Physicists From India

"In support of the West’s physical claim to the whole world, the Western history of science sought to establish an intellectual claim to all knowledge in the world, especially all scientific knowledge. To situate this claim in its proper perspective, we need to probe a little deeper to understand a bit of the unstated logic behind colonialism. According to the religious beliefs of the colonialists, such an intellectual claim of discovery, in turn, established the colonialist’s moral claim to the whole world. It was these “moral” claims that distinguished colonialism from a simple project of robbing the world by physical force."

"But the mysterious source of Mercator's precise trigonometric values, and his technique, remains unknown to this day. Mercator, who worked with Gemma Frisius at the Catholic University of Louvain, obviously had privileged access to information brought in by sailors and priests returning from India and China, via Antwerp. So it is hardly surprising that the "Mercator" projection is identical with a projection used in maps of the celestial globe from China from at least five centuries earlier—and the same principle could obviously be applied to the terrestrial globe. How- ever, since Mercator was arrested by the Inquisition, and was lucky to escape with his life, it is also not surprising that he kept his "pagan" sources of information a closely guarded secret. The tables of trigonometric values published by Clavius, in 1608, used the Indian de- finition of sines and cosines, and the then common Indian value for the radius of the circle. Hence, these tables far exceeded in accuracy the "tables of secants" provided by earlier nav- igational theorists like Stevin for calculation of loxodromes, which were (at the accuracy of) Aryabhata's values, known to the Arabs. It is hard to see how such accuracy (unprecedented for Europe) could even have been attempted without calculus techniques. Clavius, who au- thored the calendar reform proclaimed by pope Gregory, certainly had access to every bit of information brought in by the Jesuits, but could hardly be expected to be truthful enough to acknowledge his “pagan” sources. Since Clavius’ tables were published several years be- fore the first hint of the calculus “officially” appeared in Europe in the works of Kepler, and since Clavius provides no explanation of his method, it remains a mystery how these high- precision trigonometric values were calculated. The only reasonable explanation is that like his contemporaries, Tycho Brahe, who merely articulates Nilakantha’s astronomical model, or Scaliger, whose “Julian” day number system copies the Indian ahargana system, Clavius obtained his trigonometric values from India."

"The trigonometric values published by Clavius, who was at the centre of the Jesuit web, provide further circumstantial evidence that the Jesuits had obtained the latest Indian texts on mathematics and astronomy, and had studied them. Thus, Clavius’ trigonometric values use exactly the Indian definition of the sine and also the same value of the radius?? used by Indian sources in stating Madhava’s sine values. Further, Clavius was unable to give any explanation for the way those trigonometric values were derived, and, obviously enough, the derivation of such precise values required essentially calculus techniques. Had Clavius himself discovered a striking new procedure, by which to obtain more precise trigonometric values, would he not have announced it, to establish his priority, especially since this was towards the end of his life? In fact, Clavius, though he published sophisticated trigonometric tables in his name, lacked a proper understanding of even elementary trigonometry, since he was unable to use trigonometry to determine a key navigational parameter—the size of the globe."

"When Indian astronomy works, translated by Jesuits in Cochin, started arriving in Europe, Tycho, as one of the most famous astronomers of his day, and the Mathematician of the Holy Roman Empire, would naturally have been chosen as the person to whom they were referred. Nilakantha's model was what later came to be called the “Tychonic” model, which Tycho was trying to check against observations. Why, after all, was Tycho so secretive about his papers, not even allowing his trusted assistant Kepler to see them? In any case, on Tycho's sudden death, Kepler obtained not just Tycho's observations, but also the rest of his papers which contained the underlying theory."

"... formal mathematics is no more than a culturally-dependent system of aesthetics, ... it may continue to be taught like Western music..."

