{"id":190,"date":"2020-03-18T20:01:03","date_gmt":"2020-03-18T14:31:03","guid":{"rendered":"http:\/\/ckraju.net\/blog\/?p=190"},"modified":"2020-03-18T20:01:03","modified_gmt":"2020-03-18T14:31:03","slug":"did-indian-learn-trigonometry-from-greeks-responses-to-the-aryan-race-conjecture-in-the-african-context-and-the-relevance-to-indology","status":"publish","type":"post","link":"https:\/\/ckraju.net\/wordpress_F\/?p=190","title":{"rendered":"Did Indian learn trigonometry from Greeks? Responses to the Aryan race conjecture in the African context, and the relevance to Indology"},"content":{"rendered":"

Recently, I presented my talk<\/a> on \u201cPre-colonial appropriations of Indian ganita: epistemic issues<\/a>\u201d. This was at a round table at IIAS Shimla which replaced the now-postponed conference on Indology<\/a>. My talk was primarily about the inferior math we teach in school today based on the European misunderstanding of the Indian ganita which Europe imported.<\/p>\n

\"Shimla<\/p>\n

But as a sidelight, I took up a novel aspect of the Aryan race conjecture. Indologists have so far talked about the Aryan conjecture solely in the Indian context. However, I pointed out the need to link this discussion also to the Aryan race model as it applies to the African context. In particular, to the issue of the Aryan model vs Ancient model as in Martin Bernal\u2019s Black Athena, vol. 1: The fabrication of ancient Greece 1785-1985<\/em>. (The date of 1785 alludes to William Jones whose philological researches started these wild speculations on race.)<\/p>\n

The fabrication of ancient Greece has a direct bearing on the history of Indian math. But first let us understand how racists did it.<\/p>\n

Racist history<\/strong><\/p>\n

Bernal\u2019s key point was that after 1785 racist historians systematically rewrote history to appropriate all achievements of Black Egyptians to White Greeks. This aligned with George James\u2019 Stolen Legacy:<\/em> Greek philosophy is stolen Egyptian philosophy<\/em>. But instead of philosophy, Bernal applied it, for example, to architecture where the evidence of Greeks copying Egyptians is not easily contested: the so-called Greek architecture of columns is manifestly copied from Egypt and Iran (Persepolis).<\/p>\n

Bernal made only scattered remarks on math and science, perhaps out of deference to his father J. D. Bernal, who wrote his famous (but now hopelessly dated) volumes on the history of science. However, after going through my PHISPC volume Cultural Foundations of Mathematics<\/em>, Bernal (Jr) strongly encouraged me to look at the related issues of concern to the history of math where undue credit has been given to Greeks (as explained in an earlier blog \u201cGreediots and Pythagoras\u201d, which also provides the relevant background to this post).<\/p>\n

One point in my above book relates closely to Afrocentrist concerns about undue credit to Greeks in the history of math.<\/p>\n

Thus, <\/span>my point (<\/span>later <\/span>summarised <\/span>e.g. in Is Science Western in Origin?<\/a>) was that <\/span>the church falsified history <\/strong><\/span>even <\/strong><\/span>before racist <\/strong><\/span>historians<\/strong><\/span>. <\/span> <\/span>T<\/span>his process <\/span>of falsifying history <\/span>went virulent during the Crusades against Muslims. <\/span>(Bernal agreed with me here.) <\/span>The Toledo mass translations of Arabic texts into Latin, beginning 1125, involved learning from the books of the religious enemy. The church, which had earlier consistently burnt heretical books, <\/span>needed to justify <\/span>learning from <\/span>the books of the religious enemy. It provided this justification through the coarse falsehood that all scientific knowledge <\/span>in Arabic books came from the <\/span>sole<\/span> \u201cfriends of Christians\u201d, the early Greeks. <\/span>As such, it claimed that knowledge <\/span>in Arabic books<\/span> as a Christian inheritance: <\/span>and that Arabs contributed nothing to it. <\/span> <\/span>Later racist historians <\/span>modified the church thesis by <\/span>insist<\/span>ing<\/span> that the author<\/span>s<\/span> of Greek books, even in Africa, <\/span>were<\/span> white-skinned, <\/span>hence claimed it as part of White achievements.<\/span> <\/span>The racist historian Florian Cajori is an example of how religious chauvinism was absorbed into racist chauvinism. <\/span>No evidence <\/span>exists, and none was <\/span>needed!<\/span><\/p>\n

