Sunday, 26 November 2017

Decolonizing maths at UCT - Part 2

09-10-17
From: Crowe
To: C. K. Raju <c_k_raju@hotmail.com>;Henri Laurie <henri.laurie@gmail.com>

Dear Prof. Raju and Dr Laurie,

Thank you for your rapid, frank and highly informative comments and response, BOTH now and at the seminar/panel discussion.

Since several Fellows of UCT have indicated that matters relevant to these should be discussed at the upcoming annual Fellows' Dinner on 11 October.

May I assume that all mentioned in these e-mails and Prof. Raju's attached "Response" are in the public domain.

If I hear nothing from you, I will assume that this is the case.


11-10-17
From: Henri Laurie
To: Crowe and several other UCT colleagues

I really do think we need to spell out in simple terms what Raju is saying, why it is in part believable (yes, Euclid the historical person is poorly attested, yes, it is possible, even likely, that results from India were known to and influenced Wallis, Fermat and others in their work on what became calculus) but in large part is nonsense (no, the maths of 17th century Europe is not a mere copy of the Kerala school's work, no, Euclid's elements definitely date from far earlier than Hypatia, and no, ancient and Hellenistic Greek writings are not forgeries made to cover up intellectual theft) and in particular the things that are wrong in his work amount to India- and self-aggrandising mythmaking.
His teaching claims are probably the easiest to demolish, in that not only is his method demonstrably ineffective and his experiments unscientific, but clearly they are ludicrously narrow, so limited that even if they were successful they would not give access to the bulk of modern applications of mathematics. (partial list: cryptology, asymptotic methods, dynamical systems, complexity, networks, artificial intelligence, tensors ... and even linear algebra). On the other hand I find the notion of putting differential equations at the heart of analysis very appealing (not original, of course: the Five Colleges Consortium ran a long experiment doing exactly that, and Postmodern Analysis by Jost is a rigorous and advanced text placing ODEs at the heart of the initial development of the subject), and it irks me that by championing it he probably consigns it to eternal neglect.


10-10-17
From: C. K. Raju
To: Crowe

I have absolutely no difficulty in keeping things public, except that there is a lot of misunderstanding, and misrepresentation. This may be exacerbated by prematurely making a partial discussion widely public.

Therefore, I suggest that you wait till the discussion is complete, and not make an incomplete discussion entirely public. No great harm in waiting. A particular social event (Fellow's Dinner) is of little consequence compared to the long-term suffering of black students. Floating a misrepresentation may do a decided disservice to them. You have to also keep in mind that the math department did not allow me to talk about it publicly on their turf. And, who will correct the misrepresentations in my absence?

While some of the misrepresentation of my work (such as Murugan's) is decidedly mischievous, there may be a lot of genuine confusion as well.

For example, there was this elderly person in the audience during the UCT panel (not sure whether he was from UCT) who was so abysmally out-of-date that he wanted to revert to the terminology of falsifiability which Popper discarded four decades ago. Further, he was confused about the criterion, and imagined that there are “degrees of falsifiability”, like 20% falsifiable, and 30% falsifiable, etc.! If there is confusion about so elementary a notion, imagine what could happen with the other novel things under discussion.

So, please wait before widening the audience.



10-10-17
From: Henri Laurie
To: C. K. Raju; llg@sun.ac.za; NCBYOL001@myuct.ac.za; NGWBLE001@myuct.ac.za; Josh Hayes; Loretta Feris; Sané Erasmus; Timothy Crowe
Subject: Re: Decolonisation programme

Dear Prof Raju

Thank you for your response. I would like to continue with my summary of your suggestions. If I understand you correctly, each of the points in my summary should be extended. This I have tried to do below, mostly guided by your comments.

-------------

0. Accept that mathematics did not arise in Europe and that the contributions attributed to Greek and other mathematicians from Europe (up to approximately 1700 CE) were in fact first done elsewhere and appropriated by Europeans.

1. Reject the metaphysics of the infinite as asserted for example in the construction of real numbers based on ZFC set theory.

2. Reject formalism as a philosophy of mathematics and formal proofs based on two-valued logic.

3. In place of 1. and 2. above, adopt zeroism as expounded in the work of C. K. Raju.

4. Formulate calculus as the solution of ordinary differential equations (as defined within zeroism), teach calculus as the numerical solution to ODEs, situate the origin of this approach in India,  and, if formulae are required to express these solutions, have recourse to computer algebra systems like Mathematica, Maxima and Wolfram Alpha. 

-----------

As you can see, I also disagree with you that only via a completely extended discussion can one understand your suggestions. My view is that each person is to some extent idiosyncratic in how their understanding works. In my case, I need to have an overview of the whole system I am trying to understand. I have always found it hard simply to learn bit by bit without having a sense of the whole that the bits fit into. What I am trying to do here is to construct such an overview of your suggestions.

Do you find my revised summary to be more accurate? How should it be improved?

All the best
Henri

PS --- This is from my point of view off topic, but I think it best to add a general comment. Although we agree on the need for a practical approach to mathematics, we disagree on what that means and in particular we disagree on the role of formal mathematics in the practice of mathematics. As I made clear on the night of your presentation, I believe that formal logic is the basis of computer science, and that without the contributions from logicians including at the very least Frege, Russel and Godel, the foundational work of Turing and von Neumann would not have been possible, and without their work computers would have developed very differently and in my opinion much more slowly. I further believe that formal logic remains essential to the practice of computer science. Indeed, I think formal techniques are of great value in many of the applications of mathematics.


11-10-17
Article in Daily Maverick
Surely good scholarship means having our perspectives challenged?
  • Adam Cooper
If universities of the future are to be relevant and contribute to building an inclusive, just society, one that nurtures reflection and deep learning, they should be places where we are intrigued by opinions that differ from our own. Such perspectives may challenge the status quo and our assumptions about the world we live in.
Last year during a lunch break at a conference at Unisa, a tall, lean Indian man with wispy grey hair asked if he could sit next to me. I was eating alone and felt a bit awkward, so I said that he was welcome to join me, relieved to have a companion and avoid appearing to be the conference attendee with no friends. The scholar told me that he had designed the first Indian super computer, but that he was now more interested in the history of mathematics. He spoke eloquently and complained about all of this nonsense in South Africa about science and mathematics being “white man’s knowledge”, that all peoples have practised science of some sort since antiquity and that he was determined to set the record straight.
He explained that while the West usually draws a straight line connecting the Greeks and Romans to the enlightenment and then proceeds to link this genealogy to modern-day European and North American scientists, many Indian, Arab and African scholars have contributed to the reservoir of global scientific knowledge that we now inherit.
In ancient India, he continued, where people used pieces of string instead of geometry sets, mathematicians were more concerned with the use of science for the benefit of community needs than generating abstract proofs. So if a solution was incorrect by the time you arrived at the fiftieth decimal point, something that would render it simply “wrong” in the modern academy, this would not matter for community based science because the difference would not be able to be seen by the naked eye.
He told me that in modern mathematics one cannot use an empirical example in order to prove a theorem. You have to prove theories through abstract languages or sets of symbols. This astounded me. I had always thought of mathematics as that most scientific of scientific subjects and yet in certain instances the scientific method could not be used as the basis for knowledge generation. Rather than saying that this practice was “wrong” or not good for science, he was interested in learning about how these rules of the game were established.
I thought further of my time at school, spending hours memorising proofs of theorems that had no meaning to me and which taught me nothing other than the fact that to do well at school you had to commit to memory large bodies of information that leave your brain the minute you exit the examination room.
The Indian scholar from whom I learnt a great deal during that lunch break is called CK Raju.
This week a storm broke loose because Professor Loretta Ferris Deputy Vice-Chancellor for transformation at UCT invited Dr Raju to address the university community. People, many of whom complain that students shut down debate and behave barbarically by burning paintings, demanded that this man not be given a platform to speak, that he be silenced and denied the opportunity to share his ideas. They then questioned the credentials of the black female deputy vice-chancellor who invited him, sending her a barrage of abusive emails. 
In all the controversy I did not read a single critique of Dr Raju’s work, his ideas or his scholarship. I don’t think most of his critics even realise that he is primarily a historian of mathematics, rather than a mathematician. All I read was mud-slinging and name calling by the very people that hypocritically proclaim that South African students scream and shout rather than develop good arguments. I observed these sentiments from former vice-chancellors and Nobel prize winners alike.
We do not have to believe everything we are told. Neither are we forced to like everything to which we are exposed. But if universities of the future are to be relevant and contribute to building an inclusive, just society, one that nurtures reflection and deep learning, they should be places where we are intrigued by opinions that differ from our own. Such perspectives may challenge the status quo and our assumptions about the world we live in.
Rather than feeling threatened and defensive about these opinions, we should engage with them in the spirit of dialogue. Is that not what constitutes good scholarship? To have our perspectives challenged by different ones? I am not a mathematician, but my discussion with Dr Raju made me want to learn more about mathematics, the philosophy behind it and the difference between culturally specific traditions and rigorous science. Our would-be-educators who spent a portion of last week castigating Dr Raju would be better off working on their own curricula and pedagogical techniques, such that they may begin to interest South African students. It is remarkable, considering the events that have taken place in this country since 2015, that these learned people have yet to realise that their futures depend on this. DM
Dr Adam Cooper is post-doctoral fellow and research specialist in the Human and Social Development programme at the Human Sciences Research Council. He holds a PhD in Education Policy Studies from Stellenbosch University and is a fellow of the Centre for Commonwealth Education at the University of Cambridge.


11-10-17
From: Henri Laurie
To: Crowe
                        
Of course, you may quote my emails to Raju. I am doing my best to stay polite to him and not get drawn into directly contested claims, time will tell whether I succeed.
I see he has responded dismissively and continues his attack on Jeff [Murrogan]. He also doesn't seem to realise that he is insulting you directly as well!






12-10-17
From: Henri Laurie
To: Raju

It is of course possible that I misunderstand your position, but on present evidence I don't think so. From what you say, my point 0 is accurate: you do claim that what you term Western mathematics contributed nothing original to the early history of mathematics; you merely want my point to include your low opinion of their understanding of what they imported. From what you say, my point 2 should be reformulated as saying "Reject the supposed infallibility of formal logic and the false primacy of formal reasoning over empirical evidence", thank you for the improvement.
Although it is likewise possible that my thinking is clouded, it is not clouded by the myths to which you refer, because you are simply in error about those.

