Ganita vs mathematics: Ten myths of Western math

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.

Read the rest of this entry »

Education policy, secularism and traditional values

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 )  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.

Read the rest of this entry »

Science and Islam

November 1st, 2015

As part of a series of workshops on science and various religions, there was a day-long workshop on science and Islam at the Universiti Sains Islamic Malaysia.

USIM workshop-1

USIM workshop-2

USIM workshop-3

My presentations are posted online: Part 1, Part 2, Part 3.

This developed the paper on Islam and science presented as a keynote address at a previous international conference on Islam and Multiculturalism at the University of Malaya.

Decolonisation in South America-2

July 2nd, 2015

Became an honorary member of the the Institute of Complex Thought at the University Ricardo Palma. Good to know that they want to try the 5-day course on calculus.

Institute of Complex Thought

University Ricardo Palma

University Ricardo Palma

Decolonisation in South America-1

July 2nd, 2015

A few years ago, when a friend, Jorge Ishizawa from Lima, asked for a copy of my book Cultural Foundations of Mathematics, I wondered what he would do with it. (I sent it, but it bounced back.) On a recent visit to Peru, I had a conversation with people at his organization PRATEC, which works with traditional Andean knowledge.  Interestingly, many of them were aware of my work.

Found out that Bolivia has a full-fledged Ministry for Decolonisation! India should have one too!



Group photo

MIT Talk: Calculus the real story

May 19th, 2015

The abstract of my talk at MIT differs from my presentation, posted at

The point I made in the talk was that MIT teaches calculus and trigonometry wrongly. This is just because Europeans failed to understand the mathematics they imported from India. For example, the very words “trigonometry”, “zero”, “surd”, “sine”, indicate European conceptual mistakes and failure to understand imported Indian mathematics. We should therefore not blindly copy the MIT MOOC courses, but teach calculus differently, contrary to the recommendation made by Sam Pitroda.

A video of the question and answer session would hopefully soon be online.

Raju’s paradox: all formal mathematicians are fools

May 12th, 2015

For almost two decades now, I have been pointing out that formal mathematics (and much Western philosophy) is based on the false belief that proof based on two valued logic (”deduction”) is “superior” to empirical proof (”induction”). This belief is NOT universal (e.g. Indian mathematicians used empirical proofs, e.g. Buddhists used a different logic), it is NOT empirically certain (e.g. quantum logic), it is anchored in Crusading myth (e.g. there was no “Euclid”, and the book Elements begins with an EMPIRICAL proof, and ends with an EMPIRICAL proof of the “Pythagorean” “theorem”). Formalism, the prevailing philosophy of mathematics, arose from an attempt to “save” that rotten myth that Westerners did something “superior” in math. This math has religious roots in bad Crusading theology (Aquinas’ bowdlerization of al Ghazali that logic binds God). All this mythology and theology has NOTHING to do with any practical application of mathematics, mostly done on computers today, and can be safely eliminated (e.g. using zeroism) without diminishing the practical value of math by an iota. Doing so makes math easy, and actually improves science. That is, it leads to a truly superior math.

At a recent conference in Vizag, I even tried to initiate a public discussion on this, which mathematicians have avoided so far. However, a discussion did take place, and the draft minutes are posted at

In a more recent conversation with an award-winning formal mathematician, I was asked to give a concrete example of how formal mathematics can lead to wrong conclusions. I have already given examples such as the Banach-Tarski paradox, but they involve technicalities. So, here is a simple example.

Theorem: All formal mathematicians are fools.

Proof. Step 1. If Schrodinger’s cat is both alive and dead then all mathematicians are fools. (Instance of the tautology hence theorem of 2-valued logic that “A and not-A implies B”, where A and B are any propositions whatsoever.)

Step 2. It is an empirical fact that Schrodinger’s cat is both alive and dead. (More precisely, the cat is a macrophysical metaphor for an electron in the two-slit diffraction experiment: the electron both passes through a given slit 1 (A), and does not pass through it, i.e., passes through slit 2 (not-A). For more details see The Eleven Pictures of Time.)

Step 3. Therefore, all formal mathematicians are fools. (By modus ponens.)


Buddhism and science on Ambedkar jayanti

April 14th, 2015

Recently I participated in a panel on science and religion in the Netaji Subhash Institute of Technology. The students who were brought up indoctrinated with Western stories of the conflict between science and religion were dumbfounded when I asked the following question. If science and religion were at war, why then did the church bring science to India? For the manifest fact, contrary to the story of a conflict between science and church, is that the best science colleges in India are still mostly church institutions. The students appreciated it, though it is hard for them to get out of the mental frame imposed by the story. Hopefully, it will set some of them thinking about the use of scientific authority to impose church dogmas.