"Briefly, Europe inherited not one but two mathematical traditions: (i) from Greece and Egypt a mathematics that was spiritual, anti-empirical, proof-oriented, and explicitly religious, and (ii) from India via Arabs a mathematics that was pro-empirical, and calculation-oriented, with practical objectives.' Much mathematics taught at the K-12 level is of Indo-Arabic origin: (1) arithmetic, (2) algebra, (3) trigonometry, and (4) calculus. Despite the obviously different philosophical orientations of these two streams of mathematics Europe recognized only a single possible philosophy of a "universal" European mathematics, into which it forcibly sought to fit both mathematical streams."

"The linkage of time perceptions to ethics applies also to Buddhism. The relevant notion of time here is the notion of paticca samuppada , an understanding of which was equated by the Buddha with an understanding of the dhamma. This is a deep and tricky point about Buddhist ethics"

"Unfortunately, there are double standards in the matter: one standard for Greek history, another for Indian."

"But the primary rule of Western faith-based history of math, as one should well understand by now, is that myth is evidence, and all evidence contrary to the myth, even if this is evidence in front of one's eyes, should be thrown out to preserve the myth."

"This plays on the psychology of the colonized, who are persistently taught that only Western sources are reliable, a cardinal principle of Wikipedia even today."

"The history of astronomy and physics in texts should be fundamentally revised. It should be pointed out, for example, that a scientific evaluation of the evidence indicates that Claudius Ptolemy did not exist (this would also teach students a lesson on how and why to do physics practicals in a more genuine way). It should also point out that Copernicus was no revolutionary, that Newton was a deeply religious person, and that Einstein might have played legalistic tricks which a patent clerk is expected to know. There are many other aspects of history and physics nomenclature which need to be revised (in texts)."

"No Western historian, to my knowledge, has commented on the curious fact that the theory of planetary motion in the West developed without the availability of appropriate planetary data. To begin with, every purported observation in “Ptolemy’s” Almagest is fabricated, and obtained by back-calculation. There is not a single known exception to this."

"To recapitulate, in mathematics, the East-West civilizational clash may be represented by the question of pramâna vs proof: is pramâna (validation), which involves pratyaksa (the empirically manifest), not valid proof? The pratyaksa or the empirically manifest is the one pramâna that is accepted by all major Indian schools of thought, and this is incorporated into the Indian way of doing mathematics, while the same pratyaksa, since it concerns the empirical, is regarded as contingent, and is entirely rejected in Western mathematics. Does mathematics relate to calculation, or is it primarily concerned with proving theorems? Does the Western idea of mathematical proof capture the notions of ‘certainty’ or ‘necessity’ in some sense? Should mathematics-as-calculation be taught primarily for its practical value, or should mathematics-as-proof be taught as a spiritual exercise?"

"If one excludes the philosophy of science from the ambit of a study of its history, then one is obliged to do history with the default philosophy of science. In our case this means that one must then accept the present-day Western philosophy of mathematics, not only as a privileged philosophy, but as the only possible philosophy of mathematics."

"From the historiographic angle, the confounding of Euclid of Megara with Euclid the supposed author of the Elements is interesting. While the occurrence of such a mistake is understandable, its persistence for five centuries is not. The persistence of this error for centuries shows that that stories about "Euclid" were propagated, by historians in Europe, exactly in the uncritical manner of myth."

"the term “sine” derives from sinus meaning fold, from the Arabic jaib, meaning fold for a pocket. This was written as “jb” omitting the vowels, but was intended to be read as jı̄bā, from the Indian term jı̄vā corresponding to the earlier Sanskrit jyā used for the chord. Possibly, the name “Euclid” was inspired by a similar translation error made at Toledo regarding the term uclides which has been rendered by some Arabic authors as ucli (key) + des (direction, space). So, uclides, meaning “the key to geometry”, was possibly misinterpreted as a Greek name Euclides."

"The rope (or string) is flexible in more ways than one and can be used to do everything that can be done with a compass-box. It can further be used to measure the length of a curved line, impossible with the instruments in a compass- box. This is helpful for the measurement of angles, and the subsequent transition to trigonometry and calculus."