1. It is not the case that the likes of Fermat and Newton simply copied Indian texts---the much weaker claim that they had access to some of the results of Indian texts is indeed likely, but the historiography for establishing exactly what they knew about, say, Madhava, remains to be done (I reject your claim that you have already established this). As any reading of their work will reveal, the mathematicians of Italy in the 14th and 15th century had their own set of problems they were grappling with, and their own approach (although indeed in part originating from imperfectly known work done elsewhere). They established many results that occur nowhere in any earlier mathematical tradition. This work led directly to Galileo and the controversies around infinities and infinitesimals, which far from what you claim, the Catholic church attempted to suppress. In fact, the Jesuits were the most active of all in this suppression, specifically because they felt it introduced into mathematics techniques of proof that fell short of the Euclidean standard. Indeed, the teaching of concepts that resemble modern infinitesimals had disappeared from Italy by the middle of the 17th century, although it had originated there. Your account of the "myth" of the work on calculus is entirely incorrect. You are furthermore clearly in error about Euclid: it is true that the historical person is poorly attested, but the books and the name were well known and occur in many places. Also, the historiography about works of others such as Eudoxus that made their way into Euclid's Elements is well established. Finally, important later works, such those of Diophantus and Appolonius would surely have appeared in a compendium such as the Elements if it was as late as you have claimed. Indeed, Appolonius is clearly later than Euclid yet still BCE. In order to discredit the achievements of Greek mathematics, you would have to discredit the entire corpus of ancient writings in Greek, and with it the works of Byzantine and Muslim scholars. That is clearly not a tenable position.
2. Your account of the "myth" of the philosophy of mathematics is likewise completely wrong. It is simply not the case that any mathematician now refers to Russell and Whitehead's Principia as the source of proofs about integers or looks to it for adding value to arithmetic; the Principia is indeed valued, but for quite other reasons. More than that, after the "philosophy wars" of 1920s and 1930s in mathematics, the community of mathematicians as a body turned away from philosophical argument and simply got on with doing such mathematics as they were able to communicate. The philosophy of mathematics is alive as a branch of philosophy, but it is dead as a part of mathematics. Our undergraduate students are not in any sense taught any of the philosophies of formalism, intuitionism, constructivism or whatever. They are not taught a "metaphysics of the infinite", they are taught mathematical systems, some of which use the concept of infinite sets. Contrary to what you say, there is no mathematical problem with this at all.
3. I agree with you that much of what you call "normal" maths does not directly call on what you call "formal" maths. But this is like saying that a carpenter using a measuring tape does not refer to the bureau of standards. Contrary to any "myth" you claim, nobody conflates bridge building and category theory. We understand that mathematics, worldwide, is a whole: there is no clear dividing line between "pure" and "applied", nor is there such a thing as mathematical concepts that are "Indian" or "Western". There is just mathematics. On the other hand, many extremely useful formulae and concepts did indeed first arise in formal/pure mathematics. This is actually very well established and I am astounded that you seem to claim otherwise. It is no "myth".
Let us now turn to the teaching of calculus. Yes, I believe it is essential for a full understanding of calculus to have a good understanding of real numbers and limits. At UCT however we do not start with an axiomatic construction of real numbers, nor do we do formal delta-epsilon proofs in first year. Moreover, we do emphasise that calculus is much more than a formal system relating some expressions to others: we emphasise that functions establish meaningful relations between variables, and we insist on interpretations the concepts of calculus in terms of rates of change, areas, cumulative change and so on. It is true that differential equations are neglected in first year (I would prefer they weren't) but on the other hand there is only so much one can fit in. Part of what we fit in is a bit of complex arithmetic. I wonder how one teaches complex numbers purely in terms of the practical value of the concept, as opposed to teaching the formalism? A great virtue of formalising mathematics is that it can then be compressed into much shorter accounts, and sometimes (as with complex numbers) be easier to teach.
I feel that there is some value in your work and suggestions, but that you make extreme claims for it on a flimsy basis. I am now thinking that you say so many things that are clearly wrong, and you make so many grandiose claims that turn out to contain only a little bit of truth and a lot of speculation, that in the long run you may actually do the cause of decolonisation more harm than good.
I offer these rejoinders not because I wish to belittle you in any way, but because I think they are true.

12-10-17
From: Raju
To: Henri Laurie

Dear Dr Laurie,

Your expanded summary is a caricature.

For example, I don't just reject the historical claims about Western achievements, I assert that the West did not UNDERSTAND the math it imported. For example, it took CENTURIES for Europeans to understand even the elementary arithmetic algorithms taught in primary school today, which were imported in Europe from the 10th c. I teach that European confusion over imported math is reflected in the very terms, such as zero, surd, sine, trigonometry. The confusion peaked with the infinite series of the imported calculus. Eventually, the West developed a bad philosophy of math which I reject. Hence, the title of my censored article included both history AND philosophy.

Again, for example, contrary to your caricature, I do NOT reject 2-valued logic; I accept inference based on 2-valued logic as a valid practical APPROXIMATION in many situations, provided it is based on empirically valid hypotheses (absent from formal math). What I reject are the inflated claims about “reason” (based on 2-valued logic) arising from the post-Crusade Christian theology of reason (that logic binds God, or that deductive proofs based on 2-valued logic are infallible or less fallible than empirical proofs, etc.)

Your caricature shows you are unable to understand my position. This is because formal mathematicians accept three categories of myths without proof.

1.    Myths about history of math (Greeks like Euclid, Archimedes etc.), then Newton, etc.
2.    Myths about the philosophy of math (that mathematical proof has some value, for example that the ugly 378 page proof of 1+1=2 in the Principia adds to the practical [or epistemic or aesthetic] value of 1+1=2 in some way).
3.    Myths about the achievements of math: the achievements of normal math, such as bridge building, are uncritically conflated with the achievements of formal math, to argue against me, though I advocate normal math against formal math.
Your thinking is clouded by the constant appeal to these myths: for example, your claim that computer technology is an achievement of formal math. If so, why do computers use floating point numbers and not real numbers? Floating point numbers do not constitute ANY algebraic structure (semi-group, group, ring, integral domain, field) as taught in formal math courses, since even the associative law for addition fails. You mistake the formal theory of Turing machines with real-life computers.

Your difficulty in understanding my position is on account of these myths. Hence, they must first be destroyed: destruction must precede fresh creation.

Accordingly, we should start the discussion at the other end: by examining the existing body of formal math, and the way things are currently taught. This will expose the above myths. Only after that will you be able to understand my point of view.

So, let us start with a central issue: the way calculus is today taught using real numbers and limits. Since I trained as a formal mathematician, I taught this for years, asserting that real numbers and limits were needed for “rigor”. I have now abandoned that belief as mere myth.

But, according to you, are real numbers and limits essential for teaching and doing calculus?


16-10-17
From: Raju
To: Henri Laurie

Dear Dr  Laurie,

It seems you are hurt by my statement that your mind is clouded with myths. However, just examine your emails: at a rough estimate you may have told around a 100 stories. But you provide ZERO EVIDENCE. Stories without evidence are called myths, especially if they have been around for long. A web of interwoven myths is one in which one myth supports another, but the whole has no evidence. This is a common propagandist strategy to cloud the mind. This is what I meant by saying your mind is clouded with myths. All Western history of science is in the dock. So just repeating its stories is NOT a valid defence.

So, please desist from repeating your myths (Diophantus, Eudoxus, Apollonius, etc.) If you have any PRIMARY EVIDENCE for ANY story you want to tell, first produce that evidence or refer to the primary source, and we will then discuss the story after looking at the evidence. I repeat, please don't take for granted even a single story about “Greek achievements”: produce the evidence or desist from repeating your myths. And start from the actual PHYSICAL evidence not a mere story about the evidence, to avoid the trick of using one myth to support another.

Please also note that late Byzantine Greek texts, from a thousand years after the fact, are NOT reliable primary evidence, for any claim attributed to early Greeks. This is commonsense, but I have advanced several reasons. For example, scientific texts are accretive. Thus a 16th c. text attributed to Archimedes is evidence only of 16th c. knowledge, not evidence for the claim that Archimedes wrote on the Sphere and the Cylinder. Likewise, a 12th c. text attributed to Claudius Ptolemy is evidence only of 12th c. knowledge, e.g. as in the case of the current pole star heading the list of stars in the Almagest. The belief that no intermediate person added anything to a scientific text in a thousand years is a wild claim based on the racist denial of creativity to others. It is also contrary to commonsense. In those days, copying a text involved huge expense. so, it was done for utility, not posterity, hence any scientific text would be updated with current knowledge, exactly as we do today.

There are many further arguments: but, in brief, produce evidence from the purported times. An example of such evidence is what Diop correctly noted: the Rhind papyrus and Moscow papyrus provide PRIMARY evidence that Egyptians knew about the sphere and the cylinder 1300 years before the purported date of Archimedes. I will only engage with such serious evidence, not your wild guesswork based on a bunch of myths.

But, perhaps I am mistaken. It seems your calculated strategy is to avoid engaging with the evidence. For example, during the panel you flipped through my 500 page book, in about 5 seconds, and summarily dismissed my evidence and arguments. No serious scholar would do that. Do you teach your students in UCT to flip through their math texts the same way? You did that because summary dismissal is easy, engaging with the mass of evidence and details is hard; everyone understands that.

Likewise, in your recent email you summarily assert that my views on Euclid are in error. But you have not produced an iota of (primary) evidence, or claimed my challenge prize, only given “arguments” from myth.

See, also, the admission by David Fowler, the leading Western expert on Greek mathematics, 15 years ago, in response to my statements about Euclid. He honestly admitted that NOTHING is known about “Euclid” and that our first actual manuscript of the Elements is from the late 9th century: http://mathforum.org/kb/message.jspa?messageID=1175733&tstart=0. All else is speculation.

The fact is that book Elements was later used by the church which misinterpreted it and used it as a text to teach “reason” in support of its post-Crusade rational theology. (The Bible says nothing about reason; the word occurs less than a 100 times.) Since the book Elements became a key church instrument, it is surrounded by all sorts of false myths. E.g. the myth is that the book Elements (of Geometry) is about deductive proofs, but the fact is that the book has not a single pure deductive proofs of any proposition. So, let us stick to actual facts. The Elements is NOT a book about deductive proofs.

Of course, any myth can be made compatible with any facts by piling on the hypotheses. So, to "save the story" the West piled on the hypothesis that the the mythical Euclid erred in executing his intentions and wrote a wrong book! How absurd! For, how do you know the intentions of a mythical person and say that he actually wanted to write a different book? But it is on that ridiculous assertion that the book was rewritten (as a book on synthetic geometry!) by Hilbert. That was the farcical beginning of formal math.

Anyway, you do not engage with anything I have said, for example that the evidence points to the real author of the Elements as a black woman. Or that it is a actually a religious book in the tradition of Egyptian mystery geometry described by Plato. That is, apart from “argument from myth”, your other argument is an “argument from dismissive adjectives”. Anyone who knows English can apply adjectives, but hard work is needed to engage with hard evidence! Do you really think people are so blind they don't see what is happening?

Thirdly, it is by now quite clear that your summary is intended to caricature: set up a straw man whom you can then easily dismiss without getting into details. Thus, on the strength of your summary point 1, you assert “It is not the case that the likes of Fermat and Newton simply copied Indian texts”. The false insinuation is that that is my claim. Now please scroll down to my earlier email, which makes no such general claim, but refers SPECIFICALLY to Fermat's challenge problem to European mathematicians. Unlike you, I have also provided a reference to my article published in the Springer encyclopedia. Please download it, and search for “Fermat”. You will see that my specific assertion is the following.

