Re: Functions computed by Turing Machines MUST apply finite string transformations to inputs

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 Scaffolding first (not for publication):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