How does this concern Indians? Because the colonial myth of civilizational superiority of the West mutated from the myth of racist superiority of Whites. Both myths are based on essentially the same false history of science and mathematics. We still teach that false history of science to our schoolchildren, under colonial influence. See the chapter 5 on “Introduction to Euclid’s geometry” in the class IX NCERT school math textbook.
Despite an enormous amount of secondary literature, there is no primary evidence for the existence of “Euclid”, or that he, or any person or group near his purported date, was the author of the text attributed to him, or that the author was a white male, as shown in our school texts (or Wikipedia etc), or that the text was written for remotely the purposes attributed to “Euclid”. (My challenge prize of Rs 2 lakhs for such primary evidence has been standing unclaimed for the last ten years.) But our government has laid down that, for Western history, we must follow the Wikipedia “standard” that SECONDARY Western (or Western-approved) sources MUST be regarded as definitive proof, because the colonized have no right to demand primary evidence for the master’s tales.
Indian historians seem to have implicitly accepted this historical “principle” of differential evidence, for there was never any hullabaloo regarding false Western history in Indian school texts. Indeed, in two centuries no one else ever checked even the blatantly false and propagandist history of science used by Macaulay, though we changed our education system based on it. Cross-checks will not happen in the near future either, for there are no serious historians of science in any of our numerous university history departments. (It is necessary to emphasize publicly this persistent and collective failure of our historians, because in these time of a Corona tidal wave no one can be sure how long they will last, so if the bitter truth is not stated now it may never be stated.)
“Euclid” (= Uclides = aql-i-des = rational geometry) is a Christian chauvinist myth concocted by the Crusading church in the 12^{th} c. The myth of Greek origins of all science was first used to appropriate all scientific knowledge in Arabic texts to early Greeks. The Crusades failed because Christian Europe was far behind Muslim Europe in scientific knowledge, badly needed even for a religious war. But the church also required an excuse to appropriate it, since the church had earlier declared all non-Christian books as heretical. Attributing the origin of that knowledge to Greeks made it a theologically correct Christian inheritance, since Eusebius had declared early Greeks as the sole “friends of Christians”.
The same trick was later used for a purpose more vital to the church—to support its sudden theological shift to Christian rational theology (set up during the Crusades to compete with Islamic rational theology or aql-i-kalam), by giving “reason” a false Greek origin, to appropriate reason as a Christian inheritance. Note that the fake history of “Aristotle” (of Toledo, not Stagira) alone^{1} was not enough to appropriate the kind of “reason” the church needed, since “Euclid”, or rather the brazen church “reinterpretation” of the book falsely attributed to him, provided the sole purported example of axiomaticreasoning prior to the Crusading church. Since then, the “Euclid” myth was used to dodge the reality that such peculiar metaphysical reasoning was actually an invention of the crusading church for its political gain.
The world-over everyone used normal reasoning based on facts, as e.g. in India in the Nyaya, Buddhist, or Jain syllogisms. But Christian rational theology used a special type of reasoning, called formal (or faith-based) reasoning, which began from (faith-based) axioms, rather than facts, because facts are so often nakedly contrary to church dogmas. An example is Aquinas’ axiomatic reasoning about angels (which don’t exist, in fact), to deduce that many angels can fit on a pin, in his Summa Theologica. However, most people confound normal reasoning (based on facts) with formal reasoning (why bypasses facts, and is based on faith in axioms), because of the church doublespeak of using only one word “reason” for both.
The Western claim that axiomatic reasoning is a “superior” form of reasoning is a mere church superstition, which glorifies church metaphysics. However, this claim of a “superior” form of reasoning is critical to the claim of civilizational superiority. Hence, even though it has been publicly exposed, over a century that the book, purportedly authored by “Euclid”, does not contain a single axiomatic proof, from its first proposition to its last, even supposedly responsible historians like Needham keep regurgitating this false myth of axiomatic proofs in “Euclid”, as proof of Western civilizational superiority.
And, of course, this myth of axiomatic proofs in “Euclid’s” book is repeated in our school texts, because of our differing standards of history, that for Western history we must blindly trust Western authority, and that no one should actually read an easily available book, imitating Cambridge dons who foolishly avoided reading the book carefully for over 750 years until the end of the 19^{th} c.
Today, the myth of civilizational superiority is used to promote axiomatic mathematics as a “superior” type of mathematics, involving “infallible” deduction, though it is trivial to show that axiomatic deduction is highly error-prone, and, of course, even valid deduction need not result in valid knowledge, since any desired nonsense proposition whatsoever can be proved axiomatically as a theorem, by suitably selecting the axioms, as Aquinas did.
The axioms of mathematics (such as those of set theory) are a pure metaphysics of infinity (aligned to church dogmas of eternity), which are empirically irrefutable. They result in nonsense mathematical theorems such as the Banach-Tarski theorem that one ball of gold can be subdivided and reassembled, without stretching, in to two balls of gold identical to the first. These unrealistic theorems are then defended by further metaphysics such as “measurability” which few understand.
The axioms are to be accepted solely on the strength of Western authority: e.g. calculus must be taught using formal “real” numbers, not the “non-Archimedean” arithmetic and the normal mathematics with which the calculus originated in India, and as I teach it. All practical value (e.g. calculation of rocket trajectories) still comes from normal mathematics: e.g. calculation of rocket trajectories is today done on computers which cannot use formal real numbers, declared essential for calculus, but use floating point numbers instead, which are quite different. Similar remarks apply to AI.
Unlike the claim of racist superiority, which is firmly rejected by Blacks, the closely related claim of civilizational superiority, especially in mathematics and science, has been accepted and internalised by the colonized today, who rush to defend it, typically by abusing the critic. They resort to abuse because so few (none to my knowledge), even in our premier universities, understand or can state even the axiomatic proof of 1+1=2 in formal real numbers, for which I offered a reward of Rs 10 lakhs in JNU. Surprisingly, not a single faculty member in our premier university claimed this reward, or even the reduced reward of Rs 1 lakh offered for the full proof of 1+1= 2 in real numbers, if given in a week’s time.
The cure, as I stated in my censored article, which was censored worldwide, is to stand up to the false history AND bad philosophy of mathematics, at the base of the secular justification for the claim of religious/racist/civilizational (Christian/White/Western) superiority.
