Rudra on his marriage procession. The bluish violet Viṣṇu is said to have joined them with his four forms, i.e., Pāñcarātrika vyūha-s, and was introduced by Nandin.

-Rudra enters the marriage hall and the marriage is concluded.
-Brahman and the other gods send Vāyu as their messenger to urge Rudra to produce a son with Pārvatī. However, Nandin turned him back asking him not the break the marital privacy of the deities.
-All the gods went to Kailāsa themselves and beseeched Rudra, whose half was occupied by Ambikā, to produce the promised son who would relieve them from the Asura-s.
-Rudra assumed a six-headed form blazing like a crore suns and enveloped the realms of the universe terrifying all beings. Then, from the third eye of each of his six heads, the upward seminal flow (ūrdhvaretas) exploded as six flashes of intense light that vaporized the directions (dudravaḥ sarvato diśaḥ). Terrified by this manifestation, all sought refuge in Rudra, praising him with hymns.
-He gathered back those six blazes and they came together as six pacified minute sparks. He then instructed Vāyu and Agni to take them to the arrow-reed forest on the banks of the Gaṅgā and vanished along with Ambikā. Thereafter, Vāyu and Agni, each getting tired after a while, with much effort bore the sparks to the Gaṅgā and deposited them there. The other gods eager to see what would happen also arrived there.
-The Marut-s with their joyful selves filled the quarters with a pleasant breeze (diśaḥ prasedur maruto vavuś ca sukhamātmanāṃ). Then, in the midst of a lotus in the arrow-reed forest, a six-headed, twelve-armed, two-footed divine boy took shape (note recurrence of the ancient motif of the birth of Agni in the lotus: Ṛgveda 6.16.13).
-Viṣṇu called upon the six Kṛttikā-s to nurse him. Instantaneously, becoming six separate kids he drank from their breasts.
-Even as the six flashes from Rudra were vaporizing the directions, Pārvatī too was startled and jumped away. As a consequence, the anklet fell from her feet and broke spilling the gems within it. Ambikā was reflected on those nine gems and appeared tenfold — herself and the 9 reflections. These became the Kālikā goddesses, who were fertilized by the rays emanating from Rudra and became pregnant.
-The droplets of the sweat of the startled goddess were also fertilized by Rudra. From them were born a 100,000 fierce gaṇa-s (who became the retinue of Skanda).
-Ambikā was displeased by seeing these goddesses pregnant and cursed them that they would have an unending and painful pregnancy. They went to Rudra seeking his aid and upon his counseling Ambikā released them from her curse and each gave birth to a mighty son of the complexion of their respective mothers.
-Goddesses and the corresponding sons were: Raktā (ruby) — Vīrabāhu; Taralā (pearl) — Vīrakesarin; Pauṣī (topaz) — Vīramahendra; Gomedā (garnet) — Vīramaheśvara; Vaiḍūryā (beryl) — Vīrapuraṃdara; Vajramaṇi (diamond) — Vīrarākṣasa; Marakatā (emerald) — Vīramārtāṇḍa; Pravālā (coral) — Vīrāntaka; Indranīlā (sapphire) — Vīradhīra. These nine Vīra-s became the companions of Skanda and were known as his brothers.
-Then Rudra told Ambikā that they have actually generated a mighty son and asked her to come along on his bull vehicle to see him.
-They set out with thousands upon thousands of Rudrakanyā-s, Mātṛ-s, gaṇa-s and the Marut-s.
-Then Umā hugged the six separate kids who became a single Ṣaṇmukha and fed him with her milk.

The narrative of the birth of Kumāra up to this point presents several interesting points:
1. There is a prominent role for Vāyu along with the usual Agni in the birth of Skanda. We believe that this is the survival of an ancient motif that is already seen in the Veda, where on rare occasions, apart from the usual Rudra, Vāyu is presented as the father of the Marut-s. This is not a mere slip, because in the Indo-Iranian world we see an overlap in the Rudra- and Vāyu class deities. On the Indian side that goes back to the worship of Rudra in the context of the rites of the Proto-Śaiva-s, the vrātya-s, and in the Eastern Iranian world in the character of the deity Vāyu Uparikairya, who is iconographically identical to the Hindu Rudra.
2. We see the subliminal presence of the Marut-s, even in this late reflex of the Kaumāra origin myth suggesting a long survival of this memory in the circles conversant with the Veda.
3. A variant of the “fertilizing sweat motif” attested in this myth presents the origin of the 100,000 Skanda-gaṇa-s from the sweat of Gaurī.
4. The Nava-vīra-s are a unique feature of the South India Kaumāra cycle. However, the number nine is also mentioned as the total of the Kaumāra-vīra-s even in one of the most ancient surviving variants of the Kaumāra cycle, which is seen in the Mahābhārata:
kākī ca halimā caiva rudrātha bṛhalī tathā ।
āryā palālā vai mitrā saptaitāḥ śiśumātaraḥ ॥
etāsāṃ vīrya-saṃpannaḥ śiśur nāmātidāruṇaḥ ।
skandaprasādajaḥ putro lohitākṣo bhayaṃkaraḥ ॥
eṣa vīrāṣṭakaḥ proktaḥ skandamātṛgaṇodbhavaḥ ।
chāga-vaktreṇa sahito navakaḥ parikīrtyate ॥
This account in the Mbh states that by the grace of Skanda, the 7 goddesses (Skandammātṛ-s), i.e., Kākī, etc., gave birth to the terrifying red-eyed deity Śiśu, who was called the eighth vīra. However, when Nejameṣa = Bhadraśākha with the head of a ram, generated by Agni is taken into account, Śiśu is said to be the ninth vīra. Then the question arises as to who were the remaining seven? From the preceding account in the Mbh we can infer that these were Viśākha and other Kumāraka-s who were emanated by Skanda when struck by Indra’s vajra. We believe that these vīra-s were ectypes of the Marut-s filtering down through later mythic overlays. It also appears likely that in the Śivarahasya, the most prominent of the nine vīra-s, Vīrabāhu, is essentially an ectype of Viśākha as the younger brother of Skanda. This connection to one of the oldest surviving versions of the Kaumāra cycle suggests that this aspect of the Southern tradition was a memory coming down from its ancient layer originally brought from the North.

-Thereafter Skanda displayed his childhood līlā-s, some of which bring out his roguish (dhūrta) aspects that are known from the oldest layers of the Kaumāra tradition. One notable set of such cosmic sports is expressed in beautiful Mandākrāntā verses:
jyotiś cakraṃ dhruva-kara-gataṃ vāta-raśmi-praṇaddhaṃ
chitvā bālaḥ prathita-mahimā svānugānāṃ karāgraiḥ ।
dikṣv aṣṭāsu svayam api dadhan dhārayan vyoma-gaṅgā
nakrān badhvā vyasṛjad abhisaṃbhāvya-pāthaḥ punastān ॥
The boy putting forth his greatness, having taken in his hands the self-moving ones (planets) split the reins of propellant force (wind ropes) which bind them to the polar rays around which the celestial wheel revolves. Giving to himself the eight quarters, he then took on the Celestial Gaṅgā (Milky Way); binding the crocodiles (the constellation of Scorpius) he released them again into the Sun.
paścād ūrdhvam mahar api janas tat tapaḥ satya-lokaṃ
gatvā gatvā tad adhi vasatīn viśva-sādhyāmarendrān ।
līlā-lolo nava ca kalayan vedhaso bhīmabhūtān
lokālokaṃ girim api mudā prāpa cikrīḍa bālaḥ ॥
Thereafter, he ascended upwards to the Mahar, Jana, Tapa and Satya realms [of the universe], and kept going on to the excellent dwellings of the Viśvedeva-s, Sādhya-s, the immortals and Indra. Making anew celestial fierce beings, joyfully attaining the boundaries of the universe (lokāloka mountain), the playfully sporting boy sported.

This displacement of the celestial bodies by Skanda already has a germ in the Mbh account: pracyutāḥ sahasā bhānti citrās tārāgaṇā iva ।. The celestial army of Indra attacked by Skanda is said to have been like the clusters of stars thrown off their orbit. Another notable point is a subtle astronomical allegory in the first verse. The constellation of Scorpius is called the nakra in Hindu tradition. Hence, we take the account of Skanda seizing the nakra-s and releasing them into the solar blaze as an allusion to the Kārttika month (when Skanda was born) when the Sun is opposite to the Kṛttikā-s in Scorpius.

-Alarmed by Skanda’s sports the gods fought him.
-Skanda defeated the gods and shows them his viśvarūpa (macranthropic) form.
The viśvarūpa of Skanda, while comparable to other viśvarūpa-s in the Itihāsa-purāṇa tradition, has some interesting cosmic verses:
tasmin tejasi te devā vaiśvarūpe jagat-trayam ।
koṭi-brahmāṇḍa-piṇḍānām mahā-vapuṣi romasu ॥
yūkāṇḍānīva koṭīni caikaikasmin sahasraśaḥ ।
tat-tad āvaraṇaiḥ sārdhaṃ tatratyair bhuvanair janaiḥ ॥
bhūtair bhavyair bhaviṣyadbhir brahma-viṣṇavādibhiḥ suraiḥ ।
jānu-pradeśa-mātre ‘sya dṛṣṭvā vismayam āgatāḥ ॥
In his radiance, were the gods of all forms and the triple world. In the hairs of his great body were the crores of spheres of galactic realms (brahmāṇḍa-piṇḍā-s). They were like the eggs of lice [of the hairs], in each one of the crores there were thousands of world-systems, each with its own set of orbits and local inhabitants of those worlds. Seeing the past, the present and the future, the Brahman, Viṣṇu and like of gods all coming only to the height of his knees, they reached bewilderment.

-Realizing who he was, the gods crowned Skanda as the commander of their army.
-The incident of the runaway sacrificial ram of Nārada. Skanda dispatched Vīrabāhu to capture it and bring it back. Skanda then took it as one of his vehicles. A homologous episode is found in the Ajopākhyāna of the Śivapurāṇa; there, instead of a ram, it is a goat. It may be noted that the Tamil allusion to this myth in the poem by the Saṅgam poet Maturai Nakkīranār (Tirumurukārruppaṭai 200-210) also records a caprine animal that might be interpreted as either a goat or a ram.

-Skanda chastised and imprisoned Brahman for his lack of gnosis of the praṇava.
-He then stationed himself at Kumāraparvata. At Rudra’s behest, Nandin tried to get him released, but Skanda warned Nandin that he might have him join Brahman and asked him to leave right away. Then Rudra and Umā finally made their son release Brahman and he taught Brahman the secrets of the praṇava, associating it with the Yajurvedic/Sāmavedic incantation  subrahmaṇyom । (the mantra used in the Soma ritual to invite Indra for the libation).
-Kumāra initiated the campaign against the Asura-s by marching against the fortress of Tāraka.
-Skanda sent Vīrabāhu to launch an attack on Tāraka and Krauñca (an asura who had assumed a mountainous form due to a curse of Agastya).
-Being informed by his spies of the assault, Tāraka sallied forth to meet the gaṇa-s led by the nine vīra-s. Fierce encounters took place between Vīrakesarin, Vīrabāhu and Tāraka. Vīrabāhu repelled Tāraka’s māyā with the Vīrabhadrāstra. Tāraka drew Vīrabāhu into a feigned retreat and traps him in the mountainous cavern of Krauñca, putting him to sleep. He then routed the gaṇa-s showering missiles on them. Tāraka is described as having an elephantine head.
-Skanda entered the field to rally his gaṇa-s with Vāyu as his charioteer. Skanda routed the Asura-s. Taraka said that while he is a foe of Indra and Viṣṇu, he had no enmity with Rudra. But Skanda pointed to his sins and crimes against the deva-s and attacked him. After a fierce fight, Skanda cut off his trunk and tusks and pierced his head. He fell unconscious but on getting up he hurled the Pāśupata missile at Skanda. Skanda caught it with his hand and took it for himself. Tāraka then asked Krauñca to aid him with his māyā. After repulsing their magic, Skanda finally killed both Tāraka and Krauñca with his śakti.
-Skanda took his station at Devagiri and gifted the Pāśupata missile he had caught to Vīrabāhu.
-Rājanīti section where the court suggested to Śūrapadma, who was enraged by the death of Tāraka, that they should avoid a confrontation with Rudra’s party.
-Skanda goes on a mostly Śaiva (apart from Kañci and Veṅkaṭācala, where Skanda is said to have run away when Umā did not give him the mango) pilgrimage.
-Skanda releases the Pārāśara-s from a curse they had gotten from their father due to their cruelty towards fishes in their youth.
-Skanda goes to Śentīpura.

The Sambhava-kāṇḍa ends here. We believe that the core of this kāṇḍa derives from an older Kaumāra tradition that was of pan-Indospheric distribution. The structure of the narrative is such that Śūrapadma and Siṃhamukha, who are unique to the Southern tradition, only have a minor role in it. The break in the narrative between the killing of Tāraka and Krauñca on one side of the remaining Asura-s on the other side supports that part as being an accretion to this archaic core.

2) The Asura-kāṇda. From here on the narrative starts paralleling the Rāmāyaṇa in several ways.
-Asurendra, the lord of the Asura-s and his wife Maṅgalakeśī birthed a daughter named Surasā. She became a student of Uśanas Kāvya and acquired the moniker Māyā due to her proficiency in Māyā. When she reached adulthood, Kāvya lamented the condition of the Asura-s due to their crushing defeats at the hands of Indra and Viṣṇu. He asked her to have sons of great might through Kaśyapa and have them learn the praxis of ritual from him.
-Seduced by the beauty of Surasā, Kaśyapa abandoned his austerities and cohabitated with her. From their coitus when they assumed celestial forms Śūrapadma was born. When they engaged in coitus as lions, Siṃhamukha with a leonine head was born. From their coitus as elephants Tāraka was born with an elephantine head. When they mated in the form of goats they birthed the demoness Ajāmukhī. Taking many other animal forms they birthed several other fierce Asura-s. From their sweat, during each intercourse, numerous other demons arose.
-Kaśyapa then taught his sons the Śaiva lore.
-Then abandoning Kaśyapa, Surasā took her sons away and instructed them to perform a great sacrifice to Rudra to gain boons from him.
-Having pleased Rudra with his mighty ritual, where Śūrapadma offered himself as the oblation, he obtained the boons of the overlordship of a 1008 galactic realms (aṣṭottara-sahasrāṇām aṇḍānāṃ sarvabhaumatām ।), overlordship over the gods with enormous equipment and wealth, an adamantine body, invulnerability and the Pāśupata missile. Rudra granted him and his brothers such boons with the condition that no force except that originating from Rudra himself could destroy them.
-Armed with these boons and blessed by Kāvya, the Asura-s attacked Kubera and conquered his realm, taking him prisoner.
-They then conquered the realms of the gods and subjugated them.
-Viṣṇu fought Tāraka for long but realizing his invulnerability from Rudra’s boons retreated after congratulating him.
-Śūrapadma then had Tvaṣṭṛ build great forts for himself and his brothers.

At this point the narrative takes detour into Agastya cycle.
-Ajāmukhī forced Durvāsas to engage in congress with her. As a result, she birthed two sons Ilvala and Vātāpi. They went to Durvāsas and asked him to transfer his tapas power to them. He refused but offered them an alternative boon. They remained adamant and got into an altercation with him. He escaped from the place with his magic after cursing them that someday Agastya will slay them.
-They obtained their peculiar boon of resurrection from Brahman.
-They slew many brāhmaṇa-s through their well-known goat trick.
-They were finally slain by Agastya, who digested Vātāpi and hurled the Pāśupata that he had obtained from Rudra at Ilvala slaying him.
-Śūrapadma tried to abduct Indrāṇī. The Asura-s caused a drought; as a consequence they dried up Indra’s gardens.
-With the aid of Vināyaka, Indra caused the Kāverī river to flow out of Agastya’s pot and water the gardens.
-After the churning of the ocean, Rudra wanted to engage in coitus with Mohinī, the alluring female form of Viṣṇu. Viṣṇu indicated that it was impossible. Rudra pointed out that Viṣṇu was actually one of his śakti-s and thus a valid female. They copulated beneath a Sāla tree in Northern Jambudvīpa. The sweat from their passionate intercourse gave rise to the Gaṇḍakī river. In it, the mollusks known as vajradanta-s gave rise to the Sālagrāman-s used in the worship of Viṣṇu.
-From their conjugation, the god Śāstṛ was born.
-Rudra placed Śāstṛ in charge of protecting Indrāṇī from abduction.
-Śāstṛ in turn brought in Mahākāla as the bodyguard for Indrāṇī.
-Ajāmukhī and her friend Durmukhī tried to abduct Indrāṇī for Śūrapadma. However, Mahākāla swung into action and chopped off their hands.
-Ajāmukhī complained to Śūrapadma of her dismemberment.
-Śūrapadma forced Brahman to heal her and Durmukhī.
-Śūrapadma’s son Bhānukopa seeking revenge attacked the realm of Indra.
-He fought a fierce battle with Jayanta, the son of Indra, and eventually took him prisoner.
-Unable to find Indra or Indrāṇī, Bhānukopa destroyed the realm of Indra.

3) The Vīramāhendra-kāṇḍa.
-Before attacking the fortress of Vīramāhendra, Skanda sent Vīrabāhu as a messenger to Śūrapadma to ask him to peacefully surrender, release the deva-s he had incarcerated and return their realms that he had occupied.
-Vīrabāhu went to the Gandhamādana mountain and prepared to fly to Vīramāhendra. He mounted the massif assuming a gigantic and fierce form and laughed terrifyingly (aṭṭahāsa). He felt like extending his arms so that he could crush the Asura-s fortifications and cities with his hands like an oil-press crushing sesame seeds.
-As he pressed on the mountain the surviving warriors of Tāraka who were hiding in the caves came forth and were crushed by Vīrabāhu.
-Thinking of his guru, Skanda, Vīrabāhu flew into the sky causing the world to quake as he sped through the welkin.
-As he arrived at Lankā, which was the capital of Śūrapadma’s general Vyālimukha (who was visiting his lord), he was challenged by his deputy Vīrasiṃha and his troops. After a quick fight, Vīrabāhu chopped off Vīrasiṃha’s arms and head with his sword.
-Vīrabāhu leapt on Lankā and pushed it under the ocean.
-Vīrabāhu was then attacked by Vyālimukha’s son Ativīra and his troops who emerged out of the water. Vīrabāhu cut down the daitya troops and took on Ativīra who fought with a cleaver obtained from Brahman. However, Skanda’s Vīra cut his head off.
-Flying a thousand yojana-s he reached Vīramāhendra. As he was wondering which might be the best gate to make an entrance he arrived at the southern gate. There, he was challenged by Gajāsya, a monstrous demon with a thousand trunks and two thousand arms. After a closen fight, Vīrabāhu chopped off his trunks and hands and slew him with a kick.
-Realizing that this fight would bring more Asuras into the fray, he used his magic to become minute and entered via the eastern gate.
-There he saw the enslaved gods and the dwellings of mighty demons.
-Kumāra appeared in the dreams of Jayanta and the gods who were being subject to indignities by the Asura-s. Skanda told them that he had already killed Tāraka and Krauñca and that he had sent Vīrabāhu as his emissary who would wreak havoc among the Asuras. He assured them that thereafter he himself would attack the Dānava stronghold and slaughter them.
-Vīrabāhu met Jayanta and the other imprisoned gods and told them that their sufferings were due to their siding with Dakṣa during his ritual. He assuaged them by stating that the spear-wielding god would destroy the Asura-s and relieve them shortly.
-Vīrabāhu audaciously appeared before Śūrapadma and intimated him of the conditions for his surrender placed to him by Skanda.
-Śūrapadma rejected the terms and sent his general Śatamukha to capture Vīrabāhu. A fierce battle broke out between them during which Vīrabāhu demolished 20,000 Asura fortifications. In the end, he slew Śatamukha by thrashing him.
-Taking a giant form he crushed many other Asura warriors.
-Uprooting a mountain he smashed the Asura city.
-After another fierce fight, Vīrabāhu slew Śūrapadma’s ten-headed son Vajrabāhu by chopping off his heads with his sword.
-As Vīrabāhu was flying away, the polycephalous Vyālimukha challenged him. Another fierce fight ensued and Vīrabāhu finally killed him by chopping off his heads.
-Returning to Śentīpura, Vīrabāhu bowed thrice to Skanda.
-The Asura-s rebuilt their capital demolished by Vīrabāhu and prepared to fight Skanda.
-Skanda built the fort of Hemakūṭa as the base for this attack on Vīramāhendra.
-Śūrapadma’s spies informed him that Kumāra was gearing for an attack on Vīramāhendrapura.
-He called his son Bhānukopa and asked him to attack Skanda and his troops right away as they had approached the Asura city and fortified themselves at Hemakūṭa.

4) The Yuddha-kāṇḍa.

ṣaṇmukhaṃ dvādaśa-bhujaṃ triṣaṇṇayana-paṅkajam । kumāraṃ sukumārāṅgaṃ kekī-vāhanam āśraye ॥

-Bhānukopa donned his armor and mounting his car sallied forth with numerous Asura heroes.
-Skanda sent heavily armed, ruby-colored Vīrabāhu at the head of the bhūtagaṇa-s to intercept him. Wielding a bow like the pināka of Rudra he sallied forth. The two armies met amidst a shower of arrows from warriors on both sides.
-The fight was evenly poised but eventually, the gaṇa-s of Skanda started gaining an upper hand as the bhūta commanders slew their Asura counterparts.
-Seeing his forces retreating from the assault of the bhūtagaṇa-s of Skanda, Bhānukopa rallied them back. Bending his bow to a circle he released an unending stream of arrows on them striking down many and causing the gaṇa-s to fall back. Seeing this, the gaṇa Ugra got close to Bhānukopa and attacked him with a rod. Bhānukopa destroyed that rod with his arrows and struck down the gaṇa with the Brahma-spear. Then the gaṇa Daṇḍin attacked Bhānukopa with a mountain and struck his chariot and driver. Bhānukopa furious felled Daṇḍin with a shower of arrows. Next, he fought the gaṇa Pinākin who had rushed at him and struck him down with a shower of thousand arrows. Thereafter, several other gaṇa-s mounted a massed attack on Bhānukopa who routed them with his unending shower of arrows.
-He then fought the navavīra-s of Skanda. Vīrasiṃha was struck down by the Nārāyaṇa weapon of Bhānukopa.
-Then Vīramārtāṇḍa attacked the Asura. He got close to Bhānukopa and broke his bow; however, Bhānukopa struck him down with his cleaver.
-Vīrarākṣasa next attacked him from close quarters and both fell to the ground. Bhānukopa recovered consciousness and mounting a fresh car resumed the battle. Five of the remaining Vīra-s surrounded him and fought a great bow-battle for a while. Striking some of them down and brushing aside the rest he rallied the Asura troops and marched straight at Vīrabāhu.
-They fought a terrific battle in which both lost their bows but taking up new bows resumed the assault. Vīrabāhu smashed Bhānukopa’s helmet but he donned a new one and continued. Finally, tiring from the fight, Bhānukopa swooned.
-Immediately, the Asura forces surrounded their hero to protect him even as the gaṇa-s recovering from his assault surged forward. By then Bhānukopa stood up and continued the battle with Vīrabāhu.
-Despite all his attempts he could not dispel Vīrabāhu’s showers of arrows. Hence, he deployed the Mohāstra, a missile that caused the gaṇa-s to be paralyzed and fall to the ground. Even Vīrabāhu was paralyzed in his car. Taking advantage of this Bhānukopa shot numerous arrows at Skanda’s forces drenching them in blood.
-Skanda seeing his gaṇa-s in dire danger fired the Amoha missle from Hemakūṭa. This destroyed the Mohāstra and revived all the gaṇa-s.
-Seeing the nullification of all his tactics, Bhānukopa retreated for the day deciding to resume the battle later.
-Realizing the seriousness of the situation, Śūrapadma himself decided to join the battle. He sallied forth along with Atiśūra, the son of Siṃhamukha and Asurendra, the son of Tāraka.
-Indra saw them and informed Skanda of the impending attack. Having saluted Indra, Skanda decided to lead his forces personally in the battle. Indra asked Vāyu to be Skanda’s charioteer.
-A great battle broke out between the gaṇa Ugra and Atiśūra. Atiśūra discharged numerous divine missiles at his adversary but they failed because Skanda provided immunity against those missiles to his follower. Finally, Atiśūra discharged the Pāśupata, but it did not harm its own party and returned to Mahādeva. Frustrated thus, he leapt out of his car and struck Ugra with a rod. However, Ugra survived that blow and snatched the weapon from the demon and pummeled him to death with it.
-Tāraka’s son Asurendra rushed to shore up the ranks after his cousin’s death. He faced the gaṇa-s Kanaka, Unmatta, Siṃha, Daṇḍaka, and Vijaya in fierce encounters, defeating each of them.
-Then Vīrabāhu flew in on his car and started showering arrows on the demon. After a prolonged encounter, Vīrabāhu smashed his enemy’s chariot. The two engaged in a great battle flying in the skies, with Asurendra wielding a rod and Vīrabāhu, a sword. The latter finally beheaded Asurendra.
-Seeing his nephews slain, Śūrapadma launched a fierce attack on the bhūtagaṇa-s. He was attached by the nine Skanda-vīra-s. Fierce fights took place between him and Vīrarākṣasa, Vīramahendra, Vīradhīra, and Vīramāheśvara in that order and he overcame all of them. Vīrabāhu then entered the fray to shore up his half-brothers. He deployed the Aindra and Vāruṇa, Brahma, Vaiṣṇava missiles on the demon and Śūrapadma countered those with his Māyāsurāstra. Then both deployed the Pāśupata missile but it returned back to the respective users. Then they both deployed śakti-s that neutralized each other. Finally, Śūrapadma struck Vīrabāhu on his chest with a daṇḍa.
-Seeing his champion’s discomfiture, Kārttikeya attacked Śūrapadma and a great fight ensued. Bending his bow Skanda fired a profusion of arrows at the Asura lord. They cut each other’s shafts in mid-flight. Śūrapadma hurled his śakti at Skanda, who cut it off with 14 arrows. Then Śūrapadma uttering a loud roar hurled a trident at Skanda who cut it off with four and the seven arrows thereafter. Then with another missile, Skanda smashed the helmet of Śūrapadma and destroyed his armor with further shafts.
-Thereafter, the six-headed son of Ambikā hurled a cakra and cut down the Asura hordes that accompanied Śūrapadma and the piśāca-s feasted on their corpses.
-Śūrapadma replenished his gear and returned to the fight. He tried deploying many divine missiles but they were all nullified by Kumāra with his śakti missile. Thus, on the brink of defeat, Śūrapadma vanished and flew back to his fortified city thinking he would return later to fight Kumāra.
-Skanda ordered his bhūtagaṇa-s to storm the fortifications of the Asura stronghold.
-The gaṇa-s launched a massive assault on the fortifications of Vīramāhendrapura. In course of this assault, they killed the demon Atighora.
-Bhānukopa sallied forth again to fight Vīrabāhu, this time armed with his grandmother Māyā’s Sammohana missile.
-After prolonged use of various missiles both tried to get better of the other with the Pāśupata. Both Pāśupata missiles neutralized each other.
-At this point, Bhānukopa deployed his grandmother’s Sammohana missile, which not only made Vīrabāhu but also the rest of the Skandapārṣada-s unconscious and hurled them into the ocean.
-Bhānukopa returned to this father to tell him of his great victory and promised him that he would head out the next day to slay Skanda.
-On receiving intelligence that his army had been drowned by Bhānukopa, the six-headed son of Rudra launched his śakti, which sped to the ocean, and, destroying the Sammohana weapon, led his forces out back to the Asura capital.
-The Skandapārṣada-s now launched a ferocious assault on the defenses of the city. The Asura Vyāghrāsya advanced to defend the fortifications. He was slain after a trident fight by the Skandagaṇa named Siṃha.
-As the Skandapārṣada-s demolished the defenses of Vīramāhendrapura, Vīrabāhu hurled the Āgneya and Vāyava missiles and set the city on fire.
-Śūrapadma’s men informed him of the reversal and the impending destruction of his city by the fires. He brought in the mahāpralaya clouds to douse the fires. As they were putting off the fires, Vīrabāhu struck back with the Vāḍava missile to vaporize the clouds. Seeing the havoc in his city, Śūrapadma wanted to head out himself to fight Skanda and his forces.
-Just then Śūrapadma’s son Hiraṇya came to him and told him that it might be prudent to surrender to the six-headed son of Rudra, reminding him that there was no one who could counter him and his dreadful gaṇa-s.
-Śūrapadma warned his son that he would kill him if continued speaking thus. Hiraṇya calmed him down and decided to enter the battlefield himself.
-Hirāṇya baffled the Skandapārṣada-s for a while with his display of māyā. Finally, his māyā was overcome by the Cetana missile shot by Vīrabāhu. Hirāṇya fought Vīrabāhu for a while but the latter cut his bow and smashed his car with his astra-s. Hirāṇya knew that he would be killed shortly. He also realized that nobody would be left to perform the funeral rites for his family once Skanda’s troops stormed the city. Hence, he took the form of a fish and vanished into the ocean.
-Śūrapadma’s son Agnimukha next took the command of the Asura forces and led them against the Skandagaṇa-s with a vast force of Asura-s. In the battle that followed, Vīrapuraṃdara slew the Asura-s Somakaṇṭaka and Megha with his arrows. After a pitched battle, Agnimukha slew seven of the Vīra-s, barring Vīrapuraṃdara and Vīrabāhu with the Pāśupata. Agnimukha the advanced on Vīrabāhu. After an even astra-fight, Agnimukha got Bhadrakālī to fight on his behalf. Vīrabāhu defeated her and she left saying no one could stop the Skandapārṣada-s. Then Agnimukha returned to the fight showering thousands of arrows. Vīrabāhu hurled the Vīrabhadrāstra which burst Agnimukha’s head.
-As Vīrapuraṃdara and Vīrabāhu were lamenting the fall of their brothers, the latter flared up and shot an arrow into Yamaloka engraved with the message that, he the younger brother of Kārttikeya, wanted Yama to release his seven half-brothers. Duly Yama released their ātman-s and they reanimated their bodies.
-A great battle next took place between three thousand Asura-s born of Śūrapadma and a thousand of the chief Skandapārṣada-s. The battle was evenly poised for a while, but the Asura-s started gaining the upper hand as their severed limbs were restored by a special gift they had obtained from Brahma. Hence, the gaṇa-s turned to Skanda, who appeared in their midst, and gave one of their leaders, Vijaya, the Bhairava missile. As he deployed it, one of three thousand Asura-s named Matta deployed the Māyāstra. However, the Bhairavāstra destroyed it and cut off the heads of all three thousand Asura-s.
-Next, Dharmakopa, another son of Śūrapadma advanced with his troops against the Vīra-s. His troops were destroyed by the Vīras-s even as Dharmakopa closed in on Vīrabāhu. After an exchange of missiles, Dharmakopa struck down Vīrabāhu’s charioteer. Then they engaged in a closen fight where Dharmakopa tried to strike Vīrabāhu with a rod and then a thunderbolt. Evading both, Vīrabāhu killed him with a kick.

-Bhānukopa received the news that while he thought he had won, the forces of Skanda had returned and wreaked enormous destruction on the Asura-s. He told his father perhaps it was a futile attempt, and they should surrender to Skanda. His father refused; hence, Bhānukopa set forth again to fight the Skandapārṣada-s. After a great fight Bhānukopa overthrew the bhūtagaṇa-s attacking him and rushed forward with a shower of arrows. Vīrabāhu bent his bow and destroyed the missiles hurled by Bhānukopa. Thereupon, Vīrabāhu hurled a śakti and struck Bhānukopa. However, recovering from the blow he resumed the fight. For a while, neither could get better of the other in their exchange of astra-s. Bhānukopa then baffled Vīrabāhu with his māyā powers. Vīrabāhu destroyed the māyā display with his own magic. As their fight raged on, Bhānukopa smashed Vīrabāhu’s chariot. But Vīrabāhu retaliated by breaking the Asura’s chariot and cutting his bow with his shafts. Finally, they closed in for a sword fight. Vīrabāhu chopped off the right hand of Bhānukopa but he took the sword in his left and continued. Vīrabāhu cutoff that hand too. Handless, he tried to deploy the Māyā missile but Vīrabāhu swept his head away with a blow from his sword.
-Śūrapadma on hearing of the death of his son fainted. He lamented much when he received his son’s mutilated body parts. He called his brother Siṃhamukha to come from his city of Āsurapura to join the fight. Shocked by the news of the defeat of the Asura-s, and the death of his sons and nephews, Siṃhamukha flew over from his city to aid his brother.
-Donning his armor, he set forth for battle with his great troop of Asura-s. Skanda called Vāyu to get his chariot ready. Vīrabāhu with his half-brothers wanted to lead the 100,000 Skandapārṣada-s to the encounter first. Skanda let him do so and a fierce fight ensued. Showering balls, arrows, axes, and plows on the gaṇa, the great lord of the Asura-s advanced. His demons fought several gaṇa-s in melee as they exploded each other’s weapon discharges to smithereens. Vīramārtāṇḍa used the Jñānāstra to counter the māyā being deployed by the demons. Siṃhamukha cut through the gaṇa ranks like a great mountain on the move. He put to flight the 100,000 Skandapārṣada-s with showers of missiles. He then proceeded to crush them as though one would crush mosquitoes. Seeing this, Vīrabāhu counter-attached showering thousands of arrows with his bow. The hundred sons of Siṃhamukha surrounded him and returned the showers of arrows. With his missiles, Vīrabāhu smashed their chariots and broke their bows. Then they rushed at him with their swords but Vīrabāhu slew all hundred with an arrow and his sword.

-Infuriated and saddened by this, Siṃhamukha rushed at Vīrabāhu. They ground each other’s missiles to dust and had a prolonged astra fight. Vīrabāhu slew his charioteer. Siṃhamukha hurled a gadā at him, but it burst on striking his adamantine form born of Rudra. Vīrabāhu then demolished the Asura’s car. He resumed the battle taking new cars over and over again and deploying thousands of bows. Vīrabāhu kept breaking them repeatedly. Seeing himself unable to get better of Skanda’s warrior, Siṃhamukha deployed the Māyāpāśa. The great lasso weapon immediately bound Vīrabāhu and the gaṇa-s who were on the field and hurled them atop the Udaya mountain in a state of paralysis. Sensing victory, Siṃhamukha roared loudly and thought that Skanda too had fled. However, his spies informed him that Skanda was still very much there with the remaining gaṇa-s at Hemakūṭa. Mātariśvan informed Skanda of the events and Siṃhamukha’s advance towards their fort.
-Mounting his car driven by Vāyu, Skanda led his forces into battle. In the battle that ensued the Asura-s began to retreat. At that point, Siṃhamukha assumed a gigantic form with two thousand arms. Grabbing all the gaṇa-s of Skanda he swallowed them. Śūrapadma’s spies informed him of his brother’s deeds and he ascended an observation turret to see the great form of his brother.
-Skanda then strung his bow and twanged the string causing the whole universe to resound and the Asura vehicles fell to the ground from the sound emanating from the bow twangs of the son of Umā. Siṃhamukha rushed at him to do battle. Kumāra fired a mighty missile that split open the firm belly of the demon and from the fissures through which blood was pouring out, some of the gaṇa-s who had been swallowed emerged forth. Stanching the slits in his belly with his many arms, the demon hurled a dreadful rod at Skanda. He split it up with four missiles, which then proceed the strike the demon on his forehead. Losing his strength, he lifted his hands off his belly and the remaining gaṇa-s too escaped.
-Skanda then fired a missile that proceeded to the Udaya mountain and destroyed the Māyāpāśa. Then turning into an airplane the missile brought Vīra-s and gaṇa-s back to the field and returned to the six-headed god’s quiver.
-To shore up their leader, the Asura-s who had retreated returned to attack Skanda upon hearing his terrifying roar. As they surrounded the god, he hurled thousands of projectiles and also attacked the demons with rods, swords, spears and axes. Vāyu maneuvered the car with great speed even as Skanda dispatched his missiles that lit up the entire universe like the Vaḍava fire. The great god pierced the many galactic realms with his weapons and rent asunder the limbs of the demons and shattered their vehicles. The cluster missiles shot by Skanda branched repeatedly giving rise to crores upon crores of arrows and penetrated all the galactic realms slaying numerous Dānava-s wherever they were. Seeing these weapons being fired by their commander, all the deva-s sang the praises of the son of Rudra.
-The whole field was filled with corpses of the demons. Wielding a thousand bows Siṃhamukha again attacked the commander of the deva-s.
-He then struck Vāyu on the chest with numerous arrows and the god fainted. But Skanda controlling his own car destroyed the Asura’s chariot with a hundred arrows. Then with a thousand arrows, the son of Mahādeva, cut down all the bows of the demon at once. Siṃhamukha hurled a trident at the god, who cut it down with fourteen arrows. Then he rushed at the god with a rod who powdered it with seven shafts. The demon then sent the death-dealing pāśa but Skanda cut it up with a thousand projectiles. Then he cut up the two thousand arms of the Asura. The great demon (termed māhāmada here) uttered a “mahākilikilārāva” and rushed at Skanda. The god sliced off his thousand heads with an equal number of arrows.
-Siṃhamukha regenerated his severed limbs and reentered the fray. Skanda let this happen eight times as part of his battle sport. Then he cut all his hands except for a pair and heads except for one. The demon roared that he would slay the god with just those and uprooted a mountain and rushed at his adversary. Kārttikeya rent asunder that mountain with a single arrow. The Asura now attacked him with a terrifying daṇḍa. Thereupon, Guha hurled his vajra which blazed up like several crores of suns. It destroyed that daṇḍa and striking the Asura on his chest annihilated him.
-Having bathed in the Celestial Gaṅgā Kārttikeya returned to the Hemakūṭa fort with his Vīra-s and gaṇa-s.

-Hearing of the death of his brother from his agents, Śūrapadma fell down from the observation turret he had mounted to witness the battle. Regaining his composure, he decided to himself lead the Asura-s in the war against Guha. He ordered all the surviving Asura-s from the numerous galactic realms that he controlled to come over and join him for the battle.
-Mounting his special battle car armed with all the divine missiles, with a great force of Dānava-s he headed out of his fortified city with their roars filling the whole universe.
-The gods called on their commander Skanda to enter the field against the evil demon. Worshiped by all the gods and his 100,009 Vīra-s, Skanda took up all his weapons and set forth for battle on the car driven by the god Vāyu:
ādāya paraśuṃ vajraṃ śūlaṃ śaktiṃ vibhīṣaṇāṃ ।
khaḍgaṃ kheṭaṃ bṛhac cakraṃ daṇḍaṃ musalam eva ca ॥
dhanuś-śarān mahāghorāṃs tomarāṇi varaṇy api ।
vinirgatya rathaṃ ramyaṃ vāyunā nītam agnibhūḥ ॥
āruroha surais sarvaiḥ pūjitaḥ puṣpa-vṛṣṭibhiḥ ।
nava-saṃkhyādhikair lakṣair vīrair api mahābalaiḥ ॥

-The other gods asked Viṣṇu if Kārttikeya might meet with success in the impending encounter. Viṣṇu assuaged their doubts saying that their troubles would end soon as Skanda would definitely triumph.
-As the battle was joined, Śūrapadma’s demons charged with a great shower of weapons. Skanda twanging his dreadful bow, which resounded like the flood at the end of the Kalpa, entered the field. He launched into an orgy of slaughter with his missiles reaching the limits of the universe. Wherever the demons went, his bolts cruised after them. Breaking through the walls of the galactic realms they entered whichever region the Asura-s flew to and slew them. Floods of blood and mountains of corpses of the Asura warriors started to pile all around.
-Furious, Śūrapadma joined the fray and laid low most of the Skandapārṣada-s with his terrifying missiles. Vīrabāhu rushed forth to engage him and cut his bow with his cleaver. But Śūrapadma punched with his fist and he fainted. Deciding not to kill him for he was just a messenger of Skanda, Śūrapadma seized by his feet and hurled him into the sky.
-He then charged at Skanda and engaged him in a fierce bow battle with the exchange of innumerable arrows. Finally, Śūrapadma struck down the flag of Skanda with a shower of arrows and blew his conch as a mark of victory. Skanda however quickly retaliated cutting and hurling Śūrapadma’s banner into the sea with seven shafts. Then, the thousand-headed gaṇa Bhānukampa blew on a thousand conchs and Viṣṇu too blew on his. Agni turned into the cock banner and went to adorn the car of Guha. The cock crowed loudly. All this created a terrifying din.
-Angered, Śūrapadma now turned to the gods were and attacked them with his weapons. Skanda followed him with Vāyu driving his car at top speed. Skanda protected the gods and attacked the demon with a shower of weapons. As the chariots of the two of them wheeled around in battle the whole universe to vibrated violently and whole mountains were reduced to atoms.
-Śūrapadma attacked his enemy with halāyudha-s, bhindipāla-s, kuliśa-s, tomara-s and paraśu-s. Then Skanda destroyed his vehicle completely with fourteen missiles.
-The demon then mounted the Indralokaratha (the space-station he had captured from the gods) and started tunneling into the various galactic realms he had conquered. However, he found the tunnels into them blocked by the arrows of Mahāsena and found that many of his demons were trapped in each one of them. He broke down the obstructions with his weapons and let out his demons. Those Asura-s came out and mounted a furious attack on Skanda. With his cakra, paraśu, daṇda and musala the son of Umā slaughtered them, and chasing them to each of the realms, he burnt them down with his weapons to a fine ash.
-The Asura then deployed the deadly Sarvasaṃhāraka-cakra, but Mahāsena sportingly captured it for himself. Next, he tried māyā tactics but Skanda easily overcame those with the Jñānāstra.
-Thus, defeated he finally went to his mother and asked if she might have a means of victory. She told him that she did not see a way out against the son of Rudra, but the only thing he could do is to get the Sudhāmandara mountain to revive the dead demons.
-He mounted a lion-vehicle and sent the Indralokaratha to bring the said mountain. The craft brought the Sudhāmandara to the field and the wind blowing from it started reanimating the dead demons. Seeing this, Skanda deployed the Pāśupata missile that started branching and emitting numerous Rudra-s, the Marut-s, Agni-s and vajra-s. These destroyed all the reanimated demons and also the vivifying mountain. Thereupon, the Asura sent the Indralokaratha to scoop up Vīrabahu and the remaining 100,008 troops of Skanda and stupefy them. Guha retaliated with a series of missiles that grounded the craft and brought it back to him. The gaṇa-s got out of it safely and the space-craft became the property of Skanda.
-Then the Asura injured Vāyu with his shafts and briefly Skanda’s chariot was out of control. But regaining control he cut the bow of the demon. Śūrapadma thereafter attacked him with the terrifying missile known as the Sarvasaṃhāraka-śūla. Skanda shot numerous arrows to destroy his lion-vehicle and then hurled the Ghora-kuliśa that neutralized the said śūla and brought it back to Skanda.
-The Asura assumed the form of a gigantic fierce bird and started pecking at Skanda’s car and blowing his gaṇa-s away with the blasts from his wings.
-Skanda then looked at Indra and the latter took the form of a peacock. Mounting the peacock Skanda and Indra fought the demon. Indra pecked him and clawed him in the form of the peacock, even as Skanda pierced him with many arrows. Śūrapadma dived in his bird form and broke Skanda’s bow, but Guha drew out his sword and hacked the bird-formed demon to pieces.
-The demon then took the form of the earth. Skanda taking a new bow drowned that earth-formed demon with the oceanic missile. The demon then took the form of the sea. With a hundred fiery missiles Skanda dried up that form. He successively took various forms, including the gods, but Skanda destroyed all of those with his missiles.
-Finally, to reveal that those forms of the demon were merely fictitious forms, Skanda assumed his macranthropic form with all existence and all the gods comprising his body — the planets and stars his feet; Varuṇa and Nirṛti his ankle joints; Indra and Jayanta his thighs; Yama and time his hips; the nāga-s and the ambrosia his genitals; the gods his ribs; Viṣṇu and Brahman his arms; the goddesses his fingers; Vāyu his nose; Rudra his head; the numerous galactic realms his hair follicles; the omkāra his forehead; the Veda his mouth; the Śaivāgama-s his tongue; the seven crores of mantra-s his lips; all knowledge his yajñopavīta.
-Seeing this macranthropic form of Kumāra, Śūrapadma had the doubt for the first time in his existence if after all this god might be undefeatable — many great Asura-s had fought him and many great missiles, which were previously infallible had been, used yet he triumphed over all of those. However, the demon brushed aside these feelings and assumed a gigantic form with numerous arms, heads and feet, and casting great darkness that enveloped the whole universe he rushed forward to eat Skanda and the other deva-s.
-Skanda immediately hurled his mighty śakti. Blazing like crores of suns it destroyed the overpowering darkness of the Asura and cruised after him. He dived into the sea of the fundament even as the śakti chased him there. The Dānava immediately became the “world-tree” — a giant mango tree stretching across the limits of the universe. Blazing like the trident of Rudra, the śakti split that tree in half. Śūrapadma assumed his own form and drawing his sword rushed at Skanda. The śakti struck him immediately and slew him.
-His remains were transformed into a peacock and a cock that respectively replaced Indra and Agni as the mount and the banner of Skanda, even as the two gods returned to their prior state. Thereafter, the gods praised Mahāsena for his glorious acts.
-Śūrapadma’s primary wife expired on hearing the news of his death and his son Hiraṇya who had hidden as a fish in the ocean performed the last rites of the dead demons with help of Uśanas Kāvya.

The final battle between Skanda and Śūrapadma has some mythic motifs of interest. First, the many transmogrifications of the demon in course of his battle with the god are reminiscent of the shamanic transformations. This motif is encountered in several distant traditions — most vividly in the folk Mongolian account of Chingiz Khan’s final fight with the Tangut emperor composed by his descendant Sagang Sechen (Also note the motif of the nine heroes of the Khan in that account). There, Khasar, the brother of the Khan (one of the nine heroes) plays a role similar to Vīrabāhu in destroying a witch who was guarding the Tangut capital and preventing the entry of Subetei. Khasar killed her with his arrows allowing the Mongols to storm it. Then the Khan and the Tangut lord fought a magical battle with both of them taking on many forms like a snake, Garuḍa, tiger, lion, and the like. Finally, the Khan took the form of Khormusta Khan Tengri (the great Mongol god) himself and put an end to the shape-shifting of the Tangut. Though he struck the Tangut with many arrows and swords he still could not kill him. ṭhe Tangut let slip the secret of his death in the form of a magical wootz steel sword hidden in his boot that the Khan seized and slew him. Thus, we suspect that the shape-shifting of Śūrapadma in the final battle is from an ancient shamanic layer of the Kaumāra tradition that is attested in the Saṅgam Tamil tradition (the muruka-veri, e.g., Tirumurukāṟṟuppaṭai 200-210).

Second, the final dive of Śūrapadma into the ocean and/or his transformation into a mango tree is a motif that has deep roots in Tamil Kaumāra tradition. It is mentioned in multiple Saṅgam texts such as: 1) Pattiṟṟupattu: here the Cēra king Neṭuñcēralātaṉ, who built a fleet to fight a naval battle with the Romans, is said to have destroyed his enemies even as Skanda cut down the tree of the Asura-s. 2) The Paripāṭal 18.1-4 mentions how Skanda pursued the demon into the deep ocean. Paripāṭal 5.1-4 mentions both his pursuit into the ocean and his destruction by the Skandaśakti in the form of a mango tree. 3) Tirumurukāṟṟupaṭai 45-46 mentions his pursuit into the ocean. Tirumurukāṟṟupaṭai 58-61 mentions his destruction in the form of the mango tree and also his centaur transmogrification, which is absent in the Purāṇa. We take these mythemes to be reflexes of the famous precessional myth — i.e., the shattering of the old world axis that is widespread across Hindu tradition and beyond. A variant of this myth is associated with the submerging of the old equinoctial constellation beneath the equator (the world ocean, e.g., the Varāha myth): thus, both of these are combined here in the final fight of Śūrapadma. Notably, both in the Pattiṟṟupattu and the Paripāṭal, Skanda is described as riding an elephant rather than a peacock in the final battle against Śūrapadma. This is probably an archaism as this elephant vehicle is mentioned in the ancient Kaumāra material found in the medical Kāśyapa-saṃhitā (129) as having been generated from Airāvata by Indra for Skanda.

5. The Deva Kāṇḍa.
-The rule of the gods is restored.
-Skanda is engaged to Indra’s daughter Devasenā.
-The marriage of Skanda and Devasenā.
-Skanda seeks the daughter of Viṣṇu born as Vallī in a sweet potato excavation among the pulinda hunter-gatherers.
-He appears as an old man to her. Gaṇeśa frightens her as an elephant, and she comes into the hands of Skanda in the form of the old man seeking help from the elephant.
-Vallī recognizes Skanda and starts a clandestine affair with him.
-When she elopes with Guha, the hunters, including Vallī’s brothers and father chase and attack Skanda, who strikes them down with his arrows.
-Kumāra revives the dead huntsmen and marries Vallī and returns to his abode with his two wives.
-The praise of emperor Mucukunda.
-Mucukunda installs the image of Rudra known as Tyāgarāja.

6. The Dakṣa-kāṇḍa
This section is mostly Śaiva material relating to the cycle of Dakṣa. One notable point is that here Rudra generates Vīrabhadra and Umā generates Bhadrakālī to destroy Dakṣa’s ritual. Notably, this parallels the Ur-Skandapurāṇa wherein Umā generates Bhadrakālī by rubbing her nose. There Rudra generates Haribhadra. This might indicate a connection to that ancient Skandapurāṇa version of the Dakṣa cycle. However, we may note that a similar situation is also seen in the Brahmapuraṇa ((39.51), where Rudra created the lion-formed Vīrabhadra, whereas Umā creates Bhadrakālī to accompany him. Further, interestingly, here as Vīrabhadra destroyed the male partisans of Dakṣa, Bhadrakālī destroyed the females of Dakṣa’s clan. This symmetry appears to be an ancient motif — in the Greek world we have Apollo kill the male Niobids while Artemis killed the female ones. Apart from the Dakṣa cycle, this kāṇḍa contains:
-The ṛṣi-s’ wives at Dārukavana run after Rudra. They attack him with various beings and he destroys them.
-The killing of Gajāsura by Rudra.
-Churning of the ocean and Rudra consumes the Hālāhala.
-The appearance of eleven crore Rudra-s at the Madhyārjuna shrine (Tiruvidaimarudur in the Drāviḍa country).
-The beheading of Brahman by Bhairava.
-Dharma becomes Rudra’s bull.
-Rudra destroys the universe and smears the residue as his ash.
-Rudra slays Jalandhara.
-The birth of Gaṇeśa.
-Jyotirliṅga-s and Aruṇācala.
-Paurāṇika geography.

7. Upadeśa-kāṇḍa
The only Kaumāra-related material in this kāṇḍa are: 1. The praise of Skanda’s peacock and chicken. 2. The “backstories” of the birth of Śurapadma, his mother and his clan. 3. The Skandaṣaṣṭhī festival.

The rest of this kāṇḍa is again largely Śaiva material pertaining to Śivadharma for lay devotees. Indeed, chapters in this section seem to self-identify as a Śiva-purāṇa. It begins with an account of the Rudra-gaṇa in Kailāsa. It contains several accounts of humble animals (including men like cora-s) attaining higher births from acts of Śaiva piety. Similarly, sinners who defile/steal from Śaiva shrines or take even things like lemons or bananas from them attain hell. The observance of key festivals of Rudra and the Bhairava-Vīrabhadra festival are laid out. Further, it gives the 1008 names of Rudra, the practice of Aṣṭāṅga-yoga, the theological principles of Siddhānta and the iconography of the twenty five images of Rudra that are displayed in Śaiva shrines.

It also contains accounts of: 1. Rudra destroying the Tripura-s. 2. Rudra slaying Andhaka. 3. The rise of the most terrible demon Bhaṇḍāsura. Rudra performs a fierce ritual, offering Brahman, Viṣṇu, Indra and other gods as samidh-s in a fire altar where he himself was the fire. From it arose the youthful goddess Tripurā who slew Bhaṇḍāsura. This minimal account lacks the details seen in the Lalitopākhyāna, where this myth takes the center-stage. 4. The killing of Mahiṣa by Durgā through the grace of Rudra as Kedāreśvara. 5. The killing of Raktabīja by Kālī and her dance with Rudra.

Some notes on the runiform “Altaic” inscriptions and the early Turk Khaghanates: Orkhon and beyond

The early Turkic inscriptions from Mongolia and their discovery
On February 27th, 731 CE (17th day of the Year of the Sheep), Kül Tegin, the great hero of the second Gök Türk (Blue Turks) empire, passed away in his 47th year (literally flew away to the realm of Tengri). He was greatly mourned by his clansman — his elder brother, Bilge Khaghan, the ruler of the Turks, had his elegy inscribed on the now-famous Kül Tegin funerary stele. On the northern face of the stele, we read:
“My younger brother Kül Tegin passed away. I mourned. My bright eyes seemed unable to see and my sharp knowledge seemed unable to know. I mourned. Tengri arranges the lifespan. Humans are born to die. I mourned thus: when tears were running out of my eyes, I restrained them; when lamentation was coming out of my heart, I held it back. I thought [of him] deeply. [I feared] the eyes and eyelashes of the two shad-s (title of generals; derived via contraction from Old Iranic kshāyathiya= warrior via Sogdian xshedh= chief), of my brothers, my sons, my officials and my people were to be ruined [because of tears]. I mourned.” (translation based on Talat Tekin, Hao Chen and Denison Ross]

On November 1 of 731 CE, Bilge Khaghan held a grand funerary ritual for his brother. It is said to have been attended by several dignitaries from East and West. Again, the inscription on the northern face of the monument states:
“General Udar, representing the people of Khitan and Tatabi, came to attend the funeral feast and mourned. From the Chinese Khaghan came the secretary Likeŋ. He brought ten thousand pieces of silk, gold, silver and various things. From the Tibetan Khaghan came Bölün. From Sogdiana, Bercheker (i.e., Persia) and Bukhara in the sunset west came General Enik and Oghul Tarkan. From the On Ok, from my son [-in-law] the Türgish Khaghan, came Makarach and Oghuz Bilge, who were officials holding seals. From the Kirghiz Khaghan came Tardush Inanchu Chor. The shrine-builders, fresco-painters, memorial-builders and the nephew of the Chinese emperor, General Zhang, came.”

The artisans who arrived with General Zhang helped furnish the Kül Tegin marble stone under the direction of Toyghut Elteber and funerary inscriptions were composed by Yollugh Tegin, son of Kül Tegin’s sister. This funerary stele bearing these inscriptions was erected the following year on August 1, 732 CE and the posthumous title Inanchu Apa Yarghan Tarkhan was conferred on him (c.f. the conferment of a comparable posthumous title on prince Tolui, the younger brother of the second Mongol Khan, Ogodei). On the stele, the great acts of Kül Tegin in raising the floundering Turk empire are narrated in the words of his brother Bilge Khaghan in almost epic terms. At this juncture, it is worth mentioning that the Ashina clan of Turks from which the Blue Turks hailed were married into the Tang royal family. Despite denials in some modern Chinese quarters, Taizong himself likely had immediate Turkic and/or Mongolic ancestry. They had played a central role in raising Taizong to the apex — a time when Turkic fashion was the rage in China — Taizong himself took on the title of the Khaghan graced by Tengri and had a funerary monument with imitations of the Turko-Mongolic balbal stones. However, on the other hand, he pursued an aggressive policy to annex the Turkic khaganate to the Tang empire. The events described on the stele follow the destruction of the original Turkic Khaghanate by the Tang. Thus, Bilge Khaghan, while narrating the biography of his brother, first talks of how the divinities aided their father to salvage the Turks when the Tang emperor decided to exterminate them:
“Without thinking of how Turks had fulfilled their allegiance, [the Tang emperor] said: “I shall kill the Türk people! I shall leave them no descendants!” The Turks were perishing. [However], Tengri of the Turks above, along with the goddess Yer (Earth) of the Turks and the water deity held my father Elterish Khaghan and my mother Elbilge Khatun at the top of the sky and raised them up so that the Turks would not perish and would become a nation.”

After describing the numerous campaigns of his father on the steppes, Bilge Khaghan moves on to talk of the achievements of himself and Kül Tegin:
“I did not ascend the throne over a prosperous people. The people over whom I ascended the throne were without food inside and without clothes outside, bad and evil. I discussed this with my younger brother Kül Tegin. So that the name and fame of the people, for whom my father and uncle had striven, should not disappear. I neither slept at night nor sat down in the daytime by reason of the Turk nation. I, together with my younger brother Kül Tegin and the two shad-s, toiled to exhaustion. Having thus toiled, I prevented the united people from being like water and fire. The people who had gone elsewhere when I was ascending the throne came back again, exhausted, on foot and naked. In order to feed these people, I campaigned twelve times with a sizable army northwards against the Oghuz people, eastwards against the Khitan and Tatabi people, and southwards against the Chinese. I battled against them there. Then, as Tengri blessed [me]; because of my good fortune and fate, I revived and fed the dying people. I clothed the naked people, and made the poor people rich. I enlarged the small population and made my people superior to those who had a strong realm and a powerful khaghan.”

Giving the biography of Kül Tegin he says:
“When my father, the khaghan [Elterish], died, my younger brother Kül Tegin was only seven years old. Thanks to the kindness of my mother Khatun, like the goddess Umai, my younger brother Kül Tegin became a grown-up man. When [Kül Tegin] was sixteen years old, my uncle, the khaghan, was working hard for his realm and laws. [When Kül Tegin was seventeen years old,] we went on a campaign against the Sogdians in the Six Prefectures and destroyed them. The Chinese prince commander came with fifty thousand. We fought. Kül Tegin fiercely charged on foot. He caught the prince commander’s brother-in-law with his own armored hands. Still armored, he presented [the captive] to the khaghan. We wiped out that army there.”

After giving a long account of his many battles he concludes with the great act of Kül Tegin during the siege by the Oghuz Turks:
“The enemy Oghuz laid siege to [our] royal camp. On a white Ögsüz (horse caught on the steppe?) [horse], Kül Tegin speared nine men. He did not lose the royal camp. [Otherwise] my mother the Khatun, together with my [step-] mothers, aunts, sisters-in-law, princesses, and the [other] surviving [women] would have become slave-maids, or their corpses would have remained lying in the abandoned campsites and on the road. If it had not been for Kül Tegin, you would all have died!”

An Altai petroglyph showing the Turks on a campaign clad in lamellar armor. Above the deer one can faintly see the ibex, the animal on the tamgha of the Ashina clan.

The Kül Tegin funerary stele is one of the five famous early Turkic stelae that record the history and great deeds of key figures from the second Turkic Khaghanate. Kül Tegin stele and that of his brother Bilge Khaghan were erected in Khoshoo-Tsaidam, Central Mongolia, by the Orkhon River in the 730s of the CE. A third monument describing the deeds of Tonyukuk, the prime minister and commander of the Turkic army, also the father-in-law of Bilge Khaghan, was erected at Bain Tsokto near modern Ulaanbataar, in the Tuul River basin. Given that it mentions the deeds of Tonyukuk as though he were speaking, it is disputed if this was a funerary stele or merely an autobiographical record of the deeds of the prime minister. Tonyukuk was prime minister and commander through the reigns of the Khaghan-s Elterish, Qapaghan, Inal and Bilge, dying at an advanced age in 725-726 CE. A record in Chinese prepared for a remote descendant of Tonyukuk during the Chingizid period mentions that he lived for 120 years (see below). This was almost 6 centuries after his time; hence, it can only be taken to mean that there was a clear memory of this long life rather than an exact record of his lifespan. The deeds recorded on the stele are more or less till 716 CE. This might mean that the stele was erected then or in the year of his death. It is possible he was a semi-retired in his last years during the reign of his son-in-law and thus had no additional deeds to record after 716 CE. The fourth monument, the Ongi monument (now badly damaged), was located at the confluence of the Tarimal River and Ongi Rivers. This was erected by Īshbara Tamghan Tarkhan, a cousin of Bilge Khaghan, for his father Eletmish Yabghu who may have died in an intra-family battle in 716 CE between the supporters of Inal Khaghan and Kül Tegin, who was trying to seize the throne for his brother Bilge Khaghan. This stele was likely erected between 725-732 CE. The fifth is the funerary inscription of Īshbara Bilge Küli Chur, who also appears to have had the title of Chikhan Tonyukuk. He is said to have lived to a full 80 years and “grown old” during the reign of Elterish Khaghan. His stele mentions him killing “nine ferocious men”, probably while still in his teens. He is also recorded as “fighting the Chinese so many times that he gained much fame by virtue of his courage and manly qualities…” As a minister and general of the Turk Khaghan who grew old in the reign of Elterish Khaghan, he might have preceded the famous Tonyukuk as the highest minister. The Küli Chur inscription does not mention Bilge Khaghan or Kül Tegin, suggesting that stele bearing it was likely erected during the late 600s or early 700s of CE.

The Bain Tsokto stele with the Tonyukuk inscription

The discovery of these monuments was among the greatest moments in archaeology as they are the earliest substantial written records of the history and the deeds of the Turkic people in their own words. The German, Philip von Strahlenberg, fighting on behalf of the Swedes, was captured by the Russians in 1709 CE during the battle of Poltava. As a prisoner in Siberia, he carried out an extensive ethnographic and geographic survey of the eastern possessions of the Rus. In course of this exploration, he observed runiform inscriptions on stones in the upper course of the Yenisei River in Southern Siberia (see below) — his account was the first notice of the old Turkic inscriptions in the modern era. However, their script and contents remained mysterious to him and they were mostly ignored thereafter. More than a century later, the Finnish explorers in Siberia rediscovered them in 1887-1888 CE. An year later, the Russian-born Siberian separatist, Yadrintsev, heard from Mongol pastoralists of the presence of inscribed stelae by the Orkhon river — these were what later came to be known as the Kül Tegin and Bilge Khaghan monuments. In the 1890s, the Finnish explorers and the Germanized Russian, Vasily Radloff, along with Yadrintsev conducted further separate explorations of the Mongolian sites. In 1891 CE, some Mongols led Yadrintsev to the Ongi monument and he made a realistic drawing of the same, recording the inscribed stele and the several balbal stones erected beside it — an important record, given the subsequent damage it suffered. These explorations made it clear that the Yenisei, Orkhon and Ongi inscriptions were all in a similar runiform script recording an ancient language.

The key to breaking the mystery of these inscriptions was offered by the Kül Tegin monument, which had a subsidiary inscription in old Chinese. It contained the condolence letter written by the Tang emperor on being informed of Kül Tegin’s death — evidently, he saw him both as a worthy rival and some kind of “colleague” given the links the Tang had with the Turks. The German Sinologist Georg von der Gabelentz was able to immediately recognize based on the work of the Finnish exploration that the inscription on the stele honored a Turkic prince. He published a translation of the Chinese inscription albeit replete with errors. This led to the Danish scholar Vilhelm Thomsen deciphering the runiform inscription based on his knowledge of the Turkish language in late 1893 CE. On the Russian side, in the same year, their ambassador in Peking showed the inscription to the Ching scholar Shen Zengzhi who provided similar suggestions regarding its identity. Subsequently, Radloff made a better translation of the Chinese inscription with the help of the Ching ambassador to Moscow and published the Turkic runiform Orkhon inscriptions. These were followed by editions and translations by Thomson, Radloff, and others. In the following years, Aurel Stein discovered a Turkic book on omenology-based dice prognostication (Irk Bitig) written in the same runiform script along with two Chinese bauddha hymns, evidently based on Sanskrit originals, in the hall of the thousand Buddha-s at Dun Huang. This text, either from the 700s or 800s of the common era, offered a further body of old Turkic material in the same script. Since then, thousands of papers have been written on these old Turkic texts leading to much improved readings of them.

The preservation of this book hints that the script was not just used for inscriptions but also in books. The Irk Bitig is unique in preserving purely Turkic content even if its author was a bauddha Turk — he says he wrote it for his elder brother, the general Itachuk, in a vihāra after having listened to a bauddha guru. The dice omenology of the text relies on using three Indo-Iranian style dice with four faces each. Thus, one gets combinations and one combination with two corresponding omens giving a total of 65 readings. Such dice have been recovered in the pre-Turk Kuṣāṇa site at Khayrabad Tepe, Uzbekistan (a parallel Hindu dice prognostication invoking deities such as Rudra, Viṣṇu, Ṣaṣṭhī, the Marut-s, Kubera, and the goddesses Mataṅgī and Mālinī is seen in the Bower manuscripts). It seems these omens are dreams — that leads to the question as to what function the roll of the dice played? We suspect there was a correspondence between the prognosis of the two — you either got a prognosis by the dice roll or if you had the corresponding dream. Alternatively, there was something coded in the omen that is lost to us. For example, the 6th omen reads thus with the corresponding dice roll:
A bear and a boar met on a mountain pass. (In the fight) the bear’s belly was slit open (and) the boar’s tusks were broken, it says. Know thus: (The omen) is bad (translation by Talat Tekin).
This omen reminds one of the statement regarding the dog and the hog in the Mahābharata; however, there it is good for the śvapāca. Another interesting point is the word üpgük = hoopoe in omen 21. While onomatopoeic, it seems like a cognate of the IE word for the bird suggesting an ancient “Nostratic” origin for it.

Imprints of the Ashina clan and the Blue Turks beyond the Khaghanate
The history of the steppes teaches us that great clans have deep impacts over time and space both at the genetic and the memetic level. This is well-known for the founding fathers of the Ārya-s, Chingiz Khan and the founder of the Tungusid Manchu empire. Was there any comparable impact of the Türk Khaghanate? A comprehensive genetic study by Yunusbayev of the impact of the Turkic expansion indicates that it is hard to assess the early signals of the Turkic expansion relative to the later ones where it was coupled with the expansion of Mongolic populations. Moreover, even though the Altaic monophyly looks increasingly unlikely, the Mongolic and Turkic peoples emerged from the same region and their languages show signs of prolonged interactions. This is also apparent in their genetics. In any case, the above study found the first signals for Turkic admixture outside the core Mongolian domain starting around 600-800 CE — this appears to correspond to the rise of the Blue Turk and Uighur Khaghanates.

A neighbor-joining tree based the single nucleotide polymorphism from ancient Central Asian samples indicting the relationship between Altaic groups speaking Turkic and Mongolic languages

On the philological side, there is strong evidence for the long-term persistence of the clan of Tonyukuk. To understand that, below we briefly recap the history of the fall of the second Blue Turk Khaghanate. On the Mongolian steppe, in 742-743 CE, three Turkic tribes, the Uighurs (originally from the region of the Selenge river), the Qarluks and the Basmyls, sensing the weakness of their Gök Türks overlords began asserting their independence. The Basmyls moved first to capture the Gök Türk capital and slay their Khaghan. The next year, the Uighurs and the Qarluks followed them to overthrow and destroy the Basmyls. The Uighurs then asserted themselves by driving the Qarluks towards Kazakhstan. Thereafter, the Uighurs moved on the remnants of the Blue Turk Khaghanate in a tacit alliance with the Chinese and beheaded their last Khaghan in 745 CE thereby erasing their empire off the eastern steppes. The Uighur lord declared himself the Khaghan under the title Qutlugh Bilge Köl Khaghan. The other branch of the Blue Turks descending from the first Khaghanate, Türgish, the “in-laws” of the second Khaghanate, had valiantly fought the Islamic Jihad and Chinese expansionism in Central Asia under their brilliant Khan Su-lu. When they encountered the Qarluks fleeing from the Uighur onslaught, they were in a weakened state from those struggles. After a prolonged fight lasting around 22 years, the Qarluks overthrew the Türgish, thus ending the line descending from the western branch of the first Turkic Khaghanate. With the old empire now gone, the famous clan of Tonyukuk, shifted their allegiance to the Uighur overlords of the Turkic world. It is notable that in this period the Kashmirian emperor Lalitāditya of the Kārkoṭa-s appointed a Turk (Cankuna) as his minister and general. We speculate that he too could have been a member of the Tonyukuk clan looking for new opportunities (though, one cannot rule out a high-ranked Türgish).

The story of the survival of the Tonyukuk clan goes back to the discovery of the earliest Turkic writings and its more recent re-investigation. In 1909 CE, a fragment of an old runiform manuscript from the period of Uighur ascendancy was procured in Khocho (Idiqutshahri). Radloff published the same the next year but he felt its contents were largely uninteresting. However, more recently, Erdal and Hao noted its parallels to another manuscript fragment from the same place in the Manichaean script that explicitly talks about the same events recorded by Tonyukuk on his stele — i.e., the revival of the Turk Khaghanate after its fall to the Chinese assault by Elterish Khaghan with his wise advice. Based on these parallels Erdal was able to interpret the contents of the first runiform manuscript as talking of the role played by Tonyukuk in the nomination and enthronement of Elterish Khaghan during the revival of the empire. Hao brought to light a work composed during the reign of the Chingizid rulers Temür Khan (son of Qubilai Khan) or his son Külük Khan that records the history of a remote descendant of Tonyukuk, Xie Wenzhi (name as recorded in Chinese), an Uighur official under the Mongols. The text states that:
1) Tonyukuk married his daughter to Bilge Khaghan.
2) After the death of Bilge Khaghan, his wife (i.e., daughter of Tonyukuk) led the Turks for some time.
3) After the conquest of Mongolia by the Uighurs, who were from the Selenge river (i.e., where three rivers join to form it), Tonyukuk’s descendants switched allegiance to them as their ministers.
4) The Uighurs saw the Tonyukukids as being “swift as falcons”.
5) The Uighurs of Khocho had a long tradition of worshiping the 20 deva-rāja-s and used Sanskrit in their liturgy.
6) Tonyukuk and Kül Tegin aided the Tang during the An Lushan convulsion in China. This is clearly an anachronistic and an ahistorical record. However, it suggests that possibly a descendant of Tonyukuk along with the Uighur Khaghan had aided the Tang during the rebellion of An Lushan and this was superimposed onto the founder Tonyukuk and Kül Tegin.
7) A certain Kezhipuer is mentioned as being a prominent minister from the Tonyukuk clan several generations after the An Lushan rebellion.

During the Chingizid Mongol rule of China, Xie Wenzhi, Xie Zhijian and other descendants of Tonyukuk were part of the elite and were prominent as scholars, artists and administrators. At the fall of the Mongol empire in China, some of these fled to Korea where they founded a prominent clan. Other members of the clan persisted under the Ming as ministers and officials in Liyang and Southeast China despite the nationalist backlash against the Mongols and their officials. Thus, the clan of Tonyukuk is a remarkable example of the human capital of a great founder lasting for over 700 years across Central Asia, China and Korea.

Looking backward in time, a major question is the provenance of the influential Ashina clan from which the Blue Turk Khaghanate, the Basmyls and the Qarluks arose. They were characterized by the famous ibex tamgha, which is seen on their inscriptions in runic script, both in Mongolia, along the Yenisei River and the Altai mountains. The clan also gave rise to Turkic elite that had intermarried with the Tang elite and conquered the western territories for the Tang emperor Taizong. It is also likely that the Ashina clan gave rise to other influential Turkic lineages of later Khaghanates like those of the Bulgars and the Khazar Khaghans. Their elite status seems to be repeatedly emphasized in their textual sources as they are distinguished from bodun — the Turkic word for the plebeians. Based on the Chinese sources one may infer that the Ashina clan might have been already present in the early Hun period of the Xiongnu Khaghanate. They were definitely present as vassals of the Rouran Hun Khaghanate and are mentioned in multiple Chinese sources as being their iron smiths. These sources also hint that the conflict between the Uighur branch of the Turks and Ashina clan might have begun in this period itself. In 546 CE, the Oghuz Turkic confederation, at whose head were the Uighurs, rebelled against their Mongolic Rouran Hun overlords. The Ashina clan is said to have aided the Huns in suppressing this revolt. However, it appears to have weakened the Rouran state and six years later, as the land thawed in the spring of 552 CE, the Ashina clan, which had risen in power from their recent exploits, overthrew their Hun overlords and drove them westwards from Mongolia. The leader of the Ashina clan declared himself the new Khaghan. Thus, there was a history of the Turkic peoples under early Mongolic rule that remains poorly understood. However, it may be reasonably inferred that there was already some diversification among them. We already see the Oghuz alliance with which the Uighurs were associated and the On Oq (10 arrows) alliance led by members of the Ashina clan. Indeed, the ethnogonic myths of the clan repeatedly mention the 10 sons of the founder, which is consistent with the On Oq having 10 sub-clans within it.

There has been a string of discordant theories regarding the origin of the Ashina clan. However, the majority of the plausible theories posit that the etymology of Ashina was not originally Turkic but Indo-European. Among the Indo-European etymologies, we have:
1) Beckwith proposed a Tocharian origin from Arśilas = noble kings. It is also related to one of the self-designations of the Tocharians for themselves (Ārśi). In further support of such a proposal, Golden noted the Turkic word for ox as öküz (note Kentum state) is likely derived from Tocharian B: oxso or Tocharian A: okās. While their probable homeland in the southern slopes of the Altai mountains would not be inconsistent with some late-surviving Tocharian imprint, there is no other evidence for a connection between the Turks and the Tocharian elite in the region.
2) Atwood proposed a similar root form, but with an Indo-Aryan etymology: ṛṣi > ārṣa > ārṣila. He notes the parallel rendering of ṛṣi as Arsilas in Greek. While an interesting proposal, it is odd that a ruling warrior clan would have such a typically brahminical etymology, unless, like certain Hindu dynasties, they sought to present ancestry from a ṛṣi.
3) Another Indo-Aryan etymology proposed by Klyashtornyj (along with proposals of Golden, Beckwith and Mair) is: Aśvin (one with a horse)>Ashina. A key point in this proposal is the status of the Wusun, who were an Indo-Iranian steppe people recorded in Chinese sources. Therein, the ethnogonic myth of the Wusun mentions that they believed that their ancestor was orphaned in an attack by the Huns (the first Khaghanate of the Huns, i.e., Chinese Xiongnu). This ancestor was then raised on the steppe by a female wolf and ravens. Multiple versions of the ethnogenesis of the Ashina clan of the Blue Turks also mention that their ancestress was a she-wolf and that they were feudatories of the Xiongnu first and the Rouran Huns thereafter (a version of this wolf motif was remembered long after the fall of the Turks to Mohammedanism by Gardīzī, the minister of the monstrous sultan Mahmud of Ghazna. He states that the Turks have sparse facial hair and a dog-like nature due to their ancestor, as per Abrahamistic tradition, Japeth, being fed wolf’s milk and ant eggs as a medicine. His teacher al Bīrūnī also records that ancestor of the Turks of Afghanistan was a long-haired dog-prince. Victor Mair proposes that wolf’s milk might have meant the slime mold Lycogala). The wolf motif is also found in the origin myth of the Uighur lineage of Turks (the Chinese sources mention their origins from the coitus of the ancestor wolf with the daughter of the Hun [Xiongnu] Khan). As per Golden, the Uighur Oghuznāma mentions “Blue Wolf” as being their war cry. The same pattern is again seen in the case of the Chingizid Mongols, where the male ancestor is the wolf. Thus, even though the wolf motif is widespread in the Turko-Mongol and Indo-European world (e.g., the founding of Rome), the Wusun and the Ashina clan share the female nurse/ancestress. Thus, the etymology of Wusun and Ashina is seen as deriving from a common root Aśvin. Beckwith correctly reasons that this group was likely a steppe Indo-Aryan remnant rather than Iranian, given the root form Aśva as opposed to Aspa (e.g., in steppe Iranian Arimaspa).
4) Finally, we have Bailey’s suggestion that it derives from steppe Iranian Śaka word āṣṣeiṇa for blue. This would match the Blue Turk appellation of the clan. However, we suspect that, while there might be something to this etymology, it is more likely an instance of retro-fitted etymologizing based on the Śaka word in one branch of the Ashina clan. There is no evidence that all branches of the clan called themselves Blue Turks.

Thus, we cautiously posit that the most likely origin of the Ashina clan was via the Turkification of an originally Indo-European (likely Indo-Aryan) steppe people that retained its elite status through multiple admixtures with East Asian groups that spoke a Turkic language. We suspect that this Turkification of the Ashina-s probably occurred over a prolonged period ranging from the Xiongnu Khaghanate all the way to the early Rouran period. Yet some imprints of the IE affinities can be gleaned even as they become more prominent on the historical landscape. It is likely that cremation was the primary funerary practice among the Ashina elite as opposed to the traditions of the Hunnic elite, linking them to an old IE tradition. In further support of a specific Indo-Aryan connection, we may point out that the names of the founding brothers of the Blue Turk Khaghanate Bümin and Ishtemi do not have an explicit Turkic etymology. However, Bümin can be transparently derived from Indo-Aryan Bhūmin (note Indic bodhisattva > early Mongolic bodi-satva on Khüis Tolgoi Brāhmī inscription) or Iranic Būmin = “the possessor of the land”. Similarly, the name Īśbara kept by multiple early Turkic Khans can be derived from Indo-Aryan Īśvara. However, the apparent decipherment of the Khüis Tolgoi, Bugut and the short Keregentas (Kazakhstan) Brāhmī inscriptions by Vovin, Maue and team suggest that there was Indic influence on the steppe which might have gone along with the missionary activity of the Bauddha-s (as opposed to remnants of steppe Indo-Aryans like the Wusun). One cannot rule out the role it might have had in transmitting Indic names and terms to the early Turkic and Mongolic groups. In the Khüis Tolgoi Brāhmī inscription we already encounter a Blue Turk Khaghan if Vovin’s reading is correct: Niri Khaghan türüg khaghan: Niri Khaghan, the Khaghan of the Turks. This would point to contact with Indic cultural elements early in their history.

In this regard, we would like to point out one further, more tenuous connection. The Chinese sources, like the Zhoushu mention that the Khaghan of the Turks performs a ritual at the ancestral cave in Ötükän mountain where Ashina was born from/suckled by the female wolf. Suishu further adds that on the eighth day of the 5th month the Turks perform a great sacrifice and send a ritualist into the cave to make offerings to their ancestors. Ethnological investigations have indicated that the Siberian Turks make offerings to the gods and ancestors with the incantation cök usually coupled with a formula. For example, Inan notes the following (in translation):

O my ancestor Kayra Khan, the Protector! cök! Here it is, offering to you Kayra Khan!
Cök! Here it is, offering to you! My mother (like fire) with thirty heads.
My old mother with forty heads; when I recite cök! Have mercy!

The latter two appear to be offerings to polycephalous female deities one of whom is associated with the fire (c.f. the Mongol fire goddess). Similarly, Anohin also recorded several formulae with offerings made with the cök incantation, including to the ancestor Kayra Khan.
Ak-it purul piske polush, cök! = Grey and white dog! help us! Cök!

Interestingly, Aydin found that this incantation found in modern Turkic formulae is already seen in several runiform Yenisei inscriptions from around the time of the Blue Turk Khaghanate and Erdal interpreted it (in our opinion correctly) as something that implies “I offer my sacrifice”. For example, we have: “Tengrim cök! bizke” = To Tengri cök!; [may he favor] us (in the Yenisei inscription cataloged as Tuba II [E 36], 2). In another Yenisei inscription, we encounter a similar formula invoking Tengri in the context of a holy rock and a cliff — perhaps a parallel to the cave offerings of the Blue Turks.

A closer examination of the known exemplars of the Turkic cök incantations reveals a parallel to the mantra incantations that end in svāhā, sometimes with an additional phrase reminiscent of idaṃ [devāya etc.] na mama. Zhang He noted (following the Song dynasty scholar Shen Kuo) that the “sai” incantation, which was usually present at the ends of the formulae deployed by the mysterious Chu kingdom (from 300 BCE or before) was likely originally svāhā or a derivative thereof (Chinese sa-po-he). The Chu kingdom is believed to have originally had a non-Cīna soma- and fire-sacrificing elite, likely of steppe Indo-Iranian origin who might have been absorbed by the Huns. Thus, it is not far-fetched to propose that the Turkic cök formula was also inspired by or derived from svāhā — something that would be compatible with the proposed Indo-Iranian roots of the elite Ashina clan.

The runiform scripts origins and spread beyond the “Orkhon” horizon
Shortly after his decipherment of the Turkic runiform inscriptions, Thomsen proposed that the runiform script was probably derived from Aramaic via Sogdian or additional Iranic intermediaries. This hypothesis came to be widely accepted in a manner parallel to the Aramaic hypothesis for the origin of the Indian Brāhmī script. However, it should be noted that some of the same problems confront the Aramaic hypothesis for both Brāhmī and runiform. Talat Tekin notes that the Orkhon inscriptions contain 38 characters and there are two additional characters that he takes to represent syllables in the Bain Tsokto stele of Tonyukuk. Of these, there are 4 vowel signs — something that Aramaic does not use. Brāhmī has an even more elaborate vowel system based on the Indo-Aryan grammatical tradition that is necessary to encode Indian languages — something which is unparalleled in the Aramaic family. The runiform script does not distinguish some long from short vowels and totally devotes 4 signs for these (/a, ä/; /i, ï/; /o, u/; /ö, ü/). 20 signs represent either a plain consonant or a/ä+consonant; e.g., at/ät. The remaining 16 signs represent various other consonants that are neutral with respect to the vowels, syllables like “ash” and sounds like ich, uk etc. Thus, the organization is quite unlike the Iranic scripts derived from Aramaic or old Aramaic itself. Now, we know that Aramaic was used in southern Central Asia within the Indosphere — e.g., Aśoka Maurya’s inscription in the northwest. There was also Kharoṣṭhī which appears to have represented a genuine Indian adaptation of Iranic administrative Aramaic with vowel diacritics for better encoding of Indo-Iranian languages. Thus, while Aramaic and Aramaic-inspired scripts were in vogue in Central Asia and India, directly deriving Brāhmī and runiform from Aramaic is not well-supported. Instead, both seem to be scripts that were probably inspired by the “presence of writing” rather than being direct adaptations of other scripts. In the Indian situation, the possibility of some memory of the Harappan signs (believed by most to be a script) is another factor, whereas in the Central Asian situation there were multiple local scripts, including possibly Aramaic, that could have provided some indirect influence.

With this background we may examine the actual situation on the ground. In Mongolia, the earliest inscriptions, Khüis Tolgoi and Bugut, which appear to go back to the Rouran Hun Khaghanate, are in Brāhmī. The Keregentas inscriptions indicate Brāhmī was in use over a wide part of the “Altaic” domain. We know that Brāhmī and its derivatives rapidly spread through central Asia concomitantly driving Kharoṣṭhī to extinction. Given its superior representation of vowels, it was evidently adaptable for non-Indo-Aryan languages and was likely seen as the script of choice when the second Hun Khaghanate sought to adopt one. Three of the faces of the Bugut stele have Sogdian inscriptions that appear to go back to the first Blue Turk Khaghanate. This suggests that after the overthrow of the Hun Khaghanate, the Turks decided to break from Brāhmī and adopt the Sogdian script. Apart from these inscriptions, there is the mysterious silver bowl which was discovered in 1969-70 during the excavation of a richly furnished grave at the Issyk Kurgan about 50 Km East of Almaty, Kazakhstan. The date of the grave remains contested but is believed to be at least as early as 150-200 BCE. The bowl contains a two-line inscription comprised of 25 or 26 characters. Many authors thought this was an early version of the Turkic runiform script. Ünal and Xursudjan instead understood it to be a version of the Aramaic script based on comparisons to Aśoka Maurya’s Aramaic inscriptions and the other mysterious Ai Khanum silver ingot inscription. Based on the Aramaic interpretation, it has been read by Ünal as having some clearly Indo-Iranian words. The first word is read as yuvan= youth in Indo-Iranian languages. The second word is read as zyād, which is interpreted as a version of shad, a word seen on the Orkhon inscriptions and again of Iranic provenance (i.e., chief or prince). In contrast, the remaining words are read as an early form of Mongolic, and Ünal links this script to the script-like markings found in some Xiongnu era graves. The proposed lower bound age of 150-200 BCE and location would be consistent with the first Hun Khaghanate of the Xiongnu. Thus, it would seem that the Huns initially adopted Aramaic, at least in the western reaches of their empire, probably via interactions with Iranic groups (supported by the loans in the proposed reading). While Ünal further thinks it provides an intermediate between Aramaic and the Turkic runiform script, there seems to be quite a temporal gap between the two with no evidence for the use of Aramaic (leaving aside Iranic descendants like Sogdian) in the region during the intervening period. Hence, we believe that the evidence for the Aramaic hypothesis for the origin of the runiform script still remains weak.

The Issyk silver bowl inscription

If we set aside the Issyk inscription, we are still left with the question as to when the runiform script started being used? An interesting clue in this regard comes from the recent discovery of bone plates used as a grip for a composite bow that were found in an Avar grave at Szeged-Kiskundorozsma, Hungary. These plates are inscribed with a runiform script that is related to but not identical to that used in the Eastern Turkic texts. The bone plates gave calibrated radiocarbon dates ranging from 660-770 CE, whereas thermoluminescence dating of a pot from the grave site gave a central date of 695 CE. These are in the general age range of the second Turkic Khaghanate’s inscriptions. These join a relatively small set of comparable short runiform inscriptions that have been found in Eastern Europe from the Avar horizon but without the secure dating of the above. All of these remain undeciphered. However, the recent discovery of several runiform inscriptions in the Altai has uncovered signs that are similar to those in these Eastern European exemplars. Further, we know that the Khazar Khaghanate also used a runiform script. At least one clear example of this found at the end of a letter written by a Jew has a short Khazar phrase (interpreted as “I have read”) in runiform (probably by a Turk in response) that can be read largely on the basis of the Eastern Turkic Khaghanate’s runiform script. Beyond this, there are several other short Khazar inscriptions that remain undeciphered — in part because the exact Khazar dialect of Turkic remains poorly understood, the inscriptions are short, and some signs are distinct from those of the Eastern runiform corpus. However, some of these signs overlap in form with those seen in the Eastern European inscriptions attributed to the Avars.

Mammoth bone runiform inscription from Yakutia — the northern reaches of the Turk domain

Recent genetic evidence has strongly established that the Avars are the remnants of the Rouran Hun Khaghanate that was overthrown by their Turk feudatories to establish the first Turk Khaghanate. Thus, it would be reasonable to propose that the script was invented in some form before the destruction of the Rouran Khaganate, most likely among the Turkic tribes. Given that the Rouran Huns themselves appear to have preferred Brāhmī, it is possible that this was a “national” script that Turks devised to specifically distinguish themselves and their language. However, it is likely that the script was also known to at least some of the Rouran Huns or Turkic groups allied to them that carried it west as they fled. Thus, in part, the inability to decipher the Eastern European Avar exemplars might come from the fact that they encode an early branch of the Mongolic language rather than a Turkic language (c.f. the Chingizid use of the Uighur script for Mongolian). In this regard, the case of the mysterious jug inscriptions can also be considered. Before the Bratsk Reservoir in Russia was flooded, six silver jugs were found on the Murujskij island by a fisherman before it went under. The form of these jugs is similar to the silver/gold jugs found at the funerary monuments of Bilge Khaghan and other members of his family. Only two of the Murujskij jugs survive and the bottom of one of them has an interesting inscription in the runiform script that can be completely transcribed on the basis of the Eastern Turkic runiform script like that seen on the Orkhon stelae. However, the transcription cannot be deciphered as Turkic (and so far as anything else). Nevertheless, the inscription is associated with the Ashina clan’s ibex tamgha (also seen on the second jug). This indicates that even though the jugs with the inscription are from the Turkic Khaghanate, the runiform script on them was used to encode a language other than Turkic. Recently, another inscription was found on a mammoth bone amulet far north in Yakutia, indicating the spread of the script and possibly the extent of the Turkic Khaghanate. Such a scenario of expansion and subsequent splintering of the Khaghanate would be consistent with: 1) the runiform script being adopted by languages unrelated to but geographically proximal to Turkic; 2) The divergence in form between different Turkic groups (e.g., those in the West which eventually gave rise to the Khazar version and those in the east which gave rise to the Uighur version); 3) Loss — once the Turks lost their self-identity as a nation and became satellites or vehicles of the Abrahamistic religions.

The mysterious Murujskij silver jug and runifrom inscription

Finally, we can say that as more inscriptions are found in Mongolia, the Yenisei and Altai we might still learn some poorly understood facets of early Turkic history. Recently (in 2017), a further monument with 14 pillars was discovered at Dongoin Shiree in Eastern Mongolia with several inscriptions and tamghas that are yet to be published in detail. The preliminary report by Japanese researchers indicates that it was the monument of the one of the shad-s of Bilge Khaghan, the yabhgu or viceroy of the eastern territories. With respect to the Yenisei inscriptions, Klyashtornyj has recently read evidence for some facets of the history of the Western Ashina Khaghans. For example, he believes that the branch of the Türgish who left the inscriptions found in Minusinsk basin near the lake of Altyn-köl were the predecessors of the Kirghiz Khaghans who eventually conquered the Uighur Khaghanate. One of the inscriptions mentions a certain general Chabysh Ton-tarqan from this clan — the name Chabysh seems to be an early attestation of the root of Chebyshev, the famous Russian mathematician who is supposed to have descended from a Chingizid Mongol chief. Another runiform funerary inscription from the Yenisei (Uibat VI) commemorates a certain hero named Tirig-beg who is said to have fought like a wild boar when the mighty Uighurs were overthrown. These complement the Suja inscription found in the early 1900s by the Finnish expedition in Northern Mongolia, which was commissioned by Boila Qutlugh-yargan who also participated in the great Kirghiz-Uighur clash of 840 CE. It is likely that this event and the subsequent Kirghiz invasion of the Chinese territories was what formed the core of their oral epic of the hero Manas.

Vikīrṇā viṣayāḥ: India and the Rus

Our sleep was disturbed by a dream with a circulating motif whose exact story line, if any, was lost upon awakening. It started with a tall elderly man of West African ancestry playing cricket (batting) with the swagger of a young star at the peak of his career. Striking the ball along the ground or smashing it high into the stands he scored on with ease reminding one of the great black emperors of yore from the Caribbean. Then the dream entered the motif phase with the same man, rather paradoxically, in a classroom repeatedly explaining a single-peaked statistical distribution he claimed to have discovered — we tried hard to capture the equation of that distribution but failed at every repetition of the motif. This kind of REM sleep can be rather troubling, and we tossed and turned around before settling into another scene that seemed to have no connection to the above (unless of course, we forgot that snatch upon awakening). In this scene was an elderly Russian Jewish woman — we would estimate her age as being around 85-90 years — who sat on a chair with a table in front of it. Soon another bearded man appeared beside her — he seemed to be in his 60s but in great health. He exuded a profound ambivalence that strongly impressed upon us — while a part of him presented features consistent with a good character, the rest of him was filled with rapacity, cunning and a taskara spirit. He told the old woman in an unusual accent that seemed either German or Russian that we spoke German. The woman responded in a feeble voice: “Die beiden Grenadiere.” We then saw ourselves in the dream reading out the famous poem of Heinrich Heine:

Nach Frankreich zogen zwei Grenadier’,
Die waren in Russland gefangen.
Und als sie kamen ins deutsche Quartier,
Sie liessen die Köpfe hangen.

Two grenadiers were marching back to France
They had been held captive in Russia,
And when they reached German lands
They hung their heads in shame.

Da hörten sie beide die traurige Mär:
Dass Frankreich verloren gegangen,
Besiegt und geschlagen das tapfere Heer—
Und der Kaiser, der Kaiser gefangen.

For here they learnt the sorry tale
That France had been conquered in war,
Her valiant army beaten and shattered,
And the Emperor, the Emperor captured.

…

“Dann reitet mein Kaiser wohl über mein Grab,
Viel Schwerter klirren und blitzen;
Dann steig ich gewaffnet hervor aus dem Grab—
Den Kaiser, den Kaiser zu schützen!”

“That will be my Emperor riding by my grave;
Swords will be clashing and flashing;
And armed, I’ll rise up from the grave
To defend the Emperor, my Emperor!”

The old woman said: “Sollen wir mit Russland oder Frankreich sein, das war die Frage…” We either did not catch or forgot the rest of her words except for the very last: “Russen und die heidnischen Indianer”. We awoke soon thereafter and the memories of the rest of the dream were lost. It was the 100th day of the Russian invasion of Ukraine.

There are two things have are remained fairly stable in the politics of our times: the mleccha-marūnmattābhisaṃdhi and Galtonism. Much else of what concerns the Hindu nation develops around these two. The concluding words that we remembered from our dream brought to mind a clear parallel that has long existed but recently raised its head again in the H world. In our previous note, from shortly after the start of the current European war, we traced the path of the rise of the new mleccha religion, navyonmāda, and its role in the overthrow of the Nārīṅgapuruṣa and beyond. Indeed, any sane, politically aware heathen living in mahāmleccha-land will get of sense of how it might have been for the last heathens of the classical world as the frenzied followers of the śūlaprotapreta were starting to gain the upper hand in enforcing their cult. We observed that when it comes to the Rus, the navyonmatta backers of Vṛddhapiṇḍaka and their internal opponents among the mleccha-s, i.e., the more protapreta-aligned folks or some of the more secularized uparimarakata-s are quite aligned in their rhetoric. As we have noted several times on these pages, the mleccha-marūnmatta-yāśu overrides even the yauna-sambandha between the paśchima-mleccha alliance and the Rus. Briefly, the inclusion of the Turuṣka in the rotten soybean soup has its deep roots in the Crimean war against the Rus. This continued to the recent times in the form of the first Afghan war, the “soft underbelly strategy”, the Chechnyan war, and the support for the marūnmattātaṅka in Rus cities. Similarly, when it comes to the H both sides of the mleccha political spectrum are quite aligned. In the case of navyonmāda, given its natural attraction for marūnmāda, it usually proceeds via active fostering of the mleccha-marūnmattābhisaṃdhi. In the case of the mleccha “right” and uparimarakata “classical liberals” or “neoconservatives” it proceeds either via support for the kīlitapreta-bhānaka-s or “enlightenment values” (e.g., the anti-H garbage spouted by the scientist Stuart Kauffman in a talk is just one example among the many from that group).

Both among the Rus and H there exist many who are truly in love with the mahāmleccha sphere (i.e., the pañcanetra-s) and identify closely with them. For the Rus the path of assimilation in the mahāmleccha mass is trivial but for the H it is formidable. Yet, the H have tried hard to do so. Among the Rus who managed to immigrate this process is mostly complete, but among those who could not, for one reason or another, different levels of yearning still exist. We could argue that even the pro-Rus elite, including Putin, wanted to be accepted as respectable members of the Occidental sphere; however, their being spurned resulted in a return to antipathy. Among the H who have immigrated and those who hold the hope to do the same, the yearning is more like that of a guy pining for a beautiful girl who does not cast a glance his way. Ironically, both the anti-Rus or anti-H policies of the Occident end up hurting those who are mostly friendly to them. However, the Indian situation is more complex. There is a sizable pro-mleccha class in India that finds work that is metaphorically not very different from that of the sepoys under the English tyrants. The Indian system and its deep penetration by the Occident, has meant that this class will actually aid the Occident in implementing any anti-H moves. It seems this class was largely eliminated or defanged among the Rus by Putin. Those of that class who were mūlavātūla-s have mostly left for their own or to the mahāmleccha lands. In contrast, the Indian equivalents of that class are going nowhere and the government neither has the awareness nor the courage to defang them as of now.

As we have again noted on these pages, the pañcanetra-s are master shadow warriors — their conquest of India and humiliation of the Cīna-s was a masterly exposition of the same. In the case of the Rus, when their marūnmatta allies failed to play the proxy role successfully they had to personally intervene in the form of the Crimean war. But even there, the core of the pañcanetra of the age (the English) lost fewer men while letting France to take the heaviest losses. Since the conclusion of the Crimean war, the (proto)pañcanetra has vigorously sought to obtain useful rentier states in the region that can do their bidding against the Rus. The current Ukrainian state was the fructification of this dream. In the subcontinent, when WW2 forced the English to retreat, following the usual doctrine of the mleccha-marūnmattābhisaṃdhi, they created TSP as the rentier state to the keep the H in check. Though the English retreated, the mantle of pañcanetra power was now in the hands of the mahāmleccha-s, who continued that policy with respect to TSP. The people of the rentier state itself might suffer, but it will be kept afloat as long as it serves the purpose of the pañcanetra-s in the realist goals against the target state. As result, these rentier states are among the most corrupt systems in the world. So far, the mleccha-s seem to have a high tolerance for the blowback that comes from these volatile pets of theirs. The mahāmleccha-s even accepted an assault of the magnitude of 9/11 to keep TSP afloat. The blowback from Ukraine has been much less, but the role it has played in frauds and cybercrimes in mleccha-land going all the way to Vyādha-piṇḍaka is immense. It is possible in the future is brings in more terrorism with all the arms the mleccha-s have pumped into the state.

Given that the history of the current conflict goes back to at least the Crimean war, we cannot but help get to its essence: the pañcanetra-s and their vassals essentially wanted to fulfill the aims of that war, viz. degrade the Rus to the point that they are no longer a great power. This is essentially the basis for the expansion of the rotten soybeans confederation right into the land of the “Mother of all Russian cities”. A parallel to the H world cannot be missed — aiding TSP, that festering rump of the Mogol empire, to take over much of the pāñcanada, which was the mother of all the Indian cities was not very different. Thus, the Rus were confronted with an existential predicament: were they going to resist this encroachment of the Occident into their natural domain by means of a rentier state or were they going to back down with a whimper. Like the Hādi-śūlapuruṣa in the old days, Putin too desired to be accepted by the pañcanetra-backed West as a part of their world. However, as it became increasingly clear that the Occident had no such intention but the contrary, he decided to take back Crimea first, and try the strategy of a low-key war in the Donbas. That later strategy seemed to have worked poorly. Second, he probably sensed that the duṣṭa-Sora-bandhu in Danu-Apara-deśa might have more aggressive plans (likely backed by Sora himself, especially given that his anuyāyin-s have successfully taken control of the mahāmleccha government). Of course, the more cynical mahāmleccha-s think it might have been triggered by the realization of his impending mortality from a cancer — in a sense, he personally had nothing to lose in some big stakes gamble. However, we believe it is a very rational fork the Rus were confronted with and had to take one of the two paths mentioned above.

The expectations and the commentary on the conflict have been wild. The mleccha-s have been claiming exaggerated victories for duṣṭa-Sora-bandhu and his paradoxical allies from the Hādi-puruṣa-pakṣa On the other hand, many expected the Rus to overrun the Dānu-Apara-deśa within a month. However, that has not happened, and the fourth month of the conflict will soon dawn. This was the limit placed by the Rus nationalist Karlin as the boundary beyond which discontent might arise in Rus against their lord. Hence, many have shifted to the mahāmleccha view of things. However, as we had remarked earlier, neither of these paths should have been expected. Historically, the Rus have not shown overwhelming military dominance from the get-go and have tended to have spotty performance in battle (Crimean war, loss to Japan, Afghanistan). However, over time they have repeatedly shown the capacity to doggedly stick to and achieve their military goals. To reiterate, they initially floundered against both the Napoleonic French (Heine’s poem) and the Germans but they came back strongly on each occasion. Thus, their performance in the current war is consistent with this past. In our assessment, while they initially lost impetus, they have subsequently made steady progress. While you may not hear it in the Occidental media, there are clear indications of this: First, the Hādi-puruṣa-pakṣin-s, whose existence the Occident grudgingly accepted, appear to have faced heavy losses and many have been taken alive. These were some of the most committed fighters in the East of that deśa. Second, if one heard the latest interviews of the sora-bandhu with his backers in the Western press, one could hear between the lines that he is hard-pressed. Third, and importantly, the mahāmleccha-s are growing increasingly silent in their news coverage of the glorious wins of their Hādi-puruṣa-pakṣin allies. The mahāduṣṭa Cumbaka, even paradoxically noted that the Dānuka-s may have to cede territory to the Rus. We still do not know how far the Rus would advance. However, it is clear that the Rus-majority regions have now been or will be soon lost by the Dānuka-s despite the spectacular victories claimed on their behalf by the mahāmleccha-s. Will the Rus be able to hold on once their strongman lord attains Vaivasvata or will the mleccha-backed rump of the Kievans make a new advance to recover their losses? That remains to be seen.

Finally, it should be noted that for whatever inconvenience the sanctions of the mleccha-s have caused to the Rus, the mahā-mleccha economy itself is floundering under its navyonmatta leadership. In the end, any sane person would realize that as of today there is no way to maintain the comforts of a modern society without consuming liquid fossil fuels. Beyond being an energy source, they are also the industrial raw material for a wide range of products that are the quintessence of modern life. Indeed, the rout of Germany in WW2 was due to their limitations in accessing liquid fossil fuels. While they captured the French reserves and managed to obtain some from Romania after their eastward thrust, they simply could not match the Soviet supplies. Nor could they capture the Soviet oil fields. The Japanese initially secured their fuel supply after the conquest of the archipelago. However, the American fightback and defeat of the Japanese in the naval battle of Midway limited their safe transportation of fuel in face of the American assaults. After their rout in WW2 at the hands of the Rus in Manchuria, the Japanese decided to surrender to the mahāmleccha-s to save their sacerdotal monarch. Thus, they learnt the hard way that the key to maintaining a modern economy was to have a reliable and proximal fossil fuel supply. Hence, they decided to restore better relationships with the Rus to access oil via Sakhalin. The mahāmleccha-s are now pressurizing them to get off Rus fuel. However, the Japanese industrial leaders have correctly realized the serious negative impact this would have and called on their government to continue dealing with the Rus. The śūlapuruṣa-s too depend heavily on Rus fuel and could lose their preeminent status as the industrial powerhouse of continental Europe if they decide to go along with the mahāmleccha directives. We even suspect that the aṅglamleccha-uparimarakata alliance might be seeing this as a means to kill two birds with one stone — sink both their old enemies the śūlapuruṣa-s and the Rus. Hungary too, which knows well of the evil of duṣṭa-Sora, seems unwilling to sacrifice its comforts by going all out against the Rus. Thus, we remain skeptical as to whether the maṇḍala-dhvaja-s and śulapuruṣa-s would really decouple from the Rus. Moreover, so far the Rus scheme for ruble payments in return for fuel, grain and fertilizers continues despite the sanctions. Hence, we hold that the Occident has failed to achieve the victory it desired in its proxy war with the Rus. That said, we accept this conflict is far from over.

In late Hindu antiquity, H thinkers realized that the restoration of the dharma-raṣtra cannot occur without a decisive and complete victory over the ekarākṣasonmāda-s. This was presented metaphorically as the kali being brought to a close only upon the uccāṭana of the unmāda-s by Kalkin. The tāthāgata-s recognized the same even as their centers were being reduced to cinders by the bearded ruffians. The catastrophic first war of independence in 1857 CE was fought on fundamentally unsound foundations on the part of the H. After that they have not really fought for the reestablishment of the dharma state as they continued with the same or worse premises on which the 1857 effort was founded. Moreover, freedom came only because the English had already sucked India dry and for practical purposes, they lost the bigger war elsewhere as they had to cede their preeminence in the pañcanetra system to their mahāmleccha cousins. To add to the H woes, while they had freedom from the English tyrants, they had lost key tracts of their land to their old ekarākṣasa enemies, who had not yet been completely overthrown when the English struck. Thus, the H had merely kicked the can down the road in a world where few could act independently without being policed by the pañcanetra confederation and its vassals. The one power that gained the capacity to act with some independence via a combination of the old Galtonian bond and the mleccha rapacity for cheap manufactures was the Cīna-s, who too had become an enemy of the H. Thus, just like the Rus, the H too were presented with a fork on the road: either die with a whimper like a śvan strangled for a Yulin feast or attempt to regain the dharma state by the overthrow of the ekarākṣasa yoke on their necks. The latter path would mean fighting the combined power of the mleccha-marūnmattābhisaṃdhi with the Hans potentially fishing in the troubled waters. The H leadership decided to simply postpone any confrontation of the question as it was too painful to even contemplate. Neither road was pleasant, and the human cost was going to be huge.

But nations without power do not have the choice of their battlefields. Even as we woke from the strange dream the news reached us that the Indian state had abjectly capitulated to the marūnmatta-s, with the mleccha-s and first responders cheering them on. The details of this need no elaboration as they are rather well known to all. Nevertheless, just for the historical record, we would simply say that, as is usual of them, the marūnmatta-s are baying for the head of a government official for speaking the truth about the rākṣasa-mata. There is nothing new in that, but the following are notable: 1) The Lāṭeśvara was brought into power with the hope that he would deal firmly with the marūnmatta-s, even as he did so when they burnt the H alive in his province. However, he meekly caved to the pressure from the West Asian marūnmatta hellholes even as his predecessor the nāmamātra-vājapeyin had done when the marūnmatta-s hijacked the Indian plane to occupied Gandhāra. Then the mistake was done of keeping those three ghāzi-s above the ground after their capture when they should have been promptly dispatched to one of Citragupta’s chambers (it seems the security forces have mostly learnt their lesson since). 2) Moreover, the capitulation of the Lāṭeśvara took place against the backdrop of the renewed ghāzi activity in Kaśyapa-deśa. Residual Vaṅga and Cerapada are tottering under regular marūnmatta assaults too. 3) Most galling thing was that the Lāṭeśvara’s government sent a message to the H that they were more concerned about their enemies who seek to annihilate them rather than the H themselves. 4) It is rather telling that the government even abdicated its mandate for law enforcement under the secular constitution to which they cleave – simple cut and dry cases of freedom of expression and incitement of violence – that could put the ruffianly marūnmatta-s in place (thankfully a couple of state leaders are following that in the least). One could go into any number of explanations (and few of them are entirely valid) of why the Lāṭeśvara capitulated but the bottom line is that the Indian government under electoral politics is too weak to confront the foes of the H. While one could raise parallels to the Mūlasthāna Sūrya temple hostage situation with the Pratihāra-s, a modern state aspiring great power status should have the means of countering such blackmail – they are quite obvious though they cannot be mentioned in public. Hence, the Lāṭeśvara and his court should have at least made that honest confession to the H people that they and probably their army are too weak to confront the mleccha-marūnmattābhisaṃdhi; hence, they would need to capitulate.

We believe that, as with the Rus, the H have been taken to the fork in the road. The Lāṭeśvara, the only patriotic leader with a mass appeal, has shown the weakness of his position. This has cast serious doubt on his ability to take the H through the confrontation — rather he has stuck with the old practice of kicking the can down the road. The government’s hope is everything will be hunky-dory after some cycles of Freitag Eruptionen, but, make no mistake, the marūnmatta-s have sensed that the aging Lāṭeśa is no longer the man he was when he held sway in Lāṭa. If the woman is killed, then it will embolden them even further. They have won this round and will come back for more. Duṣṭa-sora and the navyonmatta-s also want to overthrow the Ānartapa — hence, their natural alliance will swing into action. They have already planted the deśī equivalent of the Dānu-apara’s sora-bandhu along with his band of uśnīśātatāyin-s. Sora and his agents have also succeeded in corrupting the judiciary along the lines of what they have done in mahāmleccha land. Hence, we believe that whether H like it or not they will find themselves on one or the other fork sooner than later and they may not even have a choice. The default endpoint would be that of a camel garroted by a marūnmatta.

Alkaios’ hymn to the Dioskouroi: Hindu parallels

In this note we shall see how even a short “sūkta” of the yavana Alkaios to the Dioskouroi (individually named Kastor and Polydeukes), the Greek cognates of the Aśvin-s, offers several parallels to the Hindu tradition in the Veda. In the Veda, the Aśvin-s are the sons of Rudra hinting at his overlap with Dyaus (tvam agne rudra asuro mahodivaḥ | or bhuvanasya pitṛ). In the Greek and Roman traditions, they are the son of Zeus or Jupiter maintaining that old connection going back to the Proto-Indo-European tradition and probably beyond to prehistoric times. In Greece, the memory of their Rudrian character is recorded in a 600-500 BCE stele from Sellasia in the Spartan realm where Plestiadas, a pious votary of the deities, inscribed a verse stating that he erected it “out of fear of the fury of the Tyndarid twins (the Dioskouroi)”.

Figure 1. A denarius of the Roman emperor Antoninus Pius showing the twin gods Castor and Pollux with the eagle of Jupiter between them. This iconography closely parallels that of their para-Vedic relatives Skanda and Viśākha. The stars above them signify their association with the constellation of Gemini — an ancient association also reflected in the Taittirīya Brāhmaṇa.

deũté moi nãson Pélopos lípontes,
paĩdes íphthimoi Díos ēdè Lḗdas,
eùnóōi thúmōi prophánēte, Kástor
kaì Polúdeukes,
oì kát eùrēan khthóna kaì thálassan
paĩsan èrkhesth’ ṑkupódōn ep’ ìppōn,
rē̃a d’ anthrṓpois thanátō rúesthe
zakruóentos,
eúsdúgōn thrṓiskontes ep’ ákra náōn
pḗlothen lámproi próton’ ontrékhontes
argaléai d’ en núkti pháos phérontes
nãï melaínai;

Come to me all the way from Pelops’ island,
powerful sons of Zeus and Leda,
make your appearance with a kindly soul, Kastor
and Polydeukes!
You ride over the wide earth and the entire sea
on your quick-footed horses;
you rescue men with ease from death
due to freezing,
leaping from afar to the tops of their well-benched ships,
shining brightly as you run up the forestays;
to that in trouble in the night you bring light,
to the ship in darkness.

We shall now consider both linguistic and philological equivalences with Sanskrit usages:
• paĩdes = putra son; This occurs in the phrase “paĩdes íphthimoi Díos” the powerful sons of Zeus (and Leda). That parallels the phrase: divo napātā vṛṣaṇā: the manly offspring of Dyaus.
• We render thúmōi as soul. The thumos is a cognate of dhūma is Skt (= smoke/steam going back to PIE with same meaning). In Greek, one of its meanings, breath, is related to the original meaning, from which we get soul. The equation of soul and breath is also seen in H tradition: For instance, prāṇa is called the “soul”. The other Skt word ātman is related to an old IE word for breath (e.g., German Atem= breath).
• eùrēan khthóna uruvyachasam pṛthivīm. The first word is an exact cognate of uru = wide. The khthóna= kṣmā (kṣa) earth;
• ṑkupódōn ep’ ìppōn parallels the phrase used for the Aśvin-s in RV 1.117.9 and RV 7.71.5: āśum aśvam: swift horse; podon = padam = foot; āśu = ōku swift; ippos = aśvaḥ horse. A comparable phrase is used by Gṛtsamada Śaunahotra in his spell for the chariot: āśavaḥ padyābhiḥ in RV 2.31.2: with swift steps/feet.
• rúesthe rakṣathaḥ; c.f. rakṣethe dyubhir aktubhir hitam in RV 1.34.8: you protect through day and night. The protection at night is also mentioned in the Greek hymn(below).
• núkti = nakta (0-graded to aktā) = night; pháos = bhAs shine/light. phero > phérontes = bhara = to bear; náōn= nāvam boat. This protection offered to sailors by the Dioskouroi is mirrored in the marine rescue of Bhujyu stranded at sea that is mentioned in the śruti: yad aśvinā ūhathur bhujyum astaṃ śatāritrāṃ nāvam ātasthivāṃsam | RV1.116.5: when, Aśvin-s, you ferried Bhujyu to the shore after he mounted your ship of a hundred oars.

Figure 2. Castor and Pollux on a coin of the Roman republic with the ship on reverse.

Some notes on the Indo-European aspects of the Anatolian tradition

Prolegomenon
This section is primarily for students of the old religion who approach it from the Indo-Aryan direction and tend to be less aware of the West Asian material. The Anatolian branch of “Indo-European” (in quotes because this appellation becomes inaccurate once Anatolian is brought into the picture; see below) has no living representatives. Modern linguists usually recognize 5 major branches: Hittite, Luwic, Palaic and Lydian, of which the Luwic dialect of Pisidian is the last attested from around 1-200 CE. In 1812 CE, Burckhardt discovered Anatolian monuments with strange hieroglyphic inscriptions in an unknown language. Eventually, this language was deciphered as Luwian. The archaeological excavations conducted by Winckler and Makridi at Boghazköy in 1906 CE led to the discovery of the erstwhile capital of the great Anatolian power, the Hittites. This site yielded a massive library of thousands of clay tablets in the cuneiform script originally developed for the Sumerian language. However, the language of these texts was clearly neither Sumerian nor Akkadian (a Semitic language that adopted the cuneiform script). In 1915 CE, Hrozny made a major breakthrough in the grammatical structure of the language by recognizing that it had vibhakti-s similar to old Indo-European (preserved in an archaic form in Sanskrit). These corresponded to sambodhana (vocative), prathamā (nominative), dvitīyā (accusative), tṛtīyā (instrumental), caturthī+saptamī (a common dative-locative), pañcamī (ablative), and ṣaṣṭhī (genitive). This finding led to the realization that the Hittite language might be an Indo-European one. In the following years, relatively easy texts were deciphered, and over time an increasing diversity of texts, spanning religion, politics and administration, were at least partially understood.

These developments have led to the unequivocal realization that Anatolian is a branch of the Indo-European family. However, its grammatical structures and linguistic features suggest that it was the earliest known branch of the “Indo-European family”; hence, the more correct term for the hypothesis describing the family would be Indo-Hittite. Linguistic phylogenetic analysis strongly suggests that the next branch to diverge from the stem was Tocharian. Archaeogenetic evidence is consistent with the progenitor of this branch corresponding to the Afanasievo Culture, which branched off from the early Indo-European Yamnaya Culture in the Caspian-Pontic region and rapidly moved eastwards by around 3300 BCE. On the western steppe, the remaining early Indo-Europeans interacted and admixed with the European farmers, represented by the Globular Amphora culture, to give rise to the clade that might be termed “core Indo-European”. These had begun rapidly splitting into the stems of the other major Indo-European lineages (e.g., Italo-Celtic, Greco-Armenian, Germanic, Balto-Slavic, and Indo-Iranian) latest by 3000 BCE. Over the next 1000 years, they launched several invasions radiating out of their homeland to cover much of mainland Eurasia. Together, these observations would mean that Hittites were not part of these Indo-European expansions but represent an early movement that happened prior to 3300 BCE.

So far, neither archaeogenetics nor archaeology has given any definitive clues regarding how the Anatolians reached their destination from the steppes. While both routes, via the Balkans and the Caucasus, have been proposed, there is currently sparse evidence in support of either scenario. Given that the above-mentioned branches of Anatolian are restricted to Anatolia and its immediate environs, the divergence likely happened in situ. Given the degree of their divergence, one may conservatively infer that they had arrived in the region sometime between 2800-2300 BCE, if not earlier. However, the actual records of Anatolian are later than that — Hittite words are first seen as loans in the records of Akkadian (an extinct Semitic language) businessmen operating in Anatolia from around 1900-1800 BCE. The Hittite kingdom emerged even later — only around 1700 BCE, with the names of their first great kings, Labarna I and Hattusili I, being recorded a little after that. This first kingdom of the Hittites lasted till around 1500 BCE. Between 1500-1380 BCE, the Hittite lands were dominated by Hurrian rulers, who were probably aided by Indo-Aryan warriors from the Sintashta-Andronovo expansion. In 1380 BCE, the Hittites made a comeback and waged war against the Hurrian state of the Mitanni led by an Indo-Aryan elite (e.g., their king *Sātavāja>Sattivaza), who were likely in an alliance with the Egyptians and had arisen to considerable power between 1600-1500 BCE. The treaty between Suppiluliuma I and Sattivaza is famous for listing the Indo-Aryan gods, Mitra, Varuṇa, Indra and the Nāsatya-s.

The aggressive military action of these new Hittite kings eventually led to the collapse of the Mitanni kingdom to their east; however, their growing power brought them new rivals, such as the Egyptians. The transport of Egyptian prisoners to their capital is suspected of having transmitted a disease. As the Hittites were weakened by the epidemic, which lasted 20 years, an alliance formed against them in western Anatolia led by the Arzawa, who spoke a distinct branch of Anatolian (Luwic or Lydian), several Hittite vassals and the Mycenaean Greeks. While the Hittites were wilting from the disease and the attack, they are believed to have used biological warfare by sending infected rams to the Arzawan alliance. In the aftermath of this event, the Hittites finally turned the tables on these rivals in the final phase of the reign of Mursili II. With this victory and the epidemic drawing to a close, the Hittites reached the climax of their power around 1300 BCE. However, this intensified their conflict with the imperial Egyptians — they fought a great chariot battle at Kadesh, but neither side could gain a decisive victory in the war. Thus, they settled for a marriage treaty in 1270 BCE. New enemies arose in the East in the form of the aggressive Assyrians, who had occupied the former Mitanni lands and waged destructive wars on the Hittites. In 1237 BCE, the Assyrians led by Shalmaneser I and Tukulti-Ninurta I defeated the Hittites in a major showdown at Nihriya, which was perhaps in the vicinity of the upper reaches of the Balih River. The Assyrian emperor Tukulti-Ninurta I then forced the Hittites to stop aiding the Kassites and conquered Babylon. While the Hittites continued to retain control over the Anatolian heartland, their power declined after this rout, and they were destroyed around 1170 BCE by unknown invaders. It is conceivable these invaders had some connection to an Iranic group (perhaps related to the Hakkari stelae) that came down from the steppes to the North.

The Anatolian languages were proximal to several distinct languages. When they arrived in Anatolia, they appear to have conquered a pre-Indo-European people, the Hattians, who spoke the Hattic language. This language might have descended from the ancestral language of the Anatolian farmers. Hattic influenced Hittite and was used alongside it. There are bilingual texts; for example, in one called “When the Storm-God thunders frightfully” following the ritual injunctions in Hittite, the ritualist is called to recite some Hattic incantations. Then there were the Urarto-Hurrian languages of unclear affinities that were spoken by the Hurrians. Several texts were translated from Hurrian into Hittite. The use of the cuneiform script and geographic proximity brought them in contact with the Sumerian language; Sumerian logograms were often used for Hittite words. To the East, the successors of the Sumerians, the Akkadians, who spoke an East Semitic language also influenced the Hittites and they deployed Akkadian logograms in their written language. To their south, their contacts with Egypt brought them into the sphere of Egyptian, a distant cousin of Semitic within the Afro-Asiatic family.

In addition to these local languages that preceded the presence of the Hittites in the region, there were the two core Indo-European languages that appeared in the locale as a result of their later expansions. To the West, the Greeks appear to have closely interacted with the Lydian and Luwian branches as part of the Arzawan alliance (probably the Greek memory of this event relates to the Trojan war that many believe relates to their attack on the Hittite province of Wilusha). To the East, the Hurrian state of the Mitanni had an Indo-Aryan elite, which appeared in the region by at least 1800 BCE (probably the western branch of the same Indo-Aryan group that conquered India). In the Kizzuwatna kingdom (today’s southern Turkey), which was allied with the Mittani before their conquest by the Hittites, we again find some of the kings or elites, such as Pariyawatri (<Paryavatri) and Śūnaśūra of likely had Indo-Aryan ancestry. Similarly, other Indo-Aryan (*Devātithi, *Subandhu, *Sumitra and *Suvardāta) and Iranic chiefs (Vidarṇa) were also operating in the Levant and Syria to the East and the Armenian states of Hayasa and Isuwa through the period of 14-1200 BCE. The direct contact with the Hittites is indicated by the Indo-Aryan loans seen in the famous equestrian manual of Kikkuli from the Hittite lands. Moreover, as suggested by Mayrhofer and Petrosyan, the theonym Akni found in a Hittite source and identified with the Sumerian Nergal/East Semitic Erra (fiery god; literally the scorcher) was most probably the Indo-Aryan Agni. Given the evidence for the Indo-Aryans in the Pontic steppes (Sindoi and Maeotians), it is not clear if they arrived in West Asia in a single invasion or multiply via the Caucasus (given their Armenian presence) from a base in the North.