Egyptian and Persian texts were translated into Greek, by Alexander and the Ptolemy dynasty, but <\/span>any material coming from these texts was <\/span>all attributed <\/span>by racist historians<\/span> to Greeks. Western historians against Afrocentrism, such as Lefkowitz, falsely state that there is no evidence for such translation. <\/span>As I pointed out in my UNISA lectures<\/a>, <\/span>Zoroastrians have been complaining about the burning and Greek translation of their texts for over 2000 years. <\/span>Western historians <\/span>rightly assume that their <\/span>parochial <\/span>readers would be unfamiliar with those texts. Obviously, also, f<\/span>or the G<\/span>r<\/span>eediotic brain it is <\/span>equally<\/span> easy to <\/span>imagine<\/span> <\/span>(when required)<\/span> that <\/span>skin color relates to the language of the text: thus, <\/span>any Indian author writing in English, such as this one, must be white-skinned! <\/span>There are no early original Greek sources available, but even if they were a claim of <\/span>any <\/span>Greek originality <\/span>(e.g. on Sphere and Cylinder, attributed to Archimedes), <\/span>would need proof, <\/span>since this is also found in the Ahmes papyrus <\/span>from a thousand years earlier<\/span>, as pointed out by Diop. <\/span>Lefkowitz has only some utterly foolish comments to offer claiming that Archimedes compared the area of a cylinder to the volume of a sphere. That is the typical standard of racist historians.<\/span><\/p>\n

R<\/span>elevance to Indology<\/span><\/strong><\/p>\n

Anyway, <\/span>the fact is (1) that the Abbasid khilafat in Baghdad made huge investments in knowledge (e.g. Bayt al Hikma), so that, <\/span>following the knowledge gradient, <\/span>numerous Arabic texts were translated <\/span>FROM <\/span>Arabic into Byzantine Greek <\/span>(then Constantinople was a tributary of Baghdad).<\/span> The fact also is that (2) much Indian knowledge travelled to Baghdad, as <\/span>is well known and as repeated <\/span>and explained <\/span>during my talk (e.g. al Khwarizmi\u2019s <\/span>Hisab al Hind<\/em>). <\/span>As stated in the abstract, a<\/span> striking example of both <\/span>(1) and (2) <\/span>is the case of the <\/span>Panchatantra<\/em> which was translated from Sanskrit to Farsi to Arabic <\/span>and then <\/span>to Byzantine Greek to other European languages as Aesop\u2019s fables. <\/span>Knowledge of Indian math could similarly have got into late Arabic and Byzantine Greek texts.<\/span><\/p>\n

So, the question that arises, and was raised in <\/span>Cultural Foundations of Math<\/em>ematics,<\/em> <\/em>was this: <\/span>could Indian knowledge have been mis-attributed to Greeks <\/strong><\/span>in<\/strong><\/span> the process of appropriating Arabic texts to Greeks<\/strong><\/span>? Specifically, <\/span>on the strength of this appropriation, <\/span>people <\/span>like Pingree <\/span>and his students <\/span>have been clam<\/span>ouring <\/span>that trigonometry was transmitted from Greeks (\u201cPtolemy\u201d) to Indians. <\/span>My question <\/span>challenged <\/span>this claim <\/span>(and Pingree ducked the challenge in 2004 <\/span>when, on a trip to the US, I directly challenged him to publicly debate the claim<\/span>).<\/span><\/p>\n