Anyone interested in attending the meeting may please get in touch with me or the organizers.
1The published version of this article on logic in the Springer Encyclopedia has gathered some gross gratuitous errors because of the reflexive and unilateral application of this false history by the editor/publisher: e.g. Organon dating factually to the Crusading time of 12^{th} c. CE, has been dated by Springer to 12^{th} c. BCE! 😀
This is a video recording my concluding seminar (25 March 2021) as a Tagore Fellow at the Indian Institute of Advanced Study.
Twitter summary:
1. Ganita (गणित) differs from (formal) math,
2. it makes math easy, and
3. makes science better.
4. This is an obituary of formal math.
Slogan formulation
Formal math is dead,
long live normal math (गणित)
Detailed “abstract” (synoptic contents etc.) in three layers..
Best run on site (without downloading). Space bar moves presentation forward. Blue text indicates hyperlinks (for those who would like to examine the briefly displayed material in detail).
]]>Greek history for idiots: Greediots and Pythagoras. 1: No axiomatic proofs in Greek math.
Of course, I have been raising this point abut logic and math from much earlier.
“Mathematics and Culture”, in History, Culture and Truth: Essays Presented to D. P. Chattopadhyaya, ed. Daya Krishna and K. Satchidananda Murthy, Kalki Prakash, New Delhi, 1999, 179–193.
“Computers, Mathematics Education, and the Alternative Epistemology of the Calculus in the YuktiBhāā”, Philosophy East and West, 51:3 (2001) 325–362.
Cultural Foundations of Mathematics: the nature of mathematical proof and the transmission of calculus from India to Europe in the 16th c. CE, Pearson Longman, 2007.
Of course, the belief that logic is metaphysical and metamathematical, and decided by authority, is one with which I disagree. I had even earlier argued that the nature of logic (in the real world) depends upon the nature of time; hence quantum logic, at the microphysical level, is quasi truth-functional. (Schrodinger’s cat can be both alive and dead at one instant of time.) See
C. K. Raju, Time: Towards a Consistent Theory, Kluwer Academic, Dordrecht, 1994. (Fundamental theories of physics, vol. 65.)
For a quick account of how Buddhist logic is quasi truth-functional and gives rise to quantum probabilities, see
CKR, “Probability in Ancient India”, Handbook of the Philosophy of Science, vol 7, Philosophy of Statistics, ed. Prasanta S. Bandyopadhyay and Malcolm R. Forster. General Editors: Dov M. Gabbay, Paul Thagard and John Woods. Elsevier, 2011, pp. 1175–1196.
An account of why I disagree with Haldane’s account of Jain logic as three valued, and Kothari’s attempt to incorporate it into an interpretation of quantum mechanics, see
C. K. Raju, The Eleven Pictures of Time, Sage, 2003.
In particular, as I pointed out in passing long ago, with reference to Udyotkara, that Buddhists and Naiyayikas debated inconclusively across 1500 years, because they had different notions of time, hence logic. (Nyaya logic is two-valued.)
CKR, “Time in Indian and Western Traditions and Time in Physics.” In: Mathematics, Astronomy and Biology in Indian Tradition, PHISPC Monograph Series on History of Philosophy, Science, and Culture in India, No. 3 (D. P. Chattopadhyaya and Ravinder Kumar eds) ICPR, New Delhi (1995) 56–93.
Therefore, there is no such thing as “Indian” logic in the singular. Alas, in the English language, “logics” is ungrammatical! And “whereof one cannot speak, thereof one must be silent”.
And, of course, the long-standing belief in Western thought that deductive proofs are infallible, is a completely wrong idea.
CKR, “Decolonising mathematics”, AlterNation 25(2) (2018) pp. 12-43b, https://doi.org/10.29086/2519-5476/2018/v25n2a2.
All best,
C. K. Raju
–
]]>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’s 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’s 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’ 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 “Greediots and Pythagoras”, 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 “friends of Christians”, 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’s 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’s 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 (“Ptolemy”) 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.
(0) Non-existence of primary Greek sources. There are no primary sources for claims about Greek achievement in math. (This was admitted by the famous historian of Greek math, David Fowler: “We possess no original versions of any Greek mathematical text, and most texts survive only in the form of Byzantine minuscule from the mid-ninth century AD onwards”. That is all the primary sources for Greek math are from another land, in another language, and from another time, thousand years or more later. For the source of the quote, see my lecture 3 on “Not out of Greece” at the University of South Africa, posted online at http://ckraju.net/unisa.)
That is, the earliest available sources for Greek math date to at least a century AFTER the known arrival of Indian math among Arabs, and some are from many centuries later as in the case of “Ptolemy’s” Almagest etc. As such, it is easily possible that Indian math and astronomy went into Arabic or Byzantine Greek manuscripts, and some of it was later indiscriminately attributed with Crusading and racist fervour by credulous or dishonest Western historians to the Greeks.
(1) Epistemic test. Then, of course, there is the epistemic test that (leave alone early Greeks) even later-day Europeans did not understand trigonometry properly as the very term “trigonometry” shows. The Jesuit general Clavius did publish in 1607 in his own name trigonometric values stolen from India. Though these values had the same ten decimal place precision, as found in India, neither Clavius nor any other European was then able to use them to correctly calculate the size of the earth (as the students of my history and philosophy of science course do, and as explained in my Class IX school text on Rajju Ganita). As explained in my talk, it was because of its mathematical backwardness that Europe hence had a navigational problem with longitude, which persisted until (at least) the mid-18th c. (The relation of earth size to longitude determination was already mentioned in my abstract by quoting Brahmagupta’s statement that ignorance of earth’s radius makes longitude calculations futile. The matter is discussed at length in Cultural Foundations of Mathematics. That is, the epistemic test and the European longitude problem show the persistent European lack of understanding of trigonometry until the 17^{th} c.
But dishonest historians like Pingree (and his students) keep insisting that trigonometry was transmitted to India from the early Greeks. They want people to believe the quaint story that early Greeks had this knowledge which then suddenly vanished from Europe exactly like fairy godmother appears and disappears! This is an obvious case of anachronistic attribution of knowledge to early Greeks.
