Abstract for webinar: JNU, 16 Sep 2020

Statistics for social science and humanities:
should we teach it using normal math or formal math?

C. K. Raju

Indian Institute of Advanced Study
Rashtrapati Nivas, Shimla 171 005
ckr@ckraju.net

Abstract. Statistics has long been used in social sciences such as economics, psychology, education, medicine (including gender studies) etc. Further, a classic example of the application of statistics to history is the use of punch-marked coins by D. D. Kosambi. Statistics has also started being increasingly used in humanities, especially literature, in the analysis of texts (including ancient texts) given the digitization of numerous texts, though the few attempts on “digital humanities” in India have focussed on the use of digital rather than statistical techniques.

The key stumbling block in the use of statistical techniques is the general ignorance of mathematics among practitioners of social science and humanities. This ignorance arises from the extreme difficulty and complexity of the underlying formal math (measure theory, Lebesgue integral, Wiener measure etc.) involved in the current understanding of probability. (This applies also to many who use statistical techniques in AI, without understanding their limitations.)

However, historically speaking, probability and statistics (sampling theory) first developed in India, in connection with the game of dice, as described in the अक्ष सूक्त of the Rgveda, in the द्युत क्रीडा and also the romantic story of Nala and Damayanti, in the Mahabharata.¹ The related quantitative theory of permutations and combinations, and binomial expansion is described in numerous early Indian texts including the मेरु प्रस्तार (centuries before “Pascal’s triangle” made its appearance in Europe or even in China; there isn’t even the usual fake Western chauvinistic story of how the “Greeks” did it first!). This knowledge of probability was stolen from India by Cochin-based Jesuits in the 16^th c., and taken to Europe along with Indian calculus texts,² where Europeans suddenly “discovered” both calculus and probability, on the same genocidal “doctrine of Christian discovery” which enabled them to “discover” India, and Americas etc.

Like most intellectual thieves, Europeans understood some practical aspects, but failed to understand the subtleties of both calculus and probability, just as they had earlier failed to understand zero. Hence, they eventually evolved an inferior but extremely complicated solution (“formal mathematics”) to those epistemic problems,³ which already had an easy and elegant solution in the original normal mathematics.

In particular, the use of “real” numbers and limits, as in calculus, does NOT work in the case of probability, since relative frequencies converge to probability only in a probabilistic sense (convergence in measure), so that probability cannot be defined as the “limit” of relative frequency without begging the question. The subjectivist interpretation of probabilities clearly does not work in e.g. the case of peculiar probabilities in quantum mechanics.⁴ Popper’s “propensities” are mere verbiage linked to his wrong belief that he had solved the “problem” of induction.

In this connection, I describe how a decolonised course in calculus, designed by me, was conducted in universities in many countries, including Ambedkar University Delhi,⁵ to demonstrate that teaching calculus the way it originated as normal math, makes it very easy even for social scientists. This clears the way for students of social science and humanities to learn statistics. I briefly explain how this new course ENHANCES the ability to apply statistics in complex practical situations where formal math fails (e.g. stochastic processes driven by Levy motion). On this basis, a decolonised course in statistics for social science and humanities was designed per the requirements of the Malaysian Qualifications Agency. But, of course, this course is meant for those who want to USE the knowledge, and not for those who just want to ape the West.

About the speaker

C. K. Raju holds a PhD from the Indian Statistical Institute, Kolkata, preceded by an MSc in mathematics and a BSc (Hons) physics from Mumbai. He initially taught math and statistics, and researched in formal math (advanced functional analysis and applications to relativity and quantum field theory) for several years. Later, he was responsible for porting large applications (space, oil etc.) on India’s first supercomputer, Param, and that experience first led him to doubt formal math.

He has authored numerous research papers and several acclaimed books. In Cultural Foundations of Mathematics (Pearson Longman, 2007) he compiled evidence for the development of calculus in India (with a different philosophy, now called zeroism) and its transmission to Europe in the 16^th c., where it was not properly understood. In Time: Towards a Consistent Theory (Kluwer, 1994) he earlier explained why Newtonian physics failed for theoretical reasons, and was replaced by relativity (by Poincare), because Newton (failing to understand the Indian calculus) had made time metaphysical. He went on to outline a new physics, using functional differential equations, forced after relativity, but which Einstein failed to understand. In the Eleven Pictures of Time (Sage, 2003) he proposed a new way to relate science and religion through time. He has developed and taught decolonised courses on math, and the history and philosophy of science. His shorter books include Is Science Western in Origin? (Multiversity 2010), Ending Academic Imperialism (Citizens International, 2011) and Euclid and Jesus (Multiversity, 2012).

He has wide-ranging interests: he has headed India’s largest computer science department, been editor of the Journal of Indian Council of Philosophical Research and Vice-President of the Indian Social Science Academy. He has received several awards. Currently he is an Honorary Professor of the Indian Institute of Education, and Tagore Fellow at the Indian Institute of Advanced Study.

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