My counter-points to that claim are the following.
\n<\/strong><\/span><\/p>\n

(0) <\/strong><\/span>Non-existence of primary Greek sources.<\/strong><\/span> <\/span>There are no p<\/span>rimary sources for claims about Greek achievement in math. (This was admitted by <\/span>the famous historian of Greek math,<\/span> David Fowler: \u201cWe possess no original versions of any Greek mathematical text, and most texts survive only in the form of Byzantine minuscule <\/span>from the mid-ninth century AD onwards<\/span>\u201d. <\/span>That is <\/span>all the primary sources for Greek math are from another land, in another language, and from another time, thousand years or more later.<\/strong><\/span> <\/span>For the source <\/span>of the quote<\/span>, see <\/span>my<\/span> lecture 3<\/a> on \u201cNot out of Greece\u201d at the University of South Africa, posted online at http:\/\/ckraju.net\/unisa<\/a>.) <\/span><\/p>\n

That is, the <\/span>earliest<\/span> <\/span>available sources for Greek math <\/span>date to at least<\/span> a century <\/span>AFTER<\/span> the known arrival of Indian math among Arabs, <\/span>and <\/span>some are from <\/span>many centuries <\/span>later <\/span>as <\/span>in the case of \u201cPtolemy\u2019s\u201d Almagest etc. <\/span>As such,<\/span> <\/span>it is easily possible that Indian math and astronomy went into Arabic <\/span>or Byzantine Greek <\/span>manuscripts, and <\/span>some of <\/span>it was later indiscriminately attributed with Crusading <\/span>and racist<\/span> fervour by <\/span>credulous or dishonest Western historians<\/span> to the Greeks. <\/span><\/p>\n

(1) <\/span>Epistemic test.<\/strong><\/span> Then, of course, there is the epistemic test that <\/span>(leave alone early Greeks) even later-day <\/span>Europeans did not <\/span>understand<\/em> trigonometry <\/span>properly as the very term \u201ctrigonometry\u201d shows.<\/span> <\/span>The Jesuit general Clavius <\/span>did<\/span> publish <\/span>in <\/span>1607 in<\/span> his own name <\/span>trigonometric values <\/span>stolen from <\/span>India. Though these values had <\/span>the same<\/span> ten decimal place precision, <\/span>as found in India, <\/span>neither Clavius nor any other European was then <\/span>able to <\/span>use them to <\/span>correctly calculate the size of the earth <\/span>(as the students of my history and philosophy of science course do<\/a>, and as explained in my Class IX school text on Rajju Ganita<\/a>).<\/span> <\/span>As explained in my talk, i<\/span>t was because of <\/span>its<\/span> mathematical backwardness that <\/span>Europe <\/span>hence<\/em> had a navigational problem with longitude, which persisted until (at least) the mid-18th c. <\/span>(The relation of earth size to longitude determination was already mentioned in my abstract<\/a> by quoting Brahmagupta\u2019<\/span>s<\/span> statement that ignorance of earth\u2019s radius makes longitude calculations futile. The matter is discussed at length in <\/span>Cultural Foundations of Math<\/em>ematics<\/em>. <\/em>That is, the epistemic test and th<\/strong><\/span><\/span>e <\/strong><\/span><\/span>European longitude problem show the persistent European lack of understanding of trigonometry until the 17<\/strong><\/span><\/span>th<\/strong><\/span><\/span><\/sup> c. <\/strong><\/span><\/span><\/p>\n

B<\/span>ut dishonest historians like Pingree (and his students) keep <\/span>insisting<\/span> that trigonometry was transmitted to India from the <\/span>early <\/span>Greeks. <\/span>They want people to believe the quaint story that early Greeks had this knowledge which<\/span> then <\/span>suddenly vanished <\/span>from Europe <\/span>exactly <\/span>like fairy godmother <\/span>appears and disappe<\/span>a<\/span>rs<\/span>! <\/span>This is an obvious case of anachronistic attribution of knowledge to early Greeks.<\/span><\/p>\n

In my presentation, <\/span>I <\/span>also <\/span>quickly <\/span>made several other points, <\/span>related to my general theory that there has been a whole lot of fraud in the Western history of science, <\/span>so that there is an urgent need to <\/span>correct and <\/span>decolonise the history and philosophy of science <\/span>(as I have been <\/span>trying to <\/span>do).<\/span> <\/span><\/p>\n

