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 http://ckraju.net/issa/conversation-draft-minutes.html.
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.)
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 »
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.
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.
As for actual alternatives in math education, my experiments with my decolonised course on calculus have already been reported in scholarly articles such as
My article on the claim that Vasco “discovered” India. On the religious and legal “Doctrine of Christian Discovery” any land belongs to the first Christian to sight it whose Christian duty it is to murder or enslave the original inhabitants. That is what happened in the Americas and Australia, but that is a genocide we celebrate not condemn. The original article, and the one published in Nai Dunia, with changes below.
A partial (but documented) English version has appeared online in Frontier Weekly as The “discovery” of India (part 1).
Here are my responses. (A separate response in Hindi to Dinanath Batra’s associate’s comments on my Jansatta article in Hindi of 10 Aug 2014 is given below.)
- Abuse. Some people have turned abusive and chanted abuses like mantras! Funnily, their abuses are always the same, no matter what the critique! After working on decolonisation for the last 4 years, and mentioning the use of Indian ganita in the above articles, it is excessively funny to be accused of being a follower of Macaulay! Pathetic. These abusers have an equally pathetic knowledge of Hinduism, and hence are its worst enemies, not its owners, as they claim, for they confuse the fakes for the real stuff. (Incidentally, I have also given what is possibly the strongest possible scientific basis for Upanishadic philosophy, relating it to scientific and refutable notions of time, but it is beyond even their leaders.) Anyway, such ignorance of the purva paksa (the critique) permanently disqualifies these abusers from being taken seriously, according to the Nyaya sutra.
- It is ancient hence it is Vedic.
- Wrong! Ancient does not mean Vedic. Buddhism, Jainism, and Lokayata are also ancient, but all reject the Veda as a means of knowledge. Lokayata said that Brahmins are hypocrites. Is that also Vedic knowledge!? If not, the claim “vedic = ancient” is just a second lie invented to “save” the first (claim of “Vedic” math). A third lie is now needed to “save” the second one! (Note that Lokayata are Hindus on present-day tax laws, or the Indian census.)
- Besides, how do we know it is ancient? What is the pramana? Our source (Krishna Tirtha) is recent. He hid his real sources, obviously for a good reason. If they were really ancient, why did no one else mention them in so many thousands of years? How do we even know this system is Indian in origin?
- The article pointed out that the usual algorithms are Indian in origin (unknown to Krishna Tirtha and his followers), and based on the place value system which can be traced to the Veda. They are definitely Vedic. Why abandon the real Vedic for the fake Vedic?
- It is useful for CAT etc.It is a very narrow and colonial vision of education that imagines that education is intended only to pass competitive exams The real social use of mathematics is on the frontiers of science and technology, where the mental arithmetic of “Vedic” math is irrelevant.
- Caste and Shakuntala Devi. Read the rest of this entry »
Here is a link to a video interview (over 9 hours) with Claude Alvares on a variety of issues concerning decolonisation of education. This has been posted by Multiversity TV, and I should have posted it long ago on my blog.
History and Philosophy of Science
Part 5 of the above video series has interviews with students of the new “decolonised” course on History and Philosophy of Science (HPS). Some details of the new course, pictures of students etc. were earlier posted on this blog at
The genesis of the HPS curriculum, the international conference which preceded it, and minutes of discussion at Universiti Sains Malaysia are posted at
The actual curriculum of the courses which ran at AiU are posted at
As for math education, my experiments with my decolonised course on calculus have already been reported in scholarly articles such as
MH 370 has been in the news for some time, so I expressed my views on a visit to Penang, and this led to a press conference the next day.
The press has been harping on human factors, terrorists, hijacking by hacking, pilot suicide and all sorts of exotic theories. The terrorist theory was clearly wrong from day one: why should someone intending to kill himself want a fake passport? Hijacking or hacking also does not fit the facts: else there should have been some related demands by now. It is important to understand the correct causes to prevent a recurrence of this tragedy.
The most likely possibility is a failure of technology, not human error. Very likely there was structural failure and an explosive decompression. What would the pilot do in that case? He would turn back to Malaysia (hoping to land), and would dive down (aiming to get oxygen back in the cabin, not to evade radar). [Why would a pilot intent on suicide turn back and fly across Malaysia, that too while trying to avoid radar?] Clearly, despite his heroic attempts, the pilot and passengers must have succumbed to hypoxia and hypothermia very quickly.
At this stage some people with pitiful faith in technology ask what about the oxygen masks? Obviously they also failed. If the plane cracks open, the oxygen tank and pipelines too can get torn apart. A known example where the oxygen supply failed is the case of Helios flight 522 of 14 Aug 2005 (a Boeing 737), in which all passengers and crew died, and which continued its zombie flight until crash, despite jets being scrambled to intercept it.
There is a wrong expectation that the plane would have disintegrated into bits and fallen on the spot. Even if the aircraft suffers explosive decompression, the plane can continue to fly and may even land safely as demonstrated by Aloha Airlines flight of 28 April 1988 in which explosive decompression tore out an 18 foot hole.
Obviously, in this case of MH-370 (a Boeing 777-200ER) after the failure of the oxygen supply and the quick onset of hypoxia, the plane presumably continued on auto pilot mode, like a ghost flight, like the Helios flight, until it ran out of fuel and fell into the sea.
