Archive for the ‘History and Philosophy of Mathematics’ Category

A fitting response to racist censorship: “Pythagoras”, earth’s radius, and navigation

Saturday, February 4th, 2017

My article first published and then censored by Conversation (but remained on the Wire), has now been published in full as part of another article “Black thoughts matter: decolonized math, academic censorship and the ‘Pythagorean’ proposition”, in the Journal of Black Studies. Click the link to download from the journal site, as an Online First article.

Apartheid did not disappear overnight with a change in the political system in South Africa. Black students are still the victims of covert apartheid which persists in academics, and thereby perpetuates inequity. Hence their protests and demand for decolonising the university.

Macaulay argued that colonial education was needed for science, an argument still used today. Therefore, math and science must first be decolonised to be able to decolonise the education system. Colonially indoctrinated people wrongly believe Western formal math and science are universal, so there is no choice but to imitate the West. My Conversation article explained in brief why this belief is false, and how math can be and has been decolonised, and through it science. This struck a major blow against colonial/Western/White power; hence that article was censored with a silly excuse lacking credibility, as another article in Wire noticed.

Now, colonial education was instituted with the help of a false history of science—that science is Western in origin. This colonial history built on an earlier false racist history arising from ultra-chauvinistic Crusading history. George James resisted racist history arguing that the achievements of Egypt were falsely credited to Greeks. More recently James was attacked by Lefokowitz, an attack applauded by covert racists all over the world. My JBS article explains in passing the error in Lefkowitz’s response to James about Aristotle’s plagiarism. (Of course, she was wrong, and, in fact, incoherent, about Archimedes too, as I explained in my recent lectures at UNISA, but that is another story.)

The JBS article also expands an earlier brief remark on the myth of Pythagoras and its connection to navigation. (more…)

Western superstitions in science

Wednesday, February 1st, 2017

The Black House Kollective initiated a welcome conversation in Soweto on decolonisation in relation to Western superstitions in science.

Soweto poster

For example, the first lesson in science is typically about Newton’s “laws”. But how do we know there are any eternal laws of nature? That was just a church dogma enunciated by Aquinas in Summa Theologica.  (Recall how a priest given a PhD in philosophy of science by Cambridge tried to turn the classroom into a pulpit, at Universiti Sains Malaysia, but could not state a single eternal law of nature when repeatedly challenged to do so.) Of course, a non-mechanistic physics is possible, as I have shown.

More subtle is the creep of superstitions into science through the metaphysics in formal mathematics, falsely declared to be universal (or superior) with the help of false myths like those of Pythagoras and Euclid PLUS false myths of the deductive proofs in the Elements PLUS false myths about the infallibility or superiority of deductive proof.

However, colonised minds, who believe in and propagate these superstitious beliefs, are terrified when asked to publicly explain why 1+1=2 in formal math. So far, no formal mathematician, anywhere in the world, has shown the guts to try to defend formal math in public. That itself tells everyone that the truth is with normal math.

Here is the initial part of the very interesting conversation in Soweto (3.5 MB mp3 file) and a photo of the participants.

Trailer of conversation in Soweto

Participants in Soweto meet

The Scroll and racist censorship: an open letter to the Scroll Reader’s Editor

Friday, November 4th, 2016

4 Nov 2016

Dear Dr Rammanohar Reddy,

Thank you for your response.

  1. I was under the impression that the Reader’s Editor is not a mere glorified post box, to forward mail to the editor, as you say you have done. In the event of a disagreement with the editor, I imagined that the Reader’s Editor performs an independent function. In the present circumstances there are several issues, as listed below.

  2. My article was taken down by Scroll.in when the Conversation took it down. There was no legal requirement to do so, since the Conversation articles are under a Creative Commons license. Please give your judgment on whether the failure on your part to exercise independent editorial judgment in taking down the article is justified.

    1. The wider context of the article is a big political agitation going on in South African universities where whites dominate the academic system (only 5% of black students succeed in higher education).

    2. The immediate context is false history which was the traditional justification for the promoting the belief in racial superiority of whites, and was explicitly used for that purpose by numerous prominent Western philosophers such as Hume, Kant, Hegel etc. Macaulay similarly justified colonialism using the same false history. My article challenged an earlier article in Conversation which reiterated that false history saying “Much, though certainly not all, math was the creation of dead white men”.

