Archive for the ‘History and Philosophy of Mathematics’ Category

Did Indian learn trigonometry from Greeks? Responses to the Aryan race conjecture in the African context, and the relevance to Indology

Wednesday, March 18th, 2020

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. 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.

Shimla Indology lecture

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. (more…)

Greediots and Pythagoras. 3: Was Euclid a black woman?

Wednesday, March 18th, 2020

My point in part 1 and part 2 of this post was that there were no axiomatic proofs among Greeks, and that the cult of Pythagoreans as also the book Elements were both concerned with religious beliefs about the soul linked to geometry. The church reinterpreted the book Elements, to suit its politics. Church education then spread the ridiculous false belief that Euclid’s” book was somehow allied to its theology of reason, which used faith-based reasoning. Colonial education spread these beliefs far and wide.

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 5th 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.

Greediots and Pythagoras. 2: How church/colonial education spreads false myths

Wednesday, March 18th, 2020

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? (more…)

Greek history for idiots: Greediots and Pythagoras. 1: No axiomatic proofs in Greek math

Wednesday, March 18th, 2020

Greek history for idiots: Greediots and Pythagoras.
1: No axiomatic proofs in Greek math

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 2nd, 3rd, and 4th 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.

(more…)

Plagiarism by ex-president of the Royal Society. 3: Lessons for decolonisation of math

Friday, November 8th, 2019

So, what are the lessons for decolonisation from part 1 and part 2?

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.

(more…)

Plagiarism by ex-president of the Royal Society. 2: The cover-up by the American Mathematical Society

Friday, November 8th, 2019

Part 1 of this post restated the facts regarding my novel mathematical point about “Einstein’s mistake”, how it was copied by Michael Atiyah during his AMS Einstein Centenary lecture of 2005, and its subsequent report published in the Notices of the AMS, 2006. Also copied was the claim that the point was novel enough to constitute a paradigm shift. It was also related to quantum mechanics as I had done earlier. For sure, Atiyah did it knowingly, for (a) my novel point about Einstein was very widely disseminated through two books and several journal articles, and newspapers, and (b) Atiyah persisted in falsely claiming credit even after (c) he was directly informed of my past work, and acknowledged being so informed.

But before going to an ethics body (which later indicted Atiyah) I first approached the American Mathematical Society for redress.

So how exactly did the AMS respond to this plagiarism?

As the AMS ethics states (see excerpt):

  • The knowing presentation of another person’s mathematical discovery as one’s own constitutes plagiarism and is a serious violation of professional ethics. Plagiarism may occur for any type of work, whether written or oral and whether published or not.

And how ought the AMS to respond to plagiarism? It says:

  • “the Society will not knowingly publish anything that violates this principle, and it will seek to expose egregious violations anywhere in the mathematical community.”

The AMS cover up: part 1

But what did the AMS actually do? Did it expose this egregious violation of its ethics to the maximum extent possible?

Not at all. To the contrary, it covered up. How? The AMS did publish a note acknowledging the indubitable similarity of my earlier published work with the ideas attributed to Atiyah in the offending article published in the Notices. But this was not enough. Not even an apology was offered: that is the belated acknowledgement subtly tried to pass off Atiyah’s plagiarism as an “acceptable” oversight. It suggested that, in preparing for his Einstein centenary lecture, Atiyah had somehow missed noticing my two prominent books and journal articles on Einstein. But that Atiyah too had independently arrived at the very same novel mathematical (though not social) conclusions about Einstein in his Einstein centenary lecture, as I had done a decade earlier. The conclusions were so novel that the offending article had, like me a decade earlier, called it a paradigm shift, and had even linked it to quantum mechanics exactly as I had.

My letter objected to this. It was already plagiarism when it happened the first time, in 2005 because my extensively published work was widely disseminated, and wide dissemination is the test of plagiarism on the stated AMS ethics. It was plagiarism beyond all reasonable doubt when it happened a second time, through the prominent 2006 article published in the Notices of the AMS, AFTER Atiyah was directly informed of my past work, and had acknowledged being so informed.

But Andy Magid the then editor of the Notices refused to publish my letter. He wanted to hide the  full facts that Atiyah plagiarised twice, and that the second time there was not a shred of doubt that he plagiarised knowingly. Obviously, hiding these key facts would mislead many people into thinking the Atiyah case was one of “innocent” oversight. That is, the editor misused his editorial authority to suppress facts and mislead people by refusing to publish my objection. (His intent must be judged from his actions, and not what he preaches to his students.) That is, instead of upholding the stated AMS ethics, the AMS editor connived at its violation. Haensch, in her blog post, is furthering conniving in that unholy effort to water down Atiyah’s plagiarism, by twisting facts into allegations.

