Re: What is the Result from Invoking this Halt Function?

From: Dave Vandervies (dj3vande_at_csclub.uwaterloo.ca)
Date: 08/24/04 

Date: Tue, 24 Aug 2004 17:25:33 +0000 (UTC)

In article <P9hUc.266078$a24.121278@attbi_s03>,
Marc Goodman <marc.goodman@comcast.net> wrote:

>Please note there are two separate possible statements here:
>1). It is not possible to do X
>2). Doing X is possible but adds no computational power.
>
>You may be making one or both of these statements.
>I have no argument with the second statement, it's the
>first statement I've been objecting to, and it's the first
>statement that I believe has been argued by many of the
>posters here.
>
>If you want to argue statement 2, then you should have
>no difficulty convincing Peter that Turing's proof
>still applies without having to argue that he can't
>use his "special mechanisms."

My eyes have glazed over on this particular subthread, but it started
with PO's claim that 'X'=='introspection' allows his "proof" to work.

When we're working with a turing machine, (1) is true; there's no way
in the definition of a turing machine for the machine to examine its
own state transition functions.

When we're working with PO's augmented turing machine, (1) is false,
but (2) is true. Outline of proof: For any augmented TM and augmented
UTM, we can run the AUTM on a UTM and run the ATM on the AUTM, and this
collection will do, in all cases, exactly what the ATM would be doing
with only the AUTM and not the UTM underneath, without any introspection
on the part of the UTM (which is what's "really" running).

dave 

-- 
Dave Vandervies        dj3vande@csclub.uwaterloo.ca
Don't blame me, blame Georg Cantor.
         --James Riden in the scary devil monastery

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