The Mesopotamian Origin of Early Indian Mathematical Astronomy

Abstract

(ProQuest: ... denotes formulae omitted.)In this paper I intend to advance and offer evidence in support of an hypothesis concerning the dependence of the mathematical astronomy of the Jyotifavedâftga on Mesopotamian science of the Achaemenid period.1 I believe that the evidence in support of the theory that some elements of early Indian astronomy are derived from Mesopotamia is overwhelming, and that the evidence for the rest of my hypothetical reconstruction is persuasive. But I must enter a cautionary note with regard to that portion which relates to the Indian intercalation-cycle: the evidence in both the cuneiform and the Sanskrit sources is so fragmentary that no hypothetical reconstruction of the development or of the interrelation of their respective intercalation-cycles is more than a reasonable guess. I hope that the reader will find my guess more plausible than those of my predecessors.Though the Vedas and Brahmanas provide us with some crude elements of observational astronomy, such as the standard list of 27 or 28 nakcatras or constellations associated with the Moon's course through the sky, and some rough parameters, such as the twelve months and 360 nychthemera of a year, mathematical astronomy begins in India with a group of related texts which I intend to explain in this paper. The basic text of this group is the Jyotifavedâftga * one of the six angas or limbs studied by Vedic priests; its purpose was to provide them with a means of computing the times for which the performances of sacrifices are prescribed, primarily new and full moons. This brief work has come down to us in two recensions: a shorter one of 36 verses associated with the Rgveda, and a longer one of 43 verses associated with the Yajurveda, which latter incorporates 29 verses of the Rk-recension. That Rk-recension was composed by one Lagadha, who is otherwise unknown, or, according to another interpretation, by Suci on the basis of Lagadha's teachings; the Yajur-recension names no author, but has the dubious benefit of a bhâcya or commentary by one Somakara. It is the Yajur-recension that has generally been used by modem scholars also, as it, in two of its additional verses, attempts to adjust the older system of the Rk-recension to the familiar terms of medieval Indian astronomy. In this paper the shorter and surely older Rk-recension will be used.We are justified in asserting the originality of the Rk-recension not only by its shortness, but also by its parallelism to other pre-medieval Sanskrit texts. In particular we must discuss here the following seven works in addition to the two recensions of the Jyotifavedâftga:1. The Arthasâstra of Kautilya3 is an ancient work on political science. Many scholars have identified the author with the minister of Candragupta Maurya, who established the Mauryan Empire in northern India shortly before 300 b.c., though it seems fairly secure that our recension of Book Two of the Arthaiâstra does not antedate the second century a.d.4 The twentieth chapter of the second book of the Arthasâstra prescribes the duties of the Mânâdhyakca or Super- intendant of Measurements, among which is included the duty of supervising the measurements of time. These time-measurements are closely related to those of the Jyotisavedanga.2. The Sardulakarnavadana5 is now the thirty-third story in a Buddhist collection of tales about Bodhisattvas, the Divyavadana. Originally it was an anticaste tract in which a king of the Matangas (that is, Candâlas), Trisafiku, asks a Brâhmana, Puckarasârin, to give his daughter, Prakfti, to the outcaste's son, aardulakarna. Upon the Brahmana's refusal of this unorthodox request, Trisafiku proves his status as a Brâhmana by displaying his knowledge of astral divination and astronomy. Our present Sanskrit version is full of interpolations, both in prose and in poetry; but the history of the basic core of the text can be traced back to translations into Chinese by the Parthian prince An Shih-kao, who settled in Loyang in a. …