In my presentation, I also quickly made several other points, related to my general theory that there has been a whole lot of fraud in the Western history of science, so that there is an urgent need to correct and decolonise the history and philosophy of science (as I have been trying to do).
(a) Non-textual evidence: numerals. Because textual evidence in the early Greek case is not at all reliable (see below) we need to examine the non-textual evidence. Greeks and Romans were backward even in arithmetic, and lacked knowledge of fractions, and therefore could not have done any trigonometry. There are other pointers to Greek and Roman arithmetic backwardness: e.g. the largest number they had was the myriad (10000) pitifully small compared to the number of 10^{53}
named as tallakshana by the Buddha. (No name for it even today in English.)
(b) Non-textual evidence: calendar. For what purpose did Greeks do trigonometry? Indians did it for astronomy and navigation. Forget about navigation, the Greek ignorance of astronomy is further corroborated by the highly defective Greek calendar. The Greek calends were a butt of jokes for Romans, as even the OED accepts, though the Romans themselves had a highly defective calendar.
(c) Social conditions. The social conditions of early Greeks (e.g. the death-sentence on Socrates on the charge of impiety by doing astronomy) demonstrates that the early Greeks were a superstitious lot, who punished astronomy with death. How, then, could astronomy (or any science) flourish among Greeks under these circumstances? Likewise, it is strikingly strange that a Euclid should have written a text so well suited to the political requirements of the Crusading church, 1500 years later, that the church adopted the book as a text for centuries. (But Greediots are gullible people with no brains, which is OK, except that they demand the same from others!)
(d) Accretion in scientific texts. Later-day (Arabic or even later Byzantine Greek) sources of Greek math are likely to be accretive. As I teach in my decolonoised HPS course, scientific texts tend to be accretive since frequently updated with the latest knowledge. The Almagest is such an accretive text, e.g. its star list is headed by the present-day pole star which was not even remotely near the pole in the time of its purported Greek author Claudius Ptolemy (2^{nd} c. CE). As such, attributing authorship of, or all knowledge in, these late texts to early Greeks (such as Ptolemy and Archimedes) is grossly anachronistic. (But Greediots are bent on self-glorification.)
(e) Scriptural significance given to isolated passages. Since early Western historians were Christian priests, or trained by them, they assigned scriptural significance to isolated passages in these late texts. For example, the supposed “evidence” for “Euclid” is one such single passage in a text by Proclus. As in scriptural analysis, reliance on individual passages conveniently ignores the context; it invites us to overlook that this passage contradicts the rest of Proclus’ prologue which speaks of the religious significance of geometry. (Theology, of course, can digest all contradictions by demanding faith.)
(f) Interpolation, either innocent or deliberate. The more natural approach is to regard such misfit passages as later-day interpolations. The late texts, which are the source of Greek history of science, come to us from the hands of dishonest Christian priests who could easily have interpolated remarks or passages. It has always been the official tradition of church history (since Eusebius and Orosius) to write falsehoods to glorify itself and denigrate others. There are well documented cases of forgeries by Christian priests, such as the fake “Testimonium Flavium”, or the spurious “Award of Constantine” on which the Vatican is founded. They introduced extensive forgeries even into the Bible (“gospel truth”) as the scientist Isaac Newton pointed out in his suppressed seven-volume History of the Church, suppressed to this day. Of course, some interpolations could also be non-malicious errors, as in the wrong claim that Euclid was from Megara in the first English translation of the Elements from Byzantine Greek in the 16^{th} c. In short, isolated passage in late sources of Greek math are not reliable for they may involve interpolations, whether deliberate or introduced innocently.
In view of all the above arguments, in my talk I repeated the point made in Cultural Foundations of Mathematics that the Almagest (of Egyptian origin) a later version of which was mis-attributed to a non-existent early Greek called Claudius Ptolemy could have accreted from later-day Indian math and astronomy texts. In fact, I argued that the version available to us did so accrete, for example because it speaks of the difficulty of multiplication exactly as do Arabic zijes of the 9^{th} c. And it starts with a paraphrase of a long-drawn controversy in Indian tradition over Aryabhata’s statement that the earth rotates.
Someone in the audience (a Greediot?) understood only the point about the lateness of sources for claims about Greek math. Looks like the rest of my arguments went above his head, or he just ignored them since he had no answer to them. He objected that physical sources for Aryabhata are similarly late. This is an objection raised even by school children (while teaching them Rajju Ganita) hence here is my response in detail.
First, I have no objection to valid inference: only to wild speculation as used in the Greek case. To reiterate, one needs to separate valid inference from wild speculation.
Thus, the physical Indian sources of math come from the same land, and in the same language, only from a different time, unlike the Greek sources which are not only from a different time, but also from a different land, and in a different language. Apart from wild racist assumptions, by what process exactly do we know what percent of the text, if any, was actually the work of Greeks? How much was of Egyptian origin, and how much due to accretion from Indian texts? Obviously, Western historians never explained. They never will be able to.
Second, the objections (a), (b), (c), (d) obviously do NOT apply to Indian sources of math. E.g. there is evidence for sophisticated arithmetic and a sophisticated calendar right from Vedic and Buddhist times (the Buddha has a name, tallakshana, for 10^{53}). The social conditions in India were against superstition, as I have repeatedly pointed out (e.g. see this magazine article on scientific temper in ancient India, and this extract describing Indians against superstition), though, of course, all sorts of false and derogatory stories have been spread about India. This situation is contrary to Greeks where even Socrates was killed for doing astronomy, and disbelieving the divinity of the sun and the moon, a charge he denied. But Greediots are stuck to their myths and just neglect any contrary textual or non-textual argument, 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.
Further, Indian sources are free from 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’s आर्यभटीयभाष्यwe can clearly separate Aryabhata’s contribution from that of Nilakantha a thousand years later. No anachronistic attribution here.
Because there are so many different commentaries from different times and places, all of which verbatim reproduce the original text on which they comment, we can also rule out accretion. But Greediots don’t seem understand this argument. They are bent upon glorifying Greeks by falsely and anachronistically attributing knowledge to mere names like Archimedes.
