Education - History and Philosophy of Mathematics - Science and Society

National Knowledge Commission and Math Education: An Open Letter to Sam Pitroda

Dear Mr Pitroda,

It was nice to meet you again at the FICCI gathering a few days ago.

There wasn’t enough time for me to clarify what I was saying, so let me do so here.

1. First, I agree with you that a major change is needed in the current system of higher education and research.

2. However, for the National Knowledge Commission (NKC) to make the right recommendations, you need to know the real causes of past failures. So what went wrong? I could find no NKC document which studied the past record of knowledge management in India, as I have done.
3. In the field of telecom, you are an acknowledged expert, and I personally think you did a wonderful job with C-DOT. However, in the field of higher education and research in India, which was the point being discussed, you lack both personal knowledge and personal experience. You are forced to rely on others.

4. Which others? According to my studies, the single central cause of the failure of knowledge management in India was that ignorant people attempted to manage knowledge. Certainly, these people—politicians, bureaucrats etc—wanted control for obvious reasons. But the single biggest problem was their ignorance.

5. Sure, they consulted experts. My point was that they were too ignorant even to decide correctly who the right experts were. That is why science management in India has been such a colossal failure—even more so than sports management: as a crude index, we could produce at least one gold in Olympics but no Nobel prize in the last sixty years. (People at least understand a good sportsperson when they see one, but they judge the worth of a scientist solely by the stories they hear, and without any personal understanding of the scientist’s work.)

6. That brings me to the point I raised. The NKC is repeating the same mistake.

7. Let me illustrate this with the case of mathematics (and science) education, a point to which NKC has accorded priority. My comments apply to both school education and higher education.

8. The NKC seems to have selected experts by branding. Now, where a product has some direct practical value, branding has value, for it refers to the experience of a large number of people. But, where there is no clear-cut practical value, as in religion or astrology, or formal mathematics, the value of branding is suspect. Is the largest-selling religion the truth? I doubt it very much.

9. Before you rush to say that mathematics is not religion, you ought to know that the very word “mathematics” derives from “mathesiz”, a term with deep religious connotations. To understand how that affects present-day math, do take a look at my paper on “The Religious Roots of Mathematics” (Theory, Culture and Society, 23, 2006, pp. 95–97, ed. Mike Featherstone et al.) or, better, my book on Cultural Foundations of Mathematics (Pearson Longman, 2007). The religious dimension of formal (theorem-proving) mathematics can be brought out quite easily: most of the theorems of present-day formal mathematics would fail with Buddhist logic (or Jain logic for that matter). Why should one use one type of logic rather than another? No one in the world could answer this objection in the last ten years (see my article, “Computers, mathematics education, and the alternative epistemology of the calculus….” Philosophy East and West, 53, 2001, 325-62). Why, then, should a secular country, India, encourage this sort of religiously biased formal mathematics?

10. Let us set aside these abstruse matters which you may not understand nor perhaps appreciate. Let us look at simple practical value. Most certainly, mathematical calculations do have tremendous practical value, they are used everywhere in science and engineering. But what practical value has, say, the TIFR math school, the bastion of formal mathematics, produced in the last 50 years? Possibly, they could show you certificates from the West. Such endorsements are useful for brand-building, but that’s no guarantee of practical value: endorsement by film stars may lead to higher sales but are no assurance of a higher-quality soap. This is especially true when the practical value of the product is not clear, as in the case of formal mathematics. Did the NKC conduct a study to answer the question about practical value posed above? If the knowledge commission goes by guesswork, it naturally risks making exactly the same mistake that decision makers made earlier in the manner of naive shoppers.

