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 \texttt{TOOLKIT} 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.

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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, 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. The effects of this were seen in 605 CE when according to the New Book of Tang, the Turks retaliated by forming an alliance with the Tang and launched a genocidal assault on the Khitans resulting in their defeat. 4000 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, they were not done, and their time was to come 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. 1283 states that “The Khitan…their language of 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.

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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.

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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.

yajna_etc_barFigure 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.

yajna_strchFigure 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: 6 \times, RV7: 1 \times, RV8: 1 \times, RV10: 2 \times). 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 7 \times; Taittirīya-brāhmaṇa 6 \times. However, it occurs more commonly in the distinctive smaller Atharvan collections: AV-vulgate 25 \times; AV-Paippalāda 30 \times. 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

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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 (\approx 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.

chariot_TrundholmFigure 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 \S1 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.

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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 \LaTeX 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 \LaTeX 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.

IntelligenceGPTGPT3.5 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 V_1s 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.

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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 possibly 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 V_1 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 V_1 girl of a high clan serve him dinner. However, he was very dubious of the whole thing: He told Clotilde: “No truly traditional V_1 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 V_1 as yourself if I were to accept such an offer. Incidentally, I’m getting married in the coming months once she graduated.” V_1: “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 V_1 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 V_1 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 V_1: “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.”
V_1: “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.”
V_1: “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.”
V_1: “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.”
V_1: “Ma’am that is very kind of you.”
Vr: “Why did the Śaṃkarācarya-jī ask you to stay away from encounters with such entities?”
V_1: “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 V_1 in his retinue diagnosed that I was seized by the bhūta-s from the cemetery. It took many different ritual attempts before a V_1 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 V_1‘s tale but felt it might not be proper to ask him too much and simply mumbled something in sympathy and kept quiet.


On getting home from the meeting with the V_1 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.


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 V_1 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 \bullet 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.”


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 V_1 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 V_1 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 V_1. 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.

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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 \times 2 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.

Screenshot (24)

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 (\approx 465 Ma) while Clearwater West is from the Permian (\approx 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 P_J is the orbital period of Jupiter then: (1) The Hungarias are concentrated at a period of \tfrac{P_J}{5} \approx 867 days followed by an exclusion gap at \tfrac{P_J}{4} \approx 1083 days. (2) The inner and the central belt are separated by the resonance of \tfrac{P_J}{3} \approx 1444 days. (3) The \tfrac{2P_J}{5} \approx 1733 days and \tfrac{2P_J}{5} \approx 1857 days resonances respectively bound the Psyche peak from the central and outer belts. (4) The outer belt is bounded by the \tfrac{P_J}{2} \approx 2167 days resonance and the Cybeles are concentrated by the \tfrac{4P_J}{7} \approx 2476 days resonance. (5) The Hildas are concentrated by the \tfrac{2P_J}{3} \approx 2889 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 D to energy (bottom right panel of Figure 4):

E = 6.286D^{3.4} mT

Here, the energy E is in mT, i.e., megatons of TNT; in turn 1 mT \approx 4.184 \times 10^{15} J 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.

Meteorites_Fig5Figure 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.

Meteorites_Fig6Figure 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.

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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 20 \times 70. It was easy to track given its proximity to \iota Aurigae. Below \iota, 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 \approx 6.2-6.4. 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 20 \times 70.


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).