Also, in the Indian case, there are so many commentaries on Aryabhatiya from so many different places in India. This is quite unlike the Greek case, where there is just one (out-of-context) passage in one manuscript used as evidence for Euclid. That is the Indian sources are (probabilistically) independent, so that any later-day interpolations can easily be identified, and can also be easily excluded from a critical edition. In short, anachronistic attributions, accretion, and interpolations, can be ruled out in the Indian case of Aryabhata, say, but not in the case of Greek “sources”.
Again, because of the existence of both commentaries and objections (raised by opponents of Aryabhata, such as Varahamihira, and critics such as Brahmagupta) and responses to them, there is a continuity in Indian sources, which is completely absent in the Greek case, where all we have is a single late text. We are asked to rely on wild (and sometimes demonstrably dishonest) speculations (such as those of Heiberg) based on a single late text such as the Archimedes palimpsest.
Anyway, the simple upshot is that contrary to what has been stated by dishonest Western historians like Pingree, trigonometry (and aspects of Indian astronomical controversies) were accreted into the Almagest, and the early Greeks were innocent of both trigonometry and the crime of astronomy. This is one of the reasons Western historians have failed to engage seriously with my book Cultural Foundations of Mathematics on the origin of calculus and trigonometry in India. They have no answer, and instead have the cheek to ask me to engage with their later texts, and not tell a different story.
The time has come to puncture the bloated Western self-image, based on falsehoods. By beginning to tell our own stories, we are nearing the end of false Greek glorification since the Crusades and by racist historians who never dare take our objections into account.
]]>But the church was hardly the only culprit. Following in the footsteps of the church, this technique of using false history for self-glorification and denigrating the other was later picked up by racist historians.
As a result, our current class IX school text poisons the minds of young children by showing them a racist image of a white-skinned Euclid as does Wikipedia a partner in the crime of racist propaganda.. There is no evidence for even the existence of Euclid (my prize of Rs 2 lakhs for serious evidence about Euclid is still open after a decade) so how did these Greediots know the color of Euclid’s skin? But Greediots will be Greediots!
I shook this equilibrium by arguing to the contrary that the author of the Elements was a black woman as depicted on the cover of my book Euclid and Jesus. Curiously, because of childhood indoctrination, people ask for “evidence” only when one speaks of black skin; these are the very same people who, as children, never asked for evidence and never objected to the depiction of Euclid as white-skinned without the slightest evidence.
Anyway, what is my evidence? How exactly do I know the gender or skin color of the author? Well, all Greek manuscripts of the Elements describe the book Elements as authored by Theon or based on his lectures. (Euclid is never mentioned as the author in any Greek manuscript or commentary, one more nail in the coffin of utterly Greediotic history.) Theon was the last librarian of the Library of Alexandria before it was burnt down by rampaging Christian mobs. Proclus a short while later writes a commentary on the Elements. So, the real author of the Elements must be between Theon and Proclus. (The subject of Egyptian mystery geometry, of course, existed from long before, we are speaking of the author of a particular book on the subject, the Elements.) That leaves Theon’s daughter as the most likely author of the Elements. This is, of course, some 800 years after the purported date of Euclid, and in vastly different social circumstances.
This belief in the gender of the author is further corroborated by the fact that Greek commentaries speak anonymously of “the author of the Elements”, though they mention all others from Aristophanes to Zeno by name. Why the anonymity? Obvious: none else is a woman, and we know that Christians regard women as inferior, and never accepted a woman as a pope. This anonymity further suggests that something terrible happened to the author. Indeed, as is well known Hypatia was raped and brutally killed on the altar of a church.
As the last event demonstrates, changing the author (hence the date) changes the social circumstances. That naturally does change our understanding of the book: a book written in another time and another place would have different motivations.
In accord with Proclus’ stated understanding of the Elements as a religious text intended to arouse the soul, Hypatia was trying to defend her pagan beliefs about the soul through geometry. But this was at a time when those pagan beliefs about the soul were under vicious attack by the church which had demolished every last pagan temple in the Roman empire. Hypatia hence aroused the ire of the church. This atrocious hate crime by a Christian mob led by a hate-mongering bishop was no local rivalry as church apologists maintain: it was part of a dirty religious war waged by Christians against pagans, the first religious war known to mankind.
And how do I know the color of her skin? Well, I go by the standard of “balance of probabilities” for history. The author of the Elements (i.e., Theon’s daughter the 5^{th} c. Hypatia) was from Alexandria in Egypt which is part of the African continent. So, black is the default skin color until proved otherwise. Go ahead, produce contrary evidence for the skin color of the author from the text and I will change my views, provided the remark is not an obviously forged one. And if you can’t produce the evidence for the skin color of the author (and no one has for so many centuries) then accept that I am right. Accept that the depiction of Euclid as a white man is false racist propaganda carried on for centuries.
My reasoning about the author as a black woman writing to defend her religious beliefs is certainly far better than the mere myth that the author was a white male, or the contra-factual claim that the book is about axiomatic proofs, a belief so politically convenient to the Crusading church that it adopted the Elements as a text book to teach faith-based (axiomatic) reasoning to its priests.
At this stage there are those who will jump up to say, as a person did after my talk, that skin color (or gender) of the author does not matter. First the real author does matter, because changing the author changes our understanding of the book from a book about axiomatic proofs to a semi-religious text of little practical importance. But the skin color of the author also matters: else why did my article on “Was Euclid a black woman?” create such a storm in South Africa? Tens of thousands of people found it interesting, therefore it was reproduced worldwide. But then the South Africa editor of the Conversation censored it: she wanted to preserve the false myths of white achievements in math. She exercised her editorial authority to censor it. On the system of blind faith in editorial wisdom, the article was censored worldwide (e.g. by Scroll in India). Why censor it if the skin color really does not matter? (See, Mathematics and censorship.)
At this stage, when racists ;have no arguments to offer, they resort to the church technique of vilification: this requires no academic skill, any dog can bark. The racist press in South Africa and the related church reports in US called me a “conspiracy theorist”. Obviously, their greatest and best formal mathematicians can think of nothing better to do than to serially plagiarise my work. (See this blog on Plagiarism by the President of the Royal Society.) This racist slur of “conspiracy theory” was repeatedly used by another participant in the Shimla round table, as an acknowledgment of his lack of academic skills All the above arguments are a conspiracy theory aren’t they?