(a) <\/span>Non-textual evidence: numerals.<\/strong><\/span> <\/span>Because textual evidence <\/span>in the early Greek case<\/span> is not <\/span>at all<\/span> reliable (see below) w<\/span>e need to examine the non-textual evidence. Greeks and Romans <\/span>were backward even in arithmetic, and <\/span>lacked knowledge of fractions, and therefore could not have done any trigonometry. <\/span>The<\/span>re are other pointers to Greek and Roman arithmetic backwardness: e.g. <\/span> the largest number they had was the myriad <\/span>(10000) pitifully small compared to the number of 10<\/span>53<\/span><\/sup>
\n<\/span>named<\/em> <\/span>as <\/span>tallakshana<\/em> <\/span>by the Buddha. <\/span>(No name for it even today in English.) <\/span><\/p>\n

(b) <\/span>Non-textual evidence: calendar<\/strong><\/span>. <\/span>For what purpose did Greeks do trigonometry? <\/span>Indians did it for astronomy and navigation. Forget about navigation, t<\/span>he <\/span>Greek <\/span>ignorance<\/span> of astronomy is <\/span>further <\/span>corroborated by the highly defective Greek calendar. The Greek calends were a butt of jokes for Romans, <\/span>as even the OED accepts, though the Romans <\/span>themselves had a highly defective calendar.<\/span><\/p>\n

(<\/span>c<\/span>) <\/span>Social conditions.<\/strong><\/span> <\/span>The social conditions of early Greeks (e.g. the death-sentence on Socrates<\/a> <\/span>on the charge of <\/span>impiety by <\/a><\/span>doing astronomy<\/span><\/a>) demonstrates that the early Greeks were a superstitious lot, who punished astronomy with death. <\/span>How, <\/span>then,<\/span> could astronomy <\/span>(or any science)<\/span> flourish <\/span>among Greeks <\/span>under these circumstances?<\/span> <\/span>Likewise, it is strikingly strange that a Euclid should have written a text so well suited to the <\/span>political<\/span> requirements of the Crusading church, <\/span>1500 years later,<\/span> that <\/span>the church <\/span> adopted the book as a text for centuries. <\/span>(But Greediots are gullible people <\/span>with no brains<\/span>, <\/span>which is OK, except that they <\/span>demand <\/span>the same<\/span> from others!)<\/span><\/p>\n

(<\/span>d<\/span>) <\/span>Accretion in scientific texts<\/strong><\/span>. <\/span>Later-day (Arabic or even later Byzantine Greek) sources of Greek math <\/span>are likely to<\/span> be accretive. <\/span>As I teach in my <\/span>decolonoised <\/span>HPS course, <\/span>s<\/strong><\/span>cientific texts tend to be accretive <\/strong><\/span>since<\/strong><\/span> frequently updated with the latest knowledge<\/strong><\/span>. <\/span>The<\/span> <\/span>Almagest<\/em> <\/span>is <\/span>such <\/span>an accretive text, e.g. its star list is headed by the present-day pole star which was not even remotely <\/span>near <\/span>the pole in the <\/span>t<\/span>ime of <\/span>its purported Greek author Claudius <\/span>Ptolemy <\/span>(2<\/span>nd<\/span><\/sup> c. CE)<\/span>.<\/span> <\/span>As such, attributing <\/span>authorship of, or all knowledge <\/span>in, these late texts to early Greeks <\/span>(such as Ptolemy and Archimedes) <\/span>is <\/span>grossly <\/span>anachronistic. <\/span>(But Greediots are bent on self-glorification.)<\/span><\/p>\n

(<\/span>e<\/span>) <\/span>Scriptural significance given to isolated passages.<\/strong><\/span> <\/span>Since early Western historians were <\/span>Christian <\/span>priests, <\/span>or trained by them, <\/span>they assigned<\/span> scriptural significance to isolated passages in these <\/span>late <\/span>texts. <\/span>For example,<\/span> the supposed \u201cevidence\u201d for \u201cEuclid\u201d <\/span>is one such<\/span> single passage in a text by Proclus. <\/span>As in scriptural analysis, <\/span>reliance on individual passages<\/span> <\/span>conveniently <\/span>ignor<\/em>es<\/em> the context<\/em>;<\/em> <\/span>it<\/span> <\/span>invites us to overlook that <\/span>this passage <\/span>contradicts <\/span>the rest of Proclus\u2019 prologue which speaks of the religious significance of geometry. <\/span>(Theology, of course, can digest all contradictions <\/span>by <\/span>demanding<\/em> faith.<\/span>) <\/span><\/p>\n