    3. I asserted, to the contrary, that people should stand up to the false history and bad philosophy of math. Under these circumstances even a political novice would have been sceptical of a vague “editorial reason” offered for taking down an article which went viral. That was an unambiguous act of censorship. And your act of taking down the article, without applying your mind, amounts to extending support for that censorship to defend the claims of racist history. If there was anything wrong in the article you could have have carried a rebuttal. That would have given correct information to your readers instead of mere insinuations used by you to support racist history (whatever your intentions).

    4. In fact, there is no way to contest my claims on factual grounds. My Rs 2 lakh prize for Euclid stands unscathed, even after the article was pulled down. You or your readers are welcome to try their hand at it. But instead you have chosen to insinuate that there was something wrong with the article.

    5. So, once again, please state your judgment as Reader’s Editor whether the Scroll editor erred in taking down the article without applying his mind to its contents and to the political context of the prevalent racism in South Africa, which my article provided a concrete way to oppose.
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Protest against racist censorship

Friday, November 4th, 2016

False history of the kind that “Much, though certainly not all, mathematics was the creation of dead white men” has been traditionally used to defend racism. My Euclid challenge prize for Rs 2 lakhs is offered to demonstrate that this racist history is based on faith not any facts. Therefore, the only way to save that rotten history is to prevent its articulation. Hence the Conversation took down my article “To decolonise math, stand up to its false history and bad philosophy.” Here are two protest letters and an article.

1.Protest letter to Conversation from Decolonial International Network

2. Protest letter from Mr S. M. Mohamed Idris, Chairman, Citizens International, to International Association of Universities.

3. Note on censorship of decolonised math.

As a mark of protest against this censorship do reproduce the  original article re-posted at http://ckraju.net/blog/?p=117. Or link to it. Feel free to reproduce the protest letters, (more…)

Afraid of the truth: article against racist history and bad philosophy taken down for MANIFESTLY FALSE and frivolous reasons, which Conversation hides to insinuate

Friday, October 28th, 2016

Synopsis: My article “To decolonise math stand up to its false history and bad philosophy” published in Conversation (Global edition) became very popular, but was then taken down on “editorial grounds”. These “editorial grounds” did NOT relate to a single factual flaw or defect in my argument. The “editorial” ground stated in an email from an editor Southey, was this: “you have sited [sic] only your own work to back up your key points.” This frivolous editorial reason is NOT stated publicly just because it is manifestly false (my article did cite plenty of others), so stating it publicly would immediately expose the dishonesty involved in taking down the article. Before announcing the decision to take down the article, no one asked me to explain my side, presumably because asking me would have brought out the truth on record. Such an editorial reason is especially comic in the context: thus, my article principally aimed to rebut Brodie’s earlier article on decolonisation of math which had very carelessly neglected to cite a huge amount of my prior work on the decolonisation of math and science, work which easily shows up even on a Google search. That large amount of my earlier work therefore HAD to be cited in my article. The flaw was in Brodie’s careless article, not in my attempt to rectify that carelessness.

The real reason why my article was taken down is that it was a dangerous piece of dissent. It  hit a crucial weak spot in claims used for racist and colonial domination: the false history which was traditionally used to support the bad philosophical claims of “superiority” whether of the white race or of formal math. The article knocked out the prejudices needed for racist and colonial domination, prejudices of the kind accepted also by those who are not explicit racists. My article explained that a decolonised math is possible; taking it down is also an attempt to derail and misguide the push for decolonisation of universities in South Africa. Hiding the public articulation of the exact “editorial reason” for taking down the article helps preserve racist prejudices in the only way possible: by insinuation, not by appeal to facts or arguments. Had any easy refutation of my deeply researched article been possible, the editors would have simply published a rejoinder, not taken down the article. Such editorial excesses aptly illustrate the weaknesses of the Western academic tradition, which allowed the concoction of racist history in the first place.

