Archive for the ‘History and Philosophy of Science’ Category

The Kerala school vs calculus teaching today

Wednesday, August 16th, 2017

As pointed out in the previous post, calculus started not with the Kerala school but with the dalit Aryabhata, of Patna, in the 5th c. The Aryabhata school in Kerala acknowledged him as their master, and Nilakantha somasutvan wrote a commentary (bhashya) on the Aryabhatiya. To repeat, the Indian calculus was a pan-India development, and NOT a product of the Kerala school alone.

In particular, though infinite series are an easily recognized aspect of calculus, the emphasis on them is misleading, especially for the purpose of teaching Indian calculus in universities today. The above quote in the earlier blog post continues:

“Further, if we teach the Indian calculus today in universities (as I do) the focus will be only on what Aryabhata did. So, the plagiarists’ false understanding of history also prevents us from reforming calculus teaching today. Neither of the plagiarists understands the calculus well enough to teach it.”

Another quote, in the earlier blog post, closely related to this is the following.

“Like all plagiarists, Joseph and Almeida made horrible blunders while restating my thesis (stated in the Hawai’i paper,1 that the calculus developed in India with a different epistemology). For example, in one of their papers in Race and Class they asserted “the Kerala mathematicians used the floating point numbers”, used in modern-day computers. Ha! Ha! Ha! What a joke! Only complete ignoramuses like the two plagiarists could have thus misunderstood my thesis about floating point numbers stated in my Hawai’i paper, which was part of a course on C-programming that I was then teaching as Professor of computer science.”

No doubt this was a blunder, but why was this a horrible blunder? Because a different number system was at the heart of the Indian method of summing infinite series, but Europeans did not understand it (and did not understand how to sum infinite series), and Western historians like Plofker do not understand it till today.

This lack of understanding of Indian calculus by Europeans had serious consequences: it led to the failure of Newtonian physics. I have analysed Newton’s error in understanding the Indian calculus, the consequent conceptual error in the notion of time in his physics, responsible for the failure of his physics, and proposed a corrected theory of gravitation.2 (An expository account of the new theory of gravitation is also available.3) The point about floating point numbers used to do calculus on computers is further explained in the course of this analysis, as is the point about avyakt ganit. Floats are a finite set, smaller than formal reals, with no recognizable algebraic structure, because the associative law fails even for addition; avyakt ganit results in a “non-Archimedean” ordered field larger than formal reals. Calculus can be done with number systems smaller or larger than formal reals, university calculus as taught today is not the only way to do calculus as some foolish historians assume.

The matter is simple, the Indian use of avyakt numbers very naturally led to avyakt fractions which are today called rational functions and correspond to the use of so-called non-Archimedean arithmetic. (more…)

Kerala school vs Bihar university

Wednesday, August 16th, 2017

The previous blog post contains two important points which need some elaboration. The first is elaborated in this post the second in the next.

To quote:

“They made out the Indian calculus to be solely a product of Kerala, when in fact, as explained in my book, it originated in Patna, in the 5th c., with Aryabhata, a lower caste person. The Kerala school certainly developed it further (and these highest-caste Brahmins from the south, such as Nilakantha Somasutvan, had no difficulty in honestly calling themselves disciples of the low-caste Aryabhata from the north). Even the later achievement of Madhava involved essential inputs from Narayana Pandit of Benaras, as explained in my calculus book. That is, the Indian calculus was a pan-India development, and NOT a product of the Kerala school alone. But, this important story of national integration across regions and castes, in pre-colonial India, is lost in the story of regional chauvinism personally profitable to the thieves who did not understand the subtleties of what they stole.”

The reference to Aryabhata as a lower-caste person is explained in this article first presented at a seminar on “Dalit Narratives in Philosophy”, at Patna, and variously published.

The infinite series from Kerala are known to Western scholars since the 1832/1835 paper of Whish. These include the sine series claimed by Newton and the series for π claimed by Leibniz. These claims of “discovery” were based on the genocidal Doctrine of Christian Discovery, that a piece of land (or knowledge) belongs to the first Christian to spot it. (As in the beliefs that Columbus “discovered” America or Vasco da Gama “discovered” India, so also in scientific discoveries.) As the US Supreme Court observed, though this was a papal doctrine, Protestant countries like Britain (from which US inherited its laws) fully accepted it. Newton implicitly referred to this doctrine when he called Leibniz the “second discoverer” of the misnamed “Leibniz” series or the equally misnamed “Gregory” series, chauvinistic nomenclature, a Western mumpsimus which must be abolished.

Because colonial pride and power were both based on false history (of early Greeks, “the friends of Christians” as Eusebius called them, followed by such Christian “discoveries”), the finding of infinite series in India was a shock. Since infinite series are an easily identifiable aspect of calculus, today, many people who do not properly understand the calculus, have taken up the refrain of the “Kerala school”.