(f) <\/span>Interpolation, either innocent or deliberate.<\/strong><\/span> <\/span>The more natural approach is to regard such misfit passages as <\/span>later-day <\/span>interpolations. <\/span>The late texts, <\/span>which are the source of Greek history of science,<\/span> come to us from the hands of dishonest Christian priests who could easily have interpolated remarks or passages. <\/span>It <\/span>has always been the <\/span>official <\/span>tradition of church history (since Eusebius and Orosius) to write falsehoods <\/span> <\/span>to glorify itself and denigrate others. <\/span>There are well documented cases of forgeries by <\/span>Christian<\/span> priests, such as <\/span>the fake <\/span>\u201cTestimonium Flavium\u201d, or <\/span>the spurious <\/span>\u201cAward of Constantine\u201d <\/span>on which the Vatican is founded.<\/span> <\/span>They<\/span> introduced extensive forgeries even into the Bible <\/span>(\u201cgospel truth\u201d)<\/span> as the scientist Isaac Newton pointed out in his suppressed seven-volume History of the Church, <\/span>suppressed to this day.<\/span> <\/span>Of course, s<\/span>ome<\/span> interpolations could also be non-malicious errors, as in the <\/span>wrong <\/span>claim that Euclid was from Megara in the first English translation of the <\/span>Elements<\/em> from Byzantine Greek <\/span>in the 16<\/span>th<\/span><\/sup> c. <\/span>In short, isolated passage in late sources <\/span>of Greek math <\/span>are not reliable for they may<\/span> involve <\/span>i<\/span>nterpolations, <\/span>whether deliberate or introduced innocently. <\/span> <\/span><\/p>\n

In view of all the above arguments<\/span>, in my talk I repeated the point made in <\/span>Cultural Foundations of Math<\/em>ematics<\/em> that the <\/span>Almagest<\/em> <\/span>(of Egyptian origin) <\/span>a later version of which was <\/span>mis-<\/span>attributed to a non-existent early Greek called <\/span>Claudius <\/span>Ptolemy could have accrete<\/span>d<\/span> from <\/span>later-day <\/span>Indian<\/span> math and astronomy<\/span> texts. In fact, I argued that <\/span>the version available to us<\/span> did so accrete, for example because it speaks of the difficulty of multiplication exactly as <\/span>do<\/span> Arabic zijes of the 9<\/span>th<\/span><\/sup> c. <\/span>And it starts with a paraphrase of a long-drawn controversy in Indian tradition over Aryabhata\u2019s statement that the earth rotates. <\/span><\/p>\n

Someone in the audience (a Greediot?) understood only the point about the lateness of sources for claims about Greek math. <\/span>Looks like t<\/span>he rest of my <\/span>arguments<\/span> went above his head, <\/span>or he <\/span>just <\/span>ignored them since he had no answer to them.<\/span> <\/span>He objected that <\/span>physical <\/span>sources for Aryabhata are similarly late. This is an objection raised even by school children <\/span>(while teaching <\/span>them <\/span>Rajju Ganita) <\/span>hence here is my response in detail.<\/span><\/p>\n

F<\/span>irst, I have no objection to valid inference: only to wild speculation as used in the Greek case. <\/span>To reiterate, one needs to separate valid inference from wild speculation.<\/span><\/p>\n

Thus<\/span>, the <\/span>physical <\/span>Indian sources <\/span>of math <\/span>come from the same land, and in the same language, only from a different time, unlike the Greek sources which are <\/span>not only <\/span>from a different <\/span>time,<\/span> <\/span>but also from a different land, <\/span>and<\/em> <\/span>in a different language. <\/span>Apart from wild racist assumptions, <\/span>by what process <\/span>exactly do we know what percent of the text, <\/span>if any,<\/span> was <\/span>actually <\/span>the work of Greeks? <\/span>How much was of Egyptian origin, and how much due to accretion from Indian texts? Obviously, Western historians never explained. <\/span>They<\/span> never will be able to. <\/span><\/p>\n