Indeed, Atiyah pressed his false claim so brazenly for a good reason: the value of formal mathematics is judged solely by authority, and as the authority, Atiyah was confident that many formal mathematicians would throw ethics and facts to the wind and jump to defend him (for quid pro quo, or because of their deep respect for authority).

Act 2: “Atiyah’s hypothesis”, Atiyah’s mistake

Therefore, Atiyah continued brazenly. In Atiyah’s second act of plagiarism he got two of his stooges, Johnson and Walker, to write the report of his lecture for the Notices. Why? First it provided a fig leaf of cover, which I later tore apart by pointing out that Atiyah was consulted. Second, the real aim of the Notices article was to attach his name to my ideas. Only by a third party (though not Atiyah writing himself) could coin a new term linking Atiyah to the grand “discovery” (not C. K. Raju’s book in the library, but the ideas in it!).

To further press Atiyah’s claim to the ideas, these two named it “Atiyah’s hypothesis”. This was done on the socially savvy principle, that people go by the name attached to a discovery, irrespective of the real discoverer. Therefore, merely naming it “Atiyah’s hypothesis”, while again suppressing any reference to my prior work, would forever mislead people into believing it was Atiyah who first thought of the idea.

This devious plan to plant that term “Atiyah’s hypothesis” in the most widely read math journal was probably Atiyah’s idea. At any rate, this nomenclature certainly had his approval, since Atiyah was consulted, as Walker was eventually forced to explicitly admit.

But there was another, even more subtle aspect of social savviness. Calling it “Atiyah’s hypothesis” (instead of “Einstein’s mistake”, as I did) would not arouse social opposition (as, for example, in Israel denying me a visa to talk about it in Palestine). Atiyah understood the value of my mathematical point, but he was interested in promoting himself, not in speaking the truth about Einstein.

However, despite this crafty way of plagiarising my work, Atiyah slipped up, because he lacked the knowledge which went into shaping my ideas. Atiyah the mathematician made a blunder about the physics involved. (more…)

Plagiarism by ex-president of the Royal Society. 1: The facts

Friday, November 8th, 2019

Background: What the decolonisation activist should know

By way of background theory, decolonisation activists need to understand the following. Western wealth was initially built on the obvious theft of land (e.g. of “Red Indians” by killing them) and the theft of labour (of blacks by enslaving them) and forcing them to work on the land. However, colonial power was built on a lesser known and more intangible theft: the intellectual theft of knowledge. This intellectual theft was used to glorify the West by systematically creating fake intellectual heroes from early Greeks to the “renaissance” (see Is Science Western in Origin?). This self-glorification was then used (e.g. by Macaulay) to impose colonial education, the key and continuing source of colonial power. (See, Ending Academic Imperialism: a beginning.)

To dismantle continuing colonial power, decolonisation activists must understand two key ways of covering up intellectual theft. The first is to use the “doctrine of independent rediscovery”, to let off the intellectual thief, and, indeed, continue to give credit to him. The second is the systematic technique of demonisation, to attack the one whose idea is stolen. Recall, how, instead of condemning genocide, it was the “Red Indians” who were demonised e.g. through “Western” films and narratives of “cowboys and injuns”. Likewise, instead of condemning slavery, it was the blacks who were demonised, and continue to suffer from the resulting prejudice even after slavery and apartheid officially ended. That is, apart from creating fake heroes, the West also systematically creates fake villains by demonising all its opponents to make even genocide and slavery “morally righteous”.

The following should be regarded as a case study which explains how these tricks continue to be used today at the highest level of the most reputed Western academic organizations to perpetuate colonial power and academic imperialism.

Introduction

Recently, a blog post “Putting math in context” came to my notice. It “tangentially” links (a) decolonisation of math (in which I have been involved over the past decade) to (b) the brazen and repeated plagiarism of my earlier published mathematical work by a former President of the Royal Society, Sir Michael  Atiyah and (c) its cover-up by the American Mathematical Society (AMS). This post on the AMS official blog, is written by Anna Haensch, an Assistant Professor at Duquesne University, and former AMS-AAAS mass media fellow. Her job as a blogger is supposedly to improve the public understanding of science. But the post is misleading. It distorts facts. Since this is a matter of great public importance, the issues need to be clraified, especially in the context of attempts by racists and formal mathematicians to protect their power (and jobs) by derailing the effort to decolonise math.

My response is in three parts. (1) The facts, (2) the cover-up by the American Mathematical Society, and (3) the lessons for decolonisation.

