Le 31-juil.-06, à 23:32, John M a écrit :

> 1Z:
> I liked your examples, would have liked better if you do not base the 
> entire
> list on "matter to exist". It may not.
> I have a notion - cannot put my finger on an adequate formulation of 
> it into
> words - that mathematics cannot be computed by mathamatics - I think 
> Goedel
> would have some objections to that.
> Somebody tell me if this is a wrong idea. I will not fight it. (Not my
> table).

It is ok. Godel would have approved: the whole of formal mathematics 
cannot be "computed" by any formal mathematics. It is a little vague 
but this convey the main godelian point.

Concerning some of tyhe conversation between Brent, 1Z and Stathis, I 
would say that I don't see the relationship between computations and 
random string. Computations, or their description can be shown to be 
necessarily redundant, (and deep in Bennett' sense).

For Tom and Georges:
Take the Fi corresponding to 0-argument (fortran) programs. Any such 
program stops or does not stop. Consider the function which associates 
to n either 1 or 0 according to the fact that the nth program stop or 
does not stop. you get a deep complex and subtly redundant sequence of 
0 and 1.
If you decide to compress it maximally you will get Chaitin OMEGA 
number, which gives the probability that a Fi will stop or not, (but 
this cannot be done algorithmically). There is no reason to related 
consciousness to those random compression of computation. Look at 
nature from genome to the number PI: you will always see many 
redundancies. They are absent in the Putnam Chalmers rock. I don't 
think it makes sense to attribute computations in there (but then I 
don't care given that UDA makes us having to (re)define physics by 
winning (in some relative probabilistic sense) sheaf of relative 
computations existing in platonia.



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