Re: Turing vs math

From: Jacques M. Mallah <jqm1584.domain.name.hidden>
Date: Wed, 27 Oct 1999 17:09:50 -0400 (EDT)

On Wed, 27 Oct 1999, Juergen Schmidhuber wrote:
> Jacques:
> >On the contrary. Why assume the lack of *any* given type of
> >mathematical stucture? A true everything-hypothesis surely would not.
> >Occam's razor says: don't add extra distinctions such as a restriction
> >like that.
> >Note also that, as I said, computability isn't the real issue. A
> >Turing machine can not be a continuous (but computable) structure. Of
> >course the non-computable stuctures should exist too in an everything -
> >hypothesis.
>
> The "non-computable structures" are just an ill-defined fidget of our
> imagination. They do not exist in the sense that we cannot formally
> describe them with a finite number of bits. Textbooks and theorems about
> real numbers are computable (finite symbol strings, finite proofs), most
> real numbers are not.

        I don't really know what you mean, but it sounds like you're
saying, you don't think real-valued quantities can exist because real
#'s can't be described with a finite # of bits.
        But as you admit, *sets* of real #'s can easily be described by
us. Remember, the whole point of the everything-hypothesis is that a set
is simpler than the sum of its parts, and that all the parts exist.

> Occam's razor really says: do not add any bits beyond those necessary
> to explain the data. Observed data does not require more than a finite
> number of bits, and never will.

        The claim of the everything hypothesis is that it requires 0 bits.

> Non-computability is not a restriction. It is an unnecessary extension
> that greatly complicates things, so much that we cannot even talk about
> it in a formal way.

        No one said it was a restriction. I said your approach involves
an extra restriction. And if you're claiming that non-computable
structures are not well defined, that's just false.

                         - - - - - - -
              Jacques Mallah (jqm1584.domain.name.hidden)
       Graduate Student / Many Worlder / Devil's Advocate
"I know what no one else knows" - 'Runaway Train', Soul Asylum
            My URL: http://pages.nyu.edu/~jqm1584/
Received on Wed Oct 27 1999 - 14:13:22 PDT

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