Monday 31 August 2015

Prof M M Kalburgi--A Tribute

Avishrant Anveshaka 

Prof M M Kalburgi--A Tireless 


Prof M M Kalburgi at Dharwad Sahitya Sambhrama Jan 25, 2013 

Today morning, (Aug 30, 2015) the town of Dharwad a major educational and cultural centre of Karnataka was shocked out of its contented and cultured life, when one of its leading lights Prof M M Kalburgi a renowned researcher into Kannada culture and prolific writer was shot down at his residence. The tragic loss has shocked the entire literary world of Karnataka and thousands of Prof Kalburgi's admirers and students. Speculation is rife on who might have ordered a gangland Mafiosi style hit on a 77 year old writer. The day was filled with shocked admirers and VIPs streaming to his residence, hospital and to the grounds of the famed Karnatak College, where he once studied and where now he was lying in state.

The funeral will be tomorrow noon in the grounds near Karnatak University Campus, according to Lingayat burial traditions, not too far from the lecture halls where he once taught thousands of students for over three decades on the nuances of Kavirajamarga the 9th century Kannada classic on poetics or the correct way to read and interpret the works of Adikavi Pampa the great 10th century Jain Kannada poet or the radicalism in 12th Century Vachana literature of Basavanna and other Lingayat Sharanas of Karnataka.

Dharwad unlike other cities, does not count its IT billionaires or the Real Estate Rajas but it does proudly reel off the names of its Gyan Peeth and Kendra Sahitya Akademi Award winners; poets, novelists, playwrights, researchers and of course an unending stream of top notch Hindustani musicians. Hence the shocked town and the rest of Karnataka hope that the supari style killers who came into his home acting as students-- perhaps knowing that it was always an open house to researchers-- and shot him in the head, in cold blood at close quarters, and those who hired them, would be caught soon by police investigators.

Prof M M Kalburgi a master of Halegannada (Ancient Kannada), explaining the nuances of Adikavi Pampa's poetry (10th C CE) at an intimate gathering in Dharwad

I was not his student in a formal sense but my parents being his neighbours and close friends afforded me an ease of entry into his warm friendship whenever I visited my Janmabhoomi Dharwad from my Karma Bhoomi, Mumbai. He gladly shared his vast knowledge, his concerns and his flashes of new insights into the radicalism of 12th century Sharana Sahitya, which was our common ground. Every time I met him he would wave with great enthusiasm a bunch of new books that he had either written or edited. His energy was infectious. He was equally an indefatigable organiser and motivator who cajoled others into his numerous projects.

He was prolific. His four volumes of research papers; Marga I-IV and literally dozens of volumes of Vachana literature that were edited, were part of his academic output during his teaching career. After a brilliant teaching career in Karnatak University Dharwad he became the Vice Chancellor of Kannada University at Hampi where he once again showed his organising abilities. Post retirement he continued to write and edit profusely.

His recent output in the past five years alone is mind boggling. He edited and published the complete literary and journalistic works of Basavaraj Kattimani, a progressive writer from Belagavi (formerly Belgaum). He also edited and published several volumes of the great early 20th century researcher, F G Halakatti from Vijayapur (formerly Bijapur). He also made a great gift to medieval historians by getting seven volumes of world history written in Persian by a scribe in the 18th century Adilshahi court of Vijayapur (Bijapur), translated and published in Kannada.

He was now engaged in editing a volume of over 2500 selected vachana poems to be published in 20 different languages. His long introduction to the volume is a classic commentary on the essence of Lingayat sharana movement. He supervised and guided the translators in different languages as well. As a result, in 2012 Kannada, Sanskrit, English, Urdu, Bengali, Hindi, Marathi, Telugu, Punjabi, Tamil editions were published by Basava Samiti.

