Archive for the ‘History and Philosophy of Mathematics’ Category

Rajju Ganit workshop from today

Monday, June 25th, 2018

We have never re-examined our math education since independence to eliminate the trash myths and bad philosophy brought in by colonial education. Since people don’t understand the problems at the level of the calculus, this workshop takes up issues at the school level. For links, download the pdf of the poster.

Rajju Ganit poster p 1
Rajju Ganit poster p 2

The racist (and church) strategy: censor and defame, do NOT debate

Saturday, June 23rd, 2018

Racists are stupid nitwits. The whole business of racism is based on a stupid lie that people with a certain colour of the skin are superior. I thought everyone understood the stupidity of racists.

Therefore, at a recent meeting in India, I was surprised when a couple of young people used the polemic of “conspiracy theory”. This was the polemic used by the racist press in Cape Town which attacked me in the manner of a racist lynch mob. Of course, the press report did not and could not specify what conspiracy theory I was accused of. Nor even did it name any stupid racist as the actual source of that polemic, since it was indefensible.

Obviously, anyone who believes that polemic of “conspiracy theorist” without the slightest evidence is even stupider then the racists themselves. It is one thing that young people mindlessly believe Wikipedia. It is another that they believe what is so obviously trash racist propaganda. It is this sort of gullibility which led to the persistence of racism for centuries.

The simple fact is that the racist academics in UCT were frightened by my challenge to them to openly debate the decolonisation mathematics and science. They ran away from open debate, which would have exposed their inadequacies. It was to justify running away from debate that they planted that racist press report. Obviously in a press report they were free to state any kind of falsehood and stupidity, without fear of contradiction. They hoped (perhaps correctly) that there would be enough gullible people to believe them. Running away from debate was the same church strategy of censoring heretics used by the editor of Conversation who censored my article on decolonising mathematics. Defame, do not debate, is their strategy, just because they know they would lose an open debate. Nobody could point to a single error in my censored article. Nobody could even claim my Euclid prize in so many years. And formal math is based on that silly church myth so they cannot junk it.

The real reason for the great fright in UCT was my challenge to GFR Ellis, of the UCT math department. He co-authored Stephen Hawking’s serious book, and got the Templeton award for putting together science and religion. In my UCT lectures, I objected strongly to the claim that general relativity (and particularly Hawking’s singularity theory) proves the truth of Judaeo-Christian theology and its notion of creation. I argued that the work of Hawking and Ellis is an example of thoroughly bad science which can be decolonised. I explained (as in my book Eleven Pictures of Time) that such bad science is the result of church metaphysics in formal math. Eliminating that metaphysics would decolonise mathematics and science.

Obviously, not only racists but also the church was afraid that an open debate on this issue would expose the trick of using science to support church theology. This is a trick which few people understand, since few people (perhaps 4 or 5 in the whole world) understand singularity theory.

Ellis shamelessly operated through his pliable student Murugan, to plant more lies against me. The hope was that using an Indian-sounding front would confuse people. My point was that my five day course on calculus makes math easy and hence enables students to solve harder problems such as elliptic integrals not covered in usual calculus courses. Murugan brazenly lied that teaching elliptic integrals is Bantuization. Obviously he would have been laughed out of existence had he tried to use that lie in an open recorded debate. Obviously also, as Fanon emphasized, there is no shortage of nonwhites who wear white masks and effectively turn into racist boot-lickers. Murugan does not care if blacks in South Africa do not get quality education in math, and works to ensure that they remain forever subordinate to Western authority.

As an easy example of bad math, in my speech at UCT I said invisible geometric points are as unreal and foolish as the emperor’s new clothes. The racist reporter thought he could deal with that. He justified the use of invisible points by (1) foolishly confounding invisible with infinitesimal (I reject invisible, but advocate “infinitesimals” ) and (2) claiming that mathematicians “routinely” handed the invisible. (Of course, the reporter could not explain the magic used by mathematicians to deal with invisible points, or how ordinary persons could measure the distance between two invisible points; as I said racists are stupid and will tell any lie and believe anything, so long as it serves their interest.) Conflating invisible with infinitesimal was particularly foolish because current university calculus uses “real” numbers which have no infinitesimals. But the mathematical authority he relied on was too ignorant, and of course I was not allowed to respond: the whole point was to suppress debate.

Hunting for invisible points

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Stephen Hawking: Genius or crook?

Thursday, April 5th, 2018

Faustian pact?

Millions of people across the world have heard of Stephen Hawking, whose recent death hence made headlines.   Everyone speaks of his ALS. But is it proof of his indomitable will? Or did he hence make a Faustian pact with the devil incarnate: the church? Daring to raise this question will doubtless arouse the rage of his admirers. But if we weigh it against the possibility that millions have been deluded using their trust in science, it is our public and ethical duty to raise the question. To answer the question Hawking’s disease is irrelevant, and we need to examine the merits of Hawking’s scientific work dispassionately.