Thus, in addition to their early divergence (usually linked to their retention of the laryngeals), their long presence in Anatolia with several neighboring cultures resulted in the Anatolian languages acquiring some peculiarities setting them apart from the rest of the Indo-Europeans. One example of this is the ergative formation (like Hindi and other Apabhramśa-s in India) that was probably acquired from Hattic. This influence also probably resulted in the loss of the feminine gender and the development of a new saptamī-like vibhakti, which has been termed the allative (could also be Semitic influence). Other simplifications are also seen in parallel with some of the later IE languages, such as the loss of the dual number and a reduced verb gradation — for instance, Hittite has a verbal distinction comparable to that between parasmaipada and atmanepada but does not have a true passive. Likewise, Hittite has only a single preterite and lacks the complex gradation of the past tense seen in the ancestral core IE. Moreover, most verbs conjugate comparably to Sanskrit asmi. Nevertheless, the Indo-European form is quite recognizable for several words. Below, we tabulate some well-known examples (it is not clear if the Hittite s was pronounced as s or ś; hence we simply render it as s):

Hittite	Sanskrit	Comment
ĕsmi	asmi	I am
ĕssi	asi	you are
eszi	asti	s/he is
asanzi	santi	they are
estu	astu	may he be (Skt loṭ: imperative)
asantu	santu	may they be (loṭ)
esun	āsam	was (Hittite preterite; Skt laṅ)
paah-si	pāhi	protect (loṭ)
dah-hi	dhiye	take
daskimi	dedhīye	take repeatedly (yaṅanta: frequentative)
hartkas	ṛkṣas	bear (Ursus)
yugan	yugam	yoke
tāru	dāru	wood
nĕpis	nabhas	cloud
hastai	asthi	bone

The dynamics of the IE conquests were evidently related: 1) the mass of the mobilization in each of the invasions; 2) the density of the local populations and the resources they could command; 3) Potential military alliances with local groups. The core IE conquests in Asia and Europe can be loosely compared to those of the much later Chingizid Mongols — they were rapid and vast in their scale, often overthrowing and dominating deeply entrenched and densely populated agrarian centers. This evidently implies an effective military apparatus, even though we do not fully understand all its dimensions and how it was applied. In the first phase of the conquest of Europe, it is conceivable that a mixed economy combining some farming (probably related to the interaction with the Globular Amphora Culture) and mobile pastoralism provided the backbone for their military strategy. The latter evidently involved a degree of horse- and cattle-drawn transport. The second phase of the expansion, which also provided a new impetus throughout the rest of the IE world, was probably dependent on the invention of the spoked-wheel chariot and the breeding of superior horses by the Aryan branch. Both waves of core IE expansions were associated with either large scale replacement of the pre-IE populations (in places like Scandinavia or Central Asia) or the incorporation of the pre-IE populations (accompanied by admixture) within a new IE framework (e.g., Southern and Central Europe, India and East Asia). In contrast, the Anatolian conquest was apparently more gradual. This might reflect the fact that the Anatolians diverged at a relatively early stage before the more effective versions of the IE “military package” were in place. Moreover, they were potentially a smaller invading force entering a territory with long-established sedentary populations with aggressive military capabilities. Nevertheless, even the Anatolian version of the IE package was sufficient to allow their eventual dominance in the region.

Approaching the Anatolian tradition
Due to the above elements the Anatolian tradition, as it has come down to us, will necessarily be somewhat less recognizably IE in its form. This is also influenced by the workers in the field who are strongly affiliated with the study of West Asian and North African languages and traditions and have a strong Afro-Asiatic bias. While Sanskrit (starting with Hrozny) played an important role in the decipherment and apprehension of the Hittite language, the Hittitologists have paid less attention to Aryan philology in understanding the Anatolian tradition. Instead, there has been a much greater emphasis on interpreting Hittite tradition from an Afro-Asiatic perspective. There has also been a long-standing tendency of connecting the Hittite and the Greek tradition — the latest in this direction are the works of Archi, Bachvarova and Rutherford, who continue on the foundation laid by the earlier scholar Singer. This has also overlapped with the tendency to find West Asian or North African roots for various Greek traditions, even when obvious IE parallels exist — a misapprehension going back to Herodotus. While Bachvarova has correctly emphasized the need to turn to Aryan philology for understanding the later West Asian religious traditions, this aspect is quite under-appreciated in Anatolian studies, despite the repeated finding of a proximal, even if subtle, Indo-Aryan presence, in West Asia during the Hittite period.

A leader in Hittitology, Harry Hoffner, Jr, stated in the introduction to his landmark tome on Hittite mythology:

“The key to understanding any society is its living context. No amount of research into the events that transpired during its history, examination of its material remains, or analysis of its language can substitute for the intuitive understanding which comes from being a part of that era and society. Obviously, it is impossible for us to have this experience for any society of the past.”

We agree that this intuitive understanding is a key — no amount of linguistic palavering can substitute for it. While we do not belong to the Bronze Age steppe, we should emphasize that we are the only surviving practitioners of a reflex of the old IE religion quite close to its ancestral state. Thus, we are indeed in possession of a share of that intuitive understanding, which is key to the understanding of these texts. Hence, even though we are no Hittitologist, we believe that looking at the Anatolian texts with a comparative lens from an Aryan perspective is of considerable value in understanding that tradition and more generally the early IE religion. Before we move on with that, we must acknowledge that our presentation owes a debt to the translations and textual work by scholars such as C Watkins, I Singer, HA Hoffner Jr, B-J Collins, M Bachvarova, I Rutherford, JD Hawkins, J Puhvel, C Karasu and D Schwemer among many other contemporary and earlier ones. When we present their translations, we use the terms adopted them by such as “Sun God” or “Storm God”; however, it should be understood that the literal meaning of these translated terms does not carry the valence of the original deities hiding under those terms. However, we cannot do much in that regard as most of these terms stem from Sumerograms or Akkadograms whose actual Hittite equivalents might be unknown unless there are further attributes in the text.

How IE is the Anatolian tradition? We address this question by taking up many aspects of the religion as it has come down to us.

Thousands of gods
The first thing that strikes one about the Anatolian religion is that the Hittites have a large number of named gods, even by the standards of complete IE pantheons, like those of the Indo-Aryans. Now, there are three theological facets to this:

1) IE tradition acknowledges that there are a large number of gods, several thousands or more, even though only tens of them are actually named and distinctly recognized in ritual. Thus, in the Ṛgveda, Viśvāmitra states that:
trīṇi śatā trī sahasrāṇy agniṃ triṃśac ca devā nava cāsaparyan । RV 3.9.9

Thus, the number of gods is given as 3339 (also given in the Vaiśvadeva-nivid) — a number related to the synchronizing of the eclipse cycle and moon phase cycles. However, elsewhere in the RV, this number is given as 33 (with the corresponding goddesses):
patnīvatas triṃśataṃ trīṃś ca devān anuṣvadham ā vaha mādayasva । RV 3.6.9

This latter number is closer to the count of actually named gods. Hence, one could state that the thousand gods of the Hittites are merely a reflection of this. Indeed, we see a reference to a 1000 gods in a similar sense in a Hittite incantation against an imprecatory deployment (CTH 429.12):

“And you, O Sun-god, O Storm-god, O Patron-god, O [all] go[ds], with bow (and) arrow sho[ot the evil tongue], drive away the ev[il] tongues made [before the gods?]! And to the mar[iyani]-field we will take th[e]m, and bur[y] them there. And [let] them disappear from the sight of the gods: away from the Sun-god, the Storm-god, the Pa[tro]n-god, [a]nd from the Thousand Gods let them disappear.” Translation by Haroutunian.
Here, the 1000 gods appear to be a reference to the large number of unnamed gods — only three gods are explicitly named.

2) From the Indo-Aryan and Greek tradition we know that the same god might manifest as a distinctly named deity (devatā) specific to a particular incantation or a specific ritual. Thus, in the different Vedic rituals belonging to the ādhvaryava tradition of the Yajurveda the one god Indra might manifest as a multiplicity of deities, each specific to the ritual like: Indra Kṣetraṃjaya (for conquest of pastures); Indra Gharmavat (Pravargya); Indra Gharmavat Sūryavat (for prosperity); Indra Dātṛ (for amicability of subjects); Indra Punardātṛ (recovery of lost goods); Indra Prababhra (overthrow of rivals); Indra Vajrin (for abhicāra); Indra Vaimṛdha (victory in battle); Indra Indriyāvat (for attaining Indrian strength/senses); Indra Amhomuc (freedom from distress); Indra Manyumat (for performing a heroic deed in battle or capture of foes); Indra Manasvat (godly intelligence); Indra Prasahvan (when the yajamāna’s ritual cow might be seized by a raiding force or victory in Aśvamedha battles); Indra Vṛtrahan (if the new moon ritual is performed after the new moon time); Indra Marutvat; Mahendra; Indra Ṣoḍhaśin (in multiple rituals); Indra Sutrāman (Rājasūya and Sautrāmaṇi); Indra Arkavat; Indra Aśvamedhavat (if one is facing destruction or loss of power); Indra Svarāj (supremacy among rulers). This does not mean that there are 22 different gods but merely that the same god manifests as 22 devatā-s specific to the respective incantations and rites. Further, incantation-specific deification might be extended to items that are not gods, such as the soma-pounding stones or the ritual grass. A comparable tendency is also recorded in the Hittite tradition. In the above list of Indra devatā-s, those with the ancient Indo-European -vant/-mant suffixes are most common. This usage is also seen for other devatā-s (e.g., for Agni devatā-s we have Agni Anīkavat and Agni Tantumant) in the ādhvaryava tradition. We also observe similar theonyms of Hittite deities that we believe stem from a comparable principle. For instance, we have Inarawant (note parallelism to Vedic Indravant; see below), Assunawant (=endowed with excellence?) and Hasauwant (we believe this is a cognate of Skt asu-vant = endowed with life force; Prajāpati is called a related name Asumant in the Taittirīya Brāhmaṇa).

3) In Indo-Aryan, Iranian and Germanic traditions we have the many names of a god — the 300 names of Rudra in the Śatarudrīya incantation and the names of Vāta-Vāyu in the Vāyavya incantation; the incantation of the 101 names of Dātar Ahura Mazdha in the Zoroastrian tradition; the 54 names of Odinn preserved in the Gylfaginning (totally the North Germanic kennings feature at least 207 names of Odinn). This was greatly expanded in the nāmāvali-s of the later Hindu tradition starting from the epics. Thus, one unacquainted with this ancient tendency and the equivalence of the names might mistake their multiplicity for an actual multiplicity of the gods.

From a historical viewpoint, the early Hittite texts contain fewer named gods than the later ones from close to their high point, where the list keeps growing in size. This can be seen as pantheonic accretion from associated cultures, with the addition of Hattian, Sumerian, Akkadian, Hurrian and even Indo-Aryan deities to the mix. However, this does not mean that the accretion proceeded without any identification or syncretism. One could say that a pathway for identification and syncretism was always latent in IE tradition. For example, far removed in space and time, we hear Odinn explain the multiplicity of his names in the Gylfaginning thus:

“It is truly a vast sum of knowledge to gather together and set forth fittingly. But it is briefest to tell you that most of his names have been given to him by reason of this chance: there being so many branches of tongues in the world, all peoples believed that it was needful for them to turn his name into their own tongue, by which they might the better invoke him and entreat him on their own behalf.”

When we take this into account, the Hittites probably had a relatively circumscribed pantheon of specifically recognized gods. The evidence for this comes from the Yazilikaya temple from 1300-1230 BCE. While the iconography and the name-markers of many of these deities are obviously Hattic, Hurrian or Semitic, their organization is unlike anything else in West Asia, indicating a Hittite organizing principle, which is likely of IE provenance. A total of over 80 reliefs are carved in two main chambers, A and B, of the rock-cut shrine. The more elaborate chamber A seems to have originally contained 64 figures (2 of which are largely lost), all or most of which can be identified as gods of the celestial Hittite pantheon. Chamber B with 12+3 figures and is identified with the nether world. Of these, the 12 gods seem to be identical to the 12 in chamber A and the remaining 3 are deities (apart from the Hittite king) which may also be represented in chamber A. Thus, conservatively, we may see the core Hittite pantheon as featuring 64 deities. In chamber A, the pantheon of gods and goddesses are shown as though in procession a towards the central deities, the Storm God and the Chief Goddess placed in the northern direction, from either side of the chamber. A pyramidal crag rises above these central gods — the site was evidently chosen to represent the mountain of the world axis. Chamber B in contrast represents the netherworld. One of the prominently displayed Chamber B deities is indicated by iconography related to the Sumerian Nergal, who was likely associated with Fire God (=Agni) on one hand the lord of the netherworld on the other (c.f., the Iranian relief from Parthian age Hatra where Nergal is syncretized with an Arabian netherworld deity (Zqyqa) and an Iranic deity and shown holding the tricephalic Kerberos in a manner similar to the Greek Herakles. Like Agni, he holds an axe — a characteristic IE feature).

Figure 1. The Yazilikaya pantheon from “Celestial Aspects of Hittite Religion: An Investigation of the Rock Sanctuary Yazılıkaya” by Zangger and Gautschy,  JSA 5.1 (2019) 5–38

Keeping with the world axis symbolism, as has been proposed before (e.g., Zangger et al., most recently), we agree that the organizing principle is astronomical, with symbolism likely derived from IE tradition. On the god side, the procession opens with 12 identically depicted gods — these have been identified with the deities of the 12 months of the year — a number also reflected in other IE traditions, like the Greek Dodecad of Olympians and the 12 Āditya-s of the para-Vedic Hindu tradition. RV 10.114.5 also mentions the offering of 12 soma cups, implying that they are for a count of 12 gods. The 28th and 29th figures of this pantheon are identified as the bulls of heaven (Hurris and Seris in Hurrian), who draw the chariot of the Storm God. These hold up a large lunar symbol; thus, they likely represent the point of the full moon and the duration of the lunar month (since both 28 and 29 hold up the moon symbol, it is likely that both the synodic and sidereal months are implied). This mapping of the gods with the lunar cycle is also seen in the Indo-Iranian world; hence, the Yazilikaya frieze is likely a depiction of the Hittite reflex of the same ancestral tradition. The goddess side of the procession opens with 18 or 19 female deities. Zangger et al propose that this corresponds to the 18/19 year eclipse/lunar cycle — this might again present a mapping related to the number of gods in the RV.

The Storm God
The Storm God of the Anatolians went by the name: Tarhunna (Hittite); Tarhuwant>Tarhunz (Luwian). His name is a cognate of the Sanskrit Tūrvant (e.g., applied to Indra: sanīḻebhiḥ śravasyāni tūrvan marutvān no bhavatv indra ūtī  । RV 1.100.5). Some have proposed that, while it has a clear IE etymology, it might have been adopted to mimic Taru the name of a functionally similar Hattian deity. However, we propose (also apparently favored by Schwemer) that it was transferred from IE to Hattic. We suspect that the Anatolian theonym has an etymological equivalence to the Germanic Indra-class deity. As the Indra-class deity of the Anatolian branch he was identified with a wide range of local, functionally similar deities of cities. In terms of the more widely distributed gods, we can see his identification with the Hurrian Teshub and Semitic (H)Adad. The Hittite exemplar in the Yazilikaya temple is not shown with prominent horns. However, elsewhere his Hittite images (e.g., Mursili III’s seal) and the Luwian depictions frequently show the characteristic bovine horns. While we cannot be sure where this iconographic convention originated, it is clear that it was already widespread across bronze age Eurasia, encompassing, the Bactria-Margiana complex in Central Asia, the Harappan civilization in India, and Mesopotamia and the Anatolian-Hurrian world in West Asia. The same iconography is also textually alluded to in the RV for Indra and other deities (Agni, Rudra), e.g., yas tigmaśṛṅgo vṛṣabho na bhīma ekaḥ kṛṣṭīś cyāvayati pra viśvāḥ ।. Hence, we can say that even if the specific features might have been local, the horned iconography for this deity was likely rather naturally adopted by the Anatolians as they might have had a certain “pre-adaptation” for the same from the ancestral IE tradition. He is also often shown standing on a bull, which is aligned with the frequent references to Indra as the bull. Indra was decoupled from this iconography in the later Hindu world; however, it persisted in association with Rudra who also shows that connection even in the śruti.

Figure 2 Anatolian and Mittani depictions of the Storm God

In terms of weapons, he is depicted as bearing a mace (comparable in form to the classic Indo-Iranian gadā) in the Yazilikaya temple and on the famous seal of the Hittite king Mursili III. A comparable mace is also held by the Hurrian Storm God from a seal from the early Mitanni realm. In this version, he also holds a spear and is shown trampling mountains, suggesting the possible influence of the Indo-Aryan Indra, the terror of the mountains. He also holds a spear while fighting the famous serpent demon in the Luwian site of Malitiya (Arslantepe). The Luwian versions from Malitiya and elsewhere, and the version from the Aleppo temple in Syria show him as holding a trident and sometimes also an axe in the other hand. The axe is reminiscent of one of the types seen on the Yamnaya anthropomorphic stelae suggesting potential IE influence. The trident on the other hand with its wavy prongs is a representation of the famous thunderbolt. We posit that both the mace and the trident are alternative visualizations of the same weapon — the cognate of the Aryan vajra. Some of these iconographic conventions first seen in the Anatolian exemplars persisted till much later in India (the trident-like vajra of Indra, the axe and the triśūla of Rudra) and the Roman empire (Jupiter the thunderer slaying the anguipedian = snake demon and Jupiter Dolichenus; see below). The repeated adoption of this iconographic convention by different IE branches supports an IE inspiration or, in the least a compatibility, following the ancient spread of the convention similar to the horned headgear of the deity. The version from the Aleppo temple also shows him bearing a sword on his belt in addition to the axe and trident. This is reminiscent of the later anthropomorphic stelae from IE sites on the steppes.

Both in Luwian iconography and Hittite mythological texts we have depictions of the Storm God slaying the serpent demon (Hittite: Illuyanka). This myth is found in every branch of IE; thus, it unambiguously belongs to the ancestral stratum of IE mythology. Its Hittite variants mention: 1) baiting of the serpent demon with food: A parallel is found in the Kaṭha Saṃhitā where Indra takes the form of a glob of honey to draw the serpent demon Śuṣṇa to eat it up. 2) At least one Hittite version states that the serpent demon has stolen the heart and the eyes of the Storm God, i.e., something essential for life. He has to then be tricked into giving those back. The Kaṭha Saṃhitā similarly implies Śuṣṇa had stolen the ambrosia (amṛta) of the gods. Indra takes it back by entering his maw in the form of a glob of honey. He then flies out with it in the form of an eagle (a famous IE myth). 3) A preserved Hittite myth mentions an eagle being sent to search for the vanished Storm God. However, a more direct depiction of their connection is seen on the seal of Mursili III, where an eagle is placed in front of the Storm God on his bullock cart (He is also shown holding the eagle on a silver rhyton; see below). Finally, one could also point to the reuse of the West Asian eagle wing symbol with a solar disc in IE contexts, like as the emblem above the Storm God on Luwian stelae.

Finally, the Hittites also preserved a myth of the disappearance of the sun resulting in paralyzing hahhimas (ice; cognate of Skt hima of PIE provenance). While one could imagine a winter frost in Anatolia, the concomitant “disappearance” of the sun is a motif specifically associated with more northern latitudes and is again seen across the IE world. Thus, the appearance of this myth in Anatolia is a clear sign of its IE provenance. In other IE traditions, the Indra-class deity recovers the sun, often doing battle with his vajra-like weapon against the demons, who have hidden the sun. While its details are poorly preserved, the Storm God is repeatedly mentioned in that Hittite text as confronting the freeze with other gods.

The consort and the sister of the Storm God and West Asian syncretism
The Yazilikaya temple pairs the Storm God with his consort who stands on a lion. This chief goddess of the Hittite pantheon is usually identified with the Hurrian deity Hebat and Hattic Wurusemu. We have a remarkable sūkta-like incantation (CTH 384) composed by the ritualist-princess Puduhepa (wife of king Hattusili III), the “rājarṣikā” among the Hittites:

1. O my lady, Sun Goddess of Arinna, lady of the Hatti lands,
2. Queen of the heaven and the earth!
3. Sun Goddess of Arinna, my lady, queen of all the lands!
4. In the Hatti land you take (for yourself) the name of the Sun Goddess of Arinna,
5. but besides (in the land) that you made the Cedar Land (Hurri),
6. you take (for yourself) the name of Hebat.
7. However I, Puduhepa, (am) your maid from the outset…
(translation from Karasu)

Thus, we see that Puduhepa identifies the Hittite Sun Goddess, the queen of heaven and earth (a dvandva like Dyāvāpṛthivī), with Hebat of the Hurrians. On the Hurrian side, we see no evidence for Hebat being the Sun Goddess. On the Semitic side, epithets comparable to those used for the Anatolian Sun Goddess are used in Akkadian for Shamash the solar god rather than for a goddess. However, in the IE world, we see multiple manifestations of the solar goddess (e.g., the whole Indo-Aryan marriage ritual is centered on her). Thus, we posit that the Sun Goddess was inherited from the Anatolian IE tradition, and Puduhepa identified her with Hebat, not due to solar connotations, but because she was the supreme female deity of the Hurrian tradition. Hence, it is probable that the Hittite interpretation of the consort of the Storm God corresponded to their Sun Goddess. In terms of her iconography, she rides the lion — this convention, like that of the horned headdress of the Storm God, has also spread widely across Eurasia encompassing BMAC, Sumeria and its Semitic successors, and Anatolia. A direct parallel can be seen in an Akkadian seal, where the consort of the Semitic Storm God rides in front of his cart on a lion hurling rain or lightning. In textual terms, the large felines (lion, tiger and leopard) are associated with the supreme mother goddess Aditi in the early Vedic layer of the Indo-Aryan tradition.

Figure 3. The consort of the Storm God and the mirror-wielding goddesses

The pairing of the bull-riding Storm God and the lion-riding goddess was an iconographic convention that traveled widely over space and time. In the East, it manifested in the iconography of Rudra and his consort Umā (Rudrāṇī) in India. In the West, it formed the basis of images of Jupiter Dolichenus in the Roman empire. Another Anatolian goddess, who rode a lion, was identified with the ancient goddess Kubaba of the Mesopotamian world. Here name is likely also behind the theonym Cybele, a later goddess from the region, who is iconographically comparable. Interestingly, she is associated with the Anatolian Rudra-class archer deity Santa (see below) in certain texts. Her distinctive feature in the Anatolian world is the mirror, which she shares with Rudrāṇī in India, Tapatī (Tabiti) in the steppe Iranic world, and Juno Regina Dolichena, the consort of Jupiter Dolichenus in the Roman empire. In the Far East, the mirror as an attribute of the goddess was also transferred to the Japanese solar goddess probably from a steppe Iranic source. This mirror iconography is primarily seen in the Luwian reflexes of the Anatolian religion (e.g., at Carchemish), where this goddess might have been identified or syncretized with the supreme Hittite goddess. Consistent with this, like her consort, she may be shown with the cow horns in some depictions. Indeed, such a Luwian pairing might have been the ultimate inspiration for the Dolichenian deities. Given that the mirror is not typical of Mesopotamian or North African goddesses, we posit that the mirror was probably acquired from an Aryan source relatively late in the development of the Anatolian religion. Nevertheless, its eventual wide adoption across the IE world suggests that it resonated with a deeply rooted solar aspect of the goddess.

Finally, we come to the third major Eurasian goddess called Innana in the Sumerian realm, Ishtar by their East Semitic successors (= West Semitic Ashtart) and Shaushka/Shaushga by the Hurrians. She was evidently functionally related to a comparable goddess from the BMAC in Central Asia and probably also to the horned pipal tree goddess of the Harappans. Right from her Sumerian manifestation, she is a transfunctional goddess associated with war, love and medicine. This transfunctionality made her easy to syncretize with high goddesses sharing some of these functionalities from across diverse traditions. Her transfunctionality is amply testified in the historical record: Her Hurrian iconography depicts her heavily armed, emphasizing her military nature. The Indo-Aryan Mitanni ruler Tushratta (<Tveṣaratha) sent such an image of hers with a maninnu necklace having the form of a “bed of her plant” to the Egyptian Pharaoh Amenhotep III perhaps to heal him of his illness — this exemplifies her healing aspect. Finally, the Hittite monarch Hattusili III writes that Shaushga led him to his future wife Puduhepa, the ritual expert, when he was returning from the Egyptian campaign as the commander of the Hittite army under his brother. He specifically mentions that the goddess brought them together in mutual love — exemplifying her sexual facet.

Figure 4. Shaushga and Ishtar. The drawing of Shaushga from the Aleppo is an accurate reproduction by Gestoso Singer in “Shaushka, the Traveling Goddess”, TdE 7 (2016)  43–58

In the Hittite realm, she is indicated by the Ishtar Akkadogram; hence, we do not know the actual form of her Anatolian name. However, we posit that the Hurrian Shaushga had already received influences from the Indo-Aryans in the region that might have also fed into her equation with a Hittite goddess. First, we have the maninnu necklace sent by Tushratta to the Pharaoh that may be etymologized on the basis of the IA word maṇi (amulet/bead/gem) potentially related to her healing power (c.f. Atharvavedic healing maṇi-s). Second, in Shaushga’s Syrian images (e.g., at the Aleppo temple; the other temple depicting her at Ain Dara was recently destroyed by the Turkish and their ISIS Khilafat allies) her iconography shows the following elements: 1) Horned head gear comparable to the Mesopotamian Ishtar. 2) two quivers on either shoulder — this has a Mesopotamian parallel in the form of the weapons rising from Ishtar’s shoulder in more than one depiction. We also have an image of an iconographically equivalent goddess which was stolen and possibly damaged by the Americans during their conquest of Iraq, which shows her with a similar quiver; however, we do not know its exact provenance; 3) She wields a mace which is seen in some Mesopotamian images or a vajra-like weapon; 4) Finally, she also bears an axe that is close in shape to the steppe axes from IE zone (also note Indo-Aryan personal name, Svadhiti = axe, recorded in the region from the Hittite period), such as those found on the anthropomorphic stelae and that borne by Tarhunz; hence, we suggest this element of Shaushga’s iconography was probably due to Indo-Aryan influence. Third, in the Hurrian-Mitanni realm, Shaushga was distinctively seen as the sister of gods starting with the Storm God. In the Indo-Aryan world, the important lunar goddess Sinīvālī is praised as the sister of the gods (and likely also her companion lunar goddesses Rākā, etc. They are probably the sisters of Indra mentioned in RV 4.22.7). This deity persists in later Hindu tradition as the mighty goddess Ekānaṃśā. Hence, the sisterly relationship of Shaushga to the gods could again be a configuration that developed either under Indo-Aryan influence or was an old IE feature coming from the Hittites. Even in the Mesopotamian tradition, in addition to Venus, Ishtar appears to be associated with the moon. Her bull-horn headgear might represent the same. This would have allowed for her easy syncretism with IE lunar goddesses.

Innarawant
Whether the Hittite Innara (Inara) is related to the Vedic Indra has been subject to some debate. The daughter of the Storm God named Inara is well known in the Hittite mythic tradition. A text coeval with the Yazilikaya names Inar(a) as the male god from the Hurrian land, suggesting that the knowledge of a male equivalent existed in the Anatolian world. Thus, Innarawant, which has been taken to mean strong/manly/majestic as a masculine theonym might tie the two together — Hittite often maintains homosemy between the base form and the old IE -vant augmentations. Keeping with the meaning of the name, the ritual in which the singular deity Innarawant is invoked is related to restoring the strength or manliness of the patron. This association calls to mind the Vedic term nṛmṇa (manly) used for Indra. It also reminds one of the ādhvaryava ritual invoking Indra Indrīyāvat for special strength. We list below some of the incantations and ritual actions relating to this theonym (CTH 393: “Anniwiyani’s Rituals”, transcribed and translated by B-J Collins in “Hittite Rituals from Arzawa and the Lower Land”; upper case are Sumerograms or Akkadograms):

I take blue wool, red wool, barley, karsh-grain, and coriander and they roast them. One pitcher of beer, sixteen small thick breads, one goat, one puppy, fourteen pegs of poplar, two small NUNUZ-stones, fourteen small cups, and twelve small pitchers. They make all of the birds out of clay. Whichever bird the augurs observe, they do not omit any.
As soon as night falls, she ties blue wool to the ritual patron—first to his feet, his hands, and his neck, his middle; to his bed (and) the four bedposts the first time. She [the auguress] ties (it) in the same way to his chariot, his bow, and his quiver.
Afterwards she ties red wool in the same fashion. Then the roasted seeds, the thick breads, the implements of fired clay, the pegs, and the clay birds and the small pitchers she arranges in a pitcher. She places it under the bed on behalf of the ritual patron and it remains under the bed for him.
At dawn they cut the blue and red wool off the ritual patron entirely and she places them in the basket. They bring a consecrated girl into the inner house, and they situate her in the entrance. She holds a bird of dough in her hand. The consecrated girl calls, “Go away Protective Deity Lulimi! Come in Protective Deity Innarawant!”
This is followed by dog and goat sacrifices to Innarawant.

One may note the following: 1. The blue and red threads — a close parallel is seen in the Veda in the form of the nīla-lohita threads — RV 10.85.28: an amulet in the marriage ritual. This practice is elaborated in the Śāṅkhāyana Gṛhyasūtra 1.12.8 which recommends tying an amulet of 3 maṇi-s (= gems) to the bride by her kinsfolk with blue-red wool or silk threads. Similarly, as per the Kauśikasūtra a blue-red thread is used with the mantra AV 8.8.24 in the battle ritual. 2. Āpastamba recommends that: sūtre vartmanor vyavastṛṇāty uttarayā nīlaṃ dakṣiṇasyāṃ lohitam uttarasyām । (To the ends of the [spokes of the] wheels [of the chariot by which the groom takes the bride is taken home] a blue thread is tied to the right wheel and a red thread to the left). The tying of the threads to the chariot again presents a parallel to the Hittite ritual. 3. The use of a chariot in the Hittite ritual for manliness is paralleled by the ritual prescribed by the Mānava Gṛhyasūtra 1.3.7 or the Vārāha Gṛhyasūtra 15.3.1 of the Maitrāyaṇīya-s for manly power: anu māyantu  devatā anu-brahma suvīryam । anu-kṣatraṃ tu yad balam anu mām aitu madyaśaḥ ॥ iti prāṅ abhiprayāya pradakṣiṇam āvartayati  । (VGs has upa in place of the particle anu; Tr: “May the deities come following (drive along with) me; may brahma power; good manliness, royal power and whatever is strong come to/follow me” reciting thus, facing east he drives his chariot in a clockwise circle).

The Hittite texts also show a plural form of the Innarawant — the Innarawantes deities — these accompany the fierce archer deity Santa/Sanda who is the bringer of epidemics. This is recorded in the ritual of Zarpiya, the physician of Kizzuwatna (CTH 757), in Hittite and Luwian that is performed when an epidemic strikes the land (which might be related to the great epidemic that swept through the Hittite empire). In that, the ritualists utter an incantation (translation based on those by Collins and Schwartz): “ O Santa (indicated by the Marduk Akkadogram) and the Innarawantes deities, do not approach my gate again.” The Luwian part of the text calls upon these gods to evidently eat the sacrificial sheep or cattle and not the men: “ Do not again approach this door in malice. Eat sheep and cows; do not eat a man, zaganin, tuwiniya.”. The Innarawantes accompanying Santa are rather notably described thus:

They bring in one billy-goat and the master of the estate libates it with wine before the table for Santa. Then he holds out the bronze ax and recites: “Come Santa! Let the Innarawantes-deities come with you, (they) who are wearing blood-red (clothes), the mountain-dwellers, who are wrapped in the huprus garments;
who are girt (?) with daggers, who hold strung bows and arrows. “Come and eat! We will swear (an oath to you)…”

In addition to an animal sacrifice, the ritual involves the offering of 9 libations of wine and 9 offerings of bread. Then 8 virgin boys are called in and one wears a goatskin cloak (c.f. cloak of the vrātya) and howls like a wolf. The others follow him, and they eat the sacrificial meat like wolves. This suggests that the total number of deities in this part of the ritual is 9 = 1 Santa + 8 Innarawantes.

Thus, the cast of the epidemic-associated archer deity Santa and his fierce Innarawantes companions brings to mind the Indo-Aryan Rudra and the Rudra-s or Marut-s. Some specific points include: 1) The term Innarawantes in the plural brings to mind the epithet of the Marut-s, Indravant:  ā rudrāsa indravantaḥ sajoṣaso hiraṇyarathāḥ suvitāya gantana । RV 5.57.1; 2) The Innarawantes are described as being like mountain-dwellers, an epithet used for the Marut-s in the RV: pra vo mahe matayo yantu viṣṇave marutvate girijā evayāmarut । RV 5.87.1; 3) The special mention of their garments in which they are wrapped reminds one of the RV epithets for the Marut-s focusing on their armor and their ornaments: varmaṇvanto na yodhāḥ śimīvantaḥ pitṝṇāṃ na śaṃsāḥ surātayaḥ । RV10.78.3; naitāvad anye maruto yatheme bhrājante rukmair āyudhais tanūbhiḥ । RV 7.57.3; 4) Their being heavily armed again matches the descriptions of the Marut-s: vāśīmanta ṛṣṭimanto manīṣiṇaḥ sudhanvāna iṣumanto niṣaṅgiṇaḥ । RV5.57.2; 5) More tenuously, the participation of 8 lupine youths in the ritual might be a mimicry of the Innarawantes. This brings to mind the repeated emphasis on the youth of the Marut-s in the Veda and the old count of 8 for the Rudra-s.

In conclusion, while the term Innarawant refers to both singular and plural deities we believe that the usage is consistent and reflective of an ancient connection inherited from a PIE tradition. We believe that in the singular form it reflects characteristics inherited from the archetypal Indrian deity and in the plural reflects the Rudrian archetype found in the Marut-s who show an intimate connection with the Indra-class.

Other Anatolian manifestations of the Archer deity
Santa is not the only manifestation of the archer deity in the Anatolian world. Collins points to the Hittite ritual text of the female ritualist Āllī (CTH 402) from the Arzawan locus for countering abhicāra that mentions an Archer deity likely associated with the Orion region of the sky. The opening incantation of the rite goes thus (Collins’ translation):

“Then the wise woman speaks as follows: “O Sun God of the Hand, here are the sorcerous people! If a man has bewitched (lit. treated) this person, herewith he is carrying it (the sorcery) with (his own) back. May he take them back! He is carrying (var. May he carry) it with (his own) back!
If however, a woman has bewitched him, you O Sun God know it, so it should be a headdress for her, and she is to put it on her head. May she take them back for herself! It should be a belt for her, and she is to gird herself; it should be for her a shoe, and she is to put it on!”

These incantations are followed by the invocation of the Hunter:
The Sun God of the Hand and the (divine) Huntsman (are) in front. He (the Huntsman) has his bow [and] he has his [arr]ows. For his dogs let it be bread. [For] the [h]orses let it be fodder. And for the ritual patron [let it be] figurines of clay.” The wis[e woman] puts [them] (the ritual figurines) down.

This is followed by the winding of the blue-red wool (see above) around ritual figurines and their burial. The ritual figures are shown carrying “kursa-s”, which are thematically equivalent to valaga-packages in the Indo-Aryan world.

This is followed by the below ritual actions and incantations:
She steps a little away from there, and at the side of the pit breaks one flatbread for the Dark Ones. Those who turn before the Huntsman, (for them) she (the wise woman) breaks a flatbread with the miyanit tongue. She breaks one flatbread for the dark earth; she breaks one flatbread for the Sun God and recites: “You must guard this!” She breaks one flatbread for the Sun God and places it on the ground. She libates beer before the gods. And she says: “You must keep this evil witchcraft fastened (in the earth)!”
She steps back a little and breaks one flatbread for Ariya and places it to the right of the road. She libates beer and says: “You, seize this evil and do not let it go!” She breaks one flatbread for the crossroad and places it to the left of the road. She libates beer and says: “You, gods of the road — the evil — guard it! Do not let it return!”
She steps forward a little and breaks one flatbread to the salawana-demons of the gate. She sets it down, libates beer, and recites: “Upward [ … ] may you always say good things! GALA-priests, [you] lock up the evil (words/things)!” She breaks a pitcher, and they enter the city.
She puts kars-grain, passa-breads, a bow, and three arrows in a basket and places them under the bed. It remains under the bed (overnight). She ties a strip of wool to the head and foot of the bed.
On the second day, when it becomes light, she takes the basket out from under the bed, waves it back and forth over the person, and speaks: “O Huntsman, you return the sorcery to the sorcerer! Let it be your cure!” She cuts the wool from the bed and places it in the basket.

In general terms, these incantations are notable for the following points: 1) It invokes a solar deity translated as “Sun God of the Hand” — this brings to mind the major Indo-Aryan solar deity Savitṛ whose hands are a prominent feature (c.f. Yajus incantation: devo vaḥ savitā hiraṇyapāṇiḥ pratigṛhṇātu ।; hiraṇyapāṇim ūtaye savitāram upa hvaye । RV 1.22.5 ). 2) Multiple incantations in this ritual have a resemblance to the Atharvan pratyaṇgirā incantations where the kṛtyā is sent back to the sender (e.g., the yāṃ kalpayanti… ṛk). 3) The statements, “you O Sun God know it” and “You must guard this!” are reminiscent of the Atharvan anti-kṛtyā incantation invoking the sun: sūrya iva divam āruhya vi kṛtyā bādhate vaśī । AV-vulgate 8.5.7 (Like the Sun ascended the heaven, blocks sorcery with might.) 4) Here again, we see the use of the blue-red threads; this is similar to the use of the nīla-lohita wool is used in the Indo-Aryan marriage ritual to block the kṛtyā (sorcery): nīlalohitaṃ bhavati kṛtyāsaktir vy ajyate ।AV-vulgate 14.1.26 (Tr: The sorcery becomes the blue-red thread; the sorcery which clings [to the bride] is driven off).

The most notable feature of this ritual is the invocation of the archer deity who goes by the epithet the “Huntsman”. We cautiously follow Collins in accepting Ariya as the likely name of the “Huntsman”, which, in turn, is related to the Greek Orion. The etymology of the Hittite Ariya and Greek Orion remains unclear. However, it is possible that both are related to the PIE root, which is behind forms such as: Hittite arāi (rise up); Tocharian A ar- (bring forth); Avestan ar- (set into motion) comparable to Sanskrit iyarti (liṭ form āra or bhāvakarman for arye; go forth); Greek ornūmi (set into motion); Latin orior (to proceed from source), orīgo (origin). Over a century ago, Lokamanya Tilak had boldly proposed that on the Indo-Aryan side the terms Āgrayaṇa or Agrahāyana might represent a cognate of Orion suggesting, just like Collins for Hittite, that “a” in Indo-Aryan can be seen as validly corresponding to the Greek “o”. While one could question the direct etymological homology of Āgrayaṇa and Orion, Tilak’s semantic equivalence might still be valid. The term Āgrayaṇa arose because Orion in the PIE days stood close to the equinoctial colure in the PIE days — it was the leader of the constellations even as Kṛttikā ( Pleiades) was in the later times. Thus, the Orion/Ariya could have derived from the root related to the “origin” or the point from which the sun goes forth on its journey starting with the vernal equinox. Hence, it is even possible that the terms Āgrayaṇa or Agrahāyana were adopted as semantically appropriate homophones of an ancient word that was a cognate of Orion/Ariya. In this regard, we should point out that the constellation of Mṛgaśiras ( Orion; see below) was apparently known by the name Āryikā in Sanskrit lexicographic manuscripts āryikāstu mṛgraśiraḥ śiraḥ sthāḥ pañca-tārakāḥ ।). However, this manuscript has not been published to confirm the reading (it was also recorded by German Indologist Albrecht Weber). If this reading is upheld, then it might represent the survival of a name of the constellation linking it to the Hittite and Greek versions.

The evidence from the Greek, Iranian, and Indo-Aryan sources suggest that the association of the Orion region of the sky with the Rudrian deities goes back to the ancestor of core IE. Even if the Ariya etymological link does not hold up, there are other features of the Hittite ritual which link the Huntsman to the Orion region of the sky and to the core IE archetype of the Rudra-class deity. Greek, Iranian and Indo-Aryan sources concur that this part of the sky was associated with dogs and an archer/hunter — this association is recapitulated in the Hittite incantation. Rudra is both specifically associated with dogs and is the hunter of the god Prajāpati ( constellation of Orion), who may take the form of a deer. In the Greek tradition, Orion’s death is brought about by the Rudrian deities Artemis and/or Apollo. In one well-known narration of the myth, Apollo directs his sister Artemis to shoot Orion with an arrow. On a painted Greek pot, Apollo is shown killing Orion as he tries to assault Artemis. In other versions, Artemis shoots him down on her own or apparently kills him with a cakra; in yet another, either she or Apollo kills him with a scorpion (constellation of Scorpio) or a snake (depicted on Greek pottery).

There are further parallels between the Greek and Indo-Aryan traditions regarding Orion. The first relates to the myth wherein the goddess Eos and Orion were to join in a liaison. The gods objected to this and directed Artemis to shoot down Orion. This again presents a remarkable parallel to the Vedic tradition: The god Prajāpati was to join in an illicit incestuous liaison with the goddess Ushas (cognate of Eos). The enraged gods sent Rudra to slay Prajāpati, whose corpse is represented in the sky by the constellation of Orion. This cognate Greek and Indo-Aryan mytheme evidently preserves an astronomical allegory relating to the sun being in the vicinity of the constellation at the vernal equinox in ancient times. The other Greek-Hindu parallel relates to the myth of the blindness of Orion. Orion is said to have been blinded by Oinopion when he tried to assault a Pleiad. He then walks eastwards hoping to catch the rays of the sun so that it would cure his blindness. The Śāntikalpa of the Atharvan tradition invokes the constellation under the name the blind one (Andhakā):

āvāhayāmi varadām andhakāṃ śaśivallabhām ।
ehi me andhake devī mṛdu-karmasu śobhane ॥
I invoke the boon-granting consort of the Moon, the [goddess of the] Andhakā constellation. May the auspicious goddess of the Andhakā constellation come to me for the gentle rites.

This name for the constellation evidently comes from the “blindness” demon Andhaka who was killed by Rudra. Thus, the constellation of Orion is not identified with the Rudra-class deity himself/herself, but with the target of that deity in both Hindu and Greek traditions. Hence, we cannot automatically assume that the Huntsman of the Hittite ritual is the constellation of Orion, but rather the Rudra-class deity who is linked to that part of the sky. Both the Indian and Iranian branches of the Aryan tradition concur in identifying the Rudra-class deity with the adjacent star Canis Majoris (the brightest star as seen from the earth) while also identifying the asterism containing that star with a dog.

Beyond, the astronomical connection, even this relatively meager Hittite incantation offers several key connections to the Rudra-class deities in the Anatolian world and beyond: 1) As in the Hittite rite, Rudra-class deities are frequently invoked to repel/hurl back abhicāra in the Atharvan tradition (e.g., in the yāṃ kalpayanti sūkta and the bhavā-śarvīya offerings in the Mṛgāreṣṭi). 2) The horses of the Huntsman are specifically mentioned in addition to his dogs. This is mirrored in the incantation to invite Rudra to the ritual of the Īśāna-bali or Śūlagava, where his horses are specifically mentioned: ā tvā vahantu harayaḥ sucetasaḥ śvetair aśvaiḥ saha ketumadbhiḥ । vātājirair mama havyāya śarvom ॥ 3) In addition to the Huntsman, and the Sun-god of the Hand, the ritual invokes the Dark Ones (marwayanza) and the salawana demons. These two are also associated with another notable manifestation of the Archer God in the Anatolian world going by the name Runta (Dark Ones in CTH 433.2; salawana-demons in CTH 433.3). The epidemic-causing Archer God also receives another name, Iyarri, in Dandanku’s Arzawan plague ritual, where he is again accompanied by the Dark Ones. Finally, the Dark Ones are also mentioned together with Santa in a Hieroglyphic Luwian inscription. This suggests that Santa, Runta and Iyarri are all likely manifestations of the same Rudra-class deity, with the Dark Ones either being cognates of the Innarawantes of Zarpiya’s ritual or a group of beings possibly paralleling the Marut-s or the gaṇa-s or Rudra. In this regard, it might be noted that in some Kṛṣṇa-yajurveda traditions (e.g., Maitrāyaṇīya and Kaṭha) the constellation of Mṛgaśiras is assigned to the Marut-s. The association with the demons is also mirrored in Rudra being called the Asura (tvam agne rudro asuro mahodivaḥ । RV 2.1.6). Likewise, on the Greek side, Apollo is called a Titan in the incantation from the Magical Papyrus for the ritual that was performed at sunrise when the moon is in Gemini.

4) A key connection to the Rudra-class deities is seen in the injunction to make the beer and bread offering to the deity at crossroads. This has a close parallel in the autumnal, disease-curing Vedic Tryambaka-homa:

tānt sārdham pātryāṃ samudvāsya । anvāhārya-pacanād ulmukam ādāyodaṅ paretya juhoty; eṣā hy etasya devasya dik; pathi juhoti; pathā hi sa devaś carati; catuṣpathe juhoty; etad dha vā asya jāṃdhitam prajñātam avasānaṃ yac catuṣpathaṃ tasmāc catuṣpathe juhoti ॥ Śatapatha Brāhmaṇa 2.6.2.7

Having collected all (the cakes from the potsherds) into one dish, and taken a fire-brand from the Anvāhārya-fire, he walks aside towards the north and offers — for that is the direction of the god (Rudra). He offers on a road — for on roads the god roves. He offers on a cross-road — for the cross-road, indeed, is known to be his customary haunt. This is why he offers on a cross-road.

This connection is also seen on the Greek side: The Apollo devatā, Apollo Agyieus (literally Apollo of the road), was worshiped as the manifestation of that deity associated with the road. Like the Hindu Rudra in the classical age, he tended to be worshiped aniconically in the form of liṅga-s. Further, the goddess Hecate, who likely emerged as an ectype of Artemis, is specifically associated with crossroads. 5) The use of a bow and three arrows in the ritual has a specific parallel in the ritual for the Rudra-class deity in the Indo-Aryan soma ritual. After the five-layered altar is piled in the somayāga, a major series of oblations are offered to Rudra with Yajuṣ-es and Sāman-s. In course of this, after the Śatarudrīya oblations are made, another is offered with the famous mantra “yo rudro agnau…” Then the sacrificer or another brāhmaṇa takes up a bow and three arrows and goes around the altar even as the incantation paying homage to Rudra to ransom the sacrificer from the god is recited. The Yajus texts explain it thus:

rudro vā eṣa yad agnis; tasya tisraḥ śaravyāḥ pratīcī tiraścy anūcī । in Taittirīya Saṃhitā 5.5.7
This fire is indeed him, Rudra. His missiles are three — one that comes straight on, one that strikes transversely, and one that follows up.

Indeed, this triplicity of Rudra’s arrow is explicitly connected with the slaying of Prajāpati (Orion) — he was pierced by the trikāṇḍa (tripartite or triple-headed) arrow standing for the 3 stars of Orion’s belt (Skt: Invakā-s) in Aitareya Brāhmaṇa 3.33 and:

atha yasmān nā mṛgaśīrṣa ādadhīta । prajāpater vā etac charīraṃ; yatra vā enaṃ tad āvedhyaṃs tad iṣuṇā trikāṇḍenety āhuḥ sa etac charīram ajahād; vāstu vai śarīram ayajñiyaṃ nirvīryaṃ tasmān na mṛgaśīrṣa ādadhīta ॥ Śatapatha Brāhmaṇa 2.1.2.9
Now, on the other hand (it is argued) why one should not set up his fire under Mṛgaśīrṣa (Orion). This [constellation] is indeed Prajāpati’s body. Now, when they (the gods) on that occasion pierced him with what is called a tripartite arrow he abandoned that body. As that body is a mere husk, unfit for worship and sapless, he should therefore not set up his fires under Mṛgaśīrṣa.

Figure 5. Depictions of the Anatolian deity Runta

This finally brings us to a key association of the Rudra-class deities seen both in the Greek and Hindu worlds — the deer — often their target in their role as huntsmen-archers. This animal figures in the Anatolian world in the context of the archer deity going by the name Runta/(Ku)Runtiya, sometimes identified with Inar. As noted above, the iconographic correspondence and the association with the Dark Ones establishes the equivalence between Runta on one hand and on the other Santa and the Huntsman/Ariya of the above ritual. Runta is indicated by the stag-horn hieroglyph making his connection to that animal explicit. There are several notable depictions of this deity making his connection to the deer explicit:

1) In a scene depicted on an Anatolian silver rhyton, ritualists offer libations and bread to Runta standing on a stag with an aṅkuśa and the Storm God. Both gods hold eagles. The insignia of Runta, namely his quiver, two spears and the slain stag are also shown again separately.
2) In the Aleppo temple, he is shown in a procession of gods and goddesses (including the Shaushga image depicted above) holding a bow and a spear and is labeled prominently with the deer-horn hieroglyph.
3) At Yazilikaya temple Chamber A he is shown with what might be a bow and labeled again with a prominent deer-horn hieroglyph.
4) Altinyayla stele depicts him in the mountains standing on a stag with a bow and holding a stag antler even as a worshiper pours out a libation in front of him.
5) Collins also notes several seals from Nişantepe on which the same deity is similarly depicted.
6) These depictions also suggest that the deity holding a bow and spear behind the storm god on Mursili III’s seal is likely to be the same Archer God.

In conclusion, this web of connections and iconography establishes the deer-associated Archer/Hunter God of the Anatolians as the likely reflex of the Rudra-class deity inherited from the PIE tradition.

Conclusion
While Sanskrit and IE linguistics played a central role in the decipherment of the Anatolian language texts, the prevalent tendency has been to interpret the Anatolian religion quite independently of its IE background based on local West Asian and North African models. This is rather evident in the leading Hittitologist Hoffner’s tome on Hittite myths. While there is no doubt the Hittite religion was imbrued with elements from the West Asian substrata and neighbors, we hold that, with some diligence in the comparative method, one can pick out a clear IE “signal”. However, this signal might be complicated by the interactions with other IE groups such as the Indo-Aryans and Greeks who were also operating in the vicinity during the height of Anatolian power. More recently, workers such as Archi, Bachvarova, Rutherford and Collins admit the Greek connection and explore it further. However, they (to a degree, Bachvarova is an exception) tend to ignore the rest of the IE material, especially Indo-Iranian, when approaching this issue. Here, we present a preliminary redressal of that. We believe that it helps better understand the Anatolian religion and also helps reconstruct the ancestral IE tradition. We propose that while understanding the great diversity of names among Hittite deities we have to be guided by iconographic parallels and the principle of a god presenting as a multiplicity of devatā-s — an important feature of the ādhvaryava tradition within the Vedic layer (subsequently pervasive across traditions) of the Hindu religion. Thus, by the comparative method, we propose that this ādhvaryava tendency had roots in the PIE religion.

It also helps better understand some elements of the Anatolian religion, like the Rudra-class deities. The Hittitologist Archi noted several key features of the Anatolian archer deities and suggested that they inspired the Greek Apollo. Collins hinted at a possible pre-Greek origin for the Ariya/Orion tradition in the Anatolian locus. However, we think these are misapprehensions coming from ignoring the Indo-Iranian parallels. Orion region of the sky is indeed associated with the Rudra-class deity right from the early Indo-Iranian tradition. Once those connections are considered along with their Greek parallels, the Anatolian manifestations are best seen as a PIE inheritance. We are thus led to the conclusion that the association of the Orion region of the sky with the Rudra-class deity was probably a PIE tradition with ancient calendrical associations noted over a century ago by Tilak.

The death of Miss Lizzie Willink

Late that spring, Somakhya and Lootika were visited by their mleccha friend Irmhild. Letting her sleep off the jet lag, they left for work. Given the good weather, Lootika returned early to check on their friend and go out with her prospecting spiders in the nearby woods for their work on endosymbionts. L: “Hope you had some good sleep and are all set to lead our battle-charge? Let me get you something to eat and we’ll head out when the sun goes down a bit. Somakhya and a student will join us in the woods.” Even as Lootika brought Irmhild some snacks, she said: “Restful, but strange. At least I can confess this to you without any embarrassment — After a while, I had a visitation from Lizzie — I’m sure you have heard of her from Somakhya and your folks. In any case, it may be a good sign given what we intend to do.” L: “Ah! they mentioned her in passing, but my recollection is they were not successful in getting her to say anything.” Ir: “I would not be so negative — I learned her name from that really exciting sitting they arranged.” L: “I’d like to hear it straight from your mouth — ain’t it interesting we never got to talk about that in length?”

Ir: “Sure. Taking the story back to the beginning — it relates to the start of my interest in arthropods — I may have been 12 or 13 then. One night, I had what seemed like a dream in which I felt the presence of a woman. I say felt because she was not visually very apparent though I could feel her touch clearly. She seemed very kind and stroked my hair gently in the manner of a parent — I felt her do that even today. Though I did not have much of a visual impression — just something shadowy — I had the very clear impression of her showing me shiny beetles, colorful spiders, mantids and cowrie shells in that dream. On waking from that dream, I was left with a profound curiosity for these little beasties and was driven to learn more about them. As you know, Lootika, it became my life’s work. From then on, she would occasionally drop in, in the form of a vague presence, mostly when I was wide awake. Sometimes she would just stroke my hair or kiss me; other times she would concretely tell me something — her visits often led me to discover something significant. For example, she came on the day I discovered the novel spider bacterial endosymbiont that I subsequently worked on with Somakhya and Indrasena. When we were working on that, the two came to collect some specimens from me at the museum. I can tell you precisely that it was a week before you joined Somakhya at his old place. That evening, I went with them and your sister Vrishchika for dinner. Given the things we got chatting about, it was for the first time I told anyone of the visitations from this shadowy woman — I used to be really scared to tell anyone about it. But your folks were totally cool with it. While interested, they did not seem alarmed that it was pathological. In fact, I specifically asked Vrishchika about that possibility and she just brushed it aside. Instead, she suggested that we make her manifest, and explained how they could do that.

After dinner, they applied one of those magical techniques you followers of the old religion possess and summoned her. I entered into some kind of a trance and they gave me a pen, hoping I’d take a dictation from her. I did take directions from the phantom lady, but there were hardly any words; instead, I had drawn out a beautiful, detailed image of a Madraspatanum mud dauber wasp. While I have a good hand, it was better than anything I had ever drawn. I had never been to India or seen that wasp before. I know that you and Somakhya had obtained an actinobacterium associated with it, but I know you’ll had not illustrated it in your paper. Hence, I believe it was truly a ghost drawing. Below the sketch, in my trance, I had written out the words: ‘Lizzie is really happy with your progress.’ I really do not have a close friend or family by the name of Lizzie; so I was puzzled. However, just before I came out of the trance, I saw a young woman sitting beside me who despite being a total stranger felt strangely familiar. She was clearly an apparition because she wore clothes from a bygone era — I’d say the 1800s. I would estimate her as being no older than in her early twenties. The white sleeve on one of her arms was soaked in blood and she seemed to bleed from one of her eyes that was clearly stabbed by something. I was utterly shocked by the ghastliness of her injuries that marred her otherwise stately appearance. That sight itself totally snapped me out of the trance. Even as that happened, I distinctly heard her say: ‘Dear child Irmhild, stay well.’ While this was in keeping with her maternal attitude towards me, I was surprised by the mismatch it had with her appearance as a young woman. I must remark her accent was clearly of a different era when the flavors of English had not diverged much. Neither Somakhya nor Indra felt anything, but Vrishchika said that she felt a bit of a presence. She also remarked having a mental impression at that point that she was a benevolent and protective phantom who was afraid of being bound. Hence, she said that they would not try a more active procedure to bind her. But I felt happy to have learnt her name and to have seen her for the first time. But that sight left me feeling a bit depressed as her injuries seemed really bad. I wonder if they were the cause of her untimely death and transition to phantomhood.”

Lootika agreed that it would be unwise to try anything aggressive with such a phantom: “I suspect she doesn’t want to make a visual impression as she does not want to scare you with that injured manifestation of hers.” Ir: “That makes sense. However, for some reason, I’ve been feeling a pressing curiosity to discover more about this mysterious Lizzie.” L: “I could try again to get her to speak.” Accordingly, Lootika performed a bhūtākarṣaṇa and waited to see if her friend might experience an āveśa. Irmhild suddenly stopped talking and after a couple of minutes asked for writing material. She slowly wrote out a few words and drew something. Seeing her remain in that state for some time doing nothing, Lootika sprinkled some water on her from her kamaṇḍalu and brought her out of it. Ir: “It looks as though she did not say much even this time, but this is interesting. I seem to have written just a single line though it felt as though I was writing quite a bit. It says: ‘Tombstone 66, Surat European cemetery.’ Lootika, what do you make of this drawing?” L: “Hmm… well, it looks like the map of the said cemetery. I’m sure she is referring to an old cemetery in a city in India, in a state known as Gujarat. Hence, we can look up the map and locate that grave if it still survives. But did you have any other sensation of her?”

Ir: “I must confess to being a bit shocked by her visual apparition again. She seemed very cheerful, but I could not take my eyes off another dab of blood on her collar. The strange thing was she sat just beside you and pointed to her neck and tried to say something that I could not hear. Lootika, did you experience something — you just did not seem to react?” L: “That is part of performing these procedures safely. While we draw in the ghosts, we shield ourselves from them for you never know what they might spring at you. These apparitions from the days of the English tyranny often have a particular hate for my people not unlike their modern counterparts — we have had more than one encounter with such phantoms that needed us to exert all our defenses. However, I too tend to believe this girl is a good phantom.” Ir: “Now the tales of your encounters only make me more curious about this Lizzie. Let us search for this place called Surat. Ain’t it strange she points to a place in India? Could it merely be a projection of me being with you guys?” L: “I think this is genuine. As for Surat, I can take you there on the map in a moment.” Soon Lootika was able to locate the likely cemetery in the satellite image and using the map Irmhild had drawn out they seemed to locate the stated grave. L: “At least that grave seems to be still there — apparently the cemetery is in the care of the Archaeological Survey. Unfortunately, I don’t have anyone in my immediate circle with associations with that city, else I could have gotten more direct information. Let us see if Somakhya or Vrishchika might give us some leads but now it is time for us to make our foray.”

The next day, Vrishchika and Indrasena came over for a visit and they got yarning about their days in graduate school and the like. The topic soon moved to Irmhild’s phantom aide and Lootika told the rest of her latest attempt. As Irmhild’s curiosity remained unquenched, they told her that they could make another attempt with a planchette. Somakhya brought out a Roman letter board and smeared it with a bit of powdered borax: “We have rarely used this one but let us try.” Ir: “Wow! I’m really excited to try that out.” For objectivity, they had Irmhild sit out, while the remaining four operated the pointer. They asked her to silently ask the ghost the questions once she made an appearance. They performed the bhūtākarṣaṇa and waited, but for a while, no one appeared. Somakhya wondered if the ghost might need some comforts and made her an offering of madhuparka. That seemed to work, and she answered in the affirmative regarding her presence. Then Irmhild silently asked the phantom to say more about herself. The pointer moved with some assertiveness right away and she recorded the letters. After that one answer, the board seemed to rattle and Irmhild and Vrishchika said that they sensed her leaving. L: “I guess we should just let her be. She doesn’t seem to want to say much.” When they put the letters together and tried to parse them, they read: “Mr. Blyth’s papers. Zoological Survey. Madraspatanum.” Ir: “Now, what is that even supposed to mean?” In: “I presume she means that we’ll have to consult these papers of a certain Blyth. Who knows if they even survive… Nowadays, her Madraspatanum goes by the name Chennai.” Ir: “Since this is in your country, I guess you guys might be able to find something.” S: “We can try but something so far back in time can be notoriously difficult to track. We can keep inquiries going spanning the breadth of the land from Surat to Chennai, but Irmhild, I fear you won’t have an answer soon.”

All their initial inquires came to naught in the knotty tangle of the Byzantine bureaucracy surrounding the old records from that dark phase of Indian history. Sometime later, Irmhild called Somakhya and Lootika to ask if they could help with a course she was conducting. Before concluding the conversation, she asked if they had any new leads on her phantom visitor. She mentioned that when Indrasena and Vrishchika had visited her a little while back, they had tried the planchette once again and it had issued two words — “Krishnan” and “Charuchitra” — they were taken to be nonsense words, especially given that the second was merely the name of one of Somakhya’s cousins. Nevertheless, she preserved them wondering if it was after all a genuine clue. S: “Dear Spidery, what do you make of those. I have a feeling this is not nonsense.” L: “Why? Charuchitra is a historian. She might be able to find us something about that grave via her connections, But who is this Krishnan?” S: “Indeed. I believe this chap Krishnan is the fellow who maintains the annelid and mollusc collection at the Zoological Survey. Have you forgotten that we had once gone through a torturous series of inquiries to get him to show us their museum collection? Given that we did tarpaṇa to him on that occasion, he might prove helpful in accessing these Chennai archives if they still survive. Let us activate these connections and see if we can give Irmhild something when we meet her.”

In the evening after the classes, Somakhya and Lootika were hanging out with Irmhild. L: “We have big news for you. We have unraveled the mystery of your phantom clanswoman!” Ir: “What? I cannot wait to hear what you have gotten! Why do you say clanswoman? I’m not aware of any such ancestor as far as our records go.” Somakhya: “From her story, we can say that she cannot be your direct ancestor, but you may have to search your family records for a collateral line which would feature her.” Lootika handed over a copy of the document found among the papers of Blyth that had an autobiography of the phantom. L:“Irmhild, given the inferred connection to your clan, I must warn you that parts might be difficult to read. Nevertheless, it seems to bring some closure and solace too.” It was preceded by the following prefatory note from Blyth:

I must now turn to a most singular experience while in my camp near Rayghur, a fort of the chieftain of the Morettos, who had fought our men with much distinction during the mutiny. LW, who had been deceased for nearly 2 years then, suddenly appeared before me in her phantom form on the evening of March 13th, 1872. It was the first and only time in my life I have had an auditory or visual hallucination — I certainly have never experienced anything so vivid and prolonged as this. I affirm that I am stout of heart and of a most unimaginative constitution — yet, this apparition felt as real as anything from this world. She commanded me to record the story of her life and inquired if I had fitted her grave at Surat with the most abominable Hindoo grotesques she desired. I felt in no position to disobey her command. Below, I record her words as I noted them before she vanished and have not attempted to insert any parenthetical notes regarding my own appearance in the third person in the narrative. I can vouch that whatever she said with regard to the events concerning me is entirely veridical.

The words of LW’s phantom:
I was born in what was to soon be the colony of Victoria in Australia where my father JW was then the military surgeon. I was the second of four siblings; my elder brother was Robert; my younger siblings were Edward and Minnie. It was a rough place as we started taking in convicts, but I have considerable gratitude for having spent my early youth there. An important consequence was that I became a skilled equestrian early in life. The second consequence came about when I rode out to the cliffs and discovered fossil shells of cowrie snails. I compared these to the cowries we have today and realized that those from the past were notably different. I began wondering — why had they vanished? From where did the ones we have today come? I asked my mother about this. She said that the Lord the God was unhappy with some of his ante-antediluvian creations and destroyed them in their entirety. But that did not answer how the ones we have today came into being — after all, had the Lord not finished his creation within the first seven days of existence? I got some answers when the naturalist Mr. Sowerby came visiting. He became interested in my collection and in return for them gave me some coins and lent me some books by Sir Lyell and Mr. Owen. I labored through them with much interest. Later I learnt that Mr. Sowerby described the fossil cowries I had found under his name. Shortly, thereafter I found a few more new giant cowries but my family left Australia for the Bombay Presidency in our Indian possessions. My parents insisted that I should go to finishing school and sent me back to England. I abhorred the regimental order of the finishing school and was most certainly amongst the worst of their pupils. Thankfully, my father’s friend, Dr. Parkinson, was rather kindly and took interest in my shells and introduced me to the latest intricacies of natural history. He helped me publish my discovery of the Australian fossil cowries as an appendix to his own tome on fossils.

Around that time, I witnessed a most dreadful apparition. It was a wet evening and after a meager supper, I was buried for a few hours in a tome published by Mr. Wallace. All of a sudden, I was roused from my reading by an unexpected knock on the dressing table. I looked up at the mirror and instead of seeing my reflection, I saw my brother Robert walk out of it. He appeared rather unwell and almost translucent. I feared I might be losing myself or having an attack of nerves. However, he spoke in a most assuring voice that calmed me. Then he said something that frightened me: “The promises of the church are mere platitudes. I neither see the angels nor hear the choir of God. But what the dark Hindoos worship is indeed the truth. I find myself in the retinue of the great god Seeva, who is none other than Dionysos. I’m at peace and so will you be when your time comes.” It took me some time to process this apparition, and when I did so, I feared that my dear brother had passed away in distant India. My apprehensions were confirmed when the Indian mail finally arrived informing me of the tragedy. Robert had caught an ague whilst supervising the opium fields and perished as result far from his native land. I had completed finishing school but was gripped with melancholy and lost interest in my many suitors. Hence, I traveled to Switzerland to spend some time with my mother’s sister. Her family was to go to Cairo; I took that chance to take to the sea with them and return to my family in India.

As I disembarked the smooth-sailing Fairlie at Bombay, the warm air lifted my spirits. I felt a sudden sense of purpose and eagerly scanned the quay for my parents. I finally joined my father and his koelie Joognoo Raum Pondee who took care of my luggage. As we were returning to his post to the south of Bombay, a frightening riot had broken out among the natives. The tillers known as the Ryots wished to rid themselves of their debts and turned on their native bankers known as the Mawrwarees. The Bombay Army under Sir Rose, who had formerly played a pivotal role in crushing the Mutiny, along with some natives of the Scinde Division were deployed to put down the rowdy Ryots. Unfortunately, our convoy came upon a large band of hideous Ryots who were throatily screaming cries that could blanch the stoutest heart. I froze as they threw the bleeding corpse of a decapitated Mawrwaree on the path ahead of us. Our koelie Pondee suggested that we mount the horses that were conveyed by the Scindes and make our way home swiftly via the hills. However, he worried about my safe conveyance as the Ryots closed in. Everyone in our party heaved a sigh of relief when they learnt that I was a skilled equestrian. Thus, after quite an adventure I reached home with my father. Soon, I found myself pampered by more than one dashing suitor, but my mind-numbing job as the governess to the magistrate’s children abraded any joy I might have felt from the ample attention I was receiving.

Thankfully, Pondee, who also worked as a native assistant to Mr. Blyth, put in a word to him about my abilities as a naturalist. Ere long, I had an interview with Mr. Blyth and provided him a letter of reference from Dr. Parkinson. Thus, I became his assistant, and he suggested to me the most interesting possibility of systematically discovering and recording the mantids, hemipterans and coleopterans from the Western Ghats in the Bombay Presidency. I set out twice every week on my horse with Mr. Blyth or Edward and prospected the ravines and hills where the Alexander of the warlike Morettos had once held sway and fought the armies of the Mahometans. I found considerable success in discovering hexapods new to science. Following his advice, I started classifying the insects and increasingly saw the truth in the theories of Mr. Wallace and Mr. Darwin. I had intended to describe these observations together with my mentor Mr. Blyth and had never felt happier before. Unfortunately, my mission met with an unexpected interruption as little Minnie caught a cold and went into decline. I helped my mother in nursing her. One day, when she had to be confined to the bed, I heard the peculiar blare of a strange instrument followed by a strange vocal song. I looked around — neither my mother nor my brother who were in the room with Minnie heard it; nor did Minnie herself. However, our maid, Pondee’s wife, and our native cook, Tauntia, affirmed hearing the same. Pondee’s wife informed me that a great disaster was impending — it was the conch-blare and the dolorous dirge of the Yum-doots — the agents of the Indian Hades who whisk souls away. The next day poor Minnie expired.

It took me a while to recover from my dear sister’s death, but now I returned with an even greater purpose to complete my survey of Insecta. One morning, Pondee informed me that during his prospecting rounds he had found a conglomeration of horned beetles near the Kulwunt eminence; however, he had failed to collect any. I was heading that way; hence, I took the directions from Pondee and set out with Mr. Blyth. On reaching the base of the Kulwunt, we forked onto our respective paths agreeing to meet at 2:00 PM in the afternoon. In my wandering, I came across an old derelict shrine of the Hindoos, which had within it a phallic emblem — a symbol of the god Seeva. In niches on the walls of the shrine were the images of his sons the gods Kaurtic with six heads, the Mars of Hindoos, and the Indian Janus, who bore the head of a pachyderm. Maybe I felt a bit of a swoon from the blazing Indian sun. I decided to drink some water and rest a bit at the platform of the shrine. I began thinking thus: after all, just as the cowries on the Australian cliffs and the terrible lizards of Mr. Owen had gone extinct, even religions had come and gone. Would that not explain why our ancestors had once cleaved to a religion, not unlike that of the natives. I was increasingly drawn to the view, as my brother’s ghost had said, that the religion of the Bible was utterly false and had been foisted on us by the blade of the sword, even as we Europeans have tried to impose it on the black natives. As I got up from my introspection to resume my prospecting, I felt some strange urge to place wildflowers on the images of the gods in the shrine.

Then, as I went to mount my horse, I saw a most dreadful apparition. I now know that it was a mātṛ from the retinue of the great god Rudra. That most frightful divine lady said to me that my allotted term of life was drawing to a close. I asked if I would be joining Minnie and Robert. She responded that due to my act of piety I would join her host and vanished. I brushed it aside as a mere hallucination from the heat and rode on towards the spot where Pondee had spotted the horned beetles going up a narrow path. In retrospect, I should have dismounted but, as the Hindoos say, who can escape what the god Bruhmah has written out for you? For some reason, my seasoned horse bolted and threw me off into the defile bristling with bamboos. I was severally skewered through my arm, neck and eye and could not extricate myself. However, Mr. Blyth heard my cry and was able to locate me after a search. He had to get Pondee along before he could finally get me down from my hellish impalement: by then, I had lost consciousness. Finally, I was taken home and my father started treating my wounds. After the initial treatment, I regained consciousness briefly and spoke once to bid my family, friends, and my suitor Captain Atkinson goodbye for the last time. I instructed them to decorate my tomb with the tridents and drums of the great god Seeva. Only my brother Edward assented but he too expired last year after being hit by a ball while playing cricket. My grieving parents left for England shortly thereafter. My life’s work will not see the light of the day. Hence, as I rejoice in the retinue of the great gods, I will aid a future member of my clan realize more of it than I did.

This was followed by a concluding note from Mr. Blyth:
I had no intention of fulfilling the delirious requests of the dying Ms. LW to place the symbols of the Hindoo Termagants and Baphomets on her tomb. I suspected that she had come under the evil influence of my assistant Pondee’s wife, who clouded her otherwise logical intellect with ghastly superstitions. However, this apparition near Rayghur filled me with such terror that I commissioned a blacksmith to make the needful auxiliaries and decided to fit them on poor Ms. LW’s tomb when I got a chance to visit Surat.

Somakhya: “Irmhild, here is a picture of her tomb. My cousin Charuchitra was able to obtain it via her connections to the Archaeological Survey. Evidently, Blyth never got to furnish it with the symbols of Rudra — he himself passed away a few months later with a fever following a cut to his thumb. The epitaph has not survived in its entirety, but it gives her name as Lizzie Willink — this matches the initials in Blyth’s account. Also note, while they did not furnish it with the tridents and the ḍamaru-s she wanted, they engraved a beautiful copy of one of the fossil cowries she discovered — it bears the unmistakable siphon and whorl peculiar to the Australian exemplar. No doubt she was able to grasp an evolutionary lesson from that. These indicate that the grave pertains to the very same person whose initials are in Blyth’s document.” Ir: “Tragic! The epitaph says that she was only 22 when she died. It now strikes me that the aunt she mentioned in her narrative must be a lineal ancestor of mine.”

[Any resemblance to real incidents or people should be taken as merely convergence in story creation under constraints]

Indo-European expansions and iconography: revisiting the anthropomorphic stelae

Was there an early Indo-European iconography? The anthropomorphic stelae
There is no linguistic evidence for the presence of iconic or temple worship among the early Indo-Europeans. However, after their migrations, when they settled in the lands of sedentary peoples, they adopted a range of religious icons often stylistically influenced by local traditions. Nevertheless, there are some clear iconographic features of their deities and other divine entities that shine through these local styles (to be discussed in later notes). This suggests that, even if iconic worship was not the central focus of their religion, they had definitive visualizations for their deities that emerged early in IE tradition. Moreover, barring the Iranian counter-religion, most branches of IE people adopted iconic and temple worship in the later phases of their tradition. This observation, together with some of the textual features of the early iconic worship of Hindu deities (e.g., caitya-yāga and gṛhya-pariśiṣṭa-s), suggest that early IEans probably did have iconic worship on the steppes itself; it was just not a major expression of the religiosity of their elite.

The archaeology of the IEans was fraught with much confusion until archaeogenomic studies over the past decade greatly clarified the situation. Hence, we can now say with some confidence that we do have a body of archaeological records for early IEan iconography, even if we do not fully understand it. The earliest evidence for this comes from the Yamnaya horizon on Pontic–Caspian steppe that is associated with early IEans. The striking body of iconic images from this locus and time is comprised of the so-called anthropomorphic stelae (Figure 1). These stelae caught the attention of researchers right from the early work of Gimbutas and were subsequently discussed at length by Telegin and Mallory. While their iconographic content and functions continue to be debated, several authors, starting from Gimbutas, have proposed an IEan interpretation. Further, most of these authors have tended to explicitly or implicitly invoke Indo-Aryan themes (e.g., Vassilkov most recently) to provide the imagery with an IE interpretation.

Figure 1. Examples Anthropomorphic stelae from different parts of Africa and Eurasia (2, 4, 6 from Vierzig).

That said, it should be noted that the basic form of these anthropomorphs is widely distributed across Eurasia starting from the chalcolithic-Bronze Age transition, with a core temporal window of 3500-1800 BCE. A survey by Vierzig indicates that apart from commonly occurring in the Yamnaya horizon, they are also densely present in the Northern Italy-Alpine region, Iberia and Sardinia. Moderate to sparse occurrences of such anthropomorphic stelae are also seen in France, Germany, the Italian and Greek peninsulas, Sicily, Caucasus and Northern Arabia (e.g., Hai’l and Tayma’ in modern Saudi and also probably Jordan — the Israeli exemplar). A miniature terracotta version was also reported by Sarianidi in Bactria (see below for more on this). In the East, they are found in the Dzungarian Basin associated with the Chemurchek Culture (2500–1700 BCE) that succeeded the Afanasievo, the Far Eastern offshoot of the Yamnaya. Another successor of the Afanasievo, to the north of the Chemurchek culture, is the Okunevo culture in the Minusinsk Basin. This culture shows some remarkable menhirs that seem to have been influenced in some features by the classic anthropomorphic stelae. These also share features with the stelae from Shimao (roughly 2300 BCE) and later expressions of this theme such as the deer stones of Mongolia (see below) and even the totemic structures in the North American horizon. Finally, we could also mention the menhirs from Dillo in South Ethiopia that might be seen as sharing some general features with the Eurasian stelae under consideration. However, their iconography is again too distinct to be included in this discussion. The distribution of the anthropomorphic stelae suggests that, like certain other iconographic conventions (e.g., the horned deity), this convention too spread widely, even if some versions might have a convergent origin. Thus, a priori, it cannot be identified with a specific culture, though specific versions of them might show a narrower cultural affinity (see below).

The typical anthropomorphic stele under consideration is a simplistic depiction of a human form — usually only a basic outline of the body. The minority of the stelae are furnished with more elaborate embellishments. Despite their simplicity, they display a certain unity that distinguishes most of them from the more divergent menhirs with human features. Further, across the above-mentioned zone, the better preserved and more elaborate versions display some common features: 1) The male figures (which tend to be the majority) are often shown as ithyphallic. This feature is shared by the Arabian, Yamnaya (and its western successors Corded Ware) and possibly at least some of the Iberian versions. 2) The figures often wear a belt around the waist reminiscent of the Iranic avyaṅga. This feature is definitely shared by exemplars from across the above-stated distribution zone. 3) The arms and legs when shown are always presented in a static manner, even when associated objects, like weapons, are depicted. 4) Across their distribution zone, the stelae are frequently but not always associated with graves (this is also true of the Ethiopian anthropomorphic menhirs of Dillo). Even the most elaborate early versions of these anthropomorphic stelae appear simpler than the coeval religious icons of Egypt, West Asia and possibly also the Harappans. Thus, we believe that the anthropomorphic stelae did not have their primary origin in the Egypt-West Asia-Harappan corridor but in the steppes or among the Early European Farmers or in the Caucasus.

Anthropomorphic stelae IE heartland and their dispersal
The early Arabian and steppe versions show sufficient divergence to suggest memetic diffusion rather than direct transmission via invading groups; however, from the time of the Yamnaya expansion onward there are specific features to suggest the presence of an iconographic convention governing their production that was likely transmitted by expanding IE groups. We will first consider this in the context of the Yamnaya artefacts and the western expansion of the IEans. It can be best understood by comparing some famous stelae namely: 1) the so-called Kernosovskiy and Federovsky (Poltava region) idols from what is today Ukraine. 2) The Natalivka stele, again from Ukraine. 3) Cioburciu stele from what is today Moldavia. 4) The Hamangia stele from what is today Romania. 5) The Floreşti Polus stele from interior Romania. All these stelae depict male figures that are unified by the presence of a common weapon the battle axe. Importantly, in the Kernosovskiy, Federovsky, Cioburciu, Hamangia and Floreşti Polus stelae at least one axe is secured via the waist belt of the anthropomorph. These stelae (barring Floreşti Polus: fragmented? and Natalivka: not clear), as well as several others from the Yamnaya horizon (Novoselovka, Svatovo, Kasperovka, Novocherkassk and Belogrudovka), are also unified by the depiction of the outlines of the feet (Skt: pādukā-s). The Kernosovskiy, Natalivka and Svatovo stelae from Ukraine display a bow as an additional weapon. The profile of the axe common to all these stelae is boat-shaped and corresponds to the battle axe seen in the western successor of the Yamnaya, viz., the Corded Ware culture. Such axes are frequently buried in the Corded Ware graves believed to belong to elite males. One of the ārya words for the axe is paraśu, which has cognates going back to proto-Indo-European. It is quite possible this type of axe was indeed known by that ancestral IE word. On the whole, these features support the IEan provenance and westward movement of this type of anthropomorphic stele into Europe.

Figure 2. Yamnaya-associated stelae.

The Kernosovskiy idol depicts a second kind of axe with a distinct head profile. This may be compared to a recently reported massive metal axe, weighing just shy of a kilo and blade length of about 21 cm from the Abashevo culture (in the middle Volga and adjacent Ural region), which likely represented the Aryans before their southward expansion. The Ṛgveda mentions two distinct types of axes, the paraśu and the vāśī. The word vāśī does not appear to have cognates outside the Indo-Iranian branch among the IE languages. It is possible that the eastern movement of the Corded Ware-like cultures acquired a distinct type/word for axe from other local populations. But the presence of two distinct types of axes on the Kernosovskiy idol from the Yamnaya period suggests that a second type of axe might have been acquired even earlier but only used in certain descendant IE cultures.

Figure 3. Chemurchek stelae. 1 and 2 from Kovalev. 3 from Betts and Jia.

Turning to the eastern transmission, we find that a bow held in a manner similar to the Yamnaya stelae is featured in at least three anthropomorphic stelae at Chemurchek sites (2750-1900 BCE). One of these (published by Kovalev) holds another weapon, which could be either an axe or an aṅkuśa paralleling the Yamnaya stelae. A similar axe or aṅkuśa is held without a bow in the hands of three other stelae from the Chemurchek culture and can be seen on the Belogrudovka stele in the Yamnaya group. One of the Chemurchek anthropomorphs holds something like a mace comparable to what is found on the Kernosovskiy idol. Until recently the affinities of the Chemurchek people were uncertain. However, the archaeogenetic study of Zhang et al provides some clarity in this regard. First, the eastern offshoot of the Yamnaya, the Afanasievo underwent local admixtures with the Tarim early Bronze Age population (the source population of the famous Tarim mummies) and to a smaller degree with the East Asian “Baikal Early Bronze Age” giving rise to the “Dzungarian Early BA1” population. Next, this mixed, again with the Tarim BA, and a Namazga/Anau-I chalcolithic-related population (Geoksyur) to give rise to the Chemurchek people. Thus, the genetic evidence supports an ultimate link between these cultures and the Yamnaya derived populations, suggesting that iconographic similarities in the eastern anthropomorphic stelae are related to the Indo-European movement to the east. In this scenario, a Chemurchek-related population rather than the Tarim mummies population likely gave rise to Tocharian languages. However, a wrinkle remains regarding the Afanasievo situation: while Mallory claims that stelae have been recovered in that horizon, we have found no evidence for such so far in the literature. This may point to greater diversity within the early Eastern extension of Yamnaya than previously appreciated (see below section).

Figure 4. Okunevo and Shimao stelae. 1-4 Okunevo stelae (from Polyakov et al and Leontiev et al). 5 Shimao stelae (from Sun et al).

Before we leave the footprints of the Yamnaya expansion on the eastern anthropomorphic stelae, it would be remiss if we do not touch upon the Okunevo menhirs and the Shimao stelae. Like the Chemurchek culture, the Okunevo culture (2600-1700 BCE) represents a bronze age admixture between the IE and East Asian populations that arose from a comparable, but distinct, admixture of the Afanasievo with Tarim BA and Baikal BA populations, probably driven primarily by males. The Okunevo anthropomorphic stelae/menhirs share the general similarity of the round facial profiles with some of the Chemurchek stelae from the Kayinar Cemetery. However, beyond this they show much diversity and several striking and unique features, such as: 1) a halo of elements emanating from the faces, like rays, waves (often terminating in lunes) and dendritic structures. 2) A frequent motif featuring a central dyad of concentric circles surrounded by four cusps shaped like an astroid. 3) Peculiarly curved mouth on the anthropomorph. 4) Depictions of stylized animals like wolves and elk (both of which acquire mythic significance in the much later Turko-Mongol world). 5) Unlike the Yamnaya stelae they lack a belt. The earliest Okunevo specimens are close in form to the simplest versions of the Chemurchek stelae. Some of these early Okunevo versions also share a bovine motif with the Yamnaya stelae (e.g., Kernosovskiy). They acquire the greatest complexity in the middle Okunevo period with all the above-mentioned distinctive features. The first half of the middle Okunevo period is marked by the unusual tall menhirs (up to 5m tall) often depicting multiple anthropomorphic or theriomorphic faces. The Okunevo stelae/menhirs are distinguished from the Yamnaya and Chemurchek versions in almost entirely lacking weapons — we are aware of only a single exemplar from the middle Okunevo period where the anthropomorph is flanked by two tridents. To our knowledge, tridents are unknown in any of the other early steppe stelae.

We propose that the Afanasievo-like founder populations of Chemurchek and Okunevo were probably either the same or close, but distinct from other sampled Afanasievo groups that seem to have lost the ancestral stelae (contra Mallory?). This population introduced relatively simple stelae to founders of both these populations at the time of the admixture with local groups. The Chemurchek retained these in a largely conservative form, whereas Okunevo innovated upon it probably drawing on the mythemes coming from their Northeast Asian founder population with links to Siberia. This might explain the parallels between the later and the Inuit and American totems. The weaponless Okunevo stelae with exaggerated facial features and expressions are also mirrored in the iconography of the stelae from the early neolithic urban site from Shimao, Shanxi province of China (2250-1950 BCE). As these have no Chinese antecedents, it is quite possible that they were influenced by the contemporary IE-admixtured cultures to their north (a contact possibly also responsible for the dawn of the metal age in China). Currently, the archaeogenetic information from the Shimao is limited but suggests affinities to the Northern East Asian populations related to that contributing to the ethnogenesis of the Okunevo. Thus, it points, in the least, to a role for a similar population as that involved in the emergence of the Okunevo and the potential diffusion of iconographic elements.

Stelae associated with subsequent pulses of steppe expansions
We shall next survey the reflexes of the stele iconography associated with the later pulses of expansions from the steppes. The first of these was the Aryan expansion which is associated with the Sintashta culture and its successor Andronovo culture that spread out over the steppe. Based on the phylogeny of extant horses and the spread of chariotry through the old world, we believe that the Aryan expansion marked the second great IE wave from the steppes after the initial Yamnaya expansions. In cultural terms, this wave might have played a role in reinforcing old IE steppe traditions even among the earlier branches emanating from the first Yamnaya expansion — sort of an Aryanization of the earlier IEans. Archaeogenetics has established that, while the Aryans appeared at the BMAC horizon by around 2100 BCE, they did not carry any of that genetic admixture to India. After 1500 BCE we find both noticeable BMAC and East Asian admixture in the steppe Aryans of the Andronovo expansion. This East Asian admixture was also not carried into India. Further, these results indicate that: 1) The Aryan conquerors of India did not tarry much at the BMAC or only marginally skirted it as they entered the subcontinent. 2) In the subcontinent they underwent admixture with the Harappan people. The subsequent presence of individuals with both Aryan and Harappan ancestries back on the steppe in Central Asia (Narasimhan et al) suggests that the Indo-Aryans initially established a polity that spanned the Indian subcontinent and the steppe. 3) This should have happened between 2000-1500 BCE. After that, the Indo-Aryans remained in India and the connections with the central Asian steppes diminished. In contrast, the Aryans who remained on the steppe interacted and underwent admixture with the BMAC. We can say that this played a major role in the emergence of the Iranic tradition. The key marker for this is the camel — an important domesticate and cultural animal in the BMAC culture. While the camel is known by the cognate word (uṣṭra) in the Ṛgveda, it is neither prominent nor a part of human names (unlike the old IE horse names). In contrast, the camel is a common part of early Iranic names (Zarathuštra, Frašauštra, Vohūštra, Aravauštra) and is more frequently encountered in their early mythosphere as a holy animal (e.g., as an incarnation of the god Verethragna). This indicates that the counter-religion of Zoroastrianism developed in close proximity to the BMAC probably influenced by its substratum religion. Consistent with this, after 1500 BCE, we start observing increasing BMAC admixture among steppe Aryans along with East Asian admixture.

Figure 5. BMAC anthropomorph (from Sairanidi).

In terms of anthropomorphic stelae, we find a signal for iconography portrayed on it at the gateway to India. At the BMAC site of Bactria, in the temporal window approximately corresponding to the arrival of the Aryans at this horizon, Sarianidi reported an anthropomorphic terracotta icon in a ritual vessel. This closely resembles the Yamnaya stelae with the trademark belt with an axe of the classical Corded-ware type attached to it. This object along with some other terracottas from ritual vessels are distinct from all other BMAC artefacts suggesting their origin from an extrinsic culture. Asko Parpola has claimed that the axe is related to the adze-axe found by Mackay in a late layer of Mohenjodaro, which he identifies as a marker of Aryan presence. While we tentatively agree with his proposal of it being a signal of the Aryan entry into the Harappan lands, there is no evidence that the axe on the belt of this anthropomorph is the adze-axe. A possible signal of a Sintashta/Andronovo derived pulse reinforcing steppe traditions among the western groups is found in the Iberian Peninsula from around 1700-1000 BCE. These Alentejo-type stelae combine motifs of the older Yamnaya stelae and the later stelae (see below). On the Yamnaya side we see the footprint motif (e.g., Alentejo stele of Gomes Aires), the bow, and the bovine or equine motif and on the later side, motifs shared with the Mongolian deer stone-khirigsuur complex and Śaka-like stelae (see below), such as the use of the sword and its mode of fastening to the belt.

As for the Aryans who remained on the steppe there was definitely some diversity with groups closer to both the Indic and Iranic branches and perhaps a third branch with relics like the Kalasha. One such group followed in the footsteps of the older Afanasievo expansion to invade the Eastern steppes. Their appearance is indicated by Mongolian deer stones found in a circumscribed latitudinal band defined by the Baikal Lake and the steppes of Mongolia and spanning the region starting between the Ili and Irtysh to the western reaches of the Amur. These artefacts are named so for dramatic depictions of the Asian elk (sometimes avicephalous) with prominent antlers — a feature shared with some of the Okunevo stones. On rare occasions, the stone might also depict reindeer or moose. They are often associated and with stone circles that are sites of horse sacrifices and are connected to the coeval emergence of khirigsuurs (Mongolian equivalents of Kurgans) on the open steppe. Thus, this culture has been referred to as the deer-stone-khirigsuur-complex (DSKC). These stones have a much more elongated rectangular form than the Yamnaya versions with the top usually depicting an anthropomorphic face to the east. Below the “face” are the depictions of the deer and below them is the characteristic belt of the anthropomorphs. Often weapons and sometimes other implements are shown attached to the belt. While weapons associated with the belt are a feature shared with the Yamnaya stelae, their mode of attachment in the deer stones, i.e., suspended below the belt, is very uncommon in the former stelae. This mode of attachment, to our knowledge, is seen in a single Yamnaya stele, namely the Kalitche exemplar from Bulgaria (probably marking the early IE movement towards the Balkans). It is also seen on the Olkhovchik stele (probably early Śaka or other steppe Iranian), several later Śaka stelae, and the Śaka-inspired Slavic Zbruch idol, all from a later phase of steppe IE (see below). The weapons include axes, bows, quivers, swords and daggers. The axe is generally of the second type found on the Yamnaya stelae. This overlap in the weapons associated with the belt suggests a connection of the Mongolian DSKC to the IEans from the Western Eurasian steppe. The other implements are fire starters and chariot rein hooks. The latter indicates a connection to a distinct IE culture from the Afanasievo, namely one with chariots. Consistent with this, a large body of C14 dates over the past 2 decades has indicated that the DSKC is from 1350-900 BCE, which is a much later period than Afanasievo or even the Chemurchek and Okunevo cultures. Jeong et al’s archaeogenetic analysis indicates that the DSKC people emerged from an admixture of the Andronovo expansion of the Aryans with the Baikal Early Bronze Age population. A few individuals also show some Bactria-Margiana Archaeological Complex (BMAC) component, which as noted above was picked up en route to the East. Thus, the DSKC stelae, like the Okunevo situation, probably represent a synthesis of IE (e.g., the belt-associated weapons) and Northeast Asian motifs (e.g., the elk) coming from the two divergent founder populations.

Figure 6. DSKC, Śaka and Turkic anthropomorphs (From Telegin and Mallory and Fitzhugh).

By 1000-800 BCE certain horse-borne (as opposed to chariot riding) Iranic groups started dominating the steppes. In Indo-Iranian tradition, these groups are referred to as the Śaka (the Achaemenid Iranian inscriptions mention several distinct types of Śaka-s) and the Greek tradition remembers the same or related groups as Cimmerians, Scythians and Sarmatians (likely Iranian Sairima). There were probably other steppe Iranic groups, like Alani, Arimaspa-s, Massagetae, Kuṣāṇa-s, that might have been distinct from the Śaka-s but for this note, we simply refer to Śaka and other steppe Iranics as Śaka for short because they seem to have been the primary authors of the stelae under discussion. Archaeogenetic work by Unterländer and Gnecchi-Ruscone has shown that the Śaka emerged in East Asia and shows a three-component admixture with Aryan, Mongolian Baikal Bronze Age and BMAC ancestry. Given that a similar admixture is seen in the Mongolian DSKC people, a population related to the DSKC was potentially the progenitor of the Śaka-s. These proto-Śaka-s then moved across the steppes, all the way to the western Eurasian Pontic end — this is established by the presence of this Mongolian ancestry even the Sarmatians of the Caspian-Pontic region. Thus, one could say that the proto-Śaka expansion was the first great Mongolian expansion — a pattern of steppe expansions that was to be followed by the Huns, Turks and Khitans, Chingizids and Jurchen over the next 3000 years. However, this one was by a group with a notable Aryan ancestry. This proto-Śaka expansion is dated on archaeogenetic and archaeological grounds to around 1300-900 BCE. This was followed by two secondary pulses of steppe-Iranic expansions between 800-100 BCE in the form of the Sarmatian expansion from North Kazakhstan, just east of the Caspian, and the Eastern Śaka expansion from the Mongolia-Kazakhstan borderlands. The latter one eventually brought the Śaka-s to India, where they established kingdoms before their defeat and absorption by the Andhras and Gupta-s.

Figure 7. Hakkari stelae.

The mysterious Hakkari stelae from what is today Turkey are also perhaps related to the proto-Śaka expansion. These are believed to date from 1000 BCE and correspond to the kingdom known as Hubushkia in the Assyrian sources. The artistic quality of these stelae is much higher than any of their steppe counterparts and they include both male and female figures. The male figures are all well-armed in ways closely paralleling the Yamnaya versions, like the Kernosovskiy idol. The weapons include axes, spears, maces, shields, aṅkuśa-s, bows, and a dagger that is usually fastened via the belt. Like in the case of some Yamnaya ones, many of them feature secondary human figures, and several other animals including the horse, ram, deer, snake and a possible felid. They also show the primary human figure as holding or drinking from a cup. This feature persisted in the later Śaka and Turko-Mongolic stelae and balbals. Given the iconographic correspondences in the Hakkari stelae to the Śaka versions from a younger period and the Yamnaya/other steppe stelae from an earlier period, we believe that they were commissioned by a steppe group that entered west Asia, probably by crossing the Caucasus (see below). If the dating of these Hakkari stelae is correct, then they fill an important gap between the earlier steppe versions and the classic Śaka versions which we shall look at next.

The Olkhovchik stele might represent a proto-Śaka exemplar followed by a profusion of such stelae from across the Eurasian steppe down to the Caucasus. It is believed that by 1000-900 BCE they appeared in the highlands of Armenia and by 700-300 BCE in Georgia, Crimea and the Pontic steppe. The northernmost reaches of the Śaka expansion are indicated by the recently reported anthropomorphic stelae/menhirs from Ust-Taseyevsky in Siberia. While these stelae are relatively simple, their Śaka connections are hinted by the Bactrian mirrors featuring camels and bronze-horse harness ornaments found alongside the stelae. There are two broad types that might be discerned among these which differ in terms of whether the anthropomorph holds a drinking horn (similar to the cup on the Hakkari stelae) or not. They also assume somewhat more concrete human forms than the earlier stelae from across the steppe. In terms of the weapons, while axes and maces still persist, they lose out the sword/dagger as the most common weapon on the stelae. These Śaka stelae are strongly associated with funerary Kurgans and horse sacrifices, again hearkening to the DSKC sites.

From roughly around 200-100 BCE, a new series of Mongolian expansions began on the eastern steppes — the Mongolic and Para-Mongolic expansions — the Hun and the Xianbei Khaganates. While some of the male elites of this expansion might have descended from the old steppe Aryan groups, their dominant ancestry was predominantly a distinct Northeast Asian one. Northeast Asian ancestries continued to dominate through the later Turk, Khitan and Chingizid expansions out of the region (with different degrees of southern admixture from Han-related groups) and was accompanied by a displacement of the IEans of the steppe by Turkic and Mongolic peoples. Remarkably, the Śaka style of stelae persisted among at least a subset of these peoples (Turks and Chingizids) as the well-known balbal stones. The rise of the Turks is in no small measure attributable to the Ashina clan, which also played a major role in the rise of Chinese power — the Tang emperor Taizong descended on one side from this clan and his military successes depended heavily on that alliance. Following Beckwith’s suggestion, it appears that the Ashina clan’s ethnonym was probably derived from the Indo-Āryan name aśvin (also likely behind the Chinese rendering of the ethnonym Wusun). Thus, it is conceivable that the Turks acquired the anthropomorphic stelae via an ancestral connection to the steppe Aryans. Though the stelae continued to be associated with funerary monuments among the Turks, some ideological changes were seen in their use. First, there are cases among Kök Türük (Blue Turks) and On-Oq (the 10-arrows Turkic confederation), where both the Khaghan and his Khatun might be shown on the same stele (e.g., the Kogaly menhir, Kazakhstan and the Apshiyakta menhir in the Altai region — just the faces are shown on this). Second, there are cases where a single Turkic grave might be accompanied by several balbals. We have the following Turkic statements: “khaniem khaghan-kha bashlayu baz khaghaniegh balbal tikmis”, which means: “first I erected Baz Khaghan as a balbal for my father, the Khaghan; “bashlayu khirgiz khaghaniegh balbal tikdim”, which means: “first I erected the Kirghiz Khaghan as a balbal.” This suggests that effigies of enemy leaders slain by or for the deceased leader were also erected as balbals. We do not know if such conventions persisted through the Chingizid period. Finally, it also appears that this tradition crossed the sea to reach Japan. Evidence for this is seen in some of the stelae housed at the Rakan-ji temple. It remains to be seen if this might have something to do with the proposed role of the steppe nomads in transmitting certain traditions to Japans.

Figure 8. The Zbruch idol.

Finally, we shall touch upon the Slavic stelae and idols which remain poorly understood. Those which are believed to be clearly Slavic show elements of steppe-Iranian influence, as indicated by the presence of the drinking vessel on more than one of them. However, at least some of them also seem to be from purely deific rather than funerary monuments suggesting that they were functionally distinct from the Iranic ones. Two of the well-known ones are the Zbruch idol and the Ivankovka group. The Zbruch idol, now housed in Poland, is most remarkable — a tall menhir featuring three tiers of images. The top-most level features a tetracephalic, 8 handed being with a hat. The four heads face in the four directions like those of the god Brahman-Prajāpati of the Indo-Āryan tradition. On one side, the tetracephalic being holds a drinking horn, just like the Śaka stelae. Another side holds a small cup or bowl. the third side shows a sword hanging from the belt again just as in the Śaka stelae and a horse below it (a feature shared by multiple steppe stelae). The next tier depicts four human figures, one on each side, likely a pair of males and a pair of females. Finally, the third tier has, on three of the sides, figures similar to the naras-like yakṣa-s who hold up Rudra, Kubera and yakṣiṇi-s in Indian sculptures (e.g., those from Barhut or Gudimallam). The Ivankovka exemplar is a comparable four-headed idol which is believed to have been housed in a shrine with two other images — one a tall menhir with a face on the top and another a smaller figure similar to the Śaka stelae. The Stavchany shrine is similar believed to have housed two idols in the least, one of which has a figure with a drinking horn on one side and a horse on the other. The Zbruch and the Ivankovka idols do give the vibe of being a four-headed Slavic deity housed in shrines that were demolished by the Orthodox Church. Apart from sharing the multi-tier imagery with some of the middle Okunevo stelae, it should also be pointed out that the Slavic idols have some likeness to the wooden idols made by the Mansy, a Uralic people related to the group contributing to the ancestry of the conquering Magyars. These in turn are related to the Shigir idol recovered from a bog near Kirovograd on the eastern slope of the Middle Urals. This one shares the tall menhir-like form (reconstructed as being original 5.3 m in height) and the multi-tiered structure with the Slavic and Uralic idols. Several of the tiers show anthropomorphic heads placed along the vertical axis of the idol. If it was not dated, it could have passed off as a Slavic one. However, recent C14 dating suggests that wood was up to 11-12K years old making a pre-neolithic object. If it was indeed made that far back, then it would be one of the oldest human iconic artefacts and suggests the persistence of some iconographic conventions coming down from the Eastern Hunter-Gatherer populations.

Figure 8. The Shigir and Mansy idols (from Bobrov).

Back to philology
In conclusion, we see both conservation and innovation of elements among the Eurasian anthropomorphic stelae spanning several millennia from the latest neolithic (with related forms like the Shigir idol going back to pre-neolithic times) down to the last millennium. A notable point with regards to their evolution is seen in weaponry and other military accessories. The earliest exemplars from the steppe feature the axe and the bow prominently — the former shows continuity with the stone versions of the neolithic. In the later versions, whereas the bow persists to a degree, the axe declines and is replaced by the sword which is almost never seen in the early versions. This is paralleled by Indo-European textual evidence — the Ṛgveda hardly ever mentions the sword; however, it abundantly references the bow and, to a degree, two versions of the axe. Even in the later Vedic texts, the sword is not that prominent. Only in the Mahābhārata do we encounter the stuti of the sword. Likewise, the chariot rein hooks vanish by the time of the core Śaka phase where cavalry had all but replaced chariotry. The iconography was also influenced by the cultures with whom the IEans interacted and mixed in course of the wide-ranging migrations. We saw this influence in the form of East Asian motifs like the elk and the Okunevo reconfiguration. While the iconic and temple worship of many IE branches, such as the Ārya-s, Iranians, Greeks, Romans, and the Celts was strongly influenced by the wide-ranging iconographic conventions of the North African, West Asian and BMAC cultures, we suspect that some elements of the steppe stele iconography lingered in these new images spanning a wide swath of time. First, we agree with Vassilkov’s hypothesis (some of his other infelicities aside) that the vīrakal/pāliya (Gujarāti) tradition inheres its essence from the steppe stelae via the Indian megalithic expansion. We also suspect that the Hittite/Luwian stelae with the Indra-class deity and the Jupiter Dolichenus stelae retained some iconographic inheritance from the older steppe versions.

This leads us to the final point — the ancient IE provenance of the stelae and its widespread distribution are at odds with the absence of an early IE linguistic signal for the same. Nevertheless, we argue that the early Hindu tradition records Aryan customs that might be related to the stelae. Before we delve into this, we have to briefly ask what were the functions of these stelae? The archaeological evidence consistently points to the presence of a funerary context across time. However, the Slavic idols and the above-mentioned possible connection to stelae with gods on them suggest that at least some of these had a specific link to the worship of the gods. We will argue based on Hindu sources that the two functions are not mutually exclusive and might have a link to early iconic worship. Coming to the old Hindu funerary rituals we see evidence for both burials and cremations. Allusions and ritual incantations pertaining to both are found in the RV. The “earthen house” alluded to by Vasiṣṭha (mṛṇmayaṃ gṛham) does point to potential burial like those seen in the Yamnaya pit graves. However, the classic pitṛmedha texts of the different Vedic schools indicate a combination of the two, often in the context of a Kurgan burial (a comparable version is also seen in Greek tradition, e.g., the funeral of Achilles). Broadly, it specifies the following: 1) The cremation of the deceased with the three or the single ritual fire(s), sometimes along with his weapon (bow) and/or ritual implements. This is usually accompanied by the sacrifice of a goat or a cow and the animal’s remains are placed on the corpse and burnt along with the deceased. 2) An odd number of days after the fire dies down the ashes are gathered and fashioned into an anthropomorphic effigy and bones are collected and placed in an urn. While not the most prevalent practice, one subsequent ritual ground up the bones and re-incinerated the powder mixed with ghee in a ritual offering with the appropriate incantations. 3) The more prevalent ritual was the burial of the urn or the bones (arranged anatomically) beneath a funerary monument known as the śmaśānavedī or the loṣṭaciti, i.e., a kurgan.

Given that the pitṛmedha texts describe a funerary ritual consistent with the piling of a kurgan (also mirrored by the Iliad), one would expect that there might be some reference to the stelae that have been found in funerary contexts. A closer examination of these texts reveals multiple candidates that might help understand the archaeological exemplars. The first is a conserved feature prescribed by multiple schools that is likely to have been present in the ancestral pitṛmedha of the early Indo-Āryans. A person who has only performed the rites up to the havis sacrifice gets a re-cremation of his powdered bones or as per Śatapatha-brāhmaṇa/Kātyāyana, a kurgan piled with stones. A person who has performed the soma rite gets a full-fledged kurgan. After the cremation, a pacificatory rite is done between the cemetery and the settlement. Here, the adhvaryu and the survivors of the deceased one set up a fire altar and place a bull-hide rug to its west. The survivors stand on that hide; the adhvaryu touches each one of them and makes the pacificatory oblations in the fire. Then touching a live bull, they walk eastwards towards the settlement. The last person to walk back wipes off their footprints with a śamī twig broom. Then a memorial stone is erected at the midpoint between this ritual fire altar and the cemetery. The Mānava pitṛmedha states that this stone is installed by digging a ditch for it and by uttering the name and gotra of the deceased. Thereafter, a mixture of milk and water is offered at that spot. After this is done, if the dead man is survived by his wives, they smear themselves with fresh cosmetic ointment and put collyrium on their eyes. Then a dish of barley and mutton is prepared and served. We posit that this stone which is placed between the spot of the pacificatory fire, and the cemetery is equivalent to the stele. It is conceivable that ordinary ritualists just got a simple stone whereas the more elite ones got a prominent memorial stone.

There are some other rituals that might have influenced or played a role in the anthropomorphic iconography of stelae seen in the archaeological record. For example, Vaikhānasa’s pitṛmedha suggests that the funerary ritualist should make a clay piṇḍa, and having invoked Rudra in it take it to the site of the pyre and place it there with a piece of gold after having made the oblation to Yama Dahanādhipati. The corpse is then cremated beside it. Hence, it is conceivable that this clay lump evolved into or evolved from a stone marker in which divinities like Rudra and/or Yama were worshipped. As noted above, the ashes after the cremation are made into an anthropomorphic effigy (e.g., detailed in Bhāradvāja-pitṛmedha). The Gautama-pitṛmedha specifies that this effigy should be covered with moss, decorated with herbs and flowers, and offered cooked rice with an incantation to Yama Pretarāṭ. It is possible that this anthropomorphic effigy served as an inspiration for stone versions of the same. The Śatapatha-brāhmaṇa/Kātyāyana specifies that if a śmaśāna-citi is piled over the bones then a stone piton should be placed at its southern corner that has an image of the dānava Vṛtra on it. This again hints at a potential demonic image also being erected at the site of the funerary monument.

In light of these Vedic parallels, we can revisit the best-preserved Yamnaya stele, the Kernosovskiy idol, to analyze some of the motifs found on it: 1) there appears to be a flayed skin on the Kernosovskiy idol (probably also on some of the Iberian stelae). Parallel to this, the funerary ritual mentions the placement of the ritual animal hide on the corpse of the ritualist at his cremation. 2) The square on the front side, and likewise, the square and circle with what appear like trees inside them on the rear are respectively reminiscent of the shapes of the āhavanīya and gārhapatya altars of the ārya-s. The ritualist is cremated with the fires from these altars — thus this imagery might signify the same funerary motif. 3) The backside depicts (below the belt) what looks like the darvi ladle and the praṇītā-pātra of the ārya ritual. These ritual implements are placed on the corpse of the ritualist and burnt along with it. Thus, again this might be symbolized on the stele. 4) The bovine and equine images: a cow might be sacrificed in the antyeṣṭi, dissected and the organs placed on the corpse. Horse sacrifices are known from some of the steppe funerary sites. In some pitṛmedha texts, a horse is brought to the site for ritual purposes but not sacrificed. 5) The ithyphallic male figure with axes, a spear, a mace and a bow suggests a deity of the Rudra-class. This is again reminiscent of the worship of Rudra in a funerary clay piṇḍa in at least certain traditions.

Geopolitical summary: March 2022

The autumn dawn
As the 40th day of the autumn of 2016 CE dawned, the mahāmleccha left-liberals were sunning themselves in the last rays of the setting Ardhakṛṣṇa. He was the hero of the age for them, a veritable yuganātha, who had reified all they had stood for. The left-liberal biologists (the majority of them are such) celebrated his manifold vibhava-s by naming no less than 14 newly discovered organisms, from a fungus to a dinosaur-age lizard, after him. His pakṣa rested in the content surety that he would be succeeded by yet another of their chosen ones, the old Ṣiḍgapatnī, who had caused their hated antagonist, al-Qadhdhāfī of barbara-prathamonmatta extraction, to be meet his end by being skewered through his arse by their ghāzī allies on the North African sands. His reign had also seen the execution of at least 10 varṇa-kopa-s, following up on the Neocon-backed efforts of his predecessors, the mahāduṣṭa-s Guccaka and Vakrās, and the Ṣiḍga before him. It was hoped that the Ṣiḍgapatnī who had overseen many of those operations would continue the tradition without any break with financial backing from duṣṭa Sora and others. After all, they had propped up Vijaya-nāma-vyāparin as a strawman to demolish and overthrow the hastipakṣa.

The left-liberal gardabha-s had not yet turned full navyonmāda at that point. However, as we have been stating on these pages, the navyonmatta-s were waiting in the wings to take the center stage under a gardabha mleccharāṭ. They were being churned out by the thousands in the liṇga-śāstra, tunda-śāstra and varṇa-śāstra departments of the mleccha academe. These young graduates were flocking to the centers of cala-citra-s, government, science, and technology, armed with their unmāda, which they claimed to be an overarching śāstra. Thus, backed by Sora-nāma-mahāduṣṭa and the like they were penetrating every center of power and education in the mleccha world. At that point, their action was mainly seen on the fringes, overthrowing opponents in cala-citra production, small universities and at academic conferences. Not many realized then that the future belonged to them — they were to play a decisive role not just in the politics of the post-Ardhakṛṣṇa Mahāmleccha land, but in geopolitics itself, unfurling their Indrāyudha-dhvaja-s wherever they went. But they were not able to break out right away because the majority of the American people were not yet in on their program.

However, as November 9th dawned, the gardabhin-s were utterly shocked to see that Vijaya had indeed become Vijaya, wiping out Ṣiḍgapatnī at the saṃvara-krīḍa the mahāmleccha-s had participated in. This sent alarm bells ringing at the highest amplitude across the trans-continental mleccha-mūlavātūla elite. The nāriṅgapuruṣa was everything they were opposed to: he was a man of the people; he communicated directly with them in short sentences funneled via duṣṭa-jāka’s medium; he did not want to waste the mleccha exchequer on useless wars in foreign lands (a favorite project of Ṣiḍgapatnī and the Neocons; even Ardhakṛṣṇa was brought on to that program against his own wishes); he wanted the mahāmleccha to look inwards at their own growing issues. Importantly, after the failed attempt at a varṇa-kopa in the midst of the Cīna-s in 2011 CE, the mahāmleccha-s reverted to going “full Galton”. The nāriṅgapuruṣa wished to break this key Galtonian edge, irking the elite even more. Finally, he wanted to restore good relationships with the reign of the Khagan of the Rus, who had repeatedly offered the olive branch to the aṅglamleccha-led confederation. This again ran completely counter to the intentions of the praṇidhi-s of the Deep State — after all the mahāmleccha antaryāmin-s and Ṣiḍgapatnī’s pakṣa, from the Chechnyan war to the Snow Revolution of 2013 CE, had plotted to bring down the Rus.

Emperor Vijaya and his overthrow
Thus, the mahāmleccha antaryāmin-s tried their best to overthrow him by whatever means they had at their disposal. As soon as he took the āsandi, they unleashed the navyonmatta bhañjaka-s to cause mayhem and take the sheen of his rājyābhiṣeka. Then they tried to accuse him of being an agent of the Rus, even as they shielded their Galtonian lovers and those honey-trapped by agents of the Prācya-s. When that did not dislodge him, they tried to pin all kinds of sexual scandals on him — after all he had been a veśyā-pradarśaka in the past. Still, not making progress, they had to finally turn to the time-tested technique in their book — the varṇa-kopa — this time it had to be deployed within the US itself. By then, the Galtonian embrace of the mleccha-s had brought the Wuhan corruption to the shores of the Krauñca continent and it was raging through the cities causing much fear and death. With the people frustrated by the lockdowns, their livelihoods upended and with no respite from the rogāṇu in sight, they had become an absolute tinder-keg waiting for the proverbial spark. And, as the spring of 2020 CE drew to a close that spark did come due to well-known arrogance and celebration of the “police culture”, among the śveta-tvaṅ-mahāmleccha-s.

This was the moment the antaryāmin-s were waiting for. To their advantage, the brewing storm perfectly aligned with the interests of duṣṭa Sorādi and the allied navyonmatta-s. They realized that they could not overthrow Vijaya without aid from the navyonmatta-s, both their “intellectual” wing in the academe and now in Big Tech, and their street wing in the form of the kālāmukha-s. The two coordinated their program with the antaryāmin-s to paralyze the nāriṅgapuruṣa and place Vṛddha-piṇḍaka and Aṭṭahāsakī on the āsandī. There were three key procedures they deployed in this process: (1) The coordination between the mainstream media and Big Tech to tilt the playing field entirely in favor of Piṇḍaka. This included total suppression of the devastating (for Piṇḍaka) news regarding Vyādha-piṇḍaka. Instead, they gave a positive spin highlighting the (possibly oṣadhi-addled) citra-kalā of Vyādha-piṇḍaka. (2) Rioting on the ground with the kālāmukha troops of the navyonmatta-s to take the sheen off the achievements of Vijaya (especially in West Asia) and to sow doubt in the minds of the fence-sitters in the crucial months leading to the saṃvara-krīḍa. (3) Manipulation of public health initiatives at many points: rioting for navyonmatta causes was encouraged, whereas assembling for the nāriṅgapuruṣa’s rallies was discouraged. It also seems games were played to delay the vaccine announcement until the slanted saṃvara-krīḍa ensured Piṇḍaka’s victory.

The new master puppeteers
Enraged by how Vṛddha-piṇḍaka was taken to victory by his backers, the nāriṅgapuruṣa’s anuyāyin-s swarmed into the rājyapīṭha of the mahāmleccha (probably goaded and abetted by the antaryāmin-s) on the historic day of Jan 6th, 2021. As this was catching the attention of much of the naive world, a much bigger event played out in Mlecchavarṣa — the nāriṅgapuruṣa’s uccāṭana was completed. Throughout his reign, he had used vikūjana as his primary tool to reach the masses. The antaryamin-s realized that as long as he could do so, he might be able to rally a resistance around him. It had to be smashed. Thus, with Big Tech they effected an absolute mūkī-karaṇam of Vijaya. With that, they showed who was really in power. Piṇḍaka was merely a puttala and they were the sūtradhārin-s who ran him along with their agents in Big Tech. This point was missed by most — the saṃvara-krīḍa was merely a facade and the true bosses were Deep State and their arborizations in Big Tech. Their religion was navyonmāda, the latest of the eka-rākṣasa-mata-s — a secular mutation of older ones. This should have sent the highest decibel fire sirens ringing through the capitals of the non-āṅglamleccha world, like say Bhārata, but we are not sure the leadership even registered it (especially given the awards they conferred on Bhikṣāsundarī and the Dvārānuyāyin). The emperor and the legalistic mandarins of the Cīna-s had already understood this and had banned the evildoers, Guggulu, Mukhagiri-Reṇugirī, Vi and also Sora on their soil, even as they completely took control of their own people. Thus, they were suddenly in a position of power as they had immunity against this. Moreover, emboldened by this and the Galtonian caressing from the mleccha-s they moved swiftly to put down resistance from their ever-restive marūnmatta-s. Now, with the fall of the nāriṅgapuruṣa social credit was implemented in the mleccha lands with navyonmatta driving the ever-changing norms.

Reading the Russia-collusion hysteria
One thing that struck us as the operation against the nāriṅgapuruṣa was ongoing was somewhat anachronistic “Russia-collusion hysteria”. After all, the mahāmleccha had comprehensively beaten the Soviet Rus empire in the Cold War-1 — so, why did they have to bring up Rus operations in second decade of the 2000s, long after that war was won? Serious students of the mahāmleccha antaryāmin power structure would know that the Cold Warriors never went away. They merely regrouped to form the core of a bipartisan Neocon elite that advised both Ṣiḍga and Guccaka. After all, Vakrās was their plant to guide Guccaka who was seen as dull by many. Control of state policy by this elite meant that, Ṣiḍga and Guccaka, while overtly belonging to different pakṣa-s, were merely shadow puppets played by the same operators. This became apparent in aftermath of the historic day of Jan 6th, 2021, when Ṣiḍga, Guccaka and Ardhakṛṣṇa came together to denounce their former friend, the nāriṅgapuruṣa, and celebrate the recapture of the āsandī by the old elite. This elite, many of whom occupy positions in the DoS and associated advisory bodies, has always had a deep grudge against the Rus. While the āṅglika-s had beaten Rus in the Crimean war and forced them to sell their foothold in America (Alaska) to the mahāmleccha, they had repeatedly failed to bring them down in their entirety.

The defeat of the Rus in Cold War-1 brought up such an opportunity for their successors. Their vindictive mindset made them deploy the “Treaty of Versailles doctrine”, which had been enacted by the older leader of the Pañcanetra confederation, the āṅglika-s. Briefly, the śūlapuruṣa-s, while taking heavy losses in WW-1, were hardly defeated. They could have effectively resisted the āṅgla-phiraṅga-mleccha alliance for a while and could have even reached something more like a draw (though with very heavy losses to them). However, their āṅglika cousins tricked them into an armistice, even as they did not lift the naval siege, finally forcing them into the humiliating and totally degrading Treaty of Versailles. Thus, they ended up not only having to endure the blow of WW-1 but also the continued assault after agreeing to a truce without a corresponding infliction of damage on their evil-minded enemy, dismemberment, ethnic cleansing by other Europeans, and the crushing economic collapse that followed. Essentially, the anti-Rus warriors of the DoS have been wanting something equivalent for the Rus. They nearly got there in the Yeltsin years, but the current Khagan of the Rus proved to be a roadblock to its complete enactment. Nevertheless, exploiting the weakness of the Rus, that he admitted, the mleccha DoS elite successfully carried a varṇa-kopa in Ukraine during Ardhakṛṣṇa’s reign. This action had also been enormously lucrative for Vyadha-piṇḍaka and his retinue with their Kievan money-laundering operation. Hence, we had some premonition that the Russia-collusion hysteria meant that when the gardabhin-s seize power they would move for a subversion operation against the Rus.

The new state religion is unveiled
Whereas the older version of the antaryāmin-s had been left-liberals operating under a dvayonmatta covering (one might remember the repeated ejaculations of the dvayonmatta phrase heard during the Guccaka era), as we saw above, they adopted navyonmāda in the current era. A good example is Nimeṣaka who seamlessly moved from prathamonmāda to flying Indracāpaketu-s on his dūtya-s. That Piṇḍaka’s court is essentially run by and for navyonmatta is seen from the never-ending, daily attempts to push navyonmatta on all their subjects across the board in Big Tech, government offices, sports/entertainment, and scientific and educational institutions. It might soon become embodied in the law of the land via the nyāyādhīśa-s that Piṇḍaka gets to appoint during his tenure. For a normal heathen, it indeed feels like how it might have been for one in the closing days of heathen Rome. Navyonmāda is a two-edged sword — while it is an extremely virulent and infectious disease of the mind, it has drastic fitness-reducing tendencies by encouraging tundatvam, ṣaṇḍatvam, and abalīkaraṇam. Thus, it has more of a straiṇa-saṃgrāma-kalā rather than a pumryuddha-nīti — the former, irrespective of sex, is also suited for the characteristic (often video-game playing type) who finds him/her-self in modern Big Tech. The former is rather ineffective against some ideologies that show resistance to navyonmāda, namely tṛtīyonmāda. This was plainly seen in the ignominious retreat of the Mahāmleccha-s and their pūtimāṣa allies from marūnmatta-occupied Gandhāra and Bāhlika.