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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 9 \times 9 = 81 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 \times 2 31. vyāpin \times 2 32. arūpin \times 2 33. prathama \times 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 \times 2 66. asaṃsthita \times 2 67. pūrvasthita \times 2 (total: 32)
(12) Kamala (center of the lotus throne): 68. sākṣin \times 2 (total: 1)
(13) Indrādi-devatā-s (the gods of the directional ogdoad): 69. turu \times 2 70. piṅga \times 2 71. pataṅga \times 2 72. jñāna \times 2 73. śabda \times 2 74. sūkṣma \times 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 10^5 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 9 \times 9-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 \to (1) Ananta \to (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 \to (1..9) Bindukā, Bindugarbhā, Nādinī, Nādagarbhajā, Śaktī, Garbhinī, Parā, Garbhā and Arthacāriṇī.
Kapāla \to (10..18) Suprabuddhā, Prabuddhā, Caṇḍī, Muṇḍī, Kapālinī, Mṛtyuhantā, Virūpākṣī, Kapardinī, Kalanātmikā
Caṇḍeśa \to (19..27) Caṇḍamukhī, Caṇḍavegā, Manojavā, Caṇḍākṣī, Caṇḍanirghoṣā, Bhṛkuṭī, Caṇḍanāyikā, Caṇḍīśanāyikā.
Yogeśa \to (28..36) Vāgvatī, Vāk, Vāṇī, Bhimā, Citrarathā, Sudhī, Devamātā, Hiraṇyakā, Yogeśī.
Manonmana \to (37..45) Manovegā, Manodhykṣā, Mānasī, Mananāyikā, Manoharī, Manohlādī, Manaḥprīti, Maneśvarī, Manonmanī.
Hāṭakeśvara \to (46..54) Hiraṇyā, Suvarṇā, Kāñcanī, Hāṭakā, Rukmiṇī, Manasvī, Subhadrā, Jambukāyī, Bhaṭṭanī.
Kravayāda \to (55..63) Lambinī, Lambastanī, Śuśkā, Pūtanā, Mahānanā, Gajavaktrā, Mahānāsā, Vidyut, Kravyādanāyikā.
Mudreśa \to Vajriṇī, Śktikā, Daṇḍī, Khaḍginī, Pāśinī, Dhvajī, Gādī, Śūlinī, Padmī.
Diñmaheśvara \to 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 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 \times 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 \times 2 । vyāpin \times 2 । arūpin \times 2 । prathama \times 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 \times 2 । asaṃsthita \times 2 । pūrvasthita \times 2 । sākṣin \times 2 । turu \times 2 । piṅga \times 2 । pataṅga \times 2 । jñāna \times 2 । śabda \times 2 । sūkṣma \times 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 \times 2 । vyāpin \times 2 । arūpin \times 2 । prathama \times 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 \times 2 । asaṃstuta \times 2 । pūrvasthita \times 2 । sākṣin \times 2 । turu \times 2 । piṅga \times 2 । pataṅga \times 2 । jñāna \times 2 । śabda \times 2 । sūkṣma \times 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 \times 2 । vyāpin \times 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.

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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.

Polygon_SineFigure 1.

It is easy to see (Figure 1) that for a circle of diameter d the side s of an inscribed regular polygon of n sides is s=d\sin\left(\tfrac{\pi}{n}\right). 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 \sin\left(\tfrac{\pi}{n}\right) for n=3..9. 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 \sin\left(\tfrac{\pi}{x}\right):
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 d, its circumference c, the length of the given arc a and y its chord. Then the above can be written in modern notation as:

y= \dfrac{4da(c-a)}{\frac{5c^2}{4}-a(c-a)} = \dfrac{16da(c-a)}{5c^2-4a(c-a)}

Now, the arc can be written as the x^{\mathrm{th}} fraction of the circumference, \therefore a=\tfrac{c}{x}. By plugging this into the above equation, we get:

y= \dfrac{16d\tfrac{c}{x}(c-\tfrac{c}{x})}{5c^2-4\tfrac{c}{x}(c-\tfrac{c}{x})}

This allows us to eliminate c and write


Thus, we get an algebraic function approximating y=\sin\left(\tfrac{\pi}{x}\right):


Figure 2.

In the below table we show the values of the polygon sines for n=3..9 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.

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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 \approx 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 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 8 \times, 28 \times, 108 \times 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 28 \times 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.

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

The Ur-Skandapurāṇa (SkP) or the “archaic” Skandapurāṇa ( \approx 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 \to Hiraṇyākṣa \to Andhaka \to Prahlāda \to Virocana \to 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

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_kaumAraAvicephalous 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.

