symmetric icon attractors

•April 10, 2007 • Leave a Comment

For several years we have been fascinated by the symmetric icon attractors popularized by the physicist Sprott. The above attractors discovered by Golubitsky and Field gain their symmetry because of the step r=(x+i*y)^n, where n is an integer power. Thus they spread the xn+1 and yn+1 values over the imaginary plane resulting in symmetry decided by the power n. The z-value is not used in the calculation of x and y so it appears rotationally symmetric around the z axis.

The last Arya

•April 10, 2007 • Leave a Comment

Through the corrupt gramophone recording we heard the voice of Kareik, the last devlole of the Kalash, reciting the ancient hymns of dishani, bhagiShT, sutarem, imra and mahandeu. These were recorded by Morgenstierne in 1929 and five years later the devalole was dead and with that the oral tradition of the Kalash was lost. Several decades earlier the Kalash had already faced the death blow from the Jihad of Abd-ar-Rahman, the murderous Ghazi from Afghanistan. Per say there was nothing new in the event — Islam and the cult of Jeshua ben Yusuf had annihilated, and were to continue annihilating, numerous religions and cultures of the world. Yet, there was something in this that struck a chord in us. We heard some time back from both Sh and Hayasthanika that the pArShu-s were reduced to a tribe and amongst them those maintaining the oral Avestan tradition were on their way out. These people were our Indo-Iranian sister groups, their religions and deities homologous of ours. Despite bearing head on blow from Islam they had survived this long due to the innate resilience that characterizes our ancestral culture. But the effects of time could not be overcome and they were on the path of extinction. We, last of this great superior tradition, were the next in line and are seen sliding down that path. The vedic shAkhas being denuded, simultaneously attacked by the two Abrahamisms, we seem like a pretty Hindu girl surrounded by unwashed, bearded Meccan ruffians.

Why have we reached this condition ? Some parasitoid wasps inject polydnaviruses into their host and with that they lose their ability to mount a immune response on the inserted wasp larva. This is what has happened to Hindu society because the Hindu immune surveillance has just failed to recognize the parasites. The prolix Balagandadhara of Ghent’s researches provide data to visualize this problem.

In the samarA~NgaNa

•April 8, 2007 • Leave a Comment

The news reached that our most skilled senAnI had captured the fort of amukhAsthika after a very fierce and prolonged struggle. In the thick of battle with shara-s raining all over it was not known who was friend or foe, but in the end he held his cool and we routed our foemen. At that point we turned our attention to personally lead the forces against a fort that had for long kept slipping from us, though we had planted our flag on that parvata before our foes. But even as we were closing into to make a large attack on it, our skilled senAnI sent us a messenger that the young commandant who had fought with great distinction on the battle of shulbAri hala had been ambushed by a combine of our most dreaded shatru-s who possessed a large force. Our young commandant panicked greatly. But our senAnI tried to calm him down and asked him to remain bold on the field. We saw the grim advance of our hated bhrAtR^ivya and spent a sleepless night wondering over the battle plan. We drew our battle plans and to protect the front manned by our young commandant, when we faced another unexpected attack. The abhichAraymAna-s had earlier slowed us down with a dreaded attack, which is another story in itself. Now they incited the khANDavans into a rebellion. Just before we set forth for the other front we were probed by the khANDavans and spent a while in a prolonged skirmish. While we drove them away ,like the bhR^igus driving away dIrghajihvI, they were resorting to mitra-bheda to try to break up our allies. Suddenly we found ourself under a massive alignment of our enemies, all hoping that we never see the sun again. We turned to maghavan to confer victory on us.

Some considerations on Hindu atomism

•April 8, 2007 • Leave a Comment

tanIyAMsaM pAMsuM tava charaNa pa~NkeruhabhavaM
viri~nchiH saMchinvan virachayati lokAn avikalam
vahaty enaM shauriH katham api sahasreNa shirasAM
haraH saM-kShubhyainaM bhajati bhasitod-dhUlana-vidhim || (saundarya lahari 2)

Minute particles have arisen from the dust of your feet,
gathering these together brahmA constructs the orderly universe,
viShNu with his thousand heads verily holds these,
hara in destroying the universe splits these apart and smears himself with them as ash.

