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The Rediff Special/ Amartya Sen

What goes by the name of 'Western science' or 'Western mathematics' is not exclusively a product of the West

The spread of science, mathematics and culture

I come now to the second issue: the difficulty in deciding what exactly is the origin of an idea or an object. Sometimes a thing may come, proximately, from the west, but its earlier origin may have involved non-Western influences in a crucial way. This is particularly the case when we talk about science or mathematics, since these subjects absorbed the contributions of many different societies and cultures. To the immediate recipient, the arriving ideas and beliefs may look identifiably 'Western,' since they are brought in by people from the west, and yet these ideas and beliefs may not be, in any sense, specifically Western in nature or in origin.

Perhaps I can illustrate the point with an example I have used in a different context (in the Satyajit Ray Memorial Lecture I gave in Calcutta in 1995 under the title 'Our culture, their culture') namely, the arrival of modern mathematics in British India. The subject arrived in Indian high schools in a distinctly British form, and the terminology as well as the exact propositions were a reflection of what was then standard in English high schools. There is, however, nothing quite essentially 'British' or 'Western' about contemporary mathematics, even though some conservatives in Indian did see it as an intrusion of Western modes of thought. As it happens, some of the basic ideas, for example of Trigonometry, that were being introduced by the British in Indian schools had, in fact, been developed in India itself, even though these came back to India through Western textbooks.

Perhaps nothing illustrates the point better than the origin of the term 'sine' -- a central concept in Trigonometry. Aryabhata, the Indian mathematician, had discussed the concept of 'sine' in the late fifth and early sixth century, and he called it jya-ardha (half-chord) in Sanskrit, and sometimes abbreviated it simply as jya. When the Arabs took on this notion, they Arabised the term jya, and with that began a remarkable story of international transformation of terminology. Howard Eves, the historian of mathematics, describes it thus: Aryabhata called it ardha-jya ('half'chord') and jya-ardha (chord-half'), and then abbreviated the term by simply using jya ('chord'). From jya the Arabs phonetically derived jiba, which, following Arabic practice of omitting vowels, was written as jb. Now jiba, aside from its technical significance, is a meaningless word in Arabic. Later writers who came across jb as an abbreviation for the meaningless word jiba substituted jaib instead, which contains the same letters, and is a good Arabic word meaning 'cove' or 'bay.' Still later, Gherardo of Cremona (ca 1150), when he made his translations from the Arabic, replaced the Arabian jaib by its Latin equivalent, sinus (meaning a cove or a bay), from whence came our present word sine.'

Given the migration of ideas in mathematics and in science, it is hard to see any particular concept or discipline as being specifically from any part of the world -- the West or anywhere else. In fact, as we look at the time around the end of the first millennium, cross-cultural comparisons bring out the spread of Eastern influence on Western mathematics. While the decimal system was well developed in India by the sixth century and used extensively by Arab mathematicians soon thereafter, the arithmetic notation and procedures reached Europe mainly in the last quarter of the tenth century. Also, the related use of zero, which too was well established by then in Indian and Arab mathematics, still needed some championing, and the Indian mathematics, still needed some championing.

The Indian mathematician Sridhara produced a definitive treatment of this issue around 1000 AD. Indeed, these two are the only items of mathematical interest between 975 and 1000 AD that are noted in the well-known reference books The Timetables of History, and in Kulturfahraplan, in German, edited respectively by Bernard Grun and Werner Stein. Similarly, the only scientific invention in physics and chemistry that is recorded for this period in the world, in these reference books, is the perfection of gunpowder by Chinese scientists, just around 1000 AD.

What goes by the name of 'Western science' or 'Western mathematics' is not exclusively a product of the West, even though it is in the West that some of the integration and recent developments have tended to occur. Indeed, in nearly every field of knowledge and art and craft, influences run across boundaries at impressive speed, and it is just as hopeless to find fully homegrown Western science or mathematics or literature or the arts, as it is to resent innovations coming from other countries for the fear that its foreign origin would itself undermine local culture.

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Amartya Sen, continued

Amartya Sen, the world renowned economist, delivered this UNESCO lecture in Delhi recently.

The Rediff Specials

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