Cīna-s and others react to the new religion
This set the stage for what may prove to be one of the biggest turnings of the geopolitical wheel in our age. Pandemics go together with the coming of war and the falling of empires. This occasion was no exception. The mahāmleccha adoption of navyonmāda and the subsequent defeat in Bāhlika triggered reactions across the world. A serious fraction of the Bhārata elite adopted navyonmāda with elan. Even the Lāṭeśa’s government has been dangerously pushing navyonmatta policies in places like the army. The Cīna, the Rus, the Ugrians and the Poles saw it as either an outright danger or in the least something deserving suspicion. Even the French, who had played a key role in incubating a strand of it in the early days, saw it correctly as an American disease. The Cīna-s saw an opportunity. Navyonmāda has been extremely resonant with Galtonism. This meant that the Cīna-s would get the much-needed reprieve from the strictures of the nāriṅgapuruṣa. Indeed, it is likely that there was actually a Cīna-mahāmleccha-antaryāmin collusion to put Piṇḍaka on the throne — not for nothing, Vijaya had called him Bījapura-piṇdaka. This now has allowed them to resume penetration operations at a deep level in Mlecchavarṣa. The resurgence of the Needhamistic strain of Galtonism has allowed the stealing of mleccha technology. At the same time, they were also relieved that the abalīkaraṇam caused by navyonmāda could offset their own plummeting fertility in terms of the balance of real military power vis-a-vis the mahāmleccha.

This has to be placed against the background of the recent geopolitical situation of the Cīna-s. At home, they had achieved considerable success by suppressing their marūnmatta rebels and attempted varṇa-kopa-s and acquiring legalistic mastery over their citizens. While they unleashed the pandemic on the world, they initially supposedly had some control over it even as the rest of the world was reeling from its effects. This gave them a chance to act on their ambitions. Since the Opium Wars, where the Indians were used as cannon fodder by the English to achieve their objectives, the Cīna-s have seen the H as sepoys whom the mleccha-s can use to do their dirty work. Thus, they correctly read the mahāmleccha intention of using India as a balancer against the Cīna ambitions of Asian hegemony. At the same time, they also suspect that mahāmleccha might try to separate the Anglicized pretonmatta-s in the Indian Northeast to create a foothold for them to reach Cīnadeśa. Thus, they thought that if they downsized India in a punitive expedition, then they would send a strong message to the mleccha-s that they are already the Asian hegemons and that any mleccha action against them would be dead on arrival. They saw this as preparation for potentially moving against Taiwan. On the other side, they also shored up the Goryeo strongman Kim and helped build his missile capacity to threaten the mahamleccha in the Far East and their protectorate, the Uṣāputra-s. Thus, they put this plan into action along the border with India. One major skirmish occurred at Galwan involving Song dynasty polearms on the Cīna side and perhaps even bare hands on the Indian side. Despite losses of men on both sides, one could say the Indian forces prevailed and the maximalist aims of the Cīna-s were thwarted. While the conflict continues to simmer, the Cīna-s are currently tied up with the return of the Wuhan corruption to East Asia. In conclusion, the Cīna-s have realized that they cannot attain their ambitions right away; hence, they are trying to use the leash handed to them by navyonmāda to the maximum even as they build their capacity for a new thrust. However, their biggest limitation cannot be addressed anytime time soon.

The Rus play their card
The other major player watching the navyomatta turn of the mahāmleccha were the Rus. There were occasions when the great Chingiz Khan, disregarding his council’s advice to wait till spring to fatten the horses, chose to attack his foes right away in winter. He had the intelligence and the correct military intuition regarding the paramountcy of timing and the fact that his enemies would be in no better state with respect to the nourishment of their cavalry. Very few military leaders have that kind of eye for the right decision. We cannot say that the Khagan of the Rus has anywhere near that kind of eye. This was seen in his handling of Ukraine. After the varṇa-kopa in Ukraine and their new regime’s intention to join the pūtimāṣa, the Khagan of the Rus correctly divined that he needed to act there quickly. Consequently, he took back Crimea. He also laid the ground for the Donbas war that met with mixed success. However, for reasons which are unclear, he did not proceed right away with a more full-fledged operation, even though the situation was more favorable than now. Of course, Ukraine is not Georgia, which he had earlier quickly brought to its heels when it attempted to join the pūtimāṣa incited by the mleccha agents lodged in the country. One possibility is that he knew that his army was not ready for such an operation — there is some evidence for this based on the way the Donbas conflict played out. He might have wanted to wait till he could add the hypersonic missiles to his panoply. However, we suspect that the most important reason was the vulnerability of the Rus economy to the Occidental mleccha economic warfare. Thus, over the years he took several economic measures that insulated the Rus to a degree from such shocks. During that period, other than in Donbas, he carried out some operations to test his troops on the battlefield by shoring up the Alawi protectorate in Syria against the mahāmleccha-al Qaeda alliance (a tempestuous long term on-off relationship going back to its bearded Arabian founder). Thus, with the pūtimāṣa’s retreat from his underbelly in Gandhāra and Bāhlika, he felt it was time to act. Perhaps, his actions were precipitated by some intelligence he had received regarding a new round of mleccha-backed varṇa-kopa-s. His suspicions were probably confirmed by the Kazakhstan uprising in Jan 2022 that had all the hallmarks of a mahāmleccha subversion operation. It was quickly crushed by Rus-backed troops.

Thus, as Feb 2022 CE drew to a close, the Rus recognized the Donbas oblasts as independent and launched a full-fledged invasion of Ukraine from the Russian and Belarusian territories. The war has gone on for over a full month now. A subset of Russian nationalists and Occidental commentators felt that the Rus would conquer Ukraine in about a month. That has not turned out to be the case. It has exposed some of the suspected weaknesses of Rus infantry and the shortcoming in their ability to protect and advance their tank columns despite smashing the Ukrainian air force early in the conflict. In terms of historical precedence, this weakness is not a new thing — even in the heydays of their empire, Karl-12 of Sweden defeated a much large Russian force in the first battle of Narva. Then there was the Japanese victory over the imperial Rus in 1904-1905 CE. Here most of the Occident (even the English backers of the J) was quite stunned by the rout of the Rus. Finally, even the comprehensive Rus victory against the Nazi advance came at huge human cost. The Occidental backers of the Ukrainians are spreading the uplifting news (for their audience) that the Rus are on the brink of defeat and have lost tens of thousands of men. As the war grinds on, the mahāmleccha continue to back their prathamonmatta protege and his neo-Nazi allies with anti-armor and other weaponry and satellite intelligence on the Rus movement to preempt their operations (parallels to the English role in the Russo-Japanese war cannot be missed). Thus, even if Bandera was bumped off by the KGB in the Śūladeśa, his dream lives on to date. True to his spirit, over the past month, they have displayed their legendary brutality that even surprised the Hādi śūlapuruṣa’s men.

Our own assessment (admittedly based on incomplete information) is that the Rus have not advanced to the degree of the optimistic estimates and have certainly suffered more losses/prisoners of war than they would have wished. However, it is clear that as of now the mleccha-s are overstating the weakness of their position. We suspect the mleccha-s know this heart of heart but are hoping that their wishes come true in the coming days. A lot of commentators seem to assume that Rus have maximalist aims (articulated clearly by the Russian nationalist named Karlin on the internet) of seizing the whole of Ukraine. It is not clear if that was/is their intention. One can unambiguously game (from great power geopolitics) that they would take the necessary steps to prevent the mahāmleccha-alliance from encroaching into their sphere of influence. They were too weak to prevent it in the Baltic states and their peripheral Slavic cousins, but they seem to have a clear red line in the Caucasus, Central Asia, and obviously the Kievan lands (after all it was the mother of the Rus cities as they say). Hence, one can expect their ultimate strategic objective to make the Kievan lands unusable for the mahāmleccha and their vassals. Hence, in the least, the Rus might declare victory with the Donbas territory in their control. Given that the mahāmleccha-alliance would try their best to stiffen the rest of Ukraine, they might opt to thoroughly demolish it so that its ability to threaten the territories gained in the conflict would be severely limited. Though we understand the advantage of the maximalist position from a Rus perspective, we really do not know if they have the wherewithal to achieve it, given the above-noted shortcomings. The fact that they have repeatedly attempted “peace talks” (if true) suggests that they are either not trying a complete conquest, or want to take it relatively intact, or are admitting the relative weakness of their position (how the mleccha see it). It cannot be denied that it is a total tragedy for the Ukrainians. However, as the American political thinker Mearsheimer indicated, that is exactly how great power politics plays out. Nevertheless, in our admittedly poorly informed opinion, the military course of the conflict still remains wide open, and the Rus are far from defeated as the West would like to claim. There might even be further complications in the coming days if Azerbaijan moves against Armenia and Iran joins the mix. If the supposed deployment of the Kinzhal missiles and thermobaric bombs is true then the Rus are sending a clear signal to the Occident that, even if their ground troops might not be doing great as the West thinks, they have devastating fire-power to pose a real threat to the Occident. Despite his blabberings from jaraṇa, to his credit, Piṇḍaka has not escalated to the degree the “hawks” in his retinue want him to. However, the probability of a larger and deadlier conflict remains high (~15%) in our estimate.

Navyonmāda’s first war: what is in it for the H?
While the uncertainty on the prospects of the Rus remains, what we would like to draw attention to is the nature of this war between the mahāmleccha-led confederation and the Rus. It is seen by many as Cold War-2. We divide things a bit differently. The period from the start of the perimeter-creep strategy of the pūtimāṣa following the collapse of the Soviet empire to the Russia-collusion hysteria should be seen as the actual Cold War-2. However, starting from the Rus invasion of Ukraine it should be seen as a real war between the navyonmatta Occident and the Rus (could be called a hybrid strategy as much of the heavy fighting is done by the neo-Nazi-allied groups backed by mahāmleccha advisers). While it draws on the old conflicts between the Western churches and the Orthodox church, its mode of operation is primarily that of navyonmāda — the first great war that navyonmāda is engaging in (even their Kievan puppet is pulling all the right strings to appease this disease). Thus, they fight this war by employing the same methods adopted by navyonmāda in its other campaigns, like that against Vijaya — the idea is to essentially “cancel” the Russians, keeping with their favorite mode of action. That is exactly how all the navyonmatta duṣṭa-s who rule the Occident have acted. Overnight they canonized the rogues and the hādi-ghātaka-s are now being feted as heroes much like their own kālāmukha-s. This is a warning for all other free nations — it will be the mechanism by which navyonmāda launches against them. The hate, which navyonmāda is so good at channeling, dovetails with the old vindictiveness characteristic of the āṅgla-mleccha-s: the same cartoons as those they made of the German, Japanese and Hindus and actions mirroring the killing of Dachshunds and shepherd dogs. Keeping with navyonmāda being essentially a philosophy of suffering and misery they are inflicting misery on themselves and even more so on the rest of the world from the commodities shortages that are resulting from the Occidental mleccha imposing sanctions and causing the war to prolong.

From an H perspective matters are complicated. Hopefully, it has delivered yet another lesson that any kind of alliance or entanglement with the Occident is likely to prove fatal. Ukraine is only the latest casualty of the quest of unchosen nations to become a part of the West when they do not really belong to it. Many H feel a deep resonance with the West and yearn for communion with it. This will only bring ruin to their posterity and nation. The H depend heavily on the Rus for their armaments; hence, a defeat of the Rus at the end of this conflict is a victory for the enemies of the H. It also has the danger of compromising the H defenses. The mleccha-s would use the opportunity to harm the H (especially via their navyonmatta assets within the country) — something they already want to do, given that India has not condemned the Rus. Ideally, the H should read this situation as a war between navyonmāda and the Rus. The defeat of navyonmāda is good, perhaps even an existential matter for the H. Some are surprised when we say this — they tell us navyonmāda will only ruin the senā of the mleccha-s not that of the H. Our reasoning is simple: the Indian state and H society have developed some serious structural problems as a result of their marked decline from the prolonged struggle against marūnmada and the subsequent encounter with Occidental modernity. This has primed some of the masses and a major part of the elite towards navyonmāda. The adoption of navyonmāda will exacerbate these structural problems like the cracks in a building during an earthquake. It is already undermining the scaffold of H civilization by incapacitating its physical and memetic defenses. Notably, it could cause the masses to cannibalize the elite who hold human capital. Right now, navyonmāda is the state religion of the Piṇḍaka regime and its satellites. Hence, it also has the backing of the Occidental might in India. A Rus defeat could accelerate the same. Unfortunately, the vote-bank politics of India means one of two things, neither of which look good. On one hand, India is one election away from being seriously undermined if the pakṣa changes for they are merely the Indian equivalents of the Kievan agents of the mahāmleccha. On the other hand, the H-friendly political alliance has shown all the signs of being vulnerable to navyonmāda themselves enacting certain policies that are detrimental to the H bearing critical human capital. Thus, a secular decline can set in from their policies. The situation can be salvaged only if the H leadership seriously faces up to this issue and actively suppresses navyonmāda across Indian institutions. The discerning can read and complete the rest of the story.

Human retroviruses, sociology of science, and biographical ruminations

We learnt via a recent obituary that the French researcher Luc Montagnier died a month or so ago after living for nearly 90 years. He along with his compatriot and erstwhile colleagues, Françoise Barré-Sinoussi and Jean-Claude Chermann discovered HIV-1. Subsequently, his lab also discovered HIV-2, the second virus that causes AIDS. It was around the time of the discovery of HIV-2 and the naming of the original AIDS virus as HIV-1 that we made our own first foray into studying evolution and biochemistry in the language of the genes. Soon thereafter, we realized that the study of the biochemistry of the endless war between viruses and their hosts offered some of the deepest insights into the evolutionary process after Darwin’s work. Thus, the path for our primary investigations in the coming years “crystallized” out of these early meditations. Not being an entirely autistic type of scientific enthusiast, we also started observing the sociology of science, if anything for the selfish reason of understanding better the social systems that we would become a part of due to our chosen course. We cannot say that we saw or understood things clearly in those early days, but the germs of the realization that the heroic hagiographies of science are far from the truth dawned on us then. One early introduction to this was the drawn-out conflict between the Frenchman Montagnier and his American rival Robert Gallo.

In the late 1960s, it was becoming clear due to the work of Miller that the lymphocytes originating from the thymus (an organ, which, until a little before then, had remained shrouded in mystery) played a central role in acquired immunity. A little over a decade later these lymphocytes (T cells) took the center stage in a mysterious disease that was just beginning to be recognized. Even as the discovery of the T lymphocytes was being announced and met with skepticism among the immunologists, cases of AIDS were beginning to turn up outside Africa. In 1968, a Norwegian sailor who had engaged in sexual activity in Western Africa presented a mysterious disease with immunodeficiency symptoms comparable to AIDS. He and some members of his family died in the 1970s without a clear diagnosis. Again in 1968 an American teenager of African ancestry, who may have engaged in sexual promiscuity, was diagnosed with a mysterious syndrome that included Kaposi’s sarcoma. He died shortly thereafter. However, it took a full decade for this mystery disease to be recognized as a distinct entity. In late 1979, physicians in New York, USA, and the vicinity started noticing a cluster of cases of aggressive Kaposi’s sarcoma that was afflicting young homosexual male patients. Until then it had only been observed as a rare, slowly progressing tumor in older patients of Jewish or other Mediterranean ancestries. Around the same time, in California homosexual males were showing up with a strange syndrome of immunodeficiency. Finally, in the summer of 1981, these unusual findings were tied together, and it was recognized that indeed a new disease characterized by lymphadenopathy and strong immunosuppression was making its rounds. Over the next several months, further surveillance of this disease led to the finding that it was marked by a dramatic reduction in a specific type of T cells, which were known as the helper cells that were defined by a marker molecule on their surfaces, the CD4, a protein with domains of the immunoglobulin superfamily.

There was one man who was well-poised to exploit this finding — Gallo. By then he was already a veteran of T cell research, having discovered Interleukin-2 in the 1970s. This had allowed him to cultivate T cell cultures in the lab. Work in his lab had also shown that the Gibbon Ape Leukemia Virus transmitted from a pet gibbon to a new world Woolly monkey spawned the simian sarcoma virus. This led him on the quest for human retroviruses that culminated in the discovery of HTLV-1 in 1979 as the causative agent of cutaneous T-cell lymphoma. Subsequently, he and others were able to show that it was also the causative agent of T-cell leukemias found endemically among some Caribbean islanders of African descent and some South Japanese. In 1981, his lab discovered a second leukemia virus HTLV-2 from what was described as a “hairy cell T cell leukemia”. An interesting feature of the HTLVs was the tropism towards CD4+ T cells and transmission via sex, blood transfusion, needle-sharing, or mother to child during breastfeeding. Thus, when AIDS was described as a new disease in 1981, Gallo was already in possession of key priors and technologies that led him to suspect that this virus might also be related to his HTLVs. Not surprisingly, in 1983 he published two papers proposing a role for his HTLVs in AIDS.

However, Gallo was beaten to the real virus by a French lab, led by Montagnier. He had an interest in virology since the characterization of the tobacco mosaic virus and had a background in studying interferon inhibition to trigger retrovirus activation. He was inspired by Gallo’s earlier HTLV work to look for a retrovirus as the agent of AIDS, a disease that was brought to his attention by a colleague. The French team soon isolated the virus, now termed HIV-1, from the lymph node biopsy of a French homosexual man who was showing early AIDS lymphadenopathy. Montagnier and his colleagues published their work in the spring of 1983 reporting a new retrovirus, they named LAV, which might be a possible candidate agent of AIDS. This paper was published back-to-back with the above-mentioned two papers from the Gallo lab claiming a link between AIDS and the HTLVs. Gallo might have been a good scientist but was not a good man. Montagnier, a naturally born scientist, was a reserved personality in stark contrast to the aggressive Gallo, who had a publicity blitz going on in America. Thus, at the time of the publication of the French paper, the editorial in the American tabloid, Science, spoke extensively of Gallo’s work linking the disease to the HTLVs, while making only a passing reference to the former. Gallo soon realized that Montagnier had an edge over him, and the virus the French had in hand was the likely agent of AIDS rather than the HTLVs. Thus, when Montagnier presented his findings at a meeting shortly after the discovery of the virus by his lab, Gallo crudely attacked him and tried to put him down. Thus, Gallo wanted to downplay the French team’s work, even as he could prepare his own claim for its discovery. Under the standard procedure of sharing published reagents, Montagnier’s lab sent Gallo two samples of their virus a few months after publishing their report. Gallo soon claimed that he had identified the real causative virus of AIDS and called it HTLV-III. He was backed by the muscle of the US Department of Health and Human Services, whose secretary claimed that they would soon have a diagnostic test and vaccine as a result of Gallo’s discovery of the AIDS virus. The former turned out to be true but not the latter. Finally, in May of 1984 Gallo published four papers comprehensively presenting his side of the story and making the case that his HTLV-III was indeed the causative agent of AIDS. The following month Montagnier and Gallo made a joint announcement that their virus was likely the same. In the summer of the same year a group led by Jay Levy from UCSF also independently published the identification of the same virus, which they called ARV, from AIDS patients in California.

The subsequent years saw a major battle between Gallo and Montagnier for priority and patents on AIDS diagnosis. Over the years the credit and patent battles reached the highest level and were taken up by the heads of state of France and the USA. They eventually settled for joint credit. Gallo and scientists in this lab were initially accused of scientific misconduct in their 1984 papers by a US government investigation. The accusations mentioned him “intentionally misleading colleagues to gain credit for himself and diminish credit due to his French competitors” and “impeding potential AIDS research progress by leading scientists away from working with the French researchers.” However, he was later absolved of it under the new definitions of misconduct by the US government while being accused of being non-collegial. When their sequences were determined it turned out that Gallo’s HTLV-III was more or less identical to Montagnier’s LAV. This was unusual given the high variability of HIV-1. Investigations eventually established that Gallo’s virus was indeed derived from the French lab. Does this mean that Gallo stole the French virus? The neutral investigations suggest that the French samples had a rapidly growing version of the virus isolated from a French AIDS patient then diagnosed as having Kaposi’s sarcoma. This strain dominated the strain from another patient in the sample Montagnier sent Gallo in 1983 after the publication of his original LAV paper. It subsequently contaminated the cultures and overran the strains in Gallo’s lab once he received it. Thus, both the French and the American labs ended up with the same strain. However, these investigations also showed that Gallo’s lab had genuinely isolated other strains by themselves at that time but what they published was the same as the French one. Thus, it argued against them having deliberately stolen the French virus.

Our take on this story is that the French had the priority. However, Gallo’s earlier contribution to human retrovirology and T cell biology is undeniable. He was correct in his hunch that AIDS was caused by a retrovirus, like his HTLVs. Where he was wrong was in assigning agency to them for AIDS. However, he quickly realized that the French had the right virus and tried to claim it for himself — this matches his personality. It is not surprising that he felt bad to be headed off in a discovery that he felt rightfully belonged to him, given his role in the discovery of human T cell retroviruses. Thus, he used all the advantages he had in the field along with his scientific network to bolster his claim. In the process, his lab might have been less than honest or in the least willfully negligent while rushing to stake their claim. Some like Levy who reached the right conclusions around the same time were largely forgotten in the race.

We had the chance to speak to two individuals, one who was close to Gallo’s rush for glory, and another who had been involved in the AIDS gold rush that followed. The first told us with some disquiet a tale that contained paradoxical narratives. Firstly, he felt that Gallo and members of his team were subjects of a “witch-hunt” due to unnamed enemies in the American academe and national labs. Secondly, he also confessed that Gallo’s lab was a high-pressure environment like many industrial-style Euro-American scientific groups. The demand for rapid results in face of the competition from France, coupled with the hierarchy, favoritism, and immigration status intimidation of foreign researchers pushed them to cut corners and do things in a less than honest way. He vacillated for a while regarding whether he himself might have engaged in dishonest activities. He then went on to add that those who failed to understand the ways of the “big man’s” lab were quickly turned into sacrificial goats even if they got the results that brought the big man glory — there was no intention of rewarding those in the trenches equitably. The second individual mentioned how it was “hot” to be an AIDS researcher and how she enjoyed the well-paying fellowships/stipends relative to other researchers laboring on less hot science. However, that came at a cost. She soon realized that she was not getting the attention despite the first authorships in the manuscripts — perhaps due to her demure ways. Rather it was all going to her boss who flew from continent to continent giving talks even as she labored to provide him the pictures on the slides. Thus, she soon crashed and burned out. These events and conversations informed me that despite the glamour that is portrayed in the popular hagiographies, behind the facade science was still very much like any other activity undertaken by a troop of apes with its characteristic dominance hierarchies. It also informed us that not all that you see in the journals, including the tabloids, might be produced in an entirely honest way.

Nevertheless, as we entered our teens these events surrounding the discovery of HIVs and the HTLVs made us interested in both the broad and the narrow ways of the retroviruses. Walking on the broad path, from the 13th to the 15th years of our life we studied the reverse transcriptase with great intensity and pushed ahead to studying its relationship to the RNA polymerases of positive-strand RNA viruses and double-stranded RNA viruses, and cellular and viral DNA polymerases. This early experience we gained in detecting and analyzing their evolutionary relationships was to hold us in good stead in life and led us to many great discoveries in the future. At the same time, we also studied the RNase H and integrase enzymes of the HIVs and related retroviruses, and that opened yet another world to us, whose significance we continue to understand in gradual steps to this date. With the rising excitement in HIV-1, the interest in HTLV-1 and HTLV-2 took the back seat. However, on the narrow path, we became intrigued by the pathology of the HTLVs. First, HTLV-1 causes severe disease only in somewhere between 2-8% of the infected individuals. The rest remain asymptomatic, though one study suggests these might show mild cognitive decline. Second, even in the cases when it proceeds to a severe disease there is a prolonged asymptomatic phase post-infection that can last several years to decades. Third, the severe, as well as milder but chronic manifestations of the disease, are rather pleomorphic. The most severe version is of course T-cell leukemia/lymphoma. The next most severe manifestation is tropical spastic paraparesis, where the HTLV-1 infected T cells cross the blood-CNS barrier to enter the spinal cord and stimulate the astrocytes to produce cytokines to draw more T cells into the CNS. The resulting inflammation causes spinal cord damage and progressive weakness of the legs and loss of urinary bladder control. Beyond these, the virus also causes pediatric infectious dermatitis, conjunctivitis, uveitis, joint inflammation, and other forms of muscular weakness (polymyositis) in places where it is endemic. Coming to HTLV-2, it is even less pathogenic than HTLV-1 — other than rare T-cell leukemia, it also causes a neuro-inflammatory disease similar to tropical spastic paraparesis. Their more recently discovered relatives, HTLV-3 and HTLV-4 are as yet known only from asymptomatic cases. These peculiarities of the disease have puzzled us over the years.

As noted above, HTLVs and HIVs share similar transmission modes; however, HTLV-1 shows remarkable differences in heterosexual transmission between the sexes — 60% of the transmission is from infected males to females and only 0.4% from infected females to males! However, the prevalence increases in females after age 50, though the chance of it developing into leukemia is higher in males than in females. The pleomorphism, the dominance of asymptomatic cases, and epidemiological peculiarities go along with unusual patterns of geographic endemism in these viruses (barring HIV which has become more cosmopolitan). Studies on their origins take us back to Africa where the majority of events of transfer of retroviruses to humans have seemed to have occurred. The table below summarizes this situation.

Of the above, at least 16 transmission events from non-human primates (both apes and monkeys) to humans have occurred in Sub-Saharan Africa. Field studies have indicated a particular prevalence of such infections among African monkey and ape hunters/butchers. We cite from the field studies by Richard et al to illustrate some cases of this. A 65-year-old hunter/butcher from the Ogooué-Ivindo region in Central Africa was reported as being simultaneously infected by 3 retroviruses — SFV, HTLV-1, and HTLV-4. He was severely bitten in the arm by a gorilla. A 58-year-old primate hunter/butcher from the Ngounié region of Central Africa was severely bitten on the left thigh by an adult male silverback gorilla. He seems to have developed HTLV-4 infection as a consequence. The frequent crossover of retroviruses to humans in Africa appears to result from blood/saliva contacts during primate hunting/butchering activities. A parallel transmission between monkeys and apes appears to take place in Africa, which in part might be mediated by hunting — e.g., chimpanzee predation on monkeys or gorilla-chimpanzee conflicts. The current phylogenies suggest that the chimpanzees received their SIV (HIV-1 cognate) from monkeys on at least two occasions; the chimps in turn transmitted it to the gorilla. Humans appear to have received HIV-1 twice, once from a chimpanzee and once from a gorilla. The natural human infections from other primates are paralleled by similar infections of primate-laboratory workers. To date, all known SFV (Simian Foamy Virus) cases are apparently asymptomatic and have not been sexually transmitted to the partners of the infected individuals. A notable case is of SIV (the simian strain of the virus related to HIV-2) being transmitted to a primate-researcher in the lab, probably while handling the blood of experimentally infected macaques. He seems to have developed a sudden severe but temporary dermatitis, which might have been due to the virus, and has a low-level chronic infection. However, beyond that, there was no other evidence of persistent illness or transmission to the sexual partner.

Thus, to date, the majority of the transmissions — SFV, SIV, HTLV-3 and HTLV-4 — have been mild, asymptomatic, or even dead-end infections. Taken as a whole, HTLV-2 is again not very severe. Of course, HIV-1 has been severe and HIV-2 to a lesser degree than the former. That leaves us with HTLV-1 which appears to occupy a peculiar intermediate niche. On the zoonotic side, it appears to repeatedly transmit from non-human primates to humans. Within humans, its relatively low level of severe disease coupled with remarkably slow progression has allowed it to become endemic in populations across the world. While most of its diversity is related to the multiple African transmissions from non-human primates, the slave trade of Sub-Saharan Africans appears to have dispersed it to several regions of the world. However, there is a trans-continental clade of HTLV-1 that apparently has a more ancient origin. A part of its transmission might be via the Mohammedan slave trade of Africans. Consistent with a potential transmission via this older slave trade, the Indian strains are related to the West Asian strains. Interestingly, despite the extensive monkey-human contacts, there is no evidence for HTLV-1 or other retroviral crossovers to humans in India. One possible reason could be the rare or absent consumption of monkeys/apes in India. However, there is the mysterious HTLV-1c clade that is found among natives of Australia and Melanesia. This clade is the most divergent of the HTLV-1 clades and is very unlikely to be a transmission from Africa. Moreover, no non-human primates are found in Australo-Melanesia. This suggests that the infection was likely acquired by humans in Asia and then transmitted to this region. The current phylogenetic analysis favors a model wherein it was transmitted from macaques to humans, perhaps in prehistoric India, and then borne eastwards. Given that the orangutans also appear to have acquired their strain from the macaques, it is not possible to rule out that they were an alternative source for the HTLV-1c clade.

As this story developed, we remained intrigued by the overall biology of retroviral infections in primates. There was clearly a long history of primate retroviral infections spanning several viral clades and exchanges that occurred time and again between primate species, followed by dissemination within a species via promiscuous sex and feeding of infants by lactating females. Thus, theory would predict that a generally high degree of natural resistance would evolve against retroviruses in primates. It seemed to us that the prediction was generally borne out in the case of most primate retroviruses given the dead-end and mild/asymptomatic infections. Thus, it struck us that the general resistance to retroviruses was worthy of a more detailed investigation. With this lens, it seemed that HIV-1 was an exceptional snapshot of bad luck for the human species. We realized early on that the HIV-1 tragedy was an unexpected consequence of globalization. This meant that a part of the resistance emerged from social strategies that limited sexual contacts between distant tribes and perhaps taboos on eating other primates. Therefore, the more virulent transmissions, like HIV-1, might have been relatively contained in the past and self-limited themselves by burning through smaller tribal populations with limited contact with others. Nevertheless, we also realized that such defenses alone were facile and there had to be stronger molecular ones. Thus, we became particularly interested in Apobec3 and CIITA families of proteins. Both these lines of investigation proved rather fruitful for us. The first led us to discover the origins of the anti-retroviral deaminases and this has, in turn, spawned some recent biotechnology of note. It also helped us develop a proper theory for lymphotropism and the origin of vertebrate adaptive immune systems. The latter contributed to our understanding of the roots of innate immunity. Thus, decades after we first started, we finally acquired a fairly clear understanding of some of the mysteries of retroelements and their ongoing collaboration and battles with their hosts.

Transcripts of conversations: the addiction principle:

A friend recorded some of our verbalizations and made transcripts of them. He sent them to us to and we decide to edit them and post them as and when we get the chance — not out of a narcissistic impulse but simply to record some of these thoughts.

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Q: You keep mentioning the “addiction principle” as yet another feature shared by biological conflicts at the microscopic level and human geopolitical conflicts. Could you explain that?
Aham: In geopolitics, the use of addiction in a very literal sense was seen in the opium wars that were fought around the mid-1800s between the British-led Occidental drug-trafficking regimes (other than the Brits, there were French and some Americans) and the Manchu Ching empire in China. The Brits cultivated opium in their Indian conquests and sold it for huge profits in China by encouraging its recreational rather than pharmaceutical use. Due to the alarming rates of addiction, Ching banned its use and blocked the Occidental drug traffickers from selling it. The latter retaliated with two wars at the end of which they had crushed the Ching empire, imposed humiliating strictures, and extracted territorial concessions from them. The key point to note here is the two-fold strategy – the introduction of an addicting substance and retaliation when the addiction was cast aside.

In biology, this was observed at multiple levels. One of the most famous is the phenomenon of plasmid addiction in bacteria. The plasmids in question are DNA elements that reside in bacterial cells outside their primary chromosomes. They might be totally parasitic elements, or they may give something in return by conferring benefits to the cell, like resistance against viruses or antibiotics. Now, many of them carry a further selfish element integrated into them known as a toxin-antitoxin system. These systems are usually made up of two genes, one coding for a toxic protein (the toxin) and the other codes for its antidote. One common principle involves a labile antidote that is easily degraded and a toxin that is stable. Thus, only if the two-gene selfish element is intact, the cell survives as both the toxin and antitoxin are made, and the former is suppressed. Now, if the cell gets rid of the parasitic plasmid, the labile antitoxin degrades rapidly and is no longer made afresh. However, the stable toxin persists, and once the antitoxin is degraded, it is unleashed and kills the cell by one of many mechanisms. Thus, the cell cannot get rid of the plasmid and is “addicted” to it.

There are many variants of this in biology. For example, there are the Medea elements that have evolved from transposons in the flour beetle Tribolium. The restriction endonuclease superfamily enzyme of the transposase encoded by this element elicits its toxic action by cutting DNA, and its ATPase domain acts as the antidote. Here, the toxin kills all progeny that lacks at least one Medea locus inherited from their parents. Thus, it ensures that the lineage is ever-addicted to the Medea element. A similar addictive phenomenon is observed with Rickettsia-like bacteria such as Wolbachia that are inherited via the female germline (they enter the eggs). These bacteria encode toxins that evince many effects such as parthenogenesis, feminization, cytoplasmic incompatibility, and killing of male progeny, all of which ensure that only infected females will transmit the bacterium to the next generation are produced.

In all these biological examples, we see the enforcement of addiction as a critical feature shared with geopolitical conflicts. There are some variations on this theme in biology that are again apposite to geopolitics. These are the immunity elements of prokaryotes such as Restriction-Modification and CRISPR systems. These confer a clear advantage to their host in the form of providing immunity against invasive genetic elements. However, they also have a sinister side to them. The same weapon they use against the invader or an alternative toxin embedded within them can turn against the cell to kill it, operating under the same principle as the toxin-antitoxin systems — i.e., the persistence of the toxic component after the loss of the antidote. Thus, they can first induce adoption by providing a selective advantage in the form of an immune mechanism. However, once the invader threat is gone, the cell cannot eliminate this costly defensive apparatus because the addiction is enforced via a toxic attack on the host cell.

Q: Ah! One can see multiple parallels here to the current geopolitical situation. What in your opinion are important points in this regard?
Aham: There are several. An overt drug like opium is no longer widely used. However, the Cīna-s might be playing a comparable hand in the USA (e.g., fentanyl?) with a more indirect enforcement mechanism exploiting the Galtonian edge, which we just talked about. We do not know for sure if the Sackler family was the agent for some other nation or group. The most obvious substance in a modern geopolitical sense is, of course, petroleum. Addiction to it has clearly limited the options for a republic like India and also puts the Hindu nation in danger from the marūnmatta-s. Here India/ the Hindus have opted to play prokaryotes and pay the costs for CRISPR systems rather than go eukaryote and get rid of them. As I have told you before, perhaps conflicts like this stabilized the eukaryotes and allowed their radiation. Then again, like Restriction-Modification, CRISPR, and other such systems, we have defense addiction. Nations that depend on other nations for their weaponry have or will learn it the hard way. Finally, we have that most important form of modern addiction, the penetration of whole nations by addictive in silico financial and service systems run by the navyonmatta technocrats like Guggulu, Mukhagiri-Reṇugirī, Bejha and Jāka-now-talcum-powder. The response of the Occidental regimes backed by these by these most evil forces to the Russian attempt to reconquer Ukraine illustrates the classic enforcement strategy in the addiction process. The Hindu addiction to these is deep, and it is not clear if their leadership even realizes that.

Phantom impressions-1

Lootika had gotten her kids engaged with the beauty of the connections between multiplication tables, division and geometry. Leaving them to their labors, she went over to Somakhya’s desk to bring him to join her for the afternoon tea. Lootika looked at the cardioid that had formed on the surface of her beverage from the declining sun glancing off her cup with an amused smile. Pointing to that, she remarked: “This is it, dear. An interesting byproduct of teaching our kids some mathematics was that I cracked that mysterious divine riddle of yours:

tanutaḥ svasārau ubhe । kṛṣṇā ca śvetā ca । viṃśatyuttara-sapta-śatam agner mayūkhāḥ । ayam bhājakaḥ । aśvamedhe .aśvasya pārśvāḥ । ayam eva guṇakaḥ । paryeti trayastriṃśatam arān nemiḥ । sarve devās tiṣṭhanti teṣu । āvirbhavati madhye navaḥ ṣaḍguṇo devaḥ kumāraḥ । trayāginā parivṛtaḥ । idaṃ rahasyaṃ devānāṃ jāla-cakram ॥

As you stated, it was indeed a profound religious experience to see it manifest — a mysterious emergence at the center of the spider’s web. At once it brought together the realm of numbers with the ribs of the sacrificed aśvamedha horse, the days and nights of the saṃvatsara, and the count of the gods as stated in the operation of the numerical sequence in the Taittirīya śruti, the three-fold Agni, and our family divinity in, the new god, in the center of the web. I was struck by how it tied together the Taittirīya chant of the sequence with its opening ṛk: tvam agne rudro asuro mahodivaḥ । tvaṃ śardho mārutam pṛkṣa īśiṣe …”
S: “Spidery, I was sure you would have that experience once you cracked it — as though you were coming to rest in the midst of your own cobweb experiencing a revelation.” Lootika smiled and handed over her phone to Somakhya: “What do you make of this?”

S: “Why? This is a long message from your friend Bhagyada. I’m sure you have given her the memo that, like me, you would rather that people not send you long messages via the written medium with the expectation of a similar-sized response.”
L: “I have, but, in this case, it is a good thing she has recorded it. I think she could not reach me because I was busy with the kids. Read it and say what you think?”

Somakhya read out Bhagyada’s message aloud: You may recall the old traumatic events that I faced beginning with our visit to the dolmens at Siddhakoṭa. I have always tried to keep them out of my head, but my husband was asking me about those events due to some turn in the conversation relating to our impending visit to Kalakausha’s place tomorrow. I had some of those events flashback in my mind in a rather vivid and present manner. Then a strange thing happened — I moved on with my cooking for the day when I saw the image of a Paleolithic-looking chap on the white porcelain tiles of the kitchen wall. His face was obvious and quite clear, but the rest of his brownish body was hazy. I’m pretty sure he was the guy interred under the dolmen at Siddhakoṭa where I was afflicted. My mind immediately flew over to you, Lootika — after all, I would not have made it out of that dolmen had it not been for you and Somakhya.

As you know well, being a good coethnic of yours, I neither drink alcohol nor use hallucinogenic preparations. I’m certainly in decent health these days and taking no psychoactive medication. Hence, the manifestation of that fellow was rather distressing, but it was very real. I was intensely wishing you were around to dispel or bind that grayish-brown chap who was appearing on the wall. Then something even stranger happened. As I kept thinking of you, I saw you briefly in a room busy with your kids! But that vision went blank right away, and I saw an image of myself bouncing off the kitchen walls as though I was out of my own body. The dark chap went after those images of mine. Frightened by this, I switched off the stove and went to the bedroom and pulled out that inlaid stone disc you had given me. I again very briefly felt that I was with you, and I saw the dolmen guy being flung into the sky. Suddenly a calm came over me, and the everyday mundane world returned.

L: “So what do you think, Bhārgava?” S: “Your defenses are good and nearly impenetrable, susmeratā. You would certainly recall how I had performed a parakāyapraveśa to enter you during those tumultuous days when we had gone our solitary ways. I have done it a few times with others, but you were the hardest to seize both due to your svabhāva and mantra-s. I was rebuffed several times bounced off, and indeed I saw myself bouncing off the walls of my room and yours like a projected image. Finally, though captivated and lost in the splendid charms of your beauty as you lay on your mattress, I hardened myself to perform a stambhana, paralyzing your defenses, like Vīrabhadra the gods. After that, I took control of you. I believe your friend underwent one of those mysterious translocations and was subconsciously impressing on you, but your strong defenses bounced her off and then the dolmen-dweller as he followed her to you!”

L: “Ah! So, we indeed converge in our interpretation of this curiosity. If you recall, when we were young, we needed some especially susceptible people for phantoms to manifest when we plied the planchette — Bhagya and Vidrum were among the best. When it was just our inner circle, the success would be much less barring some special bhūta-s and vetāla-s that would seek us out. I was always struck by the ease with which Bhagya would perceive bhūta-s. Once, when my sisters and I were plying the planchette along with Bhagya, a bhūta manifested that tried to speak to Varoli. Neither Varoli nor the remaining three of us sisters noticed it, but Bhagya did. At first, we thought she was uncharacteristically pulling a fast one on us. However, conversing with it via her we were convinced of its reality after the bhūta answered some secret questions whose answers only my sisters and I could have ever known.”

S: “It is interesting you mention this because I believe it goes along with another phenomenon that I would term the capacity for easy “delocalization”. As you know, Bhagya used to live near my house in our youth and her mother knows mine well. In the days before you joined our school, her mother used to bring her over for help with schoolwork once in a while. One day her mother had brought her over for help with some problems in chemistry. I was not at home, having gone with Sharvamanyu to explore a deep fissure on the side of the Vānaraparvata. When I returned, she asked me if I had seen a snake in a hole beside one of the walls of the fissure. I was shocked as to how she knew of this. I was pretty sure she was not shadowing us as we were wandering around in the hills. What she said surprised me. She was bored sitting at my place waiting for me to come home and wondered where I might be. At that point, she apparently caught a few fragments of my conversation with Sharvamanyu on our way back home that contained the mention of the snake. You would recall that the path where Sharvamanyu’s way would diverge from mine was about a kilometer from my house – remarkably, we did speak about the snake just before we parted. There is no way she could have heard that directly from within my house — it seemed more of a delocalized impression.”

L: “That’s fairly notable — I believe in the current incident, we can see elements of both her facility for delocalization and proclivity for phantasmagorical impressions. I think the intense focus on the traumatic experiences following her encounter with the dolmen-dweller delocalized her to his orbit, and he followed her. Then she seems to have delocalized twice to my vicinity as she intensely thought of me, though I never perceived any presence at all. This caused the dolmen-man to follow her image, and he was bounced off by my defenses. We learned early that while we have a capacity from our mantra-s and svabhāva to bring down or bind the bhūta-s, we have to develop strong defenses to survive their impact. Hence, most of the time it comes at the cost of our ability to interact with them directly. It is in a sense the converse with Bhagya and Vidrum who tend to have that svābhāvika capacity to sense them but little by way of defense.”

S: “There seems to be a spectrum in that svābhāvika capacity, which may have some genetic foundations. This genetic component has long been observed among students of ghostly lore throughout the world across very different cultures. However, it has been mostly forgotten with modernism despite the advances in our understanding of genetics. Indeed, that may be true even of you and your sisters who have a certain controlled capacity for delocalized perception when deploying the mantra-s of the Vāmasrotas for which you have a siddhi of the svāyambhuva type. I’m particularly intrigued by your sister Vrishchika’s investigations that one determinants might be certain polymorphisms in some of the variable cadherin domain modules of the PCDHA1 cluster of proteins. But phantasms can manifest even among those not normally prone to being impressed by them. We know the case of Vidrum’s aunt Vaidoorya, who had only one impression, even as Vidrum routinely saw them as part of his daily reality. You would also recall the unfortunate example experienced by my cousin Saumanasa of most prosaic temperament [Appendix]. Before that experience, had she heard of our many adventures, like Vidrum’s aunt, she would have happily paid to have us examined by a modern “evidence-based” psychiatrist. As far as we know, her experience is so far a solitary one. At the other end of the spectrum, we have guys like a Polish man named Ossowiecki who had some svābhāvika magical capacity, which he honed after meeting with a Russian Jewish man who had lived in India for a while and acquired his capacity from some unknown Hindu magicians. In 1925 CE, he was said to have been given a lump of mud scooped up from the basement of the pretālaya of Praxeda. The Pole was apparently told nothing about the mud, but on taking it in his hands and focusing, he described a vision he had of a shrine where men and women had gathered to sing as part of some ceremony. He described it as a single-story white building that was then suddenly destroyed. He also apparently stated that the mud he was given was from that shrine and seemed to be from deep down in the cellars. It so happened that the shrine was a Roman temple of Mithra that had been demolished by the preta-sādhaka-s, and the said pretālaya was built atop its ruins. This and several other incidents suggested that he was able to delocalize both in space and time and on occasion others might experience his delocalized manifestations.”

L: “I would also link this to the variation observed in the hypnogogic, hypnopompic and dream experiences of people. Those who tend to see dream solutions for problems seem to have a greater propensity for the direct phantasmagorical experience — this is consistent with us not solving problems in the dream. People who tend to see geometric or previously known images in their hypnagogia or hypnopompia tend to be less prone to experiencing phantasms. On the other hand, those who tend to see persistent photo-realistic faces or whole bodies of unknown people tend to be more prone to direct phantasmic experience. One could even say that natural selection seems to have generally acted in the direction of suppressing this capacity, even as it does to excessive mathematical genius or synesthesia. Indeed, more generally, it seems selection shapes the senses not necessarily towards what is veridical but what enhances fitness. There are other indications that this biological or genetic component might also manifest in more tangible ways. For example, Vrishchika has told me of the dangers of unmanaged empathy for a medical practitioner. She said there is a tendency to slide towards two extremes. The student physician might acquire a certain type of involved or affective empathy wherein they have a participatory sense in the patient’s suffering. This ends up deeply affecting them such that they usually evolve along either of two pathways. In the first, they suffer some type of post-traumatic stress disorder that pushes them to crash out. In the other, they gain a shell that cuts off all concern for the patient. It may drive them towards psychopathy or a sense of omnipotence that only damages the patient. Due to this, it is not uncommon for a patient to complain that the physician with a fancy education is no good compared to a lesser-educated one who has some other magic ingredient. After an initial struggle, Vrishchika told me that it suddenly clicked that the best spot to be in was no different from the well-defended but completely aware position we have cultivated regarding the bhūta-s and vetāla-s. With that in place, she was able to develop a state of detached empathy, where she can feel committed to alleviating the torture and death without those impressing on her like a bhūta. It was in the course of trying to decipher that she initiated that Protocadherin locus study.”

At that point, they were done with their afternoon break and returned to their respective duties.

Appendix: Saumanasa’s tale
Saumanasa once frantically contacted her cousin Somakhya and his wife Lootika to tell them about a strange experience. Her narration ran thus: Dear Somakhya, I hope you would not consider me as having lost sanity or hallucinating. I would have said that to anyone who told me something like what I experienced. However, our cousin Charuchitra told me that, if anyone, I must speak to you and your wife. I was editing a manuscript in my office in morning of the 12th of Bhādra (Kīlaka) and was to meet with my student in about 20 minutes. I suddenly heard a loud noise as though something heavy had crashed into my office. It repeated thrice. I was alarmed and came out into my lab to see if something heavy was smashing into the walls. To my surprise, I saw no one showing the slightest reaction, and my students were quietly proceeding with their work as though nothing had happened. I asked if they had heard something. All of them said no and looked at me a bit surprised. Just then, one of them remarked loudly “Wow, what’s that?” pointing to something behind me. I, too, felt as if someone had just passed behind me. But my student quickly withdrew her statement, saying: “It must have been a power fluctuation — maybe it just made your office lights flash brightly.” I went back into my office feeling something was amiss. As I sat in my chair, I vividly saw the image of my student who was to meet with me as if printed out of silvery gossamer. But there was something strange — the top of her head was indistinct and smudged out. I clearly heard her voice saying: “I’m sorry I cannot give you the sequences.” It repeated itself a few times after the vision died out, and the whole place went quiet. I thought it must be because I did not have my fix of coffee as the machine was broken. The time for the appointment came, and my student did not come. Annoyed, I sent her an email and then a message that she should come right away. Later that afternoon, I heard she had died just before our meeting. As she was coming into the campus, she was confronted by another woman over their competing interest in a male. That woman then repeatedly shot her in the head from close quarters. She was to have come with some ancient DNA sequences to discuss the same with me.

A note on Śrī, Viṣṇu and śṛṅgāra

yaḥ pūrvyāya vedhase navīyase
sumaj-jānaye viṣṇave dadāśati ।
yo jātam asya mahato mahi bravat
sed u śravobhir yujyaṃ cid abhy asat ॥ RV 1.156.2
Whoever repeatedly performs rituals to the wise one
to the ancient and the new one, Viṣṇu, along with his consort,
whoever speaks of the great birth of the great [god],
he alone will surpass his peer in glory.

While the aspect of the Viṣṇu as a manly warrior of great might (like as the suppressor of the malignant wolf) is well-expressed in his cognates from more than one branch of the Indo-European tradition (going by extant material), his fertility and erotic aspects are less-known. By the latter, we are not referring to the prominent reflexes of these seen in the Kārṣṇi cult of the Sāttvata branch of the religion but to those pertaining to the form of the deity in the mainstream of the Indo-Aryan religion. These aspects are already alluded to in the Ṛgveda itself. For example, with regard to his role in fertility, we have:

saptārdhagarbhā bhuvanasya reto viṣṇos tiṣṭhanti pradiśā vidharmaṇi । RV1.164.36ab
The seven embryos of the world-hemispheres, the semen of the universe,
stand in the expanding space by the institutes of Viṣṇu.

viṣṇur yoniṃ kalpayatu । RV 10.184.1a
Viṣṇu prepares the womb. (An incantation that is used in the main Hindu fertility ritual of garbhādhāna)

The above mantra-s present the function of Viṣṇu in preparing the womb for the embryos both in the cosmic (in relation to Dyaus and Pṛthivī or the world hemispheres) and the human realms. The god’s famous name Śipiviṣṭa that is used by Vasiṣṭha in RV 7.99 and 7.100 ties together his erotic and fertility aspects. The fertility aspect of Viṣṇu under this name is remembered down to Bhāgavata from the late Paurāṇika stratum, wherein we hear of the brāhmaṇa-s performing a rite for the king of Aṅga to bear a son:

iti vyavasitā viprās tasya rājñaḥ prajātaye ।
puroḍāśaṁ niravapan śipiviṣṭāya viṣṇave ॥ Bh 4.13.35
Having decided thus, the vipra-s offered a cake to Viṣṇu Śipiviṣṭa for the sake of progeny for that king.

Finally, we may also note Viṣṇu’s association with a retinue of consort goddesses in the RV:

viṣṇuṃ stomāsaḥ purudasmam arkā
bhagasyeva kāriṇo yāmani gman ।
urukramaḥ kakuho yasya pūrvīr
na mardhanti yuvatayo janitrīḥ ॥ RV 3.54.14 
To Viṣṇu of many marvels the songs and chants
have gone, like singers on the road of Bhaga.
The wide-striding bull whose followers are many [goddesses];
The youthful mother goddesses never forsake him.

In the tāntrika tradition straddling the border of Pāñcarātra and Śaiva sects, the Śipiviṣṭa aspect of Viṣṇu is made explicit in the iconography of his erotic form Māyāvāmana. The erotic aspect of Viṣṇu and Śrī is also inherited by the smārta Śrikula tradition (recorded in the Brahmāṇḍa-purāṇa), where a lay devotee couple might recite an incantation to Viṣṇu and his consort Śrī so that their coitus might become an act of kaula offering. The existence of a now extinct vaiṣṇava tāntrika tradition with erotic rituals paralleling those of the śaiva yāmala tantra-s and bauddha-s of the vajrayāna stream is indicated by the bauddha commentator Ānandagarbha, who in his commentary on the Guhyasamāja-tantra tries to explain why the Buddha expounded this tantra while in coitus with the Buddha-yoṣit-s. He remarkably states that this was done to draw away the worshipers of Viṣṇu to the bauddha-mata. He goes on to state those vaiṣṇava-s worshiped Viṣṇu (the etymologies he provides makes it clear that he is not referring to a Kārṣṇi cult) via erotic pleasure-giving rituals. Thus, it appears that the bauddha-s were themselves mimicking a tāntrika vaiṣṇava tradition and trying to justify their own rituals within a “conversion” framework. We believe that the tradition on consideration was focused on the form of Viṣṇu known as Viṣṇu Trailokyamohana, whose mantra-s are found in several extant texts, but a more detailed consideration of those is beyond the scope of this note.

Reflexes of the ancient erotic aspect of Viṣṇu also find considerable expression in classical kāvya. In the rest of this note, we provide some examples culled from various anthologies where Śrī or Viṣṇu are invoked in the context of their erotic sports.

kiñjalka-rājir iva nīla-saroja-lagnā
lekheva kāñcana-mayī nikaṣopala-sthā 
saudāminī jalada-maṇḍala-gāminīva ।
pāyād uraḥ sthala-gatā kamalā murāreḥ ॥ (Vasantatilakā)
Like an array of pistils clinging to a blue waterlily,
like the streaks of gold marking a touchstone,
like lightning flashing against a mass of rain clouds,
May Kamalā lying on the chest of Murāri protect us.

kiṃ yuktaṃ bata mām ananya-manasaṃ vakṣaḥ-sthala-sthāyinīṃ
bhaktām apy avadhūya kartum adhunā kāntā-sahasraṃ tava ।
ity uktvā phaṇa-bhṛt-phaṇā-maṇi-gatāṃ svām eva matvā tanuṃ
nidrāc chedakaraṃ harer avatu vo lakṣmyā vilakṣa-smitam ॥ (Śārdūlavikrīḍita; attributed to Bhāsa)
“Why, alas, is it appropriate that, abandoning me who single-mindedly lies on your chest
full of attachment, you now take a thousand others as your wives?”
She said so, taking the [reflections] of her own body in the gems borne on the serpent’s hoods.
May that embarrassed smile of Lakṣmī that broke the sleep of Hari protect you!

This verse potentially plays on the multiplicity of consorts, already alluded to in the RV, being reflections of the singular Śrī.

keli-calāṅguli-lambhita-lakṣmī-nābhir-mura-dviṣaś caraṇaḥ ।
sa jayati yena kṛtā śrīr anurūpā padmanābhasya ॥ (Āryā)
The toe of the foot of Mura’s foe playfully tickled the navel of Lakṣmī;
victorious is that which makes Śrī a suitable wife of lotus-naveled one.

Here a pun is played on Viṣṇu being Padmanābha — lotus-naveled — and also having lotus feet. By tickling Śrī on her navel with his toe, he has also made her “Padmanābhā” and thereby a suitable female counterpart of his.

kaca-kuca-cubukāgre pāṇiṣu vyāpṛteṣu
prathama-jaladhi-putrī-saṃgame .anaṅga-dhāmni ।
grathita-nibiḍa-nīvī-bandha-nirmocanārtha
caturādhika-karāśaḥ pātu vaś cakra-pāṇiḥ ॥ (Mālinī)
With her hair, breasts and chin-tip engaged in his hands,
in the first erotic congress with the ocean’s daughter,
may the wheel-bearer wishing for more arms than four,
for untying the tightly fastened knot of her skirt, protect you!

uttiṣṭhantyā ratānte bharam uraga-patau pāṇinaikena kṛtvā
dhṛtvā cānyena vāso vigalita-kabarī-bhāram aṃśaṃ vahantyāḥ ।
bhūyas tat-kāla-kānti-dviguṇita-surata-prītinā śauriṇā vaḥ
śayyām ālambya nītaṃ vapur alasa-lasad-bāhu lakṣmyāḥ punātu ॥
(Sragdharā; attributed to Vararuci)
Raising herself at the end of coition by holding on to the serpent-lord with one hand,
bearing her garment in the other, with her mass of heavy disheveled tresses on her shoulder
But again, with the beauty of her form doubling his desire for love, Śaurin pulls her back
to the couch. May the body of Lakṣmī with her indolently embracing arms purify you.

lakṣmyāḥ keśa-prasava-rajasāṃ bindubhiḥ sāndra-pātair
udvarṇa-śrīr ghana-nidhuvana-klānti-nidrāntareṣu ।
dor-daṇḍo ‘sau jayati jayinaḥ śārṅgiṇo mandarādri-
grāva-śreṇi-nikaṣam asṛṇa-kṣuṇṇa-keyūra-patraḥ ॥ (Mandākrāntā, attributed to certain śrī Bhagīratha)
With the droplets of pollen falling thickly from the flowers in Lakṣmī’s hair,
brightly decorating it as he wearily sleeps in between intense erotic sports [with her],
may that cudgel-like arm of the conquering wielder of the Śārṅga bow, be victorious,
for whose irresistible polished armband the rocky array of mount Mandara was the touchstone.

The above is an allusion to the incarnation of Viṣṇu as the gigantic turtle bearing the axial Mandara mountain during the churning of the ocean.

Are civilizational cycles the norm?

Nearly two and half decades back, we used to have several conversations with a late śūlapuruṣīya professor, mostly on topics with a biological angle. While not a mathematician, he had a passing interest in dynamical systems, for he felt that they held the clues to great secrets of biology. We, too, were interested in dynamical systems for the lessons they offered at a certain abstract level that went beyond biology — as far as biology was concerned, we are of the firm opinion that there is no substitute to understanding its actual molecular details and no amount of mathematics can fill in for insight from that domain. Once, while chatting more generally, the śūlapuruṣīya professor was piqued by our interest in the ideas of his compatriot Oswald Spengler. He confessed that though they were no longer popular in academic circles, he too had a deep interest in Spengler’s ideas. Our śūlapuruṣīya professor had a friend who had (then) recently died, a mahāmleccha professor of upari-śūlapuruṣīya extraction, who in life was a deep student of macroevolution although little known outside his circles — precisely the kind of personality who would be buried in the current mleccha Zeitgeist. That dead professor, in turn, was close to a remarkable Russian of several talents — an evolutionist, an adventurer, an author of fiction and a prognosticator. Our late śūlapuruṣīya professor was in possession of a discussion on Oswald Spengler and related matters between the upari-śūlapuruṣa and the Rus, with the former taking the view that ultimately Spengler was right in his broad account on the life-history of civilizations. The Rus, in contrast, had a peculiar view that our śūlapuruṣa was puzzled by but knew little about. He correctly realized we might be the best to take a look at that.

In the exchange with the upari-śūlapuruṣa the Rus had said that inspired by his readings of Hindu lore, he believed that all civilizations would go through cycles, large and small, rising and falling with some quasi-periodicity. We were amused to see that he had explicitly stated we were verily in the Kaliyuga whose terminal days would see a decline and collapse of civilizations across the globe. Our śūlapuruṣīya professor remarked that people could have felt like that in every age; thus, it becomes a self-fulfilling prophecy with little reality to it. Nevertheless, he stated that the Spenglerian termination would by no means be pleasant either, and the question remains of what comes after that? He wished us to present our views on this topic. He had a vague sense that perhaps unbroken civilizations, such as those we came from, might have different memories than those of the Occident. We mentioned to him that indeed many civilizations of the old world had the concept of the end of times, which had been borrowed by the Abrahamists and incorporated into their own framework. However, our tradition had a concept of many cycles of existence, yuga-s and kalpa-s, with things going up and down, which is unique in terms of its time scale and detail. In our teens, we wondered about this peculiarity of our tradition and felt it might represent an inductive projection from a long-lasting tradition that had memories of cycles of booms and busts.

The average human life is long enough to see change in course of it but is too short relative to the existence of a species to place this change in the context of historical time. Thus, it is not surprising if the lifetime experience tilts one towards a unidirectional view of change. This not only affects an individual but a whole civilization if it has a short tradition. Indeed, the ascendant Occident might be viewed as a civilization with such an abbreviated tradition. Hence, there is a stronger tendency to view civilizational dynamics as a simplex and an insistence that growth is forever in some quarters. Even if someone were to see through this, it sometimes benefits them to maintain the lie because, in the least, it deflects the frustration of the masses away from them if the yuga was indeed on an avasarpiṇi course. In contrast, a civilization with a long tradition might see the risings and fallings of civilization to be a natural process — something which is unavoidable even if one were to swim against the tide desperately. One could say that Hindus have existed in such a state for a while. The notable feature of the Hindu model is its scale — going hand in hand with the much-maligned Hindu love for big numbers, the cycles are said to span huge temporal registers. This is closely intertwined with the Hindu mathematical approach to astronomy (going back to the śruti), wherein cycle synchronizations using solutions to indeterminate equations play an important role. Thus, it admits the space for the perception gained over a human lifespan being a misreading of the real trend of the slowly plodding yuga.

However, we kept wondering if such cyclicity should really be the norm of civilizational existence, especially when so many so-called intellectuals from the modern Occident kept assuring us that a great future of eternal progress was what we should look forward to. We were well conversant with the logistic growth curve; hence, we knew that such a dream was ultimately delusional. However, the scale was not clear — were we in the early stage where growth can be close to exponential, or were we nearing the inflection towards the eternal plateau. We did realize that certain resources, like energy, which were fueling our growing frenzy, were finite; hence, once they were exhausted, we would have to simplify. Finally, works like that of Tainter, which we have discussed before, indicated that civilizational collapse was the norm. Hence, the same could befall us. The most profound impact in this regard came in the 16th year of our life from our learning of the 2D cellular automaton of Ulam, the original investigator of cellular automata (CA). We had explored several CA before and after this period, which yielded deep insights germane to the topic under discussion. However, here we shall limit ourselves the classical Ulamian automaton, which offers useful insights, despite its extreme simplicity. After that study, we have been rather convinced that chaotic civilizational cycling, albeit with some predictable features, is unavoidable. We gave a demonstration and an account of the same to our śūlapuruṣīya professor, and it seemed to excite him greatly. We must reiterate that this is only a demonstration of an analogy, not a proof of anything. However, such dynamics with the simplest of rules lead us to conjecture that is also true of the more complex systems of everyday life, although with different parameters.

The Ulamian CA is played on a 2D grid with each cell in it capable of assuming 2 states, either 0 or 1 (shown below as red and blue). The system can be represented by a square matrix whose elements are either 0 or 1. The state of each cell in the subsequent step is dependent on the states in a neighborhood of 5, i.e., the cell itself and its 4 neighbors as shown below . The rule for assigning the state of a given cell in step is: if the sum of a cell’s neighborhood is even (0, 2, 4), the cell is 0; if the sum of the neighborhood of a cell is odd (1, 3, 5) is it 1.

The neighborhood for the Ulamian CA; the value of the neighborhood is 2 in this case

Thus, the simple system is balanced — there is an equal number of neighborhood states that can lead to it being 0 or 1. It allows for “autocatalytic” conversion, i.e., single 1 cell to convert its neighbors in an outward growth at the same time it has inbuilt inhibition of crowding by setting the even neighborhoods to 0. Hence, it may be seen as capturing some of the basics of processes seen in life or structure like a civilization that grows by the expansion of its units.

Figure 1. The Ulamian CA on an infinite planar grid

Figure 2. The first 65 steps of the Ulamian CA on an infinite grid

The CA can be played on an infinite planar grid or a finite torus. We first consider the former case by initializing it with a single 1 cell at and playing it till . This is shown as an animation in Figure 1 and statically in Figure 2. Above the CA, we show 2 numbers; the one to the left is the step ; the one to the right is the total number of cells in state 1 at that step. The latter gives rise to the below sequence (graphically depicted in the top panel of Figure 3):

1, 5, 5, 17, 5, 25, 17, 61, 5, 25, 25, 85, 17, 85, 61, 217, 5, 25, 25, 85, 25, 125, 85, 305, 17, 85, 85, 289, 61, 305, 217, 773, 5, 25, 25, 85, 25, 125, 85, 305, 25, 125, 125, 425, 85, 425, 305, 1085, 17, 85, 85, 289, 85, 425, 289, 1037, 61, 305, 305, 1037, 217, 1085, 773, 2753, 5 …

Figure 3. Number of 1 cells and entropy in the evolution of the Ulamian CA on an infinite grid

One observes that new “big” maxima (Figure 3) are attained at steps equal to powers of 2: 1, 5, 17, 61, 217, 773, 2753, 9805, 34921, 124373, 442961, 1577629… that are followed by minima of value 5. The value at the step just before the maxima is the same as the value at the step. The value at step 2 before the step is the value at step. We had discovered that the ratios of successive pairs of these values are convergents of the positive root of the polynomial . Thus, the values at the steps define a Nārāyaṇa type Meru sequence that can be generated by the following recurrence formula: , where .

Further, from the above relationships we obtained a closed form for the above sequence of the total number of cells with value 1 in the Ulamian CA:
$f[1]=1; f[2k-1]=f[k]; f[4k-2]=5f[k]; f[4k]=3f[4k-1]+2f[4k-3]$

Figure 4. The number of 1 cells in the evolution of the Ulamian CA to 513 steps

Thus, we can compute the number of 1 cells of the CA on an infinite grid at any step without actually having to run it (Figure 4). This shows us that this sequence has a fractal structure with cycles of length and more detail being added at each successive interval . As we noted above, the values attained in each cycle are intimately linked to the constant . In the middle of each cycle, we have a local peak located a . The ratio of the peak to this mid-cycle peak at step is . The balance between the conditions producing 0 and 1 states results in a predictable but intrinsic boom and bust cycle with booms at and the busts at the step immediately after the boom. This shows that even though infinite space for growth is available, the balance between growth and death from local crowding can lead to cycling in a population modeled by such an Ulamian CA. We can use Shannon’s entropy to measure the complexity of the structure of the pattern formed by the CA. Given that the CA is initiated from a central cell, it is symmetric in the 4 quadrants; hence, we only need to look at one quadrant. There we look at all possible 5 letter words (32 possible words) formed by the 2-letter alphabet (i.e., 1, 0) that are formed as the CA evolves and measure the Shannon entropy in terms of these 5 letter words (bottom panel of Figure 3). We find that the complexity of the CA at a given step as measured by entropy tracks its growth — when it attains maximal occupancy (in terms of 1 cells) it also has the highest complexity and vice versa.

Figure 5. First 300 steps in the evolution of the Ulamian CA on a torus of circumferences of 37

Figure 6. First 300 steps in the evolution of the Ulamian CA on a torus of circumferences of 37

A more interesting situation arises when we play the automaton on a finite torus (Figure 5 shows an animation on a torus flattened out as a square; Figure 6 shows statics of the same). Here we notice that by step 19 the circumferences of the torus are spanned, and the CA starts “folding” on itself. As a result, the CA’s dynamics are chaotic beyond this point. There are no longer predictable great booms at step (the step is always a high value, though not the highest). However, the bust at step predictably continues to be the greatest. There are several other busts of different magnitude. However, there is a significant tendency for one to occur at . If we let the CA to evolve to 1100 steps (Figure 7, top panel), we can see that there are also certain significant “golden ages” where relatively high occupancy (1 cells) is maintained over a large number of steps. For the CA on the torus, its complexity at a given step defined by Shannon entropy in 5-letter words becomes a good measure (Figure 7, bottom panel). While generally recapitulating occupancy, it tends to be more stable to the fluctuation in the number of 1 cells. Tracking entropy, we see that after the deep bust of step 897 (the 28th event), there is a “lean patch” and some volatility that lasts till step 905. After this, a great golden age is seen with high complexity and occupancy till the predictable wipe out of step . In the interim there are only 3 minor dips and a remarkable passage through with hardly a dip. There are likewise “dark ages”. For example, from the great bust of step 1025 to step 1059, low complexity states dominate the landscape with quick reversals of high complexity states by busts in the next step.

Figure 7. Number of 1 cells and entropy in the evolution of the Ulamian CA on a torus for 1100 steps

Thus, the Ulamian CA played on a torus captures key features of real-world populations in a very simple way: The rules of the CA establish the need for preexisting founders for growth as well as a local effect of death from over-crowding. The torus mimics the finiteness of resources or space for growth. Thus, after reaching the maximal circumference, the populations have to fold onto themselves, which on one hand can allow more complexity by fostering a greater diversity of local configurations and, on the other, cause overcrowding leading to a bust. Thus, when we first watched the Ulamian CA play out on our computer screen, we realized that civilizational cycles are likely to be inevitable — both in terms of population density and complexity of organization. It also told us that, in qualitative terms, the cycles would be chaotic; however, there would be certain statistically predictable elements. This brings to mind a popular adage: “History may not repeat itself. But it rhymes (pseudo-Mark Twain).” It also offered us three key insights regarding the complexity of civilizations. First, high densities can only be sustained via structural complexification — an approximation of fractal organization. Second, there is usually close to maximal complexity before a great bust — the end is usually sudden. Third, the maintenance of a protracted golden age goes with constant reconfigurations of high complexity states, i.e., there is no stable high complexity convergence. So the golden ages are not marked by a single stable state but a constant churn that results in a certain quasi-fractal complexity being maintained without tipping over to collapse from overcrowding and loss of that fractality. This again reminds one of the ideas of authors like Tainter, who have closely studied civilizational collapse — there is increasing complexification followed by a collapse.

Real population and civilizations are way more complex in their specifics than a 2D automaton operating under simple rules. Yet, our intuition is that if a system with the simplest of assumptions to capture growth and local resource competition can produce great complexity of behavior, then the same should be expected of a more parameterized system. Among other things, the various specifics can be seen as vectors acting in different directions and canceling out each other. Thus, it leaves us with the relatively simple inescapables — just as population dynamics and life-history can be modeled by simple equations like the logistic curve even though the actual elements contributing to the parameters are of immense biological complexity. Moreover, while these vectors might cancel each other, their multiplicity means that the evolution of the system is likely sensitive to initial conditions leading to chaotic dynamics. Hence, while the simple Ulamian automaton is unlikely to be a specific model of civilizational cycles, it is likely to be a realistic picture of its general patterns. Thus, we were left with an appreciation of the inevitability of civilizational cycling and skepticism for the ideas of eternal growth and utopianism which are prevalent in the Occidental academe.

On the rise of the mātṛkā-s and the goddess Cāmuṇḍā

The roots of the mātṛkā-s in the śruti and the Kaumāra tradition
The standard list of 7/8 goddesses known as the mātṛkā-s is a hallmark feature of the classical religion: Brāhmī, Māheśvarī, Kaumārī, Vaiṣṇavī, Vārāhī, Indrāṇī, Cāmuṇḍā, sometimes with the central Caṇḍikā (Mahālakṣmī), to make a list of 8. Most of them are the female counterparts of the prominent gods of the classical pantheon. These goddesses have a relatively constant iconography throughout the Indosphere, starting from the Gupta age. Despite this relatively late arrival on the iconographic landscape, they have deep roots going back to the ancestral Indo-European religion and its earliest Indo-Aryan manifestation. Right in the Ṛgveda, we have the incantations for the Patnī-saṃyāja or the worship of the goddesses at the Gārhapatya altar (e.g., RV 2.32.4-8; RV 5.46.7-8), along with Agni Gṛhapati. Similar ṛk-s are also seen in the Atharvavedic tradition. Three types of goddesses can be discerned in these incantations: 1) The great trans-functional goddess of proto-Indo-European provenance, Sarasvatī; 2) The deva-patnī-s or the wives/female counterparts of the gods; 3) The “lunar goddesses”, Kuhū (Guṅgū), Sinīvālī, Rākā, Anumatī. Below we provide an Atharvavedic version of these incantations (the subset which is found in RV is effectively the equivalently).

yā rākā yā sinīvālī yā guṅgūr yā sarasvatī ।
indrāṇīm ahva ūtaye varuṇānīṃ svastaye ॥
I call she who is, Sinīvālī, who is Guṅgū, who is Rākā, who is Sarasvatī, for my aid I call Indrāṇī, and Varuṇāṇī for my well-being.

sinīvālīm anumatīṃ rākāṃ guṅgūṃ sarasvatīm ।
devānāṃ patnīr yā devī indrāṇīm avase huve ॥
I invoke for protection Sinīvālī, Anumatī, Rākā, Guṅgū, and Sarasvatī, the wives of the gods, and she who is the goddess Indrāṇī.

senāsi pṛthivī dhanaṃjayā aditir viśvarūpā sūryatvak ।
indrāṇī prāṣāṭ saṃjayantī tasyai ta enā haviṣā vidhema ॥
You are Senā (the goddess of the divine army), the Earth, the conqueress of wealth, Aditi, multiformed, and sun-skinned. O Indrāṇī, [for you] the prāṣāṭ call, O all-conquering one; we pay homage to her with this offering.

uta gnā vyantu devapatnīr indrāṇya1 gnāyy aśvinī rāṭ ।
ā rodasī varuṇānī śṛṇotu vyantu devīr ya ṛtur janīnām ॥
May the goddesses, the wives of the gods, come, Indrāṇī, Aśvinī, Agnāyi, and the Queen. May Rodasī [wife of the Marut-s] and Varuṇāṇī hear us, and the goddesses come to the ritual of the mothers.

yā viśpatnīndram asi pratīcī sahasra-stukābhiyantī devī ।
viṣṇoḥ patni tubhyaṃ rātā havīṃṣi patiṃ devi rādhase codayasva ॥
The Queen of the folks, you are Indra’s equal, the goddess with a thousand tresses, coming to us. O wife of Viṣṇu, to you, these offerings [are] made. O goddess, urge your husband to be liberal [towards us].

A five-headed Indrāṇī from a Nepalian mātṛkā-pūjā manuscript

Of these goddesses, Indrāṇī and Viṣṇupatnī (Vaiṣṇavī) are featured in most classic mātṛkā lists of the later religion. Another goddess from the classical mātṛkā list, Rudrāṇī, is seen in yajuṣ incantations of the Taittirīya and Kaṭha schools of the Kṛṣṇa-yajurveda. The goddess Senā is associated with the divine army. In the Kṛṣṇa-Yajurvedic Kaṭha and Maitrāyaṇi schools, Senā identified with Indrāṇī: indrāṇyai caruṃ nirvapet senāyām uttiṣṭhantyām । sénā vā indrāṇī । This association continues in the late Yajurvedic incantation known as the Āyuṣya-sūkta (Bodhāyana-mantra-praśna), where the same goddess is explicitly termed Indrasenā. In later tradition, she is seen as the wife of Skanda (Devasenā), who is also mentioned in the Āyuṣya-sūkta by her other name Ṣaṣṭhī.

A persistent pattern in these Vedic rituals is the presence of a single male god accompanying a cluster of goddesses. As noted above, Agni Gṛhapati is the single male deity who accompanies the goddesses receiving offerings in the Patnī-saṃyāja. The RV also repeatedly states that the wives of the gods arrive at the ritual accompanied by the god Tvaṣṭṛ (RV 1.22.9; 1.161.4; 2.31.4; 2.36.3; 6.50.13; 7.34.20; 7.34.22; 7.35.6; 10.18.6; 10.64.10; 10.66.3) Additionally, in the Taittirīya school we have two versions of the Devikā oblations. In the first of them, the god Tvaṣṭṛ accompanies the goddesses Sarasvatī and Sinīvālī. In the second, the god Dhātṛ (a later ectype of Tvaṣṭṛ [Footnote 1]) is invoked together with the goddesses Aditi, Anumatī, Rākā, Sinīvālī and Guṅgū. This pattern may be seen as analogous to the usual situation, wherein several male gods associated with different functions are spanned by a single transfunctional goddess — Sarasvatī [Footnote 2]. Here, a single male generative deity is associated with a multi-functional cluster of goddesses who actualize the dormant generative capacity of the former. While the Patnī-saṃyāja associated with the Śulagava ritual of the Śukla-yajurveda invokes the goddesses with Agni Gṛhapati as usual, it presents a unique set of them (Pāraskara-Gṛhya-Sūtra 3.8):

śūlagavaḥ ।
The impaled bull [sacrifice]

svargyaḥ paśavyaḥ putryo dhanyo yaśasya āyuṣyaḥ ।
It procures heaven, cattle, sons, riches, renown, long life.

aupāsanam araṇyaṃ hṛtvā vitānaṃ sādhayitvā raudraṃ paśum ālabheta ।
Having taken the aupāsana fire to the forest, and having performed the spreading [of grass], he should obtain the animal for Rudra.

sāṇḍam ।
With testicles (i.e., not castrated)

gaur vā śabdāt ।
Or a cow as the name [of the ritual specifies]

vapāṃ śrapayitvā sthālīpākam avadānāni ca rudrāya vapām antarikṣāya vasāṃ sthālīpāka-miśrānyavadānāni juhoty agnaye rudrāya śarvāya paśupataye ugrāyāśanaye bhavāya mahādevāyeśānāyeti ca ।
Having cooked the omentum, a plate of rice, and the cuts from [the victim], he offers the omentum to Rudra, the fat to the atmosphere, and the cuts of meat with the rice to Agni, Rudra, Śarva, Paśupati, Ugra, Aśani, Bhava, Mahādeva and Īśāna.

vanaspatiḥ ।
The Vanaspati (offering to the sacrificial post is made).

sviṣṭakṛd ante ।
At the end [offerings are made to Agni] Sviṣṭakṛt.

dig vyāghāraṇam ।
Then the sprinkling to the directions [is performed].

vyāghāraṇānte patnīḥ saṃyājayantīndrāṇyai rudrāṇyai śarvāṇyai bhavānyā agniṃ gṛhapatim iti ।
At the end of the sprinkling the offer the Patnī-saṃyāja oblations to Indrāṇī, Rudrāṇī, Śarvāṇi, Bhavānī, and Agni Gṛhapati.

lohitaṃ pālāśeṣu kūrceṣu rudrāya senābhyo baliṃ harati yās te rudra purastāt senās tābhya eṣa balis tābhyas te namo yās te rudra dakṣiṇataḥ senās tābhya eṣa balis tābhyas te namo yāste rudra paścāt senās tābhya eṣa balis tābhyas te namo yās te rudrottarataḥ senās tābhya eṣa balis tābhyas te namo yās te rudropariṣṭāt senās tābhya eṣa balis tābhyas te namo yās te rudrādhastāt senās tābhya eṣa balis tābhyas te nama iti ।
He [then] offers the blood [of the sacrificed bull] as bali with a bunch of Butea frondosa leaves to Rudra and his troops with [the incantations]: “O Rudra, those armies, which you have to the East (to the South; to the West; to the North; upwards; downwards), to them is this bali. Obeisance be to them and to you.”

ūvadhyaṃ lohita-liptam agnau prāsyaty adho vā nikhanati ।
He casts the gut and the blood-smeared remains into the fire or buries them beneath.

anuvātaṃ paśum avasthāpya rudrair upatiṣṭhate prathamottamābhyāṃ vā .anuvākābhyām ।
Having [placed the remains of] the animal such that the wind blows from himself to it, he goes towards it by [reciting] the Rudra incantations, or the first and last anuvāka [i.e., Śatarudrīya].

naitasya paśor grāmaṃ haranti ।
They do not take anything of the animal to the village.

etenaiva goyajño vyākhyātaḥ ।
By this the cow-sacrifice is also expounded.

pāyasenānartha-luptaḥ ।
It is done with an offering of milk, and the [rituals] not meant for it are omitted.

tasya tulyavayā gaur dakṣiṇā ।
A cow of the same age (as the sacrificed animal) is the ritual fee.}

Thus, the Patnī-saṃyāja of the Śulagava departs from the classical one in combining Indrāṇī with the three raudra goddesses, Rudrāṇī, Śarvāṇi and Bhavānī. Hence, we are already seeing a hint of the tendencies in the mātṛkā system of the classical religion, wherein the māṭṛkā-s typically have an explicitly raudra connection. Indeed, this triad of raudra goddess might indicate a connection to the old name of Rudra, Tryambaka, which implies his association with three mothers. Other than the above-mentioned male deities coming with a cluster of goddesses, in the late Taittirīya tradition of the Bodhāyana-mantrapraśna, we see Skanda appearing with a cluster of 12 māṭṛkā-s:

aghorāya mahāghorāya nejameṣāya namo namaḥ ॥
āveśinī hy aśrumukhī kutuhalī hastinī jṛṃbhiṇī stambhinī mohinī ca ।
kṛṣṇā viśākhā vimalā brahmarātrī bhrātṛvyasaṃgheṣu-patanty amoghās tābhyo vai mātṛbhyo namo namaḥ ॥

Similarly, another late Taittirīya tradition, the Vaikhānasa-mantrapraśna, provides an incantation for a set of goddesses who are said to be born of Guha (i.e., Skanda) and said to bear the gaṇa of Rudra:

jvālā mālā gumbhinī guha-jātā raudraṃ gaṇaṃ yā bibhṛyāt surūpī svāhā ॥ VP 6.36.5

A second incantation describes a set of goddesses, including the one who bears Skanda:

mohī vimohī vimukhī guha-dhāriṇī ca nidrā ca devī virajās tu bhūtyai svāhā ॥ VP 6.37.9

Starting from its late Vedic roots, the association of Skanda with the mātṛ-s was remembered over a prolonged period in Indian historical tradition. For instance, it figures in the famous maṅgalācaraṇa of the Cālukya monarchs where they describe themselves thus: …mātṛ-gaṇa-paripālitānāṃ svāmi-mahāsena-pādānu-dhyātānām… Protected by the troop of mātṛ-s and meditating on the feet of lord Mahāsena. This association of a cluster of goddesses with Skanda is further developed in the Mahābhārata:

tataḥ saṃkalpya putratve skaṃdaṃ mātṛgaṇo .agamat ।
kākī ca halimā caiva rudrātha bṛhalī tathā ।
āryā palālā vai mitrā saptaitāḥ śiśumātaraḥ ॥ Mbh 3.217.9 (“critical”)
Having established the sonship of Skanda, the band of mātṛ-s went away: Kākī, Halimā, Rudrā, Bṛhalī, Āryā, Palālā and Mitrā, these are the seven mothers of Śiśu.

A similar list is given in the “mega”-Skandapurāṇa:

kākī ca hilimā caiva rudrā ca vṛṣabhā tathā ।
āryā palālā mitrā ca saptaitāḥ śiśumātaraḥ ॥ SP-M 1.2.29.175-76

Notably, in this cluster of goddesses, we see, for the first time, an explicit list of 7 mātṛ-s — a number that became characteristic of the classical group of mātṛkā-s. In subsequent narrations of the Kaumāra cycle in the medical and paurāṇika traditions, the number of mātṛ-s who accompany Skanda is numerous and varied. Nevertheless, one of the archaic versions from the Mbh we encounter for the first time the description of these mātṛ-s as having the form of female versions of the gods:

yāmyo raudryas tathā saumyāḥ kauberyo .atha mahābalāḥ ।
vāruṇyo .atha ca māhendryas tathāgneyyaḥ paraṃtapa ॥
vāyavyaś cātha kaumāryo brāhmyaś ca bharatarṣabha ।
vaiṣṇavyaś ca tathā sauryo vārāhyaś ca mahābalāḥ । [missing in some recensions]
vaiṣṇavyo .atibhayāś cānyāḥ krūrarūpā bhayaṃkarāḥ । [Alternative for above]
rūpeṇāpsarasāṃ tulyā jave vāyusamās tathā ॥ Mbh 9.45.35-36
O scorcher of foes, possessed of great might [these goddesses took the forms] of Yama, Rudra, Soma, Kubera, Varuṇa, the great Indra and Agni. O bull among the Bharata-s, yet others of great might took the form of Vāyu, Kumāra, Brahman, /Viṣṇu, Sūrya, Vārāhī/Viṣṇu and other terrifying and fierce forms evoking great terror./ Endowed with the beauty of Apsaras-es, they were possessed of the speed of wind.

Thus, within this Kaumāra context, we see the first expression of a matṛ list converging on the classical system. Kaumāra-mātṛ-s appear first in iconography in the company of Skanda in Kuṣaṇa and pre-Kuṣaṇa sites like the holy city of Mathura. Even the earliest iconographic exemplars of the 7 classical mātṛ-s are connected to Skanda (Gupta age; see also the Patna inscription which speaks of Kumāragupta’s brother-in-law installing a shrine for Skanda at the head of the matṛ-s). However, in the post-Gupta age, the connection of Kumāra and the classical mātṛ-s gradually faded away. However, the old Vedic template of a multiplicity of goddesses in the company of a single god continued to be expressed. Among the gods of taking the place of Skanda in the mātṛkā panels were Kubera, Rudra, both in his classic form and as Tumburu, Vīrabhadra and Gaṇeśa. Of these, as we have noted before, the association with Rudra is archaic, having Vedic roots. It is reiterated in the Mbh:

vanaspatīnāṃ pataye narāṇāṃ pataye namaḥ ।
mātṝṇāṃ pataye caiva gaṇānāṃ pataye namaḥ ।
apāṃ ca pataye nityaṃ yajñānāṃ pataye namaḥ ॥ Mbh 7.173.38
Salutations to the lord of the trees, men, the mātṛ-s, the gaṇa-s, the waters, and ever the lord the rituals.

Indeed, a large host of 190 ferocious therocephalic and avicephalic mātṛkā-s, comparable to those accompanying Skanda, is described as being generated by Rudra to drink up the blood of Andhaka in the Matsyapurāṇa. In the same narrative, Nṛsiṃha also generates 32 mātṛkā-s to pacify the former. These latter goddesses are the arṇa-devī-s of the famed 32-syllabled mantra of Nṛsiṃha. A band of piśācī-s, who eat up the corpse of the daitya Hālāhala killed by the gaṇa-s of Nīlalohita-rudra, when he comes to take the skull of Brahman, are also known as Kapālamātṛ-s and associated with Rudra as per the proto-Skandapurāṇa (7.15-23). The association between Rudra and the mātṛkā-s is also emphasized in the historical record by the famous Gupta age inscription from Bagh, Madhya Pradesh, which mentions the Pāsupata teacher, Lokodadhi, installing a temple that is the station of the mātṛ-s in the village of Piñcchikānaka:  … bhagaval lokodadhi pāsupatācārya-pratiṣṭhāpitaka-piñcchikānaka-grāma-mātṛ-sthāna-devakulasya … In conclusion, the conceptualization of the mātṛkā-s in the classical religion can be traced back to the Vedic layer of the religion, with an organic evolution in the Mahābhārata and the early medical literature, and close associations to the Kaumāra and Śaiva sects.

Cāmuṇḍā, her distinctness, and preeminence

Cāmuṇḍā from a prayoga manual from Nepal

However, there is one mysterious mātṛkā in the classical list who does not fit the general deva-patnī prototype inherited from the śruti. She goes by the common name Cāmuṇḍā or is alternatively known as Bahumāṃsā in some early paurāṇika texts. She is often distinguished by a corpse-, an owl- (e.g., Paraśurāmeśvara temple in Kaliṅga) or a vulture (the Mayamata pratiṣṭhātantra of saiddhāntika tradition) ensign. While she is explicitly linked to Rudra, she is often distinguished from his typical female counterpart Rudrāṇī. Cāmuṇḍā does not occur in any Vedic text (except in masculine form in a late addendum to the Vaikhānasa-mantra-praśna); nor does she occur in the epics.

In contrast, she appears profusely in paurāṇika texts. However, even here, in one of her early occurrences, directly pertaining to one of her holiest shrines, Koṭivarṣa, she is presented under a different name, Bahumāmsā, which appears to be a euphemistic double entendre. An apparently archaic version of the Koṭivarṣa-māhātmya, the famous pīṭha in Vaṅga, also known as Devīkoṭa (see below), was incorporated into the “proto”-Skandapuraṇa. Briefly, the frame story goes thus: Brahman once performed saṁdhyā at the Bay of Bengal for a crore years. Then he founded a beautiful city that eventually came to be known as Koṭivarṣa, where people lived a youthful existence. Once the god left the city, it was invaded by daitya-s, who committed many atrocities and slew thousands of brāhmaṇa-s and desecrated rituals. To remedy this, the gods went to Brahman and with him they went to Rudra. There Gaurī was performing tapasya in a grove and turned all the gods into females. Rudra then told them that they could slay the daitya-s only in their female forms. Thus:

tato devo .asṛjad devīṃ rudrāṇīṃ mātaraṃ subham ।
vikṛtaṃ rūpam āsthāya dvitīyām api mātaram ।
nāmnā tu bahumāṃsāṃ tāṃ jagat-saṃhāra-rūpiṇīm ॥
niyogād devadevasya tato viṣṇur api prabhuḥ ।
mātarāv asṛjad dve tu vārāhīṃ vaiṣṇavīm api ॥
abhūt pitāmahād brāhmī śarvāṇī saṃkarād api ।
kaumārī ṣaḍmukhāc cāpi viṣṇor api ca vaiṣṇavī ।
vārāhī mādhavād devī māhendrī ca puraṃdarāt ॥
sarvatejomayī devī mātṝṇāṃ pravarā subhā ।
bahumāṃsā mahāvidyā babhūva vṛṣabhadhvajāt ॥
sarveṣāṃ devatānāṃ ca dehebhyo mātaraḥ subhāḥ ।
svarūpabaladhāriṇyo nirjagmur daitya-nāsanāḥ ॥
vāyavyā vāruṇī yāmyā kauberī ca mahābalā ।
mahākālī tathāgneyī anyās caiva sahasrasaḥ ॥
tā gatvā tat puraṃ ramyaṃ daityān bhīmaparākramān ।
jaghnur bahuvidhaṃ devyo ghoranādair vibhīṣaṇaiḥ ।
daityahīnaṃ ca tac cakruḥ purāgryaṃ hemabhūṣitam ॥ “proto”-KM17-23
Then the god (Rudra) generated the goddess, mother Rudrāṇī. Taking an auspicious yet grotesque form, he also generated a second mother going by the name Bahumāṃsā, she of world-destroying form. At the mandate of the god of the gods, the mighty Viṣṇu also generated two mothers, Vārāhī and Vaiṣṇavī. From the Grandfather came Brāhmī and from Śaṃkara [came] Śarvāṇī. Kaumārī from Skanda (note irregular saṃdhi: ṣaḍmukhāt similar to that found in the Kaulajñānanirṇaya of Matsyendra. This supports the archaic nature of this narrative). Vārāhī from Mādhava and goddess Māhendrī from the smasher of forts (Indra). All these foremost of mothers were full of luster and auspicious. Bahumāṃsā, the great wisdom goddess, came into being from the bull-bannered one (Rudra). From the bodies of all these deities emerged auspicious mothers, each bearing their respective form and might, and set forth for the destruction of the demons: Vāyavyā, Vāruṇī, Yāmyā, Kauberī, Mahākālī, then Āgneyī of great strength, and thousands of others. The manifold goddesses slew [the demons], uttering terrifyingly ferocious yells. They made that foremost city decorated with gold free of the demons.

On one hand, the mātṛkā-s of narrative are reminiscent of the older Kaumāra cycle, and the Vedic Patnīsaṃyāja in naming a more inclusive set of goddesses including those generated by Vāyu, Varuṇa, Agni, etc. On the other hand, the core set of goddesses, who are named first, has crystallized to the classical 7-mātṛkā list. The only difference is that Bahumāṃsā replaces Cāmuṇḍā. However, their equivalence is clear from the account as Rudra specifically assumes a grotesque to generate her. As the narrative continues, Bahumāṃsā’s preeminent place in Koṭivarṣa is made amply clear:

hetukeśvara-nāmāhaṃ sthāsyāmy atra varapradaḥ ।
yuṣmābhiḥ saha vāsyāmi nāyakatve vyavasthitaḥ ॥
yas tu yuṣmān mayā sārdhaṃ vidhivat pūjayiṣyati ।
sarva-pāpavimuktātmā sa parāṃ gatim āpsyati ॥
dānavā nihatā yasmāc chūlena bahumāṃsayā ।
śūlakuṇḍam idaṃ nāmnā khyātaṃ tīrthaṃ bhaviṣyati ॥
iha sūlodakaṃ pītvā bahumāṃsām praṇamya ca ।
avadhyaḥ sarva-hiṃsrāṇām bhaviṣyati narottamaḥ ॥  “proto”-KM29-32
Under the name of Hetukeśvara, I (Rudra) will station myself here as the boon-giver. I will stay with you all, taking the position of leadership. Whoever worships you all together with me as per the ritual injunctions shall become free of sins and attain the highest state. From the trident with which Bahumāṃsā slew the demons, this holy pond will be known by the name of Śūlakuṇḍa. He who drinks the Śūla-water here and worships Bahumāṃsā will become unassailable to all harm-doers and will become the foremost of men.

Keeping with the preeminence of Bahumāṃsā in the early Koṭivarṣa cycle, in a subset of her early paurāṇika occurrences, Cāmuṇḍā appears independently of the classical mātṛkā lists. For example, Cāmuṇḍā is described in the Varāhapurāṇa as the slayer of the danava Ruru independently of the classical mātṛkā-s. This episode with the specific etymology furnished therein for the name Cāmuṇḍā (see below) is also told in the Devīpurāṇa in an expanded form (DP 83-88). However, in the DP version, Cāmuṇḍā is presented as one of the 7 classical mātṛkā-s. The slaying of Ruru is also retold in the Mātṛsadbhāva, an auxiliary text of the Brahmayāmala tradition. While other mātṛ-s are mentioned therein as being in the company of Rudra as Hetuka Bhairava (Hetukeśvara in the KM narrative), the main protagonist is Cāmuṇḍā in the form of Karṇamoṭī (Karṇamoṭinī), who pursues Ruru into pātāla and slays him after a battle lasting a crore years. This is used as an alternative etymology for Koṭivarṣa. The same text also mentions that Rudra emanated the goddess Ekavīrī from his forehead (third eye; note the Athena motif shared with the Greeks) to slay the daitya Dāruka. In the Cera country, the cult of Rurujit is widespread and closely associated with that of Bhadrakālī, who is described as the slayer of Dāruka. Indeed, the Brahmayāmala tradition preserved in south India tends to equate Bhadrakālī, the killer of Dāruka, with Cāmuṇḍā:  bhadrakāli tu cāmuṇḍā sadā vijaya-vardhinī ॥ Interestingly, while the Mātṛsadbhāva’s focus is Koṭivarṣa, its extant manuscripts are found in the Cera country, suggesting that the cult was carried south from Vaṅga after the destruction of Devīkoṭa by the Meccan demons. Below we provide the account of the slaying of Ruru from the Varāhapurāṇa 96:

tasyā hasantyā vaktrāt u bahvayo devyo viniryayuḥ ।
yābhir viśvam idaṃ vyāptaṃ vikṛtābhir anekaśaḥ ॥
pāśāṅkuśadharāḥ sarvāḥ sarvāḥ pīnapayodharāḥ ।
sarvāḥ śūladharā bhīmāḥ sarvāś cāpadharāḥ śubhāḥ ॥
tāḥ sarvāḥ koṭiśo devyas tāṃ devīṃ veṣṭya saṃsthitāḥ ।
yuyudhur dānavaiḥ sārdhaṃ baddhatūṇā mahābalāḥ ॥
kṣaṇena dānava-balaṃ tat sarvaṃ nihatantu taiḥ ।
devāś ca sarve sampannā yuyudhur dānavaṃ balam ॥
kālarātryā balañ caiva yac ca devabalaṃ mahat ।
tat sarvaṃ dānava-balam anayad yama-sādanam ॥
eka eva mahādaityo rurus tasthau mahāmṛdhe ।
svāñ ca māyāṃ mahāraudrīṃ rauravīṃ visasarja ha ॥
sā māyā vavṛdhe bhīmā sarva-deva-pramohinī ।
tayā vimohitā devāḥ sadyo nidrāntu bhejire ॥
devī ca triśikhenājau taṃ daityaṃ samatāḍayat ॥
tayā tu tāḍitasyāsya daityasya śubhalocane ।
carma-muṇḍe ubhe samyak pṛthagbhūte babhūvatuḥ ॥
rurostu dānavendrasya carma-muṇḍe kṣaṇādyataḥ ।
apahṛtyāharad devī cāmuṇḍā tena sā ‘bhavat ॥
sarvabhūta-mahāraudro yā devī parameśvarī ।
saṃhāriṇī tu yā caiva kālarātriḥ prakīrtitā ॥

As she [Rudrāṇī] laughed, from her mouth arose numerous goddesses with many strange forms, by whom this universe was enveloped. These terrifying and auspicious goddesses all held lassos, goads, tridents, and bows, and all had full breasts. All those crores of mighty goddesses stood surrounding the [primary] goddess, bearing quivers, together fought with the dānava-s. The whole dānava force was rapidly assaulted by those [goddesses], and together with them, the gods fought the dānava force. The great deva-force, together with the army of Kālarātri, sent the entire dānava force to Yama’s abode. The great daitya Ruru stood alone in the great battle. He then released his terrible rauravī magic. That terrible all-god-deceiving magic grew, and, overcome by it, the gods immediately fell asleep. Then the goddess struck the daitya on the battlefield with her trident. Thus, struck by the beautiful-eyed goddess, the skin and the head of the daitya were cleanly separated. As the goddess instantly seized and took away the skin and the head of the lord of the dānava-s, she came to be known as Cāmuṇḍā. From the terrifying form of the supreme goddess that destroys all beings, she came to be known as Kālarātrī.

The text then provides the below praise of Raudrī, where she is clearly identified as Cāmuṇḍā:

jayasva devi cāmuṇḍe jaya bhūtāpahāriṇi ।
jaya sarvagate devi kālarātre namo’stu te ॥
viśvamūrte śubhe śuddhe virūpākṣi trilocane ।
bhīmarūpe śive vedye mahāmāye mahodaye ॥
manojave jaye jambhe bhīmākṣi kṣubhitakṣaye ।
mahāmāri vicitrāṅge jaya nṛtyapriye śubhe ॥
vikarāli mahākāli kālike pāpahāriṇī ।
pāśahaste daṇḍahaste bhīmarūpe bhayānake ॥
cāmuṇḍe jvālamānāsye tīkṣṇadaṃṣṭre mahābale ।
śata-yāna-sthite devi pretāsanagate śive ॥
bhīmākṣī bhīṣaṇe devi sarvabhūtabhayaṅkari ।
karāle vikarāle ca mahākāle karālini ।
kālī karālī vikrāntā kālarātri namos’tu te॥

In the above cycles, Cāmuṇḍā is identified with Rudrāṇī and also as the primary dānava-slaying goddess, a role otherwise performed by Durgā. A folk memory of this was probably prevalent throughout the Indosphere and is today mainly seen in South India (e.g., the Cera country or Mysuru in the Karṇāṭa country). Additionally, Cāmuṇḍā is also presented as a distinct goddess, who is part of Rudra’s retinue, independently of the other mātṛka-s. This being a popular position is established by multiple such references in post-Gupta kāvya. In one such, she is paired in her skeletal form with the equally skeletal gaṇa Bhṛṅgiriṭi in a beautiful Śārdūlavikrīḍita verse of Yogeśvara regarding the celebration in Rudra’s retinue of the birth of Skanda:

devī sūnum asūta nṛtyata gaṇāḥ kiṃ tiṣṭhatety udbhuje
harṣād bhṛṅgariṭāvayācita-girā cāmuṇḍayāliṅgite ।
avyād vo hata-dundubhi-svana-ghana-dhvānātiriktas tayor
anyonya-pracalāsthi-pañjara-raṇat-kaṅkāla-janmā ravaḥ ॥ Subhāṣita-ratna-kośa 5.1
The goddess [Rudrāṇī] has birthed a son. O gaṇa-s rise up and dance!
Why? From joy, Bhṛṅgiriṭi raising his arms sings unasked embraced by Cāmuṇḍā.
On top of the loud din from the beating of the resounding drums
is the rattling born of the bones from the skeletal cages of those two — may it protect you!

She is also praised as the goddess slaying Niśumbha by Bhavabhūti in another masterly Śārdūlavikrīḍita with an allusion to the famous axial motif:

sāvaṣṭambha-niśumbha-saṃbhramanamad-bhūgola-niṣpīḍana-
nyañcat-karpara-kūrma-kampa-vicaṭad-brahmāṇḍa-khaṇḍa-sthiti ।
pātāla-pratimalla-galla-vivara-prakṣipta-saptārṇavaṃ
vande nandita-nīlakaṇṭha-pariṣad-vyakta-rddhi vaḥ krīḍitam ॥ Subhāṣita-ratna-kośa 5.3
From your whirling of Niśumbha, the earth-globe, with the axis, is pressed,
down on the turtle’s shell shaking it, shattering the support of the universe’s hemisphere.
The seven oceans trying to flood the netherworld instead fall into your cavernous cheeks.
I praise your perfectly performed dance that delights the retinue of the blue-necked one.
*Also could be a double entendre for the pressed down foot.

While she is not explicitly named here, the cavernous cheeks indicate that the goddess being referred to is none other than Cāmuṇḍā (see below). The two notable points in this verse are: first, Rudra’s retinue is the audience for her dance, again suggesting that she is an integral part of it. Second, as we noted above, she is shown as assuming the role normally assigned to the goddess Durgā/Caṇḍikā, i.e., killing Niśumbha, again reinforcing the idea of a folk memory of Cāmuṇḍā as the primary demon-slayer. This overlap with Caṇḍikā will be further explored below.

Cāmuṇḍā also occurs independently of the classical mātṛkā list but as part of other clusters of goddesses in certain paurāṇika and tāntrika traditions, e.g., the Dakṣa-yajña episode at the beginning of the Mega-Skandapurāṇa (1.1.3.49-53; Māheśvara-khaṇḍa, Kedāra-khaṇḍa):

vīrabhadro mahābāhū rudreṇaiva pracoditaḥ ।
kālī kātyāyanīśānā cāmuṇḍā muṇḍamardinī ॥
bhadrakālī tathā bhadrā tvaritā vaiṣṇavī tathā ।
nava-durgādi-sahito bhūtānāṃ ca gaṇo mahān ॥
śakinī ḍākinī caiva bhūta-pramatha-guhyakāḥ ।
tathaiva yoginī-cakraṃ catuḥṣaṣṭyā samanvitam ॥
nirjagmuḥ sahasā tatra yajñavāṭaṃ mahāprabham ।
vīrabhadra-sametā ye gaṇāḥ śatasahasraśaḥ ॥
pārṣadāḥ śaṃkarasyaite sarve rudra-svarūpiṇaḥ ।
pañcavaktrā nīlakaṇṭhāḥ sarve te śastrapāṇayaḥ ॥
Impelled by Rudra himself, the mighty-armed Vīrabhadra marched forth right away to the grove of the yajña with Kālī, Kātyāyanī, Īśānā, Cāmuṇḍā, Muṇḍamardinī, Bhadrakālī, Bhadrā, Tvaritā and Vaiṣṇavī, the nine Durgā-s and the rest: the great bhūta-gaṇa-s, Śakinī, Ḍākinī, the ghosts, pramatha-s and Kubera-s agents (guhyaka-s). The circle of 64 yoginī-s also accompanied him. Hundreds of thousands of gaṇa-s accompanied Vīrabhadra. These troops of Śaṃkara all had the form of Rudra, with five heads, blue-throats, and weapons in their hands.

The mention of the nine Durgā-s, after the list of nine goddesses, implies that these nine, including Cāmuṇḍā, are those Durgā-s. The remaining mātṛkā-s (barring Vaiṣṇavī, who is also counted among the nine Durgā-s) are not featured in this list. Similarly, in the iconographic section of the Agnipurāṇa (a similar account is also found in the iconographic manual, the Pratiṣṭhā-lakṣaṇa-sāra-samuccaya), we encounter a tradition, where multiple Cāmuṇḍā-s are presented as part of a group of 8 cremation-ground mothers, the Ambāṣṭaka, again almost entirely distinct from the classical mātṛkā-s (AP 50.30-37):

kapāla-kartarī-śūla-pāśa-bhṛd yāmya-saumyayoḥ ॥
gaja-carma-bhṛd ūrdhvāsya pādā syāt rudracarcikā ।
Rudracarcikā [is depicted] holding a skull, battle scissors, trident, lasso to the right and left. She holds an elephant hide, and her leg is raised up.

saiva cāṣṭabhujā devī śiro-ḍamarukānvitā ।
tena sā rudracāmuṇḍā nāṭeśvary atha nṛtyatī ॥
Rudracāmuṇḍā is verily the eight-handed goddess holding a severed head and a ḍamaru. She is shown dancing as the goddess of the dance (c.f. the above verse of Bhavabhūti).

iyam eva mahālakṣmī-rupaviṣṭā caturmukhī ।
nṛ-vāji-mahiṣebhāṃś ca khādantī ca kare sthitān ॥
The goddess Mahālakṣmī is indeed shown in a four-faced form. She [is depicted] eating a man, horse, buffalo, and elephant held in her hands.

daśa-bāhus trinetrā ca śastrāsi-ḍamaru-trikaṃ ।
bibhratī dakṣiṇe haste vāme ghaṇṭāṃ ca kheṭakaṃ ॥
khaṭvāṅgaṃ ca triśūlañ ca siddha-cāmuṇḍakāhvayā ।
Siddha-cāmuṇḍakā is depicted, with ten arms and three eyes, bearing a weapon, a sword, a ḍamaru, a trident, in her right arms; a bell, a shield, a skull-topped brand and a trident in her left arms.

siddhayogeśvarī devī sarva-siddhapradāyikā ॥
etad rūpā bhaved anyā pāśāṅkuśayutāruṇā ।
The goddess Siddhayogeśvarī (the goddess of the kaula Pūrvāmnāya = Trika), who bestows all accomplishments, is shown with another form, crimson in color, holding a lasso and a hook.

bhairavī rūpa-vidyā tu bhujair dvādaśabhir-yutā ॥
Bhairavī, the beautiful wisdom goddess, is shown with 12 arms.

etāḥ śmaśānajā raudrā ambāṣṭakam idaṃ smṛtaṃ ।
These raudra [goddesses] of the cremation ground are known as the cluster of eight-mothers.

kṣamā śivāvṛtā vṛddhā dvibhujā vivṛtānanā ॥
Kṣamā is shown surrounded by jackals as an old female with two arms and a gaping mouth.

danturā kṣemakarī syād bhūmau jānukarā sthitā ।
The fanged Kṣemakarī is shown [seated] on the ground with her hands on her knees.

These Ambāṣṭaka goddesses, Rudracarcikā, Rudracāmuṇḍā, Mahālakṣmī, Siddha-cāmuṇḍā, Siddhayogeśvarī, Bhairavī, Kṣamā and Kṣemakarī are likely associated with the 8 mahāsmaśāna-s of the tāntrika tradition. This is supported by the presence of Mahālakṣmī in the list, who is associated with the mahāsmaśāna of Kollagiri or Lakṣmīvana (modern Kolhapur). In the list, we find two explicitly named Cāmuṇḍā-s, which hearkens back to the mega-Skandapurāṇa Navadurgā-s, where Cāmuṇḍā is followed by Muṇḍamardhinī, who on etymological grounds could be seen as the second Cāmuṇḍā. A third goddess of the Ambāṣṭaka, Kṣamā, is depicted as an old female with jackals — again, iconographically similar to Cāmuṇḍā. The ogdoad also features Rudracarcikā, another ectype of Cāmuṇḍā (see below). Thus, we have at least four goddesses in the Ambāṣṭaka group, who can be described as conforming to the Cāmuṇḍā type. This multiplicity hints at Cāmuṇḍā being worshiped as the primary goddess at several of the mahāsmaśāna-s.

Cāmuṇḍā with her husband Bhiṣaṇa-bhairava: the deities of Ekāmra (a Nepalian depiction)

At least one of these mahāsmaśāna-s featuring Cāmuṇḍā was perhaps located at Ekāmra (modern Bhubaneswar) in the Kaliṅga country. The association of Cāmuṇḍā with this site, along with her Bhairava consort and Kubera or his female counterpart Kauberī, is abundantly attested in the kaula tradition: tantra-s (e.g., Kubjikāmata) and prayoga manuals of the Paścimāmnāya (e.g., Siddhi-lakṣmī-kramārcanā-vidhi-s), the Uttarāmnāya traditions like Niśi-saṃcara, and Ḍāmara texts like the Tridaśa-ḍāmāra-pratyaṅgirā. For example, we have the below mantra-s from the Paścimāmnāya (or its combination with the Uttarāmnāya in the case of the last mantra) tradition:

aiṁ OṂ ekāmraka-mahākṣetra-bhīṣaṇa-mahā-bhairavāya yaṁ cāmuṇḍā-śakti-sahitāya ekapāda-kṣetrapālāya dhanādhipataye namaḥ ॥
OṂ aiṁ yaṁ raṁ laṁ vaṁ śaṁ ekāmrake ohāyī kālarātrī chippinī cāmuṇḍā kauberī । au-kṣaḥ (o-kṣaḥ) bhīṣaṇa-bhairava śrīpādukabhyāṃ namaḥ ॥
OṂ aiṁ yaṁ bhīṣaṇa-bhairavāya cāmuṇḍā-sahitāya ekāmraka-kṣetrādhipataye namaḥ ॥
OṂ ekāmrake kṣetre yaṃ bhīṣaṇabhairava yāṃ cāmuṇḍā ambāpāda khphreṁ ॥

Coming to Carcikā, her equivalence with Cāmuṇḍā is established by multiple sources. For example, Amarasiṃha in his lexicon says: karmamoṭī tu cāmuṇḍā carmamuṇḍā tu carcikā । (AK 1.1.92). The great Bhāskararāya Makhīndra reiterates this in his gloss on the Lalitā-sahasranāma. Consistent with this, we also have the Śārdūlavikrīḍita verse of Tuṅga, which mentions Carcikā in Rudra’s retinue, separately from Rudrāṇī, in a manner similar to Cāmuṇḍā, as noted above.

carcāyāḥ katham eṣa rakṣati sadā sadyo nṛ-muṇḍa-srajaṃ
caṇḍī-keśariṇo vṛṣaṃ ca bhujagān sūnor mayūrād api ।
ity antaḥ paribhāvayan bhagavato dīrghaṃ dhiyaḥ kauśalaṃ
kūṣmāṇḍo dhṛti-saṃbhṛtām anudinaṃ puṣṇāti tunda-śriyam ॥
How does he ever protect his garland of fresh human heads from Carcā?
Also his bull from Caṇḍī’s lion and his snakes from his son’s peacock?
Thus, wondering to himself about the lord’s deep mental skill
Kūṣmāṇḍa daily nourishes the growing satisfaction of his belly’s corpulence.

The presence of Carcikā in Rudra’s retinue, independently of the classical mātṛkā-s, is also seen in some paurāṇika traditions, such as the Vāmana-purāṇa (70 in vulgate; 45 in short edition). Here, in the final battle with Andhaka, Rudra then took all the gods and his gaṇa-s into his body (c.f. Greek Kronos motif). When Andhaka struck him with his mace and caused him to bleed, from his own blood, Rudra generated the 8 Bhairava-s. Then from his fertilizing sweat, Rudra generated the virgin goddess Carcikā from his forehead (c.f. Greek Zeus-Athena motif) and then Kuja (the planetary archon of Mars) from his sweat that dropped on the ground. Together, Carcikā and Kuja drank up the blood of Andhaka. This myth, with Carcikā drinking up the blood of Andhaka, is widely depicted in images throughout India.

Finally, Carcikā replaces Cāmuṇḍā in some classical 7/8 mātrikā lists in tāntrika mantra-prayoga-s, like those in the Hāhārava or the Picumata of the Brahmayāmala tradition. Below are the famed Aṃbāpāda mantra-s of the Hāhārava belonging to the Atharvaṇa-guhyakālī tradition (Uttarāmnāya), where the 8 classical mātṛkā-s are associated with the eight Bhairava-s and manifest as Kālī-s, each surrounded by a retinue of 64 yoginī-s:

OṂ hrīṃ huṃ chrīṃ phreṃ [bhairava] +āsanāya aṣṭāṣṭaka-yoginī-sahitāya [devī] kāli 2 aṃbāpāda huṃ phreṃ namaḥ ।
Asitāṅga-bhairava : Brahmavatī
Ruru-bhairava : Rudravatī
Caṇḍa-bhairava : Kumāravatī
Krodha-bhairava : Viṣṇumatī
Unmattabhairava : Ghoraṇavatī/Varahāvatī
Kapāla-bhairava : Mahendravatī
Bhīṣaṇa-bhairava : Carcikāvatī
Saṃhāra-bhairava : Mahālakṣmīvatī
OṂ hrīṃ hūṃ chrīṃ phreṃ muṇḍinyai [devī] 2 aṃbāpada chreṃ hūṃ namaḥ ॥
devī= Kālī, Mudgalā, Daṃṣṭrinī, Śṛṅgārā, Śūlinī, Vajriṇī Pāśinī, Aṃkuśinī

Carcikā is associated with two great shrines at the Western and Eastern extremities of India, respectively Hiṅgulā (Vamanapurāṇa vulgate 70.47) and Koṭivarṣa. Of these, Koṭivarṣa in the Vaṅga country is explicitly known as a mahāsmaśāna. Hence, we may identify Rudracarcikā, who heads the Ambāṣṭaka list, as the goddess associated with this site. In support of this proposal, we have the famous Vaṅgīya inscriptions found in the vicinity that specifically mention the shrines of Carcikā (e.g., the Siyān and Bangarh inscriptions). The Parbatiya inscription of the Vanamālavarman, the king of Assam in the 800s of CE, also mentions the renovation of the temple of Hetukeśvara, the Rudra associated with Koṭivarṣa. King Nayapāla (r. 1043–1058 CE) says that he built a temple for the image of Carcikā his ancestor, emperor Mahendrapāla (r. 845–860 CE), had installed:

… mahe[ndra]pāla-carcāyā mahendra-sadṛśodayaḥ । yaḥ śailīm vaḍabhīm śaile sopānena sahākarot …
He who presented like Mahendra built for Mahendrapāla’s Carcā a stone vaḍabhī temple on the hill with steps [leading to it] (Siyan inscription, unfortunately, damaged by the Meccan demons).

The saiddhāntika-śaiva-deśika, Mūrtiśiva, a preceptor of the Pāla monarchs, mentions that he installed a similar temple for Carcikā and worships her in two verses, in anuṣṭubh and śārdūlavikrīḍita, thus:
OṂ namaś carcikāyai ।
surāsuraśiraḥ-śreṇi-paṭa-vāsa-samā jagat ।
pāntu viśvakṛtābhyarcāś carcā-caraṇa-reṇavaḥ ॥
daṃṣṭrā-saṃdhi-nilīnam eka-kavalam viśvaṃ tad aśnāmi kiṃ?
saptāmbhodhi-jalāni hasta-suṣire guptāni kim pīyate ?
ity āhāra-daridratākulatayā śuṣyat tanum bibhratī
kalpānte nṛ-kapāla-maṇḍana-vidhiḥ pāyāj jagac carcikā ॥ (Bangarh inscription)
Obeisance to Carcikā.
Like perfumed powder for the turbans of the array of gods and demons,
worshiped by the world-maker (Viśvakarman), may the dust from Carcā’s feet protect the world.

“The universe is a single morsel that will lodge in space between my teeth. Then what shall I eat?
The waters of the seven oceans will be hidden in the hollow of my palm. Then what may be drunk?”
Thus, anxious from the poverty of her meal, with her body becoming desiccated, observing,
at the end of the age, the rite wearing a garland of human heads, may Carcikā protect the world.

In the above verse, one may note the parallel to the drinking of the oceans seen in Bhavabhūti’s verse cited above. In addition, Koṭivarṣa, the same region of Vaṅga (Varendrī) also had another famous Cāmuṇḍā shrine, Puṇḍravardhana, which is mentioned along with Ekāmra by the great Kashmirian mantravādin Abhinavagupta in his Tantrāloka. The Uttarāmnāya has the below incantation remembering this now lost site:
OṂ hrīṃ śrīm śrī-puṇḍravardhana-mahopakṣetre cāmuṇḍā ambāpāda khpreṃ namaḥ ।

Pāla Carcikā 

The recovery of at least 24 images of the ekavīrā type, i.e., Carcikā or Cāmuṇḍā independently of other mātṛkā-s, from the Pāla age sites ruined by the Mohammedans, in the vicinity of Koṭivarṣa and Puṇḍravardhana, attests to the importance of her cult in the Varendrī region. One of these images is remarkable in depicting Carcikā, flanked by Gaṇeśa and the Bhairava or Mahākāla, surrounded by 20 Carcikā-s (totally with the central figure 21 goddesses; c.f. the 21 Tārā-s of the bauddha tradition). This multiplicity of Carcikā-s brings to mind the array of 20 Carcikā-s mentioned the Siddhāṅga-pañcaka-mantra-s of the Śaktisūtra:

ghasmarā carcikā vicceśvarī śrīviccāvvā- pāduke pūjayāmi aiṃ ॥
svarūpavāhinī nava-sthānagā śrīnandinī- viccāvvā pāduke pūjayāmi aiṃ ॥
padmā śobhā vikāśinī viccāvvā- pāduke pūjayāmi aiṃ ॥
mahāśāntā vikasvarā vikāśinī viccāvvā- pāduke pūjayāmi aiṃ ॥
nāda-carcikā śabdādyā śrīṣaṭkā viccāvvā- pāduke pūjayāmi aiṃ ॥

If we count the last goddess, Viccāvvā, who is the same in each of the five, then we get a list of 16 comparable to the 16 Cāmūṇḍā-s mentioned in the southern Brahmayāmala with roots in the Vaṅga country.

The scorpion-goddess

Vṛścikā from Prayāga

We next consider a goddess who is iconographically similar to Cāmūṇḍā but distinguished by a scorpion ornament on her belly. Images of this goddess are widely distributed across India, but a scorpion is never mentioned as an ornament in any of the numerous iconographic accounts of Cāmūṇḍā. Moreover, this scorpion goddess is only found in ekavīrā form, never with the other mātṛkā-s. To decipher who she is, we have to turn to the mega-Skandapurāṇa, which mentions scorpions as the medallion of Caṇḍī, a member of the entourage of Rudrasadāśiva:

tathodyato yoginī-cakra-yukto gaṇo gaṇānāṃ patir eka-varcasām ।
śivaṃ puraskṛtya tadānubhāvās tathaiva sarve gaṇanāyakāś ca ॥
tad yoginī-cakram ati-pracaṇḍaṃ ṭaṃkāra-bherī-rava-svanena ।
caṇḍī puraskṛtya bhayānakāṃ tadā mahāvibhūtyā sam-alaṃkṛtāṃ tadā ॥
kaṇṭhe karkoṭakaṃ nāgaṃ hāra-bhūtaṃ cakāra sā ।
padakaṃ vṛścikānāṃ ca dandaśūkāṃś ca bibhratī ॥
karṇā-vataṃsān sā dadhre pāṇi-pāda-mayāṃs tathā ।
raṇe hatānāṃ vīrāṇāṃ śirāṃsy urasi cāparān ॥
dvipi-carma-parīdhānā yoginī-cakra-saṃyutā ।
kṣetrapālāvṛtā tadvad bhairavaiḥ parivāritā ॥
tathā pretaiś ca bhūtaiś ca kapaṭaiḥ parivāritā ।
vīrabhadrādayaś caiva gaṇāḥ parama-dāruṇāḥ ।
ye dakṣa-yajña-nāśārthe śivenājñāpitās tadā ॥
tathā kālī bhairavī ca māyā caiva bhayāvahā ।
tripurā ca jayā caiva tathā kṣemakarī śubhā ॥
anyāś caiva tathā sarvāḥ puraskṛtya sadāśivam ।
gantu-kāmāś cogratarā bhūtaiḥ pretaiḥ samāvṛtāḥ ॥
Then the accompanied by the circle of yoginī-s, the gaṇa, the lord of the gaṇa-s (Nandin) of singular splendor and all the leaders of the gaṇa-s followed, keeping Śiva at their head. The circle of yoginī-s was most-terrifying and resounding with their yells, like the beating of kettledrums. They kept at their forefront the terrible Caṇḍī adorned with great magnificence. She had made the Karkoṭaka snake in the form of a necklace on her neck. She had a medallion of scorpions and bore snakes. Her earrings were made of severed hands and legs. She wore the severed heads of warriors slain in battle on her chest. She wore a skirt of elephant-hide and was accompanied by the circle of yoginī-s. She was surrounded by Kṣetrapāla-s and likewise by Bhairava-s. Similarly, she was accompanied by zombies, ghosts and deceiver ghosts. With Vīrabhadrā at their head, were the most-terrifying gaṇa-s, who had been ordered by Śiva to destroy Dakṣa’s sacrifice (the Raumya-s). Likewise, there were Kālī, Bhairavī, the frightful Māyā, Tripurā, Jayā and the auspicious Kṣemakarī. These and all others, of great ferocity, keeping Sadāśiva at their head, surrounded by ghosts and zombies, desired to march forth.

