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

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> 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.
Bruno
http://iridia.ulb.ac.be/~marchal/
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