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computers / comp.ai.philosophy / Re:_My_honest_reviewers:_André,_Ben,_Mike,_Dennis,_Richard_[_Where_are_the_tapes?_]

SubjectAuthor
* Refuting the Peter Linz Halting Problem Proof --- Version(10) [ keyolcott
+* Re: Refuting the Peter Linz Halting Problem Proof --- Version(10) [olcott
|`* Re: Refuting the Peter Linz Halting Problem Proof --- Version(10) [olcott
| +* Re: Refuting the Peter Linz Halting Problem Proof --- Version(10) [olcott
| |`- Re: Refuting the Peter Linz Halting Problem Proof --- Version(10) [olcott
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| +* Re: Refuting the Peter Linz Halting Problem Proof --- Version(10) [olcott
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| || `- Re: Refuting the Peter Linz Halting Problem Proof --- Version(10) [olcott
| |`* Re: Refuting the Peter Linz Halting Problem Proof --- Version(11) [olcott
| | `* Re: Refuting the Peter Linz Halting Problem Proof --- Version(11) [olcott
| |  +* Re: Refuting the Peter Linz Halting Problem Proof --- Version(11) [olcott
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| |  `* Re: Refuting the Peter Linz Halting Problem Proof --- Version(11) [olcott
| |   +* Re: Refuting the Peter Linz Halting Problem Proof --- Version(11) [olcott
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| |   `* Re: Refuting the Peter Linz Halting Problem Proof --- Version(11) [olcott
| |    `- Re: Refuting the Peter Linz Halting Problem Proof --- Version(11) [olcott
| `- Re: Refuting the Peter Linz Halting Problem Proof --- Version(10) [olcott
+* Re: Refuting the Peter Linz Halting Problem Proof --- Version(10) [olcott
|`- Re: Refuting the Peter Linz Halting Problem Proof --- Version(10) [olcott
+- Re: Refuting the Peter Linz Halting Problem Proof --- Version(10) [olcott
+- Re: Refuting the Peter Linz Halting Problem Proof --- Version(10) [olcott
+- Re: Refuting the Peter Linz Halting Problem Proof --- Version(11) [olcott
+- Re: Refuting the Peter Linz Halting Problem Proof --- Version(11) [olcott
+* Re: Refuting the Peter Linz Halting Problem Proof --- Version(11) [olcott
|`- Re: Refuting the Peter Linz Halting Problem Proof --- Version(11) [olcott
+- Re: Refuting the Peter Linz Halting Problem Proof --- Version(11) [olcott
+- Re: Refuting the Peter Linz Halting Problem Proof --- Version(11) [olcott
+* Re: Refuting the Peter Linz Halting Problem Proof --- Version(11) [olcott
|`- Re: Refuting the Peter Linz Halting Problem Proof --- Version(11) [olcott
+- Re: Refuting the Peter Linz Halting Problem Proof --- Version(11) [olcott
+* Re: Refuting the Peter Linz Halting Problem Proof --- Version(11) [olcott
|+- Re: Refuting the Peter Linz Halting Problem Proof --- Version(11) [olcott
|`* Re: Refuting the Peter Linz Halting Problem Proof --- Version(11) [olcott
| +* Re: Refuting the Peter Linz Halting Problem Proof --- Version(11) [olcott
| |`* Re: Refuting the Peter Linz Halting Problem Proof --- Version(11) [olcott
| | `* Re: _My_Dishonest_reviewers:_André,_Ben,_Mikeolcott
| |  +* Re: _My_Dishonest_reviewers:_André,_Ben,_Mikeolcott
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| |  ||`* Re: _My_honest_reviewers:_André,_Ben,_Mike,olcott
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| |  |`- Re: _My_Dishonest_reviewers:_André,_Ben,_Mikeolcott
| |  `- Re: _My_Dishonest_reviewers:_André,_Ben,_Mikeolcott
| `- Re: Refuting the Peter Linz Halting Problem Proof --- Version(11) [olcott
`- Re: Refuting the Peter Linz Halting Problem Proof --- Version(11) [olcott

