Special session of the 38th Indian Social Science
29 March-2 April 2015
The Indian Social Science Academy will be holding the 38th Indian Social Science Congress at the Andhra University, Vishakapatnam from 29 March to 2 April 2015. (See details at http://www.issaindia.com/welcome.php.) This meeting expects to deliberate on the existing knowledge system and its relevance for the Indian people. This is a call for participation in a special session on decolonisation of mathematics planned during this Congress. Because of the novelty of this session, it calls for detailed explanation.
The present-day university system is modelled on the Western university. Historically, that system was set up by the church during the Crusades, and globalised by colonialism. Because the Western university system was designed for the “needs” of the church, it developed “academic” processes designed to preserve church myths (“authorised knowledge”) and insulate them from critiques. One simple method was to eliminate critics: it is well known how the church tortured and killed critics (or suspected critics) during the long centuries of the Inquisition. Another method was to silence critics through censorship: no material was allowed to be published without prior approval based on a secretive evaluation; secrecy being the essence of the method. There were numerous other propagandist methods such as abusing the critic (typically denounced as a heretic) or simply striking a pose of superiority, and maintaining it by debate avoidance.
Our concern is with the way the legacy of these propagandist methods still flourishes in the present-day university system. The critic is not killed but is ostracised: as every young woman knows, there are no jobs for people who question prevailing academic orthodoxies. Secretive reviews are an integral and essential aspect of present-day academics; the performance of universities and their faculty is evaluated on that basis. While peer review is good, such reviews should be public, and post-publication, as argued in my booklet Ending Academic Imperialism. Secretive processes can be easily manipulated; no one will accept secrecy in a method of resolving property disputes, so why should secrecy be essential to settle academic disputes? That church method of critic control is often passed off as “quality control” using the hate technique of denouncing the critic (as a “crank” not “heretic”, etc.).
These methods achieve what they were designed to do: preserve myths and beliefs which would not survive public debate. Thus, these methods avoid ever publicly engaging with the critique; that was useful to the church which aimed for myth preservation, not truth. But such Western “academic” traditions ought to have no place in education or processes related to knowledge in a free society.
As a concrete example, consider the myth of “Euclid” who was declared in the West as the father of “real” mathematics. There is no evidence for “Euclid”, and plenty of counter evidence that the book Elements was written at a completely different time, by a different author, for a different purpose. No one came forward to claim the “Euclid” challenge prize of USD 3300 for serious evidence about “Euclid”. However, editors of Western scholarly journals will summarily refuse to entertain papers related to the non-existence of “Euclid”, for that is the only way to preserve the myth. Further, because of these bad Western “academic” processes, our school texts remain unchanged, and preserve that myth despite lack of evidence. Those school texts, exactly like Wikipedia, continue to indoctrinate millions in the false history of “Euclid”. That myth of “Euclid” was propagated by the Crusading church, to support its sudden adoption of rational theology (adapted from Islamic rational theology) as a way to persuade Muslims after the military failure of the later Crusades.
The persistent effects of such myths are amazing. Contrary to the myth, the book Elements purportedly written by “Euclid” is not, in fact, about axiomatic proofs: even its first proposition involves empirical proof, as does its proof of the 47th proposition (“Pythagorean theorem”). Because of bad Western academic processes, this elementary fact in an elementary book remained suppressed for centuries, for it was contrary to the myth. Though the fact was finally admitted in the 20th c., the attempts to preserve the myth continued with Russell, Hilbert, and Birkhoff who tried to recast the book to fit the myth. Those attempts failed. For example Hilbert's synthetic geometry does not fit the Elements beyond proposition 34 which is metric. Birkhoff's metric axiomatisation trivialises the book. There is not as yet any way to reconcile the book with the myth that it concerns axiomatic proof.
Nevertheless, mathematics education today continues to be anchored on those myths or the derivative philosophies of formalism, just by declaring that to be “superior”, as racist historians did, or claiming it is “rigorous”. Such declarations are dishonestly combined with persistent debate-avoidance, for decades, for example on the issue of whether 2-valued logic on which deductive mathematical proofs are today based comes from culture or experience (or from God). (Any choice is fatal to the claim that deductive proofs are superior to empirical proofs.)
Another myth is about the “aesthetic” value of mathematics. Plato and “Neoplatonists” did indeed club mathematics and music, as ways of literally arousing the soul. Hence they declared mathematics and music was important for its spiritual and religious value, not practical value. The book Elements aimed to demonstrate that mathematics leads to the “blessed life”. However, today, while the aesthetic value of music is manifest, it is equally manifest that formal mathematics has turned into an ugly nightmare for most students, not an aesthetic experience. That honest experience of the common student is more important than the empty claims of “experts” with vested interests.
