pA~ncharAtrika vaiShNava elements in the astronomy textbook sUrya-siddhanta and other notes

When it comes to astronomy, more than any other field, the white indologists and their Japanese apers have sought to show Hindus as frauds or idiots (of course, nowadays they cushion it in all manner “sophisticated” jargon, such as “Indo-Moslem scientific collaboration in pre-modern South Asia”, etc) [Footnote 1]. Everything worthwhile in our old astronomy is attributed to Mesopotamians, Greeks and more recently the Chinese (incidentally, we are supposed to have learned about 0, yes about nothing, from them). The 4th book of the dEnkart, informs us that Sassanian emperor kShayathiya-puthra-I (shapur-I) in 250 CE collected books on astronomy, grammar and time-keeping from the Hindus and the megale-syntaxis (Almagest) of Claudius Ptolemy from the Greeks for his library. This illustrates that, at least in the eyes of the Iranian court, it was not just the yavana-s but who also the Hindus who had something useful to contribute regarding astronomy. One of the early textbooks of Hindu mathematics is the sUrya-siddhAnta, which has been at the center of much controversial attention of the mlechCha-s. We are told that it contains incontrovertible evidence for the enlightenment of the Hindus by the yavana-s, alternatively we are informed that it is a rather inferior piece of science. But the few people have investigated the history of this text as it survives from the viewpoint of a Hindu insider, for whom it marks the early tradition of trigonometry and geocentric astronomy. In Hindu tradition it appears after the siddhAnta of brahmA and before the Greek work of Paulos (paulisha siddhAnta); thus, technically it could contain a core of pre-yavana material. We outline below a few interesting features that have a bearing on the history of the text.

The text itself is presented as an interesting interlocution, as is typical of several shAstra-s, between sUrya and the asura maya. Pleased with the penance of maya, sUrya projects a being from his person (as he is very busy with his duties in the sky and too blazing to behold) who taught the asura astronomical lore. The text itself later informs us that the knowledge of astronomy and astronomical instruments is lost at the end of each kalpa and has to be regained from sUrya. Now the text begins thus:
achintyaavyakta-rUpAya nirguNAya guNAtmane |
samasta-jagadAdhAra-mUrtaye brahmaNe namaH ||

Salutations to the god brahmA, who has an inconceivable and unmanifest form, without guNa-s and also of nature of guNa-s, the form [i.e. hirANyagarbha] which is the foundation of the whole universe.

Thus, on the whole while this siddhAnta is a saura text, the opening ma~NgalAcharaNa is to brahmA. This is an important marker: brahmA, who emerged as a neo-ectype of vaidika prajApati towards the concluding phases of the Vedic period, became the focus of the brAhmaNa concept of a central deity. In this capacity of the central deity he inherits all the features of his vaidika manifestation, first outlined in the hiraNyagarbha sUkta (RV 10.121) and also serves as some kind of personification of the upaniShadic brahman. His centrality in the junction between the vedic and the epic period is seen in the form of of the brahma-yAga, a new ritual initiated in this time. This ritual is outlined in some depth in the AV parishiShTa 19, and includes the iconic, yantra and fire worship of brahmA as ordained by the bhArgava-s. This central position of brahmA is affirmed in the rAmAyaNa and some some degree in the mahAbhArata. The early purANa-s such as the core of the mArkaNDeya purANa also retain this preeminent position of brahmA. It is this brahmA, who is also seen as the personification of the brahman who is repeatedly attacked by the tathAgata and his immediate successors. Thus, there was a period of supremacy of brahmA, which certainly overlapped in time with the beginnings of the bauddha mata. After this period brahmA declined even within the Astika sphere and became secondary to the other two gods of the crystallizing trinity. Thus, we see the ma~NgalAcharaNa to brahmA as being a marker for a relatively early layer in the extant sUryasiddhAnta.

