On 5/31/2012 10:57 AM, Bruno Marchal wrote:
it even has something to do with intelligence. When Alan Turing designed the first
stored program electronic digital computer, the Manchester Mark 1, he insisted it have
a hardware random number generator incorporated in it because he felt that
pseudo-random numbers being produced by a numerical process could not be truly random.
He thought that if a machine could sometimes make purely random guesses and then use
logic to examine the validity of those guesses it might be able to overcome some of the
limitations he himself had found in pure Turing Machines (although he never used that
name for them), and then you could make what he called a "Learning Machine. He thought
that in this way the limitations all deterministic processes have that he and Godel had
found might be overcome, at least in part.
For problem solving this in vindicated by the result that Random Oracle can enlarged
classes of problem solving. Those are given by necessary non constructive proofs. This
does not overcome Incompleteness or insolubility, but can reduce complexities in
relative way. That might play a role in the first person indeterminacy comp measure
problem, as it gives freely a first person "random Oracle" a priori, relativized by
their many computational extensions.
And it is a very likely trick for evolution to have developed since making random choices
is part of optimum strategies in games with incomplete information.
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