Sunday, 26 November 2017

Decolonizing maths at UCT - Part 3

14-11-17
From: Crowe
To: Raju; Loretta Feris; Daya Reddy; VC; Judith Du Toit; Dean of Science; Elelwani Ramugondo; Peter Dunsby; Chris Mitchell; Gerda Kruger; Sipho Pityana; Kasturi Behari-Leak; Goitsione Mokou; Kenneth Hughes; Henri Laurie; Nicola Illing; Ed Rybicki; David Benatar; Andy Buffler; Muthama Muasya; Shadreck Chirikure; simonrakei.sr@gmail.com; Russell Ally; llg@sun.ac.za; Harry Garuba; Maano Ramutsindela; Arthur Ngwenya; SRC President
 
Thank you for keeping me briefed. Thanks also for your response, I’ll reply to it in due course.
Chris Mitchell is a fine person, but seems to be constrained by his bosses concerning what gets published and was does not in the UCT NEWS.  Most of my pieces (which are accessible in my Blog Site – timguineacrowe.blogspot.co.za) are rejected out of hand.
What does get published (and is therefore available to the whole UCT Community – including students) is in Views from Campus, e.g.
https://www.news.uct.ac.za/article/-2017-09-26-decolonisation-at-the-university-of-cape-town-what-is-ita-how-should-it-be-achieveda
I wouldn’t hold my breath waiting for our pieces being published, let alone endorsed by pro- or anti-Fallists.
Further regarding students, I have lectured to literally thousands to them over my 40 years at UCT and mentored nearly 60 postgrads, six of whom became professors.  I look forward to seeing a list of your academic offspring.
At the height of Apartheid, I designed and implemented a de novo, Afrocentric, academically/ demographically inclusive and socio-economically relevant, one-year master’s programme in Conservation Biology, a discipline that was then in its academic infancy and untainted by Western devils.
During its 24-year history, the CB Course has had a high academic ‘fitness’.  More than 80% of the nearly 300 graduates to date have found relevant employment and published +-130 peer-reviewed scientific papers.  Thus, in cold financial terms, the CB Course more than earns its keep through the generation of government subsidies for published papers and graduated students.
In terms of government demographics, 25% of CB grads so far have been ‘black’ and 52% female.  They hail from 43 countries, 23 African.  For a more complete story, see:
https://www.uct.ac.za/dailynews/?id=10155
It’s good that you’re sending a copy of your piece to the SRC.  Its new bunch of councillors are adamantly opposed to destructive decolonization you seem to advocate.
Yes, there is hypocrisy in some faculty in the UCT.  These are the ones queuing up to sacrifice academic excellence developed over decades in the name of decolonization.
Yes, there may be closet-racists in UCT, although I’m confused how they can shower abuse from their closed quarters.  Regardless, I am not one of them.  Just take the time to read my history of UCT and other pieces included in my Blog Site.
With regard to your claim about the author of the Elements, it is, in fact:
“On the actual evidence, the anonymous “author of the Elements” was a black woman who was raped and killed in a church.” 
All the evidence available is your revision of a history that doesn’t exist.
Euclid was probably a bunch of people.  But, no one will ever know for sure, except you.

14-11-17
From: Raju
To: Crowe; Loretta Feris; Daya Reddy; VC; Judith Du Toit; Dean of Science; Elelwani Ramugondo; Peter Dunsby; Chris Mitchell; Gerda Kruger; Sipho Pityana; Kasturi Behari-Leak; Goitsione Mokou; Kenneth Hughes; Henri Laurie; Nicola Illing; Ed Rybicki; David Benatar; Andy Buffler; Muthama Muasya; Shadreck Chirikure; simonrakei.sr@gmail.com; Russell Ally; llg@sun.ac.za; Harry Garuba; Maano Ramutsindela; Arthur Ngwenya; SRC President