And (if skin color really does not matter) are Greediots willing to change the image of “Euclid” children see in our school texts from a white man to a black woman? Will they even try changing it in Wikipedia which is supposedly open to change? Will they openly admit there is no evidence for the white skin of the author of the Elements as they have been falsely peddling for centuries? Like the worm turning, could they even add a comment in Wikipedia about the existence of different opinions? No way! Actions speak louder than words. If skin color really does not matter, don’t just say it, show it with your actions! And if you don’t we know what your true beliefs are for we judge by actions!
The trick to spread these Greediotic and racist lies is to use childhood indoctrination, through education, and reinforce it by propagandist and racist instruments like Wikipedia. Greediots everywhere, evidence nowhere.
]]>As pointed out in the previous blog entry, there are, in fact, no axiomatic proofs in Greek math. But there is a widespread and sticky belief to that effect.
Why is this false belief about axiomatic proofs among Greeks so widespread and sticky? In fact, Western/church education spread the false myth.
Cambridge foolishness
Thus, on (1) that false myth of axiomatic proofs among Greeks, linked to (2) the false myth about the person Euclid and his intentions, (3) the order of theorems in the Elements was regarded as very important, and the key contribution made by “Euclid”.
This third myth was so important that the Cambridge Board of Studies foolishly laid down in its exam rules in the 1880’s that students must follow that order. This Cambridge foolishness is extraordinary because the Cambridge syndics commissioned a new text, which liberally uses empirical proofs, including, of course, the empirical proof of SAS (Side angle Side or proposition 4). Order is unimportant once an empirical proof is used: for instance the Indian proof of the “Pythagorean theorem” in the युक्तिभाषा proves the theorem in one simple step, without needing 46 earlier propositions.
The Cambridge foolishness in insisting on the order of the propositions, while using a text which gives empirical proofs tells us how the education system propagates Greediotic myths for centuries, and teaches students to ignore facts.
Church hegemony over the Western mind
Even Bertrand Russell, as a product of Cambridge, continued to believe in the “Euclid” myth of axiomatic proofs, though he realized the myth did not fit the actual book. He foolishly declared it to be Euclid’s error and not the error of the false myth of Euclid and his intentions!
That is the effect of the church control over the Western education system, and consequent hegemony over the Western mind, including the minds of those opposed to the church. This church “education” from Cambridge widely spreads myths and superstitions, which were then globalised by colonial education. It created “Greediots, Greediots everywhere and not a stop to think”.
A politically convenient reinterpretation
As Proclus explains (and the reason why he wrote his Commentary on the Elements), the Elements is a “pagan” religious text, i.e. a text on Egyptian mystery geometry which is meant to arouse the soul, exactly as Plato argued in Meno. The book Elements was never intended to be about axiomatic proofs. How did “Euclid” fit church needs to a T?
The church simply re-interpreted the book to suit its politics of reason. The church was well aware that most people are gullible, because of childhood indoctrination. And such was the fear of the church (not only the Inquisition, but even in England), that the church as well aware that no one would dare to challenge its interpretation. The facts is the no one did so for centuries.
During this time the church used the Elements to teach reasoning to its priests: a special kind of metaphysical reasoning, which suited the church, since its divorced from facts, and involving faith based or axiomatic proofs.
The church monopoly on education, through the “reputed” institutions it set up and controlled, such as Oxford and Cambridge, resulted in spreading this superstition widely among Westerners.
So widely, that when the myth of axiomatic proofs in “Euclid” ultimately collapsed (among the knowledgeable), people like Russell and Hilbert created formal mathematics to save it.
The Pythagorean calculation
Curiously, Greediots and Western historians, intent on glorifying themselves, never ever speak of the “Pythagorean CALCULATION”, though a formal proof of the “Pythagorean proposition” has no practical value, and all practical value derives from the ability to use it to CALCULATE the diagonal of a rectangle whose sides are known.
Western historians are silent about the process of calculation among Greeks. Why? Because, as stated in the Manava sulba sutra 10.10, that calculation requires square roots and Greeks and Romans did not have fractions or square roots or any part of the mathematical apparatus needed to carry out that calculations as Egyptians (Ahmes papyrus), Iraqis, and Indians did. See this article in Journal of Black Studies or its manuscript version. Many non-Greeks had the “Pythagorean” calculation which was SUPERIOR since it offers practical value than the mere “Pythagorean” theorem, and its sham epistemic value.
This dishonesty of Western historians (in not comparing the calculation and the theorem) is not accidental: false history is a deep seated part of Western culture. Western culture has obvious church roots, and the church discovered long ago that lies are a terrific source of power, and can be used to rule over gullible people even without weapons. Since then, the West has been systematically writing false history in the manner of Orosius’, History Against the Pagans, with the calculated intent to glorify itself and portray all others as inferior.
It has propagated these lies through the Western education system over which it had a monopoly for centuries.
Globalisation due to colonialism
The problem is that colonialism globalised this church education system, and our children are its victims, suffering its evil consequences until today.
For example, our class X school text in math uses the term “Pythagorean theorem” 32 times to hammer the lie home in the minds of children. A thousand lies are not needed to make a truth, 32 times is quite enough.
Naturally, children start believing it to be true, and they disbelieve other ways to understand the proposition. No room is provided to students or anyone else to disagree or challenge the school text or even ask for evidence: if you do, all that NCERT does is to say that this is the way it is done in Western texts. So, we the colonised must slavishly imitate it. That is the purpose of colonial/church education: to teach slavish imitation.
To repeat, teaching the Greediotic history of the “Pythagorean theorem” is like teaching the literal belief in virgin birth: no evidence for it, it is contrary to known evidence and contrary to common sense. Yet millions of people hang on both beliefs because of childhood indoctrination through “education”.
It is high time we repaired our text books to eliminate this kind of nonsense Western history by eliminating all references to the Pythagorean theorem in them.
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Recently, I presented my talk on “Pre-colonial appropriations of Indian ganita: epistemic issues”. This was at a round table at IIAS Shimla which replaced the now-postponed conference on Indology.
