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devel / comp.theory / On recursion and infinite recursion (reprise)

SubjectAuthor
* On recursion and infinite recursion (reprise)Mr Flibble
+* On recursion and infinite recursion (reprise)olcott
|+* On recursion and infinite recursion (reprise)Ben
||`* On recursion and infinite recursion (reprise)olcott
|| `* On recursion and infinite recursion (reprise)Ben
||  `* H(P,P) == false is correctolcott
||   `* H(P,P) == false is correctBen
||    `* H(P,P) == false is correctolcott
||     `* H(P,P) == false is correctBen
||      `* H(P,P) == false is correctolcott
||       `* H(P,P) == false is correctBen
||        `* H(P,P) == false is correct [ verified facts ]olcott
||         +* H(P,P) == false is correct [ verified facts ]Dennis Bush
||         |`* H(P,P) == false is correct [ verified facts ]olcott
||         | +* H(P,P) == false is correct [ verified facts ]André G. Isaak
||         | |`* H(P,P) == false is correct [ verified facts ]olcott
||         | | `* H(P,P) == false is correct [ verified facts ]André G. Isaak
||         | |  `* H(P,P) == false is correct [ verified facts ]olcott
||         | |   +* H(P,P) == false is correct [ verified facts ]Dennis Bush
||         | |   |`* H(P,P) == false is correct [ verified facts ]olcott
||         | |   | `* H(P,P) == false is correct [ verified facts ]Dennis Bush
||         | |   |  `* H(P,P) == false is correct [ verified facts ]olcott
||         | |   |   `- H(P,P) == false is correct [ verified facts ]Richard Damon
||         | |   `* H(P,P) == false is correct [ verified facts ]Richard Damon
||         | |    `* H(P,P) == false is correct [ verified facts ]Dennis Bush
||         | |     `* H(P,P) == false is correct [ verified facts ]olcott
||         | |      `* H(P,P) == false is correct [ verified facts ]Dennis Bush
||         | |       `* H(P,P) == false is correct [ verified facts ]olcott
||         | |        `* H(P,P) == false is correct [ verified facts ]Dennis Bush
||         | |         `- H(P,P) == false is correct [ verified facts ]olcott
||         | +* H(P,P) == false is correct [ verified facts ]Dennis Bush
||         | |`* H(P,P) == false is correct [ verified facts ]olcott
||         | | `* H(P,P) == false is correct [ verified facts ]Dennis Bush
||         | |  `* H(P,P) == false is correct [ verified facts ]olcott
||         | |   +* H(P,P) == false is correct [ verified facts ]Dennis Bush
||         | |   |`* H(P,P) == false is correct [ verified facts ]olcott
||         | |   | +* H(P,P) == false is correct [ verified facts ]Dennis Bush
||         | |   | |`* H(P,P) == false is correct [ verified facts ]olcott
||         | |   | | `* H(P,P) == false is correct [ verified facts ]Dennis Bush
||         | |   | |  `- H(P,P) == false is correct [ verified facts ]olcott
||         | |   | `- H(P,P) == false is correct [ verified facts ]Richard Damon
||         | |   `* H(P,P) == false is correct [ verified facts ]Richard Damon
||         | |    `* H(P,P) == false is correct [ verified facts ]Malcolm McLean
||         | |     +* H(P,P) == false is correct [ verified facts ]Ben
||         | |     |`* H(P,P) == false is correct [ verified facts ]olcott
||         | |     | `* H(P,P) == false is correct [ verified facts ]Dennis Bush
||         | |     |  `* H(P,P) == false is correct [ verified facts ]olcott
||         | |     |   `- H(P,P) == false is correct [ verified facts ]Richard Damon
||         | |     `* H(P,P) == false is correct [ verified facts ]olcott
||         | |      `* H(P,P) == false is correct [ verified facts ]Dennis Bush
||         | |       `* H(P,P) == false is correct [ verified facts ]olcott
||         | |        `* H(P,P) == false is correct [ verified facts ]Dennis Bush
||         | |         `* H(P,P) == false is correct [ verified facts ]olcott
||         | |          `* H(P,P) == false is correct [ verified facts ]Dennis Bush
||         | |           `* H(P,P) == false is correct [ verified facts ]olcott
||         | |            `* H(P,P) == false is correct [ verified facts ]Dennis Bush
||         | |             `* H(P,P) == false is correct [ verified facts ]olcott
||         | |              +* H(P,P) == false is correct [ verified facts ]Dennis Bush
||         | |              |`* H(P,P) == false is correct [ verified facts ]olcott
||         | |              | `* H(P,P) == false is correct [ verified facts ]Dennis Bush
||         | |              |  +- H(P,P) == false is correct [ verified facts ]olcott
||         | |              |  `* H(P,P) == false is correct [ verified facts ]Dennis Bush
||         | |              |   +- H(P,P) == false is correct [ verified facts ]olcott
||         | |              |   `* H(P,P) == false is correct [ verified facts ]Dennis Bush
||         | |              |    `* H(P,P) == false is correct [ verified facts ]olcott
||         | |              |     `- H(P,P) == false is correct [ verified facts ]Richard Damon
||         | |              `* H(P,P) == false is correct [ verified facts ]André G. Isaak
||         | |               `* H(P,P) == false is correct [ verified facts ]olcott
||         | |                `* H(P,P) == false is correct [ verified facts ]André G. Isaak
||         | |                 `- H(P,P) == false is correct [ verified facts ]olcott
||         | `- H(P,P) == false is correct [ verified facts ]Richard Damon
||         `* H(P,P) == false is correct [ verified facts ]Ben
||          `* H(P,P) == false is correct [ verified facts ]olcott
||           +* H(P,P) == false is correct [ verified facts ]Python
||           |`* H(P,P) == false is correct [ verified facts ]olcott
||           | `- H(P,P) == false is correct [ verified facts ]Python
||           +* H(P,P) == false is correct [ verified facts ]Ben
||           |+- H(P,P) == false is correct [ verified facts ]olcott
||           |+* H(P,P) == false is correct [ Simple TM Interpreter ]olcott
||           ||`* H(P,P) == false is correct [ Simple TM Interpreter ]Ben
||           || `* H(P,P) == false is correct [ Simple TM Interpreter ]olcott
||           ||  `* H(P,P) == false is correct [ Simple TM Interpreter ]Ben
||           ||   +* H(P,P) == false is correct [ Simple TM Interpreter ]olcott
||           ||   |`* H(P,P) == false is correct [ Simple TM Interpreter ]Ben
||           ||   | `* H(P,P) == false is correct [ Simple TM Interpreter ]olcott
||           ||   |  `- H(P,P) == false is correct [ Simple TM Interpreter ]Ben
||           ||   `- H(P,P) == false is correct [ Simple TM Interpreter ]olcott
||           |`* H(P,P) == false is correct [ Simple TM Interpreter ]olcott
||           | `* H(P,P) == false is correct [ Simple TM Interpreter ]André G. Isaak
||           |  +* H(P,P) == false is correct [ Simple TM Interpreter ]olcott
||           |  |`* H(P,P) == false is correct [ Simple TM Interpreter ]André G. Isaak
||           |  | `* H(P,P) == false is correct [ Simple TM Interpreter ]olcott
||           |  |  `* H(P,P) == false is correct [ Simple TM Interpreter ]André G. Isaak
||           |  |   `* H(P,P) == false is correct [ Simple TM Interpreter ]olcott
||           |  |    `* H(P,P) == false is correct [ Simple TM Interpreter ]André G. Isaak
||           |  |     `* H(P,P) == false is correct [ Simple TM Interpreter ]olcott
||           |  |      `* H(P,P) == false is correct [ Simple TM Interpreter ]André G. Isaak
||           |  |       `* H(P,P) == false is correct [ Simple TM Interpreter ]olcott
||           |  |        `* H(P,P) == false is correct [ Simple TM Interpreter ]André G. Isaak
||           |  |         +* H(P,P) == false is correct [ Simple TM Interpreter ]olcott
||           |  |         |`* H(P,P) == false is correct [ Simple TM Interpreter ]André G. Isaak
||           |  |         `* H(P,P) == false is correct [ Simple TM Interpreter ]Ben
||           |  `- H(P,P) == false is correct [ Simple TM Interpreter ]olcott
||           +- H(P,P) == false is correct [ verified facts ]Richard Damon
||           `* H(P,P) == false is correct [ verified facts ]Mikko
|`* On recursion and infinite recursion (reprise)Mikko
+* On recursion and infinite recursion (reprise)Richard Damon
+* On recursion and infinite recursion (reprise)Mikko
`* On recursion and infinite recursion (reprise)Mikko

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On recursion and infinite recursion (reprise)

<20220502164732.00004e01@reddwarf.jmc>

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From: flib...@reddwarf.jmc (Mr Flibble)
Newsgroups: comp.theory
Subject: On recursion and infinite recursion (reprise)
Message-ID: <20220502164732.00004e01@reddwarf.jmc>
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 by: Mr Flibble - Mon, 2 May 2022 15:47 UTC

Not all infinitely recursive definitions are invalid however infinitely
recursive definitions that arise out of a category error (as is the
case with the halting problem) are invalid.

The halting problem (as currently defined) is invalid due to the
invalid "impossible program" [Strachey, 1965] that is actually
impossible due to the category error present in its definition and
*not* because of any function call-like recursion; confusion between
these two types of recursion are why Olcott is having difficulty
communicating his ideas with the rest of you shower.