Mitchell has not responded to my email, and a reminder. I guess this shows the shape of things to come.
So, I attach my response, assuming the UCT News is purely online.
I notice that you do not seem to regard the students as part of the UCT community, and have not kept them informed. As pointed out in my response, they are actually the paymasters of the faculty, and it is high time the faculty realized that they are responsible to the students and the public.  So, I have marked a copy also to the President of the SRC.
Let them also know about the hypocrisy of some faculty in the UCT. You keep asking the students to engage, in the matter of decolonising science, and all that the closet-racists in UCT are doing is to shower abuse, and avoid engaging. They could not even engage with the easiest of my claims that the author of the Elements was a black woman. Are these UCT faculty setting an example which they would want the students to emulate?
UCT debate on decolonising science and the Crowe report
C. K. Raju
Indian Institute of Education, and SGT University
Summary: I nail some wild lies by Crowe. To build a false case, he also suppresses my key affiliations: the one's relevant to decolonisation of math and science.
Colonisation involved mind capture using myths. To decolonise, those myths must be critically scrutinized, and new narratives may be needed. The racist methodology, however, is to dodge critical scrutiny, by (a) avoiding engagement with evidence, and arguments, and (b) demand blind faith in colonial myths and (c) and blind faith in the opinions of residual colonial authority. (Apart from being untrustworthy, that may be irrelevant; in particular, decolonisation rejects formal math, globalised by colonialism, so it does NOT need the prior permission of formal mathematicians.)
Crowe nevertheless sticks to the above excessively weak methodology; for example, he reiterates the myth of (a white) Euclid, but fails to provide evidence for it. This, despite my ZAR 40K “Euclid” challenge prize. On the other hand, there is counter evidence for my claim that the book Elements was written in the +4th c. CE, by a black woman. Her religious leanings were with the Egyptian notion of soul which Greeks from Plato to Proclus persistently connected to mathematics. However, that “pagan” notion of soul was later cursed by the post-Nicene church which smashed all pagan temples at that time: that is why she was lynched in a church.
The false history of Euclid is linked to a bad philosophy of math used today: that the white man did math in some “superior” way which must be imitated. First, contrary to the Euclid myth, there are no formal proofs in the actual book Elements. Second, formal proofs are not superior: mere deductive proofs do not lead to valid knowledge. Instead, they make math difficult without adding to practical value, which comes from normal math, which accepts empirical proofs as also empirical tests of postulates, and logic. Therefore, the right remedy for the problems about math-teaching facing blacks is to reject formal math and revert to universal normal math. Since normal math is easy, it enables students to solve harder problems.
Changing math also changes science by eliminating the redundant metaphysics in formal math: for example, eliminating the metaphysics of time in Newton's misunderstanding of the calculus changes his theory of gravitation.
I briefly go into the Atiyah case to show that even high mathematical authority cannot be trusted. (In 2005, on the centenary of Einstein's special relativity paper, Atiyah tried to grab credit for my theory.)
Crowe has banked on the opinions of George Ellis and his student Jeff Murugan. However, he suppresses a key fact. During the UCT debate, I raised my long-standing critique of the singularity theory of Stephen Hawking and Ellis for arriving at their creationist conclusions and for leading to the utterly superstitious conclusion that “Judeo Christian theology is part of physics”. I had offered to discuss also the related technicalities of formal math (non-standard analysis applied to Schwartz distributions) in the math department. Afraid to be exposed, and nervous about the technicalities, Ellis and Murugan fled from the academic battle. They continue to avoid the critique but attack the critic—in “safe” forums where I am not allowed to respond. Crowe relies on that opinion which fails even to acknowledge the conflict of interests. Between reciting myths and citing such dishonest opinions, Crowe does not make a single valid point.
The students should note that faculty salaries are funded by students fees and public money: therefore the faculty must be made publicly accountable. Till such time, an interim solution is to start teaching decolonised courses in parallel to existing courses, and to let the students choose what the prefer.
Some lies
The purpose of a constructive debate is to arrive at truth, but that requires adherence to the truth. Timothy Crowe seems unable to stick to the truth: in a widely circulated earlier email exchange with me, Crowe lied wildly about what I said about Karl Popper's handwritten letter to me. Then Crowe tried to fudge issues, proving that the distortion was no accidental misreading.
Therefore, first let me nail some more of Crowe's lies, in his report on the UCT debate. Since I warned Crowe beforehand against lies and misrepresentations, he has corrected some lies in the earlier version of his report, but has introduced new one's! He now has no excuse for them.
Thus, Crowe gives a long series of “quotes” from me. The very first of those concerns some French astronomical observation missions. The content of the quote may well be true. But it is false that I said it; I have not written anything about Haiti. Crowe provides no source for his “quote”.
Crowe goes on to lie about my work concerning relativity. He says that I claim
“that Albert Einstein's theories of special and general relativity were anticipated much earlier by Henri PoincarĂ© and were flawed [corrected by Raju].”
Yes I have claimed that special relativity was anticipated by Poincare (shortly before Einstein), and I stand by that. However, it is a wild lie that I ever claimed that special relativity is flawed. To the contrary, I stated in my acceptance speech for the TGA award,
“There is no doubt at all that the theory [of special relativity] was the work of a genius. The question is who was that genius: PoincarĂ© or Einstein? The second question follows naturally from the first: compared to PoincarĂ©, a mathematician, did Einstein, a non-mathematician, even understand the full mathematical implications of the theory of relativity?
I NEVER said special relativity is flawed. That is just another wild Crowe lie. What I said was Einstein did not understand its full mathematical implications. There is a huge difference. I have repeatedly emphasized since 1992 that Poincare DID understand that relativity necessitates functional differential equations (FDEs), though he used only retarded FDEs or delay differential equations, which he called equations of finite difference. [More about Einstein below in the 2005 case when Atiyah, a leading mathematician, advanced claims similar to mine on the centenary of Einstein's special relativity paper.]
It is possible that Crowe is a total ignoramus and so bound by myths that he does not understand the difference between Einstein and special relativity. In that case he should rectify his ignorance and not harbor vainglorious dreams of debating with me. I will not consider this possibility further; as I stated at the start of the UCT debate, lies or misrepresentations, for whatever reason, mark the end of debate.
Such persistent lies by Crowe are an admission he knows he is on weak ground. The use of lies also shows that he is not interested in a constructive debate but only in domination by hook or crook. He has earlier revealed his general trick to defend himself: whenever a specific lie is nailed, he will call it an ad hominem attack! Pitiable.
I will not bother to refute all of Crowe's lies here: my purpose is decolonisation and not to nail Crowe's lies, for Crowe seems beyond reform or repair. Nailing two lies is enough for the perceptive. Suffice it to say that Crowe is not even approximately trustworthy especially when (a) he “quotes” without citing a source, or (b) tries to paraphrase without understanding, both of which he frequently does.
Fudging facts
Crowe goes on to fudge key facts about my career. Specifically, he suppresses all key aspects related to decolonisation. Thus, my experiments on teaching decolonised calculus were performed at the Universiti Sains Malaysia (then the apex Malaysian university) when I was a long-term visiting professor in the mathematics department there. This affiliation was stated, for example, in my papers reporting on those experiment, “Teaching mathematics with an alternative philosophy”, cited at 7 and 22 in my advance summary for the UCT debate, and Crowe himself provides a link to one of those papers. So, Crowe knowingly suppressed facts, and does so to build a false case.
Next I joined Al Bukhary International University, where I designed and taught courses on decolonised history and philosophy of science, as explained on these blogs (1, 2), and shown in this short video. This affiliation too was stated in my paper on gravitation, published by the American Institute of Physics, and cited at 14 in my summary for the UCT debate.
Currently, I am an Honorary Professor with the Indian Institute of Education, based at its centre in the Mumbai University campus, carrying out a project on alternative math teaching in schools: basically rejecting the myths associated with Euclid and using African/Indian cord geometry to teach school geometry in an easy and better way. Experiments are on to teach decolonised cord geometry in Indian schools. My current affiliation with IIE was stated clearly in the summary circulated for the UCT panel.
I am also concurrently a Professor Emeritus at the SGT University, Delhi, teaching regular decolonised courses, on calculus and history and philosophy of science (as publicly declared by the University; click the above link to see also the pictures of students which too I showed in UCT). These are the ONLY decolonised courses on math and science, well-tested and running as regular university courses ANYWHERE in the world. Therefore, the UCT was absolutely right to invite me to talk about decolonisation of math and science during my visit to South Africa. Who else could they have invited?
Crowe suppresses these four key affiliations because accepting them shoots down his case to bits, as he knows. Pictures of students of these decolonised courses were also shown during my UCT presentation. Crowe admits he was there. This suppression of the truth is Crowe's other best argument, and he calls it “research”! Unethical.
The new narrative
I am also very proud of having initiated the Project of History of Indian Science, Philosophy and Culture (PHISPC) in the early 90's. The aim of the PHISPC project was that we, the colonised, should tell our own stories, and not be tied down by the stories told about us by the coloniser (e.g. Hegel's rant that all Africans were cannibals). The new stories turned out to be very, very different. This telling of one's own stories (in over hundred volumes) was very fruitful and marked the beginning of emancipatory decolonisation. I strongly advocate that Africans too must start telling their own stories, to break free from the narratives with which the coloniser has bound them.
The PHISPC was housed in the Centre for Studies in Civilisations, and has produced over a hundred volumes, an enormous academic effort by any standards. My volume on Cultural Foundations of Mathematics (Pearson Longman, 2007) was the 50th. Crowe suppresses this very important fact, though a long list of PHISPC volumes is printed on the jacket of my book, and a glance at it will show that it involved the cream of Indian scholarship from across the political spectrum. In typical racist style, Crowe only seeks to belittle the whole effort by calling the Centre an NGO, which it technically is, but only to preserve its autonomy, since it is fully government funded.1
The telling of new narratives is the beginning of decolonisation, but that also marks the end of colonisation for it involves the destruction of old narratives and old structures of authority.
Decolonisation methodology
Indeed, false colonial narratives were a key aspect of colonial rule. Colonial rule was not a simple military conquest: it was con-all-ism, and used con-tricks, myths, and superstitions to capture the colonised mind. Colonial education (which was church education when it first came to the colonised) systematically indoctrinated the colonised into those Western myths and superstitions.
Therefore, as I explained in Ending Academic Imperialism, a key strategy of decolonisation is to dismantle colonial soft power by confronting colonial lies, myths and superstitions. Decolonisation is NOT a demand to reject everything Western, as is often caricatured; it is a demand to “be critical and choose what is best” .
Incidentally, decolonised math rejects the formal math globalised by colonial education and seeks to restore normal math. Therefore, it is wrong to demand, as Crowe does, that decolonised math requires the prior permission of the colonised mathematicians (who do formal math). The equitable counter proposition is that formal mathematicians are welcome to debate publicly, and one formal mathematician was invited to the UCT panel. Having nothing to say, he used up his time to recount his autobiography! While many formal mathematicians are understandably annoyed by the decolonisation proposal, they have so far come up with only hot air and abuses. Not a single cogent counter-argument from them yet. Because the debate was public this was quickly exposed. This is discussed in more detail below.
Being critical of Western myths and superstitions is a simple process: just demand EVIDENCE for every colonial myth (whether historical or philosophical). If no evidence is forthcoming, discard the myth, and eliminate the related lies from the education system.
The racist methodology: avoiding evidence
But a critical analysis threatens the soft power of the coloniser and the racist—which power persists in education—even after the notional end of colonialism or apartheid.
Therefore, racists and pro-Western elements dodge a critical analysis of their myths. (1) They totally avoid engaging with the evidence, and instead (2) demand reliance on authority—their authority. This racist methodology was also used in apartheid and slavery which could not have survived critical engagement with the evidence, but recall how the Bible,2 Kant and Hume etc. were cited in defence of racism and slavery.
The UCT debate exposed these tactics of evidence-avoidance and demanding reliance on (Western) authority. For example, Henri Laurie demanded that Western myths must be accepted without evidence (in an earlier email exchange). He said the onus of disproving colonial myths was on the challenger who must produce counter-evidence! This is unreasonable enough, but Laurie went further, to an amusing extreme: he said when counter-evidence is produced, he had the right to dismiss it without examination. During the UCT panel, he demonstrated his belief that mere racist arrogance is a valid substitute for scholarship: he flipped thorough my 500 page volume in 5 seconds and rejected it! The whole world should know that this is what passes for academics among some in UCT. Shame.
In simple terms, racism uses BLAA (Boasts of white superiority, Lies about non-Whites, accompanied Adjectives and Abuses). The use of these tactics identifies the closet racists who may outwardly pretend to be against racism today (though they never suffered for any anti-apartheid views under apartheid, like Steve Biko).
Both Crowe and the GroundUp article against me followed this racist methodology. For example, the GroundUp article called me a “conspiracy theorist” but couldn't even say WHAT conspiracy theory I was accused of! For the racist, any remark by a closet-racist for some undisclosed reason is ultimate proof. Racists can “prove” anything in this way.3 For others, this only shows that the racists are frightened and desperate and unable to come up with anything better.
Likewise, Crowe relies on “quotes” (in quotes) from me; but alas he is unable to contest any of my statements with any sort of counter-evidence or counter-argument. He just uses the excessively naive assumption (“Crowe's postulate”?) that anything surprising and contrary to colonial myths and superstitions is wrong. Crowe's postulate is the same as Laurie's: both claim colonial narratives must be accepted without asking for evidence because they don't have the evidence.
Let me now move on to the real substance.
The myth of Euclid provides an excellent illustration of how new decolonised narratives displace the old, and why #EuclidMustFall.
Was “Euclid” a black woman?
The role of myths is especially important for math, a key stumbling block for blacks in higher education. The myths are con-trickery, a substitute for the real history and philosophy of math, which philosophy is poorly understood by the vast mass of people.
Because myths are at the core of colonial power, Crowe begins by reiterating the myths of math. But he offers nil evidence. Consequently, EVERY claim in his opening section is false. Instead of dealing with that mass of falsehoods, here I will focus on Euclid, a myth used to justify the way math is taught today. To change the way math is taught, we must first shoot down that myth.
To demonstrate the lack of evidence, I have long offered a Euclid challenge prize of ZAR 40K for any serious evidence about Euclid.4 No one could claim the prize. Crowe amusingly imagines mere verbiage will hide lack of evidence. His other defence is to cite the opinion of the UCT math department which apparently finds this mere demand for evidence an ad hominem attack, and a terrible distortion of history, not to mention a “conspiracy theory”, and a “crank” demand and charlatanry! So many adjectives are needed because they KNOW there is no evidence. Thus, David Fowler, the leading Western expert on ancient Greek mathematics, admitted long ago (in response to an angry query against me) that NOTHING was known about Euclid, and that our earliest copy of the book Elements is from +888 CE, closer in time to us than to the purported date of Euclid. That admission is archived here.
So why does Crowe desperately try to hang on to that myth of Euclid? One reason is clear enough. “Euclid” is depicted as a white man through his images (just google). But there is nil evidence for Euclid, so how did anyone know the color of his skin? This only shows what kind of trash history the highest Western “authorities” have peddled for centuries; it is proof that they should NOT be trusted an inch.
The educational consequences of this “white-Euclid” myth are clear enough: last year in an article in Conversation, Karen Brodie opined that “mathematics is the work of dead white men”. She further stated that blacks and women are bad at math, and insinuated that the right way to “decolonise” math is to retrain the psyche of blacks and women to teach them to think like the dead white men who invented math. It was to preserve such obnoxious racist nonsense that Conversation censored my article in response, after my article was published.
My censored article aroused a lot of resentment and surprise among whites. One reason for the resentment was my claim that the author of the Elements was a black woman, not a white man. The surprise is manifest: Science 2.0 still carries that censored article under the changed title “Was Euclid a black woman?...”. Racists find this galling, and Crowe puts up this proposition as proof of my unreasonableness! How very unreasonable and “illogical” that someone disbelieves the false myths of the white origins of math, because those myths lack evidence! How very unreasonable that someone claims the Elements was authored by a black woman! However, unlike Western or racist historians, I back ALL my claims with EVIDENCE.
Thus, while there is nil evidence that a person or persons called “Euclid” wrote the book Elements in the -3rd c. CE, there IS counter evidence that the book was written, some seven hundred years later, in the +4th c. CE, by Theon of Alexandria. As Thomas Heath, another leading Western authority on “Greek math”, noted, “All our [Byzantine] Greek texts of the Elements up to a century ago. . . purport in their titles to be either “from the edition of Theon”. . .or “from the lectures of Theon”.”5 Therefore, the book Elements was completed after the 4th c. Theon. But it was before the 5th c. Proclus who wrote a commentary on the book. That narrow range leaves Theon's daughter, the mathematician Hypatia, as the best candidate.
The further corroborative evidence is that commentaries on the book speak anonymously of the “author of the Elements”, though they name others from Aristophanes to Zeno. Why the anonymity? What terrible thing rendered the “author of the Elements” anonymous? Was it because she was a woman? And someone to whom something terrible happened, too terrible to be mentioned? Hypatia again fits the bill.
How do I know the color of her skin? Well, she lived in Alexandria in the African continent, where the default skin color is black. Therefore, she was black on the balance of probabilities which is the standard of proof for history. I am willing to revise my opinion, but ONLY if someone produces solid EVIDENCE to the contrary. I will not budge an inch on the mere racist prejudices of even thousands whites (or compradors) still in authority, who are baying for my blood and hurling all sorts of abuse against me. Let them howl.
That beautiful and wise black woman, Hypatia, was brutally lynched in a church, as is well known. I draw attention to that fact because it has an important bearing on the history and philosophy of math. Why was the church against her?
Thus, Crowe recites also the false myth that the Greeks did formal math. This is total bunkum. In fact, the book Elements does not have a single formal proof in it. Just check even the “authoritative” doctored 19th c. source. Its first and fourth proposition use empirical proofs on which its proof of the penultimate proposition, the “Pythagorean theorem”, depends. Those who make the false claim about Greeks giving formal proofs, should produce the purported formal proofs supposedly given by Greeks, or desist from making false claims. So far all that people like Laurie have said is to lie that my arguments are only against the person Euclid.
In fact, the truly special feature of Greek mathematics was its relation to religion, and the soul. There is solid textual evidence for this, for example, in Plato's Meno. There, Socrates links mathematics to mathesis, meaning learning, and claims that “all learning is recollection” of the eternal ideas already known to the soul from its past lives. He demonstrates that Meno's slave boy has an innate knowledge of geometry. Socrates then argues that is because his soul acquired that knowledge in a previous life. This connection of math to the soul is reiterated in Plato's Republic (Book VII), where Socrates asserts that geometry must be taught, NOT for its practical value, but because, by arousing the soul, it makes people virtuous.
Centuries later, Proclus in his +5th c. commentary, places the book Elements in the very same religious tradition, and explicitly derives the word “mathematics” from mathesis (NOT mathema, as Crowe false asserts using unreliable Wikipedia). There is a more detailed discussion of this in the chapter on “Geometry and the soul” in my book Euclid and Jesus.
