Dear Friammers,
We have decided to carry on from our seminar on Emergence to one on
Mathematical Thinking. Although we don't meet for a month, I found myself
reading the first assignment, Thurston's On Proof and Progress in Mathematics.
Now Thurston loves mathematics and is apparently good at it, but he is firm in
arguing that the process of proof is not as the normative account would have
it. Given our local debates about the ideal of formalism and given my
suspicion that many computer programmers suffer from math envy (the way
experimental psychologists suffer from physics envy), I was astonished by the
following paragraphs.
The standared of correctness and completeness necessary to get a computer
program to work at all is a couple of orders of magnitude higher than the
mathematical community's standard of valid proof.
Astonished, and yet, instantly convinced that it was true. Note that Thurston
is proud of how mathematicians do their work; no criticism here.
I think that mathematics is one of the most intellectually gratifying of huan
activities. Because we have a high standard for clear and convincing thinking
and because we place a high value on listening to and trying to understand each
other, we don't engage in interminable arguments and endless redoing of our
mathematics. We are prepared to be convinced by others. Intellctually,
mathematics moves very quickly. Entire mathmatical landscapes change and
change again in amazing ways during a single career.
When one considers how hard it is to write a computer program even approaching
the intellectual scope of a good mathematical paper and how much greater time
and effort have to be put into it to make it 'almost'formally correct, it is
preposterous to claim that mathematics as we practice is any where near
formally corrrect.
You would almost think that computer programming was the Queen of the Sciences.
Nick
I wonder what you all think about it.
Nick
Nicholas S. Thompson
Emeritus Professor of Psychology and Ethology,
Clark University ([email protected])
http://home.earthlink.net/~nickthompson/naturaldesigns/
http://www.cusf.org [City University of Santa Fe]
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