From:

**S. Kalyanaraman**

**Probability in Ancient India: a debate**

An interesting debate is ongoing between Prof. C.K. Raju and Prof. Michael Witzel on the topic: Probability in Ancient India. This is at H-Net online (Humanities and Social Sciences – Discussion Networks).

Here is the abstract from the draft referred to by Prof. Raju in his message of June 25, 2011: http://multiworldindia.org/wp-content/uploads/2010/05/ckr-Tehran-talk-on-academic-imperialism.pdf

**Ending Academic Imperialism: a Beginning**

Abstract: Academic imperialism begins with Western education, which has not been seriously challenged in hard sciences. Colonialism changed the system of education as a key means of containing revolt, and stabilising Western rule. The change was possible (e.g. by Macaulay in India) just because a large section of the colonised elite had already swallowed the racist beliefs of the 18th c., that only the West had innovated in science. Those racist beliefs, in turn, were based on a bad history and philosophy of science violently distorted by the religious fanaticism which overwhelmed Europe from the Crusades in the 11th c. until the 17th c. Therefore, to end academic imperialism it is necessary to take the following steps. (a) Dismantle and expose the falsehoods of this Western history of science. (b) Change also the accompanying philosophy of science. (c) Use this to construct a new pedagogy, particularly in the hard sciences, and demonstrate its practical value, to dismantle the colonial education system. (d) Dismantle the Western power structure at the level of higher-education and research.

The immediate action items relate to (c) and (d). (1) Help repeat an experiment to test a new pedagogy of the calculus ("5-day course on calculus without limits") based on a new history and philosophy of mathematics, which enables the calculus to be taught very easily, with the help of computers, even to non-math students. (The calculus is at the base of hard science.) (2) Join and contribute to a new society and web-journal for History and Philosophy of Non-Western Science (HAPONOWS), which will not permit reliance on secondary Western sources, so that authors will have to assume that all such material is doubtful and untrustworthy.

Kalyanaraman

*********************

__Probability in Ancient India__

by

Visiting Professor

School of Mathematical Sciences

Universiti Sains Malaysia

Penang

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 historians of Asia need not be technically well-informed?)

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