The learned kaivalyAshrama, the late medieval tantric guru from an orthoprax maTHa in the southern Konkans, in his commentary on the saundaryalahari clearly explains this shloka as describing the paramANus as emerging from the feet of tripura-sundarI and being used by the trimurti in their loka-kAryam. In his commentary mentions how the fundamental particles the paramANu-s combine to give rise to the basic aNu combinations like dvyANu-s and tryANu-s. This is consonant with the mantra prayoga of this shloka — mastery over the knowledge of all matter or nature (Long back while studying this shloka I was inspired by ShoDashikA that great mistress of the kula path, flanked by sa~nketA and sachiveshI).

In my opinion, one of the pinnacles of Hindu thought, along with pANini’s study of language are the vaisheShika sUtra-s of kaNAda. The vaisheShika thought in its pristine form was largely dead in the later days of Hindu thought. Yet, it was the beginning of physics in India, and the foundation of a very productive line of addressing the universe. To us (this a very personal view) vaisheShika is the best of the darshana-s for a veda-practicing AstIka in the context of modern knowledge. Many Hindus are unable to grasp the significance vaisheShika. We believe that vaisheShika is a prelude to scientific thought and not just a metaphysics. Thus, a “modern darshana” that an AstIka can follow without a contradiction in Weltanschauung would build from the base of vaisheShika, just as medieval Hindus built on early vaisheShika thought (e.g. vAchaspati mishra). Sadly many early works of the pristine vaisheShika period are now lost. It was once a great challenge to the nAstIka-s who expended their efforts to undermine or co-opt it.

Some early lost vaisheShika works are preserved in citations of nAstIka-s in their debates against the AstIkas. One example is given by paramArtha (499-569 CE), an AchArya who traveled from bhArata to the land of the chIna-s to teach darshanas and translated a number of works from Sanskrit to chIna-bhASha. In one such, the lakShaNAnusAra shAstra, he describes vaisheShika, albeit mistaking certain points. He gives an account of tIrthaka, a successor of prashastapAda, on the universe, which in broad outline agrees with the idea that saundaryalahari 2 has as its background: 1) The universe has two kinds of saMvarta-s (end or dissolution) — the antara saMvarta and the tejaH saMvarta. 2) The former saMvarta occurs at the end of each kalpa comprised of approximately 10^10 years, the total life of the universe being roughly 3*10^10 years. 3) The first kalpa is known as the tapah kalpa (the period of heat), the second the the jala-kalpa (the period of liquid) and the third the vAyu-kalpa (the period of gas). 4) At the end of each kalpa all matter is dissolved into the constituent paramANu-s (fundamental particles of vaisheShika) and exist in state of disjunction. 5) At the beginning of each kalpa the paramANu-s combine due to the unseen forces (as kaNada states) and produce aNu-s that grow larger in size to produce the entire universe. 5) The consciousness and mind are conjoined or separated when atoms do the same. 6) After three rounds of tejah saMvarta one coming at the end of each triadic universal period the universe lapses into a state of pure disjoint paramANu-s and consciousness.

A certain parallel with jaimini’s sUtra-s and the vaisheShika sUtra-s exists suggesting that their authors belonged to a common intellectual tradition (i.e. successors of the veda):
athAto dharma jij~nAsA | (MS1)
athAto dharma vyAkhyAsyAmaH | (VS1)
both mean the approximately same (jij~nAsA= inquire into or vyAkhyAsyAmaH – explain) and are clearly distinguished from the inquiry into brahman or yoga or causes of sorrow or principles of logic.
chodanAlatho artho dharmaH | (MS2)
yato.abhyudaya niHshreyasa siddhiH sa dharmaH | (VS2)
The constructs are very similar between mImAmsa and vaisheShika, but the former declares that the veda’s prescription is dharma. Whereas, vaisheShika declares that one that produces abhyudaya and niHshreyasa is dharma (Note that there two distinct terms used and not mokSha. Much after the pristine vaisheShika faded away, later authors thought that these terms were related to mokSha of vedAnta).

tasya nimitta-parIShTiH | (MS3)
tadvachanAd AmnAyasya prAmANyaM | (VS3)
Here again the two darshana-s probably imply similar (not same) things: The mImAmsaka-s seem to mean (going by shabara svAmin): examination (of veda) is proof of that (dharma).
The aNuvAdins state: authoritativeness rest with that vedas because it is a declaration of that (dharma).

