Archive for the ‘History and Philosophy of Mathematics’ Category

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?

Second grievance against NCERT

Thursday, May 16th, 2019

Since the NCERT tried to evade all issues in the first grievance, a second grievance has been filed, asking NCERT to produce primary evidence for “Euclid” or delete all 63 mentions and image of Euclid from its 9th standard text. Further falsehoods will be taken up subsequently.

The new grievance is given below.

DOSEL/E/2019/01645

This grievance is raised as a response to the response received to grievance DOSEL/E/2019/01152 (signed Smt. Tulika Verma, Under Secretary).
The response received from Smt. Tulika Verma, unfortunately, does not address all the five points (falsehoods) DOSEL/E/2019/01152 contained, and at best, can be seen as a partial (and unsatisfactory) response to FALSEHOOD 2.

Vide this grievance, we request clarity on FALSEHOOD 1 in DOSEL/E/2019/01152:

1) Does NCERT consider Euclid a historical person who lived in the past (Yes / No / Not sure)
(There are 63 references to Euclid, and one image, in just the 9th standard NCERT math text)

2) If the answer to question 1 above is a yes, what is the serious evidence NCERT can furnish to support the claim that Euclid is historical

Serious evidence means evidence from PRIMARY sources. Tertiary sources like Wikipedia are unacceptable, as are secondary sources. The related point also being made is that Euclid is part of church propaganda. Therefore, merely producing some Western secondary text in support of the propaganda is NOT acceptable. (Or if NCERT regards it as acceptable, it must also agree to put a bold warning at the beginning of the school text that it has no serious evidence for the story stated about Euclid, and that its policy is that all Indian children are obliged to accept whatever nonsense is stated in Western secondary texts, and have no right to challenge those texts by demanding primary evidence).

Thank you for your attention.


NCERT unable to produce evidence for “Euclid”

Monday, April 29th, 2019

The NCERT class IX textbook on mathematics has its chapter 5 entitled “Euclid’s geometry”. A public grievance was lodged with the government pointing out numerous other falsehoods in the book. The grievance in the 4000 character text format specified for grievances is posted at http://ckraju.net/geometry/NCERT-grievance-note.txt. There is also a detailed version, posted at http://ckraju.net/geometry/NCERT-grievance-detailed-note.pdf.

The NCERT in its response failed to supply any evidence for Euclid. This laughable response is further proof of the total irresponsibility of the NCERT. Its implicit policy is that students dare not ask questions, for if NCERT cannot answer, obviously the teachers would be unable to answer similar questions in class.

George Gheverghese Joseph serial plagiarist and mathematical ignoramus, invited for conference on math education by Hyderabad University. Part III The false claim of social justice

Sunday, January 27th, 2019

This is part 3 of a three part series of posts. It is better if you first read part 1, which pointed out the long-term plagiarism by Joseph violating all academic and editorial norms, and part 2 which explained its ill effects on math education.

I know the defence that will be offered for the Hyderabad conference, on mathematics education and society. That the participants do not care about plagiarism and lack of editorial and academic ethics, because they are campaigners for social justice in relation to math. This is false.

Colonialism, or invasion of the mind through colonial education, is the most pernicious and oppressive form of social injustice today, affecting the largest number of people. For social justice in relation to math we need to decolonise math. To decolonise math we need to critically re-examine its false history and bad philosophy, as I pointed out in my censored article, now in Journal of Black Studies, and Rhodes Must Fall. But critical re-examination of the West (except the lightweight criticism pre-approved by the West) is taboo for the indoctrinated and superstitious colonised mind.

Let me take a simple example. The fake church-story of Euclid is used today to teach formal mathematics by glorifying metaphysical reasoning in the manner of the church theology, and contrary to common sense. The story is fake and NCERT or anyone else in the world is unable to provide serious evidence for Euclid despite my Rs 2 lakh prize for such evidence. There are five lies in that false claim about “Euclid” (see the related section on five lies in my IIT-BHU talk). These multiple lies aim to indoctrinate young children into church dogmas. Why do we still have these false church stories in our school texts? Did our social-justice-mongers ever object. No way! They cannot because they have to show their loyalty and submissiveness to the Western master. They think that keeping silent is a great way to support not only plagiarism but also all kinds of Christian chauvinism packaged with colonial education.