When I was looking after the initial application group in C-DAC, in the 1980’s, I desperately needed some mathematicians who could contribute some practical value to the big task at hand. You will recall that C-DAC was required to port several applications of national importance on the target machine, and every such application (space, oil etc.) involved a mathematical problem. Unfortunately, I could find no appropriate mathematicians in this country who could work on these problems: thanks to the pervasive influence of the TIFR math school which pushes the wrong kind of mathematics. (This applies also to its branch at IISc Bangalore, which purportedly does some “applied math”). But it is from this very school that the NKC has drawn its member, basing itself on brand value rather than practical value for the Indian people.

11. Then there is the question I raised of the veracity of expert opinion. Apart from its immediate members, NKC has a large number of experts advising it. You do not understand the basis of these expert opinions, so how can you be sure that the opinions will benefit the country and not the expert? The point that I raised was that the President of the Indian National Science Academy was found guilty of plagiarism. (Therefore, he did not look into my complaint against a well-known mathematician and the former President of the Royal Society.) He rubber stamped the views of a foreign organization which had perhaps spent more money on him in ten years than the Indian government. He did not resign. Nobody objected. Does anything more need to be said about the ethics of such experts?

This high-level case shows that the phenomenon of biased expert opinions is very widespread. Experts anyway get a free hand in a scientifically illiterate society that India is. Because opinion and judgment cannot be a matter of adjudication, experts can be completely brazen. Blame management is simple: experts always get the credit for success, but never the discredit for failure: can you give a single case in which an expert in India was penalised for having given a bad opinion? Like the patient of a dishonest doctor, it is only the country which loses. Anyone who objects is excluded from the system. All this may not amount to corruption under Indian law, but when government policy (and even law) is based on such expert opinions it can be ruinous for the country. As for those who watch silently, again there is nothing illegal either in silently watching something wrong—but it is unethical. So why should one trust the opinion of experts who find excuses to compromise so readily? Clearly the standard of honesty for experts has to be of a different order.

What did the NKC do to ensure this? Mere assurances about the absence of a bias are not acceptable. You are convinced, but your personal conviction is not enough: for you are simply not knowledgeable enough to judge whether there is a bias in the expert’s opinion. Good management would have seen the problem and would have brought in objective and transparent mechanisms and institutions to ensure the ethics (and competence) of the experts who have been guiding the country and who guide also the NKC. Good management would have brought in countervailing expert opinions and so on.

12. For the specific case of the TIFR maths school, its funding came from the Department of Atomic Energy, hence under the false pretence that this work was somehow useful for atomic energy. Why hasn’t the nation been informed loud and clear that the purported connection of formal mathematics to atomic energy is bunkum? Why don’t they get their funding in a more straightforward way?

There are further issues of biased expert opinion considered below.

13. I agree with you that mathematics and science education ought to be a priority. But what _sort_ of mathematics should we teach? The one which produces demonstrable practical value for the people of country as a whole? or the one which suits the experts who advice the NKC? Your math expert in NKC probably does not even understand any types of mathematics beyond “pure” and “applied” mathematics, so I want to emphasize that what I am talking about is a fundamentally new type of mathematics, as explained in my book, cited above. This is incidentally better suited to computer technology. But it does not mimic the West.

14. To drive home the point that the ghost of Macaulay still haunts our education system, just take a look at the racist history that is propagated in current school texts (see my article, “Teaching Racist History”, Indian Journal of Secularism 11, 2008, 25–28, also Jansatta, 23 Jan 2008). None of the “experts” responsible for these school math texts was able to produce the evidence for these absurd racist stories, when I publicly demanded it. They could only cite secondary Western sources, or make up more stories—about me for example. This is exactly the way the priest and the astrologer operate: when someone demands evidence, produce a story instead. When that story is challenged, produce another story, and so on. But without evidence there can be no knowledge. And it is the same clique of “experts” who are advising the NKC in various ways.

