2002 Indic Colloquium
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Roddam Narasimha

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National Institute of Advanced Studies
Indian Institute of Science Campus
Bangalore, INDIA 560 012



91 80 360 1969



91 80 360 8781


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Background Information

Prof. Roddam Narasimha FRS is the Director of the National Institute of Advanced Studies at the Indian Institute of Science Campus in Bangalore, INDIA.


Some thoughts on the Indian half of the Needham question

Read the entire paper in PDF format (88K, 19 pp.)

Much debate has taken place on the famous question raised by Needham regarding "the failure of China and India to give rise to distinctively modern science while being ahead of Europe for fourteen previous centuries . . ." . A variety of explanations have been offered in India for the failure mentioned in the above quote. These explanations have ranged from an (alleged) preference for idealist philosophies and an inward looking, other-worldly culture, to the prevalence of a rigidly stratified social system etc. It is argued in the paper that while there is some truth in many of the explanations that have been offered, they are in the final analysis not truly convincing for three major reasons: (a) the philosophical systems of India are very diverse, (b) at the end of the first millennium the sciences in India were in a relatively strong position in the civilized world of the day, and had indeed become very influential, and (c) (as the quote above from Needham admits) India (and China) were in fact ahead of Europe for fourteen centuries before the European scientific revolution and there is no evidence that the explanations offered were not operative in that long period.

The proposal in the paper is that it would be more useful to approach the question by looking at what happened in Europe in the 16th century and later as the manifestation of a European miracle. In order to understand the roots of this miracle it is important to study earlier developments in Europe, say during the 12th to 15th centuries. It is now well known that several Eastern inventions travelled to the West during and after the Crusades. Among these were a variety of technologies from China, and the new numeral and mathematical inventions that went from India (both through creative West Asian intermediaries). The renowned mathematician Hermann Weyl wrote in 1929: 'Occidental mathematics has in past centuries broken away from the Greek view and followed a course which seems to have originated in India and which has been transmitted, with additions, to us by the Arabs; in it the concept of number appears as logically prior to the concepts of geometry.' Indeed the history of mathematics in India can be interpreted as indicating the occurrence of a mathematical revolution heralded by Aryabhattta, and leading in the next several centuries to the development of the Indian numeral system, algebra, techniques for solving both linear and quadratic indeterminate equations, and the germs of the calculus. These new mathematical techniques travelled West over the course of centuries and appear to have played a decisive role in the mathematization of science that was such an essential ingredient of the European scientific revolution -- in ways that still have to be more completely studied.

The Needham question then rephrases itself to ask why the Indian mathematical revolution did not lead to a corresponding 'distinctively modern' scientific one. One reason could be that it was not accompanied by the generation of new technologies -- or their absorption from elsewhere (e.g. China). (Quite possibly no economic or political need was felt for them in India at the time.) But there appears to have been another fundamental philosophical reason, illustrated by the totally different approaches to science taken in classical Greece and classical India. By a detailed comparison of two texts in geometry (the Indian Shulba-sutras and the Greek Euclid) and in astronomy (Ptolemy and Aryabhatta), it is proposed that, in a useful over-simplification, the Greek approach may be thought of as that of axiomatizers and model-makers and the Indian approach as that of pattern-seekers and algorisers. The style of the Indian intellectual approach indicates a deep suspicion of axioms and models, but great ingenuity in handling numbers and discerning patterns (for example in the motion of heavenly bodies). It is suggested that the European scientific revolution, which may be traced to Copernicus, Galileo and Newton, came about in part because of a powerful fusion of the ideas of model-making and algorithms. It is also argued that while the distrust of universal axioms and models in Indian logical systems appears to have been philosophically justified, and may be said to have been vindicated by 20th century developments in quantum mechanics and logic (e.g. wave-particle duality, Gödel's theorems, deterministic chaos), the use of a somewhat less fastidious approach in Europe towards understanding nature led to unreasonably and unexpectedly spectacular successes in the development of science there.

We can say that European model-making could not progress without the mathematical tools whose roots can be traced to India, and similarly that Indian science could not progress without the model-making abilities of the West. The distrust of models, while not philosophically unjustified, has turned out to be historically expensive for India.

Read the entire paper in PDF format (88K, 19 pp.)