The Revolt Continues
Conversation with Shivanand Kanavi, Vice President, Tata Consultancy Services in Ghadar Jari Hai.
Ghadar Jari Hai, Vol III, Issue 3 & 4, 2009
“Indian mathematics is practical whereas the European is metaphysical”
C K Raju has been arguing passionately through several lectures and books about the uniqueness of ancient Indian mathematics and how it influenced the rest of the world. He says what is taught as standard modern mathematics today, is based on theological positions taken by the Church after the Crusades. Shivanand Kanavi conversed with Raju on the results of his research in the history and philosophy of mathematics.
(Excerpts below. The full conversation is available on the website www.ghadar.in)
Shivanand Kanavi: Dr Raju, welcome to peepul he neeche. Having looked at some of your writings, I see that you have researched deeply into the mathematical tradition of India as well as that of Persia, Arabia and Europe. Could you give us an overview of exchanges between India and West Asia in the field of mathematics?
C.K.Raju: As I have stated in the book (Is Science Western in Origin?-By C K Raju), the process of exchange with Arabs started with Barmakids (barmak from pramukh, Persian-Buddhists who were wazirs to Abbasid Khalifas-Ed). This was around the 8th century CE, after the conquest of Persia by the Arabs. Besides the spread of Islam in Persia, Persian customs spread to the Arabs. There was a tradition in Persia of importing knowledge from all over the world. It was based on a philosophy which regarded knowledge itself as virtue, like the Socratic philosophy. To make people virtuous you gather knowledge from all corners of the world. It was begun by Khusrow Noshirvan in the 6th century. At that time Justinian closed all the schools of philosophy in the Roman empire and many philosophers took refuge in the court of Noshirvan. According to the Shahnama of Firdausi, his wazir came to India and took chess, Panchatantra, etc. back to Persia.
There was also an astronomical tradition in Jundishapur (Gundeshapur) in Persia. This astronomy also traveled from India. Which is interesting, because Khusrow’s court already had the most knowledgeable people in the Roman empire, and if the Almagest or any other advanced astronomical text existed at that time then it would have been similarly collected and translated, but we do not hear about it. On the contrary, the Almagest itself starts off by addressing an unknown “Cyrus”. So it was probably constructed in Persia. Certainly, Greek knowledge was translated into Persian and later into Arabic. But, so far as astronomy is concerned we know that the very fact that first it went from India to Persia and then Baghdad shows that Greek knowledge at that point did not compare in any way with the present-day versions of Ptolemy’s Almagest.
There was also a strong tradition of neo-Platonism which came through texts in the Greek language, which probably originated in Egypt. This was called the “theology of Aristotle”, and that was the primary extent of “Greek” knowledge at that time. There was no Greek knowledge available from Byzantium at that time since all the schools of philosophy there had been closed by Justinian.
We also know that Arabic knowledge travelled in the other direction, to Greek texts. The proof is that Panchatantra is translated from Sanskrit to Pahlavi (and you find its reference in Firdausi’s Shahnama) and from Pahlavi it was translated into Arabic and then from Arabic to Greek. Among the Arabs it became the basis of a movement -Ikhwan as- Safa (the Brethren of Purity); so we know the route that knowledge took from India to Greek texts.
It also traveled directly, as in Ashoka’s time, when Indian texts and medicinal plants went to Alexandria. The process really took off with Bayt al hikma (The House of Wisdom of Baghdad) which was linked to Islamic rational theology that valued knowledge as a virtue. It was closely related to aql-i-kalaam, which taught that Allah has given you aql and one must apply that aql in order to interpret the Koran.
SK: Was there any exchange between Persia and Greece and Persia and India during Alexander’s (Sikander) travel through Persia up to India?
Raju: There is an account in the Zoroastrian book of Nativity that Alexander got his books from the Persian emperor and got them translated. The question is: what happened to them? Presumably, some of them, the looted books, went to Aristotle, Alexander’s teacher, and some of them went to the corpus of the library of Alexandria. Aristotle was supposed to be the first person in Greece to have a library, so where did his books come from?