When I met him last week he assured me that the remaining 10 language editions in Dogri, Maithili, Assami, Bodo, Gujarati, Malayalam, Konkani, Nepali, Odiya, Santhali, Kashmiri and Sindhi are also in the final stage and would be published in the last quarter of this year. Translations into Mandarin, Japanese, French and Spanish were also on the cards.

He then pointed to me a heap of corrected proofs of over 20,000 vachanas in Kannada, which would be published in two slim volumes in literally Bible style with similar paper and asked me if I knew printing experts who could deliver a high quality product soon.

And all this after "retirement" ! I joked with him that the name plate outside his house was a mistake. It said Vishrant Kulapati (Retired Vice Chancellor) and it should have read Avishrant (tireless) Kulapati instead !

His researches and speculations were bold and were often iconoclastic. He was a great admirer of Basavanna the 12th century sharana and founder of Lingayatism. The radicalism of Basavanna and his sharana colleagues inspired Prof Kalburgi to take on all those who claimed to be leaders and moral guides of Lingayats today but who would not stand the test of Basavanna's radicalism.

The 12th century sharana movement with Basavanna as the spearhead founded Lingayatism and in short stood for: complete dignity of labour; dismantling of caste discrimination; gender discrimination; temple worship and all meaningless rituals. It also gave a prominent egalitarian social twist for the first time to the older experiential Bhakti movement that had primarily advocated paths to individual spiritual salvation. It was not only inclusive towards all castes and communities but also put forward an egalitarian economic and social philosophy and not renunciation of the world for other worldly goals. 

In today's India very few would of course stand Basavanna's test. This led Prof Kalburgi to not only take on casteist and conservative forces in general but also some powerful conservatives among Lingayats.

Conservatives found him polarising and some researchers disagreed with his speculations while admiring his scholarship but he posited that culture studies and historians have to perforce join the dots, speculate, interpret, interpolate, extrapolate and take leaps to make progress even if some of them later turn out to be wrong.

While scholars may not disagree with his approach in principle and listened to him with interest, students lapped it up. Status quoists or those who feared his criticism however would adopt extra-academic methods like demonstrations and stone throwing outside his residence.

Shrill elements in the media would be all too happy at times to take his remarks out of context or even misquote him to create a controversy. For example a remark he had made about superstitions in a public meeting in Bengaluru which had been organised to discuss the draft Anti-superstition bill prepared by Karnataka Government led to screaming headlines in one of the news papers leading to death threats and cowardly acts of vandalism at his residence last year.
But he carried on and when I asked him once about such threats he quoted me a vachana by Basavanna himself:

ನಾಳೆ ಬಪ್ಪುದು ನಮಗಿಂದೆ ಬರಲಿ,
ಇಂದು ಬಪ್ಪುದು ನಮಗೀಗಲೆ ಬರಲಿ,
ಇದಕಾರಂಜುವರು, ಇದಕಾರಳುಕುವರು
`ಜಾತಸ್ಯ ಮರಣಂ ಧ್ರುವಂ' ಎಂದುದಾಗಿ

ನಮ್ಮ ಕೂಡಲಸಂಗಮದೇವರು ಬರೆದ ಬರೆಹವ ತಪ್ಪಿಸುವಡೆ

Let what could happen tomorrow come to us today,
Let what could happen today come to us here and now,
Who is afraid of this!
One that is born will also die
Neither Hari nor Brahma can override what my Koodala Sangama Deva has writ.

Perhaps a fitting epitaph for a tireless researcher. May he rest in peace.

Tuesday 18 August 2015

Roddam Narasimha Interview on Ancient Indic Science

A Conversation with Roddam Narasimha:

“For 1400 years India and China led 

the world in science and technology”

Prof Roddam Narasimha, FRS, is a distinguished aerospace scientist, and among the first few Indian engineers to be elected to several leading international academies like the Royal Society, the US National Academies of Sciences and Engineering and the American Academy of Arts and Sciences. He has contributed enormously to the development of aeronautical and space sciences in India. He is presently at the Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore. One of his current areas of research is the study of cloud evolution and dynamics, a subject of great relevance to the Indian monsoons and global climate change. He has written several papers and articles on how ancient Indians ‘thought’ science. These are excerpts of a conversation between Shivanand Kanavi and Roddam Narasimha.

Published in Ghadar Jari Hai, Vol 9 Issue 3

And in

SK: What got you interested in Indian science and what is your approach?

It began during my student days in the US, when I was working for a PhD in aeronautical engineering at the Graduate Aeronautical Laboratories, California Institute of Technology (Caltech) in the late 50s. At Caltech one had the opportunity to make friends with students from all over the world – from Europe to Vietnam and Burma, and to meet and get to know an equally diverse but distinguished international faculty. (I worked with one of them, Prof. Hans W. Liepmann.)

There were great cultural differences among both faculty and students, but as far as intelligence was concerned I did not see any great differences. Intelligence seemed fairly uniformly distributed across the world. So if intelligence was not the problem why were so many countries in the world (including India in particular) rather backward economically and technologically? After meeting many distinguished American scientists, including some Nobel Prize winners, for example, I saw that they had indeed made extraordinary contributions, and some of them (like Richard Feynman) were one-in-a million kind of truly exceptional people, but they did not seem superhuman. And the science I had learnt in Bangalore, while not as advanced as in California, was not dissimilar in kind; its heroes were the same, and had come almost entirely from what one may call the Euro West.

So the question arose: hadn’t there been any science or any scientific geniuses in India, and if there had been what were they like?

I started reading about ancient Indic science. This was not easy because not many books were available on the subject then at Caltech, but I did come across a few very interesting ones. The first was Al Biruni, (Persian encyclopedic, 973-1052 CE, among many other books author of Taḥqīq mā li-l-hind min maqūlah maqbūlah fī al-ʿaql aw mardhūlah: “Verifying All That the Indians Recount, the Reasonable and the Unreasonable”--Ed), who had come to India about a thousand years ago with Mohammed of Ghazni as a kind of scholar-in-residence in his moving court. Several chapters of Al Biruni’s book are on Indian astronomy, and they were fascinating to read. He complains that the Hindus think there is no science like theirs, no art like theirs, no religion like theirs and so on. He said, there were pearls in their science, but they were mixed with dung (mostly puranic stories)!

He comments that some Indians believe in the wildest superstitions: how could the reasoning and logic of somebody like Aryabhata (476–550 CE) be reconciled with such superstitions? He is especially harsh on Brahmagupta (598–670 CE), who compromised his science by upholding the mythologists, e.g. Rahu-Ketu myth on eclipses.

However another scholar in the same century, the Spanish-Arab Said al-Andalusi, (1029-1070 CE, mathematician, astronomer, wrote  "history of science": Altarif bi-tabaqat al-umam (Exposition of the Generations of Nations) seems to have found mostly pearls in Indic science: in his history of world science he surveyed the contributions of several peoples – Greek, Egyptian, Arab, Hindu (i.e. Indian) etc., but among them the Hindus were the premier nation. They were intelligent, innovative and creative, and a nation favoured by God, he said.

One must remember that at that time the Arab world was a great centre of international scholarship. I found later that the Arabs were usually generous in acknowledging what they learnt from other civilizations (including the Indian and the Greek). There was an internationally known Hall of Wisdom in Baghdad, and the books of Aryabhata, Brahmagupta, Charaka and Susruta had all been translated into Arabic, and some into Persian and Chinese.

It looked as if India had been a major player in science at that time, raising the question when and why things changed. So when I returned home from the US I started trying to read Indic science in the original Sanskrit. It was not easy, but slowly it got to be absorbing.

SK: Can you give an example of Aryabhata’s thinking?

Aryabhata was rational, and there is hardly anything that you can call superstitious in his writing. He knew that a solar eclipse occurred when the moon’s shadow falls on the earth, and a lunar eclipse when the moon enters the earth’s shadow. From the shape of the shadow on the moon he inferred that the earth must be round. This may now be common knowledge, but at that time it was heresy. He went on to propose that night and day were caused by earth’s rotation around its axis.

SK: Does he say whether the system was geocentric or heliocentric?

He does not make an explicit statement about it because for him relative motion was what mattered. Actually he used a version of what is today called the Galilean principle of relativity, and gives the example of how, as a boat sails down the river, the trees on land appear to move in the opposite direction to the occupants of the boat. What is stationary and what is moving? To him it does not make a difference (to the dynamics).

SK: Did you study Sanskrit?

Sanskrit was my second language at school but I did not learn enough, so at my father’s prodding I attended early morning classes at a temple in Gandhi Bazar. At college I continued my contacts with Sanskrit by attending the late Shri D V Gundappa’s remarkably multi-lingual, multidisciplinary Sunday classes at the Gokhale Institute of Public Affairs in Basavanagudi. I started picking it up again towards the end of my stay in the US, and began a rather desultory programme of reading books in the original when I came back.

It slowly became clear to me that Aryabhata, Bhaskara (Known as Bhaskarachrya or Bhaskara II, 1114–1185 CE, mathematician, astronomer ) were very smart people indeed, and would be comparable to the best I had seen anywhere. At the same time their style of reasoning, their philosophy, and the way they ‘thought’– all of these seemed very different. Thus the question became: why and how was it that science in India was so strong in what the West calls its Dark Ages, but had in more recent times stagnated and lagged behind?
SK: Can we go back to the dispute between Aryabhata and Brahmagupta?

Aryabhata rejected the story of a daanava named Raahu swallowing the sun or 
his tail Ketu covering the moon during eclipses. Eclipses occurred due to shadows, he said, and he did not see any shadow of a tail ! Brahmagupta, who came more than a century later, was a great mathematician himself, but did not agree with Aryabhata about rejecting the Rahu-Ketu myth and criticized him and his followers scathingly.

However, one of these, Varahamihira (505-587 CE), dismissed Brahmagupta’s arguments as ‘absurdities’, as Brahmagupta’s predictions of eclipses were also based on the shadow theory ! (This inconsistency in Brahmagupta was Al Biruni’s main target.) One thing I learnt from all this was that the debate between mythology and ‘rational’ science in India is at least as old as Aryabhata and Brahmagupta, and to this day has not been resolved in Indian popular thinking on science.
I think there is a wonderful play waiting to be written, a play involving Aryabhata and Brahmagupta, Plato, Newton, Ramanujan, Neelakantha and so on, arguing across the ages !

In spite of the dispute, Brahmagupta and Aryabhata continued to be treated with respect by later Indic mathematicians like Bhaskara and Neelakantha. Unlike in Europe Aryabhata did not suffer an inquisition or punishment.

I remember wondering as a kid what the Ontikoppal panchanga (published in Mysore, brought home every Ugadi by my father), meant when it claimed it was made ‘Aryabhatiyareetya’ (following Aryabhata’s text the Aryabhateeya), mentioned ‘drg.ganita’ (syllables that sounded strange and fascinating to my childish ears), and so on. Clearly Aryabhata was the father of an Indic approach to astronomy that remained foundational for nearly 1500 years. 

SK: What was drg.ganita?

 It signified an important concept in the Indian philosophy of astronomical science. The major objective was to achieve agreement between drik (seeing, observation) and ganita (calculation).

In today’s language drg.ganita's outlook was that the computed prediction must agree with observation.

This may not seem surprising, but Greek thinking needed a conceptual model (sometimes very elaborate, with assumptions many of which we now know to have been wrong) before one got down to calculations (which they had largely learnt from the Babylonians). Of course they also wanted agreement between prediction and observation. On the other hand according to Plato a smart ‘geometer’ should be able to figure it all out by pure thinking.

