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
| From: Frank F Conlon <con…@U.WASHINGTON.EDU> List Editor: Frank F Conlon <con…@U.WASHINGTON.EDU> Editor’s Subject: H-ASIA: Probability in Ancient India Author’s Subject: H-ASIA: Probability in Ancient India Date Written: Fri, 17 Jun 2011 13:45:35 -0700 Date Posted: Sat, 17 Jun 2011 16:45:35 -0400 |
H-ASIA
June 17, 2011
Probability in Ancient India
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From: C. K. Raju c_k_…@hotmail.com
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?)
- K. Raju
Visiting Professor
School of Mathematical Sciences
Universiti Sains Malaysia
Penang
H-ASIA
June 18, 2011
A comment re: posting Probability in Ancient India
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From: Michael Witzel <wit…@fas.harvard.edu>
With reference to yesterday’s posting on “Probability in Ancient India”:
The scientific claims made in this message apart, the note certainly is not historical but another case of “Antiquity Frenzy”: commonly found nationalistic claims to be/ to have “the oldest” (whatever). <http://www.umass.edu/wsp/methodology/delusions/antiquity.html>
> 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.
Dating the Rgveda (RV), the oldest Indian text, at 4000 BCE is common with traditionalists,but runs afoul of the scientic facts:
The RV is full of horses and chariots, but horse-drawn, spoke wheel chariots were invented only around 2000 BCE (either in the Ural steppes or in Mesopotamia, scholars disagree); and: the steppe animal, the horse (equus caballus), was absent in South Asia until it was introduced from the steppes around 1800/ 1700 BCE (just as in Mesopotamia and Egypt).
Other (inscriptional, linguistic, and archeological) data point to composition of the RV around 1400-1000 BCE.
As for Wilson, this early Sayana-inspired translation (1888) is certainly outdated in several respects. Even the contemporary translations by Oldenberg and M.Müller (Sacred Books of the East) and others are better and closer to the original meaning of the text. Since then, there have been many other translations.
> 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 “dice” game (from RV 10.34 onward) is not one played with cube dice (found already in the Indus Civilisation), but one of grasping a handful of the 150 Vibhitaka nuts thrown. They must devisable by 4.
See H. Falk, Bruderschaft und Würfelspiel, 1986, for the most recent update. The Nala story about leaves (below) actually hints at this.
> 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!)
Thus, there are no “permutations and combinations” as in playing with cube dice but there is just the question of the remainder being divisible by 4 and whether the rest is 3, 2, or — worst- 1 nut left (kali). As in the Yuga theory.
> 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.
This paper has the erroneous idea about cubes (due to old translations), when the translation of the Gambler Hymn in the RV 10.34.8 says:”The 53 dice dance like the sun playing with its rays” — while the text clearly says ” the 3 times 50 (tripancaasah) [vibhidaka nuts 10.4.1] play…”
— As expected…
[See: Miyakawa, Hisashi: Die altindischen Grundzahlwörter im Rigveda [Indologica], Diss.2001, or Miyakawa, Hisashi: Die Grundzahlwörter im ältesten indischen Literaturwerk, dem Rigveda. Dettelbach : Röll, 2003]
Cheers!
Michael Witzel
Michael Witzel
<www.fas.harvard.edu/~witzel/mwpage.htm>
Dept. of Sanskrit & Indian Studies,
Harvard University
1 Bow Street,
Cambridge MA 02138, USA
phone: 1- 617 – 495 3295, 496 8570,
fax 617 – 496 8571;
my direct line: 617- 496 2990
H-ASIA
June 25, 2011