The background

In an article in the Conversation, Karen Brodie made the absurd statement that “Much, though certainly not all, of mathematics was created by dead white men”. There is nothing new about this absurd claim: numerous “reputable” Western philosophers, such as Hume and Kant have used this argument from false history to assert the non-creativity of blacks, to morally justify racism and slavery. Likewise, Macaulay used the same false history to assert the non-creativity of the non-West in science, to impose colonial education. That education was designed to created a slave mentality1 which the British very much needed to offset their military weakness as colonisers.

To contest the roots of racism and colonialism it is, therefore, necessary to contest this argument from false history, especially the false history of mathematics and science. This is what I did in my article “To decolonise math stand up to its false history and bad philosophy”, published in Conversation (Global edition) on 24 October. In fact I went a step further. I pointed out that the claim that Western math is “superior”, since based on deductive proof, is analogous to claims of racial superiority: not only is there no evidence for Euclid, there are no deductive proofs in the book Elements he supposedly wrote, AND deductive proofs are inferior and more fallible than empirical proofs, contrary to the deep-seated but erroneous belief in Western philosophy. (more…)

To decolonise math stand up to its false history and bad philosophy

Wednesday, October 26th, 2016

[This article was first published in the Conversation (Global edition) on 24 October 2016. It quickly reached a readership of 16737, before being taken down, obviously because it represents a dangerous piece of dissent against racism and colonialism. For more details see the next blog post. ]

A false history of science was used to initiate colonial education, in support of colonialism. This false history persists. In a recent article about decolonising mathematics, for instance, Professor Karen Brodie asserts that “Much, though certainly not all, of mathematics was created by dead white men.”

This is not true.

A false history

Consider the most elementary mathematics of fractions. Did the white man invent it? No. The Rhind papyrus shows that black Egyptians knew about fractions from at least 3700 years ago. Moreover, Greeks and Romans did not: there is no systematic way to represent fractions in traditional Greek and Roman arithmetic. Europe imported the arithmetic of fractions, and it came into the Jesuit syllabus only around 1572, and the white man finally started learning what Ahmose the scribe was teaching black children 3000 years earlier.

What mathematics could “dead white men” have created without even a knowledge of fractions?

Of course, Western historians have long claimed that “real” math was invented by Greeks: Pythagoras, Euclid and so on. However, Pythagoras is myth and there is no historical evidence for Euclid, as I’ve explained in my book Euclid and Jesus.

The “evidence” for Euclid is so thin, that I’ve instituted a challenge prize of around R40,000 for serious evidence about Euclid. This stands unclaimed and has done for several years.

Further, though the text Elements (which Euclid supposedly wrote) comes from Alexandria in Africa, its author is commonly visualised as a white man. But it is rather more likely that the anonymous “author of the Elements” was a black woman.

When this is pointed out, some people try to save the myth: they say they don’t care about the author, only the book. However, it is another false Western myth that the book Elements is about deductive proofs. The actual book contains no pure deductive proofs. Its very first proposition is proved empirically, as is its fourth proposition (the side angle side theorem), needed for the proof of its penultimate proposition (“Pythagorean proposition”).

Deductive proof doesn’t lead to valid knowledge

Stripping off the false history exposes the central philosophical claim: that “real” math is about deductive proofs which are infallible and lead to “superior” knowledge. However, that claim too is false: deductive proofs are fallible. So an invalid deductive proof can be easily mistaken for a valid one. For centuries, the most authoritative Western scholars collectively made this mistake, when they wrongly praised “Euclid’s” Elements as a model of deductive proof.

Worse, even a validly proved mathematical theorem is only an inferior sort of knowledge, since we never know whether it is valid knowledge. For example, the “Pythagorean theorem” is not valid knowledge for triangles drawn on the curved surface of the earth. However, Europeans kept applying the “Pythagorean theorem” to such triangles to determine latitude and longitude on their navigational technique of “dead reckoning”. This led to centuries of navigational disasters and made navigation – and determination of longitude – the key scientific challenge for Europeans from the 16th to the 18th centuries.

In fact, a mathematical theorem need have no relation at all to valid knowledge. For example, we can easily prove as a mathematical theorem that a rabbit has two horns: 1. All animals have two horns. 2. A rabbit is an animal. 3. Therefore, a rabbit has two horns. This is a valid deductive proof, but is the conclusion valid?