Indic philosophy emphasized calculation without insisting on the elaborate models of the Greeks– a philosophy that I like to think of as ‘computational positivism’. This philosophy served us well till about a century after Newton – Indian ganita predictions were as good as or better than the best elsewhere.
However in the 19th century the power of the Newtonian revolution coupled with the use of algebra and computation changed the character of astronomy (and other physical sciences). And progress in Europe was so rapid and spectacular that the level of accuracy achieved there surpassed that of Indic methods by large margins early in the 19th century.

SK: So was all Indic science rational?

No, we have already talked about Brahmagupta, for example. However, I gradually came to the conclusion that classical Indic science was indeed generally rational, but it was rationality of a different kind; and it did have conflicts with mythology.

We must however remember that, although Newton is generally seen as rational about his science, he did not consider it as important as what he secretly wrote about theology. Not many know or remember that. Around that time and later in Europe the possible existence of great ancient civilizations in Asia and Africa became a serious issue, as estimates of their age were approaching the Biblical date of Creation.

If you compared the views expressed in Europe during the so called Dark Ages there (before the Renaissance), Indian science was perhaps more rational than European science of the time.

Nobody tried or convicted Aryabhata just because he said Rahu-Ketu is nonsense. At the same time Brahmagupta’s criticism did not affect his reputation as a brilliant scientist. Both of them, I believe, were computational positivists, so their other views seem to have been seen as secondary, lost in the indifference of traditional Indic tolerance of different views.

SK: So how long did this classical science last, and when and why did it end?

Some twenty years ago I came across Joseph Needham, a distinguished British scientist who had studied Chinese science and technology in great depth and also wrote a bit on the sides about Indic science. He concluded that as the West got to know more about Eastern science, the question that demanded an answer was why neither China nor India gave birth to modern science, despite the fact that they were ahead of the West in science and technology for 1400 years (say 200 CE to 1600 CE).

 Why was modern science born in Pisa and not in Patna or Peking? – Needham asked.

It was the first time that I had seen a distinguished western scholar acknowledge so readily that India and China had earlier been ahead for 1400 years. This question is not much discussed in India. Some Indians take the extreme view that everything was known to our ancients, but some others go to the opposite extreme and consider everything Indian was superstition and rubbish (an imperial British view typified by Macaulay’s comment about how one shelf of good European books was worth the whole literature of India and Arabia). It slowly became clear to me that both sides were wrong: the history of science is not linear – it is chequered.

The European dark ages were anything but dark in India; our dark ages have been the last several centuries.

A study of European opinion in the 15th-16th century leads to the conclusion that Europe was becoming aware at that time that the East had been ahead of them. They had encountered the more advanced Arabs during the crusades, Indian numerals and algebra in the 16th-17th century, Chinese technologies in between – and they began to see advances in Asia which they did not know about.
If you read Francis Bacon you will see that he recognized the power of new inventions like the printing press, the nautical compass, and gun powder (all from China, as we now know) – inventions that had changed the world more than any empire, sect or star, he said); and then there was sugar, which came from India. He was dazzled by them, just as I was dazzled by all the things that the West had done when I first went to the US.

Bacon blamed the Greeks for the sad state of European knowledge. He called them a set of quacks and charlatans; his criticisms of Plato and Aristotle were scathing. Europe had taken the wrong path, and had to change. It is almost like what some Indians began to say in the 19th and 20th centuries as our classical epistemology collapsed: ‘all that we have learnt is worthless’.

As one begins to analyse classical Indic and European texts, it becomes clear that, deep down, at a fundamental level, it is all really about how one acquires reliable new knowledge, i.e. about epistemology.

In the 17th century Newton almost implemented what Bacon had said. What changed at that time? The standard western answer is mathematicization of science, but that characterization is misleading. It depends on what you mean by mathematicization. Surely one cannot say that ancient Greeks and Indians were not mathematical?
Actually what happened in the 16th-17th century was that the meaning of mathematics changed. Till then it was geometry and Euclid in Europe (borrowed back, incidentally, from the Arabs and their Arabic translations from the Greek a few centuries earlier).