“Thus, in Feb 1657, Fermat (Ouvres, p. 332 et seq.) asked European
mathematicians to solve the problem Nx2+1 = y2 for a given (positive, non-
square) N. As examples, he listed, for the case N = 3, that x = 1; y = 2
are solutions, and x = 4; y = 7 are also solutions. Then he asked for the
smallest integer solutions for the case N = 61, and N = 109. This is today
called “Pell's equation", and the smallest solutions are the numbers x =
226153980; y = 1766319049 given by Bhaskara II centuries earlier. Given
how large these numbers are, an independent rediscovery would represent a
fantastic coincidence.”

You stick to your easy caricature because you are unable to tackle such specific statements: these large numbers could not have been “independently rediscovered”. Why not admit it honestly? In fact, this is just one proof that Indian mathematical texts were available to Western mathematicians: the West stole knowledge before it stole wealth, and is now trying to hide the theft. Among the Indian texts in question was the Kriyakramakari, a commentary on a work of Bhaskara II, which also has (in the chapter on the circle) Madhava's value of ?, and the infinite “Leibniz” series for the circumference, etc. This was one of the texts prevalent in the vicinity of Cochin where the Jesuits had set up a college by 1550, and were mass-translating Indian texts. They were motivated to steal precise sine values because precise sine were badly needed for navigation (determination of latitude, longitude, and loxodromes) the chief scientific challenge then facing Europe. 

Your claim that Jesuits avoided this is laughable. The top Jesuit, Christoph Clavius published a whole book on an interpolated version of Madhav's sine table to 10 decimal place precision in 1608. (Flip through my book more carefully for the detailed primary reference.) Are you denying the existence of that book? Or asserting it is yet another “independent rediscovery” eh? A long chain of fantastic coincidences? My epistemic test destroys even that defence. Clavius was so ignorant of trigonometry that he could not correctly determine the radius of the earth, which students of my decolonised courses do. (That Clavius did not understand the knowledge he claimed as his own is proof that he copied, on my epistemic test. This test applies also to students who cheat in an exam and copy from others; if they don't understand or are unable to explain what they have written, that is proof they copied.)

And from where did Clavius get the correct figure for the duration of the tropical year? It was not native to Europe, for the Julian calendar had been wrong for 1600 years by then. The figure was wrong just because Greeks and Romans were arithmetically so challenged they did not understand general fractions. Even Clavius' Gregorian reform of 1582 states the duration of the tropical year not in terms of fractions but using a roundabout system of leap years. That method is inferior to stating a precise fraction, for it only gets the tropical year right on a thousand-year average, so equinox does not come on the same day on the calendar. (It also causes confusion as in whether the year 2000 was a leap year.) There were no native observations in Europe regarding the tropical year. Hence, Protestants rejected the reform until 1752, long after Newton's death, despite the great economic significance of an accurate calendar for navigation and determining latitude in daytime. (For details of how that is done, see my 9th standard school text.)

There are numerous other such cases of copying, apart from Fermat and Leibniz and Newton: Tycho Brahe (Royal Astronomer to the Holy Roman Empire) produced a “Tychonic” model which is a carbon copy of Nilkantha's astronomical model! And Clavius' contemporary and rival, Julius Scaliger, started bJulian day numbers, a copy of the Indian ahargana system. Each such case is evidence that Europeans in the 16th c. had access to Indian mathematical and astronomical texts.

Since you persistently avoid engaging with such specifics, it is taken that you have admitted them, as is the legal practice.

You may continue to wait for a Western historians to “fix” the “storio-graphy” by stuffing it with the usual Western lies about history! But decolonisation will proceed irrespective of Western approval. We will tell our own stories. Stop us if you can. Unlike the West we are concerned with truth, and dismantling the colonial power that flows from false history. So, you are welcome to contest the evidence (if you can), but your mere dismissive opinions are utterly inconsequential. Keep them to yourself, for the concern is with public knowledge not your private beliefs.

To reiterate, your summary caricature is just an easy way to to hide your inability to engage with a whole lot of specific but “inconvenient” evidence.

Apart from your argument from (1) myth, (2) adjectives, and (3) caricature, you argue from (4) abuse. This is the stock method used by Western “scholars” when in trouble. It seems beyond their understanding that abuse loses the argument. Grandiosity lies in the false Western claims glorifying the West that, e.g., there was a Euclid who did something very special which everyone else should imitate. There is no grandiosity in demanding evidence for Euclid, or in rejecting the false claim that the book Elements has any special proofs. You abuse to cover-up for lack of evidence, and sidetrack the issues. The abuse is a symptom of academic bankruptcy, as in the reactions of some of your colleagues in the Daily Muck.

Your claim that you genuinely believe your stated opinion is equally a worthless claim: doubtless many of your colleagues genuinely believed in apartheid and the inferiority of blacks. Probably some still do. Does that make their beliefs true? No. It just exposes the rot in the apartheid brain. That rot stems from false racist history. So, the only cure is to destroy that false history so that the brains of future generations are not similarly infected by that rot.

To reiterate, all these arguments of yours are an admission of failure.

So, let us move on from history to something you perhaps understand: formal math, and how calculus is taught today.

I asked you what value, if any, did the 378 page proof in Principia add to 1+1=2. You evaded the question by saying that the Principia proof is not taught. I take it, you are admitting it is not taught because its proof of 1+1=2 has no value, else you would have explained what value it has instead of beating about the bush.

So, what kind of formal proof of 1+1=2 would you give from first principles? (Don't assume naive set theory etc; if you use set theory, develop it formally, all from first principles, write out formal proofs in full, and count all the pages needed for that.) And please do explain, if you can, what value does any such formal proof add to 1+1=2? And if they have no value, why teach prolix formal math for something which can be easily understood in another way?

Indeed, formal math only obfuscates normal math, does not add to its value. Its claim to "understanding" is bogus. Just another story. 

Thus, the common calculus syllabus is well known. You admit you teach THAT real numbers and limits are required but do not teach even the definitions of real numbers or limits. Naturally students are left confused. Nor do you teach the philosophy why real numbers and limits are required. What a wonderful way to teach "real understanding"! This is exactly as I claim: in the name of teaching "real understanding" what you actually teach them is blind imitation and ritual symbolic manipulation, of little practical value. You are not imparting knowledge, but indoctrinating them. The aim is to create obedient mental slaves who do not understand what they learnt. Will they be able to pass my pre-test question paper even after doing your calculus course? I doubt it very much, but am willing to experiment. Your math department is the one disallowing pedagogical experiments which I have done elsewhere, and which demonstrate that your teaching is detrimental to students.

And why do you hide from students other possibilities such as using non-Archimedean arithmetic, which I recommend? Some of your colleagues seem desperate even to stop a public discussion of the same. This happens only when you know that what you do cannot withstand public scrutiny. 

Calculus with real numbers fails in many common situations. According to it, a differentiable function must be continuous. So, what do you do with the differential equations of (classical) physics (including general relativity) when discontinuities arise, in practice, and limits fail to exist, as in shock waves or singularities. Turn to creationism like your colleague Ellis? Is that the real reason you teach ignorance: to be able to spread superstitions on the strength of authority?

