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computers / comp.ai.philosophy / Re: On recursion and infinite recursion (reprise)

SubjectAuthor
* Re: On recursion and infinite recursion (reprise)olcott
`* Re: On recursion and infinite recursion (reprise)olcott
 `- Re: On recursion and infinite recursion (reprise)olcott

1
Subject: Re: On recursion and infinite recursion (reprise)
From: olcott
Newsgroups: comp.theory, comp.ai.philosophy, sci.logic, sci.math
Followup: comp.theory
Organization: A noiseless patient Spider
Date: Tue, 3 May 2022 15:19 UTC
References: 1 2 3 4 5 6 7 8 9 10
Path: i2pn2.org!i2pn.org!eternal-september.org!reader02.eternal-september.org!.POSTED!not-for-mail
From: polco...@gmail.com (olcott)
Newsgroups: comp.theory,comp.ai.philosophy,sci.logic,sci.math
Subject: Re: On recursion and infinite recursion (reprise)
Followup-To: comp.theory
Date: Tue, 3 May 2022 10:19:29 -0500
Organization: A noiseless patient Spider
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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


Subject: Re: On recursion and infinite recursion (reprise)
From: olcott
Newsgroups: comp.theory, comp.ai.philosophy, sci.logic, sci.math
Followup: comp.theory
Organization: A noiseless patient Spider
Date: Tue, 3 May 2022 16:39 UTC
References: 1 2 3 4 5 6 7 8 9 10 11 12
Path: i2pn2.org!i2pn.org!eternal-september.org!reader02.eternal-september.org!.POSTED!not-for-mail
From: polco...@gmail.com (olcott)
Newsgroups: comp.theory,comp.ai.philosophy,sci.logic,sci.math
Subject: Re: On recursion and infinite recursion (reprise)
Followup-To: comp.theory
Date: Tue, 3 May 2022 11:39:44 -0500
Organization: A noiseless patient Spider
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On 5/3/2022 10:36 AM, Dennis Bush wrote:
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.


No I can't understand what you mean.
I think that I see it now, I had forgotten the notation.

An input having a pathological self-reference relationship to its decider H would necessarily derive a different halt status than an input not having a pathological self-reference relationship to its decider Hb.

The P having a pathological self-reference relationship to H is not the same as the Px NOT having a pathological self-reference relationship to Hb. Because P.H calls itself and Px.Hb does not call itself P is not the same input as Px.


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).


Different computations must give different answers.
That you don't fully understand all of the nuances of how this applies to H/P and Hb/Px is OK, it is difficult to understand.

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.

Which is *NOT* halting. A halting input must reach its own final state.

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.

It it not Hb(Pa,Pa) it is Hb(Px,Px). That P calls H makes it an entirely different input than Px that does not call Hb.

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.

That P calls H makes it an entirely different input than Px that does not call 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.


That P calls H makes it an entirely different input than Px that does not call Hb.

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

That P calls H makes it an entirely different input than Px that does not call Hb.


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.

I can't *wait* to see your movie theater.  Such a expert at projection must have a great picture.


--
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: On recursion and infinite recursion (reprise)
From: olcott
Newsgroups: comp.theory, comp.ai.philosophy, sci.logic, sci.math
Followup: comp.theory
Organization: A noiseless patient Spider
Date: Tue, 3 May 2022 22:08 UTC
References: 1 2 3 4 5 6 7 8 9 10 11 12 13 14
Path: i2pn2.org!i2pn.org!eternal-september.org!reader02.eternal-september.org!.POSTED!not-for-mail
From: polco...@gmail.com (olcott)
Newsgroups: comp.theory,comp.ai.philosophy,sci.logic,sci.math
Subject: Re: On recursion and infinite recursion (reprise)
Followup-To: comp.theory
Date: Tue, 3 May 2022 17:08:27 -0500
Organization: A noiseless patient Spider
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On 5/3/2022 4:49 PM, Dennis Bush wrote:
On Tuesday, May 3, 2022 at 12:39:49 PM UTC-4, olcott wrote:
On 5/3/2022 10:36 AM, Dennis Bush wrote:
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.

No I can't understand what you mean.
I think that I see it now, I had forgotten the notation.

An input having a pathological self-reference relationship to its
decider H would necessarily derive a different halt status than an input
not having a pathological self-reference relationship to its decider Hb.

The P having a pathological self-reference relationship to H is not the
same as the Px NOT having a pathological self-reference relationship to
Hb. Because P.H calls itself and Px.Hb does not call itself P is not the
same input as Px.

The P we're talking about is a *specific* P, namely Pa which is built from Ha, and Ha is a *specific* H.  So Pa and Px are the *same*.

Not at all because H(P,P) has itself as part of its input and Hb(P,P) does not have itself as part of its input.


So just because Pa contains an embedded copy of Ha but not an embedded copy of Hb doesn't means that it's not the same.


Sure it does. The correctly simulated input to H(P,P) specifies infinitely nested simulation where as correctly simulated input to Hb(P,P) DOES NOT specify infinitely nested simulation.

How much longer are you going to continue the verified facts?
This does make you look quite foolish or dishonest.

Ha(Pa,Pa) and Hb(Pa,Pa) have the *exact* same input.


The correctly simulated input to Ha(Pa,Pa) specifies infinitely nested simulation where as correctly simulated input to Hb(Pa,Pa) DOES NOT specify infinitely nested simulation.

How much longer are you going to continue the verified facts?
This does make you look quite foolish or dishonest.

Just because it appears from a glance that Ha is starting its simulation of Pa "in the middle" doesn't mean that's what's actually happening.  That's just how the incorrect simulation is manifesting itself.  It's kind of like undefined behavior in a C program.

You only have to do a correct execution trace of Ha(Pa,Pa) and Hb(Pa,Pa) to see that:

The correctly simulated input to Ha(Pa,Pa) specifies infinitely nested simulation where as correctly simulated input to Hb(Pa,Pa) DOES NOT specify infinitely nested simulation.

How much longer are you going to continue the verified facts?
This does make you look quite foolish or dishonest.


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).

Different computations must give different answers.
That you don't fully understand all of the nuances of how this applies
to H/P and Hb/Px is OK, it is difficult to understand.

Just because Pa contains an embedded copy of Ha but not an embedded copy of Hb doesn't means that it's not the same.

You only have to do a correct execution trace of Ha(Pa,Pa) and Hb(Pa,Pa) to see that:

The correctly simulated input to Ha(Pa,Pa) specifies infinitely nested simulation where as correctly simulated input to Hb(Pa,Pa) DOES NOT specify infinitely nested simulation.

How much longer are you going to continue the verified facts?
This does make you look quite foolish or dishonest.

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.
Which is *NOT* halting. A halting input must reach its own final state.
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.
It it not Hb(Pa,Pa) it is Hb(Px,Px). That P calls H makes it an entirely
different input than Px that does not call Hb.

No it is *exactly* Hb(Pa,Pa).  The same encoding passed to Ha is passed to Hb.

You only have to do a correct execution trace of Ha(Pa,Pa) and Hb(Pa,Pa) to see that:

The correctly simulated input to Ha(Pa,Pa) specifies infinitely nested simulation where as correctly simulated input to Hb(Pa,Pa) DOES NOT specify infinitely nested simulation.

How much longer are you going to continue the verified facts?
This does make you look quite foolish or dishonest.

Trimmed extraneous / redundant material to stay focused on the most essential point.


--
Copyright 2022 Pete Olcott "Talent hits a target no one else can hit;

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