"The second consequence follows from the first: for if the Indian infinite series were established using a method of calculation and demonstration that does not constitute a formal mathematical proof, valid according to the present-day belief in the potency of formalism, then the Indian infinite series may forever have to be consigned to the status of "proto- calculus", or at best "pre-calculus", for that is how Western historians of science would surely like to classify them, if at all they are compelled to link these Indian infinite series to the infinitesimal calculus in Europe. After all, Indian infinite series were very similar to, if not identical with, the series used by Cavalieri, Fermat, Pascal, Barrow, Gregory, and Wallis, and these efforts are already classified as “pre-calculus” by Western historians of science. While such a strategy of classification and labelling may suit the political interests and the morbid narcissism of the West, it works against the grain of history regarded as an attempt to reconstruct the past."

"Of course, it is well known from the philosophy of science that any evidence whatsoever can be made consistent with any theory whatsoever by introducing enough auxiliary hypotheses."

"It seems part of human nature that if one desires something strongly one pretends that it is true. If the pretence is carried out long enough, it becomes difficult to distinguish between pretence and reality."

"It is a common error to confound quasi-cyclic time with eternal recurrence. It was not generally believed that these cosmic cycles were exact or eternal. The whole possibility of deliverance – moksa, nirvāna – was premised on the idea that these cycles were neither exact nor eternal. (However, the category of cyclic time encourages such an error by suggesting that various types of cyclic time are the same.) In India, this was the traditional view of time and life after death held from before the time of the Buddha. The Lokāyata denied the belief in life after death as a fraud. An interesting feature of this denial is how Pāyāsi sought to establish the non-existence of the soul by performing some 37 experiments with dying men, and condemned felons. It is unlikely that such experiments were ever performed anywhere else."

"In writing about physics, as distinct from mathematics or astronomy, in early Indian traditions, one is immediately struck by the apparent paucity of material—the available commentaries in English suggest that there is little beyond the Purusa Sukta, the pancabhutis and atomism."

"The trigonometric values published by Clavius ... provide further circumstantial evidence that the Jesuits had obtained the latest Indian texts on mathematics and astronomy.’"

"We have seen a number of difficulties raised by sceptics about the belief in life after death; these difficulties evaporate in the context of cosmic recurrence."

"Moving to pragmatic and people-oriented standards rather than the Westerm-oriented standards of the elite will hopefully also restore the idea of science as relating to our immediate surroundings, both social and natural."

"The Elements not only acquired a theologically-correct origin, it also acquired a theologically-correct interpretation. Plato and Neoplatonists had linked geometry and mathematics to the soul. The revised interpretation rejected this linkage as heretical. Mathematics was reinterpreted as “a universal means of compelling argument”."

"This book, since it presents a new account of Indian history, inevitably involves a critique of Western history. However, some Western scholars, recognizing the intrinsic weakness of that history, tend to respond to any critique of Western history not by examining the evidence (which would expose it) but by launching personal attacks on the critic with labels—in this case, the label "Hindu nationalist" seems to commonly arise to the tongues of shallow scholars. Now I completely fail to see why the only choice one has is between different kinds of hate politics— why the rejection of Western racist history necessarily implies the acceptance of some other kind of hate politics. ... It is easy to find many people who oppose one kind of hate politics while being "soft" on another set: however, as stated above, I fail to see why one's choice should be restricted to different brands of hate politics. I am not in any such camp, my stated system of ethics does not admit hate politics of any kind, and I oppose all attempts to mix religion with politics... Suppose “Hindu nationalists” were to seize power, strangle dissent by passing laws to kill dissenters, in painful ways, and then continuously expand their power through multiple genocide for the next 1700 years. What sort of history would emerge? We do not need to imagine very hard, for we have a concrete model before us, in the sort of Western history that has been written since Eusebius! Because of the long history of brutal suppression of dissent in the West, various fantasies, contrary to the barest common sense, have been allowed to pile up, and these continue today to masquerade as the scholarly truth."

