The Logic of Non-Western Science: Mathematical Discoveries in Medieval India

By Pingree, David | Transactions of the American Philosophical Society, May 1, 2014 | Go to article overview

The Logic of Non-Western Science: Mathematical Discoveries in Medieval India


Pingree, David, Transactions of the American Philosophical Society


(ProQuest: ... denotes formulae omitted.)

One of the most significant things one learns from the study of the exact sciences as practiced in a number of ancient and medieval societies is that, while science has always traveled from one culture to another, each culture before the modern period approached the sciences it received in its own unique way and transformed them into forms compatible with its own modes of thought. Science is a product of culture ; it is not a single, unified entity. Therefore, a historian of premodern scientific texts - whether they be written in Akkadian, Arabic, Chinese, Egyptian, Greek, Hebrew, Latin, Persian, Sanskrit, or any other linguistic bearer of a distinct culture - must avoid the temptation to conceive of these sciences as more or less clumsy attempts to express modern scientific ideas. They must be understood and appreciated as what their practitioners believed them to be. The historian is interested in the truthfulness of his own understanding of the various sciences, not in the truth or falsehood of the science itself.

In order to illustrate the individuality of the sciences as practiced in the older non-Western societies, and their differences from early modern Western science (for contemporary science is, in general, interested in explaining quite different phenomena than those that attracted the attention of earlier scientists), I propose to describe briefly some of the characteristics of the medieval Indian sastra of jyotisa. This discipline concerned matters included in such Western areas of inquiry as astronomy, mathematics, divination, and astrology. In fact, the jyotisls, the Indian experts in jyotisa, produced more literature in these areas - and made more mathematical discoveries - than scholars in any other culture prior to the advent of printing. In order to explain how they managed to make such discoveries - and why their discoveries remain largely unknown -1 will also need to describe briefly the general social and economic position of the jyotisls.

Sastra ('teaching') is the word in Sanskrit closest in meaning to the Greek 'éjciorrínn* and the Latin 'scientia.' The teachings are often attributed to gods or considered to have been composed by divine rsis ; but since there were many of both kinds of superhuman beings, there were many competing varieties of each sastra. Sometimes, however, a school within a sastra was founded by a human ; scientists were free to modify their sastras as they saw fit. No one was constrained to follow a system taught by a god.

Jyotih is a Sanskrit word meaning 'light,' and then 'star' ; so that jyotihsästra means 'teaching about the stars.' This sästra was conventionally divided into three subteachings : ganita( mathematical astronomy and mathematics itself ).samhitä (divination, including by means of celestial omens), and hora (astrology). A number of jyotisis (students of the stars) followed all three branches, a larger number just two (usually samhitä and horä), and the largest number just one (horä).

The principal writings in jyotihsästra, as in all Indian sästras, were normally in verse, though the numerous commentaries on them were almost always in prose. The verse form with its metrical demands, while it aided memorization, led to greater obscurity of expression than prose composition would have entailed. The demands of the poetic meter meant that there could be no stable technical vocabulary ; many words with different metrical patterns had to be devised to express the same mathematical procedure or geometrical concept, and mathematical formulae had frequently to be left partially incomplete. Moreover, numbers had to be expressible in metrical forms (the two major systems used for numbers, the bhütasafikhyä and the katapayädi, will be explained and exemplified below), and the consequent ambiguity of these expressions encouraged the natural inclination of Sanskrit pandits to test playfully their readers' acumen. …

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