Path: ...!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!eternal-september.org!.POSTED!not-for-mail
From: Richard Heathfield <rjh@cpax.org.uk>
Newsgroups: comp.theory
Subject: Re: Halting Problem: What Constitutes Pathological Input
Date: Tue, 6 May 2025 07:10:03 +0100
Organization: Fix this later
Lines: 27
Message-ID: <vvc93r$29pp8$3@dont-email.me>
References: <GE4SP.47558$VBab.42930@fx08.ams4> <vvamqc$o6v5$4@dont-email.me>
 <vvan7q$o4v0$1@dont-email.me> <ts5SP.113145$_Npd.41800@fx01.ams4>
 <vvat0g$vtiu$1@dont-email.me> <vvatf3$o4v0$3@dont-email.me>
 <vvaut0$vtiu$4@dont-email.me> <vvav6o$o4v0$4@dont-email.me>
 <vvb329$15u5b$1@dont-email.me> <vvb37g$1451r$1@dont-email.me>
 <vvb43f$15u5b$4@dont-email.me> <vvb8fm$1a9jr$1@dont-email.me>
 <vvc4ok$26dgq$1@dont-email.me>
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 7bit
Injection-Date: Tue, 06 May 2025 08:10:04 +0200 (CEST)
Injection-Info: dont-email.me; posting-host="4489552a91c35915dbf980ce94c452ca";
	logging-data="2418472"; mail-complaints-to="abuse@eternal-september.org";	posting-account="U2FsdGVkX1/lLb9lUK+XEEvjHtgFcZvl80PGRXUuVgNBBaKdXl6hEg=="
User-Agent: Mozilla Thunderbird
Cancel-Lock: sha1:FiKHye413poTSCQPcEEiqsubHeY=
In-Reply-To: <vvc4ok$26dgq$1@dont-email.me>
Content-Language: en-GB
Bytes: 2536

On 06/05/2025 05:55, olcott wrote:
> *EVERYONE IGNORES THIS*
> It is very simple the mapping from inputs to outputs
> must have a well defined sequence of steps.

What you're ignoring is that not every well defined sequence of 
steps we can imagine writing will necessarily produce a correct 
mapping from inputs to outputs.

To convince yourself of this, try to construct an algorithm that 
will universally and correctly decide whether any program you are 
given will halt for the input you're given. When you think you 
have done so, let Turing know, and he will show you how to build 
a program that your 'universal' program can't analyse.

Your problem is not that you don't understand Turing's logic, but 
that you can't believe the place it takes you. Logic isn't a 
matter of belief, of course, any more than Pythagoras is; it's 
more of a failure to accept the counter-intuitive result that 
there really are some programs that can't be written.

-- 
Richard Heathfield
Email: rjh at cpax dot org dot uk
"Usenet is a strange place" - dmr 29 July 1999
Sig line 4 vacant - apply within