SK: That does not sound very different from Elgin’s marbles!
Raju: (Laughs) Yes. People have not talked about the sources of books for the library of Alexandria. It could not have been those small city states in Greece, which did not have the capacity to produce them. If you look at the trial of Socrates, there were supposed to be 600-odd jurors. If you take ten persons in the population for every citizen then there would still be only about 5-6000 people in Athens so how could they produce books on the scale of the library of Alexandria-half a million books as is normally mentioned? Only a Persia or an Egypt could have done that. In the case of Alexander, as with other military conquerors, knowledge flowed towards them in the case of barbarian incursions.
SK: Arabs have been depicted as carriers and safe keepers of knowledge rather than creators of knowledge. Can you comment on that.
Raju: There is an enormous amount of evidence to the contrary. My book mentions the case of Copernicus, where the Arabs were clearly the creators and the Europeans merely the carriers of knowledge. So it is good to look at the question: how did this story start, that Arabs were mere safe keepers of Greek knowledge.
SK: In fact they have been depicted as barbaric nomads killing each other, who did not have any culture till the British formed various nation states in Arabia in the 20th century. Thus there were Pharaohs and then there were Bedouins till the Anglo-Saxons came…
Raju: If you look at Arab literature (pre-Islamic) there is a depiction of a freewheeling society living in the desert. Post Islam, they conquered Persia and absorbed a lot of the administrative structure of the Persians and then there was this culture of books and libraries. It is undeniable that Arabs were creative and made contributions. So one should investigate about when the story started that Arabs were only safe keepers.
It started during the Crusades. They [the Christians of Europe] were fighting a religious war and Europe had a tradition of book burning. In fact, there were many fiats [by Christian emperors] right from 4th century to burn books. The library of Alexandria was burnt down. There was a tradition of burning heretical books which included secular knowledge. Within Christendom, there was not much of a culture of books and when they were fighting the Arabs they realized that they needed secular knowledge which was available in books. They captured Toledo which had a massive library [coming from] the Umayyad khilafat.
It took a lot of time [for the church] to arrive at the decision to translate those books [and not burn them]. This needed a justification. That was concocted by saying that this knowledge belonged to Greece and the Greeks were theologically ‘correct’. This was regarding the early Greeks, mind you, since they were pre-Christian, whereas they [the church] had conflicts with later Greeks like Proclus, Theon, etc. The advantage of inventing a person like Euclid was that you can attribute a philosophy to that individual which suits you.
SK: One of the important theses put forward by you is that mathematics has cultural foundations. Can you say that there is an Indian way of doing mathematics and if so, what are its features?
Raju: There are some clear cut features. In India there was just one notion of proof or pramana which was applied everywhere: be it philosophy, mathematics or physics. The first pramana was pratyaksh (direct demonstration). Empirical means were accepted as proof. This you find in Sulbasutras, in Aryabhata, and right down to Yuktibhasa.
For example the so called ‘Pythagorean theorem’ could be proved by drawing the triangle on a palm leaf, and it could be shown that the square on the’ diagonal’ was equal to the sum of the squares on the other two sides. This could be shown by cutting, rotating etc. Whereas the European tradition would disagree and say that mathematics is purely metaphysical and by bringing in motion you are bringing in physics and it violates the basic idea of geometry as concerned with immovable space. That is one major source of tension.
Secondly, today the notion of proof is seen in a very rigid manner in a completely metaphysical way. How do you carry out deduction, on what logical basis? After all there are different systems of logic which are prevalent. There is the Jain system of advanced and paperhanging, there is Buddhist logic of Khachaturian and so on. In fact, in the debates between Naiyayikas and Buddhists over a thousand year period you find that they are not addressing each other’s issues because of differing concepts of anumama [inference or deduction] . Europeans declare their logic as universal, when it is not.