Now this “pagan” (Egyptian) notion of soul was accepted also by early Christianity (Origen), but the post-Nicene church cursed it and distorted Christianity for its own political benefits (See, e.g. “The curse on 'cyclic' time”, chp. 2 in my Eleven Pictures of Time, Sage, 2003). Because the book Elements championed that same notion of soul, associated with equity, it aroused the church's wrath. Hence a Christian mob brutally lynched Hypatia at this time when the church got every last “pagan” temple in the Roman empire physically smashed by inciting mobs. More details in my book Euclid and Jesus,which displays the image of that revolutionary black woman on its cover, alongside some images of the archaeological finds of broken statues of “pagan” gods from Alexandria.
Many centuries later, the church freely “reinterpreted” the book Elements as a book on deductive proofs (which it is not), ascribed to it a false (but theologically-correct) origin in an unknown “Euclid”,6 and used it to teach reasoning to its priests. This was done in support of the post-Crusade Christian theology of reason copied from the Islamic theology of reason (aql-i-kalam), so as to persuade the Muslims who were military too strong then to be converted by force. I have explained this in various places.
If Crowe or anyone else wants to challenge my conclusions they need to contest specific facts and arguments, not merely point to the sweeping evidence-less opinion of this or that person in UCT, who merely uses BLAA. Those dirty days of apartheid are over, and the sooner the closet racists accept this, the better for them.
The bad philosophy of formal math
The false myth of Euclid and his deductive proofs is linked to the bad philosophy of formal math that deductive proofs are “superior”. This bad philosophy determines the way math is taught today. Crowe reiterates the false Western myth that everyone other than “Greeks” did “inferior” math as mere rules of the thumb. Contrary to that myth, normal math (which I advocate), used BOTH facts (empirical proofs) and reasoning (deductive proof), like science. The special feature of formal mathematics is that it is anti-empirical and prohibits empirical proofs (facts), and uses ONLY deductive proof. By avoiding empirical proof formal math claims superiority. But is this claim of “superiority” any better than the racist claim of white superiority? It is not.
To show this, it is important to point out, as I have done, that a mere deductive proof does NOT lead to valid knowledge. Consider the following deductive proof. (1) All animals have two horns, (2) A rabbit is an animal, therefore, (3) A rabbit has two horns. This is a valid deductive proof, but is the conclusion valid knowledge? Obviously not; it is nonsense. In the same way, a deductive proof may be given for any pre-desired conclusion whatsoever from appropriate premises.
Indeed, it is very well known that deductive proof does not lead to “truth”, but leads at best to relative truth, relative to the premises. Crowe seems ignorant of this basic thing. He goes by myth and faith. And neither the mathematician nor the philosopher on the UCT panel engaged with my critique of formal mathematical proofs. (Crowe says he was there, and they engaged, but don't trust him, watch the video, and tell me where they engaged with this critical point that the philosophy of formal math is bad.)
The above deductive proof led to invalid knowledge because the first premise (“All animals have two horns”) is false. But we know this only EMPRICALLY. However, formal math, rejects the use of facts. As its name suggests, it is purely about form: substance and facts do NOT matter. Crowe believes in the authority of Russell who explained formal math thus: “We...take any hypothesis that seems amusing, and deduce its consequences”. 7 I find horned rabbits distinctly amusing, even though the trolls of apartheid were not amused!
As Russell further explained, in the same paragraph, in formal math, one ought NOT to check whether the hypotheses are true as facts: “It is essential not to discuss whether the first proposition is really true”. [Emphasis added] So, let us not discuss further whether, in fact, all animals have two horns: such discussions about facts are irrelevant to formal math which is divorced from facts. Russell concludes, “Thus [formal] mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true.” [Emphasis added] That is just what I claim, mere deductive proof provides no guarantee of valid knowledge. Crowe does not know the abc of the philosophy of formal math, and the UCT philosopher on the panel did not engage with any of these claims of mine. (Note: Those who resist decolonisation of math in UCT must recruit some competent debaters!)
Can't we empirically check the starting postulates of formal math? No, we cannot. Formal math is metaphysics, i.e., it cannot be empirically tested. As a simple example, geometric points are declared invisible. So how can we EMPIRICALLY verify the postulate that a unique straight line passes through two points? (A line is made up of points; if the points are invisible, so is the line!) Moreover, unlike an invisible electron, an invisible point does not affect anything in the real world, so we cannot even indirectly infer its existence the way we can infer the existence of an electron by its track in a bubble chamber.
In fact the postulate is contrary to experience: most people did geometry in school only with visible dots, and visible lines. Two real dots may be connected by multiple lines which differ slightly. That is a fact, and the practical experience, contrary to the postulate. But, by teaching formal math, young children are indoctrinated to reject this commonsense, and blindly trust Western authority on the nature of invisible points! Why do theycomplain if I laugh at those who believe in invisible points and recall the story of the emperor's new clothes? Can Crowe (or anyone in the UCT math department) explain how the above postulates about invisible points and invisible lines may be EMPIRICALLY tested?
Apart from the inability to verify postulates there are other reasons why deductive proof fails to provide valid knowledge. An invalid deductive proof may be passed off as valid. The classic example is how the proofs in the Elements were mistaken for valid deductive proofs for centuries. Again, formal mathematical proof uses 2-valued logic which is not universal, that choice needs to be justified empirically, and is only approximate.
Riddled with so many failings, the fact is that formal math not only fails to provide any assurance of valid knowledge (rigor), it makes math extremely complicated (mortis)! That is why the proof of 1+1=2 in Whitehead and Russell's Principia needs 378 pages. Formal mathematics distinguishes between integers and real numbers. So, things become even more complicated when we try to deductively prove 1+1=2 in formal real numbers, from first principles, because this needs that we first develop set theory, which involves an enormous metaphysics of infinity altogether beyond empirical verification. To bring out these problems, I asked Laurie to prove 1+1=2 for real numbers from first principles, writing out the formal proofs in full. But even that first step was too complicated for him. How on earth will students understand calculus based on real numbers? My point is this: why do this absurdly complicated thing when it provides no assurance of valid knowledge and no practical advantage for application to science and engineering? Why not do 1+1=2 in the normal way?
The real reason is found by examining Western tradition. The avoidance of empirical however was part and parcel of the church dogma of reason, because any engagement with the empirical might damage its doctrines like virgin birth. Therefore, the church glorified reason (“deduce how many angels can fit on the tip of a pin”) but ran down the empirical (“do angels exist?”). It suited the church well to lay down postulates authoritatively; testing them did not. Crowe just repeats the myths around those dogmas, like the myth of Euclid and his (absent) deductive proofs which were part of church mythology and believed for long by Western authorities. Crowe is entitled to his faith, but why should such faith be treated as public knowledge and taught in universities? My demand is to teach math solely for its practical benefits. There are many more issues, some of which (including the false claim of aesthetics in formal math) are taken up at the popular level in this article on “Math and censorship”,
To summarise, (a) we need to discard Western/racist myths (b) including myths linking the false history of math and its purported Greek origins to a bad philosophy of math, for formal math offers no demonstrable practical advantage, and (c) revert from formal math to teaching normal math which makes all math (not just calculus) a whole lot of easier. This results in no loss for practical applications of math, since real world applications of math to science and engineering invariably involve normal math and approximations. On the contrary it results in a gain, since making math easy enables students to do harder problems. Therefore, to overcome the pedagogical problems facing blacks in math, we should decolonise and teach normal math.
New theory of gravitation
The concrete benefit of decolonised normal math for pedagogy is clear enough (it makes math easier, and enables students to do harder problems). But there is a deeper question: will a different way of doing math affect science? The answer is yes. Briefly, because science uses math, and formal math involves metaphysics, that metaphysics may creep into science through formal math. But this is complicated to explain. The easiest illustrative case mentioned in my UCT summary was the case of Newtonian gravitation.
What specific statement is Crowe denying? That Newtonian physics and Newtonian gravitation failed over a century ago? That Newton made time metaphysical8? That the conceptually incoherent notion of a “flowing time” was the basis of Newton's attempt to understand calculus using “fluxions”? That correcting Newton's error about time led to special relativity? That relativity needs FDEs? That my new theory hence reformulates gravitation using FDEs?
The resulting differences of my theory from Newtonian gravitation are explained for the layperson in this press release. On the new theory, the gravitational effect of earth's rotation is experimentally testable, using the NASA flyby anomaly, or using a controlled experiment with a pair of satellites in orbit around earth. Laurie was dismissive, as usual: “experiments are a dime a dozen” he said in response! The sole important thing is to trust racist and colonial authority, he implied.
By the way, my new approach to calculus involves what is today called non-Archimedean arithmetic, in addition to zeroism. (As usual, Crowe does not provide a source for the quote.) This is clearly explained in the original paper on “Retarded gravitation theory”9 That paper explains that calculus can be and is and was done without formal real numbers, (1) using floating point numbers as on a computer, and (2) using what is formally called a non-Archimedean ordered field larger than real numbers. (This was the way calculus originally developed in India as explained in my articles for the Springer encyclopedia.)
Demanding the use of formal real numbers for calculus forces time to be like a line, on grounds of authority, not physics. A brief and popular-level account of the complex issue of how this relates to religious beliefs is in the video of my Berlin lecture on “Decolonising Time: time at the interface of science and religion”.
The Atiyah case
As another example, Crowe suggests that it is incredible that Michael Atiyah regarded as the world's leading mathematician, tried to grab credit for my analysis of Einstein's mistake. I take up this example to demonstrate the unreliability of Western authority at the highest level.
The math may be beyond Crowe, but he ignores even the simple evidence. First, three experts of the Society for Scientific Values found a valid case was made out against Atiyah, and this is posted online. (Click the above link, and scroll down to case number 3 of 2007.) This has been cited as a stock case of plagiarism.
Of course it is a fact that my book Time: Towards a Consistent Theory (Kluwer, now Springer, 1994) advocated functional differential equations (FDEs) in physics. It also pointed out a mathematical mistake related to FDEs made by Einstein and many others. (The mistake was to replace FDEs by ordinary differential equations (ODEs), which are qualitatively different.) My book pointed out that even retarded FDEs already lead to a paradigm shift in physics.
By a curious “coincidence”, Atiyah in his 2005 Einstein centenary lecture also advocated the use of retarded FDEs. By a further “coincidence”, he too called it a paradigm shift in physics. He did not cite my work, but instead ended his lecture by saying “Don't forget that I suggested it”. He did not speak explicitly of Einstein's mistake, but in a side interview to the press Atiyah mentioned the Poincare-Einstein priority issue, and also that Einstein was not a good mathematician and “he needed help” (from Marcel Grossmann) to formulate the general theory of relativity.
It is a fact that Atiyah was later compelled to acknowledge the similarity with my earlier published work in this 2007 letter published in the Notices of the American Mathematical Society. But this was AFTER the publication of the 2006 article, reporting his 2005 speech and giving him credit for the theory. Claiming credit by not acknowledging prior published work is recognized as an ethical violation in the published ethics of the AMS.
Further, Atiyah's pretence that this was an innocent oversight is false. Contrary to that, Atiyah was personally informed of my work through emails including this one, of 26 Oct 2005 (which he acknowledged), long before he got his lecture published in a 2006 article in the Notices of the AMS. This was done through two American authors who explicitly acknowledge that they consulted Atiyah, as is natural. But, the 2006 article again failed to cite me. It again repeated Atiyah's claim “Don't forget that I suggested it”. Indeed, it went further, and tried to cement Atiyah's priority by naming the thesis as “Atiyah's hypothesis”, all with Atiyah's concurrence. Some innocent mistake this! Because my study of history had made me well aware of the dirty tricks of Western authorities, I threw a spanner into the works which derailed Atiyah's game plan.
There are many more details, but let Crowe first engage with the above facts. So far, like Laurie, Crowe simply follows the stock racist methodology: to dismiss everything contrary to his faith, though he is completely unable to engage with a single relevant argument or piece of evidence!
Ellis and Murugan
Both Crowe and the GroundUp article bolster their attack against me by citing the opinions of Jeff Murugan and George Ellis of the UCT math department.
First, Murugan lies that my calculus course offers no advantage. As just one example, my calculus course teaches elliptic integrals and elliptic functions left out of standard undergraduate calculus courses. As explained in “Time: what is it that it can be measured?” (cited earlier) elliptic integrals are needed to properly perform the first serious science experiment in schools: the simple pendulum.
Second, both Ellis and Murugan hide their conflicting interests: I have a long-standing critique of the book Ellis jointly authored with Stephen Hawking, on singularity theory. (My UCT summary referred to this as “Hawking singularities” because I have long regarded Ellis as a mere sidekick of Stephen Hawking, but obviously he is important in the UCT context.) Murugan is a student of Ellis.
Two key grounds for my critique of Hawking and Ellis are the following. First, singularity theory has been used to push post-Nicene church dogmas into science. My public critique of the similarities between Hawking and Ellis and Augustine—their postulates and creationist conclusions—is standing since my book Eleven Pictures of Time (Sage, 2003). In UCT, I specifically pointed to the claim that singularity theory claims to prove “Judeo Christian theology is part of physics”. This is a clear attempt to spread superstitions through abuse of mathematical authority. Why didn't Ellis or Murugan come to my talk and reject or defend this devastating claim against Ellis? Why do they want to hide that critique? Obviously they find it easier to make unsupported claims against the critic in newspapers.
Third, as stated in my summary for the UCT panel, I was willing to discuss the formidable technical details in the math department based on this paper (see citation at no. 17) and how my earlier use of non-standard analysis, applied to Schwartz distributions, can be replaced simply by non-Archimedean arithmetic.
I also briefly explain how the apparent breakdown of the differential equations of physics at a singularity is due to the limitations of university calculus, and can be easily avoided, even within general relativity, by reverting to the philosophy with which calculus originally developed. This, is technical, and would be taken up in more detail in my lecture on decolonising math.
That is I critique both the politics and formal math involved in singularity theory; this threatened to expose Ellis' lifework to ridicule. Hence, he desperately did not want me to lecture in the math department. Instead of confronting me at an academic level, he and his student Murugan avoided the critique and chose to plant tales against me in newspapers, which will not permit me to respond. Note how they stick to such sheltered positions: Crowe laughably speaks of Murugan's “devastating critique” which is kept secret.
My devastating critique of Hawking and Ellis is public for some two decades.
Other issues
Crow quotes me again without naming a source.
“Since bad history and philosophy of science [e.g. my historical summary above] was violently distorted by the religious fanaticism which overwhelmed Europe from the 11th to 17th Centuries, it is necessary to dismantle and expose the falsehoods of this Western history of science and its accompanying philosophy of science.”
The broad quote seems genuine, but the word “bad” is obviously a typo. This issue is explained in my booklet Is Science Western in Origin? To quote from the back cover.
during the Crusades, scientific knowledge from across the world, in captured Arabic books, was given a theologically-correct origin by claiming it was all transmitted from the Greeks....Second, during the Inquisition, world scientific knowledge was again assigned a theologically-correct origin by claiming it was not transmitted from others, but was “independently rediscovered” by Europeans. The cases of Copernicus and Newton (calculus) illustrate this process of “revolution by rediscovery”. Third, the appropriated knowledge was reinterpreted and aligned to post-Crusade theology. Colonial and racist historians exploited this, arguing that the (theologically) “correct” version of scientific knowledge (geometry, calculus, etc.) existed only in Europe.
Then there is the idea that colonial education was introduced with the specific purpose of curbing revolts and uprisings. As explained in this article on Education and counter-revolution, this thesis was argued by Macaulay (a name as detested in India as Rhodes is in South Africa) in a speech in British Parliament. He was referring to the revolts then going on in Europe, as also stated by Marx a few months later. Further, the fact is that the British were easily overthrown in India in 1857 and the first Western universities (Mumbai, Kolkata, Chennai) were immediately afterwards introduced in India. Crowe's ignorance is vast, whether about colonialism or math or science, and his laughable method is to conclude that anything he finds surprising is wrong!
Concluding remarks
To conclude, Crowe fails to raise any reasoned and specific objections, and thus requires no specific answers. In accordance with the racist methodology (BLAA) he boasts about the reputation of the math department, and lies about me. He recites myths and cites the opinions of Ellis and his student Murugan, without revealing that I critiqued the life work of Ellis, and exposed it—and that the two are apprehensive of addressing in an academic forum either the relation of singularities with theology or the technicalities involved.
Basically, Crowe is arguing that racist and colonial authority must prevail over evidence: the blacks must be suppressed and subjugated again through academics. The game plan is evident: Crowe is desperate to derail the decolonisation effort, hoping to take it over by bullying. He then plans to implement recolonisation by playing on words to call it decolonisation!
So how should the majority confront it? First don't fall for the old colonial con-trick again, and watch out also for the compradors. Watch the actions not the words: demand evidence, and specific arguments. Did anyone raise any substantive point against me? Or contest any single piece of evidence or arguments I raised? Which were the specific sentences they contest? If not their claim of “engagement” is false. Discard it. And, if they are unable to engage, why do they demand that students should engage?
Second, students and the wider public should remember that the salary of the faculty at UCT comes from THEIR fees, and PUBLIC money. So, the faculty must be held PUBLICLY accountable. The local community must demand to know what benefits it gets in return for the money it invests. If any “expert” refuses to explain, and thinks he or she is responsible only to the formal math community, then let them take a 50% salary cut for non-performance each year. That might be a good way to make fees fall!
That solution may be hard to implement. But a simple interim way to improve teaching AND keep the “experts” publicly accountable is to expose them to the threat of being rendered irrelevant. Allow parallel decolonised courses to run in the University, so students can choose the decolonised courses over the existing course if they so wish. Students must raise the demand for such parallel decolonised courses.
1There are other facts Crowe suppresses. For example, that I was Professor and Head of the Computer Science department at the National University of Journalism in Bhopal, for five years, at a time when it was the largest computer science department in the country (with some 38000 students). He suppresses that it was as a Distinguished Professor of Computer Science that I joined Inmantec. After all, the success of the Indian software industry presupposes good teaching of computer science for which there has been a great demand. Also, my association with Inmantec ended long ago.
2E.g., Josiah Priest, Bible Defence of Slavery...and A Plan of National Colonization Adequate to the Entire Removal of Free Blacks, by Rev. W. S. Brown, Louiseville, Kentucky, William Bush, 1851.
3My detailed response to the GroundUp article, which GroundUp refused to carry appropriately, is put up at http://ckraju.net/papers/Ground-up-ckr-response.pdf,
4This was reiterated in my censored article in the Conversation last year. The censored article was later reproduced in full in the article “Black thoughts matter” in Journal of Black Studies, and the contents explained further in a popular-level article on “Math and censorship”. I had asked for these articles to be circulated prior to the UCT debate.
5Thomas Heath, A History of Greek Mathematics, Dover, New York, 1981, p. 360.
6The late Martin Bernal (personal communication) agreed that Uclides was just another translation howler, but favoured deriving it from aqli + des (rational geometry) rather than Ucli + des (key to geometry).
7B. Russell, “Mathematics and the metaphysicians”, chp. 5 in: Mysticism and logic and other essays, Longman Green and Co., London, 1919.
8For an expository account, see C. K. Raju, “Time: what is it that it can be measured?” Science & Education, 15(6) (2006) pp. 537–551. Draft available from http://ckraju.net/papers/ckr_pendu_1_paper.pdf.
9C. K. Raju, “Retarded gravitation theory” in: Waldyr Rodrigues Jr, Richard Kerner, Gentil O. Pires, and Carlos Pinheiro (ed.), Sixth International School on Field Theory and Gravitation, American Institute of Physics, New York, 2012, pp. 260-276. http://ckraju.net/papers/retarded_gravitation_theory-rio.pdf.