Second, the objections (a), (b), (c), (d) obviously do <\/span>NOT<\/span> apply to Indian sources of math. E.g. there is evidence for sophisticated <\/span>arithmetic<\/span> and a sophisticated calendar right from Vedic <\/span>and Buddhist <\/span>times <\/span>(the Buddha has a name, <\/span>tallakshana<\/em>,<\/span> for 10<\/span>53<\/span><\/sup>). <\/span>The social conditions <\/span>in India<\/span> were against superstition, as I have repeatedly pointed out (e.g. see <\/span>this <\/span><\/span>magazine <\/span><\/span>article on scientific temper in ancient <\/span><\/span><\/a>India<\/a>, and this extract describing Indians against superstition<\/a><\/span>), <\/span>though, of course, all sorts of false <\/span>and derogatory <\/span>stories have been spread <\/span>about India.<\/span> This <\/span>situation <\/span>is <\/span>contrary to Greeks where even Socrates was <\/span>killed for doing astronomy<\/span>, <\/span>and <\/span>disbelieving<\/span> the divinity of the sun and the moon, a charge he denied.<\/span> <\/span>But Greediots are stuck <\/span><\/span>to<\/span><\/span> their myths<\/span><\/span> and just neglect any <\/span><\/span>contrary textual or <\/span><\/span>non-textual argument, <\/span><\/span>and they justify this neglect by refusing to provide space for counter-views in the journals of the history of science which they control, like Pingree did.<\/span><\/span><\/p>\n

Further, <\/span><\/span>Indian sources are free from <\/span><\/span>the objection of accretion and anachronistic attribution, which applies to Greek sources. Thus, for example, the tradition in India was that commentaries reproduced the original text in full. As such, by examining Nilkantha\u2019s <\/span>\u0906\u0930\u094d\u092f\u092d\u091f\u0940\u092f\u092d\u093e\u0937\u094d\u092f<\/span><\/span><\/span>we can clearly separate Aryabhata\u2019s contribution from that of Nilakantha a thousand years later. <\/span>No anachronistic attribution here. <\/span><\/p>\n

Because there are so many different commentaries from different times and places, all of which <\/span>verbatim <\/span>reproduce the original <\/span>text on which they comment<\/span>, we can <\/span>also <\/span>rule out accretion. <\/span>But Greediots don\u2019t <\/span><\/span>seem <\/span><\/span>understand this argument. <\/span><\/span>They are bent upon <\/span><\/span>glorifying Greeks by <\/span><\/span>falsely and <\/span><\/span>anachronistically <\/span><\/span>attributing knowledge to <\/span><\/span>mere <\/span><\/span>names like Archimedes.<\/span><\/span><\/p>\n

Also, <\/span><\/span>i<\/span><\/span>n the Indian case, <\/span><\/span> there are so many commentaries <\/span><\/span>on Aryabhatiya <\/span><\/span>from so many different places <\/span><\/span>in India. <\/span><\/span>This is quite<\/span><\/span> unlike the Greek case, where there is just <\/span><\/span>one<\/em><\/span> <\/span><\/span>(out-of-context) <\/span><\/span>passage in <\/span><\/span>one<\/em><\/span> <\/span><\/span>manuscript<\/span><\/span> <\/span><\/span>used <\/span><\/span>as evidence for Euclid.<\/span><\/span> <\/span><\/span>That is<\/span><\/span> the Indian sources are (probabilistically) independent, <\/span><\/span>so that <\/span><\/span>any later-day<\/span><\/span> interpolations can <\/span><\/span>easily be identified, and can <\/span><\/span>also <\/span><\/span>be easily excluded from a critical edition. <\/span><\/span>In short, <\/span><\/span>anachronistic attributions, accretion, and interpolations, can be ruled out in the Indian case <\/strong><\/span><\/span>of Aryabhata<\/strong><\/span><\/span>, <\/strong><\/span><\/span>say, <\/strong><\/span><\/span>but not in the case of Greek \u201csources\u201d.<\/span><\/span><\/p>\n