16-10-17
From: Henri Laurie <henri.laurie@gmail.com>
To: C. K. Raju
Cc: llg@sun.ac.za; NCBYOL001@myuct.ac.za; NGWBLE001@myuct.ac.za; Josh Hayes; Loretta Feris; Sané Erasmus; Timothy Crowe; Elelwani Ramugondo; Daya Reddy
Subject: Re: Decolonisation programme
Dear Prof Raju
My primary objective with these emails is to form a clear impression of what you actually claim and propose, to bring clarity (for me) to a mass of detail. That is why I keep returning to a simple outline of your claims. For me, it is important to summarise what you claim before going into details. I do that at the end of this email. Before that, I respond at far too great a length to some of your points.
I stand by my rejection of your allegation that what we call Greek mathematics is a fraud and that the work was done much later than the usual attributions. I agree, as I have said more than once, that the historical person Euclid is poorly attested. This is trite and can be found in any proper history of mathematics. The prize you promise for evidence makes this gap dramatic, but your pointing out that it exists is very far from new. The onus of proof rests on you, not us who think that yes, Plato really existed and did write the dialogues attributed to him, he did describe the platonic solids (and it is no coincidence, in my opinion, that these same solids appear at the end of Euclid's Elements), the man Socrates whom Plato describes really did exist, likewise the battles between Greek and Persian armies really did happen and the plays attributed to Aeschylus, Sophocles and Euripedes really were written by them, who were men who really existed at the dates that are currently in encyclopedias. Likewise Aristotle really existed and was a teacher of Alexander the Great, who really did conduct military campaigns deep into Asia. I think Eratosthenes really existed, and that he did make a remarkably accurate estimate of the size of the earth, and that he did so within a generation or three from the dates traditionally given for Euclid.
There are dated buildings and inscriptions in stone that attest to this reality. I have not visited them, but friends of mine have and their eye-witness accounts accord with what I have seen in books. There are documents that date to not much later, admittedly in Latin (for example by Cicero and Plutarch), that attest to the historical reality of these figures. There is also a large body of linguistic work that places the Greek writings in a well-attested chronological order, and indeed have in some cases clarified that some writings had been incorrectly attributed. These include writings in mathematics. Are you seriously claiming that all of the writings of ancient and Hellenistic Greece are frauds, or are you claiming that only the mathematical texts are frauds?
I take this large body of scholarly work seriously. You cannot with a word dismiss it as a mere web of myths: you have to demonstrate point by point that they are false. Or at least, you cannot be expected to be taken seriously as a scholar if you don't. Instead, as far as I can see, you simply elaborate a very small number of well-known facts (such as the lack of biographical detail about Euclid) into a grand accusation that this is all invention. The onus of proof is on you: please demonstrate, for example, that Archimedes was not well-known as a mathematician and an inventor to Cicero and Plutarch. Demonstrate that Appolonius of Perga's works all date from far later than is currently believed.
Moreover, although there are very few original documents from ancient Greece and Hellenistic culture, there aren't none. A few actual fragments on papyrus, vases and and so on actually exist, and are linguistically consistent with writings traditionally attributed to those times and places.
I think the products of Greek thought and creativity are well-established, and it is well-known that they took mathematics extremely seriously. It is entirely consistent that they should have produced a large body of mathematics.
You might concede that, but then point out that they were not entirely original. You would then be repeating what is found in any serious history of mathematics: that the earliest Greek mathematicians were said to have learnt their mathematics in Babylon and Egypt (and possibly even further from home), and that this is consistent with what is now known. I hold that this was typical of the age, from roughly 800 to 200 BCE, when in the Middle East (Greece, Turkey, Mesopotamia, Egypt) and India and China, an emphasis on what I would call the philosophical impulse led to amazingly similar developments in all three regions. I also believe they all influenced each other. However, only in the Middle East did an ideology/religion based on the laws given by a god develop (and only in those regions do we have these laws codified as principles in religious texts; all three regions have ancient texts but my understanding is that this is a distinct difference between them), and I think the identification of mathematics with the nature of god that is so characteristic of Pythagoreanism and Platonism is a direct outcome of believing that the nature of god can be codified logically. There is no reason to think that somehow Europe between 1100 and 1500 lucked and cheated itself into a dominant position and retrospectively invented the entire Greek corpus (or perhaps you would say only the mathematical part of it?). No, Europe fell off the Middle Eastern axis due to the so-called "movement of the peoples" which destroyed the western part of the Roman empire, and Europe had to recover literate culture over a period of several hundred years. The little bit of learning that survived in monasteries was indeed not the major source of the sudden blossoming of learning that happened after 1100. As you say, it was because they started translating the writings of Arabic scholars. But this is well-known, and those scholars really existed and attested to the reality of Euclid and Archimedes and Appolonius and Eratosthenes and Eudoxus quite independently of the medieval Christians.
I find it astonishing that you attempt to wipe all that out. But even more astonishing is that you base this merely on the fact that Euclid as a person is poorly attested.
If I may be permitted an analogy, it is with the theory that the historical person identified as William Shakespeare did not write the plays that by scholarly consent are attributed to him. That claim is likewise based on the fact that very little is known about this historical person. But not nothing, and everything we do know is consistent with him really being the author, and it is entirely the norm for us to know very little about people from Shakespeare's time, unless they were of very high status, likes kings and lords, cardinals and bishops (and even then, not in all cases). Of course we don't know much about the historical person Euclid. But we do know about the books and we do know about styles of writing mathematics, and what we know about how people wrote mathematics is consistent with the idea that a specific style, in terms of definitions, propositions and proofs and analysis and synthesis did originate in Greek writings approximately at the time of Euclid, and to call it Euclidean is entirely appropriate. Likewise, the Elements of Euclid has been a massively influential text for a very long time, and on internal documentary evidence (including other documents such as the writings of Appolonius) it dates to the time attributed to Euclid. The Elements of Euclid really does summarise very succinctly almost all of a particular mathematical tradition, and it clearly predates Appolonius and Democritus. It really isn't permissable scholarship to claim otherwise without very detailed evidence on every point. As I say, the onus of proof is on you, not on us.
And yes, I flipped through your book in few seconds. I was hoping for substantial evidence that I would have to read in more detail, but I didn't see any sign of it. Of course, it may be there but not be obvious in such a brief look. But I have read a review of that book (in Philosophia Mathematica) saying much the same thing as I do: that you have very little direct evidence (like everybody else, of course), and that your exaggerations are likely to obscure the real value some of your suggestions do have.
I could go on to your discussion of Clavius and so on, in a similar vein, but this email is already too long. I will content myself by repeating, firstly, that I believe the detailed historiography of Western appropriation of Indian results remains to be done (but yes, it has started) and secondly, that there are many results and preoccupations in Western mathematics that are not found elsewhere. There is for example the much, much richer set of curves that they were studying, and in general far more emphasis on geometry. There are the developments in negative numbers and complex numbers, and in algebraic notation. There are several systems of logarithms. The mathematicians that you call Western did many things the mathematicians you call Indian did not do, and so, no, they did not merely try to copy them. (I find the terms "Western" and "Indian" somewhat inappropriate, as the independent societies that participated in these events have perhaps an abstract unity but emphasising the use of modern categories obscures their internal differences and conflicts, and also I really don't think one should encourage people to think that mathematical results differ according to social context ... 1+1=2 and all that).
As to your methods of teaching calculus, I do take them seriously for a very limited purpose: to introduce students to calculus via ODEs. However, I find the courses and results you have so far presented entirely unconvincing. Moreover, I am far more ambitious about what I want our students to be able to do. I want them to be able to think of families of solutions to ODEs, I want them to be able to do formal integration by hand (not merely by typing things into a computer algebra system), I want them to be able to do dynamical systems analysis that includes a very abstract view of linear algebra. And I want them to be able to do numerical analysis, in which they would learn that yes, floating point numbers are very strange as a number system, that fixed point numbers and integers are numbers of different types (and I might well want to refer to Russel's type theory here, and to formal logic) and that all three types lead to quite different ways of doing calculations on a computer, right down to the level of hardware. It seems to me that your philosophy of zeroism hasn't yet been developed to deal with types in the sense of computers. But when it does, it is my belief that a properly axiomatic approach would nevertheless be superior to empirical evidence. Beyond computation I would want the students to develop a deep understanding of vector spaces and indeed of normed spaces, and I would want them to understand complex analysis and abstract algebra. I believe that numbers properly speaking are as abstract as rings and topologies and categories, and I further believe that stating mathematics in terms of axioms and proofs is the only way to build a mathematics that can be reliably transmitted over many centuries and many cultures. We have been doing exactly that for hundreds of years, and it is the reason that I believe our South African mathematicians can contribute exactly the same way as any other mathematician to the world-wide totality of mathematics. There is no coloniality in the axioms and the proofs. The coloniality consists entirely in who gets to have access and who gets to control mathematics and who gets to decide what mathematical research gets funded. We fix that not by replacing mathematics with something easy (which merely removes us from the world-wide community of science), but by teaching it properly to our students, and by counteracting the systematic exclusion that many of them face, and by changing the power structures that control mathematics.
Oh, and to prove 1+1=2 I would say that the natural numbers are any structure that satisfies Peano's axioms, within which the proof is very easy and very short (and resembles learning to count, but isn't identical to it). Then those same axioms make it possible to prove multiplication properties without merely postulating them. As for empirically studying multiplication, I don't see it. What one *can* study are the properties of algorithms. But how do you prove that a given algorithm for multiplication is correct? How else than by the way mathematicians usually do it now, as I mention above: via Peano's axioms. We could go on to the properties of prime numbers, so vitally important these days in computing and communications, but for so long merely the province of number theory, one of the purest of branches of mathematics. And the cryptosystems using those pure mathematical results are most definitely not empirical mathematics. Then there's the remarkably subtle concept of random numbers. Yes, I definitely want our students to do what you call formal mathematics, as well as what you call normal mathematics!
Let me end by saying I still believe that the following is an accurate and fair summary of your programme for decolonising mathematics:
0. Accept that before about 1700, the Western tradition in mathematics did not contribute anything original.
1. Reject the metaphysics of the infinite as embodied in ZFC set theory and the construction of real numbers based on that theory.
2. Reject the supposed infallibility of formal logic and the false primacy of formal reasoning over empirical evidence.
3. Replace 1 and 2 above with the philosophy of zeroism, as formulated by CK Raju.
4. Define calculus as solutions to ODEs, and introduce calculus via numerical solutions, going on to computer algebra systems for formal solutions.

In the meantime

09-10-17
From: David Gammon, Assistant Dean of Science for, amongst other things, academic support
To: several UCT colleagues
--
Dear Colleagues,

I have been a silent participant in this thread, but I write now with growing concerns. I read this report (http://www.universityworldnews.com/article.php?story=20171006102945514) on the weekend, in what I believe is a fairly widely read news forum.

I am not a Fellow of the university, nor currently a member of UCT’s Senate. I am, however, increasingly concerned at the implications of the apparent silence of our distinguished scientists and mathematicians (and other academics), in the face of (a) the misleading and almost fraudulent behavior of CK Raju, (b) the fact that he is being given significant platforms from which to purvey his views, and (c) the style of much of the reporting of his contributions – which often comes across as mildly approving and certainly seldom with the stern critique that is warranted. Incidentally, a more critical contribution (https://www.groundup.org.za/article/uct-invites-conspiracy-theorist-talk-about-decolonisation-science/) has been written by Nathan Geffen in GroundUp.

I do understand the reticence to get involved in this, but I would ask you as senior scholars whether we can afford to not respond? Perhaps I am particularly concerned about our current students, where sadly they might not have the intellectual frameworks to evaluate the various claims. Is there not perhaps scope for a small group to get together to compile a reasoned response to some of the key claims of Professor Raju?


09-10-17
From: Peter Dunsby – HoD MAM
To: David Gammon

Dear David,

I also have great concerns and share the views of Jeff [Murrogan] and George [Ellis]. I believe that the visit of Dr Raju has severely undermined transformation efforts in the department and in particular are engagements with students. 



09-10-17
From: George Ellis
To: David Gammon

Raju has a powerpoint presentation http://ckraju.net/papers/ckr-usm-presentation-6.pdf where he demonstrates that his teaching methods are a disaster - see the section at the end labelled `Results'. This should be made widely known.

The basic issue is that there is no such thing as Western Science, there is just science. This is what needs to be sung out loud and clear.


27-10-17
From: Crowe
To: C. K. Raju; Loretta Feris; Mamokgethi Phakeng; Daya Reddy; Chris Mitchell; VC; Judith Du Toit; Gerda Kruger
Subject: Debate at last?
Dear Prof. Raju,
Why not submit your rebuttal (endorsed by Prof. Feris' and her SLG maths colleagues Profs Reddy and Phakeng) to Chris Mitchell so BOTH can be published in the UCT NEWS?
Or, is debate really dead at UCT?
By the way, I'm the "elderly" chap who took issue with concering your use of "refutation" insteadof "falsification" vis-a-vis Popper. 
Your reply that his English was poor and he really meant to use refutation is simply false.  I am a well-read Popper scholar, especially with regard to his views on evolution; have published in Biology and Philosophy; and participated in a published debate on biology philosophy with Daniel Dennett.
Let's see if the powers at UCT will back you.


23-10-17
From: Raju
To: Henri Laurie llg@sun.ac.za;Yolisa Ncobo;Arthur Ngwenya;Josh Hayes;Loretta Feris;Sané Erasmus;Timothy Crowe;Elelwani Ramugondo;Daya Reddy

Dear Dr Laurie,

Not so fast! Let me first put on record that you failed also to provide a full, formal proof of 1+1=2, in formal REAL numbers. What a shame! You advocate the teaching of real numbers for rigor and can't rigorously prove even this simple thing! Obviously you teach blind trust, not rigor. The FULL proof (ab initio) of 1+1=2 in reals is a huge effort (500 pages?), and you probably never did it in your life. But the point was to make this complexity of formal math manifest to others.

The other question was what value does this horrendous complexity add? Let me also record that you were unable to explain what value formal (anti-empirical) proof adds to the value of 1+1=2. The issue is NOT “some proof” versus “no proof”; the central issue is that the anti-empirical proof of formal math are WEAKER and less certain than the empirical proofs of normal math. This is fundamentally contrary to the myths of the coloniser, but you could not engage with this issue, and are unable to justify what you teach. Why not do things the simple way?

The anti-empirical proofs of formal math directly imitate the anti-empirical proofs of the post-Crusade church theology of reason,: for example, the proof of how many angels fit on the head of a pin. And they are just as worthless, for the answer obviously depends on what postulates we use to describe angels, who have no real existence, any more than “real” numbers exist in reality. By choosing postulates appropriately, one can arrive at any answer one pleases about these imaginary entities. The church glorified such anti-empiricism because contact with the empirical would destroy its dogmas, such as virgin birth. But why should we?

The bulk of the students are interested only in the practical value of math. So, whatever your faith, you should accept empirical proofs, at least for math applied to science, engineering, commerce, which are all empirical. (The usual wild escapist myth of aesthetics in formal math deserves no consideration since it is contrary to the fact that most students find formal math ugly.) Therefore, we should revert to normal math.

