Path: news.eternal-september.org!eternal-september.org!.POSTED!not-for-mail
From: Mikko <mikko.levanto@iki.fi>
Newsgroups: comp.theory
Subject: Re: How do computations actually work?
Date: Sun, 25 May 2025 12:09:28 +0300
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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.

-- 
Mikko