Examination of the sUryasiddhAnta reveals the imprint of yet another tradition, which was on the ascent in the post-Vedic period. In the 12th chapter maya asks sUrya to explain to him the geocentric model of the solar system and its orbital parameters. In answering him sUrya takes off on an unexpected detour that goes thus:

vAsudevaH paraM brahma tanmUrtiH puruShaH paraH |
avyakto nirguNaH shAntaH pa~nchaviMshAt paro .avyayaH ||

vAsudeva is the primal brahman whose primal form is the puruSha. It is imperceptible, unmanifest, without guNa-s, unperturbed and beyond the twenty five tattva-s.

prakR^ity antargato devo bahir antash cha sarvagaH |
sa~NkarShaNo .apaH sR^iShTvAdau tAsu vIryam avAsR^ijat ||

This god [vAsudeva] pervaded the prakR^iti from within, without and entirely, [and emanated] sa~NkarShaNa, who gave rise to the liquid element and emitted his seed into that.

tad aNDam abhavad dhaimaM sarvatra tamasaavR^itam |
tatraaniruddhaH prathamaM vyaktIbhUtaH sanAtanaH ||

That gave rise to a golden egg entirely covered in darkness. In that egg the eternal aniruddha first became manifest.

hiraNyagarbho bhagavAn eSha Chandasi paThyate |
Adityo hy AdibhUtatvAt prasUtyA sUrya uchyate ||

He [aniruddha] is called hiraNyagarbha in the Vedic recitations. Due to him being the first manifestation [of the universe] he is called Aditya, and as the universe emanates from him he is called sUrya (word play on Adi-> Aditya and pra-sU-> sUrya).

paraM jyotis tamaH pAre sUryo .ayaM saviteti cha |
paryeti bhuvanAn eSha bhAvayan bhUtabhAvanaH ||

This great light which dispels the darkness is sUrya also known as the god savitar. As sUrya he is generator of all the worlds and the cause for sustenance of life.

prakAshAtmA tamohantA mahAn ity eSha vishrutaH |
R^icho .asya maNDalaM sAmAny usrA mUrtir yajUMShi cha ||

This embodiment of light , the destroyer of darkness, he is well-known as the primal matter. His sphere [is identified] with the R^ik-s, his rays with the sAman-s and his mass with the yajuSh-es.

trayImayo .ayaM bhagavAN kAlAtmA kAlakR^id vibhuH |
sarvAtmA sarvagaH sUkShmaH sarvam asmin pratiShThitam ||

This great, auspicious deity [assumes the] form of time and is the maker of time. He is all-pervasive, moving in all ways, atomic and everything is established in him.

rathe vishvamaye chakraM kR^itvA saMvatsarAtmakam |
ChandAMsy ashvAH sapta yuktAH paryaTaty eSha sarvadA ||

He rotates the chariot wheel of the universe which is of the form of the year. The seven Vedic meters are yoked as his horses and thus he eternally revolves

tripAdam amR^itaM guhyaM pAdo .ayaM prakaTo .abhavat |
so .aha~NkAraM jagat sR^iShTyai brahmANam asR^ijat prabhuH ||

The indestructible 3/4th of him remains hidden, with the remaining ¼ generating the visible universe. He the lord having generated the consciousness of I and emitted brahmA.

tasmai vedAn varAn dattvA sarva-loka-pitAmaham |
pratiShThApy ANDa-madhye .atha svayaM paryeti bhAvayan ||

Having conferred on the grandfather of all worlds [brahmA] the boon of the veda-s, he installed [brahma] in the cosmic egg and himself illuminated it.

atha sR^iShTyAM manash chakre brahmAha~NkAra-mUrti-bhR^it |
manasash chandramA jaj~ne sUryo .akShNos tejasAM nidhiH ||

brahmA bearing the consciousness of I, [had the first person experience] of the thought of origination. From his mind was born the moon, and the sun the mass of light from his eyes.

manasaH khaM tato vAyur agnir Apo dharA kramAt |
guNaikavR^iddhyA pa~nchaiva mahAbhUtAni jaj~nire ||