The categories involved in the category error are the decider and that
which is being decided. Currently extant attempts to conflate the
decider with that which is being decided are infinitely
recursive and thus invalid.

/Flibble

Re: On recursion and infinite recursion (reprise)

<t4p08u$5ar$1@dont-email.me>

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https://www.novabbs.com/devel/article-flat.php?id=31422&group=comp.theory#31422

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From: polco...@gmail.com (olcott)
Newsgroups: comp.theory
Subject: Re: On recursion and infinite recursion (reprise)
Date: Mon, 2 May 2022 11:18:36 -0500
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 by: olcott - Mon, 2 May 2022 16:18 UTC

On 5/2/2022 10:47 AM, Mr Flibble wrote:
> Not all infinitely recursive definitions are invalid however infinitely
> recursive definitions that arise out of a category error (as is the
> case with the halting problem) are invalid.
>

It seems to me that all infinitely recursive definitions are invalid and
I am having an excellent dialogue with some Prolog folks about this in
comp.lang.prolog.

> The halting problem (as currently defined) is invalid due to the
> invalid "impossible program" [Strachey, 1965] that is actually
> impossible due to the category error present in its definition and
> *not* because of any function call-like recursion; confusion between
> these two types of recursion are why Olcott is having difficulty
> communicating his ideas with the rest of you shower.
>

I created the x86 operating system taking at least a man-year so that I
could encode the HP counter-example P in C/x86 and then create a halt
decider H in C that examines the behavior of its correct simulation of P.

void P(u32 x)
{ if (H(x, x))
HERE: goto HERE;
return;
}

int main()
{ Output("Input_Halts = ", H((u32)P, (u32)P));
}

_P()
[000009d6](01) 55 push ebp
[000009d7](02) 8bec mov ebp,esp
[000009d9](03) 8b4508 mov eax,[ebp+08]
[000009dc](01) 50 push eax // push P
[000009dd](03) 8b4d08 mov ecx,[ebp+08]
[000009e0](01) 51 push ecx // push P
[000009e1](05) e840feffff call 00000826 // call H
[000009e6](03) 83c408 add esp,+08
[000009e9](02) 85c0 test eax,eax
[000009eb](02) 7402 jz 000009ef
[000009ed](02) ebfe jmp 000009ed
[000009ef](01) 5d pop ebp
[000009f0](01) c3 ret // Final state
Size in bytes:(0027) [000009f0]

machine stack stack machine assembly
address address data code language
======== ======== ======== ========= =============
....[000009d6][00211368][0021136c] 55 push ebp // enter P
....[000009d7][00211368][0021136c] 8bec mov ebp,esp
....[000009d9][00211368][0021136c] 8b4508 mov eax,[ebp+08]
....[000009dc][00211364][000009d6] 50 push eax // Push P
....[000009dd][00211364][000009d6] 8b4d08 mov ecx,[ebp+08]
....[000009e0][00211360][000009d6] 51 push ecx // Push P
....[000009e1][0021135c][000009e6] e840feffff call 00000826 // Call H
....[000009d6][0025bd90][0025bd94] 55 push ebp // enter P
....[000009d7][0025bd90][0025bd94] 8bec mov ebp,esp
....[000009d9][0025bd90][0025bd94] 8b4508 mov eax,[ebp+08]
....[000009dc][0025bd8c][000009d6] 50 push eax // Push P
....[000009dd][0025bd8c][000009d6] 8b4d08 mov ecx,[ebp+08]
....[000009e0][0025bd88][000009d6] 51 push ecx // Push P
....[000009e1][0025bd84][000009e6] e840feffff call 00000826 // Call H
Local Halt Decider: Infinite Recursion Detected Simulation Stopped

It is clear that the input to H(P,P) specifies infinitely nested
simulation to H.

> The categories involved in the category error are the decider and that
> which is being decided. Currently extant attempts to conflate the
> decider with that which is being decided are infinitely
> recursive and thus invalid.
>
> /Flibble
>

I already applied your idea of category error to Gödel's Incompleteness
and Tarski Undefinability. In both of these cases the Gödel H and the
Tarski p are incorrectly placed in the category of truth bearer / logic
sentence. They cannot be correctly evaluated because they are
semantically incorrect.

Now in comp.lang.prolog we are getting Prolog to agree that they are
semantically ill-formed.

--
Copyright 2022 Pete Olcott "Talent hits a target no one else can hit;
Genius hits a target no one else can see." Arthur Schopenhauer

Re: On recursion and infinite recursion (reprise)

<87wnf3ga8h.fsf@bsb.me.uk>

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https://www.novabbs.com/devel/article-flat.php?id=31424&group=comp.theory#31424

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From: ben.use...@bsb.me.uk (Ben)
Newsgroups: comp.theory
Subject: Re: On recursion and infinite recursion (reprise)
Date: Mon, 02 May 2022 17:39:10 +0100
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 by: Ben - Mon, 2 May 2022 16:39 UTC

olcott <polcott2@gmail.com> writes:

> It is clear that the input to H(P,P) specifies infinitely nested
> simulation to H.

What two pointers must be passed to H for H to tell up about the halting
of P(P)? If H can't report on the halting of the computation P(P) it is
not a halt decider, and you have already told use that H(P,P) == false
and that P(P) halts.

You have nowhere to go with H, hence your switching topics to being
wrong about Gödel again.

--
Ben.
"le génie humain a des limites, quand la bêtise humaine n’en a pas"
Alexandre Dumas (fils)

Re: On recursion and infinite recursion (reprise)

<t4pesp$d9n$1@dont-email.me>

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From: polco...@gmail.com (olcott)
Newsgroups: comp.theory
Subject: Re: On recursion and infinite recursion (reprise)
Date: Mon, 2 May 2022 15:28:07 -0500
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 by: olcott - Mon, 2 May 2022 20:28 UTC

On 5/2/2022 11:39 AM, Ben wrote:
> olcott <polcott2@gmail.com> writes:
>
>> It is clear that the input to H(P,P) specifies infinitely nested
>> simulation to H.
>
> What two pointers must be passed to H for H to tell up about the halting
> of P(P)? If H can't report on the halting of the computation P(P) it is
> not a halt decider, and you have already told use that H(P,P) == false
> and that P(P) halts.

If H can report on the halting of non-input P(P) then it is not a
decider because deciders only compute the mapping from inputs to final
states.

>
> You have nowhere to go with H, hence your switching topics to being
> wrong about Gödel again.
>

That you expect a halt decider to compute the mapping from non-inputs is
a little nuts when you know that deciders can't possibly do this.

It turns out that I can create a whole TM interpreter from scratch
quicker than I can learn the extraneous complexity of the TM Interpreter
http://www.lns.mit.edu/~dsw/turing/turing.html

It will have the same eight-bit quintuples of the TM, The Turing Machine
Interpreter. These will be at the beginning of the file, followed by
BEGIN_TAPE on a line by itself. Followed by the initial tape as
contiguous ASCII characters.

It will output a full execution trace. The only parameter to the command
line system with be filename.tm. This system is easily extended to
16-bits or 32-bits. These larger systems will use 4-8 hex digits for
state / character representation.

--
Copyright 2022 Pete Olcott "Talent hits a target no one else can hit;
Genius hits a target no one else can see." Arthur Schopenhauer

Re: On recursion and infinite recursion (reprise)

<NZYbK.49$UWx1.11@fx41.iad>

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From: Rich...@Damon-Family.org (Richard Damon)
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 by: Richard Damon - Mon, 2 May 2022 22:32 UTC

On 5/2/22 11:47 AM, Mr Flibble wrote:
> Not all infinitely recursive definitions are invalid however infinitely
> recursive definitions that arise out of a category error (as is the
> case with the halting problem) are invalid.
>
> The halting problem (as currently defined) is invalid due to the
> invalid "impossible program" [Strachey, 1965] that is actually
> impossible due to the category error present in its definition and
> *not* because of any function call-like recursion; confusion between
> these two types of recursion are why Olcott is having difficulty
> communicating his ideas with the rest of you shower.
>
> The categories involved in the category error are the decider and that
> which is being decided. Currently extant attempts to conflate the
> decider with that which is being decided are infinitely
> recursive and thus invalid.
>
> /Flibble
>

Except that the "impossible program" isn't part of the definition of the
Halting Problem.

By your definition, I suspect much of Mathematics becomes a category error.

If you are willing to say that this is a natural result of your logic
system, fine, but just remember that consequence, which actually says
your logic doesn't refute Gobel, as the Theorm specifically requires
working in a field that supports some minimums that your logic doesn't
handle.

Re: On recursion and infinite recursion (reprise)

<20220502233810.000023d2@reddwarf.jmc>

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From: flib...@reddwarf.jmc (Mr Flibble)
Newsgroups: comp.theory
Subject: Re: On recursion and infinite recursion (reprise)
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 by: Mr Flibble - Mon, 2 May 2022 22:38 UTC

On Mon, 2 May 2022 18:32:16 -0400
Richard Damon <Richard@Damon-Family.org> wrote:

> On 5/2/22 11:47 AM, Mr Flibble wrote:
> > Not all infinitely recursive definitions are invalid however
> > infinitely recursive definitions that arise out of a category error
> > (as is the case with the halting problem) are invalid.
> >
> > The halting problem (as currently defined) is invalid due to the
> > invalid "impossible program" [Strachey, 1965] that is actually
> > impossible due to the category error present in its definition and
> > *not* because of any function call-like recursion; confusion between
> > these two types of recursion are why Olcott is having difficulty
> > communicating his ideas with the rest of you shower.
> >
> > The categories involved in the category error are the decider and
> > that which is being decided. Currently extant attempts to conflate
> > the decider with that which is being decided are infinitely
> > recursive and thus invalid.
> >
> > /Flibble
> >
>
> Except that the "impossible program" isn't part of the definition of
> the Halting Problem.