14-11-17
From: Raju
To: Crowe; Loretta Feris; Daya Reddy; VC; Judith Du Toit; Dean of Science; Elelwani Ramugondo; Peter Dunsby; Chris Mitchell; Gerda Kruger; Sipho Pityana; Kasturi Behari-Leak; Goitsione Mokou; Kenneth Hughes; Henri Laurie; Nicola Illing; Ed Rybicki; David Benatar; Andy Buffler; Muthama Muasya; Shadreck Chirikure; simonrakei.sr@gmail.com; Russell Ally; llg@sun.ac.za; Harry Garuba; Maano Ramutsindela; Arthur Ngwenya; SRC President 
Mitchell has not responded to my email, and a reminder. I guess this shows the shape of things to come.
So, I attach my response, assuming the UCT News is purely online.
I notice that you do not seem to regard the students as part of the UCT community, and have not kept them informed. As pointed out in my response, they are actually the paymasters of the faculty, and it is high time the faculty realized that they are responsible to the students and the public.  So, I have marked a copy also to the President of the SRC.
Let them also know about the hypocrisy of some faculty in the UCT. You keep asking the students to engage, in the matter of decolonising science, and all that the closet-racists in UCT are doing is to shower abuse, and avoid engaging. They could not even engage with the easiest of my claims that the author of the Elements was a black woman. Are these UCT faculty setting an example which they would want the students to emulate?

