Hal Ruhl wrote:
> Here is a revised version of my comments on this subject.  I think it fixes 
> several aspects of what I have had to say earlier.
> Standalone deterministic evolving universes:
> Such a universe is describable as a concatenation of single output programs 
> of the form:
>           Rj(Aj) -> B; Rj(B) -> C; ... Rj(F) -> G; Rj(G) -> H; Rj(H) -> I; 
> ....
> "Rj" is a subset of the rules of an N-bit FAS.  "Aj" is an axiom of that 
> FAS.  There are no potential branches in or out.  It is an elegant proof 
> and defines the complexity of each of its objects B,C,...F,G,H,I ...
> Because the proof is everywhere elegant each successive object is more 
> complex than its preimage.  This is the type of theorem cascade I was 
> trying to identify.

This last statement is surely incorrect. Because the map Rj is a
mechanical application of rules, the complexity of B is no greater
than that of Aj - you can only get out what you put in.


Dr. Russell Standish                     Director
High Performance Computing Support Unit, Phone 9385 6967                    
UNSW SYDNEY 2052                         Fax   9385 6965                    
Australia                                [EMAIL PROTECTED]             
Room 2075, Red Centre                    http://parallel.hpc.unsw.edu.au/rks

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