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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:

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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 sp^3, sp^2, 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 x 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 \tfrac{Z}{\sqrt{\pi}}, where Z is the atomic number, and we set the Bohr radius a_0=1 But for our purposes just the shape matters:
f_{1s}\left(x\right)=e^{-x}\left\{0\le x\right\}
f_{2s}\left(x\right)=\left(2-x\right)e^{-\frac{x}{2}}\left\{0\le x\right\}
f_{2p}\left(x\right)=xe^{-\frac{x}{2}}\left\{0\le x\right\}
f_{3s}\left(x\right)=\frac{1}{6}\left(27-18x+2x^{2}\right)e^{-\frac{x}{3}}\left\{0\le x\right\}
f_{3p}\left(x\right)=\left(6x-x^{2}\right)e^{-\frac{x}{3}}\left\{0\le x\right\}

From these, you get the shape of the probability distributions as x^2f_{o}(x)^2, where o 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!’’


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:

\displaystyle \sum_{j,k=0}^{\infty} x^j y^k

Charuchitra: “What answer did you guys get?”
Somakhya: “An area bounded by a square of side with length 2 defined by the diagonal points (\pm 1, \pm 1).’’
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 \sqrt[3]{2} 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 \sqrt[3]{2}?’’
C: “You can use \tfrac{5}{4}\left(1+\tfrac{3}{125}\right)’’
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 1-1+1-1+1-1+1 \cdots=\tfrac{1}{2} — 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 \textrm{Al(OH)}_3’’
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.’’

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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) also 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.

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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.

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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.

\pi and squaring of a circle
Ramanujan is well-known for his numerous approximations of \pi 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 \tfrac{9}{5}. Use that segment to construct a circle with diameter 1+\tfrac{9}{5}.
3. Apply the geometric mean theorem on that circle (Figure 1) to obtain a segment of length \sqrt{\tfrac{9}{5}}. Use that to construct a segment of length \tfrac{9}{5}+\sqrt{\tfrac{9}{5}}. With that segment construct a circle of diameter 1+ \tfrac{9}{5}+\sqrt{\tfrac{9}{5}} (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: \pi \approx \tfrac{9}{5}+\sqrt{\tfrac{9}{5}}. This is very close to Āryabhaṭa’s approximation: \pi \approx \tfrac{62832}{20000} = \tfrac{3927}{1250}. 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 3\tfrac{16}{113} 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 \pi

4n-3 defines the alternate odd numbers: 1, 5, 9, 13, 17, 21, 25, 29, 33, 37…
4n-1 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 \pi:

\displaystyle \pi = 4\sum_{n=1}^{\infty} \left( \dfrac{1}{4n-3} - \dfrac{1}{4n-1}\right)

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

\displaystyle \pi\cot(\pi z) = \sum_{n=1}^{\infty} \left(\dfrac{1}{n-1+z} - \dfrac{1}{n-z}\right)

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

\displaystyle \psi(x+1)=\dfrac{\Gamma'(x+1)}{\Gamma(x+1)}=\sum_{n=1}^{\infty} \left(\dfrac{1}{n}-\dfrac{1}{n+x}\right) -\gamma

Here \gamma is Euler’s constant.

\sqrt{10}, cubes of triangular numbers and \pi


Figure 2. 10-\pi^2 

In old India (e.g., Brahmagupta and the Jaina Prajñāpti texts) we find \sqrt{10} as an approximation for \pi. This is interestingly close to the Egyptian approximation \left(\tfrac{16}{9}\right)^2. We can ask the converse question of how close is \pi^2 to 10 (Figure 2). Ramanujan discovered an interesting answer for this.

The triangular numbers, T_n, are the sums of successive integers up to n, i.e, T_n = \tfrac{n^2+n}{2}: 1, 3, 6, 10… Then,

\displaystyle 10-\pi^2 = \dfrac{1}{8}\sum_{n=1}^{\infty} \dfrac{1}{T_n^3}

Reciprocals of the cubes of odd numbers and \zeta(3)
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 \infty:

\displaystyle \sum_{n=1}^{\infty} \dfrac{1}{n} =\infty

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., \tfrac{1}{3}>\tfrac{1}{4}; \tfrac{1}{5}, \tfrac{1}{6}, \tfrac{1}{7} > \tfrac{1}{1/8} 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 z on the complex plane:

\displaystyle \zeta(z) = \sum_{n=1}^{\infty} \dfrac{1}{n^z}

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 \zeta(2) = \tfrac{\pi^2}{6}. Euler subsequently established that the reciprocal of \zeta(2) gives the probability of two integers drawn at random from the interval between n_1 and n_2 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:

\displaystyle \zeta(z) = \sum_{n=1}^{\infty} \dfrac{1}{n^z} = \prod_{p} \dfrac{1}{1-\dfrac{1}{p^z}},

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 -\tfrac{1}{12} (found in his first notebook and communication with Godfrey H. Hardy) — this was essentially his auto-discovery of the value of \zeta(-1). 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 \zeta(3) that is today sometimes called Apéry’s constant. After the days of Ramanujan, this constant has appeared in several areas of physics.