"Only when it started emerging from the Dark Age did Europe first come to know of the Elements—through 12th c. translations from Arabic into Latin by Adelard of Bath and Gerard of Cremona—after the capture of the Toledo library, and the setting up there of a translation factory. However, at this time of the Crusades, there was a strong sense of shame in learning from the Islamic enemy. Also at the time of the Inquisition, the fears that Toledo was a Trojan horse that would spread heresy could not be lightly discounted. The shame was contained by the strategy of "Hellenization"—all the world knowledge, up to the 11th c. CE found in the Arabic books (including, for example, Indian knowledge) was indiscriminately assigned an early Greek origin, with the Arabs assigned the role of mere transmitters (and the Indians nowhere in the picture). The fear of heresy was contained by the strategy of Christianization of this incoming knowledge, by reinterpreting it to bring it in line with the requirements of Christian theology."

"Soon we will have people on Mars, and we truly will be multi-planetary. And the young boy or the young girl who will be going to Mars could be in this audience or listening today. I have wanted to work at JPL on these missions since I was 14 years old and I am privileged to be a part of it. And this is a remarkable time in the space program, and we are all in this journey together. So the next time you think you don't have enough time in your day, just remember, it's all a matter of your Earthly perspective."

"The atomistic theory of matter appears in well established and elaborated form in various systems of Hindu philosophy... The oldest of these systems... appears to be that of the Vaiseshika, attributed to Kanada... Whether or no the... theory antedated Democritus... is... uncertain. Professor Garbe's opinion is that beyond a doubt the Indian theory is a long time after the theory of Leucippus and Democritus. L. Mabilleau, on the other hand, considers the Vaiseshika system as several centuries earlier than Democritus. ...This theory recognizes nine distinct entities constituting the universe. These are earth, water, fire, air (or wind), ether (akasa), time, space, soul, and "manas." ...Time, space, and soul are not material, though existent. The "manas" is the medium through which impressions of sense are conveyed to the soul. The first four, therefore, correspond to the four elements of Empedocles; the fifth, ether, can be compared with little similarity to the ether of Aristotle. The first four elements are composed of atoms which are eternal, never created nor destroyed. Each of these four elements exists as atoms and also as aggregates of atoms. As atoms, they are imperishable. The elements which we see or feel are aggregates of atoms and as such are subject to change, but the atoms, which are invisible, do not change. ...Akasa, or ether, is assumed not to consist of atoms, but is infinite in extent, continuous and eternal. It cannot be apprehended by the senses, but is the carrier of sound. It is also described... as all-pervasive, occupying the same space that is occupied by the various forms of matter, and therefore devoid of the property of impenetrability, characterizing the atoms of other elements."

"Two systems of Hindu thought propound physical theories suggestively similar to those of Greece. Kanada, founder of the Vaisheshika philosophy, held that the world was composed of atoms as many in kind as the various elements. The Jains more nearly approximated to Democritus by teaching that all atoms were of the same kind, producing different effects by diverse modes of combination. Kanada believed light and heat to be varieties of the same substance; Udayana taught that all heat comes from the sun; and Vachaspati, like Newton, interpreted light as composed of minute particles emitted by substances and striking the eye."

"As Gautama is the Aristotle of India, so Kanada is its Democritus. His name, which means the “atom-eater,” suggests that he may be a legendary construct of the historical imagination. The date at which the Vaisheshika system was formulated has not been fixed with excessive accuracy: we are told that it was not before 300 B.C., and not after 800 A.D. Its name came from vishesha, meaning particularity: the world, in Kanada’s theory, is full of a number of things, but they are all, in some form, mere combinations of atoms; the forms change, but the atoms remain indestructible. Thoroughly Democritean, Kanada announces that nothing exists but “atoms and the void,” and that the atoms move not according to the will of an intelligent deity, but through an impersonal force or law — Adrishta, “the invisible.” Since there is no conservative like the child of a radical, the later exponents of Vaisheshika, unable to see how a blind force could give order and unity to the cosmos, placed a world of minute souls alongside the world of atoms, and supervised both worlds with an intelligent God.66 So old is the “pre-established harmony” of Leibnitz."