Anyway, the fact is that most students today study mathematics for its practical value (for commerce, science, engineering). Setting aside false Western history (church history, racist history, colonial history), much of this mathematics (arithmetic, algebra, trigonometry, calculus, probability) originated in India, and was transmitted to Europe for its practical value. For example, Greek and Roman ways of doing arithmetic with an abacus were primitive, and Europeans (starting with Florentine merchants) themselves abandoned the Roman system of arithmetic as inferior, and disadvantageous for commerce. They adopted Indian arithmetic techniques called algorithms, or “Arabic numerals”, for they first came to Christian Europe through Cordoba via al Khwarizmi's (“algorismus”) book Hisab al Hind. Just as the phrase “Arabic numerals” incorporates Gerbert's misunderstanding of that arithmetic (that there was some magic in the shape of the numerals, which made arithmetic efficient) the very words “zero”, “surd”, “sine”, “trigonometry”, still in current use, tell the story of centuries of European incomprehension of that imported mathematics, which led to centuries of struggle before its eventual acceptance.
The most severe conceptual difficulties were created by the infinite series of the Indian calculus which did not fit the European religious understanding of mathematics as “eternal truth” or “perfect” and error free. That European incomprehension, accompanied by the attempts to make infinite series “theologically correct”, led to the creation of an enormous body of metaphysics which has nil practical value. Indeed, that metaphysics is of negative practical value: for example, Newton's metaphysics of the calculus (fluxions) led to his conceptual error about time (that “mathematical time flows equably”) because of which Newtonian physics failed. That huge overhead of the redundant metaphysics of infinity/eternity is also what makes math difficult. However, historically speaking, the practical math which Europe had earlier imported, was loaded with that add-on Western metaphysics, and was returned to India and globalised during colonialism. This dangerous cocktail of metaphysics and practical value was, as usual, declared a “superior” way to do mathematics. That is how it is taught today while dishonestly avoiding any public questioning of that claim of superiority.
While an alternative philosophy and pedagogy of mathematics has been developed, and its advantages demonstrated, there seems little possibility that this would ever be discussed in the West. After all, it wasn't only Western philosophers like Kant, Hume, Carlyle etc. who declared themselves superior, for some trivial and fallacious reason, passed off as deep philosophy. The philosophy curriculum of most Western universities still reflects the church abhorrence of “heresy”, by excluding Indian philosophy, for example. That can be studied only as part of “cultural” studies, but not philosophy proper. Likewise, an alternative philosophy of mathematics can be discussed in the West only under the rubric of “ethnomathematics”, that is by marginalising it to cultural studies, so it would not impinge on “mainstream” school and university teaching, but would only provide a wailing wall.
However, the demonstrated fact is that new decolonised pedagogy of math, which focuses on the practical value of math, not only makes hard math (such as calculus, or stochastic differential equations) easy, it enhances practical value, since students can do harder problems. The bad methods of university calculus are responsible for the problems related to infinities which still plague contemporary physics (as in the renormalization problem of quantum field theory, or shock waves in general relativity, or runaway solutions in electrodynamics), can be better resolved using the new philosophy of zeroism, and the traditional Indian “non-Archimedean” arithmetic. This is true also for the philosophical problems which still plague the Western metaphysics of probability. Therefore, we refuse to blindly accept that Western metaphysics as “superior”. On the contrary, the persistent Western debate avoidance on that claim is a tacit admission of inferiority.
Since the Western academic system is not open to a discussion of such issues, it is hardly possible to discuss within that system the numerous further issues associated with decolonisation and curricular reform, which involves a large-scale critique of Western “authorised knowledge”, in mathematics and science. Such a discussion has to be done outside of Western “editorial” or political control. Therefore, for any decolonisation of the curriculum to proceed, it is necessary first to reform the Western system of validating knowledge and break the Western taboos on discussing non-Western knowledge except as cultural artefacts.
Accordingly, we plan to go back to the ancient Indian tradition of public debate as the most transparent way to tackle fundamental disputes related to knowledge and its validation. There must be public criticism and debate on the Western belief in “superiority” of Western knowledge: and for asking whether that works for the benefit of non-Western people or against them. We believe knowledge must be subject to the most stringent tests and public review: therefore alternative viewpoints too must be subject to the same norm of public debate. That is something not possible within the tradition of church-inspired academics, which seeks to marginalise them.
Our goal, of course, is a practical one, and we intend to proceed beyond discussion to action: if the claims of the superiority of Western knowledge cannot be publicly established, we fully intend to proceed to petition the government to change the school and university education system, so as to teach knowledge relevant to the needs of our people, and avoid blind imitation of the West, especially as regards mathematics and science.
Accordingly, a special session involving public debate on some or all of the preceding propositions related to mathematics, its pedagogy, its practical use in physics (or the stock market) is planned. Note that this is NOT a session on paper-reading or polemics or sermonising. This is a call for physical participation in public disputation between scholars. Those who participate do NOT need to submit a paper. But they should indicate their intent to participate, and possibly also indicate in a few lines any specific propositions that they would be challenging. They are expected to come prepared with the purva paksa: knowledge of the opponent's position, since Ignorance (or misrepresentation) of the purva paksa is a traditional ground for losing the debate. To facilitate this, an initial list of books, articles and videos supporting the above propositions (some of which may seem strange) is put up at http://ckraju.net/papers/Reading-list-Bengaluru.html. The list should ideally be traversed recursively, for there are many more references involved.
C. K. Raju
President, Indian Social Science Academy,
and Chairperson, Mathematics and Statistics Research Committee