It is according to [Wikipedia, 2022].

/Flibble

Re: On recursion and infinite recursion (reprise)

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 by: Richard Damon - Mon, 2 May 2022 22:46 UTC

On 5/2/22 6:38 PM, Mr Flibble wrote:
> On Mon, 2 May 2022 18:32:16 -0400
> Richard Damon <Richard@Damon-Family.org> wrote:
>
>> On 5/2/22 11:47 AM, Mr Flibble wrote:
>>> Not all infinitely recursive definitions are invalid however
>>> infinitely recursive definitions that arise out of a category error
>>> (as is the case with the halting problem) are invalid.
>>>
>>> The halting problem (as currently defined) is invalid due to the
>>> invalid "impossible program" [Strachey, 1965] that is actually
>>> impossible due to the category error present in its definition and
>>> *not* because of any function call-like recursion; confusion between
>>> these two types of recursion are why Olcott is having difficulty
>>> communicating his ideas with the rest of you shower.
>>>
>>> The categories involved in the category error are the decider and
>>> that which is being decided. Currently extant attempts to conflate
>>> the decider with that which is being decided are infinitely
>>> recursive and thus invalid.
>>>
>>> /Flibble
>>>
>>
>> Except that the "impossible program" isn't part of the definition of
>> the Halting Problem.
>
> It is according to [Wikipedia, 2022].
>
> /Flibble
>

Nope, you comprehend worse that PO.

Note, and Encyclopedic entery, like Wikipedia, is NOT just a definition
but a full article explaining the subject.

Maybe if you look for a FORMAL source, that states what is the ACTUAL
definition, you would learn something.

Re: On recursion and infinite recursion (reprise)

<20220502234711.00000216@reddwarf.jmc>

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From: flib...@reddwarf.jmc (Mr Flibble)
Newsgroups: comp.theory
Subject: Re: On recursion and infinite recursion (reprise)
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 by: Mr Flibble - Mon, 2 May 2022 22:47 UTC

On Mon, 2 May 2022 18:46:00 -0400
Richard Damon <Richard@Damon-Family.org> wrote:

> On 5/2/22 6:38 PM, Mr Flibble wrote:
> > On Mon, 2 May 2022 18:32:16 -0400
> > Richard Damon <Richard@Damon-Family.org> wrote:
> >
> >> On 5/2/22 11:47 AM, Mr Flibble wrote:
> >>> Not all infinitely recursive definitions are invalid however
> >>> infinitely recursive definitions that arise out of a category
> >>> error (as is the case with the halting problem) are invalid.
> >>>
> >>> The halting problem (as currently defined) is invalid due to the
> >>> invalid "impossible program" [Strachey, 1965] that is actually
> >>> impossible due to the category error present in its definition and
> >>> *not* because of any function call-like recursion; confusion
> >>> between these two types of recursion are why Olcott is having
> >>> difficulty communicating his ideas with the rest of you shower.
> >>>
> >>> The categories involved in the category error are the decider and
> >>> that which is being decided. Currently extant attempts to
> >>> conflate the decider with that which is being decided are
> >>> infinitely recursive and thus invalid.
> >>>
> >>> /Flibble
> >>>
> >>
> >> Except that the "impossible program" isn't part of the definition
> >> of the Halting Problem.
> >
> > It is according to [Wikipedia, 2022].
> >
> > /Flibble
> >
>
> Nope, you comprehend worse that PO.
>
> Note, and Encyclopedic entery, like Wikipedia, is NOT just a
> definition but a full article explaining the subject.
>
> Maybe if you look for a FORMAL source, that states what is the ACTUAL
> definition, you would learn something.

If Wikipedia is wrong then correct it and have your corrections
reviewed; until then please shut the fuck up.

/Flibble

Re: On recursion and infinite recursion (reprise)

<87fslrfs3t.fsf@bsb.me.uk>

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Subject: Re: On recursion and infinite recursion (reprise)
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 by: Ben - Mon, 2 May 2022 23:10 UTC

olcott <polcott2@gmail.com> writes:

> On 5/2/2022 11:39 AM, Ben wrote:
>> olcott <polcott2@gmail.com> writes:
>>
>>> It is clear that the input to H(P,P) specifies infinitely nested
>>> simulation to H.
>> What two pointers must be passed to H for H to tell up about the halting
>> of P(P)? If H can't report on the halting of the computation P(P) it is
>> not a halt decider, and you have already told use that H(P,P) == false
>> and that P(P) halts.
>
> If H can report on the halting of non-input P(P) then it is not a
> decider because deciders only compute the mapping from inputs to final
> states.

TM deciders compute mappings from inputs to final states /according to
some property of the inputs/ -- whether the input represents, for
example, an even number, a prime number or a halting computation.

According to you there is no "input" (in reality a pair of pointers)
that represents the halting computation P(P). Why should anyone care
about this H if it does not decide what we want -- the halting of the
function call represented by the two arguments to H? Whatever H is
actually deciding is not interesting.

Also, I wonder why you wasted so much time justifying the fact that
H(P,P) == false "even though P(P) halts" when H(P,P) is, apparently, not
even supposed to be deciding the halting P(P). Well, we know, of
course. You realised you were in a hole so you started to dig sideways.
You used to know that H(X,Y) had to decide the halting of X(Y). You're
now pretending it never did!

> That you expect a halt decider to compute the mapping from non-inputs
> is a little nuts when you know that deciders can't possibly do this.

Don't be silly. They decide properties of inputs -- parity, halting and
so on. You'd know this if you'd done even the warm-up exercises I set.
How are they coming along? It looks like you have found an excuse to
bail out again:

> It turns out that I can create a whole TM interpreter from scratch
> quicker than I can learn the extraneous complexity of the TM
> Interpreter http://www.lns.mit.edu/~dsw/turing/turing.html

I doubt it. But I suppose you think that's a reasonable excuse. Of
course, some of us remember you saying writing such a thing would take
about a week three years ago. I remember wondering how such a simple
program could take you a week to write.

Of course you don't need an interpreter to write E or specify P, but you
must find some excuse for bailing out.

--
Ben.
"le génie humain a des limites, quand la bêtise humaine n’en a pas"
Alexandre Dumas (fils)

Re: On recursion and infinite recursion (reprise)

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 by: Richard Damon - Mon, 2 May 2022 23:16 UTC

On 5/2/22 6:47 PM, Mr Flibble wrote:
> On Mon, 2 May 2022 18:46:00 -0400
> Richard Damon <Richard@Damon-Family.org> wrote:
>
>> On 5/2/22 6:38 PM, Mr Flibble wrote:
>>> On Mon, 2 May 2022 18:32:16 -0400
>>> Richard Damon <Richard@Damon-Family.org> wrote:
>>>
>>>> On 5/2/22 11:47 AM, Mr Flibble wrote:
>>>>> Not all infinitely recursive definitions are invalid however
>>>>> infinitely recursive definitions that arise out of a category
>>>>> error (as is the case with the halting problem) are invalid.
>>>>>
>>>>> The halting problem (as currently defined) is invalid due to the
>>>>> invalid "impossible program" [Strachey, 1965] that is actually
>>>>> impossible due to the category error present in its definition and
>>>>> *not* because of any function call-like recursion; confusion
>>>>> between these two types of recursion are why Olcott is having
>>>>> difficulty communicating his ideas with the rest of you shower.
>>>>>
>>>>> The categories involved in the category error are the decider and
>>>>> that which is being decided. Currently extant attempts to
>>>>> conflate the decider with that which is being decided are
>>>>> infinitely recursive and thus invalid.
>>>>>
>>>>> /Flibble
>>>>>
>>>>
>>>> Except that the "impossible program" isn't part of the definition
>>>> of the Halting Problem.
>>>
>>> It is according to [Wikipedia, 2022].
>>>
>>> /Flibble
>>>
>>
>> Nope, you comprehend worse that PO.
>>
>> Note, and Encyclopedic entery, like Wikipedia, is NOT just a
>> definition but a full article explaining the subject.
>>
>> Maybe if you look for a FORMAL source, that states what is the ACTUAL
>> definition, you would learn something.
>
> If Wikipedia is wrong then correct it and have your corrections
> reviewed; until then please shut the fuck up.
>
> /Flibble
>

It isn't that the article is "Wrong", it is a fairly good Encyclpedic
article. It just is that the first two paragraphs aren't all a
definition, and it doesn't say they are.

