Remark on History of Anthropology and Mathematics

 

This remark inspired by David Mills (Department of Education, University of Oxford) paper "After Malinowski..." ( Ethnicity seminar at ISCA 1.03.2013 ). David described Malinowski style of doing anthropological seminar at LSE with its interactive way of presentation, formalism,"raumkunst" and, of course, pub. It became puzzling for today's anthropologists because mathematical aspects of Malinowski functionalist thinking ( as well as Levi-Strauss algebraist thinking) are ignored usually in anthropological departments.Mathematically speaking, however, it is quite understandable - Malinowski was mathematician among anthropologists, he had training in Calculus,theory of functions, functional analysis and, purhaps, in theory of differential equations. Hence, he tried to reproduce traditional mathematical style of seminar with freedom to ask questions, freedom of associations, and with exactness of definitions at the same time in ethnography of 1930s. Even today such details of mathematical seminars ( including pub) remain unchangable.It is interesting that Malinowski had opposition to algebraic style as well ( his snobish remark on "kinship algebra", for example ). In comparison with Levi-Strauss, working under applications of category mathematics and modular algebra in kinship classifications ( together with Andre Weil ), B. Malinowski ,probably, could be defined as "topologist",indeed. As is known it is the most ancient division into mathematical thinking at all. Thus,mathematical aspects of anthropology history are also essential ...

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Comment by Michael Alexeevich Popov on March 18, 2013 at 12:42pm

Thank You.

Bronislav Malinowski's PhD "On Principle of Economy of Thought " was connected with Mach's mathematical physics and he used his knowledge of calculus for applications in social anthropology ( culture as integral function, for example ). As a founder of social anthropology ( as social science ) he understood that real applications of mathematics is not simple re-writing of well-known patterns. In particularly, reality contains equations having complex roots ,probabilities expressed by complex numbers etc. Andre Weil showed that some ethnographic problems could be solved by applications of elementary algebra as well as contemporary category mathematics. Thus, in order to represent holistic reality in anthropology we cannot avoid mathematics ( incl. number theory, zeta functions, complex analysis of social networks, simulations, some areas of mathematical physics, etc ). However,cross-cultural differences between culture of arts and culture of science are essential today. Malinowski and Levi-Strauss knew how to overcome it

Comment by M Izabel on March 17, 2013 at 6:15am

Why are these mathematical? Do you mean symbolic? 

"freedom to ask questions, freedom of associations, and with exactness of definitions"

As far as mathematicalization of anthropology is concerned, besides statistics and econometrics, only these four seem applicable: mathematical logic, set theory, category theory, and computational theory.  I wish I were a mathematician. I would definitely explore culture using foundations of mathematics.  My logic is simple: if zero exists in reality as nothingness and infinity as limitlessness, mathematics to me seems a representation of reality using a different language.    

Comment by Alice C. Linsley on March 8, 2013 at 12:11pm

In kinship analysis finding the pattern is easier for people who think mathematically, I think. It took me over 20 years to identify the marriage and ascendancy pattern of the Horite ruler-priests. These brilliant men would have discovered it readily.

Thanks for this thoughtful remark.  Excellent!   

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