So of all darshana-s these are the two that directly express their intent on dharma and its vedic roots. [As an aside- Since the tathAgata and his successors wanted to subvert precisely this, namely dharma, they used the same term dharma and tried to give it an entirely different meaning. It is not a big surprise that the initial conflicts of the bauddha nAstIka-s was precisely with these two darshanas (e.g. buddha attacking uruvelA jaTila kAshyapa).]

We observe that vaisheShika thought is present in the bhArata and the purANa-s. In the former it is seen in the lecture of the great kShatrIya woman sulabhA prAdhAnI during the discourse with the king of mithilA. In the purANa-s, for example the bhagavata purANa, it appears in the lecture of maitreya. However, unlike sAMkhya (yoga) and in the much latter paurANic milieu, vedAnta, neither mImAmsa nor vaisheShika are discussed in their technical details in these texts. Again, chANakya only mentions sAMkhya, yoga and lokAyata, suggesting the former two were the “popular” philosophies that were seen as successors of the upaniShadic philosophical speculation. Both mImAmsa and vaisheShika instead appear to have arisen in a specialized setting of vedic ritualists (ironically bauddha nAstIka-s also later arose in this setting), but assumed very different paths despite certain similar foundational concepts.

Many philosophers have noted the points of divergence of mImAmsa and vaisheShika after a similar opening of their darshana sUtra-s. vaisheShika is not interested in the two prime issues of mImAmsa: 1) The veda being by its very nature valid. 2) The eternal existence of the veda. While not bothered about these issues, in the very last sUtra-s (adhyAya 10, Ahnika 2), kaNAda stresses the authoritativeness of the veda. Then both vaisheShika and mImamsa agree upon a critical point: There is no creator for the universe and there is no Ishvara. The universe is entirely a result of combination of the fundamental particles and the sole agent for their combination is karma. Finally, mImAmsa depends heavily on the position that sound is eternal, and this is connected with its world view of the apauruSheyatva of the veda. kaNAda examines the possibility of the eternality of sound and then rejects it. To me in addition to the above positions, it is this position on sound that makes vaisheShika an over all superior philosophy of all the hindu systems.

If the opening stress on dharma and the closing stress on the veda is an important feature of vaisheShika, then the question arises as to its specific vedic antecedents if any. The use of vaisheShika terminology in charaka’s medical treatise is an important pointer in this regard. In charaka, vaisheShika is heavily overlayed by the “populist” saMkhya thought. It is possible that in the yajur-vedic school of charaka and kaThas arose the early formal vaisheShika which continued to linger on the later medical treatises produced by the former school. [Of the kR^iShNa yajurvedin-s the kaThas appear to be closest to the charakas. The brAhmaNa of the kaTha-s preserved now as the terminal brahmaNa of the kAThaka section of the taittirIya-s has a mImAmsa on the chyana with different metals, like gold, silver, lead etc. It is in this context that the paMsu-s (atoms) are mentioned.] An important corollary to this use of vaisheShika thought by the charaka-s is that vaisheShika actually served as a proto-scientific naturalistic base in hindu analysis of nature’s phenomena. The charaka-s saw that vaisheShika theories provided a reasonable frame to understand chemistry of substances, and there by determine the behavior or particular substances in the animal body or guide the deployment of particular substances in therapeutics.

