FOM: infinity of the universe and other points holmes at
Fri Nov 3 13:35:21 EST 2000

Dear All: 

Dr. Kanovei is misinformed about the position of "science"
on the infinity of the universe.  The current best opinion is that the
universe is infinite in extent (though only a finite part of it is
accessible in practical terms).  It will also apparently have infinite
future duration.  This is based on the current estimates of the
density and rate of expansion of the universe.

If the universe is infinite in extent, then it is straightforward to
model the natural numbers and even the reals using physical objects;
such models will not be useful in practice, but they would serve to
eliminate some kinds of ontological objections.

In particular, Goldbach's conjecture (or any assertion of arithmetic)
could be phrased as an assertion about physical objects (though not an
assertion in which a physicist would be interested).

I think that the basis of Kanovei's position is philosophical rather
than scientific, and in fact stems from an extreme philosophical
position (not an unusual one (for non-mathematicians), but not one
that commands universal "of course..." assent).

And God posted an angel with a flaming sword at | Sincerely, M. Randall Holmes
the gates of Cantor's paradise, that the       | Boise State U. (disavows all) 
slow-witted and the deliberately obtuse might | holmes at
not glimpse the wonders therein. |

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