Re: Two dozen people were simply wrong --- Try to prove otherwise

On 5/31/2024 3:30 AM, Mikko wrote:

On 2024-05-31 01:54:52 +0000, olcott said:
 

On 5/30/2024 8:37 PM, Richard Damon wrote:

On 5/30/24 9:31 AM, olcott wrote:

On 5/30/2024 2:40 AM, Mikko wrote:

On 2024-05-30 01:15:21 +0000, olcott said:

>

x <is> a finite string Turing machine description that SPECIFIES behavior. The term: "representing" is inaccurate.

>
No, x is a description of the Turing machine that specifies the behaviour
that H is required to report.

>
That is what I said.

>
Note, the string doesn't DIRECTLY specify behavior, but only indirectly as a description/representation of the Turing Mach
>

>
The string directly SPECIFIES behavior to a UTM or to
any TM based on a UTM.

 An UTM interpretes the string as a specification of behaviour

YES, exactly !!!

and another Turing machine may interprete likewise. But in a
different context the interpretation is different.
 

When Ĥ is applied to ⟨Ĥ⟩
Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qy ∞
Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
When embedded_H <is> a UTM or <is> a halting computation based on a
UTM then the ⟨Ĥ⟩ ⟨Ĥ⟩ input to embedded_H SPECIFIES that ⟨Ĥ⟩ ⟨Ĥ⟩ correctly
simulated by embedded_H cannot possibly reach its own simulated final
state at ⟨Ĥ.qn⟩.

Note that there are specifications of behaviour that do not
describe. A specification can be an algorithm that takes
the input and output of a Turing machine and from then computes
whether the output is correct. That kind of specification cannot
be used as an input to an UTM or other Turing machine that expects
a description.
 

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