\displaystyle \zeta(3)=\dfrac{8}{7} \sum_{n=0}^{\infty} \dfrac{1}{(2k+1)^3}

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

y= \dfrac{x^{2}}{2\left(e^{x}-1\right)}

Figure 3. \zeta(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 k_1 \pi^3+k_2 \zeta(3), where k_1, k_2 are constants specific to each sum:

\displaystyle \sum_{n=0}^{\infty} \dfrac{1}{(3k+1)^3} = \dfrac{1}{27}\left(\dfrac{2}{3\sqrt{3}}\pi^3+13\zeta(3)\right)

\displaystyle \sum_{n=0}^{\infty} \dfrac{1}{(4k+1)^3} = \dfrac{1}{16}\left(\dfrac{1}{4}\pi^3+7\zeta(3)\right)

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 n \to \infty 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 \psi(x) \Rightarrow \psi^{(2)}(x):

\displaystyle \sum_{n=0}^{\infty} \dfrac{1}{(5k+1)^3} = -\dfrac{1}{250} \psi^{(2)}\left(\dfrac{1}{5}\right) \approx 1.0059121444577

The Ramanujan primorial plus one fourth sequence
The prime numbers 2, 3, 5, 7, 11… are denoted by p_1, p_2, p_3, p_4, p_5 \dots. By analogy to the factorial product, one can define the primorial as the product of successive primes:

\displaystyle p_n\# = \prod_{k=1}^{n} p_k

Ramanujan defines a sequence such that 2 \sqrt{p_n\# + \tfrac{1}{4}} is an odd integer. This holds for the below values of n:


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 ad=bc then for n=2, 4:
(a+b+c)^n+(b+c+d)^n+(a-d)^n = (c+d+a)^n +(d+a+b)^n+(b-c)^n

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: 14n^2 + 70n + 98; \; n=1, 2, 3 \dots The sum of the 4th powers is given by 98 (n^4+ 10 n^3 + 39 n^2+ 70 n +49 ).

The next problem in this genre is to find rational solutions to the indeterminate equations:
2w^2=x^4+y^4+z^4 \; ; \; 2w^4=x^4+y^4+z^4 \; ; \; 2w^6=x^4+y^4+z^4

Ramanujan gives parametrizations to solve such equations: if a+b+c=0 then,
2(ab+bc+ac)^2 = a^4 +b^4+c^4 \dots \S 1
2(ab+bc+ac)^4 = (a(b-c))^4+(b(c-a))^4+(c(a-b))^4 \dots \S 2
2(ab+bc+ac)^6 = (a^2b+b^2c+c^2a)^4+(ab^2+bc^2+ca^2)^4+(3abc)^4 \dots \S 3

The equation \S 1 is quite trivial. For the equation \S 2, using Ramanujan’s parametrization one can obtain several sets of tetrads. Below is an example where we take a to be successive integers starting from 0 and b to be 1 more than a:
a=0,1,2,3\dots; b=a+1

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 y is the sequence of odd numbers. w (first column) are the hex numbers, i.e., the centered hexagonal numbers given by the quadratic expression 3n^2+3n+1. The sequence defined by w 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. x (second column) is the square star numbers (Figure 4), i.e., square numbers with triangular numbers on each side, given by the quadratic expression 3n^2+2n, while z (fourth column) are the square grid numbers given by the expression 3n^2-2n (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 \S 2 with a=1 and b 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 w in this tetrad is specified by n^2 - n + 1. 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 1, the second side is 1, 2, 3 \dots and the angle between these two sides is \tfrac{\pi}{3}. Then the squares on the third sides of this sequence of triangles will have an area equal to the sequence w (Figure 8). In this tetrad x is the sequence of odd numbers, y takes the form n^2 - 2n and z is the same sequence as y 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.