Fact, not allegation

First, referring to my webpage on Atiyah’s  plagiarism of my work and its cover-up by the AMS, Haensch calls it an “allegation of intellectual theft”, and “a really wild ride”.

But, it is a FACT that Atiyah plagiarised my work. There is a public finding by an ethics body that Atiyah was prima facie guilty of plagiarism. This is the first entry on the Atiyah webpage:

Hence, this is today an established and cited case of plagiarism. There is a distinction between a convicted criminal and an alleged criminal! Journalists are required to respect facts, but Haensch does not. (Perhaps because she is also a formal mathematician. Formal math is divorced from empirical facts, and hence can reach any false conclusions through bad postulates. This is one good reason to decolonise math.) A formal mathematician can simply postulate that “fact=allegation”. :) How else does Haensch reduce the public finding of three experts of an ethics body to a mere allegation made by me? For she has not offered a single new fact, or argument. Her related journalistic trick of avoiding facts is “proof by adjectives”, to persuade people who are too lazy to check facts.

AMS belatedly acknowledged my prior work

The other fact is that even before the judgment by the ethics body, the Notices of AMS itself eventually admitted the similarity of my earlier published ideas to those falsely claimed by Atiyah. This is again stated on the Atiyah webpage:

Is the journal (the most widely read math journal) so abysmally lacking in standards that it published such an admission merely on the strength of a wild allegation? Haensch’s insinuation implies this!  Actually, the strong similarity with my ideas is indubitable, and anyone can cross check it: just use the links to various documents on my Atiyah  webpage.

To recall, I first linked functional differential equations to a paradigm shift in physics on the one hand, and to quantum mechanics on the other. This was published as part of a long series of journal articles later consolidated into a book, Time: Towards a Consistent Theory, Kluwer Academic, 1994. (Fundamental theories in Physics, vol. 65.) These novel ideas were exactly the one’s for which Atiyah dishonestly claimed credit in his AMS Einstein centenary lecture 2005 and in its report published in 2006. This was done in full knowledge of my past work.

Why a post-facto acknowledgement is NOT enough

OK, so why is the post-facto acknowledgement to my prior work not enough? (more…)

Ganita vs formal math

Sunday, June 16th, 2019

My first “official” seminar at the Indian Institute of Advanced Study, Shimla, introducing the topic of my research project as a Tagore Fellow.

Ganita vs formal math: re-examining mathematics, its pedagogy, and the implications for science.

Here is the extended abstract, and the official tweet from the Director (seated, extreme left). (Will get a better photo.)

Tweet from Makarand R. Paranjape, Director, IIAS (Official) (@ShimlaIias)
Makarand R. Paranjape, Director, IIAS (Official) (@ShimlaIias) Tweeted:
Prof. C.K. Raju, Tagore Fellow, IIAS, made a presentation yesterday on “Ganita vs Formal Mathematics: Re-Examining Mathematics, its Pedagogy and the Implications for Science” in the Seminar Room of the Institute. Prof. R.C. Pradhan chaired the session.@MakrandParanspe https://t.co/jpzGuDh1oX https://twitter.com/ShimlaIias/status/1139432721946595328?s=17

Decolonising mathematics: discarding church myths and superstitions

Tuesday, May 28th, 2019

Colonial education was church education, which changed our traditional math teaching by bringing in myths and superstitions, directly related to the post-Crusade church theology of reason. Most people fail to understand this, since colonial education ensured they know nothing about (a) mathematics or its philosophy, or (b) the church theology of reason, and (c) stuffed them full with prejudices (e.g. that math is universal).

But this understanding of colonial math makes  it easy to decolonise math. We need only to critically examine and junk church myths (such as Euclid) and related superstitions about axiomatic (or faith-based) math, and focus on the practical value of (normal) math. A key such superstition, brought in by colonial education, is that formal math is “superior” because deductive proofs are infallible.

The foolishness of this belief (irrespective of its church origins) has been argued out in detail in the article on Decolonising mathematics, published in AlterNation 25(2) pp. 12-43b. Download the whole paper by clicking on the link above or below.

Not only are deductive proofs highly fallible, they are more fallible than empirical/inductive proofs. The purported infallibility of deductive proofs is just another church superstition like the purported infallibility of the popes who erred in understanding even elementary arithmetic algorithms for addition and multiplication. Laughably, much Western  thought is founded on this superstition (because the church first hegemonised the Western mind).

The above article covers part of the keynote address I gave on “Decolonising math and science education” at the 11th Higher Education Conference, Univ. of Kwazulu Natal, Durban, in 2017. The video, presentation, and other details were given in an earlier post.