There was little time to explain it during the panel, but Buddhism accepts only the two principles of pramana (proof): namely, pratyaksa (empirically manifest) and anumana (inference). Those two means of proof are also the basis of (real) science. Specifically, Buddhism rejects authority-based proofs, such as the authority of editors of Western scientific journals, based on secretive refereeing, and their ranking system. Buddhists point out that authority must either be manifest or based on inference. Therefore, what possible source of conflict can there be between Buddhism and (real) science?

Clearly, the only source of conflict is similar to that between science in theory, and science as practised, for science in practice relies heavily on authority, such as editorial authority. It also relies on secrecy (such as secretive refereeing) to preserve authorised knowledge in the manner of the church. Finally, most people cannot judge the validity of science on their own and rely on stories about who can be trusted, and who not. Naturally, they get taken for a ride.

There are other differences. Thus, for example, ethics is an important aspect of Buddhism. (Those interested in seeing how Buddhist ethics relate to present day science may like to see my paper on “Harmony Principle”, in Philosophy East and West and elsewhere.) Practising scientists, however, often disregard ethics. A whole lot of Nobel prizes were given to people who participated in the Manhattan project and then coolly washed their hands off the blood of millions affected by the nuclear bombs dropped on Hiroshima and Nagasaki. The same thing can be said of medical practitioners today who are almost totally sold out to the pharmaceutical companies, and care little for patients. Thus, practising scientists are required to be loyal to their masters, the state or capital, and suppress ethical objections.

Though there is no conflict between Buddhism and real science, there can be a conflict between Buddhism and science as it exists, because of intrusion of church dogmas in the content of present-day science and mathematics. I have commented on this intrusion of dogma into science in the context of Stephen Hawking, in the my paper on Science and Islam, and in the public debate with a Christian evangelist with a PhD from Cambridge, intent on turning the classroom into a pulpit. In all cases, the attempt was to use the authority of science to impose dogmas of Christian theology, as in claims about eternal laws of nature, or “causality” (meaning mechanistic causality), or Hawking’s singularities interpreted to suit creationism. The above paper on the harmony principle also briefly indicates why the correct scientific position is not mechanistic causality but very similar to conditioned coorigination (that the future co-originates, conditioned by the past, but not decided by it). That is also the central Buddhist principle of paticca samuppada. Read the rest of this entry »

Dalits and Science in India: Aryabhata on Ambedkar jayanti

April 14th, 2015

Some months ago, I was invited to Patna for a meeting organized by Sanjay Paswan, dalit leader and former Union Minister of State for HRD. Unfortunately, I had to cancel the visit at the last minute, but wrote a short account of my speech. The speech was a response to Sanjay Paswan’s learned book Cultural Nationalism and Dalit which makes the point that the conditions for lower castes were not so oppressive in pre-colonial times. He has documented numerous cases of famous lower-caste religious figures from the ancient Valmiki to Kabir and Ravidas. Of course, he includes Dharmpal’s point about the prominence of dalit teachers and students in pre-colonial education according to British statistics. The same thesis is illustrated by Sri Narayana Guru.

This thesis is important. My point is that the thesis is a priori credible, for. when Buddhism flourished, in India, or, later, when there were many powerful Islamic rulers, it would have been easy for dalits to opt out of the caste system by converting. This was what Ambedkar emphasized when he proclaimed that he was born a Hindu but would not die one. Therefore, also, he converted to Buddhism and urged other dalits to do so. Therefore, also, there should not be a law against conversion, since that would be anti-dalit.

In my planned speech, apart from putting this forward, I also thought of extending the thesis argued by Sanjay Paswan by pointing out that famous dalits included scientific figures like Aryabhata, not only religious one’s. That Aryabhata was dalit is clear from his name Aryabhata, often misspelled as Aryabhatta. As any Sanskrit dictionary will confirm, bhata refers to a slave, a soldier etc., while bhatta is the title of a learned Brahmin. Thus, the misspelling changes Aryabhata from a dalit to a Brahmin. In some cases this misspelling may be due to sheer ignorance, but in some cases it is surely due to mischief, as I pointed out many years ago.

Since I had written out my speech, on “Dalits and Vigyan”, but could not present it, I sent it to a couple of newspapers and magazines. Read the rest of this entry »

Teach religiously neutral math

October 24th, 2014

My article published today in The Hindu, was heavily abbreviated. The more detailed original article in about 1200 words is easier to understand. The petition to teach religiously neutral math, and related material is already on this blog. A draft of a more detailed paper on “Eternity and Infinity” delineating how the West misunderstood Indian math, and its consequences for science today is also posted online for those who want to go into depth about the connections of present-day formal math to church theology on the one hand, and its failures in present-day science on the other. Imitating the West in mathematics is bad idea.

Hindu article 24 October 2014

As for actual alternatives in math education, my experiments with my decolonised course on calculus have already been reported in scholarly articles such as

Teaching math with a different philosophy 1 and

Teaching math with a different philosophy 2