FOM: Effective and feasible computability (reply to Davis)

[Martin Davis]

At 02:44 PM 11/2/98 -0500, Joe Shipman wrote:

>
>Martin --
>It is the "strong finiteness of everything real" that is one of the questions
>at issue here.  The current best theories of fundamental physics contradict
>that assumption in several ways (use of real numbers in the formulation,
>physically measurable quantities as sums over infinite sets of scenarios,
>countably infinitely many "energy levels" even for a single particle, infinite
>potential energy for a gravitating system, infinite future time horizon), and
>Dyson and Tipler have each argued in extensive detail that one consequence of
>this is the possibility of arbitrarily large computations.  Is your "strong
>finiteness of everything real" a philosophical presupposition or do you have
>independent evidence for it?  If you do have independent evidence, how does it
>fit with the infinitary theories referred to above?
>-- JS
>
>
I am ignorant of this work by Dyson & Tipler, and can't comment on it. I
have two comments, nevertheless:
1. I do not agree that CT can in any way be effected by whether this physics
is or is not correct.
2. Even if there are infinitely long computations being physically realized,
thta does not in itself imply that there can be a physical device that can
compute with infinitely many different inputs.

Martin