Again, b<\/span><\/span>ecause of the existence of <\/span><\/span>both <\/span><\/span>commentaries and objections <\/span><\/span>(<\/span><\/span>raised <\/span><\/span>by opponents of Aryabhata, such as Varahamihira, and critics such as Brahmagupta)<\/span><\/span> <\/span><\/span>and responses <\/span><\/span>to them<\/span><\/span>,<\/span><\/span> there is a <\/span><\/span>continuity<\/em><\/span> in Indian sources, which is completely absent in the Greek case, where <\/span><\/span>all we have is a single late text. W<\/span><\/span>e are asked to <\/span><\/span> rely on wild <\/span><\/span>(and <\/span><\/span>sometimes <\/span><\/span>demonstrably <\/span><\/span>dishonest<\/span><\/span>) <\/span><\/span>speculations <\/span><\/span>(such as those of Heiberg) <\/span><\/span>based on a single late text such as the Archimedes palimpsest.<\/span><\/span><\/p>\n

A<\/span><\/span>nyway, the simple upshot is that <\/span><\/span>contrary to<\/span><\/span> what has been stated by dishonest Western historians like Pingree, trigonometry (and aspects of Indian astronomical controversies) were accreted into the <\/span><\/span>Almagest<\/em><\/span>, and the early Greeks <\/span><\/span>were innocent of both trigonometry and the crime of astronomy. <\/span><\/span>This is one of the reasons Western historians have failed to engage seriously with my book <\/span><\/span>Cultural Foundations of Mathematics<\/em><\/span> on the origin of calculus and trigonometry in India. <\/span><\/span>They have no answer, <\/span><\/span>and <\/span><\/span>instead <\/span><\/span>have the cheek to ask me to engage with their later texts, <\/span><\/span>and not tell a different story.<\/span><\/span> <\/span><\/span><\/p>\n

The time has come to <\/span><\/span>puncture<\/span><\/span> the bloated Western self-image, based on falsehoods. <\/span><\/span>By beginning to tell our own stories, w<\/span><\/span>e are nearing the end of false Greek glorification since the Crusades and by racist historians <\/span><\/span>who never dare take our objections into account. <\/span><\/span><\/p>\n","protected":false},"excerpt":{"rendered":"