Widespread ignorance

But it is near impossible to do so. While millions revere him, very few understand the mathematical intricacies about calculus related to his work, especially on Penrose-Hawking singularity theory. That theory was the basis of his best-selling book A Brief History of Time. The widespread ignorance about it became starkly obvious during my debate with Roger Penrose, in Delhi, in 1997, attended by various professors of physics from Delhi University and JNU whose blank faces told the story.

What the vast majority believe is a story about science, a story they blindly trust. So deep is their trust that, from a position of ignorance, they are quite certain a contrary opinion is not to be trusted! “Millions of people believe this, they can’t all be wrong can they?”.  Such a “proof by numbers” is convincing because it has survival value, as explained in my book The Eleven Pictures of Time: there is often safety in being part of the herd. But this psychology also provides an easy route to propaganda to fool a mass of people.  For centuries, millions of Westerners fervently believed in the idea of a powerful God who appointed the church as his broker. The belief persisted just  because the church reviled any dissenters as heretics and atheists, and, for centuries, killed them most brutally.

The Christian theology in Hawking’s work

Therefore, common sense may be a better guide to the truth than guesswork based on trust. What even the most gullible person cannot fail to notice is the way singularity theory connects to the notions of a Judeo-Christian God and a specifically Judeo-Christian notion of creation.

I have pointed this out repeatedly over the last twenty years, but the faithful, and our secular liberals, just ignore it. So, it is necessary to point it out yet again. Hawking’s popular book was preceded by an academic book, The Large Scale Structure of Space-Time, which he co-authored with G. F. R. Ellis who won the Templeton award for connecting science and religion. That book concludes that the cosmos has a singularity. What does that mean? The authors interpret it to mean a moment of creation. The bottom line of the book [p. 364] asserts: “the universe began a finite time ago. However, the actual point of creation, the singularity, is outside the presently known laws of physics.” God created the cosmos and then set the clockwork of eternal laws in motion.

For those who don’t understand this, the meaning is made explicit in a book co-authored by Hawking, “A briefer history of time”. It explained [p. 141] that:  “At the big bang and other singularities, all the laws [of physics] would have broken down, so God would still have had complete freedom to choose what happened and how the universe began.”
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Decolonising mathematics and science: new reading list

Thursday, March 29th, 2018

Q. 1. I would like to know how I can decolonise myself mathematically. (I am an Aircraft Maintenance Engineer with engineering back ground.)
Q. 2. Do u suggest any videos of yours or any books? subsequently how I could prevent my kids from mental colonization.
A.

Step 0.

Proposed videos. The general good news is that I plan to produce a series of videos aimed at school children to prevent their indoctrination through colonial/church school texts. Hope to get them out within the next 3 months.

Step 1.

Read the non-technical accounts. A good starting point is 1000 word article for the layperson which went viral but was censored. The full version is still available on my blog.

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

As the first lesson in decolonisation, ask yourself: why was an article on mathematics censored after publication? Did it contain obscenity? And if there was something wrong in it why was anyone unable to point to a single mistake till now? As for people, they protest censorship of sex but not of mathematics: why?

Journalists mould your opinion, but today’s journalists look at the social backing, not the evidence. They call it “quality control” (meaning social control).  At least one editor did apply his mind, at  the Wire which put back the article (but forgot about the key issue of philosophy included in the title). Similarly,  Science 2.0 highlighted the claim that “Euclid” was a black woman, obviously something to be censored in South Africa.

Decolonisation is NOT only about history alone. Another philosophy is important for the contemporary value of decolonised math and science. So, why is it taboo? A preliminary exposition is in the article on

Mathematics and censorship

In short, there are two issues regarding math: (1) the myths, and (2) the superstitions surrounding formal (Western) math.

The myths

Myths are the anchor of superstition. If you have heard a story, such as that of Euclid, and have no evidence, it is probably a myth. Here is an easy book on myths: the myth that science is Western in origin.

Is Science Western in Origin?

It is available on Kindle and from the Other India Bookstore, Goa. Hindi version from Daanish Books, Delhi, and Multiversity, Penang. It is suitable for children (but they should skip the scholarly preface by Vinay Lal).

The superstitions

For some 1500  years, Western civilization was dominated by the church, whose power is based on falsehoods. It is an idle fantasy of the colonised mind that this effect of the church just disappeared overnight. The manifest fact is that the church is still powerful in large parts of the world, including the US. And the West is still steeped in church myths and superstitions which creep even into science in a variety of ways, especially through math. (more…)

Cape Town “debate” exposes Stephen Hawking’s racist co-author

Tuesday, February 20th, 2018

The panel discussion at the University of Cape Town (UCT) achieved something important: it exposed Stephen Hawking’s co-author G. F. R. Ellis, a star of the racist apartheid regime. He ran away from UCT debate, because he could not defend through open debate the awful church propaganda he along with Hawking and some others have been trying to promote as great science.