This is an account of the bridal procession of Rudra’s retinue on the occasion of his marriage to Pārvatī. Though he was displaying this sport of marrying his wife again following Sati’s reincarnation as Pārvatī, his Śakti-s never really left him. The chief among them is Caṇḍī, wearing a badge or medallion of scorpions. Thus, it appears that this ever-present Śakti of Rudra is depicted as the ekavīrā vṛścikodarī goddess. It is possible that the scorpion was identified with the eponymous constellation. Thus, its placement on the belly of the destroying goddess might have had an astronomical symbolism related to the constellation’s position at the southern point of the ecliptic (associated with her seasons: autumn/winter: right in the Yajurveda) and its connection to the Vedic goddess of the netherworld and doom, Nirṛti. In another account of the destruction of Dakṣa’s sacrifice from the Kāyāvarohaṇa-māhātmya (5.82), Rudrāṇī herself generates a goddess by rubbing her nose, who is described by the epithet śahasracaraṇodarī. This might be interpreted either as she with a 1000 feet and bellies or with a millipede on her belly, giving a possible parallel for this iconography.

Despite her widespread presence in Śaiva temples, the presence of this goddess in the mantra-śāstra is limited. The goddess Kubjikā is described as having scorpion ornaments like her husband Aghora in the prayoga-texts of the Kaula tradition (e.g., Ṣaḍāmnāyapūjāvidhi):

agni-jvālā-prabhābhair jvalana-śikhi-piccha-vṛścikair hāramālā ।
muṇḍasraṅ-muṇḍa-bhāgābhaya-durita-harā kubjikeśī namas te ॥
Obeisance to you. Goddess Kubjikā, who takes away misfortune has the glow of blazing flames, is garlanded by a wreath of shining peacock feathers and scorpions, and a garland of severed heads, holds a severed head, and shows the gestures of protection and boon-giving.

The scorpion-goddess Vṛścikā also figures in the Śrikula practice of the meditation on the six cakra-s along the path of the suṣuṃṇa. In the Anāhata-cakra, she is worshiped in the circle of the goddess Rākinī presiding over blood along with her Rudra. Here, she is worshiped along with several other goddesses, including Cāmuṇḍā, on the 12 spokes of the cakra. The Vaṅgīya mantravādin Pūrṇānanda explains it thus in his Tattvacintāmaṇi:

anāhate nyaset paścāt paritaḥ ka-ṭha-varṇakaiḥ ।
kālarātriḥ khātitā ca gāyatrī ghaṇṭikā tataḥ ॥
ṅā vṛścikā ca cāmuṇḍā chāyā jayā tathaiva ca ।
jhaṅkāriṇī tathā jñānā ṭaṅkahastā ca vinyaset ॥
ṭhaṅkārī ca kramādetā dhyātvā vīraśca pūrvavat ।
The equivalence between the goddesses and the bīja-s formed from the arṇa-s is thus: kaṃ: Kālarātriḥ; khaṃ: Khātitā; gaṃ: Gāyatrī; ghaṃ: Ghaṇṭikā; ṅaṃ: Vṛścikā; caṃ: Cāmuṇḍā; chaṃ: Chāyā; jaṃ: Jayā; jhaṃ: Jhaṅkāriṇī; ñaṃ: Jñānā; ṭaṃ: Ṭaṅkahastā;
ṭhaṃ: Ṭhaṅkārī.

This meandering discussion establishes that, while Cāmuṇḍā was seen as part of the 7/8 mātṛkā-s, she also had a separate existence either as a preeminent figure among the mātṛkā-s or as an independent goddess. In the latter capacity, she both iconographically and mythologically, overlapped with the domains of two independent goddesses Bhadrakālī and Caṇḍī/Caṇḍikā. An example of this overlap in folk tradition is the poem of Bhuṣaṇa Tripāṭhī on Śivājī, where he says that Caṇḍī is growing fat from eating the Mohammedans offered to her by the Marāṭhā advance — thus, he equates Caṇḍī to the emaciated Cāmuṇḍā.

Cāmuṇḍā’s place in the mantra-śāstra
We now turn to the mantraśāstra to examine some aspects of her worship. The KM already signals that the worship of the goddesses at Koṭivarṣa was according to the tantra-s known as the Yāmala-tantra-s:

ahaṃ brahmā ca viṣṇus ca ṛṣayas ca tapodhanāḥ ।
mātṛtantrāṇi divyāni mātṛ-yajñavidhiṃ param ।
puṇyāni prakariṣyāma yajanaṃ yair avāpsyatha ॥
brāhmaṃ svāyambhuvaṃ caiva kaumāraṃ yāmalaṃ tathā ।
sārasvataṃ sagāndhāram aiśānaṃ nandiyāmalam ॥
tantrāṇy etāni yuṣmākaṃ tathānyāni sahasrasaḥ ।
bhaviṣyanti narā yais tu yuṣmān yakṣyanti bhaktitaḥ ॥
narāṇāṃ yajamānānāṃ varān yūyaṃ pradāsyatha ।
divyasiddhipradā devyo divyayogā bhaviṣyatha ॥
yās ca nāryaḥ sadā yuṣmān yakṣyante sarahasyataḥ ।
yogesvaryo bhaviṣyanti rāmā divyaparākramāḥ ॥ KM 34-38
I [Rudra], Brahman, Viṣṇu and the sages with a wealth of tapas will compose the pure and divine Mātṛ-tantra-s [expounding] the foremost procedures for the rituals to the Mātṛ-s, by which you all would be worshiped. Brāhma, Svāyambhuva, Kaumāra-yāmala, Sārasvata with Gāndhāra, Aiśāna, Nandi-yāmala — these tantra-s of yours and thousands of others will come into being, and men will piously worship you all with them. You, O goddesses, endowed with divine yoga, will grant boons to the men who worship you and confer magical powers on them. Those women who will continuously worship you with the secret rituals will become the mistresses of yoga, beautiful and possessed of magical prowess.

Consistent with the above, the root tantra of the Brahmayāmala tradition, the Picumata, has a major section devoted to the yoginī-kula-s associated with each of the mātṛkā-s. Given the preeminence of Cāmuṇḍā at Koṭivarṣa, one would expect a special place for her among the mātṛkā-s in the mantra-śāstra. We believe that imprints of this are seen throughout the Śaiva- and Śākta- mantraśāstra and their arborizations. For example, the pratiṣṭhā-tantra, Mayamata, after giving the iconographic specifications for the 7 mātṛkā-s flanked by Vīrabhadra and Vināyaka, provides a second section only for Cāmuṇḍā. There it describes the installation of her images with 4, 6, 8, 10, 12, or 16 arms made from wood, clay, or stucco. It states they should show her dancing (see above) the twilight dance either by herself or place her beside Rudra, shown performing the same dance. It further mentions that the images with 4 or 6 arms are helpful for pacificatory purposes. It is again specified that the worship/festivals should be officiated as per the Yāmala-tantra-s (e.g., Southern Brahmayāmala).

The dominance of Cāmuṇḍā in the Śaiva systems is also apparent in the archaic mantra-śāstra recorded in the Ḍāmara-tantras. There, Cāmuṇḍā is invoked in a “fever-missile” incantation deployed to strike adversaries with a wasting fever thus:
OṂ bakāmukhā cāmuṇḍā kṣīra-māṃsa-śoṇita-bhojinī [amukaṃ] khaḥ khaḥ jvareṇa gṛhṇa gṛhṇa gṛhṇāpaya gṛhṇāpaya huṃ phaṭ svāhā ॥
Remarkably, the goddess is described as being heron-faced. While this is not encountered in any of her later extant iconographies, on one end, it connects her to the archaic avicephalous goddesses associated with Skanda in the early Kaumāra cycles and the avicephalous goddesses of the Kumārī (Kauśikī Vindhyavāsinī) cycle of the proto-Skandapurāṇa. On the other end, it connects her to the terminal Śaiva-śākta Mahāvidyā tradition, which features the attacking goddess Bagalāmukhī, whose name likewise means heron- or stork- headed. Bagalāmukhī too is not commonly shown with an avian head, but we have multiple prominent exemplars of such iconography in her case. First, we have such a painting from Kangra, Himachal. There is also the avicephalous Bagalāmukhī with 16 hands at the Saṇkaṭa Ghāṭa temple in Vārāṇasi. In a painting from the Bagalāmukhī temple at Bankhandi, Himachal, she is shown riding a crane, which also attacks the daitya whom she slays. Notably, at the Bagalāmukhī temple at Nīlācala, Assam, she is depicted with an owl ensign, another feature shared with Cāmuṇḍā. This suggests that grotesqueness of Cāmuṇḍā’s form included within it a long, iconographically unexpressed memory of the ancient avicephalous goddesses, which was subsequently passed on Bagalāmukhī. She is also identified with another of the Mahāvidyā-s, Chinnamastā, in the opening verse of her famous stotra, though their iconography is rather distinct:

OṂ chinnamastā mahāvidyā mahābhīmā mahodarī ।
caṇḍeśvarī caṇḍa-mātā caṇḍa-muṇḍa-prabhañjinī ॥

Her presence is also felt across the Śakti-para Śaiva systems. Kubjikā, the supreme goddess of the Paścimāmnāya, is seen as having several deities (Rudra and Dūtī-s) associated with her respective nyāsa aṅga-s:
Hṛdaya: Kālī
Śiras: Siddhayogeśvarī or Juṣṭācāṇḍālī
Śikhā: Svacchanda-bhairava (the deity of the Bahurūpī ṛk)
Kavaca: Śivā
Netra-traya: Raktacāmuṇḍā (Parā in some traditions)
Astra: Pratyaṅgirā or Guhyakālī
As one can see, the deity of the eyes of Kubjikā is none other Raktacāmuṇḍā. Her mantra is given as:

OṂ rakte mahārakte chāmuṇḍeśvarī svāhā ॥
aiṃ rakte mahārakte chāmuṇḍeśvarī khphreṃ svāhā ॥
The first is the root form and the second version is the kaula deployment.

Raktacāmuṇḍā’s deep presence is indicated by her presence in other Śaiva mantra traditions. For example, the Ḍāmara tradition deploys her mantra for the successful procurement of medicinal herbs:
OṂ hrīṃ raktacāmuṇḍe hūṃ phaṭ svāhā ॥

The Ḍāmara tradition also worships her in the company of Rudra as Nṛsiṃha, a feature shared with the Guhyakālī tradition:
OṂ hrīṃ śrīṃ klīṃ draṃ caṇḍogre trinetre cāmuṇḍe ariṣṭe hūṁ phaṭ svāhā । hrīṃ namāmy ahaṃ mahādevaṃ nṛsiṃhaṃ bhīmarūpiṇaṃ OṂ namas tasmai ॥

At the root of the Śākta tradition are the famed mantra-s of Cāmuṇḍā, the most fundamental of which is the Navārṇa-mantra. Tradition hails it as the best of the best of the Śākti-mantra-s: vicce navārṇa-mantro .ayaṃ śakti-mantrottamottamaḥ ।. It goes thus:
(OṂ) aiṃ hrīṃ klīṃ cāmuṇḍāyai vicce ॥
It might be expanded to include Cāmuṇḍā at the end of the mātṛkā-list as the Sarva-mātṝ-maya-mantra:
(OṂ) hrīṃ brahmāṇī-māheśvarī-kaumārī-vaiṣṇavī-vārāhī-aindrī-cāmuṇḍāyai vicce svāhā ।
We then have the Padamālā-mantra found in several texts like the Devīpurāṇa and the Yuddhajayārṇava-tantra (which in turn is included in Agnipurāṇa; AP 135). This long mantra, while including all the mātṛkā-s as the above, has as its primary deity the 28-handed Cāmuṇḍā. It ends with the mantra-pada:
OṂ cāmuṇḍe kili kili OṂ vicce huṃ phaṭ svāhā ॥
These mantra-s indicate the intimate connection between Cāmuṇḍā and the mysterious mantra utterance “vicce”. Indeed, Abhinavagupta even calls her Viccikā in his Tantrāloka, making one wonder if there is some connection to Vṛścikā via a Prākṛta form. In any case, the ending of the Padamālā-mantra is remarkably similar of the root mantra of the Paścimāṃnāya, the Samayāvidyā, which is the female counterpart of the Bahurūpī ṛk (the Aghora-brahma-mantra [Footnote 3]). Every syllable of the Samayāvidyā corresponds to one of the 32 syllables of the metrical Bahurūpī. The standard Paścimāṃnāya Samayāvidyā:
OṂ bhagavati ghore hskhphreṃ śrīkubjike hrāṃ hrīṃ hrauṃ ṅa-ña-ṇa-na-me aghoramukhi chrāṃ chrīṃ kiṇi kiṇi vicce ॥
The Paścimāṃnāya Samayāvidyā as per the Vaṅgīya tradition:
OṂ namo bhagavati hskhphreṃ hauṃ kubjike aiṃ hrīṃ srīṃ aghore ghore aghoramukhi klīṃ klīṃ kili kili vicce ॥
This suggests that the Cāmuṇḍā mantra influenced the construction of the Samayāvidyā.

Moreover, the Aṣṭa-mātṛkā-mantra-s of the Paścimāmnāya also parallel the Sarva-mātṝ-maya-mantra:

aiṁ aghore amoghe varade vimale [bīja] [devī] vicce ॥
śrīṃ: brahmāṇī; caṃ: kaumārī; ṭaṃ: vaiṣṇavī; thaṃ: vārāhī; paṃ: indrāṇī; yaṃ: cāmuṇḍādevī; śaṃ: mahālakṣmī

As noted above, we have the Śakti-sūtra of the Paścimāmnāya, which as has the Siddhāṅga-pañcaka-mantra-s to the array of Carcikā-s. Finally, a similar kind of influence of the Cāmuṇḍā mantra, likely via the Paścimāmnāya, is also seen on the construction of the long mantra of the erotic goddess Bhagamālinī of the Dakṣiṇāmnāya (note pada bhaga-vicche):

OṂ āṃ aiṂ bhagabhage bhagini bhagodari bhagāṅge bhagamāle bhagāvahe bhagaguhye bhagayoni bhaganipātini sarvabhage bhagavaśaṅkari bhagarūpe nityaklinne bhagasvarūpe sarvabhagāni me hyānaya varade rete surete bhagaklinne klinnadrave kledaya drāvaya amoghe bhaga-vicche kṣubha kṣobhaya sarvasattvān bhageśvari aiṃ blūṃ jaṃ blūṃ bheṃ moṃ blūṃ heṃ blūṃ ai/ blūṃ klinne sarvāṇi bhagāni me vaśamānaya strīṃ blūṃ hrīṃ bhagamālinī-nityā-kalāyai namaḥ ॥ (As per the Jñānārṇava–tantra 15)

The etymology of Cāmuṇḍā
Finally, we come to the peculiar issue of the etymology of Cāmuṇḍā. The Purāṇa-s offer multiple alternative “folk etymologies,” e.g., from carma+muṇḍa (Devī- and Varāha- purāṇa-s) or from Caṇḍa and Muṇḍa; however, none of these are by any means grammatical Sanskrit derivations. Moreover, the multiplicity also suggests that its actual roots were forgotten by the time the name was in common use. Yet, it seemed deserving of an explanation to the Sanskrit speaker as it did not seem “natural”, unlike the names of the other mātṛkā-s with deep Indo-Aryan roots. This goes with the fact that she is not a straightforward female counterpart of the gods, unlike most other mātṛkā-s.

Interestingly, some of her earliest mentions in the Koṭivarṣa-māhātmya and the Vindhyavāsinī section of the proto-Skanda-purāṇa, furnish her with a bivalent, but proper Sanskrit name, Bahumāṃsā. However, this name did not persist. Indeed, the other names of Cāmuṇḍā, Carcikā and Karṇamoṭī, or the peculiar mantra-pada vicce are also not attested in the earliest Sanskrit texts and lack a transparent Sanskrit etymology. This suggests that the names of this goddess adopted from a non-Aryan language eventually acquired wide currency within Sanskrit. This was hinted at even by Bhaskararāya. Moreover, as we noted above, Cāmuṇḍā overlaps with the domain of the related goddess known as Caṇḍī/Caṇḍikā, who is traditionally an ectype of Durgā. It does seem like Caṇḍī and Carcikā too might have originated from different attempts at Sanskritization of the same non-Aryan word that also gave rise to Cāmuṇḍā.

Its absence in the Vedic and epic layers of the language suggests that the word was unlikely to have been borrowed from a language the ārya-s encountered en route to India (Uralic or Bactria-Margiana) or upon first entering India (the Harappan language). We cannot etymologize it as Dravidian or Austro-Asiatic either. Hence, we have to tentatively admit that it might be from a now-extinct tribal language. Adopting such a name when an early Sanskrit name Bahumāṃsā was already in use suggests that simple syncretism with tribal goddesses was not at play. Instead, foreign words might be adopted to indicate special powers in incantations (e.g., the jharbhari-turphari sūkta to the Aśvins right in the RV itself). Thus, in the tāntrika tradition, the adoption of words from or which sound like from other languages is part of the same process. We posit that this was the mechanism by which the Navārṇa-mantra was constructed and, in turn, this made Cāmuṇḍā a more popular name displacing Bahumāṃsā. This also goes hand in hand with a widespread tendency to show the universality of the deity. In the case of the great Rudrian goddesses, this was also associated with a tendency to emphasize her links to the Rudrian domain of the exterior, which includes the tribal groups (already seen in the Yajurveda). This is also signaled by indicating the worship of the goddess in distant or non-Aryan lands. For instance, in the proto-Skandapurāṇa, the virgin goddess Kauśikī born of the black slough of Pārvatī emanated numerous avicephalous and therocephalous goddesses to aid her in the killing of Śumbha and Niśumbha. Thereafter, these goddesses were installed for worship in various countries, like the owl-headed Upakā in Pārasīka (Iran); the raven-headed Vāyasī in Yavana (Greek lands); the lion-headed Pracaṇḍā in Tukhara (Tocharia); Vānarī among the Śabara tribesmen; several others in the provinces of Lankā. This is reflected in the mantra-śāstra by the names of the goddesses like Gāndhārī or Dramiḍi.

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Footnote 1: First appears as theonym of Tvaṣṭṛ in his aspect as Viśvakarman in RV 10.82.02. There Viśvakarman is explicitly described as Dhātṛ. The equivalence of Dhātṛ, Viśvakarman and Tvaṣṭṛ is established in the late Yajurvedic version of the Puruṣa-sūkta with the appendix termed the Uttaranārāyaṇa.

Footnote 2: This pattern is reproduced in the national epic on the earthly plane in the unusual polyandry of the five Pāṇḍava-s to Draupadī.

Footnote 3: The Kashmirian Kaṭḥa tradition preserves a form of the Bahurūpī that combines both the Rudra-s and the Rudrāṇī-s; recorded by the mantravādin Svāmin Lakṣmaṇa Jū

Huns, Uralics, and empires of the steppe

A map by Savelyev et al. for the geographic orientation of the reader of the below article.

The Huns of Europe
“The lord of the Huns, King Attila, born of his father Mundzuk, lord of the bravest tribes, who with unprecedented power alone possessed the kingdoms of Scythia and Germania, and having captured their cities terrorized both Roman empires and, that they might save their remnants from plunder, was appeased by their prayers and took an annual tribute. And when he had by good fortune accomplished all this, he fell neither by an enemy’s blow nor by treachery, but safe among his own people, happy, rejoicing, without any pain. Who therefore can think of this as death, seeing that no-one thinks it calls for vengeance?”

This is a prose translation of a poem on the death of Atilla based on the rendering from the Latin furnished by E.A. Thompson. It is believed to have been narrated by a German to Priscus of Panium, a Greek who had lived among the Huns. In turn, it was transmitted in Latin by Cassiodorus and from him to Jordanes, from whom it has come down to us. This describes the death of Attila, the lord of the Huns of Europe, who had died after heavy drinking celebrating his marriage to his latest wife, a Germanic woman Hildegund (rendered as Ildiko). He seems to have had a hemorrhage in his respiratory tract leading to bleeding into his lungs and probably unable to raise himself in the drunken stupor “drowned” in his own blood.

This marked the climax of the great wave of Hun invasions in the West in early 453 CE. Who were these Huns who terrorized the Roman and German worlds, which were steeping into a “dark age” under the terrible West Asian mental disease, the second Abrahamism, following the death of the great Julian in 363 CE? Shortly after Julian’s death, the Huns appear to have invaded from the distant East and beaten the Iranic tribe (hereinafter, we use Iranic for the people and Iranian specifically for the Sassanian empire) of the Tanaitae sometime between 370-380 CE. Priscus tells us: “The Huns killed and plundered the Tanaitae and joined the survivors to themselves in a treaty of alliance. Then in company with them, they made more boldly a sudden inroad into the extensive and rich cantons of Ermenrichus (Hermannaric, the Gothic German)” — translation by Otto Maenchen-Helfen. Who were these Tanaitae? From their name, we can say that they were people living on the Don (the Dānu of the Indo-Iranians). The heathen Roman general Ammianus Marcellinus tells us: “The Huns overran the territories of those Alani [bordering on the Greuthungi (=the Eastern Gothic Germans, or Ostrogoths)] to whom usage has given the surname Tanaitae (the people of Dānu).” Thus, these can be identified with the steppe Iranics, who still retained the old ethnonym (airya>Alan).

The German ruler Hermannaric was said to be like a second Alexander of Macedon, who had subjugated various Iranic, Uralic (i.e., Mari), Baltic and Slavic tribes, in addition to unifying various German groups under him. Hermannaric had a woman named Sunilda, likely from a (married to) subjugated Iranic tribe, torn to shreds and her brothers attacked the Germans to avenge this. While they failed to kill Hermannaric, they stabbed him on the side in the skirmish, and the injury greatly weakened him. Seeing this, the king of the Huns, who is named as Balamber, launched a strike on the Germans. While the details of the Eastern German-Hun conflict in this period remain murky, there are reports that suggest that in 378 CE, the western Gothic branch of the Germans and the Huns formed an alliance against the Romans. As a result, the Hun cavalry came to the aid of the Germans at Adrianople in 378 CE and helped them massacre the Roman legions. There are further reports of a German-Hun-Iranic alliance raiding Roman provinces around this time and other German-Hun alliances attacking the Romans a little later in the early 380s of CE. In 384 CE, the Huns completed the conquest of much of what is today Hungary, and their cavalry was raiding as far as Gaul.

Then, we hear that in 395 CE, a great Hun horde broke through the Caucasus and invaded the Iranian empire as well as Roman provinces to the south of Armenia. The force invading the Iranian empire is said to have been led by two Hun commanders named Basich and Kursich, who marching along the Tigris and Euphrates, eventually struck Ctesiphon and, evading the Iranian army, passed through Azerbaijan back into the steppes. Another branch of this horde launched a blitzkrieg on Syria and then Anatolia. There is also a report of a Hunnic assault on the city of Edessa during this invasion. There was soon talk of a Hun-Sassanian alliance against the Christian Roman empire, but the Roman embassy reached a peace agreement staving this invasion.

In 400 CE, we hear of a certain Uldin becoming the lord of the Huns. He attacked the Germans led by a commander named Gainas, killed him, and sent his head over to the Romans at Constantinople. In 404-405 CE, taking advantage of the winter, Uldin invaded the Balkans and devastated Thracia. In 408 CE, the Romans faced a crushing defeat at their hands with heavy losses of men in Thracia. After that, the historical accounts become murky again. However, in the 420s of CE, during the intra-Roman wars, there appears to have been some kind of alliance between some Roman factions and the Huns. Some Huns were operating as far as North Africa as part of this alliance. Some time in the second half of the 430s of CE, the Hun situation heats up again with the rise of two brothers, Bleda first, and then Attila, the sons of Mundzuk, lord of the Huns. Bleda seems to have first been the king of the Huns and, together with Attila, led the invasion of Illyria around 441 CE. In 442 CE, the Romans met defeat after defeat at the hands of the Huns in the Balkans, and the Romans were forced to pay tribute to them. Around this time, an intra-Hun conflict broke out, and Bleda was overthrown and possibly killed in the early 440s by his brother Attila. Taking advantage of this, the Romans stopped paying the tribute.

On taking over the Hun leadership, Attila first decided to set the tribute situation right. He calculated the arrears to be 6000 pounds (?) of gold and demanded that it be paid as a single lump sum. Not surprisingly, this demand sparked the Roman-Hun war of 447 CE that went badly for the Romans. Marcellinus Comes, the Illyrian states: “In a tremendous war, greater than the first one (the earlier Hun-Roman war of the early 440s), Attila ground almost the whole Europe into the dust … Attila came as far as Thermopylae. Arnegisclus (the Roman general from Marcianople), after fighting bravely and killing many enemies, fell in a battle against Attila near the river Utus in Dacia Ripensis.” The Christian Nestorius in course of trying to give a spin to the events as a consequence of the lack of Abrahamistic dogma states: “The barbarians (Huns) were masters and the Romans slaves. Thus, the supremacy had changed over to the barbarians.” Callinicus adds: “The barbarian people of the Huns, the ones in Thracia, became so strong that they captured more than a hundred cities and almost brought Constantinople into danger, and most men fled from it … There was so much killing and blood-letting that no one could number the dead. They pillaged the churches and monasteries and slew the monks and nuns. And they devastated the blessed [church] of Alexander [a Christian “martyr”]”.

This was the pinnacle of Hunnic power in Europe. While it is hard to estimate the full extent of Attila’s empire or understand its relationship to the Asian power center (he might have just been a “viceroy” of the Khan — sort of like Batu or Hulegu to Mongke or Qubilay), Priscus tells us that he was seen as the “king, commander and supreme judge of his people” after the great victory of 447 CE. However, unlike with the Chingizid Mongols, the end came nearly as precipitously as his rise. In 451 CE, Attila attacked the Germans in Gaul and unexpectedly suffered heavy losses to his cavalry from the resolute German counterattack. He then tried to make up for this by invading Italy. During this phase, he met with some renewed success by taking the fortified city of Aquileia, then Milan and Pavia. However, with an epidemic raging in the ranks of the Huns and their German allies, they had to retreat soon, allowing the Roman forces to consolidate their defenses. With Attila’s death early in 453 CE, major internal conflicts broke out among the Huns and their Germanic subjects. In 467 CE, Dengizich, Attila’s son, fought desperately with the Germans on the Danube but faced a major defeat. Two years later, the European Hunnic power came to an end as Dengizich was beheaded by the German Anagast, fighting on the Roman side. However, remnants of Hun power appear to have persisted in the Caucasus, where we hear of Hun leaders Glones and Styrax leading them against the Sabirs, who may have been a Turkic group. Further east, the Kutrigurs and Utigurs may have also been surviving Hunnic groups situated on the north shore of the Black Sea.

The affinities of the Huns of Europe
As we can see from the sources cited above, the Hunnic horde was a multiethnic assemblage from the beginning of their record in Europe. Priscus says: “His (Attila’s) Scythian subjects were swept together from many nations… Besides their own barbarian tongues, either Hunnish or Gothic, they spoke Latin as many have dealings with the Western Romans, but not one of them easily speaks Greek, except captives from the Thracian or Illyrian frontier regions.” One of the groups of this assemblage is still prominent as the Germanic people in the regions the Huns conquered in Europe. Attila’s last wife, Hildegund, was clearly a German woman. Her tale is remembered (in a somewhat garbled form) in surviving Germanic legends like Atlakviða of the Nordic Poetic Edda, where she goes by the name Gudrun. Some Hunnic leaders seem to have taken up Germanic names. Attila’s brother Bleda’s name seems to have been derived from the Germanic name Blatbert. One of Attila’s generals killed in the great showdown with the Germans was named Laudareiks — clearly Germanic — probably a Germanic ally of the Huns. Another Hun leader is named Ragnaris, again Germanic. Thus, there are multiple lines of evidence that the Germanic folks were incorporated into the Hun horde of Europe.

The Iranics no longer exist in Europe, but their long presence in the region and the Roman empire is well-attested (e.g., the origin of Roman Mithraism). Thus, their figuring in the Hunnic assemblage is also not a matter of much surprise. Right from when the Huns were first noticed, this association is stated, i.e., their conquest and absorption of the Alani. Again, their presence in the Hunnic assembly is hinted by Priscus’ usage of “Scythian subjects”. After the death of Attila in the 460s, the Huns were led by a certain Hormidac in a devastating assault on Dacia. This is clearly a rendering of the Iranic name, Hormizdak, one also found among the Sassanian royalty. Iranic names are also seen among the Kutrigur, like the Hun leader Zabergan who defended his land against the Eastern Christian Roman attack in the 550s of CE. Likewise, Glones might have also had a name of Iranic provenance.

This leaves us with the “original Hunnish” language — it was clearly distinct from Iranic or Germanic and seemed to come from East Asia. It is here that the greatest confusion exists, as nothing other than personal names and a few terms have come down from that language, that too mostly via Latin or Greek sources. The early experts tended to favor a Turkic etymology for them. However, there was always a lingering doubt among some researchers that it might belong to the larger Mongolic clade after all. First, irrespective of whether Altaic languages are a monophyletic group (there are many different formulations of this; for the latest iteration, one can consult the work of Robbeets, who supports the hypothesis under the name“Transeurasian”) or not, there is little doubt that Turkic and Mongolic have closely interacted over a prolonged period resulting in a substantial shared vocabulary. Hence, single words that are given a Turkic etymology could be from a Mongolic source, after all. But distinguishing these from Turkic is not trivial. For instance, Attila’s father, Mundzuk reminds one of the second part of the name of the Chingizid Mongol general Qizil Monchuk; however, the said general could have been of Turkic ancestry. Second, there are some tantalizing hints of clearly Mongolic etymologies.

Unraveling this is complicated because while we have the runic Turkic inscriptions of the Gök (Blue) Turks, early Mongolic from the corresponding period is poorly attested. Substantial Mongolic texts are only available from the Chingizid period onward. But the extant Mongolic is only the crown group of a larger extinct language family — the greater Mongolic clade. That family included the language of the Khitan who founded the Liao (in North China) and Qara Khitai empires. Though many Khitan words are now known from bilingual texts with Chinese equivalents, the Khitan language remains partly undeciphered (despite the efforts of the Mongolic scholars led by Qīnggéěrtài in studying old and newly discovered Khitan texts), posing yet another challenge for understanding the early development of the greater Mongolic clade. The greater diversity of these para-Mongolic languages from the greater Mongolic clade is also hinted at by the original language of the Tangut royal family, the Tuoba clan, who descended from the leaders of the Xianbei confederation. Long before the formation of the Tangut kingdom, the para-Mongolic Tuoba clan, as the Khans of the Xianbei confederation, held sway approximately between the late 300s-500s of CE. This brings us exactly to the time of the Hun activity in the West. In turn, this suggests that there were already powers of the greater Mongolic clade active in the East, making it possible that the Asian core of the Huns, after all, had their origins among these greater Mongolic groups.

Recently, Vovin’s study of the Khüis Tolgoi (Brāhmī; 604-620 CE) and Bugut (Brāhmī and Sogdian; 584-587 CE) inscriptions in Mongolia, established that the Ruan-Ruan Khanate, who displaced the Xianbei to establish as second “Hun” Khaganate contained an elite who spoke a Mongolic language even closer to the Chingizid Mongolian than the Khitan or Tuoba languages. They were eventually displaced by the Blue Turks and moved westwards following the trail of the earlier Huns all the way to Hungary as the Avar Khanate. Given the evidence for a relationship between the Huns and the Avars (see below), Vovin’s decipherment, if true, strengthens the idea that the Asian core of the Huns and the Avars who came later were likely Mongolic.

The Huns of India and Iran
This brings us to the elephant in the room — the relationship of the European Huns to the other groups that go under the same name. Beginning around the first half of the 450s of CE, a Huṇa force invaded India, probably towards the very end of mahārāja Kumāragupta’s reign. We hear from the inscriptions of his son, emperor Skandagupta, that he defeated the Hūṇa-s in a fierce battle to restore the fortunes of the Gupta empire (the Bhitari inscription). This first wave of Hūṇa-s is usually identified with the horde established by the lord known as Kidara and is known after him as the Kidarites. The Hūṇa incursions into India did not stop with that. As the Gupta empire declined in the 490s as a second wave of Huns, usually termed the Alchon Huns (Hara-hūṇa or the Red Huns), invaded. These Huns had been raised to power in Central Asia in the 430s by their lord Khingila. A successor of his, the Hūṇa king Toramāṇa, broke through to briefly conquer large swaths of northern India. The Gupta resistance against them continued from the East for another 20-30 years with the main star of this fightback being mahārāja Nṛsiṃhagupta Bālāditya. Toramāṇa was succeeded by his son Mihirakula who lasted until around 530 CE.

In the meantime, a second nationalist resistance began in central India under Prakāśadharman and his son Yaśodharman, the rising Aulikara kings. By 528 CE Yaśodharman had defeated the Hūṇa-s and subjugated them — he even mentions capturing the women of Mihirakula’s harem. However, new Hūṇa invasions, now under a third horde, the Śveta-hūṇa (Hephthalites), generally believed to be related to the Alchon Huns, continued until around 606 CE. The Puṣyabhūti princes, Rājyavardhana and Harṣavardhana, defeated them comprehensively and reduced the survivors to the vassal province of the Hūṇamaṇḍala. While the Hūṇa-s who invaded India bear unambiguously Iranic names, evidence from Sanskrit sources hints that they had an East Asian genetic component and used the characteristic horse ornaments of the eastern Central Asian groups. Apart from the Hūṇamaṇḍala province, we hear of a very late mention of the Huṇa-s in India during the reign of the Kalacuri king, Lakṣmī-karṇa, in the 1050s of CE — his wife was the Hūṇa princess Avalla-devī — it remains unclear if she was from the same Hūṇamaṇḍala or elsewhere (like a śāhīya Hūṇa from Gandhāra, survivors of the old Alchons, fleeing the Mohammedan horrors to inner India).

In parallel, the Sassanian empire had similar invasions by related Hūṇa groups. The Kidarite Huns (the Iranians seem to have called them the Red Huns) and the Iranians had a complex relationship. Having founded a Central Asian state, probably centered at a mighty fort near Samarkand, in the early phase of their career (350s of CE), the Kidarite Huns invaded the eastern part of the Sassanian empire even as the great Iranian shahanshah Shāpur-II was in the midst of the war with the Romans. Shāpur-II had to turn to his rear and wage a nearly 5-year war on these Huns before forcing them to sue peace. As a part of the deal, they allied with the Iranians to fight the Romans. Thus, their lord (probably named Krum-pat; c.f. the name of the later Bulgar Khan) aided Shapur-II in major victories against the Romans. This association and their occupation of the former Kuṣaṇa lands in Central Asia explains the extensive Iranicization of these Hun groups. Based on the names of the leaders, we can also see a degree of Hinduization of the later Kidarites (e.g., Salanavīra and Vinayāditya). Down the line, the relationship between the Iranians and these Huns soured again, and between 400-460 CE, the Iranians suffered multiple defeats against these Huns. Thus, they were forced to pay tribute to the Kidarites along the lines of what Attila levied on the Romans. In a parallel situation, when the Iranians stopped the tribute, a major war broke out. In an expedient move, the Sassanian shahanshah Phiroz formed an alliance with the rival Hun horde, the Śveta-hūṇa-s, and, in the 460s of CE, overthrew the Kidarites who were by then already greatly weakened by the Gupta assault.

What goes around comes around. Thus, in the 470s, the Śveta-hūṇa-s aggressively turned against their erstwhile Iranian allies, forcing Phiroz to war against them. In an engagement southeast of the Caspian, in the old lands of the Dāsa-s (Hyrcania), the Iranians were smashed by the Huns, and Phiroz was taken prisoner. He had to pay a heavy ransom and prostrate himself before the Śveta-hūṇa lord Akhśunwar. He agreed to do so, facing east in the morning, and claimed that he had actually only bowed to the god Mithra. Stinging from this defeat, 4-5 years later, Phiroz tried to reclaim the lost ground in a second campaign against the Huns. The Iranian force was demolished again, Phiroz’s son was taken hostage by the Huns, and he had to pay a hefty tribute. Now Akhśunwar declared himself the shahanshah of the Sassanian empire and added the Iranian crown on his head in his coins. To add insult to injury, Phiroz had to pay a huge amount to get his son released. At the same time, taking advantage of his routs, Judaistic and Christian subversionists were causing unrest in parts of the Iranian empire. Smarting from his prior defeats, Phiroz thirsted for revenge, but his forces were reluctant to fight the Huns again. Yet, Phiroz pressed ahead for a war with the Huns in 484 CE with the cream of the Iranian army south of the Caspian. Akhśunwar lured them into a hidden trap in the form of a concealed ditch while feigning retreat and claiming not wanting to initiate hostilities. Phiroz fell into the ditch in wild pursuit of the Huns and was killed by their archers. Many of his brothers, sons, and several of the Iranian elite were also slain as they attempted to aid him. Phiroz’s surviving brother then successfully rallied with their chief generals to defend the Iranian core from the Huns. However, the Huns helped overthrow him and placed Phiroz’s son, who was earlier their hostage, as a more pliant ruler on the throne. It took the Sassanians about 80 years to recover their losses and eventually overthrow Śveta-hūṇa-s under shahanshah Kushrau-I in an alliance with the Blue Turks.

The Huns of the East
Some historians have long recognized that there must be a common basis for these groups with a shared ethnonym operating across the breadth of Eurasia in the same general period. Moreover, their mode of action with respect to the settled empires of India, Iran and Rome shows striking parallels. Notably, there are other indications of the connections between these groups. For example, Kidarite coins have been found in Eastern Europe and Hungary, where the Attilan Huns operated. Further, Priscus tells us that the Kidarites were the Chionites, an alternative term for the Huns with deep roots to the East (see below). To understand this, we have to look further East and farther back in time to around 250 BCE. Simultaneously with the ascent of the nationalist Cīna empire of the Chin, the peoples of the Mongolian steppe appear to have started consolidating. Part of this might have been driven by technologies they acquired from their Indo-Iranian neighbors. Another factor seems to have been the Chinese unification, which started threatening their existence with wall-building activities of Chin Shi Huang and aggressive military action the Chin took against the peoples of Mongolia in 215 CE. The first organization appears to have occurred under a leader named Touman. His son Modun (probably Bagatur in the original Mongolic language) Shanyu appears to have unified them and began a series of expansive campaigns to build the first great Mongolian empire of the steppes in history. The memory of this old empire lasted to the times of Chingiz Khan, who referred to the ancient times of the Shanyu. These first Mongolic conquerors were known to the Chinese as Xiongnu, a word likely pronounced as something similar to Hūṇa and perhaps something like (C)hunu in a Mongolic language. This, in turn, is close to the name Chuni occasionally used for the European Huns and Chionite, who Priscus says were the Kidarites. This suggests that the Xiongnu were indeed the “original” Huns and strengthens the linkage between these ancient groups across Eurasia.

After a long struggle with the Hans, the Mongolian core of this first empire of the Xiongnu appears to have fallen to the para-Mongolic Xianbei group sometime between 150-200 CE, and the survivors fled West into the Saka and Kuṣāṇa lands. This suggests that the demise of the old Xiongnu empire resulted in the westward movement of its people and their mixing with various steppe Iranic groups while carrying the Hun ethnonym. The Kidarite takeover of the Kuṣaṇa lands in Central Asia is attested both in coinage and Cīna historical records. Over time, the Iranic components might have become dominant in some of these Hunnic hordes. It is even possible that the very title Khagan is derived from the Iranic hva-kama (=“self-ruler”) and was transmitted back eastwards to Mongolia. As they moved further West, they started absorbing Germanic, possibly Slavic, and also other tribes (see below). The connections of some of the more Western groups, like the Śveta-hūṇa-s, to the Eastern ones, continued via the Central Asian borderlands: as noted above, the Xianbei confederation was displaced by Ruan-Ruan Khanate, who were probably derived from underling Xiongnu, who persisted under the former. In the 490s, the Hephthalites and the Ruan-Ruan Khanate formed an alliance (probably based on their old familial connections according to Golden) and conquered the Turkic horde of the Teleuts (T’ieh-le). Then, the Hephthalites again allied with the Ruan-Ruan Khanate to strike their arch-enemies, the Xianbei kingdom of the Northern Wei. Around 520 CE, the Ruan-Ruan Khan turned against his powerful uncle, a brāhmaṇa minister whose sister was married to the former Khan. This brāhmaṇa’s other sisters were married to the king of the Hephthalites. In a change of alliances, the Hephthalites then aided this brāhmaṇa in Kokonor in the drawn-out struggle against the Ruan-Ruan and the Xianbei.

The Hungarians
While Attila is remembered mostly negatively both in the Christian Occident and the Germanic historical lore, he is a national hero for the Hungarians even after their conversion to the cult of Jesus. This seems to be a rather deep memory given the time that has elapsed since the Hunnic conquest of Hungary. However, we should note that this memory was likely reinforced by the Avar Khanate that arose from the overthrow of the Ruan-Ruan by the Blue Turks and the Hephthalites by the Sassanian-Blue Turk alliance. A horde of these neo-Hunnic peoples moved West under the Khans Kandik and Bayan, just as the classical European Huns before them, and erupted into Eastern Europe and Hungary starting around the 550s of CE. Over the next 60 years, they rose in power, forming shifting alliances with Germans, such as the Langobardi, and also the Slavs, to subjugate a vast territory from the steppes of the Black Sea-Caspian regions to nearly the gates of Vienna. This brought them into prolonged conflict with the Eastern Roman empire, in course of which they allied themselves with the Iranians and launched a striking attack on Constantinople in 617 CE. Over the next 100 years, their power declined, and they were eventually defeated by the Frankish crusade and the Slavs. The survivors were converted to the second Abrahamism thereafter.

Despite the memories of these Hunnic connections, the extant Hungarians speak an Uralic language. There is no evidence for this being the language of the Huns or the Avars who followed them. This is also in stark contrast with much of the surrounding regions, which speak Indo-European languages — predominantly of the Germanic, Slavic and Albanian branches. So how did the Hungarians come to speak an Uralic language? While this is not the place to get into the debates of the cladogenesis of the Uralic languages, it can be confidently said that the Hungarian language is not closest to the other Uralic languages of Northern Europe, like Estonian, Finnish, Karelian, or Saami. Nor is it specifically related to the Eastern European Uralic tongues like those of the Mari, the Udmurts and the Mordovians. Instead, it is closer to the Siberian languages Mansi and Khanty that are spoken to the East of the Urals. This linguistic observation by itself points out that the language of the Hungarians has come from some other group that invaded Europe from the East.

Historical records vindicate this conclusion. After the destruction of the Avar Khanate in Hungary, there was a further invasion from the East by a group known as the “conquering Hungarians” led by the Magyars. The first mentions of them on the eastern fringes of Europe are seen through the 800s of CE. Around 862 CE for of Magyars launched a raid on Central Europe. They returned 20 years later, sacking Germanic lands as far as Vienna. Close to 890 CE, the Hungarians launched a major westward thrust, probably triggered by the conflicts between the Turkic khanates of the Khazars and the Pechenegs. Shortly thereafter, they crushed the Slavs in what is today the Hungary region and established themselves there. In the first decade of the 900s, they advanced rapidly, smashing a Frankish German army in Slovakia and cleared the path for more extensive conquests. Over the next 50 years, the Germans suffered defeat after defeat at the hands of the Magyars, who led spectacular raids covering what are today Spain, France, Germany, Poland, the Balkans and the Eastern Roman territories of Europe. Finally, in 955 CE, the Hungarians were annihilated by a fierce German counterattack near what is today Augsburg, Germany, and the Magyar leaders were captured and executed. The survivors held on to Hungary and were eventually converted to Christianity and “accepted as Europeans”. This still leaves us with the conundrum of why the Hungarians, who have acquired their language from a distinct eastern conquering group, which invaded long after the classical Huns, still recall the Hunnic connection.

Genomics of the Huns, Avars and Hungarians
Historical hypotheses and reconstructions are often hard to corroborate due to the incompleteness of the records. However, over the past two decades, genomics is providing us with a serious independent mechanism for testing various historical hypotheses. Its spectacular success was seen in resolving many aspects of the first great expansions from the steppes, i.e., of the Indo-Europeans. It is also providing deep insights into the situation of the next set of expansions from the steppes, namely that of the Hunnic, Turkic and later Mongolic peoples. The Hungarian conundrum is another place where genomics can be brought to bear. The initial genetic studies on the extant Uralic peoples (e.g., by Tambets et al.) only deepened this mystery. They showed that the “pure” Uralic ancestry is largely restricted to the easternmost Siberian groups like the Nganasans. That, too, is mainly restricted to the Y-chromosome. However, the mitochondrial genome shows some European admixture. In contrast, as one moves West, there is increasing European admixture in all Uralic groups, and it is clearly more in terms of the mitochondrial genomes, suggesting that the Uralic movements to the West were likely mediated by males who took local females. Strikingly, even though the majority of the Y-chromosomes of the Khanty and the Mansi (Siberian sister groups of the Hungarians) are of Uralic affinity is only a very small minority in the Hungarians. The Uralic signal is nearly invisible in the Hungarians in terms of the mitochondrial genome. While the same is seen in the mitochondrial genomes of the Estonians and the Finns, their male lines respectively show a large or a majority Uralic fraction. This means that though the Hungarians acquired the language of their conquering national founders, their extant genome is of mostly Germanic ancestry. Thus, the Magyar conquerors hardly left a genetic impact. This means that the extant Hungarian genomic sequences are not sufficient to answer questions of the ethnogenesis of the founders of the nation or their connection to the Huns.

Here is where a recent preprint published by Maróti et al. becomes crucial in clarifying Hungarian ethnogenesis and the complex relationships between the various steppe groups. They obtained human genomic sequences from 271 ancient samples from Great Hungarian Plain and 73 direct C14 dates. Thus, they have a collection spanning the Hunnic, Avar and Magyar periods, which can help probe the above issues. They found that the majority of the samples had European ancestry, suggesting that the invaders did not greatly alter the local ancestry, unlike the Indo-European invasions, which left much deep genetic imprints in both Europe and Asia.

However, they strikingly found a subset of both the Hun and Avar age samples forming a cline in the principal component analysis that went from the Germanic-type European ancestry on one end to the Turko–Mongolic East Asian ancestry on the other. Notably, on the East Asian end of the cline, two of their Hungarian Huns group tightly with the Kalmyks and the Mongols, among extant populations, and the close to two historical Hun samples, namely a Hun from Kurayly, Kazakhstan from 380 CE and a Tian Shan Hun. Modeling this ancestry suggested a major late Xiongnu component marked by Han admixture. They could model one further sample as having Xiongnu and Germanic or Sarmatian (a steppe Iranic group close to the Alani) ancestry, pointing to the admixtures indicated by the historical records. In an independent study, Veeramah et al. looked at the genetic affinities of individuals from Sarmatian and other graves across western Eurasia. Interestingly, one early Sarmatian individual from the Orenburg region of Russia (~400-200 BCE) and a Crimean individual (200-400 CE) with a deformed skull in the style of the Alchon Huns show specific evidence for Indian admixture with SNPs potential private to greater India. This suggests that, as in the earlier Aryan invasion of India, there were individuals from the subcontinent who were also entering the steppe hordes. This provides independent genetic support for historical records such as the brāhmaṇa, who was allied with the Hephthalites and the Ruan-Ruan Khanate. Thus, the Hunnic movement through Asia into Europe, while having its ultimate origins in Mongolia, swept in a wide range of ancestries on their path. The Avar age samples formed an Europe-East Asia cline entirely overlapping with the Hunnic samples. Several Early Avar and a few Middle Avar age samples group with the Huns, Xiongnu, Xianbei, some early Turkic, and Chingizid Mongol samples at the East Asian end of the cline. These Avars at the East Asian end of the cline show a specific Ancient North-East Asian admixture that was also noted among the early Xiongnu, Ulaanzuukh, and Slab Grave samples from Mongolia. This establishes the Mongolian origins of the Avars and supports their deep shared ancestry with the Xiongnu.

In terms of Y chromosomes (also see earlier work of Keyser et al.), both the Hunnic and Avar male samples from this Hungarian study show a presence of the Q haplogroup, which was also found in East Asian Xiongnu samples, such as those from the spectacular Middle Xiongnu Tamir Ulaan Khoshuu cemetery at the confluence of the Tamir and the Orkhon Rivers in Central Mongolia. Additionally, both these Hungarian samples also show the same R1a Y haplogroup that was widely dispersed across Asia by the Indo-Iranians. The presence of this haplogroup in the above Middle Xiongnu cemetery males in Mongolia suggests that a major fraction of these were not derived from later absorption of Indo-Iranians on the western steppes. Rather, this male line likely descended from the Middle-Late Bronze age Indo-Iranian Andronovo horizon that had expanded into the Mongolian steppe. Consistent with this, we find mentions of some of these steppe Indo-Iranians in the Xianbei successor states down to the Chingizid period as the Aran or Asud (<arya). It also indicates that the male line of these old Indo-Iranians persisted through the “Mongolization” of the East, especially among the Hunnic elites (e.g., the 2000-year-old Xiongnu elite cemetery at Duurlig Nars in Northeast Mongolia studied by Kim et al.). The word Hun itself probably has an Indo-Aryan or secondarily Iranicized origin (We hope to discuss this point further in the future). The recovery of these Y-chromosomes in the Hungarian Huns suggests that the male lines of these elites were likely still in action centuries later in the West. These observations further strengthen the connection between these groups from the two ends of the Eurasian landmass.

Finally, coming to the conquering Hungarian elite samples, Maróti et al. found that they show a more spread out distribution on their PCA plot. Few of them squarely fall in the above-described Hun and Avar clines shifted towards Western Eurasian groups with respect to the easternmost members of these clines. This suggests that a minority subset of the Magyars were indeed derived without any further admixture from a Hunnic group that had already mixed with steppe Iranic groups to their West. However, the major clusters of the Magyars show a further shift towards the Siberian groups, namely the Mansi, the Selkup and the Yukagir (the former two are unambiguous Uralic speakers). Remarkably, these ancient Magyar samples also show close genetic affinities to the peoples of Bashkortostan in what is today Uralic Russia. Medieval Hungarian records from the 1200s mention this land as the ancestral domain of the Magyars of Hungary. The authors found that the Magyar elite with Uralic ancestry could be modeled as a mixture of Mansi up to 50%, with the rest being made of late Xiongnu and Iranic Sarmatian ancestry. Based on these admixtures, they posit that there was an initial admixture between the ancient Sarmatians and an Uralic group close to the Mansi around 643-431 BCE and later with the Huns around 217-315 CE, even as the remnants of the Xiongnu empire were moving West.

This fits well the inferences from linguistic data. The Hungarian language is a sister of the Mansi language, which suggests that an Uralic group was central to the ethnogenesis of the original Magyars. This has now been independently supported by the archaeo-genomic evidence, filling lacuna from the paucity of such ancestry in extant Hungarians. The Hungarian language shows clear Iranic loans relative to Mansi and Khanty, indicating that they had contact with the Iranics. The genetic evidence suggests that this happened around 500 BCE when a steppe Iranic group related to the Sarmatians (Avestan: Sairima) probably moved into the Uralic zone and were absorbed by a Mansi-like group. This contact left both a genetic and linguistic impact on this Uralic group. It also probably introduced elements of a steppe nomad lifestyle and warfare to these proto-Magyars (since there is no evidence of their sister groups engaging in similar military nomadism). This priming was probably reinforced as a Hunnic group originating from the fragments of the Xiongnu empire, which had also mixed with steppe Iranic elements, was absorbed into the proto-Magyars in steppe-Siberian borderlands. It is likely that this proto-Magyar group had participated as an auxiliary of the European Hun and Avar invasions because few of the Magyar elite were plainly Hunnic without much Uralic admixture. This is consistent with the accounts of the Magyar military tactics, which are frequently compared to those of the Huns and Avars. Thus, we probably had a situation where the proto-Magyars retained the Uralic language of their demographically dominant Mansi-like core but also inherited legends of the old heroes, like Attila, from the Hunnic peoples embedded their midst. This might explain the importance of Attila and his successors in their national consciousness (c.f. Geser Khan epics in the East).

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Further reading:
Maróti et al. https://doi.org/10.1101/2022.01.19.476915
Tambets et al. https://doi.org/10.1186/s13059-018-1522-1
Veeramah et al. https://doi.org/10.1073/pnas.1719880115
Amorim et al. https://doi.org/10.1038/s41467-018-06024-4
Fóthi et al. https://doi.org/10.1007/s12520-019-00996-0
Savelyev et al. https://doi.org/10.1017/ehs.2020.18
Jeong et al. https://doi.org/10.1016/j.cell.2020.10.015
Kim et al. https://doi.org/10.1002/ajpa.21242
Keyser et al. https://doi.org/10.1007/s00439-020-02209-4
Robbeets et al. https://doi.org/10.1038/s41586-021-04108-8
P. Golden, An Introduction to the History of the Turkic Peoples: Ethnogenesis and State-Formation in Medieval and Early Modern Eurasia and the Middle East (1992)
A. Kurbanov, Hephthalites: Archaeological and historical analysis (2010)

Some observations on the Lekkerkerker-Zeckendorf decomposition of integers

In our youth, we learned of a nice arithmetic theorem of Lekkerkerker (more popularly known after Zeckendorf; hereinafter L-Z) that relates to the famous Mātrā-meru sequence : 0, 1, 1, 2, 3, 5, 8… defined by the recurrence relationship . The theorem states that all positive integers can be uniquely expressed as a sum of one or more distinct non-consecutive terms of . A proof for this theorem can be visualized through a simple geometric construction (Figure 1).

The graphical L-Z decomposition of integers from 1..12

Pile rectangles whose sides are two successive terms of so as to make a half-square (Figure 1). One can see that every integer can be reached by a horizontal path of such rectangles. This also specifies the algorithm for the L-Z decomposition of an integer . Find the largest term of such that . If then continue the same procedure on the difference till . This gives us the decompositions shown in Figure 1.

One can define sequence that counts the length of the L-Z decomposition of each integer . For example, we see that 12=8+3+1, i.e., it is decomposed into 3 terms. Thus, ; similarly . goes as: 1, 1, 1, 2, 1, 2, 2, 1, 2, 2, 2, 3, 1, 2, 2, 2, 3, 2, 3, 3, 1, 2, 2, 2, 3, 2, 3, 3, 2, 3, 3, 3, 4, 1, 2,

One see that the value jumps by 1 for the first time at certain values of (Figure 2): . Using these we define a new sequence : 1, 4, 12, 33 We can then ask what is its convergent? We found that,

,

where is the Golden ratio .

We can then ask if there is a closed expression for . We derived this to be:

Figure 2

Another class of sequences we explored was , the lengths of the L-Z decompositions of , where and , i.e., the powers of integers. For example, goes thus: 1, 1, 2, 1, 2, 3, 3, 3, 3, 6 . Plots of against show a good fit for a linear growth in the range in which we computed these values (Figure 3; it is computationally intensive), albeit with increasing dispersion as increases. If we take their growth to be linear, we then can ask the question: what would be the slope of these lines? Interestingly, we empirically found the slopes of the lines approximating the L-Z decomposition lengths of to be respectively . Can this be proven or is there an alternative description of the growth of these sequences?

Figure 3

Subjective and objective insight

The black American scientist Sylvester Gates mentioned a curious personal anecdote in a talk. To paraphrase him, when he was in college, he had to take a calculus course. He mentioned how he could cut through differentiation as it was a largely mechanical process. Then came integration, where he said he was stuck with the problems involving multiple substitutions to arrive at the final integral. The inability to crack difficult problems of that genre gave him a headache, and he fell asleep. Something happened to him in his sleep that when he awoke, he suddenly emerged with a new understanding to solve those problems, and they no longer seemed difficult. We can completely identify with that experience of his. However, it was not a night’s sleep that flipped the switch in our case. We had to wait for that testosterone burst, that elixir of masculinity, which allows males to perform great acts. We clearly remember how, a few months before it, we struggled to derive the equations of certain loci for which we had figured out mechanical constructions. But, upon the passage to manhood, suddenly we found ourselves possessed of svāyambhuva insights that allowed us to penetrate such problems with ease — it was as if the doors to a deeper realm of understanding had been opened. Other people have told us of similar experiences — we recently heard from a friend how he had a phase transition at some point in his life (overlapping with puberty), which made him suddenly grasp a mathematical entity that had previously defied him and led him to pursuing a degree in physics.

Our life-history-associated flips may be relatively easily explained in neurological terms — the gonadal hormones are known to trigger extensive neurogenesis, and these new neurons and the reorganization of neuronal connections, which they case seem to provide the firepower for apprehending mathematical and conceptual ideas that were previously difficult to process. However, the experience narrated by Gates is of a different kind. He definitely did not grow a bunch of neurons over his nap, but it seems his “subconscious” kept working and churned up the solution back to his conscious mind on awakening. Such experiences are not isolated. In fact, they might have played a big role in the history of science in the form of dream revelations. We first learnt of this from the famous story of how August von Kekulé solved the structure of benzene in a dream. Subsequently, we learnt of several other examples: 1) Ramanujan obtained formulae concerning several elliptic integrals from the goddess Śri in a dream. 2) Niels Bohr had a dream of electrons revolving like planets around the nucleus in fixed orbits. 4) Dmitri Mendeleev had a dream of the periodic table of elements. 4) AR Wallace had a dream while suffering from a tropical fever in the Far East that left him with the evolutionary theory. We have never made any of our major scientific discoveries in a dream. However, we have had a couple of mathematical problems, and the path to their solution appear in dreams — these were very rare events — we had exactly two so far in life!

While the pubertal and the dream switches might seem like different things, we hold that they have a commonality. Both are marked with the acquisition of a new insight after which the world might not appear to be the same. Before the switch, there was no way of solving the problem with a purely workmanly approach. That switch happens at a “subconscious” level, but it impinges into conscious action with a fundamentally changed framework that allows you to see a new order or a system where none seemed to exist before — everything makes sense in this framework but not outside it.

This has implications for the process of science. It has become popular to tell students that science is generated via the “scientific method”, whose realization is seen as a major development for science itself. Ideas related to the formalism of the scientific method are widespread. As we have discussed before, we encounter them in the nyāya (+vaiśeṣika) theory of knowledge production wherein from a kalpanā (tentative hypothesis) we proceed to a nirṇītā if it passes the test (vinigamaka) as opposed to the alternative hypothesis. The established hypothesis becomes the theory or siddhānta. A similar formulation emerged the Occident starting with the pioneering work of the French savant Rene Descartes (apparently, he got this framework in a dream) and culminating in the Jewish thinker Karl Popper who presented a clear “flow-chart” encompassing hypothesis generation, prediction, testing and falsification. That such a formalism sprung up convergently across cultures implies that there might be something deep to them. In general, we agree it is a good way to understand how science works. However, we should stress that this is not how it actually happens.

The actual process of scientific discovery depends heavily on the welling up of those perspective-changing insights from the subconscious to the conscious that we mentioned above (for why we term it perspective-changing, see below). However, it should not be held that the profound perspective-shift that bubbles up to you is necessarily scientifically correct even if it were mathematically beautiful, technically sound, or seemingly robust as a device. It has to be tested against actual data. Here is where the Popperian idea of making a prediction based on it and testing it comes in. We have several famous examples of how the perspective-changing explanation might be beautiful but scientifically wrong. We could mention the great German astrologer Johannes Kepler‘s original planetary model, where he fitted each of the five Platonic solids between the orbits of the six then known planets. He felt he had stumbled upon a profound insight: “The intense pleasure I have received from this discovery can never be told in words…” However, the predictions of this model did not fit the mass of astronomical observations, the great legacy of Tycho Brahe. Where Kepler emerged as a scientist was in his ultimate rejection of this hypothesis despite its beauty (he drew a diagram of it rivaling the hand of Leonardo da Vinci himself) and personal appeal. Thus, the role of the Popperian process was relatively limited in this example of how science actually happened. The Popperian hypothesis rejection did not result in an automatic path ahead for Kepler. Indeed, he might have been consigned the heap of many a forgotten scientist had he stopped there. Kepler’s effort in constructing his original model and testing it provided him with many insights into the problem at hand. He also had key observations that did not fit his initial hypothesis in his head. These provided the grist for his renewed attack on the problem. Here again the subconscious churning through the paths taken by the great yavanācārya-s, Archimedes and Apollonius, going back to the Delian oracle of Apollo resulted in Kepler arriving at the correct hypothesis that was striking in its generality, even if more abstruse than the earlier one for the pre-Newtonian layman.

From a neurological perspective, this subconscious production of science is not surprising. It is well known that most of our neural processes, which might be termed thinking, are unconscious. Even in a conscious experience, like vision, there is an enormous amount of neural calculation and information processing that we are entirely unaware of. In fact, it might even be dangerous for a regular individual to be exposed to this data, its processing, and its presentation. This is strikingly illustrated by the case of the black English artist savant, Stephen Wiltshire, whose very existence might be denied by people who have not seen him in action. However, his extraordinary capture of visual detail comes at the cost of strong autistic traits that are potentially fitness-nullifying. Indeed, on very rare occasions, such capacities might get unmasked by brain injury, as in the case of Jason Padgett, suggesting that natural selection is likely working to keep them masked rather than expressed. Hence, the subconscious, which is screened from the conscious, is the most likely seat where the perspective-shifting insight arises. We hold that there is a pure Platonic realm of mathematics and “linguistic content” that contains the foundation of “all knowledge” of existence. The conscious surfing of this realm is likely not possible for most people. Many of those who are able to access it often have a cost, such as being on the autistic spectrum. Thus, this realm is in part surfed only subconsciously by most.

Anyone who has solved a difficult (to the person doing the job) scientific or mathematical problem knows the sensation Kepler talks about — that first-person experience. The perspective-changing insight usually comes first, but it is in a sense “raw”, i.e., the details are not precise at all, but there is something in the subconscious that tells you that you have the right solution. It feels as if the “surfing” process apprehends it in the Platonic realm, but its clarity is smudged when it is dredged up to the conscious realm. After that, there is a workmanly phase wherein one implements the solution in concrete terms. In this phase, one’s intelligence and breadth of knowledge are vital determinants of how well one converts the insight into the finished product of a scientific discovery or a mathematical theorem. What emerges usually has a formalism that allows it to be communicated mechanically to the recipient. However, this communication, as well as its reception by peers, might not be easy. A common adage goes that once you announce a new insight, your peers first ridicule it — this is usually because they are not in possession of the new framework you have, and even to apply it mechanically, they need at least a limited perspective-shift. Eventually, the peers learn to apply it mechanically and see that it gives correct results. This causes them to shift towards the new framework even if they do not fully grasp it. Finally, the flip occurs in the minds of the peers and a subset of them might declare the discovery as trivial or claim that they knew it all along — this in part stems from a total conversion that makes them lose their prior framework (some of this is captured in the paradigm shift model of the Jewish thinker Thomas Kuhn).

In the end, all this still lies in the domain of what might be termed the objective because once the insight is gained, it can be formally transferred to others by a mechanical procedure. For example, most Indian “crackers” in our days who exuberantly integrated all manner of complicated functions often did not have any insight into calculus — they had merely mastered its protocol. On the other end, there might be mathematicians turgid with formalism who think all common presentations of calculus are fundamentally flawed. In between are the reasonable practitioners who know that there is a certain insight, which becomes very natural at a certain point in one’s study of the field. Once one knows this, it no longer seems like a black box but as natural a procedure as 2+2=4 (unless you are possessed by the Neo-American disease). Thus, for many who have “mastered” calculus, the original perspective shifts that its discoverers might have had are no longer very important. Because of this one might also see a devolution of the field if the continuity with the original insight is lost. We believe that a good example of this is the loss of the great astronomical insights of Āryabhaṭa in Hindu astronomy until it was in a sense rediscovered by the Nambūtiri school or their (as yet unknown) predecessors. This might also be a major factor in the loss of technological insights, such as the Antikythera mechanism of the Archimedean tradition or the yantra-s of Āryabhaṭa or king Bhoja. This might even happen in our age.

In any case, the bottom line is that these perspective shifts, once realized, can be transferred to others. Hence, we see this as being in the domain of “science” or objective knowing. However, over the years, we have come to realize that there is an equivalent of this switch that intrudes into the subjective domain that might not be entirely transferable, at least by the same way we transfer the objective insights. There are several versions of this straddling the domain between the purely subjective and the objective. To explore this, we start with the existence of hard biological barriers that stand in the way of the first-person experience of one group from being replicated in the other. An easily understood case of this comes from the innate differences between men and women (notwithstanding the neo-American simulacrum of West Asian diseases of the mind, which tells you that they do not exist). One domain where this is very apparent is vision — men and women literally see things differently. Women tend to see a greater richness of color than men, especially in the middle wavelengths of the visual range, and men see finer detail (especially changing light intensity) and subtler movements than women. While we do not entirely understand the biology behind this, it may proximally stem partly from the X-chromosomal linkage of opsin genes, which encode visual sensors, and partly from the massive role of testosterone in modeling the visual cortex during development. There may be good teleologies for this going back to our evolutionary past, especially given that primates are very visual animals, which recognize color on faces (among other things for mate choice), and the behavioral differences between males and females in several primate lineages. Thus, males and females have distinct subjective experiences of color and detail conditioned by their biological differences — this is analogous to the pubertal neural transformations that lead to new insights. However, in this case, the first-person experience of one group cannot be replicated by the other due to the fundamental biological distinction between them.

This leads us to the question as to whether, in some cases, this barrier to the subjective experience can be turned off by a switch such that you see things in a wholly new way — something analogous to man being able to suddenly see all the gradation of colors a woman was talking about that he never understood. For this, let us consider the effects of N,N-Dimethyltryptamine (DMT). Those who have not had a DMT experience (that includes us, to be clear), can get some picture of the self-reported objective part. For example, a survey of 561 DMT users [Footnote 1] showed significant coherence in the prominent features experienced by them. They reported an encounter with a “being, guide, spirit, alien or helper” that appeared “conscious, intelligent, and benevolent” and “continued to exist after the encounter”. The majority also stated that they received “a message or a prediction of the future”. We cannot make complete sense of what they experienced, but we can agree that the compound made them see something unusual. However, the users also show a significant trend of saying that the experience results in a profound change of world view, and they did not see things the same way after it. For example, more than half of those who identified as “atheists” no longer did so after the experience. Thus, no amount of explaining or description of the experience in an objective sense can flip the perspective switch for those who have not gone through it. Therefore, this tells us that there is a perspective switch in the subjective realm, similar to what we see in the objective sphere in the scientific process; however, that cannot be simply transmitted through a formal framework to others. Instead, one may have to subject oneself to the compound to see if such a shift might be experienced in the first person. Indeed, the commonality and distinction between these subjective and objective perspective changes is illustrated by the lysergic acid diethylamide (LSD) experiences that are said to produce both objective scientific perspective shifts, which can be formally communicated, and subjective ones which result in a “changed perspective on existence,” which seem untransmittable.

The limiting case of the subjective perspective-shift is something that educated Hindus can understand; however, others might find it incredibly difficult to grasp. At a general level, it might be something that overlaps with the flipping of the switch, which occurs with psychedelic compounds, but, typically, the Hindu praxis related to it does not go via such compounds. This may be termed, for the lack of a better word, “brahmānanda.” While the use of the term brahmānanda might indicate that we are privileging Advaita vedānta, we should clarify that it is not the case. The percipient, either due to a yogasādhanā or vicāra has a switch flip within him, which shines the light of a profound subjective experience, that might be liked to awakening from a dream. In the regular dream world, one is conscious and doing things with a unified first-person experience despite the absence of much sensory input. In that state, one takes that experience to be reality. But when one awakens, one realizes that it was not reality but some “illusion”. Similarly, in the brahmānanda experience, the percipient is said to awaken from the everyday world into that new brahmānanda state, at which point he sees the everyday world just like a dream. Some such condition and transformation into it is widely accepted in H tradition (including the vedabāhya schools). What they differ in is the ontological status they accord it and the theological framework into which they incorporate it. We will not labor on this point because educated H will get it right away, and others probably will make no sense of what we are talking about.

There are more “secular” examples in the same general domain that again a subset of people can find difficult or impossible to apprehend. Below we give a couple of such anecdotes. To understand the “reality” of subjective experience, one has to be able to appreciate what is called, in modern Occidental philosophical terminology, the “hard-problem” of consciousness. It goes hand-in-hand with the “first-person-experience” available for mental reflection; it is given the technical term quale (plural: qualia). Simply put, the hard problem is then the question of how we can get to the qualia from an understanding of all the biochemistry and biophysics (the “easy problem”). This is a philosophically difficult chasm to bridge between the objective realm of science and the subjective realm of consciousness. A physicist with a prodigious head once asked us if we felt that the “human brain” and “consciousness” were the last great frontier of biology, which would draw the biggest brains in the field. We responded that it might suck in the big brains but that there were more fundamental problems in biology. This led us to talk about consciousness, and soon we realized that he thought consciousness was the same as the biochemistry and biophysics of the brain. Hard as we tried, he could neither apprehend the very existence of qualia nor the concept of the philosophical zombie — it almost seemed like he was one. We put this aside as simply an issue with our attempt at explaining the concept to him. More recently, we had a similar conversation with a set of friends. Of the two of them, one, who was formerly a physicist, again simply failed to apprehend the concept of qualia or that the hard problem could even exist. The other one, a biologist with a reasonable general knowledge of neurobiology, had considerable difficulty grasping the existence of qualia. He fumbled along, insisting, like many before him, that they must be just “illusions” not unlike optical illusions. However, midway into the conversation, a switch suddenly flipped within him. He exclaimed something like: “I get what you are saying! This is profound, a hard problem indeed! Now I see why this might be a big issue.” In this case, we could not transfer an algorithm to him for making the switch — something within him flipped while he was trying to process our words and imagery objectively.

We finally come to the specific case where there seems to be an interaction between the subjective and objective domains of knowing. We illustrate it with an example that would make the typical modern occidentally conditioned scientists (usually one with left-liberal beliefs) very uncomfortable (though the protagonists in the narrative are Occidental scientists). The narrator somehow felt we would “get it” even if we do not believe him. A senior colleague told an elderly biochemist of European ancestry of his observations on the apparent “ghostly” transmission of information from deceased individuals to those born after them in West Africa. The senior colleague had systematically gathered this information and presented what may be termed objective data with statistics to support his contention that this unbelievable thing (in the modern paradigm) happens. Unlike some who would have normally laughed it off, our biochemist heard out his colleague attentively and studied his data. He found nothing wrong in the report but could not believe that what his colleague told him could really happen. He felt there could be other mundane explanations. The said biochemist, himself a man of travel and adventure, was interested in the anthropology and genetics of certain human diseases prevalent in West Africa. Hence, he had the chance to travel there and check things out with the tribesmen himself. What he saw in “pratyakṣa” — the subjective first-person experience he had in West Africa — caused a dramatic perspective shift. After this first-hand encounter, he began believing what his senior colleague had presented to be true, even if he did not have an explanation for it. He did not publish it because he knew others would have the same disbelief as him unless perhaps they reproduced his experience for themselves — something not easily achieved when it needs serious fieldwork among the tribes of West Africa.

This is not restricted to the domain of such unusual things, though it might be enriched there. We have had at least one personal example of the same in ordinary science in our youth. A researcher had published an unusual scientific discovery whose full implication he did not grasp. When we read it, we realized how unusual it was and the major implications of it being true. However, we simply could not get ourselves to believe it, for it was not easy to reproduce it by any means at our disposal in our youth. We also found that other respected researchers in the field could not reproduce it and disregarded it. However, a few years later, we were able to reproduce it for ourselves and see it plainly with our own eyes. At that point, we managed to develop a formalism to present it quite plainly to the rest of the community. Seeing our presentation, several saw its reality and started claiming it as their profound discovery! Because it was in the realm of the objective, once the formalism was presented, people could make the flip by following it. However, to develop that, we had to have a first-person experience of it — enter a state of being a believer — before proselytizing it. Not all such flips necessarily result in correct insights. Some of those could be false, both in the domain of science and religion.

Finally, why do we call it a “perspective shift”? Early on, we read of a mathematical construct that led us to an analogy of how these insights work. It is the famous construct of a 2D world — the flatland. For the flatlander, objects accessing and using the third dimension for motion will mysteriously appear and vanish. Moreover, a flatlander moved into the third dimension will suddenly acquire X-ray vision into other flatlanders. Thus, the insights we have discussed in this note have the feel of such a vision of a flatlander suddenly gaining access to 3D space; hence, we term them perspective shifts. Might such a thing also apply to our 3D space? Some rare people, like Henri Poincare and Alicia Stott, the daughter of the well-known mathematician Boole, had the capacity to “see” 4D space. Thus, Stott was able to construct shadows and cross-sections of 4D and higher dimensional objects in 3D space and make discoveries in this regard. This led to the great mathematician Coxeter using her extraordinary ability to assist his geometrical research even though she had never formally attended college. This was a genetic siddhi, elements of which she got from her parents and passed on to her son. For the typical individual, there might even be an inhibition against such special insights, for it could come at a fitness cost, as noted above. In this regard, we note the case of a fellow graduate student who was a virtuoso programmer. One day he had a mental quake, after which he remarked to us how he was apprehending 4D space naturally and seeing hyper-Platonic solids. Sadly, a few months later, he lapsed into dysfunctionality with a severe mental condition.

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[Footnote 1] Davis et al; https://doi.org/10.1177/0269881120916143

On the passing of E.O. Wilson

E.O. Wilson, one of the great biologists of the age, has fallen to the noose of the king, the black son of Vivasvān. He lived a long, productive, and eventful life, just 8 years shy of a century. He was a major influence on our scientific development. We learnt of kin and group selection and r- and K-selection from reading his classic tome, “Sociobiology: The New Synthesis” in our youth. The introduction to these concepts of the evolutionary theory kept brewing in our minds, and we kept thinking about the molecular consequences of the same. In the 13th summer of our life, we studied the immunoglobulin domain and the generation of antibody diversity in jawed vertebrates. It was then that first connections clicked into place. We realized that must be general evolutionary parallels between the immunological molecular machinery for self-non-self discrimination and the apparatus relating to kin-nonkin discrimination in social contexts. A few years later, we read John Maynard-Smith’s “Evolutionary Genetics”, which we were lucky to borrow shortly after its publication. By then, we were armed with some agility in calculus; thus, the mathematical framework provided by Maynard Smith allowed us to apprehend some key ideas of the selective process relating to the logistic growth curve and related issues. These also came together with the ideas of Pāṇini/Patañjali on linguistic systems and those of Shannon regarding the relationship between entropy in statistical mechanics and linguistic strings. Finally, one fine evening it all came together, and we realized the foundations of understanding the imprints of the selective processes we first learnt of from Wilson’s book on the information in biological macromolecules. Exploring this story has kept us occupied to this date.

We found our journey to be somewhat ironic when we learnt much later of the famous clash between J.D. Watson and Wilson when they were both at Harvard University. Old Jimmy felt that molecular biology had made Wilson’s type of biology (“stamp collector” science) unimportant. Watson is famously reputed to have said: “Smart people didn’t go into ecology … It’s not intellectually demanding.” While we also feel a degree of intellectual kinship with Watson, there is a palpable aspect of Wilson’s statement regarding Watson — “the most unpleasant human being I have ever met” — in molecular biology. Indeed, molecular biology has quite a share of the “most unpleasant” people you can meet outside of a street in some rough city of the world. We believe that some of this culture stems from the founder of that science Watson himself. While we admit this is a subjective and anecdotal impression (we do not have controls to say if scientists are more or as nasty in experimental physics or organic chemistry), it cannot be denied that the cultural defects of modern molecular biology are reflected in the mounds of fake results and credit stealing (best termed plagiarism) corrupting scientific publications from the constricted highways of the magazines and to the toxic byways of preprint servers. Even more troubling for the foundations of the science is the triumph of the Watsonian metaphor over the Wilsonian call for consilience — something that deeply resonates with the Hindu tradition of knowledge. Wilsonian consilience was put to practice by his late friend, the great entomologist, T Eisner, who brilliantly brought together the study of biological conflicts with an exploration of the chemical virtuosity of insects. Thus, we have numerous practitioners of the modern branches of biology, championed by old Jimmy, who lack an understanding of the foundational ideas of their science — imagine physicists practicing their science with only a smidgen of knowledge of the Lagrangian or the Hamiltonian. It would indeed do the science good if the practitioners were to pay more sincere attention to the Wilsonian philosophical outlook. However, this may not come to be for other reasons that intersected with Wilson’s journey through life (see below).

Kin selection was discovered by J.B.S. Haldane and elaborated in a proper theoretical framework by W. Hamilton. Wilson’s seminal contributions to hymenopteran biology were critical in establishing kin selection on a firm footing. However, ironically, Wilson tended to have a soft corner for group selection, which eventually became a full-blown attack on kin selection as the explanation for eusociality in his last years. He sought to provide this idea with a mathematical foundation with the help of Nowak and Tarnita. We feel that much of that complicated mathematics is probably more a smokescreen than real fire and does not displace kin selection, at least in the contexts that were close to him — eusociality as reported in arthropods or the mole rats. Nevertheless, unlike many other biologists, we do think Wilson had a point regarding the place of group selection in social systems. To a degree, this might have been critical in human sociality, much like the hypersocial ants that Wilson had studied. The lineage as a whole provides a way to understand this. Men unrelated to great leaders like Chingiz Khān or Shivājī sacrificed their lives for them. In return, these leaders ensured the survival of their offspring. Say they had not sacrificed themselves for the new group identity forged by the Khān, they might have been wiped out in entirety like the many bands on the steppe before them. Thus, while the Khān got to propagate his genes to leave an oversized genetic imprint that stands out even today, these men might have raised the probability of the survival of their lineage from 0 to something small but non-zero. Our investigations suggest that group selection might have a role in the stability of bacterial biofilms too.

This brings us to an important point elaborated by Wilson: the superorganism. The same genome is differentially expressed to generate a diversity of castes that dramatically diverge in appearance, size, and behavior. This provides a striking illustration of a molecular principle, namely the use of epigenetic regulatory processes to add information over and beyond that encoded in the four bases of DNA. Thus, different parts of the same code are unveiled in different individuals making them look almost as if they were different species. This led to the formulation of the evolutionary hypothesis of how epigenetic regulation in eukaryotes might provide the initial “capacitance” for changes that might then be hardwired into the genome. At the social level, it showed the remarkable success and stability of the caste system as an evolutionary strategy. It has repeatedly emerged in multiple hymenopterans and the cockroach-like clade. Thus, it should not be a surprise to see it emerge in humans though we can only be considered nearly eusocial. Nevertheless, the basic principle of a superorganism with castes can be seen as applying to our societies. That is how our ancient social theorists saw the varṇa system — the 4 varṇa-s (mirroring the numbers of castes seen in arthropods) are seen as aṅga-s of the metaphorical puruṣa who is the society. The stability of these castes for over 90 million years in hymenopterans should serve as food for thought to the left-liberals who strive to have it abolished. This should be placed against the backdrop of the many evolutionary successes of the hymenopterans and isopterans, which anticipated some of those that we pride ourselves on, like the discovery of farming or antibiotics.

This finally brings us to what brought Wilson and Watson back together. Wilson was one of the first to face the assault of the navyonmatta-s — the left-liberals with deep connections to the H-haters of American school led them — Lewontin, Gould, Kamin, and Rose, among others. They orchestrated a band of thugs, the predecessors of the kālāmukha rioters of the American gardabha-pakṣa, to attack Wilson. Watson was a member of the old mleccha guard and, like his collaborator, F. Crick, saw the reality of genetic differences between ethnicities. This made him an enemy of navyonmāda, driving him close to his old foe, Wilson. In the end, the first wave of navyonmāda orchestrated by the uparimaragata left-liberals failed to storm the scientific branches of academia completely. Instead, due to the lack of Wilsonian consilience in the Occidental academe, it festered on in the non- and less- scientific domains of the same. In the end, it has to be kept in mind that both Wilson and Watson belonged to the mleccha elite. Their fortress is still pretty strong despite being sapped by navyonmāda. Wilson was a quiet personality. He generally maintained a dignified public profile, kept writing his books, and moved to other areas of interest. Thus, the navyonmatta-s lost interest in him. In contrast, Watson has an abrasive personality who liked to focus on the most uncomfortable of human genetic differences in a public and, sometimes, crude way. This resulted in his fall from grace as an American hero. In the end, Wilson’s personality offers a better model to emulate than Watson. He was productive until late into his long life. He explored a range of ideas brought many of them to the public with elegant writing. However, this would have only been possible in the height of the mleccha academic ecosystem. Even if one had the genetic wherewithal to emulate a Wilson, it would be tough to achieve the same in the absence of that type of ecosystem, which is now under threat from navyonmāda.

Some words on mleccha cartels

An embedded anthropological study of social substructures is vital to grasp some of their features that seem baffling to the outsider or the “uninitiated” insider. Much of what we will be talking about here has been said in some form on these pages before, and some of it will necessarily be vague for the mleccha and his agents are still in control of the world. Yet, we felt it is worth recording this as there is no guarantee that the whole story can be said in plain language. If the time does come when it can be told in such a way, then the tendency will be to focus on the distracting specifics rather than the general significance, and the focus will be through the lens of inter-personal feelings rather than objectivity. Another point to note is that in the past decade navyonmāda, whose long fuse was smoldering for decades, finally exploded on the world scene along the lines its founders wanted. This means that the old lenses used to view the mleccha are no longer a perfect fit — cognizance should be taken of the deep divergences within the mleccha world. Nevertheless, as we have often remarked before, there is an alignment of the preta, garden variety liberal and nayonmatta positions when it comes to the H. Indeed, this is a continuation of the deep anti-H sentiment in the mleccha world, especially among the āṅgla-gaṇa, which goes back to over a century and a half. For example, the popular mahāmleccha mouthpiece, the Washington Times, was as anti-H a century ago as today. Hence, despite the deep schisms within the mleccha worlds, like those between the overt Abrahamisms, there is a common pith (much like the marūnmatta scientist, Al Bīrūni, had remarked regarding the Hindu-s and the Yavana-s).

Over the past few years, two H (they not educated about H traditions but do not tilt against them either. Their knowledge of Indian politics is next to non-existent), whom we know well, brought us in contact with three influential mleccha organizations. The power of two of them, while extensive, is in no way directly related to national- or geo- politics, and their influences are relatively domain-specific. The third has a more local character but exerts considerable influence on one of the two bigger organizations. We will hereinafter refer to them as “cartels,” but it should be emphasized that they do not trade in recreational substances or weapons or the usual things the word cartel is commonly used for. However, we learnt that they operate very similar to cartels. To be clear, we are not a member of any of the three though our H contacts are. They entered those cartels through either prolonged pro bono service or playing middleman in key access networks for powerful mleccha insiders. In the process, they learnt how to play in those circles via mlecchānusāra. In short, it involves an elaborate process of delegation while claiming credit for oneself. The lower-ranked individuals actually doing the dirty work are paid primarily with “biscuits” like those tossed to the faithful dog Tom for fetching a stick. The mlecchānusāra has a subtlety to it, despite seeming simple to the naive onlooker. Indeed, a couple of such naive V3s thought they could play the boss-mleccha but ended up much like the nāpita mimicking Maṇibhadra.

While our H contacts are insiders, they still felt that there were deeper secrets that only the mleccha and mūlavātūla players could access. However, they got one key perk — immunity to random attacks from the thugs (see below). A prathamonmatta insider brought to the attention of one of our contacts the case of a non-H deśīya who entered the cartel by presenting himself as a “traditionally oppressed and excluded minority.” However, after some study, we realized that it was only half the story. He had a long track-record of serving the mleccha by playing middleman in important networks like our other H contact. There is a particular knack to the whole thing that these two individuals have mastered. It is probably how arms dealers operate. A śūlapuruṣa and a kṛśapuruṣa, who are high-level players in one of these cartels, and with deep moles in the other two, revealed to us some of their deeper dealings. The śūlapuruṣa knew well that we are an outsider with no means of harming the cartels. He had also gotten a big favor from us (to be open, a calculated action on our part that benefited us) and thought a return favor might be to reveal some secrets of his power. The kṛśapuruṣa had also benefited from us (at no particular cost or gain to us); however, he also felt some kind of “ethical discomfort” about the cartel of which he is a deep insider. Thus, they ended up revealing some of the actions that went on within.

One key feature of these cartels is the multi-leveled defensive layering like the prākāra-s of maṇḍala bristling with deities capable of deploying all manner of weapons. The outer facade is carefully painted to present a picture of being “free and fair”. However, in reality, it is anything but that. But how is that facade maintained? The main element of this is the first layer of the system — a large body of “peripherals”, who are not members of the cartel and know nothing of its inner workings. However, they are dependent for their survival on the exclusive products of the cartel and have fear and admiration for the cartel leaders, much like a low-ranked individual might have for the player. These peripherals are the ones who buy and use the cartel products and are occasionally given some small rewards for doing so. Whenever survival is hard, it is possible to easily earn the gratitude of those in the struggle by giving them a few tidbits that seem like encouragement or moral support. The second element of this involves the cartel members choosing a few individuals from among the peripherals for two kinds of things: (i) those who would do advertisements of the virtues of the “free and fair” system operated by the cartel and show how their products are chosen entirely due to merit in a competitive Turkish bazaar. (ii) The second set of individuals are chosen for doing the hard and dirty work of running the cartel’s production systems — sapping and utterly boring job if one were to have an avenue to lead a free and self-respecting life. The cartel members pay these chosen peripherals for these jobs a little more in terms of the “biscuits” they toss to them. The first mechanism is closely related to the “toolkit” approach in geopolitics that is used widely in social and legacy media and national destabilization activities of the navyonmatta-s (often backed by duṣṭa-sora and the like). Thus, at the whistle of the managers from Sora’s organization, the peripherals will start yelling “dog-whistle” and claim that the imaginary H canine is shredding them.

The next layer is that of the “thugs” who are again not cartel members but offer their services for the cartel. These thugs themselves are individuals of lower intelligence than the cartel members or the peripherals. Thus, they do not pose a significant danger to the cartel members by themselves as they cannot easily organize a rebellion against the cartel. Moreover, being good-for-nothings, they strongly depend on the cartel for their very survival. Coming from the lower rung of the social ladder, they are full of resentment and get great satisfaction from acts of vandalism and violence (even if of the metaphorical kind). This feeds into their fantasies of being maverick vigilantes doing their part for the “noble cause”. Often these types are high on navyonmāda and have time on their hands to offer themselves for “policing” on behalf of the cartels. They perform two operations: (i) intimidation of the peripherals who may start discovering the cartel’s ways, fall out of line, or show independence. (ii) they attack those producers who lead lives independently of the cartels so that they cannot sell their products in the open market. These attacks are orchestrated such that they appear rather random, and the independent producers are left wondering what hit them and who is behind the attacks. The result is to force the independents into being subservient peripherals or be entirely driven out of the business. These tactics have a mirror in political navyonmāda, such as the kālāmukha thugs of the gardabha-pakṣa among the mahāmleccha. It also resembles the tactics of marūnmāda, where the kaffrs (=independents) are offered the option of either losing their foreskin or their head.

The next notable layer is made up of cartel insiders, who form the cartel’s public face. Among the mahāmleccha and their satellites, the keyword is “diversity”. Usually, the individuals in this layer are chosen so as to hide any signs of ethnic enrichment in the cartel. The members are there to create the illusion that anyone can “make it” and that the cartel does not really have any exclusive principles beyond pure merit. The cartels we are talking about includes a large number of true believers of navyonmāda, but most members would hardly give up their yachts or sprawling villas for the kṛṣṇa on the street for whom they proclaim unreserved love. Hence, they pay great attention to camouflaging this with effusive public declarations of the creed of navyonmāda. This layer also features the appointed spokespeople who direct the advertisement activities of the peripherals — e.g., updating the toolkit and setting agendas for them. A related layer is one of “managers” who interface with the thugs and peripheral workers and set goals for them.

An essential aspect of the system is an elaborate chain of scapegoating. If something bad happens and the cartel comes under fire (e.g., their egregious mistakes during the Middle Kingdom corruption or the uncovering of major sexual misconduct by a member), this chain ensures that the fuse does not burn all the way to the cartel members. Thugs and peripherals might be immolated with little remorse as sacrificial victims as long as the cartel’s interests and inner circle are preserved. Thus, it is hard to pin the blame on the cartel — it will get pinned on to someone lower down in the elaborate chain of scapegoats, and that little tentacle will be amputated like that of a Hydra leaving the rest of the animal intact to regrow it. If due to a major mishap, the blow-back happens to breach the inner rungs of the cartel, then scapegoating action follows along ethnic lines. Those ethnicities with strong internal bonds quickly close their ranks to protect and secrete away their tainted members leaving the loosely bonded ethnicities to take the blow. The H fall in that latter category as most H members of these cartels have a poor sense of religious solidarity and have a tendency to splinter along the lines of their deśa-bhāṣā. Indeed, an H player from one of the said cartels, who had achieved extraordinary power, thought himself to be immune to attack. However, his rivals trapped him using the perennial device of seduction by women. Thus exposed, he had no ethnic network to shore him up for when in power he thought he was one of the mleccha-s and shunned the H. Thus, without an ally, the mleccha-s and others closed in to finish him off. In contrast, when a mūlarogin was exposed for a major scandal affecting the core principles of the cartel, he was quickly encapsulated by his ethnic network and after a while rehabilitated with an advertisement campaign with high production values. So much so that a peripheral who spoke to us of his case was surprised that he could even have engaged in wrongdoing. A small cīna peripheral and an H thug were chosen and duly offered up as the bali-s that wiped away the enas of our mūlarogin.

Once one gets acquainted with these systems and is freed from self-censorious fear of being called a “conspiracy theorist”, one realizes that the same model is duplicated in the mleccha world across organizations diverse in size and domain of action. To our knowledge, the H have not been able to read these well and have mostly been overrun by them — the H commoner tends to believe the stated objectives of the respective cartels (we have seen H repeatedly do so with utter sincerity). The Cīna-s have realized their existence and, with their growing power, tried to penetrate them to a degree by bribery and seduction. They have definitely had a degree of success for their efforts, especially given that they have more or less captured certain other critical domains of mleccha production.

An author who experienced and described the collapse of the Soviet Rus empire said that it is not entirely bad to live a life in the margins. The basic argument is that a gale might uproot the oak at the center of the plot but do little to the pinkweed growing on its margins. Having led such a life ourselves, we agree with such an assessment for the most part. On the plus side, the margin-dweller is less-affected by catastrophic collapses and upheavals that the cartels might engineer. On the downside, this option is not easy for most as they have to make bigger gambles to sustain their families. However, we have observed that above-average but not supersmart individuals can sustain good family lives as long as they have small but reasonably talented marginal leaders. However, herein lies a potential danger. The cartels realize that such nucleations have the power to trigger marginal revolutions that can eat into their pie. Thus, the cartels try their best to quash these even threatening life in the margins. We suspect that the following factors will only make it easier for them to put down marginal revolutions: (i) the cartels gaining exclusive control of the world of the internet (e.g., culminating in the overthrow of the Nāriṅgapuruṣa among the mahāmleccha). (ii) The rise of an internet-only generation with short attention spans and a tendency to acquire knowledge from secondary sources. (iii) the belief that unreal gratifications can be achieved. (iv) the rise of “meta-software” that accesses the lives of people, which they have wholly surrendered to the cartels (the details of that might be a story for another day). The only thing that remains unclear is the timeline for this action to play out.

Relationships between incircles of the “equilateral triangles in a square” system

This note relates to geometric relationships that may be likened to the Japanese temple-tablet problems. The inspiration for discovering and exploring it came from an origami construction presented by the pioneer in that field, Sundara Rao of Kumbhaghoṇa, in the late 1800s. Given a square piece of paper, how does one fold it into an equilateral triangle? The construction which Rao gave was that of an equilateral triangle with sides equal to that of the starting square and sharing one side with it (Figure 1). Based on Figure 1, it is easy to see how that might be achieved. When we first folded this in our youth, we realized that it is not the largest equilateral triangle that can be placed inside a square. However, examining the origami construction for the above, we realized that it also gave us an easy origami construction for the largest equilateral triangle that can be inscribed in a square (the blue triangle in Figure 1). That construction should be self-evident once the first equilateral triangle sharing a side with the square is in place). These two equilateral triangles and the square result in a configuration of 7 other triangles (Figure 1).

The below study concerns the relationship between the incircles of these 7 triangles and two additional incircles, namely that of the starting square and the Raoian triangle constructed from it . Their radii, which the relationships connect, will be respectively, and . We outline the proof rather than present all the tedious trigonometry and radical algebra. If you like to do that with paper and pencil and are good at that, you can try the same. However, we cut through the tedium of the at times complicated algebra using a combination of recognizing key patterns and the open-source computer algebra system from GeoGebra that seamlessly interfaces with its geometric constructions. Nevertheless, we will show a few obvious ones to lay the background.

Figure 1.

• First, with is straightforward trigonometry to show that

• The proportion of the radii of the incircles is equal to the proportion of the equivalent sides of their triangles.

• Let the side of the largest inscribed equilateral triangle (blue) be and the smaller one (sharing the side with the square) be . We can use the half-angle formula to show that . In turn, that means

• We can see that triangles with incircles , , and are similar triangles. Using the Sine Law we can show that the sides of such a triangle are in the ratio . With this and the above we can get the proportionality of these triangles. For example, we can show that the sides of the triangles with and are in the proportion: . :

• Next, we use Brahmagupta’s formula for the incircle of a triangle, , where is the semiperimeter (half the perimeter) of the triangle. From the proportions of the triangle sides, we can show that the ratio of the areas and the perimeters of the triangles whose incircles are and are both

• Thus, from above we have: and , i.e., a geometric mean relationship.

• Similarly, we use Brahmagupta’s formula to obtain the incircle radii of and . With that, we get the following relationships:

, i.e., a harmonic mean relationship.

, i.e., is the harmonic mean of .

• One can also get relationships connecting the radii of all the 7 incircles and also all 9 incircles in the configuration (Figure 1):

Thus, one can see the “2-ness” of the square in the form of and the “3-ness” of the equilateral triangle in the form of pervades the system.

The Rāmāyaṇa in numbers: meters, sarga- and kāṇḍa- structure

In the extant Indo-European textual corpus, only in the Hindu collection do we find two complete early epics to complement the śruti. The Iranian epics come from a much later age than the core Avestan corpus, and in the Greek and Celtic cases, the śruti-equivalents have been mostly or entirely lost. As they have come down to us, the Hindu epics postdate much of the Vedic corpus but are still in a distinct language register that largely predates the classical Sanskrit. Thus, the numerical study of the epics gives us essential information regarding the evolution of the Old Indo-Aryan language and compositional technique, with general implications for earlier branching events within Indo-European. Contrary to the deeply flawed mainstream white indological opinion (and its imitators), and in line with Hindu tradition, we hold that the original Rāmāyaṇa was composed prior to the Mahābhārata. However, it is also clear that both epics were at some point “held” by the same expositors and redactors, resulting in some convergences. We had earlier presented some key details about the structure of Rāmāyaṇa and the earliest para-Rāmāyaṇa (the Rāmopākhyāna) via numerical analysis and pointed out how the kāṇḍa-s show both a certain unity and divergence relating to the compositional history of the epic. Here, we extend that analysis further and draw some inferences regarding the above-stated issues.

The so-called Baroda “critical edition” is available in an electronic format and forms the basis of the below analysis. We have corrected several errors in that text; however, we cannot rule out that some errors remain, affecting some of the below numbers. Nevertheless, these will not affect any of the basic inferences presented below. The Rāmāyaṇa is mostly a metrical text with 17810 verses having 2 hemistiches each. There are 79 verses with 1 hemistich, i.e., standalone verses; 576 verses with 3 hemistiches: verses; 5 with 4 hemistiches which are essentially agglomerations of 2 complete verses. It is unclear if some of the 1 and 3 hemistich verses were originally complete verses that lost one hemistich. However, many of these odd-hemistich verses are genuine “capping” verses that occur at the ends of sarga-s. The 17810 “properly formed verses” fall into the below metrical classes (Table 1)

Table 1

Syllables	Frequency	Meter
32	16949	Anuṣṭubh (Śloka)
44	476	Triṣṭubh (Upendravajrā)
48	285	Jagati (Vaṃśastha)
50	26	Puṣpitāgrā
45	22
47	20
46	16	Aparavaktrā etc.
33	8
52	7	Rucirā

The primary meters are given in the third column with major, specific subtypes in brackets. It should be noted that the type in the bracket is just a widespread version and not the sole version found in the epic. For example, we have triṣṭubh-s of other types like jāyā, buddhi, kīrti, etc. in addition to the common upendravajra. Likewise, with the jagati-s we have versions like kumārī in addition to the prevalent Vaṃśastha. The dominant meter is, of course, the śloka anuṣṭubh. Now, some verses do not match any meter. Since we did not individually check all of them, some may be errors in the preparation of the electronic text — indeed, we corrected several of these. However, some of the 33s are genuine hypermetrical anuṣṭubh-s, like the famous ancient statement in the second hemistich that is hypermetrical:

idaṃ bhuṅkṣva mahārāja prīto yad aśanā vayam ।
yad annaḥ puruṣo bhavati tad annās tasya devatāḥ ॥
O great king, be pleased and partake this, such food as we [eat],
for the gods are offered the [same] as what food the man takes.

The 45 syllabled verses seem to be hypermetrical triṣṭubh-s, and the 47 syllabled ones seem to be primarily hypometrical jagati-s. Thus, there appears to be a total of about 50 hypo/hyper-metrical verses among the “properly formed” verses . The 46 syllabled verse is a bit of a mystery. Many of these can be shown to be aparavaktrā-s; however, several do not match the aparavaktrā properly. It is not clear if these were variant aparavaktrā-s that are no longer in vogue or an error of transcription or something else.

This pattern of strong metricality is in contrast to the Veda. Looking at the most metrical of the Vedic texts, the Ṛgveda, we find below distribution (Figure 1).

Figure 1. Frequency of verses of a given syllable count in the Ṛgveda.

The RV widely uses the Gāyatrī meter (2nd most common) that fell out of vogue in the later Sanskrit tradition. However, the other widely used meters Anuṣṭubh (4th most common), Triṣṭubh (most common) and Jagati (3rd most common), are shared with the epic tradition. We also have internal evidence from the śruti that their syllable count was precisely as in the later dialect, like in the epic. Hence, it is striking to note that, unlike in the epic, the meter is far more loosely maintained in the RV, with a dominance of hypometrical verses. This suggests that whereas the Rāmāyaṇa was composed more or less in the same dialect as it has come down to us, the RV was likely originally composed in an older dialect closer to the PI-Ir state, with a distinct system of saṃdhi-s than in later Sanskrit. The language in which it has come down to us has shifted in register closer to later Sanskrit, with the new saṃdhi-s resulting in losses of syllables from the old language. In a smaller number of cases, this shift in register has also resulted in the likely resolution of old saṃdhi-s and consequent hypermetricality. This shall be separately discussed in the future in the context of the Veda.

We shall next look at the distribution of the different meters in each kāṇḍa per 1000 proper verses in Table 2.

Table 2

Based on this distribution we can compute the Euclidean distance between kāṇḍa-s and construct an unrooted single linkage tree (Figure 2).

Figure 2. Relationship between kāṇḍa-s based on distribution of meters.

To better understand the above groupings, we next go down to the sarga level and compute two metrics for each sarga in a kāṇḍa: (1) metrical heterogeneity, i.e., the mean syllable count per sarga and (2) length of a sarga in number of verses (as previously discussed). The metrical heterogeneity measures how “pure” a sarga is in terms of the meter. For example, a sarga composed entirely of Anuṣṭubh-s will have metrical heterogeneity of 32. We show the plots of these metrics in Figure 3.

Figure 3. Sarga heterogeneity metrics by kāṇḍa.

Here, we can see that the kāṇḍa-s 1 and 7 are dominated by sarga-s with pure Anuṣṭubh-s of similar mean length, explaining their grouping in the tree. The kāṇḍa-s 2, 3, and 4 are somewhat more heterogeneous in terms of their metrical structure and have similar mean lengths consistent with their grouping. Finally, kāṇḍa-s 5 and 6 are metrically the most heterogeneous with on an average significantly longer sarga-s. This structure and grouping throw some light on the history of the text. Kāṇḍa 1 (Bāla) states that Vālmīki composed the epic in 6 kāṇḍa-s along with an “uttara” or addendum: tathā sarga-śatān pañca ṣaṭ kāṇḍāni tathottaram ॥ (From Vulgate; absent in “Critical”). This hints that there was a memory of the uttara-kāṇḍa (7) as an addendum to the core 6. This is apparent from the nature of several parts of kāṇḍa-7, which fill in the narrative gaps in the core kāṇḍa-s or provide explanatory commentary. The same feature is evident in kāṇḍa 1 (including the above statement). Their grouping, together with an anuṣṭubh-rich structural uniformity reminiscent of the purāṇika verses, suggests that they are likely entirely (7) or partly (1) the product of a later redactional effort to fill in parts of the epic that were either lost or needed further explanation/augmentation. Even the supposed names of the sons of Rāma, Kuśa and Lava, appear to be derived from an old term for a minstrel, the kuśīlava (the twins are mentioned as such in the beginning of 1 and end of 7), suggesting the emergence of these parts within the oral tradition of such minstrels, which used the relatively-easy-to-compose anuṣṭubh-s uniformly. Kāṇḍa 1 also hints that the original epic had two subsections to it:

kāvyaṃ rāmāyaṇaṃ kṛtsnaṃ sītāyāś caritaṃ mahat ।
paulastya vadham ity evaṃ cakāra caritavrataḥ ॥
He (Vālmīki) composed the great poem, the Rāmāyaṇa, the story of Sītā.
Even so, he of firm vows composed that known as the slaying of the Paulastya.

We could interpret this as implying two larger sections of the narrative centered on the tale of Sītā (i.e., her birth and marriage to Rāma, etc.) and the killing of Rāvaṇa. Thus, we suspect the two structurally unified parts the kāṇḍa-s 2-4 (probably with parts of the ancestral 1) formed the first of these sections, and kāṇḍa-s 5-6, which are again structurally similar, and organically related to the killing of Rāvaṇa, formed the second. Kāṇḍa 5 (Sundara), which shows maximal metrical and length heterogeneity, was likely composed thus on purpose (as we noted before). This kāṇḍa foreshadows the tendency in later classical kāvya, where the kavi-s set aside specific sections of their work, to showcase their virtuosity in terms of composing in a diverse array of meters or displaying various alaṃkāra-s, including citrakāvya. We do not see the much longer and complex metrical expressions of classical kāvya nor the constraint-based composition using techniques of citrakāvya in the Sundarakāṇḍa. Yet, it is clear that Kāṇḍa 5 elegantly intersperses diverse meters on top of the basic anuṣṭubh background to bring about pleasing changes of cadence. Like later kāvya-s, it also has entire sarga-s in long meter-s.

Next, we study the structure of the sarga-s by themselves and see if we can discern: (1) specific structural classes of sarga-s; (2) whether the sarga class has a relationship to the kāṇḍa it comes from. To do this, we first construct a matrix where every row corresponds to a sarga. The first 9 columns correspond to the fractions of the sarga in verses of a particular number of syllables (32, 33, 44 etc.). Column 10 corresponds to the length of the sarga in number of verses normalized by the longest sarga (5.1). We then use this matrix for unsupervised classification of the sarga-s using the random forest predictor as implemented by Breiman and Cutler. Briefly, this is a machine-learning method that uses an ensemble of individual classification tree predictors (i.e., decision trees to classify the given data). The decision process specified by an individual tree uses each observation to vote for one “class” and the forest of such trees is used to choose the class with the plurality of votes. For the classification process, the number of randomly selected variables that are searched for deciding the best split at each node in the tree is taken to be , where is the total number of variables. The unsupervised mode works by making the RF predictor discriminate the observed (i.e., the above sarga matrix in our case) from synthetically produced data. The synthetic data is made by randomly sampling from the product of marginal distributions of the variables from our input matrix. As a result, one can obtain a proximity matrix between the input observations (i.e., sarga-s in our case). This proximity matrix can be converted to a distance matrix and used as the input for multidimensional scaling (MDS), representing the observations as points in an Euclidean space of dimensions, with the Euclidean space distances between these points approximately equal to the distances in the distance matrix. By choosing the first two dimensions in this Euclidean space and plotting them, we can reduce dimensionality and obtain visual clusters or classes of the observations. Figure 4 shows the first two dimensions of the MDS plot for our data following unsupervised random forest classification (655 trees and minimal terminal node size of 90).

Figure 4

We see 4 broadly delineated clusters, although their “smearing” indicates a degree of a continuum. Examining each cluster individually, we see that they provide a meaningful classification of the sarga-s: (1) The first class (ellipse to the left) is composed of sarga-s that are pure anuṣṭubh-s. (2) The second class (top right ellipse) comprises of sarga-s that have anuṣṭubh-s combined with triṣṭubh-s. The core of this class is defined by a very characteristic form of the sarga that contains a triṣṭubh as the capping (final) verse. (3) The third class (bottom right ellipse) consists of sarga-s combining anuṣṭubh-s with jagati-s. The core of this class uses a jagati, usually of the vaṃśastha type, as the capping verse. (4) Finally, the central ellipse contains a group of sarga-s typified by interspersing of different meters on an anuṣṭubh background or those with irregular (hypo/hyper-metrical) verses.

Figure 5

One can see from the color-coding of the sarga-s by kāṇḍa in Figure 4 that there might be distinct patterns — e.g., class 1 appears enriched in kāṇḍa-s 1 and 7, which are rare in the other classes. Hence, we next examined if each of the above classes differ significantly in terms of the kāṇḍa-s from which their sarga-s are drawn (Figure 5). This confirms that the kāṇḍa-s 1 and 7 dominate class 1 . The pattern is inverted for class 2 with triṣṭubh capping verses. This is in keeping with the above proposal of kāṇḍa-s 1 and 7 having a distinct compositional pattern and history. Another notable feature that emerges is the enrichment of kāṇḍa 2 in the class with jagati capping verses . In conclusion, this suggests that the older aitihāsika kāvya tradition had a style of capping a long run of anuṣṭubh-s with a triṣṭubh or a jagati to mark the end of a section. This practice appears to have given way to the purely anuṣṭubh composition, probably among the kuśīlava-s who subsequently preserved the itihasa-s and the emerging purāṇa-s as an oral tradition.

Sneha, snowstorms, the sun and the moon in enigmatic ṛk-s

That the Indo-European homeland was a cold place with snow is evidenced by widespread survival of two hon-homologous words for snow. Recently, a discussion on one of these words, sparked by some linguist, landed on my timeline on Twitter. From that, it seemed that people were unaware of the attestation of its cognate in Old Indo-Aryan. This, in turn, reminded me of a discussion we had with our friend in college on the very same issue. Hence, we thought it worthwhile to put down this discussion — this apposite since the winter solstice is approaching, and as we write this note, it is a new moon with a solar eclipse in Antarctica.

The two words for snow that can be traced back to early Indo-European, probably even PIE, are attested in Sanskrit as sneha and himá/hímā. The udātta is represented by the acute sign and differs between the masculine form that is usually used for snow and the feminine for winter.

Sneha is represented by many cognates that include snow itself; Old Iranian has snaēža = to snow; Baltic: (Lithuanian) sniẽgas; Germanic: (Old English): snīwan. There are the 0-graded forms in: Greek: niphás = snowflake; Latin: nivis; Celtic (Welsh): nyf. Thus, it is a solid IE word. Interestingly, it has also been transferred to Sumerian in a form that suggests either early Indo-European or the Satem clade (Balto-Slavo-Aryan) as the possible sources. This might point to a potential trade contact between Sumerians and the Indo-Europeans in their colder lands to the north of the former. Coming to Indo-Aryan, while etymologists recognize the ancestral form as being Sanskrit sneha, they usually only cite Prakritic siṇeha or siṇhā as cognates bypassing Sanskrit as though it is not attested in it. However, as we shall see below, this is not true. In New Indo-Aryan languages that are still familiar with snow we have descendants of the Prakritic forms as the primary word for snow, e.g., Kashmiri shīna (pronounced these days with terminal schwa loss).

The second word hima, was probably paralogously polysemous right from the early stages of PIE, meaning both winter and snow. It is clearly inherited from PIE in the Indo-Hittite sense as we have Hittite gimmanza = winter. We have Baltic (Lithuanian): žiemà = winter; Greek: kheima = snowstorm/cold; khion = snow; Armenian: jiun = snow; Latin: hiems= winter; Celtic (Old Welsh) gaem = winter. In Sanskrit we see all the senses being attested. The usage śata-himā is literally a 100 winters, meaning hundred years. A similar usage is seen in Latin, e.g., bīmus from *bihimos — lasting two years. The form hemanta again denotes a season marking the end of winter. On the other hand, the form himavant means a mountain [covered] with snow. Similarly, in the Ṛgveda hima can be directly used to indicate snow, for example:

himenāgniṃ ghraṃsam avārayethām
pitumatīm ūrjam asmā adhattam ।
ṛbīse atrim aśvināvanītam
un ninyathuḥ sarvagaṇaṃ svasti ॥ RV 1.116.8

With snow, you two averted the scorching fire,
you two bestowed nourishing food for him [Atri],
You two Aśvin-s, led out Atri from the fuming crater,
into which he been led, and all the troop to weal.

This ṛk attributed to Kakṣivant Dairghatamasa [Footnote 2] is an allusion to the famous deed of the Aśvin-s that is repeatedly alluded to in the RV, where they saved Atri from a fuming crater. The simple reading of the verse would imply that Atri was led into it along with his troops. They were cooled with snow and then brought up. The phrase sarvagaṇaṃ svasti occurs only one other time in the RV, in a sūkta of the Atri-s; however, there it refers to the gaṇa-s of the god Bṛhaspati. Nevertheless, one wonders if there is a subtler, undiscovered connection furnished by this cognate phrase from these relatively late sūkta-s of the RV. Finally, one may comment that this tale hints at the possibility of Atri and his men having fallen into one of the geothermal craters in the Caspian-Black Sea region close to the IE homeland.

Returning to sneha-, we tabulate below the occurrence of this word in some old Vedic texts relative to hima- (while we count both senses of hima- we do not count the season hemanta in the below table).

Text	sneha	hima
Ṛgveda	2	11
Atharvaveda (vulgate)	1	16
Atharvaveda (Paippalāda)	0	35
Taittirīya Saṃhitā	0	10

Thus, it is clear that sneha, while attested in the oldest surviving Indo-Aryan text (the single AV-vulgate instance is identical to the ṛk found in the RV), it is absent in the successor texts though hima- remains as common or is more frequently used. However, we should also add that a related form snīhiti (snowstorm) occurs once in the RV and once in the Taittirīya Āraṇyaka. In the case of sneha, a semantic shift occurred in Sanskrit, where it came to denote a wide range of things, including fluidity, smoothness, oil/fat and love. We will next examine the two occurrences in the RV and suggest that they are semantically aligned with the Middle and New Indo-Aryan forms. Both occur in enigmatic sūkta-s/ṛk-s that need further discussion.

The first occurrence is in a long sūkta of Tiraścī Āṅgirasa on the many glorious acts of Indra, which needs to be described to give some context. The first three ṛk-s (1-3) describe the might of Indra and his vajra and also allude to his act of piercing the mountains with his arrow. This motif is reused by Vālmīki in the Rāmāyaṇa when Rāma pierces the seven trees to prove his might (Indra-hood displacing that of the mighty Vālin) to the ape Sugrīva. The following triad (4-6) describes how Indra, in his cosmogonic form as the generator of all beings, slew Ahi with his vajra, even as the mountains shrieked. The Marut-s seeing his valor, approached him for an alliance, like brāhmaṇa-s reciting mantra-s to praise him. The next tṛca (7-9) describes a Marut-centric version of the Vṛtra myth. When Vṛtra violently sallied forth, the other gods, who were the companions of Indra, retreated, leaving him alone in the battle. However, the 360 Marut-s (an unusual count associated with the days in an year) singing the praises of Indra joined him in battle, asking for a share of the ritual offerings. They urged Indra to scatter the anti-deva asura-s with his vajra and cakra, assisted by their battle formation fronted by their sharp spears.

In the next tṛca (10-12), the Āṅgirasa calls on his fellow ritualists to send forth their chants to Indra. In the tṛca (13-15), which includes the ṛk of specific interest to us, the narration moves to the battles fought by Indra against the enemies of the gods in alliance with Bṛhaspati. This triad is soaked in astronomical allegory, with the god Bṛhaspati himself likely being represented in the sky by the planet Jupiter. The main feature of this triad is the mention of a black (shrouding like a cloud) drop, kṛṣṇa drapsa, which is said to wander to the solstitial colure along a sinuous river Aṃsumati. We interpret this river as the lunar ecliptic. The whole myth seems to encode a solar eclipse close to the winter solstice (The old Aryan New Year), in which context the snowstorm is mentioned. The next tṛca (16-18) describes the following acts of Indra: 1. Right when he was born, he became the foe of the seven unrivaled ones (not entirely clear who they are). 2. He discovered Dyaus and Pṛthivi, which were hidden. 3. He set into motion the wide-ranging worlds. 4. He smashed the unrivaled one (Vṛtra) with his vajra. 5. He slew Śuśna. 5. He discovered the hidden cows. 6. He demolished the fortifications. 7. He released the frozen rivers and slew the demoness (an allusion to Dānu) lording over the waters. The final tṛca (19-21) praises Indra as Vṛtrahan and the lord of the Ṛbhu-s, calling on him for the soma offering.

ava drapso aṃśumatīm atiṣṭhad
iyānaḥ kṛṣṇo daśabhiḥ sahasraiḥ
āvat tam indraḥ śacyā dhamantam
apa snehitīr nṛmaṇā adhatta ॥ RV 8.96.13
The drop stood at the Aṃśumatī,
the black [drop] wanders with the ten thousand.
Indra helped it [the drop] blowing along with his skill.
The manly-minded [Indra] repulsed the snowstorm.

drapsam apaśyaṃ viṣuṇe carantam
upahvare nadyo aṃśumatyāḥ ।
nabho na kṛṣṇam avatasthivāṃsam
iṣyāmi vo vṛṣaṇo yudhyatājau ॥ RV 8.96.14
I saw the drop wandering at the solstice,
in the sinuous path of the River Aṃśumatī,
going down like a black cloud,
I impel you, bulls, to fight in the battle.

adha drapso aṃśumatyā upasthe
.adhārayat tanvaṃ titviṣāṇaḥ ।
viśo adevīr abhy ācarantīr
bṛhaspatinā yujendraḥ sasāhe ॥ RV 8.96.14
Then, the drop, in the lap of the Aṃśumatī,
bore the body sparkling with light.
As the deva-less folks moved forth [to attack],
united with Bṛhaspati, Indra conquered [them].

Commentary: The black drop (drapsa, an old IE word) is interpreted as the new Moon. The drop is associated most commonly with soma (with a lunar equivalence in several cases; on rare occasions it is used for Venus). Normally, the soma is silvery — ṛjīśin (like earlier in this sūkta) — reinforcing the lunar connection. However, here the drop is explicitly and atypically described as black, suggesting that the new Moon is alluded to. The first ṛk mentions the drop wandering with a ten thousand: we take this large number to denote the stars. The drop is seen as blowing along: we consider this an early allusion to the primitive Hindu astronomical theory (shared with the Greeks and likely of old IE provenance) of celestial bodies being blown on their paths by cosmic winds. In the second ṛk, the composer states that he sees the black drop which is likened to a cloud — suggesting its shrouding nature — wandering near a colure. He also mentions the sinuous course of the river Aṃśumatī. Given that the word aṃśu is used for soma (or the soma stalks before extraction of the juice) and metaphorically connects the soma plant and the Moon, Aṃśumatī would mean the riverine path with soma/the Moon. Hence, we take this to be an allusion to the lunar path/ecliptic [Footnote 3].

We take the colure (viṣuṇa) to be solstitial. Winter is the season that corresponds to the battle between the gods, led by Indra, and the demons. The verb, ava-sthā = going own, suggests the nether point of the ecliptic path analogized to a river. Hence, we hold that the solstice referred to is specifically the winter solstice. Thus, it is not any new moon but likely the new Moon closest to the winter solstice, corresponding to the old Aryan New Year. This, in turn, supports the idea that the snehiti which Indra averts is indeed a snowstorm. The final ṛk of this triad mentions the black drop in the lap of Aṃśumatī, where it paradoxically takes on a body sparkling with light. We take this to allude to a solar eclipse happening close to the solstice. The at the point of emergence of the sun from the total eclipse or an annular eclipse would indeed give the impression of the black drop (the Moon) taking on a glittering body. Thus, this is a variant of the famous Svarbhānu eclipse myth of the Atri-s but probably referring to a specific eclipse near the solstice. In this context, the attack adevī folks should be taken as a purposeful conflation of the earthly enemies with the asura-s causing the eclipse as in the Svarbhānu myth. Moreover, given the overall celestial setting, the specific involvement of Bṛhaspati, as a companion of Indra, in this conflict suggests the potential presence of Jupiter in the vicinity during this event (Or perhaps in the nakṣatra of Tiṣyā).

We may also point out that the deployment of snow or other “weather weapons” is a feature of the battles of Indra with the dānava-s elsewhere in the RV. For example, Hiraṇyastūpa Āṅgirasa gives an account of the battle between Indra and Ahi, when the latter had frozen the rivers and corralled the cows. Here, Ahi, first tries to pierce Indra with his spear, but Indra evades him by becoming the tail of a horse. Having evaded his strike, Indra conquered the cows and the soma and released the waters. Then he closed in for combat with Ahi:

nāsmai vidyun na tanyatuḥ siṣedha
na yām miham akirad dhrāduniṃ ca ।
indraś ca yad yuyudhāte ahiś ca
utāparībhyo maghavā vi jigye ॥ RV 1.32.13
Neither the lightning nor the thunder scared away [Indra] for him,
neither the snow (/mist) nor the hail that he [Ahi] spread out.
When Indra and Ahi fought each other,
Maghavan triumphed, [then] and also for the time that came.

Here, Ahi deploys various “weather weapons”, reminiscent of the steppe “rain-stone” magic of the Turkic and Mongolic world, but they fail to scare away Indra. The first two, lightning and thunder are unambiguous, and so is the final one, hail (hrāduni). The word miha could mean snow or mist. In either case, it supports the deployment of such weather weapons, consistent with the interpretation of sneha- as snow, i.e., in a snowstorm.

Strikingly, the second occurrence of sneha- is again in the context of the same eclipse myth. This account occurs in the monster sūkta of maṇḍala 9, which agglomerates shorter sūkta-s of various Vasiṣṭha-s and Kutsa Āṅgirasa. We shall consider the whole tṛca with this reference below:

ayā pavā pavasvainā vasūni
māṃścatva indo sarasi pra dhanva ।
bradhnaś cid atra vāto na jūtaḥ
purumedhaś cit takave naraṃ dāt ॥ RV 9.97.52
Bring (addressed to soma), by purifying yourself with this filtering, riches.
At the hiding of the Moon, O drop (moon/soma), run forth into the lake.
The yellowish (sun) is also here as if impelled by the wind.
the wise one (Soma) has indeed given us the man (Indra) for the sally.

uta na enā pavayā pavasva
adhi śrute śravāyyasya tīrthe ।
ṣaṣṭiṃ sahasrā naiguto vasūni
vṛkṣaṃ na pakvaṃ dhūnavad raṇāya ॥ RV 9.97.52
Also with this filtering purify yourself,
at the front of the famous ford of celebration.
Sixty thousand treasures the destroyer of rivals,
like a tree with ripe fruits, will shake down for triumph.

mahīme asya vṛṣanāma śūṣe
māṃścatve vā pṛśane vā vadhatre ।
asvāpayan nigutaḥ snehayac ca
apāmitrāṃ apācito acetaḥ ॥
The bull is his name [Indra], great and fierce, are his two,
deadly weapons, in the hiding of the Moon or in the touching.
He put to sleep the rivals and snowed down on them.
Repulse the enemies, repulse the senseless ones.