Recently, I presented my talk on \u201cPre-colonial appropriations of Indian ganita: epistemic issues\u201d. This was at a round table at IIAS Shimla which replaced the now-postponed conference on Indology. My talk was primarily about the inferior math we teach in school today based on the European misunderstanding of the Indian ganita which Europe imported. But as a sidelight, I took up a novel aspect of the Aryan race conjecture. Indologists have so far talked about the Aryan conjecture solely in the Indian context. However, I pointed out the need to link this discussion also to the Aryan race model as it applies to the African context. In particular, to the issue of the Aryan model vs Ancient model as in Martin Bernal\u2019s Black Athena, vol. 1: The fabrication of ancient Greece 1785-1985. (The date of 1785 alludes to William Jones whose philological researches started these wild speculations on race.) The fabrication of ancient Greece has a direct bearing on the history of Indian math. But first let us understand how racists did it. Racist history Bernal\u2019s key point was that after 1785 racist historians systematically rewrote history to appropriate all achievements of Black Egyptians to White Greeks. This aligned with George James\u2019 Stolen Legacy: Greek philosophy is stolen Egyptian philosophy. But instead of philosophy, Bernal applied it, for example, to architecture where the evidence of Greeks copying Egyptians is not easily contested: the so-called Greek architecture of columns is manifestly copied from Egypt and Iran (Persepolis). Bernal made only scattered remarks on math and science, perhaps out of deference to his father J. D. Bernal, who wrote his famous (but now hopelessly dated) volumes on the history of science. However, after going through my PHISPC volume Cultural Foundations of Mathematics, Bernal (Jr) strongly encouraged me to look at the related issues of concern to the history of math where undue credit has been given to Greeks (as explained in an earlier blog \u201cGreediots and Pythagoras\u201d, which also provides the relevant background to this post). One point in my above book relates closely to Afrocentrist concerns about undue credit to Greeks in the history of math. Thus, my point (later summarised e.g. in Is Science Western in Origin?) was that the church falsified history even before racist historians. This process of falsifying history went virulent during the Crusades against Muslims. (Bernal agreed with me here.) The Toledo mass translations of Arabic texts into Latin, beginning 1125, involved learning from the books of the religious enemy. The church, which had earlier consistently burnt heretical books, needed to justify learning from the books of the religious enemy. It provided this justification through the coarse falsehood that all scientific knowledge in Arabic books came from the sole \u201cfriends of Christians\u201d, the early Greeks. As such, it claimed that knowledge in Arabic books as a Christian inheritance: and that Arabs contributed nothing to it. Later racist historians modified the church thesis by insisting that the authors of Greek books, even in Africa, were white-skinned, hence claimed it as part of White achievements. The racist historian Florian Cajori is an example of how religious chauvinism was absorbed into racist chauvinism. No evidence exists, and none was needed! Egyptian and Persian texts were translated into Greek, by Alexander and the Ptolemy dynasty, but any material coming from these texts was all attributed by racist historians to Greeks. Western historians against Afrocentrism, such as Lefkowitz, falsely state that there is no evidence for such translation. As I pointed out in my UNISA lectures, Zoroastrians have been complaining about the burning and Greek translation of their texts for over 2000 years. Western historians rightly assume that their parochial readers would be unfamiliar with those texts. Obviously, also, for the Greediotic brain it is equally easy to imagine (when required) that skin color relates to the language of the text: thus, any Indian author writing in English, such as this one, must be white-skinned! There are no early original Greek sources available, but even if they were a claim of any Greek originality (e.g. on Sphere and Cylinder, attributed to Archimedes), would need proof, since this is also found in the Ahmes papyrus from a thousand years earlier, as pointed out by Diop. Lefkowitz has only some utterly foolish comments to offer claiming that Archimedes compared the area of a cylinder to the volume of a sphere. That is the typical standard of racist historians. Relevance to Indology Anyway, the fact is (1) that the Abbasid khilafat in Baghdad made huge investments in knowledge (e.g. Bayt al Hikma), so that, following the knowledge gradient, numerous Arabic texts were translated FROM Arabic into Byzantine Greek (then Constantinople was a tributary of Baghdad). The fact also is that (2) much Indian knowledge travelled to Baghdad, as is well known and as repeated and explained during my talk (e.g. al Khwarizmi\u2019s Hisab al Hind). As stated in the abstract, a striking example of both (1) and (2) is the case of the Panchatantra which was translated from Sanskrit to Farsi to Arabic and then to Byzantine Greek to other European languages as Aesop\u2019s fables. Knowledge of Indian math could similarly have got into late Arabic and Byzantine Greek texts. So, the question that arises, and was raised in Cultural Foundations of Mathematics, was this: could Indian knowledge have been mis-attributed to Greeks in the process of appropriating Arabic texts to Greeks? Specifically, on the strength of this appropriation, people like Pingree and his students have been clamouring that trigonometry was transmitted from Greeks (\u201cPtolemy\u201d) to Indians. My question challenged this claim (and Pingree ducked the challenge in 2004 when, on a trip to the US, I directly challenged him to publicly debate the claim). My counter-points to that claim are the following.<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[2,3,5],"tags":[],"class_list":["post-190","post","type-post","status-publish","format-standard","hentry","category-education","category-history-and-philosophy-of-mathematics","category-history-of-astronomy"],"_links":{"self":[{"href":"https:\/\/ckraju.net\/wordpress_F\/index.php?rest_route=\/wp\/v2\/posts\/190","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ckraju.net\/wordpress_F\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/ckraju.net\/wordpress_F\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/ckraju.net\/wordpress_F\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/ckraju.net\/wordpress_F\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=190"}],"version-history":[{"count":0,"href":"https:\/\/ckraju.net\/wordpress_F\/index.php?rest_route=\/wp\/v2\/posts\/190\/revisions"}],"wp:attachment":[{"href":"https:\/\/ckraju.net\/wordpress_F\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=190"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ckraju.net\/wordpress_F\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=190"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ckraju.net\/wordpress_F\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=190"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}