Neither meaning nor truth (nor practical value) in formal mathematics

January 23rd, 2019

At my IIT (BHU) lecture (see also previous post), I emphasized Bertrand Russell’s remark that there is neither meaning nor truth in (formal) mathematics. Hence, any nonsense proposition one desires (such as “All rabbits have two horns”) can be proved as a formal mathematical theorem from appropriate postulates: Russell’s sole criterion being that the postulates should be “amusing”.

To drive the point home, I pointed out how, long ago, when I still believed in formal math, I used to teach a course (A) on Real Analysis while also teaching a more advanced course (B) on Advanced Functional Analysis, in the math department of Pune University. In the elementary course (A) I taught

Theorem: A differentiable function must be continuous. (Therefore, a discontinuous function cannot be differentiated.).

In the more advanced course (B) I taught

Theorem: Any (Lebesgue) integrable function can be differentiated infinitely often. (Therefore, a function with simple discontinuities can be differentiated infinitely often.)

I have made exactly this point earlier in this blog.

“Now, for several years I taught real analysis to students and mathematically proved in class that a discontinuous function cannot be differentiated. I also taught advanced functional analysis (and topological vector spaces and the Schwartz theory according to which every Lebesgue integrable function can be differentiated). In the advanced class, I mathematically proved the exact opposite that a function with a simple discontinuity can be differentiated infinitely often (and the first derivative is the Dirac δ).”

The question is which definition of the derivative should one use for the differential equations of physics? As pointed out in Cultural Foundations of Mathematics (or see this paper) the issue can only be decided empirically, unless the aim, like that of Stephen Hawking and G. F. R. Ellis, is to spread Christian superstitions about creation using bad mathematics.

Superstitions go naturally with ignorance. One such ignorant professor from the IIT mathematics department was present during my lecture. His knowledge was limited to the first of the theorems above, and he ignorantly believed that it was some kind of absolute truth, which everyone was obliged to believe. He objected to my claim that a discontinuous function can, of course, be differentiated, and walked out to show his contempt of my claim.

Even the students had heard of the Dirac δ, and agreed with me. The next day during the workshop, I explained that I had engaged with this question since my PhD thesis. But the professor remained absent, though his ignorance was exposed before the students. He is welcome to respond by email; I will post it publicly since it is sure to further expose his ignorance.

Oliver Heaviside applied first applied this to problems of electrical engineering over a century ago, and Dirac, formerly an electrical engineer, then applied the Dirac δ to physics. It remains very useful because it is the Fourier transform of white noise (flat spectrum or the unit function), and used even in the formal mathematical theory of Brownian motion.

Earlier in the lecture, the same professor, contested my claim that probability was invented in ancient India, and taken from India in the 16th c., where credit for it was later falsely given to people like Pascal and Poisson. Read the rest of this entry »

Institute lecture and workshop at IIT (BHU)

January 9th, 2019

Will be giving the institute lecture at IIT (BHU), the century old first engineering college in India, on the 18th of Jan, followed by a workshop on “Alternative math” on 19th of Jan.

Poster for lecture and workshop at IIT (BHU)

(The Workshop is from 10 am to 5 pm with tea breaks and a lunch break.)

Core question: Indians are proud of our ganita tradition, but today we teach Western formal math believing it to be superior; but what if Indian ganita were superior?

Outline answer: (1) The West was backward in math. It imported most basic math from India, including arithmetic, algebra, trigonometry (via Arabs) and calculus and probability (directly from Cochin). (2) This import created a crisis because practical ganita differed philosophically from religious Western math. To fit it into their framework, the West changed ganita to mathematics by adding religiously-loaded metaphysics. (3) During colonialism, our own ganita wrapped in religiously biased metaphysics and packaged with a false history was returned to us and declared superior. We never cross-checked either that fraud history against evidence or that superstitious Western claim of superiority against commonsense by critically comparing formal math with ganita (normal math) to decide which is really superior. (4) Eliminating the religious/metaphysical elements (a metaphysics of eternity/infinity) in formal math  does NOT affect practical value which all comes from normal math. (5) Instead it makes math easy hence enables students to solve harder problems. It also results in better science.

Further details about the lecture and workshop are posted at http://ckraju.net/IIT-BHU/. Explicit links below.

Abstract of Lecture

Extended abstract of lecture

Workshop details

Alternative math 1: Rajju Ganit

Alternative math 2: Calculus without limits.

Detailed schedule

Jan 18, 2019
5.30 pm Welcoming the gathering
5.32-5.40 pm Slide Show on Ramanujan
5.40 pm Introduction of the speaker
5.45 pm Address by the Speaker
6.45 pm Q and A and Vote of Thanks
7.00 pm High tea
Jan 19, 2019
10.00 am Very brief Intro to the workshop followed by Session 1
11.30 am Tea break
11.45 am Session 2
1.00 pm Lunch break
2.00 pm Session 3
3.00 pm Tea break
3.15 pm Session 4
4.30 pm Open house (interactive session)
5.00 pm Conclusion and Vote of Thanks

Honoured before mass audience at Bijapur

January 9th, 2019

Was honored before a mass audience at Bijapur.

