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From: Mikko <mikko.levanto@iki.fi>
Newsgroups: comp.theory
Subject: Re: How do computations actually work?
Date: Tue, 27 May 2025 11:29:40 +0300
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On 2025-05-26 16:40:25 +0000, olcott said:

> On 5/25/2025 10:46 AM, Fred. Zwarts wrote:
>> Op 25.mei.2025 om 16:50 schreef olcott:
>>> On 5/25/2025 4:09 AM, Mikko wrote:
>>>> On 2025-05-24 15:25:21 +0000, olcott said:
>>>> 
>>>>> On 5/24/2025 2:54 AM, Mikko wrote:
>>>>>> On 2025-05-23 16:04:49 +0000, olcott said:
>>>>>> 
>>>>>>> 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.
>>>>>> 
>>>>>> No, they don't. Some proofs derive the same conclusion with an essentially
>>>>>> different approach.
>>>>>> 
>>>>>> However, in spite of the differences, they do share a common fieature:
>>>>>> your HHH is not a part of any of the proofs.
>>>>> 
>>>>> All of the conventional proofs of the HP assume that
>>>>> there is an *input D* that can actually do the opposite
>>>>> of whatever value that HHH returns.
>>>> 
>>>> Depends on what you mean by "conventional". If you merely mean proofs
>>>> that apply ordinary logic then there are proofs with a different
>>>> strategy. If you mean only proofs that use the same strategy that
>>>> Turing used then you are closer to the truth. But there is no assumption
>>>> about the exstence of such D. Its existence is proven.
>>>> 
>>> 
>>> In seems that way until you pay much closer attention.
>>> 
>>> int main()
>>> {
>>>    DDD(); // The HHH that DDD calls cannot report on the
>>> }        // behavior of its caller because it cannot see
>>>           // is caller.
>>> 
>>> Even if HHH could see and report on the behavior of
>>> its caller because its caller is not its input this
>>> too is no good.
>> 
>> It seems that way to you, until you pay somewhat closer attention.
> 
> The HHH(DDD) must report on the behavior that its actual input
> actually specified CANNOT BE VIOLATED.

Of course it can. In fact HHH does violate that. DDD specifies a halting
behaviour but HHH reports that DDD specifies a non-halting behaviour.
That is a violation of that rquirement.

-- 
Mikko