After the 16th century it began to include numbers and algebra, both of which had come from India. Algebra or beeja-ganita had developed into a ‘new maths’, and was transmitted to Europe through creative Arabs and Persians; and the trajectory of that diffusion can now be traced fairly well.

The word algebra started getting used in Europe in the 15th-16th centuries, and slowly grew in usage, even as the use of the word geometry declined. Indeed the new mathematics even affected geometry, leading to what we now call analytical geometry.

Thus what really happened in Europe then was the algebraization of mathematics and (a little later) of the exact sciences like physics. As the renowned mathematical physicist Hermann Weyl said, Europe moved away from Greek ideas to follow a path that had originated in India, where the concept of number had been considered logically prior to the concept of geometry. I believe this was a strong factor in the revival of science in Europe.

Bacon’s formula of knowledge = power (in contrast to the Indic equation knowledge = salvation) translated to growing power over the East. The European languages did not have a word for algebra at the time so they took over the Arabic word al jabr, just as we too have taken over TV, radio, etc. from English.
Descartes once referred to algebra as ‘barbarous’: it was clearly not a direct Greek or European legacy. Francis Bacon realized that much new knowledge had come from outside the European culture area – presumably the East.

SK: What is the concept of beeja and ganita, which you have spoken of recently as 'Indic concepts that changed the world'?

Ganita is literally reckoning, counting and manipulating numbers; gan is ‘to count’ in Sanskrit. In the west a mathematician was, and was called, a ‘geometer’ for long; and in India a mathematician was a gan aka, a numerist.

India was number-centric. Bhaskara said beeja-ganita (algebra) is avyakta-ganita, i.e. ganita with unmanifest (i.e. unknown) quantities, which need to be found out from the data available and so made to become vyakta, ‘known’. That unknown, the hidden, is beeja. Thus computing with the unknown so that it becomes known is beeja ganita, which went as algebra to Europe through the Arabs (who made their own creative contributions).It appears as if the modern scientific revolution in Europe was a response to the inventions, both mathematical and technological, that went from the east through the Arabs. These inventions dazzled the Europeans, just as their inventions in turn dazzled us two or three hundred years later.

SK: So what was the difference between Europe and India in the way science was done?

Neelakantha, a 15th-16th century mathematician-philosopher from Kerala, explicitly tells us how to do science. I had been trying to infer from Aryabhata and Bhaskara what their attitude towards science and mathematics might have been, and then I came to know about the Kerala school and Neelakantha’s Jyotirmimamsa (which unfortunately has not yet been translated into English).
He actually talks about epistemology, i.e. the science of knowledge-making, and describes what methods lead to the generation of valid, reliable and belief-worthy knowledge. Neelakantha’s views throw light on where Indians and westerners differed in their epistemology.

Indic methodology was primarily based on observation, experience (pratyaksha, anubhava) and inference , skill (anumana, yukti). The Greek conception was based on deductive two-valued (i.e. yes or no type) Aristotelian logic, often following from stated axioms considered ‘true’ or self-evident (typified by Euclid).

In the 15th -16th century a fusion seems to have started taking place between the two in Europe. Though Indians were in touch with the Greeks, at least since the times of Alexander, they only borrowed some tools from them but did not accept their philosophy or ideology.

After having rubbished Greek philosophy, Francis Bacon went on to invent a kind of hybrid that combined experience, observation (in particular through experimentation) with inference of axioms. Axioms thus ceased to be self-evident truths, and became instead tentative inferences.

