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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory
Subject: Re: Turing Machine computable functions apply finite string
 transformations to inputs VERIFIED FACT
Date: Wed, 30 Apr 2025 09:58:52 -0500
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On 4/30/2025 1:05 AM, Richard Heathfield wrote:
> On 30/04/2025 03:45, Richard Damon wrote:
>> On 4/29/25 3:57 PM, olcott wrote:
>>> On 4/29/2025 10:33 AM, Fred. Zwarts wrote:
>>>> Op 29.apr.2025 om 15:11 schreef olcott:
> 
> <snip>
> 
>>>>> No H can possibly see the behavior of P(D)
>>>>> when-so-ever D has defined a pathological
>>>>> relationship with H this 
>>>>
>>>> makes it impossible for H to see the behaviour of P(D).
>>>> The behaviour of P(D) does not change, but H does not see it.
>>>
>>> H MUST REPORT ON THE BEHAVIOR THAT IT DOES SEE
>>>
>>
>> No, it must report on the behavior that exists.
>>
>> It is only ABLE to correctly report on behavior it can "see", but 
>> there is no structural restriction that says we can't ask it about 
>> something that it can't see.
> 
> Nor is there any restriction that says it can't deduce behaviour it 
> can't see, simply by reading the tapes.
> 

It is ONLY allowed to derive its output by
applying finite string transformations to its input.
For the HHH/DD pair these must be the finite string
transformations specified by the x86 language.

For the embedded_H / ⟨Ĥ⟩ ⟨Ĥ⟩ pair these
transformations are specified by the Linz template.

When Ĥ is applied to ⟨Ĥ⟩
Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qy ∞
Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn

Above adapted from bottom of page 2
https://www.liarparadox.org/Linz_Proof.pdf

(a) Ĥ copies its input ⟨Ĥ⟩
(b) Ĥ invokes embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩
(c) embedded_H simulates ⟨Ĥ⟩ ⟨Ĥ⟩
(d) simulated ⟨Ĥ⟩ copies its input ⟨Ĥ⟩
(e) simulated ⟨Ĥ⟩ invokes simulated embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩
(f) simulated embedded_H simulates ⟨Ĥ⟩ ⟨Ĥ⟩
(g) goto (d) with one more level of simulation

> Mr Olcott seems unable to recognise this possibility. Having built his 
> hammer, he is determined to see the Halting Problem as a nail that 
> cannot withstand being pounded hard enough.
> 
> Unfortunately for him, the problem is more like a 16 puzzle with two 
> tiles swapped. If he plays by the rules there is no solution, no matter 
> how hard he hits it.
> 
> This is why he keeps trying to change the rules, with word salad like 
> 'pathological self-reference', when self-reference is the whole reason 
> the proof works.
> 


-- 
Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer