Ĥ.q0 wM ⊢* Ĥ.qx wM wM ⊢* Ĥ.qy ∞
Ĥ.q0 wM ⊢* Ĥ.qx wM wM ⊢* Ĥ.qn

The above is adapted from (Linz:1990:319).
It shows that Turing machine Ĥ copies its input at (q0) and begins
executing an embedded copy of the original halt decider with this input
at (qx).

The (qy) state indicates that the halt decider has determined that its
input would halt.

The appended (qa) and (qb) states cause Ĥ to infinitely loop if the halt
decider has determined that its input would halt.

The ((qn)) state indicates that the halt decider has decided that its
input would not halt.

Linz, Peter 1990. An Introduction to Formal Languages and Automata.
Lexington/Toronto: D. C. Heath and Company.

It can be understood from the above specification that when the embedded
halt decider at state Ĥ.qx bases its halting decision on simulating its
input,
and it has ([Ĥ],[Ĥ]) as its input that:
Ĥ.q0 would copy its input and then Ĥ.qx would simulate its input with
this copy then
Ĥ.q0 would copy its input and then Ĥ.qx would simulate its input with
this copy then
Ĥ.q0 would copy its input and then Ĥ.qx would simulate its input with
this copy...

Several people here accept that it is true that when the simulating halt
decider at state Ĥ.qx is replaced with a UTM that Ĥ would never halt
because the simulation of the input: ([Ĥ],[Ĥ]) to Ĥ.qx would never halt.

(A) Every simulation of input P that never halts unless simulating halt
decider H aborts this simulation <is> a non-halting computation. This
remains true even after H stops simulating P.

∃H ∈ Simulating_Halt_Deciders
∀P ∈ Turing_Machine_Descriptions
∀I ∈ Finite_Strings
(UTM(P,I) = ∞) ⊢ (H(P,I) = 0)

In English this says that whenever the input (P,I) to a simulating halt
H decider would never halt if the simulating halt decider was replaced
by a UTM then the simulating halt decider correctly decides not halting
on this input.

This halt deciding principle overcomes the pathological self-reference
error of the halting theorem:

(B) The simulation of: ([Ĥ][Ĥ]) by the simulating halt decider @ Ĥ.qx
never halts unless Ĥ.qx aborts this simulation.

(C) ∴ The simulating halt decider @ Ĥ.qx correctly decides its input
([Ĥ][Ĥ]) as non-halting.

http://www.liarparadox.org/Halting_problem_undecidability_and_infinitely_nested_simulation.pdf

--
Copyright 2021 Pete Olcott

"Great spirits have always encountered violent opposition from mediocre
minds." Einstein

On Fri, 21 May 2021 08:37:57 -0500
olcott <NoOne@NoWhere.com> wrote:

> Ĥ.q0 wM ⊢* Ĥ.qx wM wM ⊢* Ĥ.qy ∞
> Ĥ.q0 wM ⊢* Ĥ.qx wM wM ⊢* Ĥ.qn

Please refrain from using mathematical symbols that aren't present in
most fonts; Usenet readers often don't support displaying them as they
don't support fallback fonts.

/Flibble

On 5/21/2021 11:31 AM, Mr Flibble wrote:
> On Fri, 21 May 2021 08:37:57 -0500
> olcott <NoOne@NoWhere.com> wrote:
>
>> Ĥ.q0 wM ⊢* Ĥ.qx wM wM ⊢* Ĥ.qy ∞
>> Ĥ.q0 wM ⊢* Ĥ.qx wM wM ⊢* Ĥ.qn
>
> Please refrain from using mathematical symbols that aren't present in
> most fonts; Usenet readers often don't support displaying them as they
> don't support fallback fonts.
>
> /Flibble
>

I can't do that because it would reduce the effectiveness of my
communication far too much.

What concrete instances are you referring to a ten year old Linux client?

Anyone with a modern PDF reader can read the PDF version because it has
the fonts embedded.

http://www.liarparadox.org/Halting_problem_undecidability_and_infinitely_nested_simulation.pdf

--
Copyright 2021 Pete Olcott

"Great spirits have always encountered violent opposition from mediocre
minds." Einstein

On Fri, 21 May 2021 11:55:34 -0500
olcott <NoOne@NoWhere.com> wrote:

> On 5/21/2021 11:31 AM, Mr Flibble wrote:
> > On Fri, 21 May 2021 08:37:57 -0500
> > olcott <NoOne@NoWhere.com> wrote:
> >
> >> Ĥ.q0 wM ⊢* Ĥ.qx wM wM ⊢* Ĥ.qy ∞
> >> Ĥ.q0 wM ⊢* Ĥ.qx wM wM ⊢* Ĥ.qn
> >
> > Please refrain from using mathematical symbols that aren't present
> > in most fonts; Usenet readers often don't support displaying them
> > as they don't support fallback fonts.
> >
> > /Flibble
> >
>
> I can't do that because it would reduce the effectiveness of my
> communication far too much.
>
> What concrete instances are you referring to a ten year old Linux
> client?
>
> Anyone with a modern PDF reader can read the PDF version because it
> has the fonts embedded.

Then stop posting your fucking shit to Usenet and write a fucking blog
instead.