However, how were the Indian infinite series summed? No one else has given an answer. Not when the calculus first went to Europe in the 16th c. Not in the last two centuries since Whish. The only answer is the one I have provided. (more…)

George Joseph: serial plagiarist

Tuesday, August 15th, 2017

1-The fraud-news blitz

Ten years ago, on 14/15 Aug 2007, on the 60th anniversary of India’s independence, PTI London released a piece of fraud news. All major newspapers in India prominently carried it, Hindustan Times on the front page, The Hindu on the back page etc. According to the news, two British researchers from Manchester and Exeter universities had established that the calculus developed in India before Newton. But they added that this left Newton’s greatness unaffected.

The news was based on a press release posted on the Manchester university website (now removed from its site, since it was a fraud, but archived here).

The news was also carried internationally, for example, by the London Telegraph. I phoned them, and pointed out that I had recently published a whole book dealing with the transmission of the calculus. Cultural Foundations of Mathematics (Pearson Longman. 2007). The subtitle of the book itself said this: it was “The nature of mathematical proof, and the transmission of the calculus from India to Europe in the 16th c. CE”. The book emphasized the development of calculus in India with a different philosophy of mathematics, and its theft by Cochin-based Jesuits. This theft of knowledge was carried out to solve the major scientific challenge then facing Europe: navigation. But, after stealing it, the same churchmen wrote utterly false histories glorifying the West by claiming that Newton and Leibniz invented the calculus. Colonialism was built on this false history, not any technological superiority, as I have explained elsewhere.

My calculus book was the culmination of a ten year effort since 1997, partly funded by two agencies: the Indian National Science Academy since 1998 (Project on Madhava and the Origin of the Calculus), and the Project of History of Indian Science, Philosophy and Culture, with which I was associated since its inception in the early 90’s, but accepted an Editorial Fellowship only in 1999. The 500-page book (an authored volume, not an edited volume) was the 50th volume in the PHISPC series.

When I brought this to the notice of the London Telegraph they said they had not checked the news, and removed the fraud news item from their website.

In Hindustan Times the front page news carried the signature of Vijay Dutt their London correspondent.

HT front page news
I contacted the HT office, and further pointed out that one of the purported authors of the Manchester paper had been earlier involved in plagiarising my work and warned in 2004 by Exeter University. The HT had given prominent coverage to that news in 2004.HT plagiarism report 8 Nov 2004

(If the above is difficult to read, download the pdf file posted here.) (more…)

Myth, math, and censorship

Thursday, August 3rd, 2017

My article on “Mathematics and censorship” appeared in Kafila on 25 June 2017.

The original censored article “To decolonise math stand up to its false history and bad philosophy” was first published in the Conversation (global edition), in October 2016. It went viral and was removed by the South Africa editor on the lame ground that “You sited [sic] yourself”. Meaning, you brown man, what right do you have to talk of a new philosophy of mathematics? What right do you have to demand evidence for Greeks like Euclid? What right do you have to say that mathematics may have had a black mother not a white father? Don’t you know Conversation boasts of academic rigor, and that means you can only cite the work of others approved by White/Western reviewers. That is our (unstated) editorial standard.

In India the censored article was re-published by Wire and Scroll. Both took it down when the Conversation did. But Wire put it back with an apology. The article currently survives here on this blog, on Wire, and on Science 2.0. The article was recently reproduced in full as part of a peer-reviewed scholarly article published in Journal of Black Studies, a draft of which is available online.

To reiterate the Conversation failed to find anything wrong with the article. It was unable to refute a single point or a single sentence in the censored article. So, the real reason to censor the article was to protect vested interests. What are those vested interests?

One such vested interest obviously relates to White domination, which persists not only in post-apartheid South Africa but elsewhere. On a myth that is still taught to Indian school children “Euclid” is declared the father of mathematics and our school texts carry an image of him as white-skinned.

However, as my censored article pointed out, there is nil evidence for the very existence of Euclid leave alone for the color of this skin. I objected to it, but the NCERT did nothing; Narlikar, Sinclair and Co,  wanted to propagate false stories. To drive the point home, I then offered a prize of Rs 2 lakhs for the slightest serious evidence about Euclid. No one claimed the prize.

Obviously there is ample counter evidence that the book Elements attributed to Euclid, was written long after his purported time, by someone else, a woman who was in all probability black as portrayed on the cover of my book Euclid and Jesus.

Black mother of math?

This “black mother of mathematics” was raped and killed on the altar of a church (though the censored article did not mention this last fact because it was tightly edited in collaboration with the Conversation editor and limited to 1000 words,). Myths are a source of power, so this attack on their myths enraged the racist Whites in South Africa. They first tried the usual technique of “proof by abuse”. When that failed, censorship was applied.

However, the actual vested interests are deeper than one imagines. (more…)

Decolonising math and science: Amsterdam

Saturday, July 8th, 2017

My talk to the Critical Collective co-organized by the New Urban Collective and the University of Color at the University of Amsterdam on Decolonising mathematics and science.

This was followed by an interview with Grapevine TV.

Decolonising time: Time at the interface of science and religion

Saturday, July 8th, 2017

A video of a talk at Berlin. Berliner Festspiele, MaerzMusik festival, “Thinking together: Decolonising time”.

Some people with attention-span restricted to the twitter limit thought this was only about the calendar. So, here is the abstract: Decolonising time: time at the interface of science and religion, and the full presentation.

Here is the video.

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

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 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…)