From his mind sprung space; from space gas; from gas arose heat; from heat arose the liquid element and from it the solid element in order.

agnIShomau bhAnuchandrau tatas tv a~NgArakAdayaH |
tejo-bhU-khAmbu-vAtebhyaH kramashaH pa~ncha jaj~nire ||

The sun and the moon arose from agni and soma and thereafter the five planets arose from the five primal elements in order: heat/light->Mars; solid->Mercury; space->Jupiter; liquid->Venus; gas->Saturn.

punar dvAdashadhAtmAnaM vyabhajad rAshi sa~nj~nakam |
nakShatra-rUpiNaM bhUyaH saptaviMshAtmakaM vashI ||

The self-possessed [brahma] divided himself 12 fold to give rise to the rAshi-s and 27-fold to give rise to the nakShatra-s.

tatash charAcharaM vishvaM nirmame devapUrvakam |
Urdhva-madhyAdharebhyo .atha srotobhyaH prakR^itIH sR^ijan ||

Thus, through the combinations of the three streams of prakR^iti (3 guNa-s) he gave rise to the universe made of all the mobile and immobile entities filled with the gods.

guNa-karma-vibhAgena sR^iShTvA prAgvad anukramAt |
vibhAgaM kalpayAmAsa yathAsvaM veda-darshanAt ||

Thus having successively given rise to the various entities classified as per their properties and activities, he ordained the various divisions of the universe as in the Vedic tradition.

graha-nakShatra-tArAnAM bhUmer vishvasya vA vibhuH |
devAsura-manuShyANAM siddhAnAM cha yathAkramam ||

The great [brahmA] then ordered the planets, lunar constellations, other stars, the earth and the realms of the deva-s, asura-s, men and siddha-s in order.

brahmANDam etat suShiraM tatredaM bhUr-bhuvAdikam|
kaTAha-dvitayasyeva sampuTaM golakAkR^iti || SS 12.12-29

The universe is a void within which the earth, the atmosphere etc are situated is shaped like a sphere comprised of the fusion of two kaTAha-s (=Indian cooking vessels; colloquially called called kaDAhi).

What is of note here is the introduction of the theistic vaiShNava form of sAMkhya that is typical of the pA~ncharAtrika tradition. It is comparable to that observed in the proto-pA~ncharAtra narrated in the mahAbhArata. It describes the basic emanation from the primal vAsudeva of the vyUha-s culminating in aniruddha who manifests as brahmA in the primordial cosmic egg. This aniruddha is identified with savitAr who is primal manifestation of light. On the whole this emanational sequence described here is entirely consistent with that described in the mahAbharata even though pradyumna is not explicitly mentioned. Thus, it is rather clear that the sUrya-siddhAnta was redacted by the pA~ncharAtrika vaiShNava-s who were responsible for this section. When this section is compared with the initial ma~NgalAcharaNa to brahma it becomes clear that the pA~ncharAtrika-s did not seek to completely rework the shAstra – they merely sought to interpolate their material at points which they felt allowed an organic placeholder for their material. This interpolation should be compared with other comparable interpolations by vaiShNava-s in certain other non-sectarian works. As we have shown earlier, they appear to have introduced a mantra associated with the preparation of an agada termed the mahAgandhahasti in the chikitsAsthAna of the charaka saMhitA (23.90). There is also an interpolation into the R^igvidhAna of shaunaka, which is clear of vaiShNava origin and attributed to a certain viShNukumAra. In that the mantra verses containing the famous vaiShNava recitation beginning with the following are present:

jitam te puNDarIkaakSha namas te vishva-bhAvana |
namas te astu hR^iShIkesha mahA-puruSha pUrvaja || RVdh 3.33.174

This suggests that the vaiShNava interpolation might have even been pA~ncharAtrika in origin as this stotra is central in later pA~ncharAtrika tradition. Thus, there appears to have been a phase of vaiShNava/pA~ncharAtrika interest in the transition of a variety of non-sectarian texts into which were interpolated elements of pA~ncharAtrika worship. When exactly this happened is harder to establish in the case of the sUryasiddhAnta from the interpolation noted above. It does not show the more derived features clear in the later tantra-s and purANa-s, so it cannot be ruled out that it was from a relatively early layer of pA~ncharAtrika tradition.

