[FOM] Directions for Computability Theory Beyond the Pure Mathematical

[Ryan Paul Nurmela]

Peter Gerdes wrote:
> Suppose we get lots of support for a theory like QM which postulates 
> random events.   

For the record, it is disputable as to whether or not QM is actually
postulating random events.  In fact, in the early part of this century
Einstein argued strongly against such an interpretation.  The view that
won out is referred to as the Copenhagen view, and it is this "view"
that claims QM is actually postulating random events.  The other
interpretation held by Einstein and those of like mind is that QM is
merely a formalism for determining the *statistics* of large numbers of
quantum interactions.  And indeed there is nothing in the mathematical
development of QM that forces one to believe in random events.
Randomness from QM is rather suggested at by its results and certainly
had a philosophical appeal for those who proposed it (Bohr) especially
when one considers the philosophical prejudices of that time.

While this is clearly not the popular viewpoint, it is not at all
inconsistent with QM itself.  This alternate viewpoint, however, forces
one to accept the belief that QM is not the final word on the quantum
world and begs for one to reach further as Einstein did in his
later years.  Modern developments in physics such as quantum loop
gravity seek a far more deterministic model of the world than that
proposed by many string and field theorists.

As for the future of mathematics in science I would hope that many
mathematicians are secretly of the mind that the world truly is
deterministic at its deepest level.  Godel, the true platonist, despised
the Copenhagen-view and had little appreciation for those who proposed
it.  But of course Godel and Einstein were good friends.

Ryan Nurmela
Physics graduate student