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

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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 x_n at a given point in time in a population. Under the selective pressure acting on it, in the next generation, it will become x_{n+1}. Thus, the selective pressure can be conceived as a function that brings about the transformation x_{n+1} = f(x_n). 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 f 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.

FP_fig1_cobweb1Figure 1. Cobweb diagram for the functional iterates of f(x)=\tfrac{1+x}{2+x^2}

For example, let us take the function acting on x_n to be f(x)=\tfrac{1+x}{2+x^2} (Figure 1). We can see that the iterative application of this function on any starting x_0 (point B in Figure 1) eventually leads to convergence to a fixed point that can be determined by obtaining the intersection between f(x) and the line y=x. In this case, one can prove that it will be 0.6823278…, the only real root of the equation x^3+x-1=0. 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 f(x)=\tfrac{1}{x}-x

Instead, consider the same process under the function f(x)=\tfrac{1}{x}-x (Figure 2). Here, we can show that there would be two points that emerge as a result of the intersection between f(x) and y=x: the two roots of the equation 2x^2-1=0, \pm \tfrac{1}{\sqrt{2}}. These two points draw the iterates towards themselves but the competition between them results in the outcome being chaos unless x_0 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 \sin(x), which shows a gradual convergence to 0. The gradual convergence in cases like this is related to their limit as x\to 0; e.g., \lim_{x \to 0} \tfrac{\sin(x)}{x} =1. In the below catalog, \phi denotes the Golden Ratio and \phi' 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.
\sqrt{1+|x|}: \phi

1+\dfrac{1}{x}: \phi; This attractor also extends to the complex plane. For more discussion of this system see our earlier note.

2+\dfrac{1}{x}: 1+\sqrt{2}; This attractor also extends to the complex plane.

1+\dfrac{1}{2x}: \dfrac{1+\sqrt{3}}{2}

2+\dfrac{1}{2x}: 1+\sqrt{\frac{3}{2}}

\dfrac{1+x}{2+x}: \phi'

FP3_algebraic_mapFigure 3. Chaotic functional iterates of some simple algebraic functions

\dfrac{1}{x}-x: symmetric sawtooth chaos: \phi, \phi' are repellors.

x-\dfrac{1}{x}: sawtooth chaos: \phi, \phi' 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.

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

4x^3 -3x (Chebyshev 3): chaotic (-1,1)

These next two functions are the Chebyshev polynomials 2 and 3, which show chaotic behavior if x_0 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.

FP4_cheb3_histFigure 4. Distribution of the functional iterates of 4x^3 -3x

(2) Circular trigonometric functions

FP5_cos_complexFigure 5. Number of iterations to convergence or divergence to \infty of iterates of \cos(x)

\cos(x): 0.73908513321516 (the solution of the equation x=\cos(x)) 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 \tan(x) from different starting points.

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

\sin(2x): 0.94774713351699

FP7_cos2x_histFigure 7. Distribution of the functional iterates of \cos(2x)

\cos(2x): chaotic. The iterates are contained in the interval (-1,1) with certain exclusion zones. The most prominent exclusion zone contains the primary repellor 0.514933264661… (solution of the equation x=\cos(2x); red point in Figure 7).In the negative part of real line, the exclusion begins at \cos(2) (purple point in Figure 7). The points of the other exclusions zones (black points) are more mysterious.

\tan(2x): chaotic

\sin(x)-\cos(x): -1.25872817749268

\sin(x)+\cos(x): 1.2587281774927

\cos(x)-\sin(x): bicycle: -0.83019851706782, 1.41279458572762; These attractors are also valid in the complex plane.

Figure 8. Functional iterates of 160801 starting points of \sec(x) in the complex plane

\sec(x): 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 \pi Figure 8; red points).

\cot(x): While it is chaotic on the real line, on the complex plane it converges to either \pm 1.1996786402577i depending on the initial point.

\csc(x): 1.1141571408719

FP9_cossquaredFigure 9. Regions of convergence or divergence to \infty of iterates of \cos^2(x). The light-yellow regions converge to the attractor indicated as a blue point

\cos^2(x): 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).