/Flibble

On 5/21/2021 12:00 PM, Mr Flibble wrote:
> On Fri, 21 May 2021 11:55:34 -0500
> olcott <NoOne@NoWhere.com> wrote:
>
>> On 5/21/2021 11:31 AM, Mr Flibble wrote:
>>> On Fri, 21 May 2021 08:37:57 -0500
>>> olcott <NoOne@NoWhere.com> wrote:
>>>
>>>> Ĥ.q0 wM ⊢* Ĥ.qx wM wM ⊢* Ĥ.qy ∞
>>>> Ĥ.q0 wM ⊢* Ĥ.qx wM wM ⊢* Ĥ.qn
>>>
>>> Please refrain from using mathematical symbols that aren't present
>>> in most fonts; Usenet readers often don't support displaying them
>>> as they don't support fallback fonts.
>>>
>>> /Flibble
>>>
>>
>> I can't do that because it would reduce the effectiveness of my
>> communication far too much.
>>
>> What concrete instances are you referring to a ten year old Linux
>> client?
>>
>> Anyone with a modern PDF reader can read the PDF version because it
>> has the fonts embedded.
>
> Then stop posting your fucking shit to Usenet and write a fucking blog
> instead.
>
> /Flibble
>

I propose that there are no actual cases of any properly configured
modern hardware that cannot read the symbols that I post.

Citing something that would have been a problem 20 years ago is ridiculous.

--
Copyright 2021 Pete Olcott

"Great spirits have always encountered violent opposition from mediocre
minds." Einstein

On Fri, 21 May 2021 12:22:15 -0500
olcott <NoOne@NoWhere.com> wrote:

> On 5/21/2021 12:00 PM, Mr Flibble wrote:
> > On Fri, 21 May 2021 11:55:34 -0500
> > olcott <NoOne@NoWhere.com> wrote:
> >
> >> On 5/21/2021 11:31 AM, Mr Flibble wrote:
> >>> On Fri, 21 May 2021 08:37:57 -0500
> >>> olcott <NoOne@NoWhere.com> wrote:
> >>>
> >>>> Ĥ.q0 wM ⊢* Ĥ.qx wM wM ⊢* Ĥ.qy ∞
> >>>> Ĥ.q0 wM ⊢* Ĥ.qx wM wM ⊢* Ĥ.qn
> >>>
> >>> Please refrain from using mathematical symbols that aren't present
> >>> in most fonts; Usenet readers often don't support displaying them
> >>> as they don't support fallback fonts.
> >>>
> >>> /Flibble
> >>>
> >>
> >> I can't do that because it would reduce the effectiveness of my
> >> communication far too much.
> >>
> >> What concrete instances are you referring to a ten year old Linux
> >> client?
> >>
> >> Anyone with a modern PDF reader can read the PDF version because it
> >> has the fonts embedded.
> >
> > Then stop posting your fucking shit to Usenet and write a fucking
> > blog instead.
> >
> > /Flibble
> >
>
> I propose that there are no actual cases of any properly configured
> modern hardware that cannot read the symbols that I post.
>
> Citing something that would have been a problem 20 years ago is
> ridiculous.
It isn't ridiculous: Usenet is 40 years old and hasn't changed much in
that time. Either follow the established norms of the forum you post to
or fuck off.

/Flibble

On 5/21/2021 12:24 PM, Mr Flibble wrote:
> On Fri, 21 May 2021 12:22:15 -0500
> olcott <NoOne@NoWhere.com> wrote:
>
>> On 5/21/2021 12:00 PM, Mr Flibble wrote:
>>> On Fri, 21 May 2021 11:55:34 -0500
>>> olcott <NoOne@NoWhere.com> wrote:
>>>
>>>> On 5/21/2021 11:31 AM, Mr Flibble wrote:
>>>>> On Fri, 21 May 2021 08:37:57 -0500
>>>>> olcott <NoOne@NoWhere.com> wrote:
>>>>>
>>>>>> Ĥ.q0 wM ⊢* Ĥ.qx wM wM ⊢* Ĥ.qy ∞
>>>>>> Ĥ.q0 wM ⊢* Ĥ.qx wM wM ⊢* Ĥ.qn
>>>>>
>>>>> Please refrain from using mathematical symbols that aren't present
>>>>> in most fonts; Usenet readers often don't support displaying them
>>>>> as they don't support fallback fonts.
>>>>>
>>>>> /Flibble
>>>>>
>>>>
>>>> I can't do that because it would reduce the effectiveness of my
>>>> communication far too much.
>>>>
>>>> What concrete instances are you referring to a ten year old Linux
>>>> client?
>>>>
>>>> Anyone with a modern PDF reader can read the PDF version because it
>>>> has the fonts embedded.
>>>
>>> Then stop posting your fucking shit to Usenet and write a fucking
>>> blog instead.
>>>
>>> /Flibble
>>>
>>
>> I propose that there are no actual cases of any properly configured
>> modern hardware that cannot read the symbols that I post.
>>
>> Citing something that would have been a problem 20 years ago is
>> ridiculous.
>
> It isn't ridiculous: Usenet is 40 years old and hasn't changed much in
> that time. Either follow the established norms of the forum you post to
> or fuck off.
>
> /Flibble
>

If you want to follow 40 year old norms that have become moot because of
advances in technology feel free. You are not the boss of me.

--
Copyright 2021 Pete Olcott

"Great spirits have always encountered violent opposition from mediocre
minds." Einstein