samarA~NgaNa marsha

khaT phaT jahi !
In the tales of Sherlock Holmes many a time the great narrative of Dr. Watson could see the light of day only after a long silent interlude. Even so perhaps the whole history of the great struggle will be narrated only in the future. For that the only person who can be the narrator should remain alive at the conclusion of the story. Hence, there are some stories which never have an ending. With such thoughts we wondered how it might be possible to send the signal even if we were to be sent to vaivasvata’s domain. Three past statements came to mind: 1) The learned Acharya before going on the southward path had said: “All my vidyA-s will become divided among you all. Each with some, but none with all.” 2) When we stood there before the greatest of the great indra, he said: “Chose the choice of mArkaNDeya. There is glory in it but only one who lives the life of mArkaNDeya can complete it” 3) pretty mAnasikA said: “You will hear me call you on the night of the turning of the 9th year of the decade of that mAnusha yuga. A grAhI of the terrible kind would have seized you then. You would turn back to look who called but you will see no one.”

I continued walking on that weary path after mAnasikA made that statement. After having gazed at pita dyauH with our Aptavarga we shook off that above-said grAhI by a great yAga where we saw the thunderer as the eagle. We kept walking on that path. When PM was routed for his final journey by the abhichAra of Fourier of maNgala-grAma we were seized by the second grAhI.

The abhichAra-s of Fourier had probably gone with him. It was prayoga against the “secular ari”. Much had happened between the great strike of the durNama, a terrible piShAcha and a vile mohini at mid-night. Those events will form part of the great narrative if comes to pass. It was a quite night and we had just rebuilt our fort which had smashed to smithereens by the ari. Suddenly we sighted the troops of the duShTA trailing us. With the usual taskara-like slyness, they slipped through our defenses to take a stab at us. We had placed a decoy that they promptly pummeled with all their hate. This gave enough time for our dUra-dR^iShTi prayoga to detect their line of action. They had broken through our second wall in the mean time. We knew where the kR^ityA was by then. We immediately reacted from our secret fort and carried out an immediate uchChATana on her. While retreating she however placed two valaga-s against us and was lying in wait in the nest. We invoked vinAyaka to protect us against her and escaped to the northern nest. Seeing this she retreated to the southern lair. We feared the strange Apya-valaga that she had placed right in the path – we are still a bit puzzled why it was still unbroken after so many hours.

khaT phaT jahi !

Posted in Life

Mhasvad: The lost western chAlukya-s and the exploits of kAla-bhairava

In the halcyon days, when our knowledge of chAlukyan history was still sketchy, we were seated on the parapet at the foot of the vAnara hillock and yarning away after having cut a monotonous zoology lecture. It is for these pleasures of life I am still thankful to the much maligned Indian education system (imagine if this could ever have been done in the structured and over-bearing American education system). With us were shANDilya and shUdra-shreShTha to whom I was expressing my idea of finding an old chAlukyan outpost in the hamlet of Mhasvad (pronounced mhAsvAD). S and SS had taught me an important lesson in life- enjoy pleasures when you can for who knows when they might go away and you fall head-long like nahuSha or yayAti. S and SS immediately suggested that we should make a trip to Mhasvad and check things out. SS who knew precisely how to manage such adventures suggested that rather than taking a direct bus we should couple it with a visit Satara and then proceed to Mhasvad (all part of the ancient chAlukyan kingdom). As per SS’s plans we set out precisely timing our dinner at Satara and then catching sleep and proceeding the next morning to Mhasvad in an eastward flourish on the Satara-Pandharpur road. The hamlet is located on the banks of a shallow river the mANga~NgA, which empties into the bhIma.

The large temple of Mhasvad is a historian’s delight. It was built during the rule of Shahu by funds provided by the Maratha ruler to a certain bALoji dubaL a local chieftain. It is clearly built atop an older larger temple complex. Ruins of a temple from this older complex are seen immediately in front of the current temple. In front of these ruins we noticed a slab with a nearly 1000 year old image of shiva riding a horse and battling an asura. Even in the current temple the image of bhairava is one where he rides a horse with a huge sword. We were reminded of the opening mantra of the shUlagava ritual to rudra, where rudra is invoked charging on a white horse. In the current temple’s AvarNa we noticed a slab with an inscription in Kannada script. Epigraphic Indica provided a translation of the same: In 1138 CE the kalachUri king bijjala from Mangalvedha who was a vassal of the chAlukya king jagadekamalla of Kalyani gave a brahmadeya grant of to a brAhmaNa of the kapi gotra (pravara R^iShi-s named) to provide daily naivedyam and upachAra for the li~Nga of siddheshvara which was housed in the original temple [The belief is that the current li~Nga is the same as that of the original siddeshvara. Even today numerous local people, including tribals and nomadic herders still remember and fervently worship the shiva of this shrine as shidoba]. The place is described as a mahiSha-vADA or a buffalo pen in the inscription, mentioning that it was surrounded by 12 smaller herder settlements. The modern temple had certain shUdra priests who perform services for most of the visitors to the shrine.

There a small shop sold a certain “sthala-mAhAtmyaM” which was printed in a vulgar Maharatti. The mAhAtmyaM had some interesting stories not found in any canonical purANa:
“Originally the place was in the uninhabited daNDakAraNya. There a terrible demon name mahiShAsura lived. He was killed here by mahAlakShmI in the famous battle (devI mAhAtmyaM) and the place came to be known as mahiSha-vADA. Then in the vicinity a new asura succeeded mahiSha. He was shoNita-daitya, grew uncontrollably in size and caused great terror. From shiva emerged a terrifying being — his name was kAla-bhAirava he first descended in kAshI on the banks of the real ga~NgA and he then traveled as a nAtha mendicant to appear in the buffalo hamlet on the banks of the mAN-ga~NgA. He held a trident and a Damaru. Here rudra told him that he would not be able to kill the demon unless he lived the life of a householder and followed the norms of life. He agreed and asked where he could find a wife. rudra told him that in pAtAla lived the venomous serpentiform viShNu—shesha-nArAyaNa, whose daughter siddha-yogeshvarI would be a suitable wife.

So kAla-bhairava set off to pAtAla in the quest of his bride. The road to pAtAla was supposed to be a journey on land to Andhra followed by a descent through a hole there to pAtAla. As he was journeying to Andhra he came across two fierce goddesses – mArI (mArI-AI in the vernacular) and jagadambA (yelamma-AI in the vulgar Maharatti). They said this young fellow needs help. So mArI gave the bhairava a stone and asked him to throw it at his enemies and jagadambA gave him a kerchief to wipe his face if he ever felt he was dying. Taking these he went to pAtAla. There he was confronted with the ajagara hordes of shesha-nArAyaNa. After a fierce fight with them he was hard pressed when he threw the stone of mArI at them. They were all scattered by it and ran away from sheshanArAyaNa’s abode. The kAla-bhairava declared to shesha that he wanted shesha’s daughter, yogeshvarI (jogu-bAi in the vernacular). shesha first asked him to first sit down and eat. shesha bit into the food before serving kAla-bhairava. Upon eating the food kAla-bhairava felt dizzy and thought he might die, but he remembered jagadaMbA’s kerchief and wiped his face with it. On doing so the poison of shesha was countered and he was fine again and asked for yogeshvarI. sheshanArAyaNa said he could get her if he could enter a rocky chamber, with no doors, inside which she lived. Hurling his trident and shattering the rock he got in and was dazzled by the appearance of siddha-yogeshvarI. He asked her to reduce brilliance and when she did so he married her. Now that he was married he could pursue the job of killing the daitya.

This frightful bhairava arrived on a horse and attacked shoNita-daitya. After a fierce fight the asura was pierced in the chest by a trident of kAla-bhairava. The wrathful bhairava then struck his head off with his sword. Hence, they worshiped the terrifying bhairava there as siddheshvara, holding the asura’s head. The bhairava asked for a reward from the deva-s for his service. The deva-s and the great goddess Adi-mAyA-shakti promised that they would institute a kalasha to worship kAla-bhairava from the pratipad to the dvAdashi of the kArttika shukla pakSha.”

The mAhAtmyam added that the bALoji who built the current temple was a descendant of the chAlukyas from brahmApurI (Karhad) further south. He used to come to Mhasvad repeatedly to worship the bhairava there. He decided to build a temple for the image in the ruins of the old shrine. The temple was finally completed by his son. Near the temple there was an old vIra-kal showing a daNDanAyaka who was killed in the defense of young ladies who were being abducted by the marauding tribes. We wandered further up and found another little river coming in to join mANga~NgA. We could not find its name. On its bank were a cluster of shrines. There was one to sheshanArAyaNa (locally called nAgoba), one to kAla-bhairava (with a sword, trident, a shield and a skull-bowl, accompanied by a dog) and uniconic rocks to yelammA-AI and marI-AI. There we saw another large stone slab with a remarkable relief of kAla-bhairava and siddha-yogeshvarI, both wielding bows and hunting a boar and antelope with a pack of dogs.

The original bhairava worship under the kalachUris and chAlukyas was during the height of the royal patronage to other mantra-mArga shaiva-s in addition to the siddhAnta shaiva-s. After the decline of the chAlukya-s there was a period of cattle raids before the yAdava-s restored a semblance of order. The destruction of the yAdava-s by the Islamic assault was followed by a brief revival under the Kalyani chAlukyas who bravely resisted the army of Islam. But the terrible Jihad of the Bahmanid’s in 1469 under Khwaja Mahmud Gawan devastated the chAlukya-s and destroyed their strongholds and temples, returning most of the Mhasvad region to forest. But, strikingly the memory of their old shrine seems to have remained in the descendants of the chAlukya-s in maharAShTra who rebuilt this temple after Islam was rolled back from the region. That is the origin of the modern temple. East of Pune there is another place Sonari, where shoNIta-daitya is also said to have been killed, where an aShTa-bhairava temple is seen. Again it was rebuilt in the Peshva period after an older chAlukya shrine was destroyed by the Moslems. It retains the 8 fold symmetry of the old temple and there are different bhairava-s like asitA~Nga and ruru in the niches, but the local devotees or priests know nothing about the 8 bhairava-s of mantra-mArga. While the old deities survive, the bhairava of mantra-mArga seems to have passed from the rahasya-s of mantra-mArga shaiva shAsana to the folk religion of the local shepherds and goatherds who replaced the original buffalo breeders of the region.

Posted in Heathen thought, History

The guNa-s of sAMkhya as physical concepts

See also:
Elements of sAMkhyan theories of atomism and consciousness in early Hindu thought
The case of AchArya vArShagaNya

A pervasive element of Hindu thought is the concept of the tri-guNa-s. Their use is common in colloquial discussion: food might be classified in terms of guNa-s or even people might be categorized based on their dominant guNa. The same tri-guNa terminology might also be used to describe other abstract entities such as organismal behavior, moral qualities of a person or properties of material. The concept of tri-guNa-s while intuitively grasped by a Hindu is a very fluid in terms precise definition. Despite its pervasiveness in modern Hindu discourse its origins lie in the late- and post- vedic developments leading to sAMkhya thought. Because of the imprecise and intuitive understanding of guNa-s in general usage there has been much confusion amongst many modern students of Hindu thought when the guNa-s are used in the context of technical ancient literature. In course of my study of the sAMkhya-yoga system, I became increasingly aware of this issue.

Amongst modern Hindus one of the first to correctly grasp the technical meanings of the guNa terminology was the scholar from va~Nga, Brajendranath Seal. He correctly saw that the early sAMkhya thinkers considered guNa-s to be not just “qualities” but real physical concepts. That this was the original understand becomes clear from the vyAsa-bhAShya. In explaining the sUtra 3.44 of pata~njali the VB clearly explains each term of the sUtra as an increasingly basic description of matter – evolute of the original prakR^iti. The VB telling uses atypical descriptors for the 3 guNa-s, namely khyAti, kriyA and stithishIlA. These terms along with the context clearly imply that guNa-s of sAMkhya were physical concepts. The sattva (=khyAti) in the most mysterious in modern terms by a distinctive feature of sAMkhya – it might be taken to mean “information” or that aspect of matter that responds to/interacts with the puruSha (of sAMkhya) or consciousness. rajas (=kriyA) is energy and tamas (=stithishIlA) is mass. That these were viewed as physical entities becomes assumes great significance in the context of a sAMkhyan conservation principle guNa-s. In its formulation this principle resembles the modern physical conservation principle of mass/energy. This is provided by the vyAsa bhAShya in the commentary on sUtra 2.19 of pata~njali:
visheSha-avisheSha li~Nga mAtra-ali~NgAni guNa-parvan ||
VB: guNAstu sarva dharmAnupAtino na pratyastam ayante na+upajAyante | vyaktibhir eva-atIta-anAgatavyaya-AgamavatIbhir guNa-anvayinIbhir upajananaapAyadharmakA iva pratyavabhAsante |
“Though guNa-s go through all kinds of transformations/evolution (*anupAt) they are neither destroyed nor created. They appear to as if they had properties that come into being and disappear on account of the various forms of matter formed by the guNas past and yet to come (i.e. the forms of matter) those come and go out of existence.”

As mentioned above the vyAsa- bhAShya in describing the guNa-s clearly conceives them as the basis of matter. When we take that with above explanation in the context of sutra 2.19 it becomes apparent that the vyAsa-bhAShya is implying the physical conservation of guNa-s. Some points of note are: 1) The word dharma here is used in conjunction with the word “anupatinaH”. In technical Sanskrit this word is used to imply arithmetic progression or a series. So what is meant by dharma are the states of matter that form via the sAMkhyan transformation or evolutionary process from the guNa-s of prakR^iti to the paramANu-s of the bhUta-s. 2) In this light the word vyakti in the next sentence implies the various manifestations or forms of matter/energy. Thus, the sAMkhyan statement of the principle of conservation parallels the modern physical principle: “Matter+energy is neither created nor destroyed; it is only transformed from one form to another”. Is this explanation provided the bhAShya and its physical interpretation as presented above compatible with the original content of the sUtra of pata~njalI? It strongly appears this is the case because the vyAsa bhAShya does consistently show a close understanding of the sUtra text. While the sUtra text is hard to render in a modern language, it does seem the bhAShya is very much in the right context. We can with some trepidation render 2.19 thus: “The evolutes of the guNa-s [which are the basis of matter] are particular and unparticular, which are differentiated and undifferentiated [matter].”

As far as I know the saMkhya statement is the most sophisticated statement of the conservation principle in the ancient world. Amongst the Greek equivalents of the Hindus Thales had a conservation principle but it was much less sophisticated as far as I can see.

Posted in Heathen thought, History, Scientific ramblings

The case of AchArya vArShagaNya

It is extremely common for ancient Indian AchArya-s to remain mere names, with little if anything else known about them. As a result their dates and biographies are subject to wild speculations and debates. Such debates, often spearheaded by White indologists and their oriental imitators, show a general tendency to mistrust Hindu sources, obfuscate matters and apply an ad hoc system of decisions to decide whether someone is early or late. It would seem that their general their rule of the thumb is to provide as late dates as possible for most Hindu sources, and try to make it appear that most philosophical development happened after the Buddhists or the contact with the Greeks.

One Acharya of considerable interest in the development of Hindu thought is vArShagaNya, the great proponent of the sAMkhya-yoga school. He could perhaps be credited with being the first to formulate a version of the law of conservation of mass (energy) and thus becomes an important individual in the history of Hindu science. He is cited as an ancient authority in the vyAsa-bhAShya on the sUtra-s of pata~njali. vAchaspati miShra suggests that he as the author an ancient sAMkhya text termed the ShaShThI-tantra from which the vyAsa-bhAshya draws its citations. In the least it is certain that in discussing sUtra-s of pata~njali the commentator vyAsa had access to a text by vArShagaNya. He is also mentioned in a commentary named yuktidIpikA on Ishvara-kR^iShNa’s kArika-s as a prior authority of sAMkhya.

Multiple Chinese sources also describe vArShagaNya as an authority of the sAMkhya school. One of these is the Indian Acharya paramArtha who settled in Nanjing, China (around 550 CE) and composed a biographical work on the philosopher vasubandhu of the kaushika gotra from school of puShpapura (modern Peshawar in the Islamic Terrorist state). In this work he states that the great sage of the sAMkhya school was vArShagaNya who was king of the nAga-s living at the base of the Vindhya mountains. His student vindhyavAsa reworked and revised the sAMkhya doctrine and composed a collection of shloka-s containing this revised version of sAMkhya. He participated in a philosophical debate with the bauddha AchArya buddhamitra in Ayodhya, presided over by the king vikramAditya. vindhyavAsa routed buddhamitra in this debate and as result won a great reward from king vikramAditya and thus brought the ascendancy of sAMkhya. It was in order to counter vindhyavAsa that the bauddha-s rallied under vasubandhu to compose the polemical work paramArtha-saptati against sAMkhya.

The chInAchArya Hsuen-Tsang’s student Kuei-chi considered the positions of the sAMkhya theorists as the pUrva-pakSha in defending the bauddha mata. Here, he mentions that the chief sAMkhya teacher was a certain ba-li-sha in chIna-bhAShA, which meant “rain” in deva-bhAShA. His followers were known as the “rain-host” (which would be a Chinese translation of varSha=rain; gaNa=host). Their chief work is supposed to have been some thing called the hiraNya-saptati, which was used in debating against Indian bauddha Acharya-s who were the teachers of the chIna-s.

Thus, the available Chinese and Hindu material clearly indicate that vArShagaNya was a major sAMkhya teacher who had influenced the course of its development.

paramArtha mentions that buddhamitra was vasubandhu’s teacher. Now the White Indologists and their fellow travelers concluded that since vArShagaNya was a teacher of vindhyavAsa, vArShagaNya should have in turn been a senior contemporary of vasubandhu and place him at around 350 CE. This claim has since accepted and used over and over again to date vyAsa bhAShya, the yoga-sUtra etc. However, this claim when examined closely has problematic issues and arises from the indological habit of accepting certain traditional presentations as facts over others, to suit the late dates typically favored by White Indologists.
1) The Chinese work of paramArtha is clearly mythologizing vArShagaNya- it calls him the king of the nAga-s. 2) It calls buddhamitra as the teacher of vasubandhu during vikramAditya’s reign. But this is contradicted by the accounts of Hsuen-Tsang and Kuei-chi who state that vasubandhu was brAhmaNa manoratha’s student and do not establish a direct connection between the bauddha Acharya defeated by the sAMkhya-s and vasubandhu. 3) paramArtha skips from vikramAditya to bAlAditya in his narrative (around 470 CE) suggesting his account of gupta chronology was contrived. 4) The Chinese sources also conflate the hiraNya-saptati with the kArika of Ishvara-kR^iShNa – something for which we have no evidence from any Indian source. In conclusion we see 1) the general sketchiness of paramArtha’s narrative from the historical viewpoint, 2) its variance from other chIna sources, and 3) the tendency of both paramArtha and Kuei-chi to mythologize vArShagaNya, though to different degrees. Thus they can hardly be used to conclusively anchor the date of vArShagaNya to the exclusion of evidence from all other Indian textual sources.

In the Hindu sources vArShagaNya is associated with the tradition of the sAmaveda. There was a major sAmavedic redactor of that name who is mentioned in the jaiminIya gR^ihya sUtra, and there might have even been a shAkha of the sAmaveda (or sub-school of jaiminIya) by that name. The vaMsha brAhmaNa of the sAmavedic tradition provides his full name as sushravas vArShagaNya and places him as a student of prAtarAhna kauhala. A certain vArShagaNya is also referred to in bharata’s nATya shAstra as the founder of a technique of discharging a weapon. The most important mention of vArShagaNya is in the mahAbharata (vulgate/Ganguli edition 12[shAnti parvan].319). The specific context of his mention is notable: Chapters 12.302-12.316 (vulgate) contain an elaboration of different forms of sAMkhya thought – including some of the high points of Hindu thought, namely early formulations of the evolutionary theory of life. This is followed by chapters 12.317-13.320 that delve into yoga. The yoga presented here (12.317), while brief, is definitely related to the presentation in pata~njali’s sUtra-s. It mentions the prANAyama, the eight limbs of yoga, the attainment of siddhi-s and the state of samAdhi. However, it is important to note that there is no mention what so ever of pata~njali. Instead in the subsequent chapter (12.319) in a brahmodaya between yAj~navalkya and the gandharva vishvAvasu we are given a list of yoga-sAMkhya teachers, which includes the name vArShagaNya, along with other sAMkhya teachers like kapila, jaigishavya and pa~nchashikha but not pata~njali. This, together with the general indication of the epic sAMkhya preceding the classical sAMkhya, suggests that pata~njali, unlike kapila, was a later figure and was systematizing in his sUtra-s the yoga already presented in the epic. It also shows that vArShagaNya was an early pre-pata~njali teacher of the sAMkhya-yoga school rather than a senior contemporary of vasubandhu of the abhidharma.

In all likelihood given vArShagaNya’s mention in the Mbh, he was a pre-bauddha teacher of an atomic sAMkhya theory. Perhaps this also explains why the vyAsa bhAShya is termed so. It was probably based on a sAMkhya text of vArShagaNya associated with the mahAbhArata and thereby vyAsa. Hence, it could have inherited that name, although it is entirely possible that the author was simply named vyAsa and conflated with the Epic author (e.g. vAchaspati in his commentary calls the yoga-bhAShya’s author veda-vyAsa). Ultimately, in all accounts it was the followers of his school who revised the original teachings of vArShagaNya that the bauddha-s debated, rather than vArShagaNya, consistent with him being earlier than the dates of those debates.

We may reconstruct the following from the prior discussions the following relative temporal series:
vedic brAhmaNa authors->(yAj~navalkya and his school)-> kapila-> pa~nchashikha-> jaigishavya and vArShagaNya-> pata~njali-> vyAsa of bhAShya + other members who follow vArShagaNya school-> Ishvara-kR^iShNa (classical sAMkhya)-> gauDapAda-> sha~Nkara-> vAchaspati mishra

The four following the vedic brAhmaNa authors, along with the parallel tradition of the bhR^igu smR^iti, constitute the saMkhya of the mahAbhArata. We would place all AchArya-s prior to Ishvara-kR^iShNa as being before 400 CE.

Posted in Heathen thought, History

Elements of sAMkhyan theories of atomism and consciousness in early Hindu thought

I was told by some pious modern Hindus attached to advaita thought that I was either a strange case of a “Westernized Hindu” (!) or an “atheistic scientist (what ever that was)” to express such a proclivity for bhUta-chaitanya-vAda (or at least qualified bhUta-chaitanya-vAda) as I have done before. On being prodded by them I had to point out that I accepted the shruti (in particular the brAhmaNa portion) to have a diversity of thought, rather than being a monolithic authority. Perhaps, on this very point I lost some of them. Keeping with the spirit of this diversity of thought in the brahmavAda of the shruti, I had to point to the rest that I definitely favored certain ideas over others. This apart, I was questioned about whether there was any evidence for ideas of atomic thought (of the sAMkhyan or vaisheShikan kind) and bhUta-chaitanya vAda in the shruti itself. In this regard I would like to point to my interpretation of particular teachings from the shAnkhAyana AraNyaka 6.19 and 7.21, kaushItaki upaniShad 3.5 & 3.8 (~=>shAnkAyana AraNyaka 5.5 & 5.8) and KU 4.19 of the R^igvedic tradition:

In SA6.19 and KU4.19 (both of which narrate the same tale) the kShatriya teacher ajAtashatru the kAshi-rAja teaches the brAhmaNa scholar gArgya bAlAki regarding the nature of the consciousness of a person. ajAtashatru makes a striking statement about where the consciousness is localized at the time of the deep sleep state: “The vessels named hitA extend from the heart to the pericardium. [Here] they from a capillary bed of 1000 slender hair-like branches. They contain molecules of orange, white, black, yellow and red. In these [molecules] the [consciousness] is localized when he has no dreams.”

In his teaching to the king of kAshi, pratardana daivodAsi, the god indra presents an early version of the sAMkhya theory (KU 3.5 & 3.8 ~=>SA 5.5 & 5.8). While these paragraphs are simply constructed, their true purport is very difficult to grasp for the modern mind. In essence the first paragraph delivers a sAMkhya model stating that an explanation will be provided as to how every bhUta becomes one for the consciousness (praj~na). The paragraph describes 5 j~nAnendriya-s, 5 karmendriya-s and the manas as particular entities that feed information into consciousness. Now the indriya-s and manas in turn receive their signals from corresponding external particles they recognize [The word used in the shruti for these particles is bhUta-mAtra, a precursor of the more widely known word tanmAtra used in saMkhyan atomism]. In the subsequent paragraph (i.e KU 3.8 or SA 5.8) it is stated that molecules constituting the stimuli and the molecules corresponding to the receptors (in the 5 j~nAnendriya-s, 5 karmendriya-s) are inter-connected in such a way that (the information exchange of) their interaction/correspondence is necessary condition for conscious experience.

Then there is the teaching of the great vAlishikhAyani (SA 7.21). He states that all is made up of combinations of the 5 elements akAsha, vayu, jyoti, ApaH and pR^ithivi. These elements in turn are made up from the combinations of minute atoms.

Thus, we notice that various elements of atomic thought, especially of the sAMkhya type, originate in the vedic brahmodaya. Most importantly these early vedic presentations while supplying several of the major elements of the full-blown sAMkhya seen in the Great Epic is distinct from it. In it vedic version we sense a clear tendency towards an “particular” or “atomic” explanation for consciousness. Unlike the classical bhUta-chaitanya-vAda of the chArvAka-s, we do not exactly encounter the claim that consciousness is directly the interactions between the particles (molecules) –this argument faces the same problems as the modern issue of the “hard problem” of consciousness (vide Chalmers). However, the vedic expositors had a collection of views that saw: 1) consciousness as being a distinctive entity, which, however, did have direct association and interaction with particles (elementary particles or molecules) 2) consciousness as appearing to intimately depend on this interaction for the production what is termed the conscious experience. 3) The interaction between sensory systems and the stimuli as a purely “molecular” process which in itself was not the consciousness (i.e. the conscious experience).

The imprint of the above-mentioned vedic ideas on classical sAMkhya and its twin yoga is very apparent. yoga right from it vedic antecedents was always linked in terms of “world-view” to sAMkhya, which was emerging as the dominant theoretical frame to explain the origin of existence. One striking example from the classical period of yoga was the expansive work on the yoga-sUtra-s of pata~njali – its original commentary the vyAsa-bhAShya [Footnote 1]. The vyAsa bhAShya extensively uses the sAMkhya framework in order to explain the sUtra-s of pata~njali. In the commentary to the sUtra 3.44 [on the “subjugation” of matter by the yogin] the vyAsa-bhAShya provides an introduction to sAmkhyan atomism.

sthUla-svarUpa-sUkShma-anvaya-arthavattva saMyamAd bhUta jayaH || YS 3.44

The vyAsa bhAShya explains that sthUla is the bulk matter, which in turn in made up of an assembly of molecules or atoms – denoted by the term svarUpa in the sUtra. The VB does consider that bulk matter might be made up of combinations of the same or different types of molecules or atoms. But the molecule (or atom) is the smallest indivisible entity bearing the attributes of the gross substance – hence, he says pata~njali terms it svarUpa [ayuta-siddhAvayavaH saMghAtaH sharIraM vR^ikShaH paramANuriti | ayuta siddhAvayava-bhedAnugataH samUho dravyaM iti pata~njaliH ||] Beyond the molecules/atoms VB proposes that the tanmAtra-s exist – these are sub-atomic particles that tend not to exist on their own but tend to only exist as conjoined together to constitute the atoms. VB states that this is what is implied by the term sUkShma of the sUtra [atha kimeshAM sUkShma rUpaM? tanmAtraM bhUta-kAraNaM | tasyaiko .avyavaH paramANuH sAmAnya visheShAtmA .ayuta siddhAvayava bhedAnu gataH samudAya ity-evaM sarva-tanmAtrANy-etat-tR^itIyam |]. Further, the VB explains that the basis of all matter lies in the 3 guNa-s that are described as khyAti [information], kriyA [energy] and stithishIlA [mass], which in the saMkhya theory are the primary evolutes of prakR^iti [evidently these 3 guNa-s are descriptive physical terms for what are usually referred to as sattva, rajas and tamas]. This is what in the sUtra is denoted as anvaya. Finally, the sUtra has the term arthavattva. This term, the VB explains, corresponds to consciousness, which it says is inherently linked to the guNa-s. The guNa-s are inseparable linked to the tanmAtra-s which form the paramANu-s and their combinations that form all substance. Hence the consciousness inherited by these evolutes of guNa-s.

It can be seen that vAlishikhAyana’s theory of atoms, the bhUta-mAtra-s in indra’s teaching and their link to consciousness have all been inherited and elaborated into the atomic model of classical sAMkhya thought.

Another important idea that might derive from the vedic idea of the division of time (kalA-muhUrtA-kAShTha etc.) is that, like matter, time also exists as quanta. The vyAsa bhAShya explains this in the context of the commentary to sUtra 3.52 of pata~njali [kShaNa tat kramayoH samyamAd vivekajam j~nAnam |]. The VB states:
yathA .apakarSha-paryantam dravyam paramANur evam paramApakarSha-paryantaH kAlaH | kShaNo yAvatA vA samayena chalitah paramANuh pUrva-desham jahyAd uttara-desham upa-sampadyeta sa kAlah ksaNah ||
Just as the “atomic particle=paramANu” is the irreducible unit of matter, so also the kShaNa is the irreducible unit of time. Indeed, the time taken by a moving paramANu to leave origin and reach the next unit space in the coordinate system is defined as a kShaNa.

The advaita vedAnta darshana (despite constantly positioning itself as the true successor of vedic thought), increasingly tended to view things differently – especially so amongst the modern vedAntavAdin-s. Now, this is a subtle act of internal doctrinal subversion without really breaking with old allegiances in the ritual sense. sha~Nkara began by the process by taking up the yoga-sUtra-s for producing a commentary which moved yoga in the direction of vedAnta away from its sAMkhya moorings. The predecessor of sha~Nkara, gauDapAda, wrote a commentary on the sAmkhya kArika-s of Ishvara-kR^iShNa where he presents the concept of the dyvANuka (“diad atom”), suggesting that lineage of sha~Nkara might have had sAMkhya affinities to start with. Of course a similar process was at hand with respect to the core vedic material (i.e. the upaniShad-s as also the domain of pUrva mImAmsa).
[Footnote 1]This is a detour from the above discussion and deals with the issue of authorship of the vyAsa-bhAShya. The name vyAsa bhAShya has been taken by many later authors to mean a bhAShya by vyAsa, the author of the original mahAbhArata (or jaya) and the original purANa saMhitA. vyAsa is also considered by the vedAntins to be the same as bAdarAyaNa, the promulgator of their sUtra-s – the brahma sUtra-s. Vedic tradition starting from the aruNa section of the taittirIya AraNyaka and the subsequent lists of prior textual redactors in yajurvedic sUtra texts (E.g. hiraNyakeshin gR^ihya 2.7.2) mention the original vyAsa kR^iShNa dvaipAyana. Thus, he is of considerable antiquity. The earliest major yoga texts are found in the mahAbhArata- they appear to belong to the layer of the bhR^igu redaction of the Great Epic. The yoga systematized by pata~njali is a successor of this earlier yoga of the Mbh and the vyAsa bhAShya follows it. Thus, the vyAsa of the VB was definitely not the same as the original kR^iShNa dvaipAyana vyAsa, but someone else. His thinking shows affinities to the sAMkhya and vaiSheshika thought seen in the medical saMhitA-s like that of sushruta and charaka and he was known to sha~Nkara. More specifically he appears to have followed the works of the great early sAMkhya-yoga AchArya vArShagaNya (possible author of ShaShThI-tantra and the first proposer of the law of conservation of matter (energy)), whose ideas he cites. This would make vyAsa of the Vb one of the vArShagaNya school of sAMkhya mentioned by the chInAchArya Kuei-chi and the Indian brAhmaNa paramArtha who was an adviser to emperor Wu in Nanjing, China (Mid 500s of CE). As per their accounts the members of the vArShagaNya school of sAMkhya had beaten the AchArya-s of bauddha yogAchara in great debates in the city of Ayodhya about 150 years ago. Now, the chIna authors were aware of the sAMkhya kArika-s of Ishvara-kR^iShNa and they were translated into chIna-bhASha by paramArtha by mid-500 CE. This meant that Ishvara-kR^iShNa was definitely before 550 CE and given the history of debates with sAMkhyans recorded by the bauddha-s was probably at least around 400 CE. The vyAsa-bhAShya has no knowledge of Ishvara-kR^iShNa’s kArika-s while mentioning various older authorities. Thus we can be sure that this vyAsa was after pata~njali but before ishvara-kR^iShNa (thus mostly before 400 CE) Beyond this we have little specific information to pinpoint vyAsa’s identity and the time of composition of this bhAShya.

Posted in Heathen thought, History, Scientific ramblings

Construction of the geya-chakra

The geya-chakra of saMgIta-yoginI

Very few good specimens of the geya-chakra of shrI-vidyA are currently available. There are a few historical yantras of shyAmalA available and they are often inaccurately drawn. However, I happened to obtain access to see some pristine forms that were prepared in vArANasi and nepAl. These versions clearly indicate the symmetries and the geometric ideas involved. As per the tradition of the mantra-mahodadhi of the medieval tantric mahidhara, we also have evidence that the yantra of sa~NgIta-yoginI was congruent to that of mAta~NgI in the dasha-mahAvidyA series.

Like the shrI-chakra the geya-chakra encodes the Golden ratio rather extensively, even if more directly: It has an innermost golden triangle of the shrIchakra type which makes contact with the inner pentagon of a pentagonal star polygon. This star polygon of course encodes the Golden ratio in the construction of its sides with respect to the pentagon in which it is inscribed. The pentacle in turn is inscribed within a circle which in turn is bounded by an aSTha-dala padma and a ShoDasha-dala padma. They are all enclosed within a square bhUpUra. The entire construction as shown above can be achieved using a compass and straight-edge. Such a construction was performed using C.a.R. to generate this ideal representation of the yantra.

Posted in art, Heathen thought

The Ara and the Arbelos

When I was young, I was fascinated by the blade held by the clobber and the way in which he plied it in fixing shoes and slippers. This blade (Ara in saMskR^ita) had a special shape and I realized a weapon like that was held by some of our deva-s. There was an Indian arrow that had a head much like this tool. Much later, I learnt of the great yavanAchArya Archimedes having studied a curve derived of 3 circles that he named the Arbelos or the clobber’s knife. Obviously he was meaning the same object apparently still in use in leather-work. I wondered if the proto-Indoeuropeans or at least the common ancestor of the Hindus and Greeks had a common device like that (Arbelos and Ara) used in leather work. The Arbelos fascinates mathematicians and laymen alike, and I was no exception to it. I simply wished to relive my journey through the Arbelos – perhaps relive a fantasy of the halcyon days of my childhood. Many fascinating properties of the Arbelos are apparent even at sight:

The most obvious being that the perimeter of the upper boundary of the curve = perimeter of the lower boundary because: d=d1+d2; pi*d/2=pi*(d1+d2)/2;

The hemichord formed by the shared tangent of the two smaller semi-circles is indicated by T. It is the geometric mean of their respective diameters: T²=d1*d2

Further, the area of the Arbelos (A) can be expressed independently of the 3 radii of the semi-circles using just the value T: A=pi*T²/4; thus, the area of the Arbelos is the same as that of a circle with diameter T. this is obvious from baudhAyana’s (Pythagoras) theorem and that any angle inscribed in a semicircle is a right angle.

There are many other interesting properties of the arbelos that have made it a fertile object of investigation in Euclidean geometry over the ages. Even the great geometer Jakob Steiner worked on its properties, like the issue of Pythagorean triplets in the chain of circles. Even in the past 100 years it has been a source of rich new results. One of the most famous features of the arbelos from ancient Greek mathematics concerned the chain of circles inscribed within it. The first circle (K1) in this chain is a tangent to all the 3 semicircles of the arbelos. The next K2 is a tangent to K1 and two of the other semicircles. In this chain of circles the height of the of the center of Kn from the base line is equal to n*dn, where dn is the diameter of Kn. The centers of K1-Kn lie on an ellipse whose foci are the centers of the two semicircles that bound the chain. If the ratio of the diameters of the two smaller semicircles of the arbelos (d1/d2) is rational then the following is observed:
The right triangle formed by the center of Kn, the center of the largest semicircle of the arbelos and the foot of the perpendicular dropped from the center of Kn to the baseline has sides forming a Pythagorean triplet. This chain of circles can be constructed using the method of reflection of points on a circle. Here the reflecting circle is of radius=d and it reflects the right line as the largest semicircle, the left parallel line as the second largest semicircle and the first semicircle bounded by these two lines as the 3rd semicircle of the arbelos. All other inscribed tangential circles are reflected to form the chain.

The family of circles – Archimedean twin, the Bankoff circle and the quadruplet are shown.

Finally there are the famous Archimedean twin circles of the arbelos, which are the tangential to the largest semicircle, either one of the two other semicircles and the segment T. Archimedes showed that these two circles are congruent. Strikingly, numerous other congruent circles come up all over the arbelos, and their discovery and properties has formed a major area of modern studies on this figure. One of these discovered by Bankoff, a rich dentist who was an amateur mathematician: One takes the following 3 points- 1) & 2) the two touches by the first circle of the chain of inscribed circles on the smaller two semicircles of the arbelos. 3) the point where the two smaller semicircles of the arbelos touch. Then one draws the circumcircle of these points. It is congruent to the Archimedean twin circles.Another more recently discovered quadruplet of the family is described thus: Take the perpendiculars from the centers of the smaller semicircles of the arbelos and let them intersect the semicircles at A and B. Draw the lines from the center of the biggest semicircle of the arbelos to the A and B. Then there are two circles passing through each of these points which are tangential to each other and the lines from the former sentence, which are also tangential to the biggest circle to the arbelos. These two pairs of circles form a quadruplet which is congruent to the Archimedean twin circles.

Posted in Scientific ramblings