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devel / comp.theory / Re: Black box halt decider is NOT a partial decider

SubjectAuthor
* Black box halt decider is NOT a partial deciderMr Flibble
`* Black box halt decider is NOT a partial deciderChris M. Thomasson
 `* Black box halt decider is NOT a partial deciderDavid Brown
  `* Black box halt decider is NOT a partial deciderChris M. Thomasson
   +* Black box halt decider is NOT a partial deciderRichard Damon
   |`* Black box halt decider is NOT a partial deciderChris M. Thomasson
   | `* Black box halt decider is NOT a partial deciderRichard Damon
   |  `* Black box halt decider is NOT a partial deciderChris M. Thomasson
   |   +- Black box halt decider is NOT a partial deciderRichard Damon
   |   +* Black box halt decider is NOT a partial deciderBen Bacarisse
   |   |`* Black box halt decider is NOT a partial deciderChris M. Thomasson
   |   | +* Black box halt decider is NOT a partial deciderBen Bacarisse
   |   | |`* Black box halt decider is NOT a partial deciderChris M. Thomasson
   |   | | +- Black box halt decider is NOT a partial deciderRichard Damon
   |   | | `* Black box halt decider is NOT a partial deciderBen Bacarisse
   |   | |  `* Black box halt decider is NOT a partial deciderChris M. Thomasson
   |   | |   +* Black box halt decider is NOT a partial deciderAndré G. Isaak
   |   | |   |`* Black box halt decider is NOT a partial deciderChris M. Thomasson
   |   | |   | `* Black box halt decider is NOT a partial deciderMike Terry
   |   | |   |  `* Black box halt decider is NOT a partial deciderChris M. Thomasson
   |   | |   |   `* Black box halt decider is NOT a partial deciderChris M. Thomasson
   |   | |   |    +- Black box halt decider is NOT a partial deciderMike Terry
   |   | |   |    +* Black box halt decider is NOT a partial deciderBen Bacarisse
   |   | |   |    |+* Black box halt decider is NOT a partial deciderJeff Barnett
   |   | |   |    ||+- Black box halt decider is NOT a partial deciderJeff Barnett
   |   | |   |    ||`* Black box halt decider is NOT a partial deciderMike Terry
   |   | |   |    || +- Black box halt decider is NOT a partial deciderChris M. Thomasson
   |   | |   |    || `* Black box halt decider is NOT a partial deciderJeff Barnett
   |   | |   |    ||  `- Black box halt decider is NOT a partial deciderMike Terry
   |   | |   |    |`* Black box halt decider is NOT a partial deciderChris M. Thomasson
   |   | |   |    | `* Black box halt decider is NOT a partial deciderBen Bacarisse
   |   | |   |    |  `* Black box halt decider is NOT a partial deciderChris M. Thomasson
   |   | |   |    |   +- Black box halt decider is NOT a partial deciderChris M. Thomasson
   |   | |   |    |   `* Black box halt decider is NOT a partial deciderChris M. Thomasson
   |   | |   |    |    `- Black box halt decider is NOT a partial deciderChris M. Thomasson
   |   | |   |    `- Black box halt decider is NOT a partial deciderwij
   |   | |   +* Black box halt decider is NOT a partial deciderRichard Damon
   |   | |   |`* Black box halt decider is NOT a partial deciderChris M. Thomasson
   |   | |   | `* Black box halt decider is NOT a partial deciderRichard Damon
   |   | |   |  `- Black box halt decider is NOT a partial deciderChris M. Thomasson
   |   | |   `* Black box halt decider is NOT a partial deciderBen Bacarisse
   |   | |    +* Black box halt decider is NOT a partial deciderChris M. Thomasson
   |   | |    |`* Black box halt decider is NOT a partial deciderBen Bacarisse
   |   | |    | `* Black box halt decider is NOT a partial deciderChris M. Thomasson
