How do computations actually work?

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.
int main()
{
   DD; // HHH cannot report on the behavior of its caller
}     // *That is just not the way that computations work*
It is the same thing with the Linz proof.
When Ĥ is applied to ⟨Ĥ⟩
Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qy ∞
Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
embedded_H cannot report on the behavior of
the computation that itself is contained within.
*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