Probability in Ancient India: Response to Witzel

As modified and posted on H-ASIA, June 25, 2011. 

Witzel will be remembered for the amusing botch he has made. This sort of thing is an extremely common occurrence among Western scholars whose scholarship is hence unreliable, for they are so often so eager to demonstrate their own superiority by trying to score a point. (Remember that editor of a  Cambridge journal who solicited my book for review, and passed it on to an “expert” so  illiterate in philosophy that he did not even understand that the philosophy was in chp. 8!)

Response to comments re: Probability in Ancient India
Ed. note: This response was received on June 22 whilst I was travelling. Dr. C. K. Raju had sent an earlier response to Michael Witzel’s post on his earlier Probability in Ancient India posting. I had requested some modifications in that post and the June 22 post was the result therefrom.  Because some editing was still required, I had to delay working on the post until my return to Seattle from extensive travels.  Today I received a post from C. K. Raju in which he “regrets” that I have delayed his post so long and “apprently suppressed” his response.  Rather than spend more time negotiating modifications of the tone of language in the ‘response’ post, I have exercised some editorial authority and omitted a few somewhat unfortunate phrases.  The edited version appears below, without excluding any of C. K. Raju’s points and, I hope, conveying his sincerely felt unhappiness.  If Professor Witzel cares to respond, we will post his view, but otherwise, this subject is closed.                         FFC
  From: C. K. Raju 

This refers to Professor Witzel’s comment on my post on probability in ancient India.

First, the exact date of the RgVeda is completely irrelevant to my probability paper, and is consequently not mentioned in it at all! It was mentioned in my post, since I was sure that some or the other historian would pick on this irrelevant point to the exclusion of everything else, for this point has been continuously and fruitlessly disputed for the last 150 years at least.

Thanks to Witzel for helping me to make my point that the focus of Asian history needs to move on to matters of contemporary significance.

Second, Witzel’s comment that I am “nationalistic” is contrary to the fact, for example, that I was thrown out from the Editorial Board of the Journal of Indian Council of Philosophical Research, for political reasons, when a “nationalistic” government came to power. The ‘nationalistic allegation is incorrect and unfortunate.

In the same vein, Witzel attributes to my paper things that I did not write. Thus, Witzel  says, “This paper has the erroneous idea about cubes (due to old translations)”. In fact, the word “cube” does not occur anywhere in my probability paper. Anyone can download my paper and check this simple fact in a few seconds. Yet Witzel categorically talks of my “erroneous ideas about cubes”! Clearly and demonstrably, it is Witzel who has erred.

Amazingly, Witzel has even given an imaginary explanation for the imaginary error he has imputed to me, by saying it was “due to old translations”. This concocted “explanation” too is equally baseless, for I did my own translation, as always, as can easily be checked. Is this a sample of how Witzel defines history?

These errors are already inexcusable, but Witzel amusingly goes on to suggest that permutations and combinations somehow relate to the shape of the dice! He says: “Thus, there are no ‘permutations and combinations’ as in playing with cube dice”. However, it is school mathematics that permutations and combinations can be applied to dice with any number of faces whether 6 or 5 (which is the number of faces for Indian dice I have stated in my paper).

Did Witzel intend to say something else? In fact, contrary to what Witzel glibly imputes to me about the game of dice, in my paper, I very explicitly said nothing at all about how the game of dice was played in Vedic times. Therefore, no matter how one interprets what Witzel says, it is entirely false to claim, as he does, that I linked the Vedic description of the game of dice to permutations and combinations. Hence, it is quixotic of him to imagine that he is contesting any part of my thesis simply by contesting how the game of dice was played in Vedic times!

In fact, my paper made a completely different point about permutations and combinations (unrelated to dice): that the theory of permutations and combinations is built into the Vedic metre! It is also built into the theory of Indian music, but that is a longer (and more difficult) story. Of course, I also pointed out that the formulae for permutations and combinations are found in a long series of early Indian mathematics texts (other than the RgVeda) in direct relation to strategies of betting and winning in gambling based on chance, which texts I have cited in detail. However, the point about Vedic metre is especially important because the metre serves as a checksum to validate the content. If Witzel (a non-practitioner) does not also know the theory of the metre, his opinion about the contents of the Veda is unreliable.

Next, the number of dice is 53 as in the number of cards (52 cards + 1 joker), and relates to the number of weeks in a year (with one inter-calary week). I am sure about my version, and I reject Witzel’s authority in the matter. I also reject Witzel’s description of the game as excessively far-fetched, and his secondary sources as unreliable. But I will not go into details, since none of this matters very much for this discussion, for the exact way the game was played in Vedic times is completely irrelevant to my probability paper, as already pointed out.

Finally, I agree with Witzel that antiquity frenzy is very apparent in the “history” which makes out that everything in science was first done by Greeks or by Christians in the European renaissance. Western history books and encyclopedias are full of this and I agree with Wtizel that it is pure delusion. As I have explained in my book “Is Science Western in Origin?” (Multiversity, 2009) this history originated during the Crusades and Inquisition, and it needs to be corrected. That is exactly what I am doing by rejecting the thesis that Newton first created the calculus and Pascal probability theory, etc.

Unfortunately, there are double standards in the matter: one standard for Greek history, another for Indian. For example, consider the origin of trigonometry. Any current encyclopaedia would say that trigonometry originated with the Greeks. Exact dates are very critical to this claim. Thus, while Claudius Ptolemy is dated to the 2nd c., trigonometry was certainly known in India from the time of the Surya Siddhanta (3rd. c.), and Aryabhata (5th c.) had proposed a revolutionary new method to replace the old way of calculating trigonometric values geometrically. An error of a couple of centuries in Ptolemy’s date would change priorities. However, Claudius Ptolemy is dated to the 2nd c. CE using a very bad process, for (a) there is no evidence that he existed, (b) the Roman calendar shows no trace of the knowledge of astronomy in the Almagest text, (c) the star list in the Almagest text is headed by the current pole star so tat the Almagest *must* post-date the 9th c. Further, (d) all observations” in the Almagest were back-calculated based on a wrong atronomical theory as R. R. Newton convincingly pointed out (”The Crime of Claudius Ptolemy”, Johns Hopkins, Baltimore, 1977), so such pseudo observations are not a reliable way to date the late and accretive text of the Almagest. (For more details, see my booklet, cited above.)

Going just by the point (c) above, and following Witzel’s procedure of dating Indian texts, the Almagest should be dated to after the 9th c. That change of date would be fatal to the claim of Greek priority in trigonometry. It would mean that trigonometry originated in India (where, unlike Greece, there were excellent material reasons for it).

Now, I am not, right now, arguing the case for the origin of trigonometry in India. I am only saying that double standards (for whatever reason) cannot be taken lightly, for they help to maintain false history. False history had dangerous consequences in the past, for it misled prominent Indians, and thus enabled Western education to be imposed in India, and other colonies, a move critical to colonisation. Accordingly, decolonisation requires this false history to be rejected. (See my booklet “Ending Academic Imperialism:a Beginning”, 2011, draft available at This is due to be released at the international conference on “Decolonising our Universities” next week in Penang.) Therefore, I cannot accept double standards in dating texts, for whatever

To conclude, Witzel’s way of arguing, by concocting a false position for the opponent and attacking it, is unethical, whether it was done deliberately or because of lack of understanding, and on my tradition of debate it entails a conclusive and permanent loss in debate.

C. K. Raju

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