Re: Turing Machine computable functions apply finite string transformations to inputs VERIFIED FACT

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