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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory
Subject: Re: Functions computed by Turing Machines MUST apply finite string
 transformations to inputs --- MT
Date: Tue, 6 May 2025 15:38:25 -0500
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On 5/6/2025 3:25 PM, joes wrote:
> Am Tue, 06 May 2025 12:49:13 -0500 schrieb olcott:
>> On 5/6/2025 6:23 AM, Richard Damon wrote:
>>> On 5/5/25 10:36 PM, olcott wrote:
>>>> On 5/5/2025 8:23 PM, Richard Damon wrote:
>>>>> On 5/4/25 9:23 PM, olcott wrote:
>>>>>> On 5/4/2025 8:04 PM, Ben Bacarisse wrote:
>>>>>>> Mike Terry <news.dead.person.stones@darjeeling.plus.com> writes:
>>>>>>> ...
>>>>>>>> As explained above, UTM(⟨Ĥ⟩ ⟨Ĥ⟩) simulates Ĥ run with input Ĥ
>>>>>>>> (having the same halting behaviour) and Ĥ run with input Ĥ HALTS.
>>>>>>>> So embedded_H does not "gather enough information to deduce that
>>>>>>>> UTM(⟨Ĥ⟩ ⟨Ĥ⟩) would never halt".  THAT IS JUST A FANTASY THAT YOU
>>>>>>>> HAVE.
>>>>>>>> UTM(⟨Ĥ⟩ ⟨Ĥ⟩) DOES halt, so embedded_H can't possibly gather
>>>>>>>> information that genuinely implies it DOESN'T halt.  The
>>>>>>>> explanation is obvious: embedded_H gathers information that *YOU*
>>>>>>>> believe implies that UTM(⟨Ĥ⟩ ⟨Ĥ⟩)
>>>>>>>> would never halt, but *YOU ARE SIMPLY WRONG*.
>>>>>>>
>>>>>>> He used to claim that false ("does not halt") was the correct
>>>>>>> answer,
>>>>>>> /even though/ the computation in question halts!  Those were
>>>>>>> simpler days.  Of course cranks will never admit to having been
>>>>>>> wrong about anything other than a detail or two, so anyone who
>>>>>>> could be bothered could try to get him to retract that old claim.
>>>>>>>
>>>>>> <MIT Professor Sipser agreed to ONLY these verbatim words
>>>>>> 10/13/2022>
>>>>>> </MIT Professor Sipser agreed to ONLY these verbatim words
>>>>>> 10/13/2022>
>>>>>>
>>>>>> When Ĥ is applied to ⟨Ĥ⟩
>>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qy ∞
>>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
>>>>>>
>>>>>> In other words embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ is correct to reject its input if
>>>>>>
>>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* UTM ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qy ∞
>>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* UTM ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn Would not halt.
>>>>>
>>>>> Nope, because that isn't the input that it was given.
>>>>
>>>> *Wrong*
>>>> <MIT Professor Sipser agreed to ONLY these verbatim words 10/13/2022>
>>>>       If simulating halt decider H correctly simulates its input D
>>>>       until H correctly determines that its *simulated D would
>>>>       never stop running unless aborted* then
>>>>
>>>> *simulated D would never stop running unless aborted*
>>>> simulated D (the actual input)
>>>> never stop running unless aborted (hypothetical H/D pair)
>>>>
>>> No, that is changing the input.
>>>
>> *would never stop running unless aborted* means the hypothetical same
>> HHH that DD calls except that this HHH does not abort.
> Yes, that is not the same HHH.
> 

Yet is the HHH that Professor Sipser agreed would be
the correct measure of the behavior of the actual input.

-- 
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer