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From: Richard Heathfield <rjh@cpax.org.uk>
Newsgroups: comp.theory
Subject: Re: Functions computed by Turing Machines MUST apply finite string
 transformations to inputs
Date: Mon, 5 May 2025 09:55:05 +0100
Organization: Fix this later
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On 05/05/2025 05:00, Mike Terry wrote:
> On 04/05/2025 22:18, Richard Heathfield wrote:
>> 

<snip>

>>>[Of course, PO cannot provide such an H.]
>>
>> Well, it's not hard. Scaffolding first (not for publication):
>>
>> 1) he writes H(P,D), which hashes P and D (md5 hash, say? Or 
>> even just add up the bits!) and returns mod 2 of the result, 
>> interpreting 0 as 'loops' and 1 as 'halts'
>> 2) he waves Turing's magic wand and sees whether he gets the 
>> result he needs for (<H^><H^>).
>> 3) if so, great! But if not, he reverses the meanings of 0 and 1.
>> 4) remove from the docs all signs of fiddling the mod 2 meanings.
>>
>> Having 'tuned' his PPHD, he can now publish and claim his place 
>> in history.
> 
> Ah, that's not what I thought you were thinking.

Why do I get the feeling that I'm not quite as clever as you 
thought I was? :-)

> What you're suggesting doesn't work!  Remember the order

We choose a door /first/, and /then/ Monty shows us a goat...

I have absolutely no doubt that you're right and that my 'hack' 
is ill-considered, but my eyes are starting to bleed, so instead 
of point-to-pointing you I'm going to bail and retreat to my 
LaTeX coal face.

<snip>

> PO likes to imagine that there's something Wrong with H^ or H2^ 
> which warrants them being excluded from HP or treated differently 
> re. definition of halting etc..  Normally he does that by 
> pretending that H and H1 are "one machine", and "whichever 
> decision that machine makes it will be wrong!!", so we have 
> Pathelogical Self Refernce or some kind of paradox or what not.  
> Thinking clearly as above (and giving distinct names for distinct 
> objects helps) makes it clear he's just muddling things up.

Mike, thy name is Sisyphus.

-- 
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