Christopher Maloney <[EMAIL PROTECTED]> posted:
To: everything-list <[EMAIL PROTECTED]>
Sent: Saturday, November 13, 1999 10:25 PM
Subject: Re: White Rabbits and QM
> Russell Standish wrote:
> > Introduction
> > Wigner[8] once remarked on ``the unreasonable effectiveness of
> > mathematics'', encapsulating in one phrase the mystery of why the
> > scientific enterprise is so successful. There is an aesthetic
> > principle at large, whereby scientific theories are chosen according
> > to their beauty, or simplicity. These then must be tested by
> > experiment -- the surprising thing is that the aesthetic quality of a
> > theory is often a good predictor of that theory's explanatory and
> > predictive power.
>
> I would go so far as to say that it is a good predictor of a theory's
> validity, or truth.  Explanatory or predictive power is not dependent
> on simplicity.

It always seemed to me that Eugene Wigner's epigram was made possible only
by ignoring the effect of Darwinian selection. We should recall that the
famous formula n(n+1)/2 for the area of a circle with radius n has fallen
into total disuse, not because of its lack of elegance but because it is
ridiculously inaccurate.

For exactly the same reason, nobody any more uses the slick p*r^2 to sum the
numbers from p to r. It's a nice looking expression, catchy even, but it
gives wrong answers.

This is why the Platonic mood of so many math aficionados strikes me as odd.
The correspondence between mathematical structures and the real world -- or
anything else -- is utterly of our choosing, it seems to me.

                                      Cheers,

                                           -dlj.



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