Jan/100
The Unreasonable Effectiveness of Mathematics
Today I came across and insightful discussion on a dark-ish corner of the philosophy of science: why does math describe the universe so well?
The Unreasonable Effectiveness of Mathematics by Richard. W. Hamming (of Hamming distance and Hamming window fame). Originally this article appeared in The American Mathematical Monthly Volume 87 Number 2 February 1980.
It's a bit of a long read, but here are some highlights:
Just as there are odors that dogs can smell and we cannot, as well as
sounds that dogs can hear and we cannot, so too there are wavelengths
of light we cannot see and flavors we cannot taste. Why then, given
our brains wired the way they are, does the remark "Perhaps there are
thoughts we cannot think," surprise you? Evolution, so far, may
possibly have blocked us from being able to think in some directions;
there could be unthinkable thoughts.
Having given four widely different examples of nontrivial situations
where it turns out that the original phenomenon arises from the
mathematical tools we use and not from the real world, I am ready to
strongly suggest that a lot of what we see comes from the glasses we
put on.
Mathematics has been made by man and therefore is apt to be altered
rather continuously by him. Perhaps the original sources of
mathematics were forced on us, but as in the example I have used we
see that in the development of so simple a concept as number we have
made choices for the extensions that were only partly controlled by
necessity and often, it seems to me, more by aesthetics. We have tried
to make mathematics a consistent, beautiful thing, and by so doing we
have had an amazing number of successful applications to the real
world.
Science in fact answers comparatively few problems. We have the
illusion that science has answers to most of our questions, but this
is not so. From the earliest of times man must have pondered over what
Truth, Beauty, and Justice are. But so far as I can see science has
contributed nothing to the answers, nor does it seem to me that
science will do much in the near future. So long as we use a
mathematics in which the whole is the sum of the parts we are not
likely to have mathematics as a major tool in examining these famous
three questions.
It makes me feel slightly less of a complete nutcase for holding some less-than-conventional ideas on the philosophy of science and mathematics. On the other hand, maybe Richard Hamming was a nutcase too.
Peter