My long-standing critique of the book Large Scale Structure of Spacetime, by Stephen Hawking and G. F. Ellis is in my book the Eleven Pictures of Time (Sage, 2003). The critique is this: Hawking and Ellis use bad math (bad calculus) to support church dogma. They interpret a cosmological singularity as a moment of Christian creation, as in the Bible story. That is the bottom line of their book:

the actual point of creation, the singularity, is outside the scope of the present-day laws of physics”.

In his popular book Brief History of Time, Hawking explained this further. The breakdown of the laws of physics at the “moment of creation” would leave God free to create the laws and world of his choice. For this piece of trash, Ellis got the million dollar Templeton award for putting together science and religion.

Tipler, who published in the “reputed” journal Nature, furthered this trash thesis. He said singularity theory proved

“Judeo Christian theology is part of physics”!

More recently, I tried to explain some of the implications of such claims in my review of Hawking’s latest book, which review was published as a full-page article in the newspaper DNA as “The Christian propaganda in Hawking’s work”.

These singularities involve bad math in two ways.

(1)  Hawking and Ellis use a bad postulate (chronology condition, exactly like the church curse on ‘cyclic’ time, which postulate they justify using Augustine’s bad critique of Origen).

(2) Secondly, they use a bad understanding of calculus (that differentiating a discontinuous function leads to singularities on the equations of general relativity).

Long ago, in 1997, I debated these aspects of singularity theory publicly with Roger Penrose, and no one could refute my published arguments for the past 15 years.

Specifically, I explained long ago (in 1988) how singularities in general relativity can be easily handled using non-standard analysis. More recently, I explained, as in the appendix to Cultural Foundations of Mathematics, that the non-standard analysis can be replaced simply by non-Archimedean arithmetic with which the Indian calculus developed.

I recapitulated the above arguments in the UCT panel discussion. The point was to explain how bad math is used to create bad science. I expected to debate further in the math department, the next day, on the technical aspects as my abstract shows.

But Ellis was frightened sick at the prospect of an open debate with me would crush his lifework. He was also afraid that would expose him. He knows he is mathematically too incompetent to tackle the points such as non-standard analysis raised by me.

So, he resorted to a simple but unethical device within his technical competence: he used his student Jeff Murugan as a sock puppet to hurl falsehoods at me through the press. To me this reveals Ellis’ true character as a racist and a charlatan: he well knew what he wrote with Stephen Hawking is all false and written just to fool people. Surely Stephen Hawking did too.

Church and racists use similar tactics: they defend one lie by means of a thousand lies. The fresh set of lies against me were planted in a report in GroundUp.

But racists tell stupid lies.

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Decolonising science: Victory in Cape Town

Monday, December 18th, 2017

The panel discussion on decolonising science at the University of Cape Town (UCT) was a great victory. It publicly exposed that no one in  the UCT had a single serious argument against me. Indeed, in the last two decades not a single person in the West has put forward a single serious argument against my proposals for decolonising science.

My advance summary of points was posted here.

My claims involved three broad areas: (a) mathematics and science, (b) its philosophy, and (c) its teaching. Accordingly, the panel which responded to me had three senior faculty members from (a) math (Henri Laurie), (b) philosophy (Bernhard Weiss), and (c) education (Leslie Le Grange).

Below is a video record of my presentation.

The panel response is here.

Summary

My three fundamental arguments were that

(1) The current philosophy of formal math involves a bad metaphysics related to church theology,

(2) this bad metaphysics results in bad science

3) eliminating it and reverting to normal math makes math easy and results in better science.

None of the respondents engaged with any of these three fundamental arguments.

The mathematician spent most of his time telling his autobiography.  The philosopher could not go beyond some irrelevant quibbles. The educationist did a good thing by summarising my points, but then made some general statements  unconnected with my claims.

More details (more…)

Decolonising math: Amsterdam lecture

Thursday, December 14th, 2017

Thanks to Djehuti Ankh-Kheru for making and posting a video of my lecture on decolonising math at Amsterdam.

Decolonising math and science: Durban keynote

Saturday, October 14th, 2017

Here is a video of the  11th Higher Education Conference at the University of Kwazulu Natal, Durban.

https://youtu.be/seEc6V_rJ5I

My keynote address: https://www.youtube.com/watch?v=cpS6MfzJr2E

www.youtube.com
Chair - Professor Kesh Govinder, University of KwaZulu-Natal Title - Decolonising Maths and Science Education

The presentation is put up, as usual, at http://ckraju.net/papers/presentations/ckr-Durban-keynote.pdf.

Professor Kesh Govinder is with the math department at UKZN, and was earlier its head. Here is a longer conversation with him and Professor Nyna Amin on decolonizing math on the Teaching and Learning TV

https://www.youtube.com/watch?v=NcuVaJA_SSc


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…)