Re: Provable vs Computable

From: Hal Ruhl <hjr.domain.name.hidden>
Date: Mon, 07 May 2001 22:15:03 -0700

Dear Bruno:

At , you wrote:
>Hal Ruhl wrote:
>
> >This is particularly due to my stand that true random noise is
> >inherent in each universe within the Everything.
>
>Remember that true random noise appear in the UDA because we don't know
>in which computation ("universe") we belong. So random noise does
>not need to be added. It is something we cannot avoid from our first
>person point of view of embedded observer.
>It is the point where Schmidhuber disagrees so much. We will come back
>on this question soon.

My position is a bit different - I think - in that I do not see observers
as essential to the presence of true random noise in a universe. The UD,
IMO - after a concatenation of its output strings into one long one that is
then altered at the knit points in some pattern - is within itself a single
valued elegant cascade. This would hold even if the activity around the
knit points is spread out along a region of the string as in Juergen's
model [If I have it right]. It is one out of an infinite number of similar
cascades that form a sub set within the more general isomorphism tree I
described.

My position is that all these attempted single valued elegant cascades run
into the complexity limit imposed by Chaitin's incompleteness in such a way
as to be unable to halt absent contradiction. The contradiction can only
be cured by an increase in complexity of the FAS governing the
cascade. The added information can only come from outside the
cascade. Not from outside the isomorphism tree.

If I have it right your approach is that the UD has an inherent true random
noise content if some of its sub strings define universes sufficiently rich
in logic to be subject to other incompleteness mechanisms especially if
observers are present. Actually I think you may be saying that the entire
UD is rich enough in any manifestation to necessarily posses this
characteristic. With this I would agree if a minimum possible complexity
UD can be shown to meet the threshold of these incompleteness mechanisms.

If you rely on the scanner transporter duplicator for this demonstration I
consider it to be the same as my E/N alternation.

However, in my approach the UD [all of them] are a small part of the
Everything.

> Well, I hope, because for teachers may and june are
>terrible :-(.

Perhaps this will allow me a chance to catch up with your logic posts.

Yours
Hal
Received on Mon May 07 2001 - 19:27:02 PDT