   |   | |    |  `* Black box halt decider is NOT a partial deciderRichard Damon
   |   | |    |   `- Black box halt decider is NOT a partial deciderChris M. Thomasson
   |   | |    `* Black box halt decider is NOT a partial deciderAndré G. Isaak
   |   | |     +* Black box halt decider is NOT a partial deciderBen Bacarisse
   |   | |     |+- Black box halt decider is NOT a partial deciderAndré G. Isaak
   |   | |     |`* Black box halt decider is NOT a partial deciderMike Terry
   |   | |     | +* Black box halt decider is NOT a partial deciderBen Bacarisse
   |   | |     | |+* Black box halt decider is NOT a partial deciderAndy Walker
   |   | |     | ||`* Black box halt decider is NOT a partial deciderMike Terry
   |   | |     | || +* Black box halt decider is NOT a partial deciderMalcolm McLean
   |   | |     | || |+* Black box halt decider is NOT a partial decider [ H(P,P)==0 is always correct ]olcott
   |   | |     | || ||`- Black box halt decider is NOT a partial decider [ H(P,P)==0 isRichard Damon
   |   | |     | || |+* Black box halt decider is NOT a partial decider [ H(P,P)==0 is always correct ]olcott
   |   | |     | || ||+- Black box halt decider is NOT a partial decider [ H(P,P)==0 isAndré G. Isaak
   |   | |     | || ||+* Black box halt decider is NOT a partial decider [ H(P,P)==0 isRichard Damon
   |   | |     | || |||`* Black box halt decider is NOT a partial decider [ H(P,P)==0 isMalcolm McLean
   |   | |     | || ||| `* Black box halt decider is NOT a partial decider [ H(P,P)==0 isRichard Damon
   |   | |     | || |||  `- Black box halt decider is NOT a partial decider [ H(P,P)==0 isJeff Barnett
   |   | |     | || ||`- Black box halt decider is NOT a partial decider [ H(P,P)==0 is always correct ]Ben Bacarisse
   |   | |     | || |+* Black box halt decider is NOT a partial deciderBen Bacarisse
   |   | |     | || ||`* Black box halt decider is NOT a partial deciderMalcolm McLean
   |   | |     | || || `* Black box halt decider is NOT a partial decider [ paradox ratherolcott
   |   | |     | || ||  +- Black box halt decider is NOT a partial decider [ paradox ratherRichard Damon
   |   | |     | || ||  `* Black box halt decider is NOT a partial decider [ paradox ratherAndré G. Isaak
   |   | |     | || ||   `* Black box halt decider is NOT a partial decider [ H refutes Rice's Theorem ]olcott
   |   | |     | || ||    +- Black box halt decider is NOT a partial decider [ H refutesRichard Damon
   |   | |     | || ||    `* Black box halt decider is NOT a partial decider [ H refutesAndré G. Isaak
   |   | |     | || ||     `* Black box halt decider is NOT a partial decider [ H refutes Rice's Theorem ]olcott
   |   | |     | || ||      +* Black box halt decider is NOT a partial decider [ H refutesAndré G. Isaak
   |   | |     | || ||      |`* Black box halt decider is NOT a partial decider [ H refutesolcott
   |   | |     | || ||      | `- Black box halt decider is NOT a partial decider [ H refutesRichard Damon
   |   | |     | || ||      `* Black box halt decider is NOT a partial decider [ H refutesJeff Barnett
   |   | |     | || ||       `* Black box halt decider is NOT a partial decider [ H refutesolcott
   |   | |     | || ||        `* Black box halt decider is NOT a partial decider [ H refutesAndré G. Isaak
   |   | |     | || ||         +* Black box halt decider is NOT a partial decider [ H refutesolcott
   |   | |     | || ||         |+- Black box halt decider is NOT a partial decider [ H refutesAndré G. Isaak
   |   | |     | || ||         |`- Black box halt decider is NOT a partial decider [ H refutesRichard Damon