UCT debate on decolonising science and the Crowe report

C. K. Raju
Indian Institute of Education, and SGT University

Summary: I nail some wild lies by Crowe. To build a false case, he also suppresses my key affiliations: the one's relevant to decolonisation of math and science.

Colonisation involved mind capture using myths. To decolonise, those myths must be critically scrutinized, and new narratives may be needed. The racist methodology, however, is to dodge critical scrutiny, by (a) avoiding engagement with evidence, and arguments, and (b) demand blind faith in colonial myths and (c) and blind faith in the opinions of residual colonial authority. (Apart from being untrustworthy, that may be irrelevant; in particular, decolonisation rejects formal math, globalised by colonialism, so it does NOT need the prior permission of formal mathematicians.)
Crowe nevertheless sticks to the above excessively weak methodology; for example, he reiterates the myth of (a white) Euclid, but fails to provide evidence for it. This, despite my ZAR 40K “Euclid” challenge prize. On the other hand, there is counter evidence for my claim that the book Elements was written in the +4th c. CE, by a black woman. Her religious leanings were with the Egyptian notion of soul which Greeks from Plato to Proclus persistently connected to mathematics. However, that “pagan” notion of soul was later cursed by the post-Nicene church which smashed all pagan temples at that time: that is why she was lynched in a church.
The false history of Euclid is linked to a bad philosophy of math used today: that the white man did math in some “superior” way which must be imitated. First, contrary to the Euclid myth, there are no formal proofs in the actual book Elements. Second, formal proofs are not superior: mere deductive proofs do not lead to valid knowledge. Instead, they make math difficult without adding to practical value, which comes from normal math, which accepts empirical proofs as also empirical tests of postulates, and logic. Therefore, the right remedy for the problems about math-teaching facing blacks is to reject formal math and revert to universal normal math. Since normal math is easy, it enables students to solve harder problems.
Changing math also changes science by eliminating the redundant metaphysics in formal math: for example, eliminating the metaphysics of time in Newton's misunderstanding of the calculus changes his theory of gravitation.
I briefly go into the Atiyah case to show that even high mathematical authority cannot be trusted. (In 2005, on the centenary of Einstein's special relativity paper, Atiyah tried to grab credit for my theory.)
Crowe has banked on the opinions of George Ellis and his student Jeff Murugan. However, he suppresses a key fact. During the UCT debate, I raised my long-standing critique of the singularity theory of Stephen Hawking and Ellis for arriving at their creationist conclusions and for leading to the utterly superstitious conclusion that “Judeo Christian theology is part of physics”. I had offered to discuss also the related technicalities of formal math (non-standard analysis applied to Schwartz distributions) in the math department. Afraid to be exposed, and nervous about the technicalities, Ellis and Murugan fled from the academic battle. They continue to avoid the critique but attack the critic—in “safe” forums where I am not allowed to respond. Crowe relies on that opinion which fails even to acknowledge the conflict of interests. Between reciting myths and citing such dishonest opinions, Crowe does not make a single valid point.
The students should note that faculty salaries are funded by students fees and public money: therefore the faculty must be made publicly accountable. Till such time, an interim solution is to start teaching decolonised courses in parallel to existing courses, and to let the students choose what the prefer.
Some lies
The purpose of a constructive debate is to arrive at truth, but that requires adherence to the truth. Timothy Crowe seems unable to stick to the truth: in a widely circulated earlier email exchange with me, Crowe lied wildly about what I said about Karl Popper's handwritten letter to me. Then Crowe tried to fudge issues, proving that the distortion was no accidental misreading.
Therefore, first let me nail some more of Crowe's lies, in his report on the UCT debate. Since I warned Crowe beforehand against lies and misrepresentations, he has corrected some lies in the earlier version of his report, but has introduced new one's! He now has no excuse for them.
Thus, Crowe gives a long series of “quotes” from me. The very first of those concerns some French astronomical observation missions. The content of the quote may well be true. But it is false that I said it; I have not written anything about Haiti. Crowe provides no source for his “quote”.
Crowe goes on to lie about my work concerning relativity. He says that I claim
“that Albert Einstein's theories of special and general relativity were anticipated much earlier by Henri PoincarĂ© and were flawed [corrected by Raju].”
Yes I have claimed that special relativity was anticipated by Poincare (shortly before Einstein), and I stand by that. However, it is a wild lie that I ever claimed that special relativity is flawed. To the contrary, I stated in my acceptance speech for the TGA award,
“There is no doubt at all that the theory [of special relativity] was the work of a genius. The question is who was that genius: PoincarĂ© or Einstein? The second question follows naturally from the first: compared to PoincarĂ©, a mathematician, did Einstein, a non-mathematician, even understand the full mathematical implications of the theory of relativity?
I NEVER said special relativity is flawed. That is just another wild Crowe lie. What I said was Einstein did not understand its full mathematical implications. There is a huge difference. I have repeatedly emphasized since 1992 that Poincare DID understand that relativity necessitates functional differential equations (FDEs), though he used only retarded FDEs or delay differential equations, which he called equations of finite difference. [More about Einstein below in the 2005 case when Atiyah, a leading mathematician, advanced claims similar to mine on the centenary of Einstein's special relativity paper.]
It is possible that Crowe is a total ignoramus and so bound by myths that he does not understand the difference between Einstein and special relativity. In that case he should rectify his ignorance and not harbor vainglorious dreams of debating with me. I will not consider this possibility further; as I stated at the start of the UCT debate, lies or misrepresentations, for whatever reason, mark the end of debate.
Such persistent lies by Crowe are an admission he knows he is on weak ground. The use of lies also shows that he is not interested in a constructive debate but only in domination by hook or crook. He has earlier revealed his general trick to defend himself: whenever a specific lie is nailed, he will call it an ad hominem attack! Pitiable.
I will not bother to refute all of Crowe's lies here: my purpose is decolonisation and not to nail Crowe's lies, for Crowe seems beyond reform or repair. Nailing two lies is enough for the perceptive. Suffice it to say that Crowe is not even approximately trustworthy especially when (a) he “quotes” without citing a source, or (b) tries to paraphrase without understanding, both of which he frequently does.
Fudging facts
Crowe goes on to fudge key facts about my career. Specifically, he suppresses all key aspects related to decolonisation. Thus, my experiments on teaching decolonised calculus were performed at the Universiti Sains Malaysia (then the apex Malaysian university) when I was a long-term visiting professor in the mathematics department there. This affiliation was stated, for example, in my papers reporting on those experiment, “Teaching mathematics with an alternative philosophy”, cited at 7 and 22 in my advance summary for the UCT debate, and Crowe himself provides a link to one of those papers. So, Crowe knowingly suppressed facts, and does so to build a false case.
Next I joined Al Bukhary International University, where I designed and taught courses on decolonised history and philosophy of science, as explained on these blogs (1, 2), and shown in this short video. This affiliation too was stated in my paper on gravitation, published by the American Institute of Physics, and cited at 14 in my summary for the UCT debate.
Currently, I am an Honorary Professor with the Indian Institute of Education, based at its centre in the Mumbai University campus, carrying out a project on alternative math teaching in schools: basically rejecting the myths associated with Euclid and using African/Indian cord geometry to teach school geometry in an easy and better way. Experiments are on to teach decolonised cord geometry in Indian schools. My current affiliation with IIE was stated clearly in the summary circulated for the UCT panel.
I am also concurrently a Professor Emeritus at the SGT University, Delhi, teaching regular decolonised courses, on calculus and history and philosophy of science (as publicly declared by the University; click the above link to see also the pictures of students which too I showed in UCT). These are the ONLY decolonised courses on math and science, well-tested and running as regular university courses ANYWHERE in the world. Therefore, the UCT was absolutely right to invite me to talk about decolonisation of math and science during my visit to South Africa. Who else could they have invited?
Crowe suppresses these four key affiliations because accepting them shoots down his case to bits, as he knows. Pictures of students of these decolonised courses were also shown during my UCT presentation. Crowe admits he was there. This suppression of the truth is Crowe's other best argument, and he calls it “research”! Unethical.
The new narrative
I am also very proud of having initiated the Project of History of Indian Science, Philosophy and Culture (PHISPC) in the early 90's. The aim of the PHISPC project was that we, the colonised, should tell our own stories, and not be tied down by the stories told about us by the coloniser (e.g. Hegel's rant that all Africans were cannibals). The new stories turned out to be very, very different. This telling of one's own stories (in over hundred volumes) was very fruitful and marked the beginning of emancipatory decolonisation. I strongly advocate that Africans too must start telling their own stories, to break free from the narratives with which the coloniser has bound them.
The PHISPC was housed in the Centre for Studies in Civilisations, and has produced over a hundred volumes, an enormous academic effort by any standards. My volume on Cultural Foundations of Mathematics (Pearson Longman, 2007) was the 50th. Crowe suppresses this very important fact, though a long list of PHISPC volumes is printed on the jacket of my book, and a glance at it will show that it involved the cream of Indian scholarship from across the political spectrum. In typical racist style, Crowe only seeks to belittle the whole effort by calling the Centre an NGO, which it technically is, but only to preserve its autonomy, since it is fully government funded.1
The telling of new narratives is the beginning of decolonisation, but that also marks the end of colonisation for it involves the destruction of old narratives and old structures of authority.
Decolonisation methodology
Indeed, false colonial narratives were a key aspect of colonial rule. Colonial rule was not a simple military conquest: it was con-all-ism, and used con-tricks, myths, and superstitions to capture the colonised mind. Colonial education (which was church education when it first came to the colonised) systematically indoctrinated the colonised into those Western myths and superstitions.
Therefore, as I explained in Ending Academic Imperialism, a key strategy of decolonisation is to dismantle colonial soft power by confronting colonial lies, myths and superstitions. Decolonisation is NOT a demand to reject everything Western, as is often caricatured; it is a demand to “be critical and choose what is best” .
Incidentally, decolonised math rejects the formal math globalised by colonial education and seeks to restore normal math. Therefore, it is wrong to demand, as Crowe does, that decolonised math requires the prior permission of the colonised mathematicians (who do formal math). The equitable counter proposition is that formal mathematicians are welcome to debate publicly, and one formal mathematician was invited to the UCT panel. Having nothing to say, he used up his time to recount his autobiography! While many formal mathematicians are understandably annoyed by the decolonisation proposal, they have so far come up with only hot air and abuses. Not a single cogent counter-argument from them yet. Because the debate was public this was quickly exposed. This is discussed in more detail below.
Being critical of Western myths and superstitions is a simple process: just demand EVIDENCE for every colonial myth (whether historical or philosophical). If no evidence is forthcoming, discard the myth, and eliminate the related lies from the education system.
The racist methodology: avoiding evidence
But a critical analysis threatens the soft power of the coloniser and the racist—which power persists in education—even after the notional end of colonialism or apartheid.
Therefore, racists and pro-Western elements dodge a critical analysis of their myths. (1) They totally avoid engaging with the evidence, and instead (2) demand reliance on authority—their authority. This racist methodology was also used in apartheid and slavery which could not have survived critical engagement with the evidence, but recall how the Bible,2 Kant and Hume etc. were cited in defence of racism and slavery.
The UCT debate exposed these tactics of evidence-avoidance and demanding reliance on (Western) authority. For example, Henri Laurie demanded that Western myths must be accepted without evidence (in an earlier email exchange). He said the onus of disproving colonial myths was on the challenger who must produce counter-evidence! This is unreasonable enough, but Laurie went further, to an amusing extreme: he said when counter-evidence is produced, he had the right to dismiss it without examination. During the UCT panel, he demonstrated his belief that mere racist arrogance is a valid substitute for scholarship: he flipped thorough my 500 page volume in 5 seconds and rejected it! The whole world should know that this is what passes for academics among some in UCT. Shame.
In simple terms, racism uses BLAA (Boasts of white superiority, Lies about non-Whites, accompanied Adjectives and Abuses). The use of these tactics identifies the closet racists who may outwardly pretend to be against racism today (though they never suffered for any anti-apartheid views under apartheid, like Steve Biko).
Both Crowe and the GroundUp article against me followed this racist methodology. For example, the GroundUp article called me a “conspiracy theorist” but couldn't even say WHAT conspiracy theory I was accused of! For the racist, any remark by a closet-racist for some undisclosed reason is ultimate proof. Racists can “prove” anything in this way.3 For others, this only shows that the racists are frightened and desperate and unable to come up with anything better.
Likewise, Crowe relies on “quotes” (in quotes) from me; but alas he is unable to contest any of my statements with any sort of counter-evidence or counter-argument. He just uses the excessively naive assumption (“Crowe's postulate”?) that anything surprising and contrary to colonial myths and superstitions is wrong. Crowe's postulate is the same as Laurie's: both claim colonial narratives must be accepted without asking for evidence because they don't have the evidence.
Let me now move on to the real substance.
The myth of Euclid provides an excellent illustration of how new decolonised narratives displace the old, and why #EuclidMustFall.
Was “Euclid” a black woman?
The role of myths is especially important for math, a key stumbling block for blacks in higher education. The myths are con-trickery, a substitute for the real history and philosophy of math, which philosophy is poorly understood by the vast mass of people.
Because myths are at the core of colonial power, Crowe begins by reiterating the myths of math. But he offers nil evidence. Consequently, EVERY claim in his opening section is false. Instead of dealing with that mass of falsehoods, here I will focus on Euclid, a myth used to justify the way math is taught today. To change the way math is taught, we must first shoot down that myth.
To demonstrate the lack of evidence, I have long offered a Euclid challenge prize of ZAR 40K for any serious evidence about Euclid.4 No one could claim the prize. Crowe amusingly imagines mere verbiage will hide lack of evidence. His other defence is to cite the opinion of the UCT math department which apparently finds this mere demand for evidence an ad hominem attack, and a terrible distortion of history, not to mention a “conspiracy theory”, and a “crank” demand and charlatanry! So many adjectives are needed because they KNOW there is no evidence. Thus, David Fowler, the leading Western expert on ancient Greek mathematics, admitted long ago (in response to an angry query against me) that NOTHING was known about Euclid, and that our earliest copy of the book Elements is from +888 CE, closer in time to us than to the purported date of Euclid. That admission is archived here.
So why does Crowe desperately try to hang on to that myth of Euclid? One reason is clear enough. “Euclid” is depicted as a white man through his images (just google). But there is nil evidence for Euclid, so how did anyone know the color of his skin? This only shows what kind of trash history the highest Western “authorities” have peddled for centuries; it is proof that they should NOT be trusted an inch.
The educational consequences of this “white-Euclid” myth are clear enough: last year in an article in Conversation, Karen Brodie opined that “mathematics is the work of dead white men”. She further stated that blacks and women are bad at math, and insinuated that the right way to “decolonise” math is to retrain the psyche of blacks and women to teach them to think like the dead white men who invented math. It was to preserve such obnoxious racist nonsense that Conversation censored my article in response, after my article was published.
My censored article aroused a lot of resentment and surprise among whites. One reason for the resentment was my claim that the author of the Elements was a black woman, not a white man. The surprise is manifest: Science 2.0 still carries that censored article under the changed title “Was Euclid a black woman?...”. Racists find this galling, and Crowe puts up this proposition as proof of my unreasonableness! How very unreasonable and “illogical” that someone disbelieves the false myths of the white origins of math, because those myths lack evidence! How very unreasonable that someone claims the Elements was authored by a black woman! However, unlike Western or racist historians, I back ALL my claims with EVIDENCE.
Thus, while there is nil evidence that a person or persons called “Euclid” wrote the book Elements in the -3rd c. CE, there IS counter evidence that the book was written, some seven hundred years later, in the +4th c. CE, by Theon of Alexandria. As Thomas Heath, another leading Western authority on “Greek math”, noted, “All our [Byzantine] Greek texts of the Elements up to a century ago. . . purport in their titles to be either “from the edition of Theon”. . .or “from the lectures of Theon”.”5 Therefore, the book Elements was completed after the 4th c. Theon. But it was before the 5th c. Proclus who wrote a commentary on the book. That narrow range leaves Theon's daughter, the mathematician Hypatia, as the best candidate.
The further corroborative evidence is that commentaries on the book speak anonymously of the “author of the Elements”, though they name others from Aristophanes to Zeno. Why the anonymity? What terrible thing rendered the “author of the Elements” anonymous? Was it because she was a woman? And someone to whom something terrible happened, too terrible to be mentioned? Hypatia again fits the bill.
How do I know the color of her skin? Well, she lived in Alexandria in the African continent, where the default skin color is black. Therefore, she was black on the balance of probabilities which is the standard of proof for history. I am willing to revise my opinion, but ONLY if someone produces solid EVIDENCE to the contrary. I will not budge an inch on the mere racist prejudices of even thousands whites (or compradors) still in authority, who are baying for my blood and hurling all sorts of abuse against me. Let them howl.
That beautiful and wise black woman, Hypatia, was brutally lynched in a church, as is well known. I draw attention to that fact because it has an important bearing on the history and philosophy of math. Why was the church against her?
Thus, Crowe recites also the false myth that the Greeks did formal math. This is total bunkum. In fact, the book Elements does not have a single formal proof in it. Just check even the “authoritative” doctored 19th c. source. Its first and fourth proposition use empirical proofs on which its proof of the penultimate proposition, the “Pythagorean theorem”, depends. Those who make the false claim about Greeks giving formal proofs, should produce the purported formal proofs supposedly given by Greeks, or desist from making false claims. So far all that people like Laurie have said is to lie that my arguments are only against the person Euclid.
In fact, the truly special feature of Greek mathematics was its relation to religion, and the soul. There is solid textual evidence for this, for example, in Plato's Meno. There, Socrates links mathematics to mathesis, meaning learning, and claims that “all learning is recollection” of the eternal ideas already known to the soul from its past lives. He demonstrates that Meno's slave boy has an innate knowledge of geometry. Socrates then argues that is because his soul acquired that knowledge in a previous life. This connection of math to the soul is reiterated in Plato's Republic (Book VII), where Socrates asserts that geometry must be taught, NOT for its practical value, but because, by arousing the soul, it makes people virtuous.
Centuries later, Proclus in his +5th c. commentary, places the book Elements in the very same religious tradition, and explicitly derives the word “mathematics” from mathesis (NOT mathema, as Crowe false asserts using unreliable Wikipedia). There is a more detailed discussion of this in the chapter on “Geometry and the soul” in my book Euclid and Jesus.
Now this “pagan” (Egyptian) notion of soul was accepted also by early Christianity (Origen), but the post-Nicene church cursed it and distorted Christianity for its own political benefits (See, e.g. “The curse on 'cyclic' time”, chp. 2 in my Eleven Pictures of Time, Sage, 2003). Because the book Elements championed that same notion of soul, associated with equity, it aroused the church's wrath. Hence a Christian mob brutally lynched Hypatia at this time when the church got every last “pagan” temple in the Roman empire physically smashed by inciting mobs. More details in my book Euclid and Jesus,which displays the image of that revolutionary black woman on its cover, alongside some images of the archaeological finds of broken statues of “pagan” gods from Alexandria.
Many centuries later, the church freely “reinterpreted” the book Elements as a book on deductive proofs (which it is not), ascribed to it a false (but theologically-correct) origin in an unknown “Euclid”,6 and used it to teach reasoning to its priests. This was done in support of the post-Crusade Christian theology of reason copied from the Islamic theology of reason (aql-i-kalam), so as to persuade the Muslims who were military too strong then to be converted by force. I have explained this in various places.
If Crowe or anyone else wants to challenge my conclusions they need to contest specific facts and arguments, not merely point to the sweeping evidence-less opinion of this or that person in UCT, who merely uses BLAA. Those dirty days of apartheid are over, and the sooner the closet racists accept this, the better for them.
The bad philosophy of formal math
The false myth of Euclid and his deductive proofs is linked to the bad philosophy of formal math that deductive proofs are “superior”. This bad philosophy determines the way math is taught today. Crowe reiterates the false Western myth that everyone other than “Greeks” did “inferior” math as mere rules of the thumb. Contrary to that myth, normal math (which I advocate), used BOTH facts (empirical proofs) and reasoning (deductive proof), like science. The special feature of formal mathematics is that it is anti-empirical and prohibits empirical proofs (facts), and uses ONLY deductive proof. By avoiding empirical proof formal math claims superiority. But is this claim of “superiority” any better than the racist claim of white superiority? It is not.
To show this, it is important to point out, as I have done, that a mere deductive proof does NOT lead to valid knowledge. Consider the following deductive proof. (1) All animals have two horns, (2) A rabbit is an animal, therefore, (3) A rabbit has two horns. This is a valid deductive proof, but is the conclusion valid knowledge? Obviously not; it is nonsense. In the same way, a deductive proof may be given for any pre-desired conclusion whatsoever from appropriate premises.
Indeed, it is very well known that deductive proof does not lead to “truth”, but leads at best to relative truth, relative to the premises. Crowe seems ignorant of this basic thing. He goes by myth and faith. And neither the mathematician nor the philosopher on the UCT panel engaged with my critique of formal mathematical proofs. (Crowe says he was there, and they engaged, but don't trust him, watch the video, and tell me where they engaged with this critical point that the philosophy of formal math is bad.)
The above deductive proof led to invalid knowledge because the first premise (“All animals have two horns”) is false. But we know this only EMPRICALLY. However, formal math, rejects the use of facts. As its name suggests, it is purely about form: substance and facts do NOT matter. Crowe believes in the authority of Russell who explained formal math thus: “We...take any hypothesis that seems amusing, and deduce its consequences”. 7 I find horned rabbits distinctly amusing, even though the trolls of apartheid were not amused!
As Russell further explained, in the same paragraph, in formal math, one ought NOT to check whether the hypotheses are true as facts: “It is essential not to discuss whether the first proposition is really true”. [Emphasis added] So, let us not discuss further whether, in fact, all animals have two horns: such discussions about facts are irrelevant to formal math which is divorced from facts. Russell concludes, “Thus [formal] mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true.” [Emphasis added] That is just what I claim, mere deductive proof provides no guarantee of valid knowledge. Crowe does not know the abc of the philosophy of formal math, and the UCT philosopher on the panel did not engage with any of these claims of mine. (Note: Those who resist decolonisation of math in UCT must recruit some competent debaters!)
Can't we empirically check the starting postulates of formal math? No, we cannot. Formal math is metaphysics, i.e., it cannot be empirically tested. As a simple example, geometric points are declared invisible. So how can we EMPIRICALLY verify the postulate that a unique straight line passes through two points? (A line is made up of points; if the points are invisible, so is the line!) Moreover, unlike an invisible electron, an invisible point does not affect anything in the real world, so we cannot even indirectly infer its existence the way we can infer the existence of an electron by its track in a bubble chamber.
In fact the postulate is contrary to experience: most people did geometry in school only with visible dots, and visible lines. Two real dots may be connected by multiple lines which differ slightly. That is a fact, and the practical experience, contrary to the postulate. But, by teaching formal math, young children are indoctrinated to reject this commonsense, and blindly trust Western authority on the nature of invisible points! Why do theycomplain if I laugh at those who believe in invisible points and recall the story of the emperor's new clothes? Can Crowe (or anyone in the UCT math department) explain how the above postulates about invisible points and invisible lines may be EMPIRICALLY tested?
Apart from the inability to verify postulates there are other reasons why deductive proof fails to provide valid knowledge. An invalid deductive proof may be passed off as valid. The classic example is how the proofs in the Elements were mistaken for valid deductive proofs for centuries. Again, formal mathematical proof uses 2-valued logic which is not universal, that choice needs to be justified empirically, and is only approximate.
Riddled with so many failings, the fact is that formal math not only fails to provide any assurance of valid knowledge (rigor), it makes math extremely complicated (mortis)! That is why the proof of 1+1=2 in Whitehead and Russell's Principia needs 378 pages. Formal mathematics distinguishes between integers and real numbers. So, things become even more complicated when we try to deductively prove 1+1=2 in formal real numbers, from first principles, because this needs that we first develop set theory, which involves an enormous metaphysics of infinity altogether beyond empirical verification. To bring out these problems, I asked Laurie to prove 1+1=2 for real numbers from first principles, writing out the formal proofs in full. But even that first step was too complicated for him. How on earth will students understand calculus based on real numbers? My point is this: why do this absurdly complicated thing when it provides no assurance of valid knowledge and no practical advantage for application to science and engineering? Why not do 1+1=2 in the normal way?
The real reason is found by examining Western tradition. The avoidance of empirical however was part and parcel of the church dogma of reason, because any engagement with the empirical might damage its doctrines like virgin birth. Therefore, the church glorified reason (“deduce how many angels can fit on the tip of a pin”) but ran down the empirical (“do angels exist?”). It suited the church well to lay down postulates authoritatively; testing them did not. Crowe just repeats the myths around those dogmas, like the myth of Euclid and his (absent) deductive proofs which were part of church mythology and believed for long by Western authorities. Crowe is entitled to his faith, but why should such faith be treated as public knowledge and taught in universities? My demand is to teach math solely for its practical benefits. There are many more issues, some of which (including the false claim of aesthetics in formal math) are taken up at the popular level in this article on “Math and censorship”,
To summarise, (a) we need to discard Western/racist myths (b) including myths linking the false history of math and its purported Greek origins to a bad philosophy of math, for formal math offers no demonstrable practical advantage, and (c) revert from formal math to teaching normal math which makes all math (not just calculus) a whole lot of easier. This results in no loss for practical applications of math, since real world applications of math to science and engineering invariably involve normal math and approximations. On the contrary it results in a gain, since making math easy enables students to do harder problems. Therefore, to overcome the pedagogical problems facing blacks in math, we should decolonise and teach normal math.
New theory of gravitation
The concrete benefit of decolonised normal math for pedagogy is clear enough (it makes math easier, and enables students to do harder problems). But there is a deeper question: will a different way of doing math affect science? The answer is yes. Briefly, because science uses math, and formal math involves metaphysics, that metaphysics may creep into science through formal math. But this is complicated to explain. The easiest illustrative case mentioned in my UCT summary was the case of Newtonian gravitation.
What specific statement is Crowe denying? That Newtonian physics and Newtonian gravitation failed over a century ago? That Newton made time metaphysical8? That the conceptually incoherent notion of a “flowing time” was the basis of Newton's attempt to understand calculus using “fluxions”? That correcting Newton's error about time led to special relativity? That relativity needs FDEs? That my new theory hence reformulates gravitation using FDEs?
The resulting differences of my theory from Newtonian gravitation are explained for the layperson in this press release. On the new theory, the gravitational effect of earth's rotation is experimentally testable, using the NASA flyby anomaly, or using a controlled experiment with a pair of satellites in orbit around earth. Laurie was dismissive, as usual: “experiments are a dime a dozen” he said in response! The sole important thing is to trust racist and colonial authority, he implied.
By the way, my new approach to calculus involves what is today called non-Archimedean arithmetic, in addition to zeroism. (As usual, Crowe does not provide a source for the quote.) This is clearly explained in the original paper on “Retarded gravitation theory”9 That paper explains that calculus can be and is and was done without formal real numbers, (1) using floating point numbers as on a computer, and (2) using what is formally called a non-Archimedean ordered field larger than real numbers. (This was the way calculus originally developed in India as explained in my articles for the Springer encyclopedia.)
Demanding the use of formal real numbers for calculus forces time to be like a line, on grounds of authority, not physics. A brief and popular-level account of the complex issue of how this relates to religious beliefs is in the video of my Berlin lecture on “Decolonising Time: time at the interface of science and religion”.
The Atiyah case

