**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.

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 10

^{th}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 16

^{th}c. text attributed to Archimedes is evidence only of 16^{th}c. knowledge, not evidence for the claim that Archimedes wrote on the Sphere and the Cylinder. Likewise, a 12^{th}c. text attributed to Claudius Ptolemy is evidence only of 12^{th}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 Nx

^{2}+1 = y^{2}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 9

^{th}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 16

^{th}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.” [C*onjectures 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.” [C*onjectures 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 6

^{th}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 -

**. 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.**__The Elements__
Perhaps the first ‘pure’ mathematician was another Greek, Archimedes, who studied at Alexandria, also in the 3

^{rd}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
20

^{th}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 20^{th}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 11

^{th}to 17^{th}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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