Re: Probability in Ancient India: a debate
S. Kalyanaraman
Babylonian and Indian Astronomy: Early Connections
Did the Indian and Babylonian astronomy evolve in isolation, was there mutual influence, or was one dependent on the other? Scholars have debated these questions for more than two centuries, and opinion has swung one way or the other with time. The similarities between the two systems that have been investigated are: the use of 30 divisions of the lunar month; the 360 divisions of the civil year; the length of the year; and the solar zodiac. Some have wondered if the Babylonian planetary tables might have played a role in the theories of the siddhantas. I shall in this essay go over the essentials of the early Indian and Babylonian astronomy and summarize the latest views on the relationship between them. I shall show that the key ideas found in the Babylonian astronomy of 700 BC are already present in the Vedic texts, which even by the most conservative reckoning are centuries older than this period. I shall also show that the solar zodiac (rashis) was used in Vedic India and I shall present a plausible derivation of the symbols of the solar zodiac from the deities of the lunar segments. This does not mean that the Babylonian astronomy and astrology is derived from the Indian tradition. If at all there was borrowing, that was restricted to the most general ideas only. The nature of Indian and Babylonian astronomical methods is quite different. I propose that it is most likely that Babylonian astronomy emerged independently.
| Comments: | 37 pages; with minor corrections |
| Subjects: | History and Philosophy of Physics (physics.hist-ph); Popular Physics (physics.pop-ph) |
| Journal reference: | History of Science, Philosophy & Culture in Indian Civilization, vol. 1, part 4 (A Golden Chain, G.C. Pande, ed.), pp. 847-869, 2005. |
| Cite as: | arXiv:physics/0301078v2 [physics.hist-ph] |
I quote and discuss David Pingree in great detail in my book.On Sun, Jun 26, 2011 at 2:23 PM, navaratna rajaramnavaratna <rajaramn...@gmail.com> wrote:
Setting double standards aside-- the late David Pingree fabricated a 'Greek source' using Indian texts to later claim that Indians derived their mathematics from the greeks, we need a forum to explore these ideas.I will see if I can organize a workshop on these topics for 2012. If I have my way it will be limited to mathematically literate people only and exclude pseudo-scholars and propagandists of all stripes.N.S. Rajaram
navaratna rajaramnavaratna
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 are the three messages of June 17, 18, 25, 2011 on a discussion log which may be of interest to researchers studying history of mathematics in ancient India and Greece.
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
View the H-Asia Discussion Logs by month
View the Prior Message in H-Asia's June 2011 logs by: [date] [author] [thread]
View the Next Message in H-Asia's June 2011 logs by: [date] [author] [thread]
Visit the H-Asia home page.
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 -0400H-ASIA
June 17, 2011
Probability in Ancient India
************************************************************
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?)
C. 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
**************************************************
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
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 <c_k_...@hotmail.com>
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 that the Almagest *must* post-date the 9th c. Further, (d) all "observations" in the Almagest were back-calculated based on a wrong astronomical 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).
ademic-imperialism.pdf. This is due to be released at the international conference on ‘Decolonising our Universities’ next week in Penang.)
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 http://multiworldindia.org/wp-content/uploads/2010/05/ckr-Tehran-talk-on-ac
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 H-Net online (Humanities and Social Sciences – Discussion Networks).
Here are the three messages of June 17, 18, 25, 2011 on a discussion log which may be of interest to researchers of history of mathematics in ancient India and Greece.
Here is the abstract from the draft referred to by Prof. Raju: 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
View the H-Asia Discussion Logs by month
View the Prior Message in H-Asia's June 2011 logs by: [date] [author] [thread]
View the Next Message in H-Asia's June 2011 logs by: [date] [author] [thread]
Visit the H-Asia home page.
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 -0400H-ASIA
June 17, 2011
Probability in Ancient India
************************************************************
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?)
C. 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
**************************************************
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
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 <c_k_...@hotmail.com>
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 that the Almagest *must* post-date the 9th c. Further, (d) all "observations" in the Almagest were back-calculated based on a wrong astronomical 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 http://multiworldindia.org/wp-content/uploads/2010/05/ckr-Tehran-talk-on-academic-imperialism.pdf. 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 reason.
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.
Cheers
C. K. Raju
Source of the messages: http://h-net.msu.edu/cgi-bin/logbrowse.pl?trx=lx&list=H-Asia&user=&pw=&month=1106
navaratna rajaramnavaratna
S. Kalyanaraman
navaratna rajaramnavaratna
Apropos pf the charge of Anxiety Frenzy , I quote from my book