The key point of my talk was that much present-day school math is an inferior sort of math which Europeans appropriated from Indian ganita without fully understanding it, and then returned during colonial times by packaging it with a false history and declaring it superior. A philosophical comparison between ganita and math was done in earlier posts and publications.
This post focuses on the false history aspect, going back to the purported Greek origins of the “Pythagorean theorem”.
False Western claim
Egyptians built massive pyramids very accurately. One would assume that to achieve that marvellous feat of engineering they knew the so-called “Pythagorean theorem”.
But in his book Mathematics in the time of the pharaohs, Richard Gillings speaks of “pyramidiots”: people who claim various sorts of wonderful knowledge is built into the pyramids of Egypt. Gillings’ argues in an appendix (citing the Greek historian Heath) that “nothing in Egyptian mathematics suggests that Egyptians were acquainted with…[even] any special case of the Pythagorean theorem.” Heath adds, “there seems to be no evidence that they [Egyptians] knew [even] that the triangle (3, 4, 5) was right-angled”. The Egyptologist Clagett chips in, “there have been exaggerated claims that Egyptians had knowledge of the Pythagorean theorem which is, of course, a formal Euclidean theorem of the Elements.”
First, Gillings, Heath etc. are not honest enough to add that there is no evidence for Pythagoras. Nor is there any evidence for the claim that he proved any sort of theorem. So, one should rightfully say, “There have been persistent false claims about a Pythagoras having proved a theorem, though there is no evidence that there was any Pythagoras nor any evidence that he proved any theorem.”
Obviously, Western history of Greeks is of very inferior quality, since the tacit norm is that stories about Greeks need no evidence and must be accepted on mere faith in Western authority: it is only stories about others which require evidence!
That is why I use the term Greediots to describe people who fantasize about all sorts of scientific achievements by Greeks without any evidence, starting from the “Pythagorean theorem”: if they can believe in that they can believe anything on their blind faith.
Religious connection of geometry
A key point: not only is there nil evidence for the story of the “Pythagorean theorem”, it is CONTRARY to all available evidence.
The Pythagoreans were a religious cult: their interest was in the connection of geometry to the RELIGIOUS belief in the soul as described by Plato, in Meno, Phaedo, Republic, etc. Anyone can check in two seconds this connection of geometry to the soul by searching for the 2^{nd}, 3^{rd}, and 4^{th} occurrence of “soul” in Meno, a primary source for Plato readily available online from the MIT repository. But for Greediots the story of a theorem is what is important: so they don’t and won’t check facts. (Is Plato evidence for Greek thought? If not, why has no one ever explained the grounds for rejecting Plato? And what are the other “reliable” sources, if any, for Greek history? )
Proclus, in his Commentary, explicitly asserts that this religious belief linking geometry to the soul was the sole concern of the Pythagoreans with geometry. But Greediots not only have no evidence for their beliefs, they ignore all the counter-evidence.
As Proclus further explains in his Commentary (on the book Elements today falsely attributed to an unknown “Euclid”) the book does geometry with exactly the same religious concerns. The subtle issue here is to understand Egyptian mystery geometry (and related Greek mathematics) as a sort of meditative discourse which drives the attention inwards and away from the external world.
All this is explained at great length in my book Euclid and Jesus: how and why the church changed mathematics and Christianity across two religious wars, Multiversity, 2012. See the webpage, or look inside. But Greediots will be Greediots they not only have no concern with facts they will not tolerate a counter-narrative or allow any space for it.
No axiomatic proofs in Elements
The interesting thing is how this “virgin-birth history” propagated by Greediots creates false “facts”. Clagett’s claim that “the Pythagorean theorem…is, of course, a formal Euclidean theorem of the Elements” is one such false “fact” which is widely believed.
The real fact is there is no axiomatic or formal proof of the “Pythagorean theorem” in the book Elements of “Euclid”. One has only to read the book; its very first proposition has an empirical proof not an axiomatic one. But just as most people do not read Plato, most people do not read the Elements. They just naively assume that even if the myth about its author as Euclid is false, the myth about the book must be correct. (Ha, Ha, they don’t know how thick are the layers of church lies!)
After centuries, some including Bertrand Russell finally understood the absence of axiomatic proofs in the Elements. What is shocking is for how many centuries Western scholars collectively failed to realize that even the first proposition of the Elements is contrary to the myth of axiomatic proofs in it.
Unfortunately, Russell referred to the absence of axiomatic proofs in the Elements as “errors” made by Euclid. That is, he foolishly assumed, merely on the strength of the “Euclid” myth, that such was “Euclid’s” intention. He should instead have inferred the intent of the author from an actual reading of the book. Thus, there is (1) no evidence for Euclid, (2) there is no evidence he wrote the book, (3) there are no axiomatic proofs in the books, but (4) Plato and Proclus’ commentary on the book do tell us about a different religious intention of geometry and (5) a different author of the book.
Further, Westerners with their faith-based history of Greeks expect others to be gullible enough to believe that this mythical Euclid, writing in a social context far removed from that of the Crusades, was so perfectly tuned to the politics of the Crusading church that the church used the book as a text for centuries. Obviously, any intention can be attributed to a mythical figure, as politically convenient, and the gullible flock will swallow whatever nonsense their priest says. The remedy is to actually read the book, and apply one’s mind to it, which ALL Western scholars hilariously failed to do for centuries.
Collective failure
That collective failure speaks very poorly for the quality of Western academics: we need to laugh at them, not follow them.
Specifically, the proof of the “Pythagorean theorem” (47^{th} proposition) in “Euclid’s” Elements depends on the 4^{th} proposition of the book, which is the side angle side or SAS proposition. However, in all manuscripts of the Elements, the SAS proposition is proved EMPIRICALLY, by putting one triangle on top of another and seeing that the two are equal. An empirical proof is NOT the same as an axiomatic proof. There are no axioms in the book from which SAS can be proved. In fact, there is no known way to prove SAS axiomatically except in the trivial way of assuming the theorem as an axiom, as is done today.
Therefore, today SAS is taught as a POSTULATE/AXIOM in our class IX school texts. This is proof of the absence of axiomatic proofs in the Elements. But Greediots don’t do their ninth standard math either: they are fixated on false myths, and worried only about how to save those lies.