Millions of students fail to understand the resulting metaphysics of invisible points, as in current Indian class VI math texts. This “education” forces them into a state of ignorance about math, hence, science, to force them to accept Western authority as the sole index of truth about both. It enables continued colonial exploitation, even after the supposed end of colonialism. When our social justice-mongers peddle inclusiveness in education (without any critical check on its nature): all they are peddling is inclusiveness into church propaganda to keep people colonised! Note, incidentally, that the related myth of :”Euclid” was invented, like Christian rational theology, during the Crusades, long before capitalism!

Note, also, that this Christian chauvinism in history relates to the genocidal “doctrine of Christian discovery” on which Vasco “discovered” India, or Columbus “discovered” America. How many times did our social-justice seekers condemn this genocide, the largest human genocide known to the world? (On my principle of proportionate condemnation, they should condemn inustices proportionately.) This evil doctrine of Christian discovery is still part of “ideal” British and US law, and states that any land or knowledge is “owned” by the first Christian to “discover it”, i.e. they are at liberty to steal it.

Joseph and Dennis Almeida know that plagiarism by Christians from a non-Christian was regarded as a high act of Christian morality, as was the genocide in three continents. Joseph, a trained lawyer, knows this evil Christian doctrine is part of US and British law. Hence, also, Joseph et al., have been serially and shamelessly plagiarising my work: they believe as Christians they have a right and duty to steal from non-Christians. And our purveyors of social justice concur by keeping quiet not only about the genocide, but also about the present-day plagiarism! Ha, some social justice this!

Finally, no doubt, people like Guru will say they are fighting for dalits even if they know nothing about math education. But is even that really true? Joseph is peddling nothing but a dirty mix of Kerala and British chauvinism, as already shown in part 2. Hence, Guru is doing a a great disservice not only to academic and editorial standards of integrity but also to the dalit cause by tacitly supporting Joseph.

The truth will eventually out, and ignorance is no excuse for scholars. Therefore, this is how they will be remembered, Joseph and Almeida as academic thieves of the worst kind, and those who tacitly support them as staunch supporters of academic and editorial dis-integrity and social injustice.

George Gheverghese Joseph serial plagiarist and mathematical ignoramus, invited for conference on math education by Hyderabad University. Part II: the ill effects of cheater-teachers on mathematics education

Saturday, January 26th, 2019

Please read part 1 of this blog post first.

Plagiarism, or the theft of knowledge, whether of the calculus, or of the calculus transmission thesis, has ill effects on mathematics education. This is not just about cheating in exams. When cheaters turn teachers it will naturally create a problem for the students.

As explained in part 1 of this blog post, in my Hawai’i paper of 2000 I had proposed a tough new standard of evidence for the history of transmission of calculus, as “proof beyond reasonable doubt” as in criminal law. This paper involved the very thesis that Joseph and Almeida have serially plagiarised over the last 18 years in the most shameless way imaginable.

However, later on, in my book 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) I introduced a further test for transmission: the epistemic test. Those who cheat and copy, like students in an exam, do not fully understand what they copy. Hence, lack of understanding is positive proof of copying in a suspicious context. (I used to apply this test to my students,) Therefore, imitating the plagiarists spreads a wrong understanding of mathematics. Let us first take the case of calculus.

Though Europeans stole the Indian calculus (for their navigational needs) and understood some of its practical value, they did not fully understand it, exactly in the way they had earlier failed to fully understand imported Indian arithmetic for centuries.

Two simple examples are as follows. Precise trigonometric values were a key motive for the theft of the calculus. The Indian calculus was used to calculate the most precise trigonometric values then known (accurate to 9 decimal places). Arithmetically challenged Europeans desperately needed those values for a solution of their navigational problems (to determine loxodromes, latitude, and longitude at sea), as acknowledged in the huge prizes instituted by various European governments from the 16th to the 18th c.