Honored at Bijapur

The award was conferred by Karnataka MP Shri Basavraj Patil, and the Vice Chancellor of the Central University Karnataka. Kalaburagi, Prof. H. M. Maheshwaraiah.

Below is a picture of the audience.

Mass audience at Bijapur

Speech at Bijapur

For more honors earlier this year see http://ckraju.net/blog/?p=150.

Decolonising humanities in Beirut

December 24th, 2018

A conference on decolonisation of humanities was organized at Al Maaref University, Beirut.

General view of the conference

The big concern was how colonial education has altered human values. But Western education did not come for humanities, therefore my point was that merely changing humanities education won’t result in the desired change.  The facts are (1) Western education came to the colonised as church education. (2) It was and is justified  on the grounds that the colonised need science. The net effect of (2) is that the colonised foolishly trust the authority of church institutions like Cambridge, Oxford, and Paris. This way the church is able to mix all sorts of subtle poison in university education, even through math and science.

CKR at Beirut conference

Though Western education ostensibly came for science it ensures that the mass of educated are ignorant of math and science, so they are forced to trust authority (of the West, obviously). It further anti-educates them by planting myths, and teaching them to think in terms of stories. For example, due to such indoctrination, the colonised are trapped in the myth that science and church are at war. They failed to notice the obvious fact, contrary to this myth, that colonial education came as 100% church education, and that, for example, the best science colleges, even in India, are still church institutions.

Mind control of the colonised was the work of the church, in  collusion with the colonial state. This persists, like Western education, even after direct political control of the colonised ended. Once the colonised are rendered ignorant, and taught to trust Western authority and myths, as Western education teaches, there is no solution for them.

Read the rest of this entry »

The racist nitwits of Cape Town

December 13th, 2018

A reporter from Africa met me recently in India to find out about the events concerning the panel discussion on decolonisation in Cape Town, a year ago. Someone here asked: could he be a church agent, who may again present a biased picture? I don’t know. But he does not seem to know any math, and may not have understood my critique of formal math. So, to make sure that others (especially the ill-informed) do not “control the narrative”, and totally misrepresent it, it is time I put up my side of things.

An important background, to the debate last year in the University of Cape Town, which has not been adequately mentioned, is my book The Eleven Pictures of  Time (Sage 2003). In it I extensively criticised the book Large Scale Structure of Space-Time by Stephen Hawking, and G. F. R. Ellis, of the University of Cape Town. (Note, in passing, that Hawking unethically collaborated with Ellis at a time when there was an academic boycott of apartheid.) My key issue with the Hawking and Ellis book was that their conclusions about a “singularity” involved bad mathematics, and a bad understanding of calculus (even from within  formal mathematics).

But let us go one step at a time. First, their conclusion that the cosmos began with a  “singularity” was not science (since not refutable on Popper’s criterion). Second, their conclusion was of great political significance to the church, through the claim that science supports the church’s religious dogmas of creation. The  mathematical conclusion of a singularity is explicitly connected by Hawking and  Ellis to religious beliefs about creation and other dogmas. The key takeaway of their book (p. 364) is that “the actual point of creation, the singularity, is outside  the presently known laws of physics.”

The belief that God rules the world with eternal “laws” of nature is itself a religious church dogma first articulated by Aquinas, not a scientific (refutable) belief. Simply put, the church supports it, but Hinduism, Buddhism and Islam deny it.  (See this minuted discussion for example, which explains that Hinduism accepts rta, but not immutable laws, for Buddhism, see the video “Buddhism and science”, for Islam see the keynote and article on Islam and science.) Further, other religions accept continuous creation, or the creativity of living organisms (not continuous creation in the mechanistic sense of the theory of Bondi, Gold, Hoyle and Narlikar). The big bang theory alone is NOT the opposite of continuous creation. The “singularity”, interpreted as a beginning of time, relates to creation  more clearly than the big bang, which need not be a true beginning of time, but could be just the other side of a big crunch in an oscillating cosmos.

There is no doubt about the religiosity of the book by Hawking and Ellis. Ellis got  the million dollar Templeton award, for putting together science and religion, and Hawking never got the Nobel prize! The church greatly glorified Stephen Hawking, and that church propagandist support helped sell millions of copies of his book  Brief History of Time which restated the conclusions of singularity theory for a lay audience.  But singularities and creationism are simply not physics. Therefore, much as Hawking desired the Nobel prize, and much as the Nobel prize committee may have wanted to give it to him, they simply could not do so.

The physicist F. J. Tipler (Physics of Immortality) pushed this connection of science and religion via singularity theory. He explicitly claimed that singularity theory proves the truth of Judeo-Christian theology. In the opening paragraphs, Tipler said his book aimed

“to show that the central claims of Judeo-Christian theology are in fact true, that these claims are straightforward deductions of the laws of physics as we now understand them. I have been forced into these conclusions by the inexorable logic of my own special branch of physics…the area of global general relativity…created…by the great British physicists Roger Penrose and Stephen Hawking.”