There is a third aspect which I have called zeroism, which has to do with what is mathematics good for. In the neo- Platonic view it is good for the soul. The European view is that mathematics is good for providing proof. But in India, the aim of mathematics was not to provide pramana but to do something vyavaharik, something practical. If I am doing something vyavaharik, I don’t mind making approximations. If I am computing, then the computer is going to make so many approximations. Many things are discarded or zeroed, and that is acceptable as floating point arithmetic.
European mathematics demands perfection, where you cannot discard the smallest entity. The belief in perfection comes from a religious view of mathematics. It then gets into the theology that God made the world and he wrote the laws in the language of mathematics, which must hence be perfect. In India, mathematics is ganit, which is counting and calculations.
SK: Modern mathematicians claim that mathematics is universal and not Indian or European. Would you comment on that?
Raju: Universality is factually incorrect. The way mathematics was done in India was different from Europe. So the Indian place value system and algorithms or calculus took such a long time to be absorbed by the Europeans. Metaphysics is never universal. The moment mathematical proof becomes metaphysical it ceases to be universal. In fact it can become ‘universal’ only to the extent that it is demonstrable empirically (pratyaksh). Universality is just a European prejudice as they are ill informed about other cultures, so they declare universality from a parochial point of view.
SK: The crude way in which universality is put forward is by saying that 2+2=4, no matter where you are; in Greece or Arabia, India or China…
Raju: It is not true, and I have argued it at great length in my paper presented in Hawaii. Let us say we are using a computer to add. Since 2+2 is a complicated case, let us take 1 + 1. The answer could be 1 or even 0 depending on what kind of logic gate one is using. So, I have to specify and say I am using integers. But what are integers? If I do arithmetic with integers on computers say using a C program on a 16 bit machine it will not give 2 as the answer but something else, unless I do rounding off. In order to specify what are integers I need infinite time and infinite memory.
In a commercial transaction we get into an agreement saying Rs 2 plus Rs 2 would be Rs 4. But that is an agreement. It is not a universal truth. If I have two stones and if I take up two more stones then I get four stones but if I break one of them into two then I get five stone pieces. So I have to be careful about them as universal truths. At a practical level there is no problem. Even if there is no formal agreement or legal frame work, I would simply say you broke the stone. An agreement is not a universal truth or ultimate truth.
SK: What is the European view on standard of proof, etc.
Raju: There is the Platonic deprecation of the empirical. Then there is the clerical elevation of metaphysics over the empirical. The clergy said the metaphysical is a higher truth than the empirical truth. That is fallacious. Metaphysics is decided by a coterie.
SK: One last comment. Many mathematicians have objections to the way the Indian mathematical results are written in the form of a sutra without explaining how they arrived at it. Is there any insight into how they achieved these results? Secondly, we know of one person who wrote many results, filling up many note books, which are still being researched, viz Srinivasan Ramanujan, though it was in the field of mathematical analysis in the western tradition.
Raju: I am not arguing for an absence of process. To question the value of axiomatic, deductive proof is one thing, and to say that there should be complete absence of process is another thing. A sutra has to be terse to make it easy to remember. It is a cultural matter, in the oral tradition, that communication should be from one mind to another and not filtered through a derivation on a dead parchment, where it is liable to be misunderstood. Right or wrong that is the tradition. However, it is not a critical issue as far as validity of the result is concerned. It is a pedagogical matter. Certainly a process has to be there and a justification [pramana] has to be there. The first text book on philosophy that I picked up from my father said, there is no philosophical tradition in India but only poetry! For philosophy you have to read the Greeks! So now I can say that there is no mathematical tradition in Europe and it is all theology which was imported here through colonialism!
I would say a religious belief is being universalized and I find it highly objectionable. I would say, in fact, that our principles are universal since they are empirical and physical. I would characterize present-day mathematics as European ethnomathematics tainted by theology.
(Dr C K Raju is a mathematician, historian and philosopher and has made important contribution through many articles and monographs towards combating Eurocentric rendition of the history of Mathematics. He has particularly brought out the impact of theological controversies in Europe on revisionist history of mathematics.)