Pages:123
Subject: Re:_My_honest_reviewers:_André,_Ben,_Mike,_Dennis,_Richard_[_last_step_of_my_proof_]_(_Mind_Reader_? )
From: olcott
Newsgroups: comp.theory, comp.ai.philosophy, sci.logic, sci.math
Followup: comp.theory
Date: Sat, 23 Apr 2022 15:44 UTC
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Subject: Re:_My_honest_reviewers:_André,_Ben,_Mike,
_Dennis,_Richard_[_last_step_of_my_proof_]_(_Mind_Reader_
? )
Content-Language: en-US
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Followup-To: comp.theory
From: NoO...@NoWhere.com (olcott)
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On 4/22/2022 10:06 PM, André G. Isaak wrote:
On 2022-04-22 20:54, olcott wrote:
On 4/22/2022 4:42 PM, André G. Isaak wrote:
On 2022-04-22 14:58, olcott wrote:
On 4/22/2022 3:42 PM, André G. Isaak wrote:
On 2022-04-22 14:09, olcott wrote:
On 4/22/2022 2:37 PM, Ben wrote:
olcott <NoOne@NoWhere.com> writes:

On 4/21/2022 8:23 PM, Ben wrote:
olcott <NoOne@NoWhere.com> writes:

On 4/21/2022 6:10 PM, Ben wrote:

Still, I expect there's a few years more chatting to be done before you
get to an editor's day.

People here have gotten the conventional halting problem dogma so
ingrained in their psyche that they believe that even when it is
proven to be a verified fact that the input to H(P,P) specifies a
non-halting sequence of configurations it is somehow incorrect for H
to report this.

H(P,P) == false is wrong because P(P) halts.  The problem of exhibiting
an H such that H(X,Y) == false if, and only if, X(Y) does not halt has
not gone away.  It's called the halting problem.  There are famous
theorems about it.  At one time you were interested in addressing it.

If the correctly simulated input to H(P,P) specifies a non-halting
sequence of configurations on the basis of its actual behavior then
this actual behavior supersedes and overrules anything any everything
else that disagrees.

The halting problem is about H(P,P) being right about P(P), not about
anything else you might find to waffle about.

The halting problem *is not* about P(P) when P(P) is not computationally equivalent to the correct simulation of the input to H(P,P).

This is simply an ignorant statement. Rather, it was initially an ignorant statement but since there have been many attempts made to remedy your ignorance, it has since graduated to a willfully-ignorant-grasping-at-straws-statement.

A halt decider is a Turing Machine which computes the halting *function*.

The halting function is a mathematical function. it is not defined in terms of 'inputs' or 'simulators'. It is not defined in terms of halt deciders at all since a function is logically prior to any algorithm for computing that function.

The halting *function* is simply a mathematical mapping from computations to {yes, no} based on whether they halt.


No. A decider computes the mapping from (finite string) inputs to an accept or reject state.

I was defining the halting *function*. That is an entirely different animal from a halt *decider*. Do you still not grasp the distinction between a Turing Machine and the function which it computes?

So the halt decider computes the halting *function* on some other basis than what its input actually specifies (What is it a mind reader?)
You really don't think these things through do you?

The halting *function* is defined entirely independently of any halt decider or computer program. It maps computations to yes or no based on whether they halt.

Whether it is possible to design a Turing Machine or program which actually computes this function, or whether it is possible to encode elements of the domain of the halting function in a way which allows them to even be passed as inputs to such a Turing Machine or program are entirely separate questions.

André


None-the-less H(P,P) does correctly compute the mapping from its inputs to its own reject state therefore H(P,P) correctly decides the halt status of the halting problem's "impossible" input.

Anyone that is an expert in the C programming language, the x86 programming language, exactly how C translates into x86 and what an x86 processor emulator is can easily verify that the correctly simulated input to H(P,P) by H specifies a non-halting sequence of configurations.

All of my reviewers expect H(P,P) to compute the halt status of P(P), yet the behavior specified by the input to H(P,P) is not the same as the behavior specified by P(P).

Since my reviewers expect the halt decider to compute the halt status of P(P) yet the input to H(P,P) specifies a different halt status my reviewers expect H to read their mind so that it can compute different behavior than the behavior that the input actually specifies.


Halting problem undecidability and infinitely nested simulation (V5)

https://www.researchgate.net/publication/359984584_Halting_problem_undecidability_and_infinitely_nested_simulation_V5 --
Copyright 2022 Pete Olcott

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


Subject: Re:_My_honest_reviewers:_André,_Ben,_Mike,_Dennis,_Richard_[_last_step_of_my_proof_]
From: olcott
Newsgroups: comp.theory, comp.ai.philosophy, sci.logic, sci.math
Followup: comp.theory
Date: Sun, 24 Apr 2022 00:54 UTC
References: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22
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Subject: Re:_My_honest_reviewers:_André,_Ben,_Mike,
_Dennis,_Richard_[_last_step_of_my_proof_]
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Followup-To: comp.theory
From: NoO...@NoWhere.com (olcott)
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On 4/23/2022 7:38 PM, Ben wrote:
olcott <NoOne@NoWhere.com> writes:

On 4/22/2022 7:00 PM, Ben wrote:
olcott <NoOne@NoWhere.com> writes:

On 4/22/2022 1:49 PM, Ben wrote:
olcott <NoOne@NoWhere.com> writes:

It does not matter at all that P(P) halts when we have proven that the
input to H(P,P) specifies a non-halting sequence of configurations.
The halting problem -- a function D such that D(X,Y) returns true iff
X(Y) halts and false otherwise -- does not go away just because you
decide to address some other question, even if it sounds superficially a
bit similar.

This is merely a very persistent {learned by rote from the book}
misunderstanding of the actual halting problem definition.
Let's imagine we are in PO land...  We've finally understood the mistake
that everyone else has been making -- it's not about what P(P) does but

about the actual behavior of the actual input: H(P,P)
int X = sum(3,4); must produce 7 or it is wrong.

No, the answer must be 12.  No, sorry, it should be g, surely?  Perhaps
you should specify this "addition problem" properly?

that <mindless monotone>the input to H(P,P) specifies non-halting
behaviour</mindless monotone>.  We publish.  No one cares.  We are
surprised; people /still/ want to know if a function call halts or not.
They /still/ want a function D such that D(X,Y) returns true iff X(Y)
halts and false otherwise and our telling them that what matters is that
<mindless monotone>the input to H(P,P) specifies non-halting
behaviour</mindless monotone> seems to leave them cold.
Strange, I know, but they seem to want to now of their programs halt,
not if <mindless monotone>the input to H specifies non-halting
behaviour</mindless monotone>.  There's no accounting for taste.

No comment on the substantive point, as usual: the problem you are now
ignoring -- the halting problem -- does not go away.  It's still there,
even in PO land.


The key fact (that is perpetually over your head) is that the input to H(P,P) specifies a non-halting sequence of configurations making it necessarily correct for H to reject this input.

It is your failure to acknowledge this key fact (because of your woefully inadequate technical competence on the x86 language) that keeps us stuck on this point.