This method began to be used with Newton, and led to what has spectacularly become the global enterprise of ‘modern’ science. In his great work Principia Mathematica Philosphiae Naturalis (The Mathematical Principles of Natural Philosophy) – perhaps the biggest ever game-changer in the world of science – Newton starts like Euclid in the first book, stating and discussing three ‘axioms’ (i.e. his three laws of motion); the rest is full of theorems, lemmas, QED etc.
In the third book he changes gear, introduces numbers from observations, and inferences from them in the light of the axioms and results of Books I and II.
Book III (of Principia-Ed) seems to me, partly Indic in style, because of the use of inference: QIE (~ ‘what may be inferred’) often replaces the Euclidean QED (~‘what had to be demonstrated’).

Newton presumably realized that the third book is not in the Greek spirit, so he inserts a short prefatory note on ‘The Rules of Philosophical Reasoning’ before embarking on Book III, where he justifies his new procedure. He sets out and explains four (new) rules, which have very little to do with the Greeks. But there are also curious commonalities between India and Europe.

Calculus was thought to be a purely European invention (as we are taught at school even now), associated with the names of Newton and Leibnitz, but it was not. Many important parts of it, at least, were known in Indian gan ita centuries earlier. This included infinite series, for example, of the Taylor-Mclaurin type, second-order difference schemes, the idea of limits – and so on.

Correspondingly, it cannot be said that Archimedes (or some other Greek) started science (compare Bacon); nor did it all start in India, for some little science must have been there even at very early times.

There were different contributions from different cultures. Ideas did travel (both ways), but not all of them were accepted along their way by local cultures. For example Indians borrowed the idea of epicycles from the Greeks, but used it very differently: the smaller circle moving along the circumference of the bigger one could keep changing its diameter. This would have shocked the Greeks because for them it would spoil the symmetry and beauty of a model based on just circles. To the Indians, however, the resulting kinky ellipse-like curve was computationally simpler and more efficient. It was the sort of thing that Bhaskara said would bring aananda to the ganakas !

Indians never really took to Euclid till it came out of Macaulay’s bookshelf into the educational system he prescribed for India in the 19th century. In the Indic Nyaya system of knowledge creation (although it makes no reference to the Greeks), the method of hypothesis to conclusion based on (deductive) logic is frowned upon, because the basis for taking the hypothesis as a given truth could not be justified. You have to compare it with or base it on observation. This is where Bacon made his leap, coupling hypothesis and inference.

Pratyaksha (observation, including experiment) was the number one pramaana (i.e. source of valid knowledge) in all schools of Indian philosophy; it was universally accepted. This must have been one of the few things that all of them agreed on! The second was anumaana (inference), accepted by every school except the Lokaayatas. As Neelakantha says, knowledge arises pratyakshena anumaanena – from observation and from inference.

SK: What about the aagamic pramaana?

After getting an interesting mathematical result, Neelakantha says etatsarvamyukti-moolam, natuaagama-moolam: all of this [comes] from intelligent reasoning, not from the aagamas. Such a statement could not have been safely made in the Europe of his time (~ 1500 CE).

SK: Aagama can also be taken as existing accumulated knowledge rather than scriptural, an important if not decisive source of knowledge.

The aagamas were indeed accepted as a third pramaana in some Indic philosophical systems. What you mention is close to what the Saamkhya philosophers call aapta vacana (the word of the trust-worthy), which they accept as the third pramaana after pratyaksha and anumaana, but they make it clear that Vedic knowledge is not privileged, because it is also essentially human in origin, so potentially fallible like any human work. In Nireeshwara Saamkhya they say there is no evidence (pramaana-abhaava) for God. Of course they don’t say that there is no God, but only that there is no evidence for it.

Classical Indic scientists rarely appealed to scriptural knowledge in their science; however many of them, including Neelakantha, were also very accomplished Vedic scholars. In general, the great scientists (e.g. Charaka, Bhaaskara) had respect for Saamkhya thinking. How can you say all this was not rational?

The history of ideas, it seems to me, is chequered, and that makes it fascinating – more fascinating than that of kings and battles.