"To be at the height of their calling, men of Science have to reject the very possibility of Materialistic doctrines having aught to do with the Atomic Theory; and we find that Lange, Butlerof, Du Bois Reymond—the last probably unconsciously—and several others, have proved it. And this is, furthermore, demonstrated by the fact, that Kanâda in India, and Leucippus and Democritus in Greece, and after them Epicurus—the earliest Atomists in Europe—while propagating their doctrine of definite proportions, believed in Gods or supersensuous Entities, at the same time. Their ideas upon Matter thus differed from those now prevalent... the Atomic Theory kills Materialism."

"In physics, the thinker Kanada, explained light and heat as different aspects of the same element, thus anticipating Clarke Maxwell's Electro-magnetic Theory, which unified different forms of radiant energy. Sankaracharya, in his Advaita thought expanded the concept of unity of matter and energy. Vacaspati recognized light as composed of minute particles emitted by substances, anticipating Newton’s Corpuscular Theory of Light and the later discovery of the Photon. In Botany, Sankara Mishra and Kanada have discussed the circulation of sap in the Plant and the Santiparva of Mahabharata has clearly stated that the plants develop on the strength of nutrients made through interaction of sunlight and materials obtained from the air and ground. Bhaskarcharya's concept of Differential Calculus preceded Newton by many centuries. His study of time identified Truti: The 3400th part of a second as the unit of time."

"In the fuzzball paradigm, the black hole microstates have no interior, and radiate unitarily from their surface through quanta of energy E ∼ T. But quanta with E ≫ T impinging on the fuzzball create large collective excitations of the fuzzball surface. The dynamics of such excitations must be studied as an evolution in superspace, the space of all fuzzball solution |Fi⟩."

"The black hole information paradox is probably the most important issue for fundamental physics today. If we cannot understand its resolution, then we cannot understand how quantum theory and gravity work together. Yet very few people seem to understand how robust the original Hawking arguments are and what exactly it would take to resolve the problem."

"The exact description of any physical process must include the effects of quantum gravity. But our experience suggests that there is a separation of scales, so that under suitable conditions we get 'lab physics'; i.e., physics described to good accuracy by quantum fields on gently curved spacetime."

"Another project which keeps the Bourbaki name alive is the Seminaire Nicolas Bourbaki, which is a series of seminars, about 12–20 per year, on contemporary mathematics started in 1948. It is considered an honour to be invited to give a seminary in this seminar in this series; the only Indian to figure in the seminar so far is Harish Chandra, who gave a talk in the 1957–58 series and, apparently, thus lost the chance of winning the Fields medal in 1958! (Siegel was the chairman of the Fields medal committee in the ICM 1958!)"

"I have often pondered over the roles of knowledge or experience, on the one hand, and imagination or intuition, on the other, in the process of discovery. I believe that there is a certain fundamental conflict between the two, and knowledge, by advocating caution, tends to inhibit the flight of imagination. Therefore, a certain naiveté, unburdened by conventional wisdom, can sometimes be a positive asset."

"In mathematics we agree that clear thinking is very important, but fuzzy thinking is just as important."

"String theory work done in India is pretty good. … There’s no other country with a GDP per capita comparable to India’s whose string theoretic output is anywhere as good. In fact, the output is better than any country in the European Union, but at the same time not comparable to the EU’s as a whole. So you get an idea of the scale: reasonably good, not fantastic. The striking weakness of research in India is that research happens by and large only in a few elite institutions. But in the last five years, it has been broadening out a bit. TIFR and the Harish-Chandra Research Institute (HRI) have good research groups; there are some reasonably good young groups in Indian Institute of Science (IIS), Bengaluru; Institute of Mathematical Sciences, Chennai; some small groups in the Chennai Mathematical Institute, IIT-Madras, IIT-Bombay, IIT-Kanpur, all growing in strength, The Indian Institute of Science Education and Research (IISER), Pune, has also made good hires in string theory."