But how does this go with the incontrovertible evidence for Greek influence? When we look at the text as we have it we cannot deny the presence of Greek words. For example:
-The word kendra (Gk:kentron) is used 5 times, but nowhere other than in chapter 2.
-The word koNa (Gk: gon = corner).
Now even the occidental indologists agree that sUryasiddhAnta does not contain material of Ptolemy’s megale-syntaxis so, at least its core, cannot be younger than around 150 CE when he lived. On the other hand the geographical section alludes to the ascendency of Rome (romAka) not the yavana-s in the west. So we get a window between the Roman conquest of Greece around 130 BCE to 150 CE. This window is fairly consistent with the sUryasiddhAnta’s pA~ncharAtrika elements being from the layer of the pA~ncharAtrika tradition that was already known to and adopted by some of the yavana successors of Alexander of Macedon prior to the common era (E.g. the Heliodorus garuDa pillar from 140 BCE).

On certain Hindu astronomical ideas in the sUrya-siddAnta
The presence of multiple layers in the extant sUrya-siddhAnta suggests that the presence of Greek words cannot automatically mean that all ideas therein are of Greco-Mesopotamian origin. The multiple redactions of the text imply that they could have been introduced later when the siddhAnta-s were consolidated by later naturalists like varAhamihira. The pA~ncharAtrika origin mythology positions itself as being founded upon vaidika origin mythology. This position is indeed valid because the ideas presented there are part of various traditions found in the R^igveda itself, such as in the hiraNyagarbha sUkta, puruSha sUkta, vishvakarmA sUkta (10.82) and nAsadIya sUkta. It should be noted that it clearly indicates a spherical universe with spherical earth. Now white indologists and historians of science have argued that the idea of a spherical earth emerged first in Greece perhaps due to their early sages such as Empedocles or Parmenides between 500-450 BCE and was solidified by Plato and Aristotle. From the Greek world it is supposed to have reached the Hindus after the Alexandrian conquest, who till then were flat-earthers. Thus, the spherical earth in the sUrya-siddhAnta is supposed to be due to Greek influence. This idea is plainly wrong. Long ago the great patriot B.G. Tilak had shown that the vaidika cosmography conceived the earth as spherical surrounded by the multiple rajas and not as a flat plane above which the sky was anchored. Further, some have argued that the vaidika cosmography saw the earth as a concave counterpart of the sky, based on the common refrain in the veda dyAva-pR^ithivI (the deities of the sky and earth). This has also been shown to be erroneous by Tilak who pointed out the veda clearly knows of space beneath the earth. The sphericity of the earth is alluded to in the secret language in the famous cosmographic sUkta of the RV (1.164) in R^ik 1.164.34-35. It is further clarified in the shatapatha brAhmaNa as:
ayaM vai loko gArhapatyaH | parimaNDala u vA ayam lokaH | (ShB
This world, i.e. the earth is the gArhapatya; this world is verily spherical. Any educated shrauta ritualist knows that he meditates on this statement while he installs the gArhapatya altar which is explicitly equated with the earth.
Similarly in ShB and the sun is similarly described as being spherical:
evaitad Adityam upadadhAti sa hiraNmayo bhavati parimaNDala |
asau vA Adityo hR^idayaM shlakShNa eSha shlakShNaM hR^idayam parimaNDala eSha parimaNDalaM |