   |   | |     | || ||         `* Black box halt decider is NOT a partial decider [ H refutesolcott
   |   | |     | || ||          +* Black box halt decider is NOT a partial decider [ H refutesAndré G. Isaak
   |   | |     | || ||          |`* Black box halt decider is NOT a partial decider [ H refutes Rice's Theorem ]olcott
   |   | |     | || ||          | `* Black box halt decider is NOT a partial decider [ H refutesAndré G. Isaak
   |   | |     | || ||          |  `* Black box halt decider is NOT a partial decider [ H refutesolcott
   |   | |     | || ||          |   +- Black box halt decider is NOT a partial decider [ H refutesAndré G. Isaak
   |   | |     | || ||          |   +- Black box halt decider is NOT a partial decider [ H refutesRichard Damon
   |   | |     | || ||          |   `* _Black_box_halt_decider_is_NOT_a_partial_decider_[_André_doesn't_know_Rice's_Theolcott
   |   | |     | || ||          |    +* _Black_box_halt_decider_is_NOT_a_partial_decider_[André G. Isaak
   |   | |     | || ||          |    |`* _Black_box_halt_decider_is_NOT_a_partial_decider_[olcott
   |   | |     | || ||          |    | +* _Black_box_halt_decider_is_NOT_a_partial_decider_[André G. Isaak
   |   | |     | || ||          |    | |`* _Black_box_halt_decider_is_NOT_a_partial_decider_Malcolm McLean
   |   | |     | || ||          |    | | `* _André_doesn't_know_Rice's_Theorem_[_Malcolm_]olcott
   |   | |     | || ||          |    | |  +* _André_doesn't_know_Rice's_Theorem_[_MalcRichard Damon
   |   | |     | || ||          |    | |  |`* _André_doesn't_know_Rice's_Theorem_[_Malcolcott
   |   | |     | || ||          |    | |  | `* _André_doesn't_know_Rice's_Theorem_[_MalcRichard Damon
   |   | |     | || ||          |    | |  |  `* _André_doesn't_know_Rice's_Theorem_[_Malcolm_](_attention_deficit_disorder_)olcott
   |   | |     | || ||          |    | |  |   `* _André_doesn't_know_Rice's_Theorem_[_MalcRichard Damon
   |   | |     | || ||          |    | |  |    `* _André_doesn't_know_Rice's_Theorem_[_Malcolcott
   |   | |     | || ||          |    | |  |     +- _André_doesn't_know_Rice's_Theorem_[_MalcRichard Damon
   |   | |     | || ||          |    | |  |     +* _André_doesn't_know_Rice's_Theorem_[_Malcolm_](_attention_deficit_disorder_)olcott
   |   | |     | || ||          |    | |  |     `* André doesn't know Rice's Theorem [ MalcolmBen Bacarisse
   |   | |     | || ||          |    | |  +* _André_doesn't_know_Rice's_Theorem_[_MalcAndré G. Isaak
   |   | |     | || ||          |    | |  `- _André_doesn't_know_Rice's_Theorem_[_MalcJeff Barnett
   |   | |     | || ||          |    | +- _Black_box_halt_decider_is_NOT_a_partial_decider_[Richard Damon
   |   | |     | || ||          |    | `* _Black_box_halt_decider_is_NOT_a_partial_decider_[_André_doesn't_know_Rice's_Theolcott
   |   | |     | || ||          |    `- _Black_box_halt_decider_is_NOT_a_partial_decider_[Richard Damon
   |   | |     | || ||          `- Black box halt decider is NOT a partial decider [ H refutesRichard Damon
   |   | |     | || |`* Black box halt decider is NOT a partial deciderMike Terry
   |   | |     | || `- Black box halt decider is NOT a partial deciderAndy Walker
   |   | |     | |`* Black box halt decider is NOT a partial deciderMike Terry
   |   | |     | `* Black box halt decider is NOT a partial deciderwij
   |   | |     `- Black box halt decider is NOT a partial deciderChris M. Thomasson
   |   | `* Black box halt decider is NOT a partial deciderRichard Damon
   |   `* Black box halt decider is NOT a partial deciderMalcolm McLean
   `* Black box halt decider is NOT a partial deciderJeff Barnett