FP10_cscsquaredxFigure 10. Regions of convergence of iterates of \csc^2(x) or divergence to \infty. The light yellow regions converge to the attractor indicated as a blue point

\csc^2(x): 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).

\sec^2(x): chaotic

FP11_xbytanxFigure 11. Number of iterations of function \tfrac{x}{\tan(x)} for convergence or divergence to \infty

\dfrac{x}{\tan(x)}: The attractor on the real line is \dfrac{\pi}{4}. 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).

\sin(\cos(x)): 0.69481969073079

\tan(\sin(x)): 1.5570858155247

\sin(\tan(x)): -0.99990601241267

\sin(\sec(x)): 0.97678326638014

\cos(\sec(x)): 0.44604767999913 (root of the equation \cos(x)= \tfrac{1}{\arccos(x)}) it the attractor both on the real line and the complex plane.

\sin(\csc(x)): \pm 0.94403906661161 is the attractor both of the real line and the complex plane depending on the starting point defined by (root of the equation \sin(x)= \tfrac{1}{\arcsin(x)}

\tan(\cos(x)): bicycle: 0.013710961966803, 1.55708579436399; These values are remarkably close to but not identical to the solution of the equation \arccos(x)= \tan(\cos(x)), i.e., r=0.01371006057 and \arccos(r)=\tan(\cos(r))=1.55708583668. Thus, the sum of these two values is close to \tfrac{pi}{2}.

\cos(\tan(x)): bicycle: 0.013710102886935, 0.999906006233481; These values are remarkably close to but not identical to the solution of the equation \arccos(x)= \cos(\tan(x)), i.e., r=0.999906018592 and \arccos(r)=\cos(\tan(r))=0.01371006057.

\cos(\csc(x)): 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 r=\arcsin(\tfrac{1}{\pi})=\mathrm{arccsc}(\pi)=0.323946106932 and \cos(\csc(r))=-1

(3) Hyperbolic trigonometric functions
\coth(x): converges to either \pm 1.19967864026 (solutions of the equation x= coth(x)) depending on the starting point.

\mathrm{sech}(x): 0.7650100

\dfrac{1}{\mathrm{arcsinh}(x)}: \pm 1.07293831517215 depending on the starting point.

(4) Exponential functions
e^{-x}: 0.5671433; remarkably this is \mathrm{W}(1), where \mathrm{W}(x) is the function discovered by the polymath Johann Heinrich Lambert, in the 1700s. This value can be computed using the below definite integral:

k= \displaystyle\int_{-\pi}^{\pi}\log\left(1+\dfrac{\sin(x)}{x}e^{\tfrac{x}{\tan(x)}}\right) dx

Then the fixed point of the exponential function, \textrm{F}(e^{-x})=\dfrac{k}{2\pi} \approx 0.5671433 \cdots latex

FP12_expdecay_complexFigure 12. Number of iterations for convergence of functional iterates of e^{-x} or divergence to \infty

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

2^{-x}: 0.64118574450499; comparable behavior as above in the complex plane. The closed form for this fixed point can be derived from the Lambert function: \textrm{W}(x):

\displaystyle \textrm{W}(x)=\dfrac{1}{2\pi}\int_{-\pi}^{\pi}\log\left(1+\frac{x\sin\left(t\right)}{t}e^{\frac{t}{\tan\left(t\right)}}\right)dt

Then the \textrm{FP}(2^{-x})= e^{-\textrm{W}(\log(2))}

e^{-\tan(x)}: 0.54522571736464

FP13_gaussianFigure 13. Number of iterations for convergence of functional iterates of e^{-x^2} or divergence to \infty

e^{-x^2}: the attractor 0.652918640419 is the solution to the equation x^2+\log(x)=0. We can again find a closed form for this fixed point using \textrm{W}(x):

\textrm{FP}(e^{-x^2})= e^{-\frac{\textrm{W}(2)}{2}}

In the complex plane, all points within the fractal boundary (Figure 13) converge to the same attractor at different rates or diverge to \infty (white regions). It is interesting to see that one of the convergence contours recapitulates the curve y=e^{-x^2} reflected about the real axis (Figure 13).