--
Copyright 2022 Pete Olcott

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


Subject: Re:_My_honest_reviewers:_André,_Ben,_Mike,_Dennis,_Richard_[_Where_are_the_tapes?_]
From: olcott
Newsgroups: comp.theory, comp.ai.philosophy, sci.logic, sci.math
Followup: comp.theory
Date: Mon, 25 Apr 2022 16:51 UTC
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Subject: Re:_My_honest_reviewers:_André,_Ben,_Mike,
_Dennis,_Richard_[_Where_are_the_tapes?_]
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From: NoO...@NoWhere.com (olcott)
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On 4/23/2022 8:43 PM, Ben wrote:
Richard Damon <Richard@Damon-Family.org> writes:

On 4/23/22 8:57 PM, Ben wrote:
olcott <NoOne@NoWhere.com> writes:

The following simplifies the syntax for the definition of the Linz
Turing machine Ĥ.
Oh, no!  I thought you'd given up on TMs (you really should).

There is no need for the infinite loop after H.qy because it is never
reached.
    "No nitwit H ⟨Ĥ⟩ ⟨Ĥ⟩ transitions to H.qy as I have told you many
    times."
What that a mistake?  A lie?  Poetic license?

The halting criteria has been adapted so that it applies to a
simulating halt decider (SHD).
No, you can't alter the "halting criteria".  The problem you claim to be
addressing is about halting, the criterion for which is not for you to
alter.
So, from here on, you are not talking about a halt decider as it should
be specified...  OK.

Ĥ.q0 ⟨Ĥ⟩ ⊢* H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qy
If the correctly simulated input ⟨Ĥ⟩ ⟨Ĥ⟩ to H would reach its own
final state of ⟨Ĥ.qy⟩ or ⟨Ĥ.qn⟩.

Ĥ.q0 ⟨Ĥ⟩ ⊢* H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qn
If the correctly simulated input ⟨Ĥ⟩ ⟨Ĥ⟩ to H would never reach its
own final state of ⟨Ĥ.qy⟩ or ⟨Ĥ.qn⟩.

You are free to use your made-up "altered" halting criterion, but I
would urge you not to use junk notation like ⟨Ĥ.qy⟩.  The ⟨⟩s go round
TMs to indicate a string encoding, but Ĥ.qy is a state.  But since this
is not about a halt decider as specified by the textbooks, it's probably
not worth trying to find out what thoughts this poetic use of notation
is meant to conjure up in the reader's mind.

When Ĥ is applied to ⟨Ĥ⟩
Ĥ copies its input ⟨Ĥ0⟩ to ⟨Ĥ1⟩ then H simulates ⟨Ĥ0⟩ ⟨Ĥ1⟩

There is no machine H0 or H1 so there can be no strings ⟨Ĥ0⟩ or ⟨Ĥ1⟩.  I
know you are writing a poem here, so I can guess what you want the
reader to think of, but in technical writing one should use notation
constantly and clearly.

I will defined him a bit here, while he isn't being very clear about
his notation (which is normal for him) I think the trailing numbers
are supposed to be "indexes" indicating which of a number of identical
strings we are refering to. In a more expressive notation they would
be subscripts.

Well that's why I wrote that the reader can guess.  But the problem goes
much deeper than writing <Ĥ0> rather than <Ĥ>_0.  The <> notation is
supposed to indicate actual strings on the tape,



but when H is
simulating, and when that simulation is simulating these strings won't
appear anywhere.  They simply don't exist on the tape.  If PO had
written a UTM, he'd know this.


So when Ĥ copies its input this copied input goes no where?




You still have not cleared up your huge gaff about the location of the tape of machines that are simulated by a UTM.

When a UTM simulates the TM description of another UTM
which simulates the TM description of another UTM
simulates the TM description of a TM where are the tapes?