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Re: Black box halt decider is NOT a partial decider [ H(P,P)==0 is always correct ]

<eN2dndJR4fe4NGD9nZ2dnUU7-cPNnZ2d@giganews.com>

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Subject: Re: Black box halt decider is NOT a partial decider [ H(P,P)==0 is always correct ]
Newsgroups: comp.theory
References: <20210719214640.00000dfc@reddwarf.jmc> <sd4pbc$f1b$1@gioia.aioe.org> <sd76r9$r63$3@dont-email.me> <sd7cgs$1qmn$1@gioia.aioe.org> <uMGJI.28030$qk6.2244@fx36.iad> <sd7een$js8$1@gioia.aioe.org> <zyHJI.20655$7H7.13829@fx42.iad> <sd8bim$1set$1@gioia.aioe.org> <87eebrlv2m.fsf@bsb.me.uk> <sdckqo$cm8$1@gioia.aioe.org> <87a6mehx5q.fsf@bsb.me.uk> <sdfbv2$14bi$2@gioia.aioe.org> <875yx0he2s.fsf@bsb.me.uk> <sdffqm$jsh$1@gioia.aioe.org> <87zgucfux4.fsf@bsb.me.uk> <sdi9vb$r9b$1@dont-email.me> <87eebnfc8c.fsf@bsb.me.uk> <19Kdna-u6-AOSWH9nZ2dnUU78QXNnZ2d@brightview.co.uk> <87tukjdqmi.fsf@bsb.me.uk> <sdjlo4$1oct$1@gioia.aioe.org> <eOadnfv1CNxEEGD9nZ2dnUU78RPNnZ2d@brightview.co.uk> <4826ab33-061b-472e-a1a5-e2ded35ecd82n@googlegroups.com>
From: NoO...@NoWhere.com (olcott)
Date: Sun, 25 Jul 2021 13:10:45 -0500
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 by: olcott - Sun, 25 Jul 2021 18:10 UTC

On 7/25/2021 12:40 PM, Malcolm McLean wrote:
> On Sunday, 25 July 2021 at 17:14:20 UTC+1, Mike Terry wrote:
>>
>> I think this is all a bit like Malcolm suggesting that PO is raising
>> "interesting ideas" that might be useful with more study, or that some
>> basic idea of PO's is "really quite clever...". It is NOT. PO has no
>> incling of those possibilities and really no interest in them. He is
>> simply saying things he naively thinks are true, without any logical
>> reasoning going on. No cleverness at all. He is not "performing a
>> magic trick", where he will pull a rabit out of a hat - he genuinely
>> believes he is refuting the Linz proof, no tricks. Pretending otherwise
>> may be being nice to PO, making him feel better, but is ultimately
>> unhelpful IMO. I'd say it seems like "dishonest niceness" to me. (But
>> maybe Malcolm really thinks PO is producing worthwhile results, or is on
>> the path to that, in which case it's just being "actually nice"!)
>>
> I've always been very clear that I haven't yet seen from PO anything that
> constitutes a refutation of Linz. However when we have, for example, the
> "H is the operating system" ruse, I do tend to say "that's a clever cheat"
> rather than "how could you make such a simple and obvious error?".
> Largely because it's a nicer way of conveying essentially the same
> information.
>
> I did say recently that PO had constructed his own paradox. It's this. If
> H is simulating halt decider, and is called on H, it creates a series of
> nested recursions. If it doesn't detect the situation, it never halts. If
> it does detect the situation and terminates the simulations, it halts.
> However if it halts, the nested recursions were not infinite.
>
> I do wonder if this could form the nucleus of an another proof that
> halting is undecidable.
>