\dfrac{1}{e^x-x}: 0.7384324007018

\dfrac{1}{(e^x-x)^2}: 0.63654121332649

FP14_1bylogofxsquared_complexFigure 14. Number of iterations for convergence of functional iterates of \tfrac{1}{\log(x^2)}

\dfrac{1}{\log(x^2)}: 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.

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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 \beta-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, \beta Lyrae and \delta 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 \approx 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 \beta 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.

ecl.bin_AlgolFigure 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 M_\odot (solar masses) and 2.90 R_\odot (solar radii); the dimmer star is of spectral type K2IV of 0.81 M_\odot and 3.5 R_\odot. An approximate depiction of an Algol-like system is shown in Figure 2.

algolFigure 2. An Algol-like binary system

Figure 3 shows the TESS light curve of \beta 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 \delta Pictoris a \approx 4.72 magnitude star near Canopus.

ecl.bin_beta_Lyrecl.bin_Delta_PicFigure 3. Light curves of \beta Lyrae and \delta 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 \delta Pictoris (with a bit of sharpness) is in between the EAs and a full-fledged EB like \beta 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.

beta_LyraeFigure 4. A \beta 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.

ecl.bin_W_UMaFigure 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).

WUrsaMajorisFigure 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.

ecl.bin.01_Kepler_EB_L.curvesFigure 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 \lambda Tauri and the EB \delta 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.

ecl.bin_VSX_per.ampFigure 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 \approx 0.62 then the stars are typically EAs. A morphology parameter greater than \approx 0.62 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.

ecl.bin_gbulge_per.ampFigure 9. The period amplitude diagram for the Milky Way galactic bulge colored by the morphology parameter (categories: 0 \le x \le 0.25 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 \ge 0.75, we start seeing the emergence of two populations belonging to distinct period bands.

ecl.bin_Kepler_per.morphFigure 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 \le 0.66. However, for values \ge 0.66 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.

ecl.bin_bulge_per.morphFigure 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).

ecl.bin_bulge_morphdistFigure 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 \delta Pictoris like EBs and the higher one closer to \beta 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).

ecl.bin_Rus_SpectypeFigure 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 \beta 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 \beta 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).

ecl.bin_bulge_col.perFigure 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 (\le 0.5), 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).

ecl.bin_Kepler_Per.TempFigure 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 m_1, m_2; \; m_1 \ge m_2 in the x-y plane with the origin in rectangular coordinates, (0,0), 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 a to be a unit distance. This yields its dimensionless coordinates as (1,0). Then the magnitude of the position vectors to a point on this x-y plane from the two stellar centers will be:



We define the stellar mass ratio: q=\dfrac{m_2}{m_1}

Then, the distance of the center of mass C of the two stars from the origin will be:

\dfrac{m_2}{m_1+m_2} =\dfrac{q}{1+q}

Thus, the coordinates of C would be (\dfrac{q}{1+q}, 0)

The gravitation potential \phi at a point on the x-y plane is specified thus:

\phi= -G\left (\dfrac{m_1}{s_1(x,y)} + \dfrac{m_2}{s_2(x,y)} + \dfrac{(m_1+m_2)r(x,y)^2}{2a^3} \right)

Here, G 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 C: here r(x,y) is the magnitude of the position vector from C and a is the distance between the centers of the two stars. Since we have already set a=1, i.e., taken it as the distance unit, and computed the coordinates of C, we write the equation of \phi after factoring out \dfrac{m_1+m_2}{2} in a dimensionless form in -G\dfrac{m_1+m_2}{2} units on the x-y plane as:


With this equation, we can plot the Lagrangian equipotential curves for k a given potential value (Figure 16):


Euler_LagrangeFigure 16. The Lagrangian equipotential curves for an Algol-like system with the five Lagrangian points.

The (x,y) for which the equipotential curve first takes on a real value, i.e., it appears as just two points, define the two Lagrangian points L_4, L_5. 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 L_3 (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 L_2. 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 L_1. 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, L_1-.L_5, 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 x values for which the gravitational forces cancel each other yielding L_1, L_2, L_3 (Figure 16):


The inner loop of the equipotential curve defining L_1 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 L_1 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.

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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.

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.

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.

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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.
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 ॥

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 ।