The debate seems to have generated wide interest, so I thought I would record it here. Here is my original post on H-Asia. The comment from Michael Witzel, of Harvard University, is given in the comments section under that.
Probability in Ancient India
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The history of Asia is somehow understood in the West in such a way as to *exclude* the history of science, and, by extension, the possibility that the Asian philosophies can ever contribute significantly to present-day science.
However, mathematics in India was not just about the place-value system for numbers and zero and algorithms. Some years ago I showed that the calculus (not the “pre-calculus”) originated in India and was transmitted to Europe where it was not properly understood by Newton et al. (Cultural foundations of mathematics: The nature of mathematical proof and the transmission of the calculus from India to Europe in the 16th c. CE, Pearson Longman, 2007, PHISPC vol x.4). My new philosophy of zeroism, related to sunyavada and the philosophy with which calculus developed in India, has demonstrated advantages over the older way to teach calculus based on the European notion of “limits”, and the university curriculum in mathematics is accordingly being reformed in this part of the world.
This note is just to bring to the notice of Asian historians that probability too originated in India, where the game of dice is described in detail in the RgVeda (ca.-4000 CE), though bad translations like those of H. H. Wilson could not capture the spirit of that poetic description. The game of dice also played a key role in precipitating the Mahabharata war (traditional date-3100 CE). The epic clearly has a notion of a fair game, hence some notion of unbiased dice and consequently probability. The game of dice is related to sampling theory in the romantic story of Nala and Damayanti, where a king knowledgeable in dice (and a prospective suitor for Damayanti) explains to her husband Nala how to count the number of leaves in a tree. (Sad that romance, like poetry, never mixes with serious science in the West!) Early Indian mathematical texts had worked out the theory of permutations and combinations. More details are in my paper, “Probability in Ancient India” published in the Handbook of Philosophy of Science, vol 7. Philosophy of Statistics, Elsevier, 2011, a draft version of which is available at http://ckraju.net/papers/Probability-in-Ancient-India.pdf.
One contemporary application is to the frequentist interpretation of probability, which is what is needed for statistical physics, for relative frequency is what can be measured. But relative frequency cannot be used to *define* probability (in a non-circular way), since probability is the limit of relative frequency only in a probabilistic sense. The philosophy of zeroism provides a way out of this paradox which actually arises due to the notion of “limits”.
The other contemporary application is to show that probability defined using Buddhist logic (as distinct from Jain logic used by D. S. Kothari) corresponds to quantum probabilities, involved in quantum computing. This part is only for the technically well-informed. (But, then, again, why should it be the norm that hstorians of Asia need not be technically well-informed?)
C. K. Raju
Visiting Professor
School of Mathematical Sciences
Universiti Sains Malaysia
Penang