_P()
[00000c25](01) 55 push ebp
[00000c26](02) 8bec mov ebp,esp
[00000c28](03) 8b4508 mov eax,[ebp+08]
[00000c2b](01) 50 push eax // 2nd Param
[00000c2c](03) 8b4d08 mov ecx,[ebp+08]
[00000c2f](01) 51 push ecx // 1st Param
[00000c30](05) e820fdffff call 00000955 // call H
....

machine stack stack machine assembly
address address data code language
======== ======== ======== ========= =============
Begin Local Halt Decider Simulation at Machine Address:c25
[00000c25][00211776][0021177a] 55 push ebp // P1 begins
[00000c26][00211776][0021177a] 8bec mov ebp,esp
[00000c28][00211776][0021177a] 8b4508 mov eax,[ebp+08]
[00000c2b][00211772][00000c25] 50 push eax // push P
[00000c2c][00211772][00000c25] 8b4d08 mov ecx,[ebp+08]
[00000c2f][0021176e][00000c25] 51 push ecx // push P
[00000c30][0021176a][00000c35] e820fdffff call 00000955 // call H1

[00000c25][0025c19e][0025c1a2] 55 push ebp // P2 begins
[00000c26][0025c19e][0025c1a2] 8bec mov ebp,esp
[00000c28][0025c19e][0025c1a2] 8b4508 mov eax,[ebp+08]
[00000c2b][0025c19a][00000c25] 50 push eax // push P
[00000c2c][0025c19a][00000c25] 8b4d08 mov ecx,[ebp+08]
[00000c2f][0025c196][00000c25] 51 push ecx // push P
[00000c30][0025c192][00000c35] e820fdffff call 00000955 // call H2
Local Halt Decider: Infinite Recursion Detected Simulation Stopped

In the above computation (zero based addressing) H0 aborts P1
No P(P) ever stops running unless H0 aborts its simulation of P1

(1) H does perform a pure simulation of its input until after it makes
its halt status decision.

(2) It can be verified that this is a pure simulation on the basis that
the execution trace does what the x86 source-code of P specifies.

(3) Because there are no control flow instructions in the execution
trace that can possibly escape the infinite recursion the execution
trace proves that a pure simulation of the above input cannot possibly
ever reach its final state.

(4) Therefore H was correct when it decided that its input never halts.

--
Copyright 2021 Pete Olcott

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

Re: Black box halt decider is NOT a partial decider

<87czr6dztx.fsf@bsb.me.uk>

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https://www.novabbs.com/devel/article-flat.php?id=18910&group=comp.theory#18910

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From: ben.use...@bsb.me.uk (Ben Bacarisse)
Newsgroups: comp.theory
Subject: Re: Black box halt decider is NOT a partial decider
Date: Sun, 25 Jul 2021 19:15:54 +0100
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 by: Ben Bacarisse - Sun, 25 Jul 2021 18:15 UTC

Mike Terry <news.dead.person.stones@darjeeling.plus.com> writes:

> On 25/07/2021 15:26, Ben Bacarisse wrote:
>> Mike Terry <news.dead.person.stones@darjeeling.plus.com> writes:
>>
>>> Anyway I would be with you on the "static" vs. operational (temporal)
>>> process question, but we might both be outliers I guess. [Something
>>> you said a few years back raised the possibility in my mind that
>>> perhaps we had both studied at the same university, possibly even
>>> around the same time. (Cambridge, 1979-1981.)]
>> Blimey, yes. Peterhouse.
>>
> (Trinity Hall... (Probably I don't need to add my usual "not
> Trinity"))

Indeed not. Just up the road, and one of the loveliest colleges. I
don't think we met.

--
Ben.

