Archive for June, 2011

Probability in Ancient India

Thursday, June 16th, 2011

Like calculus, probability too started off in India. People have long been asking me to write about it, and I finally did so. My article on “Probability in Ancient India” is finally out in the Handbook of the Philosophy of Science, vol. 7. Philosophy of Statistics by Elsevier.

The first account of a game of dice is in the aksa sukta of the Rgveda which dates to approximately -4000 CE (as Lokmanya Tilak first pointed out). I had to translate the sukta myself given the mangled and undecipherable translation by H. H. Wilson. (Likewise, I naturally don’t take seriously the dates given by Eurocentric scholars like Max Mueller, whose purported literary “evidence” is hard to take seriously since he didn’t know even the Sanskrit alphabet, and misspelt Chandogya Upanishad as Khandogya Upanishad, and since he believed like Wilson in the Biblical date of creation, in -4004 CE, so he thought no books could have been written that early!)

The next account of probability is in the Mahabharata (traditional date -3100 CE), a war which started around cheating in a game of dice. (Cheating presupposes a notion of fair game, hence a notion of probability.) There is an interesting connection of dice to sampling theory, in the story of Nala and Damayanti.

Of course, Indian mathematics texts long contained formulae for permutations and combinations (involved even in the Vedic metre) though unreliable Western historians of mathematics, like Smith, erroneously stated that this started only with 12th c. Bhaskara II.

What is the practical relevance of this revised history? First, there is the connection of calculus to probability: how zeroism resolves the difficulty with the frequentist interpretation of probability, used for most practical applications, but which currently defines probability circularly as a limit (in probability) of relative frequency. That is advantage zeroism over limits.

Then, of course, there is the issue of the logic on which probabilities are defined, which connects Buddhist logic to quantum logic and quantum computation. Wonder how many people can really understand that (except through prejudice).

The details are here.