Re: On recursion and infinite recursion (reprise)

<20220503003041.00001407@reddwarf.jmc>

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From: flib...@reddwarf.jmc (Mr Flibble)
Newsgroups: comp.theory
Subject: Re: On recursion and infinite recursion (reprise)
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 by: Mr Flibble - Mon, 2 May 2022 23:30 UTC

On Mon, 2 May 2022 19:16:03 -0400
Richard Damon <Richard@Damon-Family.org> wrote:

> On 5/2/22 6:47 PM, Mr Flibble wrote:
> > On Mon, 2 May 2022 18:46:00 -0400
> > Richard Damon <Richard@Damon-Family.org> wrote:
> >
> >> On 5/2/22 6:38 PM, Mr Flibble wrote:
> >>> On Mon, 2 May 2022 18:32:16 -0400
> >>> Richard Damon <Richard@Damon-Family.org> wrote:
> >>>
> >>>> On 5/2/22 11:47 AM, Mr Flibble wrote:
> >>>>> Not all infinitely recursive definitions are invalid however
> >>>>> infinitely recursive definitions that arise out of a category
> >>>>> error (as is the case with the halting problem) are invalid.
> >>>>>
> >>>>> The halting problem (as currently defined) is invalid due to the
> >>>>> invalid "impossible program" [Strachey, 1965] that is actually
> >>>>> impossible due to the category error present in its definition
> >>>>> and *not* because of any function call-like recursion; confusion
> >>>>> between these two types of recursion are why Olcott is having
> >>>>> difficulty communicating his ideas with the rest of you shower.
> >>>>>
> >>>>> The categories involved in the category error are the decider
> >>>>> and that which is being decided. Currently extant attempts to
> >>>>> conflate the decider with that which is being decided are
> >>>>> infinitely recursive and thus invalid.
> >>>>>
> >>>>> /Flibble
> >>>>>
> >>>>
> >>>> Except that the "impossible program" isn't part of the definition
> >>>> of the Halting Problem.
> >>>
> >>> It is according to [Wikipedia, 2022].
> >>>
> >>> /Flibble
> >>>
> >>
> >> Nope, you comprehend worse that PO.
> >>
> >> Note, and Encyclopedic entery, like Wikipedia, is NOT just a
> >> definition but a full article explaining the subject.
> >>
> >> Maybe if you look for a FORMAL source, that states what is the
> >> ACTUAL definition, you would learn something.
> >
> > If Wikipedia is wrong then correct it and have your corrections
> > reviewed; until then please shut the fuck up.
> >
> > /Flibble
> >
>
> It isn't that the article is "Wrong", it is a fairly good Encyclpedic
> article. It just is that the first two paragraphs aren't all a
> definition, and it doesn't say they are.

The first two paragraphs define the halting problem as that is what the
currently extant halting problem "proofs" are predicated on (and why
they are invalid).

/Flibble

Re: On recursion and infinite recursion (reprise)

<t4ptcr$287$2@dont-email.me>

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From: polco...@gmail.com (olcott)
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Subject: Re: On recursion and infinite recursion (reprise)
Date: Mon, 2 May 2022 19:35:38 -0500
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 by: olcott - Tue, 3 May 2022 00:35 UTC

On 5/2/2022 5:47 PM, Mr Flibble wrote:
> On Mon, 2 May 2022 18:46:00 -0400
> Richard Damon <Richard@Damon-Family.org> wrote:
>
>> On 5/2/22 6:38 PM, Mr Flibble wrote:
>>> On Mon, 2 May 2022 18:32:16 -0400
>>> Richard Damon <Richard@Damon-Family.org> wrote:
>>>
>>>> On 5/2/22 11:47 AM, Mr Flibble wrote:
>>>>> Not all infinitely recursive definitions are invalid however
>>>>> infinitely recursive definitions that arise out of a category
>>>>> error (as is the case with the halting problem) are invalid.
>>>>>
>>>>> The halting problem (as currently defined) is invalid due to the
>>>>> invalid "impossible program" [Strachey, 1965] that is actually
>>>>> impossible due to the category error present in its definition and
>>>>> *not* because of any function call-like recursion; confusion
>>>>> between these two types of recursion are why Olcott is having
>>>>> difficulty communicating his ideas with the rest of you shower.
>>>>>
>>>>> The categories involved in the category error are the decider and
>>>>> that which is being decided. Currently extant attempts to
>>>>> conflate the decider with that which is being decided are
>>>>> infinitely recursive and thus invalid.
>>>>>
>>>>> /Flibble
>>>>>
>>>>
>>>> Except that the "impossible program" isn't part of the definition
>>>> of the Halting Problem.
>>>
>>> It is according to [Wikipedia, 2022].
>>>
>>> /Flibble
>>>
>>
>> Nope, you comprehend worse that PO.
>>
>> Note, and Encyclopedic entery, like Wikipedia, is NOT just a
>> definition but a full article explaining the subject.
>>
>> Maybe if you look for a FORMAL source, that states what is the ACTUAL
>> definition, you would learn something.
>
> If Wikipedia is wrong then correct it and have your corrections
> reviewed; until then please shut the fuck up.
>
> /Flibble
>

I think that the problem is that Richard has disagreeably as his highest
priority, thus doesn't really give a rat's ass for the truth. An

An impossible program C. Strachey
The Computer Journal, Volume 7, Issue 4, January 1965, Page 313,
Published: 01 January 1965
https://academic.oup.com/comjnl/article/7/4/313/354243

It is very common knowledge that the Wikipedia description is true and
this is affirmed in Sipser.

For any program f that might determine if programs halt, a
"pathological" program g, called with some input, can pass its own
source and its input to f and then specifically do the opposite of what
f predicts g will do. https://en.wikipedia.org/wiki/Halting_problem

Now we construct a new Turing machine D with H as a subroutine. This new
TM calls H to determine what M does when the input to M is its own
description ⟨M⟩. Once D has determined this information, it does the
opposite. https://www.liarparadox.org/Sipser_165_167.pdf

--
Copyright 2022 Pete Olcott "Talent hits a target no one else can hit;
Genius hits a target no one else can see." Arthur Schopenhauer

Re: On recursion and infinite recursion (reprise)

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 by: Richard Damon - Tue, 3 May 2022 00:40 UTC

On 5/2/22 7:30 PM, Mr Flibble wrote:
> On Mon, 2 May 2022 19:16:03 -0400
> Richard Damon <Richard@Damon-Family.org> wrote:
>
>> On 5/2/22 6:47 PM, Mr Flibble wrote:
>>> On Mon, 2 May 2022 18:46:00 -0400
>>> Richard Damon <Richard@Damon-Family.org> wrote:
>>>
>>>> On 5/2/22 6:38 PM, Mr Flibble wrote:
>>>>> On Mon, 2 May 2022 18:32:16 -0400
>>>>> Richard Damon <Richard@Damon-Family.org> wrote:
>>>>>
>>>>>> On 5/2/22 11:47 AM, Mr Flibble wrote:
>>>>>>> Not all infinitely recursive definitions are invalid however
>>>>>>> infinitely recursive definitions that arise out of a category
>>>>>>> error (as is the case with the halting problem) are invalid.
>>>>>>>
>>>>>>> The halting problem (as currently defined) is invalid due to the
>>>>>>> invalid "impossible program" [Strachey, 1965] that is actually
>>>>>>> impossible due to the category error present in its definition
>>>>>>> and *not* because of any function call-like recursion; confusion
>>>>>>> between these two types of recursion are why Olcott is having
>>>>>>> difficulty communicating his ideas with the rest of you shower.
>>>>>>>
>>>>>>> The categories involved in the category error are the decider
>>>>>>> and that which is being decided. Currently extant attempts to
>>>>>>> conflate the decider with that which is being decided are
>>>>>>> infinitely recursive and thus invalid.
>>>>>>>
>>>>>>> /Flibble
>>>>>>>
>>>>>>
>>>>>> Except that the "impossible program" isn't part of the definition
>>>>>> of the Halting Problem.
>>>>>
>>>>> It is according to [Wikipedia, 2022].
>>>>>
>>>>> /Flibble
>>>>>
>>>>
>>>> Nope, you comprehend worse that PO.
>>>>
>>>> Note, and Encyclopedic entery, like Wikipedia, is NOT just a
>>>> definition but a full article explaining the subject.
>>>>
>>>> Maybe if you look for a FORMAL source, that states what is the
>>>> ACTUAL definition, you would learn something.
>>>
>>> If Wikipedia is wrong then correct it and have your corrections
>>> reviewed; until then please shut the fuck up.
>>>
>>> /Flibble
>>>
>>
>> It isn't that the article is "Wrong", it is a fairly good Encyclpedic
>> article. It just is that the first two paragraphs aren't all a
>> definition, and it doesn't say they are.
>
> The first two paragraphs define the halting problem as that is what the
> currently extant halting problem "proofs" are predicated on (and why
> they are invalid).
>
> /Flibble
>

No, lets actually look at what is says, and parse it:

In computability theory, the halting problem is the problem of
determining, from a description of an arbitrary computer program and an
input, whether the program will finish running, or continue to run
forever. Alan Turing proved in 1936 that a general algorithm to solve
the halting problem for all possible program-input pairs cannot exist.

For any program f that might determine if programs halt, a
"pathological" program g, called with some input, can pass its own
source and its input to f and then specifically do the opposite of what
f predicts g will do. No f can exist that handles this case. A key part
of the proof is a mathematical definition of a computer and program,
which is known as a Turing machine; the halting problem is undecidable
over Turing machines. It is one of the first cases of decision problems
proven to be unsolvable. This proof is significant to practical
computing efforts, defining a class of applications which no programming
invention can possibly perform perfectly.

Jack Copeland attributes the introduction of the term halting problem to
the work of Martin Davis in the 1950s.[1]

The FIRST SENTENCE is the definition of the Problem.

The Second Sentence is the Theorem about it that says that no solution
exists.

That ends the first paragraph.

The Second Paragraph, is a continuation of the idea of the Second
Sentence, giving a summary of the proof that no solution exist.

It is a category error to confuse the Statement of the Problem with the
Proof of the Theorem that not answer to the Problem exists.

A Proof is NOT a Problem.