That vaisheShika theory was principally meant as a system of proto-scientific explanation is seen in its application within its tradition starting from kaNAda. udyotakAra following the tradition used it to explain refraction of light. udayana used it to explain how heat from the sun was the ultimate source of all earthly heat stores. bhaTTa jayanta used it to explain photo-chemical reactions. It also influenced the great nAstIka intellectual, the jaina umAsvati who incorporated the vaisheShika concept of saMyoga, vibhAga in the form attractive and repulsive forces between paramANu-s and aNu-s.

In conclusion it might be said that the ancient Hindus had in vaisheShika a proto-scientific frame work whose important features included: 1) The absence of a creator for the universe or an Ishvara as the cause of the universe; 2) The construction of the universe through the combination of fundamental particles paramANu-s- “atoms” to give rise to “aNu-s” molecular particles. 3) The particle nature of light and heat. 4) An explanation of natural phenomena using molecular and atomic particles and a small set of basic physical forces. 5) karma chiefly implies physical forces and force itself has a particle nature. 6) The mind is molecular in nature. 7) consciousness is not per say “non-material” but associated with matter- perhaps as a distinct particle or as a “property” of a particle, perhaps like charge.

But going by later Indian thought and modern Hindus it is clear that this naturalism has been receding to the background. In this context, I have been puzzled by certain observations: I believe that the majority of modern Hindus believe in Ishvara as the cause of the universe or are creationists of different grades. Some may restrict themselves with seeing the universe’s cause as the Ishvara, others may see all the diversity and complexity of nature as a sign of Ishvara. Yet others may believe in the special entities like the sUkShma sharIra transmitting their pApa-s and puNya-s from one sthUla sharIra to another and so on. Majority of Hindus using the Abrahamistic terminology say they believe in God and even go through some effort to say that they are not polytheistic but actually believe in one basic God. Many Hindus and particularly Hindu vedAntic achArya-s do not accept evolution of life by natural selection. Is all of this because of Abrahamistic subversion of their thought alone? Or is it because they have been pre-conditioned for this mental state due to their separation from old vaisheShika and sAMkhya thought?

I feel that it might be a combination of both factors. If this were so it is disappointing that Hindus have actually lost their intellectual rigor and are no longer philosophically innovative as their predecessors.

At this point the learned jaina muni-s bhuvana-vijaya and jambu-vijaya must be acknowledged for their tremendous services to the AstIka-s. A proper text of the vaisheShika sUtra-s had been hard to get in modern times, in part due to the above reasons. muni bhuvana-vijaya obtained pristine manuscripts of the vaisheShika sUtra-s along with a commentary of chandrAnanda (~700-800 CE) from a jaina manuscript collection in jaisAlmer, rAjasthana. His son jambu-vijaya carefully edited the text to provide a reliable version of the vaisheShika sUtra along with chandrAnanda-s commentary. chandrAnanda cites the veda-s and purANa-s showing his wide knowledge of Hindu lore in general. My teacher knowing my proclivities pointed to me to chandrAnanda’s commentary and its importance in grasping the vedic milieu in which vaisheShika arose.

Iran and middle eastern conflict

•April 7, 2007 • Leave a Comment

“And so these men of Indostan
Disputed loud and long,
Each in his own opinion
Exceeding stiff and strong.
Though each was partly right,
All were in the wrong.”

Thus, as John Saxe had elegantly stated, most people debate about the Middle East. For those who believe they have seen the elephant itself, a very important test for several geopolitical scenarios in the coming years is going to be the conflict between Moslem Iran and the Jews (not Americans). Ultimately, any one with common sense knows that Israel is the strongest of the Middle Eastern states. For all their talk the Arabs are pretty useless in war. The Americans easily defeated them in the invasion of Iraq, but committed the fatal mistake of trying to occupy them in the modern world. Israel has also learned the hard way that occupation of Arab territory is not at all an effective strategy in the long term. Anyhow, Israel has effectively neutralized the Arab threat to its *existence* unless it commits demographic suicide (Like Hindus might in India). But Iran is another claimant for the position of hegemon of the ME, though it is far from actually going nuclear. So a conflict between the Jews and Iran is almost inevitable and both sides know this fully well, and are taking steps. The Jewish action so far is subtle and covert, while Iran has been loud and open. Yet, I suspect this loudness of Iran is not really comparable to the Arab loudness (like that of Saddam; the Arabs got the take home message with his recent lynching). Iran probed Israel using the Hezbollah, which was the first sign that they might actually have a sting to back the claws. Is Israel going ever respond with an attack like that on Osirak? This is a very interesting point to get an answer on. But our feeling is that the Jewish strategy is going to be different this time. I believe it is important for Hindus to observe this carefully, especially given that Israel is a notable arms supplier for India and has cooperated in some areas of military intelligence.

