Re: Provable vs Computable

From: Hal Ruhl <hjr.domain.name.hidden>
Date: Sun, 06 May 2001 22:22:30 -0700

Dear Bruno:

At , you wrote:
>Juergen Schmidhuber wrote
>
> >Which are the logically possible universes? Max Tegmark mentioned
> >a somewhat vaguely defined set of ``self-consistent mathematical
> >structures,'' implying provability of some sort. The postings of Bruno
> >Marchal and George Levy and Hal Ruhl also focus on what's provable and
> >what's not.
>
>You know that Hal Ruhl doesn't distinguish computability and provability,
>so
>it is open for me if his approach is nearer your's or mine.

Awhile ago I did identify computability and provability, but now see
provability as a subset of the computable. But is computable enough and
computable where [inside/outside a particular universe considerations]?

I place myself nearer your work Bruno and also that of Russell
Standish. This is particularly due to my stand that true random noise is
inherent in each universe within the Everything.

This does not mean that I consider the isomorphic tree I described in
another post to contain randomly generated strings [the horizontal
isomorphisms will be a list of all strings] but rather that isomorphic
links to these strings necessarily IMO have some random nature in the
determination of acceptable successor links - the evolution of the
active/inactive mix I described.

Also IMO the logics we may find in our universe derive from this foundation
not the reverse. If one looks at the frequency of events versus event size
in the "large" event region we find that some experiments in our universe
produce slopes close to but slightly higher than -1. The field
observations I have seen produce somewhat higher valued slopes going
towards -2. A slope of -1 would as I see it indicate a deterministic
cascade. However, one must also examine the "small" event part of the
spectrum. Here a slope of +1 IMO indicates a deterministic cascade but the
two ends of the spectrum need not be symmetric.

Our logic IMO is in the "large" event part of the spectrum and a thought
experiment as well [not even a "lab" let alone the "field"] and therefore
likely to be almost deterministic in our universe. IMO the incompleteness
types we have discovered do not have a large impact on our everyday use of
our reasoning methods.

Yours

Hal
Received on Sun May 06 2001 - 19:29:33 PDT