Re: On recursion and infinite recursion (reprise)

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 by: Richard Damon - Tue, 3 May 2022 00:48 UTC

On 5/2/22 8:35 PM, olcott wrote:
> On 5/2/2022 5:47 PM, Mr Flibble wrote:
>> On Mon, 2 May 2022 18:46:00 -0400
>> Richard Damon <Richard@Damon-Family.org> wrote:
>>
>>> On 5/2/22 6:38 PM, Mr Flibble wrote:
>>>> On Mon, 2 May 2022 18:32:16 -0400
>>>> Richard Damon <Richard@Damon-Family.org> wrote:
>>>>> On 5/2/22 11:47 AM, Mr Flibble wrote:
>>>>>> Not all infinitely recursive definitions are invalid however
>>>>>> infinitely recursive definitions that arise out of a category
>>>>>> error (as is the case with the halting problem) are invalid.
>>>>>>
>>>>>> The halting problem (as currently defined) is invalid due to the
>>>>>> invalid "impossible program" [Strachey, 1965] that is actually
>>>>>> impossible due to the category error present in its definition and
>>>>>> *not* because of any function call-like recursion; confusion
>>>>>> between these two types of recursion are why Olcott is having
>>>>>> difficulty communicating his ideas with the rest of you shower.
>>>>>>
>>>>>> The categories involved in the category error are the decider and
>>>>>> that which is being decided.  Currently extant attempts to
>>>>>> conflate the decider with that which is being decided are
>>>>>> infinitely recursive and thus invalid.
>>>>>>
>>>>>> /Flibble
>>>>>
>>>>> Except that the "impossible program" isn't part of the definition
>>>>> of the Halting Problem.
>>>>
>>>> It is according to [Wikipedia, 2022].
>>>>
>>>> /Flibble
>>>
>>> Nope, you comprehend worse that PO.
>>>
>>> Note, and Encyclopedic entery, like Wikipedia, is NOT just a
>>> definition but a full article explaining the subject.
>>>
>>> Maybe if you look for a FORMAL source, that states what is the ACTUAL
>>> definition, you would learn something.
>>
>> If Wikipedia is wrong then correct it and have your corrections
>> reviewed; until then please shut the fuck up.
>>
>> /Flibble
>>
>
> I think that the problem is that Richard has disagreeably as his highest
> priority, thus doesn't really give a rat's ass for the truth. An
>
> An impossible program C. Strachey
> The Computer Journal, Volume 7, Issue 4, January 1965, Page 313,
> Published: 01 January 1965
> https://academic.oup.com/comjnl/article/7/4/313/354243
>
> It is very common knowledge that the Wikipedia description is true and
> this is affirmed in Sipser.
>
> For any program f that might determine if programs halt, a
> "pathological" program g, called with some input, can pass its own
> source and its input to f and then specifically do the opposite of what
> f predicts g will do. https://en.wikipedia.org/wiki/Halting_problem
>
> Now we construct a new Turing machine D with H as a subroutine. This new
> TM calls H to determine what M does when the input to M is its own
> description ⟨M⟩. Once D has determined this information, it does the
> opposite. https://www.liarparadox.org/Sipser_165_167.pdf
>
>

Thus you have shown you don't even know what a "Definition" is, so it is
impossible for you to reason by the meaning of the words.

You have just proved yourself to be an IDIOT.

Re: On recursion and infinite recursion (reprise)

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Newsgroups: comp.theory
Subject: Re: On recursion and infinite recursion (reprise)
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 by: Mikko - Tue, 3 May 2022 09:31 UTC

On 2022-05-02 15:47:32 +0000, Mr Flibble said:

> Not all infinitely recursive definitions are invalid however infinitely
> recursive definitions that arise out of a category error (as is the
> case with the halting problem) are invalid.

An infinite recursion cannot arise out of a category error as the recursion
stops at the category error.

Mikko

Re: On recursion and infinite recursion (reprise)

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Subject: Re: On recursion and infinite recursion (reprise)
Date: Tue, 3 May 2022 12:36:44 +0300
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 by: Mikko - Tue, 3 May 2022 09:36 UTC

On 2022-05-02 16:18:36 +0000, olcott said:

> It seems to me that all infinitely recursive definitions are invalid
> and I am having an excellent dialogue with some Prolog folks about this
> in comp.lang.prolog.

One of the rules that define Prolog language is

arguments ::= argument | argument "," arguments

which is infinitely recursive. Is it invalid? Is Prolog invalid because
of this and other infinitely recursive rules?

Mikko

Re: On recursion and infinite recursion (reprise)

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Subject: Re: On recursion and infinite recursion (reprise)
From: malcolm....@gmail.com (Malcolm McLean)
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 by: Malcolm McLean - Tue, 3 May 2022 11:08 UTC

On Tuesday, 3 May 2022 at 10:36:48 UTC+1, Mikko wrote:
> On 2022-05-02 16:18:36 +0000, olcott said:
>
> > It seems to me that all infinitely recursive definitions are invalid
> > and I am having an excellent dialogue with some Prolog folks about this
> > in comp.lang.prolog.
> One of the rules that define Prolog language is
>
> arguments ::= argument | argument "," arguments
>
> which is infinitely recursive. Is it invalid? Is Prolog invalid because
> of this and other infinitely recursive rules?
>
Kind of.
A Prolog program is a physical object, not a mathematical object, so
the recursion has to terminate somewhere.
But it might lead you into strange territory if you tried to define the result
of passing an ininite argument list to some Prolog.

Re: On recursion and infinite recursion (reprise)

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 by: wij wij - Tue, 3 May 2022 12:12 UTC

richar...@gmail.com 在 2022年5月3日 星期二上午8:48:57 [UTC+8] 的信中寫道:
> On 5/2/22 8:35 PM, olcott wrote:
> > On 5/2/2022 5:47 PM, Mr Flibble wrote:
> >> On Mon, 2 May 2022 18:46:00 -0400
> >> Richard Damon <Ric...@Damon-Family.org> wrote:
> >>
> >>> On 5/2/22 6:38 PM, Mr Flibble wrote:
> >>>> On Mon, 2 May 2022 18:32:16 -0400
> >>>> Richard Damon <Ric...@Damon-Family.org> wrote:
> >>>>> On 5/2/22 11:47 AM, Mr Flibble wrote:
> >>>>>> Not all infinitely recursive definitions are invalid however
> >>>>>> infinitely recursive definitions that arise out of a category
> >>>>>> error (as is the case with the halting problem) are invalid.
> >>>>>>
> >>>>>> The halting problem (as currently defined) is invalid due to the
> >>>>>> invalid "impossible program" [Strachey, 1965] that is actually
> >>>>>> impossible due to the category error present in its definition and
> >>>>>> *not* because of any function call-like recursion; confusion
> >>>>>> between these two types of recursion are why Olcott is having
> >>>>>> difficulty communicating his ideas with the rest of you shower.
> >>>>>>
> >>>>>> The categories involved in the category error are the decider and
> >>>>>> that which is being decided. Currently extant attempts to
> >>>>>> conflate the decider with that which is being decided are
> >>>>>> infinitely recursive and thus invalid.
> >>>>>>
> >>>>>> /Flibble
> >>>>>
> >>>>> Except that the "impossible program" isn't part of the definition
> >>>>> of the Halting Problem.
> >>>>
> >>>> It is according to [Wikipedia, 2022].
> >>>>
> >>>> /Flibble
> >>>
> >>> Nope, you comprehend worse that PO.
> >>>
> >>> Note, and Encyclopedic entery, like Wikipedia, is NOT just a
> >>> definition but a full article explaining the subject.
> >>>
> >>> Maybe if you look for a FORMAL source, that states what is the ACTUAL
> >>> definition, you would learn something.
> >>
> >> If Wikipedia is wrong then correct it and have your corrections
> >> reviewed; until then please shut the fuck up.
> >>
> >> /Flibble
> >>
> >
> > I think that the problem is that Richard has disagreeably as his highest
> > priority, thus doesn't really give a rat's ass for the truth. An
> >
> > An impossible program C. Strachey
> > The Computer Journal, Volume 7, Issue 4, January 1965, Page 313,
> > Published: 01 January 1965
> > https://academic.oup.com/comjnl/article/7/4/313/354243
> >
> > It is very common knowledge that the Wikipedia description is true and
> > this is affirmed in Sipser.
> >
> > For any program f that might determine if programs halt, a
> > "pathological" program g, called with some input, can pass its own
> > source and its input to f and then specifically do the opposite of what
> > f predicts g will do. https://en.wikipedia.org/wiki/Halting_problem
> >
> > Now we construct a new Turing machine D with H as a subroutine. This new
> > TM calls H to determine what M does when the input to M is its own
> > description ⟨M⟩. Once D has determined this information, it does the
> > opposite. https://www.liarparadox.org/Sipser_165_167.pdf
> >
> >
> Thus you have shown you don't even know what a "Definition" is, so it is
> impossible for you to reason by the meaning of the words.
>
> You have just proved yourself to be an IDIOT.

PO is incapable of logic reasoning (PO had shown he cannot even get the truth
table of logical implication/AND right). All he said is delusion including when
words from him happen to be correct to others (no real meaning).

IIRC, PO's revision that H(P,P) has no relation with P(P) is deliberately
fabricated this recent year after PO ran out his reasons to explain why HP is
wrong and he is correct. PO has no trouble to 'lie' to his bible (he can read
it his way), the HP thing is just piece of cake.