Commentary: Composite sūkta-s, like the one in which these ṛk-s of Kutsa Āṅgirasa occur, are typical of the final part of maṇḍala 9. Except for Kutsa, who is the author of the last 4 tṛca-s and the terminal ṛk with the classic Kutsa refrain, all the other authors are Vāsiṣṭha-s. However, throughout the long sūkta (longest in the RV) we find several allusions to the finding of the sun’s path, the holding of the sun, and soma as the Moon. Thus, it is not out of place to furnish an astronomical explanation for these ṛk-s. Key to the interpretation of these ṛk-s is a rare word māṃścatu/māṃścatva whose meaning has puzzled students over the ages. It occurs only thrice in the RV, and its meaning was already obscure to Yāska, who groups it with the words for horses in the Nighaṇṭu. Two of the occurrences are in this tṛca, and one is in RV 7.44.3 by Vasiṣṭha Maitrāvaruṇi. Thus, this word perhaps links the Vāsiṣṭha-s to Kutsa. It can be etymologized as maṃs+catu. Catu can be derived from the root cat- = to hide or vanish. Māṃs (with a pure anunāsika) is taken to mean the Moon, an older variant of mās, closely related to the form in early Indo-European. This form is supported by other Indo-European cognates like: Baltic (Latvian): mēnesis; Latin: mensis. Thus, the word is taken to mean the vanishing of the Moon. To their credit, some white indologists have correctly etymologized this word using comparisons across IE. However, they failed to understand its actual meaning. Notably, on the only occasions it occurs in RV, it is coupled with bradhna — the yellowish or reddish sun. This is also seen in the case of the verse of Vasiṣṭha:

dadhikrāvāṇam bubudhāno agnim
upa bruva uṣasaṃ sūryaṃ gām ।
bradhnam māṃścator varuṇasya babhruṃ
te viśvāsmad duritā yāvayantu ॥
Ever having awakened, to Dadhikrāvan and Agni
I speak; to Uṣas, and the sun, the cow.
The yellowish one from the hiding of the Moon, [becomes] Varuṇa’s brown one,
let them drive away all the bad things from us.

Notably, the first ṛk of Kutsa, explicitly states that the sun (bradhna) is also at at the same place as the hiding of the Moon. The sun is said to be impelled to that place by the wind — again, note an allusion to the old hypothesis of the cosmic winds moving the celestial bodies (c.f. the above ṛk of Tiraścī Āṅgirasa). This conjunction corresponds to amāvāsya or the sun and moon “dwelling together”, resulting in the new Moon (or the hiding/vanishing of the Moon). Hence, māṃścatva should be understood as the “hiding of the moon” at new Moon in all its occurrences. However, there are indications that it is a new moon with a solar eclipse. The final ṛk talks of two events, the māṃścatva and the pṛśana, i.e., the touching. We take this touching as the “contact” of the sun and Moon implying an eclipse. Moreover, the ṛk of Vasiṣṭha, states that the bradhna (usually yellow or red) is Varuṇa’s brown one from the māṃścatu. This suggests that the sun’s darkening, indicating a solar eclipse at the new moon [Footnote 1].

We also encounter the cryptic statements parallel to the ṛk-s of Tiraścī Āṅgirasa, such as the drop (Moon) running into the lake. This is also called the famous ford (tīrtha) — you can cross over to the “other side” there. We take these as allusions to the winter solstitial point on the ecliptic. Thus, we believe both Kutsa and Tiraścī are talking about the same or a similar eclipse close to the winter solstice. However, notably, in this case, it is Indra who showers snow on the enemies, putting them to “sleep” — again reminding us of the use of rain/snow stones in the Altaic warfare. Thus, the two occurrences of sneha+ and the one occurrence of snīh- in the RV indicate the use of this ancient IE word in the sense of snow. The interesting early polymorphism in the form of sneh- and snīh- suggests that the ancestral state of this word, perhaps even its form in the original dialect in which the RV was composed, was close to the ancestral Baltic version (at least the first syllable). Thus, we are probably seeing a fossil of the dialect diversity in early Indo-Aryan or Indo-Iranian itself.

To conclude, we may note, an eclipse at the solstice is a relatively rare event. However, if we give a leeway of about 5 days on either side of the winter solstice, one may get more of such events. Below is a list of such events that have happened or will happen over 3 centuries from 1801-2100 CE anywhere in the world grouped by their year lunar cycle from the catalog of Eclipse Predictions by Fred Espenak (provided by NASA):
21 Dec 1805; 20 Dec 1824; 21 Dec 1843; 21 Dec 1862
22 Dec 1870; 22 Dec 1889; 23 Dec 1908
24 Dec 1916; 24 Dec 1927
25 Dec 1935; 25 Dec 1954; 24 Dec 1973; 24 Dec 1992
25 Dec 2000; 26 Dec 2019; 26 Dec 2038; 26 Dec 2057
27 Dec 2065; 27 Dec 2084
17 Dec 2066

One can see that between 1900-2100 there have been/there are no events on the solstice day. However, in 1870 CE we had a very close pass within 12 hours of the solstice. In general, the 1800s saw several close events, but the following two centuries did not. Due to the 19-year clusters, we cannot be sure that the ones recorded in the RV were the same event. However, their relative rarity and clustering would mean that they might have been dramatic enough to leave a memory in the text.

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Footnote 1: This occurs in the context of Dadhikrāvan, who is typically invoked in the dawn ritual. We posit that Dadhikrāvan represents a heliacally rising old Vedic constellation, although its identity still remains uncertain.

Foonote 2: While its style is similar to that of the old Gotama founders like Kakṣivant and his father, the sūkta itself mentions Kakṣivant in the third person and talks of the later Gotama-s. This suggests that it was appended later to the Kakṣivant collection by one of his successors.

Foonote 3: In later Hindu tradition, the lunar and solar paths are often depicted on temple roofs as sinuous snakes.

The strange case of the Āpastamba sprite

This is the second of the two stories that arose from incidents during the visit of Yaśaśravas, Somakhya’s cousin. With the autumnal vacations, Somakhya was having a good time with his visiting cousin, giving him lectures on the theory and the practice of the study of variable stars. During the day, they spent their time with numerical solutions of differential equations that modeled the pulsations of stars. At night, they observed the stars in good view from Somakhya’s terrace with the smog of the fireworks having lifted. Additionally, as instructed by Somakhya’s father, he was also teaching Yashashravas sections of the hautra mantra-pāṭha. The on the second day of his cousin’s visit, the two of them were doing their evening saṃdhyā rituals together when Somakhya was disturbed by a peculiar behavior evinced by his cousin. In the midst of his prāṇāyāma or arghya, Yashashravas suddenly uttered the word Āpastamba-sūtra almost randomly a few times with a peculiar affectation and cadence. Somakhya was taken aback, but remembering his father’s words of never getting disturbed in his performance, he ignored it and continued to the end. Somakhya: “Yashashravas, what is wrong with you — have you gone crazy? Why were you randomly saying “Āpastamba-sūtra” in the course of your saṃdhyāvandana? I know you are of that school, but it makes no sense to pepper your upāsana with utterances of that word, moreover voiced in that strange manner.” Yashashravas felt as if some weight had lifted off his head and told Somakhya a strange tale. Somakhya was shocked by it, but once he had gathered himself, he said they should wait until his friend Lootika visited before taking any further action.

Somakhya’s mother had wished to invite Lootika’s mother and her daughters for the coming festival of Dattātreya that Somakhya’s family observed; she thought it might also be an opportunity for some socializing, given the visiting relatives. Somakhya was keen that his friend be around to deal with the case of his cousin Yashashravas and hear it from his own mouth. Yashashravas had already heard from their other cousin Babhru of his dramatic encounter with the four sisters; hence, he anticipated it with some excitement. However, Somakhya was a bit concerned that Yashashravas might clam up, feeling put off, if Lootika’s sisters were also around — they were only a little less formidable than his friend in terms of the impression they could produce on introduction, as Babhru had experienced first hand. Shortly after they arrived, Yashashravas quickly felt the edge of the sisters when Varoli, who was younger than him, gave them a little talk about Propynylidyne, Helium hydride, and Argon hydride their formation and energetics in interstellar space. However, as Somakhya had hoped, their mothers drew away the three younger sisters to look at jewelry, clothing and watch some video recording with them in another room. This gave Somakhya, Yashashravas and Lootika the solitude and time they wanted.

S: “Yashashravas, Lootika is our confidante and will be of great help in trying to get to the bottom of your predicament. You can reliably share all you need to with us. Let us lose no time and get started. For Lootika’s benefit, could you tell your story right from the beginning going back to your upanayana?”
Y: As you know, Somakhya, for a variety of reasons, my upanayana was performed about 6 years past the earliest recommended age at Kshayadrajanagara. It was a big affair, and a pity you could not be there due to the exams you had to give. However, our cousins and relatives like Babhru, Saumanasa, Mandara, Charuchitra and Varaha, as also our friend Indrasena and his brother, were all in attendance, and we had great fun. I recall one major untoward incident. The giant coconut tree in our grandfather’s house fell crashing the night after the upanayana and destroyed the maṇḍapa. Hence, we could not perform the Skanda-pūjā the next day, which is customary in our families. For three days after the upanayana, a snātaka from Kāśi, who, like me was an adherent of the Āpastamba school, was sent by the purohita who had performed your Atharvan upanayana. He taught me the correct performance of the saṃdhyopāsana along with some scholiastic material of Khaṇdadeva for several hours. On the afternoon of the fourth day after the upanayana, Indrasena and I were seated on the parapet of our grandfather’s house yarning away about something when we saw the said snātaka come. I was a bit surprised because he was supposed to come only for 3 days, and it was not yet the time for the saṃdhyā. I thought he had come by error and wanted to tell him so. So, I jumped down from the parapet and ran out of the gate towards him. He just ignored me and kept walking ahead, all the while repeatedly saying “Āpastamba-sūtra” in the same manner you heard me, most unfortunately, utter it during the saṃdhyā.

To my surprise, he just vanished at the end of the road on which our grandfather’s house stands. It turned to shock when Indrasena said that he suddenly disappeared from his sight too when I reached him. It got worse when Indrasena’s brother, Pinakasena, who was beside the gate making a tail for a kite, said that he thought we were playing some stupid prank when he saw me speaking to the air — i.e., he did not see the snātaka at all. It was all strange and funny for them, but for me, it was just the beginning of a horror story! That evening as we sat for saṃdhyā, I began jabbering “Āpastamba-sūtra” randomly in the course of the ritual. Indrasena admonished me to be serious with the ritual and did not believe it when I said that it was just involuntarily coming to me without any effort on my part. To my horror, the same thing happened when I was doing it with my father, and he blasted me for being frivolous with the ritual. I felt too embarrassed to tell him what was happening as I feared he might think I have gone mad. With great self-effort, I acquired the ability to control it to a degree and skipped sāyam-saṃdhyā if I could, for it came upon me only in the evenings. I also got some relief, albeit incomplete, when, after vedārambha, I started studying the rakṣohā mantra-s to Viṣṇu from the Taittirīya-śruti. It returned with a frenzy on the upākarmā day and completely ruined it. I told this to Babhru, who, as you know, is quite frivolous, and he responded it was a good reason to stop saṃdhyā altogether. But thereafter, he told me the unbelievable tale of when you had visited him with Lootika and her sisters and added: “maybe you should ask them to come over to your place too”. That is why I felt some relief when you mentioned that this is something you would like to handle with Lootika around.”

S: “So, Lootika, what do you think of this?”
L: “Most remarkable and ghastly. It should be quite a problem for a V1 male not to be able to perform his saṃdhyā properly. But I’m puzzled by this utterance of “Āpastamba-sūtra”. Is that something peculiar to the Āpastamba school? As you know, my family follows the Bodhāyana-sūtra, though, as far as I know, the Āpastamba-s are not very divergent, except that they have lost the proper recitation of the Śrīsūkta and the Skandayāga in its entirety.”
Somakhya smiled saying:“I know you Bodhāyana-s are pretty proud of your Śrīsūkta and Skandayāga”, even as Yashashravas intently turned his gaze from one to the other. Suddenly, Lootika excitedly remarked: “Ah! Somakhya, I remember you telling me of this particularly malevolent sprite known as the Āpastamba-graha. My gut tells me that your cousin has been seized by that.”
S: “Yes, Gautamī! This is indeed the first time I am encountering that sprite in person. Never thought we would do so in this life.”
L: “I remember you telling me that he can be particularly nasty if we try to bind him directly. So, how do we proceed against him?”
S: “We should first hear him out. We will get some clue about how to proceed from that.”
L: “Sounds exciting. Can we get him to speak with a Ḍāmara-mantra?”
S: “We can do so, but we have to take extra precautions and prepare Yashashravas for it. I also suggest that you recall the short Vīrabhadrāstra and keep it ready in your mind.”
Somakhya went to the sacristy and brought out a special svayaṃbhu-liṅga that he and Lootika had installed, some flowers, incense, a copper plate, and a long abhicārika nail. He asked Yashashravas to perform a Śivārchana of the liṇga with the following incantations:
oṃ rudrāya namaḥ । oṃ uḍḍīśāya namaḥ । oṃ sudurlabhāya namaḥ । oṃ kapardine namaḥ । oṃ virūpākṣāya namaḥ । oṃ sarva-graha-bhayāpahāya namaḥ ॥
Somakhya: “Lootika, why don’t you go out to the veranda and ready yourself to deploy the Ḍāmara-prayoga; I’ll prep Yashashravas for it in the meantime. Yashashravas, we diagnose you as being seized by a sprite known as the Āpastambagraha. The sprite had its origin in the distant past in the Marahaṭṭa country and has been spreading like a slow virus by capturing Āpastamba V1s throughout the southern half of Bhārata and beyond. Now, recall the great Mṛtyulāṅgala incantation. It is a powerful but also an extremely dangerous incantation. It is important that you periodically keep repeating it, if not daily. The biggest danger from the sprite lies in interfering with the performance and recall of this mantra — this can prove fatal to the victim. While I have never encountered an Āpastambagraha before, I have heard of such a fatality in the case of a V1 from the Andhra country. Now perform its nyāsa:
Mṛtyulāṅgalasya Vasiṣtha ṛṣiḥ । anuṣṭubh chandaḥ । Kālāgnirudro devatā ॥
Having done that do japa of it as per the form deployed by the vipraugha with the bīja-saṃpuṭi-karaṇa that I’ll specify and not the aiśa form heard in the śruti:
ṛtaṃ satyam param-brahma-puruṣaṃ kṛṣṇa-piṅgalam ।
ūrdhvaretaṃ virūpākṣaṃ viśvarūpaṃ namāmy aham ॥
oṃ krāṃ krīṃ huṃ phaṇ namaḥ ॥

Somakhya then drew a circle and asked his cousin to sit inside it and start a japa of the said mantra. He warned him that once Lootika deployed the Ḍāmara-prayoga he could go into a trance and asked him not to resist it. Lootika then came in having fortified herself for the Ḍāmara-prayoga. She was a bit nervous from the fact she was dealing with an Āpastambagraha with a nasty reputation. Somakhya told her to calm down: “Lootika, the Āpastambagraha only possesses men, but as a male graha with affiliations to the brahmarakṣas class, it does have a tendency to grab V1 females without possessing them. I suspect he would not have interest in possessing me as Āpastamba is not my primary school but he could still lash out. That’s why I think you should deploy the Ḍāmara-prayoga solo so that I can perform a shielding prayoga for you. Yet, be warned it might break through; therefore, be ready with the Vīrabhadrāstra if it tries to attack you.” Lootika then placed a neem stave on Yaśaśravas’s head and right away deployed the Grahavādini-mantra:
oṃ namo bhagavate mahākālarudrāya tripuravināśanakāraṇāya virūpākṣāya sarvabhūta-graha-vetālādhipataye rudrasyājñayā vada vada vada vada huṃ phaṭ svāhā ॥

About 3 minutes into the prayoga, they noticed that Yashashravas was slipping into a trance. A minute later, he started prattling like Aitaśa of yore, uttering the single word — “Āpastamba-sūtra” in spurts with a strange cadence. Lootika was taken aback by the first encounter with the graha, but regaining her composure, she continued with the prayoga and sprinkled some bhūti on him. He then signaled for writing material and launched into few minutes of frenzied writing. At the end of it, he just fell flat as though exhausted from heavy exercise. Somakhya sprinkled some water on him from his kamaṇḍalu, and he returned to his senses handing over the sheets of paper to his companions. “I cannot believe I wrote all that stuff down while feeling like being in an almost catatonic state.” S: “It looks like you have covered the first page with many repeats of “Āpastamba-sūtra”. Not surprising. There are parts where you seem to have doodled away in some South Indian script with its typical twisting curves that we cannot read. Yet, there seem to be coherent, understandable blocks. Could you kindly read those parts out?”

Y: “I used to be Gaṇḍalepa and was born in the Marahaṭṭa country. As a kid, I seemed to remember elements of my past janman as a great śāstrin of the Veda and was reciting the Aṣṭādhyāyi with svara-s by the time I was an year old. I started learning the Taittirīya-śruti at age 3, even before my upanayana. By age 12, I had mastered it and moved on to study the kalpasūtra of Āpastamba, the school to which my family adhered. By 15, I had earned the reputation that if paṇḍita Haradatta Miśra were alive, he would be the one studying at my feet. When I turned 18, I realized that my scholarship would not support me, and I had a wife too. I was desperate to get employment that paid better than the paltry stipend I got from the Chatrapati’s fund. By the grace of god Viṣṇu, I found sardār Khaṭāvkar, and he appointed me as his nyāyādhīśa, a job for which I was imminently suited given my authoritative knowledge of the dharmaśāstra-s. I also helped Khaṭāvkar with the commentary he was writing on some Pāñcarātrika texts. Khaṭāvkar, in turn, trained me in arms, and I became a reasonably proficient fighter.

However, Khaṭāvkar had an evil side to him, and it is perhaps partly due to the association with his unprincipled acts that this fate has come upon me. He was a partisan of the late Padishaw Awrangzeb and a good friend of Nawab Sahib Daud Pathan. One day, Nawab Sahib hatched a plan for a raid on Khargaon and asked Khaṭāvkar to help; I joined the raiding band too. During the raid, the Nawab Sahib, to his credit, instructed the men not to attack the temple of Aṣṭhabhairava in the town. However, some Afridis and Bohras in his band disobeyed his command and burnt the temple anyway. After the arson and looting, Khaṭāvkar observed that there were gold and silver utensils of the temple and decided to loot them. He was kind enough to ask me to join him and take a share of the plunder. Losing my sense of propriety, I did so. Soon after that, Khaṭāvkar met his end with the action the new Chatrapati took against him. The gods may take multiple janman-s to punish you. Indeed, Khaṭāvkar has taken at least four and is probably still experiencing the fruits of his deeds piecemeal. I was spared and, under the patronage of the courtiers, had an opportunity to perform śrauta rituals.

I became the adhvaryu for the great yajamāna Lakṣmaṇa Śāstrin and performed several rites for him. However, in the course of that, I committed acts that I should not have done. I kept out the Mādhyaṃdina-s censuring them as false V1s, and I also kept out the Ṛgvedin-s from being elected as Hotṛ-s because my Taittirīyaka associates and I could take up their role with our hautra-pariśiṣṭa-s. An enraged Ṛgvedin put a case in the court against me and my associates. We realized that we were likely to lose it. I had exorcised a graha from an associate of mine and kept it bound by my mantra-s. I decided to dispatch that graha against the Ṛgvedin so that he would stumble in his testimony at court. I did not realize that it was an Āpastambagraha. But the Ṛgvedin, Gore by name, had some mastery of the Atharvan lore or the Kashmirian pariśiṣṭa; thus he deployed a pratīchīna-prayoga. The moment he started reciting “yāṃ kalpayanti…” the Āpastambagraha came hurtling back and seized me. It interfered with my ability to remember the Mṛtyulāṅgala incantation, and I expired six months later. As is typical of these Āpastambagraha-s, they spawn a new one each time they slay a victim, and I soon became one in search of a host.

In the meantime, Nawab Sahib had been murdered by another Nawab and had come back as a liquor-seller. I hung out at his liquor-stall, making occasional conversation with him as a friendly graha. One day, a V1 named Kuṇṭe arrived there and helped himself to a few swigs. I was thus able to seize him right away and make him jabber just like you. However, before I could finish him off, he was taken by his people to the Piśācamocana-kṣetra at Kāśi, and a gaṇa of Rudra forced me to leave him. There I hung out in a tree for centuries before I could seize the snātaka who taught you, while he was at Kāśī. He had intoned the Mṛtyulāṅgala mantra while on a commode, thus, becoming easy prey for me. He died earlier that day when I seized you spawning another Āpastambagraha. Since your family had failed to protect you with the Skanda ritual, I knew I had a new host and duly took hold of you. I have not yet been able to entirely break your defenses either because you have firmly maintained your brahmacarya. But it will not be long before I’m able to bring your chapter to a close. I also intend taking this pretty girl who had the temerity to make me speak along as a slave maid for my ghostly wanderings.”

Terrified, Yashashravas handed the script back to Somakhya: “I seem to have scrawled another page full of Āpastamba-sūtra at the end … but is there a way out of this? I don’t want to go the way of the snātaka.” Just then, Lootika’s mother called her: “Lootika, we need to be going, hurry up!” L: “Mom, we are in the midst of something important; I’ll get back by myself later.” L.M: “Remember, you don’t have your bike with you, so you have to come.” Thankfully for her, Somakhya’s mother intervened: “They seem to be engrossed in their fun — so, let them be. My husband will drop her back in the evening when he takes the offerings to the Rudra-caitya.” After some wrangling, Lootika’s mother let her stay. Just as that was settled, they all felt the ground rattle as if there was an earthquake. Lootika felt her hairband snap and someone pulling her locks: “Ouch, I fear the distraction caused by my mother to my japa has resulted in him getting me.” Suddenly Lootika saw her bag creeping on the floor towards the door: “He’s going for my siddhakāṣṭha.” However, she managed to grab her bag and retrieve her siddhakāṣṭha and deploy the mantra:
huṃ drutam muñca muñca māṃ bhadrakālī-vīrabhadrau ājñapayataḥ phaṭ ॥
With that, she managed to shake off the Āpastamba-graha. S: “That is our chance. Yashashravas return to your japa.” Somakhya got out the nail and, going over to the liṅga performed a kamaṇḍalu prayoga with the mantra:
huṃ namaḥ ṣaṇmukhāya huṃ phaṭ duṣṭaṃ graham astreṇa vitudāmi pāśena kīle badhnāmi ॥

The nail leapt out of his hand and dropped on the plate with a prolonged jingle before coming to a rest. L: “That was a close brush but I believe we have him.” S: “Indeed, did you notice how he tried to dissimulate his name thinking we may use it in place of an amum in the prayoga?” L: “Hmm… I was puzzled by that and unsure if it was written in some strange script, and didn’t know what to make of it. That’s why I made sure not to use it in any prayoga.” They sprinkled some water on Yashashravas and asked him to conclude his japa with an arghya using the Mṛtyulāṅgala mantra. S: “Yashashravas, I believe you should have a smooth saṃdhyā this evening.” L: “The tale of the late snātaka indeed reminds me of the V1 who is mentioned to have been originally seized by a piśāca-graha in the tale of the Piśācamocana-tīrtha.” Later that evening, Somakhya’s father drove them to the caitya, where, after the initial darśana-s, they went to the sub-shrine of the Ātreya to deliver the offerings. Since Lootika and Somakhya had a fear of dogs, they let Yashashravas feed some curs while uttering vedo .asi ।. As he was doing so, Somakhya and Lootika ran up to the giant, ghostly aśvattha tree on the temple grounds and drove the nail into the ground at its base.

Agni as the divine commander in the Veda and the Purāṇa

With the Sākamedha-parvan with the oblations to Agni Anīkavat having just passed, we present a brief note on Agni as the general of the deva army. Agni is presented as the commander of the deva-s in the brāhmaṇa literature. For example, the Śatapatha-brāhmaṇa of the Śuklayajurvedin-s makes the below statement in regard to the ratnin oblations, which are made in houses of the various functionaries of the old Indo-Aryan state. With regard to the oblation to Agnī Anīkavat we hear:

araṇyor agnī samārohya senānyo gṛhān paretyā + agnaye .anīkavate aṣṭhā-kapālam puroḍāśaṃ nirvapati । agnir vai devatānām anīkaṃ senāyā vai senānīr anīkaṃ tasmād agnaye ‘nīkavate । etad vā asyaikaṃ ratnaṃ yat senānīs tasmā evaitena sūyate । taṃ svam-anapakramiṇaṃ kurute । (in Mādhyaṃdina SB 5.3.1 in Kāṇva SB 7.1.4)
Having taken up the two fires (Gārhapatya and Āhavanīya) on the two kindling-sticks, having gone to the house of the commander of the army, he prepares a cake on eight potsherds for Agni Anīkavat. Agni is indeed the leader (anīka) of the gods, and the commander is the head of the army: hence, for Agni Anīkavat. He, the commander, is verily one of his (the king’s) gems. Therefore, for him [the king], he [the commander] is thus consecrated. He [the king] makes him [the commander] his own follower.

Again, in the Gopatha-brāhmaṇa we have the following statement regarding the offering to Agni Anīkavat in the context of the Sakamedha oblations:

aindro vā eṣa yajña-kratur yat sākamedhāḥ । tad yathā mahārājaḥ purastāt senānīkāni vyuhyābhayaṃ panthānam anviyād evam evaitat purastād devatā yajati । tad yathaivādaḥ somasya mahāvratam evam evaitad iṣṭi-mahāvratam । atha yad agnim anīkavantaṃ prathamaṃ devatānāṃ yajati । agnir vai devānāṃ mukham । mukhata eva tad devān prīṇāti । (in GB 2.1.23)
These Sākamedha-s are verily that of Indra. Just as the emperor placing the commanders in the head of his army-formations advances unchecked on his path, so also, he (the ritualist) sacrifices placing the deities to the front. Just as there is the Mahāvrata of the soma sacrifices, this is the [equivalent of the] Mahāvrata for the iṣṭi-s. Now, in that, he sacrifices to Agni Anīkavat (the commander), the first of the deities. This Agni is indeed the mouth of the gods. Thus, he pleases the gods through their mouth.

As an aside, we may note that the Atharvavedic tradition sees the Sākamedha oblations as the equivalent of the Mahāvrata-s for the iṣṭi cycle. The Mahāvrata is performed at the winter solstice. The Sākamedha on the Kārttika full moon is the last full moon in autumn before the winter solstice. Hence, the two are seen as being equivalent. Now, this role of Agni as the commander of the gods is already hinted at by multiple incantations in the Ṛgveda (reproduced in the Atharvaveda) itself. For example, we have:

agnir iva manyo tviṣitaḥ sahasva senānīr naḥ sahure hūta edhi । RV 10.84.2a
Blazing like Agni, o battle fury, conquer! Our commander, the conqueror when you are invoked at the kindling.

Here Manyu (the battle fury) is implied to lead the forces, like commander Agni. We may also consider one of the Agni Anikavat incantations Atri-s:

uta svānāso divi ṣantv agnes
tigmāyudhā rakṣase hantavā u ।
made cid asya pra rujanti bhāmā
na varante paribādho adevīḥ ॥ RV 5.2.10
Also, in heaven, let there be the roars of Agni
with [his] sharp weapons for the smiting of rakṣas-es.
Indeed, in his exhilaration, his fury smashes forth,
the defense of the ungodly do not contain him.

Finally, we also have the famous Rakṣohā Agni incantations of Vāmadeva Gautama (RV 4.4.1-5), which present the most exalted account of Agni’s war-like nature in the entire śruti [Footnote 1]:

kṛṇuṣva pājaḥ prasitiṃ na pṛthvīṃ
yāhi rājevāmavāṃ ibhena ।
tṛṣvīm anu prasitiṃ drūṇāno .
astāsi vidhya rakṣasas tapiṣṭhaiḥ ॥ 1
Make your charge like a broad front.
Move forth like a mighty king with his troops,
thirsting to charge forth slaying,
You are an archer: pierce the rakṣas-es with the hottest missiles.

tava bhramāsa āśuyā patanty
anu spṛśa dhṛṣatā śośucānaḥ ।
tapūṃṣy agne juhvā pataṅgān
asaṃdito vi sṛja viṣvag ulkāḥ ॥ 2
Your swirling [weapons: cakra-s implied] fly swiftly;
touch down on [the foes] impetuously blazing.
O Agni, with your tongue [hurl] blasts of heat, flying [sparks]
unstopped hurl forth firebrands all around.

prati spaśo vi sṛja tūrṇitamo
bhavā pāyur viśo asyā adabdhaḥ ।
yo no dūre aghaśaṃso yo anty
agne mākiṣ ṭe vyathir ā dadharṣīt ॥ 3
Send out spies against (the foes). He is the fastest.
Become the uncheated protector of these people.
Whoever wishes us evil from a distance, whoever from nearby,
O Agni, may no one (enemy) evade your meandering course.

ud agne tiṣṭha praty ā tanuṣva
ny amitrāṃ oṣatāt tigmahete ।
yo no arātiṃ samidhāna cakre
nīcā taṃ dhakṣy atasaṃ na śuṣkam ॥ 4
O Agni stand up, stretch your bow against [our enemies],
Burn down the foes, o one with a sharp weapon.
Whoever makes hostile moves at us, o kindled one,
burn him down like dry shrubs.

ūrdhvo bhava prati vidhyādhy
asmad āviṣ kṛṇuṣva daivyāny agne ।
ava sthirā tanuhi yātujūnāṃ
jāmim ajāmim pra mṛṇīhi śatrūn ॥ 5
Rising upwards, jabbing against [the foes, pushing them]
away from us; make your divine powers apparent.
Slacken the taut [bows] of those incited by yātu-s,
be they kin or non-kin slay forth the enemies.

In the transition between the Vedic and Epic phases of the Hindu literary activity, the role of Agni as the commander of the gods was transferred to his son Kumāra, effectively also the son of Agni’s dual Rudra. The stage for this is set deep in the śruti itself. As noted before, the Kaumāra mythology is closely tied to the famous sūkta of the Atri-s we mentioned above (RV 5.2). Already in the fragmentary Vedic tradition of the Bhāllavi-s, we see the hint of this connection in the deployment of the ṛk-s from RV 5.2 by Vṛśa Jāna for the Ikṣvāku ruler Tryaruṇa. The Śatapatha-brāhmaṇa, explaining the duality of Agni and Rudra, explains that the 8 forms of Rudra culminating in the supreme Īśāna, the lord of all, are the 8 transformations of Agni, with Kumāra as the 9th, evidently alluding to the very same sūkta of the Atri-s:

tāny etāny aṣṭāv agni-rūpāṇi । kumāro navamaḥ saivāgnis trivṛttā ॥ Mādhyaṃdina SB 6.1.3.18
These then are the eight forms of Agni (Rudra, Śarva, Paśupati, Ugra, Aśani, Bhava, Mahādeva, Īśāna). Kumāra (the boy) is the ninth: that is Agni’s threefold state (i.e., 3 3).

This sets the stage for the final ninth form as the son of Rudra-Agni. In this process, Kumāra also inherited to connection to the old equinoctial connection to the constellation of Agni, i.e., Kṛttikā-s – he is also their son, Kārttikeya. Also contributing to the identity of the para-Vedic Kumāra are the aspects of the Vedic sons of Rudra, the Marut-s, who are also seen as leaders of the deva army. For instance, in the Apratiratha Aindra sūkta we have:

devasenānām abhibhañjatīnāṃ jayantīnām maruto yantv agram ॥ RV 10.103.8c
May the Maruts go at the forefront of the shattering, conquering armies of the gods.

Notably, the Maruts are repeatedly referred to as Agni-s (e.g., agnayo na śuśucānā ṛjīṣiṇo bhṛmiṃ dhamanto apa gā avṛṇvata । RV 2.34.1c; na yeṣām irī sadhastha īṣṭa āṃ agnayo na svavidyutaḥ pra syandrāso dhunīnām । RV 5.87.3c; te rudrāsaḥ sumakhā agnayo yathā tuvidyumnā avantv evayāmarut ।RV 5.87.7a; ye agnayo na śośucann idhānā dvir yat trir maruto vāvṛdhanta । RV 6.66.2a). This completes the circle of the connection between Agni and the sons of Rudra, who are the spear-wielding heroes of the deva army.

However, there are rare instances in the itihāsa-purāṇa corpus that furnish descriptions of the martial Agni mirroring his role as commander of the divine army in the śruti. We provide snippets of such accounts below from the third section of the Harivaṃśa, the Bhaviṣya-parvan (sometimes called Appendix I). The first snippet is from the narration of Agni leading the gods in the battle against the daitya Balin, who was subsequently trampled by Viṣṇu:

lohito lohitagrīvo hartā dātā haviḥ kaviḥ ।
pāvako viśvabhug devaḥ sarva-devānanaḥ prabhuḥ ॥
subrahmātmā suvarcaskaḥ sahasrārcir vibhāvasuḥ ।
kṛṣṇavartmā citrabhānur devāgryaś citra ekarāṭ ॥
lokasākṣī dvijahuto vaṣaṭkāra-priyo ‘rcimān ।
havyabhakṣaḥ śamīgarbhaḥ svayoniḥ sarvakarmakṛt ॥
pāvanaḥ sarvabhūtānāṃ tridaśānāṃ taponidhiḥ ।
śamanaḥ sarvapāpānāṃ lelihānas tapomayaḥ ॥
pradakṣiṇāvarta-śikhaḥ śucilomā makhākṛtiḥ ।
havyabhug bhūtabhavyeśo havyabhāgaharo hariḥ ॥
somapaḥ sumahātejā bhūteśaḥ sarvabhūtahā ।
adhṛṣyaḥ pāvako bhūtir bhūtātmā vai svadhādhipaḥ ॥
svāhāpatiḥ sāmagītaḥ somapūtāśano ‘dridhṛk ।
devadevo mahākrodho rudrātmā brahmasaṃbhavaḥ ॥
lohitāśvaṃ vāyucakraṃ ratham āsthāya bhūtakṛt ।
dhūmaketur dhūmaśikho nīlavāsāḥ surottamaḥ ॥
udyamya divyam āgneyam astraṃ devo raṇe mahat ।
dānavāṇāṃ sahasrāṇi prayutāny arbudāni ca ॥
dadāha bhagavān vahniḥ saṃkruddhaḥ pralaye yathā ।
prāṇo yaḥ sarvabhūtānāṃ hṛdi tiṣṭhati pañcadhā ॥
Red, red-necked, the destroyer, the giver, the oblation, the poet;
The purifier, all-consuming, the god, the mouth of the gods, the lord;
The soul of mantras, brilliant, thousand-rayed, full of light;
With black tracks, with wonderful rays, the leader of the gods, beautiful, the sole ruler;
The witness of the worlds, invoked by twice-born, delighting in the vaṣaṭ call, bright;
The oblation-eater, dwelling in wood, self-reproducing, doer of all acts;
The purifier of all beings, the wealth of the gods’ tapas;
The suppressor of sins, with a flickering tongue, full of heat;
With helical swirling flames, bright haired, of the form of ritual;
The oblation-eater, lord of past and future, the partaker of the ritual share, yellow;
The soma-drinker, of good great luster, the lord of beings, the slayer of all beings;
The unassailable one, the purifier, the power, verily the core of beings, Svadhā’s husband;
Svāhā’s husband, the Saman song, the filtered-soma consumer, holding the [soma]-pounding stone;
The god of gods, of great wrath, of nature of Rudra, born of incantations;
Having mounted the chariot drawn by red horses with wind-wheels, the maker of beings,
the smoke-bannered, the smoke-tufted, blue-clothed one, foremost of the gods,
having raised the divine Āgneya missile in battle, the great god
burnt down thousands, millions and tens of millions of dānava-s,
like in the cosmic dissolution, the enraged lord of fire;
He, who is the metabolism of all organisms, situate five-fold in their hearts.

The second short snippet alludes to Agni’s weapons and the manifestation of the other gods with their weapons. This comes from the narration of the fruits of the tapasya of the deities and presents the appearance of Agni within the frame of the old Vedic ritual of the churning out of the fire in the manner of the Atharvan-s of yore:

atha dīkṣāṃ samāsthāya sarve viṣṇumayā gaṇāḥ ।
puṣkarād agnim uddhatya praṇīya ca yathāvidhi ॥
juhuvur mantravidhinā brāhmaṇā mantracoditāḥ ।
haviṣā mantrapūtena yathā vai vidhir eva ca ॥
sa cāgnir vidhivat tatra vardhate brahmatejasā ।
tejobhir bahulībhūtaḥ prabhuḥ puruṣavigrahaḥ ॥
brahma-daṇḍa iti khyāto vapuṣā nirdahann iva ।
divya-rūpa-praharaṇo hy asi-carma-dhanurdharaḥ ॥
gadī ca lāṅgalī cakrī śarī carmī paraśvadhī ।
śūlī vajrī khaḍgapāṇiḥ śaktimān varakārmukī ॥
viṣṇuś cakradharaḥ khaḍgī musalī lāṅgalāyudhaḥ ।
naro lāṅgalam ālambya musalaṃ ca mahābalaḥ ॥
vajram indras tapoyogāc chataparvāṇam ākṣipat ।
rudraḥ śūlaṃ pinākaṃ ca tapasā-dhārayat prabhuḥ ॥
mṛtyur daṇḍaṃ pāśam āpaḥ skandaḥ śaktim agṛhṇata ।
jagrāha paraśuṃ tvaṣṭā kuberaś ca paraśvadham ॥
Having taken the dīkṣā for ritual all the troops [of V1s] imbued with Viṣṇu, churned out Agni from the [lotus/] pond [Footnote 2] and led him forth as per the injunctions [Footnote 3]. Invoked by the brāhmaṇā-s as per the Vedic instructions, and inspired by mantra incantations, and [fed with] offerings purified with mantra-s verily as per the injunctions, he, Agni, as per tradition, blazed forth there with brahman luster. The lord, having become manifold with rays, became anthropomorphic. He is known as the rod of brahman, appearing as though burning [all] with his body. With weapons of divine form, indeed holding a sword, shield and bow. With a mace, plowshare, discus, arrow, shield, battle-pickax, trident, thunderbolt, he is sword-armed and wields a lance and an excellent bow. Viṣṇu is armed with a discus, sword, pestle and a plowshare. Nara of great might is armed with a plowshare and a pestle [Footnote 4]. United with tapas, Indra strikes with the thunderbolt of a hundred edges. The lord Rudra by tapas has taken up the trident and Pināka [Footnote 5]. Yama took the rod, Varuṇa (literally waters), the lasso and Guha the lance [Footnote 6]. Tvaṣṭṛ took up an ax and Kubera a battle-pickax.

While the paurāṇika tradition presents accounts of several of the ancient battles between the deva-s and the daitya-s, all surviving versions aim to downgrade the pantheon as represented in the old Aryan layer of the religion for magnifying their sectarian deities. Nevertheless, we believe that the paurāṇika tradition preserves relatively unmodified fragments from an older layer of narratives. This is supported by the sharing of phrases with the old tradition (e.g., vajraḥ śataparvaṇaḥ or kṛṣṇavartman) and the fact that above snippets are replete with Vedic allusions and metaphors. Both these snippets present Agni in his old martial form; the first might be seen as mirroring and augmenting the presentation of Agni in the famous kṛṇuṣva pāja iti pañca incantations, while the second mirrors his emergence, upon being churned out, presented in the above-mentioned sūkta of the Atri-s. Thus, even with all the religious turnover, some of the primal imagery from the old Aryan past continued relatively unchanged in the paurāṇika tradition.

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Footnote 1: Notice the Vedic device of ring-linking in structuring sūkta-s with old IE roots. The words kṛṇuṣva…vidhya from the first are repeated in reverse order in the fifth of the kṛṇuṣva pāja iti pañca as vidhyādhy…kṛṇuṣva to complete the classic ring. Then an intricate network is formed by other linkages; for example: in the first ṛk, the two hemistiches are linked by prasitim. In the second ṛk, they are linked by the root patan+. Then 1 and 2 are linked by the root tap+; prati links 3, 4, 5; 4 and 5 are linked by the root tan+ and so on. For a complete graph, see Figure 1. Such intricate weaving is especially typical of magical incantations, c.f. the Apratiratha Aindra.

Figure 1.

Footnote 2: This is modeled after the action of the primordial Atharvan, which is mentioned to in the śruti:  tvām agne puṣkarād adhy atharvā nir amanthata । RV 6.16.13a. This is a likely allusion to the fire within water found in the regions closer to the homeland of the early Indo-Europeans.

Footnote 3: The Vedic ritual of Agni-praṇayana with the recitation of the Hotṛ and the carrying forth of the wooden sword along with the fire to the mahāvedi.

Footnote 4: The coupling of Nara and Viṣṇu situates this narration with the Nara-Nārāyaṇa tradition of the epic Vaiṣṇava religion where it is often juxtaposed with the more prevalent Sātvata tradition. This verse hints at their “merger” by furnishing Nara with the iconography of the Sātvata Saṃkarṣaṇa.

Footnote 5: The Pināka should be correctly understood as the bow of Rudra.

Footnote 6: This hemistich has many readings. e.g., The Gītā press text reads:  mṛtyur daṇḍaṃ pāśam āpaḥ kālaḥ śaktimagṛhṇata ।; The Pune reading from Parashuram Lakshman Vaidya reads: mṛtyur daṇḍaṃ sapāśaṃ ca kālaḥ śaktim agṛhṇata । We take an uncommon southern reading which more congruent with regard to the weapons and the gods.

The birth defects of Dhṛtarāṣṭra and Pāṇḍu and related matters

This note has its origin in a conversation with Sharada. We originally intended to incorporate the core of it into one of our usual fantastical stories. However, following a second conversation with her, we decided that it might be best to present it as a note of its own.

Vyāsa Pāraśarya was the author of our national epic, the Bhārata, in more than one way: he first sired the protagonists, and then he recorded their history as it played out. The queen Satyavatī had extracted a promise from her husband Śantanu that her son and not his older son Bhīṣma would take the throne of Hastināpura. However, to her bad luck, both her sons via Śantanu, Citrāṅgada and Vicitravīrya, died shortly after ascending the throne — an eponymous gandharva slew Citrāṅgada at Kurukṣetra and Vicitravīrya contracted tuberculosis and perished before fathering any children. He left behind his widows Ambikā and Ambālikā. Distraught, Satyavatī first asked her stepson Bhīṣma to father children on the widows; however, he refused to break the vow of celibacy he had taken for Śantanu to marry her. Before her marriage to Śantanu, Satyavatī was a boat-woman from a fisher clan who ferried people across the Yamunā. In course of her duties, she once had to ferry the great brāhmaṇa, Parāśara of the Vasiṣṭha clan. He was smitten by her beauty and started wooing her with sweet words during the boat ride. She was caught in the dilemma of her father’s wrath if she went with him and the brāhmaṇa’s curse if she refused. However, the boon he offered convinced Satyavatī to consort with him. He enveloped the region in a mist with his magical powers, and they engaged in coitus. As a result, they had a son, the illustrious Vyāsa Pāraśarya, the editor of the Veda-s and the composer of the Bhārata. Thereafter, Parāśara restored her virginity and gave her the boon by which a pleasant perfume replaced her fishy odor. Vyāsa went with his father, and Satyavatī continued as a boat-woman until her marriage to the king Śantanu. Now in this hour of need, she summoned her first son Vyāsa and asked him to sire children on her widowed daughters-in-law. Vyāsa agreed but stated that the Kausalya princesses should undergo an year of preparatory rites before engaging in coitus with him. However, fearing the dangers of a kingless state, Satyavatī pressed her son to inseminate them immediately.

Evidently, from his being a yogin performing tapas, Vyāsa was in an uncouth state with yellowish-brown dreadlocks, unshaven face and body odor. Thus, when he had intercourse with Ambikā, she closed her eyes not to see his grim visage. As a result of this “impression” of hers, Vyāsa told Satyavatī that Ambikā’s son would be duly born blind despite having the strength of 10000 elephants. Satyavatī beseeched Vyāsa to father another child, as a blind child could not be a king. This time he had intercourse with Ambālikā, who, looking at his dreadful appearance, turned pale. Accordingly, she gave birth to a hypopigmented child. Satyavatī then asked Vyāsa to bed Ambikā again. But remembering his terrifying appearance, she instead sent her slave whom she had decked with her own ornaments. The slave engaged in comfortable coitus with Vyāsa, and he manumitted her and said that she would have a brilliant son who would be the most intelligent of the men of the age. Thus were born the blind Dhṛtarāṣṭra, the blanched Pāṇḍu and the wise Vidura. Pāṇḍu’s troubles did not end with the absence of pigment. After his marriage, while living a sylvan life with his wives, he shot a brāhmaṇa and his wife while they were having intercourse in the form of deer. The brāhmaṇa duly cursed Pāṇḍu that he would too die as soon as he has sex with one of his wives and that wife too will meet her end with him. This is the platform story for the unfolding of the Bhārata, with the birth of Pāṇḍu-s through the intercession of the gods.

One may ask what is hidden behind the mythologem of the birth defects of Dhṛtarāṣṭra and Pāṇḍu? If one were to take a strongly historical position, one could argue that they probably were afflicted by a genetic defect. They could have had something like a variably expressive version of Waardenburg’s syndrome or the Hermansky-Pudlak syndrome, which are associated with both blindness and hypopigmentation. However, the language of myth has many layers. Beyond the historical layer, the Bhārata clearly conceals divine archetypes. These are best seen in the case of the Pāṇḍu-s but as the final parvan mentions, it applies more broadly to the other characters. We suspect that the background of Āditya-s was implied to be present in Dhṛtarāṣṭra and Pāṇḍu, with Vidura representing the joint Mitrāvaruṇā manifesting as dharma. This suggests that the blind Dhṛtarāṣṭra perhaps represents Bhaga (a continuation of the ancient Indo-European blind deity motif also seen in the Germanic Höðr) and the white Pāṇḍu combining the pale solar aspect of Vivasvān and still-born Mārtāṇḍa, which comes forth in greater Germania as the opposite of the blind Höðr, the white Baldr.

Finally, this mythologem also preserves a peculiar “para-medical” motif, namely the “maternal impression”. While not seen as a real thing in modern biology, there is a widespread belief that experiential impressions on the mother during pregnancy might translate into birth defects or birthmarks in her child. At some point, when we were re-reading the Bhārata, we realized that the legend of Dhṛtarāṣṭra and Pāṇḍu was embedding within it this prevalent pre-modern belief in maternal impression. Briefly, this view holds that ghastly sights of amputations or deformities seen by the mother in real life, or in a dream, or bodily transformations of the mother (like Ambikā’s closing of her eyes or Ambālikā’s blanching) from fear or dohada (dauhṛda)-s (satisfied or unsatisfied pregnancy cravings) might on occasion transmit congruent or similar defects/marks to the developing fetus. We did not pay much attention to it, but noted a parallel to the dohada of the mother of the great Chāhamāna hero Hammīradeva reported in the Hammīra-mahākāvya: she had a craving to have a bath in the blood of marūnmatta-s when pregnant with him and that is said to have conferred on him the fury that he manifested when manfully facing the monstrous Army of Islam.

However, beyond that, we mostly set aside these mythic motifs until we had a discussion with a late German professor in graduate school. He brought to our notice a peculiar story reliably narrated by the great Russo-German biologist Karl Ernst von Baer, a pioneer in the evolutionary theory and embryology. Von Baer’s sister saw a fire when looking out while she was about 6-7 months pregnant and thought that her house in the distance was burning. She became obsessed with that fire and kept seeing a vision of it constantly before her eyes until she gave birth to a daughter in due course. Interestingly, her daughter had a red birthmark on her forehead that took the shape of a flame that lasted until she was 7 years of age. I was bemused by this case of “maternal impression” close to our age, that too presented by a pioneer in embryology, whose own work should have suggested that this is unlikely. The late German professor mentioned to us that it is possible that it had some connection to von Baer’s peculiar ideas of a “teleological” force that influenced his version of the evolutionary theory.

Our conversation with Sharada brought to our attention the presence of contemporary belief in “maternal impression” relating to birth deformities and also reminded us of one of the morbid tales that our late grandmother and her relatives liked talking about, which involved such a motif. The possibility of a cross-cultural and temporal presence of this idea made us explore it a bit more. This led us to the work of the famous Canadian physician Ian Stevenson, who is well known for investigating strange things like ghosts, reincarnation, and the like. He had performed a detailed comparison of the published cases of such “maternal impressions” and uncovered some strange cases himself. One such notable case that he details is from Lankā, where a certain Siṁhala rowdy was killed by his adversaries, who chopped off both his hands. It was said that the rowdy’s mother then invoked Viṣṇu and Skanda to bring such a fate upon the child of his killer and repeatedly cursed the killer’s wife that she would have a deformed child. Subsequently, the assailant’s wife gave birth to a son lacking arms – a birth defect closely paralleling the amputations the rowdy was subject to. The deformed child died within an year or two of birth. Stevenson stressed that the deformities, of which he produced a photograph, were unusual and that there was no history of genetic defects in the family as far as his extensive investigations could tell.

In a detailed study, Stevenson gathered at least 50 cases that he considered reliable (they corresponded to rare defects, and in his estimation, in 46 of the 50 cases the similarly rare maternal impression corresponded very closely to the lesion in the neonate) and analyzed them for general tendencies. In 41/50 cases, he reported the pregnant mother directly seeing or hearing about a lesion (which may be a wound, surgery, or something else) in another person. In 6 cases, she experienced something on herself — these are more comparable to those of the Kausalya princesses of our national epic. Stevenson describes some of the cases in greater detail. One was reported in the British Medical Journal in 1886. Here a woman in the 4th month of her pregnancy dreamt that a rat had bitten off the great toe of her right foot. Consequently, “she awoke screaming, and narrated the cause of her fright to her husband, who corroborated her statement”. When she delivered her child, it lacked the very same great toe she lost in her dream. This case may be compared to the examples of Kausalya princesses, in that the impression was not the sight of a lesion in someone else but in the mother. However, the one distinguishing feature of the epic example is that the premonitory impression happened at conception rather than pregnancy proper.

By considering an additional set of less reliable cases, Stevenson drew up a more extensive list of 113 cases of maternal impressions. In this set, he found 80 cases with the impression in the first trimester, 20 in the second, and 13 in the third, which, as he noted, is a statistically significant difference . The significant over-representation in the first trimester is aligned with that period being the most susceptible period in pregnancy for birth defects from biological causes. For example, it is well-known that severe alcohol abuse during the first trimester can disrupt the development of the head, resulting in birth defects. Similarly, studies on the teratogenicity of high (>10000 IU) doses of vitamin A suggest that birth defects were concentrated among the babies born to women who had consumed it before the seventh week of gestation. Importantly, it maps to the period when morning sickness is most prevalent, which itself seems to be an adaptation to protect the fetus in early development from potentially teratogenic compounds in the food. Thus, it also corresponds to the peak period of defects from the ubiquitination-activating drug thalidomide that was wrongly used to treat morning sickness (we shall return to its action below).

From Stevenson’s cases, which are mostly from Occidental cultures and relatively close to our times (1700-1900s), it became clear that the idea of maternal impression is indeed a widespread cross-cultural one with arborizations into other “mystery” phenomena like abhicāra and reincarnation. This made us revisit the old Hindu medical tradition to consider the positions they held in this regard. As a representative, we may consider one of the great authoritative texts of early Hindu medicine: the Śarīra-sthāna of the Suśruta-saṃhitā, which starts of with an ancient theory of being. Following the sāṃkhya tradition, it lays out that from the primordial matter prakṛti, various organs constituting the body arose. While these organs are seen as being made up of matter (bhautika adhibhūta), i.e., transformations (vikārāḥ) of prakṛti, they are said to have mapping on the realm of consciousness (adhyātma) and the sphere of the gods (adhidaivata; which cuts across the material and conscious realms in a “Platonic sense”). This mapping to the gods derived from the Yajurveda (with some parallels to the puruṣa-sūkta-s and central to the nyāsa-s of later tradition) is stated thus in Suśruta:

sva svaś caiṣāṃ viṣayo .adhibhūtam | svayam adhyātmam adhidaivtaṃ ca | atha buddhe brahmā | ahaṃkārasyeśvaraḥ | manaś candramā | diśaḥ śrotrasya | tvaco vāyuḥ | sūryaś cakṣoḥ | rasanasya+āpaḥ | pṛthivī ghṛāṇasya | vaco .agniḥ | hastayor indraḥ | pādayor viṣṇuḥ | pāyor mitraḥ | prajāpatir upasthyeti | tatra sarva evācetana eṣa vargaḥ | puruṣaḥ pañcaviṃśatitamaḥ sa ca kārya-kāraṇa-saṃyuktaś cetayitā bhavati ||
The mapping is thus: Brahmā: intellect; Īśvara (Rudra): I-ness (personal identity); Moon: mind; directions: hearing; Vāyu: skin; Sun: eyes; waters: tongue; Earth: nose; Agni: vocal system; Indra: prehensile organs; Viṣṇu: locomotory organs; Mitra: excretory organs; Prajāpati: reproductive organs. The final sentence clarifies that while the evolutes of prakṛti are by themselves unconscious, the 25th tattva, puruṣa, enters the primal cause (prakṛti) and its evolutes and endows them its nature consciousness. We layout this sāṃkhya foundation of Hindu medicine because it is via that intersection of the realm of consciousness and matter that it tries to explain things that would be seen as “supernatural” in a modern sense.

The Hindu medical tradition (like that recorded by Suśruta) has a proto-biological understanding of specific issues generally pointing in the right direction:
(1) Unlike the folk idea prevalent in the Indo-European world of the sperm being a seed sown in the vagina/uterus, it understood that there was a biological contribution from both the parents. In the case of the male, it saw that as coming from the semen. That contribution was not visible in the female, but it postulated an ārtava — a theoretical ovum.
(2) It did recognize that there was some sex-determining principle coming from the semen and the ārtava, though the exact nature of it was imperfectly understood.
(3) It recognized a “proto-genetic” principle wherein the parents’ postulated contributions gave rise to different organs in the embryo.
(4) It presented a primitive theory based on “biochemical expressions” in the developing embryo for various birth defects (including those comparable to Pāṇḍu and Dhṛtarāṣṭra), atypical sexuality and pigmentation differences.

However, superimposed on this essentially biological foundation (sometimes with pioneering insights) is a belief in different forms of extra-biological impressions. The roles of the various processes involved and their effects are voiced by Suśruta thus:

san niveśaḥ śarīrāṇāṃ dantānāṃ patanodbhavau |
taleśv asaṃbhavo yaś ca romṇām etat svabhāvataḥ ||
The development of the organs in their proper locations, the fall of [milk] teeth, and the growth [of permanent teeth], non-growth of hair in palms and feet all are [examples] of development as per the natural law [for that organism].

Thus, Suśruta and other authorities acknowledge that basic human development is as per a natural law — i.e., a purely biological process typical of a given species. However, immediately thereafter, he cites śloka-s that goes on to describe a very different hypothesis regarding mental traits:

bhāvitāḥ pūrvadeheṣu satataṃ śāstra-buddhayaḥ |
bhavanti sattva-bhūyiṣṭhāḥ pūrva-jāti-smarā narāḥ ||
Those constantly conditioned in the former bodies by the study of the śāśtra-s become [even in the current birth] men endowed in sattva remembering the former birth.

karmaṇa codito yena tadāpnoti punarbhave |
abhyastāḥ pūrvadehe ye tāneva bhajate guṇān ||
Impelled by acts which he has performed [in the former birth], a person attains his [state] in the reincarnation. Those activities which were repeatedly practiced in the former body are also shared by the [current one].

Thus, there was a belief that mental traits transmitted via reincarnation from the previous birth, like an inclination toward good learning, and behavioral tendencies acquired by constant practice, were superimposed on the basic biological development (mentioned above). Combined with the reincarnational effect (which parallels beliefs in most human cultures across the world) were various beliefs that may be considered as belonging to the domain of maternal impression. One of these is believed to act at the time of conception or just before that, as was the case with Ambikā and Ambālikā. An old verse cited by Suśruta records such a belief:

pūrvaṃ paśyed ṛtu-snātā yādṛśaṃ naram aṅganā |
tādṛśaṃ janayet putraṃ bhartāraṃ darśayed ataḥ ||
Whoever is the first man the woman may see after her purificatory bath following her menstruation, the child she births resembles him; hence, she must see her husband.

The commentators add that if her husband is not around at the moment, she should see the sun. Thus, the impression of the first man she sees is said to determine the child’s appearance. The old Hindu medical tradition also records a variety of alternative causes for birth defects, some biological and other “impressional”:

garbho vāta-prakopeṇa dauhṛde vāvamānite |
bhavet kubjaḥ kuṇiḥ paṅgur mūko minmina eva vā ||
A fetus suffering insults from the derangement of vāta (one of the three basic bodily processes of old Hindu physiology humors of Greek physiology) or due to the [unfulfilled] maternal cravings (dauhṛda), may indeed become hunchbacked, defective in the arms, defective in the legs, dumb, or nasal-voiced.

mātā-pitro .astu nāstikyād aśubhaiś ca purākṛtaiḥ |
vātādīnāṃ ca kopena garbho vikṛtim āpnuyāt ||
From the mother or father being counter-religious or due to their inauspicious ways or from their misdeeds in a past incarnation or from the derangement of the vāta and the like the fetus acquires birth-defects.

Thus, while a proximal physiological cause (i.e., the derangement of the doṣa-s) is offered, meta- or “supernatural” causes are also suggested in the form of unfulfilled maternal cravings and the “impressions” of the inappropriate ways of the parents in the current and past incarnations. For the maternal cravings, the Hindu proto-scientists presented a purely physiological hypothesis within the context of embryological development:

tatra prathame māsi kalalaṃ jāyate | dvitīye śītoṣmānilair abhiprapacyamānānāṃ mahābhūtānāṃ saṃghāto ghanaḥ saṃjāyate | yadi piṇḍaḥ pumān strī cet peśī napuṃsakaṃ ched arbudam iti | tṛtīye hasta-pāda-śirasāṃ pañca-piṇḍakā nirvartante | aṅga-pratyaṅga-vibhāgaś ca sūkṣmo bhavati | caturthe sarvāṅga-vibhāgaḥ pravyaktaro bhavati | garbha-hṛdaya-pravyakti-bhāvāc cetanā-dhātur abhivyakto bhavati | kasmāt? tat sthānatvāt | tasmād garbhaś caturthe māsy abhiprāyam indriyārtheṣu karoti | dvihṛdayāṃ ca nārīṃ dauhṛdinīṃ ācakṣate | dauhṛda-vimānanāt kubjaṃ kuṇiṃ khañjaṃ jaḍaṃ vāmanaṃ vikṛtākṣam anakṣaṃ vā nārī sutaṃ janayati | tasmāt sā yad icchet tat tasyai dāpayet | labdha-dauhṛdā hi vīryavantaṃ cirāyuṣaṃ ca putraṃ janayati ||
There (in the womb), in the first month, a bag-like structure emerges. In the second, starting with metabolic action of the three (śītoṣmānila) physiological processes, the molecular combinations of the primal elements comprise a condensed structure. The presence of a lump-like structure indicates a male; a bud-like structure a female; a tumorous mass, an intersex. In the third, 5 lump-like forms of the hands, legs and head develop. The incipient divisions of the various organs and their subdivisions come into being. In the fourth, the substructures of all the organs become clearly apparent. From the full development of the fetal heart, the substance of consciousness becomes apparent. How so? From the heart being the receptacle [of consciousness]. Thus, in the fourth month, the fetus displays agency for the organs to apprehend/elicit their stimuli/actions. There are two hearts (one of the fetus and one of the mother), and from that the pregnant woman is known to be two-hearted [thus, the maternal cravings]. Hence, unfulfilled maternal cravings result in the woman giving birth to an offspring that may be hunchbacked, defective in the hands, defective in the legs, mentally defective, dwarfed, with deformed eyes or eyeless. Therefore, one must satisfy her cravings as she wishes. Indeed, the woman with satisfied cravings births a virile and long-lived son.

Thus, the Hindu hypothesis of maternal cravings stems from the old belief that the heart is the seat of consciousness [Footnote 1]. Thus, the full development of the heart causes the organs of the fetus to seek their stimuli (jñānendriya-s) or actions (karmendriya-s). These are expressed via the mother resulting in maternal cravings. The hypothesis further posits that non-fulfillment of these results in defects in the fetus. We still do not fully understand the causes for maternal cravings or their adaptive logic in their entirety. The “spandrel” hypothesis suggests that they might arise from the uterine nervous connections activating the neighboring taste-related regions in the part of the brain known as the insula. However, we find it highly unlikely that the phenomenon is a spandrel. On the other hand, modern experiments suggest that, at least in childhood, there might be a liking for the gustatory stimuli the kids were repeatedly exposed to via their mother’s food during their fetal development. It is possible the Hindu proto-scientists made similar observations and accordingly extrapolated and expanded them to propose the above hypothesis. Indeed, tradition holds that such maternal cravings in themselves have a prognostic character. We cite a few examples of these below:

āśrame saṃyatātmānaṃ dharmaśīlaṃ prasūyate |
devatā-pratimāyāṃ tu prasūte pārṣadopamam ||
darśane vyālajātīnāṃ hiṃsāśīlaṃ prasūyate
The woman with a craving to visit a dwelling of sages births a self-controlled child committed to dharma. Indeed, she who desires to see an image of a god births a child who would grace a council. She who wishes to see a carnivorous animal births a child prone to violence.
godhā-māṃsā .aśane putraṃ suṣupsuṃ dhāraṇātmakam |
gavāṃ māṃse tu balinaṃ sarva-kleṣa-sahaṃ tathā ||
She who wants to eat the meat of a Varanus lizard births a child who will sleep well and cling to material possessions. Similarly, she who craves for beef births a strong child capable of enduring all manner of hardships.
māhiṣe dauhṛdāc chūraṃ raktākṣaṃ loma-saṃyutam |
vārāha-māṃsāt svapnāluṃ śūraṃ saṃjanyet sutam ||
She who craves for buffalo-meat births a brave child with reddish eyes and endowed with hair. She who longs for pork births a sleepy though a brave child.

More generally, the tradition holds that the nature of the child would mirror the nature of the animal whose meat the pregnant woman desires. Finally, tradition also holds that there is a direct mapping between the mother’s body and that of the fetus to account for the classic maternal impressions:

doṣābhighātair garbhiṇyā yo yo bhāgaḥ prapīḍyate |
sa sa bhāgaḥ śiśos tasya garbhasthasya prapīḍyate ||
Whichever part of the pregnant woman’s body is afflicted by physiological derangement or by injury, the corresponding part of the child in the uterus is afflicted.

In conclusion, we can summarize the old Hindu medical tradition’s position on fetal development as involving: 1) natural laws expressed as biological processes with parental “genetic contributions” as the primary drivers of development; 2) impressions of past incarnations of the child; 3) impressions from deeds of parents in current and past incarnations; 4) fulfilled or unfulfilled dauhṛda-s, which are physiologically explained as the influence on the mother by the fetal organs exercising the apprehension of their objects; 5) maternal impressions from the mother’s visual images post-menstruation and the mapping of the insults to the mother’s body onto the fetal body. The widespread presence of the impressionist components of these beliefs across cultures suggests that they go far back in history. Apparently, in some Romance languages, the word for birthmark and craving are the same and reflect a belief that the unfulfilled dauhṛda-s spawn those marks. The yavana physician Galen believed in the classic maternal impressions, and Empedocles held that women who fell in love with certain statues produced offspring who looked like them. Similarly, in Greek literature, the dark Ethiopian is said to have given birth to the fair Chariclea because she kept looking at the image of the white Andromeda while pregnant.

A version of such beliefs played an important role in the history of biology closer to our times. Had the French soldier Jean-Baptiste Lamarck (1744–1829 CE) been blown to smithereens by the German guns bombarding his position that he held with great valor, we might not have had one of the famous debates in biology that is somewhat artificially presented in textbooks. Having survived his stint in the French army Lamarck went on to propose one of the early modern evolutionary theories. Lamarck’s theoretical framework lay at the transition between archaic and modern scientific thought — one could say the transition between proto-science and science. His chemistry was more primitive than that presented in early sāṃkhya, subscribing to a four-element model of the universe and opposing the leap towards modern chemistry pioneered by his compatriot Antoine-Laurent de Lavoisier. Aspects of his biology also remained primitive: on the one hand, he subscribed to spontaneous generation, apparently disregarding the work of the Italian Fransisco Redi that showed it to be a myth. On the other, he subscribed to the existence of a “life force”, which among other things, “tends to increase the volume of all organs”. Nevertheless, he was a keen biologist who, through his investigations, realized that organisms of one form must have evolved from those with another. A part of his explanation for this process involved a hypothesis based on a certain proto-biophysics of fluid flow. He argued that the rapid flow of fluids within the tissues of organisms “will etch canals between delicate tissues” much like a river erodes its bed. He then postulated that the differential flow rates that will ensue would lead to the origin of distinct organs. Simultaneously, he saw these fluids themselves becoming more complex, giving rise to a greater diversity of secretions and organ diversification. He combined this proto-biophysics with two so-called laws to explain the evolutionary process. The first law postulated that different organs of a given organism were either augmented or diminished depending on the degree of their use or disuse in the course of its life. The idea was based on the observation of real somatic adaptation to environmental pressures happening in the course of an organism’s life. The second law posited that these characters acquired during the life of an organism by the first law are passed to their offspring — the inheritance of acquired characters. In proposing this, he was more or less following the broad class of ideas coming down from the ancients that were similar to maternal impression in the general sense.

Charles Darwin’s grandfather Erasmus, who was one of the inspirations for his evolutionary theory, also accepted the inheritance of acquired characters, and Charles himself acknowledged this aspect of Lamarckism and incorporated it as a subsidiary component of his own theory. The shock waves from Darwin’s hypothesis resulted in a sizable body of biologists falling back to pure Lamarckism or some variant thereof as a counter to Darwinism that deeply disturbed them. One such was the goal-seeking evolutionary theory of the German biologist, Theodor Eimer, which incorporated the Lamarckian mechanism. Attempts claiming to demonstrate Lamarckian inheritance of acquired characters went on for a long time, including that of the famous Ivan Pavlov, but none of these studies produced reproducible or reliable results. Despite this, Lamarckism remained popular, especially in France, down to the second half of the 1900s. A variant of it had tragic consequences in the Soviet Empire in the form of Lysenkoism. Starting with the embryological work of Johannes Müller, serious questions were raised about whether embryonic development was affected by somatic characteristics acquired by the parents. After Darwin, August Weismann experimentally showed the isolation of the reproductive germplasm from the somatoplasm of the adult body in mammals casting doubt on any mechanism that allowed the Lamarckian changes acquired by the somatoplasm of an organism to be transmitted to the offspring. The subsequent advances in genetics, biochemistry and developmental biology over the 1900s made Lamarckism look less plausible until it was more or less consigned to the history of science among serious biologists.

However, by the late 1990s, a version of the “inheritance of acquired characters” started making a comeback within the Darwinian framework. Microorganisms, especially prokaryotes, show rampant horizontal gene transfer. The horizontally transferred genetic material integrated into the genome or a plasmid can then be transmitted to the offspring. Its subsequent maintenance would be subject to natural selection. In fact, the selection could act even before the transmission to the progeny; for example, the transfer of a gene confers immunity to a virus or resistance to a toxin (e.g., antibiotic). Thus, one could see it as a process of acquiring an adaptation that is then transferred to the next generation. Indeed, several organisms, like bacteria, have sophisticated mechanisms for acquiring foreign DNA. This could be in the form of the competence system that allows DNA uptake in certain phases of their life cycle or domesticated viruses that can act as transfer agents for DNA. Less understood, but potentially in a similar vein, are the lipid vesicles derived from cells that might also carry nucleic acids. Thus, the acquisition of characters encoded in the transferred DNA from the environment has been institutionalized in many bacteria. Indeed, the commonly cited prokaryotic immune mechanisms, namely the CRISPR and PIWI-based systems and other systems we have discovered, can be seen as variants of this process of controlled acquisition of genetic information (in this case, from invading elements like viruses) that is then inherited by the offspring. However, this is entirely within a Darwinian setting with selection post-acquisition explicitly taking the place of use or disuse as an augmenting or diminishing agent.

In prokaryotes, this transfer of DNA in part plays the role of sex. Eukaryotes have evolved an institutionalized sexual mechanism that is decoupled from ambient DNA transfer. Nevertheless, they too have been extensively acquiring “ready-made” adaptations through horizontal DNA transfer. That said, from relatively early in eukaryotic evolution, there have been repeated adaptations for “setting aside” a germplasm from the somatoplasm. In the unicellular eukaryotic world, we see this in the ciliates, which set aside their germplasm in the micronucleus while running their cells with a somatoplasmic macronucleus. Indeed, the macronucleus loses a good part of the genetic information maintained and transmitted to the next generation in the micronucleus. Of course, this separation of the germplasm and the somatoplasm is the norm in eukaryotes like the animals. Moreover, a similar phenomenon to the ciliate macronuclear DNA loss is seen in several animals like the Ascaris nematode worm or the lamprey, where part of the genome is shed in the somatic cells. In vertebrates, in cells like lymphocytes, the DNA is again lost or mutated as part of the generation of immune antigen receptors. In the neurons of at least some vertebrates, the genome is edited by the jumping of transposons. However, all these “acquired” somatic changes are kept out of the germplasm segregated early on from the somatoplasm. The origin of this separation seems to be due to the genetic “addiction” pressure exerted by genomic selfish elements against their loss by excision, as seen in the macronucleus or the somatic genomes of some animals. This has gone hand in hand with mechanisms that suppress the expression of these genomic selfish elements in the germline. This suppression process is achieved by a class of mechanisms collectively termed “epigenetic” or transmission of information over and beyond that transmitted by the genome. Along with this, pressures to safeguard the genomic integrity of the germline have also resulted in strong blood-germline barriers in various animals.

On one hand, these discoveries have been the strongest strike against impressionist information transmission, including Lamarckian acquired characters — a consequence of the strong shielding of the germplasm in several eukaryotes from the somatoplasm. On the other hand, the epigenetic mechanisms have revived a version of this transmission because they do seem to transfer non-genetic information inter-generationally. There have been claims that such epigenetic mechanisms might be behind the intergenerational transmission of the effects of trauma. However, the evidence for such claims is rather questionable, and at best, they remain uncertain to date. Nevertheless, at least in some animals, like insects, there are other forms of epigenetic information like endo-parasitic bacteria transmitted via the germline (e.g., Wolbachia), which influence the sex ratios by killing a subset of the offspring produced in matings that disfavor their transmission. These bacteria often encode toxins to enforce their “addiction”, several of which attack the genomic DNA of their host, including, as we discovered, by mutating it. Thus, there is a possibility of transmission of acquired effects through epigenetic mechanisms that have developmental consequences in a more limited sense.

One of the major discoveries of modern developmental biology, including ones we have contributed to, is the role of protein ubiquitination in regulating development. A major aspect of ubiquitination is its action on protein stability, i.e., tagging of key developmental regulator proteins for their degradation. Thus, both the disruption and enhancement of various ubiquitination pathways can result in a diverse array of birth defects. As noted above, the mechanism of action of thalidomide is via the enhancement of one of the ubiquitination systems, which in turn results in the degradation of a transcription factor causing birth defects. It is conceivable that other than toxic compounds, like thalidomide, certain other stresses (or, if true, transmitted epigenetic information) impinge on the ubiquitin system to affect the stability of various developmental regulators resulting in birth defects.

Coming a full circle, with an improved understanding of biological processes, beliefs in maternal impressions in the broad sense, which lay within the domain of mainstream medicine from the days of the ancient Ārya-s to the late 1800s, were gradually excluded from it. As Stevenson, perhaps, the last intrepid believer in it in the western academe noted, these reports more or less vanished in the 1900s. We are not sure if it is a useful avenue to revisit. Nevertheless, being cognizant of it being a tenacious feature of the cross-cultural belief landscape, we believe that it is something that can be better investigated with the sharper tools that are currently at our disposal. We have a range of mature technologies that span nucleic acid sequencing, biochemistry, and developmental biology, allowing us to more directly probe birth defects than ever before. These could be brought to bear more systematically on the suspected cases of impressions — in the least, the conclusions might contribute in a more humdrum way to our understanding of developmental processes.

Finally, if one were to see a case where one is inclined to bypass biological explanations for the “supernatural”, then one may ask if the relationship between the impressing stimulus and the impression is really causal or a manifestation of the mysterious “synchronicity”. While those inclined toward the rationality of the age might abhor the very mention of synchronicity, it may be simply something they have not experienced.

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Footnote 1: As an aside, we may note that Suśruta records that Śaunaka proposed the head to be the controller of the organs and director of the development of other organs rather than the heart:  pūrvaṃ śiraḥ sambhavati +ity āha śaunakaḥ | śiro mūlatvāt pradhānendriyāṇām | However, this more correct apprehension seems to have been dropped in parts of Hindu biological tradition for the more primitive heart theory proposed by Kṛtavīrya

The rise of Navyonmāda, the subversion of the Mahāmleccha-s, Cīnānusāra and beyond

The past
The dynamics of the establishment of the counter-religious unmāda-s are of some interest. The pūrvonmāda of pharaoh Akhenaten arose from the moha in his own head and was imposed on the populace due to his imperial power. It was quickly erased by the actions of his successors Tutankhamen, Ay and Horemheb and it never was able to take root. The mūlavātaroga seems to have spread rapidly within a tightly-knit ethnic group and soon evolved into an in-group marker. Hence, there was selection against it breaking out into the rest of the populace because its value to the in-group would then be lost. However, by being a strong in-group marker, it tenaciously persisted by maintaining in-group cohesion during military expeditions and raids against out-groups and became the incubator for the future unmāda-s. An infective variant of it first broke out into the general population in the form of pretonmāda. In the early days, pretonmāda appears to have been comparable to the mūlarug, providing an in-group marker for some “good-for-nothings”. However, it acquired several memes from other natural religions in the environs during this period, making it a stronger competitor. Armed with this expanded memome, it conquered the Romans through a less-appreciated strategy of subterfuge, martyr-creation and elite capture (see below). Once in power, it quickly expressed that anti-outgroup militant tendency inherited from its parent strain on a much larger scale. After a period of expansion via this virulent mode, it oscillated between explosive virulence (e.g., South America, Africa and Goa) and its earlier mode of creeping person-to-person infection (e.g., Andhra).

The same meme-complex was transferred to the marusthala resulting in marūnmāda, which codified “spread by any means” as a duty of every adherent. Indeed, the learned māhāmada Ibn Khaldun clearly explains in his Muqaddimah that it is the obligate duty of a marūnmatta to convert everyone to the unmāda by missionary activity or force. He then goes on to add that whereas this is an explicit duty of the marūnmatta-s, it is only an incidental or localized activity among the pretonmatta-s or ādivātūla-s (M 1.473-474). While he might be correct regarding the latter, the former, in reality, are closer to his own. Nevertheless, the fact that he explicitly mentions this as a feature of marūnmāda distinguishing it from the other unmāda-s suggests that it has always been more “in the face” with them. Ibn Khaldun had also emphasized the need for a strong power, like the ruler, to enforce the sharia once the Adyunmatta dies because it is this enforcement of sharia that keeps the people doing the “right thing” from which their natural tendency is to lapse (M 1.472). Ibn Khaldun himself furnishes the example of a North African woman from the Jewish priestly caste, who, distant from the ekarākṣasa core, reverted to a semi-natural religion and as a magician queen. Uniting various tribes, she valiantly blocked the advance of the rākṣasa-senā until the Ghāzī-s eventually beheaded her and her skull was gifted to the Khalif. Thus, the marūnmāda thinkers clearly understood that unmāda-s are maintained by internal and external enforcement programs, without which they can break down and disappear.

Coming to the present
These aspects of marūnmāda reemerged in the secular rudhironmāda that in turn arose out of the matrix of “enlightenment values”, dear to the deluded secular mleccha-s, which itself was a counter-religion to the older prathamonmāda-pretonmāda matrix. While rudhironmāda inherited its claims for secularity from the “enlightenment values”-roga and turned its back to the ethnoreligious mūlavātula-śūlapuruṣīya roots, in its attempt at universality, it followed marūnmāda and pretonmāda. On the one hand, this allowed it to be easily transmitted and embraced by people as diverse as the prathamonmatta-s, śūlapuruṣa-s, the Rus, the Vāṅga-s, the Cera-s, and as an outer coat by the Cīna-s. On the other, as we shall discuss below, its secular universality proved to be its undoing. At its peak, rudhironmāda was held up by the Soviet Rus in the great conflict with the Anglosphere and its vassals. However, at the end of that struggle, the Soviet empire collapsed, and rudhironmāda failed in its grand geopolitical objectives. While it failed as a geopolitical force, it quietly thrived for more than half a century in the fertile breeding grounds of the Anglospheric academia, especially among the Mahāmleccha. There, it underwent a series of mutations before eventually emerging as navyonmāda.

What rudhironmāda lacked was the religious facade of pretonmāda and rākṣasonmāda, and this was a serious downside. While both rudhironmāda and the overt unmāda-s struggled against natural religions, the latter were at least able to offer themselves as the ultimate alternative, i.e., the “only true religion”. However, rudhironmāda was not able to give anything of that kind. As a parallel, one could consider the case of Mustafa Kemal Ataturk — he took the Turks out of marūnmāda. Had he reintroduced the religion of the Tengri-s, the Turks of Turkey might have been a cured people. However, he failed to offer a different religion in its place after removing marūnmāda, and sometime later, they returned to it with a vengeance. A similar phenomenon happened to varying degrees in the marūnmatta states conquered by the Soviets. While it is not apparent to the casual observer, navyonmāda eventually corrected this critical fault of its rudhironmāda parent — the religious vacuum. Navyonmāda neither set out to do this consciously nor did it converge on it right away or in any conscious way. Instead, these features emerged organically via selection within the movement to fill in the vacuum of religiosity created by the earlier rudhironmāda within the Mahāmleccha academia. Navyonmāda gradually evolved this feature over the period from the 1980s to the 2020s. In many ways, navyonmāda resembled the religiosity of the saṃgha of the sugata with its veda-virodhaka tendencies when it exploded as a potential religion for a section of the anglospheric elite and their arborizations in vassal states of the larger leukosphere.

While the religious facet of navyonmāda helped it replace pure rudhironmāda, this aspect also created the foundations for their seizing power by creating both in-group solidarity and the ever-correcting “purge of deviations or moderation” as in marūnmāda. Coming out of academia and originally filled with lots of socially low-ranked, physically unfit individuals, outright warfare was not an option for it to capture power. Instead, it tread on a path very similar to pretonmāda in its early days of elite capture. When Gucchaka was the emperor, and the marūnmatta-s attacked the Mahāmleccha in their big strike, there was a huge surge of military and nationalist sentiment. The result was an attack on several rudhironmatta academics, as well as moderates, who now organized under the banner of navyonmāda. Gucchaka’s neo-con handlers, headed by his deputy duṣṭa Vakrās, the matta Āṇi, and the prathamonmatta-s, squandered the swelling nationalism of the mleccha-s by engaging in the useless invasion of Iraq. That was followed by throwing away a chance to normalize relations with the marūnmatta-occupied Iran, and more troubles emerged for the mleccha-s. Duṣṭa Gucchaka also set up a police state within state, and to date, unironically rationalizes it to the Mahāmleccha by saying that it is a “reminder” of the comfort they can feel. This police state, along with the financial crisis which followed, strengthened the hands of the rising navyonmatta-s when Ardhakṛṣṇa became emperor of the Mahāmleccha confederation. While in part unhinged or even evil, the cara-s like Himaguha, Harijaṅgala (anti-H), Mānavīya (navyonmatta) and Asaṅga, have revealed the depth and the power of the systems, which Gucchaka and Vakrās put in place for the pañcanetra-mleccha-s to closely monitor and control their own citizens. While not in the face, like that of the Han, it has the comparable capacity and only needed a willing player to exploit it to its fullest.

Against this backdrop, when Ardhakṛṣṇa became the lord of the mleccha-s, under his sympathetic rule, the navyonmatta-s started creeping forward aided by his dala. A key factor was the coming of age of the young students indoctrinated by professors in the universities into the newer strains of navyonmāda with prominent religious (c.f. the marūnmatta students from Gandhara in TSP madrasas — The Students). They were available to work for Ardhakṛṣṇa’s campaign and entered the śāsana upon his victory. In his kalevarā, they found their much-needed bodhisattva. With the first of these navyonmatta-s in the śāsana, they could now play filter and amplifier with their professors in the universities. They got more of their kind, while they punished and purged those who failed to fall in line in an alliance with the vālūkavatūla-s (see below). This creep leading to the control of the mainstream media, the academia, internet-social media-based big tech, and offices of the government (the deep state) was rather deep by the end of the reign of Ardhakṛṣṇa. They thought that they could easily usher in their preferred candidate Jārapatnī and establish their regime with their power. However, Mahāmleccha democracy actually worked, and Vijaya, also known as the Nāriṅgapuruṣa, became the mleccharāṭ. He tried to push back, but he was no Julian and full of his own insufficiencies and inexperience. Alarmed by his victory, the navyonmatta-s now went into high gear and used the Nāriṅgapuruṣa as an excuse for quickly pushing in their excesses. They used all their instruments to constantly hector the Nāriṅgapuruṣa and facilitated his ultimate uccāṭana by Piṇḍaka and his deputy Aṭṭahāsakī, who was an opportunistic adopter of navyonmāda and their front-end person.

Analyzing the rise of navyonmāda
Now, let us take a closer look at some of the aspects of the rise of navyonmāda among the Mahāmleccha. As noted before, when the Mahāmleccha became a superpower after their victory in WW2, the world was never more starkly divided into winners and losers. The natural resources of Krauñcadvīpa, together with the victory in war, paid dividends to them like nothing in recent history. As a result, the Mahāmleccha started building sprawling suburbs and zoomed around their vast frontier lands in their gas-guzzlers. This prosperity made them more and more detached from reality, and the myth of infinite “economic expansion” took root in them, making them blind to how unsustainable this was. This softened their elite, worsened their health, and also precipitated the decline of conventional ekarākṣasa religion in a section of their elite. This left them in need of other avenues for feeling a sense of “virtue” and piety. In our opinion, this psychological complex plowed the soil for navyonmāda to take root eventually.

As this was taking place over half a century, there were parallel developments in academia. The victory in WW2, the triumphs of the nuclear bomb, the shift of the epicenter of frontier physics from Śulapuruṣīya to Krauñcadvīpa, and James Watson’s role in the founding of molecular biology, made the Mahāmleccha academia emerge as a potent accreditation system. But over time, the myth of infinite expansion took root in these systems, turning them into pyramid schemes. One consequence of this was what some mleccha academics have termed “elite production”. Having spent a lot of time with mleccha academics, we can say that there are some very tāthāgatan qualities therein — a mix of a tendency for plagiarism and lack of attention to detail and subtlety. The result is the dominance of mediocre or half-baked models of understanding over more complete and nuanced ones. This is nowhere more starkly illustrated than the fake studies in psychology churned out by the dozen, replete with manufactured statistics. “Cancer biology” comes a close second furnished with photoshop artistry. This was mainly because a part of the expanding Mahāmleccha academia divorced itself from a test against the real world due to the fetish of “peer-review”. Here, research gets acclaimed due to publication in “high-profile” journals reviewed by peers rather than being a realistic description or nature or making predictions that proved to be correct. This was yet another fertilizer for the growth of navyonmāda — a system where one can get away with fancy beliefs without checking if they hold in the real world.

Indeed, this blindness to reality in navyonmāda’s priorities can be seen at many levels beyond the obvious. However, it is a kind of māyāvāda that not just takes the jagat to be mithyā but creates a mithyā-jagat of its own. Most plainly, it is seen in the denial of biological reality in the form of sex and race and its replacement with a celebration of pseudo-biological shape-shifting. However, this permeates more subtle matters too. On the economic front, the classic rudhironmatta-s went on endless harangues about economic unevenness in society and acted on it by killing or banishing the prosperous elite. In contrast, the navyonmatta-s do not rail much about the material; instead, they vent against something immaterial termed “privilege”, and their actions are aimed at eliminating those whom they perceive as privileged. The elite in normal societies either signaled their status or were accorded status due to either distribution of material possessions or their praxis of rituals. However, in navyonmatta society, the elite signal it via their beliefs and claims of purity therein (elite capture). In this aspect, they are remarkably similar to vālūkavatūla-s. A critical flashpoint for the māyāvāda of the navyomatta-s came with computers masquerading as phones and the internet becoming ubiquitous. This allowed commerce and social life to transition to a virtual electronic world, completing that sensation of a decoupling with reality, which the navyonmatta-s desired.

In such a system, the holders of the allowed beliefs rather than producers of work that passes real-life tests are magnified by shallow vanity articles as though they are the next bodhisattva-s on the block. Recently, we saw such an article on a navyonmatta human geneticist, who thoroughly mixes her science with the Nicene creed of navyonmāda, to provide that facade of objectivity to those in that pakṣa. A mix of such boosterism of particular types as role models and the sense of virtue from these beliefs takes the place of a key aspect of religion — the sense of belonging among the pious and a concomitant disdain for the impious. Thus, the new votary of navyonmāda, usually from a deracinated or shallow background, suddenly finds a new purpose in life by professing it. It provides for beliefs that touch the human need to feel justified and virtuous. These are often reinforced by actual mimicry of religious activities, such as rhythmic chanting of slogans against enemies (c.f. marūmatta-s stoning the “devil”), internalization of concepts such as the “power of the word”, great fear of taboo words, sacralized ethnicities and “martyrs”, marches resembling a religious procession, and community-building with opportunities for sexual encounters and “group therapy”.

Thus, the American university system slid from being institutions of accreditation to those of degeneration, furthering the capacity of navyonmāda to take over the systems. It was still not straightforward because there were still many academics who still had to give up common sense to adopt it. It breached this barrier through a series of steps. First, it evolved obfuscation of language, wherein common words were reused such that they meant something specific to the insider, whereas the outsider saw them in their ordinary sense as words of virtue. In old religions, for example, in the yoga tradition, words like gomāṃsa did not mean what the commoner might take them to mean. Here, the intention was to conceal secrets and repel the uninitiated (e.g., he may think a yoga text is recommending that he consume gomāṃsa and keep away from it). However, the intention of the navyonmatta-s was not repulsion but outright deception — it was to purposely obfuscate the uninitiated and unwittingly get them onboard with the navyonmāda project. This is rather comparable to Tathāgata redefining common religious words like trayi or ārṣa or sūkta (=sutta). Thus, the lay votary would not realize that the Buddha is subverting the religion and get sucked into the śaraṇa of the saṃgha. Thus, driven by the need to feel virtuous and pious, the mleccha liberal academics vigorously adopted and supported navyonmāda, even as unsuspecting lay ārya-s adopted the cult of the Buddha — after all who would want to reject something termed the way of the ārya-satya-s or dharma?

As they began winning votaries, they transitioned from a bauddha mode to the marūnmatta/pretonmatta mode of counter-religion. The academics who resisted navyonmāda, even left-liberals who had some commonsense left, were attacked by the mobs of navyonmatta-s, typically recruited from the frenzied student body. Some academics were kicked out of their institutions, others who were too powerful to evict were sidelined in public discourse, yet others converted under this pressure. The campus riots, like those of the American Spring (e.g., in Berkeley, a hothouse of navyonmāda), pushed the growing body of university administrators into submission to the demands of the self-righteous navyonmatta-s. The monoculture in academia allowed the capture of institutions founded on it like scientific and medical journals, which now amplified the message and pushed the credo onto young and impressionable minds. Those who sought accreditation from these bodies (academia and journals) had to now submit to the new religion, and the rest had to go silent like Thabit ibn Qurra.

In the next step, these newly minted young navyonmatta-s gushing out of the big-name universities flooded corporations and the government. Those who took navyonmāda lightly used to jocularly remark that when these indoctrinated students get a real job, they would be jolted out of their unmāda into reality. This might have indeed happened in the past with rudhironmāda, as we saw with our own classmates. However, here the reverse occurred. The navyonmatta-s captured and transformed the institutions they invaded. In the days of old rudhironmāda, they presented themselves in opposition to the “capitalist” corporations and “oppressive” government. However, navyonmatta was more agile and worked with the corporations — if the corporations paid them a jaziya and supported their demands they were more than happy to play along and support the corporations. This was an easy way for corporations to appear virtuous too. Like a king who might have committed sins in war, building a temple to expiate those, the corporations were more than happy to absolve themselves of capitalistic excesses by adopting navyonmāda themselves. The mahāduṣṭa-s like guggulu, Dvāra, Mukhagiri, Jaka and Bejha all adopted navyonmāda to differing degrees as a prāyaścitta while continuing to commit “capitalistic sins”. Thus, came about the marriage of these with navyonmāda, which would have been impossible under the old rudhironmāda, which would have attacked them for their wealth. A very real exhibition of this was the repainting of “the occupy movement” working under the old rudhironmāda premises to its new navyonmāda colors.

More sinister than even these was the māhāduṣṭa Sora, who had always channeled his money into navyonmāda being philosophically in union with it. He saw it as an opportunity to enact his grand political plans both among the Mahāmleccha and abroad, like in Bhārata. Among the Mahāmleccha, he saw navyonmāda as a potential private army to put his pakṣa headed by the vṛddha Piṇḍaka on the āsandi. In this, he was mostly aligned with other mahāduṣṭa-s. They got their golden chance when the pandemic lock-downs followed by some egregious acts of violence by daṇḍaka-s on kṛṣṇa-s caused a janakopa. This janakopa was quickly channelized by kālāmukha militant wing of the navyonmatta-s (c.f. the Mahāmlecchīya gardabha-pakṣa’s earlier militant — the ka-trayam deployed against kṛṣṇa-s). This provoked quick and correct action against them by the then mleccheśa, Nāriṅgapuruṣa. However, his effort was rendered toothless as the navyonmatta-s had subverted the deep-state and the Sorādi māhāduṣṭa-s used their riches to provide legal impunity to their kālāmukha rioters aided by the likes of Aṭṭahāsakī.

“Rus! Rus!” and Cīna-capeṭa
As navyonmāda’s priorities are not aligned with the real world, its adoption by the elite would eventually be hit by the real world. However, this does not mean a correction will be immediate, as illustrated by the Dark Ages in the Occident brought on by pretonmāda. With the sailing being smooth for the Mahāmleccha, the deep-state actors kept themselves busy going blue in the face, shouting, “Russia! Russia!”, even as the storm of the Middle Kingdom Corruption was brewing in the Orient. As the said corruption broke out of China, the Mahāmleccha were oblivious even to their own intelligence agencies; instead, they were busy in an internal conflict, with the deep-state and the gardabha-pakṣa trying to overthrow the Nāriṅgapuruṣa. Finally, when the Middle Kingdom Corruption reached the shores of Krauñcadvīpa, the gardabha-pakṣa was trying hard to prevent the appropriate steps from being taken to counter it. The compromised deep-state could not mobilize a proper supply of masks for the citizens or even guda-pramṛja-s for the mleccha-s to sanitize themselves. The result was a massive death toll, the full extent of which has definitely been under-reported. To top it all up, the mleccha-senānī betrayed his own boss, the Nāriṅgapuruṣa, to the cīna-s. Cīna-s saw an opportunity to hit hard at Mahāmleccha power using navyonmāda. Even as the navyonmatta-s disparaging their own constitution, the Cīna-dūta-s gave the mūlavātūla Nimeṣaka and the Mahāmleccha praṇidhipa as resounding slap right in their own den. However, lost in the world of their own making, they failed to wake up — Nimeṣaka was more concerned about flying navyonmāda’s Indracāpadhvaja-s at mleccha-dūtaśālā-s than managing the proper retreat of the mleccha-s from Gandhāra. As icing on the cake of their delusions, Piṇḍaka and Nimeṣaka declared that they had conducted a great operation to kill dreaded ghazi-s of the Khilafat and avenge the death of their baṭa-s, when in reality they killed a bunch of children of one of their own marūmatta friends.

In contrast, emperor Xi proceeded with strengthening the Cīna-s. He lied his way through the Middle Kingdom Corruption, even as the rest of the world was tied down by it. He delivered a definitive punch to the restive vālūkavatūla-s, whom the Han had earlier subjugated. He was able to move ahead with testing hypersonic missiles supposedly. Notably, he was above to exploit the navyonmatta movements, like the kṛṣṇajīvāndolana, to aid the overthrow of the antagonistic Vijaya-nāma-vyāpārin and bring the pliable Piṇḍaka on the āsandi — it is notable how the Cīna-s colluded with the tech-duṣṭa-s to silence any discussion on Vyādha-piṇḍaka and his yantra. The cīna-s have other assets. First, their penetration of the Occidental academia via Galtonism is incredibly deep. Thus, mleccha academics bat for their interests, provide them with cutting-edge knowledge, and might even obtain funds for their research which might ultimately be to the detriment of the mleccha-s themselves. This also provides them a conduit to slip in their spaś-es as students. Second, they have cultivated assets among the big-tech duṣṭa-s, e.g., Mukhagiri is their jāmātṛ who originally courted them before they broke up with him. Perhaps, even the break was not of his own accord but due to the pressure from the mleccha side. Finally, since the mleccha big-tech depends on delivering cheap opiates to the masses, the cīna-s hold them by their balls by controlling manufacturing. Thus, as big-tech takes control of the Mahāmleccha as the de facto government (something which will accelerate with the strides being taken in machine learning and other areas of computing, which in turn have been made effective by the more than two decades of data the masses have supplied them), the leverage on them that the cīna-s have, coupled with their immunity from them, would allow them to use navyonmāda as a potent weapon.

Onward to Bhārata
All unmāda-s, the old counter-religions, and their new secular mutants see the dharma as their natural enemy — what Viṣṇuśarman would term svabhāvavairam. The one area where this is manifest is the hatred for the brāhmaṇa-s and functional H systems. Those among the mleccha-s and their sipāhi-s who fight for the so-called “enlightenment values” (the older delusion) hate the H as they offer a robust and likely superior alternative to their system. This threatens to undermine their truth-claim that they have found the only true formula that succeeded due to being good rather than being enforced by the smoking end of the nālika. Across the mleccha elite, some of the predictions of the evolutionary theory for Homo sapiens are fundamentally incompatible with their cherished beliefs. Thus, the majority of Occidental scientists (across ideological camps) focusing on its study slip into denialism on one or the other matter. Both the “Western values” types and those who fight for navyonmāda are terrified by the fact that H succeeded because they created a system that instinctively acknowledges the pulls of biology, i.e., human nature, on social structure. Thus, Bhārata is the one frontier where there is an alignment of the enemies. Paradoxically, while navyonmāda fights pretonmāda and “enlightenment values” in the Occident, in Bhārata, these align for the break up the H. In contrast, marūnmāda-navyonmāda alliance will be strong in both India and the West. Hence, we predict that given the intrinsic lack of fecundity in navyonmāda due to celebration of biology-denial it will end up aiding marūnmāda in Bhārata.

Historically, H have had to deal with the preta-maru-rudhira triad — while there have been the classic heathen failures against these, at least they were recognized as such by a large fraction of the elite. In contrast, the capacity to recognize navyonmāda is even lower, as can be seen from the fact that even pro-H government circles so quickly and willingly propagate navyonmāda memes. This has also meant that the H elite have adopted navyonmāda memes to differing degrees. The secular elite constantly bombard the impressionable with navyonmāda packaged within opiates such as spectator sports, product advertisement and cinema, as if they were distributing adulterated heroin. Moreover, navyonmāda is also “safe for use” even for Cīna subversion operations in Bhārata. In particular, government adoption of navyonmāda memes would result in undermining the H army. This is something the Cīna-s badly want because despite all their show of tech, they have a dearth of young men needed to fight wars. On this front, the H still hold an upper hand, but if, like the Mahāmleccha, they decided to adopt navyonmāda, they could easily ruin their senā on top of having a tech gap with respect to the mleccha-s and Cīna-s. We have indeed seen evidence for mass deployment of navyonmāda by both Sorādi-duṣṭa-s and cīna-s — the CAA riots, the various khaṇḍa-jāti riots, the kīnāśa-uśnīśa-riots and Dravidianism — over the past few years. Hence, to cut the chase, we argue that the rise of navyonmāda has not only greatly multiplied the H’s threats in Bhārata and abroad but could be an existential threat.

This essay builds on an earlier one, which overlaps in scope, filing in some historical details.

Some biographical reflections on visualizing irrationals

In our childhood, our father informed us that, though the school told us that , it was not valid. However, he added that for “small fractions” [Footnote 1] it was a great approximation. Moreover, the numerical problems, which we would encounter in the tests, were designed with radii, etc., as “round” multiples of 7; hence, it was alright for vyavahāra. He also told us that in reality, was irrational and that fractions like were only approximations thereof. We asked why was the best of the “small fraction” approximations. He asked us to figure that out for ourselves but told us that we could get better approximations with bigger fractions: and .

Armed with this information, not being mathematically too endowed, we had to think long about it before arriving at an algorithm to understand this. It went thus (written using post facto terminology):
1) Given that we had a lot of sheets of graph- and ruled- paper, we first sought to draw a line with slope equal to , i.e., . This would ideally need the squaring of a circle. However, at that point, we did not know of Ramanujan’s constructions and accurately re-doing the yavana constructions with curves like the spiral and kampyle lay in the future. However, we had those approximations with the “larger fractions” that our father had given us, and with a hand calculator, we could verify that they provided more than the accuracy we needed for testing out . Accordingly, we counted out 113 and 355 small squares on the X- and Y-axes respectively on the graph paper and carefully drew the line with a pencil that had an expensive, thin graphite refill.
2) By definition, the line passed through (0,0). After that, we tracked every time the line cut the horizontal (red crosses) or vertical (green circles) grid lines of the lattice (Figure 1).
3) We saw that the line first cut the horizontal grid lines at 1, 2, 3 and the vertical grid line for the first time at 1 after cutting the horizontal line 3. The horizontal cut at 3 and the vertical cut at 1 come close to each other (Figure 2). This immediately told us the obvious: , a reasonable first-order approximation, seen in several ancient traditions, like the Ṛgveda, where it is embodied by the god Trita. Going along, we saw an even closer approach between the vertical cut at 6 and the horizontal cut at 19 (Figure 1). This yielded , which again reminds one of the kinds of values seen in old traditions like the construction for squaring the circle of the Maitrāyanīya-s or the popular value of seen in some old Indian texts or the value in the Rhind papyrus of the Egyptians. At , we saw a near-perfect matching of the vertical cut at 7 and the horizontal cut at 22. Further ahead, we saw another close approach between the horizontal cut at 25 and the vertical cut at 8, but this was worse than the approach at . It only got worse from there till the higher fraction , though there was a fairly good approach at (still worse than ). Thus, we had seen for ourselves that was indeed the best approximation among the “small fractions”. This childhood experiment was to leave us with a lifelong interest in irrationals and their fractional approximations, mirroring the fascination for things like the cakravāla seen in our intellectual tradition.

Figure 1. The cuts corresponding to

The only problem with using such a method for finding rational approximations for numbers like or is that you should know their value to a high degree of accuracy a priori or be able to construct them using special curves. For example, if you can construct a line of slope you can determine — not as good as the approximation for but has a nice symmetry with it telling us that . However, for irrationals amenable to Platonic construction, e.g., this method can be used effectively to find small rational approximations, if any. Thus, we can arrive at as a rough and ready approximation for (Figure 2).

Figure 2. The cuts corresponding to

A few years later, these experiments led us (independently of any literature on the topic) to the idea that every irrational number can be represented as an infinite string of 0s and 1. We take a line of the form , where is an irrational number. Based on the above approach, we write 1 if the said line cuts a horizontal grid-line and 0 if it cuts the vertical grid-line of the lattice. Since the line will pass through a lattice point only at (0,0), we start the sequence by writing 01. Thus, by moving along the line, we get an infinite sequence representing as a string of 1s and 0s. One can see that as the number of elements in this sequence the ratio of 1s to 0s tends to . Thus, for , the first 50 elements of this sequence are:

01101011010110101011010110101011010110101101010110101

We also represented the same as a “string of pearls” diagram (Figure 3). This kind of representation reminds one of the differentiated cells in linear multicellular arrays in biology, for example, the occurrence of heterocysts in a filament of Anabaena. This led us to realize that the irrationals have a deep structure to them that is not apparent in the seemingly random distribution of digits in their decimal representation.

Figure 3. The “string of pearls” representation of various irrationals.

As we have seen before on these pages, this structure can manifest variously. One place where we found this structure as manifesting was in strange non-chaotic attractors, which were first described by Grebogi et al. in the mid-1980s. These attractors are “strange” because they manifest a fractal structure (see below) but do not exhibit chaos, i.e., the attractor has the same structure irrespective of the values with which the map is initiated. The map which we found is distinct from that of Grebogi et al. but produces similar behavior. It is of the form:

Here is a constant for which we can choose some value , but we set it to 1.03 simply for the aesthetics of the “irrational spectrum” (see below) and the manifestation of its fractal structure (Figure 4). The other parameter is the irrational number under consideration. Irrespective of the initial conditions (as long as both ), the attractor takes the same form (Figure 4) that is determined only by the irrational , as long as remains the same. We term this the “spectrum” of the irrational. While the attractors appear superficially like curves symmetric about the -axis with positive and negative limbs, we can show that they are actually fractal. The iterates do not proceed along the curve but jump from lower limb to upper limb and vice versa, and between any two arbitrarily close points on a given limb, one can find a finer structure of points jumping between the limbs, thereby establishing its fractal structure. Indeed, as increases, the attractor acquires a structure reminiscent of the classic fractal structure seen in maps like the logistic map. The spectrum itself depends on the fractional part of the irrational (Figure 4). This can be established by comparing the spectra for (the Golden ratio), which have the same fractional part — they are identical. In contrast, the spectra of are not the same, keeping with the differences in their fractional parts.

Figure 4. The spectra of various irrationals initiated with

While this type of “spectrum” captures the structure hidden in the fractional part, we also designed a second type of “spectrum” that captures the structure relating to the rational approximations we saw in the opening discussion. This is defined as the below summatory sequence:

,

Here is the irrational number under consideration. Figure 5 shows a step plot of for and . We observe that it has a modular structure that builds up into a larger “wave”. At the lowest level, we have an up-down step of size 1. Then we see repeats of such steps with a transition between repeats at multiples of 7 (red lines). This continues until the “trough” of that wave is reached at 106 (green line). Then an ascent begins at 113, which is complete after a further 113 steps (violet line). Note that the numbers 7, 106 and 113 are the denominators of the successive best rational approximations of . Thus, these sequences have a fractal structure with larger and larger cycles whose size is determined by the denominators of the successive rational approximations.

Figure 5. Step plot of the summatory spectrum of till .

Hence, those irrationals with multiple small rational convergents tend to show more “overtones” resulting in a more complex structure (e.g., or ; Figure 6)

Figure 6. Step plot of the summatory spectrum of various irrationals till .

From the above plots, it becomes apparent that while for all irrationals will be fractal, at least small scales some show greater “complexity” than others, e.g., compare the plots for or with those for or . We wondered if there might be a way to define this visual impression quantitatively? We did so by defining sequences , the sum of the terms of in a sliding window of size . For each irrational, we considered all computed for . Then for each of these summatory sequences for a given irrational, we counted the number of times the curve changes direction, i.e., changes from going down to going up and vice versa. We then normalized the direction-change counts with each for a given irrational by the maximum number of direction changes seen for that irrational. The mean of this normalized value gives a measure of the complexity, i.e., the “wriggliness” of the curve. This is shown as in Figure 7 along with a plot of for and shows that the measure indeed matches the visual impression from Figure 6.

Figure 7. Step plot of the sliding window sequence of various irrationals with

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Footnote 1: Fractions with small numerators and denominators

Turagapadādi

This note stems from a recent conversation with a friend, where he pointed out that the graph representing all possible positions the horse (knight) can take on the chessboard from a given starting square produces interesting graphs. It struck us that this would indeed be an interesting exploration to introduce neophytes into the graph theory and computational exercises relating to it. Hence, we prepared this elementary note for pedagogical purposes and to show some pretty pictures. The origin of this class of problems lies in the Hindu tradition of citrabandha-s and yukti-s, which have been extensively discussed and illustrated by various medieval authors in kāvya and encyclopedic literature (e.g. Mānasollāsa of the Cālukya emperor Someśvara-deva). In his Śiśupāla-vadha, Māgha states:

viṣamaṃ sarvatobhadra-cakra-gomūtrikādibhiḥ ।
ślokair iva mahākāvyaṃ vyūhais tad abhavad balam ॥
That force was difficult to penetrate being equipped with
the sarvatobhadra, cakra and gomūtrikā and like of formations,
even as a mahākāvya furnished with such verses.

Here, he uses a simile to compare the military formations like sarvatobhadra (comparable to the Roman testudo), etc., with the equivalent citrabandha-s or structural constraints used in kāvya. Several of the early medieval examples of such citrabandha-s in kāvya are related to the description of battle scenes: e.g., the Haravijaya of Rājānaka Ratnākara, the Śiśupāla-vadha of Māgha, the Kirātārjunīya of Bhāravi and the Jānakīharaṇa of Kumāradāsa; thus, it seems likely that the authors were trying to embed images of the yuddhavyūha-s of the yuddha-s under description in their kāvya, as suggested by the above verse of Māgha. However, such devices are also used widely in stotra literature, for instance to depict the weapons of the deities instead of the vyūha-s — the Kaśmīrian Sāmavedin, Rudraṭa Śatānanda, uses such in his Durgāṣṭaka. Since we first learned of the use of such structural constraints in kāvya in our youth from the praise of Durgā by the great Kaśmīrian kavi Ānandavardhana, it struck us that just as they have place in illustrating battle-formations, they also represent an early example of using ideas that intersect with graph theory and symmetry with far more general implications. Indeed, even as the “Kavi-prajāpati (to use Kalhaṇa’s term)” selects for such constraints to bring meaning to his kāvya, natural selection picks such constraints in words formed by the alphabet of nucleic acids and proteins to generate biochemical function.

Keeping with the military connections of the citrabandha-s, one such citrabandha, the turagapada, is based on the horse’s movements in that ultimate “war-game” which spread widely in the Gupta age, caturaṅga, i.e., the steps of a horse on the chessboard. While we do not play chess, we found the abstraction to be of interest. On an infinite chessboard, the horse on a given square can reach 8 other squares (Figure 1).

Figure 1. Possible paths of the horse.

However, some of these are unavailable at squares on the boundary or the penultimate circuit on a board of finite length and breadth. For convenience, going forward, we shall only look at square boards. This is stated for an board by emperor Someśvara-deva in his Mānasollāsa thus:

koṇa-pārśvasthitasyāsya turagasya pada-trayam ॥
koṇasthasya pada-dvandvaṃ prānte pada-catuṣṭayam ।
dvitīya-valaye koṇe haye pada-catuṣṭayam ॥
dvitīya-valaye’nyatra pada-ṣaṭkaṃ nigadyate ।
madhye ṣoḍaśa[koṣṭheṣu] sthitasya turagasya ca ॥
padāṣṭakaṃ vinirdiṣṭaṃ caturaṅga-viśāradaiḥ ॥

In the cell next to the corners, the horse has 3 moves; in the corner cells, it has 2 moves; interior to these cells, on the border circuit, it has 4 moves; in the corner cell of the second circuit, it has 4 moves; in the interior cells of the second circuit, it has 6 moves; in the 16 interior cells, it has 8 moves each. Thus it has been expounded by the chess experts.

We can consider the cells of an chessboard, labeled from 1 to by rows, as the nodes of a graph. An edge connects two nodes in this graph if they can be reached from each other by the move of a horse — the turagapada. The horse can make no moves on boards with . Figure 2 illustrates the graph for . One can easily see that the horse can reach every cell from every other cell except for cell 5. Thus the graph is a simple cycle of 8 nodes with one disjoint node 5.

Figure 2. Moves of a horse on a board.

From board onward (Figure 3), we get single-component graphs with no disjoint nodes. From , all the graphs have 4 nodes with just two connections corresponding to the corners of the board, as mentioned by Someśvara. The nodes are colored as per the number of edges connecting to them. This graph can be rendered as a 3D object, which, in principle, could be the structure of a hydrocarbon. However, it remains unclear to us if such a hydrocarbon exists or can be synthesized in reality.

Figure 3. Moves of a horse on a board.

From onward, we get nodes all the possible connections, namely those with 2, 3, 4, 6, 8. We have a single maximal node at , node 13, with 8 connections. When we render this graph using the Kamada-Kawai force-direct spring algorithm, we get a structure with bilateral symmetry and interesting relationships between symmetrically equivalent neighboring nodes (Figure 4). For example: nodes 1, 19; 7,25, both pairs differ by 18. The nodes 9, 21; 5, 17 differ by 12. The 4 edge nodes 8, 12 and 14, 18 represent another such pair of symmetries.

Figure 4. Moves of a horse on a board.

These graphs lead us to the classic turagapada problem of kāvya and its solutions, which simply stated goes as: can you find a path such that the horse visits each cell on the board only once? In terms of the graph, it can be stated as: can you find the path passing through all nodes of the horse graph only once. In modern computational literature, this is called the knight’s tour problem. The above graphs show that no such tour can exist for . For , cell 5 cannot be reached, but the remaining cells can be visited by a closed cyclic tour path (Figure 5). For , though the graph has a single component, the fact that a pair of 2-edge nodes connect to the same pair of nodes means that a tour cannot be completed. However, 15 of the 16 possible cells can be visited on tour (Figure 6).

Figure 5. Incomplete turagapada on a board.

Figure 6. Incomplete turagapada on a board.

From onward, one can always find multiple tours that visit every cell. Figure 7 shows such an example on a board.

Figure 7. Turagapada on board

It is easy to see with the graph that solving the turagapada by brute-force walks along the graph is very inefficient and will explode as increases. However, a simple algorithm for finding a turagapada exists: (1) Start with a given node and move to a neighboring node from which the fewest non-0 number of further possible moves are available. For the possible available moves, only those neighbors which have not yet been visited are counted. (2) If a tie occurs, then one simply goes to the cell with a smaller index. (3) While these two steps are sufficient to yield solutions from several cells, it is not foolproof. Hence, one may look one level down to see if there are neighbors’ neighbors from which the fewest possible moves are available to find turagapada-s with greater certainty.

Figure 8. Turagapada on board

Figure 8 shows a solution for an board using the above algorithm starting from cell 1. Given that Someśvara explicitly lists out all the possible moves from a given cell, he implicitly seems to have used a similar algorithm with symmetry considerations to find a turagapada. He specifies it by first providing a chessboard with coordinates indicated by the syllables formed by the first 8 vowel conjunctions (a, ā, i, ī, u, ū, e ai) of the 8 consonants (c, g, n, d, ṭ, r, s, p). He then gives the turagapada asā sequence of 64 syllables shown below (Figure 9).

Figure 9. Someśvara’s turagapada.

pa si pu se ṭai ne cai gū । nī cu gi ca nā ṭa sā pī ।
sū pai re dai ge dū gu ci । ga dā ra pā sī pū sai ṭe ।
nai ce nū gai cū gī cā na । ṭā sa pi su pe rai de nu ।
ṭū rī di ṭu ri dī ru ṭi । du ni cī gā da rā ṭī rū ।

Other than this yukti presented by Someśvara, several kavi-s have given their own solutions for complete tours. We have Rudraṭa’s solution in the form of a prosodic pattern with repeating strings of nā and lī interspersed between two distinct syllables, namely se and le (supposedly you can use the principles of saṃdhi and samāsa-vigraha to read this as a Sanskrit verse). His commentator, Namisādhu, provides a mnemonic using the Sanskrit varṇamālā. Ratnākara and Veṅkaṭanātha-(Vedānta) deśika provide pairs of verses with one laying the chessboard and the other providing a solution tour. Rudraṭa, Ratnākara and Veṅkaṭanātha, exploit the fact that the anuṣtubh meter has four feet of 8 syllables each. Thus, they can cover 32 syllables or half a chessboard with a single śloka. This solution is symmetric; hence, it can be reflected to provide a full board solution. The widespread use of turagapada as a citrabandha, from Kāśmīra to Drāviḍa, suggests that a version of the algorithm stated above was imparted in traditional medieval education.

This tradition was transmitted to the Mohammedans, and from them, it appears to have been transmitted to Europe. However, to our knowledge, the first solution appears relatively late in Europe, being provided by Leonhard Euler. William Hamilton considered a related problem: let a dodecahedron represent a graph with 20 nodes and 30 edges. Find a cyclic path that passes through all edges only once. Here every node is connected to 3 edges. A similar question can be asked for the horse-graph — i.e., finding a complete tour that is also a cycle. A solution to this problem is recorded in the late medieval encyclopedia of Nīlakaṇṭha Bhaṭṭa (Bhagavanta-Bhāskara), but I do not have it handy right now. In any case, a vast body of literature exists on algorithms for tours and their use in kāvya; hence, we do not tarry any more on this point.

Finally, few other interesting questions emerge from the horse graphs. First, the diameter of a graph is defined as the longest shortest path between two nodes of a graph. The distance between two nodes is a geodesic — i.e., the shortest path along the graph. The longest such geodesic between any two pairs of nodes in the graph is its diameter. For the horse graph with we can compute this sequence to be: 4, 5, 4, 4, 5, 6, 6, 7, 8, 8, 9, 10. Can one come up with a closed expression for this?

Second, there are shortest paths between node 1 and node for a given horse graph. For this sequence goes as: 2, 2, 8, 4, 6, 108. A colleague of ours, a professional mathematician, showed us a complicated formula that can describe this strange sequence. While I am not providing that here, it shows a dramatic jump whenever . Thus, we see a jump at , making it more than the number of shortest paths found for the . Thus, it appears the inventors of the game chose to provide a maximal diversity in the movement of the horse for boards of a similar order.

Asians and Pacific Islanders: The triangle

In our youth, we read with great excitement old books on anthropology obtained from a library with considerable difficulty. The excitement was primarily from learning about the osteology of extinct apes and monkeys, including the closest sister groups of Homo sapiens. Some of those books also had a collection of plates with pictures of stone tools and various extant peoples of the world, especially hunter-gatherers who still lead a relatively archaic mode of life. Those pages too fascinated us, and we spent many an afternoon turning through them wonder-struck by how many different morpho- and eco-types of Homo sapiens were around. Of those tribes, the Melanesian in particular caught our attention with their gripping displays of headhunting, cannibalism and prion neuropathology (there was still a debate about what prions were back then). The images of Fijian tribesmen and a collection of their braining clubs left a deep impression on us (Figure 1). We had a direct experience of the same when we visited a coethnic who had been driven out of Fiji during the attack on the Hindus by the former islanders. However, in his flight back to the subcontinent, he had brought along one of those clubs of the ancestors of his Fijian enemies. We wondered about how the Melanesians and Polynesians reached their distant outposts in the Pacific. We also wondered how these Indo-Pacific peoples might be related to the tribal Indians — it did not escape our attention that some of that ancestry was visibly present in the non-tribal Indians.

Figure 1. Fijian tribal warriors with a club photographed in the late 1800s.

Answers to many of those questions have come from the genomics of extant and prehistoric peoples over the past few years. In its present form, this note is by no means a survey of all that. It is just a very brief account comprised of a few observations sparked by recent discoveries. Unfortunately, due to magazine-fever many molecular paleoanthropology papers while presenting important specimens are poorly written and illustrated. Also, due to the competing groups involved, the speed with which new specimens are piling in, differences in interpretation, and the terminological issues, these works do not afford a synthetic picture of the history of the people under consideration. So, we have had to wade through these presentations, which might ignore each other, to summarize the below points of interest regarding the evolution of the Asians and Pacific Islanders. At the broad level, the ethnogenesis of the Eurasians and Pacific islanders can be summarized by this principal component analysis of the genomic variation of extinct and extant individuals (Figure 2). Some populations are colored distinctly against the gray background of the remaining individuals and labeled. The key prehistoric genomes are indicated by big stars and labeled in the legend.

Figure 2. A plot PC1 and PC2 showing various Eurasians and Pacific Islanders. LinearBKer: Linearbandkeramik (Early European Farmers: Neolithic); Gandhara: Ancient samples from Northwestern India (what is now TSP); Aus/Papuan: Australians (squares) and Papuans (triangles); Phil/Mal Ngrt.: Aeta, Agta, Jehai and Batak peoples (Philippines/Malaysian Negritos, brown triangles); Cam: Cambodians; Twn Ausn: Taiwanese Hanben site, likely early Austronesians; Karelia HG: Eastern hunter-gatherers from Karelia (Finland-Russia border zone); Iran.Cu: Copper Age people from Hajji Firuz site; Iran.Neo: Neolithic people from Ganj Dareh site; Geoksyur Neo/Cu: Turkmenistan Neolithic and Copper Age people.

One can see that a triangle of clines describes a major fraction of Eurasians and Pacific islanders. The first is the Indian cline extending from the Andamanese populations, like the Onge, Jarawa and Great Andamanese on one end and at the other end terminating in the Sintashta steppe culture that likely corresponds to the expanding Aryans. The Paniya tribe of Kerala and Karnataka represent one of the groups from the mainland that is closer to the Andamanese end of this cline. The second notable cline is the Australasian cline, with the Papuans and Australians on one end (close to the Andamanese) and the East Asians (Hans, among others) at the other end. In between lie the Negrito tribes of the Philippines and the Malay region (brown triangles), and the Austronesians who spread into the Indo-Pacific from Taiwan in a maritime expansion, ultimately reaching New Zealand and Rapa Nui (Easter Island) of the coast of Chile. The third notable cline completing the triangle is the North Eastern Eurasian-First American cline. The Bronze Age Okunevo from Southern Siberia, the North and South American native peoples (including the prehistoric Kennewick man from the Washington state of USA), Eskimos, and Mongols are seen lying on this cline. Based on the prehistoric samples we can summarize some key events in the ethnogenesis of the Asians and Pacific Islanders thusly:

1. Before 50K, there was an unknown number of archaic Homo lineages throughout Asia all the way to the Pacific islands. Of these, the Denisovans were widespread. We have direct evidence for Denisovan admixture in Tibet, Mongolia (the Salkhit woman from 34KYA shows some Denisovan admixture), the Philippines and the Indo-Pacific islands. The ancestral Asian arrived in this landscape after splitting off from the lineage leading to the Western Eurasian in the west. Then the ancestral Asian split up into several far-ranging groups, probably by around 50KYA. These early Asian lineages included:
i. The Tianyuan-like Eastern group prototyped the Tianyuan man from the Tianyuan cave near Beijing, dating to 41KYBP. A recent study posits that the Tianyuan man might have had up to 3% archaic Homo admixture from a Denisovan source. The Tianyuan-like clade was probably basal to the later East Asian clades, which eventually split up into Northeast Asian and Southeast Asian clades ancestral to modern East Asians.
ii Onge-Hòabìnhian group, once extending from at least the Andamans (Onge, Jarawa, Great Andamanese) through Laos, Vietnam and Malaysia. This group has been recently registered in the ancient specimens from Hòabìnhian hunter-gatherers from East Asia from at least 8000 YBP.
iii. An early-diverging sister group of the Onge-Hòabìnhian clade were the hunter-gatherers of the Indian subcontinent from whom tribal Indians on an average get most of their ancestry (e.g., See Paniya in Figure 2). The Onge-Paniya gap in Figure 2 represents this deep divergence between the Onge-like clade proper and their mainland Indian sister group. Varying fractions of this ancestry persist in non-tribal Indians with a mostly south to north gradient (“The Ancient Ancestral South Indians” (AASI) of the Reich group). Today, other than this Indian HG clade, the broader “Onge-like” clade includes the Philippines Negritos, Papuans and Australians (Note their proximity in Figure 2).
iv. The Tibetan hunter-gatherer-Jomon group, which once stretched over Asia from at least Nepal-Tibet to Japan. These people played an important role in the ethnogenesis of the modern Japanese. The old Jomon were first invaded by a Northeast Asian population from the Amur River region, leading to the Yayoi period around 3000 YBP. This was followed by the classical Koreanic-type East Asian invasion of Japan, marking the emergence of the historical Japanese at the beginning of the Kofun period. Pure representatives of this group are extinct now, but their Y-chromosome and some autosomal genome survives in Nepal, Tibet and Japan. It seems the 2800-year-old Chokopani man from the Mustang cave in Nepal had 16% of this ancestry while a 3500-year-old Jomon Japanese individual shows about 44%.