Mere deductive proof does not lead to valid knowledge. We must check whether the assumptions are true. In this case the assumptions are false: simply point to an animal which has no horns. However, formal math forbids such commonsense, empirical proofs, based on its central dogma that deductive proofs are “superior”.

Anyway, the postulates of formal mathematics, say set theory, cannot be empirically checked. So formal mathematics is pure metaphysics. The only way to check its assumptions is to rely on authority – and in practice we teach only those postulates approved by Western authority. For example, calculus is done with formal real numbers (and not Indian non-Archimedean arithmetic, or floating point numbers used in computer arithmetic). School geometry is taught using Hilbert’s far-fetched synthetic postulates, not Indo-Egyptian cord geometry.

A slave mentality

Thus, formal mathematics creates a slave mentality. It creates a person who blindly relies on Western authority and conflates it with infallible truth. So finding better ways of inculcating that slave mentality – teaching the same maths but differently, as Brodie proposes in her article – is absolutely the last thing we should do.

False claims of “superiority” are a trick to impose Western authority, exactly as in apartheid. Everyone understands 1+1=2 in a commonsense way. But Whitehead and Russell took 378 pages in their Principia to prove 1+1=2. Declaring such mountains of metaphysics as “superior” knowledge has political value. People who cannot understand those 378 pages “needed” for 1+1=2 are forced to trust an “expert”.

The entire colonial tradition of education teaches us to trust only Western-approved experts, and distrust everyone else. This creates epistemic dependence for even the simplest things like 1+1=2, making epistemic dissent impossible.

But epistemic dissent is central to decolonisation. And much work has already been done to decolonise mathematics.

A successful alternative

There is an alternative philosophy of mathematics, consolidated in my book Cultural Foundations of Mathematics and now renamed zeroism.

It rejects the Western metaphysics of formal mathematics as religiously biased since the days of Plato, who related mathematics to the soul. Actual teaching experiments have been performed with eight groups in five universities in three countries – Malaysia, Iran and India.

This decolonised math is so easy that the calculus can be taught in five days. Work on this approach to decolonising mathematics and science has been reported in various meetings on decolonisation organised by the Multiversity. It was publicly discussed in newspapers, and blogs, and prominently reported in newspapers, magazine articles, interviews and videos.

Decolonised math rejects the redundant metaphysics of formal math as inferior knowledge. It reverts to a commonsense practical philosophy of mathematics as a technique of approximate calculation for practical purposes. By making math easy, it enables students to solve harder problems that are usually left out of existing courses. It also leads to a better science, the simplest example being a better theory of gravitation arising from correcting Newton’s wrong metaphysical presumptions about calculus.

(CK Raju explains how decolonised maths leads to better science. [Click image to go to video of MIT talk])

In short, math can be decolonised. The simple way to do it is to have the courage to stand up to its false Western history and bad Western philosophy, and focus solely on its practical value.

Author’s note: Publication details for cited references are available here.

Conversation with the Dalai Lama

Wednesday, October 26th, 2016

The video of my conversation with the Dalai Lama is now on You Tube.

still

It is also still available on the official site .

Reports of this appeared in Tibet Post,

Tibet Post

and in the Sunday Guardian

and sundry news agency reports.

Videos of MIT and IISc talks

Thursday, January 28th, 2016

The video of my MIT talk is now online at Calculus: the real story

The abstract and presentation were put up on an earlier blog
http://ckraju.net/blog/?p=106

The video of my talk at Indian Institute of Science is also online Calculus: ganita or math?

Ganita vs mathematics: Ten myths of Western math

Tuesday, November 17th, 2015

Note: Am locked out of my website. The following “abstract” is for the forthcoming 39th Indian Social Science Congress, Mangalore, a talk at Indian Institute of Science, Bangalore, and an international meeting on plurality in math in Kolkata. The idea is to talk and discuss publicly, not publish in secretively reviewed journals.