To reiterate, the proof of the “Pythagorean theorem” in the book Elements depends on the proof of SAS. Therefore, there is no formal mathematical proof of the “Pythagorean theorem” in the book Elements of “Euclid”. That is, while the book Elements has axioms and proofs, it has no axiomatic proofs. In fact there is no formal proof of the “Pythagorean theorem” in any Greek works or before the 20^{th} c. On the other hand, non-formal (semi-empirical) proofs are available everywhere, including in India.
Myth stronger than facts
But, even a century after the absence of axiomatic proofs in the Elements was publicly exposed, the myth proves stronger. There is no shortage of “eminent” scholars who keep repeating that false claim of formal or axiomatic proofs in the Elements. Clagett is not an isolated scholarly Greediot. Needham also believed that Greeks did something special in math, as I have pointed out.
It is high time that Western historians acknowledged the falsehood of both terms in the phrase “Pythagorean theorem”: no Pythagoras, and no formal theorem. It is even higher time that Indians understand that much Western history of science is deliberate fraud since Western historians refuse to remedy even utterly false claims about the “Pythagorean theorem”.
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An interactive workshop at the Berlin festival for time issues 24, 25 March 2020, 1500-1800 Berlin time. Facebook live stream: http://facebook.com/MaerzMusik
will be only of the conference talk on the 21st March 1430 to 1600 Berlin time (1900 to 2030 IST).
The workshop will cover the following 12 topics related to the book. Each topic will be covered in an average of approximately 20 minutes. After each hour there will be questions for around half an hour.
The book begins and ends with the Fisherman’s story: to marry a mermaid the Fisherman wants to lose his soul, but does not know how to do so.
The first step is to understand that current physics is history-dependent. This destroys the hypotheses of the recurrence theorems (whether Poincare’s or Markovian). That is, recurrence can no longer be exact or eternal (even granting that exact recurrence is conceptually meaningful).
Recommended reading
General reference:
The Eleven Pictures of Time: the physics, philosophy and politics of time beliefs, Sage 2003. See a preview of the book (Kindle: look inside at https://www.amazon.in/Eleven-Pictures-Time-Philosophy-Politics/dp/0761996249. See, also, webpage: http://ckraju.net/11picsoftime/.
Also,
Time: towards a consistent theory, Kluwer Academic, Dordrecht, 1994. Fundamental theories of physics, vol. 65. See webpage: http://ckraju.net/11picsoftime/oldbook/index.html.
For a later account of how a changed picture of time changes values see
“The Harmony Principle” Philosophy East and West, 63(4) (2013) pp. 586–604. http://www.ckraju.net/papers/Harmony-principle-pew.pdf.
For the relation of a tilt to creativity and time travel see.
“Time Travel and the Reality of Spontaneity” Found. Phys., 36(7) 2006, pp. 1099–1113. https://arxiv.org/pdf/0804.0830
For an account of how the church hijacked mathematics, see
Euclid and Jesus: how and why the church changed mathematics and Christianity across two religious wars, Multiversity, Penang, 2012.
For an account of how church dogmas of eternity penetrated into the formal mathematics of infinity see,
“Eternity and Infinity: the Western misunderstanding of Indian mathematics and its consequences for science today.” American Philosophical Association Newsletter on Asian and Asian American Philosophers and Philosophies 14(2) (2015) pp. 27–33. Posted at http://ckraju.net/papers/Eternity-and-infinity-Pages-from-APA.pdf.
For the mathematically inclined, interested in a general expository account of the mathematical reformulation of physics with a tilt in the arrow of time, using mixed-type functional differential equations, see the following:
For the ongoing efforts to decolonise mathematics and teach calculus and geometry as normal math without “real” numbers see:
Web: http://ckraju.net/. Writings: http://ckraju.net/papers/ckr-books-articles.html.
Press: http://ckraju.net/press, Videos: http://ckraju.net/videos, Blog: http://ckraju.net/blog.
Lesson 1. Do not blindly trust Western/White authority. Fight to reject any system which forces such trust.
If the editor of the most prominent math journal (Notices of the AMS) can act so shamelessly in such a public case, just imagine what mischief an editor can do in secret. Yet our whole academic system forces academics to trust editors. University academics are required to submit papers to editors and get their certificates of approval through a secretive process of refereeing. This system of valuing only publication in secretively refereed “trusted” and “authoritative” journals, whose ranking strongly correlates with their degree of Westernization, turns university academics across the world into slaves of the West. For their career advancement they are forced to keep Western authority happy. This is particularly the case in formal mathematics, where authority is the sole guide to truth.
With such secretive editorial control over what constitutes valid knowledge, no serious critique of colonial knowledge is possible. For example, the racist editor of the Conversation censored my article on decolonising math, after it was published and went viral. (For more details see “Mathematics and censorship“, Journal of Black Studies, and Rhodes Must Fall.) Her stupid excuse was that (as a non-White) I am not allowed to cite original ideas from my own published work, but must only repeat White/Western falsehoods. It is strange that so many news portals across the world, which first reproduced my article, believed that excuse, and pulled down my article.
That editor’s idea of a proper article was one which began with the fake history that “mathematics…is the work of dead white men”, and hence blacks and women are bad at math. The recommendation “imitate the West/Whites”. This way of using fake history to demand imitation of the West was the strategy of colonisation, and that is being now passed off as a strategy of decolonisation.
Reject this system of thought control. Refuse to be guided by such editors. As stated in Ending Academic Imperialism, in this digital age, there is a very easy alternative in the form of post-publication public review. (That would diminish colonial power of thought control, which is exactly what the decolonial activist wants.)
Lesson 2. Colonial authority is built on false myths of supremacy, just as racist authority was built on the false myth of racist supremacy. Tear it down by demanding evidence for those myths.
Much colonial power is based on lies propagated through colonial education. To teach the intellectual supremacy of the coloniser, math texts tell all sorts of glorious but false tales of White/Western/ colonial achievements in math, such as those of early Greeks such “Euclid”, “Archimedes” etc. for which there is no serious evidence. (See the drafts of these lectures. “Not out of Greece”, delivered at the University of South Africa, Pretoria.) The Greeks and Romans knew little math little math as shown by their defective calendar, copied, like their gods, from Egyptians.