2. The Onge-Hòabìnhian clade proper lack high Denisovan ancestry but their sister group, the Papuans and Australians, show evidence for at least two introgression events with Denisovans. The Philippines Negritos, too, had 1 or 2 Denisovan admixtures. Thus, greater Onge-like clade spreading from India to South East Asia encountered Denisovan races all the way from the Philippines to Sahul (the combined Pleistocene landmass of Papua+Australia) and annihilated them across the Indo-Pacific islands while mating with them on occasion. This raises the possibility that the dwarf Homo (e.g., Homo floresiensis and the Luzon Homo) on the Philippines and Flores were races of Denisovans. The North Asian and Central Asian Denisovans seemed to have had larger body size and a characteristic huge molar.

3. A sister group of the greater Onge-like clade group or alternatively a group branching close to the stem after the Tianyuan-like and Onge-like groups somehow reached America and contributed a small amount to the ancestry of some South Americans. While initially noted by Skoglund et al. in the Amazonian tribes like Surui and Karitiana, recent work by Brazilian researchers also recovered this ancestry on the South American Pacific coast. To date, this ancestry is missing in the North and Central Americans or their Beringian predecessors. This favors the model in which this Onge-like ancestry reached the Pacific coast of South America by sea (see below).

4. Recently, Carlhoff et al. reported the genome of a pre-Neolithic young forager woman from Leang Panninge, South Sulawesi dating to 7.2-7.3 KY from the `Toalean’ archaeological complex. This is the first genome from Wallacea, the Oceanic islands between the Sunda shelf of Indonesia and the Sahul landmass of the Pleistocene. She is modeled as having 50% of Onge-Papuan-like ancestry related to that seen in Sahul peoples along with the Denisovan admixture seen in them. However, the best fit models also suggest a prehistoric East Asian ancestry of 50%. The authors say this can be approximated by Qihe, a Southeast Asian Neolithic individual from 8.4 KYA. This suggests that not just Onge-like groups but also the Southeast Asian clade expanded into the Pacific, mixing with the former. However, this type of 50-50 Qihe-Onge-like mixture is no longer present in Sulawesi or its surroundings. They seemed to have been wiped out in turn by another Southeast Asian expansion, the Austronesian expansion from Taiwan in the past 4000 years.

5. Such a see-saw contest between representatives of the greater Onge-like clade and the Austronesians of Southeast Asian roots played out repeatedly over the Philippines and the Malay archipelago. This is supported by the Southeast Asian admixture seen in the various Negritos and the remarkable the ancient DNA results from Vanuatu. This cluster of about 80 remote islands in the South Pacific is populated by people speaking an Austronesian language but having most of the ancestry from a Papuan-like group. Like Papuans, several Vanuatu tribesmen wear phallic sheaths (koteka). However, the earliest genomes from these islands suggest that they were first occupied by the Austronesians. But they were soon joined by the Papuan-like group. These Papuan-like people seemed to have wiped out the Austronesians on several islands, but the latter seemed to have held out on some of the islands. These Austronesians then appear to have made a return to mix with the former and give rise to the extant Vanuatuans.

6. If the Austronesians expanded primarily via the maritime route to span a vast swath of the globe, another Southeast Asian group, the Austroasiatics, appears to have expanded mainly by land and probably by sea. These include the speakers of Vietnamese and Khmer in continental Southeast Asia, Aslian in peninsular Malaysia and Thailand, the Nicobarese in island India, Khasi in North East India and the Munda in Eastern and North Eastern India. These Austroasiatics seem to have expanded from the Mekong river basin as a group dependent on fisher and some neolithic farming for their subsistence. One group probably arrived in the Indian mainland around 3200 YBP, where they mixed with the original Indian hunter-gatherers to give rise to the Munda-speaking tribal groups like the Santhal (Figure 2). It is likely they also resorted to a maritime route to reach Nicobar relatively early on.

Finally, we shall make a few remarks regarding the implications of these findings for the modes of spread and various language groups. There is little evidence for any clear-cut relationships between the languages of the Andamanese, Papuans and Australians despite some claims to this effect by some of the long-rangers. Nor do they show relationships to Dravidian or whatever is reconstructible of the ancient Indian substrata. This is keeping with their split in the relatively ancient past when Denisovans were still around in the Indo-Pacific region and prolonged existence as hunter-gatherer tribes. The Austronesian and Austroasiatic languages are well-defined families like Indo-European and show the hallmarks of massive, relatively recent expansions. Linguistic investigations suggest that the languages of the Kra-Dai family (e.g., Thai) might be a sister group to the Austronesian languages. The genetic evidence is not inconsistent with this proposal. The Austronesians were the masters of maritime expansion — they probably reached their Taiwanese homeland after splitting off from mainland Kra-Dai speakers. From there, they returned to the Asian mainland and Malay peninsula (Cham in Vietnam and Malay) and spread both East and west. In the East, they first moved slowly, taking the Philippines and then around 3500 YBP covered most of the Malay Archipelago. Over the next 500 years, they took Melanesia and Western Micronesia. By around 1500 YBP, they had swung west to Madagascar off the coast of Africa. Over the next 700 years, they took every remaining Micronesian and Polynesian island all the way to Easter Island and Hawaii. The Southeast Asian admixture in pre-Austronesian Leang Panninge suggests that the Austronesians were not the first to venture into the Oceanic deep East. This is also hinted by the presence of the Onge-like ancestry in South America that likely reached there directly by sea via the Pacific coast. However, Austronesians certainly seem to have been the most successful. This raises the question of whether their boats were the critical factor that allowed the Papuan-like people to reach Vanuatu after the Austronesians got there first. This might also explain why the Austronesian language rather than genetics dominated in Vanuatu by functioning as the link language between the islands. Finally, this brings us to the recent work that has provided evidence for South American admixture from a Zenu-like South American tribe among the Polynesians, supporting the much-maligned contention of Thor Heyerdahl. Here again, it is peculiar that there is no evidence for a greater South American presence in Polynesia if they managed to reach some of the islands and transmit the sweet potato (Ipomea batatas). We suspect the initiative was with the maritime Polynesians who managed to reach the South American coast and bring back some admixture to their islands along with the sweet potato. Perhaps, as Heyerdahl speculated, this contact might have also contributed to some of the iconographic convergences that he noted, like on Easter Island.

Clear monophyletic language families like Austroasiatic and Austronesian are not seen as uniting China, the Korean Peninsula and Japan, though these East Asians are genetically very close. While Japonic and Koreanic have structural similarities, evidence for their monophyly as sister groups or as part of a larger Macro-Altaic assemblage is limited. This suggests that the Yayoi probably brought the Japonic languages to Japan. This might explain the more general structural similarities with North East Asian language families like Koreanic and Tungusic but the absence of a specific relationship. The Kofun, while contributing most of the genetics of the extant Japanese, did not bring the language itself. They instead probably rose up in the Yayoi background as an elite that adopted the Yayoi language while spreading Kofun genetics.

Thus, ancient DNA is making up for the absence of recorded history. Unfortunately, this revolution has not yet touched India. Imagine if we were to know something of Jorwe culture or Ash Mound peoples — they remain archaeological black boxes along with several other slices of Indian history.

The shape of dinosaur eggs

Readers of these pages will know that we have a special interest in the geometry of ovals. One of the long-standing problems in this regard is: what is the curve that best describes the shape of a dinosaurian egg? While all archosauromorphs hatch from eggs outside their mother’s body, the form of their eggs is rather variable; crocodylians and turtles may lay either leathery or hard-shelled eggs. The dinosaurs almost always lay hard-shelled eggs that tend to be rather uniform in shape in the wild. Being hard-shelled, the shape of a dinosaurian egg can be described by the characteristic curve of its maximal (area) cross-section. The egg itself will be the solid of rotation of this curve around its longest axis. Using this definition, the noted morphometrician and student of Aristotelian zoology, D’arcy Thompson, classified bird eggs into various forms in his famous book “On growth and form”. More recently, this was revisited by Nishiyama, who named 4 shape groups for the eggs of modern (avian) dinosaurs: (1) circular; (2) elliptical; (3) oval; and (4) pyriform. However, an examination of a large data set of eggs from around 1400 extant birds by Mahadevan and colleagues shows no strict boundaries between the shape classes. Hence, in principle, they should all be describable by a single equation of shape with varying parameters. If postmortem distortion and the effects of fossilization have been properly accounted for, the Mesozoic dinosaur eggs featured additional diversity. For example, the eggs of theropods, like the tyrannosaur Tarbosaurus, would not be described appropriately by any of the 4 purported classes. It would rather be a generalized higher-order elliptical egg (see below). Hence, ideally, the equation should not just cover extant dinosaurs but also the extinct ones.

Indeed, there has been a long-standing interest in obtaining that single equation that describes eggs’ shapes, starting with extant birds. One such early attempt was that of the Swiss geometer Jakob Steiner who proposed the oval of Descartes (defined by the bipolar equation: , where is the ratio parameter and the constant sum) as the general equation for avian eggs. However, D’arcy Thomas had pointed out that various avian eggs do not fit this curve. Subsequent explorations of this question have offered a range of solutions. In light of recent work presenting a new potential solution, we consider and compare some notable attempts, including the latest.

Maxwellian ovals: The great JC Maxwell, while still in his early teens, generalized the ellipses to describe families of ovals. Of these, one class of ovals, the “trifocal ellipse” can be described using three functions in :

Then the Maxwellian oval is described by the equation:

, where are parameters.

 Figure 1. A Maxwellian trifocal oval.

We too independently arrived at this curve in our teens but, unlike Maxwell, did not achieve any deep understanding of the physics of these curves. This curve is constructed using the same principle as an ellipse, viz., the locus of points whose distances from the foci add up to a constant, but it has 3 colinear foci instead of 2 of the regular ellipse (Figure 1). For and close values, we get a curve that even a casual observer will note as approximating the shape of common avian eggs (Figure 1). Indeed, in 1957, such a curve had been used by a certain E. Ehrhart as a possible fit for the avian egg following statistical analysis of real specimens. Unaware of Ehrhart’s work, in course of our own early experiments with this curve, we too considered this as a possible description of the shape of the most common type of avian egg prototyped by those of several galloanseran birds. This has now been borne out by the large dataset of Mahadevan and coworkers, in which the most frequently occurring morphology is close to this curve. However, it is hardly a universal equation of shape as there are several egg shapes lying outside its scope.

Hügelschäffer’s equation: The the 1940s, a German engineer Fritz Hügelschäffer, derived the equation of an oval that he felt was a good fit for the shape of avian eggs. As we have noted before on these pages, we independently arrived at the construction of this oval and derived its equation while in junior college. Hügelschäffer expressed the equation of this curve in the following form:

Here, is the major axis or length of the egg with its center placed at origin . is the minor axis or maximal breadth of the egg. is the distance between and the point of intersection of the segments and . By taking this effectively yields a 2 parameter shape curve, that accounts for more egg morphologies than the Maxwellian trifocal oval: with , we obtain the circular , elliptical and oval shape classes of extant avian eggs. Moreover, its parameters are entirely intuitive and can be measured easily from real specimens. However, it does not account for the so-called pyriform class (common in shorebirds) or the Mesozoic dinosaurian eggs like those of Tarbosaurus, the caenagnathid Beibeilong, the troodontids, or the ceratopsian Protoceratops.

Preston’s 4 parameter oval: Incited by D’arcy Thompson’s failure to give a  general equation for the shape of eggs, in the 1950s, Frank Preston, a versatile English engineer (invented a glass-melting furnace and a device to measure avian egg shapes), marksman and naturalist, derived the 4 parameter oval to describe the shape of all bird eggs. He used the following logic: the most symmetric class is the circular class for which one can easily write down the equation: . By multiplying this by the parameter , the aspect ratio (ratio of minor to major axis) of an ellipse, we get the equation , which can account for both the circular and elliptical classes. Then Preston accounted for the remaining classes using a polynomial function , where , thus yielding the final equation of a generalized oval:

Figure 2. Eggs of selected extant and extinct dinosaurs modeled using Preston’s equation.

You can try out various fits with above parameters on a collection of real eggs here

As one can see from Figure 2, Preston’s 4 parameter oval accounts for all dinosaur egg shapes extant and extinct. The egg of the Ural owl is of the elliptical class coming close to the circular class. The emu is nearly a classical elliptical with a very small parameter that adjusts it to a more generalized ellipse. The song thrush and osprey are very nearly ovals with a pronounced parameter and slight adjustments, again with a very small parameter. The guillemot and great snipe are clear pyriforms with both pronounced and parameters. The extinct dinosaur Troodon has an egg quite distinct from any extant bird but can still be modeled by Preston’s oval with positive terms. The egg of Tarbosaurs (and others like it, e.g., Beibeilong or Protoceratops) is a generalized ellipse that is again well-modeled by Preston’s equation with just a negative term with other powers in the polynomial having 0 coefficients. Preston’s equation can model most extant bird eggs using just the linear and square terms with negative coefficients. The cubic term is only needed for unusual eggs, like in this case, that of Troodon. Since Preston, several researchers have tried to duplicate his approach by using other functions in place of his cubic polynomial (see below). However, recent numerical analysis using a dataset of 132 real eggs from various modern species by Biggins et al. has shown that Preston’s curve outperforms all these other attempts in having the least and an impressively small error. Thus, the Preston 4 parameter oval can be considered a valid, universal description of the shape of the dinosaurian egg.

In light of the success of the Preston oval, we were a bit surprised when we saw a recent work by Narushin et al. claiming to introduce a universal formula for the egg shape. They acknowledge the success of Preston’s work but state that the parameters in his equation are neither intuitive nor readily determined. The former is indeed a potential criticism; however, the latter is less of any issue with modern graphing software, so long as one has good photographs. Hence, they decided to start with Hügelschäffer’s formula and applied a series of modifications to arrive at a complicated formula for a general oval:

Here, as in Hügelschäffer’s equation, is the major axis or length of the egg; is its minor axis or greatest breadth; is the breadth of the egg at the point halfway from the center at to the narrow end of the egg (Figure 3). However, is not the same as in the Hügelschäffer equation but is defined as:

, where is a positive number.

The landmarks of Narushin et al’s equation for a dinosaurian egg.

One advantage of this equation is that can be directly measured relatively simply with Vernier’s calipers and a ruler. The parameter can be empirically calculated from by adjusting . While the authors state this equation can account for all extant bird eggs, we found that, unlike Preston’s equation, it could not account for special cases of extinct dinosaur eggs, like those of Troodon and Tarbosaurus, assuming that their reconstruction is accurate. However, we rectified that by using an “inversion” flag that takes 3 values: N, Y, and H. It appears that for all extant birds (at least those considered by Narushin et al.), this flag is N; these can be modeled using their equation as is. For Troodon and related eggs, the flag is Y; here, has to be substituted by . For Tarbosaurus and related eggs, the flag is H; here for we use the equation as is and for , we substitute with . This accounts for all dinosaur egg shapes comparable to Preston’s equation (Figure 4). If we normalize it by taking , it effectively leaves us with a maximum of 4 parameters as in the case of Preston’s equation.

Figure 4. Eggs of selected extant and extinct dinosaurs modeled as Narushin et al’s oval with the inversion flag modification.

You can try out various fits with above parameters on a collection of real eggs here.

The relative merits of this equation need to be compared to that of Preston’s using real specimens. Unfortunately, this requires additional work as Mahadevan and colleagues’ large dataset does not have all the necessary measurements for such a comparison. They instead used the oval of Baker, an attempt to duplicate Preston’s work, which significantly falls short of the latter in terms of accuracy while providing a simple 2 parameter space. It is defined by the equation:

Here is the aspect ratio of the ellipse as in Preston’s equation or the equivalent of in Hügelschäffer’s equation, while is an asymmetry parameter similar to in Hügelschäffer’s equation. This curve has 3 successively tangent lobes with points of tangency at and . For and the two lobes have a divergent hyperbola-like form. For , the curve takes the form of the oval that approximates the shape of a dinosaurian egg. When , the curve becomes an ellipse.

A biologist can easily conceive each of the parameters from Preston’s or Narushin et al.’s curves as being controlled by a genetic factor, with changes in it leading to a change in the parameter. Thus, one can easily account for the diversity of egg morphologies observed among dinosaurs through genetic changes. The parameter gene mapping feeds directly into the question of what are the selective forces acting on egg shape. Several of these have been proposed and debated since Darwin. Irrespective of the correctness of some of these, one key point emerging from the suggestions made by Birkhead is that the ovoid morphology is a clear sign of a comprise solution resulting from balancing selection. The compromises themselves might involve very different factors. One such relates to spherical morphology having the smallest surface area for a given volume. Hence, it is ideal for not losing heat quickly. However, eggs also need to be externally warmed, either by direct contact with the mother or exposure to solar or geothermal heat (e.g., in titanosaurs). Here, a less spherical shape would afford a greater surface area to allow quicker external heating. Similarly, a hard-shelled egg would have the greatest strength against external force if spherical. This would be selected for better protection or bearing the weight of the brooding mother or insulating material deposited atop it. On the other hand, it should also be easy enough for the chick to break out. These opposing forces would lead to compromise solutions in the form of deviations from circularity. Mahadevan and colleagues also observed that increased flight performance is often associated with smaller aspect ratios and more asymmetric eggs. Here again, a compromise of sorts might be in play — higher flight performance selects for bigger eggs on one hand and a more streamlined body on the other. Hence, the compromise is achieved by having longer or more asymmetric eggs. A similar effect, albeit unrelated to flight, but body morphology, might have also been at play in the Mesozoic dinosaurs with long eggs. Of course, the shape diversity beyond a simple ellipse suggests that other selective forces beyond the above are also at play.

However, a morphometrician of the bent of D’arcy Thompson would still object that these equations need to be derived ground up from physics — in fact, he voices precisely that problem in his account of bird egg shapes — they need to be derived from an equation which accounts for fluid pressure in a bounded membrane. This was keeping with his wider skepticism towards one of the foundations of biology (natural selection) while emphasizing the other (geometry). Mahadevan and colleagues presented such a derivation a few years back; however, it is not clear if it can actually recapitulate the entire range of ovals seen in real-life dinosaurian eggs.

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Further reading:

Avian egg shape: Form, function, and evolution by Stoddard, Yong, Akkaynak, Sheard, Tobias, and Mahadevan

Egg and math: introducing a universal formula for egg shape by Narushin, Romanov, and Griffin

Accurately quantifying the shape of birds’ eggs by Biggins, Thompson, and Birkhead

Matters of religion: the lesson by the lake

Sharvamanyu was with his preceptors Somakhya on Lootika on the shore of a lake in the midst of the mountains on a full moon night. It was the cremation ground for a lineage of Vs, who had historically specialized in the arts of preparing medico-recreational substances from Acacias but had risen to the status of warriors during the great Jihād-s of the monstrous Mogol tyrants. Some distance from where they sat, the shore was whitened by the bones of the generations of Vs who taken the ladder to confront the glowing jaws of the fearsome Sārameyau en route to the realm of Vivasvān’s dark son. Now, those osseous remains gleamed like gold as the bowl of soma climbed over the lake to gladden the bands of Vasu-s, Āditya-s and Rudra-s with a pleasing draught. Mātariśvan, who is also known as Śambhu, drafted a pleasant breeze over the lake making waves lap the banks, even as the music of the sons of Rudra playing on the vāṇa-s sounded in the airy realm. Sharvamanyu sought the mysterious experience of yoga from his preceptors. He had been practicing a mantra for six months but had met with nothing but failure. The ensign of Soma climbing the celestial vault occulted the great mass of stars known as Tiṣyā, marking the day of the great bull-sacrifice of yore to Rudra. That conjunction is indeed a sign of the gods Somārudrā — the Taittirīya-śruti has declared: “rudro vai tiṣyaḥ |”. Somakhya and Lootika had verily received a signal of The god in that regard. It is said that on that day the dānava Maya had built the Tripura-s, and it was on that day that Rudra had destroyed the triple-planets.

They led Sharvamanyu to a small shrine of the awful Vināyaka by the cemetery with an archaic image of the god. An inscription from the Vikrama year 1532 stated that the image had been found in the lake by a Gāṇapatya siddha and installed in the shrine. The siddha was said to have joined the retinue of his chosen god as a phantom upon his death and was believed to manifest occasionally in those regions, especially to V votaries who were uncorrupted by religious degeneration that had passed through the region thereafter. Somakhya and his wife asked Sharvamanyu to worship Vighna with a short stuti and by placing some of the flowers they had collected in course of their trek to the lake at the feet of the image. Sharvamanyu recalled one their teacher Shilpika had taught them:
namas te gajavatrāya namas te gaṇanāyaka |
vināyaka namas te .astu namaste caṇḍavikrama ||
Obeisance to you, the elephant-faced, obeisance to you the lord of the hosts; obeisance be to you the Vināyaka; obeisance to you of fierce valor.

namo .astu te vighnakarte namas te sarpamekhala |
namas te rudravaktrottha-pralamba-jaṭharāśrita ||
Obeisance be to you the creator of obstacles, obeisance to you with a snake-girdle; obeisance to you endowed with a pendant belly, who emerged from Rudra’s face.

Then, they asked Sharvamanyu to do the kara- and aṅga-nyāsa-s appropriately and begin the japa of his mantra 324 times. As he was in the midst of that, Lootika pointed her siddha-kāṣṭha, whose tip bore the carving of the head of Garuḍa, at him. Suddenly, he had a vision of a huddled band of people wearing bone-ornaments singing songs in a strange language. He could catch many words, but it was not entirely intelligible to him — it was neither Sanskrit nor a modern Aprabhraṃśa. At climactic phrases in the lyrics, he felt overpowering emotions seizing him from deep within. From the midst of the band arose the ghost of a V named Kiñjalka. The phantom said: “Having performed great acts of valor, I was beset by a large band of well-armed enemies when my siddhi-s had declined. Hence, I had to do battle as an ordinary man though I was still powered by all the experience I had acquired from my assiduous practice from a young age. Thus, fighting my foes like the sūtaputra in his last fight, I was slain and passed into the retinue of Paśupati Deva.” Then, he saw the apparition of a beautiful woman. As she faded away from his vision, he felt all his strength had ebbed away, and he involuntarily fell to the ground. As he struggled to get up, he saw a dog repeatedly going to the cemetery and waiting for someone who had joined the Pitṛrāṭ. As the apparition of the dog rose up into the sky and merged with the constellation graced by the bright Procyon, he saw a cat descending from a pole and run towards a large bowl with a goldfish. It knocked down the bowl, and the fish jumped out to swim away into the great lake stretching before him clearing the prior apparitions. Then, despite the moon being there in the sky, all went pitch black — he felt he was in a subterranean cave with no lamp. That utter darkness remained for some time during which he lost track of everything except the mantra whose japa he was performing. He then saw his friend Vidrum being dragged away with a lasso around his neck by a buffalo. He wanted to shout out to his companions to aid his friend, but his voice deserted him. Now, to his utter horror, he saw Abhirosha’s corpse being eaten by a voracious dog and crows. Then, he saw himself being dragged the same way but now he felt an utter calm — death no longer seemed to cause him any concern at all and all his emotions were stilled.

Then, he saw a great procession of reptiles and other strange animals, of which he recognized only a few, but the rest still seemed vaguely familiar to him as he had seen Somakhya and Lootika draw them when they were in school. In that utter darkness, he saw a clear vision of the temple of Rudra in the cemetery with the liṅga blazing forth as though self-luminescent — he remembered his teachers telling of the term sadyojyotis — now he realized what that meant. He heard the mantra-s from the Taittirīya-śruti by which the liṅga is installed. Suddenly, the terrifying five-headed god after whom his parents had named him manifested from the liṅga. Each of the brahma-mantra-s from the upaniṣat of the Taittirīyaka-s, revealing the five-fold form of the god known as Mahādeva, sequentially manifested in his mind. The first was that of Sadyojāta with which he saw the face of Kumāra. The next was that of Vāmadeva with which he saw the perfect face of Manonmanī. Then the Aghora mantra manifested, and he saw the dreaded face of the Bhairava. After that came the Tatpuruṣa mantra, and he beheld an aquiline face with a solar orb, glowing like the eagle of the god Savitṛ. Finally, came the Iśāna mantra, and he saw that glorious face known as Rudra-sadāśiva. The apparition of Rudra was more real than any experience he had had. His mind involuntarily remarked over the japa: “He is known as Paśupati; he is Īśāna.”

Thereafter, he could discern the great bow of the god and the missile mentioned in the scriptures as the Pāśupata — the great arrow of Nīlarudra. He then saw the terrifying trident of the god with which he had impaled Andhaka in the vast White Forest; the cakra with which he had severed the head of Jalandhara who had even bound the Vaḍavānala; the Aghora-missile with which he had destroyed the triple-forts; the vajra praised in the śruti; the bhindipāla, the śataghni, the tomara, the prāsa and the terrifying sword with which had dealt death to numerous dānava-s as described in the national epic. He was accompanied by an awful troop of gaṇeśvara-s, the ape-faced Nandin, the skeletal Bhṛṅgin, the many-armed lion-headed Vīrabhadra who had beheaded Dakṣa and flayed the giant daitya Nala, the black Mahākāla, the Kṣetrapāla emitting a meteor that blazed through the firmament and Caṇḍeśa. He also saw Kīrtimukha, of the form of a standalone leonine head, and the Śiva-kṛtyā, who had emerged from the mouth of Rudra to snare the Bhārgava in her vulva, both inspiring a primal fear. He saw a great churn of rapidly moving Pramatha-s holding tridents, axes, and other weapons looking like smaller Rudra-s. Then he saw the Śiva-gaṇa-s with lion-, elephant-, horse-, donkey-, dolphin-, hog-, bovine-, goat- and ram- faces prancing along, brandishing various weapons. He also saw the axe-wielding Gaṇapa surrounded by a great host of ferocious, black elephant-headed Vināyaka-s. For a moment, the realization of the profound gaṇa-vidyā, illuminating the meaning of the multitude of gaṇa-s of Mahādeva flashed in him. He simultaneously saw the import of Rudra in the śruti and the śaiva-śāstra. At that point, he beheld the skull of Prajāpati held by Rudra. At once, he had the realization that he, together with the entire universe, was within that skull gracing the eight-fold god. He spontaneously uttered that Atharvan incantation of The god, manifesting both as himself and his son, believed to have been said by Prajāpati himself as he was decapitated by Rudra:
kāpālin rudra babhro .atha bhava kairāta suvrata |
pāhi viśvaṃ viśālākṣa kumāra varavikrama ||

Thereafter, he spontaneously uttered the devadeveśvara-stuti:
namo viṣama-netrāya namas te tryambakāya ca |
namaḥ sahasra-netrāya namas te śūla-pāṇine |
namaḥ khaṭvāṅga-hastāya namas te daṇḍa-dhāriṇe ||
Obeisance to the odd-eyed one and obeisance to you with the three goddesses. Obeisance to the thousand-eyed, obeisance to you with a trident in hand. Obeisance to the one with the skull-topped brand in hand, obeisance to you bearing the cudgel.

tvaṃ deva hutabhug-jvālā-koṭi-bhānu-samaprabhaḥ |
adarśane vayaṃ deva mūḍha-vijñānato .adhunā ||
You, o god, have the luster like that of the flames of the eater of oblations (Agni) and a crore suns. Before seeing you, o god, we were foolish; now we have been enlightened.

namas trinetrārtiharāya śambho triśūlapāṇe vikṛtāsyarūpa |
samasta-deveśvara śuddhabhāva prasīda rudrācyuta sarvabhāva ||
Obeisance to the three-eyed remover of troubles. O one, who is trident-handed, with a mouth of fierce form, the lord of all the gods, of pure nature, Rudra, the infallible and of all natures, be pleased.

pūṣṇo .asya dantāntaka bhīmarūpa pralamba-bhogīndra-lulunta-kaṇṭha |
viśāla-dehācyuta nīlakaṇṭha prasīda viśveśvara viśvamūrte ||
O destroyer of teeth of Pūṣan, one of terrible form, with the dangling lord of the snakes hanging from your neck, of gigantic body, infallible, the blue-throated one, the lord of the world, whose form is the world, be pleased.

bhagākṣi-saṃsphoṭana dakṣa-karmā gṛhāṇa bhāgaṃ makhataḥ pradhānam |
prasīda deveśvara nīlakaṇṭha prapāhi naḥ sarvaguṇopapanna ||
O one how blew up Bhaga’s eyes, of skilled actions, may you take the foremost offering of the ritual. O lord of the gods, the blue-throated one be pleased. Protect us, o one endowed with all qualities.

sitāṅga-rāgāpratipannamūrte kapāladhārims tripuraghna deva |
prapāhi naḥ sarvabhayeṣu caivaṃ umāpate puṣkara-nāla-janma ||
O god of unattainable form smeared with white ashes, the skull-bearer, the slayer of the Tripura-s, the husband of Umā, and the one born from the lotus-stalk (as Agni or from Prajāpati) protect us from all fears.

paśyāmi te dehagatān sureśa sargādayo vedavarānananta |
sāṅgān savidyān sapada-kramāṃś ca sarvān nilīnāṃs tvayi devadeva ||
O eternal lord of the gods, the root of all lineages of the universe, I see in your body the excellent Veda-s together with the Vedāṅga-s, the various branches of knowledge, and the Pada and Krama recitations of the Veda, everything is inside you, o god of the gods.

bhava śarva mahādeva pinākin rudra te hara |
natāḥ sma sarve viśveśa trāhi naḥ parameśvara ||
O Bhava, Śarva, Mahādeva, the yielder of the Pināka, Rudra, Hara. We all bow to you, o lord of the universe. Protect us, o foremost lord.

Thereafter, Sharvamanyu saw in place of Rudra, his consort, the great goddess Kālarātrī, surrounded by diverse yoginī-s filling the whole field of view up to the horizon with an eight-fold symmetry. At that sight, he spontaneously uttered the Kalarātrī-stuti:
jayasva devi cāmuṇḍe jaya bhūtāpahāriṇi |
jaya sarvagate devi kālarātre namo .astu te ||
Victory be to you the goddess Cāmuṇḍā; victory to you who snatches away all beings. Victory to the omnipresent goddess; obeisance to you, o Kālarātri

viśvamūrte śubhe śuddhe virūpākṣi trilocane |
bhīmarūpe śive vedye mahāmāye mahodaye ||
O world-formed one, the auspicious one, the pure one, the odd-eyed one, the three-eyed one, one of terrible form, benign one, one of the form of knowledge, one of great illusory powers, one of great preeminence.

manojave jaye jṛmbhe bhīmākṣi kṣubhitakṣaye |
mahāmāri vicitrāṅge jaya nṛtyapriye śubhe ||
Victory to you, o one of the speed of mind, the victorious one, the great blossoming, the terrible-eyed one, suppressoress of all agitation, the bringer of great disease, of marvelous body, lover of dance and the auspicious one.

vikarāli mahākāli kālike pāpahāriṇī |
pāśahaste daṇḍahaste bhīmarūpe bhayānake ||
O fierce one, the great goddess of time, time, the remover of sins, wielder of a noose, with a rod in your hand, of terrible form, the fear-inspiring one.

cāmuṇḍe jvalamānāsye tīkṣṇadaṃṣṭre mahābale |
śata-yāna-sthite devi pretāsanagate śive ||
O Cāmuṇḍā, with a flaming mouth, with sharp fangs, you of great might, the goddess riding a hundred vehicles, seated on a corpse, the benign one.

bhīmākṣi bhīṣaṇe devi sarvabhūtabhayaṅkari |
karāle vikarāle ca mahākāle karālini |
kālī karālī vikrāntā kālarātri namo .astu te ||
Obeisance be to you, o terrible-eyed one, frightful goddess, striking terror in all beings, terrifying one, formidable one, the great time goddess and the terrifying one. She is time, the terrible one, striding boldly and the night of dissolution.

Sharvamanyu concluded his japa and rose, wanting to ask his companions about his visions, but they pressed their fingers to their lips, directing him to be quiet and continue the japa as they climbed one of the proximal hills on the rim of the lake. As they made their way up, they paused to take yet another look at the great occultation of Tiṣya nearing its conclusion. Reaching the top of the prominence, they arrived at the little shrine of Śiva. On the wall of the shrine was the relief of a siddhayoṣit Stṛkā performing liṅgārcana. Somakhya and Lootika offered some flowers there and performed a tarpaṇa to the feet of the said siddhayoṣit. They asked Sharvamanyu to do the same and remarked: “This siddhayoṣit, Stṛkā, impelled by Mahādeva arrived from the continent of Śvetadvīpa to become a student of the charismatic siddhayoṣit Indramaṇidevī of the śūdra-varṇa at Śūrpāraka. There having studied the Śambhu-para scriptures and observing the vrata of chastity, she acquired siddhi-s in various Māheśvara-mantra-s. Then, she performed mantra-sādhanā at the cemeteries of Kollagiri, Kilakilārava, where the yadu hero had slain the giant ape Dvividha, and Avimukta, where Kālabhairava had imparted the kāpālika rite to Kubera. She then settled here under the patronage of the lord Jayakeśin. Due to her siddhi-s in the Netra, Koṭarākṣa, Vyādibhakṣa and Aghoreśvarī vidyā-s, she lived a long life free of trouble teaching the Māheśvara-śāstra-s and experiencing the glories of Nīlarudra.”

Then seating themselves on the platform around the shrine Somakhya and Lootika bade Sharvamanyu to ask them questions that he might have regarding his sādhanā. Sh: “The experience I had finally opened me to the possibility of what the lakṣya of the sādhāna might be. I had struggled for months failing with the dhyāna and, after that, with the avadhāna. But the sudden manifestation of a clear vision of the deva and his parivāra has cleared that issue in one stroke.”

L: “Indeed, succeeding at dhyāna is an impediment for many. A small number of people are endowed with sahaja-dhyāna capacity — the same is true for the other steps in sādhanā. Such folks might wonder why others should even raise the matter. Let me be clear, devatā-dhyāna does not come automatically to the majority. However, it can be achieved by multiple means: (i) through the repeated study of mantra-siddhānta-s that give accounts of the devatā-s; (ii) through purāṇa readings; (iii) through study of properly prepared texts known as devatā-citra-saṃgraha-s; (iv) by visits to temples or attending temple festivals or cala-pujā-s to behold the icons of the deities; (v) by an experience induced by teachers or other interested mantravādin-s. We attempted that last option with you, and believe it should help you going forward.”

Sh: “Still, I wonder if I might succeed at the avadhāna and if the siddhi might manifest at all? Pray tell me what are the rahasya-s of that?”
S: “Abhyāsa is the first and foremost step. As with physical exercise, for most people, the ability to perform something at a certain level does not come as sahaja. They have to use their will often with enormous force to get themselves to practice. At first, the going is hard, the fruits are limited, and there could even be negatives like pain. One has to calibrate the right level the body can take and slowly step up the gradient — you know this well in physical practice. Eventually, one starts seeing the benefits of it and liking the action. Unfortunately, the path to even a modicum of siddhi is littered with sādhaka-s who failed at this step. That is the reason many of our traditions emphasize physical yoga with āsana, prāṇāyāma, and the like. It gives you a tangible object of control — your own body. By observing how you succeeded in that control, you will develop a model that can be imitated at the mental level to acquire the control needed for avadhāna. Lootika, do you want to add something?”

L: “Regarding siddhi, I would remark that svayaṃsiddha-s are rare. The siddhayoṣit, at whose shrine we are now seated, is a case in point. However, she became one due to two points that are often overlooked. First, she had sahaja capacity for abhyāsa — without that, she could not have become a svayaṃsiddha. Second, she was an example of a daivarakṣitā — otherwise, how could she have come safely from Śvetadvīpa to Jambudvīpa — she could have been captured and borne away by any number of men in the process. Then, she managed to perform kṣetrāṭana, reaching difficult śmaśāna-s to perform sādhanā. Hence, one has to be cognizant of one’s condition. The probability of being daivrakṣita is low; one cannot make that a default assumption; likewise with sahajābhāyasa-śakti. Hence, one has to gauge one’s capacity while not faltering at the abhyāsa and set the sādhya accordingly.”

Sh: “Surely the apparition of the phantom of Kiñjalka and the dog that kept visiting the cemetery have a lesson here?”
L: “The case of said V gives an important lesson. A human is a finite being with a relatively small window of opportunity. A person usually begins life with no special endowments. Even a sahaja soul, while endowed with great potential, cannot make that manifest entirely without appropriate abhyāsa. Then he reaches a high point upon honing his sahaja capacity by abhyāsa at some point in his youth. After that, he plateaus. This is because he comes under two opposing forces, one of physical decline with age and the other of the growing wisdom and experience fueled by his constant sādhana. At some point, his physical decline overshoots his accruing wisdom and ability; thus, his downward slide begins. In some sādhaka-s, the fame of their sādhana attracts pupils from the ranks of others seeking glory. They seek para-saṃyogāt mahattvam, which in turn feeds into the sādhaka, for he is now possessed of an army of pupils. As we have told you before, vidyā is enhanced by the resonance with good antevāsin-s. Thus, he may rightly (due to wise counseling of his army) or wrongly (living off the deeds of his students) be buoyed up much longer than his true personal capacity. In the case of Kiñjalka, he was unable to get a troop of any size and had to live off his own capacity. Hence, when confronted by a bhrātṛvya with a larger force, he was killed with his own capacity limited by physical decline. Thus, the lesson is one may experience a plateau in the sādhanā, after which the decline and death follow. Thus, many sādhaka-s have come and gone, and nobody remembers them. Other things can happen. Either when human decline sets in, or when a sādhaka has had an experience like you had today, or when he witnessed the siddhi of his guru from close quarters, he might think that the siddhi is close by and will repeatedly try to grasp it. However, it would be as futile as the dog hoping day after day that its master who has taken the southern path would return from the cemetery.”

Sh: “Somakhya, I note that you are in silent contemplation with almost a tinge of disapproval. Have I done something wrong?”
S: “You know me from so long back that you picked something just from my face that you felt was disapproval. It is not — it is just that I was mentally wanting to head off certain questions that I felt would ensue from you. As for the rest of the apparitions in your experience, spend some days contemplating them in silence, and you will get your answers. You may ask other questions, though.”
Sh: “I now realize that the path can be the climb up the slopes of Kailāsa — some go up to glimpse the god and return to the world of men, but others make an exit midway to join the retinue of the god as a phantom! But in everyday life, man continues with his toils if he sees at least a few positive results else, he gives up. How does one keep toiling in face of repeated failure, when one might be reaching for the unattainable like the dog at the cemetery? Moreover, the tale of the wicks of Bhairavānanda, which Lootika had told us in school, comes to mind — would I end up with wheel on my head for my persistence?”

S: “That is indeed the hardest part. You may have the great svayaṃsiddhi but not be daivarakṣita. Thus, your attainments could be modest. However, due to your svayaṃsiddhi you might have perfect jñāna of what it would be like to be mahāsiddha but still not be one in reality. If you have that jñāna, you may keep trying, though, in the end, your fate would be no different from that of the dog. It might be frustrating, but at least you would have only failed from being a daivahataka. But then take the case of our former classmate Hemaliṅga; he definitely had enormous mathematical capacity and smashed his way to a certain level. But he sought to reach the levels of the great gaṇitajña-s of all times that lay out of his reach. Attempting hard, like trying to leap onto a high ledge, he only hit the cliff-face and dropped down. However, that was not fatal; Vrishcika tells us that his abhyāsa at least brought him comfort in life. Thus, the great failed attempt at mahāsiddhi often builds character and gives you a minor siddhi that might bring pleasure in life. However, we must warn you Sharva, that path to the highest siddhi-s is fraught with much danger even as the fourth wick of Bhairavānanda. You might see warnings as you are headed that way, which you must differentiate from benign failures. Indeed, Lootika and I have seen the ghost of more than one V, who persisted through those warnings and fell in such attempts, like the corpses of forgotten climbers on slopes of the Himavant. On the other side, if your sādhya has come in clear vision, keep toiling and change upāya-s upon repeatedly failing. Like in biology, so also here; remember, once one has entered the stream, one sinks when the toil ceases. So you have to do so just to stay afloat. The good teacher should tell those who cannot keep up to exit early.”
Lootika: “Now, let us resume our trek back to reach in time to catch the train back to the city.”

Twin Āditya-s, twin Rudra-s

This note originated as an intended appendix to the article on Rudra and the Aśvin-s we published earlier. The first offshoot from that work, which we published separately, explored the links between Rudra, Viṣṇu and the Aśvin-s in the śrauta ritual. We finally found the time to fully write down the intended appendix and present it as a separate note. To rehash, we noted an intimate connection between the primary Rudra-class deity (typically in his manifestation as the great heavenly Asura, the father of the worlds) and the twin deities (the Aśvin-class) of the ancestral Indo-European religion. This is preserved in multiple descendants of our ancestral religion, such as in the śruti, the para-Vedic material in the aitihāsika-paurāṇika corpus, in the Roman religion relating to Castor and Pollux, and probably the non-Zoroastrian strains of the Iranian religion. It was definitely there in at least some branches of the Germanic religion, but its destruction by the West Asian mental disease has only left us with the euhemeristic figment of Horsa and Hengist as the descendants of Woden. Likewise, we hear explicitly of the destruction by the Christians of the temple dedicated to the Western Slavic deity Rugiaevit and his twin sons Porevit and Porenut. It is pretty likely that Rugiaevit’s name is derived from the same root ru- as that in the name of Rudra, and these twin sons are the equivalents of the Aśvin-s.

In the śruti, this old motif manifests as the Aśvin-s being the sons of Rudra who follow on his track as he rides his heavenly chariot. As the physicians of the gods, they inherit the medical and pharmacological virtuosity of their father. In a parallel Vaidika tradition, which entered the śruti fold from a group of Aryans distinct from the ṛṣi-s who composed the RV, the twin sons of Rudra are Bhava and Śarva, who accompany their father, like the Dioskouroi of the Greco-Roman worlds. Their worship is prominent in the Atharvaveda and some texts preserved in later Vedic collections; however, in the ādhvaryava tradition, they were absorbed as names of Rudra or those of the multitude of Rudra-s. In the para-Vedic material preserved in the itihāsa-s and purāṇa-s we see them as the twin ectype of Skanda, i.e., as Skanda-Viśākhau, the sons of Rudra.

With this background, we shall consider the enigmatic sūkta of Urucakri Ātreya (RV 5.70), which on the surface is a simple 4-ṛk one in the Gāyatrī meter. The anukramaṇi specifies its deities at the twin Āditya-s, Mitra and Varuṇa. Indeed, the first ṛk of the sūkta is directed to these gods and it is embedded amid the long series of sūkta-s to Mitra and Varuṇa by different Ātreya-s:
purūruṇā cid dhy asty avo nūnaṃ vāṃ varuṇa । mitra vaṃsi vāṃ sumatim ॥
Indeed, now, in full breadth is the aid from you two, O Varuṇa! I have gained the benevolence of you two, O Mitra!

After beginning with an acknowledgment of the help gained from Mitra and Varuṇa, the next ṛk suddenly changes the focal deities:

tā vāṃ samyag adruhvāṇeṣam aśyāma dhāyase । vayaṃ te rudrā syāma ॥
O you two, may we attain you two together, in your benign state (literally: without intention to harm) for our stability. May we be so, o you two Rudra-s.

pātaṃ no rudrā pāyubhir uta trāyethāṃ sutrātrā । turyāma dasyūn tanūbhiḥ ॥
Protect us, two Rudra-s, by your defenses; also save us, since you two are good rescuers. May we overpower the dasyu-s with our bodies.

Notably, the deities remain dual in the above two ṛk-s, but they are explicitly identified as twin Rudra-s. While some students of the Veda have taken this use of Rudra to be merely an appellation transferred to the deities of the first ṛk, there is no support for that. Mitra and Varuṇa are unanimously categorized in the Āditya class, as its leading exemplars, and never placed in the Rudra class. Hence, we have to understand the twin Rudra-s of the above two ṛk-s differently. First, their raudra nature is explicitly indicated in the entreaty to be benign (adruhvāṇeṣam). Second, they are described as sutrātrā, good rescuers, which immediately brings to mind the Aśvin-s who are frequently invoked in such a capacity. In the RV, Rudra in singular denotes the god, in his unitary form, and as the father of his class. Rudra-s in the plural refer to the entire class or the Marut-s. The dual form of Rudra applies only to the Aśvin-s everywhere else in the RV. In particular, the Atri-s repeatedly refer to them as such: e.g., RV 5.73.8, 5.75.3 and in RV 5.41.3 they are invoked together with Rudra as Asuro Divaḥ. Thus, we posit that in RV 5.70.2-3, Urucakri Ātreya implies the Aśvin-s by the dual form of Rudra and not the twin Āditya-s.

The last ṛk of the sūkta goes thus:
mā kasyādbhutakratū yakṣam bhujemā tanūbhiḥ । mā śeṣasā mā tanasā ॥
May you two of wondrous deeds not make us experience some phantom with our bodies. Neither with the rest [of our people] nor with our descendants.

The word yakṣa (neuter) could be taken to mean a ghostly apparition or phantom — perhaps one which causes a disease — a yakṣma. The imploration is to avoid the possession of the ritualist’s own body or that of this people or descendants by such a phantom. On the one hand, this is rather reminiscent of the supplications to Rudra for similar protection, often with the negative particle mā. On the other, it is reminiscent of the supplication to Varuṇa to be relieved from his heḷas (=“fury”; also, a feature of Rudra) for the sins that he unerringly notices. For instance, we have in the śruti the imploration of Śunaḥśepa:

ava te heḷo varuṇa namobhir
ava yajñebhir īmahe havirbhiḥ ।
kṣayann asmabhyam asura pracetā
rājann enāṃsi śiśrathaḥ kṛtāni ॥ RV 1.24.14
We avert your fury (heḷas) O Varuṇa with obeisances,
we implore to avert it by rituals and oblations;
ruling, for us, O all-seeing Asura,
you will give release from the sins that were done.

Thus, both Varuṇa and Rudra share not only the heḷas but are also known as Asura-s (the latter being emphasized for the cognate of Varuṇa in the Iranic branch of the religion, and remembered for Odin (see below) in the Northern Germanic religion). Thus, even though Varuṇa or Mitra are never called Rudra-s, they have a certain overlap of category, particularly in the actions of Varuṇa, and perhaps, to a degree, in the Iranic world in the cognate of Mitra. We believe that in the sūkta under consideration, Urucakri Ātreya plays on this overlap in the final ṛk by not naming any deity but simply using the dual epithet adbhutakratū. Thus, we suggest that he is purposefully ambivalent to cover both sets of twin deities referred to in the sūkta — the Āditya dyad or the twin Rudra-s, i.e., the Aśvin-s. The epithet adbhutakratū will transparently apply to the Aśvin-s as they are frequently described as wonderworkers in the śruti. The ṛk could also apply to Mitra and Varuṇa in the sense of supplication to avoid their heḷas. The invocation of the heḷas of Mitra, Varuṇa, and the Marut-s, representing the intersection of their respective functional categories can be seen in RV 1.94.12 composed by Kutsa Āṅgirasa:

ayam mitrasya varuṇasya dhāyase
‘vayātām marutāṃ heḷo adbhutaḥ ।
mṛḷā su no bhūtv eṣām manaḥ punar
agne sakhye mā riṣāmā vayaṃ tava ॥
This one is to be fed ghee [literally suckled],
as the wondrous pacifier of the fury of Mitra and Varuṇa, and of the Maruts.
Have mercy on us! May the mind of these (the above deva-s) be good again
O Agni, in your friendship, may we not be harmed.

This overlap in category has confused some Indo-Europeanists of the Dumezilianist strain. They have split hairs and gone into contortions about whether the Germanic Odin represents a cognate of Varuṇa or Rudra. This ancient functional intersection has meant that one or the other class of deities could have served as a locus for absorption of traits of the other.

Self, non-self and segregation: a very basic look at agent-based lattice models

In our college days, a part time physics teacher from an old and respected V clan used to chat with us about issues of mutual interest that were beyond that of the rest of the class (or for that matter the rest of the teachers) and well out of the scope of the syllabus. He was the only one among the physics staff with an interest in science for science’s sake. We always felt he had it in him to be a scientist and he was indeed was pursuing a doctoral program at his own pace on the side. However, he clarified to us that he was the big fish in the small pond and that every man’s ambition is like a rocket set off on a Dīpāvalī night — drawing out a parabola on the board he declared with his characteristic smirk: “It will come down; hence, why trouble yourself with a dizzying fall”. In course of one involved conversation spanning thermodynamics, dynamical systems and biological ensembles, he declared to us: “I agree with you that there are several problems where the actual entities are fungible. It doesn’t matter if we are dealing with atoms, cells or animals, they could as well just be numbers. You should explore the Ising models — maybe you will find something there to answer your questions.” We are not really into “proving a few theorems”; however, playing with things on paper or a computer has always excited us. Hence, the next time we could access a computer we began looking into those models and soon realized that it could be used to understand some basic aspects of biological systems.

Here we shall describe some experiments with such models that go no further than the most basic exploration of these systems. In physics, such models were first proposed by Lenz and his student Ising. In sociology, they were introduced by Schelling (of whose work we learnt much later) who carried out the experiments with a graph paper and coins. Today we can do them easily by writing some code on a little computer. The basic rules for the games we shall look at go thus:

1) The games are played on a lattice on the surface of a torus but for visualization we shall cut open the torus and render it as a square board. Thus it would look like this:

2) Each cell of the lattice can be occupied by an “agent” of one of two colors (as above) or be empty.
3) The system has strict conservation laws: the agents can neither be created nor destroyed and the number of agents of each color will be conserved.
4) The neighborhood of an agent is determined by the “span” which defines a square grid of a centered on it with neighbors. means a grid with the agent at the center and 8 lattice positions available for neighbors around it. Thus, the agent marked with a black dot (above) has 5 neighbors at : 2 blue and 3 yellow. means a grid with the agent in the center and 24 available lattice positions for neighbors in two concentric shells around it.
5) The agency of the agent manifests as its ability to read the number and color of its neighbors and either stay put where it is or move over to a random empty cell in the lattice.
6) Beyond this is there is occupancy, , i.e. the fraction of the total available cells in the lattice that are occupied by agents.

All the experiments described below are played on a lattice, i.e. there are 2500 cells available to the agents. In all experiments, the agents move to an available empty cell if the number of its neighbors of any color are , the sociality factor. Thus, if then the agent will move from their current location if they have no neighbors at all. In the first set of experiments, they additionally sense the the absolute number of non-self neighbors, i.e. those of a different color and move if it is , the non-self count. The movements of the agents are repeated over and over until stability is reached or 30 successive rounds of movement have elapsed. The games are illustrated thus: the plot to the left is the initial configuration where the agents are randomly introduced into the lattice and the plot to the right is the final configuration that is reached as mentioned above. We measure segregation by looking at the , i.e. the mean non-self: self ratio in the neighborhood of the agents. As the agents are randomly introduced, the game would start with . The degree of segregation can be statistically assessed at the beginning and end of the run by means of the t-test to see if the mean number of self and non-self agents in the neighborhood of any given agent are significantly different. At the start of the run the difference would be insignificant.

Game 1 is a run with low occupancy and an equal number of agents of the two colors (blue and orange); , i.e. a neighborhood with 8 available cells; ; , i.e. the agents tolerate up to half of the 8 available lattice points in the neighborhoods being occupied by non-self agents.

Game 1

We see that at the end of the run remains close to 1 and the mean number of self and non-self neighbors of an agent is not significantly different suggesting that tolerating non-self agents in up to half of the available neighborhoods does not result in segregation at low occupancy and low sociality.

Game 2 is run with the same parameters as above, except that we increase sociality .

Game 2

Notably, the increased sociality results in highly significant segregation. It also results in greater clumping of the agents, resulting in clustered but clearly segregated domains.

Game 3 is run with the same parameters as Game 1 but we increase the occupancy .

Game 3

Here, we see a small but significant reduction of . Thus, increasing the population with same level of tolerance for non-self by itself results in some segregation that is not seen at low occupancy.

Game 4 is run with ; thus, the agent responds to the status of the 24 available lattice points of the neighborhood around it. The occupancy is low ; i.e. less than half the available neighborhood positions tolerated as non-self; .

Game 4

In these runs we often seen no significant segregation of the agents despite the relatively low tolerance to non-self; however, we see greater clumping of the agents resulting in a more anisotropic distribution of the agents at the conclusion of the run. Thus, when larger neighborhoods are sensed by the agents, even relatively low tolerance for non-self is overridden under low occupancy leading to paradoxical clumping of self and non-self into spatially restricted domains.

Game 5 is similar to 4 but the sociality of the agents is increased to .

Game 5

This change has the dramatic effect of moving the agents towards strong segregation along with formation closely packed monotypic domains of the two agents, with clear boundaries. Thus, the sociality parameter drives a phase transition from packing with little segregation despite relatively strong non-self tolerance to nearly complete separation into domains with shared borders.

Game 6 is different from the previous ones in that it senses the relative non-self fraction rather than the absolute count of non-self in the neighborhood, , where is the total number of occupied lattice points in the neighborhood. The sociality factor is applied just as in the above cases. In this run, we set , i.e. the agent moves only if it has no neighbors. , i.e., the agent move only if the fraction of its non-self neighbors is greater or equal to . Thus, if an agent has 5 neighbors and 4 of them are non-self then and it would move. We set it to a low occupancy of .

Game 6

We observe that even with a low occupancy, high tolerance for non-self and low sociality, relative sensing drives significant segregation. Thus, with relative sensing the is the primary determinant of segregation.

What might be some real-life scenarios where these games matter? We can easily imagine the system of agents being a set of living cells showing their agency in response to chemotactic signals. At a macroscopic level, we can imagine these as individual animals (e.g. humans). Indeed, Game 6 was the one played by Schelling as a model for the sociology of segregation. In terms of cells, we can conceive of the following mechanisms: 1) cells are primitively motile; hence, they can move. 2) they can exhibit sociality by means of adhesion molecules (usually proteins) that are expressed on the cell surface. Unless these adhesion interactions are satisfied to a given degree, they would keep moving. 3) They can sense self from non-self. In the simplest case this can again happen via adhesion molecules. Indeed, such mechanisms are used by fungi and ciliates, among others, for discriminating self from non-self for mating or hyphal anastomosis. This kind of adhesion-based self-non-self discrimination can be a mechanism of sensing the absolute number of non-self neighbors. Alternatively, it can happen through sensing of diffusible signals. This mechanism is best suited for relative sensing of the ratio of non-self to total neighbors. Either way the cellular agent could respond to nonself agents in the environment.

Thus, these simple models show how the interplay of sociality and non-self tolerance can result in segregation or paradoxical grouping. In the case of relative sensing (game 6), even with high tolerance and low sociality we see segregation. This is the reality of human societies that many modern occidentally oriented social observers find very hard to swallow. But they are simply tilting against a mathematical reality, much like their medieval representative, old Don Quixote, charging a windmill. Similarly, absolute-count-sensing shows the role of sociality and crowding in segregation (e.g. Games 2, 3 and 5). Greater crowding and sociality can lead to greater segregation when compared to the same, relatively high, tolerance for non-self under low crowding and sociality. Similarly, certain middling level of sociality with sensing of larger neighborhoods can trigger long-lasting clustering without strong segregation despite lower than half tolerance for absolute number non-self agents in the available neighborhood spots (Game 4). This scenario could explain the grouping of bacteria in mixed species biofilms or relatively long-lived clustering of distinct groups in a social setting, e.g. the jāti-s in an Indian village. In conclusion, some social phenomena can be accounted for by simple lattice models of agents which are entirely agnostic to the actual mechanism of agency and sensing.

Bhairavānanda’s wicks: a retelling

It was early in the school year and the last class for the week, the English class. The students were restless as the sea at the time of the tide from the pull of the impending weekend. For the first time in his life, school seemed to hold something of interest to Somakhya as he had just made acquaintance with the clever girl of the Aṅgiras-es. However, at that point he was lost in working out the geometry of a new chaotic map he had discovered. Vidrum, who sat beside him, peeked into his work, trying to follow it, but soon lost track of the scribbles of his algebra. Just then the English teacher entered the class and surveyed the mood in the room, twirling his chastising rod. The more rowdy students were in a raucous mood. Mahish and Gardabh were singing a cyclical song using their desks, lunch boxes and water bottles as percussion surfaces. The song ran thus in a local apabhraṃsha:
There was a man.
The man had a wife.
The wife birthed a boy.
The boy became a man
The man had a wife.
<repeat>

Episodically, Mudgar decorated the song with single-word interjections comprised of salacious apabhraṃsha words. The English teacher swung his cane and charged towards them: “If I hear anymore of this I’ll have you all stand outside the class.” Sensing the students’ mood, as he did once or twice a month, he decided to provide some exit for the steam building in his restless class: “Today we shall not have any lesson. Instead, I will let two of you all tell the rest of the class a story. You must hear the story quietly without interrupting and I will give you’ll five minutes at the end of each story to ask questions and discuss it. I’ll be choosing one boy and one girl to tell the story; however, be warned, I will not tolerate any lewd story and shall punish you if you narrate one. Today, I’m selecting Sharvamanyu as the boy who shall tell us the first story. Come to the front of the class.”

Sharvamanyu did so and narrated a tale of a Marāṭhā or a Piṇḍārī evading a wild chase from the English army and finally ending up eaten by a mugger crocodile. After a lively discussion for five minutes the teacher said: “As most of you’ll would have noticed, we have a new girl in the class this year, Lootika. She did extraordinarily well in the surprise entrance test we administered to verify her candidacy for admission to our school. As you know, our institution strives for high standards and hopes to send students to the best colleges by ranking in the highest decile in the school-leaving certificate. She shows promise to be one of our good students in the final reckoning three years from now. Hence, I select her as the girl who will tell the next story.”

As Lootika came to the front of the class, Mudgar whistled loudly, even as Mahish made an obscene gesture and shouted, “Four eyes!”, alluding to to Lootika’s spectacles. Lootika retorted: “Hey buffalo dung-skull!”. The English teacher struck Mudgar with his cudgel, even as Mudgar himself might have played a square cut on the field of cricket, and swinging it menacingly he and went up to Mahish: “Lootika, stop counter-swearing and tell your story. I’m the one supposed to maintain discipline here. Mahish, I’d already warned you. Now, you shall stand outside the class, next to the door. The next time you do something like this, my stick will mightily kiss you.”

With Mahish evicted from the class, Lootika told them the following story:
Friends, I will tell you a story that is believed by some to have been composed by a certain Viṣṇuśarman. However, it is possible that it was a folktale that was later inserted into the older work of Viṣṇuśarman. I am going to follow the plot of the original closely but tell it in my own words. In a certain town in central India lived four brāhmaṇa youths, who were great friends. They were very poor and, as is usual, the richer folk shunned them. They felt that nobody appreciated them for their good qualities and no woman showed any interest in them due to their poverty. Tired of their destitution, they decided to seek a fortune elsewhere. They declared that it was better to live in the jungle wearing bark-fiber vestures than to be among their kin while being indigent. Wandering a long way, they eventually reached the river Śiprā in the environs of Avanti and took a dip in the tīrtha. Having ritually purified themselves, they set out to the great temple of Mahākāla and worshiped the god sincerely. As they were making their way out, they ran into the great Śaiva yogin Bhairavānanda. He was a profound master of the Śaiva lore. Having toiled through the voluminous tantra-s of the tradition of Īśāna, Tumburu and the four sisters, Garuḍa and the Bhūta-s, he attained the pinnacle of his mastery through the study of the Bhairava-tantra-s. Thus, he became a renowned teacher with a school at Avanti.

Having fallen at his feet, the four youths accompanied Bhairavānanda to the hall of his school: “Young men what do you seek?”. The four: “Sir, we are very poor. We have decided that we shall either become lords of wealth or die in the attempt. We have heard of your great renown in the magical arts, the nidhividyā by which a man finds subterranean wealth or the kauberīvidyā by which one can locate the great stores of wealth that the lord of the yakṣa-s has provisioned at secluded spots on this earth. We are exceedingly brave and committed, and are willing to perform bold or arduous acts to succeed in this regard. Please inform us of the right way — whether we should seek deep cavernous mines, or perform Bhairava-sādhana in the cremation grounds, or worship the goddess Śākini, or sell human meat to attain our goal.” Bhairavānanda took pity on the youths and brought out four cotton wicks from his sacristy: “Young men, proceed north to the Himālayas towards the source of the Sindhu river along the the route I shall lay out. These wicks will act like dowsing rods. As you climb the slopes of the great mountain, if the wick accidentally drops from your hand dig at that spot. You will definitely come upon some great source of wealth. Collect it and return home.” Having consented, the four youths hurried along on their Himālayan expedition, pregnant with excitement. They made a pact that they would share whatever wealth they might obtain upon the dropping of the wick. After a few days of wandering in the regions where the Sindhu river descends from the great mountain glacier, the wick of one of the men dropped. They quickly excavated the spot and soon hit a lode of copper. The man whose wick dropped said: “Let us take this wealth and return. We can make quite a gain from selling this copper and establish ourselves.” The three other friends shot back: “You are welcome to return with all the copper you want. We have three more wicks and hope to discover even greater stuff than this red metal.”

Thus, the three proceeded; in a while one of their wicks dropped. This time their excavation yielded a lode of silver. The youth said to his friends let us take this silver and return — we have done much better than a mere mass of copper that our poor friend settled for. The two others retorted: “We hit copper first and now silver. Do we need to tell you what lies ahead?” The man who found the silver said: “I’m content with this silver and will take it and return.” The two others pressed on and neared a dizzying cataract on the Sindhu. There the third wick dropped. They dug up that spot and caught the gleam of huge nuggets of gold. The lad whose wick had fallen said that they their quest had truly ended as there was nothing more to find and urged that they split the gold between themselves and go back home. His companion thundered. You are a fool. We still have a wick left. Why should we waste this blessing, which has come to us from the great Mahādeva himself via the mantravādin Bhairavānanda. Each time around we have greater success. You may return with your gold if you choose, I am going to press on alone — I believe I’ll find diamonds and sapphires, which will yield us more wealth than gold. The youth who found gold said that he would wait for his friend to return at that spot and they could go back home together.

The fourth lad pressed on but soon realized that he had lost his way as saw none of the landmarks which Bhairavānanda had indicated to them. He found himself going in circles and ran out of water. To break the cycle and find some water he just marched ahead on a straight line. Soon he came upon a ghastly sight. A man stood in the midst of a cold plateau with his body bespattered with gore. On his head spun a wheel on a peg that seemed to trepan his skull and blood freely spurted out of that perforation. The fourth youth asked this unfortunate man: “What the hell are you doing to yourself? Is there someplace I can find water?” As soon as he spoke that wheel flew away from the man’s head and dropped on the head of the fourth lad and began drilling into it. He yelled: “Ouch, what is this!”. The man who had just been relieved of the wheel said to him: “I thank you from the bottom of my heart for relieving me. I don’t know how long I have been waiting for your arrival.” The fourth lad: “I don’t understand, please get this wheel of my head”. The original wheel-bearer: “Young man, like you, I too had sought wealth from the dropping of the final wick. Thus, I reached this spot and had the wheel jump on to my head from another unfortunate soul from Tibet who stood here bearing the wheel before me. When another man with a wick comes this way, you too will be eventually relieved.” The fourth lad:“How long have you been here?” The former wheel-bearer: “It seems like eons. Who is the emperor of India now?” The fourth lad: “When we left on our expedition, queen Mṛgāvati had just handed over the throne to her son Udayana Vatsarāja, who mightily lords over the land from Kauśāmbī.” The original wheel-bearer: “Oh, I’ve never heard of him. When I left home, Rāmacandra Aikṣvākava held sway over the land from the city of Ayodhyā, like an Indra on earth.” The fourth youth shrieked in pain: “What! that is terrible — it must be more than a 1000 years. How is that even possible!”. The old wheel-bearer: “Well, this is the punishment that has been set up by the great yakṣa Naravāhana. Indeed, it has been said that the man who seeks to plunder that which belongs to the great deity of the North is penalized thus. As you would have noticed, your thirst should have left you — deathless, hungerless, thirstless but full of unrelenting pain, like me, you too shall suffer this wheel of Kubera till someone else comes by with a wick. Thank you and I shall now take leave.”

Having waited long for his friend the third youth followed his footsteps and eventually found him suffering the torture of the wheel. Having heard his tale the third youth said: “Friend, I told you that we had met our ultimate aim in gold. But lacking sense and fueled by false extrapolations you went ahead. Now I’ll have to leave you and return.” The fourth lad: “You are such a heartless fellow to betray your friend in suffering and return to a life a wealth. You can only be called a traitor who will go to naraka.” The third lad: “That would be so if I were in a situation where I could have helped you. No human can ever free you from this punishment which has been inflicted by none other than the great Vaiśravaṇa. Seeing the pain on your face from the boring of your skull, my instincts tell me that I should leave this place right away — I sense the deepest dangers lurking in this spot from the dreadful agents of Kāmeśvara. Goodbye.”

As Lootika finished her tale, some of her classmates, Tumul, Vakraas, Skambhakay and Muhira started loudly vocalizing: “boo…boo… what a boring story! Lootika is a bore!” The English teacher intervened: “Stop it or I’ll whack you. Lootika, I want you to ignore them and quietly go back to your desk. It was an excellent story, capped with a didactic flourish, which introduced the class to trivia of history, geography and quaint superstitions reminding one of the notorious Rasgol-bābājī. Lootika also introduced few words and phrases that some of you’ll might not be familiar with. Note those, check their meanings in the dictionary, and write down sentences with each of them. Now, Tumul, stand up and tell the class what you thought was the message of the story?” Tumul: “Sir, it was just a long-winded way of saying a simple sentence: it is bad to be greedy. Other than that, the story does not make much sense, and as you said, master, it talks about all kinds of superstitions that cannot be true — Lootika doesn’t seem to know even basic physics — a wheel cannot spin by itself forever. it seems she just wants to show off that she knows some words from the dead language Sanskrit in an English class. Moreover, how much copper ore can a single man take back home from high in the mountains. Surely, it will not be enough to even pay for his food and boarding on the way back. As a Brahmin girl, Lootika is simply following the example of how her kind has operated since time immemorial — obfuscate simple, common sense things with elaborate stories packed with mumbo-jumbo.” The English teacher: “Tumul, you are unable to get the device of a metaphor. Now it is you who are being long-winded to be mean to your classmate. We need to be more welcoming to our new students. Hence, I want you to write out the whole story in your own words properly explaining its significance and bring it over to me next fortnight. Now, Somakhya stand up and tell the class what you think about the story.”

Somakhya: “I think there are two ways, not mutually exclusive, to look at it. First, due to conservation laws and the principle of entropy, growth can never be infinite. Hence, if you keep on the growth curve you will go up and eventually down. Second, you could look at it as the problem of the gambler’s ruin at a casino. Even if the gambler makes some gains, eventually he will be ruined if the probability of gain is lesser than or equal to 0.5. In both these, which have bearing on real life, the big question is when exactly to bail out. If you bail out too soon you may catch much less of the growth or gain than those who stuck on longer but stay too long and you will go bust. That’s the metaphor of the wheel of Kubera. But making that decision can be extraordinarily difficult.”

The English teacher: “That is a practical take. Vidrum, what do you have to say?” Vidrum: “Based on what Somakhya has said, I think the whole story is a metaphor for participating in pyramid schemes like cryptocurrency. If you know when to quit, you can retire with good money but if you don’t you can sink into misery like that fourth chap. Hence, I think persistence might be an overrated quality and quitting often might after all help.” E.T: “That last sentence is a rather negative take and I believe a fallacious inference from the story. Hemling, I see you gesticulating and getting excited. Did you understand the story and have anything to say?” Hemling: “ The problem looks hard because the gain function in Lootika’s example is discrete. If it were a continuous function that were differentiable throughout, then I think we could for most part use the derivative of the function to reach some conclusions regarding when it would be right to bail out. For typical gain functions in real life, you have decrease in the magnitude of the derivative as you are nearing the peak. That should give you a reasonably precise indication of when to quit.” The English teacher seemed confused: “Hemling, you better keep that stuff for your math class.”

ET: “Sumalla, what do you have to say about the story?” Sumalla smiled and puckered her lips and face, uttering a lot of filler words to make up for the lack of anything substantial to say. Finally, she managed to string a few grammatical sentences: “I love diamonds and also sapphires but I would happily to settle for gold. Lootika always has something more to say on any topic. Sir, please ask her if there is some secret message in this story.” ET: “Alright, Lootika, I’ll permit you to have the last word on your story.”

L: “First, I think Tumul is a fool. He for one should brush up his physics by reading about photovoltaic cells — something like that could have kept the wheel spinning.” E.T.: “I don’t want you to go there Lootika. Stick to your story.” L: “I think the boys have more or less covered the basic message of the difficulty that we constantly face in life with respect to the quitting problem. However, I’m not sure if Vidrum’s strategy of quitting often is the winning one in an unqualified setting. Maybe it can be explored by means of computer simulations. I’d also add that these problems are made more complex by hidden variables that we cannot see or whose causal chain is too complex for us to trace — like what decided whose wick would fall when. Hence, as a general lesson, it is good to think in terms of the nature of probability distributions and perform cost-benefit analysis accordingly while making life decisions. That said, life in the margins with some copper is much better than getting trepanned.”

Just then the bell rang announcing the end of the class and the school closed for the weekend. Lootika realized that there were classmates who hated her and might want to have a go at her for the punishment they had suffered. Hence, she quickly scurried over to Somakhya and his gang. Thus, shielded by her friend she exited the school premises.

Pandemic days: bālabodhana

As the pandemic grinds to a close or at least to a pause in some parts of the world, there is a certain fear from new mutants threaten that threaten break current the status quo. The strain that arose in the deś is a case in point. This short note is some bālabodhana on how understand some of the basics of the mutational process.

At the most fundamental level, biology is written in a 4 letter alphabet — the four nucleotides (A, G, C, T/U). A RNA virus, like SARS-CoV-2, has U, whereas cellular DNA genomes have T instead. Any biological word, i.e. string of nucleotides, occupies a node in a graph (network). This graph might be seen as multi-layered where in each layer contains all words of length . In the subgraph corresponding to any given layer 2 nodes are connected by an edge if they differ by a single letter, i.e. a single substitution can change the word corresponding to a node to that corresponding to the node to which it is connected by an edge. Thus, there are 4 words of a single nucleotide which are all connected to each other, i.e. a tetrahedral graph.

With 2 letters (dinucleotides) we have possible words and the graph is way more complicated as each node can be connected to 6 other nodes.

One can easily see that will define a tetrahedron in 3D Euclidean space. However, any biological word of cannot be faithfully visualized in our everyday 3D space, as it will require many more dimensions to render it with real edge-lengths. Thus, as Martin Nowak stated, biological words are rich in dimensions but short on distance. For simplicity, we draw our graphs in whatever dimensions are easily grasped by us (i.e. 2D as above) and simply take each edge of the graph to be measured as a non-Euclidean length. In reality, not just the topology of the graph but also the length of the edges matter. Nucleotides are more likely to mutate to the same type ( pyrimidine (U/T) pyrimidine (C), purine (A) purine (G)) rather than a different type (i.e. purine pyrimidine). Thus, the lengths of edges corresponding to heterotypic substitutions are longer than those corresponding to homotypic edges. However, for convenience we shall simplify the situation by taking all edges to be of length 1. Thus, the distance between two nodes will be length along the graph: in the dinucleotide example shown above the distance between AA and AG will be 1, while that between AA and GG will be 2. Thus, for , while paths of various lengths are possible, from one node you can reach every other node with path of at most length 2. This shortest distance along the graph, , between 2 nodes is no different from the so called Manhattan metric or Hamming distance.

Some of the nodes on a given layer are connected nodes on by an edge too because by the addition or subtraction of a nucleotide you go from a sequence of length to and vice versa. However, given that you can have in a single step such additions and deletions of arbitrary length you can also connect sequences of various lengths by these length 1 edges coming from the so-called deletions and insertions. For this simple examination we shall ignore those types of mutations.

The basic, necessary process of life may be defined as the copying of an biological word, in its maximal form a genome, by a nucleic acid polymerase. All polymerases are prone to error when they make new copy of the genome from the existing template. We may define this error by , the probability of single nucleotide substitution at a arbitrary position in the genome. Then is the probability of the genome being copied correctly. This leads us to a key equation that measures mutation in the genome, i.e. probability that the copying of genome results in a mutant genome :

Here, is the shortest distance along the graph between sequences and is the length of the genome. Wrapped into this are two simplifying assumptions: 1) is constant throughout the genome and 2) it is independent of mutations at other sites.

I could not find a proper estimate of for SARS-CoV-2. However, a closely related coronavirus, with a similar-sized genome, the Mouse Hepatitis Virus RNA-dependent RNA polymerase has . The same may be safely used for SARS-CoV-2. Hence, the probability that the viral polymerase makes a copy with no mutation at all, with , is given as:

For a comparison, the HIV-1 virus reverse transcriptase has and ; thus . Therefore, HIV-1 is a far more mutation-prone virus, which copies its genome without a mutation only 3/4th of the times. The higher fidelity of replication of the coronavirus is a consequence of its distinctive proofreading 3′-5′ exoribonuclease, which the HIV-1 reverse transcriptase lacks. This increased fidelity is keeping with its larger genome, coding for several more proteins than HIV-1.

Conversely, consider the probability that a specific point mutant arises upon replication of the coronavirus genome. For example, the mutation in the Spike protein E484K can confer resistance to some of the typical antibodies made against the wild type Wuhan strain. This is a substitution of K for E which can arise from a single point mutation. This probability can be calculated using the above formula with ; hence,

When a virus infects a cell, it makes numerous copies of itself and these “burst” out eventually resulting in the death of the cell. The number of such copies that emerge out from the cell on an average is termed the burst size. To our knowledge, there are no recent studies on burst size estimates for coronaviruses. However, a study in 1976 by N. Hirano et al estimated it to be about 600-700 virus particles, again using the Mouse Hepatitis Virus in a tissue culture system. By taking a burst size of 650, one would need successfully infected cells producing bursts of this size for a specific point mutation, like the above mentioned one in the spike protein, to emerge. During peak SARS-CoV-2 infection, an individual is estimated as carrying virus particles based on calculations of Sender et al. Hence, a particular point mutation can emerge in an infected individual times.

If a point mutation confers some selective advantage, like the above-mentioned immune escape mutation, then even with the low error replication of coronaviruses relative to HIV-1, they have ample potential for developing escape mutations. Consistent with this estimate, we saw the E484K mutation repeatedly emerge in different lineages that showed antibody escape, such as the B.1.351 variant that arose in South Africa, the P.1 variant that arose in Brazil and the within the B.1.1.7 lineage in the UK. Finally, a serial passaging experiment by Andreano et al of the virus with plasma from a recovered patient found that for 7 passages the plasma neutralized the virus; thereafter point mutations emerged that allowed escape and eventually complete resistance to the plasma. One of these was the E484K. The evolutionary history of SARS-CoV-2, assuming that it broke out in Wuhan, China, in November 2019 was one of relative stasis for about an year followed by emergence of several mutants that allowed immune escape. The among these were the multiple emergences of E384 point mutations. This suggests that for the first year the virus was rampaging through a relatively immunologically naïve population with little advantage for specific point mutations. However, as pandemic response measures and the virus load in the population greatly increased, there was an advantage for specific mutants. The above numbers show that point mutations were the easiest path to this, as seen with the emergence of variants with mutations such as D614G, E484K etc.

Yet, we see that the vaccination programs have played a big role in bringing the pandemic under control in several parts of the world. Why has it worked, given the above? For this let us take a closer look at the antibody response to SARS-CoV-2.

Roughly of the antibodies against this virus are directed at the Spike (S) protein. The above picture shows the spike with the top part being the surface which it contacts the ACE2 receptor on the host. Within the spike protein the residues that are targeted by 5 distinct classes of antibodies are marked in different colors on a single monomer colored cyan, while the other two monomers of the trimer are shown in transparent light yellow. The majority of antibodies target the Receptor Binding Domain (RBD), while the minority target the N-terminal galectin-like domain (dark violet). First, since, there are at least 5 distinct classes of antibodies, the escape via a point mutation could be compensated by the binding of one of the other classes. Second, the titer of antibodies seems to matter a lot in terms of immunity. Individuals with high titer seem to be able to overcome much of the escape by single mutants like E484K. Third, there is the cellular immunity. Thus, the vaccine are in most part likely generating high enough titers of antibodies of different classes to make up for escape by single point mutations and a reasonable cellular immunity.

Now, to escape a whole class of antibodies one might typically need 3 or more point mutations. We can compute the probability of 3 point mutations arising from one replication of the virus as . This means it is very unlikely to ever arise in a single person in single replication . For a comparison, the probability of a round of replication producing a triple mutation in HIV-1 is . On a given day, an infected person carries about HIV-1 particles; hence a person has only a of developing a triple mutant in a single replication. However, 1 in every 2455 persons infected with HIV-1 can develop such a mutant in single round of replication. Hence, it has not been possible to vaccinate against it. However, as the serial passage experiment illustrated, in successive rounds of selection for individual point mutations one could eventually get to total resistance with SARS-CoV-2. The B.1.617.2 variant has already shown the capacity to partially break through the commonly used Pfizer and Astra-Zeneca vaccines in the least. In theory it is possible that a strain that is entirely resistant to the antibodies generated by the vaccine could arise in the relatively near future. Fortunately, antibodies are not the only aspect of immunity as they can also trigger cellular immunity. Hence, at least for the near future, with all aspects of immunity put together, the vaccines are likely to provide some level of protection. However, the strong selection pressure they are imposing on the S protein could result in the emergence of more consequential escape mutants. Hence, there is a lingering danger of the disease persisting in some form.

Some further notes on the old Mongol religion-2

O fire mother,
whose father is flint,
whose mother is pebble,
whose meal is yellow feather grass,
whose life is an elm tree.
An incantation to the Fire Goddess Ghalun-eke; translation from the Mongolian by Yönsiyebü Rinchen

This note revisits some themes relating to the Mongol religion gathered in the 1950s and 1960s by the Mongol scholar Yönsiyebü Rinchen from the Mongolian Academy of Science, Ulaanbaatar. He says that he descends on his father’s side from an ancient Hunnic clan founded by a certain Yöngsiyebü, who was the lord of a tümen. He records an oral chant preserved by the clan on this ancient ancestor of theirs. On his mother’s side he claims descent from Chingiz Khan via Tsoktu Taiji (1581-1637 CE), the chief of Kokonor, who aided the practitioners of the ancient Bon religion of Tibet before they fell to the bauddha-s backed by the Oirat Mongols. Rinchen, with his connections to the old Mongol religion prior to its fall to the bauddha-s, records several notable features of its practice. As we have noted before on these pages, the fall of the old religion to the bauddha-s was neither smooth nor complete. In addition to the material collected by Heissig, we have deprecations such as this one from the old shamans against the religion and followers of the tathāgata invoking at the black (qara) “ghosts” or “spirits”:

O you, you who come to eat 90 bhikṣu-s,
and returns to eat 100,000 bhikṣu-s,
O you, you who come riding the frenzied wolves,
and feed the fire with the Kanjur and the Tanjur.
Translation from the Mongolian by Yönsiyebü Rinchen

The old Mongol religion was organized thus:

Figure 1

As one can see from the diagram their world is heavy in what might be termed “ghosts” or “spirits”, which are incorporeal presences of ancestors. Of the gods themselves, there were the 99 tengri-s who are mentioned in the famous kindling fire hymn of the clan of Chingiz Khan. They were headed by the tengri Qormusta Khan Tengri, who was also known as Köke Möngke Tengri, and associated with the great blue sky. The latter name of his seems to have been the original Mongol name that is encountered in the Chingizid epic. The former name seen in texts like the Mongolian Geser Khan epic is transparently a tadbhava of the great Iranian Varuṇa-like deity Ahura Mazda. His later iconography closely converged to that of the ārya Indra, paralleling tendencies on the Indo-Iranian borderlands. Of these tengri-s, 55 are seen as benevolent and white in color; 44 are black in color, wrathful and destructive, but their fury is directed at the enemies of the Mongol nation. We had earlier discussed some of the other Tengri-s. We know much lesser of the 77 Earth Mothers, the natigai, with the exception of the fire-goddess Ghalun-eke, whose elm tree “samidh-s” are well-known from multiple surviving Mongol kindling incantations, including the aforementioned one of Chingiz Khan. These high deities are common to the Mongol peoples, and are worshiped by the elite (tsaghan yasun or the white bones) and the high shamans in special community rituals.

Rinchen recognizes two levels of shamans. The high shamans involved in worship the tengri and the great ghosts or spirits and are known as jhigharin (shamans) and abjhiy-a (shamanesses). The lower ghosts are invoked primarily by a lower grade of shamans known as böge (shamans) and idughan (shamanesses). The former word is related to the Turkic bögü, who was a shaman-magician of the pre-Abrahamistic Turks. The words might be related to the Iranic Baga (Sanskrit: Bhaga), as the name of an Āditya god or a respected one with divine capacity (e.g. Skt: bhagavat). In this regard, it may be noted that, at least since the Kirghiz Khaganate, the Turkic shaman was more commonly known as the kham or the kham khatun (female). It was explained in the Sogdhian Iranic dialect as the prophet of Baga (Sogdhian: faghīnūn, c.f. faghfur for Bagaputhra used similarly to the Chinese title of Tianzi by Eastern Iranic emperors). The lower shamans were deployed for commonplace religion and for the quotidian needs of the lay populace (qara yasun or the black bones). For special occasions, the qara yasun might call upon the high shamans for more involved rituals. One of these was the mysterious weather magic that was shared by the Turks and the Mongols, done with what was known as a “rain stone” or a “snow stone”. In times of peace, this shamanic magic was used to help during droughts and was observed closer to our times by Russians and Russified Germans during their exploration of the Mongolian east. However, there are several accounts of such as a tactic in warfare, some of which we shall describe below.

From the Pre-Mongolic times we have the account of a Zoroastrian Iranian encyclopedist, who among other things compiled a version of the Pañcatantra, preserved via Gardīzī. He recorded that such a rain-stone magic was in the possession of the ancestral Turk and its inheritance was contested among the Khazar (the Judaistic Turks), the Oghuz (from whom descend the Black and White Sheep Turks, the Khwarizm Shahs/Qangli Turks, the Osmans and Seljuks, who may have originally been a Judaistic branch of them before becoming Mohammedans) and the Khalji-s (from who descend the monstrous tyrants of India like Jalal al Dīn and Alla al Dīn). The Oghuz are said to have obtained the stone by giving their cousins fake versions. Isma’il ibn Ahmad the Sāmānid Sultan mentions that during his slaving jihad on the heathen Turks, their high shamans deployed the rain-stone magic stirring up a hailstorm. However, the Sultan grandiosely claims that he deployed his Mohammedan Allah magic and backhurled the hailstorm on the Turks. This was perhaps an old motif in Turko-Mongol tradition because it makes its reappearance in the Chingizid epic, when the great Khan was facing the confederation of the Naiman Turks. Their shamans raised a blizzard against the Mongols but the Khan’s invocation of Köke Möngke Tengri turned the blizzard against the Naimans. However, the Mongols too described their shamans successfully deploying the rain-stone magic in war. During the sack of Khwarizm, the Mongols spared the life of a Qangli Turk who still remembered the old heathen ways and incorporated him into their shaman contingent for weather magic. When Chingiz Khan’s youngest son Tolui was leading the Mongol army against the Jin, he was ambushed surrounded by them. He is said to have had his shamans, including the said Turk, deploy the great blizzard magic, which caused confusion among the Jin, and allowed the Mongols to cut them down. Later after the fall of the Mongol Khaganate, when the belligerent Han under the Ming emperor invaded Mongolia, Biligtü Khan Āyuśrīdhara the son of Toghon Temür organized the defense of his homeland. In the fierce battle in Orkhon, when it looked like Mongolia might fall, the Mongol shamans are said to have deployed the “snow-stone” magic, resulting in many Han freezing to death in the holes they dug to keep themselves warm on the steppe. Biligtü Khan is said to have then rallied the Mongols to save Mongolia from the Cīna-s drive them beyond the wall.

This use of the rain-stones and snow-stones continued even after the Islamization of the Mongols of the Chagadai Khanate in the West. In great battle near Tashkent, between the Chagadai Khan Ilyas Khoja and the alliance of Timur and Mir Hussain, the former first attacked the Mongols and gained some success and called on Mir Hussain to attack the other flank of the Mongols. At that point, the Mongol shamans were called to deploy the rain-stones and a thunderstorm is said to have struck the side of Hussain who was then smashed by the Mongols. Timur tried to rally the forces but he too was hammered by the Chagadais and forced to retreat losing several thousands of men. Finally, the Timurid Mogol Abu Sa`id himself is said to have had Özbek Mongols in his retinue perform the same magic to obtain rain to alleviate their thirst when they ran out of water on the steppe in 1451 CE. Interestingly, the English agents at Madras note that Chatrapati Śivājī sent a brāhmaṇa Mahāḍjī Pant to obtain the same kind of stones from them. However, it is not clear if the Chatrapati wanted them for some magical purpose or as medicine. While there have been records of this ritual in inner and outer Mongolia in the last 150 years with a smooth white stone the size of a pheasant’s egg and a ceramic bottle in which it is placed, unfortunately, we know little of the incantations.

We know more of the traditions relating to the genii, which are an amalgam of ancestor worship, apotheosis and reverse euhemerism. Rinchen holds that the distinction between the different types of genii follow the status of their living progenitors. The ghosts of the great Mongol lords of clans and great Khans are said to become the “lord spirits”, who are invoked in special rites by the entire clan or nation. These usually require the great shamans and shamanesses for the invocation ritual and have survived the bauddha takeover surviving within the tāthāgata pantheon. The spirits of the noted shamans, i.e. jhigharin and abjhiy-a become the “protector spirits”, while those of the lower grade böge and idughan shamans become the “guardian spirits” who are usually genii of loci. The loci themselves, usually in the vicinity of their graves, were marked by heaps of stones known as obugh-a, where the Mongols might make offerings of food or horsehair or alcoholic drinks. The three types of lower genii were collectively known as the jhalbaril-un ghurban. These were pacified with an offering of tea from China or some strong ferment and in modern times, cigars (c.f. the cheroot offerings made in the Drāviḍa country to comparable deities such the horse-riding Mūtāl Rautan depicted like a medieval cavalryman in the retinue of gods like Ārya). These lesser spirits are important in daily life for ghost-magic to attack enemies, to avert accidents while foraging on the steppe, and to protect an individual animal or child. The lesser genii are more in line with ghost-lore from other parts of the world. With appropriate agreements before their death for pacification, otherwise inimical but notable persons might become protector spirits, like Jamuqa in the Chingizid epic. The commoners who lived a bad life upon death might become vengeful or resentful evil spirits. These might need pacification with a lower grade shaman’s assistance or could even be directed for causing harm on their enemies in life and their families.

Figure 2: A “deer stone”-like enshrinement of an ancient shaman

Some of the lord spirits often straddle the line between the tengri-s and the genii. As we have noted previously, the most notable of these are the Sülde associated with the yak or horse-hair standard known as the tuq (c.f. the Indo-Aryan symbol of royalty the cāmara or yak-tail whisks). Regarding these, in later tradition a peculiar tale, clearly inspired by the ancient ārya brāhmaṇa narratives, is told: Qormusta Khan Tengri instructed the other tengri regarding the Sülde when they were defeated by the Asura-s. This custom brought them victory. From the Chingizid times we know there were two distinct Sülde: the white one (tsaghan), which was used to protect the camp in an apotropaic deployment and the black one (qara), which was used to bring harm to the enemies. That one was planted on the holy fire hearth of the enemy once their camp was taken. Sometimes, an enemy might be sacrificed to the Sülde; as of recently even bauddha ritualists sacrificed goats to some venerated Sülde. It is not clear if the followers of the ekarākṣasa cults who were sacrificed for refusing to bow before the Mongol divine symbols were killed before a tuq for the Sülde or the lord spirits of the Khans.

Figure 3. A depiction of the qara and tsaghan tuq of Chingiz Khan at the Mongolian Hall of Ceremonies.

This latter point brings us to the worship the lord spirit of the Khans. As noted by the Jewish chronicler, Rashīd al-Dīn, who was employed by the Mongols in Iran, the lord spirits of the dead Chingizid Khans were worshiped at the Yeke Qorig (the Great Forbidden Sanctuary) that is believed to have been located in the Hentii mountain range. Here the idols of the Khans received a continuous burning of incense sticks and was restricted in access. Khan Kamala, the grandson of Quibilai built the temple of the Chingizid lord spirits at Burqan Qaldun, which Igor de Rachewiltz associates with ruins found on the bank of the Avarga river. The Japanese researcher Shiraishi Noriyuki holds that the icons mentioned by Rashīd al-Dīn and the site of Kamala’s temple were the same as this Avarga river ruin. The Mongol chronicles explicitly mention that the idol of Chingiz Khan had a golden quiver with real arrows in it. Even the Manchu, during the Ching dynasty, still maintained a temple for the youngest son of Chingis Khan, Tolui, at Ordos housing an idol of his. These life-sized stone Mongol ongon icons for housing the lord spirit follow in the long tradition of Altaic steppe peoples as seen in the form of the stone images of the old Blue Turk and Uighur Khans and lords. The Khitan Khans’s spirits were worshiped in golden idols. Similarly, we have smaller metal idols among the Chingizid Mongols, which some believe might have been for the worship of the lord spirits of leaders of clans, like those of Boghorju, Muqali and Subedei.

Figure 4. 1 and 2 are Turkic balbal-s housing the ancestor spirits of ancient Turk Khans/lords. 3 is a similar stone of an ancient Mongolic lord from Mongolia recorded by Russian researchers.

Figure 5. A comparable Chingizid era stone from the 1200s of CE housed at the Mongolian National Museum of History.

During the initial bauddhization of the Mongols, ancestor worship of the Mongols was brought into the maṇḍala-s of vajrayāna. One notable case is the placement of the pictures of the Khans in the maṇḍala of the deity Vajrabhairava. As we have noted before, since the Chingizid period the lord spirit of Chingiz Khan and his prominent successors became national deities. From lord spirits they were raised to a higher divine status, who within the bauddha system was seen as a yakṣa associated with Vaiśravaṇa — the great king in the Vedic tradition or as an incarnation of Vajrapāṇi. One such incantation that worships him in his aspect as an incarnation of the great yakṣarāṭ Mahārāja goes thus:

Chinggis Khan, who has the power of three thousand people
His body was wrapped by the ten thousand white moon rays.
He has one face, two arms, and three eyes.
He was smiling wryly,
Brandishing to the center of the sky a white spear in his right hand.
In his left hand he was holding close to his heart a plate full of treasures.
He got rid of poverty in the samsara and nirvana.
His white garment was fluttering in front of his chest.
-translation by N. Hurcha from Inner Mongolia.

Some later Chingizid lord spirits also appear to receive prominent worship in certain localities. One such as is Altan Khan, who famously reunified the Mongols to defend them against the resurgent Han belligerence under the Ming, and launched a raid on Beijing. The lord spirits of him his and of some royal women of his family are worshiped in large paintings. The spirits of Abtai Khan (A Chingizid lord of one of the Khalkha Khanates) and his family were also actively worshiped before their suppression by the Marxists. This was almost like karma visiting him as he had actively suppressed the shamanic cults upon the calling of the third Dalai Lama.

The Geser Khan epic (to be treated separately) and the work of the Heissig, and more recently that of Elisabetta Chiodo and Ágnes Birtalan, suggest that some lord spirits from a pre-Chingizid period have attained deity or near deity status. Most notable of these is Dayan Degereki (Deerh), who has survived the bauddha action and was even incorporated into their framework. His enshrinement in a stone ongon icon with a bronze casing is clearly mentioned in the litany used by the shamans invoking him. What is notable is his opposition to both the founder of the Mongol nation, Chingiz Khan and the later Dalai Lama. The latter is rather understandable given the above-noted tension between the tāthāgata-s and the shamans — we had described this in an earlier note. However, Dayan Deerh’s opposition to the great Khan hints that he might have come from a clan that was subjugated by the Khan or his successors. One possibility is that he originally belonged to the Oirats, given that he is also worshiped by them. Indeed, the litany to him mentions that after he was enshrined in a stone ongon at the Örgöö river, the warriors of Chingiz Khan tried to smash his “his unruly, damned skull” [translation by Birtalan] with their swords and scimitars. However, their weapons were blunted, and they fled. Eventually, he is said to have accepted the overlordship of Chingiz Khan and became a Sülde and a wide-ranging protector of the Mongol people along with his son Saraitan and daughter Saraimoo (who appears to be a reverse-euhemerized Sarasvatī). Saraitan appears as a healing deity as indicated in the incantation recited to him in a shamanic ecstasy:
You protect every orphan,
You enrich every poor man,
Your knowledge is perfect,
You have healing powers in your thumb,
Your index finger heals,
You know everything that is hidden,
Saraitan, you are a healer
To the seventieth generation.

Similarly, the incantation to Saraimoo invokes her vīṇā and seeks the blessing of progeny:
You put a curb on the reckless,
With sounds of music on the strings of your lute,
You show what the mountain hides,
You grant fine offspring to all
Who yearn for them.
You, Saraimoo.
[translated from the Mongolian by Birtalan]

In terms of iconography, Saraimoo is depicted exactly like Sarasvatī. The iconography of Dayan Degereki closely parallels that of two other martial deities Dayisun tengri and Dayichin tengri, who seem to have been invoked along with the Qara Sülde while proceeding for a battle. This raises the possibility that this complex of deities had evolutionary connections linking them to the lord spirits to the tengri-s. However, the exact processes involved remain unclear — euhemerization versus its reverse. Among other things, Dayan Deerh’s key pre-bauddha cultic stone image was destroyed by the Soviet-backed Marxist terrorists during the ascendancy which poses impediments to our current understanding.

Some talks at the Indic Today portal

We had a chat with with C Surendranath, Contributing Editor and (in part with) Yogini Deshpande, Editor in Chief of Indic Today. It is divided into four parts:
1) https://www.indictoday.com/videos/manasataramgini-civilization-counter-religion-continuity-collapse-i/
A few clarifications for this part: 1) We do not as personally identify “trad”, “alt-right” or whatever. However, Hindu, brāhmaṇa, Vaidika smārta (with a degree of parallel adoption of tāntrika practice) are part of our identity. 2) The name of the German philosopher Schopenhauer was mysteriously blanked out twice! 3) We did say gulag but it sounds like kulak. 4) The first German Jewish professor we were thinking about was Moritz Stern, who succeeded Carl Gauss. Moritz Cantor also Jewish was Stern’s student. Related to this part is our essay on the Lithuanian (Baltic) heathen tradition.

2) https://www.indictoday.com/conversations/manasataramgini-civilization-counter-religion-continuity-collapse-ii/
This part covers issues which we have presented in the writing here: e.g. 1) Early “free-thinkers” in the Abrahamosphere (especially see second part). 2) Further details on the extra-military aspects of the Islamo-Hindu confrontation. 3) More focused discussion of aspects of counter-religions and their interactions. 4) Military labor entrepreneurship and related issues in the last days of the last Hindu empire. 5) Some Hindu polemics against the preta-mata.

3) https://www.indictoday.com/conversations/manasataramgini-civilization-counter-religion-continuity-collapse-iii/
This part covers: 1) A basic introduction to legalism (fajia) & its manifestations in old & recent Cīna thought. 2) Comparisons between the imperial political frame in fajia and the arthaśāstra. 3) “Fads for people” as a mechanism in legalism. 4) About half of Cīna history Hans were ruled foreign powers: the consequences and responses. 5) Counter-religions and Cīna responses: some comparisons with India. 6) Hui and Cīna little brother of the preta and their suppression
Overall you can take it prolegomenon for a H analysis of one of our civilizational rivals. In the oral medium some little points can slip through the cracks: We should have explicitly mentioned that eunuch Zheng He was a Hui descending from those brought to Cīna by the Mongols.

4) https://www.indictoday.com/conversations/manasataramgini-civilization-counter-religion-continuity-collapse-iv/
The final part of this chat covers the Rus. It meanders along touching on: 1) the pagan Rus and their Christianization to the Orthodox church; 2) The Mongol conquest of the Rus. 3) The Rus fight back with Dimitri. 4) The see-saw struggle with Khan Toktamish burning Moscow. 5) Closer to our age the attempt by the Rus to present themselves as the chief of the preta world. 6) Exploration of the East – Siberia. 7) Conflicts with the Western powers and Japan. 8) Marxian subversion of Russia. 9) WW2 and the attack on Japan. 10) Rus as a Superpower. 11) Decline and demographics. It is peppered with some other excursions and a discussion on the movie on Alexander prince of Novgorod who fought the Germanic invaders by Surendranath. We should have explicitly stated that he was a feudatory of the Mongols and aided by Khan Sartaq of the Golden horde.

In our opinion the oral medium is best suited for a discursive exploration of “big themes” along with interesting trivia as as raisins in the pudding. It is not the best for “technical” or detail-oriented presentations especially when not accompanied by other aids, like figures and maps. This could compromise accuracy to a degree and also the sequence in which events are treated. Hence, these should be heard with those caveats in mind.

The cicadas return

Seventeen years after we first saw them emerge, like a great horde of Cīna-s invading Tibet, the cicadas of Brood X reemerged. 17 years is a good amount of time, making one pause to reflect on what has passed by life, in addition to the cicada-s themselves. This coming of Brood X was not very successful in our area. We first started noticing them around May 17 and surveyed them in a 2 sq km region that that we walk through by foot. They emerged alright after their 17 year underground larval development at night from holes in the ground. The 17- and 13-year cicadas seem to emerge after their fifth instar molts.

Then the crawl up to reach trees or posts.

Most of them then proceeded to molt. However, right at this stage about 1/5-1/4 seemed die even as they are emerging from the molt. In the first image below one can see a specimen that has died while molting. In the second picture one see another such being scavenged by ants.

After that, several underwent proper melanization but failed to properly inflate their wings and died.

Those that did survive started their famed song.

This emergence was already a bit shaky relative to 17 years ago. From my records they were already going well by May 22 of 2004. I examined about 100 or so and did not see any obvious signs of Massospora mycosis. It was relatively cold for several days from May 17 onward (low <15 C). However, by May 21 the temperature was pretty good (low >15) but they still struggled and hardly any of their noise was heard as of May 23. While our friend reported a similar situation in his site about 15 km away from mine, others further away reported high densities at this time. The cause their poor performance in our regions remains unclear. Was it just the temperature or some other unknown pathogen or the insecticide use by residents? We saw a couple moles scurrying around in the twilight in one wooded area as also their predator a fast-running fox. Moles are known predators of their larvae but we doubt they are numerous enough to make a difference. In any case, much of the death which we saw was post-emergence. The cicadas finally hit their stride around June 2 and the wooded paths were reverberating with their tymbals. All the noises — the choruses, females clicking the wings, the coupling noises and the distress screeches as birds attacked them — could be heard. On June 18 a precipitous decline in their calls was noticed and they were gone by June 20. However, their final act was registered in the wilting of tree shoots as the females slit the terminal branches to lay their eggs.

Thus, it was just about a month of activity with a weak start and even the peak afflicted by several days of heavy rains. How exactly this would affect their prospects 17 years down the line remains unknown. This brings us to hypotheses regarding the long periods of these cicadas. Cicadas are unique among insects in having long lifespans, most of which is spent in larval stages. A study in Ohio where there was an unusually warm January followed by a freeze resulted in maple trees producing two sets of new leaves in the same year; during that event the 17 year cicadas came out one year earlier once the late spring soil temperatures stabilized at around 18 C (their preferred emergence temperature). This suggests that they have a mechanism to track the cycles of leafing in the trees whose sap they suck deep underground and thus count the years. In this regard we propose a dendrochronological exploration wherein tree ring records are examined to see if a periodicity relating to cicada emergence can be discerned in them.

More broadly, several cicadas come out every year. However, there are those, such as Okanagana in North America, which can have lifespans in the range of 9 to 19 years. At least the 9-year ones exhibit a 9 year “proto-periodic” cycle, where they are abundant in 4 of these years and relatively rare or absent in 5 of them. This indicates a degree of synchronization among the broods of the 9-year Okanaganas. One of the Okanaganas from Canada, Okanagana synodica, and Tettigades “chilensis” from Central Chile have 19-year life cycles and could very well represent transition to the next highest prime number cycle beyond 17. The Japanese cicada, Oncotympana coreana, might have converged to a shorter prime cycle of 7 years; there are several other Japanese cicadas with even shorter 3-year cycles. There are also cicadas with 4- or 8-year cycles from India, Japan, Fiji and Australia, most of which are likely proto-periodicals with abundant years and rare years. However, of these, the so-called “World Cup Cicada”, Chremistica ribhoi from the Ri Bhoi District, Meghalaya, India, with a 4 year cycle, and Raiateana knowlesi from Fiji with an 8 year cycle, appear to be truly periodic with non-prime cycles.

One argument was that the relatively long prime cycles were selected to evade predators and parasites that might take advantage of their periodic emergences to coordinate their own generations to divisors of the cicada cycle. But long primes could throw this off. However, the alternative hypothesis has been that the long cycles are to evade prolonged periods of harsh climate and that the prime cycles are likely to throw off mating with cicadas with shorter periods that may be divisors of the longer cycle. Thus, prolonged harsh climate would segregate broods which do not mate with each other favor long prime periods. However, the discovery of the even-period cicadas from India and Fiji raise questions about these prime periodicity proposals and suggests that prime periodicity is not hard and fast in cicadas.

Whatever the case, there is support for predation being a potential selective pressure for synchronicity once a period longer than a couple of years is established. It has been proposed that a mass, synchronous emergence overwhelms the predators with satiation. There is some evidence for this from field observations. We have ourselves noted that while the initial emergents are eaten by dinosaurian and mammalian predators, they are quickly overwhelmed by the huge numbers in the case of the prime periodic cicadas. More recent observations, that need further study, indicate that once they establish a high intensity chorus, they inhibit birds by driving them away from the areas with high levels of noise. This has been observed with both tropical cicadas in Central America and 17-year periodic cicadas in the USA. Very loud cicadas are seen all over the world and their noise can be damaging to mammalian ears, like those of humans, at close range. Hence, the synchronous emergence with a chorus likely to be adaptive against predators irrespective of the period.

However, for this strategy to evolve first a relatively long life has to be in place. Most insects have annual cycles and several cicadas are no different. Hence, this was likely the ancestral condition from which early on a long-lived version emerged. The origin of such a long-lived version could have been selected by harsh climate because by skipping an year or two before emergence they could tide over period of drought or cold. It is conceivable that it first arose close to the tropics in response to drought and it allowed colonization of higher latitudes as it provide a means of tiding over cold. Per say, climatically driven selection for long life is unlikely to favor synchronicity because by hedging bets and distributing the emergence one is more likely to get a good year eventually. We see the longer periods to be more common in higher latitudes like Japan, New Zealand and North America suggesting that cold weather might have been a selective pressure for increasing the length of life cycle. Once long life was selected, it is likely that a degree of synchronicity was selected next by predator pressure. It is possible that this happened several times independently in different parts of the world giving rise to the several proto-periodic cicadas and that the transition to long periodic cycles was likely via synchronization of the proto-periodic intermediates. Yet, it seems to us that we don’t still have the strongest or cleanest hypothesis for the emergence of prime periods.

A cycle of 17 years is a big span even in human reckoning. Hence, we could not avoid looking back at the ebb and flow of life in the 17 years since the last emergence. One thing has ironically remained the same both at this emergence and that last. However, when we looked at that thing during the last emergence, we were still quite hopeful. Having seen a lot of life, we are inherently pessimistic about things that need near miracles, but at that time we were still hopeful of victory in the battle of the blind-spots — one where we had to shoot the target without being able to see it. That conquest remains as elusive now as 17 years back. In those 17 years, we did see some glimmer of the hiding foe but whatever we saw inspired no confidence whatsoever that we could beat it. A strange thing happened somewhere roughly midway in those 17 years though. Tied down by the lassos of Varuṇa and the darts of Rudra, we knew not at some point how long we may trudge on. It looked like the climb of Himalayan slope while being low on supplies. At that point, like at few other points in our life, we took a big but carefully calculated gamble. There are some such junctures when the probabilities can be relatively precisely computed, and you can make an “informed” bet. However, this bet was rather different from the rest in that we made it in a niṣkāmya manner — one where we had properly steeled ourselves for the negative outcome. There we were in a three-front war but only two of them mattered at all. The gods aided this time, unlike at the time shortly after the last emergence, and we scored several outright victories on both those fronts — like the Aśvin-s and Indra aiding emperor Trasadasyu in the demolition of forts. But that third front was a mysterious experience. We neither won nor lost. However, we got a fairly clear glimpse, late one evening, of what true victory in that front would look like. We had started doubting if there was even such possibility — maybe it was just a figment of our imagination — the quest for something that did not exist in real life. That glimpse showed that it was real; we were not chasing a gandharva-nagara — we could almost get there — but the chance that we would rule over that city was perhaps not going to come. Such are the ways of the gods — they sometimes show you after a long trial that something you thought should exist really exists, but it might indeed be out of reach, like a man yearning to reach a planet going around another star.

In the 17 years that have gone by the gods took us to many deserved victories against powerful foes — indeed, the wielder of the thunderbolt raises the Ārya yajamāna against the dasyu. At some point in the last third of those years we made another calculated gamble. We were in a position of relative power and we knew that if we did not make it our enemies would gain a complete advantage. A lot more depended on our allies than on us in that samarya. Our allies tried their best, fighting to the utmost of their abilities, but they lost, and our enemies made away with all their riches. We ourselves won most individual battles, barring one where we were betrayed by expectedly flaky fellow travelers. But the advantage our foes had gained and the flagging morale of our pakṣa placed us at the foot of yet another mountain fortress that seems formidable as that of emperor Jarāsaṃdha of Magadha. Time will tell if we might be able raise an army that will accompany us in new campaigns at a time when the physical virus from China and the mental one with ultimate roots in West Asia has widened the gulf between winners and losers.

Matters of religion: Varuṇāvasiṣṇavam, Agnāvasiṣṇavam and the vyahṛti-s

Like the clouds lifting after the monsoonal deluge to unveil the short-lived comforts of early autumn, the metaphorical pall over the nation cast by the engineer’s virus was lifting. Somakhya and Lootika were at the former’s parents’ house, relieved that they had survived and overcome the tumultuous events. Somakhya’s parents asked them to offer the Varuṇāvasiṣṇava and associated oblations as ordained by the Bhṛgu-s and Āṅgirasa-s of yore. Vrishchika and Indrasena were also present as observers of the rite. Somakhya donned his turban and identified himself with the god Indra to initiate the rite, for indeed the śruti has said: tad vā etad atharvaṇo rūpaṃ yad uṣṇīṣī brahmā । — that brāhmaṇa who is turbaned is indeed of the form of the Atharvan. He explained to Indrasena that the śruti holds the Indra took the shape of the Atharvaveda in his turbaned form to protect the ritual of the gods from the dānava-s. Indrasena: “Indeed, even the primordial śruti records that form of Indra in the ṛk of the Kāṇva-s:

yajña indram avardhayad yad bhūmiṃ vy avartayat । cakrāṇa opaśaṃ divi ॥ 
The ritual magnified Indra [with praise] when he made the earth rotate, making [himself] a turban in (= of) heaven.
One may note play on the word opaśa; by taking it as neuter one could also interpret is as the pillar or the axis of heaven.”

Then, Somakhya and Lootika took their seat before the fire on the hide of a reddish brown ox strewn with darbha grass. Thereafter, they performed an ācamana and prokṣaṇa with the incantations: apāṃ puṣpaṃ mūrtir ākāśaṃ pavitram uttamam । indra jīva sūrya jīva devā jīvā jīvyāsam aham । sarvam āyur jīvyāsam ॥ [The flower is the form of the waters, the empty space [and] that which the most pure. Enliven, o Indra; Enliven o Sūrya. Enliven, o gods. May I live. May I complete my term of life].

Thereafter, Somakhya meditated on the special connection of the founder of his race to god Varuṇa and uttered the incantation establishing his connection to the founder of his lineage, great Bhṛgu: tad bhṛgor bhṛgutvam। bhṛgur iva vai sa sarveṣu lokeṣu bhāti ya evaṃ veda ॥ [That [connection with Varuṇa] is the Bhṛgu-ness of Bhṛgu. He who knows thus shines in all the worlds like Bhṛgu]. He recited the formula: OṂ sarvair etair atharvabhiś cātharvaṇaiś ca kurvīya॥ [OṂ May I perform [this rite] by means of all these incantations of Atharvan and the Ātharvaṇa-s]. OṂ mantrāś ca mām abhimukhībhaveyuḥ । [OṂ may the [AV] mantra-s face me [favorably]]. Somakhya then explained to Indrasena and Vrishchika: “The śruti holds that like a mother can be killed by the fetus she bears, the mantra-s can kill the holder if he improperly applied them or has not been diligent in their study. Hence, he must utter this incantation beginning with OṂ. The praṇava indeed protects him from such backfiring.”

He muttered the Sāvitra incantation-s to the god Savitṛ as per the teaching of the great brāhmaṇa Śvetaketu, the son of Uddākaka Āruṇi:
OṂ BHUR BHUVAḤ SVAḤ tat savitur… prachodayāt ॥: This first cycle is done with the 3 mahāvyāhṛti-s.
OṂ BHŪR JANAT tat savitur… prachodayāt ॥: Somakhya touched Lootika with a darbha-bunch and she made an oblation as is appropriate for the sacrificer’s wife in the fire at the utterance of svāhā (idaṃ na mama ॥)
OṂ BHUVO JANAT tat savitur… prachodayāt ॥: Somakhya’s parents stepped forward and made an offering with a silent svadhā call and touched water.
OṂ SVAR JANAT tat savitur… prachodayāt ॥: Somakhya made an oblation with a svāhā (idaṃ na mama ॥)
OṂ BHŪR BHUVAḤ SVAR JANAD OM tat savitur… paro rajase ‘sāvado3m॥: Somakhya made an oblation with a vauṣaṭ uttered loudly (idaṃ na mama ॥)

Then he proceeded to the main oblations:
śrauṣaḍ
yayor ojasā skabhitā rajāṃsi
yau vīryair vīratamā śaviṣṭhā ।
yau patyete apratītau sahobhir
viṣṇum agan varuṇaṃ pūrvahūtiḥ ॥

By whose power the domains of space were stabilized,
by whose energy, the most energetic and mightiest,
who lord it unopposed by their powers,
to [that] Viṣṇu and Varuṇa have gone the first offerings.

yasyedaṃ pradiśi yad virocate
pra cānati vi ca caṣṭe śacībhiḥ ।
purā devasya dharmaṇā sahobhir
viṣṇum agan varuṇaṃ pūrvahūtiḥ ॥
vauṣaṭ + idaṃ varuṇāviṣṇūbhyāṃ na mama ॥

In whose direction is that which shines forth,
[whatever] that vibrates and observes with power
from ancient times by the god’s law with might,
to [that] Viṣṇu and Varuṇa have gone the first offerings.

OṂ BHŪH pra tad viṣṇu stavate vīryāṇi
OṂ BHUVO mṛgo na bhīmaḥ kucaro giriṣṭhāḥ ।
OṂ SVAḤ parāvata ā jagamyāt parasyāḥ ॥
OṂ BHŪR BHUVAḤ SVAR JANAD VṚDHAT KARAD RUHAN MAHAT TAC CHAM OṂ viṣṇave svāhā + idaṃ viṣṇave na mama ॥

Thus, he praises forth his heroic deeds, Viṣṇu is
like a dreadful lion wandering, stationed in the mountains
From the distant realm may he come close.

śrauṣaḍ
agnāviṣṇū mahi tad vāṃ mahitvam
pātho ghṛtasya guhyasya nāma ।
dame-dame sapta ratnā dadhānau
prati vāṃ jihvā ghṛtam ā caraṇyāt ॥

O Agni and Viṣṇu mighty is your might;
you two drink from name of the ghee’s secret.
In home after home you two place the seven gems.
may your tongue move here to meet the ghee.

agnāviṣṇū mahi dhāma priyam vāṃ
vītho ghṛtasya guhyā juṣāṇau ।
dame-dame suṣṭutyā vāvṛdhānau
prati vāṃ jihvā ghṛtam uc caraṇyāt ॥
vauṣaṭ + idaṃ agnāviṣṇūbhyāṃ na mama ॥

O Agni and Viṣṇu mighty is your dear domain;
may you two savor the secret enjoyment of the ghee
In home after home you two are magnified by good praise-chants.
may your tongue flicker upward to meet the ghee.

OṂ BHŪH yasyoruṣu triṣu vikramaneṣv adhikṣiyanti bhuvanāni viśvā ।
OṂ BHUVA uru viṣṇo vi kramasvoru kṣayāya nas kṛdhi ।
OṂ SVAḤ ghṛtam ghṛtayone piba pra-pra yajñapatiṃ tira ॥
OṂ BHŪR BHUVAḤ SVAR JANAD VṚDHAT KARAD RUHAN MAHAT TAC CHAM OṂ viṣṇave svāhā + idaṃ viṣṇave na mama ॥

In whose wide three strides all the worlds are laid down;
stride widely O Viṣṇu for wide lordship; make [that lordship] for us;
Drink the ghee, O source of ghee; prolong the lord of the ritual over and over!

mama devā vihave santu sarva
indravanto maruto viṣṇur agniḥ ।
mamāntarikṣam urulokam astu
mahyaṃ vātaḥ pavatāṃ kāmāyāsmai ॥
OṂ BHŪR BHUVAḤ SVAR JANAD VṚDHAT KARAD RUHAN MAHAT TAC CHAM OM indravantaḥ svāhā ॥

May all the gods be at my ritual invocation;
The Marut-s with Indra, Viṣṇu and Agni.
Let the broad realm of the atmosphere be mine.
May Vāta blow for favoring this wish of mine.

yo naḥ svo yo araṇaḥ sajāta uta niṣṭyo yo asmāṃ abhidāsati ।
rudraḥ śaravyayaitān mamāmitrān vi vidhyatu ॥

Whether one of ours or one who is in a truce, a kinsman or an alien, whosoever attacks us
may Rudra releasing a shower of arrows pierce those enemies of mine.

yaḥ sapatno yo ‘sapatno yaś ca dviṣan chapāti naḥ ।
devās taṃ sarve dhūrvantu brahma varma mamāntaram ॥

Whichever competitor or whichever non-competitor and whichever hater curses us,
the gods shall injure him. The incantation is my inner armor.

Having concluded the after-rites Somakhya, Lootika, Indrasena and Vrischika left to savor the fresh air and the natural world, and engage in some brahmavāda on the hills beyond the late medieval temple of the awful Caṇḍikā. They stopped at the quadrangle in the low ground facing the stairs leading to the temple on the hill before a towering bastard poon tree. Vrishchika: “There used to be an old woman with a goat who used sit in the vicinity of this skunk tree. We used to feed her goat as a representative of the god Kumāra. She has likely passed into the realm of Vivasvān’s son along with her aja. Hope Rudra was kind to her when her time came. Indrasena, sometimes, thinking about you, as though seized by Skanda or Viṣṇu, I used to feed her goat hoping that Skanda might be kind to me.” Indrasena: “O Gautamī, after all the meanderings, it seems, Skanda has brought you to your destination as he did to the Kāṇva and his goat.” Lootika: “I also recall that Somakhya’s family observes a Kaumāra rite on the Āśvina fullmoon, where they make a rare dish from payasya (curdled milk cheese; Iranic: paynīr). They would offer some of that to the woman with the goat getting the leaf in which the dish was wrapped” Indrasena: “Is that a folk Atharvan rite?”. Somakhya: “Yes, the folk Atharvan tradition holds that Skanda is the teacher of Paippalāda, one of the promulgators of the AV saṃhita-s, and the paurṇamāsya rite is held in the honor of the enlightenment of Paippalāda.”

It was a quiet time of the day with just a light stream of votaries and gawkers on the stairway to the temple. The four made their way up the steps, mostly in silent thought, to pay their respects to the enshrined parivāra-devatā-s and the wife of Rudra at the main shrine. Even as they were about to exit the circumambulatory path to resume their climb beyond the stair way further up the crag to the plateau beyond, Lootika was approached by a woman who wanted to fall at her feet. Lootika prevented her from doing so and she began pouring out a litany of medical troubles. Lootika signaled to her sister: “This lady seems to have mistaken me to be you.” Vrishchika: “Stepped in and having briefly heard her out gave her some reassuring words and asked her to attend to her father’s clinic.” Somakhya and Indrasena instinctively felt their concealed guns and knives for a dasyu could always be lurking in the shades. Having reached their favored vantage point, the site of an old megalithic stone circle, they looked on at their city below. There seemed to be some hesitancy in returning to the old normal; hence, the air seemed cleaner and the horizon clearer. The, nakṣatra of the day, the eye of Mitra and Varuṇa, had mounted the vault of the cloudless southern sky. Looking into the distance they saw that the fires in the yonder cemetery were far fewer than when Somakhya and Lootika had looked on from the same place during the height of the conflict. Lootika: “The lull between the storms.” Vrishchika: “You think it is not yet over?” L: “The clash with the rākṣasa-mata-s is like the fight between the Daitya-s and the Deva-s — the bigger disease from the mleccha-s is that of the mind — it will play out next with much spilling of blood — but then our people could end in a whisper too.”

Indrasena: “Coming to the rite of morning, I’d like understand more about the AV vyāhṛti-s — both the combination of the mahāvyāhṛtis with the incantations as also the connection of the vyāhṛti-s to Maruta Indravantaḥ.”
Vrishchika: “Could we please also have a broader discussion of role the mahāvyāhṛti-s and their transcendence by other vyāhṛti-s across the Vaidika collections?”

Somakhya: “Alright, Vrishchika, let us lay the groundwork for the exploration desired by Indrasena by first addressing the brahmavāda on the vyāhṛti-s in the śruti-s other than those of the Atharvan-s. Let us begin this discussion with testing your knowledge of the traditions regarding the vyāhṛti-s in the traditions you are familiar with. Why don’t you tell us what you know regarding the three mahā-vyāhṛti-s?”
V: “The śruti of the Aitareya-s holds that the 3 vyāhṛti-s are like connective tissue that holds together the three disjunct parts of the śruti in the form of the ṛk-s, yajuṣ-es and sāman-s — thus they are compared to procedures akin to reducing dislocations of joints or sewing up cut skin. Indeed, this analogy of the Aitareya-s provides early evidence for these medical procedures among the ārya-s, which parallel those surgical and bone-setting procedures explicitly mentioned in the Veda of the Atharvan-s and having echoes among other Indo-Europeans, like in the Merseburg spell of the śūlapuruṣa-s:
(bhūr bhuvaḥ svar) … etāni ha vai vedānām antaḥ śleṣaṇāni yad etā vyāhṛtayas . tad yathātmanātmānaṃ saṃdadhyād . yathā parvaṇā parva yathā śleṣmaṇā carmaṇyaṃ vānyad vā viśliṣṭam saṃśleṣayed । evam evaitābhir yajṅasya viśliṣṭaṃ saṃdadhāti ॥

These are verily the internal bindings of the Veda-s, these vyāhṛti-s. Even as one joins the one individual thing other separated thing; like setting one joint with another joint; like suturing with a cord, skin with another torn one. Even so, verily with these one joins the disjunct parts of the the ritual.

