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From: dbush <dbush.mobile@gmail.com>
Newsgroups: comp.theory
Subject: Re: Halting Problem: What Constitutes Pathological Input
Date: Mon, 5 May 2025 18:32:36 -0400
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On 5/5/2025 6:19 PM, olcott wrote:
> On 5/5/2025 5:03 PM, dbush wrote:
>> On 5/5/2025 5:47 PM, olcott wrote:
>>> On 5/5/2025 4:40 PM, Richard Heathfield wrote:
>>>> On 05/05/2025 22:31, dbush wrote:
>>>>> On 5/5/2025 5:08 PM, olcott wrote:
>>>>
>>>> <snip>
>>>>
>>>>>> No TM can compute the square root of a dead rabbit either.
>>>>>
>>>>> Strawman.  The square root of a dead rabbit does not exist,
>>>>
>>>> Don't be so sure. I have several on my mantelpiece and two more on 
>>>> order. For once, olcott is right; there is no way to compute them. 
>>>> They do, however, need thorough and regular polishing. Black polish 
>>>> or brown? Well, that's undecidable.
>>>>
>>>>> but the question of whether any arbitrary algorithm X with input Y 
>>>>> halts when executed directly has a correct answer in all cases.
>>>>
>>>> Indeed it has.
>>>>
>>>>> It's just that no algorithm exists that can compute that mapping, 
>>>>> as proven by Linz and other and as you have *explicitly* agreed is 
>>>>> correct.
>>>>
>>>> He's coming round to the idea, albeit slowly. He can't bring himself 
>>>> to describe the mapping as 'incomputable' or 'undecidable', but he's 
>>>> started to claim that such a mapping is 'incorrect', which is a 
>>>> tacit acknowledgement that it exists.
>>>>
>>>
>>> When the input to HHH(DD) is mapped to the
>>> behavior that this input actually specifies
>>> IT DOES NOT HALT.
>>>
>>
>> In other words, HHH doesn't meet the requirements to be a solution to 
>> the halting problem:
>>
> 
> A deeper understanding proves that those requirements

Are very useful, as an algorithm that could meet those requirements 
would allow unknowable truths to be knowable.