Dear Bruno:

At , you wrote:
>Hal Ruhl wrote:
>
> >The assumption leads to a contradiction when "String N" exceeds the
> >complexity allowed by Chaitin.  More information must be added to the
> >cascade for it to continue.
>
>Why ? Only if your FAS produces as output just the "string N"
>and then stop, then there would indeed be a contradiction.

That seems to be mostly what I said.  Each cascade is a self contained 
FAS.  Each is a one trick pony.  Each trick is a universe. Each step in the 
trick is a state of that universe.  It is a very very big pony show.  The 
result is universal computation including random history universes.

But cascades of this sort suffer the contradiction.  The FAS has to grow - 
the cascade gets an injection of complexity .

Now identify each cascade current step as actually a particular isomorphism 
linked to a particular pattern in an ocean of patterns - my 
Superverse.  Each new step is a jump to a new pattern.

The cascade steps are shifts of the link to another pattern.

Hal



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