The colonised mind may talk against creationism, in support of Darwinism, but it never dared contest this kind of religious claim of creationism backed by Western authority. Despite the millions who read Stephen Hawking’s book, Brief History of Time, I have not heard a SINGLE other dissenting voice in the last thirty years. Read the rest of this entry »

Some recent honors

November 27th, 2018

Yesterday (26 November, Constitution Day) at Constitution club, I received the Nilakantha honor from the Dalit organization “Kabir ke log” from a former Union deputy education minister (and scholar) Dr Sanjay Paswan).

Nilakantha-samman

Click for a related article on dalit scientific achievements, in Jansatta.

Earlier I had received the Bharatiya Dharohar Award from the current Union deputy education minister

Bharatiya-Dharohar-Award

Click for a related article on Indian mathematics.

Still earlier, this year,  I received the MP Ratna award from the MP Chief Minister.
MP Ratna award

Click for a related interview on math education in Dainik Bhaskar.

Oxford must fall

September 30th, 2018

The long-awaited book Rhodes must Fall, by the Rhodes Must Fall Group at Oxford has been published by Zed books, and is distributed by the University of Chicago press.
Cover image Rhodes Must Fall

It carries my censored article “To decolonise math stand up to its false history and bad philosophy” together with a supportive essay by Kevin Minors a black Bermudan doctoral student.

Recall that my article was censored by the South Africa editor of the Conversation on the false ground that it did not meet their editorial standards (though I intensively interacted with an editor for a week before publication).  Basically, the editor succumbed to the furious response of the whites, to my article. The Conversation had earlier published the foolish (and obnoxious) claim that mathematics is essentially the work of dead white males, so blacks and women should be taught to think like them. In response, I pointed out that black Egyptians knew fractions 3000 years before Greeks, Romans, or Europeans learnt about elementary fractions.

The Conversation did not mind publishing that obnoxious falsehood, but the editor had no place for any truth that was anti-West. So, she objected to my referring to my own published work. Why? What on earth is wrong with that? Why should one not refer to one’s own published work? Obviously the unstated but racist ground was her belief that what a brown man says is not reliable, therefore, she will not permit him to say anything original, even if it has been peer reviewed and published earlier. He is allowed only to repeat and quote what some white man says. (This is also the Wikipedia policy: a white man, or an article approved by white men, is the only reliable source.)

Though my censored article was initially widely reproduced, sadly it was taken down by most publications around the globe. Only one Indian newspaper, the Wire, recognized the problem of racist censorship and put it back. Another international publication retained it under the title “Was Euclid a black woman?”. This is described in my article on Mathematics and Censorship, and the censored article was published in full as part of an article in a peer-reviewed journal: Journal of Black Studies. Clearly the editor of the Conversation was using utter lies to defend racist decisions.

The important thing to emphasize now is that #OxfordMustFall.

Thus, consider what happened in the panel discussion at the University of Cape Town a year ago.

Read the rest of this entry »

Israel denies visa for talk on decolonisation exposing Einstein

August 4th, 2018

The Palestine Technical University, Kadourie, Palestine, is organizing the Sixth Palestinian Conference on Modern Trends in Mathematics and Physics PCMTMP-VI, 5th-8th August 2018.

I was invited to give two plenary talks (scheduled on 7th and 8th Aug) on
Decolonising mathematics: how and why it makes science better (and enables students to solve harder problems)

An extended summary and abstract of my proposed talk are posted online.

The Israeli embassy has, however, refused me a visa. No official reason or explanation was offered for the denial of visa. When I asked, an official from the Israeli embassy did very rudely warn me not to apply ever again for an Israeli visa.

Now five years ago, I visited Palestine (See blog post “Mathematics in refugee camps”, and a nice video on History and Philosophy of science). Of course, I did have a terrible experience with the Israelis: they charged me some USD 200 for a taxi for 8.5 km, then put me on a share taxi and promised to give the receipt after I crossed the border! Never encountered such terrible cheats anywhere else in the world. But last time the Israeli embassy in India had issued me a visa.

So, I am left wondering what has changed. Three things have changed. 1. Decolonisation, 2. Einstein, and 3. Indo-Israeli relationship
Read the rest of this entry »

Alternative math: media reports

July 5th, 2018

Here are the media reports for the Rajju Ganit workshop from Dainik Bhaskar, Nai Duniya, Talk show by Global Herald, and Free Press Journal

Global Herald talk show प्रसिद्ध गणितज्ञ सीके राजू से खास चर्चा

Global Herald talk show

Dainik Bhaskar

Dainik Bhaskar Indore 26 June 2018

Nai Duniya26 June 2018

Nai Duniya Indore 26 June 2018

Global Herald e-paper 30 June 2018

Global Heral news

Free Press journal

Free Press journal, Indore, 27 June 2018

Rajju Ganit workshop from today

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