Thus, it is clear that the spherical earth and sun was a concept among Hindus long before any later Greek influence on them. Hence, it is mention in the pA~ncharAtrika origin mythology in the sUrya-siddhAnta is not Greek in origin by simply a development of the vaidika thought. Further, in the veda it is clear that the earth is considered to be of finite size and much smaller than the universal sphere (expressed in R^ik RV 1.52.11). With this idea in place and combined with the notion of sphericity there is no reason that the Hindus did not independently seek to find the diameters of the Earth, sun and moon. Indeed, evidence for their independent attempts in this regard comes from the lecture of saMjaya to dhR^itarAShTra in the mahAbhArata 6.13.39-45 (“critical”). This so called bhUmiparvan which contains an early version of the much maligned paurAnic cosmography gives the results one of these early attempts of the Hindus. It presents a primitive planetary theory of eclipses with both the svarbhAnu (already found in RV 5.40.5 and tANDya brAhmaNa 6.6.8; also points to a tradition of astronomical observations of eclipses by the atri-s) and rAhu (already present in the AV-vulgate 19.9.9). Given that this theory falls out of vogue in the later more advanced siddhAnta-s, where the correct explanation had been discovered, and the fact that it uses the archaic vaidika term svarbhAnu, it is clear that it represents a pre-siddhAntic attempt to measure the diameter of the sun, moon and svarbhAnu. The svarbhAnu-rAhu theory with these diameters or the bizarre value of pi (~3.4) are not known from the Greeks who first attempted such estimates like Hipparchus or Mesopotamian sources. A continuation of the the same tradition of measurement is preserved in the brahmANDa purANa (BhP). Here the value of circumferences of the sun by its diameter acquires a more normal value of ~3. Thus, it establishes beyond doubt that there was a indeed an endogenous tradition of attempting to estimate planetary dimensions among the Hindus, which had a deeper history than what we know in this regard of the Greeks (they could very well have their own deep history that is now lost).

From the results of R. Balasubramanian we may take the sUrya-siddhAnta yojana to be 7.89 Km from which we get the sUryasiddhAnta planetary dimension parameters thus:
Moon diameter: 480 yojana-s=3791.1552 Km; Modern value: 3474.2 Km
Earth diameter 5000 yojana-s = 12488.21 Km Modern value: 12742 Km

sUrya siddhAnta M/E ratio 0.303
Aristarchus M/E ratio .317-.39
Ptolemy M/E ratio 0.292
Modern M/E 0.272

The white indologists inform us that the sUrya siddhAnta has definitely borrowed its Moon/Earth values from the yavana-s because they are close. We are told that till that point the Hindus were either flat-earthers, who stuck to an enormous number as the value of the earth’s length or that they had borrowed a huge radius from the Babylonians. It was Aristarchus who first derived the ratios using eclipse observations which he correctly interpreted as shadows. But Hindus had no clue that they eclipses were due to shadows but ascribed them to rAhu and ketu. While indeed the svarbhAnu/rAhu theory was the old one with which the Hindus began, it is clear that even within the realm of the svarbhAnu theory the Hindus were coming to realize that the postulated entities were actually made of shadows. This is apparent in the statement:
tulyas tayo.astu svarbhAnur bhUtvAdhas tAt prasarpati |
uddhR^itya pR^ithivIChAyAM nirmito maNDalAkR^itiH || BhP 1.24.101
svarbhAnu is equal in extant to both [the sun and moon]. It moves beneath them. It made out of the shadow of the Earth and has a spherical shape.

Thus, the Hindus had arrived at an understanding of shadows as the basis of eclipses within their own system, and could have corrected their theory regarding the dimensions of the earth without outside help. Looking at the above ratios we find that interestingly they do not match the range of Aristarchus and they are greater than that of Ptolemy, even if close. We do not have values of this type in any Babylonian source. So, rather than claim borrowing from an unknown Greek source, it is more likely that Hindu arrived at it by themselves.