15. As regards my proposal to teach more of “traditional mathematics” you are quite right that nothing prevents me from doing it on my own. I was only making a recommendation to the NKC to do the right thing. I have already started teaching this new course on mathematics. (You can find a copy of the proposal at The idea is that students find mathematics a difficult subject to learn just because of the theology that has infiltrated it. And the proposed solution is to eliminate those theological elements from mathematics. This initiative has proved very successful with all those with whom I have tried it so far (that includes my own children one of whom represented India for the olympiads and has a PhD from Harvard). However, the point is this: why should my children be forced to swallow the trash (related to formal mathematics and its racist history) that is compulsorily taught in school and college, where the syllabus is fixed by these very “experts”.

16. I must say I am very disappointed by the way the NKC has responded to this new idea, about mathematics and its teaching, which is based on over 10 years of research and publication, and has received wide critical acclaim. (Please see the publication list in the project document at the link above.) The NKC keeps advising others to be receptive to new ideas. So I thought, incorrectly as it seems, that the NKC intended to do the same, and be itself receptive to new ideas.

However, I do realize that just because you rely on the very same experts as the bureaucrats did, your responses to new ideas are also exactly the same. If you discount their linkages to the West, many of these experts would be reduced to nothing. This means you have the same old benchmark: something is valid knowledge if it is accepted by the West. This process of awaiting Western endorsement, as the sole guarantee of valid knowledge, is a guaranteed recipe to ensure that Indians permanently remain followers and will never turn into leaders. My new idea, however, attacks the foundations of Western knowledge; it shakes the foundations of Western dominance through soft power. This will not make the West happy. Neither will your math experts be happy, because formal math is the only thing they know, and if they allow such new ideas they would themselves be in danger of losing their jobs or their importance. So how did you ensure that the experts assessed an idea solely by its value for the country? How can you hope to bring about a “generational change” with the same old ways of assessing new ideas?

17. Of course, you are absolutely right that you have the power, and I don’t. However, it is also true that I have the knowledge (especially of mathematics and computing) and you don’t.

Incidentally, when C-DOT ventured beyond telecom to build a parallel computer, 20 years ago, I had advised the C-DOT team to parallelise at the algorithm level. They did not do so. Three years later, when their method of parallelisation failed, they suddenly discovered Amdahl’s law (the basis of my advice) as the reason for the failure.

Drawing from that experience, this time I would like to make my recommendations public in advance. I cannot stop the NKC from proceeding on guesswork and making the wrong guesses. But I would like to give a public demonstration of how real knowledge eventually scores over the guesswork so often used by our knowledge managers. So I am making this communication public.

18. To recapitulate, expert raj is worse than license raj. NKC cannot bring about a generational change by repeating the key mistake that led to the wrong knowledge management practice that failed over the past 60 years.

When branding by Western endorsement (and not demonstrable practical value) is the basis of expert selection, there is a serious risk of selecting the wrong experts. The risk of bad expert advice is greatly enhanced in the absence of any functioning mechanism to monitor ethics. Combined with the bureaucratic pursuit of safety in following Western precedents, this has led to continued aping of the West, a la Macaulay. Hence India failed to produce any serious original science in the last 60 years. But, the NKC is using the very same experts who contributed to this past failure. Hence the NKC has no room for any fundamental new ideas such as the new approach to mathematics and its teaching that I have proposed: while it contributes practical value, it is contrary to Western ideas hence inadmissible.

The key argument in favour of bringing in the private sector is that it would introduce good management practices, and not merely that it would introduce a new set of beneficiaries, and a new source of interference in education in addition to politicians and bureaucrats. We can be a knowledge society only when truly knowledgeable people have a significantly expanded role. That still seems a distant dream.

I hope you will take my points in the spirit of frank criticism: my ethics obliges me to speak out, though I have no wish to add to the long list of Indian science and technology managers who invariably turned hostile after I criticised them.

With all good wishes,

Yours sincerely,

C. K. Raju

Copy to:

Prof. D. P. Chattopadhyaya, Chairman, CSC
Prof. S. K. Thorat, Chairperson, UGC
Prof. Krishna Kumar, Director, NCERT

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