Thus, the suturing role of the vyāhṛti-s is critical for the terminal sviṣṭakṛt-s for fixing the errors in the ritual.

S: “That is good. So, what do you know of the thesis of the transcendence of 3 mahāvyāhṛti-s?”
V: “Well, the Upaniṣat of the Taittirīyaka-s holds that there are three primal or mahāvyāhṛti-s, bhūr, bhuvas and suvar; however, the sage Māhācamasya held that there is a fourth, i.e. mahas. In his teaching mahas is privileged over the remaining three. He establishes four homologies between them and other entities. Those are the following: 1) He sees the three primary one bhūr, bhuvas and suvar as corresponding to the earth, the atmosphere and the space beyond. The fourth, mahas, is seen as the Āditya, the sun, which causes the world material worlds to take form — perhaps in more than one way — by supplying the matter to make them and also the light by which their existence is perceived. 2) The next homology is to the first 3 and the sources of light — the fire, the wind (he implies lightning here) and the sun. The reflected light of the moon is homologized to mahas — here again we might see it as the ambient light that makes perception possible even the source themselves are invisible. 3) He also homologizes the first 3 with the 3 categories of incantations in the śruti, the ṛk-s, the yajuṣ-es and the sāman-s, and mahas with the brahman, which is to be understood here as the praṇava. 4) The next homology is between the vyāhṛti-s and the inhalation, exhalation, and retention in the prāṇāyāma cycle. Specifically, in that context mahas may be understood as the air. However, I hold that from the śruti we may infer that what was meant was more general — the physiological process of nutrient uptake, export of unwanted and secreted compounds and the anabolic processes. The free-energy-providing material in this process, i.e. the nutrients, is the fourth, mahas. Thus, as there are four homologies in each set with a total of 4 sets, the vyahṛti-s are seen as being 16-fold. The summary of these linkages is presented as the understanding that the first three are the limbs of the physical body and mahas corresponds to the consciousness. Thus, mahas in different domains is equated respectively with the link substance, the work-generating substance, the diffuse or reflected light that pervades the universe and the mantra essence — all of these are seen as analogies for the nature of consciousness with respect to matter.”

Somakhya: “Excellent upa-gautamī. Dear Lootika is there something you might want to add to what your sister has just expounded from other Vedic traditions?”
Lootika: “Sure. I actually learnt of the multiple expressions of vyāhṛtyutpatti in the scriptural readings I did with your mother. This theory of Māhācamasya, introducing the fourth vyāhṛti perhaps led up to the theory of multiple vyāhṛti-s in both Atharvan and Yajuṣ traditions. This is clearly a departure from the triple vyāhṛti system expounded in the brāhmaṇa of the Vājasaneyin-s, that of the Aitareya-s and the Upaniṣad brāhmaṇa of the Jaimini singers. There explicitly Prajāpati is described as generating only 3 vyāhṛti-s.”

Indrasena: “Indeed. However, each of those accounts have notable points — one may see a gradual build up of concepts within the 3 vyāhṛti system that led to the emergence of the fourth. In the śruti of the Vājasaneyin-s, we have an account that might be seen as retaining the archaic form which the thesis of Māhācamasya eventually emerged. That account describes the heat (tapas) of Prajāpati as the basis for the emanation of the 3 worlds. Since these worlds were heated by his tapas they emanated the same 3 primary sources of light (the deities Agni, Vāyu and Āditya) mentioned by the TU. That tapas causing those lights to radiate heat spawned the collections of the 3 types of mantra-s of the śruti. His tapas then caused those mantra collections to radiate heat from which Prajāpati extracted three generative substances (śukra-s) that are the vyāhṛti-s. We might trace the origins of the two other traditions, which Lootika just mentioned, from such a foundation — one present in the Sāmavaidika tradition of the Jaiminīya-s and the other in the Aitareya-brāhmaṇa.

In the former, Prajāpati is not presented in a protogonic context, but is competing with the other gods, probably reflecting the tension between the surging Prājāpatya religion among our people and the older Ārya-deva-dharma. Prajāpati conquered the triple-world with the 3-fold mantra collection. Fearing that the other gods might see the same and take over his conquest, he extracted the essence of the ṛk-s uttering bhūḥ. That became the earth and its essence streamed forth as Agni. From the Yajuṣ-es he extracted the essence with bhuvaḥ and that formed the atmosphere and streamed forth as Vāyu. The sāman-s were distilled with the suvaḥ call and they formed the the heaven, from which the essence streamed forth as the Āditya. However, there was one akṣara he could not distill into an essence, namely the praṇava. That remained by itself and became Vāc.

In the Aitareya text, we have a cosmogony closer to that the of Vājasaneyin-s, wherein Prajāpati’s heat generated the triple-world. As in the former account, by his heating of those, the 3 luminaries emerged and by heating those the 3 mantra-s collection were generated. By heating those again the generative essences (śukra-s), which are the 3 primary vyāhṛti-s emerged. But in this account those were heated further to generate 3 phonemes: A, U, M, which Prajāpati got together to generate the praṇava, OṂ. Thus, here too, as in the Jaiminīya-Upaniṣad-brāhmaṇa we see that there is something beyond the 3 basic vyāhṛti-s, namely the praṇava. It is the praṇava that Māhācamasya equated to the fourth vyāhṛti mahas in his thesis and that which appears as the final vyāhṛti of the Atharvan-s. Thus, we see an evolutionary process within the śruti which paved the way for the vyāhṛti-s beyond the primary three via the concept of the praṇava.”

Lootika: “There is no mention of the triple vyāhṛiti-s in the oldest layer of our tradition, the Ṛk-saṃhitā. Now, that could be because they are specialized calls that don’t fit into the metrical incantations. However, in all the accounts of vyāhṛtyutpatti, which we have discussed so far, we see the central role of the protogonic god Prajāpati. Is that the vyāhṛiti incantations arose within a Prājāpatya milieu? As Indrasena pointed out, one of the narratives might hint at Prajāpati competing with the gods of the old religion. Moreover, in specifying the deities of the vyāhṛiti-s, Śaunaka mentions in the Bṛhaddevatā that, whereas Prajāpati is the god of all the 3 vyāhṛti-s as a group, individually they have Agni, Vāyu and Sūrya as their deities. Likewise, for OṂ, Śaunaka mentions Vāc and Ka Prajāpati as in the brāhmaṇa narratives, but also Indra and the gods in general as its deity. This is indeed supported by the fundamental teaching of the upaniṣat:

yaś chandasām ṛṣabho viśvarūpaś
chandobhyaś candām̐sy āviveśa ।
satām̐ śikyaḥ provācopaniṣadindro
jyeṣṭha indriyāya ṛṣibhyo
namo devebhyaḥ svadhā pitṛbhyo
bhūr bhuvaḥ suvaś chanda om ॥

After all even in its declining days our tradition was quite unanimous about this teaching and held that: “sa praṇava-svarūpī paramaiśvarya-yukta paramātmā indra upaniṣat pratipādyo bhūtva vyāhṛti-trayātmā oṃkāraḥ ।” Indra, in the form of the vyāhṛti-s and the praṇava, is indeed is the first causal link in the “bringing together” (upaniṣat) of the sambandha-s for our ancestors — fitting well with the Aitareya statement on the vyāhṛti as the internal bonds of the śruti. These hint at a pre-Prājāpatya origin for the vyāhṛti-s and the praṇava within the old religion. So, can we find evidence for the ritual deployment of the vyāhṛti-s in the pre-Prājāpatya layer of the religion?”

S: “A superficial student could indeed reach the conclusion that the vyāhṛiti-concept emerged as part of the linking of the cosmogonic role of Prajāpati with the cosmic origin of the mantra-s, like in the accounts that Indrasena just expounded. However, as your sister noted there is an association of the vyāhṛti-s with the sviṣṭakṛt rite for setting right the errors of ritual. Indeed, as you know well, such vyāhṛti oblations and calls are a general feature of most gṛhya rites and also śrauta rituals such the sāmidhenī incantations where they make up the syllables corresponding to the rest of the year beyond the 365. I would say this pervasive use is an indication of their ancient and pre-Prājāpatya ritual roles, substantiating their conception as the internal fastenings of the Veda. An unambiguous case for their pre-Prājāpatya role is made by their central role in the silent incantations that are inaudibly recited as as part of various śastra-s, as also the similar incantations used in the morning and evening offerings of the Agnihotra. Thus, the śruti of the Aitareya-s states that one concludes the Ājya and Praüga recitation with bhūr agnir jyotir jyotir agniḥ ॥; the Niṣkevalya and Marutvatīya recitations with indro jyotir bhuvo jyotir indraḥ ॥ and the Āgnimāruta and Vaiśvadeva recitations with sūryo jyotir jyotiḥ svaḥ sūryaḥ ॥ as the inaudible incantations. This give us a glimpse of their ancient use in a śrauta context going back to pre-Prājāpatya times. But we see pervasive signs of their place in even more routine rites that reinforce the proposal that their common place use was of pre-Prājāpatya provenance — I guess you might agree Indrasena?”

I: “I was just about to interject in this regard. To build up the context, we may first note the Vyāhṛti-kalpa from the gṛhya appendix of the Bodhāyana-s, which teaches the 12000x japa of the mahāvyāhṛti-s for the attainment of specific goals and purification. It was this tradition of the japa of the vyāhṛti-s that one hand was incorporated into nitya and naimittika rituals focused on Deva Savitṛ — like the very fact that we use either the three mahāvyāhṛti-s or the seven vyāhṛti-s: BHUḤ BHUVAḤ SUVAḤ MAHAḤ JANAḤ TAPAḤ SATYAM coupled the Sāvitrī in our routine daily japa. The same applies to the coupling of the mahāvyāhṛti-s with the Sāvitrī and the Trisuparṇa in the mahat (the great) rite taught by Uddālaka Āruṇi to Yājñvalkya Vājasaneya, the founders of the śukla tradition. Indeed, this coupling of the mahāvyāhṛti-s with the Sāvitrī is extended in tradition of the Jaiminīya singers, wherein two additional vyāhṛti-s are added to the list to make it a total of five, just as the seven in the other traditions. These are SATYAM and PURUṢA, after which comes the gāyatra sāman composed on the Sāvitrī. On the other hand the pure mahā-vyāhṛti japa also developed into the song of vyāhṛti-s in the tradition of the Rāṇāyanīya and Kauthuma singers. In that song, the musically rendered vyāhṛti-s are sandwiched between two musical praṇava-s and interspersed with 3 repetitions of the magical stobha-s with the concluding bhakti-s of the suvar-jyotiḥ, reminiscent of both the śastra incantation you mentioned and the brahmaśiras that closes the Sāvitrī with the ten praṇava-s (OṂ BHUḤ । OṂ BHUVAḤ । OM̐ SUVAḤ । OṂ MAHAḤ । OṂ JANAḤ । OṂ TAPAḤ। OM̐ SATYAM । OṂ tat savitur vareṇyam । bhargo devasya dhimahi । dhiyo yo naḥ prachodayāt ॥ OM āpo jyotī raso amṛtam brahma BHŪR-BHUVA-SVAROM ॥). Similar to this connection to the Sāvitrī, the vyāhṛti-s are also incorporated into the important vyāhṛti-homa-s of the Yajuṣ tradition (bhūr annam agnaye svāhā… ityādi) which culminate in the incantation of Indra as the bull among the meters that your wife just mentioned. Notably, the last of the vyāhṛti-homa incantations include the fourth vyāhṛti, mahas. All these not only indicate the pervasive presence of the mahāvyāhṛti-s but also the other vyāhṛti-s in a range of prayoga-s, like say the offerings to Mahārāja in the Āraṇyaka of the Taittirīyaka-s. These strongly favor the idea that the Prājāpatya-s were merely incorporating a widely use mantra-tradition into their philosophizing.”

S: “Good. In this regard I would note that the special vyāhṛti, PURUṢA, of the singers is also used in other recitations. One such is during the expiatory singing of the Vāmadevya Stotra based on RV 4.31.1-3 composed by the illustrious ancestor of our wives. The last of these ṛk-s is short by 3 syllables from the gāyatrī; hence, he should insert the the 3 syllables of the vyāhṛti PURUṢA and recite this ṛk as a proper gāyatrī before the Vāmadevya Stotra is sung. Thus, we have:
OṂ abhī ṣu ṇaḥ sakhīnām PU avitā jaritṝṇāṃ RU । śatam bhavāsy ūtibhiḥ ṢAḤ ॥

Similarly, during the recitation of the Rājana incantation in the nocturnal ritual of the winter solstice we insert a PURUṢA into the intertwining of the ṛk of my ancient clansman Bṛhaddiva Ātharvaṇa and that of Priyamedha Āṅgirasa:
tad id āsa bhuvaneṣu jyeṣṭham PU
nadaṃ va odatīnāṃ |
yato jajña ugras tveṣanṛmṇo RU
nadaṃ yoyuvatīno3m ।
sadyo jajñāno ni riṇāti śatrūn
patiṃ vo aghnyānāṃ |
anu yaṃ viśve madanty ūmāḥ ṢO
dhenūnām iṣudhyaso3m ॥

Bṛhaddiva Ātharvaṇa:
He indeed was the foremost in the universes,
who was born with fierce, mighty manliness
Simultaneously, with his birth, he melts down the enemies
as all his friends [Viṣṇu, Vāyu and the Marut-s] cheer him on.

Priyamedha Āṅgirasa:
At the roaring bull among the eager females,
at the roaring bull among the coy young ladies,
at the lord of your milk-giving cows,
shoot your arrow [in the form of the chant]

As you can see, the intertwining couples a mantra indicating the manliness of Indra with one indicating him as the bull among the females; thus, the vyāhṛti PURUṢA here becomes the seed that is infused into the incantation.”

I: “Somakhya, having gone so far into the realm of the vyāhṛti-s and their prayoga-s, let us return to my original question regarding the roots of the vyāhṛti-s of the Atharvan-s. Where all are they found and what are their prayoga-s?”
S: “Prājāpatya brahmavāda for the AV vyāhṛti-s given in the Gopatha Brāhmaṇa is closely but briefly paralleled by the Jaiminīya Brāhmaṇa, which states that the local worlds was generated in fluid from the three mahāvyāhṛti-s. In contrast, the higher realms of space are said to have been generated from vyāhṛti-s KARAT, JANAT, VṚDHAT and SATYAM. This indicates that there was a wider knowledge and tradition of most of the AV vyāhṛti-s. In terms of ritual, we can see from the Gopatha Brāhmaṇa itself that the prayoga is in the context of the older Aindra religion, in the offering to the Marut-s and other deities who are in the company of Indra (the Indravant-s). Even as the vyāhṛti PURUṢA is deployed within the incantations that we just discussed, one could make a case for a similar wider presence for most of the AV vyāhṛti-s. You noted the emergence of equivalents of MAHAT and JANAD among other vaidika traditions. To that I would add the use other AV vyāhṛti-s in various traditions. For instance, the Vārāha-gṛhya-sūtra of the Maitrāyaṇīya-s specifies the use of the triad karat, janat and bṛhat (unique to that tradition, and semantically mirroring mahat or mahat) in the Garbhadhāna ritual. Coming to the Taittirīyaka-s, we have Iḍa recitations laid down by my ancestor Jamadagni Bhārgava for the drawing of the milk offerings in the Agnihotra as taught by Āpastamba: BHŪR IḌĀ BHUVA IDĀ SUVAR IḌĀ KARAD IḌĀ PṚTHIG IḌĀ ॥ In this tradition, the first three mahāvyāhṛti-s are, as usual, associated with the Agni on earth, Vāyu in the atmosphere and Sūrya in the heavens. Of the two further vyāhṛti-s, karat, matching the AV tradition, corresponds to the moon moving against the backdrop of the nakṣatra-s and the YV-specific PṚTHIK corresponding to the medicinal herbs discovered by Jamadagni Bhārgava. The Āśvalāyana-s have only four drawings of milk, and use vṛdhat instead of karat, again matching one the AV vyāhṛti-s. Interestingly, the Maitrāyaṇīya-s instead use janat in this context. Thus, these vyāhṛti-s are individually used in the other traditions but come together as a whole in the AV tradition and the svāhā offerings with them are specified in the Kauśika-sūtra-s.

This brings us to TAT and ŚAM. I’d posit that those arose from the ancient opening of the Śamyuvāka incantation which is repeatedly mentioned throughout the śruti. Its ancient use is suggested by opening of the Śamyuvāka being sought from Rudra in the ṛk of Kaṇva, the son of Ghora Aṅgirasa in the RV. In regard to TAT, one might also note that it might have a link to its use in the Yajuṣ incantation of the supreme Vāyu: OṂ tad brahma । OṂ tad vāyuḥ । OṂ tad ātmā । OṂ tat satyam । OṂ tat sarvam । OṂ tat puror namaḥ ॥ Finally, coming to the praṇava as an AV vyāhṛti, it seems to be a natural inclusion given the intimate link the mahāvyāhṛti-s share with it mīmāṃsā and prayoga. We see that, for example, in the Upaniṣat statement that identifies them with Indra as the bull among the Chandas, which Lootika just mentioned. Finally, I should also mention one of the homologies that the Atharvan tradition recognizes between these vyāhṛti-s and the wider horizon of texts. Thus, it has janat as equivalent to the compilation of the Āṅgirasa-s — the Āṅgirasa-veda; similarly we have vṛdhat and Sarpaveda, karat and Piśāchaveda, ruhat and Asuraveda, mahat and the Itihāsa-s, and tat and the Purāṇa-s. This perhaps reflects both the growing corpus of texts and awareness of texts of other traditions — like the Asuraveda — it could be some kind of memory of the Iranian texts.”

V: “What are some of the meditations one should be mindful of when performing a japa or contemplation on the progression of vyāhṛti-s?”
I: “The most important one is the japa of the threefold mahāvyāhṛti-s preceded by a praṇava. During this, as in the Vaiśvadeva songs of the Chandoga-s, one meditates on the Vasu-s associating them with BHUR; them one meditates on the Rudra-s associating them with the utterance of BHUVAS; then one mediates on the Āditya-s while uttering SUVAR. With the preceding OṂ, one meditates on Indra or Viśvedeva-s, i.e. the entire pantheon. While moving from one mahāvyāhṛti to another one perceives the connector deities: SUVAR and BHUḤ are connected by Dyāvā-Pṛthivī; BHUR and BHUVAS by Agnī-ṣomā; BHUVAS and SUVAR by Vātā-Parjanyā. When uttering the five vyāhṛti-s, i.e., mahāvyāhṛti-s + TAPAS and SATYAM one additionally meditates on the primal heat from which all arose and the very nature of existence. May be Somakhya could add more while returning to our starting point of the AV vyāhṛti-s?”

L: “Also, before rounding up this discussion it would be worthwhile if you could touch upon some of the mīmāṃsā-s on the different sets of vyāhṛti-s that are not widely aired by the extant brahmavādin-s focused on Prājāpatya and Uttaramīmāṃsā traditions.”
S: “Sure. Their connection to the Sāvitrī and the god Savitṛ is the most apparent one. The śruti holds that the inviolable laws of Savitṛ, like the probabilities of the draws of the vibhīdaka nuts from the hole, are the ones which run the universe: deva iva savitā satyadharmā: like the laws of the god Savitṛ that hold true. The mahāvyāhṛti-s illustrate their most apparent domain of action: the near realm, the mid-region and the realm of the sun. The more expanded set of seven vyāhṛti-s yoked to the Sāvitrī indicate their broader sphere of action — Mahas: the wider space. Then we move into the temporal axis: janas: the origin of space itself. What drives its emergence? tapas: heat. Finally, the very fact that something exists: satyam: also expressing the inviolable or true nature of the laws of Savitṛ, the ṛta. Indeed, Kṛṣṇa Āṅgirasa states:
ṛtena devaḥ savitā śamāyata
ṛtasya śṛṅgam urviyā vi paprathe ।
By the natural law the god Savitṛ exerts himself,
[by that] the antler of the natural law has spread widely.

The Samaveda adds the vyāhṛti, PURUṢA, after SATYAM. This may be seen as the root of the concept that was later expanded in Sāṃkhyā — the Puruṣa as consciousness. In placing the final Puruṣa, the singers posited a system in which the laws and existence itself might be objects in the conscious experience of the sole reality, the Puruṣa. The next notable mīmāṃsā of the vyāhṛti-s pertains to the way we deployed the mahāvyāhṛti triad with the three feet of the AV mantra-s to Viṣṇu. This connection is declared by the Jaiminīya-s, who state that the vyāhṛti-s were offered to Viṣṇu. The three feet of the deployed mantra-s indeed correspond to the three steps of Viṣṇu, who appeared as a dwarf and suddenly grew to a gigantic size to conquer the worlds from the Dānava-s with his famed triple strides: bṛhaccharīro vimimāna ṛkvabhir yuvākumāraḥ praty ety āhavam ॥ As the founder of your race, O Gautamī-s, states in the primal śruti, that gargantuan form of Viṣṇu is said to measure out the worlds with the ṛk-s — those are the corresponding AV ṛk-s we deploy conjoined to the vyāhṛti-s. The Kāṇva-s further add that those steps were the ones with gathered the atoms — samūḍham asya paṃsure ॥ — from which the universe condenses. Hence, while uttering that incantation the ritualist meditates on the great Viṣṇu stamping out the Asura-s and likewise calls on him to exclude his rivals from his space. This association with the vyāhṛti-s also extends to Viṣṇu’s wife in the incantation seen in the Mahānārāyaṇopaniṣat of the late AV tradition that you all know very well:
OṂ bhūr lakṣmī bhuvar lakṣmīḥ suvaḥ kālakarṇī tan no mahālakṣmīḥ pracodayāt ॥
This incantation is notable in placing Kālakarṇī in suvar. This is from her association with visible time in the form of the apparent movement of the sun in the sky. As you all know well from your Āgamika practice she is none other than the gigantic, dreadful, fanged, death-dealing eponymous goddess, armed with a bow, arrows, axe, sword, cakra, trident and a cleaver, emitted by Rudrāṇī from her mouth to terrorize the gods for their support of Prajāpati Dakṣa. The fourth vyāhṛti mahat is subliminally hinted by her name Mahālakṣmī, encompassing the wider space.

Coming the the AV vyāhṛti-s, the coupling OṂ BHŪR JANAT ॥ expiates ṛk errors and is offered in the Gārhapatya; OṂ BHUVO JANAT ॥ expiates yajuṣ errors and is offered in the Dakṣiṇa; OṂ SVAR JANAT ॥ expiates Sāman errors and is offered in the Āhavanīya; OṂ BHŪR BHUVAḤ SVAR JANAD OM ॥ expiates Atharvan errors and is also offered in the Āhavanīya. Here the JANAT is seen as regenerating the flawed incantations. Vrishchika, it may interest you that the AV tradition uses a metallurgical analogy of fusing metals for the welding role of these vyāhṛti-s, unlike the medical analogy of the Aitareya that you noted. The AV also holds that the same combination of vyāhṛti-s are the incantations uttered by the brahman before he asks the udgātṛ to sing the stoma to the god Bṛhaspati in the somayāga. Likewise he utters the entire gamut of vyāhṛti-s OṂ BHŪR BHUVAḤ SVAR JANAD VṚDHAT KARAD RUHAN MAHAT TAC CHAM OM when urging the udgātṛ to sing the song of the Indravant-s derived from the famous Evayāmarut ṛk to the Marut-s and Viṣṇu that was composed by your illustrious ancestor, O Indrasena (pra vo mahe matayo yantu viṣṇave marutvate girijā evayāmarut । pra śardhāya pra yajyave sukhādaye tavase bhandadiṣṭaye dhunivratāya śavase॥). As an aside that mantra-s is notable in more than one way but you may note the phrase girijā — Viṣṇu emerging from the mountain — a mythologem that presages his emergence from the pillar in the later Nṛsiṃha cycle — but here he emerges with the marching troop of the Marut-s to head for battle, evidently to join Indra in the battle against the Dānava-s.

In the purely AV performance, as we did earlier today (or in the muttered incantation of the brahman), it is deployed with the Indravant ṛk which illustrates the connections to various vyāhṛti-s. With Agni we are connected to Bhūr, with Vāta (Vāyu) Bhuvas, with Viṣṇu, the realm of the Āditya-s. All the special vyāhṛti-s can be seen as having deep connections with Indra and the Indravant-s. As we saw before the two praṇava-s at the beginning and the end are the mark of Indra. Janat indicates the emergence of Viṣṇu and the Marut-s from the mountain, which is a metaphor for the world axis — thus on one hand it represent the origin of time that Viṣṇu manifests as. On the other birth of the Marut-s that made the universe manifest. That manifestation and the growth of the universe, which is how the sons of Rudra manifest is indicated by Vṛdhat. Karat is action of filling the universe, as the ancient Bhārgava, Uśanas Kāvya, is quoted by Agastya Maitrāvaruṇi: karat tisro maghavā dānucitrā : Maghavan made three realms fill with glistening droplets. Ruhat, stands for the ascendance of the gods, manifesting as the rising sun in which they are worshiped. Mahat, as we saw before represent the great expanse of the universe. Finally Tat and Śam are the bliss that one attains from the gods upon the success of the ritual.”

Two exceedingly simple sums related to triangular numbers

This note records some elementary arithmetic pertaining to triangular numbers for bālabodhana. In our youth we found that having a flexible attitude was good thing while obtaining closed forms for simple sums: for some sums geometry (using methods of proofs pioneered by Āryabhaṭa which continued down to Nīlakaṇṭha Somayājin) was the best way to go; for others algebra was better. The intuition was in choosing the right approach for a given sum. We illustrate that with two such sums.

Sum 1 Obtain a closed form for the sum:

These sums define a sequence: 1, 28, 153, 496, 1225…
Given that we can mostly only visually operate in 3 spatial dimensions, our intuition suggested that a cubic sum as this is best tackled with brute-force algebra with the formulae for individual terms derived by Āryabhaṭa and his commentators. Thus we have:

The reason we wrote out the final solution in this unsimplified form is to illustrate that the above sums will always be a triangular number of the form:

, i.e sums from 1 to 1, 7, 17, 31, 49… or triangular numbers

Thus, the th terms of sequence of sums would be triangular number , where . From the above, one can also see that the difference of successive terms of our original sequence of sums will be 27, 125, 343, 729…, i.e., they are perfect cubes of the form (odd numbers 3, 5, 7, 9…). These cubes are thus the interstitial sums of the indices of the triangular numbers up to the index corresponding to the triangular number that is a term of our original sequence. Thus:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31…
then, 2+3+4…+7=27; 8+9+10…+17=125; 18+19+20+21+22…+31 =343 and so on.

Another interesting feature of the original sequence is its decadal cycle in the terms of the numbers in the last 2 places (written in anti-Hindu, i.e. modern order). They will always end in the following sequence of 10 numbers:
0, 1, 28, 53, 6, 25, 6, 53, 28, 1
Similarly, the index of the triangular numbers the define our sequence also shows a pentadic cycle in the last place of the form:
1, 7, 7, 1, 9

A comparable pattern is seen if we generate a sequence that is the sum of successive terms of our original sequence: 1, 29, 181, 649, 1721, 3781, 7309, 12881… The last place has a pentadic cycle of the form: 1,9,1,9,1. The last 2 places has a cycle of length 25: 01, 29, 81, 49, 21, 81, 09, 81, 69, 41, 61, 89, 81, 89, 61, 41, 69, 81, 09, 81, 21, 49, 81, 29, 01. Both are palindromic cycles.

Finally, the sum of the reciprocals of the original sequence converges to a constant: 1.04607799646… We suspect there is a closed form for this constant but have not been able to identify it.

Sum 2 Obtain a closed form for the sum of alternating negative and positive perfect squares: -1+4-9+16… i.e.

With the sum involving just square terms it is possible to use a wordless geometric proof along the lines of that proposed by Āryabhaṭa (Figure 1).

Figure 1.

Thus, we get the above sum as , where is the th triangular number.

Pandemic days: Vaccines and war

In American history-writing we come across various attempts to the justify the use of nuclear weapons on Japan in the closing phase of WW2. We often hear the claim that by using the nukes they avoided a large number of casualties that they would have suffered in a long-drawn conventional war to conquer Japan. Neutral outsiders who have studied the matter realize that this is merely the American narrative to justify and positively spin something, which many of their own people (some leaders included) found rather disturbing. A closer look indicates that the Japanese were brought to the brink of surrender by the demolition they faced at the hands of the Rus in Manchuria. Indeed, the Rus were poised to invade the main islands and probably kill the emperor of Japan. Faced with this, the Japanese calculated that surrendering to the Americans might help them save the emperor and perhaps avert a more brutal assault that the Soviet military would have subjected them to. Were the Americans aware of this? While we rarely hear anything pointing in this direction in the many American presentations of these events, it seems very likely to us that the Americans were fully aware of the situation. Hence, we posit that the reason the Americans used the nukes on densely populated Japanese cities was to graphically demonstrate to the Rus what the “super-weapons” in their possession could do and that their leaders were dead serious about earlier hints they had given the Rus. Hence, the intended audience for nukes was likely the Soviets rather than the Japanese. This was one of clearest examples of a technological change of game in times closer to our own. The Rus and other nations eventually developed their own nuclear weapons despite the American attempts to prevent some of them from succeeding. However, we do think that being the first to make and use the nukes contributed in a big way to the American rise to superpower status.

There are indications that the rising new religion of Navyonmāda might be turning that arc of American superpowerdom to towards the horizontal; however, even in these days of late empire the accumulated technological capital of the superpower could make a major difference in the “war of the day”. We had briefly alluded to this in the past note. In this note, we shall expand a bit on that. Right from when the Wuhan corruption exploded among the Cīna-s, it was clear that the disease was being used as a geopolitical tool. With hindsight we can say that the Cīna-s knew early on that it was a respiratory disease likely transmitted by the airborne route. Despite all the show of disinfecting the streets of Wuhan with chemical sprays, early in the epidemic they were wearing masks and practicing social distancing. However, they did little to stop international traffic despite restricting internal traffic between cities with high infection. Moreover, via the WHO, they initially held back information on human-to-human spread instead pointing to wet markets. Then they used the WHO to project messages about washing hands rather than wearing the appropriate masks (Sure, early the cruise ship incidents had a norovirus-like fomite feel to it, but the Cīna-s knew better). Thus, even as they facilitated an information blackout to the rest of the world, within their own borders they took draconian measures of isolation and blockade to curb the disease. As a result, even as the left-liberal occidental media was running paradoxical pieces on how “totalitarian” governments fare worse with pandemics and how Vijayanāma-vyāpārin was being xenophobic towards their Galtonian partners, the virus breached their defenses and established itself in their midst. The result was waves of massacres that really made the occidental powers look limp. At the end of it, emperor Xi had deftly leveraged the epidemic in his lands to hit his rivals while hiding his own losses from it.

Figure 1

With the virus established in their midst, both the Cīna-s and the mleccha-s soon realized that lasting victory could only be achieved by an effective treatment — vaccination being the method of choice for the long-term. Here is where a technological race, like the one to make the nukes, came to the fore. It was not easy, given that human coronavirus vaccination programs (like those inspired by SARS) had not really reached their culmination as the disease had been curbed by public health measures well before a vaccine became necessary. Figure 1 shows the popular vaccines in use or close to deployment (by no means comprehensive) classified by method, along with the country that developed them. One can see that the Americans were able mobilize multiple vaccines based on “advanced methods” — i.e. those using artificial mRNA with modified nucleobases, adenovirus vectors and baculovirus expression systems. The most basic of these technologies, i.e., cloning of the gene for the viral spike protein, can be easily mastered. However, to develop a truly successful vaccine, there is a lot more knowledge and technology that needs to be in place. These include: 1) the knowledge of and a repository of vector viruses like the Human Adenoviruses 26 and 5, or the Chimpanzee Adenovirus in the vector-based vaccines. 2) the capacity for chemical synthesis of nucleic acids for producing codon-optimized genes. 3) A knowledge of protein structure and evolution to produce optimal S protein constructs to be used as vaccines. 4) In the case of mRNA vaccines, the knowledge of and the capacity to synthesize modified nucleobases. The de novo development of these vaccines need a long-standing and well-developed culture of molecular biology and biochemistry. The totality of this knowledge is possessed by only a few nations in the world. Thus, developing the vaccine indigenously from scratch is not possible for most of the world. This fact in itself can be weaponized in a pandemic situation to gain a geopolitical advantage. It is in this regard that the superpower capital accumulated by the USA remains unchallenged.

Of the others, the British managed to successfully develop an adenovirus-based vaccine, showing that their accumulated intellectual capital still powers some technological propulsion in crisis. While we do not know as much regarding the success of the Russian attempt from external trials, they too seem to have achieved something comparable to the Brits with their Sputnik vaccine. Their subunit vaccine seems to deploy a rather unusual concept and its true efficacy remains entirely unclear to us. Still the gulf between these and the multiple American successes remains, illustrating the distinction between the great powers and the superpower. Several other nations possess the scientific and technological capacity to develop vaccines by themselves. In the Orient, we have Japan and Korea. In the Occident we have Germany and France. None of these have managed to develop and deploy their own vaccines to date. Some of them are even facing the adverse edge of not having a suitable vaccine that they can use. This hints that the task at hand it not easy in practice, even if a nation were to possess the theoretical know-how.

The Cīna-s have shown great prowess in molecular biology in recent times. A closer look at their research capacity in this regard has shown a tendency for plagiarism, faking and imitation of more original work coming from elsewhere. However, as the Americans say, you can fake it till you make it. Keeping with that, the Cīna-s have recently managed some pieces of high-end original research suggesting that they are coming of age. However, this is not visible in term of the vaccines that they have managed to deploy — to date they have only managed the conventional inactivated viral vaccines. There are suggestions that they have been trying to pilfer more advanced technologies and reverse engineer them, but we are yet to see the results of those attempts. Thus, the head-start the Cīna-s had with the virus has not really translated into vaccinological success. Finally, coming to India, we infer that the leadership correctly realized the danger posed by the virus to a populous country with little scope for urban social distancing and went for obtaining a vaccine as soon as possible. Perhaps, they correctly judged that the Indian biotechnological capacity was not up to the mark of developing any of the advanced vaccines indigenously in time. However, they did leverage the same low-tech solution as the Cīna-s to develop the indigenous inactivated virus Covaxin vaccine. Wisely, in a parallel track they purchased a stake in the AstraZeneca adenoviral vector vaccine developed by the Brits and the American subunit vaccine Novovax for local manufacture.

Next we come to the question of how these vaccines actually fared on the ground. The American and British image had taken a heavy beating at the hands of the virus by early 2021. The US had stacked up nearly a million deaths from the virus in an year (with almost 1 in 10 Americans being infected), while the count in UK is at least 200,000 (probably 1 in 12-15 people have been infected, keeping in mind their poorer accounting of cases ). However, both these nations have flattened their curves and have gone a long way towards mitigating the pandemic in their lands. This is in no small measure from the success of their vaccines — the capacity to develop and deploy them in time. The confidence in this success in the US is reflected in the recent CDC statement relaxing the use of masks among the fully vaccinated. From the viewpoint of both cases and fatalities, France and Germany have done poorly with respect to their island counterpart — to us this is a clear indication of their failure at vaccine deployment. A similar situation is seen with Poland — a western aligned Slavic nation. The Russian situation is harder to assess. Despite their Sputnik vaccine being apparently successful (as per their published papers) they have had no success in bringing down their deaths significantly from mid-February to mid-May 2021. The causes for this remain unclear to us.

Coming to the Cīna-s, they saw immense potential to use vaccine-diplomacy to leverage their head-start with the virus and the pandemic they had helped create. They sent their vaccines to all takers but as of date of this note there are no great results to see. Recently, a good comparison has come up in the form of two countries, the small Israel and the tiny Seychelles. Given the ties the CEO of Pfizer company has to Israel, they were able to obtain that vaccine right away. The latter received the Sinopharm (majority) and AstraZeneca (minority) vaccines. The former managed to control the epidemic within their borders with their mass vaccination program, whereas the later has so far failed to do so despite fully vaccinating 60% of its people. In large part this seems to stem from the lackluster performance of the Cīna vaccine. UAE, which also deployed this Cīna vaccine, is now thinking of going for a 3rd dose to improve immunity. The results of Sinovac in the field are not inspiring confidence either. Further evidence for the Cīna failure comes from the statements of emperor Xi asking for international collaboration on vaccines. Why would he want “collaboration” if his “guns” were firing alright? This generally poor performance of the conventional inactivated virus vaccine raises questions about how the Indian Covaxin would fare in the field — we still await the official publications in this regard.

A recent study by Khoury et al indicates that the modified mRNA vaccines developed in the US provided the strongest neutralizing-antibody response, whereas the AstraZeneca vaccine providse a lower tier response. Moreover, it also appears that the American vaccines are likely to provide sufficient (severe disease/death) protection against the B.1.351 South African strain whereas the AZ vaccine might be far less efficacious in preventing infection by that strain. In conclusion, the vaccine race has left the Americans as the clear winner both in terms of currently possessing the best vaccines (and an abundance of them) and having reasonable success in controlling the disease (As of the date of writing, the US still has a 7 day rolling average of over 500 deaths daily but we suspect in large part this can be contained if more people were proactive in getting the vaccines and observing disease-limiting behavior). This allows them to weaponize the vaccine in geopolitics.

It is precisely this point which brings us to the Indian situation. India began by handling the first wave reasonably well. This was followed by a good start to the vaccination program among elderly people with the AZ vaccine. Then we saw the Indian version of vaccine diplomacy, where the mass manufacture of the AZ vaccine was used to distribute it to several small countries, including those in the Caribbean. The overconfidence and behavioral recklessness (mask laxity and vaccination hesitancy) which ensued, along with ignorance of the function , poorly managed testing and contact-tracing, Khalistani rioting in the Panjab spreading the British B.1.1.7 strain, and the emergence of the (likely) more virulent B.1.617 strain resulted in the brutal second wave. Evidence from both within India and the UK indicates that the B.1.617 strain can displace other ambient strains, making it particularly dangerous. While this strain breaks past the AZ vaccine and causes disease, that vaccine seems to be capable of preventing death/serious disease in most vaccinated people. Thus, it was of paramount importance for India to ramp up vaccine production and vaccinate as many people as possible. While we admit that is a difficult task for a big country, we feel that the inability to keep up the vaccination program as a percentage of the population was a one of failures on the part of the nation.

The question which then arises is what the proximal cause for this might be. In our opinion, a major reason for this was the embargo placed on raw material by the Mahāmleccha led by Vṛddhapiṇḍaka. If one were to game Mahāmleccha geopolitical realism from it is foundational principle, it is obvious they would do everything to limit any rival potentate that aspires “great power” status. Even if it is regional player, it has to be broken if it marginally challenges the pañcanetra mleccha power. Moreover, Vṛddhapiṇḍaka has been placed in power by Big Tech and navyonmāda which has a svabhāva-vairam with all things H. Thus, H power, however, limited in the big picture is not something they tolerate — they were in particular pricked by Indian vaccine-diplomacy in their own hemisphere. Thus, they decided to use their victory in the vaccine war to settle scores with the Lāṭeśvara by limiting resources during the critical phase of the second wave in India. The job has been done as it took quite a bit of the sheen of the nation and showed it to be no better than a third-rate power, leave alone aspirations of “great power” status. Importantly, it has also taken the sheen of the the Lāṭeśvara, even among those generally supportive of him. The evidence for the mleccha hand is further supported by the active subversion program by Big Tech (Jāka-Bejha-Mukhagiri-Dvārādiduṣṭāḥ), Soraduṣṭa and the first responders dove-tailing their action with this wave.

That said, the deeper problem is the failure of the H to learn from history. Such perfidious mleccha action has been seen time and again — for instance the mleccha mercenaries hired by the Marāṭḥā-s or the sale of defective weapons by the English to them. Hence, the H leadership should have been prepared for mleccha action against them, especially with overthrow of Vijaya-nāma-vyāpārin in their land by the navyonmatta-s. They should have prepared to source key materials to keep themselves afloat in the vaccine war. The production failures are seen more generally with things like antifungals (e.g. amphotericin B) which are needed to tackle the ongoing epidemic of mycoses accompanying the Wuhan disease. An even deeper issue is the regard for research in India. Before the pandemic there was a generally dismissive attitude towards doing hard original science (not scientism or show-science) among the H. Instead, most people with such capacity were being funneled to quite a degree into service industries that do not ultimately make a nation a “great power”. You cannot build up scientific capacity to do hard stuff overnight and the results can be seen. The physicians and nurses on the ground are limited if there is no scientific capacity holding them up.

Generating simple radially symmetric art

Many people experience beauty in structures with bilateral, radial and rotational symmetries with or without recursion. The recursive or nested structure are the foundation of the beauty in fractal form, the generation of which has become increasingly easy for the lay person with ever-improving computing power. One could generate beautiful fractal structures using a range of open source software; however, there is no substitute for writing ones own code and taking in some of the mathematics behind the beauty — truly fractal structures provide the clearest bridge between mathematics and beauty. While we have presented some discussion on such structures on these pages, that is not the topic of this note. Here, we shall talk about stuff that is mostly art for art’s sake (We fully understand that what constitutes art can have some subjectivity) that is generated based on simple repeats of certain motifs with an emphasis on radial and rotational symmetries.

For at least three generations, there has been a strand in our family with an interest in generating such art. While there certainly exist people with much greater skill than us (you can even see manifestations of genius in this regard), the driving force for us is the pleasure derived from process of generating such art. One experiences a climax, when the process of polishing the work culminates in a first person experience of beatific satisfaction. In the two previous generations, the main medium was the powder (rice flour, stone and other colored powders) used in traditional alaṃkāra. In our case it began with spending time in our youth with a kaleidoscope. That inspiration was then transferred to paper, pen and compass but eventually it transitioned to computer-aided in silico tools. Over the years we have used many tools each with its own advantages and disadvantages. The first programs we used were CorelDraw and Canvas. The latter, at that time, was available to only on a Mac. It was a decent program but expensive. Moreover, we never owned a Mac, and using it on a public or a borrowed Mac was hardly convenient. Hence, it fell to the way side. I continue to use CorelDraw for professional stuff, especially if the work needs freedom of the hand and has some complexity; however, it is expensive and a typical user might only be able access it via a funding agency. Then the open source Inkscape came along, which evolved to be a reasonable free substitute for CorelDraw. Although CorelDraw is “smoother” to use, the current version of Inkscape is not bad at all.

However, we wanted something more “programmable” where one could adjust various numerical parameters rather than going freehand — a language for graphics. The first such we looked at was MetaPost — it had, what to us were unfriendly aspects; however, the time we spent exploring it was not a total waste because in the second decade of the 2000s of CE we learnt of the existence of the PGF/TikZ (ironically named: “TikZ ist kein Zeichenprogramm) languages that greatly improved on MetaPost in our subjective opinion. Notably it could be used from within . Thus, we finally settled on TikZ as the language to write these pieces of art in. Following is an example of such with the compiled result appended below.

\documentclass[margin=5mm]{standalone}
\usepackage{tikz}
\usetikzlibrary{arrows, arrows.meta, patterns, shapes.geometric, decorations.shapes, shapes.misc, graphs, mindmap, calc, backgrounds}

\begin{document}
\begin{tikzpicture}
\pgfdeclarelayer{background}
\pgfdeclarelayer{foreground}
\pgfsetlayers{background,main,foreground}

\definecolor{col1}{RGB}{2, 35, 54}
\definecolor{col2}{RGB}{15, 184, 184}
\definecolor{col3}{RGB}{178, 209, 107}
\definecolor{col4}{RGB}{199, 186, 99}
\definecolor{col5}{RGB}{174, 137, 199}
\definecolor{col6}{RGB}{59, 148, 126}
\definecolor{col7}{RGB}{77, 148, 255}
\definecolor{col8}{RGB}{230, 229, 202}
\definecolor{col9}{RGB}{61, 69, 67}

\foreach \x in {0,36,72, ...,324}{
%wavy background
\begin{pgfonlayer}{background}
\draw[col1, fill=col1, rotate=\x, scale=.8] (0,0) -- (22.5:3.5) to [bend left=40] (-22.5:3.5) -- (0,0)--cycle;
\end{pgfonlayer}

%wavy dots
\draw[decorate, decoration={shape backgrounds, shape=circle, shape size=.8mm, shape sep=1.512mm}, col3, fill=col3, rotate=\x, scale=.77] (18:3.5) to [bend left=40] (-18:3.5);

%onion
\draw[col4, fill=col4, rotate=\x+18, yshift=2.2cm, scale=.2] (-1,1) ..
controls (-0.5,0.5) and (0.5,0.5) .. (1,1) .. controls (1.5,2) and (0,2) .. (0,2.5) .. controls (0,2) and (-1.5,2) .. (-1,1) --cycle;

%petal
\draw[col5, line width=1.5, rotate=\x, yshift=1.75cm, scale=.75] (0,1) .. controls (-0.5,0) and (0.5,0) .. (0,1) --cycle;

%chandrabindu
\begin{scope}[rotate=\x, xshift=2.1cm, scale=.3]
\draw[col7, fill=col7] (0,-1) .. controls (-0.5,-1) and (-0.5,1) .. (0,1) ..controls (-1,1) and (-1,-1) .. cycle;
\draw[col7, fill=col7] (0,0) circle (.25);
\end{scope}
%pipal leaf
\draw[col8, line width=1, rotate=\x, xshift=1.35cm, scale=.15] (0,0) .. controls (-1,0.5) and (0,1.5) .. (1,1) .. controls (2,0.5) and (1.05,0.1) .. (2.1,0) .. controls (1.05,-0.1) and (2,-0.5) .. (1,-1) .. controls (0,-1.5) and (-1,-0.5) .. (0,0)--cycle;
\begin{scope}[col3, rotate=\x+18, xshift=1.3cm, scale=.5]
\def\y{20}
\def\z{sin(30)}
\def\w{1}
\draw[line width=\w] (0,0) to[bend right=\y] (1,\z);
\draw[line width=\w] (0,0) to (1,0);
\draw[line width=\w] (0,0) to[bend right=-\y] (1,-\z);
\end{scope}
%dot in petal
\draw[col8, fill=col8, rotate=\x+18, xshift=2.1cm] (0,0) circle (.05);

%dot in pipal
\draw[col8, fill=col8, rotate=\x, xshift=1.46cm] (0,0) circle (.05);
}

%tetrafolium
\draw[col6, fill=col9, line width= 3, scale=.75] (-1.5,0) .. controls (-1.5,-2) and (2,1.5) .. (0,1.5) ..controls (-2,1.5) and (1.5,-2) .. (1.5,0) ..controls (1.5,2) and (-2,-1.5) .. (0,-1.5)..controls (2,-1.5) and (-1.5,2) .. cycle;

\foreach \x in {0,90,180,270}{
%releaux triangle
\begin{scope}[rotate=\x, xshift=.75cm, scale=.25]
\def\y{30}
\draw[col3, fill=col3] (-.5, -0.8660254) to[bend right=\y] (1,0) to[bend right=\y] (-.5,0.8660254) to [bend right=\y] (-.5, -0.8660254) -- cycle;
\draw[col1, fill=col1, xshift=.07cm] (0,0) circle(.3);
\end{scope}
}

%central circles
\draw[col2, fill=col2] (0,0) circle (.45);
\shade[inner color=col8,outer color=black] (0,0) circle (.25);
\end{tikzpicture}
\end{document}

Figure 1.

This example uses decadal symmetry with central tetrad element. In our subjective experience tetrad symmetry can be paired with other even symmetries as long as they central or the exterior most elements.

Figure 2.

Ideally all repeated motifs should have at least bilateral symmetry. However, one can get away with a layer or two of elements with just rotational symmetry, like the “S” element in Figure 2. The choice of color is another very important element — we like a degree of contrast in all the piece. Appended below are a range of productions illustrating different color choices.

Figure 3.

Figure 4.

Figure 5.

Figure 6.

The phantoms of the bone-pipe-2

Vidrum had been introduced to a synesthetic patient by a neurologist colleague. The patient’s manifestation of synesthesia left a rather profound impact on him; thus, when he had a break of an hour in his duties, wanting to explore the issue more, he decided to do some quiet reading on his computer in the library. He took his favorite seat beside the window looking out into a sylvan patch, and thought to himself: “This display of synesthesia would have interested Vrishchika a lot.” Even as he said so to himself, to his utter shock, he saw someone looking just like Lootika or Vrishchika go past him and take a seat another a little ahead. He almost exclaimed aloud: “that cannot be true! they are away in a faraway land enjoying the pleasures of conjunction with their puruṣa-s.” He looked at the girl again and realized it had to be Jhilleeka. “What is she doing here? This is not her kṣetra.” He walked up to her: “Hey Jhilli, what are you doing here. For a moment, I thought it was one of your sisters who had manifested themselves using their ghostly powers.” Jhilleeka smiled but seemed to be a bit at a loss to say anything. Vidrum went on: “I’ve not seen you in a while, but you have become a light-eyed version of your sisters.” Jh: “I’m taking that to be a compliment, but it must be just some homozygosity that found its way into me. Hope you are alright and fully recovered from the tumultuous events that are now past us.” V: “Let the past lie. But are you alright?” Vidrum pointed to her bandaged foot.

Jh: “Sort of. But that wound is the result of what one could call an adventure of sorts.” V: “What happened?” Jh: “If you run into my parents, do not tell them the whole thing. But if you want to hear the story, we can go outside.” V: “Sure.” By some fancy, I decided to take the shortcut through Viṇmārga back home from the university, which, as you know, passes through the rougher part of the city. From there, I took the bylane that leads to Mahiṣamūtra-mārga, and I quickly sighted that a knot of roughs led by Sphicmukha and Chāgalaṇḍa, who I believe were your classmates at school, had laid a predatory trap. They had set large branches of Vachellia bramble on the road to funnel drivers onto the side they had littered with nails and other metal objects. I avoided them from puncturing my bike but, in a flash of indiscretion, decided to kick one of the pegs out of the way while still riding — that did not go well, and I ended up with a deep cut on my leg. That’s why I came here to get a tetanus shot. I’m just waiting for my father to get back home.” V: “Some of the characteristic traits of your elder sisters are very much visible in you too. In any case, is this not your last month in college? I’m sure you are pursuing graduate school like your elder sisters.”

Jh: “That is correct. Prachetas and I did contemplate whether to start a company of our own and give grad school a skip given the deteriorating environment in educational institutions abroad. Thankfully, we got over that delusion after some further thought as we realized we were v1s to our core and not v3s by nature. Nor were we inclined to take the job offers we had because we have that independent academic streak. Moreover, we got into the same graduate school; so, we would not be facing the separation and the disjunction that Lootika and Somakhya faced when in graduate school.” V: “But those two told me that their disjunction was a key part of their character-building experience where they proved their individual worth by themselves.” Jh: “That may be so, but you can hardly deny that Lootika and Somakhya had the luck of being together all the way from school to the end of college — something the rest of us did not have the pleasure of. So that disjunction is not something they needed to cry about. Moreover, for all the ice in that period, the rest of us knew how Lootika kept thinking about Somakhya. We thought grad school is a good idea because, apart from the fact that we are fundamentally academically oriented, it gives an opportunity to prove ourselves under hostile fire. If luck, for some reason, doesn’t favor us, we can always quit it and get down to more real things like furthering our genes. If everything fails, in the least, I can teach my nephews and nieces mathematics and computation as they come of age.”

V: “Well, good luck. But even if you don’t start a company, I hope someday you and maybe Prachetas will build for me a robot that is like the late lamented Meghana.” Jhilleeka chuckled: “What purpose would such a robot serve even if we were to build it? Talk to Lootika and Somakhya — they will teach you a mantra of the Southern Path. Meditating thus on Śiva and Bhairavī, you will attain your desire more satisfyingly.” V: “Young lady, they are far away, and we are not in frequent touch. It is hard to find a time that matches to talk to them — let alone them imparting me a mantra. Moreover, do you even believe such mantra-s work?” Jh: “Well, you will learn if they work or not. Never mind if you don’t want to ask them about this, there is always the musical bone-pipe my sister Vrishchika gave you.” V: “Jhilli, do you think Meghana could be summoned that way?” Jh: “She may visit you that way, but it is not something you want to look forward to. It will not be pleasant. But the other phantoms who come to you via the bone-pipe might help you reach the equilibrium you seek.” Just then, Jhilleeka got her father’s call, and Vidrum had to return to his duties.

Lootika’s medallion

The following Saturday, Vidrum’s duties had ended by the afternoon; early that evening, he went with Sharvamanyu and Abhirosha for dinner. A: “So Vidrum, when will the construction of your new house begin?” V: “Sadly, it is not happening! If anything, my luck seems to remain the same” S: “But why — were you not set to hire the contractors?” V: “It is a strange story. But I decided it is better safe than sorry.” S: “I don’t get it! But if you don’t want to share it with us, fine.” V: “Oh no! I would gladly do so, but you may think I am crazily superstitious.” A: “Now that makes us even more curious.”

V: “Have you ever been gifted something interesting by the four sisters?” A: “Now, why do you ask that of all things? But yes.” Abhirosha pulled out an inlay-work medallion from her bag and showed it to Vidrum. “This is some art Lootika made for me. I realized that it was more than just art because she said that there was no need to display it but to just keep it with me, somewhere close.” Saying so, Abhirosha handed it to Vidrum. Looking at it closely, he passed it to Sharvamanyu: “It has a nice feel to it. Our friend has some eye for symmetry. I saw Vrishchika making something similar for her husband Indrasena shortly after the tumultuous events. What I received was something more sinister — a bone-pipe made from a human femur. Vrishchika gave it to me. But they all seem to know of it, for the other day, the youngest Jhilleeka asked me to ply it.”

A: “Now, how did you run into Jhilli?” V: “Well, that is a story of its own.” S: “Fine, but what does all this have to do with your abandoning the construction of your new house.” V: “Listen, it is a long and crazy story. If you blow into that bone-pipe you can get nice and haunting tunes. The haunting part is very real — it is not at all uncommon for a phantom to manifest thereafter and tell you something. The short story is that I was rather depressed with my luck that day and vocalized that matter to Jhilli. She reminded me of the bone-pipe her sister had given me and asked me to ply it.”

S: “OK, that sounds like an interesting object — a blast from the past — you never showed it to us?” V: “Well, I’ll show it to you guys the next time you’re home. I had put it aside, given all the trauma from the last visitation. But I realized paying attention to those visitations can actually be helpful. The encounter I had was somewhat dramatic.” A: “Ah! This sounds like the old times. Tell us the story.” V: “Sure. I blew into the pipe a song I heard in a movie — I’m sure it was one I had watched with you guys. The phantom came on very fast. I had hardly blown out a couple of lines, when I heard a gruff voice with a south Indian accent. I did not see anything, but I could feel an obvious presence. He asked to be seated on the couch across from my desk, saying that he needs a proper seat to ease his distress. I took a dictation of his story that I’ll read out once we are done with dinner.” It went thus:

“My name is Gunottaman (Guṇottaman), but most of the people who knew me called me Kāttutĕran, a moniker I acquired from my capacity to drive my father’s car at incredible speeds even as a ten-year-old. My family hails from the Dravidian country but had moved to the Karnāṭa country. While we came from a brahminical background, my father was the last in our lineage to have a slung a thread on his shoulder. He was a man of vision and modernity. He told us there was nothing to be gained by studying supernatural śloka-s and songs with which the brahmins earned a living by fooling gullible people. Instead, he said we should choose the Buddha, the Christ and Mahatma Gandhi as role models for leading a good and ethical life. In my teens, I read a little information pamphlet and added a new figure to that pantheon. He was the great biochemist Yerrapragada Subbarow. I was inspired by him to discover new drugs. Accordingly, I studied for a B.Sc. in chemistry and a further degree in chemical engineering from a reputed college.

Shortly after that, I became acquainted with a biologist known as Ayyangār. He had identified an amoeba-killing compound from an actinobacterium but did not know what it was. He saw the potential for making it into a treatment for amoebiasis, which was raging in some villages. Having obtained a grant, he teamed up with me, and I showed that it was a peptaibol. Eventually, I even synthesized the peptaibol, which earned me a thesis and many accolades, including an invitation to work at a Japanese university. Having cleared that hurdle, I was now renowned as a double Ph.D. and was offered a professorship at a college. A couple of years into that, I realized that the humdrum teaching of dullards was not for me. I wanted to emulate my heroes and do good to humanity. I wished to make pharmaceuticals, but that path was not easy for a man with a modest income. By then, I was married and already had two children, and a third was on the way. But some luck came my way. I had a friend from college, Adhyankar (Āḍhyaṃkara), hailing from the merchant community. He had started a paint business that was flourishing due to the housing boom. One day, over lunch, he asked me if I could synthesize anti-fungal compounds for his paints. He had been importing these compounds and said that any breakthrough would result in a significant profit of which I would receive a share. While it was not the pharmaceutical work I wanted to do, I saw it as a break and took a one-year voluntary suspension from my college job to set up a lab funded by Adhyankar. My hard work paid off, and I synthesized a siloxane halamine derivative that could work well as an anti-fungal. With my team, we soon set up an industrial manufacturing process for producing and incorporating it into Adhyankar’s paints.

A major problem in our country is the discoloration of walls by cyanobacteria. Hence, I wondered if we could augment our paints with anti-cyanobacterials. During my Ph.D. in Japan, I had made acquaintance with a fellow graduate student who had identified and determined the structure of an anti-cyanobacterial compound which had the sequence: MeR-V-V-OHMeR-MeR. I synthesized a truncated brominated derivative thereof that had 100-fold higher anti-cyanobacterial activity. When we brought this into production, I was able to negotiate a fuller partnership in the company of Adhyankar. The profits helped me to dabble with my true interests. I realized that the antiviral field was a wide-open opportunity, and Adhyankar was willing to again partner with me, thereby giving me a long rope to explore exciting possibilities.

By then, I had a flourishing family with three sons and a daughter. What is misery to some can be a gain for others. It was around that time the Great Dhori Virus Outbreak fell upon us. Building on my anti-cyanobacterial work, I had synthesized a bacterial cyanoalkaloid, whose halogenated derivatives had an excellent antiviral capacity that played a decisive role in flattening that outbreak. From the profits materialized during this time, I wanted to build a new lab and plant. I bribed a derelict temple’s management to procure some good land bypassing the usual bureaucratic strictures. During the building of the new lab, we unearthed a religious image that the Hiṇḍū-s worship under the name of some god, I think he is called Śiva. While I cared little for such superstition, I did not want it to be destroyed because it might be an object of veneration for people who believe in such things. Hence, I handed it over to some pundits at a temple. With a new lab in place, I often took my children there to intern and develop a scientific temper.

However, my fortune seems to have peaked there, and it was all downhill thereafter. My daughter acquired an undiagnosed neurological illness and committed suicide by jumping off the balcony in a fit of delirium. Then my youngest son developed a mysterious idiopathic anemia and died despite all our attempts to treat him. My next son, like me, was a great car enthusiast, but this proved to be the tragedy of our lives. He too enjoyed the thrill of speeding but sadly lost control of the car and expired on hitting a flyover pillar. Perhaps due to this stress or maybe due to her nature, my wife upbraided and slapped our eldest son one day in front of all his friends for not doing as well as we had expected in one of his exams. He was angered by that and ran away from home, and we never saw him again despite filing many a missing person report. Then when my turn came, it almost seemed like relief from all the suffering I was going through. I was alerted by the alarm system regarding a problem in the lab. I was initially informed by the staff that there was nothing to fear. I thought it was just a false alarm and casually went in a little later to check things. At that point, there was a big phosgene leak, and I died from the exposure.

What happened thereafter was remarkable. I could see my corpse being donated by my wife to the hospital for study. With much horror, I watched it being cut up and my tissue being examined microscopically and analyzed. After what was left of my corpse was consigned to oxidation at the incinerator by Adhyankar, something even more striking happened. I found myself sitting in a ghostly corpus on a large boulder that lay outside my laboratory building. Marching in front of me was a vast horde of other ghostly beings. Some looked like skeletons, others had strange animal heads, yet others had a misty, shape-shifting nature. Far behind, I saw the leaders of that horde of ghosts — they were emitting a radiance and appeared more real than anything I had seen in life. I think they were gods, as I remember seeing images in the likenesses of them being taken out during Hiṇḍū festivals. One of them had an ape-face, another had six heads, yet another a proboscis, and still another was of a dark bluish-black hue. A ghost from that immense horde came up to me and said: `You are appointed as the regent of this land that you once purchased through underhand means from the temple. You shall sit here and keep others away from it after your lab has been demolished. I spent a while wandering in my lab as though doing experiments but finally, one day, a government crew appeared and demolished it. I sat on the stone and made it my routine to grimly haunt anyone who trespassed it. When you bought this land, you came with a brahmin and his wife to take possession. They seemed to have some spells to those very same gods I saw when I was appointed as the guardian of the land. Hence, I was rendered powerless to do anything to you or them then. But now that it is just you, I can knead you like dough. If you were to build on this land, I shall reduce you to a fate that is not very different from mine. If you do not, and let my stone remain, then I will even use my ghostly powers to aid your quest for a new vehicle, a woman and a house.”

Abhirosha: “Vidrum, even I would have acted the same if I’d had encountered a phantasmagoria as this.” V: “Even if this were just an illusion, spurred by the visitation, I did some investigations that led me to a clear decision. I dug up old reports that the city auction had hidden from me. Those showed that indeed a chemical laboratory had stood on that plot. It was demolished after being decommissioned following an accident, and the plant nearby had been shut down for safety issues. I reasoned that the mysterious deaths of our visitor’s children were probably again from the poor safety leading to their affliction by toxic compounds. Who knows, some toxic stuff might still be lingering therein. Hence, I thought it prudent to abandon the plan of building my house on that site and let the agents of Mahādeva reclaim it.”

Vrishchika’s medallion

Pandemic days: Galtonism hits India

At some point last year, we stopped writing any further dispatches regarding the pandemic catastrophe from the disease because everything was playing out more or less as laid out in the earlier notes. There was the whole public drama around the “lab-leak” hypothesis that was widely disseminated by the Jewish American intellectual Weinstein and his wife Heying. While they and their cohort made some good points, there were specific counterpoints that nobody in those academic circles was able to bring to the discussion. Having studied this virus closely and having discovered multiple new things about its evolution, we had laid those out in our earlier dispatches. So, we were not too disposed towards reiterating it.

The effects of the pandemic reached far beyond the human disaster — it played with the internal stability and politics of several nations across the world. It fueled the explosive growth of the American mental disease, navyonmāda, following incidents of police brutality, typical of the Mahāmleccha. As a result, among the Mahāmleccha, Vijaya-nāma-vyāpārī was overthrown by the navyonmatta activists in Big (primarily imaginary)-Tech and Media and replaced by their candidate Vṛddha-piṇḍaka and the sūtradhāriṇī Ardhā, who works the former like a putalikā on behalf of the operators in the deep-state and Big-Tech. Now in the driver’s seat, they moved quickly to impose the navyonmāda religion on the population of America — the full extant of the steps taken for its imposition are striking (supported by statistics and raw data) but cannot be narrated for now. Indeed, in retrospect, it now appears that the Nāriṅgapuruṣa was the last line of defense against dam-burst of navyonmāda. Its capture of a serious fraction of the Mahāmleccha elite is evidenced in nearly all the ejaculations of Piṇḍaka’s courtiers; now, they even intend flying the dhvaja of navyonmāda at their dūtya-s. In essence, the Piṇḍaka-śāsana is giving a taste of how it might have been for the heathens when the second and third unmāda-s were taking over West Asia and Europe.

If this had remained restricted to the Mahāmleccha, then the rest of the world might not be too bothered about it. In fact, rival powers would have rejoiced at it because it will eventually weaken the Mahāmleccha (at least temporarily). But like any physical infectious disease, this memetic one is also infectious. Just like the overt unmāda-s, navyonmāda too has a natural enmity towards the deva-dharma. Hence, it will act in similar ways to destabilize any political party or arrangement that might even marginally help H growth. It is brought into India via the first responders and mleccha-trained academics, and is also casually dispersed to the young urban population by the occidental media. During the Kangress era, the judiciary too was subverted by several crypto-proponents of sympathizers of this neo-religion. This is perhaps one of the most imminent dangers of navyonmāda given the power the court holds in the Indian political arrangement. It has also taken a deep root in centers of higher science and technology education such as the IITs, IISERs, and TIFRs, where several academics mimic their left-liberal counterparts in the west and engage in anti-Hindu action guided by navyonmāda. Thus, when navyonmatta-s from a scientific tabloid, like the Nature magazine, interview people for something regarding India, they goes to their co-religionists (i.e., navyonmatta-s) in Indian academia. These will invariably paint an anti-H picture. To give a concrete example, I know a senior academic who had served at the IISERs and Ashoka University (a navyonmāda nest) who wanted to give his students “a balanced view” that the great rājan Śivajī was a bandit. This means a whole crop of young H, especially those in the crucial research and technology fields, are being indoctrinated into the neo-religion. Given this situation, the rise of Piṇḍaka meant that this wing of internal navyonmatta-s would be strengthened in the deśa.

This is how it indeed played out. An uṣnīṣin rebellion passing off as a kīnāśakopa was fomented in the Pāñcanada, that too during an ongoing pandemic. The discerning clearly saw the pattern, as it followed along the lines of the earlier CAA riots, the Bhim riots, and the Patel riots. However, in this case, they were conclusively outed as a Swedish front-end for navyonmatta, who is on the Asperger’s spectrum, spilled the “toolkit” of the first responders leading to the quick arrest of some of their agents. Their subsequent interrogation revealed even more of their intent. The Indian government was rather mild with and gave a long rope to these rioters. This puzzled many nationalistic observers who were hoping for firm action that the śādhu was reputedly capable of. Our reading is that the H are relatively weak in their ground state and the security apparatus knows that. Moreover, they also feared opening of a border front with the Cīna-s while tackling internal rebellions. Hence, for good optics with the mleccha-s the H leadership did not act firmly. Thus, unlike the Cīna-s dealing with their rebels, the H have to go soft as they cannot take on the Mahāmleccha under Piṇḍaka, who will back the rioters, unlike the overthrown Nāriṅgapuruṣa. Our prediction from a little over a month back was that the Mahāmleccha would continue such action until at least the end of the year or till the possible event of their king Piṇḍaka falling prey to jara resulting in some internal turmoil.

Returning to the disease, the first wave in India was bad, but the nation as a whole fared much better than most other hard-hit countries. By the end of the civil year 2020 CE, it was coming down even as it was exploding in the USA. By the first two months of 2021, it looked as though India was on top of the pandemic and the vaccination program was initiated. It was going well by early March even though a lot of eligible people were not taking it. The corresponding program was doing much worse at that point in the US — some people were driving a long way to neighboring towns and cities to get their shots. A Pakistan physician was arrested by the mleccha-s for giving the vaccine that would be otherwise wasted to “people with Indian-sounding names!” because of their kṛṣṇa-rudhira sham policy. Unfortunately, on the H side a basic lesson of epidemiology was forgotten. Infectious respiratory disease epidemics show wave dynamics. The classic precedent of the Spanish flu of 1918 CE shows that the second wave can be worse than the first because more infectious and/or more virulent mutants can emerge, especially with the effective population size of the virus being large along with a large as yet uninfected population. The same dynamic was seen with the milder H1N1 epidemic in the USA. Even the limited SARS outbreak showed waves. Several countries had already experienced two waves of SARS-CoV-2, with the second being worse than the first. In several instances, like in UK, Brazil and Iran, we have seen SARS-CoV-2 variants with greater infectivity or virulence emerge and drive a new wave. This meant that India had to be ready for wave 2, potentially driven by a more infectious or virulent strain. It is in this regard the Health Ministry largely failed in it is messaging and warning of the public. However, nations do not fail or succeed based on their leadership alone. A much bigger part is played by the people’s social responsibility, deep state, and institutions. Modern H have been strikingly weak on each of these counts, especially when compared to the East Asians. At the times of non-crisis, the accumulated civilizational capital of the H nation could take them through, but any discerning observer knows that this could break in bad times.

Those bad times came with the entirely expected wave 2. While wave 2 was expected, the above H weaknesses poured more ghee into it, making it a conflagration of sa Devaḥ (The god). In our opinion, there were several deep failures beyond the Health Ministry’s negligence regarding the imminence of wave 2: 1) The people acted as though it was back to normal. There was no masking or social distancing, crowding at indoor entertainment spaces. 2) Wearing flimsy cloth or fashion masks in the name of comfort, frequent removal of the mask to speak and interact at close quarters, and improper use of the mask. 3) Poorly governed states like Maharashtra and Kerala let the outbreak remain bad, offering opportunities for the emergence and selection of new mutants. We suspect both the B.1.351 and B1.617 variants are major drivers of wave 2. The latter seems more infectious and clearly appears to break past any natural immunity or that acquired during wave 1. There are reliable reports of reinfection in wave 2 and might be cases of B1.617. 4) Crowded election rallies with no or improper masking in certain states and religious assemblies. While the Anti-H constituency and eventually also the Dillīśvara tend to emphasize the last one (e.g., the Kumbha), the data shows that massive outbreaks were building up far from the centers of these open-air gatherings. Hence, while such crowds might have played a role in local transmission, we do not think they were by any means the primary factor in the explosive second wave in India. 5) Many eligible people simply failed to take the opportunity to get vaccinated. 6) The weak research culture (traditionally disparaged and neglected by the rising urban middle class and in part addled with navyonmāda) in the country meant that study of the mutants, the efficacy of treatment, search for new drugs, epidemiology, bio-, and chemical technology for were all not up to mark to face a crisis. 7) Unlike some countries like the USA, India is a densely populated country where people live in close proximity with extensive casual social interaction. While the latter can be advantageous in some situations, in this situation, it is a disaster, especially when people with the illness do not self-quarantine responsibly. In the end, from all we have seen, the biggest failure was the first point — people simply not taking the threat seriously. Looking at the exponential phase of its growth, we can say that the plot was probably lost between March 15-20th when the tangent to the curve moved past . The result is an unprecedented public health crisis that the already weak institutions cannot bear. Reports on the ground mention an unending stream of cremations with people simply dying before they can even get access to supplemental oxygen.

When a nation is in crisis, its enemies and haters will try to make the most of it. With the precision of a Dutch clock, the mleccha haters from Big Media and navyonmāda-addled occidental academia who are big Piṇḍakānuyāyin-s (e.g., a Harvard University physician of Chinese ancestry who is vociferous on SM) aided by their marūnmatta allies came out like beetle-grubs from the wood-works peddling “cremation sensationalism” (aimed at their fire-hating Abrahamistic audience who mostly don’t know that H cremate), blaming it on H religious assemblies. The foreign policy of the Mahāmleccha state has a simple sūtra: Weaken, destabilize or destroy any non-pañcanetra state. To add to this, the national religion of the current regime is navyonmāda, which has a svabhāva-vairam with dharma and any political assembly that might even indirectly support it. Then there is predatory American Big Pharma which has always sought to profit off human misery (incidentally of their own people, including the śvetatvak-s). Hence, they saw a golden opportunity for 1) Playing the anger in the Indian middle class from the high death toll to engineer a janakopa against the Lāṭeśvara and his court; 2) Send a clear message to the Lāṭeśvara for being pally with their internal arch-enemy, the Nāriṅgapuruṣa; 3) Use the opportunity to aid dvitīyonmatta-s and navyonmatta-s by NGO channels by providing direct “aid” bypassing the Indian government headed by the Lāṭeśvara.

They executed this program reason fairly well until today: 1) They embargoed key ingredients for vaccine production and withheld the AstraZeneca vaccines that they are not even using. 2) They amplified the noise about the Indian failure via their usual Big Media outlets aided by navyonmatta academics (e.g., the said Harvard University academic of Cīna ancestry) to facilitate the Indian public opinion turning against the Lāṭeśvara’s court. 3) Once the situation was desperate in the deśa, over the current weekend, they suddenly got active and presented themselves as saviors (much like the English during the piṇḍāri wars). Their NSA and Secretary of State, in thinly veiled messages, talked of “working with their friends and partners” in India. Every discerning H knows who their friends and partners are and how much they work for the downfall of the H. Now everyone from the above courtiers to Piṇḍaka claimed that they would help by allowing the supply of materials to India. However, one notable point in all this was how for most part they (Piṇḍaka included) avoided directly mentioning the Indian government or leaders. This shows that, like the English tyrants of the past, they are attempting to use the dire situation to present themselves as saviors while discrediting the Indian leadership.

But why did they relent at all, especially on a weekend when they are normally relaxing? In part, they saw that the H in India were not buying their first-responder messages and were seriously angry against their blockade of material flow. Not only that, they saw that there was widespread public opinion against their actions even among the śvetatvak-s (barring some like the evil queen of the Śūlapuruṣa-s). Americans of H origin were pressing on them to release the blockade. It also appears that there was some straight-talking by the Indian NSA with his counterpart (speculation). Consequently, Piṇḍaka changed his line and claimed that he would open channels for raw material flow. As soon as he announced it, his deśī sepoys in Big Tech, Big Media, tinpot think tanks started amplifying Piṇḍaka’s announcement as a noble action of the great savior.

We do not know what exactly happened, but definitely, something hurried happened behind the scenes. One can never trust the Mahāmleccha — everyone who has done so has paid dearly. Hence, one can only hope that in this desperate situation, the Lāṭeśvara did not promise them something that could come to bite the H and him in the rear in the near future. This is a once-in-century pandemic, so there are bound to be failures, but that is no excuse for being unprepared, given all the precedence — this is analogous to the unpreparedness of the H rulers to Shihab al-dīn over 800 years ago despite the precedence of Mahmud of Ghazna. Some political setups will be better prepared for situations like this, e.g., the Cīna-s, who, unlike H, need not fear “death by democracy or judiciary” allowing them to play the long game without the wastage of time and money on constant elections, let alone the significant risks from the rallies [note, we are not per say advocating a Cīna form of government as the solution but simply stating a fact]. One can only hope this wakes up the H to the need for a way more comprehensive reform of the crappy “jugāḍ” mentality that they pat themselves on the back for, along with serious and unbiased cultivation of a more robust basic research culture. So far, the H have only mimicked the broken western system — often importing just the navyonmāda and marrying it with vicious regionalistic politics rather than bringing actual research excellence from the west into their premier institutes. This cannot change overnight, but without doing so, it is not going to be easy to meet the challenges of the current order. An example germane to the current situation is the modified nucleotide mRNA vaccines deployed in the USA. This needs an extensive biochemical knowledge base that cannot be developed without serious basic research. While along with the journey to Mars, the mRNA vaccines could very well be among the last great American achievements in the penumbra of their power being eclipsed by navyonmāda, it still has shown the gulf between their technological prowess and that of the rest of the world. While this pandemic will resolve eventually, it will be at high human cost and also we do not know for sure what it will leave behind. In the worst case scenario, there will be long term health issues (e.g. neurological and respiratory) that could hamper the work force. If the Lāṭeśvara is overthrown by the Indian democracy, as the Piṇḍaka-śāsana wants, the country will essentially be overtaken by agents of the mleccha-s and marūnmatta-s and greatly decline. But then who can predict the future?

Making an illustrated Nakṣatra-sūkta and finding the constellation for a point in the sky

The illustrated Nakṣatra-sūkta

Towards the latter phase of the Vedic age, multiple traditions independently composed sūkta-s that invoked the pantheon in association with their home nakṣatra-s as part of the śrauta Nakṣatreṣṭi or related gṛhya homa-s. Of these oldest and the most elaborate is seen in the form of the Nakṣatra-sūkta of the Taittirīya brāhmaṇa. From the time we first learned this in our youth, it has been a meditative experience that compensates for the bane of urban existence — bad skies. Passing from nakṣatra to nakṣatra, we could bring to our mind the various glorious celestial bodies that we had been recording since the 10th year of our life. Thus, the desire arose in us to create an illustrated Nakṣatra-sūkta that would aid in bringing them to mind as we recited it in an indoor urban setting. We have been making our own star maps for a while, each with its advantages and downside. For nice vector graphics (PDF), we decided to use the TikZ package for . The TikZ picture itself is generated by a script we wrote in R. The datasets used for the astronomical bodies are:

• Since we did not want it to be too cluttered nor stress the compilation with memory issues, we stuck to the Bright Stars Catalog with about 9096 stars for plotting.
• The stars were colored discretely using their spectral type from the catalog. We only include the types W (very rare), O, B, A, F, G, K, M and C for our palette.
• The double stars were obtained from the Washington Double Star catalog and mapped on the Bright Stars Catalog.
• The variable stars were taken from the confirmed variability record in the Bright Stars Catalog and supplemented with information from the Hipparchos survey.
• The deep sky objects were obtained from The NGC 2000.0 Catalog and corrected where necessary. For galaxies, the orientation angle was assigned as in Stellarium. We generally plotted only the brightest of these, which can be seen by small telescopes (e.g. 20 x 3in binoculars, 3-4in refractors, 6-10in Newtonian reflectors) that we have used in our observing career.
• For the Milky Way, we used a file specifying different contours that used to be available from old planetarium software like HNS.
• The constellations boundaries as specified by the International Astronomical Union were based on the corrected version of Davenhall and Leggett’s catalog available via Vizier.
• The constellation figures are based on those drawn by Hans Augusto Rey(ersbach) in his 1952 book “The Stars: A New Way to See Them”.

We generated the star maps by IAU constellation and mapped the nakṣatra asterisms onto them as per the earliest Vedic traditions (when known) or the traditional identification widely accepted by Hindus (when the Vedic identity was unclear; see notes in PDF for details). At the end of the sūkta we provide brief notes on the Vedic tradition of the nakṣatra-s. One issue that came up in this process was the mapping of any given point in the sky onto a constellation. This takes us back to the history of the origin of modern constellations. While most of them in the northern hemisphere have their roots in ancient cultures, the precise boundaries are of recent vintage. The man behind that was Benjamin Apthorp Gould (1824-1896 CE). Born in the USA, he showed precocious mental ability and went on to become a doctoral student of Carl Gauss at the age of 20. While with Gauss, he did considerable work advancing our understanding of the asteroid belt. Inspired by the tradition of the creation of detailed star catalogs championed by Gauss’s colleague Carl Harding and student Johann Encke, Gould also went on to be one of the most outstanding star catalogers of the age. Going to Argentina to study the southern skies, he pioneered the use of photography in mapping the heavens. As part of this work, he defined the constellation boundaries for the southern constellations in 1877 CE. This was then extended by Eugène Delporte (a prolific asteroid discoverer) for the northern constellations under the IAU in 1930 CE. So the question is, given these boundaries, how do we say which constellation a point in the sky belongs to?

Nancy Roman designed a beautiful algorithm for this in 1987 CE. It goes thus: We first need to precess the coordinates of our current epoch to those of 1875 CE, which correspond to the epoch used by Gould when he first defined the boundaries. We briefly describe below the algorithm for the precession to a given epoch without going into the trigonometry and calculus involved in arriving at it (that can be found in a textbook on basic numerical procedures in astronomy, e.g., the freely available textbook, Celestial Mechanics, by Professor Tatum). For simplicity (sufficient for most purposes in terms of accuracy), we take a constant rate of precession of the equinoctial colure as , i.e., per year. We take the inclination of the earth’s axis to be: . We then compute the parameters in degrees thus:

Let, be the Right Ascension (celestial longitude; here taken from )and be Declination (celestial latitude; here taken from ) of the point in the sky we wish to precess. We then compute the corrections:

Let be the signed difference in number of years between the epoch we wish to precess to and the current epoch. Then we get the precessed coordinates as:

If

Having precessed the coordinates to 1875 CE using the above, we look up the table created by Roman of just 357 rows which takes the below form:

The lookup procedure goes thus:
1) Read down the DE low column until you get a declination lower than or equal to the declination of your point.
2) Move to the corresponding RA up column and read down until you get a right ascension higher than that of your point.
3) Move to the corresponding RA low column and read down until you get a right ascension lower than or equal to that of your point.
4) Check the corresponding RA up column and see if it is higher than the right ascension of your point. If yes, the constellation column gives the constellation in which the point lies. If not, go back to the first step 1 and continue downward in the DE low column from the first DE you obtained lower than or equal to that of your point to find the next such value and repeat the following steps until the condition in the final step is met.
Thus, we can obtain the constellation of any celestial object given its coordinates.

Johannes Germanus Regiomontanus and his rod

Even before we had become acquainted with the trigonometric sum and difference formulae or calculus are father had pointed to us that there was an optimal point at which one should stand to observe or photograph features on vertical structures, like on a tall gopura of a temple or a tree. That point can be calculated precisely with a simple Euclidean construction. Hence, we were rather charmed when we encountered this question in a German book on historical problems in mathematics. It was posed in 1471 CE by Johannes Germanus Regiomontanus to a certain professor Roderus of Erfurt (Figure 1): At what point on the [flat ground] does a perpendicularly suspended rod appear the largest (i.e. subtends the largest angle)? Let the rod be of length and it is suspended perpendicularly at height from the ground. The question is then to find the point at which would be the largest. This is also the kind of question that often repeated itself in some form in the lower calculus section of our university entrance exams. So it is not a difficult or unusual problem, but it has a degree of historical significance. Before we look into its solution, let us first talk a little about its proposer, who as an enormously important but not widely known figure in the history of science and mathematics in the neo-Occident.

Figure 1. The rod of Regiomontanus

Born in 1436 CE at Unfinden, in what is today Germany, Regiomontanus seems to have shown signs of early genius. Seeing this, his parents sent him at age 12 to Leipzig for formal studies and then he proceeded to Vienna to obtain a Bachelor’s degree at age 15. His genius came to the notice of Georg von Peurbach, a German astrologer, who wished to produce a corrected and updated translation of the Mathematike Syntaxis (Almagest via Arabic) by the great Greco-Roman astrologer and mathematician Klaudios Ptolemaios of Egypt. He hoped in the process to establish the geocentric theory on a firm footing and use the newly introduced Hindu decimal notation for the ease of calculations. However, von Peurbach’s Greek was not up to the mark to effectively translate the original but he transmitted his mathematical and astrological knowledge to Regiomontanus, whom he treated as his adopted son, before his death at age 38. On von Peurbach’s deathbed, Regiomontanus promised to continue his work on the Syntaxis and also create a synthesis of the mathematical knowledge that was present in it with the new knowledge of the Hindus and the Arabic neo-Platonic revolution that was entering Europe from the Mohammedan lands.

The Regiomontanus took up the task with great diligence by mastering the Greek language and started composing verse in it. He then took to traveling around Greece and Italy collecting Greek and Latin manuscripts collection to revive the lost knowledge of the ancients. In the process, he found a manuscript of the yavana Diophantus that he could now handle using the elements of Hindu bījagaṇita transmitted to Europe from the Mohammedans. He then became the court astrologer of the Hungarian lord Matthias Corvinus Hunyadi who staved off the further penetration of Europe by Mehmed-II, the conqueror of Constantinople, through several campaigns. As a ruler with literary interests, he had looted several manuscripts from Turkish collections in course of his successful raids. These offered additional opportunities for the studies of Regiomontanus. Having established an observatory in Hungary for Matthias, he returned to Germany and built an observatory equipped with some of the best instruments of the age and also adopted the newly introduced printing technology to start his own press. As a result, he published a widely used ephemerides with positions of all visible solar system bodies from 1475 to 1506 CE. He also published a remarkable geometric work titled “De Triangulis Omnimodis (On triangles of every kind)” wherein, among other things, he introduced the Hindu trigonometric tradition to Europe. To my knowledge, it also contains the first clear European presentation of the sine rule and a certain version of the cos rule for triangles. Regiomontanus also recovered and published the striking Latin work “Astronomica” of the nearly forgotten heathen Roman astrologer Marcus Manilius from the time of the Caesar Augustus. This beautifully poetic work would be of interest to a student of heathen religious traditions and Hindu belief systems because neo-Hindu astrology was after all seriously influenced in its belief structure of the Classical world. As a sample, we leave some lines of old Manilius here:

impensius ipsa
scire iuuat magni penitus praecordia mundi,
quaque regat generetque suis animalia signis
cernere et in numerum Phoebo modulante referre. (1.16–19)
It is more pleasing to know in depth the very heart of the universe and to see
how it governs and brings forth living beings by means of its signs and to speak
of it in verse, with Phoebus [Apollon] providing the tune.
-translated from the original Latin by Volk

Two years after the publication of his ephemerides, Regiomontanus was summoned to Rome to help the Vatican correct its calendar. He died mysteriously at the age of 40 while in Rome. His fellow astrologers believed it was prognosticated by a bright comet that appeared in the sky in 1476 CE. Others state that he was poisoned by the sons of the yavana Georgios Trapezuntios, whom he had met during his manuscriptological peregrinations. He had a kerfuffle with Trapezuntios after calling him a blabberer for his incorrect understanding of Ptolemaios and apparently the latter’s sons had their revenge when he was visiting Rome. Thus, like his friend von Peurbach, Regiomontanus died before he could see the published copy of his work on the Syntaxis. However, it was posthumously published as the “Epitome of the Almagest” in 1496 CE, 20 years after his demise in Rome. Looking at this book, one is struck by the quality of its production and the striking synergy of its text and lavish mathematical illustrations. Even today, with the modern computer languages like (TikZ included) and and our collection of digital fonts one would be hard-pressed to produce something nearing the quality of Regiomontanus’ masterpiece published at the dawn of the Gutenberg printing revolution.

Figure 2. A yavana and a śūlapuruṣa in anachronistic conversation: The frontispiece of Regiomontanus’ Epitome of the Almagest showing him questioning Ptolemaios under the celestial sphere.

Regiomontanus is said to have had a lot more material to write and publish that never saw the light due to his unexpected death. One of these was the possibility of the motion of the earth and heliocentricity. In this regard, we know that he criticized astrologers of the age for accepting the Ptolemaic model as a given without further analysis. Moreover, he demonstrated that his own astronomical observations contradicted predictions made by the geocentric models of the time. We are also left with tantalizing material reported by his successor Schöner that hint that he was converging on the movement of the Earth around the sun. After Regiomontanus had passed away, the young German mathematician Georg Joachim Rhäticus deeply studied the former’s works to become a leading exponent of trigonometry in Europe. He befriended the much older Polish astronomer Copernicus and taught the latter geometry using the “De Triangulis Omnimodis” of Regiomontanus, a copy of which with Copernicus’ marginal notes still survives. Rhäticus also urged Copernicus to publish the heliocentric theory. This raises the possibility that Rhäticus was aware of Regiomontanus’s ideas in this regard and it helped crystallize Copernicus’s own similar views. In the least, the geometric devices that both Copernicus and later Tycho Brahe needed for their work were derived from Regiomontanus, making him a pivotal figure in the emergence of science in the neo-Occident. [This sketch of his biography is based on: Leben und Wirken des Johannes Müller von Königsberg by E. Zinner]

Figure 3. Construction to solve the Regiomontanus problem.

Returning to his problem, we can game it thus (Figure 3): The rod of length suspended perpendicularly at height subtends the at the ground. This angle can be written as the difference of two angles: . Let the distance of the point on the ground from the foot of the perpendicular suspension of the rod be . We can write the tangent difference formula for the above angles using Figure 3 as:

We can see from Figure 3 that as the point on the ground moves towards the foot of the suspension, both , thus . If the point on the ground moves away from the foot of the suspension, both and again . Thus, somewhere in between, we will have the maximum and it will be in the interval . In this interval, the tangent increases as the angle increases. Thus, it will reach a maximum when the function reaches a maximum. We would find this maximum by differentiating this function and finding where . This approach, using calculus, is how we would have answered this question in our university entrance exam. One will observe that this function has a rather flat maximum suggesting that, for the purposes of viewing a feature on a tall vertical object, a relatively approximate position would suffice. While this principle of extreme value determination by calculus was known in the Hindu mathematical tradition by at least the time of ācārya Bhāskara-II (1100s of CE), there is no evidence that any of this Hindu knowledge of calculus was transmitted to Regiomontanus. In Europe, a comparable extreme value principle was informally discovered much later by the French mathematician Michel Rolle in 1691 CE who actually rejected differential calculus. So how would Regiomontanus have solved in 1471 CE?

It is believed that he used the logic of the reciprocal. When is maximum its reciprocal would be minimum. We can see that if becomes large, then term would dominate and it would grow in size. Similarly, when becomes small, the will dominate and it would grow in size. The 2 opposing growths would balance when . This yields . With this in hand, we can easily use the geometric mean theorem in a construction to obtain the desired point (Figure 3). This also yields another geometric relationship realized by the yavana-s of yore regarding the intersection of the tangent at point P on a circle and a line perpendicular to it that cuts a chord (here defined by the suspended rod) on that circle: The distance of the point of tangency from its intersection with the line containing the said chord is the geometric mean of the distances of their intersection to the two ends of the chord.

We may conclude with some brief observations on the history of science. Regiomontanus is a rather striking example of how the founder of a scientific revolution can be quite forgotten by the casual student due to the dazzling success of his successors. In the process, the existence of scientific continuity between the Ptolemaic system and the heliocentric successor might also be missed by the casual student. His life also provides the link between the popularization of the Hindu decimal notation in the Occident by Fibonacci and the birth of science in those regions by the introduction of Greek and Hindu tradition via the Arabic intermediate. While Hindu astrology was influenced by the Classical astrological tradition there is no evidence that the Ptolemaic system ever reached India. The Hindus instead developed their own astronomical tradition that appears to have rather early on used a potentially heliocentric system of calculation culminating in the work of ācārya Āryabhaṭa-I, who also discovered a rather brilliant algebraic approximation for the sine function. However, soon there was a reversal to a geostationary, giant-earth model under Brahmagupta, the rival of the Āryabhaṭa school. In the realm of astronomy, the totality of these developments resulted in epicyclic systems or eccentric systems that paralleled the Occidental models in several ways. On the mathematical side, it spawned many high points, such as in trigonometry, ultimately resulting in the emergence of an early form of differential calculus by the time of Mañjula that was subsequently advanced by Bhāskara-II. This line of investigation culminated in the works of the Nambūtiri-s in the Cera country with the emergence of what could be termed full-fledged calculus. Remarkably, this was paralleled by the revisiting of Āryabhaṭa-I and the move towards heliocentric models by the great Nīlakaṇṭha Somayājin. Partial heliocentric models for at least the inner planets, along with the prediction of the Venereal transit of the sun was also achieved by Kamalākara, a Mahārāṣṭrī brāhmaṇa, in the 1600s. Notably, only the earlier phase of the Hindu trigonometric tradition was transmitted to the Occident at the time of Regiomontanus. None of the Hindu studies towards calculus found their way there and they appear to have been rediscovered in the Occident about 2 centuries after Regiomontanus. Despite possessing a mathematical and astronomical edge, in the centuries following Nīlakaṇṭha, the Hindu schools, facing a dilution from the chokehold of the Mohammedan incubus, did not spawn a scientific upheaval of the order that took place in Europe in the centuries following Regiomontanus.

A great statistician, and biographical, numerical musings on ancient game

Recently my friend brought it to my attention that C. Radhakrishna Rao had scored a century. Born in 1920 CE to Doraswamy Nayadu and A. Laxmikanthamma from the Andhra country, he is one of the great mathematical thinkers and statisticians of our age. He came from a high-performing family but even against that background he was clearly an outlier showing early signs of mathematical genius and extraordinary memory beyond mathematics. An example of this was seen in his youth in an award he received for his anatomical knowledge, wherein he displayed his perfect recall of all bones and structures of the body. He might have been an outstanding mathematician but the lack of opportunities to pursue research in India or elsewhere during WW2 led him to going to ISI, Kolkata and becoming a statistician. By the age 20, he was doing and publishing his research by himself and eventually was awarded a PhD for his pioneering statistical work on biometrics at the Cambridge University with Ronald Fisher as his supervisor. By the age 28, he was a professor who had authored several works at the frontier of statistics. Over his 100 years he has been prolific and actively publishing into this advanced years — an outlier in every sense — a truly rare genetic configuration.

CR Rao wrote a very accessible book for a lay audience titled Statistics and truth: putting chance to work. This small book provides a great introduction to the utility and the consequences of well-founded numerical and probabilistic thinking with examples from diverse sciences. We found the book particularly attractive because, despite being a mathematical layman, we stumbled onto the probabilistic view of existence around the 15th year of our life. Rao’s book then lent proper shape to our thoughts that had been born from several experiments and explorations. To us, the probabilistic view is the fructification of an ancient strand of Hindu thought first articulated in a ṛk from the pathetic sūkta of Kavaṣa Ailūṣa (RV10.34.8):

tripañcāśaḥ krīḻati vrāta eṣāṃ
deva iva savitā satyadharmā ।
ugrasya cin manyave nā namante
rājā cid ebhyo nama it kṛṇoti ॥

Three times fifty plays the swarm of these,
like the god Savitṛ of true laws.
To the fury of even the fierce they bow not ;
even the king verily makes his bow to them.

The ṛk is referring to the game of chance, apparently one of the favorite games of the old Ārya-s played with vibhīdaka/vibhītaka nuts. Rao’s essays inspired us to explore the basic numerical aspects of this game at the end of junior college (Also the time we were studying the RV and AV). We present a freshly illustrated version of that here for other simple-minded folks. The game may be reconstructed thus: A hole was dug in the ground and 150 nuts were thrown into it. Then the player drew a handful of those to get out nuts (probably there were some constraints against cheating by drawing just 4 nuts that are not entirely clear. A possible alternative formulation involves casting the 150 nuts towards the hole and only those that fell into the hole were considered for the ensuing operation). If then it was a Kṛta (K) or the best result. The next 3 successively lower ranked results were , a Treta (T); a Dvāpara (D); , a Kali (L). It is unclear if the results were named for the 4 yuga-s or vice versa. In our childhood, our grandmother played this game with us albeit with tamarind seeds she had saved after peeling off the fruit. We manually worked out the number of different combinations (hence, order does not matter) formed from the 4 types of results (K, T, D, L) that can be seen in 1, 2, 3… successive draws: in 1 draw you can have K, T, D or L possible combinations. In 2 draws you can have: KK, KT, KL, KD, TT, TD, TL, DD, DL or LL possible combinations. So on. The sequence of the number of possible combinations goes as: 4, 10, 20, 35… This gave us an introduction to some the principles of combinatorics that only later in life we learned to be governed by the multinomial theorem:
Kṛta, Treta, Dvāpara, Kali ; successive draws; hence, the total number of possible combinations in successive draws is:

We wondered about the precise chance of getting a combination in consecutive set of draws. We finally understood this only upon apprehending the multinomial theorem. This allowed us to compute say, the chance of getting 4 kṛta-s in 4 consecutive draws as , which is pretty low. On the other end the chance of get all the 4 results in 4 consecutive draws, i.e. KTDL, is much higher: . Since the vibhīdaka game was for gambling, we can assign the scores from 4 for K to 1 for L and measure ones cumulative gains over multiple draws. We asked, for example, in 4 successive draws what will be distribution of scores (Figure 1) — what score will one have the highest chance of obtaining. We can see that the scores will be distributed between between 4 (LLLL) to 16 (KKKK). We had intuitively realized in our childhood that one had the greatest chance of of having the midpoint score of 10. With the multinomial distribution we could calculate the precise probability of getting the score 10 as 0.171875. This gave us a good feel for the multinomial distribution and how we could get a central tendency in terms of the most probable consequence (score) even multiple scores had the same number of generating combinations (first vs second panel).

Figure 1. The number of distinct combinations and probabilities of getting a given score in 4 draws.

Thus, we can reach any integer by the sum of the scores in a certain number of draws (order does not matter as only the sum matters). The draws resulting in scores adding to the first few integers are shown in Table 1.
Table 1

Integer	Draws	Number
1	L	1
2	D, LL	2
3	T, DL, LLL	3
4	K, TL, DD, DLL, LLLL	5
5	KL, TD, TLL, DDL, DLLL, LLLLL	6
6	KD, KLL, TT, TDL, TLLL, DDD, DDLL, DLLLL, LLLLLL	9
7	KT, KDL, KLLL, TTL, TDD, TDLL, TLLLL, DDDL, DDLLL, DLLLLL, LLLLLLL	11

Inspired by Hofstadter, after some trial and error, we were able to formulate an alternating recursion formula to obtain this sequence of the total number of ways of reaching an integer as a sum of integers from 1..4. We first manually compute the first 4 entries as above. Then the odd terms are given by the recursion:

The even terms are given by:

in the floor function or first integer
Thus, we have

We also devised an alternative algorithm that is well suited for a computer to extract this sequence. This algorithm revealed a close relationship between this sequence and geometry of triangles. Effectively, the above sequence gives the total number of integer triangles that have perimeter for . Thus, for we can have only 1 integer triangle, , that has . For we have 2 triangles and so on (Figure 1, Table 2). Since the smallest integer triangle has we can get the 0th term of . Then we can state that provides the number of integer triangles with .

Figure 2. First 18 integer triangles

Figure 1 shows the first 18 integer triangles, i.e. those with . One immediately notices that in this set the isosceles triangles dominate (Table 2). Of these every divisible by 3 will yield one equilateral triangle; thus equilateral triangles are the most common repeating type of triangle. There are only 3 scalene triangles in the first 18 integer triangles of which one is the famous right triangle, which is also the first Brahmagupta triangle (integer triangles with successive sides differing by 1 and integer area). We first computed the the number of triangles with that are isosceles. This sequence goes as:

Strikingly, every alternate term in this sequence from the second term onward is a triangular number, i.e. the sum of integers from . The terms between them are the integer midpoints between successive triangular numbers. This understanding helps us derive a formula for this sequence:

Here the function is the rounding up function, wherein if is an integer and the rest are rounded to the nearest integer.
Table 2

P ≤ n	# triangles	# isosceles	# scalene
3	1	1	0
4	1	1	0
5	2	2	0
6	3	3	0
7	5	5	0
8	6	6	0
9	9	8	1
10	11	10	1
11	15	13	2
12	18	15	3
13	23	18	5
14	27	21	6
15	34	25	9
16	39	28	11
17	47	32	15
18	54	36	18
19	64	41	23
20	72	45	27
21	84	50	34
22	94	55	39
23	108	61	47
24	120	66	54
25	136	72	64
26	150	78	72
27	169	85	84
28	185	91	94
29	206	98	108
30	225	105	120
31	249	113	136
32	270	120	150
33	297	128	169
34	321	136	185

Remarkably, we find that the first scalene triangle appears at and then scales exactly as but with an offset of 9. Thus, the number of scalene triangle with . The sequence scales approximately as a polynomial with positive cubic and square terms, whereas the number of isosceles triangles with scales as . Hence, even though the isosceles triangles are dominant at low they will become increasingly rare (Table 2) and their fraction of the total number of triangles will tend to 0.

We can also look at the largest angle of the integer triangles (Figure 2). These are plotted along the arc of the unit circle defined by them and scaled and colored as per their frequency of occurrence. As noted above, every third perimeter will define an equilateral triangle. This will result in the smallest of these angles being the most common. The zone exclusion in its vicinity shows that one needs large sides to approximate the equilateral triangles (e.g. the bigger Brahmagupta triangles). Beyond these, other major angles that are repeatedly observed are: ; ; ; . For example, the common version of the triangle arises whenever the perimeter . Thus, these are all versions of the triangle. However, rare scalene versions can arise, for example, in the form of the triangle and its higher homologs. Apart from the trivial equilateral triangles, 2 other integer rational sector triangles, the right or (bhujā-koṭi-karṇa triples) and the triangles (e.g. ) appear repeatedly with a lower frequency defined by their triple-generating equations.

Figure 3. The plots of the largest angles for integer triangles with

Finally, this search of integer triangles also provides a mean to construct triangles, one of whose angles are approximately a radian (Figure 3). In first 511 triangles, , the triangle provides an angle that approaches 1 radian the closest: .

Figure 4. Triangles with an angle approximating a radian.

The above observations gave us useful introductory lesson on the path to statistical mechanics. Let us consider the isosceles triangles as representing great order (because the is less freedom in their sides) and the scalene triangles as representing greater disorder (more freedom in their sides). A simple multinomial derived score results in the proportion of the order configurations decreasing over time (more draws), i.e. disorder dominates, resembling entropy in the physical world. Among the more “ordered” states the dominant one tends to be that which is in the most “central” configuration, i.e. the equilateral triangle. Finally, certain peculiar configurations can repeatedly emerge if they happen to have special generating equations like the or triangles.

Modulo rugs of 3D functions

Consider a 3D function . Now evaluate it at each point of a integer lattice grid. Compute corresponding to each point and plot it as a color defined by some palette that suits your aesthetic. The consequence is a what we term the “modulo rug”.
For example, below is a plot of .

Figure 1:

We get a pattern of circles around a central circular system reminiscent of ogdoadic arrangements in various Hindu maṇḍala-s. From the aesthetic viewpoint, the best modulo rugs are obtained with symmetric functions higher even powers — this translates into some pleasing symmetry in the rug. Several examples of such are shown below.

Figure 2:

Figure 3:

Figure 4:

Figure 5:

Figure 6:

All the above are composite numbers. Accordingly, there is some repetitiveness in the structure. However, if is a prime then we have the greatest complexity in the rug. One example of such is plotted below.

Figure 7:

See also: 1) Sine rugs; 2) Creating patterns through matrix expansion.

A guilloche-like trigonometric tangle

Coprimality, i.e., the situation where the GCD of 2 integers is 1 is one of the fundamental expressions of complexity. In that situation, two numbers can never contain the other within themselves or in multiples of them by numbers smaller than the other. In other words, their LCM is the product of the 2 numbers. There are numerous geometric expressions of this complexity inherent in coprime numbers. One way to illustrate it is by the below class of parametric curves defined by trigonometric functions:

The human mind perceives symmetry and certain optimal complexity as the hallmarks of aesthetics. Hence, we adopt the following conditions:
1) are in the range ..1 for purely aesthetic considerations.
2) are orthogonal rotation angles that are in the range
3) , for aesthetic purposes relating to optimal complexity, is an integer in the range
4) captures the role of coprimality in complexity. It coprime with and is in the range
5) .
6)
The last two conditions are for making the curve bilaterally symmetric — an important aesthetic consideration.

The result is curves with a guilloche-like form. For the actual rendering, they are run thrice with different colors and slightly different scales to give a reasonable aesthetic. Our program randomly samples through the above conditions and plots the corresponding curves. Below are 25 of them.

Figure 1.

Here is another run of the same.

Figure 2.

Huntington and the clash: 21 years later

This note is part biographical and part survey of the major geopolitical abstractions that may be gleaned from the events in the past 21 years. Perhaps, there is nothing much of substance in this note but an uninformed Hindu might find a sketch of key concepts required for his analysis of geopolitics as it current stands. The biggest players in geopolitics are necessarily dangerous entities; hence, things will be in part stated in parokṣa — this goes well with the observation in our tradition that the gods like parokṣa.

In closing days of 1999 CE, we had our first intersection with Samuel Huntington and his hypothesis of the clash of civilizations. We found the presentation very absorbing because it lent a shape to several inferences, we had accumulated over the years both in Bhārata and on the shores of the Mahāmleccha land. The firsthand experience on shores of the Mahāmlecchadeśa was very important for there is no substitute to fieldwork in anthropology — it enabled a direct interaction with the various denizens of the land and allowed us, for the first time, to extract precise knowledge of their ways and attitudes. A key concept articulated Huntington was “the clash of civilizations”, the title of his book. This is a central concept on which all geopolitical analysis rests. However, we parsed it as a network wherein the nodes are civilizations and not all edges have the same nature or valence (Figure 1). Since the closing days of the Neolithic, the core of the civilizational network (at least in the Old World to start with) has been rather dense. Further, the civilizational network is dynamic both in terms of its nodes and edges. Some civilizational nodes decline or become extinct over time taking away the edges that were connected to them (dashed lines in Figure 1). The edges themselves might change from agonistic (shown as light cadet blue arrows in Figure 1) to antagonistic (shown as red inhibitory edges) ones or vice versa over time. Some edges might be complex and cannot be easily characterized (with no heads, e.g. the “Galtonian” edges in green linking the Anglospheric powers to China). The characterization of the edges might also vary from the viewpoint of the pakṣa of the characterizer. Regarding that last point, the characterization presented here is with limits reasonably predictive and useful from the Hindu standpoint.

So, how does basic clash of civilization articulated by Huntington play out in the framework of this civilizational network? The simplest thing is to look at the flux at a given node. This is a sum of the “weights” of the edges coming into that node. Thus, it is easy is to perceive that the Hindu civilization is currently a node with notable negative flux — this immediately indicates that it is node at the adverse receiving end of the clash of civilizations.

Figure 1. A simplified and partial view of the civilizational network.

Some literature
Since Huntington’s publication several disparate works have been published or translated that have a bearing on the Hindu construction of a geopolitical world view. We just outline a few below:
• Amy Chua, an academic of Chinese ancestry, published a work illustrating the role of strongly coherent minorities with high human capital relative to their host populations in civilizational clashes, especially the destruction of states and in some cases civilizations from within. One dynamic she highlighted relates to the Occidental itch to bring “democracy” to states containing such minorities. We may add that sometimes what comes in the name of “democracy” is in reality a “gift-wrapped” strain of the Marxian doctrine. This democratization or Marxian liberalization allows the under-performing “masses”, full of resentment against the over-performing minorities, to get back at them often resulting in intra-national civilizational clashes. If the over-performing minority was the cause for holding the nation together and/or its productivity, it results in national collapse upon their defeat or expulsion. In other cases, is festers as a long-term conflict following the Huntingtonian dynamics. The objective of the enemies of the Hindus is to make this dynamic play out on the brāhmaṇa-s.

• The translation and the publication of the English works of the German academic Jan Assmann helped introduce important terms such as “counter-religions”. While he originally introduced it to understand the rise of the ekarākṣasonmāda-s of West Asia, it also serves as an excellent framework to describe the emergence of subversive religious movements in the Indo-Iranian sphere. The first such, which seems to have marked a schism within the Indo-Iranian tradition, was the counter-religion promulgated by Zarathustra. On the Indo-Aryan side, a cluster of such movements occurred nearly 2500 years ago culminating in the counter-religions of the Tathāgatha, the Nirgrantha and the Maskarin of the cowshed. Subsequently, we had a near counter-religious movement in the form of the Mahānubhāva upheaval, which contributed to the weakening of the Hindu resistance to the Army of Islam. Few centuries later, similar memes and the half-digested ekarākṣasonmāda eventually resulted in the subversion of the pāñcanadīya saṃpradāya into the uśnīśamoha. The other term Assmann introduced was the “Mosaic distinction” that helps explain the vidharma tendencies in counter-religions, especially ekarākṣasonmāda.

• The mūlavātūla indologist Sheldon Pollock published a work on the history of Indian tradition. While recognizing the positive and enormous influence of the Sanskrit cosmopolis, Pollock tried to subtly sneak in the navyonmāda framework into Hindu studies. Along with this, he provided the foundation for the powerful American indological school to present a late date for the rise of Sanskrit as a medium of Hindu expression. This helped create the idea of a non-existent Sanskritic Hindu civilization before the common era (Sanskrit was just some hidden language used in the sacred texts of brāhmaṇa-s), thus, making it younger than the mūlavātūla and probably even the pretonmāda tradition. Further, as per this theory, the transformation did not arise from with the H but was probably fostered by the Iranians, perhaps with some Greek influence. More insidiously, it opened the door for other indologists of this school to link the dharma with their pet boogeyman, the śūlapuruṣa movement of the 1930-40s. The importance of this sleight of the hand will become apparent with the next item. Unfortunately, the positive side of Pollock’s work studying the knowledge systems of the Hindu cosmopolis should have been done by Sanskritists from our pakṣa within a proper H framework — instead the H pakṣa took off on flogging dead Germans and producing little positive work.

• The recent volume by Lindsay and Pluckrose probed deep into the proct of the navyonmāda tradition that arose in the śūlapuruṣīya lands and grew into a viṣāla-viṣa-vṛkṣa nurtured by the Phiraṅga and Mahāmleccha. This work helps understand the roots of its arborizations in the form of both the śākhā-s (i.e. the Freudian, e.g. Wendy Doniger, and philological, e.g. Richard Davis) of new American indology that subverted the tradition of the old Daniel Ingalls. Given its origins in the conflict within the śūlapuruṣīya lands, and being a pracchannonmāda itself, it is not surprising that one of its projects in the indological domain is fleshing out the above-stated point of connecting dharma to the movement of the ghātaka-netā śūlapuruṣaṇām. Additionally, it has received nourishment from the founding lords of the Soviet Rus empire and served to cover up their genocidal activities. It also has been active in furthering the Maoistic strain of Galtonism (see below). It attained ascendancy in mleccha-lands by precipitating the overthrow of Vijaya-nāma vyāpārin and placing Piṇḍaka as the puppet mleccheśa from behind whom their supporter, the ardhakṛṣṇā, operates. Aided by their longstanding backer the duṣṭa Sora, they have now taken aim at the Hindus having presented them as a movement comparable to their archenemies of yore, the śūlapuruṣa-s.

The conquest of the internet
In 1999 CE, the internet was still young and a mostly free place for expression. It was seen as heralding a new mode of expression for individuals who had no voice until then. But in the coming decade this gradually declined as the principle of freedom of expression slowly eroded. The mleccha deep-state has long sought to spy on its citizens and the opportunity to do this came with the marūnmatta attack on the mahāmleccha on September 11, 2001. The mleccha powers could now institute sweeping curbs on the people in the name of protecting them. However, this was only a bīja for the total destruction of the freedom of expression that was to come with the takeover of the internet by the guggulu-mukhagiri-jāka-bejhādi- duṣṭāḥ and the viṣāmbhonidhi Wikipedia. This take over aligned with the subversion of these vyāpāra-s by the navyonmāda. The prelude to this was seen when a servant of guggulu was expelled for voicing his opinion. While people thought it was just an internal company matter, it was clear that the navyonmāda was moving to end to freedom expression. A feedback loop developed between new social media and another major development, i.e. the ubiquity of the smart phones. The latter made every man perpetually visible to the operatives of the mleccha deep-state. The dangers of the reach of these duṣṭa-s along with the mleccha deep-state was exposed by their rogue spaś Himaguha who escaped to the khaganate of Putin. The real action was seen in the past year in collusion with the conventional media to overthrow the mleccharāṭ prajalpaka Vijaya and replace him with their favored man Piṇḍaka, now provided with a court of navyonmatta-s. With that the internet became a weapon for the navyonmatta-s who are directing its full force at their longstanding foe, the Hindus.

Some basic principles for the vigraha of the loka-saṃgrāma
• The foundations of Hindu polity lie in the actions of the deva-s in the śruti by which they overthrew the ditija-s in battle after battle by ūrja, māya and astrāṇi. This was translated for the human sphere by pouring the heroes into the divine bottles in the Itihāsa-s. Finally, it was codified by the clever Viṣṇugupta who aided the Mauryan to overthrow the evil Nanda-s and the yavana-s. It was presented for bāla-s by the wise Viṣṇuśarman, an acute observer and pioneer in the study of biological conflicts. He laid out the forms of vairam. Among those is svabhāva-vairam.

• Being ekarākṣasonmāda-s and vidharma-s (counter-religions), the unmāda-s and dharma are locked in svabhāva-vairam — a conflict that ends only in the extinction of one of the parties in the long run. The ekarākṣasonmāda-s have destroyed many of our sister religions and we remain the only remaining bulwark against them. Some object that the Cīna-s and Uṣāputra-s are also there — so why claim that we are the bulwark. We argue that the Cīna-s are seized by their own sādhana of legalism (see below) that has rendered them quite weak in terms of religion. The Uṣāputra-s, while doing well for themselves, are not a force that can restore heathenism in the world, especially given their currently aging and declining population. The graph in Figure 1 and history shows that there is some truth this “viśvaguru” quality of the H, even if it has declined over the last millennium.

• rogād rogaḥ | iti roga-paramparā | ko .ayam rogaḥ? mānasikaḥ | kutra rogasya janma? marakatānām uttare .asmadīyānām mitanni-nāma-rāṣṭrasya paścime .abrahmaś ca mūṣaś ca joṣaś cetyādīnām rākṣasa-graheṇa grasta-manaḥsu | tasmāt pretaḥ śūla-kīlitaḥ | tadanantaraṃ mahāmadaḥ | navajo rudhironmādo dāḍhikamukhasya | tasmād idānīṃtano navyonmādaḥ | parasparaṃ yudhyante kiṃ tu dharma-prati teṣām virodhaḥ saṃyuktaḥ | kasmāt? | vidhārma-bhāvād viparīta-buddhyā roga-tulyaikarākṣasa-viśvāsād deva-mūrti-dveṣāc ca | tasmād ucyate mleccha-marūnmattābhisaṃdhiḥ | tasya bṛhadrūpaṃ sarvonmāda-samāyoga-rākṣasa-jāla-śambaram | idaṃ hindūkānām paramam vairam ||

• The understanding of the Chinese state in most Occidental and Indian presentations ranges from misguided to deeply flawed. Two key concepts are required to understand its behavior and threat potential. The first, the doctrine of “legalism” or fa jia, whose early practitioner Lord Shang played a notable role in the rise of the Chin — in many ways he can be seen as the Viṣṇugupta of the Cīna-s who laid path for their unification under Chin Shi Huang, who played the role comparable to our Mauryan Candragupta. This doctrine, while often denied, has dominated Cīna imperial action since. While it is a rather sophisticated system, which is outside the scope of this note, a key feature is mutual spying that helps keep society in check — a convergent feature with other totalitarian systems. In it the ruler might keep the people busy with a benign “outer coat” that keeps the imperial designs out of their sight, or to paraphrase the neo-emperor Deng Xiaoping, they will adjust to follow the wind blowing from the rulers. Over the ages, the Cīna imperium has used Confucianism, Bauddham, Turkism, socialism and westernism as the outer coats to conceal their imperial actions. This legalism makes the Cīna-s ruthless and dangerous adversaries who are difficult to read. Even if they might not be rākṣasonmatta-s, the imperial focus of the system makes them hungry for land and ādhipatyam. For this they might play a long game, slowly encroaching on land, millimeter by millimeter and playing victim when their land-grab is noticed. Using that confusion, they would try to settle the situation in their favor. However, their aging population is the biggest road block to their total victory.

• The second concept that we have laid out in these pages in some detail is Galtonism. It describes a certain type of sinophilia that permeates the West in a form first articulated by the English intellectual Galton. In it, the Occidental center sees a great power in China and is almost in awe of it from the cracking of their psychometric yardsticks such IQ, and finds them to be of a “identifiable” fair complexion (at least the more northern subset) and a very orderly people. Thus, in contrast to the Hindu, they are willing to concede a global role for the Cīna-s, despite they being heathens. Conversely, they see in the Hindu simultaneously a defiant “other”, “an ugly people” and an idiot incapable of playing any great global role. In fact any attempt on their part to do so is seen as a dangerous challenge to their ekarākṣasam undergirding that should be squelched right away. A distinct strain of Galtonism is that seen in the navyonmatta-s (e.g. starting with their boosterist, the naked Needham, down to duṣta-Sora): for them the Cīna state is a culmination of their own utopian doctrine — of course they would ignore the fact that their own implementations fail and try to claim the genius of the Cīna-s for themselves. Thus, they play a potent role as ready apologists for the Cīna imperium.

In retrospect
Looking back, late Huntington was right in terms of the great clash between the marūnmatta-s and mleccha-s that was to play out in his own last years. He was also right in that the Cīna-s would ally with the marūnmatta-s to get back at their foes. However, this did not develop globally as the Cīna-s had their own marūnmatta terrorism, which they recognized as an unmāda and treated as such. Hence, the Cīna-s limited its use to India, since there was the ever-willing TSP available as a bhṛtya who would not blow back. In the end, despite the rise of the Khilafat under Dr. Abu Bakr al Baghdadi, the mahāmleccha triumphed in this round of the conflict though their cousins in Europe might be eventually conquered.

What Huntington did not foresee was that the battle would be brought to the world by a new force, the navyonmāda, backed by the sora-jāka-mukhagiryādi-duṣṭāḥ. Like Constantine seizing the Roman empire for the pretasādhaka-s, these have placed a pliable man Piṇḍaka at the helm surrounded by navyonmatta-s. This war has already reached the Hindus. It will ally with the Cīna-s and the marūnmatta-s against their common foes. In an extreme scenario it might provide the final bridgehead the marūnmatta-s need for their conquest of mleccha lands.

The Cīna-s and marūnmatta-s have a degree of immunity to the navyonmatta-s. That is in part because the former have sealed off their internet and created their own parallel world like that of Viśvāmitra for Triśaṅku. The marūnmatta doctrine is a superior, fecundity-supporting version of the navyonmāda; hence, it is going to be hard to breach. In the long run the dynamics of navyonmāda are unclear due its contra-reproductive strategies. However, in the short run it could wreak havoc on the Hindus, especially their elite, who seem to be particularly susceptible to this disease. Going forward, at least for the next several years, models of all the older conflicts in geopolitics have to be updated to account for the role navyonmāda will play. Whatever the case, as far as H go, it will ally with the other unmāda-s against them. It will also split the mūlavātūla-s into pro- and anti- camps, a dynamic that might cause some instability to it.

The phantoms of the bone-pipe

As Vidrum was leafing through some recent case studies to gather the literature for his own production, he received a call from his chauffeur. He had fetched Vidrum’s new car. Vidrum went out to take a look at it. As he saw it gleaming in the mellow light of the parkway lamp he thought of his old friends for some reason: “Clever Lootika or Vrishchika would have said that it looks like a work of the Ṛbhu-s. That triplet of deities meant a lot to the four sisters, but I had never heard of them before I came to know them. May be after all there is a reason why they say the brāḥmaṇa-s are the conduit for communicating with the gods. No wonder this new car looks good but for some reason I experience no thrill of the kind I experienced when I got my first bicycle or for that matter my lamented old car.” He was snapped out of his musing by his chauffeur who asked him if he would want to go out on a test drive. Vidrum: “Sure. Let us drive till the foothills of the temple of Durgā past the pond of lotuses and then go over to the hotel Kūrmahrada and buy some dinner to take home.”

Back home from the test drive, Vidrum rang in his butler and informed him that he had obtained dinner from outside and offered the butler and his wife a packet of the same too. He then asked the butler to prepare cold turmeric and almond milk for the night and dismissed him. As he was enjoying his mouth-tingling dinner he lapsed into a train of thought: “I wish Somakhya was around to cast a spell of protection on my car. Time and again my mind goes back to my lamented first car. I remember that day clearly.” As his mind drifted there, his joy from the tasty dinner flattened quite a bit. Having concluded his meal, he went over to the little shrine Somakhya had installed for him to worship the 16-handed Vīryakālī, whose original was enshrined at the edge of the cemetery in his ancestral village. When Somakhya and Indrasena had learned of that shrine they were excited. They told him of the great significance of that goddess as per some ancient text whose name he had forgotten. He had promised to take them along with Lootika and Vrishchika to his village someday. He felt his meditation gave him some focus to put a few words to paper reporting a fatal case involving the infection of a sanitation worker by Burkholderia mallei. As he was doing so, he remembered that Somakhya had given him a monologue on the bacterium when they were in college but Vidrum was not yet a suitable vessel to have imbibed any of it. He kicked himself for the same because he knew it was something important for his current investigation but he just did not recall anything. But Somakhya and his gang were far away and in limited contact; hence, he had to contend with whatever he had.

