NP Alabama Pi

[desert search for techno allah]

jporter writes:
>Yes, but we are talking about Pi, the mathematical concept, and the growing
>realization that there may be no such animal as pure math, that math is just
>as messy and experimental as physics. You see, if one is to persist in
>believing that physics and *pure* mathematics (or any pure Platonic ideal,
>for that matter) never intersect, you will inevitably be forced to accept
>supernatural explanations for why mathematics works so well. (See my reply
>to Vaska).

Even believing that physics and pure math don't intersect (which I
think pretty much no one believes anyway), you're not forced into
metaphysical explanations. At least, not immediately - how much
the various solutions to this problem result in metaphysical
hooha is a matter of debate.

Wittgenstein's solution (that statements of mathematics are "rules of
syntax"), for one, appears to avoid metaphysical quandaries without
even caring whether or not there is a "pure" mathematics separate
from physics.

>You are taking the purity for granted. But it may all be in the eye of the
>beholder. In the Euclidean space with which we are most physically
>comfortable, Pi remains constant out as far as you care to look. In a
>reality where surfaces are spherical, where diameters must be drawn along
>the surface of a sphere (and bend with it), Pi would vary. Which serves to
>demonstrate that the particular "pure mathematical constant" you are
>referring to may be more of a comfortable invention than an absolute.

Again, precision helps:

The definition of pi that you're familiar with is only a definition
insofar as you also use the definitions of circle, diameter, etc.
that are part of Euclidean geometry. Of _course_ "pi" would vary
in some other geometry where "circle" and "diameter" didn't mean the
same things as in Euclidean geometry. But those numbers are no longer
pi. Context matters.

There are definitions which don't rely on geometry.



Josh

-- 
josh blog: http://www.public.iastate.edu/~kortbein/blog/
      tdr: http://www.public.iastate.edu/~kortbein/tdr/