Re: On recursion and infinite recursion (reprise)

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 by: olcott - Tue, 3 May 2022 14:31 UTC

On 5/3/2022 7:12 AM, wij wij wrote:
> richar...@gmail.com 在 2022年5月3日 星期二上午8:48:57 [UTC+8] 的信中寫道:
>> On 5/2/22 8:35 PM, olcott wrote:
>>> On 5/2/2022 5:47 PM, Mr Flibble wrote:
>>>> On Mon, 2 May 2022 18:46:00 -0400
>>>> Richard Damon <Ric...@Damon-Family.org> wrote:
>>>>
>>>>> On 5/2/22 6:38 PM, Mr Flibble wrote:
>>>>>> On Mon, 2 May 2022 18:32:16 -0400
>>>>>> Richard Damon <Ric...@Damon-Family.org> wrote:
>>>>>>> On 5/2/22 11:47 AM, Mr Flibble wrote:
>>>>>>>> Not all infinitely recursive definitions are invalid however
>>>>>>>> infinitely recursive definitions that arise out of a category
>>>>>>>> error (as is the case with the halting problem) are invalid.
>>>>>>>>
>>>>>>>> The halting problem (as currently defined) is invalid due to the
>>>>>>>> invalid "impossible program" [Strachey, 1965] that is actually
>>>>>>>> impossible due to the category error present in its definition and
>>>>>>>> *not* because of any function call-like recursion; confusion
>>>>>>>> between these two types of recursion are why Olcott is having
>>>>>>>> difficulty communicating his ideas with the rest of you shower.
>>>>>>>>
>>>>>>>> The categories involved in the category error are the decider and
>>>>>>>> that which is being decided. Currently extant attempts to
>>>>>>>> conflate the decider with that which is being decided are
>>>>>>>> infinitely recursive and thus invalid.
>>>>>>>>
>>>>>>>> /Flibble
>>>>>>>
>>>>>>> Except that the "impossible program" isn't part of the definition
>>>>>>> of the Halting Problem.
>>>>>>
>>>>>> It is according to [Wikipedia, 2022].
>>>>>>
>>>>>> /Flibble
>>>>>
>>>>> Nope, you comprehend worse that PO.
>>>>>
>>>>> Note, and Encyclopedic entery, like Wikipedia, is NOT just a
>>>>> definition but a full article explaining the subject.
>>>>>
>>>>> Maybe if you look for a FORMAL source, that states what is the ACTUAL
>>>>> definition, you would learn something.
>>>>
>>>> If Wikipedia is wrong then correct it and have your corrections
>>>> reviewed; until then please shut the fuck up.
>>>>
>>>> /Flibble
>>>>
>>>
>>> I think that the problem is that Richard has disagreeably as his highest
>>> priority, thus doesn't really give a rat's ass for the truth. An
>>>
>>> An impossible program C. Strachey
>>> The Computer Journal, Volume 7, Issue 4, January 1965, Page 313,
>>> Published: 01 January 1965
>>> https://academic.oup.com/comjnl/article/7/4/313/354243
>>>
>>> It is very common knowledge that the Wikipedia description is true and
>>> this is affirmed in Sipser.
>>>
>>> For any program f that might determine if programs halt, a
>>> "pathological" program g, called with some input, can pass its own
>>> source and its input to f and then specifically do the opposite of what
>>> f predicts g will do. https://en.wikipedia.org/wiki/Halting_problem
>>>
>>> Now we construct a new Turing machine D with H as a subroutine. This new
>>> TM calls H to determine what M does when the input to M is its own
>>> description ⟨M⟩. Once D has determined this information, it does the
>>> opposite. https://www.liarparadox.org/Sipser_165_167.pdf
>>>
>>>
>> Thus you have shown you don't even know what a "Definition" is, so it is
>> impossible for you to reason by the meaning of the words.
>>
>> You have just proved yourself to be an IDIOT.
>
> PO is incapable of logic reasoning (PO had shown he cannot even get the truth
> table of logical implication/AND right). All he said is delusion including when
> words from him happen to be correct to others (no real meaning).
>
> IIRC, PO's revision that H(P,P) has no relation with P(P) is deliberately
> fabricated this recent year after PO ran out his reasons to explain why HP is
> wrong and he is correct. PO has no trouble to 'lie' to his bible (he can read
> it his way), the HP thing is just piece of cake.

It is an easily verified fact that P(P) and the correct simulation of
the input to H(P,P) specify different sequences of configurations, thus
have different halting behavior. That several people here deny easily
verified facts is a little psychotic on their part.

--
Copyright 2022 Pete Olcott "Talent hits a target no one else can hit;
Genius hits a target no one else can see." Arthur Schopenhauer

Re: On recursion and infinite recursion (reprise)

<t4reg6$mfk$2@dont-email.me>

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From: polco...@gmail.com (olcott)
Newsgroups: comp.theory
Subject: Re: On recursion and infinite recursion (reprise)
Date: Tue, 3 May 2022 09:33:42 -0500
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 by: olcott - Tue, 3 May 2022 14:33 UTC

On 5/3/2022 6:08 AM, Malcolm McLean wrote:
> On Tuesday, 3 May 2022 at 10:36:48 UTC+1, Mikko wrote:
>> On 2022-05-02 16:18:36 +0000, olcott said:
>>
>>> It seems to me that all infinitely recursive definitions are invalid
>>> and I am having an excellent dialogue with some Prolog folks about this
>>> in comp.lang.prolog.
>> One of the rules that define Prolog language is
>>
>> arguments ::= argument | argument "," arguments
>>
>> which is infinitely recursive. Is it invalid? Is Prolog invalid because
>> of this and other infinitely recursive rules?
>>
> Kind of.
> A Prolog program is a physical object, not a mathematical object, so
> the recursion has to terminate somewhere.
> But it might lead you into strange territory if you tried to define the result
> of passing an ininite argument list to some Prolog.

Even infinitely recursive math expressions are semantically incorrect in
that they can never be evaluated.

--
Copyright 2022 Pete Olcott "Talent hits a target no one else can hit;
Genius hits a target no one else can see." Arthur Schopenhauer

Re: On recursion and infinite recursion (reprise)

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From: polco...@gmail.com (olcott)
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Subject: Re: On recursion and infinite recursion (reprise)
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 by: olcott - Tue, 3 May 2022 14:38 UTC

On 5/3/2022 4:36 AM, Mikko wrote:
> On 2022-05-02 16:18:36 +0000, olcott said:
>
>> It seems to me that all infinitely recursive definitions are invalid
>> and I am having an excellent dialogue with some Prolog folks about
>> this in comp.lang.prolog.
>
> One of the rules that define Prolog language is
>
>  arguments ::= argument | argument "," arguments
>
> which is infinitely recursive. Is it invalid? Is Prolog invalid because
> of this and other infinitely recursive rules?
>
> Mikko
>

If would have to be invalid because it can never be resolved.

--
Copyright 2022 Pete Olcott "Talent hits a target no one else can hit;
Genius hits a target no one else can see." Arthur Schopenhauer

Re: On recursion and infinite recursion (reprise)

<t4rf0q$s97$1@dont-email.me>

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From: polco...@gmail.com (olcott)
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Subject: Re: On recursion and infinite recursion (reprise)
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 by: olcott - Tue, 3 May 2022 14:42 UTC

On 5/3/2022 4:31 AM, Mikko wrote:
> On 2022-05-02 15:47:32 +0000, Mr Flibble said:
>
>> Not all infinitely recursive definitions are invalid however infinitely
>> recursive definitions that arise out of a category error (as is the
>> case with the halting problem) are invalid.
>
> An infinite recursion cannot arise out of a category error as the recursion
> stops at the category error.
>
> Mikko
>

The category error is that an expression of language X is construed as a
logic sentence / truth bearer that is true or false. It is because of
the infinitely recursive definition that X is neither of these.

https://en.wikipedia.org/wiki/Sentence_(mathematical_logic)#:~:text=In%20mathematical%20logic%2C%20a%20sentence,must%20be%20true%20or%20false.

--
Copyright 2022 Pete Olcott "Talent hits a target no one else can hit;
Genius hits a target no one else can see." Arthur Schopenhauer

Re: On recursion and infinite recursion (reprise)

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Subject: Re: On recursion and infinite recursion (reprise)
From: dbush.mo...@gmail.com (Dennis Bush)
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 by: Dennis Bush - Tue, 3 May 2022 14:47 UTC

