Path: news.eternal-september.org!eternal-september.org!.POSTED!not-for-mail
From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory
Subject: Re: How do computations actually work?
Date: Fri, 23 May 2025 11:04:49 -0500
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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