Vedaaranya Heritage Arts and Healing Festival 2016 |
Dr C K Raju
School of Mathematical Sciences
Universiti Sains Malaysia
B-56, Tarang Apartments, 19 I P Extension, Delhi 110 092
Teaching mathematics with a different philosophy
This talk will report on a novel experiment in mathematics teaching being conducted in Malaysia. By way of background, the calculus developed in India and was imported into Europe in the 16th c. by Cochin-based Jesuits. However, it involved a mathematical philosophy which Europeans like Descartes and Newton completely failed to comprehend.1 (Descartes mistakenly thought curved lines could not be rigorously measured, while Newton thought he had made calculus rigorous by making time metaphysical, and his physics failed for that reason.) This European failure to comprehend foreign mathematics was analogous to the way Europeans like Pope Sylvester earlier failed to understand elementary arithmetic algorithms (“Arabic numerals”) when they were first imported into Europe in the 10th c. CE. This consequence of cultural differences in mathematics is in stark contrast to the Western claim that mathematics is universal but only the Greeks/Europeans correctly understood it. (This post- Crusade boast is contrary to elementary commonsense, and also relies on an ultra-chauvinistic history, with concocted characters like “Euclid” and “Claudius Ptolemy”, for whose existence there is not the slightest evidence.2)
On the principle that “phylogeny is ontogeny”, many students today hence find mathematics difficult, just because present-day mathematics teaching retraces the European trajectory of learning maths, together with its attendant difficulties.3 Furthermore, the European understanding of mathematics is deeply biased by Christian theological views4 of infinity (at the heart of set theory, and notions of limit and convergence), and this adds to the difficulties (though not to any practical value).
The new pedagogy is based on the idea that mathematics learning can be made easy by retracing the actual historical process by which that mathematics (especially calculus and trigonometry) developed. It also uses the philosophy of zeroism (a contemporary reformulation of sunyavada), which allows one to teach calculus without limits, in a way which is completely rigorous and also better adapted to computer technology. (This philosophy has various other contemporary advantages, e.g., it resolves the difficulties connected with the frequentist interpretation of probability, which cannot be handled by the old notion of limits; it also resolves difficulties connected with the formalist reformulation of calculus using Schwartz distributions etc.)
BIO :
1 C. K .Raju, Cultural Foundations of Mathematics, Pearson Longman, 2007. (PHISPC, vol X.4)
2 e.g., C K. Raju, “Towards Equity in Mathematics Education 1: Goodbye Euclid!”, Bharatiya Samajik Chintan, 7 (4)
(New Series) (2009) pp. 255 264; Teaching Racist History I,n dian J o u r n al of S e c ulari sm, 11(4), 2008, pp. 25 28.
Also, Is Science Western in Origin? (Dissenting Knowledges Pamphlet Series, No. 8, Multiversity, Penang, 2009).
3 C. K. Raju, “Math Wars and the Epistemic Divide in Mathematics , chp. 9 in ref 1. Also, paper presented at CRMSE, U. San Diego, and Episteme-1, Goa, 2004.
4 C. K. Raju, “The Religious Roots of Mathematics”, Th e o r y, Cultur e & S o ci ety 23(1 2) Jan-March 2006, Spl. Issue ed. Mike Featherstone, Couze Venn, Ryan Bishop, and John Phillips, pp. 95 97. Also, Euclid and Jesus: Mathematics and Religion Across Two Religious Wars, forthcoming.
Vedaaranya and Ramgarh Shekhawati