kAmandaki on viShNugupta and chandragupta

•April 6, 2007 • Leave a Comment

yasyaabhichAra-vajreNa vajra-jvalana-tejasaH |
papAta mUlatash-shrImAn suparvA nanda parvataH ||

ekAkI mantra-shaktyA yash-shaktyA shakti-dharopamaH |
AjahAra nR^i-chandrAya chandraguptAya medinIM ||

nIti-shAstraamR^itaM dhImAn arthashAstra mahodadheH |
samuddadhre namas-tasmai viShNuguptAya vedhase ||

darshanAt-tasya sudR^isho vidyAnAM pAradR^ishvataH |
yat-ki~nchid-upadekShyAmaH rAja-vidyA-vidAM mataM ||

By the vajra-like abhichAra of the one who shone like the flash of the vajra, the opulent mountain of the nanda-s fell root and branch.
Who alone with his ministerial power [pun on mantra power] , which was like the power of the wielder of the shakti [skanda], conferred the earth on chandragupta, the moon amongst men.
The one who churned out the nectar of political wisdom, from the vast ocean of state-craft, to that wise viShNugupta our salutations.
From the great work of that man, who had explored the limits of knowledge, we are going to extract and teach in brief the lore, as promulgated by the knowers of state-craft.

Our link to asura varuNa

•April 1, 2007 • Leave a Comment

ajIjano hi varuNa svadhAvan-natharvANaM pitaraM deva-bandhuM |
tasmA u rAdhaH kR^iNuhi suprashastaM sakhA no asi paramaM cha bandhuH || AV-S 5.11

From father bhR^igu we have acquired that connection to the great asura medhira. As kavi atharvA had said to varuNa: we have walked the 7 steps of friendship and thus become connected. When atharvan desired to know that which lay beyond the rajas he asked varuNa, for the asura is the knower of that which is “paro rajasi” (kavi atharvan asks: “kiM rajasa enA paraH ?). When bhR^igu desired to acquire supreme knowledge he went to father varuNa (bhR^igur vai vAruNiH | varuNaM pitaram upasasAra |). The wise asura answered : “annaM prANaM cakShuH shrotraM mano vAcha miti | tagM ho vAcha | yato vA imAni bhUtAni jAyante | yena jAtAni jIvanti | yat-prayanty-abhi-saMvishanti | tad-vijij~nAsasva |…”
These words inspired the founder of our clan in the quest for knowledge and they are what we continue to seek. These words of the Aditya are the ones that set us on the path of knowledge. When our ancient clansman shunaHshepa stood bound at the stake, facing certain death, with harishchandra dying in pain from the jalodara, he invoked the all-seeing Aditya:
“ava te heLo varuNa namobhir ava yaj~nebhir Imahe havirbhiH |
kShayan-nasmabhyam asura prachetA rAjan-nenAMsi shishrathaH kR^itAni ||”

We have this bond (paramam cha bandhuH of atharvan) with varuNa to which we turn. When over-powered by the abhichAra of the foemen, with our enchanting yakShiNi-s all dispersed, struck down by roga like harishchandra, we turned to rajan varuNa. We sought him like our ancestors who knew the veda did. We besought him of a 1000 snares to release us from the grip of the pAsha in which we were. The great god has bore us aid when we invoked him with his great mantra from the pit of suffering in which we were.
” bibhrad drApiM hiraNyayaM varuNo vasta nirNijam | pari spasho ni Shedire ||”


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