--
Copyright 2022 Pete Olcott

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


Subject: Re:_My_honest_reviewers:_André,_Ben,_Mike,_Dennis,_Richard_[_Where_are_the_tapes?_]
From: olcott
Newsgroups: comp.theory, comp.ai.philosophy, sci.math, sci.logic
Followup: comp.theory
Date: Thu, 28 Apr 2022 22:36 UTC
References: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
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Subject: Re:_My_honest_reviewers:_André,_Ben,_Mike,
_Dennis,_Richard_[_Where_are_the_tapes?_]
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References: <v6idnaCJifSVTtT_nZ2dnUU7_8zNnZ2d@giganews.com>
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<er19K.2090$_o6b.439@fx42.iad> <87a6cbxnlg.fsf@bsb.me.uk>
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<f56dnVd6R68NRPf_nZ2dnUU7_8xh4p2d@giganews.com>
From: NoO...@NoWhere.com (olcott)
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On 4/28/2022 1:14 PM, olcott wrote:
On 4/26/2022 7:45 PM, Ben wrote:
olcott <NoOne@NoWhere.com> writes:

On 4/26/2022 6:50 PM, Ben wrote:
olcott <NoOne@NoWhere.com> writes:

On 4/25/2022 8:30 PM, Ben wrote:
olcott <NoOne@NoWhere.com> writes:

On 4/25/2022 4:42 PM, Ben wrote:
olcott <NoOne@NoWhere.com> writes:

On 4/23/2022 8:43 PM, Ben wrote:
Richard Damon <Richard@Damon-Family.org> writes:

On 4/23/22 8:57 PM, Ben wrote:
olcott <NoOne@NoWhere.com> writes:

The following simplifies the syntax for the definition of the Linz
Turing machine Ĥ.
Oh, no!  I thought you'd given up on TMs (you really should).

There is no need for the infinite loop after H.qy because it is never
reached.
        "No nitwit H ⟨Ĥ⟩ ⟨Ĥ⟩ transitions to H.qy as I have told you many
        times."
What that a mistake?  A lie?  Poetic license?

The halting criteria has been adapted so that it applies to a
simulating halt decider (SHD).
No, you can't alter the "halting criteria".  The problem you claim to be
addressing is about halting, the criterion for which is not for you to
alter.
So, from here on, you are not talking about a halt decider as it should
be specified...  OK.

Ĥ.q0 ⟨Ĥ⟩ ⊢* H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qy
If the correctly simulated input ⟨Ĥ⟩ ⟨Ĥ⟩ to H would reach its own
final state of ⟨Ĥ.qy⟩ or ⟨Ĥ.qn⟩.

Ĥ.q0 ⟨Ĥ⟩ ⊢* H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qn
If the correctly simulated input ⟨Ĥ⟩ ⟨Ĥ⟩ to H would never reach its
own final state of ⟨Ĥ.qy⟩ or ⟨Ĥ.qn⟩.

You are free to use your made-up "altered" halting criterion, but I
would urge you not to use junk notation like ⟨Ĥ.qy⟩.  The ⟨⟩s go round
TMs to indicate a string encoding, but Ĥ.qy is a state.  But since this
is not about a halt decider as specified by the textbooks, it's probably
not worth trying to find out what thoughts this poetic use of notation
is meant to conjure up in the reader's mind.

When Ĥ is applied to ⟨Ĥ⟩
Ĥ copies its input ⟨Ĥ0⟩ to ⟨Ĥ1⟩ then H simulates ⟨Ĥ0⟩ ⟨Ĥ1⟩

There is no machine H0 or H1 so there can be no strings ⟨Ĥ0⟩ or ⟨Ĥ1⟩.  I
know you are writing a poem here, so I can guess what you want the
reader to think of, but in technical writing one should use notation
constantly and clearly.

I will defined him a bit here, while he isn't being very clear about
his notation (which is normal for him) I think the trailing numbers
are supposed to be "indexes" indicating which of a number of identical
strings we are refering to. In a more expressive notation they would
be subscripts.

Well that's why I wrote that the reader can guess.  But the problem goes
much deeper than writing <Ĥ0> rather than <Ĥ>_0.  The <> notation is
supposed to indicate actual strings on the tape,

but when H is
simulating, and when that simulation is simulating these strings won't
appear anywhere.  They simply don't exist on the tape.  If PO had
written a UTM, he'd know this.