As another example, Crowe suggests that it is incredible that Michael Atiyah regarded as the world's leading mathematician, tried to grab credit for my analysis of Einstein's mistake. I take up this example to demonstrate the unreliability of Western authority at the highest level.
The math may be beyond Crowe, but he ignores even the simple evidence. First, three experts of the Society for Scientific Values found a valid case was made out against Atiyah, and this is posted online. (Click the above link, and scroll down to case number 3 of 2007.) This has been cited as a stock case of plagiarism.
Of course it is a fact that my book Time: Towards a Consistent Theory (Kluwer, now Springer, 1994) advocated functional differential equations (FDEs) in physics. It also pointed out a mathematical mistake related to FDEs made by Einstein and many others. (The mistake was to replace FDEs by ordinary differential equations (ODEs), which are qualitatively different.) My book pointed out that even retarded FDEs already lead to a paradigm shift in physics.
By a curious “coincidence”, Atiyah in his 2005 Einstein centenary lecture also advocated the use of retarded FDEs. By a further “coincidence”, he too called it a paradigm shift in physics. He did not cite my work, but instead ended his lecture by saying “Don't forget that I suggested it”. He did not speak explicitly of Einstein's mistake, but in a side interview to the press Atiyah mentioned the Poincare-Einstein priority issue, and also that Einstein was not a good mathematician and “he needed help” (from Marcel Grossmann) to formulate the general theory of relativity.
It is a fact that Atiyah was later compelled to acknowledge the similarity with my earlier published work in this 2007 letter published in the Notices of the American Mathematical Society. But this was AFTER the publication of the 2006 article, reporting his 2005 speech and giving him credit for the theory. Claiming credit by not acknowledging prior published work is recognized as an ethical violation in the published ethics of the AMS.
Further, Atiyah's pretence that this was an innocent oversight is false. Contrary to that, Atiyah was personally informed of my work through emails including this one, of 26 Oct 2005 (which he acknowledged), long before he got his lecture published in a 2006 article in the Notices of the AMS. This was done through two American authors who explicitly acknowledge that they consulted Atiyah, as is natural. But, the 2006 article again failed to cite me. It again repeated Atiyah's claim “Don't forget that I suggested it”. Indeed, it went further, and tried to cement Atiyah's priority by naming the thesis as “Atiyah's hypothesis”, all with Atiyah's concurrence. Some innocent mistake this! Because my study of history had made me well aware of the dirty tricks of Western authorities, I threw a spanner into the works which derailed Atiyah's game plan.
There are many more details, but let Crowe first engage with the above facts. So far, like Laurie, Crowe simply follows the stock racist methodology: to dismiss everything contrary to his faith, though he is completely unable to engage with a single relevant argument or piece of evidence!
Ellis and Murugan
Both Crowe and the GroundUp article bolster their attack against me by citing the opinions of Jeff Murugan and George Ellis of the UCT math department.
First, Murugan lies that my calculus course offers no advantage. As just one example, my calculus course teaches elliptic integrals and elliptic functions left out of standard undergraduate calculus courses. As explained in “Time: what is it that it can be measured?” (cited earlier) elliptic integrals are needed to properly perform the first serious science experiment in schools: the simple pendulum.
Second, both Ellis and Murugan hide their conflicting interests: I have a long-standing critique of the book Ellis jointly authored with Stephen Hawking, on singularity theory. (My UCT summary referred to this as “Hawking singularities” because I have long regarded Ellis as a mere sidekick of Stephen Hawking, but obviously he is important in the UCT context.) Murugan is a student of Ellis.
Two key grounds for my critique of Hawking and Ellis are the following. First, singularity theory has been used to push post-Nicene church dogmas into science. My public critique of the similarities between Hawking and Ellis and Augustine—their postulates and creationist conclusions—is standing since my book Eleven Pictures of Time (Sage, 2003). In UCT, I specifically pointed to the claim that singularity theory claims to prove “Judeo Christian theology is part of physics”. This is a clear attempt to spread superstitions through abuse of mathematical authority. Why didn't Ellis or Murugan come to my talk and reject or defend this devastating claim against Ellis? Why do they want to hide that critique? Obviously they find it easier to make unsupported claims against the critic in newspapers.
Third, as stated in my summary for the UCT panel, I was willing to discuss the formidable technical details in the math department based on this paper (see citation at no. 17) and how my earlier use of non-standard analysis, applied to Schwartz distributions, can be replaced simply by non-Archimedean arithmetic.
I also briefly explain how the apparent breakdown of the differential equations of physics at a singularity is due to the limitations of university calculus, and can be easily avoided, even within general relativity, by reverting to the philosophy with which calculus originally developed. This, is technical, and would be taken up in more detail in my lecture on decolonising math.
That is I critique both the politics and formal math involved in singularity theory; this threatened to expose Ellis' lifework to ridicule. Hence, he desperately did not want me to lecture in the math department. Instead of confronting me at an academic level, he and his student Murugan avoided the critique and chose to plant tales against me in newspapers, which will not permit me to respond. Note how they stick to such sheltered positions: Crowe laughably speaks of Murugan's “devastating critique” which is kept secret.
My devastating critique of Hawking and Ellis is public for some two decades.
Other issues
Crow (sic) quotes me again without naming a source.
“Since bad history and philosophy of science [e.g. my historical summary above] was violently distorted by the religious fanaticism which overwhelmed Europe from the 11th to 17th Centuries, it is necessary to dismantle and expose the falsehoods of this Western history of science and its accompanying philosophy of science.”
The broad quote seems genuine, but the word “bad” is obviously a typo. This issue is explained in my booklet Is Science Western in Origin? To quote from the back cover.
during the Crusades, scientific knowledge from across the world, in captured Arabic books, was given a theologically-correct origin by claiming it was all transmitted from the Greeks....Second, during the Inquisition, world scientific knowledge was again assigned a theologically-correct origin by claiming it was not transmitted from others, but was “independently rediscovered” by Europeans. The cases of Copernicus and Newton (calculus) illustrate this process of “revolution by rediscovery”. Third, the appropriated knowledge was reinterpreted and aligned to post-Crusade theology. Colonial and racist historians exploited this, arguing that the (theologically) “correct” version of scientific knowledge (geometry, calculus, etc.) existed only in Europe.
Then there is the idea that colonial education was introduced with the specific purpose of curbing revolts and uprisings. As explained in this article on Education and counter-revolution, this thesis was argued by Macaulay (a name as detested in India as Rhodes is in South Africa) in a speech in British Parliament. He was referring to the revolts then going on in Europe, as also stated by Marx a few months later. Further, the fact is that the British were easily overthrown in India in 1857 and the first Western universities (Mumbai, Kolkata, Chennai) were immediately afterwards introduced in India. Crowe's ignorance is vast, whether about colonialism or math or science, and his laughable method is to conclude that anything he finds surprising is wrong!
Concluding remarks
To conclude, Crowe fails to raise any reasoned and specific objections, and thus requires no specific answers. In accordance with the racist methodology (BLAA) he boasts about the reputation of the math department, and lies about me. He recites myths and cites the opinions of Ellis and his student Murugan, without revealing that I critiqued the life work of Ellis, and exposed it—and that the two are apprehensive of addressing in an academic forum either the relation of singularities with theology or the technicalities involved.
Basically, Crowe is arguing that racist and colonial authority must prevail over evidence: the blacks must be suppressed and subjugated again through academics. The game plan is evident: Crowe is desperate to derail the decolonisation effort, hoping to take it over by bullying. He then plans to implement recolonisation by playing on words to call it decolonisation!
So how should the majority confront it? First don't fall for the old colonial con-trick again, and watch out also for the compradors. Watch the actions not the words: demand evidence, and specific arguments. Did anyone raise any substantive point against me? Or contest any single piece of evidence or arguments I raised? Which were the specific sentences they contest? If not their claim of “engagement” is false. Discard it. And, if they are unable to engage, why do they demand that students should engage?
Second, students and the wider public should remember that the salary of the faculty at UCT comes from THEIR fees, and PUBLIC money. So, the faculty must be held PUBLICLY accountable. The local community must demand to know what benefits it gets in return for the money it invests. If any “expert” refuses to explain, and thinks he or she is responsible only to the formal math community, then let them take a 50% salary cut for non-performance each year. That might be a good way to make fees fall!
That solution may be hard to implement. But a simple interim way to improve teaching AND keep the “experts” publicly accountable is to expose them to the threat of being rendered irrelevant. Allow parallel decolonised courses to run in the University, so students can choose the decolonised courses over the existing course if they so wish. Students must raise the demand for such parallel decolonised courses.
1There are other facts Crowe suppresses. For example, that I was Professor and Head of the Computer Science department at the National University of Journalism in Bhopal, for five years, at a time when it was the largest computer science department in the country (with some 38000 students). He suppresses that it was as a Distinguished Professor of Computer Science that I joined Inmantec. After all, the success of the Indian software industry presupposes good teaching of computer science for which there has been a great demand. Also, my association with Inmantec ended long ago.
2E.g., Josiah Priest, Bible Defence of Slavery...and A Plan of National Colonization Adequate to the Entire Removal of Free Blacks, by Rev. W. S. Brown, Louiseville, Kentucky, William Bush, 1851.
3My detailed response to the GroundUp article, which GroundUp refused to carry appropriately, is put up at http://ckraju.net/papers/Ground-up-ckr-response.pdf,
4This was reiterated in my censored article in the Conversation last year. The censored article was later reproduced in full in the article “Black thoughts matter” in Journal of Black Studies, and the contents explained further in a popular-level article on “Math and censorship”. I had asked for these articles to be circulated prior to the UCT debate.
5Thomas Heath, A History of Greek Mathematics, Dover, New York, 1981, p. 360.
6The late Martin Bernal (personal communication) agreed that Uclides was just another translation howler, but favoured deriving it from aqli + des (rational geometry) rather than Ucli + des (key to geometry).
7B. Russell, “Mathematics and the metaphysicians”, chp. 5 in: Mysticism and logic and other essays, Longman Green and Co., London, 1919.
8For an expository account, see C. K. Raju, “Time: what is it that it can be measured?” Science & Education, 15(6) (2006) pp. 537–551. Draft available from http://ckraju.net/papers/ckr_pendu_1_paper.pdf.
9C. K. Raju, “Retarded gravitation theory” in: Waldyr Rodrigues Jr, Richard Kerner, Gentil O. Pires, and Carlos Pinheiro (ed.), Sixth International School on Field Theory and Gravitation, American Institute of Physics, New York, 2012, pp. 260-276. http://ckraju.net/papers/retarded_gravitation_theory-rio.pdf.

