Path: news.eternal-september.org!eternal-september.org!.POSTED!not-for-mail
From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory
Subject: Re: Bad faith and dishonesty
Date: Sat, 31 May 2025 10:12:57 -0500
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On 5/31/2025 8:37 AM, Mike Terry wrote:
> On 31/05/2025 11:03, Richard Heathfield wrote:
>> On 31/05/2025 10:42, Mikko wrote:
>>> On 2025-05-30 17:27:05 +0000, olcott said:
>>>
>>>> On 5/30/2025 12:06 PM, Richard Heathfield wrote:
>>
>> <snip>
>>
>>>>> As far as I can recall, Olcott's ramblings never go within discus- 
>>>>> throwing distance of a potentially erroneous step.
>>>>
>>>> There is no *INPUT* D to termination analyzer H
>>>> that can possibly do the opposite of whatever
>>>> value that H returns.
>>>
>>> We can apply Truing'c construction to every Truing machine and
>>>  prove that no Turing machine is a halting decider. With a
>>> similar construction many other problems about Turing machine
>>> behaviour can be proven uncomputable, too.
>>
>> Indeed. In fact, if I'm reading Mr Olcott's retort correctly...
>>
>> Turing: imagine a program P...
>> Turing: ...argument goes here...
>> Turing: ...and it turns out that P can't exist.
>> Olcott: Turing is wrong, because P can't exist.
>>
>> I /seeeeee.../
>>
> 
> More like:
> 
> Turing: imagine a program P...
> Turing: ...modify P as follows to create D...
> Turing: ...argument goes here...
> Turing: ...so P decides D's halting incorrectly
> Turing: ...and so P is not a halt decider.
> Olcott: Turing is wrong, because *D* can't exist.
> 
> I /seeeeee.../
> 
> Mike.
> 

Turing wasn't even dealing with halting.
No one referred to this as the halting problem
until 1958 in a book by Martin Davis.
https://www.sciencedirect.com/science/article/pii/S235222082100050X

*Here is the orignal Linz proof*
https://www.liarparadox.org/Linz_Proof.pdf

In the following embedded_H is P and ⟨Ĥ⟩ is D

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

(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

It is at step (f) that embedded_H correctly
determines that its simulated ⟨Ĥ⟩ cannot possibly
reach its own simulated ⟨Ĥ.qn⟩ final halt state.


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