So when Ĥ copies its input this copied input goes no where?
No.  Ĥ copies its input from the tape to the tape.  There's no dispute
about that.  It's clear as day in every textbook.

You said that it exists NO WHERE !
No.  Read carefully:

On 4/23/2022 8:43 PM, Ben wrote:
but when H is simulating, and when that simulation is simulating
these strings won't appear anywhere.
They simply don't exist on the tape.

They simply don't exist on the tape.
They simply don't exist on the tape.
They simply don't exist on the tape.
They simply don't exist on the tape.
They simply don't exist on the tape.
They simply don't exist on the tape.

THEY DO EXIST ON THE TAPE SO YOU ARE WRONG
THEY DO EXIST ON THE TAPE SO YOU ARE WRONG
THEY DO EXIST ON THE TAPE SO YOU ARE WRONG
THEY DO EXIST ON THE TAPE SO YOU ARE WRONG
THEY DO EXIST ON THE TAPE SO YOU ARE WRONG

As soon as the simulated Ĥ copies its input once there are three
copies of this input on the master UTM tape.

I await your E and specification for P and I will then try to explain
why you are wrong about this.

I can't possibly be wrong about this.

Do I take it you won't be holding up your end of the deal then?


I just got out of the hospital. I was there since Tuesday. When you tell me that you are sure that some black cats are white it is easy to see that you are incorrect.

I will work through the even/odd example. I am still sick so I will do it slowly.


There is no possible way for a computable function to not be a pure function of its arguments because this is a defined to be the meaning of the term: "computable function".
https://en.wikipedia.org/wiki/Computable_function

When functions are computed by TM's the "arguments" are a set of finite strings, that is all that they have to deal with. These computations cannot possibly go on any other basis than what these finite strings specify.

It is very very nutty that Ben, Richard and Andre to all believe that it can have any other basis.

If I ask you the question: "What time is it?" and by that question I mean the question: "Where is the nearest Walmart?" as long as you provided the current time then you are correct.

If H(P,P) is asked whether or not its input halts and its answer is consistent with the correct simulation of this input, then it is necessarily correct in the same way that {the current time} is the correct answer to the question: "What time is it?"

--
Copyright 2022 Pete Olcott

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


Subject: Re:_My_honest_reviewers:_André,_Ben,_Mike,_Dennis,_Richard_[_previously_undetected_semantic_incoherence_]
From: olcott
Newsgroups: comp.theory, comp.ai.philosophy, sci.logic, sci.math
Followup: comp.theory
Date: Fri, 29 Apr 2022 04:40 UTC
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Subject: Re:_My_honest_reviewers:_André,_Ben,_Mike,
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From: NoO...@NoWhere.com (olcott)
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On 4/28/2022 8:14 PM, Ben wrote:
olcott <NoOne@NoWhere.com> writes:

On 4/28/2022 6:41 PM, Ben wrote:
olcott <NoOne@NoWhere.com> writes:

On 4/28/2022 1:14 PM, olcott wrote:
On 4/26/2022 7:45 PM, Ben wrote:
olcott <NoOne@NoWhere.com> writes:

On 4/26/2022 6:50 PM, Ben wrote:
olcott <NoOne@NoWhere.com> writes:

On 4/23/2022 8:43 PM, Ben wrote:
but when H is simulating, and when that simulation is simulating
these strings won't appear anywhere.
They simply don't exist on the tape.

They simply don't exist on the tape.
They simply don't exist on the tape.
They simply don't exist on the tape.
They simply don't exist on the tape.
They simply don't exist on the tape.
They simply don't exist on the tape.

THEY DO EXIST ON THE TAPE SO YOU ARE WRONG
THEY DO EXIST ON THE TAPE SO YOU ARE WRONG
THEY DO EXIST ON THE TAPE SO YOU ARE WRONG
THEY DO EXIST ON THE TAPE SO YOU ARE WRONG
THEY DO EXIST ON THE TAPE SO YOU ARE WRONG

As soon as the simulated Ĥ copies its input once there are three
copies of this input on the master UTM tape.