"The improved understanding of the equations of hydrodynamics is general in nature; it applies to all quantum field theories, including those like quantum chromodynamics that are of interest to real world experiments. I think this is a good (though minor) example of the impact of string theory on experiments. At our current stage of understanding of string theory, we can effectively do calculations only in particularly simple — particularly symmetric — theories. But we are able to analyse these theories very completely; do the calculations completely correctly. We can then use these calculations to test various general predictions about the behaviour of all quantum field theories. These expectations sometimes turn out to be incorrect. With the string calculations to guide you can then correct these predictions. The corrected general expectations then apply to all quantum field theories, not just those very symmetric ones that string theory is able to analyse in detail."

"There people who were leaders in their field in Cambridge and they lectured. And what impressed me the most was that all these big names never said that they were busy in their research and did not want to be burdened with lectures. They took their part in the lectures actively."

"Cambridge was my goal, so once I got admission and scholarship, I decided to go there - I went there after my B.Sc at 19, I did my Masters in 3 years, by age 22 and PhD in another 3 years, by 25 years of age."

"In 1963, when I completed my PhD, it was mostly on the steady-state theory using mathematical formulations to describe creation of matter. People always argued that you cannot have matter coming out of nothing, what would happen to the law of conservation of matter. It is a normal criticism of the steady-state theory. One could answer it either in one sentence by saying what is the big-bang theory where the entire universe came out of nothing, so you are violating the law of conservation of matter and energy in a big way. But that would be to point out the weakness of the other theories and not answering your own theory."

"A black hole is the ultimate manifestation of a region of strong gravity. The pull of gravity in a black hole is so strong that even light cannot escape from it and time stands still."

"Guru: Today I will discourse upon the violence in astronomy. Disciple: Revered Sir! Will you be describing the violent phenomenon in the Universe? Guru: Yes, and I will also dwell upon the controversies amongst the astronomers about what these events imply – controversies which are no less violent than the phenomena themselves"

"I went to Cambridge to do higher mathematics, that was my first goal and appearing in the university exams in mathematics. You are given a menu of various branches of mathematics, pure as well as applied. So I found that applied aspects, especially application to astronomy were very interesting. And the speakers on both courses, that is the lecturers were also very good. At that time, I also read a book by Fred Hoyle called ‘Frontiers of Astronomy’, which gave a very readable account for a layman for what was happening in astronomy. So, all these factors made me go into the research field of astronomy. Because one is required to choose which branch of mathematics one takes as research field. In Cambridge, astronomy is treated as a branch of mathematics. So I choose that."

"So it was better to think of formulations which could explain the creation of matter without violating the law of conservation of matter...For that we used what is called as negative energy, which at that time was considered unrealistic. There was a good example of negative energy, mainly Newtonian gravity. Newtonian gravity is a negative energy system because gravitational potential energy is negative and we i.e, Fred Hoyle and me, worked out a fairly consistent method of describing this whole thing. Today what people call phantom fields, an idea which is catching up with people trying to explain some problems of the big-bang, these phantom fields are what we had proposed way back in the 1960’s."

"in our society at all levels not only uneducated but educated as well are dominated by superstitions of various kinds. The superstitions of the educated are only more sophisticated than those of the uneducated. So one needs to introduce real knowledge in place of superstitious beliefs. You need to explain to people believing in superstitious ideas that the ideas are not correct and this can be verified experimentally. When doing science popularization you have to express some facts of the real universe or the real world to the person who is not willing to believe in it and if you express it in a very pedantic way or say to the person that you are a fool, you should not believe this then it is not good because then he will believe in his superstitions even more. So you have to persuade him to think for himself, you don’t tell him what to believe but you ask him to try this experiment and see what is the reality. So that way you may be able to convince the person."