From: George Murphy (gmurphy@raex.com)
Date: Thu Sep 04 2003 - 08:26:04 EDT
It seems to me that some of the discussion about whether math is created or
discovered &c misses the forest for the trees, especially as the questions have to do
with the relevance of math for descriptions of the physical world. Einstein, e.g.,
starting from a few basic pieces of knowledge about the world, writes down a highly
non-trivial system of equations which are supposed to describe certain important aspects
of the world. These equations, while constrained somewhat by the data then available
(1915), are highly _under_determined_ by that data. For the next ~90 years then it's
found that all relevant observations that go beyond those of 1915 are in agreement with
Einstein's equations.
I am unable to see this as anything other than the ability of a human mind to
_discover_ an approximation to a pattern that exists in the world independently of human
minds. It certainly is not (as the positivists imagined) simply a matter of organizing
observational data because the data didn't exist when the equations were first written.
& certainly Einstin's mind didn't _create_ the regularities which were later found.
Note that I said discover an "approximation." To make the sort of claim that I
have made by no means requires that one believe the Einstein equations (or whatever) to
be the ultimate truth about the world. & in fact we may never discover the true
ultimate math pattern of the world. But we can get better & better approximations to
it.
Shalom,
George
George L. Murphy
gmurphy@raex.com
http://web.raex.com/~gmurphy/
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