On Tuesday, May 3, 2022 at 10:31:21 AM UTC-4, olcott wrote:
> On 5/3/2022 7:12 AM, wij wij wrote:
> > Richard Damon 在 2022年5月3日 星期二上午8:48:57 [UTC+8] 的信中寫道:
> >> On 5/2/22 8:35 PM, olcott wrote:
> >>> On 5/2/2022 5:47 PM, Mr Flibble wrote:
> >>>> On Mon, 2 May 2022 18:46:00 -0400
> >>>> Richard Damon wrote:
> >>>>
> >>>>> On 5/2/22 6:38 PM, Mr Flibble wrote:
> >>>>>> On Mon, 2 May 2022 18:32:16 -0400
> >>>>>> Richard Damon wrote:
> >>>>>>> On 5/2/22 11:47 AM, Mr Flibble wrote:
> >>>>>>>> Not all infinitely recursive definitions are invalid however
> >>>>>>>> infinitely recursive definitions that arise out of a category
> >>>>>>>> error (as is the case with the halting problem) are invalid.
> >>>>>>>>
> >>>>>>>> The halting problem (as currently defined) is invalid due to the
> >>>>>>>> invalid "impossible program" [Strachey, 1965] that is actually
> >>>>>>>> impossible due to the category error present in its definition and
> >>>>>>>> *not* because of any function call-like recursion; confusion
> >>>>>>>> between these two types of recursion are why Olcott is having
> >>>>>>>> difficulty communicating his ideas with the rest of you shower.
> >>>>>>>>
> >>>>>>>> The categories involved in the category error are the decider and
> >>>>>>>> that which is being decided. Currently extant attempts to
> >>>>>>>> conflate the decider with that which is being decided are
> >>>>>>>> infinitely recursive and thus invalid.
> >>>>>>>>
> >>>>>>>> /Flibble
> >>>>>>>
> >>>>>>> Except that the "impossible program" isn't part of the definition
> >>>>>>> of the Halting Problem.
> >>>>>>
> >>>>>> It is according to [Wikipedia, 2022].
> >>>>>>
> >>>>>> /Flibble
> >>>>>
> >>>>> Nope, you comprehend worse that PO.
> >>>>>
> >>>>> Note, and Encyclopedic entery, like Wikipedia, is NOT just a
> >>>>> definition but a full article explaining the subject.
> >>>>>
> >>>>> Maybe if you look for a FORMAL source, that states what is the ACTUAL
> >>>>> definition, you would learn something.
> >>>>
> >>>> If Wikipedia is wrong then correct it and have your corrections
> >>>> reviewed; until then please shut the fuck up.
> >>>>
> >>>> /Flibble
> >>>>
> >>>
> >>> I think that the problem is that Richard has disagreeably as his highest
> >>> priority, thus doesn't really give a rat's ass for the truth. An
> >>>
> >>> An impossible program C. Strachey
> >>> The Computer Journal, Volume 7, Issue 4, January 1965, Page 313,
> >>> Published: 01 January 1965
> >>> https://academic.oup.com/comjnl/article/7/4/313/354243
> >>>
> >>> It is very common knowledge that the Wikipedia description is true and
> >>> this is affirmed in Sipser.
> >>>
> >>> For any program f that might determine if programs halt, a
> >>> "pathological" program g, called with some input, can pass its own
> >>> source and its input to f and then specifically do the opposite of what
> >>> f predicts g will do. https://en.wikipedia.org/wiki/Halting_problem
> >>>
> >>> Now we construct a new Turing machine D with H as a subroutine. This new
> >>> TM calls H to determine what M does when the input to M is its own
> >>> description ⟨M⟩. Once D has determined this information, it does the
> >>> opposite. https://www.liarparadox.org/Sipser_165_167.pdf
> >>>
> >>>
> >> Thus you have shown you don't even know what a "Definition" is, so it is
> >> impossible for you to reason by the meaning of the words.
> >>
> >> You have just proved yourself to be an IDIOT.
> >
> > PO is incapable of logic reasoning (PO had shown he cannot even get the truth
> > table of logical implication/AND right). All he said is delusion including when
> > words from him happen to be correct to others (no real meaning).
> >
> > IIRC, PO's revision that H(P,P) has no relation with P(P) is deliberately
> > fabricated this recent year after PO ran out his reasons to explain why HP is
> > wrong and he is correct. PO has no trouble to 'lie' to his bible (he can read
> > it his way), the HP thing is just piece of cake.
> It is an easily verified fact that P(P) and the correct simulation of
> the input to H(P,P) specify different sequences of configurations, thus
> have different halting behavior.

The easily verified fact is that the correct simulation to H(P,P) is performed by Hb(P,P) (which simulates for k more steps than H) which remains in UTM mode while simulating the same input to a final state.

Because H and Hb and both simulating halt deciders and are given the same input, they are deciding on the same sequence of configurations (namely starting with the first instruction of P). Because one answers false and one answers true, one must be wrong.

Since a simulating halt decider that simulates its input to a final state while remaining in UTM mode is necessarily correct, this proves that Hb(P,P) == true is correct and that H(P,P) == false is incorrect, and that H(P,P) does *not* in fact perform a correct simulation of its input because it aborts too soon.

You've been asked several times what input must be given to H to determine if P(P) halts. It turns out that the input (P,P) can be given to Hb to determine exactly that, so the fact that H can't give the same result for the same input just shows that it is wrong and that the halting problem is unsolvable as the existing proofs show.

> That several people here deny easily
> verified facts is a little psychotic on their part.

You're projecting. Again. In fact you're *so* good a projecting that if you opened a movie theater I'll bet the picture quality would be second to none.

Re: On recursion and infinite recursion (reprise)

<t4rh62$tkh$1@dont-email.me>

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 by: olcott - Tue, 3 May 2022 15:19 UTC

On 5/3/2022 9:47 AM, Dennis Bush wrote:
> On Tuesday, May 3, 2022 at 10:31:21 AM UTC-4, olcott wrote:
>> On 5/3/2022 7:12 AM, wij wij wrote:
>>> Richard Damon 在 2022年5月3日 星期二上午8:48:57 [UTC+8] 的信中寫道:
>>>> On 5/2/22 8:35 PM, olcott wrote:
>>>>> On 5/2/2022 5:47 PM, Mr Flibble wrote:
>>>>>> On Mon, 2 May 2022 18:46:00 -0400
>>>>>> Richard Damon wrote:
>>>>>>
>>>>>>> On 5/2/22 6:38 PM, Mr Flibble wrote:
>>>>>>>> On Mon, 2 May 2022 18:32:16 -0400
>>>>>>>> Richard Damon wrote:
>>>>>>>>> On 5/2/22 11:47 AM, Mr Flibble wrote:
>>>>>>>>>> Not all infinitely recursive definitions are invalid however
>>>>>>>>>> infinitely recursive definitions that arise out of a category
>>>>>>>>>> error (as is the case with the halting problem) are invalid.
>>>>>>>>>>
>>>>>>>>>> The halting problem (as currently defined) is invalid due to the
>>>>>>>>>> invalid "impossible program" [Strachey, 1965] that is actually
>>>>>>>>>> impossible due to the category error present in its definition and
>>>>>>>>>> *not* because of any function call-like recursion; confusion
>>>>>>>>>> between these two types of recursion are why Olcott is having
>>>>>>>>>> difficulty communicating his ideas with the rest of you shower.
>>>>>>>>>>
>>>>>>>>>> The categories involved in the category error are the decider and
>>>>>>>>>> that which is being decided. Currently extant attempts to
>>>>>>>>>> conflate the decider with that which is being decided are
>>>>>>>>>> infinitely recursive and thus invalid.
>>>>>>>>>>
>>>>>>>>>> /Flibble
>>>>>>>>>
>>>>>>>>> Except that the "impossible program" isn't part of the definition
>>>>>>>>> of the Halting Problem.
>>>>>>>>
>>>>>>>> It is according to [Wikipedia, 2022].
>>>>>>>>
>>>>>>>> /Flibble
>>>>>>>
>>>>>>> Nope, you comprehend worse that PO.
>>>>>>>
>>>>>>> Note, and Encyclopedic entery, like Wikipedia, is NOT just a
>>>>>>> definition but a full article explaining the subject.
>>>>>>>
>>>>>>> Maybe if you look for a FORMAL source, that states what is the ACTUAL
>>>>>>> definition, you would learn something.
>>>>>>
>>>>>> If Wikipedia is wrong then correct it and have your corrections
>>>>>> reviewed; until then please shut the fuck up.
>>>>>>
>>>>>> /Flibble
>>>>>>
>>>>>
>>>>> I think that the problem is that Richard has disagreeably as his highest
>>>>> priority, thus doesn't really give a rat's ass for the truth. An
>>>>>
>>>>> An impossible program C. Strachey
>>>>> The Computer Journal, Volume 7, Issue 4, January 1965, Page 313,
>>>>> Published: 01 January 1965
>>>>> https://academic.oup.com/comjnl/article/7/4/313/354243
>>>>>
>>>>> It is very common knowledge that the Wikipedia description is true and
>>>>> this is affirmed in Sipser.
>>>>>
>>>>> For any program f that might determine if programs halt, a
>>>>> "pathological" program g, called with some input, can pass its own
>>>>> source and its input to f and then specifically do the opposite of what
>>>>> f predicts g will do. https://en.wikipedia.org/wiki/Halting_problem
>>>>>
>>>>> Now we construct a new Turing machine D with H as a subroutine. This new
>>>>> TM calls H to determine what M does when the input to M is its own
>>>>> description ⟨M⟩. Once D has determined this information, it does the
>>>>> opposite. https://www.liarparadox.org/Sipser_165_167.pdf
>>>>>
>>>>>
>>>> Thus you have shown you don't even know what a "Definition" is, so it is
>>>> impossible for you to reason by the meaning of the words.
>>>>
>>>> You have just proved yourself to be an IDIOT.
>>>
>>> PO is incapable of logic reasoning (PO had shown he cannot even get the truth
>>> table of logical implication/AND right). All he said is delusion including when
>>> words from him happen to be correct to others (no real meaning).
>>>
>>> IIRC, PO's revision that H(P,P) has no relation with P(P) is deliberately
>>> fabricated this recent year after PO ran out his reasons to explain why HP is
>>> wrong and he is correct. PO has no trouble to 'lie' to his bible (he can read
>>> it his way), the HP thing is just piece of cake.
>> It is an easily verified fact that P(P) and the correct simulation of
>> the input to H(P,P) specify different sequences of configurations, thus
>> have different halting behavior.
>
> The easily verified fact is that the correct simulation to H(P,P) is performed by Hb(P,P) (which simulates for k more steps than H) which remains in UTM mode while simulating the same input to a final state.
>

I have no idea what you mean.