If math is done for its practical value, then it is most inappropriate to regard math as the beliefs, myths, and practices of the formal math community. Any community may be full of prejudices and myths as you have so clearly demonstrated. Colonial education globalised that way of doing math; but decolonisation aims to change that. In short, math is not owned by the current “(formal) mathematics community”. You must justify what you teach, but were unable to do so.

In an open society, the teaching of math can only be justified by its practical value for society at large, and all practical value comes from normal math. The anti-empirical reasoning of formal math adds nil practical value, and horrendous complexity, to math. You teach it because that complexity enhances colonial authority by teaching students to trust your beliefs about it. This teaching hurts the colonised by creating a major obstacle to their educational success, and prosperity. Hence, too, we must abandon formal math, and revert to normal math, to dismantle colonialism.

I would also like to put on record that you were unable to respond to my thrice-repeated query about the technical inadequacies of the university calculus, for practical applications to science and engineering. Presumably you are not technically competent to handle that question, and did not want to admit it publicly. The equations of physics are (nonlinear) differential equations which, on university calculus (based on formal reals and limits), don't make sense at a discontinuity. Calculus based on non-Archimedean arithmetic is not only easier, and more intuitive, but also works in that situation. Therefore, for applications of the calculus, my method is more advantageous. Therefore, we should adopt it, even if it leaves the West with egg on its face, and unable to defend its myth of having invented or improved calculus.

You altogether failed to engage with my full thesis on how science changes if calculus is corrected. I guess you don't understand any physics. Anyway, it is a matter of experiment, not your opinion.

Regarding the history and philosophy of science, blacks in South Africa urgently need to be made widely aware that bogus myths of “Greek achievements” in math and science were systematically used to belittle blacks, and that those myths need to be exposed and erased. I have already conducted a workshop in UNISA on the history and philosophy of science. Your myths will be dismantled since you could produce no evidence for these oppressive myths. Since whites do not own the country any more corresponding courses, to re-educate blacks ought to be taught, in South Africa,whatever you and your pro-apartheid colleagues in UCT may want. BTW, the situation is NOT symmetric as you pretend, for I did produce counter-evidence (e.g. Fermat, Clavius, Tycho, Scaliger etc.) which you were unable to contest.

Indeed, you have totally failed to add any value to this debate. Basically, your only strategy was to repeat stories glorifying yourself and the West and use various adjective slurs and abuse to belittle others. Your colleague Bernhard Weiss, too, was remarkably lightweight in his response which consisted of only a couple of quibbles and a deliberately misplaced accusation. This was the whole strategy of evil apartheid: to justify white rule by glorifying whites and belittling blacks. That strategy of apartheid still persists: and is being propagated in a veiled way by the educational system. It needs to be dismantled in entirety, and your stock method of planting slanderous lies to misguide people needs to be exposed.

Courses need to be systematically taught, especially in South Africa to teach people at large about the numerous lies told by the Whites/West in the history of science, and the disadvantages of imitating bad Western philosophy even in math and science. South Africans need to learn how the education system still misleads them even in math and science. They need to be presented with an alternative which they can evaluate themselves without untrustworthy colonial “guidance”.

Wish you a happy Kali new year 5118.

28-10-17
From: Crowe
To: Raju; Loretta Feris; Mamokgethi Phakeng; Daya Reddy; Chris Mitchell; VC; Judith Du Toit; Gerda Kruger; Elelwani Ramugondo
Subject: Re: Debate at last?
Dear Prof. Raju,
Let's see what happens.
In term of your rejoinder vis-a-vis Popper, English and falsifiability:
With regard to Popper’s command of English and his wish to follow your advice and replace falsifiability with refutability, your ‘evidence’ is, as all too often, specious.  Yes, his Logic of Scientific Discovery was published in German.  But, from 1937 until his death in 1994, he lived and worked in English-speaking countries.  Yes, he may have used the word “refutation” in some of his writings/commentaries. But, in the 60 years available to him, neither he nor any of his proteges or critics EVER: “replaced it [falsifiability] with the term refutability”.   You may have a letter from Popper dated 1990 that says he was considering such a replacement.  But, in the four years until he died he did not. 
Regardless, “refutability” carries a sort of ‘contextual’ or even populist ‘deniability’ that suits those in power at UCT and dogma worshipers or epistemological anarchists.  Falsifiability, exemplified by the “all swans are white hypothesis”, does not. See below.
Refutability
The core meaning of refutability is ‘prove a statement or theory to be wrong’, as in attempts to refute Einstein's theory by coming up with a ‘better’ one. In the second half of the 20th century a more general sense of refutability developed, meaning simply ‘deny’, as in I absolutely refute the charges made against me. Traditionalists object to this newer use as an unacceptable degradation of the language, but it is widely encountered.

Falsifiability
Falsifiability in the Popperian sense, ideally, requires the promoter of an hypothesis to specify [as an integral part of its formulation] an unequivocal observation(s) or an argument(s) which negates it.  In this sense, falsify is synonymous with nullify, meaning to invalidate or "show to be false".  When theories are falsified by such observations, scientists can respond by revising the theory, or by rejecting the theory in favour of a rival or by maintaining the theory as is and changing an auxiliary hypothesis. In either case, however, this process must aim at the production of new, falsifiable predictions.  Thus, the term falsifiability is sometimes synonymous to testability.
This is why Karl Popper's scientific epistemology is known widely "falsificationism". Popper stresses the problem of demarcation—distinguishing the scientific from the unscientific—and makes falsifiability the demarcation criterion, such that what is unfalsifiable is classified as unscientific, and the practice of declaring an unfalsifiable theory to be scientifically true is pseudoscience.

28-10-17
From: Raju
To: Timothy Crowe; Loretta Feris; Mamokgethi Phakeng; Daya Reddy; Chris Mitchell; VC; Judith Du Toit; Gerda Kruger; Elelwani Ramugondo
Subject: Re: Debate at last?

Dear Prof. Crowe,
I will be happy to submit a rejoinder, no endorsement necessary, except the endorsement of a right to reply. Excellent idea if both are published at the same time.
Popper's statement that he used "falsifiability" because of a poor knowledge of English is in the first of his 3 volume Postscript to Logic of Scientific Discovery. The first volume is called Realism and the Aim of Science. Recall that the original LScD was in German. He replaced it with the term refutability.
Popper wrote to me (in a handwritten letter dated 4-5-1990) that he found my critical remarks very good and would respond to my objections to his criterion of refutability, and particularly my objection to his related resolution of the pond paradox (on which he published in a series of articles in Nature in the 1950's). But died before he could do so.
My new resolution of the pond paradox is in my two books on time published by Kluwer, and Sage, and also in the article "Time travel and the reality of spontaneity", in the journal Foundations of Physics 36(7) 2006, pp 1099-1113.
PS. I may take a few days to respond since my decolonised course on the History and Philosophy of Science is going on right now at the SGT University, and there have been some unanticipated changes in schedule.

29-10-17 
From: Raju
To: Crowe
First let me nail your lie: I never claimed to have given Popper advice on English or claim that he wished to follow my advice. You resort to wild lies. That proves only that your arguments are weak, and you know it. You invent lies just because you had no answer to my real claims. Thanks for this admission of failure.
My reference to Popper's handwritten letter to me was clearly in the context of my novel resolution of the pond paradox and its bearing on my critique of his criterion of refutability, in my books and article, as stated.
Do read my email again. Regarding Popper, I referred you to his Realism and the Aim of Science, vol. 1 of the Postscript to Logic Scientific Discovery. This was published some four decades ago. In that book he defines
"the technical terms 'falsifiable' ('empirically refutable') and 'falsifiability' ('empirical refutability')”. [Realism and the Aim of Science, p. xix]
 Clearly, Popper himself equated falsifiability and refutability. This one quote is enough to demolish your claim that Popper made a fundamental distinction between falsifiability and refutability; your claim is a mere gaffe.
 Going further back, to the 1960's, we find, in Conjectures and Refutations, Popper asserts
 “this criterion of demarcation—the criterion of testability, or falsifiability, or refutability—is far from obvious.” [Conjectures and Refutations, p. 51, italics original]
 This again shows that Popper used testability, and falsifiability as synonymous with refutability, as a criterion of demarcation, contrary to what you say.
 As for Popper's knowledge of English, you give a very bad indirect argument. Yes, Popper lived in English speaking countries for long. Likewise, you have lived and worked in South Africa for long. Did you translate any books or articles on philosophy into Zulu, or Tswana, or Venda? That would have made clear the difficulties of translating philosophy from one language to another.
 Had you read even the reference I directed you to, you would have seen that Popper himself admits to his problems with English. E.g., under the head “A puzzled philosopher abroad” Popper states:
 "This statement (which I formulated as pointedly as I could manage with the little English at my disposal)" [Realism and the Aim of Science, p. 12]
Contrary to this, the sole “evidence” you offer is your boast that you are a well read Popper scholar!
 I pointed to one of my critiques of Popper to indicate that I was never his blind follower, and go only by the substance. The substance of the matter is very simple: if we use the term “falsifiability”, then we have to say that some theories are falsified. But “falsification” and “falsified” can mean something else in English. For example, a common phrase, “the falsification of history” does not mean its empirical refutation, but the introduction of falsehoods into history. Therefore, refutation is the better word, as Popper subsequently understood. (This is especially so in my context where I aim to discard both metaphysics and the related false history, e.g. of Euclid.)
 A remark on the principle of BLAA on which apartheid was founded. Obviously, apartheid could not be justified on any logical arguments or factual evidence or ethics. The nitwit supporters of that evil system justified it solely on Boasts (of white superiority), and Lies and Adjectives and Abuses about non-whites. They believed boasting harder, telling more lies, and using more adjectives made for a stronger “argument”. It seems that some of those in UCT, who benefited from apartheid, are still nostalgic about their earlier privileges. They believe the same methods will still work to preserve what remains of those privileges.
 That is why I wanted this entire debate to be public, to expose the undercurrent of hidden pro-apartheid sentiment still prevalent in UCT. That unacknowledged prejudice may well be a key cause of the poor performance of black students. So, let the whole world see how some in UCT indirectly express that prejudice by clinging on to the lowest possible intellectual level: the apartheid principle of BLAA, instead of factually informed and reasoned argument.
 In any case, as I stated at the beginning of my UCT presentation, resort to lies and misrepresentations loses the argument. Since you have lied so wildly, I regard this side-conversation on Popper as closed. Anyway, I have absolutely no interest in discussing your idiosyncratic “reading” of Popper, and will not waste any more time on it. I am concerned with the larger public issue of decolonising math and science.
 So, let us stick to that PUBLIC debate.

30-10-17
From: Crowe
To: C. K. Raju; VC; Judith Du Toit; Amanda Botha; Loretta Feris; Daya Reddy; Chris Mitchell; Gerda Kruger; Karen Van Heerden; Royston Pillay; Russell Ally; Dean of Science; Sipho Pityana
Subject: Debate on decolonization at UCT: Popper goes the weasel


Dear Prof. Raju,
First, I am removing Prof. Phakeng from this correspondence since she has formally informed me [Mon 2017-10-30 07:19 AM]: “I neither invited Prof Raju no [sic] attended any of his talks, I have also not pledged my support for his work nor endorsed his scholarship. Prof Raju himself was unimpressed with my very brief conversation with him.”
Now to debate!
Your latest e-mail (29 October 2017 and appended) descends into ad hominem attack, something that the UCT SLG condemns, albeit contextually and situationally.  I’ve been labelled, inter alia by pro-Fallists: “Jim Crow” “Apartheid activist’, “killer of black people”, “racist”, “eugenicist”.   [My wife, a prize-winning educational Ph.D. scholar was labelled “white bitch”.]
But, although one pro-Fallist has called me “ill-informed”, you’re the first to call me (a Life Fellow of UCT – see my CV on page 4 of my Blog Site – timguineacrowe.blogspot.co.za) a “liar”.  Let’s see if anyone in the UCT hegemony defends me.  N.B. Max, Karen, Amanda, Royston, Russell.
My last words on Popper.  He did use the word refutation in some of his comments demarcating pseudoscience.  But, he and no one else, other than you, uses it “interchangeably” with “falsifiability”, let alone prefers refutation.
For example, if I ‘Google’ “decolonization mathematics”, I get CK Raju.  When I do the same for “falsifiability philosophy”, I get Popper.  When I do the same for “refutation philosophy” I get: A Beginner's Guide to Philosophical Refutation | Gerol Petruzella .  Even, going on for several ‘Google’ pages fails to reveal a citation for Popper. [Although there is one for Liebniz.]
So, when informed people think of Popper, they relate him to “falsifiability” not to “refutation”.
QED
I maintain that your preference for refutation is because it fits in with your induction/empiricism position on Science in general and Maths in particular.  But, to deal with this requires open, rational, public debate at UCT.  Even if the SLG wanted it, the pro-Fallists would prevent it from happening.
But, I’m just a liar who hankers for Apartheid.  In reply to this, read:
Afrocentric, inclusive, socially relevant academic ‘evolution’ at the University of Cape Town
You say I “resort to wild lies”.  But all I’ve done is string together a series of your statements.  Henri and Jeff took on your ganita/zeroism mathematics and demolished them.  But, they’re liars too; merely puppets manipulated by senior “Apartheid scientist” bosses.  The only person that has “no answer to [your] real claims” is you, because that’s all they are.  You can indeed “fool some of the people all of the time”.
With regard to Popper's knowledge of English, not only did he live in English speaking countries for more than a half century.  He worked at English-speaking institutions and published most of his work in English.  If he wanted to recant ‘falsifiability” or use different words, he would have.  But, he didn’t.  Language as a medium of instruction and research is a major issue in South Africa.  It was, and still not is.  But, not in the UK.
Next, you seem to imply that I am a racist who supports “the principle of BLAA on which apartheid was founded”.  Well, I fail again, because I don’t know what BLAA means.  But, this now makes me a “nitwit supporter of that evil system” N.B. more defamation Amanda.  With regard to my “boasts” about being a scholar and philosopher of science, I append a list of some of my more than empirical publications.  If you doubt me still, contact world leading philosophers of science Dan Dennett or Michael Ruse.
Yes, those pushing the now ongoing witch hunt at UCT (pro-Fallists, the SLG & IRTC?) will probably find someone to label as a white-supremacist heretic.  But, during my four plus decades at UCT, and especially during the last two years, virtually all the people I’ve met with are some of the finest human beings who want to (and could) lead UCT into a future that shines for all. But, they have been rendered silent.  As I write, those who enjoyed your seminar and post-seminar antics have shut down UCT again and are determined to suppress the public debate that you and I desire.  Those who just want to study and research (especially the socio-economically oppressed) must just suck it up and be (as you describe) the “some in the UCT community [who] must bear the pain”.
But, don’t hold your breath waiting for a scheduled debate.
Raubenheimer, D. & T.M. Crowe.  1987.  The Recognition Species Concept: is it really an alternative?  South African Journal of Science 83: 530-534.
Crowe, T.M.  1987.  Species as individuals or classes: an "iconoclassificationist's" view.  Biology and Philosophy 2: 167.
Crowe, T.M.  1988.  Molecules vs morphology in phylogenetics: a non-controversy.  Transactions of the Royal Society South Africa 46: 317-334.
Crowe, T.M., A.C. Kemp, R.A. Earle & W.S. Grant.  1989.  Systematics is the most essential, but most neglected, biological science.  South African Journal of Science 85: 418-423.
Crowe, T.M.  1989.  Pan-African ornithology divided.  Nature 338: 11-12.
Crowe, T.M.  1989.  Botanists, zoologists, palaeobiologists, biogeographers, earth scientists and molecular biologists unite!  South African Journal of Science 85: 417.
Crowe, T.M.  1994.  Morphometrics, phylogenetic models and cladistics: means to an end or much ado about nothing?  Cladistics 10: 77-84.
Crowe, T.M., M.A. Isahakia & E.B. Knox.  1994.  Research and training priorities in biological conservation: African solutions to African problems.  South African Journal of Science 90: 517-518.
Crowe, T.M., W.R. Siegfried, A.T. Lombard & M.A. du Plessis.  1994.  Science and the development of strategies for the conservation of biodiversity in the 'new' South Africa.  Bulletin of the Southern African Institute of Ecologists and Environmental Scientists 13(1): 13-19.
Bloomer, P. & T.M. Crowe.  1998.  Francolin phylogenetics: molecular, morpho-behavioral and combined evidence.  Molecular Phylogenetic and Evolution 8: 236-254.
Crowe, T.M.   2000.  Daniel Dennett's views on the power and pervasiveness of natural selection: an evolutionary biologist's perspective. In: Ross, D., Brook, A. and Thompson, D., eds.  Dennett's philosophy: a comprehensive assessment.  Cambridge, Mass.: Massachusetts Institute of Technology Press.  pp. 27-40.
Crowe, T.M.  1999.  A multifaceted concept of species. Proceedings of the 22nd International Ornithological Congress, Durban. Johannesburg: BirdLife South Africa. pp.1490-1495).
Crowe, T.M.  1989.  Review of: Science as a process Hull, D.L. University of Chicago Press, Chicago.  In: South African Journal of Science 85: 632.  Also printed in Origin 1(1): 8-10.
Public intellectual articles:
Racialism is a nasty, but profitable, ‘business’
A new approach to understanding subspecies can boost conservation
Khoisan origins: why ‘race’ has no place in human ancestry
Are academic freedom and non-racialism dead at the University of Cape Town UCT? – mixed messages
African gamebirds are keys to understanding global avian evolution
The long struggle to understand species: from pre-Darwin to the present day
How science has been abused through the ages to promote racism

29-10-11
From: Raju
To: Crowe
First let me nail your lie: I never claimed to have given Popper advice on English or claim that he wished to follow my advice. You resort to wild lies. That proves only that your arguments are weak, and you know it. You invent lies just because you had no answer to my real claims. Thanks for this admission of failure.
My reference to Popper's handwritten letter to me was clearly in the context of my novel resolution of the pond paradox and its bearing on my critique of his criterion of refutability, in my books and article, as stated.
Do read my email again. Regarding Popper, I referred you to his Realism and the Aim of Science, vol. 1 of the Postscript to Logic Scientific Discovery. This was published some four decades ago. In that book he defines
"the technical terms 'falsifiable' ('empirically refutable') and 'falsifiability' ('empirical refutability')”. [Realism and the Aim of Science, p. xix]
Clearly, Popper himself equated falsifiability and refutability. This one quote is enough to demolish your claim that Popper made a fundamental distinction between falsifiability and refutability; your claim is a mere gaffe.
Going further back, to the 1960's, we find, in Conjectures and Refutations, Popper asserts
“this criterion of demarcation—the criterion of testability, or falsifiability, or refutability—is far from obvious.” [Conjectures and Refutations, p. 51, italics original]
This again shows that Popper used testability, and falsifiability as synonymous with refutability, as a criterion of demarcation, contrary to what you say.
As for Popper's knowledge of English, you give a very bad indirect argument. Yes, Popper lived in English speaking countries for long. Likewise, you have lived and worked in South Africa for long. Did you translate any books or articles on philosophy into Zulu, or Tswana, or Venda? That would have made clear the difficulties of translating philosophy from one language to another.
Had you read even the reference I directed you to, you would have seen that Popper himself admits to his problems with English. E.g., under the head “A puzzled philosopher abroad” Popper states:
"This statement (which I formulated as pointedly as I could manage with the little English at my disposal)" [Realism and the Aim of Science, p. 12]
Contrary to this, the sole “evidence” you offer is your boast that you are a well read Popper scholar!
I pointed to one of my critiques of Popper to indicate that I was never his blind follower, and go only by the substance. The substance of the matter is very simple: if we use the term “falsifiability”, then we have to say that some theories are falsified. But “falsification” and “falsified” can mean something else in English. For example, a common phrase, “the falsification of history” does not mean its empirical refutation, but the introduction of falsehoods into history. Therefore, refutation is the better word, as Popper subsequently understood. (This is especially so in my context where I aim to discard both metaphysics and the related false history, e.g. of Euclid.)
A remark on the principle of BLAA on which apartheid was founded. Obviously, apartheid could not be justified on any logical arguments or factual evidence or ethics. The nitwit supporters of that evil system justified it solely on Boasts (of white superiority), and Lies and Adjectives and Abuses about non-whites. They believed boasting harder, telling more lies, and using more adjectives made for a stronger “argument”. It seems that some of those in UCT, who benefited from apartheid, are still nostalgic about their earlier privileges. They believe the same methods will still work to preserve what remains of those privileges.
That is why I wanted this entire debate to be public, to expose the undercurrent of hidden pro-apartheid sentiment still prevalent in UCT. That unacknowledged prejudice may well be a key cause of the poor performance of black students. So, let the whole world see how some in UCT indirectly express that prejudice by clinging on to the lowest possible intellectual level: the apartheid principle of BLAA, instead of factually informed and reasoned argument.
In any case, as I stated at the beginning of my UCT presentation, resort to lies and misrepresentations loses the argument. Since you have lied so wildly, I regard this side-conversation on Popper as closed. Anyway, I have absolutely no interest in discussing your idiosyncratic “reading” of Popper, and will not waste any more time on it. I am concerned with the larger public issue of decolonising math and science.
So, let us stick to that PUBLIC debate.

31-10-17
From:. Raju
To: Timothy Crowe;VC;Judith Du Toit;Amanda Botha;Loretta Feris;Daya Reddy;Chris Mitchell;Gerda Kruger;Karen Van Heerden;Royston Pillay;Russell Ally;Dean of Science;Sipho Pityana <sipho@izingwe.com>;Elelwani Ramugondo;Kasturi Behari-Leak;Goitsione Mokou

Dear Prof. Crowe,

Amusingly, you have deleted your previous email which carried the evidence of your lie. You have also changed the title of the thread, and suddenly changed the people to whom this email is addressed (many not aware of the past context) and also are now changing the context of my statement. Perhaps that is what you meant by being an expert on falsification.

