2 I NDIA AND THE W EST AND THE H ISTORY OF S OUTH A SIAN S TUDIES David Pingree (†) Mesopotamian and Greek Astronomy in India When Wilhelm Halbfass published his magisterial Indien und Europa in 1981, the full extent of the interrelationship between the astronomies of the ancient world were not yet widely known among historians (including historians of science) nor was the methodology used for establishing those interrelationships well understood. Halbfass, of course, is particularly in- terested in the mutual influences of Indian and European philosophy upon each other in the past two centuries, but he does speak about broader influences in earlier periods. In his chap- ter assessing India’s reputation for xenophobia Halbfass (1981: 209-210) also briefly refers to the Greek influence on the Indian exact sciences. In an attempt to enlarge upon my readers’ understanding of the theoretical basis, established by Neugebauer (1956 and 1957), for as- serting that a substantial interaction between India and the rest of Eurasia did take place over the long period from about 1000 BC till the present time, during which India was both a re- cipient and transmitter of scientific ideas, and to exemplify the results of modern investiga- tions into this broad field by detailing the progressive adaptation by Indian astronomers of ideas originally formulated in Mesopotamia and in Greece I offer the following paper. While all mankind has the potential to see celestial phenomena, to attribute specific meanings to them is an intellectual act that has been repeated many times in different ways in different cultures over time. This is clear from the differences between what, for example, Pharaonic Egyptians, early Sumerians and Akkadians in Mesopotamia, Ŗ gvedic Indians, the early Chi- nese, and the ancient Mayans described and failed to describe of what they saw in the heav- ens and what significance they gave to their observations. They did not start out with the same perceptions or the same interests so that one would not expect them to have eventually arrived at similar complex theories such as mathematical models for predicting certain peri- odic celestial events or theories of astral influences on human lives. Yet, while all five cul- tures eventually possessed some forms of mathematical astronomy, those of Mesopotamia (ca. 1500 BC - AD 100), India (ca. 1000 BC - AD 1900), and Greece (ca. 800 BC - AD 600) are closely interlinked by common parameters and mathematical models. Egyptian mathe- matical astronomy, on the other hand, is very limited in its scope and evidently modelled on Mesopotamian and Greek sources, while the Chinese is quite different, though in the first two millennia of the current era variously influenced by Western ideas, and the Mayan remained both limited in scope (their principle interest was in Venus and the Moon) and uncontami- nated by external influences. The historical development of astrology reinforces these distinctions and similarities between cultures with regard to mathematical astronomy. Its beginnings can be found in cuneiform texts of the last four centuries BC, but it achieved its classical form only when Mesopotamian concepts were combined with Aristotelian physics in about 100 BC. In AD 149/150 a Greek text on the resulting horoscopic astrology was translated into Sanskrit; it, and other transla- tions from the Greek, are the foundation of Indian astrology, though it was combined with other related ideas already present in Indian thought and, of course, its predictions were al- tered to fit the expectations of Indian society. From India, through Buddhism, it spread to the Far East, and from both Greece and India to Iran and elsewhere. However, it never appeared among the Mayans, though they were much interested in making predictions based on celes- Karin Preisendanz (ed.), Expanding and MerginG Horizons: Contributions to South Asian and Cross-Cultural Studies in Commemoration of Wilhelm Halbfass, Wien: Verlag der Österreichischen Akademie der Wissenschaften, 2007, pp. 41-50. 42 D AVID P INGREE tial events. For an exposition of this vision of the early history of astral omens and astrology see Pingree 1997. We know from our own experience that “scientific” and other ideas, no matter how complex, are often transmitted from one culture to another, though they may be altered to some extent in their transmission; the historical process is still going on. The history of horoscopic astrol- ogy gives us a model for how such transmissions occurred in antiquity. The proof in the case of astrology lies in the arbitrary nature of its assumptions, such as that there are just twelve divisions of the ecliptic, bearing the names of particular types of animals (including humans); that these twelve constellations are subdivided into four “triplicities” with three constellations in each; or