> Because H and Hb and both simulating halt deciders and are given the same input, they are deciding on the same sequence of configurations (namely starting with the first instruction of P). Because one answers false and one answers true, one must be wrong.
>

It is ridiculously stupid to assume that an input having pathological
self-reference to its decider would have the same behavior as an input
NOT having pathological to its decider.

> Since a simulating halt decider that simulates its input to a final state while remaining in UTM mode is necessarily correct, this proves that Hb(P,P) == true is correct and that H(P,P) == false is incorrect, and that H(P,P) does *not* in fact perform a correct simulation of its input because it aborts too soon.
>

It is very easy to verify the fact that the simulated input to H(P,P)
would never stop unless aborted. It is pretty psychotic that many of my
reviewers deny easily verified facts.

> You've been asked several times what input must be given to H to determine if P(P) halts. It turns out that the input (P,P) can be given to Hb to determine exactly that, so the fact that H can't give the same result for the same input just shows that it is wrong and that the halting problem is unsolvable as the existing proofs show.
>

It is ridiculously stupid to assume that an input having pathological
self-reference to its decider would have the same behavior as an input
NOT having pathological to its decider.

It is an easily verified fact that H does correctly reject its input and
that deciders only compute the mapping from their inputs.

>> That several people here deny easily
>> verified facts is a little psychotic on their part.
>
> You're projecting. Again. In fact you're *so* good a projecting that if you opened a movie theater I'll bet the picture quality would be second to none.

Anyone that denies easily verified facts has (by definition) a break
from reality.

--
Copyright 2022 Pete Olcott "Talent hits a target no one else can hit;
Genius hits a target no one else can see." Arthur Schopenhauer

Re: On recursion and infinite recursion (reprise)

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Subject: Re: On recursion and infinite recursion (reprise)
From: dbush.mo...@gmail.com (Dennis Bush)
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 by: Dennis Bush - Tue, 3 May 2022 15:36 UTC

On Tuesday, May 3, 2022 at 11:19:33 AM UTC-4, olcott wrote:
> On 5/3/2022 9:47 AM, Dennis Bush wrote:
> > On Tuesday, May 3, 2022 at 10:31:21 AM UTC-4, olcott wrote:
> >> On 5/3/2022 7:12 AM, wij wij wrote:
> >>> Richard Damon 在 2022年5月3日 星期二上午8:48:57 [UTC+8] 的信中寫道:
> >>>> On 5/2/22 8:35 PM, olcott wrote:
> >>>>> On 5/2/2022 5:47 PM, Mr Flibble wrote:
> >>>>>> On Mon, 2 May 2022 18:46:00 -0400
> >>>>>> Richard Damon wrote:
> >>>>>>
> >>>>>>> On 5/2/22 6:38 PM, Mr Flibble wrote:
> >>>>>>>> On Mon, 2 May 2022 18:32:16 -0400
> >>>>>>>> Richard Damon wrote:
> >>>>>>>>> On 5/2/22 11:47 AM, Mr Flibble wrote:
> >>>>>>>>>> Not all infinitely recursive definitions are invalid however
> >>>>>>>>>> infinitely recursive definitions that arise out of a category
> >>>>>>>>>> error (as is the case with the halting problem) are invalid.
> >>>>>>>>>>
> >>>>>>>>>> The halting problem (as currently defined) is invalid due to the
> >>>>>>>>>> invalid "impossible program" [Strachey, 1965] that is actually
> >>>>>>>>>> impossible due to the category error present in its definition and
> >>>>>>>>>> *not* because of any function call-like recursion; confusion
> >>>>>>>>>> between these two types of recursion are why Olcott is having
> >>>>>>>>>> difficulty communicating his ideas with the rest of you shower..
> >>>>>>>>>>
> >>>>>>>>>> The categories involved in the category error are the decider and
> >>>>>>>>>> that which is being decided. Currently extant attempts to
> >>>>>>>>>> conflate the decider with that which is being decided are
> >>>>>>>>>> infinitely recursive and thus invalid.
> >>>>>>>>>>
> >>>>>>>>>> /Flibble
> >>>>>>>>>
> >>>>>>>>> Except that the "impossible program" isn't part of the definition
> >>>>>>>>> of the Halting Problem.
> >>>>>>>>
> >>>>>>>> It is according to [Wikipedia, 2022].
> >>>>>>>>
> >>>>>>>> /Flibble
> >>>>>>>
> >>>>>>> Nope, you comprehend worse that PO.
> >>>>>>>
> >>>>>>> Note, and Encyclopedic entery, like Wikipedia, is NOT just a
> >>>>>>> definition but a full article explaining the subject.
> >>>>>>>
> >>>>>>> Maybe if you look for a FORMAL source, that states what is the ACTUAL
> >>>>>>> definition, you would learn something.
> >>>>>>
> >>>>>> If Wikipedia is wrong then correct it and have your corrections
> >>>>>> reviewed; until then please shut the fuck up.
> >>>>>>
> >>>>>> /Flibble
> >>>>>>
> >>>>>
> >>>>> I think that the problem is that Richard has disagreeably as his highest
> >>>>> priority, thus doesn't really give a rat's ass for the truth. An
> >>>>>
> >>>>> An impossible program C. Strachey
> >>>>> The Computer Journal, Volume 7, Issue 4, January 1965, Page 313,
> >>>>> Published: 01 January 1965
> >>>>> https://academic.oup.com/comjnl/article/7/4/313/354243
> >>>>>
> >>>>> It is very common knowledge that the Wikipedia description is true and
> >>>>> this is affirmed in Sipser.
> >>>>>
> >>>>> For any program f that might determine if programs halt, a
> >>>>> "pathological" program g, called with some input, can pass its own
> >>>>> source and its input to f and then specifically do the opposite of what
> >>>>> f predicts g will do. https://en.wikipedia.org/wiki/Halting_problem
> >>>>>
> >>>>> Now we construct a new Turing machine D with H as a subroutine. This new
> >>>>> TM calls H to determine what M does when the input to M is its own
> >>>>> description ⟨M⟩. Once D has determined this information, it does the
> >>>>> opposite. https://www.liarparadox.org/Sipser_165_167.pdf
> >>>>>
> >>>>>
> >>>> Thus you have shown you don't even know what a "Definition" is, so it is
> >>>> impossible for you to reason by the meaning of the words.
> >>>>
> >>>> You have just proved yourself to be an IDIOT.
> >>>
> >>> PO is incapable of logic reasoning (PO had shown he cannot even get the truth
> >>> table of logical implication/AND right). All he said is delusion including when
> >>> words from him happen to be correct to others (no real meaning).
> >>>
> >>> IIRC, PO's revision that H(P,P) has no relation with P(P) is deliberately
> >>> fabricated this recent year after PO ran out his reasons to explain why HP is
> >>> wrong and he is correct. PO has no trouble to 'lie' to his bible (he can read
> >>> it his way), the HP thing is just piece of cake.
> >> It is an easily verified fact that P(P) and the correct simulation of
> >> the input to H(P,P) specify different sequences of configurations, thus
> >> have different halting behavior.
> >
> > The easily verified fact is that the correct simulation to H(P,P) is performed by Hb(P,P) (which simulates for k more steps than H) which remains in UTM mode while simulating the same input to a final state.
> >
> I have no idea what you mean.

In other words you don't want to admit that this proves you are wrong.

> > Because H and Hb and both simulating halt deciders and are given the same input, they are deciding on the same sequence of configurations (namely starting with the first instruction of P). Because one answers false and one answers true, one must be wrong.
> >
> It is ridiculously stupid to assume that an input having pathological
> self-reference to its decider would have the same behavior as an input
> NOT having pathological to its decider.

Which is another way of saying that H can't give a correct answer for (P,P)..

> > Since a simulating halt decider that simulates its input to a final state while remaining in UTM mode is necessarily correct, this proves that Hb(P,P) == true is correct and that H(P,P) == false is incorrect, and that H(P,P) does *not* in fact perform a correct simulation of its input because it aborts too soon.
> >
> It is very easy to verify the fact that the simulated input to H(P,P)
> would never stop unless aborted. It is pretty psychotic that many of my
> reviewers deny easily verified facts.

There is no "unless". The fixed algorithm of H, which will henceforth be referred to as Ha and similarly P will be referred to as Pa, *does* abort. Because of this, Hb(Pa,Pa) explicitly shows that the simulated input to Ha(Pa,Pa) *does* stop. The fact that Pn(Pn) does not halt and that Hn(Pn,Pn) does not halt is irrelevant.

> > You've been asked several times what input must be given to H to determine if P(P) halts. It turns out that the input (P,P) can be given to Hb to determine exactly that, so the fact that H can't give the same result for the same input just shows that it is wrong and that the halting problem is unsolvable as the existing proofs show.
> >
> It is ridiculously stupid to assume that an input having pathological
> self-reference to its decider would have the same behavior as an input
> NOT having pathological to its decider.

Which is another way of saying that Ha can't give a correct answer for (Pa,Pa).

>
> It is an easily verified fact that H does correctly reject its input

Ha does not correctly reject its input as easily verified by Hb.

> and that deciders only compute the mapping from their inputs.

And all halt deciders must compute the same mapping from the same input. Ha(Pa,Pa) and Hb(Pa,Pa) do not perform the same mapping from the same input so one must be wrong.

Since a simulating halt decider that simulates its input to a final state while remaining in UTM mode is necessarily correct, this proves that Hb(Pa,Pa) == true is correct and that Ha(Pa,Pa) == false is incorrect


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