Re: Turing vs math

From: Juergen Schmidhuber <>
Date: Thu, 4 Nov 1999 09:33:36 +0100


>But in that case Schmidhuber generates also only rationnal approximation
>of the computable real number he is generating.
>I am not looking at the output of a process (nor is Schmidhuber), I am
>looking at the limit of that process after a countable time.
>So I insist, by admitting a countable time (not something which I get
>at any step) the dovetailing on the initial segments (which of course are
>just rationnals) gives a procedure dovetailing on ALL the reals.

In countably infinite time you can compute an entire real, but not
all reals.


>> The precise probabilities are never really computed.

>....Approximate probabilities based on approximations to the
>K. complexity of a string are no more computable than precise ones.
>There is no fixed bound B which allows you to compute the K. complexity
>of an arbitrary string within accuracy B.

You should add "within a given fixed time interval." Within finite
(though unknown) time you can compute the K of finite string x. In
general you'll just never know whether your current lowest upper bound
on K is tight.

Received on Thu Nov 04 1999 - 01:06:34 PST

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