Mathematics and anthropology

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Mathematics and anthropology... how can I resist such a topic?

Most of the mathematics I know has no conceivable application to
anthropology (at least directly; the physicists use some weird stuff,
and the chemists use some of that, and...). Does anyone know of any
work in the social sciences which uses algebraic topology, functional
analysis, or category theory? (The question of why mathematics is
any use at all for understanding the universe crops up frequently in
philosophy and physics.)

The mathematical methods most commonly used in the social sciences are
some areas of statistics and basic calculus. Information theory and
chaos theory are often invoked, but rarely at a concrete enough level
to allow actual mathematical methods to be deployed. (Anyone want to
tell me what the fractal dimension of the Toraja kinship system is? :-)
These are probably the most commonly used mathematical methods in
the natural sciences too (though DEs become more prominent there).

Despite this, I believe that the most valuable thing mathematicical
training can contribute to students of anthropology is not knowledge
of a small range of methods of practical use (such as how to carry out
chi-squared tests or plot logistic growth curves), but the perspective
which mathematical intution and a training in abstract thinking can
bring. I'm not sure how easy this is to teach, however -- certainly
the lower undergraduate mathematics courses I have experience of
don't even start on it.

Danny Yee.

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