[PO] Re: Refutation of the Halting Problem's Proof (Clarifications Wanted)

From: Simon G Best (s.g.best_at_btopenworld.com)
Date: 08/25/04 

Date: Wed, 25 Aug 2004 14:25:06 +0000 (UTC)

Peter Olcott wrote:
> www.halting-proiblem.com

You didn't even get your own web address right.

> I want to make what I am saying as clear as possible.

That is an excellent idea :-)

> If anyone
> has any points that are still not clear, this is the thread to ask for
> clarifications.
>
> Also I would like to work towards a consensus of the best way
> to present the ideas that are mentioned on my website, and in
> these threads. This might require me to formalize some of these
> points. I would be happy to make my material easier to understand,
> and eliminate any ambiguities. I welcome all constructive critiques.
>
> The end result of these discussions will be a website posting that most
> everyone can agree on the meaning of. In other words it should be
> clear to everyone what I am saying.
>
> If there seem to be any major gaps in what I am saying, please point
> these out. The most significant gap that I can see is exactly how to
> construct the augmented UTM without going beyond the capabilities
> of an regular TM. That this can be accomplished seems obvious.
> Exactly how this would be accomplished is less obvious.
>
> Thanks again for your time.

The first thing is the heading on the page, "Refuting the Undecidability
of the Halting Problem". It doesn't make sense. It's like, 'refuting
the ambiguity of English', or, 'refuting the redness of ripe tomatoes',
or, 'refuting the Welshness of Tom Jones', or, 'refuting the invincible
ignorance of net.kooks'.

The second thing is that you're calling your abstract a "Quick Summary",
rather than "Abstract". Of course, an abstract /is/ a quick summary,
but I'd suggest labelling it as an abstract. Other than that, your
abstract needs to be completely rewritten. Fortunately, that's
something that can be left until the rest of your document has been
completely rewritten.

Next, "Definition of the Halting Problem". It's still wrong. The
Halting Problem is the problem of determining whether or not an
arbitrary Turing Machine, M, would halt on an arbitrary input, x. More
specifically, it is the problem of finding a Turing Machine which
carries out such determinations in the general case where M may be any
(in the sense of each and every) Turing Machine, and x may be any (again
in the sense of each and every) input.

You may also need to include a number of other definitions, or at least
clearly refer to accepted, established definitions of terms and the like.

The rest of the document also needs to be completely rewritten.

It'll still be wrong, though.

Simon

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