Re: How do computations actually work?

On 5/23/2025 2:09 AM, Mikko wrote:

On 2025-05-23 02:47:40 +0000, olcott said:
 

On 5/22/2025 8:24 PM, Mike Terry wrote:

On 22/05/2025 06:41, Richard Heathfield wrote:

On 22/05/2025 06:23, Keith Thompson wrote:

Richard Heathfield <rjh@cpax.org.uk> writes:

On 22/05/2025 00:14, olcott wrote:

On 5/21/2025 6:11 PM, Richard Heathfield wrote:

[...]

Turing proved that what you're asking is impossible.
>

That is not what he proved.

>
Then you'll be able to write a universal termination analyser that can
correctly report for any program and any input whether it halts. Good
luck with that.

>
Not necessarily.

>
Of course not. But I'm just reflecting. He seemed to think that my inability to write the kind of program Turing envisaged (an inability that I readily concede) is evidence for his argument. Well, what's sauce for the goose is sauce for the gander.
>

Even if olcott had refuted the proofs of the
insolvability of the Halting Problem -- or even if he had proved
that a universal halt decider is possible

>
And we both know what we both think of that idea.
>

-- that doesn't imply
that he or anyone else would be able to write one.

>
Indeed.
>

I've never been entirely clear on what olcott is claiming.

>
Nor I. Mike Terry seems to have a pretty good handle on it, but no matter how clearly he explains it to me my eyes glaze over and I start to snore.

>
Hey, it's the way I tell 'em!
>
Here's what the tabloids might have said about it, if it had made the front pages when the story broke:
>
  COMPUTER BOFFIN IS TURING IN HIS GRAVE!
>
  An Internet crank claims to have refuted Linz HP proof by creating a
  Halt Decider that CORRECTLY decides its own "impossible input"!
  The computing world is underwhelmed.
>
Better?  (Appologies for the headline, it's the best I could come up with.)
>
Mike.
>

>
There is a key detail about ALL of these proofs
that no one has paid attention to for 90 years.
>
It is impossible to define *AN INPUT* to HHH that
does the opposite of whatever value that HHH returns.

 That is a key detail about HHH. Your HHH is not a part of those proofs.

All of the proofs work this same way.
It is merely much easier to see in a fully defined
and fully operational language such as C/x86.

For every Turing machine presented as a halting decider it is possible
to construct a computation that that Turing machine cannot decide
correctly. If that computation cannot be presented as an input to HHH
then HHH is not a halting decider.
 

int main()
{
   DD();  // Try to show how HHH called by DD can report
}        // on the behavior of its caller.
HHH is not (and is not supposed to be) a halt decider for
its caller. That is just not the way that computations work.
--
Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer