C. K. Raju
Mathematics is compulsorily taught in school to millions each year. Therefore, it sets a very healthy democratic precedent to decide the nature of math education by a public debate which James Glover has initiated in his response (Hindu, 15 October) to my article (Hindu, 3 September) on “Nothing Vedic in Vedic math”.
The claim that “It is ancient, hence Vedic” holds no water. For, how do we know it is ancient? Our actual source is a modern one: Krishna Tirtha. He never produced the relevant parishishta, even when challenged to do so by the late Kripa Shankar Shukla. How strange that not a single mathematician from Baudhayana, Aryabhata, Brahmagupta, Bhaskara, Varahamihira, Vatesvara, Uday Diwakar, Parameswaran, Madhava, to Nilkantha noticed or commented on these aphorisms for over two thousand years. Such faith-based history—based solely on the word of one person—should be clearly separated from history based on evidence. Else we only damage the credibility of the glorious history of mathematics in India, for which there is solid evidence.
Second, if everything ancient is Vedic, what about the anatmavada of Buddhists or Carvak? Accepting the denial of atman as “Vedic” knowledge damages the core philosophy of the Upanishads. Thus, stretching the meaning of the word “Vedic”, just to save Krishna Tirtha's story, has disastrous implications for Hinduism. Hence, that quibble about the meaning of “Vedic” should be rejected.
Besides, why is that label “Vedic” important? Is Vedic math to be taught because of the label “Vedic” or because of its practical value? If the latter, the misleading label “Vedic” should be gracefully dropped. If the former, or both, that would be a religious imposition.
A recent petition, signed by fifty people, addressed to top educational administrators, asks that mathematics should be taught in school only for its practical uses, and in a religiously neutral way. India is secular; therefore, religious propaganda should not be slipped into state-controlled education, even under the cover of its correlated practical value. Decisions on such issues concerning a vast mass of people should not be taken behind closed doors, just by some people designated “experts”. These “experts” must declare any conflict of interests, and publicly explain the reasons for their decisions.
A cocktail of practical value and religious propaganda can have obnoxious consequences. Post colonisation, math teaching in India blindly apes Western practices. That is a pity because most of that school mathematics (arithmetic, algebra, “trigonometry”, calculus, and probability), actually originated in India for its practical value. Europeans imported it also for its practical value. However, contrary to popular belief, the understanding of mathematics is not universal. Indian ganita accepted empirical proofs. This differed from the European understanding of math as metaphysics. Hence, over centuries, the West adapted the imported Indian math to fit their metaphysics, linked to church theology. During colonisation, it exported back this religiously coated mathematics, which is now taught globally. That metaphysical veneer is irrelevant to the practical applications of math, but instills religious biases in millions who learn math for its practical applications.
What exactly are those religious dogmas in Western mathematics? The very word mathematics derives from “mathesis” which means learning. In Plato's Meno, Socrates demonstrates an untutored slave boy's innate knowledge of mathematics. He then argues that, since the boy did not learn mathematics in this life, he must have learnt it in a previous life, so he has proved the existence of the soul! Socrates concludes that all “learning” involves the soul recollecting its eternal ideas. In Plato's Republic, he rejects the teaching of mathematics for its practical value, but prescribes it on the grounds that it is spiritually uplifting, like music. That notion of soul was, however, cursed by the post-Nicene church; how the links of religious belief to Western mathematics evolved subsequently is a complex story told for the layperson in my book Euclid and Jesus: How and why the church changed mathematics and Christianity across two religious wars.
Mathematics was considered especially suited to arouse the eternal soul since it was believed that mathematics contains eternal truths, and “like arouses like”. The belief in eternal truths, in turn, led to the Western belief that mathematics is “perfect”, and cannot tolerate the smallest error (for it would be exposed sometime during eternity). It was further thought that this perfection could be achieved only through metaphysics and not empirically: a real dot on a piece of paper can never be a “perfect” mathematical point howsoever much one may sharpen the pencil! Today, mathematics is 100% metaphysics on the philosophy of mathematics known as formalism, initiated by Bertrand Russell and others, and used to teach math in our schools and universities.
The belief that math is perfect is certainly not universal: Indian tradition accepted mathematics as non-eternal, and imperfect. The sulba sutra-s explicitly speak of anitya (impermanent) or savisesa (with something left out), and Aryabhata speaks of asanna (near value), while Nilakantha explains why the “real value” (vastavim samkhya) cannot be given. Tiny imperfections are inevitable and of little consequence for the practical applications of math. Most practical applications of mathematics today, such as sending a spacecraft to Mars, are done using computers which do math “imperfectly”.
Other aspects of Western metaphysics too are not universal. For example, on post-Crusade church theology, logic binds God but facts don't. That is, God cannot create an illogical world, but can create the facts of his choice. Hence the Western belief that logical (deductive) proofs which bind God are “stronger” than empirical proofs which don't. But which logic binds God? Contrary to naïve Western beliefs, logic and reasoning are not universal. Buddhist catuskoti or Jain syadvada are systems of logic which are not 2-valued (or even truth-functional), so teaching 2-valued logic as “universal” involves a religious bias. To avoid this bias, one can possibly choose logic on empirical grounds, but that would destroy the very basis of formalism that logical proofs are superior to empirical proofs.
Teaching Western metaphysics spreads other biases. All systems of Indian philosophy, without any exception, accept the pratyaksa, or empirically manifest, as the first means of proof. This also applies to ganita, e.g. Aryabhata declares that verticality is tested by a plumb line. Science and engineering, too, prefer empirical proofs to metaphysics. So if math is done for its practical applications it is better to accept empirical proofs in math. But present-day math teaches that such proofs, hence all Indian philosophy, is “inferior”. This is like compulsorily teaching Lokayata which rejects anumana (inference) as fallible, and would hence dismiss all Western philosophy as inferior.
Does any of this make a difference to 2+2=4? Yes. Why is 2+2=4? Putting together two pairs of apples to show four apples is erroneous on formalism which disallows reference to the empirical. Formalism posits that 2+2=4 can be “rigorously” deduced only metaphysically from, say, Peano's axioms. Most people don't know how to do that or even what Peano's axioms are. Thus, most Western educated never even properly learn 2+2=4! Since they are taught alongside that all other systems are inferior, they are compelled to rely blindly on Western authority for every little thing. This is by design. To put an end to this mental enslavement through indoctrination, education must be decolonised. India lags behind in decolonisation of education, and the new government ought to focus on that.