His mind went back to his old car and the events around it careened across his mental screen: “I still remember those days. I had a fun ride and drove by the shuttle-stop at the college to park the car and collect some stuff from my cubicle. On my way out I saw Vrishchika and her mother waiting for the shuttle. I offered to give them a ride home. They accepted it with much gratitude but, as was typical of them, the two remained silent through much of the ride. Unfazed by the bustle of the city passing by us, Vrishchika’s mom was grading exam papers. That brought back memories of her class. Being busy with her daughters, she only taught part time, but was perhaps the only one of all our female and most male instructors who had the command and the ability to make everyone understand — some of that she had passed on to her daughters. But her exams were always hard. Nevertheless, she was kind unlike many of our sadistic lecturers, and passed everyone in the final exam. As we neared their home, Vrishchika’s mom looked up and said: `I guess you don’t have anything at hand for dinner — let me pack you some.’ I graciously acquiesced. When we got to their home, I was seated in the hall as Vrishchika and her mom went into the kitchen. Vrishchika came out with a small spoon and asked me to try a pickle and see if I liked it. It was great. Her mother then responded from the kitchen that she would aliquot a bottle of the pickle for me. As she was doing so, Vrishchika asked me if I was finding my new apartment boring without the `friends’ from the cemetery. I had to confess that I missed a bit of all that drama though I certainly found the quiet rather beneficial. Vrishchika darted into her room and brought out a curious object. It was a musical bone-pipe made from a human femur. Vrishchika waved it in the air it made some haunting music, like the wooden pipe made by the tribesmen from the northern Marahaṭṭa country or southern Mālava. She said I could blow into it and I might get a visit from interesting phantoms if they happened to be pleased with the music. I was apprehensive of any such gift but she told me it will do me good in life. I wished Vrishchika good luck because she was leaving abroad and I was not sure if I would ever see her again.

With my dinner in hand, I drove back home with the bone-pipe. That weekend I blew out of it the tune of a film song. To my surprise I felt a presence as I used to feel in my old house. There was no one in my room but I could still feel someone seated next to me. Just as we would do when plying the planchette, I asked if somebody was around. I mysteriously fell asleep at that instant and saw a vision of my new car being destroyed and me dying in the crash. I woke in fear and wished I could talk to Vrishchika, Somakhya or Lootika about it but they were all gone. I remembered a strange statement from Lootika when my first bike was stolen, which she did not elaborate on: `Wheel after wheel would be destroyed but your wheel would keep turning.’ The day that prophesy came true is still fresh in my mind. By some terrible coincidence my car fell into a ditch the very place Meghana had died. I was indeed lucky not just to evade the appointment with Citragupta but to escape unscathed from such a tremendous crash. I thought to myself — may be, l still have great acts to do in life.”

Vidrum shaken out of his reverie by his butler’s knock on the door to give him his beverage. He felt a sudden urge to play the bone-pipe. He lit a bundle of sage and as it was smoldering he took out the pipe from a box where he carefully stored it and blew out a tune of a folk song to the 1000-eyed goddess that his grandmother had taught him as a youth. For a while nothing happened and Vidrum relaxed into the wafting odor of the sage along with his beverage. With his mind crowded by various events of the past, he almost forgot that he had plied the pipe when he jolted by the presence of a strong fellow with some East Asian ancestry, albeit felt only vaguely. The intensity of the presence soon increased as it grabbed him by his legs and thrust into his chair. There he felt another presence seize his very personage and launch him into a bout of frenzied writing spanning a few pages.

Somakhya and Lootika were sipping their tea as the sun’s declining rays streamed into their room. Somakhya passed his tablet to Lootika with the scan of a manuscript on it: “varārohe, what do you make of this?” L:“Why dear, though eminently legible, this is a very strange handwriting with a form reminding one of sparklers on a Dīpāvalī night. What is this strange manuscript?” S: “That metaphor for the writing is indeed very apt. It is something Vidrum sent me. He apparently took it down some time ago in a frenzied ghost-dictation induced by the bone-pipe your first sister had found in our youth. He prefaces it with the comment that it would be of greatest interest to us. Why don’t you read it out aloud?” L: “Ah, the musical bone-pipe. I had nearly forgotten about that one. Should I call the kids; may be they would like the story?” S: “I’ve not read it yet. So, let us examine it first to make sure it might be of interest or even appropriate for them. So, let them continue practicing the workout of the conics that my father has sent them.”

Lootika read it out: “I’m glad I’ve found someone to tell my story as also a bit of that of my friend. It was my friend who thrust you into your chair so that I could tell my story. I was a brāhmaṇa, Bāẓ Nayan by name. My ancestors had come all the way from Jammu and settled in the hamlet of Indargaon. We followed the Mādhyaṃdina school of the Śukla-yajurveda. Seeing my precocious capacity in absorbing the Veda after my upanayana, I was sent far from home to the gurukula at Rishikesh. There, I acquired the śruti to completion and also become a scholar of vyākaraṇa mastering the ins and outs of sage Pāṇini and his commentator Patañjali. But tragedy struck at that point as my family was wiped out in an earthquake. Left with no one, I went and sought refuge at the feet of svāmin Ātmānanda giri, a great advaita yati. He employed me as a teacher for his brahmacāri-s. Later he acquiesced to my intention to acquire an English education and study linguistics. I did so in Shimla for 5 years and translated the pariśiṣṭa-s of Kātyāyana into English. During my stay there, I befriended a Gorkha, Jang Bahādur, who had to retire from the army after sustaining injuries in a battle with the Cīna-s. Unfortunately, svāmin Ātmānanda giri’s āśrama was washed away in a great flood and I was again left with no one in the world other than my friend Jang Bahādur.

One day he showed me an advertisement in a paper for a Sanskrit professor in a great peninsular city and suggested that we go there. He said he might find a security job there. I thought it was a great idea and after a long journey by train with barely any money we made it to the city. Thankfully, they spoke and understood some Hindi there and we could make our way to a rat-and bug-ridden lodge to stay while we found a job. The job was at the College of Antiquities which was one of premier research centers in the country. The clerks there asked me for a domicile certificate and a nationality certificate. As I had neither, they rudely shooed me away. I had to make a living initially as a cook and then as an arcaka at a temple of the terrifying Vināyaka. Jang Bahādur found a job as the nightwatchman for a street.

I still believed I was Sanskrit professor material — I was confident that few people knew the intricacies of the vyākaraṇa, as it applied to the śruti, the sāmānya language or the vulgar Prākṛta-s, as I did. Hence, I went back to the college in the hope of meeting some Sanskritists who would see my true worth. I found my way into the campus by somehow convincing the guard to let me in by claiming I was paṇḍita who had been called for a meeting. I searched around to reach to office of a brāhmaṇa from the peninsula, Somaśiva Śarman. He was a learned scholar of both the pure āryavāk as well as its vulgar vikṛti-s, who was engaged in the project of a great compendium of pre-modern knowledge. He looked at me quizzically, wondering if a brāhmaṇa could ever have a name as mine. He asked my gotra and śākhā and then asked me recite sections from the Vājasaneyi śruti. I noticed he was beginning to believe me as I did so. I took the opportunity and pulled out my precious typeset manuscript of the edition and the translation of the Kātiya pariśiṣṭa-s from my bag and handed it over to him. He studied it intensely for a while and looking up remarked that he needed to hire me right away. He moved the bureaucracy with much effort to get me the post of a staff-paṇḍit at the college.

What followed was an exciting phase of my life. I soon got a small, on-campus residence — a quaint little tiled roof house. I also managed to secure my friend Jang Bahādur a job as a security man for the campus museums. He had supplied me a manuscript from Nepal on Kiranti temples. I studied and translated it and published an article in a white indological journal. I followed it up with another paper in such a journal reflecting the linguistic knowledge that I had acquired from Somaśiva Śarman on the substrates in Indo-Aryan. The I went with Jayasvāmin, the curator of our museum, and his wife Śilpikā to study a Gupta temple of Bhairava and the 8 mothers in Mālava. In that expedition, we found a cache of Gupta gold coins that we brought back to the college museum to study. Jayasvāmin and Somaśiva with their epigraphic expertise worked out some worn inscriptions in the temple and based on that we wrote a paper that described the early phases of the Bhairava-srotas and how the worship of Kārttikeya followed by the 8 mothers was an important facet of that tradition. As part of that study, I reconstructed a verse to Skanda in the Vasantatilaka meter that was inscribed in that temple during the reign of emperor Vikramāditya, which described a fierce form of Skanda. This tradition was to be incorporated as Baṭukanātha in the later Bhairava tradition. All this work earned me some reputation in the college and mleccha visitors from aboard came to pick my knowledge. It was then that my patrons at the college suggested that I submit a dissertation for the doctoral degree at the university. Thus, I could upgrade myself from a mere staff paṇḍit to a professor. As I was wondering what I should submit as a dissertation, Śilpikā had invited a young brāhmaṇa lady to talk about a paper she had recently published on a comparative analysis of the substrates in the different Yajurveda saṃhitā-s and the implications it had for the āryan conquest of the northern India.”

Lootika paused and interjected: “O Bhārgava, this is most interesting. The phantom’s tale is directly intersecting with our lives. Śilpikā is none other than our learned language teacher, whom we gave much grief as children, and the young lady he mentions is undoubtedly your own mother — perhaps from the days just before your birth.” S: “It has to be so. I really hope Śilpikā did not cast a spell on us that our children regress to the mean. Yet, this phantom seems unfamiliar to me. Pray continue dear.”

L: “That lady’s paper suggested a topic for my dissertation, which was till then vaguely lurking at the bottom of my mind. It was a detailed comparative study of all Yajurveda texts. I worked hard and wrote an over 1000-page monograph of the subject. It featured many new translations, detailed analysis of the śrauta practices and the like. Jayasvāmin and Somaśiva presided as my preceptors and I was awarded the coveted title of Professor. I was at the height of my powers and wanted to publish my dissertation as a two-volume work. But the gods apparently had other plans. Two disasters struck our college and me personally. That summer, during the vacations, a band of uśnīśin terrorists broke into our museum. Jang Bahādur bravely defended the premises but was killed in the process and the terrorists made away with the Gupta gold coins and melted them down to finance their operations. A few months later, left-liberal activists, claiming to be righting the wrongs done to the depressed classes, demolished a wall of our college and fired our archives. As a result, my typeset dissertation was burnt down and lost.

Sometime before that, Cidānanda yati, a survivor of the advaitāśrama that was washed away, had come to city and was conducting classes on Śaṅkarācārya’s tradition. He called me to meet him and help him with the translations of the texts of Appayya Dikṣita and Girvāṇendra Dikṣita that he was preparing. In course of those discussions, he introduced me to a song composed by one of the Śaṅkaramaṭha-s and told me that no amount of yaci bham and phak were going to take me anywhere if I did not awaken from the dream of phenomenal existence into satchidānanda. The former would only take me on the path of rayi to the realm of the Moon, where the forefathers dwell. Then I would return to be born again, he said. Instead, if I followed the path of austerity, celibacy, faith and Brahmavidyā, I would have the great awakening into the sole reality that is Brahman. Soon thereafter a great comet appeared in the sky. A little later, the Japanese man who was the first man to observe that comet died.

Those events got me thinking about the arrival of the Pitṛrāṭ. I was sad on one hand about the loss of my dissertation on the other the possibility of never transcending the realms to know that there is only satchidānanda. I rationalized that there was no reason to fear death at all — after all it is something no one experiences. When one is alive there is obviously no experience of death. When one is dead there is no experience of death; so, why fear something one never experiences. However, for many death can come with suffering. There was no way to prevent that even if one did not fear death for the suffering before death was after all a real experience. But then if one experienced that which is satchidānanda then one would realize that the suffering was just like in a dream. But if one does not experience satchidānanda then what are the experiences after death, if they exist at all, I wondered.

I was to get the answer for all this soon. Sundara Somayājin was a Soma ritualist from the Drāviḍa country. He was performing a Somayāga in the city. I had long wanted to witness that kind of a Yāga and went to meet him. We had a philosophical discussion on the Vedic religion. He said that what was important was the correct svara of recitation and precise execution of ritual actions as per the ritual treatises. It really did not matter if the gods like Indra or the Aśvin-s existed. They were anyhow not gods to be worshiped in the same sense as the ‘real̍ gods’ like Śiva or Gaṇeśa or Viṣṇu, he said. I became very afraid when I heard this. I reminded him that such words were uttered by the ignorant to the great ṛṣi Nemo Bhārgava:

nendro astīti nema u tva āha ka īṃ dadarśa kam abhi ṣṭavāma ||
“Indra does not exist, o Nema” So indeed he says.
“Who ever has seen him?” “Whom shall we praise forth?”

Thus the ignorant questioned the existence of the great god. But he made his presence felt:
ayam asmi jaritaḥ paśya meha viśvā jātāny abhy asmi mahnā |
ṛtasya mā pradiśo vardhayanty ādardiro bhuvanā dardarīmi ||

Here I am, o chanter: see me here.
I’m at fore in all the species by my greatness.
The directives of the natural laws magnify me.
As the smasher, I keep smashing the worlds.

The Somayājin dismissed me by saying that it was all arthavāda and after all no Indra appeared at some given time to some Nema because the Veda was coeval with the beginning of time. In one of the talks in the college, I had heard another śrauta ritualist talk about the Seat of Vivasvān. He had mentioned that its knowledge was very important to evade the arrow of Ugra Deva when one is performing a yāga. Unfortunately, our Somayājin did not seem very aware of it and was to learn the reality of Indra very soon. Perhaps, due to some pāpa I had committed in a past janman, I too was to bound in karman with him. After the Ṣoḍaśin-graha was taken, the sky blackened with a mass of clouds and a great streak of lightning followed by a thunderous peal struck the pandal that had been erected for the yāga. An electrical explosion and fire followed and the learned Sundara Somayājin was borne to the abode of Vivasvān’s son, like Meghanāda struck by the Indrāstra discharged by the Saumitri or like Arṇa and Citraratha being felled by Maghavan beyond the Sindhu or like the Sāmavedin-s of Vaṅga or Aṅga being washed away by a blow from his vajra. I too was consumed by the fierce Kravyāda on that day.

A month or so after my expiration, a band of socialists paid by a mleccha instigator, claiming to be acting on behalf of the depressed classes, attacked my college campus again. My house and belongings were among the things consumed in their arson. In my heydays, among my many foreign visitors was a Gaulish woman, Laetitia Vernon by name, who sought my help to read Sanskrit legal texts. Despite my many stern warnings, my only son got infatuated with her and having married her left for the shores of a mleccha land. My son having adopted the mlecchānusāra did not perform any kriyā-s for me. He instead wrote an article in my memory saying that the secular India was coming of age with progress and equity even as the brahminical superstition was becoming a thing of the past. Consequently, upon my death I wander as a brahmarakṣas. At least me and my friend Jang Bahādur are united in death and we lead a mostly quiet incorporeal existence haunting the little hill that lies between my college and the river.”

Lootika told her mother-in-law about the story and asked if she had any recollection of this deceased man. Somakhya’s mother: “I never took the claims of the phantasmagorical encounters of you kids seriously. But I must say this one comes about as close to being believable as any. Yes, Bāẓ Nayan was a learned man who was borne away by the inexorable force of fate — after all, even the Yādava-s, be it the mighty Sātyaki or the brave Pradyuṁna, had to clobber themselves out of existence when their time came.” She went to the study and brought out a huge volume and gave it to Lootika: “However, here is a copy of his dissertation. While nobody knows this, it was not lost for good after all. I had made a copy of it for my own study. I wanted to give it you all for it still contains insights that will help you in your own study and practice of the śruti, but I kept forgetting. While no photo or belonging of Bāẓ Nayan Śarman seems to have survived the one who chomps through the Vanaspati-s, after all, my dear, the śruti has said: ‘na tasya pratimā asti yasya nāma mahad yaśaḥ |‘”

Some notes on the Brahmayajña brāhmaṇa and Uttama-paṭala of the Atharvaṇ tradition

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The Brahmayajña brāhmaṇa (1.1.29 of the Gopatha-brāhmaṇa) of the Atharvaveda provides a glimpse of the Vedic saṃhitā canon as known to the brāhmaṇa authors of the AV tradition. The Brahmayajña might be done as part of the basic rite as done by dvija-s of other śākhā-s or as part of the more elaborate AV tradition of the annual Veda-vrata. The annual vrata-s of the Atharvaṇ brāhmaṇa-s include the Sāvitrī-vrata, Veda-vrata, Kalpa-vrata, Mitra-vrata, Yama-vrata and Mṛgāra-vrata. The kṣatriya-s and vaiśya-s should do at least 3 and 2 of them respectively, with the first 2 being obligatory. During these vrata-s the ritualist follows certain strictures like not consuming butter milk nor eating kidney beans, common millets, or the masura lentils at the evening meal, bathing thrice a day and wearing woolen clothing. Before performing Brahmayajña, he performs the ācamana as per the vidhi which states:
sa ācamanaṃ karoti |
He performs the ritual sipping of water.

This calls for the special Atharvaṇic ācamana described in the final section of the ācamana-brāhmaṇa of the AV tradition (GB 1.1.39):
tad apy etad ṛcoktam —
It has also been thus stated in the ṛk:

“āpo bhṛgvaṅgiro rūpam āpo bhṛgvaṅgiromayaṃ |
sarvam āpomayaṃ bhūtaṃ sarvaṃ bhṛgvaṅgiromayam ||”
The waters are of the form Bhṛgu-Aṅgiras incantations. The waters are imbued with the Bhṛgu-Aṅgiras incantations.
All being is imbued with the waters; [thus,] all [being] is imbued by the Bhṛgu-Aṅgiras incantations.

•The Atharvaṇ-s justify the above ṛk is by noting that the Paippalāda Atharvaveda begins with the ṛk “śaṃ no devīḥ…” to the waters (see below).

antaraite trayo vedā bhṛgūn aṅgiraso ‘nugāḥ ||
Within these [waters] the three [other] Veda-s follow the Bhṛgu-Aṅgiras incantations.

“apāṃ puṣpaṃ mūrtir ākāśaṃ pavitram uttamam” iti ācamyābhyukṣy ātmānam anumantrayata | [sūrya jīva devā jīvā jīvyāsam aham |
sarvam āyur jīvyāsam ||]
“The flower is the form of the waters, the empty space [and] that which the most pure”. Thus, he sips the water and having sprinkled water (practically mārjanam) he recites the incantation indra jīva etc: Enliven, o Indra; Enliven o Sūrya. Enliven, o gods. May I live. May I complete my term of life.

•The flower of the waters in the above incantation is an allusion to the ṛk describing the the ancient action of the Atharvaṇ-s in kindling the fire in waters [from a lotus]: ``tvām agne puṣkarād adhy atharvā nir amanthata |”
•He does the ācamana by taking three sips each with two successive words from the mantra apām puṣpam…

iti brāhmaṇam ||
Thus is the brāhmaṇa.

Now for the Brahmayajña:
kiṃ devatam iti ? ṛcām agnir devatam | tad eva jyotiḥ | gāyatraṃ chandaḥ | pṛthivī sthānam |
“agnim īḷe purohitaṃ yajñasya devam ṛtvijaṃ | hotāraṃ ratnadhātamam ||”
ity evam ādiṃ kṛtvā ṛgvedam adhīyate ||
Who is the deity? Agni is the deity of the ṛk-s. That is indeed light. Gāyatrī is its meter. The earth is its station.
“I praise Agni, the officiant of the ritual, the god and ritualist; the hotṛ and the foremost giver of gems.”
Thus, having placed it at the beginning the Ṛgveda is studied.

yajuṣāṃ vāyur devatam | tad eva jyotis traiṣṭubhaṃ chandaḥ | antarikṣaṃ sthānam |
iṣe tvorje tvā vāyava stha devo vaḥ savitā prārpayatu śreṣṭhatamāya karmaṇe ||
ity evam ādiṃ kṛtvā yajurvedam adhīyate ||
Vāyu is the deity of the Yajuṣ-es. That is verily light; Triṣṭubh is its meter. The atmosphere is its station.
“To you for nourishment, to you for strength. You are the Vāyu-s. May Savitṛ impel you the most excellent ritual.”
Thus, having placed it at the beginning the Yajurveda is studied.

sāmnām ādityo devatam | tad eva jyotiḥ | jāgataṃ chandaḥ | dyauḥ sthānam |
“agna ā yāhi vītaye gṛṇāno havyadātaye | ni hotā satsi barhiṣi ||”
ity evam ādiṃ kṛtvā samāvedam adhīyate ||
The Āditya is the deity of the Sāman-s. That is indeed light. Jagati is its meter. The heaven is its station.
O Agni, come to the oblations, praised with songs to the ritual offering. Sit as the hotṛ on the ritual grass.
Thus, having placed it at the beginning the Sāmaveda is studied.

atharvaṇāṃ candramā devatam | tad eva jyotiḥ | sarvāṇi chandāṃsi | āpaḥ sthānam | <śaṃ no devīr abhiṣṭaya> ity evam ādiṃ kṛtvātharvavedam adhīyate ||
The moon is the deity of the Atharvaṇ incantations. That is indeed light. All are its meters. The waters are its station. “May the divine [waters] be auspicious for us…” Thus, having placed it at the beginning the Atharvaveda is studied.

adbhyaḥ sthāvara-jaṅgamo bhūta-grāmaḥ saṃbhavati | tasmāt sarvam āpomayaṃ bhūtaṃ sarvaṃ bhṛgvaṅgiromayam | antaraite trayo vedā bhṛgūn aṅgirasaḥ śritā ity ab iti prakṛtir apām oṃkāreṇa ca | etasmād vyāsaḥ purovāca:
“bhṛgvaṅgirovidā saṃskṛto ‘nyān vedān adhīyīta |
nānyatra saṃskṛto bhṛgvaṅgiraso ‘dhīyīta ||”
From the waters the families of immotile and motile organisms have come into being. Hence, all being is imbued with water; [thus] all is imbued with the Bhṛgu-Aṅgiras incantations. The three other Veda-s are situated within these Bhṛgu-Aṅgiras incantations. Therefore, indeed it is water and the origin of water is by the Oṃkāra. In this regard Vyāsa had formerly said:
“He who is sanctified by the Bhṛgu-Aṅgiras incantations may study the other Veda-s.
The one sanctified elsewhere should not study the Veda of the Bhṛgu-Aṅgiras-es.”

•Regarding the origin of all beings from water: this is articulated early on in the ṛk: yo apsv ā śucinā daivyena… (RV 2.35.8) of Gṛtsamada Śaunahotra.

sāmavede ‘tha khilaśrutir brahmacaryeṇa caitasmād atharvāṅgiraso ha yo veda sa veda sarvam |
iti brāhmaṇam ||
Now there is also the khila of the Sāmaveda: “Therefore, he who as a celibate student knows the Veda of Atharvāṅgiras-es knows all this.”

Thus is the brāhmaṇa.

•The statement from the Sāmaveda-khila is also taken to justify the punarupanayana that is performed in order for those of other traditions to study the Atharvaveda.

Notes
Several notable points are raised by the Brahmayajña brāhmaṇa of the AV, not just regarding the AV tradition but also regarding its interaction with the other Vedic schools and their own evolution. It is quite obvious that the Brahmayajña brāhmaṇa represents a relatively late brāhmaṇa composition with a specific aim of justifying the primacy of the AV, probably in the context of the intra-brahminical competition for the position of the brahman in the śrauta ritual. This is explicitly supported by the fact that it cites Vyāsa [Pārāśarya] who appears in late Vedic texts and is remembered by tradition as the redactor of the 4 fold form of the śruti. In a similar vein, the citation of the Sāmaveda-khila suggests that it was composed after the terminal sections of the Sāmavedic tradition had been completed.

The opening ṛk of the RV is compatible with any of the śakha-s of the Ṛgveda. The Yajurveda that it refers to is clearly the Vājasaneyi saṃhitā (either Mādhyaṃdina or the Kāṇva śākhā-s). The Samaveda could again be any of the Samavedic saṃhitā-s. The Atharvaveda is probably the Paippalāda saṃhitā because the vulgate and the Śaunakīya begin with “ye triśaptāḥ…” However, we must note that we do not know the beginning of the lost AV śākhā-s.

Why is this notable? The AV-pariśiṣṭa 46 (Uttama-paṭala) gives the beginning and end verses of the four Veda saṃhitā-s along with several AV verses to be used in the annual Veda-vrata. Notably, these are partly different from those of the Brahmayajña brāhmaṇa. Interestingly, according to the Uttama-paṭala, the RV ends with the famous ṛk: “tac chamyor āvṛṇimahe…”. This is not present in the Śākala-pāṭha which instead ends with the short Saṃjñā-sūkta. The former ṛk was claimed by Michael Witzel to be the last ṛk of the Bāṣkala RV. However, as Vishal Agrawal correctly noted its is stated to be the last ṛk by even the Śāñkhāyana and Kauśītaki traditions. Thus, the Uttama-paṭala is referring to some RV śākhā other than Śākala, though we cannot be sure of its identity.

The Uttama-paṭala gives the Sāmaveda’s first verse as “agna ā yāhi…”, which is known to be the first ṛk of all surviving śākhā-s of the SV. However, the last ṛk is given as:
“eṣa sya te dhārayā suto ‘vyo vārebhir havane maditavyam | krīḍan raśmir apārthivaḥ ||”
This is different from the ṛk “svasti na indro vṛddhaśravāḥ…” with which the surviving SV śākhā-s conclude. It is a divergent variant of the ṛk RV 9.108.5 not attested elsewhere. In fact the extant SV saṃhitā-s contain a version that follows the RV cognate. Thus, evidently the Uttama-paṭala is referring to a now lost SV śākhā.

The situation with the YV is the most interesting. The cited starting mantra goes thus:
“iṣe tvorje tvā vāyava sthopāyava stha devo vaḥ savitā prārpayatu śreṣṭhatamāya karmaṇa āpyāyadhvam aghnyā indrāya bhāgam ūrjasvatīḥ payasvatīḥ prajāvatīr anamīvā ayakṣmā mā va stena īśata māghaśaṃso rudrasya hetiḥ pari vo vṛṇaktu dhruvā asmin gopatau syāta bahvīr yajamānasya paśūn pāhi ||”

Remarkably, this mantra is not found in any of the extant YV saṃhitā-s. However, the “indrāya bhāgam” is reminiscent of the “indrāya deva-bhāgam” found in the Āpastamba-śrautasūtra and the Bhāradvāja-śrautasūtra or the “devebhya indrāya” found in the Maitrāyaṇīya saṃhitā. Moreover, the last mantra of the Yajurveda is given as “dadhikrāvṇo akāriṣam…”. In other YV saṃhitā-s, this mantra occurs in the Aśvamedha section and is used among other thing by the ritualists to purify their mouths after the obscene sexual dialog. However, it is not the last mantra of the Aśvamedha section in any of the extant saṃhitā-s. This indicates two things: first, the Uttama-paṭala is recording a now lost YV śākha of the Kṛṣṇayajurveda (KYV). Second, while today Āpastamba and Bhāradvāja are attached to the Taittirīya-śākhā, they were once the sūtra-s of a lost KYV śākhā. This loss likely happened relatively early. It was probably associated with the southward movement of the Āpastamba-s and Bhāradvāja-s, who then shifted to the related Taittirīya-saṃhitā (TS). The text of the Baudhāyana-śrautasūtra precisely follows the TS; hence, it was definitely one of the original sūtra-s of the Taittirīya-śākhā.

Finally, the AV of the Uttama-paṭala begins with “ye triśaptāḥ…” indicating that it was recording the original śākhā behind the vulgate or the Śaunakīya.

Thus, we see a striking difference between the two AV traditions of the Gopatha-brāhmaṇa and the Uttama-paṭala. While the tendency is to see the AV-pariśiṣṭa-s as late and post-dating the brāhmaṇa, we have to be more cautious. First, the AV-pariśiṣṭa-s are a rather composite mass recording a range of traditions that with a wide temporal span. Some material like the Nakṣatra-kalpa-sūkta could closer to the late brāḥmaṇa material in age whereas, at the other end, the tortoise-soothsaying (Kurmavibhāga) is likely a late text. We posit that the Uttama-paṭala belongs to the an early layer of the AV-pariśiṣṭa-s — this provides a reasonable hypothesis for the divergence between it and the brāhmaṇa. First, it should be noted that the AV-Paippalāda-AV-Śaunakīya/vulgate divergence is rather deep — mirroring the deep divergence of the Kṛṣṇa and Śukla branches of the Yajurveda. This split might have gone along with some geographical separation in the initial phase of their divergence. This geographical separation model would suggest that the Brahmayajña brāhmaṇa tradition was associated with the AV-Paippalāda or a related lost AV school that was in the vicinity of the old Vājasaneyin-s. This is also supported by certain parallels seen between the Gopatha-brāhmaṇa and the Śatapatha-brāhmaṇa in the śrauta sections. In contrast, the Uttama-paṭala as associated with the Śaunakīya or a related school that developed in the vicinity of a lost KYV śākhā.

We have evidence that the interactions between the KYV and AV traditions might go back even deeper in time: for example, this is clearly supported by the AV-related Bhavā-Śarvā-sūkta of the Kaṭha-s that was likely present in the lost Kaṭha-brahmaṇa and the various shared sūkta-s and upaniṣat material between the Taittirīya and the AV. Finally, we have evidence from what is today Gujarat that at a later period there was a certain equilibriation of the AV schools with the combination of the Paippalāda and Śaunakīya material. This parallels a similar acquisition of some Kaṭha material by the Taittirīya. Thus, there appears to have been a relatively complex web of fission and fusion interactions between the śākha-s over a protracted period.

Some notes on the Henon-Heiles Hamiltonian system

Anyone familiar with dynamical systems knows of the Henon-Heiles (HH) system. What we are presenting here is well-known stuff about which reams of material have been written. However, we offer certain tricks for visualizing this system that make it easy for lay readers with just a high school knowledge of mathematics to play with. The HH system was discovered by the French astronomer Henon and his colleague Heiles when they were studying the motion of stars in the galaxy under the influence of the gravity of the total matter in the galaxy. The true astronomical significance of these equations outside the scope of the current discussion. Our own original interest in this problem was primarily from the perspective experimental mathematics (“play physics”), starting as an extension to our interest in defining ovals by means of ordinary differential equations (ODEs). The system defined by Henon and Heiles considers the motion of a body in 2 dimensional Euclidean space, i.e. a fixed plane. The phase space describing the motion is thus defined by the variables , where describe the position in two dimensions and describes the momentum in the two directions. Given that the momenta are , for a body of unit mass the momenta become the derivative of the position variables with respect to time . Henon and Heiles considered a potential described by the equation:

The potential energy of a simple harmonic oscillator in the direction is . By taking a unit force constant we see that the terms in represent two orthogonal simple harmonic oscillators. The further nonlinear term, , in is a perturbation that couples these oscillators. This potential takes the form of a cubic hyperboloid-paraboloid and is visualized in Figure 1.

Figure 1.

The kinetic energy of the body is given by ; where is the velocity of the body. Thus, for the above-defined HH system we get . The Hamiltonian of a system, which represents its total energy, is given by . Since this is an energy conserving system, its total energy is equal to a scalar constant , i.e. the energy level of the system. Thus, for the HH system we get:

If we section the 3D curve by planes corresponding to different energy levels , we get the equipotential curves within which the would lie for a given energy level (Figure 2). We observe that if , the equipotential curve becomes 3 intersecting lines that form an equilateral triangle defined by the equilibrium points . Within this equilateral triangle, the body exhibits bounded motion. Thus, for all we get bounded trajectories in the plane. As becomes smaller the central equipotential boundary tends towards a circle and degenerates to a point at 0. However, for we get curves that are open; hence, at these energy levels the body can escape to infinity via the open lanes. Thus, there is a clearly defined escape energy level for this system, .

Figure 2. The energy levels correspond to

To study the trajectories under this system we first obtain the equations for the force acting on a body of unit mass (acceleration) in each direction from the above potential by taking the negative partial derivative with respect to each positional variable:

From the above can now get a system of ODEs thus:

The solutions to this system yield a curve in the 4-dimensional phase-space . To solve we first need to obtain some initial conditions for a given energy level using the Hamiltonian . We do that by setting . We then choose some values of . From those we can calculate thus:

One can see that this places a constraint on the allowed — they have to be chosen such that is real. Once we have these initial conditions we can solve the above ODEs with efficient LSODA solver written by Alan Hindmarsh and Linda Petzold or you can write your own solver by the method of Runge and Kutta as we did in our youth. Initial results below are shown using the LSODA solver. However, we will see below that we can also obtain solutions without using traditional ODE solutions. Figure 4 shows an example of solution for the energy level and initial conditions in the 3D space defined by

Figure 3.

To get a better understanding of its behavior, we can visualize the solution in several other ways Figure 4. First, we can simply look at the way change with time (first 2 top left panels of Figure 4). As expected, would be oscillatory functions that cannot be defined using any elementary functions. We can also examine the positional trajectory of the body in its plane of motion by plotting (top right panel of Figure 4). From the equipotential curves defined above from , we can see that this trajectory would be bounded by the closed loop of the curve defined by the equation (shown in blue):

We can also plot (bottom left panel of Figure 4) which shows how momentum changes with the position in the direction. This curve will be bounded by a special oval (shown in blue) that is determined by letting in the Hamiltonian . This gives us a cubic curve defined by the equation (in standard coordinates, not the of the phase space of the solutions of ):

The closed loop of the cubic is the bounding oval, which was what got us first interested in the HH system in the 16th year of our life.

Figure 4.

Finally, the bottom right panel of Figure 4 shows the Poincare section that records the points where the curve shown in Figure 3 pierces the plane (See below for further discussions). It is obvious that these are a subset of the plot and will thus be bounded by the same oval .

The way to compute the Poincare section is to search the values of solution for cases where the sign of and are different. Such successive points will bound the segments of the curve that pierce the plane . Given that our steps for numerical integration are small, we can calculate the corresponding values of using linear interpolation: . Plotting the thus calculated will give us the Poincare sections for a given starting point. Now, we can also calculate the solutions for above system without solving the ODEs by converting it into a discrete difference equation. These difference equations have a step parameter , which if kept small can yield solutions equivalent to that obtained by solving the ODEs. The system of difference equations goes thus:

Figure 5.

We empirically determined that by setting we can get results similar to the solution of the ODEs with time steps of 0.01. This provides us an easy mechanism, with somewhat higher speed than the ODE solver, to obtain equivalent solutions for the HH system. This in turn allows us to explore the Poincare sections for different initial values at a much higher density. Figure 5 shows one such exploration of Poincare sections for the energy level with 100 different initial conditions, each plotted in a different color. The result is a beautiful oval with an inner decoration by a strange attractor reminiscent of one of the ovoids produced for the Russian royalty. The attractor shows clear preferred regions for the intersections of certain orbits and regions where the intersections are chaotically distributed. To better understand the relationship between the structure of the Poincare sections and the form of the orbits on the plane we take the case of and examine 12 initial points chosen from different regions of the Poincare sections, i.e. defined , with (Figure 6).

Figure 6.

The trajectories of these initial points on the plane are plotted in Figure 7. Towards the narrow end of the bounding oval we have an oval exclusion zone and the towards the broad end of the oval we have a candra-bindu (crescent and dot) clearing zone. The initial point 1 lies at the center of the narrow end oval clearing. This initial point and the center of the crescent clearing at the broad end (not shown) yield a trajectory with a single loop with 3 apexes (top row, leftmost plot of Figure 7). The next trajectory (top row, next plot moving left to right) is a straight line at a incline and corresponds to the center of the two “eyes” of the Poincare section (point 2 in figure 6 is one of these eyes).

Figure 7. The trajectories of the points corresponding to Figure 6 in left to right in 3 rows from top to bottom.

The basis of these trajectories can be understood from the plots of the functions (Figure 8; for every point in Figure 6 and trajectory in Figure 7 the corresponding are shown one below the other from top to bottom in 2 columns). The first two trajectories result from oscillations where both and have period 1 — they show the same repeating pattern after one oscillation. Thus, these two cases can be said to be in a 1:1 resonance. In the second case, they are additionally in phase, i.e. the crest and trough at the same time.

Point 3 samples the center one of the four “islands” which surround the above-mentioned “eyes” of the Poincare section. Each of the island-centers results in a trajectory like the 3rd plot (Figure 7, top row). Point 4 samples one of the small crescents in the vicinity of the oval exclusion zone around point 1 and results in the trajectory seen in plot 4 of Figure 7. These two trajectories result from where both have a periodicity of 4, i.e. a 4:4 resonance. Of the two the trajectory 3 arises from a case where in addition to 4:4 resonance the two oscillators are also in phase.

Point 5 (Figure 6) and its corresponding trajectory (Figure 7) corresponds to two period 5 oscillators in a 5:5 resonance (Figure 8). Such 5:5 resonance oscillators are a pervasive feature of the HH system at this energy level and correspond to the 5 islands of exclusion around the oval exclusion around point 1, the center of the bindu and the two exclusion zones flanking either tip of the crescent.

Figure 8

Point 6 corresponds to a trajectory arising from a 8:9 resonance; point 7 evolves into a more complex 5:25 resonance; the trajectory of point 8 simulates a 3D ribbon and arises from the even more complex 11:37 resonance.

The trajectories arising from points 9, 10 and 11 exhibit what might be termed quasiperiodic behavior. In the case of the evolution of point 9, has a quasiperiod of 4, i.e., it has a similar pattern repetition after every 4 oscillation but the successive repeats are not identical but change slightly over time. , on the contrary, has a strict period of 1. In the evolution of point 10, has a quasiperiod of 5 which is overlayed on a nearly regular higher period of 15. These two points are representative of the evolution of the points in the zones close the bounding oval on its narrow side. One may note that the evolution of point 11 is like a “broadband” version of the 5:5 resonance points. Keeping with this, has a strict period of 5, whereas has a quasiperiod of 5 with higher-order repeat patterns of multiples of 5.

Finally, the evolution of point 12 is chaotic, i.e. the oscillations have no discernible period. The irregularity is marked in but is it manifests more slowly over time. These chaotic trajectories form the bulk of the central uniform distribution of points in the Poincare section. The appearance of chaos can be seen as the limit of the trajectories with increasingly complex or longer period resonances. The quasiperiodic orbits with a nearly regular short period internal repeat structure might be seen as lying at the edge of long periods and true periodicity. In terms of energy levels, chaos starts appearing in the central regions close to and by constitutes the bulk of the internal structure of the Poincare section with internal islands of periodicity and quasiperiodicity in the anterior periphery of the oval. By the limiting nearly all of the trajectories become chaotic.

In conclusion, the HH system qualitatively shows all the typical forms of oscillatory behaviors observed in natural systems (e.g. variable star light curves, weather patterns, population dynamics and far-from equilibrium oscillatory chemical reactions): periodicity with different resonances, quasiperiodicity and chaos. It thus provides a good example how any system whose phase space is defined by even simple ODEs with non-linear terms can exhibit the behavioral diversity characteristic of natural systems.

Yajus incantations for the worship of Rudra from the Kāṭhaka ritual manuals

This article is available as a pdf document. The notes from it are appended below.

The loss of the northern and northwestern Kṛṣnayajurveda traditions due to the Mohammedan depredations of Northern India (aided an abetted by the predatory Anglospheric regimes) has been one the great tragedies faced by Hindudom. Hence, it is rather important to collate and restore whatever remains of these traditions, namely those belonging to the Kaṭha and Kapiṣṭhala schools, which were once dominant in the greater Panjab and Kashmir. In the 1940s, vidyābhāskara, vedāntaratna Sūryakānta, saṃskṛtācārya of the Pañjāba-viśvavidyālaya, Lavapura (modern Lahore) had collated several Kaṭha fragments that came from lost texts outside of the relatively well-preserved saṃhitā. These came from the lost brāhmaṇa and the surviving āraṇyaka, as well as the lost mantrapāṭha of the Kaṭha-s that went with the sūtra-s of Laugākṣi. Notable in this regard, were the following manuscripts that Sūryakānta found in what is today the terrorist state: 1) A Śāradā manuscript which was written in 1033 Vikrama-saṃvat, bright āṣāḍha aṣṭami (approximately June of 1111 CE) in Gilgit. Ironically, this manuscript was found in the possession of a mulla named Hafiz ar Rahman of the Panjab [footnote 1] and contained 340 folios. This was an extensive paddhati with several Kaṭha mantra-s and brāhmaṇa sections used in their late gṛhya rituals. Another Śāradā manuscript, found in the possession of the same mulla, of 180 folios contains overlapping content from brāhmaṇa and mantra material used in Kaṭha rituals. Finally, there was the D.A.V. college manuscript with two parts of 189 and 169 folios respectively that was again an extensive paddhati with overlapping material. The above Rudra-mantra-s come in the sections labeled Rudra-mantrāḥ or Śatādhyāya(Rudra)mantrāḥ and comprise their second division, coming after the Śatarudrīya. The fate of these manuscripts after the vivisection of India in 1947 CE remains unclear. In the past year, the eGangotri trust has made freely available two independent texts which span the mantra-s in question from the Raghunātha Mandira Sanskrit collection, Jammu. One is a Śāradā manuscript of the Śatādhyāya-dīkṣa and another is a print version of the Śatādhyāya produced in the 1920s by the Kashmirian brāhmaṇa-s, Tārachanda Kaulā and Keśava Bhaṭṭa. These have helped correct some problematic parts of the Sūryakānta texts.

The first part of this fragment is a rather important because is the only occurrence of a variant version of this famous incantation to Rudra found outside the Atharvaveda saṃhitā-s. The said incantation occurs as sūkta 11.2 in the AV-vulgate (often taken to be the Śaunaka saṃhita) and as sūkta 16.104 in the Paippalāda saṃhitā. In totality, the two AV versions resemble each other more closely and have a more extensive set of mantra-s. This clearly establishes that it was not a late acquisition of the Kaṭha-s from the neighboring Paippalāda-s, who were also prominent in the same region (e.g. the Kashmirian intellectual bhaṭṭa Jayanta). Two further points are notable. This text is entirely rhotacizing (e.g. arikravebhyaḥ) relative the fully or partial lambdacizing AV saṃhitā-s (AV-vul: aliklavebhyaḥ; AV-P ariklavebhyaḥ). On the other hand, it has mṛḷatam, mimicking the Ṛgveda dialect, instead of the AV mṛḍatam. Similarly, this text shows the archaism of using the RV-type dual form Bhavā-śarvā as opposed to the AV Bhavāśarvau. This was likely originally part of the Kaṭha-mantrapāṭha which went the sūtra-s of Laugākṣi.

It shares with the AV and Śāṅkhāyana-RV traditions, the conception of Rudra in his twin form — Bhava and Śarva. In the Śāṅkhāyana-śrautasūtra (4.20.1-2), Bhava and Śarva are called the sons of Rudra Mahādeva, thus presenting them as ectypes of the Aśvin-s, who are the sons of Rudra in the RV [footnote 2] and mirror the para-Vedic Skanda-Viśākha dyad who are coupled with Rudra (e.g. in gṛhya-pariśiṣṭa-1 of the Kauthuma Samaveda: oṃ rudraṃ skanda-viśākhayos tarpayāmi ।). In contrast, while Bhava and Śarva are used as epithets of Rudra in other Yajurveda traditions (e.g. Taittirīya), they are not presented as twins. This suggests that the the Kaṭha tradition developed in proximity to the locale where AV traditions original diversified in which the cult of the twins Bhava and Śarva, like that of the Greek Dioscouri, was dominant.

The second part is homologous to the equivalent section of the Aruṇa-praśna of the Taittirīya āraṇyaka, which is used in the Āruṇaketukacayana ritual, where the bricks of the citi are replaced by water-filled pots. It might have been part of an equivalent lost section of the Kaṭha brāhmaṇa. It is largely equivalent to the TA version with a few variants that we have retained due to consistency across Kaṭha manuscripts. Variants of the final mantra are found as AV-vulgate 7.87.1; AV-P 20.33.7 and Taittirīya saṃhitā 5.5.9.3; Kaṭha saṃhitā 40.5.33. The Kaṭha version is oddly formed and unmetrical both in the saṃhitā and across the prayoga manuals. Hence, we retain it as is without emendation or metrical restoration based on the other saṃhitā-s.

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footnote 1: He could have descended from converted brāhmaṇa-s
footnote 2: https://manasataramgini.wordpress.com/2020/01/12/the-asvin-s-and-rudra/

RV 10.5

The Ṛgveda is replete with obscure sūkta-s but RV 10.5 might easily take a place in the top tier of those. One might even ask why even attempt to write a commentary on this. We admit we could be plainly wrong in reading the words of our ancestors but the allure of attempting to understand the recondite cannot be passed up. We know nothing of the true composer of this sūkta for the anukramaṇi attributes it to the god Trita Āptya, a watery deity of old IE provenance with cognates Thrita and Thraetona Athvya in the Iranian world and Triton in the Greek world. The sūkta itself is directed towards Agni.

ekaḥ samudro dharuṇo rayīṇām
asmad dhṛdo bhūri-janmā vi caṣṭe |
siṣakty ūdhar niṇyor upastha
utsasya madhye nihitam padaṃ veḥ || 1

The one sea, the receptacle of all riches;
he of many births from our heart looks on.
He clings to the udder in the lap of the two hidden ones.
In the midst of the fountain, the bird’s path is set down.

The opening ṛk is already fairly obscure. We believe the sea here is as literal as it gets. In later Hindu tradition, the sea is seen as the receptacle of riches and the same metaphor finds an early expression here. Now, that sea is juxtaposed with one of many births. The deity of the sūkta is given as Agni and there is no reason at all to doubt that — although he is explicitly mentioned only in the final ṛk of the sūkta, many epithets throughout the sūkta confirm him as the deity. Sāyaṇa informs us that the many births of Agni correspond to this multiple kindlings in the ritual altars of such as the Āhavanīya, the Gārhapatya and the Dakṣiṇāgni in diverse yajña-s. This just one of the ways in which Agni may be seen as having many births. Alternatively, in mythological time he is again said to have many births — a possible allegory for the precession of the equinoctial colure. However, the twist in this sūkta is the “internalization” of the yajña, as Agni is said to be in the heart of the ritualists. This takes us to the next foot where he is said to “cling to the udder in the lap of the two hidden ones”. Agni in the lap of the two parents can be a metaphor for the two pieces of the ritual fire-drill or Dyaus and Pṛthivi in a cosmic context. However, neither of them are hidden and this comes in the context of the internalized yajña implied in the earlier foot. Hence, we take hidden to mean something internal, probably the mind and the intellect (which are not visible entities), whose action composes the sūkta like Agni being generated by the fire-drill. Then in the final foot, we come to Agni being identified as a bird and his path being set down in the midst of the fountain. Sāyaṇa interprets this as Agni as the lightning in the midst of the cloud. This appears to be version of the famous representation of Agni as Apām Napāt. However, we believe that two distinct metaphors, one physical and one mental or internal, are being intertwined here. The sea and the fountain are physical — they are allusions to the famous fire in water, with the fountain as the underwater plume associated with these fires. These sites in the Black Sea-Caspian Sea region could have been accessed by the early Indo-Europeans and those sightings left an impression on their tradition.

samānaṃ nīḷaṃ vṛṣaṇo vasānāḥ
saṃ jagmire mahiṣā arvatībhiḥ |
ṛtasya padaṃ kavayo ni pānti
guhā nāmāni dadhire parāṇi || 2

The virile ones dwell in the same nest,
the buffaloes have come together with the mares,
The kavi-s guard the seat of the natural law (ṛta),
they have placed the highest names in concealment.

This may be interpreted as a metaphor for the feeding of the ritual fire with oblations. The oblations are likened to the virile buffaloes, while the mares are the tongues of Agni (seen as female Kālī, Karālī, etc). This brings us to the famous imagery of the fire within water as the Vaḍavāgni or the equine fire (something Sāyaṇa seems to intuitively grasp), whose flames might be seen as the mares. The kavi-s here might be seen as tending to Agni who is seen as the seat of the ṛta. Sāyaṇa mentions the secret names to be Jātavedas, Vaiśvānara, etc which have secret meanings.

ṛtāyinī māyinī saṃ dadhāte
mitvā śiśuṃ jajñatur vardhayantī |
viśvasya nābhiṃ carato dhruvasya
kaveś cit tantum manasā viyantaḥ || 3

The two imbued with the truth and illusion conjoin,
having measured [him] out, the two birthed the child, making him grow,
[who is the] nave of all that moves and stands still.
Indeed they [the beings] with their mind seek the connection (lit: thread) of the kavi [Agni].

Here we agree with Sāyaṇa’s interpretation that it refers to the birth of the cosmic manifestation of Agni as the sun from his parents, the two world-hemispheres. This is mirrored in the ritual by the generation of Agni by the two parts of the fire-drill. In this solar form, he is seen as a nave of all that moves and moves not and connection to him is mentally sought by all beings.

ṛtasya hi vartanayaḥ sujātam
iṣo vājāya pradivaḥ sacante |
adhīvāsaṃ rodasī vāvasāne
ghṛtair annair vāvṛdhāte madhūnām || 4

For the wheel-tracks of the law, the well-born one,
refreshing offerings, for booty, serve from the days of yore,
the world-hemispheres having worn the mantle,
with ghee and honeyed food augment [the child Agni].

Here the world halves are explicitly mentioned; this clarifies the reference to the cosmic Agni, i.e., sun. The ṛta’s wheel-tracks, i.e., movements of celestial bodies like the sun further build this connection and support the rendering of ṛta as the “natural law” which is manifest in celestial movements that have continued since the ancient days. Them following the cosmic Agni is intertwined with the metaphor of the ritualists seeking booty serving Agni with refreshing offerings. The mantle of the world-halves is a likely allusion to the days and nights.

sapta svasṝr aruṣīr vāvaśāno
vidvān madhva uj jabhārā dṛśe kam |
antar yeme antarikṣe purājā
icchan vavrim avidat pūṣaṇasya || 5

Desirous [of them], the seven shining sisters,
the knower (Agni), held up from the honey to be seen,
He held [them] up within the mid-region, the earlier born one,
seeking a mantle, he found that of the earth.

This ṛk is rather obscure. Sāyaṇa explains the seven sisters as the seven tongues of Agni (Kālī, Karālī, etc) that he has held up within the mid-region for all to see. However, the celestial connection hinted at by the sisters being held up in the sky (?) suggests that it could be an allusion to the Kṛttikā-s (Pleiades) the asterism associated with Agni. However, this interpretation will not hold if we strictly take antarikṣa to be the atmosphere. We follow Sāyaṇa to take the adjective aruṣīḥ to mean shining rather than red (which ironically would fit his tongues interpretation better). Further, we also follow Sāyaṇa in interpreting the obscure word Puṣaṇa as the Earth.

sapta maryādāḥ kavayas tatakṣus
tāsām ekām id abhy aṃhuro gāt |
āyor ha skambha upamasya nīḷe
pathāṃ visarge dharuṇeṣu tasthau || 6

The kavi-s have fashioned the seven boundaries,
just to one of those the troubled one has gone,
in the nest of the highest Āyu, the pillar
stands in foundations [situated] where the paths diverge.

Sāyaṇa takes the seven maryādā-s to be ethical strictures: sins like killing a brāhmaṇa or bedding ones teacher’s wife, beer, etc lie outside the boundaries of proper conduct. Indeed, this moral sense appears to be in play when the same ṛk is deployed in the Atharvan marriage ceremony: Kauśika-sutra 10.2.21: sapta maryādāḥ [AV-vulgate 5.1.6] ity uttarato .agneḥ sapta lekhā likhati prācyaḥ | To the north of the marital ritual fire 7 lines are drawn towards the east. Then while reciting this ṛk, the couple places a step on these lines to signify the ethical strictures that accompany marriage. While this implication might be the secondary sense of the first foot, we believe that its primary sense is distinct. In the ritual sphere, it is an allusion to the seven paridhi-s, the firesticks which enclose the fire. These in turn appear to be a symbolic representation of celestial “boundaries” for the purpose of the yajña. This implied by the yajuṣ incantation that is recited as paridhi-s are laid down (e.g., in Taittirīya Śruti): viśvāyur asi pṛthivīṃ dṛṃ̐ha dhruvakṣid asy antarikṣaṃ dṛṃ̐hācyutakṣid asi divaṃ dṛṃ̐ha agner bhasmāsy agneḥ purīṣam asi || This incantation is for the rite with three paridhi-s (madhyma, uttara and dakṣiṇa). They are respectively associated with the earth, the atmosphere and the sky. The seven-paridhi ritual might have likewise symbolized the six realms and the central plane of one version of vaidika cosmography (speculation). This ṛk returns to some of the themes found in the first and second ṛk-s. The nest and the “dharuṇa”, here meaning the foundation, are mentioned again. Āyu, in the general sense, may be understood as the ancestor of the pañcajana-s, the son of Pururavas and Urvaśi. However, when Agni is seen as the fire of Āyu-s, he is called the best of the Āyu-s. This is made explicit in the ritual context in the Yajurveda by the incantation (e.g., in the Taittirīya Śruti): vider agnir nabho nāmāgne aṅgiro yo .asyāṃ pṛthivyām asyāsuṣā nāmnehi … Thus, the pillar of Agni by the name Āyu, is the skambha referred to in this ṛk. It is said to stand in the foundation where the paths diverge. Thus, the pillar should be understood as the axial pillar with the divergent paths being that of the gods (the northern path) and that of Yama with the dead (the southern path). The point of divergence is of course the equinoctial colure which intersects the plane on which the axis stands.

asac ca sac ca parame vyoman
dakṣasya janmann aditer upasthe |
agnir ha naḥ prathamajā ṛtasya
pūrva āyuni vṛṣabhaś ca dhenuḥ ||

Both the unmanifest and the manifest are in the primal sky,
Dakṣa’s birth is in the womb of Aditi,
Agni, indeed, for us is the first borne of the law,
in his former life both bull and cow.

This last ṛk talks of the role of Agni back in time during the cosmogonic period by giving a summary of what is covered in the famous cosmogonic sūkta-s, like RV 10.72 and RV 10.129. Here the unmanifest (literally the non-existent) and the manifest all that came into being are said to exist in that primal sky (parame vyoman) just as in RV 10.129 (the famous Nāsadīya sūkta). The generation of beings is seen as occurring with the Āditya Dakṣa being born from Aditi (and vice versa as per RV 10.72). This posits initial cyclical reproductions of male from female and vice versa. But it results in an apparent paradox of who came first, the male or the female. The ṛṣi of this sūkta tries to break the paradox by stating that it was Agni who was the first-born entity of the ṛta, who in that former state was androgynous. Thus, the author invokes hermaphroditic reproduction as the ancestral state. This was also the position of Vaiśvāmitra-s of maṇḍala-3, who present a comparable set of cosmogonic constructs in the context of Indra and Varuṇa (RV 3.38), emerging from the god Tvaṣṭṛ, who in some ways is like the yavana Kronos. They are said to have partitioned the hermaphroditic ancestral bovine into male and female, similar to Zeus and Apollo cleaving the hermaphrodites into separate sexes in the yavana world.

Bṛhaspati-śanaiścarayor yuddham-2020 ityādi

The below is only for information. Parts of it should not be construed as any kind of prognostication on our part.

The great Hindu naturalist Varāhamihira describes various kinds of planetary conjunctions or grahayuddha-s in his Brihatsaṃhitā (chapter 17) thus:

yuddhaṃ yathā yadā vā bhaviṣyam ādiśyate trikālajñaiḥ |
tad vijñānaṃ karaṇe mayā kṛtaṃ sūrya-siddhānte ||
The time and nature of planetary conjunctions (graha-yuddha) can be predicted by astronomers. That science has been [taught] in astronomical work composed by me [based on] the Sūrya Siddhānta. [Here he is referring to his Pañcasiddhānta]

viyati caratāṃ grahāṇām uparyupary ātma-mārga-saṃsthānām |
ati-dūrād dṛg-viṣaye samatām iva samprayātānām ||
The planets revolve in space in their respective orbits that are positioned one above the other. [However,] due to their great distance, when observed they appear as if revolving on the same surface (i.e. the sky). [Here, Varāhamihira clarifies that even though it is called a yuddha how it must be understood in the scientific sense.]

āsanna-krama-yogād bheda+ullekha+aṃśu+mardana+asavyaiḥ |
yuddhaṃ catuṣprakāraṃ parāśara ādyair munibhir uktam ||
In the order of the proximity of the conjunct planets: 1. bheda (occultation); 2. ullekha (near tangential contact); 3. aṃśumardana (the grazing of rays); 4. asavya (apart) are the four types of conjunctions described by Parāśara and other sages.

bhede vṛṣṭi-vināśo bhedaḥ suhṛdāṃ mahākulānāṃ ca |
ullekhe śastra-bhayaṃ mantrivirodhaḥ priyānnatvam ||
In the bheda conjunction, there is drought and friends and persons of great families become enemies; in the ullekha conjunction there is fear of weapons, a rebellion of ministers, but there is [abundance of] good food.

amśu-virodhe yuddhāni bhūbhṛtāṃ śastra-ruk-kṣud-avamardāḥ |
yuddhe ca+apy apasavye bhavanti yuddhāni bhūpānām ||
In the aṃśumardana conjunction, kings go to war and people are afflicted by weapons, disease or famine. In apasavya (asavya) conjunction, rulers go to war.

ravir ākrando madhye pauraḥ pūrve +apare sthito yāyī |
paurā budha-guru-ravijā nityaṃ śītāṃśur ākrandaḥ ||
The Sun in mid-heaven is [called] ākranda; paura in the east and when stationed in the west a yāyin. Mercury, Jupiter, and Saturn are always paura. The Moon is always ākranda.

ketu-kuja-rāhu-śukrā yāyina ete hatā ghnanti |
ākranda-yāyi-paurān-jayino jayadāḥ sva-vargasya ||
Ketu, Mars, Rāhu and Venus are always yāyin-s. These are either struck (defeated) or strike (win). Depending on whether the ākranda, yāyin or paura losses or wins the objects associated with of their respective categories [suffer or prosper].

paure paureṇa hate paurāḥ paurān nṛpān vinighnanti |
evaṃ yāyy ākrandā nāgara-yāyi-grahāś ca+eva ||
A paura defeated by another paura, results in city-dwellers and kings being smitten. Similarly, if a yāyin or an ākranda is defeated by another or respectively by a paura or yāyin [the objects associated with them are affected accordingly].

dakṣiṇa-diksthaḥ paruṣo vepathur aprāpya sannivṛtto +aṇuḥ |
adhirūḍho vikṛto niṣprabho vivarṇaś ca yaḥ sa jitaḥ ||
That [planet] which is positioned to the south, at a cusp, showing rapid variability of brightness, goes retrograde immediately after conjunction, with the smaller disc, occulted, gets dimmer or changes color is said to be defeated.

ukta-viparīta-lakṣaṇa-sampanno jayagato vinirdeśyaḥ |
vipulaḥ snigdho dyutimān dakṣiṇadikstho +api jayayuktaḥ ||
If the planet appears endowed with the appearance opposite of the above-described it is deemed the victor. So also that which appears bigger, smooth in the motion or brighter is considered the winner even if stationed to the south.

dvāv api mayūkha-yuktau vipulau snigdhau samāgame bhavataḥ |
tatra +anyonyaṃ prītir viparītāv ātmapakṣaghnau ||
If both are endowed with bright rays, growing larger and smooth moving it becomes a samāgama conjunction. There is [consequentially] a conciliation between the objects associated with the two planets; if it is the opposite (i.e. both are small, growing dim, etc) both the associated objects will be destroyed.

yuddhaṃ samāgamo vā yady avyaktau svalakṣaṇair bhavataḥ |
bhuvi bhūbhṛtām api tathā phalam avyaktaṃ vinirdeśyam ||
In cases where it the characteristics are not clear as to whether the conjunction of two planets is in a yuddha or a samāgama conjunction, it is likewise unclear as to what the fruits will be for the rulers.

Thus, Varāhamihira describes the general omenology of planetary conjunctions as per hoary Hindu tradition. This year is marked by a remarkable conjunction of Jupiter and Saturn that will peak as per geocentric coordinates on the day of the winter solstice (December 21, 2020; Figure 1).

Figure 1

This has caused tremendous fear and excitement among those with a belief in such omenology. Even as we were examining the conjunction for purely astronomical reasons, we received one such call from a believer. Hence, we looked up Varāhamihira to see what he has to say. Notably, this conjunction on Dec 21 is the closest since the famous Keplerian conjunction of 1623 CE. Thus, it is definitely an aṃśumardana and nearly an ullekha. From the above, we can see that, as per tradition, it is a grahayuddha of the aṃśumardana type between two paura planets, which prognosticates death from weapons, disease, or famine. Further, it is evident that Jupiter is to the south and it reduces in magnitude as it emerges from the conjunction. So as per the Hindu typology of conjunctions, it is defeated by Saturn (Figure 2).

Figure 2

Varāhamihira further provides specific omenology for the defeat of Jupiter by Saturn (BS 17.19):

bhaumena hate jīve madhyo deśo nareśvarā gāvaḥ |
saureṇa ca+arjunāyana-vasāti-yaudheya-śibi-viprāḥ ||
If Jupiter is beaten by Mars, Madhyadeśa region, kings and cows suffer. [When beaten by] Saturn, the Arjunāyana, Vasāti, Yaudheya, Śibi [peoples] and the Brāhmaṇa-s suffer. [It is noteworthy that one of the used words for Jupiter in the last 2000 years is Jiva. This word is not encountered in the earlier layers of the Sanskrit tradition. It is a loan from Greek, the vocative declension of Zeus, and is one of the marks of the influence of Greek astrology (e.g. the Paulīśa-siddhānta and Yavana-jātakam) on its Indian counterpart.]

It was that latter prognostication that caused the fear in our interlocutor. These conjunctions of Jupiter and Saturn have an interesting geometric feature: the great trigon. For superior planets one can approximately calculate the frequency of conjunctions thus: Let be the periods of revolution of the two planets and . Then will be the mean angular speeds of the two planets respectively. The difference in their speeds would be:

Hence, the time the faster planet will take relative to the slower planet to complete one revolution (i.e. catch up with it again) will be:

This will be the duration between successive conjunctions. The period of Jupiter is 4331 days of Saturn is 10747 days. Hence, . Thus, the Jupiter-Saturn conjunctions will repeat approximately every 20 years. One can see that the next two conjunctions will occur with respect to the original one at:

Thus, the three successive conjunctions will trace out an approximate equilateral triangle on the ecliptic circle — the great trigon. This trigon caught the attention of the great German astrologer Johannes Kepler, the father of the modern planetary theory in the Occident. He described this in his work the “De Stella Nova in Pede Serpentarii” that announced the discovery of his famous supernova. Since the successive trigons are not exactly aligned, they will progress along the ecliptic (Figure 3). We see that after 40 successive conjunctions it occurs very close to the original conjunction (Figure 3). This amounts to about 290182.4 days (794.4979 years). This is the roughly 800 cycle that Kepler was excited about and thought that he was in the 8th such cycle since the creation of the world (being conditioned by one of the West Asian diseases of the mind).

Figure 3. Progression of the trigons in the cycle of 40

The above formula can also be used to calculate the successive oppositions (when the configuration is Sun–Earth–superior planet) or inferior conjunctions (Earth–inferior planet–Sun) or superior conjunctions (Earth-Sun-inferior planet). We those obtain other interesting patterns. One such is successive oppositions of Jupiter which happen every 398.878 days. Thus, they nearly inscribe a hendecagon on the ecliptic circle (Figure 4).

Figure 4. Successive oppositions of Jupiter

Now the successive inferior or superior conjunctions of Venus happen every 583.9578 days. Thus, these successive events trace out a near pentagonal star (Figure 5). This comes from the fact the ratio of the orbital periods of Earth to Venus is nearly which is a convergent of the Golden Ratio.

Figure 5. Successive conjunctions of Venus

Beyond this, we may also note that the successive oppositions of Saturn nearly inscribe a 28-sided polygon (roughly corresponding to one per nakṣatra) whereas those of Mars nearly inscribe a polygon of half that number (14 sides). The minor planet Ceres nearly inscribes an 18-sided star in the ecliptic circle (Figure 6).

Figure 5. Successive oppositions of Ceres

The cosine principle, radial effect and entropy in the generalized Lozi map

The generalized Lozi map is a good way to illustrate the cosine principle and the radial effects (in lay circles to which I belong in this regard, as opposed to mathematicians). The generalized Lozi map is a 2-dimensional map defined thus:

The map is area-preserving and yields “aesthetic” images for . Additionally, values are also somewhat aesthetic and interesting. We have previously described the cosine principle for various dynamical systems, but we reiterate it here for the generalized Lozi map as it is one of the easiest ones to explain to a layperson. First, a few words on how we visualize this map. We start with the vertices of a 60-sided polygon circumscribed by a circle of radius , centered at , and record the evolution of each vertex for a 1000 iterations under the map. Since the map has an absolute value term, it will be bilaterally symmetric along the line . Hence, we rotate the iterates by an angle of , then scale and center the points, and plot the evolutes of each vertex (orbit of the vertex) in a different color. The examples of 9 such mappings starting with the said polygon in a circle of radius are shown in Figure 1.

Figure 1

The values of of the parameter are chosen such that , where are integers. We observe that the value of determines a key aspect of the shape of the map, i.e. in each map there is a central, largely excluded area that takes the form of a polygon with -sides. This is the cosine principle. More generally, the shape of the central region of the map is determined by the corresponding to the closest to . Note that for the case , we take a number relatively close to 0, for at 0 the map is degenerate. Outside of the polygonal exclusion zone, we may find chaotic behavior but it is still bounded within a unique external shape. The chaos is particularly apparent in the cases when when the map respectively yields the headless gingerbread man, the classical gingerbread man and the tripodal gingerbread man strange attractors. At the other values of , we see bands of chaos interspersed with rings of closed loops that resemble the period-doubling phenomenon in other strange attractors prior to the outbreak of full-fledged chaos.

In Figure 2 we produce the same plot by changing the radius of the circumscribing circle of the initial polygon to . We can see that at this radius, for the low the cosine principle remains dominant, but for large the polygonal zone gets “smoothened” out (e.g. for ). This indicates the radial principle, i.e. the effect of the starting radius on the degree of expression of the cosine principle in the map.

Figure 2

The degree of chaos can be seen as the measure of entropy of the map. By following the colors, one can see that when the orbits of a given starting vertex under the map are all over the place within the attractor boundary. In contrast, for the other values of , the evolutes are mostly limited to particular bands. When then the evolute of each vertex is limited to a certain concentric curve. Thus, the former lie at the high end of the entropy spectrum and the latter at the low end. A proxy for the entropy distribution of the attractor can be obtained by computing the coefficient of variation, , i.e. the ratio of the standard deviation to the mean of the distances of the evolutes of a particular vertex from the center of the map:

, where is the standard deviation and the mean distance from the center

We plot for the maps with (Figure 1) and (Figure 2) for each vertex at 60 angles from respectively in Figures 3 and 4. The mean is shown as for each plot.

Figure 3

Figure 4

We note that for is significantly (an order of magnitude) greater than the those for the other . Further, the radial effect can also be seen affecting the entropy of a map. While it remains roughly the same or is lower for the high entropy triangular, hexagonal and octagonal , for the remaining polygonal the entropy rises at relative . In the pentagonal case, it is mostly across the board while we see specific peaks in the decagonal and heptagonal case.

We next examine the radial effect and entropy more systematically for a fixed value of by choosing the hendecagonal value . The map is shown in Figure 5 and the entropy proxy in Figure 6.

Figure 5

Figure 6

Here we see two disconnected effects of the radius. First, at certain values the inner hendecagon is lost (e.g. ) or becomes smoothened out (e.g. ). Second, the entropy of the orbits of certain vertices dramatically rises for some values (e.g. ). The radial effect on neither the entropy nor the expression of the polygonal inner zone is the same across different values. However, more generally, the lower the number of polygon sides, stronger is the polygonal expression across .

Finally, we touch upon a general philosophical point that can be realized from such chaotic systems. While it is not specific to this generalized Lozi attractor, we take this opportunity to articulate it because we have presented the entropy concept. Most people agree that the attractors with neither too much entropy nor too little entropy are aesthetically most pleasing. This also has a counterpart in biology. Selection tends to prefer systems with an optimal entropy. Too much entropy in a structure (say a protein) and it is too disordered to be useful for most functions. Too little entropy and it is again too rigid to be useful for much. Moreover, from an evolvability viewpoint, too rigid a structure offers too little option for exploring multiple functions in biochemical function space. Too much disorder again means that it explores too much space to perform any function well enough to be selected. Hence, structures with some entropy optimum tend to be selected rather than those with minimum or maximum entropy. Selection can be conceived as maximizing a certain function, say for simplicity, in a given entity under selection. This will then be the fitness function. We can see from the above that cannot directly or inversely track mean entropy because that will not maximize fitness which is at some optimal entropy. It has to hence track something else. This would depend on the optimal band of entropy that is selected by the given constraints. For example, one field of constraints could select for an optimal band of mean , like . Such a field will select corresponding to the pentagon, heptagon, nonagon and decagon while avoiding the triangle, hexagon and octagon for too high entropy and the square and hendecagon for too low entropy (Figure 1, 3). This constraint field will also select for other values (e.g. Figures 7 and 8) that have is in this interval (Panels 1, 2, 6). Thus, the will be a function with local peaks that is very different from the underlying reality of a continuous entropy distribution from low to high. Thus, selection translates the underlying reality into a sensed structure very different from it. The philosophical corollary to this is that a sensed structure will be different from and unlikely to reflect the underlying reality.

Figure 7

Figure 8

Prakīrṇaviṣayāḥ: Life, brains, warfare and society

1 On big brains
An occidentally conditioned person remarked that “we were making bad use of the great brains we have evolved. Instead of using it for human betterment, we were expending it on killing each other with sophisticated weapons.” I could not but help smiling for we have long held that the recent explosive growth of brain size in humans is a likely signal of evolution due to biological conflict. Thus, we posit (like others who have independently done so) that intraspecific and interspecific (e.g. with australopithecines, Homo naledi, Neanderthals, Denisovans and the like over time) conflict led to the escalation of brain growth in human lineages. After we emerged as victors against our related species and eventually settled down as farmers, we began a transition to domestication along with the animals we had allowed to survive as domesticates for our needs. In course of this domestication, it looks as though our brain size came down a notch. Paralleling this, domestication in other animals also appears to have caused a reduction in their brain sizes. In some cases, we see strong evidence that this arose from the reduction in conflict. This possibility was noticed early on by Charles Darwin himself: “ …no animal is more difficult to tame than the young of the wild rabbit; scarcely any animal is tamer than the young of the tame rabbit…” This has since been confirmed by a modern study, which showed that the domestication of the rabbit resulted in: 1) reduction in brain size relative to body size; 2) a reduction in the amygdala and an enlargement of the medial prefrontal cortex; 3) reduction in white matter throughout the brain [footnote 1]. These changes have been proposed to result in a decreased flight response in the domestic rabbit. Similarly, the domestic pig and probably also the domestic cat and dog have smaller brains than their wild counterparts. We saw a poignant illustration of this in the form of a domesticated white lab mouse that had escaped from the lab was savoring its newfound freedom. However, its lack of smarts for life in the wild quickly made it a victim for a crow couple. Thus, if the brain of an organism is an instrument in an arms-race, the brain-size and the level of ambient biological conflict have a positively correlated relationship. More generally, “losing the martial edge” from domestication has also been seen on a civilizational scale — for example, among the steppe peoples who transitioned to a sedentary existence.

We do not as yet fully understand all the reasons why large-brained organisms arose repeatedly among those with smaller brains. But once it is in place, biological conflict can keep it growing in size. Several birds on islands are renowned for their intelligence and might have even bigger brains than their mainland counterparts [footnote 2]. At the face of it, it might look paradoxical — an island usually has less danger from predation and related conflicts than the mainland: think of the flightlessness of the dodo or the solitaire. One hypothesis that explains this is the opening of new niches on the island to the colonizer, which increases intra-specific competition as its population expands. Given the potential habitat and resource diversity, or difficulty in accessing the latter on the island, the plasticity of behavior and therefore a larger brain can be decisive in the intra-specific conflict. An example of the use of a larger brain in exploiting difficult resources is seen in the case of the cane toad introduced to Australia. The toxic toad kills species like the Varanus lizard that eat it resulting in a major decline in their populations. On the other hand, the big-brained Torresian crow has learned to rip it apart and eat it from the ventral side and thus avoid its poison glands. Thus, the rise of smarter birds on islands via intra-specific conflict could be related to the phenomenon that drove the expansion of the human brain.

Recent studies providing constraints on the distribution of earth-like exo-planets suggest that there must be stars with Earth-like planets in the Milky Way. This is a large enough number that it brings home the reality of Fermi’s paradox: “If there are extra-solar system civilizations why have we not heard from them yet?” One noted astronomer suggested that this might mean that human-type intelligence is likely to be exceptional across the Milky Way. We take a slightly more nuanced view informed by biology with regards to the reality of Fermi’s paradox. It is clear that most organisms that profoundly modify their host planet might not do so with any intention of signaling to life forms on other planets. For example, cyanobacteria altered the earth and made its atmosphere oxidizing resulting in a whole lot of new dioxygen chemistry that made organisms like ourselves possible. Cyanobacterial metabolites might signal the presence of life to an observer on another planet, but this is hardly intentional. Similarly, William Hamilton, just before his death, proposed that the bacteria might have `caused’ the emergence of atmospheric clouds to disperse themselves or their spores. While this might seem far-fetched at first sight, since the work by Sands we have known that bacteria can nucleate clouds and ice (e.g. Pseudomonas syringae). More recently, the role of marine bacteria in seeding Arctic clouds has been demonstrated [Footnote 3]. Thus, there might be an “agency” on part of the bacteria in visibly modifying the planetary atmosphere to facilitate their spread. However, while it is likely that bacteria-like forms can effectively signal the presence of life on a planet through more than one means, they do not seem to be doing so with the intent of informing aliens. This kind of signaling seems to need a large centralized brain of the kind we have. Such brains are only present in animals among earthly life and have evolved only a few times in the past 700-1000 million years animals have been on this earth: cephalopods, some lineages of avian dinosaurs, some placental mammals. While we might not fully understand why a lineage evolves a bigger brain than its sister groups in the first place, a major driver of escalating growth appears to be biological conflicts. Thus, on other planets too we expect brain-like structures to evolve if they were to provide an edge in the arms race rather than for signaling to aliens. Its growth will be driven by the arms race and not the need for space exploration. Further, if auto-domestication happens as a consequence it might eventually decline in size. Thus, auto-domestication might be seen like how yogin-s described siddhi-s — they come as byproducts but focusing on them can take you down from the goal of yoga.

We have had the unique distinction of being born in the age of space exploration. Some people, inspired by the excitement of it, have remarked that space exploration might provide selective advantages by allowing the colonization of new planets; hence, intelligent life should eventually turn to such an endeavor. We take a dimmer view. First, we believe such colonization might be an option for the basal prokaryote-like life forms that are likely to widely populate the universe. It might not be necessarily intentional but, like the seeding of clouds and ice on earth by bacteria, certain adaptations might have facilitated such escape and transmission especially in the earlier days of the solar star cluster, and its cognates throughout the Milky Way. However, for larger big-brained organisms like ourselves both the physics and the biology make such prospects of such a gain fairly unlikely. For the most part, space exploration is a byproduct of the development of weapon delivery and surveillance systems, like rockets and satellites, which actually mean something for the conflicts (i.e. dual-use technology). Once the utility of space exploration for the main product declines, the interest in space exploration for its own sake will also be limited. In the best case, we could have many intelligent civilizations that are “mining” nearby planetary bodies for various resources that give them an edge. Thus, we would say that Fermi’s paradox should be taken as the null hypothesis because theory predicts that the primary driver of big brain-like structures would be biological conflicts on the host planet, and space exploration would merely be its rare sideshow.

Finally, we should note that a big brain is also a big memetic ecosystem where viral pathological memes can take root. This probably goes hand-in-hand with domestication, which releases some of the strong survival pressure that an organism faces in a natural environment. For instance, on the wild steppe one has to ensure that food is available to tide through the harsh winter months. This cuts out a lot of the avenue for slacking. In contrast, in a city with a well-provisioned supermarket supplying soft syrupy viands at an arm’s reach and a low price takes the mind away from survival and allows for slacking. Against this background, the emergence of diseases, like American Naxalism, which would otherwise reduce survivorship, can take root and thrive. These new diseases of the mind along with their ancestral versions, i.e. the unmāda-s from West Asia can eventually recycle the civilizational state back to a more basic condition. Thus, the civilizational state we are in would cycle up and down without for the most part reaching out to life on other planets. The same would hold for them too.

2 The parasite within
Small genomes, like those of small RNA or DNA viruses (e.g. the SV40 virus), are lean and mean. They code for little else beyond a minimal apparatus to replicate their own nucleic acid and the bare essential apparatus to take hold of the host systems for producing more of themselves. In contrast, large viruses, like say a poxvirus, a mimivirus, a pithovirus or a Bacillus virus G have giant genomes. In addition to the replication apparatus, they code for a transcription system, and have a degree of self-sufficiency and independence from the host systems. They code for several elaborate means to more subtly hijack and control the host in several ways. While the former class primarily depends on fast replication of their little genomes to overwhelm the host or at least get some copies of themselves made before the host immunity overwhelms them, the latter is a different type of player. They do not replicate as fast but compete hard with the host while taking their own time to replicate their relatively large genomes accurately. This means that they code for a diverse array of capacities to keep the host immunity at bay even as they assemble their elaborate copy-making machinery inside the host cell. A curious thing about such larger viral genomes is that they invariable carry parasites within their own genomes. These may take the form of introns, inteins, and other mobile parasitic genetic elements that invade the genome and the genes of the bigger viruses. The inteins and introns have been selected to mediate their own splicing either at the level of the protein or the RNA transcript. Thus, they do not fatally cripple their host. However, they lodge themselves in genes like the DNA polymerase; hence, the host-virus simply cannot get rid of these genomic parasites. Thus, it is given that as genome sizes grow beyond a certain point, where they shift to the paradigm of slower replication and harder competition, parasitic elements make their home in them.

We have wondered if this phenomenon extends beyond nucleic acid replicators. The bloated Microsoft and Adobe Software come to mind. Another possible example is the growth of the LaTeX system. Thus, one would expect that large complexes of memes are likely to be invaded by smaller memetic parasites that they cannot get rid of. Similarly, generationally transmitted social structures and strategies (overlapping with memes) could also become home to freeloading smaller parasitic systems. We first got a hint of its wider relevance from governmental bureaucracies, where you find various, “inserts” whose absence would make little difference to the functioning of the system. We then observed the same within the otherwise robust structure of religions. This would appear to be particularly so to a pure mīmāṃsaka for whom every word in religion goes towards a ritual injunction. Thus, the presence of extraneous stuff, what he may dismiss as “arthavāda”, would be seen mostly as such textual freeloaders transmitting themselves much like an intron or an intein in a genome. This comparison led us to realize that even as the larger genomes might not be able to rid themselves of such freeloading genetic material, these other systems like texts or bureaucracies might also not be able to do so. Why? one might ask, should selection not purge them? First, as we saw with the inteins in the DNA polymerase, the cost of purging them might be higher than letting them remain if some kind of “compromise” is reached. Sometimes a cost against purging is imposed by an “addiction module” (e.g. in toxin-antitoxin systems). Here, the intein splices itself and thus make sure the DNA polymerase is functional after all. Second, the robustness of the invaded systems might smear the effect of selection into a band rather than a discrete line — therefore within that given band, the variability (e.g. presence or absence of a freeloading genetic parasite) results in no selectable difference in fitness. This implies that the freeloaders can stay on as long as the cost imposed by their persistence mechanisms does not exceed the allowed bandwidth. While we began our example by comparing large viral genomes to small ones, this is taken to an extreme in cellular genomes. The self-splicing machinery of the introns was built into a more complex spliceosomal machinery that confers a certain resistance to introns for the cellular genomes. On the intron side, it allowed them to spread relatively benignly — freeloaders but not imposing a cost enough to derail the system. In ciliates, we see another such “compromise arrangement” taken to an extreme. The cellular RNAi machinery together with the transposases from some of the freeloading elements ensure that a functional “cellular genome” from which they are excised is put together in the macronucleus. However, they are passed on for posterity via the micronucleus where they remain intact but inert.

The relationship between the selfish elements and the cellular genomes is even more complicated: we have shown that transcription factors that regulate gene expression and transcription regulatory elements to which they bind repeatedly evolve from the freeloading mobile elements. So over evolution, they offer raw material for innovation. Sometimes they provide new weaponry for pathogenic organisms and new defensive strategies for cells against other invaders. On the other side, they might breakout to give rise to new viruses. Thus, viruses like retroviruses share an ultimate common ancestry with freeloaders like introns. Other mobile genomic parasites have similarly given rise to viruses such as adenoviruses. Thus, over evolutionary time these freeloaders come with both downsides and upsides. In an environment where the system robustness allows them to be accommodated within the bandwidth allowed by selection, they will persist and end up conferring some advantages to the host genomes that maintain them as opposed to those that do not.

We wondered if the social analogs of genetic systems might have a similar two-sided relationship with respect to freeloaders. One might protest that memes are fine but how can social systems be analogized? We say that even if the mapping is not exact, these can be usefully brought into the orbit of generalized genetic systems (much like the proposed replication of clays). While we are not sufficiently motivated to describe this in full here, we try to illustrate it by example. In essence, it may be seen as a meme or its variant. Take a social system like a government. Various positions interact in a network like a network of genes in different functional ensembles: the Department of Defense, the Department of Biotechnology, the Judiciary, etc. which house within them various positions. Now, the individuals occupying a given position can be seen as fungible, e.g. a judge position can be filled by another person, but the position remains. So, it can be seen as copying itself on that fungible substrate. It can expand too: the same organization can be reproduced recursively from state to state. In the least, the comparison made us realize that certain things that people get very worked up by, such as apparently non-functional and corrupt positions in a bureaucracy, are likely to arise organically and will not go away easily. They might possess “addiction modules” like toxin-antitoxin systems that bring the system down if an eviction is attempted. Further, if there is strong selection that forces them to become extinct it might also bring down other aspects of the organization that are considered useful. We cannot rule out that over evolutionary time some of the social freeloading positions (e.g. positions relating to some branches of the humanities academia) offer selective advantages to the system in certain environments. On the other hand, such social positions can also provide the raw material for the emergence of destructive elements that are more like viruses (e.g. certain policing, religious and academic positions in society).

3 War and innovation
There is a fractal structure to the organization of space. As a result, we have few blue whales and elephants and lots and lots of bacteria. Consequently, many more biological conflicts play out among bacteria — there is a non-stop warfare between different bacteria and also between bacteria and their viruses. These battles are life-and-death struggles — as an old English tyrant gleefully remarked about how no quarter was offered to the Hindus in the war of 1857 CE, so it is in these battles fought by bacteria — “kill or get killed’’ is the name of the game. As a result, natural selection has produced an extraordinary repertoire of weaponry. We have shown that these bacterial conflicts are at the root of all innovation in biology. The origin of eukaryotes was marked by some revolutionary structural adaptations that rendered them immune to some of the weaponry used in these conflicts. For example, the dominance of the tailed bacteriophage was passé in eukaryotes. Eukaryotes mostly do without weaponry like restriction-modification and CRISPR systems. Thus, the armaments of the old-world suddenly came to a stop in the eukaryotic realm. Notable, the eukaryotic reorganization also meant that they were going to less innovative not just in terms of weaponry but more generally in terms of inventing new stuff. Yet, eukaryotes show remarkable systems innovations: where does this come from? What we found was that they get most of their innovation from the “weapons systems” of bacteria through lateral gene transfer and reuse them mostly as “peacetime technology” for various cellular systems like their chromatin structure, RNA-processing, signaling inside and between cells, multicellularity, etc. and also their own defense needs. This brought home an important point that without the pressure of warfare there will be no fancy peacetime technology.

In human endeavor, we see this in the form of various technologies, including space exploration and medicine, being driven by the military needs as the engine of innovation. Hence, we suggest that the utopian society of peaceniks would cease to innovate meaningful technology. However, it is conceivable it turns its mind towards making technology that is primarily of the form of addictions that might eventually render it supine before a more robust culture from within or without.

4 The eternal struggle
One major difference between the Abrahamistic counter-religions of the Messianic variety and the Indo-European religions is the single endpoint utopianism preached by the former. This is the driving force behind its secular mutations, including that in whose grip the modern Occident is currently convulsing. In contrast, at least since the breakup between us and our Iranian cousins (of the Zoroastrian flavor), both sides had ingrained in them the concept of the eternal or repeated episodic struggle of the deva-s and asura-s. It probably was already present in the ancestral matrix of the religion. On the Iranian side, Zarathustra caricatures it in the form of the lands the āirya-s being repeatedly invaded by Angra Mainyu. In fact, this dualism is very important to the philosophy of the Zoroastrian branch of the Iranians. On our side, the Mahābhārata and the purāṇa-s emphasize the repeated cycles of the devāsura-saṃgrāma with neither side gaining total victory. Individual victories might be achieved: Namuci, Vṛtra, Naraka, Prahlāda, Andhaka, and so on might be eliminated but new ones arise. Most importantly, right from the brāhmaṇa texts, we have the emphasis on different upāya-s being used by either side to gain victory; in each new round, a new upāya is needed for victory. Through the teachings of the diverse upāya-s, the brāhmaṇa texts lay out important teachings for humans in daily life. We hold that the devāsura-saṃgrāma is one of the most important teachings of our tradition and a mythic codification of one of the highest realizations of the Indo-Iranians. It essentially tells us the truth of nature — the eternal struggle — like between prey and predator or virus and host or producer and consumer. For example, T4-like bacteriophages and bacteria have been fighting it out for more than 2 billion years, which from long before the Pleiades existed in the sky. Thus, this battle is eternal, and each round can be won by a new upāya which becomes part of the genetic record, much the upāya-s recorded in the brāhmaṇa passages. New ūpāya-s may be discovered which supersede old ones, much like the brāhmaṇa telling us of how the old performance of a ritual might be replaced by a new brahmavāda. The Hindu-s need to pay heed to this teaching. Just as cellular life and the viruses are locked in eternal conflict, so also are we with counter-religious viruses of the mind. They will mutate and new forms will arise, and we have to keep trying new upāya-s. There will be losses, but the end goal is not to become extinct — one cannot avoid losses entirely. Thus, rather than hoping for a utopia to be ushered in, like that wished for by our enemies upon our total destruction under a leader like the āmir al momīn, we have to be prepared for round after round of saṁgrāma.

---

Footnote 1 https://www.pnas.org/content/115/28/7380
Footnote 2 https://www.nature.com/articles/s41467-018-05280-8
Footnote 3 10.1029/2019GL083039

The old teacher

The summer of the year after the tumultuous events, Lootika and Somakhya were traveling to visit their parents. They were supposed to attend the marriage of Somakhya’s cousin Saumanasa but they found social engagements with a subset of the clan quite wearisome. Thankfully, a perfect excuse appeared for them to give it the slip, and they returned to their parents’ city after Somakhya’s parents had left for Kshayadrajanagara for the marriage. Thus, Somakhya was staying with his in-laws till his parents returned. The morning after they had arrived Lootika had risen early and left to give a talk at the university and then engage in some sartorial explorations with her old friend Kalakausha and her friend’s sister Kallolini. Somakhya after finishing his morning rituals sauntered into the kitchen to chat with Lootika’s mother who was busy at her cooking.

LM: “May Savitṛ grant success to your ritual. I’m sort of envious of your mother. She is lighting fast in the kitchen like that legendary English surgeon Liston but unlike him rather infallibly consistent.”
S: “You must tell her that…”
LM: “I did but I had to clarify that it was a compliment as I went on to narrate to her the enthusiastic `lopaharṣaṇa of the English surgeon.”
S: “I’d be happy to help if I could speed things up for you in any way.”
LM: “Don’t be stupid and just stand there just outside the kitchen and chat with me while I wrap this up. I am substituting for your mother at the temple of Rudra by the river for today’s exposition and could pick your brain a bit for that.”
S: “Sure. You’re no different from your daughter in keeping everyone out of your ‘pāka-yajña’.”
LM: “Ask your mother; she would agree too! We certainly believe that too many cooks, especially the guys, spoil the broth. Moreover, we are a bit paranoid over the purity of our yajña-kṣetra.”

S: “So, what have you all been expounding at the temple?”
LM: “Your mother does the Bhagvadgītā. But as you know, over the years I’ve come over to your side. Little Lootika and I had a tiff after she was lambasted by a learned Uttaramīmāṃsā anchorite for aggressively upholding the doctrine of the owl, which evidently you had introduced to her. You may recall that while talking about this incident when we were visiting your place, your father had brought to our attention that the last common ancestor he and I shared had written a text in 1657 CE titled the Ulūkāvabodhanam, expounding the great doctrine. Since then I started studying the doctrine more closely and came over to position closer to you kids. Hence, I introduced it to the audience by way of some variety.”
S: “I’m always inspired by its opening: nama ulūkāya rudrāya aṇuvide |”
LM: “I can see that, my dear. It is indeed that opening story that I narrated to them — where Rudra appeared in the form of an owl to teach the doctrine to the great Kāśyapa. In any case, other than that, at some point when all of you kids were out of home, we also combined our efforts to start a second course, a purāṇa exposition. While there are many expositors of Vaiṣṇava-bhakti themes, we decided to go off the beaten track and have readings from the old Skandapurāṇa — to our surprise, it has gathered much greater interest than the philosophical one. It was in that regard that I needed to consult with you regarding the tale of how Skanda helped his mother in creating Vināyaka.”

Somakhya and Lootika’s mother continued on the topic of her intended exposition until she was done with her cooking and she asked Somakhya to get ready for lunch in a short while. Just then, Lootika and her companions arrived home and Lootika reintroduced them to Somakhya, reminding him of the long past days when they had first met. Then they performed a namaskāra to Lootika’s mother, who asked them to stay on for lunch; Kalakausha and Kallolini said they had to be in the hospital shortly but agreed to take some packed food along from her. Lootika’s mother admonished them to eat properly and on time. Just as they were at the gate to leave, Kallolini remarked: “Our history teacher from school periodically asks about you all. She remarked that she would like to talk to you, Lootika or your husband, or one of your sisters, whenever you’ll are in the city. I think it is something specific that she might want to talk about. Please meet her if you get the chance and are so inclined. It might really help her.” Saying so, the two ladies sped away. After they had left, Lootika’s mother remarked: “These kids of humble provenance have come a long way. Lootika, they often recognize the role you and your sisters played in the process of raising them from an unimaginative ground state to aspiring to be part of the elite. Kallolini was quite close to Varoli just like her sister to you in the old school. So, at some point, when their financial status improved enough to afford the school bus, they transferred her to your school as Varoli’s classmate.” L: “Dear mom, I suspect you ascribe more than a required role to nurture in their case. I think there was some spark that came together in them by the churn of genetics despite their plebeian roots; without that our inspiration would have amounted to nothing. Moreover, there is not much friendship between asamāna-s; the fact that they could get along with us without a display of vulgarity indicates some deeper saṃskāra in them.” LM: “You would know better. Though, I must remark that Kallolini did even better than Kalakausha in the entrance exams. I guess that was because Varoli and Jhilli could directly help her with the intricacies of science and math. She was my student in college, and she was not bad at all. Maybe some vāsana from a past janman.”

L: “What is the deal with our old history teacher? As Somakhya would say, most of the teachers and the classmates from school with whom we have lost contact have passed out of our ken like vāsāṃsi jīrṇāni.”
LM: “Somakhya, do you recall anything of your interactions with her? I remember that she was generally, good to my other three daughters, but was among the multiple teachers who would repeatedly complain to me that your wife is rather arrogant due to her varied knowledge that was so atypical of the girls.”
Somakhya looked at Lootika and chuckled: “Actually, she was one of those teachers who was not bad to me at all. She had a Nehruvian bent of mind and liked to downplay the sultanate or the Mogol tyranny and boost the English superiority over our culture. That said, she was rather generous to me and I’d say to Spidery too when we pressed the counterpoints to these issues in class. But why would she want to see us? So much has gone by and we should have passed out of her memory too.”
LM: “I don’t know for sure, but I have a bit of gossip in her regard. Her husband, a lawyer, disappeared one day without warning and nobody ever found him dead or alive. Since then she has been rather beaten down and comes to the Śivālaya to attend your mom and my expositions. She has aged rapidly and looks bent. Hence, we did not recognize her right away. One day, Kallolini brought her up to us after the exposition and asked if we knew who she was. While I was struggling to place her face, your mother correctly called her out. She told us the tale of her husband’s sudden vanishing. It was then that we remembered that we had encountered that story in the news but had not connected it to her. It looked as though she wanted to say something more in that regard but then hesitated and went quiet. Then she asked about you kids and when she could see you all. She periodically keeps pressing your mother and me about that very point. I never made much of it and simply took it to be some form of a polite inquiry.”
Lootika waded in: “I sensed that Kallolini seemed to know something more; I was about to ask but they ran away. I’ll call her and ask.”
LM: “Lootika, you can be so callous! They would be busy with patients.”

An orthogonal thought running through Somakhya’s mind made him change the topic inadvertently as he thanked his mother-in-law for the bhiṇḍītaka dish she had made: “This brings pleasant old memories. You may not know this but now I can say this freely. This was the first dish Lootika ever shared with me. I remember the day clearly — there was a torrential downpour; hence, we had the misfortune of needing to eat in the school halls. I always dreaded that, as one would invariably end up eating in the vicinity of someone with the wafting odors of abhojya food. We were also supposed to be preparing for the talent show that was in the coming week and we had a couple of periods off after lunch. Several of our schoolmates had already begun doing so during the lunch break itself in the front of the hall. Therefore, I retired to the last bench of the hall and still not feeling like eating due to the odors in the surroundings and continued working on the unusual small serine-peptidase chaperone domain of tailed bacteriophages that I had recently uncovered. It was then that Lootika sneaked up to sit beside me and shared this dish with me. We spoke of what I was doing and that sparked a remarkable idea in her head for creating a biotechnological reagent. Taking advantage of the free time, we worked out that idea to completion. She eventually did make it a reality in the lab and used it effectively.” Blushing a bit, Lootika remarked as though to distract away from the story: “It remains a useful weapon in our armory for the purification of functional proteins.” LM: “Lootika, no wonder you asked me to make this today. Now I know its link to your romance…”

Lootika’s parents were much like Somakhya’s parents — they felt one should not tarry long at useless conversations. Lootika’s mother got up abruptly and remarked: “Dear kids, I need to get ready to go and teach a couple of classes at the college before I return to leave for the temple. You can keep lazing around here for some time but if you want to meet your old teacher you may either go and see her at school where she would be correcting answer sheets or you can come with me to the temple and catch her there. I suggest the former for that might give you some more time and also still be in a mostly public place. I somehow get the vibe that you should not meet her at her home.”
L: “Why so mom?”
LM: “Dear, do as I say. If you need a ride back home call me or dad and we can pick the two of you up while returning. You can tell me of your encounter then or tonight.” Saying so Lootika’s mother left.

After her mother left, Somakhya and Lootika napped a bit to clear their jet lag. As they were waking up Lootika remarked: “Somakhya, I have a gut feeling that there might be something interesting with the case of our former history teacher. I sensed something in Kallolini’s words and also my mother’s strange remark. Moreover, why would she want to meet us? As you remarked, whatever she might have complained behind my back, she was not bad to us in class, but neither were we particularly memorable to her or to those of our classmates whom we mutually found uninteresting.” Lootika then tugged Somkhya’s hand: “I must say that I also feel some vague uneasiness about this.” Somakhya hugged her: “varārohe, at least she was not one of those teachers who complained that you spent too much time with the boys but I agree there might be something more than the mundane here. Let us go and see her at school.”

Soon the two of them got ready and took the relatively long walk back to their old school reminiscing about the happier and adventurous side of the old days. As they walked along, they paused at the spots where they had discussed memorable old findings like the primases of viruses, the RNA-modifying enzymes they had put on the map and the like. The place had changed quite a bit since they had left — in parts swankier and in parts dirtier than before. Finally, they reached the school and rung in their history teacher who with great excitement let them in. As Lootika’s mother had remarked, she looked more haggard than her age and health would suggest. She did not linger for much of an inquiry, as would be typical of a such a meeting after so long a time, confirming their suspicion that she had some specific reason for meeting them other than catching up with past students. She broke into her story: “I have something to ask of you all. Kallolini had told me that, if anyone, it would be one of you all who could help me deal with this. Kallolini’s elder sister, who apparently knows you Lootika, affirmed the same. My husband, you may or may not know, was a respected lawyer who practiced not only at the high court in our city but also in the higher courts. I really took no interest in his cases or his clients and nor did he mention any of those at home. Our conversations were on entirely different matters of common interest. One thing I did know but again did not take much interest in was his fancy for unsolved cases. He occasionally played detective and helped people with cases where they had no recourse through the official channels. He had his connections from his long practice and could get some of these cases reopened or receive official attention due to his efforts. He was no busybody but found great satisfaction in helping people reach closure in incidents where the system had failed them. I mention this because it might have some relevance to what happened to him but I don’t know the exact connection.

It might be about 5 years ago when one evening after an early dinner my husband remarked that he needed to go out to meet with a client. Normally, he met his clients on the ground floor of our two-story house that he used as his office. However, there were some occasions when he would go out to meet his clients — I guess the discreetness of the affair required him to do so. In any case, as I mentioned, I never took a deep interest in the specifics of his cases. Hence, I thought it was just one of those days and simply asked when he expected to be back. He said it might take him at least a couple of hours. Four hours passed and he did not return. I tried calling him, but his phone did not ring. I became tense and was wondering what I should do. Just then, I heard a knocking on the door. It was very unusual for anyone to visit us that late, so I looked through the peephole full of apprehension and saw a girl who seemed vaguely familiar. Surprised to see a little girl all by herself knocking at my door at night I wondered if she was being used as a decoy. Hence, I did not open the door but went up to the balcony overlooking the door and looked all around. The street was empty, and her knocking continued at the door. This combined with the vague foreboding from my husband’s failure to return made me run to the door and open it. The girl asked me to follow her. I was pretty sure it was some kind go trap and asked her who she was and what she wanted. She simply said it was very important and asked me to follow her. I said would call the police if she did not tell me. She simply said the police would not be able to help me without her and I could be in trouble if I went to the police rather than following her. I was surprised that a little girl would talk that way and shut the door and went inside to ring the cops. The next thing I knew I was waking up in the morning. I looked around and was still alone in the house — evidently, I had fallen into an inexplicable sleep when I tried to contact the police the previous night. I recalled the events of the night and in sweat called the police to report that my husband was missing.

The search went on for days and I was repeatedly interviewed by them, subject to lie-detectors tests and what not but nothing substantial ever came out of it and the case went cold like one of the cases he might have liked to look at. In the meantime, the girl kept making her appearance every now and then at intervals of a month and kept asking me to follow her. One night something seized me and I followed her and as I was doing so she tugged me to show the way and I realized it was no real girl — you may think I have gone cuckoo — but a phantom. Her grip had no substance at all to it!”

L and S: “Ma’am we understand this is exactly why you wanted to talk to us. So, no worries. We should not rule out any explanation but tell us your story as you experienced it. Before you continue could you please tell us the dates on which the phantom girl arrives?” The history teacher looked up her phone and gave them the dates. S: “Lootika, they all seem to be trayodaśī nights. Ma’am was that the day your husband regrettably vanished?”

H.T: “I do not keep track of the lunar calendar, but I have a strong feeling that it was not the case. The periodicity set in only after the second visitation.”
L: “Pray, continue with your story.”
H.T: “That day the girl led me to the temple of Hanūmat. I had never been religious and only rarely visited that temple, but I do know my husband was quite a devotee. In fact, when I went to the temple with the girl that night I had a vague recollection of seeing her there in life on the rare occasions I did go there and giving her the prasāda for I used to always feel uncomfortable about eating it. In any case, her phantomhood was confirmed as she vanished at a door just outside the circumambulatory path around the main deity. Around that time, a strange change overcame me. I felt drawn to religion and started attending the expositions of your mothers in the old language at the Śiva temple. The visitations of the phantom-girl continued, and she kept calling me. I feared I might be going nuts and wanted to consult a psychiatrist. I wondered if I should get in touch with your mother, Lootika, to get a good referral but felt rather embarrassed to do so. By some chance, one day I saw my old student Kallolini, your younger sister’s classmate, who had just finished medical school, at the temple. I told her this story. She was accompanied by her elder sister who mentioned knowing you well, Lootika. Both of them asked me many medically relevant questions and I got a referral via her sister. The visit to the shrink was of no consequence as I was certified as merely having some anxiety and prescribed some drugs. They made no difference whatsoever and I discontinued them out of safety concerns. Your friends gave me a symptom-sheet and asked me to talk to them if I had any of the reported symptoms. I did not have any other than the persistent melancholy from the odd turn my life had taken and a sense of dread whenever the phantom girl came knocking. I mentioned that to them again. They at once looked at each other and said that I should try to talk to one of you four sisters or you Somakhya. I asked if I could mention it to your mothers. They specifically said not to tell that part of my tale to your mothers but simply ask to meet with one of you when in town.”
S: “Is there anything more you would like to add to your story?”
H.T: “Yes. I did follow the phantom girl on two other occasions. The second time she led me again towards the Hanūmat shrine but instead of going inside vanished at the cart of the śṛṇgāṭaka vendor who stands at the street just where the bridge over the river ends. The third occasion was the most frightening. She led me by the railway station and my legs were wearying from the long walk. She then turned into a narrow alley with Pakistani flags fluttering on either side. A cricket match seemed to be going on and the dwellers were all chanting in unison for the victory of Pakistan. She then stopped at the break in the wall that would take you right to the train tracks and beckoned me to enter. I just could not get myself to proceed any further and turned around to scoot out of that alley known to be a dangerous place at night and call a cab. The phantom girl cried out `there!’ pointing beyond the broken wall and vanished.”

L: “I commiserate with you. This is rather bizarre ma’am but what exactly do you want of us?”
H.T: “What does all this mean? Is my husband dead or alive? Can I have the ghost girl stop visiting me?”
L: “We cannot easily answer or solve all of those issues, but we can try to obtain some information about your husband’s fate. Would you be prepared to receive it?”
H.T.: “I’ve resigned myself for the worst. But when the law cannot give an answer; I still would like an answer. Even if the worst has happened why would he visit me from beyond in the form of a little girl? Would I not receive a more understandable signal!”
L: “OK. Could you please look straight forward and look at your eyebrows without moving your head and act as though you are seeing through them to the top of your head. Now close your eyes and open them.” Lootika noticed that the teacher’s eyeballs seemed to roll inwards.
S: “Spidery, I guess you can deploy the siddhakāṣṭha effectively.” Lootika whipped out her siddhakāṣṭha sanctified as per the traditions of bhairavācāra from her bag and deployed it on her former history teacher: “Ma’am be calm; you will see some visions and they might give you an answer. Please note everything you see carefully.” After two minutes in a trance from the kāṣṭha-prayoga, the teacher returned to her senses utterly dazed and shocked.
H.T: “I fear the worst has been confirmed.”
S: “Please tell us whatever you witnessed, however, painful that might be. It would bring you some relief at the end.”
H.T: “I saw that phantom girl being lifted by a man with a beard and thrown down a manhole-like dark abyss. Then, I saw my husband being thrown into the same. Then I saw a holy fuckeer mumble some mellifluous words, I guess in the Urdu and everything goes black. Then I heard a train passing by.”
S: “Indeed! I fear the worst is confirmed. You will have to live with this but the incubus will be lifted in part. Lootika?” Lootika deployed her siddhakāṣṭha again and their former history teacher awoke from another short trance in a state of peace.
L: “We can also perform a bhūtabandha and block that ghost girl from coming to your house.”
H.T: “That would be brilliant. I already feel a strange calm within me for the first time.”
S: “No Lootika! That might temporarily relieve you ma’am, but it could be utterly dangerous for Lootika if she tried the bandha and it will not solve your problem for good. That ghost girl is a positive element. When you go to the Śivālaya simply offer some ghee or black sesame oil by drawing this diagram on the riverbank and uttering the following incantation: yathāsthānaṃ sukhaṃ tiṣṭhatu |”. Saying so Somakhya wrote down the incantation and drew the diagram and explained to her how to do the same. He said the ghost girl will return and you might see her sitting outside your house periodically, but she might not knock frequently.”
L and S: “Now may we kindly take leave. At some point sooner or later we hope you get a more complete relief and closure.”

Evening had set in and the streets were filling with a great mass of humanity. The constant blare of horns and their reverberation rent the polluted air as a throng of officer-goers made their way back home after a soul-crushing day in the service of some mahāmleccha overlord. Buses, trucks, cars, rickshaws and motorcycles competed for a sliver of the road in many a near-collision event. The sides of the streets filled with diners looking for some tongue-tickling deep-fried delicacy or sugar-laden treat. The odors wafting from these productions mixed with the fumes of the vehicles and the products of anaerobic fermentation from a distant gutter. Those awaiting their culinary orders to arrive were lost in the virtual worlds beamed on their faces from their phones. Only subliminally recording these, leaving their former teacher to her pile of answer sheets, Lootika and Somakhya started walking back home, each in their own meditation. Lootika broke the silence: “Priyatama, it strikes me that you are quite convinced that the ghost girl and the teacher’s husband had some direct connection beyond merely coming to meet their end in the same pit.” S: “Did you think otherwise?” L: “Truth to be told, I saw it differently. But now I see your line might explain somethings. Perhaps, a marūnmatta is the edge connecting the two in death.” S: “Indeed, that is how I see it. There is a lot more real detective work needed to fill in the rest of the story and neither of us is a lokasaṃcārin to get to the bottom of that. There are too many links for which we lack the right subjects to get a handle. Moreover, a bhūtabandha by us, in this case, would mean wading into territory that we don’t fully understand and the unfulfilled bhūta filled with righteous indignation could turn on you. We should pass this by some of our lokajña friends — they might be able to throw more light on the aspects of it belonging to this world. L: “While not performing a bandha, I think still we should attempt a bhūtanivaha of that ghost-girl tonight to make her tell us her story.” S: “Not sure we have all the leads to pull that off successfully…”

⬤⬤⬤

Somakhya and Lootika with their kids as also Varoli and her family were visiting Vidrum at the rural paradise he had set up. They had spent the first part of the night stargazing. They would have gone on but realized that Vidrum and Kalakausha were not really as excited as they were by the brilliant skies. So, they decided to be a bit more involved with their hosts and settled down to yarn about the old days in the pleasant breeze of the southern country. Vidrum: “I don’t think I ever told you that the mysterious matter of our former history teacher cleared itself up rather dramatically — you had left the country by then. However, I wondered if you might have played a role in that regard.” S and L: “Truth to be told, this is news to us. Please tell us the story.”

V: “A young female civil servant in the police service was rather friendly with the suave strongman choṭā Dawood who reigned like a little shaikh of the large slumland of Kabirwadi near the railway station. But during a marūnmatta festival, she arrested some chaps for the slaughter of a camel on the street not knowing that they were Dawood’s buddies. Dawood issued her a friendly warning for her impudence; unfortunately, having taken her power to her head she arrogantly retorted that she would have the strongman spend the rest of his life in jail at a flick of her finger. Soon thereafter, she disappeared much like our teacher’s lamented husband. The force, which had no leads despite vigorously pursuing the death of their commissioned officer, suddenly got an unexpected tip-off and found her corpse in a deep old railway maintenance manhole beside the tracks. They also recovered the remains of two other people long deceased. DNA tests revealed them to be a well-known city lawyer who had mysteriously vanished, who was none other than our teacher’s husband, and a girl. It turned out that the girl was kidnapped while procuring śṛṇgāṭaka-s when returning from school for the heinous pleasure of choṭā Dawood. She died at the hands of him and his henchmen and was thrown down there. She was the daughter of the poor arcaka of the temple of Hanūmat. Just to remind you, Dawood’s man had also tried to abduct our friend Sharvamanyu’s now-wife Abhirosha in the days of our youth — but we had fought him off — I’m thankful I had my grandfather’s billhook with me that day. Our former teacher’s husband had apparently tried to help the arcaka by trying to get the case to the police. That evening he had arranged a meeting with the arcaka to help him make a complaint with the material he had uncovered. However, that was not to be for Dawood and his men intercepted our teacher’s husband and dumped him in the same place. The reports mentioned that he feared their ghosts and had the well-known fuckeer Ata mulq Alla al-Din cirāg-vālā bābājī to help him ward them off. For some reason the bābā himself claimed to be possessed by the girl’s ghost and spilt the beans — his tip-off led the māmu-s to his client’s victims.”

Somakhya: “Ah. Pretty Lootika might have indeed had a hand in that last part about the fuckeer spilling the beans. She tried to draw that ghost-girl to make her speak but someone was blocking that phantom from speaking. So, she broke the block with her prayoga and instigated the phantom against the blocker.”

Bhāskara’s dual square indeterminate equations

PDF for convenient reading

Figure 1. Sum and difference of squares amounting to near squares.

In course of our exploration of the bhūjā-koṭi-karṇa-nyāya in our early youth we had observed that there are examples of “near misses”: . Hence, we were excited to encounter them a little later in an interesting couple of indeterminate simultaneous equations in the Līlāvatī. Exhibiting his prowess as both a kavi and a mathematician, the great Bhāskara-II furnishes the following Vasantatilakā verse in his Līlāvatī:

rāśyor yayoḥ kṛti-viyogayutī nireke
mūlaprade pravada tau mama mitra yatra |
kliśyanti bījagaṇite paṭavo’pi mūḍhāḥ
ṣoḍhokta-gūḍhagaṇitaṃ paribhāvayantaḥ || L 62||

Tell me, O friend! those 2 [numbers], the sum and difference of whose squares
reduced by one result in square numbers, wherein even experts in algebra who
keep dwelling upon the mysterious mathematical techniques
stated in six ways, come up as dim-witted [in solving this problem].

-Translation adapted from that conveyed by paṇḍita Rāmasubrahmaṇyan, a learned historian of Hindu mathematics

In terms of his kavitvam, Bhāskara-II abundantly illustrates the use of figures of speech, such as the yamaka-s or alliterative duplications. Ṛāmasubrahmaṇyan also mentions that he uses the figure of speech termed the “ullāsa” via the opposition of “paṭavaḥ” and “mūḍhāḥ” in the same verse to bring out the wonder associated with this problem, i.e. it is difficult even for those who are adept at the 6 operations of traditional Hindu mathematics: addition, subtraction, multiplication, division, squaring and square-root-extraction. The problem, put in modern notation goes thus:

Let be rational numbers with . Then,

When we first encountered it, we wondered if it was really that difficult but soon our investigation showed that it was hardly simple for us. To date, we do not have a general solution in integers, placing us squarely among the dull-witted. However, in the course of our study of the integer solutions, we discovered parametrizations with interesting connections beyond those provided by Bhāskara. We suspect he was aware of one or more of these, which is why he termed it a difficult problem for even those well-versed in arithmetic operations. In essence, the problem the generation of 2 new squares plus a unit square for each of them from the sums and differences of the areas of 2 starting squares (Figure 1). Before we consider the integer solutions, let us see the parametrizations offered by Bhāskara to obtain rational fractional solutions. By way of providing several numerical examples (a white indologist of the German school but with a style more typical of the American school had once stated with much verbiage what essentially amounts to “Hindoos must be idiots” for presenting such repetitive examples. He evidently forgot the fact that it was also the style of the great Leonhard Euler), he says:

atra prathamānayane kalpitam iṣṭam | asya kṛtiḥ | aṣṭa-guṇojātaḥ 2 | ayaṃ vyekaḥ 1 | dalitaḥ | iṣṭena hṛto jātaḥ | asya kṛtiḥ 1 | dalitā saikā | ayam aparorāśiḥ | evam etau rāśī || evam ekena+ iṣṭena jātau rāśī dvikena || (Parametrization 1)

atha dvitīya-prakāreṇa+ iṣṭaṃ 1 anena dvi-guṇena 2 rūpaṃ bhaktam | iṣṭena sahitam jātaḥ prathamo rāśiḥ dvitīyo rūpam 1 evaṃ rāśī || evaṃ dvikena+ iṣṭena | trikeṇa try-aṃśena jātau rāśī || (Parametrization 2)

The second parametrization he offers is rather simple:

He illustrates it with the integers and . With integers, we see that is defined by a fractional sequence whose denominators are the successive even numbers and whose numerators are defined by the sequence . This sequence has interesting geometric connections. One can see that it defines the maximum number of bounded or unbounded regions that a plane can be divided into by pairs of parallel lines. Thus, one can see that the of Bhāskara’s second parametrization provides the ratio the maximum partitions of a plane to the total number of parallel lines drawn in dyads used for the purpose.

Figure 2. Division of plane into regions by parallel lines: 3, 9, 19… regions by 1, 2, 3 pairs of parallel lines.

Bhāskara’s first fractional parametrization takes the form:

He illustrates this with , which respectively yield the pairs of solutions , , .

The problem can also be seen as that of finding the intersection between coaxial circles and hyperbolas. Restricting ourselves to intersections in the first quadrant, we can see that the general form of the solutions would be:

;

From the above, for integer solutions we can say the following: 1) Given that must be an even number, should be even. 2) Hence, from the original pair of equations, we can say that must be of opposite parity with being even and odd. 3) Further, for to be an even number it has to be divisible by 8. 4) Hence, . Therefore, all solutions should be of the form , where are integers. Beyond this, not being particularly adept at mathematics, to actually solve the equations for integers, we took the numerical approach and computed the first few pairs of solutions. It was quite easy to locate the first solution (Figure 1) which in a sense is like the most primitive bhujā-koṭi-karṇa triplet (3, 4, 5). The first few solutions are provided below as a table and illustrated as a plot in Figure 3.

Figure 3. First few integer solutions.

Table 1

We quickly noticed that there is one family of solutions that lie on a clearly defined curve (dark red in Figure 3).

Family 1. This family has the convergents: 1, 2, 3, 4 . We can easily obtain parametrization defining this family to be:

This yields (8,9); (64,129); (216,649); (512,2049); (1000,5001); (1728,10369); (2744,19209); (4096,32769); (5832,52489); (8000,80001). This corresponds to the the third parametrization offered by Bhāskara that may be used to obtain rational fractional or integer solutions:

athavā sūtram –
iṣṭasya varga-vargo ghanaś ca tav aṣṭa-saṅguṇau prathamaḥ |
saiko rāśī syātām evam vyakte+ atha vā avyakte || L 63
Or the sūtra: Square the square of the given number and the cube of that number respectively multiplied by 8, adding 1 to the first product, the solutions are obtained both for arithmetic examples or as algebraic parametrization.

iṣṭam asya varga-vargaḥ aṣṭaghnaḥ saiko jātaḥ prathamo rāśiḥ punar iṣṭam asya ghanaḥ aṣṭa-guṇo jāto dvitīyo rāśiḥ 1 evaṃ jātau rāśī , 1 | atha+ ekena iṣṭena 9, 8 | dvikena 129, 64 | trikeṇa 649, 216 | evaṃ sarveṣv api prakāreṣv iṣṭa-vaśād ānantyam ||

By taking as the given, the square of the square of the given number is , which multiplied by 8 is . This plus 1 yields the first number of the solution . Again given , its cube is which multiplied by 8 yields the second number of the solution, 1. Thus, we have the pair (1, 3/2). Now with 1 as the given we get (8, 9); with 2 we get (64, 129); with 3 we get (216, 649). Thus, with each of these parametrizations (i.e. all the 3 he offers) by substituting any number one gets infinite solutions.

However, this parametrization hardly accounts for all the solutions. Through analysis of the remaining solutions, we could discover several further families with distinct more complex parametrizations. They are:
Family 2. This family has the convergent

Here, is the -th Chebyshev polynomial of the first kind that is defined based on the multiple angle formula of the cosine function:
; ;
Thus, we get the Chebshev polynomials as:
; ;

Thus, we get the pairs (8,9); (288,289); (9800, 9801); (332928, 332929). All these points lie on the line

One observes that where 2, 12, 70, 408

From the above, it is easy to prove that the sequence of fractions are successive convergents for . For we get , which is Baudhāyana’s convergent approximating to 5 places after the decimal point.

Family 3. This family has the convergent (green line in Figure 3). It can be parametrized thus:

Thus, the ratio of successive converges to , a number which is again related to Chebyshev polynomials of the first kind evaluated at 8:

Thus, we arrive at the pairs constituting this family as: (8,9); (80,105); (1232,1641); (19592,26121)

Family 4. This family has the convergent . It can be parametrized thus:
, i.e. is every 6th term of the mātra-meru sequence
Thus, we can also express using the Golden ratio :

Thus, the ratio of successive converges to ; we can also write using the hyperbolic sine function:

Similarly, we get:

As with we can also get a hyperbolic trignometric expression for :

Finally, we can also write compactly in terms of Chebyshev polynomials of the first kind:

Thus, the first few members of this family are: (8,9); (144,161); (2584,2889); (46368,51841)

Family 5. This family has the convergent . It can be parametrized using the continued fraction expressions of the convergent:
denominators of odd terms of the continued fraction convergents of
numerators of odd terms of the continued fraction convergents of

The relevant partial convergents are ; ; ;

Thus, we see that the convergents with odd numerators and even denominators yield the corresponding to this family, with the first term matching the second term of family 1; hence, it may be seen as branching from family 1. In practical terms, one can obtain these values using the below 2-seeded recursions:
; second term onward
; second term onward

Family 6. This family has the convergent . It can be parametrized using the partial convergent fractions approximating the convergent.

denominators of partial convergents of divisible by 8
numerators of partial convergents of

The relevant partial convergents are ; ; ;

The first term is the same as the second term of family 4. In practical terms, one can obtain these values using the below 2-seeded recursions:

; second term onward
; second term onward

In the case of families 4, 5 and 6, we observe that the sum and the difference of the squares of the numerators and denominators yield perfect squares. Further, the denominator is always an even number and the numerator a surd of the form or . This suggests an approach for discovering new families. Our search till 100000 uncovered 2 more families of this form

Family 7. This family has the convergent ;

It can be parametrized using the partial convergent fractions approximating the convergent thus:

denominators of partial convergents of divisible by 8
numerators of partial convergents of

The relevant partial convergents are:
; ;

In practical terms, one can obtain these values using the below 2-seeded recursions:

; second term onward
; second term onward

Family 8. This family has the convergent ;

It can be parametrized using the partial convergent fractions approximating the convergent thus:

denominators of partial convergents of divisible by 8
numerators of partial convergents of

The relevant partial convergents are:
; ;

In practical terms, one can obtain these values using the below 2-seeded recursions:

; second term onward
; second term onward

In families 7, 8 there are no small terms that connect them to any of the other families; keeping with Hindu love for big numbers, they start relatively large and grow rapidly. These 8 families cover all the solutions in Table 1 and Figure 3 . The relationships between them are shown in Figure 4.

Figure 4. The relationship between families.

Is there a general way to obtain all parametrizations for the integer solutions of this pair of indeterminate equations? Perhaps this has already been answered by mathematicians or perhaps not. In any case, as Bhāskara had stated, the solutions to this couple of equations is not an entirely trivial problem and sufficiently absorbing for an enthusiast of arithmetic.