Finally, we may consider the interesting issues of the planetary angular diameters provided by sUrya-siddhAnta and compare them to other estimates:

Planet sUryasiddhAnta Ptolemy Tycho Modern
Mars 2.0 1.57 1.67 0.4
Saturn 2.5 1.74 1.83 0.34
Mercury 3.0 2.09 2.17 0.16
Jupiter 3.5 2.61 2.75 0.8
Venus 4.0 3.13 3.25 1.05

What is clear is that all pre-modern observers way over-estimated their planetary diameters, illustrating the short-comings of the unaided eye. Ptolemy himself attributed these values to Hipparchus who is reputed to have said: “The sun is 30 times the apparent diameter of the smallest star and the diameter of Venus which appears to be the largest star is 1/10th the apparent diameter of the sun.” In his scheme Jupiter is 1/12, Mercury is 1/15, Saturn 1/18 and Mars 1/20 that of the sun. Now the white indologists hold that the Hindus again copied their angular diameters from the Greeks to present them in the sUryasiddhAnta. However, as we can see above the values of Ptolemy/Hipparachus, while following the same order as the Hindus, are very different. In fact the Hindu series is a far simpler one, with merely an increment of .5 per planet. We find no evidence for such planetary diameter estimates among the Babylonians or for any occurrence in the Greek world prior to Hipparchus. So just going by the sUryasiddhAnta and Ptolemy’s words either could claim priority. However, when we examine the more primitive Hindu model for planetary diameters provided in the BhP 1.24 we already see them reporting a system of planetary diameters in yojana-s:

Venus 1125
Jupiter 843.75
Mars 632.8
Saturn 632.8
Mercury 474.6

From this it is clear that the Hindus already had a tradition of planetary diameters and the new order reported in the sUryasiddhAnta could merely be an emendation of that older tradition.

While there is no doubt that the yavana-s and Arya-s participated in an interactive knowledge revolution over a prolonged period (which led to exchanges in medicine, various religious/philosophical traditions, astronomy and astrology) the presence of a clear non-Babylonian older tradition of the Hindus suggests that they were not simply plagiarists in the interaction. They are likely to have arrived at the idea of spherical planets with particular diameter entirely on their own.

Footnote 1: Below is a quote from an early American missionary indologist who collected Hindu astronomical texts: “It is now well known that Hindu culture cannot pretend to a remoter origin than 2000 B.C., and that, though marked by striking and eminent traits of intellect and character, the Hindus have ever been weak in positive science; metaphysics and grammar—with, perhaps, algebra and arithmetic, to them the mechanical part of mathematical science— being the only branches of knowledge in which they have independently won honorable distinction. That astronomy would come to constitute an exception to the general rule in this respect, there is no antecedent ground for supposing. The infrequency of references to the stars in the early Sanskrit literature, the late date of the earliest mention of the planets, prove that there was no special impulse leading the nation to devote itself to studying the movements of the heavenly bodies. All evidence goes to show that the Hindus, even after they had derived from abroad a systematic division of the ecliptic, limited their attention to the two chief luminaries, the sun and moon, and contented themselves with establishing a method of maintaining the concordance of the solar year with the order of the lunar months. If, then, at a later period, we find them in possession of a full astronomy of the solar system, our first impulse is to inquire, whence did they obtain it? A closer inspection does not tend to inspire us with confidence in it as of Hindu origin. We find it, to be sure, thoroughly Hindu in its external form, wearing many strange and fantastic features which are to be at once recognized as of native Indian growth; but we find it also to contain much true science, which could only be derived from a profound and long-continued study of nature. The whole system, in short, may be divided into two portions, whereof the one contains truth so successfully deduced that only the Greeks, among all other ancient nations, can show anything worthy to be compared with it; the other, the framework in which that truth is set, composed of arbitrary assumptions and absurd imaginings, which betray a close connection with the fictitious cosmogonies and geographies of the philosophical and Puranic literature of India.

In this context one may also see another American indologist Whitney’s comment in our earlier partial note on the vedA~Nga jyotiSha.

While one one might object that citing an old American missionary is anachronistic in this day and age of studies on “Pre-modern knowledge systems of India”, it is remarkable to note that Euro-American indologists in the tradition of Neugebauer, Witzel, Pingree and his successors, Minkowski, and the like essentially say the same thing in a sugar-coated fashion.

~ by mAnasa-taraMgiNI on May 2, 2012.

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