that the seven planets (including the Sun and the Moon) are either benefic, ma- lefic, or neutral. All these arbitrary assertions are found in cuneiform texts, and are repeated in Greek, in Sanskrit, in Pahlavi, etc. Other elements – cardines, cadents and succedents, terms and the twelve astrological places for instance – were introduced by the Greeks, and can be traced through all their successors. No one could have come up with exactly the same arbitrary ideas independently; nothing that occurs in the perceptible world would have sug- gested them. Moreover, the Greek technical terms are simply transliterated into Sanskrit, which, of course, had no words for these foreign concepts; and the Sanskrit terms are found transliterated into Pahlavi, Arabic, Hebrew, Byzantine Greek, Latin, etc., marking a clear trail of continuous transmission from one culture to another. In mathematical astronomy the arbitrary elements are the mathematical models (they, of course, are not physically present, but are invented by individuals working within particular intellectual traditions in which certain approaches to mathematics are preferred) and the pa- rameters, that is, the numbers from which the mathematical operations begin. These parame- ters could not be directly observed; they were deduced from a large number of necessarily inaccurate observations (the ancients relied on unaided vision and had no instruments for keeping time accurately). A wide range of possible parameters had to be and were considered and used. Both the mathematical models and the parameters in any text, then, while restricted in range and derivation by the tradition to which the author belonged, were arbitrary both in the sense that neither has an observable existence and in the sense that any author could make alterations in either the mathematics or the numbers. Those who so altered their traditions, if they did it cleverly and persuasively, were those who advanced science. When, therefore, we find in an astronomical text of one culture mathematical techniques that can be shown to have been developed in another culture, we must feel that there is a strong case for transmission. If the mathematical model is used to solve the same or a similar prob- lem, we become more sure. Probability increases when it can be shown that the hypothesized originator is older than the hypothesized recipient. Greater certainty follows if the same pa- rameter is used. Absolute certainty follows the recipient’s use of a transliteration of one of the originator’s technical terms. Examples of all these levels of probative evidence exist in abundance. This method of investigation was brilliantly used by O. Neugebauer in his fundamental stud- ies between the 1920’s and 1980’s; I have referred previously to two of his summaries of the results he had reached by the mid 1950’s. Seldom is certainty possible in historical investiga- tions, but the careful use of these arguments combined with common sense leads to very per- suasive results – persuasive, that is, to those who take the trouble to understand the assump- tions and the methodology. Unfortunately, many contemporary scholars do not like the re- sults for political reasons; they mistakenly believe the methodology and its practitioners to be M ESOPOTAMIAN AND G REEK A STRONOMY IN I NDIA 43 Eurocentric, but rather it and they attempt to deflate the European assumption of uniqueness, and to show that the various cultures of Eurasia in science as in art, literature, and other dis- ciplines have mutually stimulated and influenced each other over several millennia, and that none of them, as was argued by Pingree (1992a), can justifiably lay claim to superiority. Within the framework outlined above, a hypothesis concerning a specific case of transmis- sion may be regarded as achieving a low or high level of probability depending on how many of the ranked criteria are satisfied. The hypotheses I have advanced concerning Mesopota- mian influence on Indian astronomy and omens in the last millennium BC meets, in my opin- ion, all the criteria except the last. Thus various elements of the cuneiform text called MUL.APIN ( MA ), which was composed in about 1000 BC on the basis of material some of which goes back to the middle of the second millennium BC, appear, as was shown by Pin- gree (1989), in relatively late Vedic texts such as the lists of twenty-seven or twenty-eight nak atras (cf. MA 1,4,31-39) found in book 19 of the Atharvaveda, (cf. AS 19,7,2-5), in the Taittirī yas āņhitā (cf. TS 4,4,10,1-3) and Taittirī yabrā hmaň a (cf. TB 1,5 and 3,1,4-5), and elsewhere; the primacy of the Pleiades (MUL.MUL in cuneiform, K ŗ ttikāų in Sanskrit) in describing the path of the Moon among the stars; the “ideal” year of 360 days (cf. MA 1,2,36- 3,12) in maňđala 1 of the Ŗ gveda (cf. Ŗ S 1,164,11) and in book 4 of the Atharvaveda (cf.