I have restored the entire thread (there are two copies of my response of 29 Oct, one pasted in-between your response, because that is how it was in your mail).

I quote from YOUR email of 28 October 2017,
“With regard to Popper’s command of English and his wish to follow your advice and replace falsifiability with refutability, your ‘evidence’ is, as all too often, specious. ...You may have a letter from Popper dated 1990 that says he was considering such a replacement.  But, in the four years until he died he did not.” (emphasis added).
I responded, and I quote from my email of 29 October.
“First let me nail your lie: I never claimed to have given Popper advice on English or claim that he wished to follow my advice. You resort to wild lies. That proves only that your arguments are weak, and you know it. You invent lies just because you had no answer to my real claims. Thanks for this admission of failure.
“My reference to Popper's handwritten letter to me was clearly in the context of my novel resolution of the pond paradox and its bearing on my critique of his criterion of refutability, in my books and article, as stated.” (emphasis added)
The specific lies are highlighted in YOUR statement (quoted above): the lies are your statements that I gave advice to Popper on English or that he stated he wished to follow my advice, or that the letter he wrote to me pertains to such purported advice. You have been caught fair and square distorting my statements wildly, too wildly to be called a misrepresentation.
If you claim you did not lie, there was simple way to establish it; no need for a long harangue, just produce the evidence that I said I gave advice to Popper on English or that he accepted it. You were not able to do that. [For obvious reasons: my whole email of 28 October is reproduced below.] Instead you try to bury the evidence and fudge the context. Everybody understands what such acts mean. 
Also, nailing specific lies is NOT an ad hominem attack. Equating the two, as you do, means you demand a carte blanche to tell any falsehood you please, so that when caught lying you will yell “ad hominem”!
Further, in my email of 29 Oct 2017, I gave you two PRIMARY sources, that Popper equated “falsifiability” and “refutability”, AND also a third quote that he admitted his difficulties with English. I quoted from Popper's PUBLISHED work, citing page numbers. In this entire discussion, you failed to give even a single primary source to support your claim that Popper used the two terms in differing ways, as you claim; you just keep repeating empty boasts about being well-informed.
Also, do stop boring me with your inferences based on google searches. In a serious debate you need to use only primary or secondary sources.
This side discussion on Popper is now CLOSED.
Please don't send me any more emails on this topic. If you still do, I may not respond to them.
I will respond publicly to your “final” piece for the UCT News debate section in a few days.

31-10-17
From: Crowe
To: Raju

Dear C.K. or Chandra (I think of us as duelling buddies these days),

Yes, I deleted all the e-mail impedimenta from my latest rejoinder.  That's because several recipients complained about having to slog through it.

With regard to Popper, falsifiability and refutation, if all you now claim is that the words concerned are functional synonyms (are "homologous" = they ARE the same thing), then let's stop the ad hominem attacks. 

However, if by refutation, you mean one idea supercedes another through populist pressure or piles of empirical 'findings' as opposed to passing a critical test(s) linked to an unequivocal prediction (the falsifier), then you're, on again, playing fast and loose with philosophy and Science.

With regard to the relative merits of zeroism-based ganita, it seems that all the mathematical scientists and educationalists at UCT (including the eminently qualified DVC Phakeng) give it a "Zero".  Otherwise, they should append their names to your rebuttal in the UCT NEWS.

It seems that your local supporters amount to a handful of deconstructive decolonizers wanting to slip through UCT with a five-day qualification in microwaved maths.  When this doesn't emerge as viable option, as always, they will try to shut UCT down (because that's all the SLG seems to understand) and allow the Silenced Majority to bear the pain you say is necessary for the great leap forward.

06-11-17
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 <sipho@izingwe.com>;Kasturi Behari-Leak;Goitsione Mokou

My final piece to be submitted to Chris Mitchell for publication in the debats section of the UCT NEWS
Dear Prof. Crowe,

I have finally found time to write out a rejoinder.

However, you will appreciate that I can only debate against a fixed body of statements.

Therefore, I request you to review and confirm that the attachment you sent earlier, for publication in UCT news, is indeed your final version, and that this is the version which will be published without change along with my reply.

You can do this in various ways. 
(1) You can print out the attachment, and sign it and initial each page, as in a legal document, and scan it and send it.
(2) You can use a digitally signed document if you have a digital signature.
(3) As the simplest (but worst) option, you can copy the contents of your attachment for UCT news, in the BODY of an email (not as an attachment). In this case use "reply all" and do not delete any non-white member of this list. 

And I want your solemn assurance that your "final piece" will not change in the slightest way after receiving my rejoinder, and before publishing in UCT news.

Of course, you are welcome to respond to me in round 2.

06-11-17
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; Jeff Murugan; Andy Buffler; Muthama Muasya; Shadreck Chirikure; simonrakei.sr@gmail.com; Russell Ally
Thank you Prof. for requiring me to provide you with a "final fixed body of my statements" relating to our written engagements vis-a-vis decolonizing science at UCT, so we can make our positions as clear as possible.  Once you have the opportunity to rebut my comments, our final words on this matter can be made available to ALL in the UCT Community via the Communication and Marketing and Development and Alumni Departments for comment and debate.
Following Prof. Raju’s suggestion, I do this by BOTH embedding my remarks within (and attaching them to) this message.
I have REPLIED ALL to those on Raju’s e-mail list and added several new addressees whom I feel should be informed and NOT because I believe that the concur with my or Raju’s views.  I do so because I fear that potential future decolonization debates will exacerbate the negative effects of those relating to Mathematics.
Like VC Price, DVC Feris and members of the CCWG, I seek “a constructive way to engage in a discussion on decolonial thinking, regardless of the discipline”.

‘Counting’ decolonizing conspirators at the University of Cape Town (UCT)
Tim Crowe – B.A. (1970 - U Mass./Boston), M.Sc. (1972 - U Chicago), Ph.D. (1978 -.UCT), Life Fellow (UCT) and Emeritus Prof. of Biological Sciences (2013 UCT)
A key component of “decolonization” at UCT relates to transforming disciplines that “obstruct/oppress” students and staff.  Perhaps the keystone ‘obstructing’-discipline in Science is Mathematics.
Mathematics began as a formal, historically documented, discipline in the 6th Century BCE with the Pythagoreans who coined the term ‘mathematics’ from the ancient Greek ?????? (mathema).  Legend clouds Pythagoras’ ‘accomplishments’, which actually may have been collective works of predecessors/contemporaries.
Although, the oldest undisputed mathematical documents are from Mesopotamia and dynastic Egypt, c. 2000 BCE, they show no appreciation of the difference between exact and approximate solutions and scientific problem solving.  Most importantly, these documents provide no explicit statement of the need for proofs or logical principles.  Pre-Greek mathematics employed ‘bottom-up’  inductive reasoning – using repeated observations to establish ’rules of thumb’.
After Pythagoras, the next major mathematical ‘player’, the also poorly historically documented Euclid (c. 300 BCE), systematized ancient Greek and Eastern mathematics/geometry in the most widely used mathematics/geometry textbook in history - The Elements.  It collected, organized, and deductively proved geometric ideas previously used as applied techniques.  Modern, formal mathematics has been described as “a series of footnotes to Euclid”, either developing ‘his’ ideas or challenging them.
Perhaps the first ‘pure’ mathematician was another Greek, Archimedes, who studied at Alexandria, also in the 3rd Century BCE.  He produced formulas to calculate the areas of regular shapes, using a revolutionary method of capturing new shapes by using shapes already understood.’
From thereon, sectors in the East carried on the baton, particularly China, India and the medieval Islamic Empire and continued the development towards increasing generalization and abstraction in mathematics. The notion of axioms as “self-evident truths” was largely discarded in favour of emphasizing logical concepts such as consistency and completeness.  Two of the most well-known 20th Century leaders in this development of “Formal Mathematics” were eccentric British mathematician G.H. Hardy and his young Indian protégé Srinivasa Ramanujan. [There is even a film celebrating their complex relationship.] The early 20th Century also saw the rise of the field of mathematical logic, which came to fruition in the hands of maths giants David Hilbert and, particularly, Bertrand Russell and A.N. Whitehead, whose monumental joint work the “Principia Mathematica” formed the basis of today’s maths.
Some ‘pure’ mathematicians and philosophers of science view mathematics as “not a science”, because “real science” is a system in which general statements (= theories and all that) are tested against empirical observations.  Mathematics is “merely” a system of logic that can be exceedingly useful in empirical science conducted by plebeian scientists like Einstein.
Decolonization with a ‘big bang’
Context:  In response to an occupation of the Dean of Health Science’s suite, VC Price created the Curriculum Change Working Group (CCWG) to drive the process of curriculum transformation.  The CCWG is co-chaired by critical theorist / race theorists Associate Profs Harry Garuba (Centre for African Studies) and Elelwani Ramugondo (Department of Occupational Therapy).  Other members were/are similar-thinking Prof. Sandra Klopper (DVC: Teaching and Learning), Prof. Sakhela Buhlungu (Dean of Humanities), Associate Prof. Harsha Kathard (Department of Health Sciences Education), Associate Prof. Denver Hendricks (Deputy Dean of Health Sciences), Dr Kasturi Behari-Leak (Academic Staff Development, CHED), Goitsione Mokou (education master’s student), Rorisang Moseli (2016 SRC President) and Brian Kamanzi (RMF and engineering master’s student). None of the members of the CCWG is a prominent mathematical scientist.
Without consulting and/or following the advice of eminent mathematical scientist DVCs Prof. Mamokgethi Phakeng (National Research Foundation – B-rated) and Daya Reddy (A-rated) and mathematical scientists ‘up the hill’, Feris and the CCWG invited Prof. C.K. Raju to kick off the decolonization debate vis-à-vis maths.
Before I pursue this matter further, allow me to show my envy of my maths colleagues at UCT.  The Department of Mathematics and Applied Mathematics at UCT is the top-rated such department in Africa, with 20 NRF rated researchers, including 1 P and 5 A-rated researchers.  Although I don’t have access to the relevant sources, I gainsay that it ranks among the top 50 maths departments worldwide.  This pre-eminence did not happen by accident.

C.K. Raju holds a B.Sc. degree (1973) from the Institute of Science, Bombay - India, an M.Sc. (1975) from the Department of Mathematics University of Mumbai and a Ph.D. at the Indian Statistical Institute (1980).  He played a major role in developing India’s first supercomputer; and has published widely on the history and development of Mathematics.  He is perhaps most noted for his views that infinitesimal calculus was developed in India and transmitted by missionaries to Europe where it was distorted to conform to the dictates of Christian religious authoritarians; and that Albert Einstein's theories of special and general relativity were anticipated much earlier by Henri Poincaré and were flawed [corrected by Raju] to the extent that much of modern physics needs to be reformulated.
Raju’s current position as “Distinguished Professor” appears to be at Inmantec (a business school in Ghaziabad) and the Centre for Studies in Civilizations (a NGO in New Delhi) based in India.  According to its website, the Centre "aims at conducting, promoting and facilitating studies and research in the broad areas of history, philosophy, culture, science and technology", and "undertakes and promotes research in relation to the past, the present and the future courses, contents, and trends of civilizations in general, and Indian civilization in particular”.


