C. K. Raju

"Another piece of non-textual evidence is the calendar. Because of their arithmetic backwardness, Greeks made a mess of the calendar they had earlier copied from Egypt like their gods. Acknowledging that mess Julius Caesar reformed the Roman calendar with great fanfare, though the net result only aggravated the mess about months (e.g. July has 31 days in honour of Julius, so August competitively has 31 days in honour of Augustus, and February is reduced to 28 or 29)! That (Julian) calendar was adopted as the Christian religious calendar in the 4th c Nicene council to fix the date of the Easter ritual, then the main church festival. However, even that "reformed" calendar had the wrong length of the year (as 365¼ days). That was a gross error even in comparison with 3rd c calendars from India. The gross error arose because the Roman system of numeration had no way to articulate fractions, except for simple fractions like half and quarter; therefore they were unable to state the true length of the year (but that wrong figure is what the colonially educated still learn!). This error (in the second place after the decimal point) naturally led to a noticeable slip in the date of Easter within a century. The church repeatedly tried to correct the error, but even the 5th c Hilarius reforms failed. The church controlled the Roman state then, and Hilarius was a pope, so the only possible reason for this persistent failure to fix the error in the date of the key religious ritual was this : basic knowledge of astronomy was unavailable in the Roman empire. Thus the non-textual evidence states the real hilarious story of Roman incompetence in astronomy, contrary to the tall tale of a Graeco-Roman Ptolemy who authored an advanced text on astronomy in the 2nd c. That is, neither "Claudius Ptolemy" nor advanced knowledge of astronomy existed anywhere in the Roman empire in the 5th c. Lack of accurate knowledge of so basic a parameter as the length of the year nails those false claims?"

"In the Mahabharata, we find the story of Nala and Damayanti. Damayanti announces her intention to remarry by choosing a husband (swayamvara). As Nala and Rituparna (the king of Ayodhya) are rushing from Ayodhya to Vidarbha to participate, they stop near a Vibhitaka tree—the five-faced fruits of which were used in the ancient Indian game of dice. Rituparna shows off his knowledge of statistics by saying: “The number of fruits in the two branches of the tree is 2095, count them if you like.” Nala says he will do exactly that – count them by the empirical method of physically cutting down the tree. Anxious not be delayed, Rituparna dissuades Nala by offering to explain how it was done using sampling and probability theory, also used in the game of dice."

"To summarise, there were different ways to measure angles very accurately in Indian tradition. An angle was defined in the sophisticated way as the length of a curved line, not in the naïve way as something (what thing?) made by two straight lines meeting at a point. The reference to 360 and 720 as a way to measure revolutions is indeed found in the Rgveda, and relates to astronomy and the calendar. Texts like Vedanga Jyotisa (– 1500 CE) use more accurate measures of angles in fractions of degrees. Similar accuracy in angle measurement was part of navigational and astronomical practice."

"Clearly, Macaulay saw education as the most powerful (and cheapest) counter-revolutionary tool. ...Regrettably, few have bothered to study or theorise about Western education as a counter-revolutionary tool."

"This then is the real meaning of those claims of "discovery" by Vasco, Columbus and Cook: people are asked to glorify and celebrate the genocide of non-Christians on three continents. That sets the attitudes of a large mass of people today. Thus, deliberately false historical claims of "discovery" continue to assist the genocidal church politics of world power."

"Adopting this unscientific Christian Gregorian calendar ruins India's economic interests."

"The mathematical theory of probability begins with the theory of permutations and combinations, needed to calculate probabilities in games of chance, such as dice or cards. The earliest account of this theory is found in India. This theory is tied to the theory of the Vedic metre (and the theory of Indian music, in general)."

"We should change the teaching of math, and teach normal math solely for its practical value."

"Could the similarity between the Indian and the “Aristotelian” syllogism be due to transmission? Certainly, there were regular contacts between India and Greece from before the time of Aristotle, as recounted by Herodotus or as evidenced by Alexander’s attempt to find the sea route to India after his army mutinied at the frontiers of India."

"The Indian origin of infinite series, found in widely distributed texts, has long been publicly known to Western scholars (Whish 1832). Recent research (Raju 2007) has shown that these Indian developments really did amount to the calculus. (This brings to the forefront various epistemological issues, and the very philosophy of mathematics taken for granted in Western discourse.) This research has also pushed the historical origin of the calculus in India much further back, to the 5th c. CE Āryabhat.a, and his method of obtaining sine values by numerically solving the corresponding differential equation using a finite difference technique."

"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."

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

"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 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”."

"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."

"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."

"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)."

"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."

"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."

"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."

"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."

"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."

"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."