19-11-17
From: Raju ckraju@sgtuniversity.ac.in
To: Timothy Crowe;Chris MitchellLoretta Feris;VC;Daya Reddy;Elelwani Ramugondo;Maano Ramutsindela;SRC President;Harry Garuba;Henri Laurie <henri.laurie@gmail.com>;Kasturi Behari-Leak;Goitsione Mokou;Dean of Science;c_k_raju@hotmail.com

A correct description would be that the closet-racists in UCT are too frightened to allow a real public debate, and will try to stop it at any cost. Too many insecure colonial myths about math, like Euclid, which are likely to be shot down in a pubic debate.
I am sending this from a new email address (and to fewer people), since I understand that the old address might have been blocked (another way to stop debate, like the censorship of my article last year).
In my reply I have clearly stated that decolonisation is about a critical rejection of colonial myths. By calling this "destructive decolonisation" you have given away that you want black students to uncritically accept your false myths, so that you can continue to exercise colonial "soft" power over them.
Critical rejection means you must debate publicly, not keep appealing to the authority of the likes of Ellis who apparently endorses that "Judeo Christian theology is part of physics".
To reiterate, the issue is debate, NOT the endorsements of those whom decolonisation rejects---namely, formal mathematicians. A conversation did take place, but there was no serious debate. Those opposed to decolonisation have totally lost that public debate.
Examine the videos and all your emails and those of Henri Laurie. Is there a single salient point of mine anyone could argue against? They could not, they just ran away from debate, like Ellis and Murugan. 
For simplicity, let us  focus on  just one group of myths related to the teaching of math.  The first question is whether formal math, as currently taught, is valid. Contrary to the usual myths, I assert the following.
(1a) There was no Euclid. The Elements was written in the +4th c. CE.  The author of the Elements was a black woman. 
(1b) There are NO formal proofs in the Elements. It is a book in the religious tradition of (Egyptian mystery) mathematics explained in Plato, as reiterated by Proclus.
(1c) Formal proof divorced from the empirical does NOT lead to valid knowledge; it can be used to prove any proposition whatsoever from appropriate premises.
Did you or anyone else in UCT produce an iota of evidence or arguments against those statements? Just examine all the videos and also all the  emails sent so far. I repeat, there is not one cogent argument or a single piece of evidence.  All that has been said so far is against the critic not the critique.
The whole world is laughing at the closet racists of UCT who only understand medieval witch hunting tactics and the mob fascist tactics of the KKK (which came up in the US, after the supporters of slavery lost power). 
I well anticipated those tactics, even in my articles from 2012, and am not afraid of them.  There has been enough display of these tactics to totally expose the closet-racists of UCT.
One last point from your next mail which I have just glanced at: you speak of defamation. Indeed, there has been a defamation campaign against me in a certain section of the South African press, sympathetic to the KKK types. For example, calling me a "conspiracy theorist" without being able even to state what is the conspiracy theory I am accused of! This defamation was done just because the UCT faculty opposed to decolonisation had nothing better to say. Add to this all the mob fascist tactics of those charlatans who jumped in to call an extremely honest man a charlatan.
However, nailing a lie (as I did with you) is NOT defamation. So, I have not engaged in defamation, either against you or against any one else.  And, I did not notice that you were able to contest what I said, merely appealed to authority! 
Best, over and out.