Ganita vs mathematics

Ten myths underlying formal math and the need to reject them

C. K. Raju

Centre for Studies in Civilizations, New Delhi

Extended abstract

We reject the myth that Western math is universal. That was always a normative universality: while it was admitted that other ways of doing math existed, it was claimed that Western math was “superior”. This claim of “superiority” (e.g. the claim that metaphysical proofs are “superior” to empirical proofs) rests merely on some anti-scientific church dogmas born of hate politics. Further, the purported “superiority” of Western math, exactly like racist claims of “superiority”, is supported by the very same fabricated church/racist/colonial history (e.g. the myth of Euclid and the myth of his deductive proofs).

Any serious study of plurality in math must critically re-examine other ways of doing math, and select the better way of doing math. Which math should be taught in schools and universities? We cannot just assume that existing (colonial) math education should persist. Nor even can we continue to justify it merely on unexamined Western myths and dogmas, even if they are widely believed today (just because colonial education propagates them). Indeed, since math is taught as a compulsory subject in schools today, if the present way of teaching it rests on (and subtly propagates) religious dogmas, and related myths, as it does, its teaching must be changed in schools in any secular country.

To this end, of deciding which math is better, we compare formal math with religiously-neutral Indian ganita (together with the explicit philosophy of zeroism). We have selected ganita not for reasons of its Indian origins, but because it concerns practical value, which is surely more universal than Western dogmatic metaphysics. Further, most math taught in schools today (arithmetic, algebra, trigonometry, calculus, probability) historically originated as ganita. Also, those same ganita techniques of calculation continue to be used today for almost all practical applications of math to commerce, science and engineering (and indeed in all computer-based numerical calculations, such as those used to send a spacecraft to Mars, or to make stock-market predictions).

While the West imported ganita for its practical value, its epistemology clashed with the religiously-loaded epistemology of math in the West (e.g. all computer-based numerical calculations are today declared “erroneous”). Ganita was made theologically correct by (a) giving it a veneer of metaphysics (e.g. the use of metaphysical limits in calculus, to align its notion of infinity with church dogmas about eternity), and (b) packaging it with a false history (e.g. that Newton and Leibniz invented the calculus). This cocktail of practical value, religious metaphysics, and false history, was just declared “superior” and globalised by colonial education. Selecting ganita over formal math preserves the practical value, while eliminating the false history and bad metaphysics. Indeed practical value is enhanced: e.g., eliminating Newton’s conceptual confusion about calculus leads to a better theory of gravity. Or, e.g., teaching calculus as ganita enables students do harder problems.

However, the bad metaphysics and false history, underlying formal math, is a key part of colonial indoctrination (“education”). The indoctrinated cling to myths: when one myth is challenged, they try to “save” it by appealing to another (e.g. if the myth of Euclid is challenged they invoke the myth of deductive proofs in the Elements). Hence, to decolonise, the whole collectivity of myths must be simultaneously denied. If this denial is to be intelligible, it cannot also be brief: for brevity assumes shared beliefs. Thus a demand for brevity, in this context, becomes a trick to block dissent.

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Education policy, secularism and traditional values

Monday, November 2nd, 2015

Many traditionalists whether in India or in Iran regard secularism in education as the biggest enemy of traditional values. (A recent example of this thinking is Bharat Gupt’s article posted at http://indiafacts.co.in/religious-pluralism-and-distorted-notions-of-secularism-in-education/ )  These traditionalists are dead wrong: the church has succeeded so well because those it considers its biggest enemies don’t even recognize it as an enemy.

The biggest enemy of traditional values are the church dogmas, which have crept even into mathematics and hard sciences, and which are so much a part and parcel of colonial education.

The primary problem facing Indian education today is that it is a thoughtless continuation of colonial education, which itself was a continuation of church education. (The first bill for secular education in Britain dates to 1872, so Western education was 100% church education when it first came to India.) Church education, designed to produce missionaries, teaches subordination to church/Western authority. That suited colonialism but does not suit a free country.

Decolonisation of education is needed even in the hard sciences such as mathematics and physics. Few have noticed that church dogmas creep even into mathematics and science as taught in our universities today. For example, physics uses differential equations which require calculus. But calculus as taught in our universities requires that time should be like the real line. However, all Indian values, especially the value of moksha (or nirvana), are based on the notion of quasi-cyclic time.1 So, just teaching calculus, in the present way, teaches that those Indian values are fundamentally wrong and anti-science, hence lack credibility.

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