Clearly, this theory explains all the known facts, and as of now, this is the only theory which explains all the facts.
Further, structural defects are a common occurrence. In fact, the Consumer Association Penang had complained in 2011 when the Southwest Airlines flight 812 of 1 April 2011 (again a Boeing 737) was forced to make an emergency landing at a military airport, after suffering mid-air decompression. In a subsequent inspection a large number of aircraft showed up with cracks and metal fatigue.
Structural failure is a common occurrence just because the aircraft body is designed to be as light as possible, and that is obviously not the same as saying it is as strong as possible or that it is as safe as possible. Further, an aircraft being expensive, airlines continue to use it for as long as possible, increasing the chances of corrosion and structural failure. Clearly consumers ought be informed about these compromises and by how much they increase the likelihood of sudden death in the air. They can then make an informed choice.
Given the above long list of demonstrated structural failures of Boeing aircraft, this possibility ought to be vigorously investigated as the lead possibility. Instead, we are being offered all sorts of exotic explanations through the press, explanations which don’t at all fit the facts. What is being examined by the FBI is the computer of the pilot (who had a long and unblemished record), not the computers of the Boeing company. A colonised mentality? or something else?
There is a relation to the previous blog post. Many people felt outraged when a bomoh appeared at the airport to divine the location of the crash site. However, so many people blindly believe in experts. They do not see that in our present-day society experts are mostly caught in a conflict of interests which they rarely publicly declare. Therefore, there is no guarantee that aviation experts would tell the whole truth, especially if that truth hurts the very aviation industry to which their livelihood may be tied. And if one is not oneself an expert how does one know that the expert is telling the whole truth (or even that he really is an expert)? So, in a situation like this, blind belief in the unbiasedness of “experts”is just another superstition.
Here are the reports of the press conference.
- A video: http://www.youtube.com/watch?v=8V8gthtuGys&feature=youtube_gdata
Petition is given below. To sign online go to:
If you are convinced, do also SPREAD the word by forwarding this email to others.
Anyone who has children or grandchildren in school (or had a bad math experience in school) qualifies as a potential signatory, as does anyone who wants real independence.
1. Printable copy: http://ckraju.net/petition/Petition-to-teach-religiously-neutral-math.pdf
2. Detailed explanation: http://ckraju.net/petition/Math-petition-explanatory-note.pdf
3. List of relevant books, papers, news etc: http://ckraju.net/papers/Reading-list-on-history-philosophy-of-math.html
HRD Minister, Govt of India,
Ministers and Secretaries of Education of all Indian States,
Vice Chancellors of various universities,
Sub: Ensure that mathematics taught in public schools is religiously neutral.
Dear Minister/Secretary/Vice Chancellor/Chairperson/Director,
Colonial education served the interests of the coloniser, so it should have been critically reviewed after independence. Unfortunately, this was not done till now, and our education system still imitates the West. Uncritical imitation may be harmful. European universities were set up by the church and controlled by it for centuries. Long-term church control meant sustained pressure to make all knowledge theologically correct. So, religious biases are likely in Western knowledge.
Indeed, the accompanying note explains that this applies even to mathematics: mathematics developed differently in different cultures, but Europeans perceived it in religious terms relating to mathesis and eternal truth. As the note explains, most school mathematics, such as arithmetic, geometry, algebra, calculus, and probability, actually originated in the non-West and was imported into Europe for its practical value. However, Europeans attempted to make it theologically correct, and align the notion of infinity to the church notion of eternity. In the process, they turned mathematics into metaphysics and introduced elements of Christian dogma in it, so that there is a subtle religious bias in the way mathematics is taught in schools and universities today. Eliminating that religious bias does not affect any practical application of mathematics.
Teaching a religious bias through a compulsory subject in public schools is unconstitutional. Mathematics should be taught in public schools in a religiously-neutral way and for its practical value. Therefore, if the charge is right, the teaching of mathematics in schools must be changed forthwith. Mathematics is commonly regarded as a difficult subject, and the superfluous theological complexities in it may be the reason for that. We note that actual teaching experiments have been performed, in universities in various countries, to show that teaching mathematics, devoid of theological complexities, also makes it easy. If the charge were not right, then our educationists ought to have publicly refuted it long ago, since it has been published in 4 books, 32 scholarly articles and numerous newspapers, in various countries, for over a decade. The silence is strange.
This matter concerns millions of students each year, including our children or grandchildren about whose education we are deeply concerned. Accordingly, we feel that the issue must be decided in a transparent way. Usually, such decisions (regarding what mathematics to teach) are taken by experts. But to avoid a biased decision, the experts must be properly selected. The non-experts who select the experts must explain why they chose those experts. The customary practice is to select experts by blindly trusting Western endorsements and certifications, but that method is inappropriate in the present context of a critical review of colonial education, where the interests of the colonised and the coloniser may diverge fundamentally. Whose interests do these experts represent? This must be transparent, especially if there is no concrete evidence that these experts contributed to the welfare of people in India. Relying exclusively on Western certified experts just amounts to continuing the colonial system of requiring permission from the West for any change of policy.