Formal math: based on church myths and superstitions

Monday, May 27th, 2019

Many smart alecs ask: what difference would it make if “Euclid” did not exist? They believe the lie about Euclid was told for no reason, and that it persists for no reason in our school texts today which mention “Euclid” 63 times, apart from giving children an image of “Euclid” (all of which makes them believe “Euclid” was real).

It is simple commonsense, however, that a lie is always told for a reason. But the reason in this case is beyond the understanding of our smart alecs. They miss the connection of the “Euclid” myth to church theology.

Our current school texts teach children the false history that “Greeks” did mathematics in some superior way which they must imitate. The myth goes that “Euclid” gave “irrefragrable proofs”, by using the axiomatic method. For this purpose, he supposedly arranged the theorems in a particular order.

Cambridge foolishness about “Euclid”

Cambridge University, a church institution, subscribed to this myth. As pointed out in this exhibit, it initially adhered to the practice of blind imitation of “Euclid’s” Elements. Then the Cambridge Special Board for Mathematics in its Report on Geometrical Teaching dated 10 May 1887 declared the proofs in “Euclid” need not be blindly imitated but the order of theorems in the Elements must be followed. On 8 March 1888 this was adopted by the Cambridge Senate as part of the amended regulations for the Previous examination.

This move by Cambridge University to “reform” mathematics teaching was excessively foolish. Thus,   while the book Elements has axioms and proofs, the simple fact is that it has no axiomatic proofs, as today understood in formal mathematics. Specifically, the first and fourth (SAS) proposition of the Elements have empirical proofs, and a chain is only as strong as its weakest link. (See, the detailed grievance against the NCERT.) If empirical proofs are admitted in one place, the order of the theorems becomes irrelevant, because the “Pythagorean theorem”, for example, can be proved in one empirical step, as was done in India. But the dons of Cambridge University failed to understand this, and made exam regulations based on their botched understanding.

Axioms but no axiomatic proofs in the Elements

The belief in axiomatic proofs in the Elements comes only from the “Euclid” myth not from a reading of the actual book, which our smart alecs never read. Even the dons of Cambridge University had not read it carefully from 1125 (when the book first came to Europe) until 1887. This Cambridge foolishness in mathematics, driven by the Euclid myth, easily exceeds  the foolishness of Sir John Lightfoot, Vice Chancellor of Cambridge University, who, in the 17th c., refined Bishop Ussher’s absurd date of creation, to fix the time of creation at exactly 9 am according to the gospel.

Eventually, Bertrand Russell, among others, pointed out the foolishness of the belief in axiomatic proofs in the Elements, calling the proofs in the Elements a “tissue of nonsense”. But, because of his Cambridge indoctrination, he kept believing in the Euclid myth that, the mythical “Euclid” intended axiomatic proofs. Hence, Russell along with David Hilbert invented formal math on that equally foolish belief in the intentions of a non-existent person, and in the church superstition about the superiority of deductive proofs (more details on that superstition in the next blog post).

Actual Greeks tied math to religion

Actual “Greeks” (Pythagoreans, Plato, Proclus) were NOT interested in axiomatic proofs, and interested only in the religious aspects of geometry, in arousing the soul and making it recollect its past lives (mathesis). This required turning the mind inwards. I have described this in great detail in various places, including my book Euclid and Jesus.

Axiomatic proofs a church tradition

But the church adopted the method of proof based on axioms (i.e., assumptions about the unreal), as in Aquinas’ proof about the number of angels that fit on the head of pin, based on certain axiomatic beliefs about the amount of space occupied by unreal angels. The church found the axiomatic method convenient, as part of its theology of reason (advocated by Aquinas and the schoolmen as the best way to convert Muslims). Obviously, basing reasoning on facts, as in universal normal math (including Indian gaṇita), would go contrary to all church dogmas (about angels etc.). As a loyal handmaiden of the church, Cambridge University, promoted the superstition that the axiomatic (or faith-based) method is “superior” to the empirical method, and that authoritatively laid down axioms (like Aquinas’ axioms about angels) are “superior” to facts.

We started imitating this way of doing mathematics as part of colonial education (which imitated Cambridge).

“Euclid” myth teaches us to imitate the church

So, when millions of students are taught the “Euclid” myth, and told that this way of doing math (formal math) is “superior”, they are being taught a church myth about “Greeks”, to teach them to imitate a foolish church practice. Neither they, nor our smart alecs,  understand this tricky way of indoctrinating children to teach them to imitate a church practice though a myth about the only “friends of the church” — the early Greeks. So, the Euclid myth is just a simple innocent lie, is it?