FOM: infinity of the universe...  Allen Hazen a.hazen at Sat Nov
4 07:59:21 EST 2000  A propos Holmes's post on the infinity of
the universe.    Suppose the universe IS infinite in extent (for
every natural number there is a region of space of nore than
that number of cubic light-years in volume).  It doesn't
automatically follow that interesting mathematical assertions,
such as Goldbach's conjecture, have physical interpretations:
for that we need not only lots of physical entities (to take the
place of the numbers) but also physical RELATIONS to interpret
the mathematical predicates (& function-expressions), and it
isn't obvious to me that these will be available.    Simple
example.  Suppose that the infinite physical universe is like
the American Mid-west: a vast and boring plain stretching out
farther than the eye can see.  And suppose the objects chosen to
represent the numbers are the (indistinguishable except by their
position) fence-posts in a fence that stretches off to infinity.
Now, one of the mat