Challenge that false claim of Western intellectual supremacy by repeatedly pointing out the falsehood of these myths. Demand solid evidence, as I did through my Euclid challenge prize mentioned also in my censored article. And keep pointing out the falsehood of those myths for at least a century to drive home the point.
Apart from the early Greeks, in “official history, scientific discoveries are mostly attributed to post-renaissance Europeans. Atiyah is hardly the sole case where brazen theft has been passed off as “independent rediscovery”. As regards post-renaissance “discoveries” in science there are numerous fraud cases of people glorified on the strength of such “independent rediscovery” just when dependent discovery was possible. This includes cases such as Copernicus, or Newton’s purported invention of calculus, as described in my books Is Science Western in Origin? (Multiversity etc., 2009, 2014) and more elaborately in Cultural Foundations of Mathematics (Pearson Longman, 2007)
First, the simple remedy is this: the onus of proof must be on the one who claims independent rediscovery or glorifies it. This principle must be applied especially to fake Western heroes. Second, there is no reason to continue to give credit to the one who claimed the idea at a later date. Give credit only to the one who did it earlier. Thomas Kuhn in his Copernican Revolution (1956) brazenly continued to glorify the “second discoverer}, Copernicus, AFTER he was exposed in 1952 by Kennedy as having copied from Ibn Shatir. Was Kuhn such a bad researcher that he didn’t know about Copernicus’ exposure? (When I ask this question in my decolonised course on history and philosophy of science, all students opine that Kuhn tried and succeeded in a cover-up.)
Keep in mind the trick of “Atiyah’s hypothesis”: that most people go by nomenclature, not facts. Hence, insist on large-scale changes in nomenclature in history books to reflect this principle, that the numerous second discoverer’s cannot cannot continue to be credited, and delete the names of people who have been fraudulently credited with ideas on the strength of “independent rediscovery”. Smashing fake Western icons, and the related claim of intellectual superiority, by speaking the truth, would expose the true face of colonialism, and greatly diminish its continuing power.
Lesson 3. Beware of the counter-reaction when editorial authority and false myths are challenged.
Colonial power was based on lies, like the power of the church. The church developed a systematic technique of preserving its lies, and the West continues to use it. The stock technique is to demonise all those who challenge its authority . That is, the simple trick is to preserve fake heroes by painting any challenger as a villain, through further lies.
This technique of creating fake villains works exactly the way witches and heretics were demonised by the church. To reiterate, American wealth was built on theft of land (from the “Red Indians” who were all killed) and theft of labour (from black Africans who were brutally enslaved). But instead of condemning genocide and slavery, genocide and slavery were extolled for centuries as a high moral acts, and supported by copious references to the Bible. The thieves were glorified, and it was the “Red Indians” and blacks who were (and are) demonised to this day, as in “Western” (cowboy) stories. Blacks continue to suffer from the resulting prejudices, as is still evident in biased police action against blacks in the US. Something similar happened in post-apartheid Africa. Those like Mugabe were demonised for demanding some reparation through land redistribution back to blacks, not the proponents of apartheid who continue to enjoy their ill-gotten wealth. It was this sense of “righteous” racism, advocated also by top Western philosophers like Kant, etc., which generated the lynch mobs in the US, after the declaration of emancipation.
So, what should one do to counter this method of maintaining lies through demonisation? Simple. First recognize when someone is being demonised. First ask: is that person doing something right which challenges White/Western/colonial authority? If so, immediately reject such post-colonial misguidance, whether academic or journalistic.
Since decolonisation concerns education one should also expect post-colonial academic lynch mobs, as in post-emancipation US. Thus, when I challenged the academics of the University of Cape Town to an intellectual debate on decolonisation, the still dominant White academics in UCT felt threatened. They were intellectually too feeble to respond to even a single one of my substantive points. See the advance summary here, the presentation (Part 1, Part 2, Part 3) and the videos of the discussion here, here, and here.)
Therefore, some academics of the University of Cape Town took the easy way out and did what they were able to do: they systematically spread the canard that I was a conspiracy theorist. No one bothered even to specify what the conspiracy theory was: presumably they were referring to the theory Atiyah plagiarised. Hilarious isn’t it: the world’s supposedly top mathematician caught repeatedly plagiarising from an alleged conspiracy theorist! But racist nitwits who were stupid enough to believe in the silly dogma of apartheid for so long can believe anything. I will have a lot more to say on this in a forthcoming blog.
Meanwhile, note how Western journalists are spreading that canard. Lewton, a journalist from Kenya, repeated this slander against me for the US-based Undark magazine, again without verifying facts. (And why did Undark editors, not demand that facts be checked?) Haensch too cites this, neglecting facts to add her own little bit to that academic lynch mob. Little by little, after a couple of decades, the West will claim I was the villain and Atiyah the hero!
Decolonisation practitioners must learn to contest this demonisation of all opponents of colonialism. How?
The opponents of decolonisation have only lies to tell, whether about heroes or villains. Hence, the decolonisation formula is simple: focus on the facts. Just check, check, and cross-check the facts and arguments. Don’t ever trust the West/Whites one inch, for so much of their power is built on lies. Cross out every last story (there are thousands of mutually supporting stories) for which you have no solid evidence (or evidence only from Wikipedia). Cross out every last empty adjective used to supplement a lack of facts. And you will see that nothing remains!
And, even if you are ignorant of math, never consult a formal mathematician privately for an opinion about the decolonisation of math. Ask them first to respond publicly to the substantive critique of formal math. Ask them to respond even to my decade-old Euclid challenge prize, that Euclid existed, was a white-skinned man, as depicted, in our school texts (and not a black woman) or that there is a single pure deductive proof in the book attributed to him. And, if the formal mathematicians dodge, and merely engage in personal attacks, and mouth more lies, or try to pass off the opinion of authority as facts, take it as a sure sign of their total intellectual defeat.
Decolonisation activists: if you take these simple lessons to heart, decolonisation will surely triumph, including decolonisation of math. Millions of children will be saved from the torture of useless formal math that is inflicted on them today. Future generations will forever thank you.
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