25-11-17
From: Crowe
To: Raju  Loretta Feris; Daya Reddy; VC; Judith Du Toit; Dean of Science; Elelwani Ramugondo; Peter Dunsby; Chris Mitchell; Gerda Kruger; Sipho Pityana; Kasturi Behari-Leak; Goitsione Mokou; Kenneth Hughes; Henri Laurie; Ed Rybicki; David Benatar; Andy Buffler; Muthama Muasya; Shadreck Chirikure; simonrakei.sr@gmail.com; Russell Ally; llg@sun.ac.za; Harry Garuba; Maano Ramutsindela; Arthur Ngwenya; SRC President 
With regard to Raju’s “closet-racists” at UCT (whom I call the “Silenced majority”), some are just too frightened by Fallist thugs (like the perennially pardoned/registered Chumani Maxwele) to attempt to engage in public debate.  Others, are emeritus senior scientists or in-house funded younger researchers who fear that the UCT Executive will take away their privileges if they speak up. Others still, are senior professors with enough funds to ‘weather’ the Fallist storm until they reach retirement age.  But, sadly, many buy the Fallists’ false accusations that they are guilty racists, simply because they are ‘white’.  The older ones didn’t do enough to resist Apartheid while institutionally-racist UCT was “colluding” with Verwoerd/Vorster/Botha.  The younger ones, by hook or crook, still bask in pro-‘white-biased bounty from the government, UCT itself and the “white-monopoly” private sector while they humiliate ‘black’ students and deny ‘black’ academics ad hominem promotion.
Tragically, these colour-coded criminals, like Raju, either avoid reading well-documented history [e.g. mine for UCT - Was/Is the University of Cape Town (UCT) an institutionally colonialist/sexist/racist institution?  Parts 1 & 2 on my Blog Site – timguineacrowe.blogspot.co.za] or just change it to suit whatever power-based ”contextual” desire currently prevails.   The ‘truth’ (a dirty word at today’s embattled UCT) is that the old guys and gals resisted Apartheid peacefully, colluded with no one, and developed UCT into a world-class university capable of generating real “critical” thinkers and daring ‘do-ers’ needed to resuscitate South Africa, indeed the continent.  [On the downside, during the 1980s, they did evade educating poorly prepared ‘black’ students, leaving that to the failed/still-failing Academic Support/Development Programmes.]  Under the Saunders/Ramphele ‘hegemonies’, major adaptive institutional and curriculum-related change took place and racist acts were dealt with decisively and severely.  An excellent example of curriculum development is the decolonized, Afrocentric, affirmative-action M.Sc. Programme in Conservation Biology run by the FitzPatrick Institute within the Department of Biological Sciences.
Also during that period, the Faculties of Science, Health Science, Engineering and Commerce introduced and developed transparent and fair policies for ad hominem promotion that are applied equitably today.  That fact was confirmed at a well-attended meeting on 24 June 2017 by Director of the Next Generation Professoriate Programme, eminent educationalist Prof. Robert Morrell.  But, because of objections raised by pro-Fallists (especially members of UCT’s new, racialist, secret society, the Black Academic Caucus), Rob’s conclusions have been kept secret by the UCT Executive.
Raju is right when he states that decolonisation is about “critical rejection”.  But, his and Fallists’ “critical” stems not from rational debate, but from critical race theory that seeks power, regardless of the cost, for the self-identified oppressed rather than academic credibility.  
With regard to Raju’s question: “Is there a single salient point of mine anyone could argue against?”, Henri Laurie and Jeff Murugan did just that extensively, pretty much politely, at his seminar and in subsequent e-mails.  Indeed, all of UCT’s mathematical scientists, including two DVCs, refuse to endorse Raju’s ganita/zeroism alternative as a preferable way to do or teach mathematics.  I am informed by several of them that it has no academic foothold even in India.  Where are Raju’s great ganita-based research publications and who are his intellectual academic ‘offspring’ that might form a School of Ganita Mathematics anywhere on Earth, especially in the Third World? 
What respectable mathematic historians endorse his two most conclusions:
1.       there was no Euclid or Euclideans 300 years BCE and that Hypatia, a black woman, compiled The (‘proof-free’) Elements during the 4th c. CE and was raped and hanged; and
2.       Newton and Leibniz’s development of the calculus is little more than ganita hijacked in India by Jesuits and garnished in Europe with Christian metaphysics.
With regard to Euclid and The Elements, very little is known about the author(s), beyond the widely accepted conclusion (disputed by Raju) that she/he/they lived in Alexandria around 300 BCE.  The Elements is a compilation of theorems probably not developed/discovered by ‘Euclid’.  They were the work of earlier mathematicians (mainly Greeks): e.g. Pythagoras (and his school), Hippocrates of Chios, Theaetetus of Athens, and Eudoxus of Cnidos.  In The Elements, ‘Euclid’ arranged theorems in a logical manner (albeit not with the rigour of modern formal mathematics) so that they follow from simple axioms. The Elements is also credited with devising particularly ingenious proofs of previously discovered theorems: e.g., Theorem 48 in Book 1.
Hypatia, in all non-Raju references, is depicted as ‘white’ and described as the daughter of Theon, a Greek mathematician from whom she learned and developed mathematics.  Her major interests appear to have been in astronomy and Platonic philosophy.  Because she was an influential pagan who challenged the status quo, she was kidnapped by a mob of Christian monks who stripped and tortured her by scraping her skin off with tiles or oyster shells.  Then they dragged her through the streets until she died, ripped off her limbs and burned her.  Raju’s only ‘evidence’ that Hypatia was ‘black’ is that she may have been born in Egypt.
With regard to Newton, Leibniz and calculus, they ‘concocted’ it in parallel using markedly different strategies and notation.  If anyone hijacked it, it was Leibniz who benefitted from examination of Newton’s notes.  To say the least, they disliked and disparaged one another.  Indeed, the history of “Western” science is replete with similar less-than-professional behaviour.  For an excellent example of this, read David Hull’s Science as a Process that chronicles the ‘systematics wars’ that plagued evolutionary biology during the last four decades of the 20th Century.
To answer Raju’s question: “Did you or anyone else in UCT produce an iota of evidence or arguments against those statements? “, follow his advice and “just examine all the videos and also all the emails”.   Better still, go to UCT magnificent libraries and do your own research.  As film character ‘Dirty’ Harry Callaghan says: “Opinions are like assholes; everyone has got one”.
Raju concludes that: “The whole world is laughing at the closet racists, [charlatans, KKK types] of UCT who only understand medieval witch hunting tactics and the mob fascist tactics.”
Just who are “these people” that are the object of Raju’s, pro-Fallist (indeed the “whole world’s”) sniggering and smearing.
George earned his B.Sc. and Honours degrees at UCT and is a senior scholar and emeritus distinguished professor of complex systems in the Department of Mathematics and Applied Mathematics.  Although he has conducted ground-breaking, internationally acclaimed research on gravity and cosmology, he also has explored the essence of complexity and causation, especially how it relates to the brain and human behaviour. One might get some total sense of his work by reading On The Moral Nature of the universe: Cosmology, Theology, and Ethics, which has been translated into Russian and Chinese.

Ellis earned a PhD in Applied Mathematics at the University of Cambridge exploring inhomogeneous and anisotropic cosmologies and singularities and continued and expanded his research along these lines. This culminated in his co-authoring (with Stephen Hawking) The Large Scale Structure of Space-Time in 1973, now regarded (except by Raju) as a classic.
He is a founding member of the Academy of Science of South Africa, participated in the commission that recommended the construction of the Southern African Large Telescope, and served as a member of the task group responsible for drafting SA's Green Paper on Science and Technology.
He has published more than 500 (peer-reviewed – not opinion pieces) articles in the world’s top scientific journals (Nature, Physical Review and the Astrophysical Journal) and authored/co-authored 12 books and many more book chapters.  This led to his serving on the editorial boards of leading journals (Classical and Quantum Gravity and the Monthly Notes of the Royal Astronomical Society) and as editor-in-chief of General Relativity and Gravitation.
Locally, in 1984, Ellis was one of the few researchers awarded an A-rating by the National Research Foundation when it initiated its rating scheme. He is one of a less than handful of researchers that has retained an A-rating since then. 
He is a Fellow and Past President of the Royal Society of South Africa (RSSA), Founder Member and past Member of Council of Academy of Science of South Africa (ASSAf), Fellow of the Third World Academy of Science (TWAS), Past President of the International Society for General Relativity and Gravitation and Fellow of the University of Cape Town.   He earned more medals than were displayed on Idi Amin’s uniform, including the Star of South Africa Medal presented by President Nelson Mandela (1999), the Templeton Prize (presented in 2004 by Prince Philip at Buckingham Palace) and Order of Mapungubwe (Silver) conferred by President Thabo Mbeki (2006).
In recognition of his achievements as a formal mathematician, he was invited to speak at the Turing Centenary Conference in Manchester in June 2012.
His education/developmental publications include:
·         A view on the school maths syllabus. (CASME talk, 1995).
·         The Development of Quantitative Social Indicators. (Notes 2001).
·         South African Developmental Issues. SAIRR (Western Cape), 2001.
·         Science, technology and Humanity (for STIAS New Humanism Project).

Outside of academia, George is chairperson of Quaker Service (Cape), and serves on the board of the Association for Educational Transformation (ASSET). ELRU, Philani, Nalibali, and The Little Hands Trust are other inspiring local organisations (I was on the Boards of ELRU and Philani for many years). I am an avid fan and supporter of the Pro Cantu Youth Choir.

Unlike me and most other UCT ‘Ivory Tower’ academics, at the height of Apartheid he would drive to the townships with his students to the aid of people assaulted by apartheid police officers, and hide black activists in his home to protect them from the police during the state of emergency.  He used a substantial amount of his R10 million Templeton Prize money to establish a scholarship fund to pay for talented young black students who couldn't afford to take up their offered places at UCT.

Jeff Murugan

Also a UCT grad, although he never ‘self-identifies’, associate prof. Jeff is a ‘black’ South African of Indian descent who was able to come to study at UCT because his parents initially ‘invested’ in him beyond their means.  Thereafter, he earned scholarships on academic merit.  More than anyone I know, he understands fully the horrendous effects of Apartheid.

Raju is correct when he ‘brands’ Jeff as one of George’s many prominent academic ‘offspring’.  But, Jeff is not an Ellis ‘clone’.  They have disagreed more about everything from black holes to the neuro-physics of the human brain than they have agreed, and even wrote a book about their arguments.  Although he asked me not to, I’ll quote one statement from his devastating critique of Raju: “From him [Ellis, not Raju] I learnt two things: always be curious and never compromise on your principles.” 
With regard to academic achievements, Jeff is currently, deputy head of department, president of the South African Gravity Society, a founding member of the South African Young Academy of Science, an Associate of the American Museum of Natural History (like me!), Vice-President of the BRICS Association of Gravity and Cosmology and a former member of the Institute for Advanced Study, the single most prestigious institution for theoretical research in the world. He has graduated 4 PhD students at UCT, two of whom are female and two of whom are black.  All have the most significant letters (other than B.Sc. and Ph.D.) after their names: JOB.  They have successfully competed for either faculty positions (University of Surrey, University of Khartoum and the Ecole Normal in Mauritius) or postdoctoral positions (WITS).

In 2020, his research group here at UCT will host the Strings 2020 annual conference, the single most prestigious meeting in his primary field of research.  Raju’s son was one of the organisers for the 2015 meeting held in India.  This is the first time it will be held in Africa, or for that matter the Southern Hemisphere.

Henri Laurie
I’ve known Henri for decades.  He is a coal-face educator who brilliantly taught my daughter mathematics she uses today in her job – salaried far beyond that of a UCT professor.   Henri’s main interest is using mathematics to sharpen debates in plant ecology. To that end, he has worked on pattern analysis, the effect of size distribution, lottery models for Cape fynbos, heuweltjies, projective geometry for human motion and spatial dynamics.  As his e-mails above indicate, he emphasizes the meaning of mathematical statements, and he cultivates enthusiasm for mathematics as a meaningful and therefore useful activity.
With regard to me and my laughable life, have a look at the following pieces (and others) in my Blog Site (timguineacrowe.blogspot.co.za).
My (and my spouse’s) ‘white’ privilege
Races within modern humans are artificial, nefarious, perverse constructs
My history; lived experience; views on race, racialism and racism; and philosophy, ‘white privilege, Fallism, decolonization in a nutshell
T.M. CROWE - CURRICULUM VITAE
I close with questions to Raju and those who spent thousands of UCT’s limited Rands in promoting his ‘efforts’ to decolonize her.
Who’s honest and who’s laughing at whom? 
To Max – is there any hope of you at least admonishing Raju for his latest defamation of the mathematicians?  Or, are they going to join me in being “left behind”?


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