I await your E and specification for P and I will then try to explain
why you are wrong about this.

I can't possibly be wrong about this.

Do I take it you won't be holding up your end of the deal then?

I just got out of the hospital. I was there since Tuesday. When you
tell me that you are sure that some black cats are white it is easy
to see that you are incorrect.
I will work through the even/odd example. I am still sick so I will do
it slowly.
OK.

There is no possible way for a computable function to not be a pure
function of its arguments because this is a defined to be the meaning
of the term: "computable function".
A computable function is a mathematical function.  The term pure is
never applied to mathematical functions since that are all pure.

https://en.wikipedia.org/wiki/Computable_function

When functions are computed by TM's the "arguments" are a set of
finite strings, that is all that they have to deal with.
The input is a single string.  Always.  (Funny that you switch to using
the term argument when it's usually called an input, but when it's
usually called an argument you use the term input!)

OK so a halt decider computes the mapping from a TM description and
must ignore its input of this TMD because it cannot deal with more
than one string?

No.  Years ago I tried to explain that you need an encoding for a pair
of string, but you never took that on board.  I always wrote <[M],I> as
the single string input where [M] is the encoding of TM M and <x,y> is
the encoding of the pair of strings x and y.  Both [M] and <x,y> are
just notations for some agreed encoding.  Maybe we agree that if x="abc"
and y="010" then <x,y> is the string "abc//010".

Eventually, belatedly, you accepted that you need a notation from a TM's
encoding and you chose <M> from, I think, Sipser, but you never agreed
to use a pair notation.

These computations
cannot possibly go on any other basis than what these finite strings
specify.
Never in doubt.

It is very very nutty that Ben, Richard and Andre to all believe that
it can have any other basis.
We don't.  You don't understand (or pretend not to understand) what's
being said.

If I ask you the question: "What time is it?" and by that question I
mean the question: "Where is the nearest Walmart?" as long as you
provided the current time then you are correct.

The question being asked of your H is "does the function pointed to by
the first argument halt when called with the second pointer as it's
argument?".  H has access to the full address space of the machine (at
least it does in your x86 model) so there's nothing hidden from H.  Your
H returns false for H(P,P) which is incorrect because P(P) halts.

Do you not comprehend the idea of computational equivalence, or do you
simply "not believe" that P(P) and the correctly simulated input to
H(P,P) could lack computational equivalence?

I know what the definition of the halting problem is.  It's as above.
Your H does not meet the spec.
You have to think it ALL THE WAY THROUGH.

The above definition simply assumes that the behavior of the correctly simulated TM description will have the same behavior as the direct execution of the underlying machine.

Ĥ.q0 ⟨Ĥ⟩ ⊢* H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.final-state

It turns out that the behavior of the correctly simulated input to H has different behavior than the direct execution of Ĥ ⟨Ĥ⟩.

Expecting that H always report on the behavior of the direct execution of its input even when the behavior specified by this input is not the same as the behavior of the direct execution of this input is exactly the same as this case:

I always ask the question: "What time is it?"
Most of the time the current time is considered the correct answer, some of the time when I ask: "What time is it?" I want the location of the nearest Walmart and will consider every other answer incorrect.

To solve these age old self-reference paradox problems we must pay enormously more attention to how semantic meanings connect together or fail to connect.

All of the things that I have been addressing are only answered through the philosophy of semantics. The math, computer science and logic systems are merely how these connections are encoded.

The Gödel G, (of incompleteness) the Tarski Undefinability x
https://liarparadox.org/Tarski_275_276.pdf
and the Halting problem counter-examples all have previously undetected semantic incoherence.

It is the same sort of thing as the:
"What time is it (yes or no)?"
example that I posted in the forum many years ago,
only much more difficult to see.

--
Copyright 2022 Pete Olcott

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


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