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