The Indian half of Needham's question: some thoughts on axioms, models, algorithms, and computational positivism

Abstract

Much debate has taken place on Joseph Needham's question regarding 'the failure of China and India to give rise to distinctively modern science while being ahead of Europe for fourteen previous centuries'. It is argued in this paper that while there is probably some truth in many of the sociocultural explanations that have been offered for the failure in India, they are in the final analysis not entirely convincing. The proposal in this paper is in two parts. The first is that the scientific revolution, which was part of a European miracle, was triggered in part by the advent of a variety of technologies from China and the new numeral system and other mathematical inventions from India - both via creative West Asian intermediaries. India had experienced a mathematical (more specifically algoristic or computational) revolution heralded by Ārya-bhata in the fifth century CE. The new computational power unleashed by this revolution combined with the classical Greek penchant for axiomatised modelmaking and a technology empowered experimental philosophy, in what appears to have been a very creative and uniquely European cultural fusion that led to the scientific (and later the industrial) revolution. The second part of the proposal is that there was an epistemological reason why the Indian mathematical revolution did not lead to a corresponding 'distinctively modern' scientific one. The Indic approach was basically not that of modelmakers but of ingenious algorisers, and showed a deep and studied distrust of axioms and physical models. This led to an attitude described here as 'computational positivism', which considers observation and computation as the only things that matter. In retrospect, that distrust appears not unjustified, especially in the light of twentieth century developments in quantum and classical mechanics and in logic; but it was historically expensive for India, as Europe achieved unreasonably and unexpectedly spectacular successes in science. To the Indians, it was Newton who was the extraordinary epistemological revolutionary, not Heisenberg or Gödel. In summary, Indian science could not move forward without the modelmaking and technology enabled experimental abilities that grew in the West, just as European modelmaking had earlier been unable to progress without the advent of powerful technologies and computational tools whose roots can be traced to China and India.