Brownian thought space

Cognitive science, mostly, but more a sometimes structured random walk about things.

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Chronically curious モ..

Tuesday, May 15, 2007

Maths has no structure

Imagine a Martian; perhaps the same Martian that Chomsky & colleagues saw as looking down (up?) onto Earth and noticing the funny thing about language. Imagine that the Martian is a Bayesian dude, much like computational linguists (and others) today are, and he gets his hands on a bunch of mathematical derivations by, to pick random examples, Einstein and Bohr. If said Martian is anything like the computational people today, he would look at all the symbols, and try to extract the statistical probability that, say, the ')' symbol was followed by the '=' symbol, and so on. Then, being an empiricist, the Martian would involve him(her)self in a textbook alien abduction scenario and test how good this Bayesian statistical model of the Einstein/Bohr symbols was against a carefully chosen subject (it wouldn't make sense to pick a Tibetian monk to test a theory of maths symbols, just as it wouldn't make sense to pick a Navajo tribesman to test a Bayesian model derived from an English corpus). Let's assume that the fit is good. the Martian would claim that he(she) had now a good theory of (a) what the end state of a mathematically minded person is and (b) by adding a few more parameters, how acquisition would proceed, by updating a flat distribution against the data - p('='|')') would go from a small, (null) prior to a high value, given the data. Q.E.D.!
(Einstein himself might have objected)


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