The ‘Debate’ and ‘Conspiracy’
Raju and three panelists spoke/debated at UCT on 19 September 2017.  My comments on this event are summarized elsewhere.  Here, I summarize my research on what might be described as the post-debate “Raju Conspiracy/Affair”.
According to the vast majority (ALL?) of UCT’s mathematical scientists, Raju grossly mis-represents the history of Mathematics in general and formal maths in particular and uses ad hominem attacks rather than logical arguments to ‘deal’ with his critics.  More disturbingly, his presentation style panders to Fallists who subsequently shut UCT down.
I list but a few [of many, many] noteworthy Raju quotes to back up my conclusions:
Formal mathematicians “facilitated and directed astronomical observation missions in order to help the French better determine the location of St. Domingue, the island that houses the modern nations of Haiti and the Dominican Republic. Why? Because this would help make the delivery of slaves and export of the products of their labor more efficient.”
“Many in the UCT faculty judge on prejudice rather than academic content: thus residual prejudices from apartheid may be a major cause of the poor performance of black students.”
“The report about me [Raju] in the Daily Maverick (29 September) is character assassination, at its worst.“
“A false history of science was used to initiate colonial education, in support of colonialism. This false history persists.”
 “Deductive proof doesn’t lead to valid knowledge.”
“Formal mathematics creates a slave mentality.”
“The entire colonial tradition of education teaches us to trust only Western-approved experts, and distrust everyone else.”
The superiority of [ganita] his alternative philosophy of  zeroism-based mathematics -, has been demonstrated by “teaching experiments performed with eight groups in five universities in three countries – Malaysia, Iran and India”.
“My decolonised math is so easy that the calculus can be taught in five days”.  This has been “publicly discussed in newspapers, and blogs, and prominently reported in newspapers, magazine articles, interviews and videos”.
“Using Zeroism, I have provided a better theory of gravitation arising from correcting Newton’s wrong metaphysical presumptions about calculus”.
“Academic imperialism begins with Western education, which has not been seriously challenged in hard sciences. Colonialism changed the system of education as a key means of containing revolt, and stabilising Western rule.”
“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.”
“We need to construct a new pedagogy, particularly in the hard sciences, and demonstrate its practical value, to dismantle the Western power structure at the level of higher-education and research.”
“The point about academic imperialism is not just to talk about it, but to end it.”
“The UCT panel discussion gave the panellists and audience another chance to academically engage with my views and contest them publicly. This did not happen, though it had a mathematician, a philosopher, and an educationist, all senior faculty members from UCT and Stellenbosch.  The respondents hardly engaged and did not refute any of my central points. Many in the audience agreed with me. Hence, the panel discussion was widely seen as an academic victory for decolonisation.”
N.B. I was there.  The panellists engaged/contested with him.  Due to his confrontational and confusing mode of presentation, it was impossible to “refute” anything he said.  Those in the audience who “agreed” with him were mainly young people (students?).  There was no “victory”.
 “The top mathematician in the world, Sir Michael Atiyah, had tried to grab credit for one of my theories (Time: Towards a Consistent Theory, Kluwer ,1994), and connived to get published a prominent article giving him credit for it.”
 “The formal mathematician on the UCT panel [Dr Henri Laurie] asserted he had such magical powers to work with invisible points (obviously not able to transmit it to others!). I then said that talk of invisible points is a deliberate con-trick. Anyone who denies this is deluded.”
 “Euclid must fall. some in the UCT community must bear the pain, which is nothing compared to the pain inflicted on blacks during apartheid.”
 “On the actual evidence, the anonymous “author of the Elements” was a black woman who was raped and killed in a church.”
  “The students who do my course would get better jobs, because they learn to do things well beyond anything done in current school or first-year calculus courses.”
 [Jeff] “Murugan [deputy HoD – UCT Maths] might lose his job if decolonisation is implemented and he doesn’t retrain.  He did not reveal his other conflict of interests. He is a collaborator - and a student - of G.F.R. Ellis, an influential UCT academic from apartheid days, whose work I attacked at the UCT panel discussion.”
 “Ellis won the million-dollar Templeton award, for science and religion, for helping to pass off such key politically-motivated church dogmas as ‘reputable’ though not refutable “science”.
 “The singularities of Hawking/Ellis are just an artefact of bad (formal) math.”
 N.B. George Ellis, FRS, Hon. FRSSAf, and Life Fellow of UCT is the Emeritus Distinguished Professor of Complex Systems at UCT. He co-authored The Large Scale Structure of Space-Time with physicist Stephen Hawking, and is one of the world's leading theorists in cosmology.  He is an active Quaker and in 2004 he won the Templeton Prize. He was President of the International Society on General Relativity and Gravitation and the International Society for Science and Religion. He is NRF A-rated. Ellis was a vocal opponent of Apartheid during the 1970-80s, when his research focused on the more philosophical aspects of cosmology, for which he won the Templeton Prize. He was also awarded the Order of the Star of South Africa by Nelson Mandela, in 1999.  In 2007, he was elected a Fellow of the British Royal Society.
 “That is UCT math department for you, no evidence needed for anything. The UCT math department is clearly part of the math problem facing blacks in the country, for it uses lies and mere authority to block serious alternatives from being tried out.”
 “Deductive proofs [core of formal maths] can be used to prove any pre-desired conclusion.”
 “Students must choose to eliminate the myths and superstitions of formal math. It leads to greater conceptual clarity. This is beneficial to the students even though it diminishes colonial authority. Black students still suffering under that authority need to be liberated. They should not wait for approval. Students must claim the right to choose between the practical value of normal math against the myths and superstitions of formal math, unreasonably enforced by the formal math community. They must claim the right to institute parallel decolonised courses, and decide for themselves which courses are better.”
 “I would like to take this occasion to thank the Deputy Vice Chancellor Loretta Feris and the Curriculum Change Working Group for showing the courage to organize this panel discussion in the midst of such a muck of prejudice. What is has achieved is to expose the academic bankruptcy of the fuming opponents of decolonisation: they have used up the entire arsenal of academic and non-academic swear words, without advancing a single serious academic argument! This shows it was a greater victory for South Africa.”
Views of others
In the cyber journal Ground Up, Prof. Jeff Murugan best summarizes the views of UCT’s mathematical scientists.
“I believe deeply in the freedom of ideas and information. As such, all ideas should be heard.  However, with Raju, UCT has just given an official platform to a set of ideas that are, at best, fringe, and lauded them as a revolutionary challenge to mainstream science.  They are not.  Much of what Raju says either reflect a very shallow understanding of the nature of science or, when they are correct, trivial.”
Jeff also wrote privately and at length on Raju’s ‘views’ to DVC Feris, VC Price, DVC and Maths colleague Daya Reddy and Dean of Science Anton Le Roux, stipulating that I do not pass on his comments verbatim.  But, I will say this much; his analysis is a devastating refutation (to say the very, very least) of Raju’s views and ‘style’ from socio-cultural as well as academic perspectives.
Rebuttal
In response to a question whether giving official sanction to Raju, who dismisses almost the entire body of work done by UCT’s mathematic scientists and the West, is a productive way of taking forward the decolonisation debate, Feris replied expansively:
“Professor Raju was invited not so that his views by necessity replace existing ones, but rather as a departure point for debate. Raju challenges existing dogma at a time when we as a university are reflecting on our colonial history and the ways in which we as a country have embraced colonial epistemology. Raju’s message to students is that they should question Western Authority on science and insist instead on empirical evidence on truth. To faculty, he asks that if we teach the exact similar science as taught in the West, we should be able to justify why that is so. First – we must explain our exclusion of other approaches to science from other parts of the world. Secondly, we should demonstrate the benefits of science as taught and understood in the West, and explain why local communities may be rendered only beneficiaries, and never co-producers of scientific knowledge. Professor Raju essentially rejects the notion that the Western philosophy of science and maths is objective and universal. This aligns with the decolonial questioning of Western thought as the singular truth. Professor Raju invites us to think about philosophy other than that which originated in the West, Eastern and African philosophies of science and maths. It seems to me like a constructive way to engage in a discussion on decolonial thinking, regardless of the discipline.”
Rejoinder
I close with a George Ellis quote:
“His [Raju’s] talk has nothing positive to contribute to the discussion, not just because he advocates replacing the internationally agreed approach to mathematics and physics by his own idiosyncratic views, but particularly because he explicitly advocates ignoring the views of international experts on scientific topics in his decolonial approach to science and maths.  If UCT were to follow that route, we’d better close down the science and engineering faculties. The degrees we will produce will be worthless.”
In short, a handful of UCT non-mathematical, critical (race?) theorists invited a ‘conspiracy theorist’ to talk about decolonisation of mathematics as taught by its world-renowned Maths Department.  The Transformation DVC and CCWG should consider the impact of Raju’s visit on the morale of ALL of UCT’s best, brightest and dedicated academics, by choosing to favour, dare I say conspire with, Fallists who ‘lapped up’ his ‘views’.
A potentially important ‘side issue’
During the Raju “Conspiracy/Affair”, he and I engaged in a mini-debate on the meaning use of the terms “falsifiability” and “refutation” in science philosophy.
Raju claims that falsifiability and refutation are philosophically functional synonyms (are "homologous" = they ARE the same thing).
 However, if by refutation, he means one idea can supersede another through populist pressure or piles of ‘contextual’ empirical 'findings', as opposed to passing a critical test(s) linked to an unequivocal prediction (the falsifier), then, once again, he’s playing fast and loose with philosophy and Science.
 Concluding comments on the current approach to decolonization at UCT
With regard to the relative merits of zeroism-based ganita, it seems that all the mathematical scientists and educationalists at UCT (including the eminently qualified DVC Phakeng) give it a "Zero".  Otherwise, they should append their names to Raju’s rebuttal to this piece.
 It seems that Raju’s local supporters amount to a handful of deconstructive decolonizers wanting to slip, or have their students slip, through UCT with a five-day qualification in microwaved maths.  When this doesn't emerge as viable option, as always, they will try to shut UCT down (because that's “all the Senior Leadership Group seems to understand”) and allow the Silenced Majority to “bear the pain” Raju claims is necessary for the great leap forward.
 A way forward
Does UCT need to repeat a fruitless discipline-based, curriculum-decolonizing ‘exercise’ coordinated by a non-specialist DVC and non-specialist members of a small theoretically narrowly focused ‘working group’?  Must such exercises be conducted by ‘experts’, simply because they convinced the DVC/CCWG that they are a bona fide decolonists; cloaked their evidence-free arguments with claims of racism, epistemic fraud and geographical chauvinism?  This is especially questionable when the ‘expert’ resorts to ad hominem attack and defamation when her/his views are challenged.
 Instead, why not challenge pro-Fallist/decolonist academics, students and alumni (e.g. from the now formally recognized Black Academic Caucus) within departments (and further afield) to produce coherent, evidence laden critiques of the oppressive/obstructive extant curriculum status quo?  These could be circulated by UCT-controlled media for transparent, unfettered debate between staff, students, potential employers, alumni and other interested and affected parties.


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