The Jesuit general Clavius published exactly those Indian trigonometric values (to exactly the same precision) in his own name in 1607. Clavius cheated, but though he claimed to have calculated trigonometric values to such high precision, he did not understand how to apply elementary trigonometry to calculate the radius of the earth, a critical parameter for navigation. Ha! Indians accurately calculated the size of the earth, from at least a thousand years before Clavius (as confirmed by al Biruni who cross-checked also Khalifa Mamun’s physical measurement of one degree of the arc).

Likewise Clavius authored the Gregorian reform of 1582 based on Indian calendrical texts (as his favourite student Matteo Ricci confessed; see Ricci’s handwritten letter in my MIT video or presentation “Calculus the real story”.) But arithmetically backward Europeans even then did not know the correct duration of the tropical year, hence Protestant Europe did not accept the Gregorian reform for the next 170 years, until 1752, long after Newton’s death, leading to many more European deaths at sea.

Likewise, George Joseph and his accomplice Dennis Almeida reveal their utter lack of understanding of basic concepts (taught in 9th standard math texts) and have made terrible mathematical blunders, on the record, which show that they are complete mathematical ignoramuses. Some of these have been discussed in my book, in the section on the transmission of the transmission thesis: for example, they foolishly and repeatedly say that solar declination can be measured at sea (how?), thereby also completely failing to understand my point that the Gregorian reform was needed to be able to measure latitude at sea in daytime.

Again in their Race and Class 45(4) 2004 article, written even as the Exeter ethics committee was going on, Joseph and Almedia copied from my Hawai’i paper of 2000, shamelessly failing to acknowledge it, though they had access to it since 1999, which they themselves acknowledged only in 2007 (but not in 2003, or 2004 when they copied from the Hawai’i paper). While some of my points about Indian pramana vs deductive proof are copied with only a few inaccuracies (but copied without acknowledgement, even while an ethics committee was on in which both participated)Joseph and Almeida some interesting statements which expose their mathematical illiteracy. Thus, my Hawai’i paper mentioned floating point numbers, and used a computer program which I then used to teach as part of my C programming course, to make a philosophical point about the failure of the associative law with floating point numbers. I pointed out that present-day practical computations with calculus are all done on a computer which uses floating point numbers.

Not understanding this mathematical subtlety, Joseph and Almeida blundered that (p. 46) “the use of irrationals…was accepted in Indian mathematics by the use of floating point number approximations“. How foolish! This was no typo, for they repeat , even more amazingly (p. 51), “the Kerala mathematicians employed…floating point numbers to understand the notion of the infinitesimal and derive infinite series.” My foot! Floating point numbers are a recent  IEEE technical standard (No. 754 of 1985) specifically adapted to digital computation. Nothing to do with the Kerala school. And there is absolutely no way in which floating point numbers can be used to derive infinite series. Utter balderdash. Possibly neither Gopal Guru nor Rochelle Gutierrez understands the huge mathematical blunder involved here. But they are all ready to address a conference on math education!

As a matter of fact (see e.g. IIT-BHU presentation for the reference and sloka) Nilakantha states the EXACT sum of an INFINITE geometric series. (Finite geometric series were known from several thousand years earlier since the Eye of Horus fractions, and the Yajurveda.) So Joseph also proved he is a historical ignoramus. He lacks knowledge of the original sources or even the related language (but is ever ready to bluff and cover up one crude lie with another, as he did about rajju ganit in my presence in Berlin in the year 1999). Rajju Ganit, by the way, is a major alternative decolonised course on mathematics that I am proposing at school, as preparation for my decolonised course on calculus without limits, as clear from the linked articles in the IIT-BHU workshop. Obviously, these ignoramuses don’t understand any of its concepts. That damages mathematics education.

Why because a valid history is important to arrive at the correct philosophy with which the calculus originated, and the way it ought to be taught today. (more…)