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Raman's question (fwd)
Sender: jw@newt.phys.unsw.edu.au (Joe Wolfe)
Subject: WSN: Raman's question
> _/ E-mail: raman@bioc01.uthscsa.edu _/
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> _/ How can it be that mathematics, a product of human thought _/
> _/ independent of experience, is so admirably adapted to the _/
> _/ objects of reality? "-Albert Einstein" _/
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This question has appeared several times lately, along with its enigmatic
attribution in quotation marks. Here's my response:
Human thought itself is admirably adapted to objects of reality (or at
least that part/version of reality of which we conceive and of which
we talk and philosophise). Human thought has survived a natural selection
in culture just as the hardware that supports it has survived a genetic
natural selection. Ways (and means) of thinking, less admirably adapted,
might not have conferred a sufficient survival advantage.
Further, the mathematics that we have developed and used are almost
entirely those which are also "admirably adapted". They too have survived
a selection process: a little different, but with similar result.
Of course we are capable of developing poorly adapted systems of
mathematics. These are not widely known simple because they are poorly
adapted. Lie groups is one case that springs to mind - this topic lay
in obscurity until the sixties when it found a use in particle theory -
but I suspect that the dustier mathematical journals can boast quite
a few systems of mathematics that have yet to find their admirable
adaptation.
Finally a selection pressure operates on professional mathematicians:
quite a few ending up doing such things as molecular dynamics and
mathematical modelling for reasons that have more to do with the
proclaimed "realities" of grant-awarding bodies than with personal
inclination or with the inspirations and vagaries of "human thought
independent of experience".
Joe Wolfe, Physics, University of New South Wales, Sydney 2052 Australia
J.Wolfe@unsw.edu.au