Re: Turing vs math

From: Gilles HENRI <Gilles.Henri.domain.name.hidden>
Date: Wed, 27 Oct 1999 10:52:04 +0200

>>> Why assume non-computable stuff without compelling reason?
>>> Shaved by Occam's razor.
>
>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.
>
>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.
>
>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.
>
>Juergen Schmidhuber www.idsia.ch

It seems that the confusion is always the same...confusing a physical
reality with the approximate (computable ) theories that we have to
describe it. Of course physical theories are computable BY DEFINITION (the
aim of physics IS to find computable models of reality). But the assumption
that the reality itself is a computation is indeed a very strong,
restrictive and unneccessary one. Occam's razor deals with the world of
approximate theories, not with the physical world itself. For example it
justifies the use of Ptolemeus system to describe the motion of planets as
long as you don't require a dynamical theory...
I think you should just read again some ancient Greek philosophs who had
already understood the difference with the reality and the description that
we give from it..


Gilles
Received on Wed Oct 27 1999 - 01:57:33 PDT