Re: Black box halt decider is NOT a partial decider [ H(P,P)==0 is always correct ]

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Subject: Re: Black box halt decider is NOT a partial decider [ H(P,P)==0 is always correct ]
Newsgroups: comp.theory
References: <20210719214640.00000dfc@reddwarf.jmc> <sd4pbc$f1b$1@gioia.aioe.org> <sd76r9$r63$3@dont-email.me> <sd7cgs$1qmn$1@gioia.aioe.org> <uMGJI.28030$qk6.2244@fx36.iad> <sd7een$js8$1@gioia.aioe.org> <zyHJI.20655$7H7.13829@fx42.iad> <sd8bim$1set$1@gioia.aioe.org> <87eebrlv2m.fsf@bsb.me.uk> <sdckqo$cm8$1@gioia.aioe.org> <87a6mehx5q.fsf@bsb.me.uk> <sdfbv2$14bi$2@gioia.aioe.org> <875yx0he2s.fsf@bsb.me.uk> <sdffqm$jsh$1@gioia.aioe.org> <87zgucfux4.fsf@bsb.me.uk> <sdi9vb$r9b$1@dont-email.me> <87eebnfc8c.fsf@bsb.me.uk> <19Kdna-u6-AOSWH9nZ2dnUU78QXNnZ2d@brightview.co.uk> <87tukjdqmi.fsf@bsb.me.uk> <sdjlo4$1oct$1@gioia.aioe.org> <eOadnfv1CNxEEGD9nZ2dnUU78RPNnZ2d@brightview.co.uk> <4826ab33-061b-472e-a1a5-e2ded35ecd82n@googlegroups.com>
From: NoO...@NoWhere.com (olcott)
Date: Sun, 25 Jul 2021 13:22:25 -0500
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 by: olcott - Sun, 25 Jul 2021 18:22 UTC

On 7/25/2021 12:40 PM, Malcolm McLean wrote:
> On Sunday, 25 July 2021 at 17:14:20 UTC+1, Mike Terry wrote:
>>
>> I think this is all a bit like Malcolm suggesting that PO is raising
>> "interesting ideas" that might be useful with more study, or that some
>> basic idea of PO's is "really quite clever...". It is NOT. PO has no
>> incling of those possibilities and really no interest in them. He is
>> simply saying things he naively thinks are true, without any logical
>> reasoning going on. No cleverness at all. He is not "performing a
>> magic trick", where he will pull a rabit out of a hat - he genuinely
>> believes he is refuting the Linz proof, no tricks. Pretending otherwise
>> may be being nice to PO, making him feel better, but is ultimately
>> unhelpful IMO. I'd say it seems like "dishonest niceness" to me. (But
>> maybe Malcolm really thinks PO is producing worthwhile results, or is on
>> the path to that, in which case it's just being "actually nice"!)
>>
> I've always been very clear that I haven't yet seen from PO anything that
> constitutes a refutation of Linz. However when we have, for example, the

I made my refutation of Linz a little more clear by changing all of the
subscripts to be numeric. My refutation of Linz cannot be properly
understood until after my refutation of simplified Linz / Strachey is
first understood.

https://www.researchgate.net/publication/351947980_Halting_problem_undecidability_and_infinitely_nested_simulation

The key thing that must be understood is that [ H(P,P)==0 is always
correct ] even though int main(){ P(P); } halts.

> "H is the operating system" ruse, I do tend to say "that's a clever cheat"
> rather than "how could you make such a simple and obvious error?".
> Largely because it's a nicer way of conveying essentially the same
> information.
>
> I did say recently that PO had constructed his own paradox. It's this. If
> H is simulating halt decider, and is called on H, it creates a series of
> nested recursions. If it doesn't detect the situation, it never halts. If
> it does detect the situation and terminates the simulations, it halts.
> However if it halts, the nested recursions were not infinite.
>
> I do wonder if this could form the nucleus of an another proof that
> halting is undecidable.
>

--
Copyright 2021 Pete Olcott

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

Re: Black box halt decider is NOT a partial decider [ H(P,P)==0 is always correct ]

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Subject: Re: Black box halt decider is NOT a partial decider [ H(P,P)==0 is
always correct ]
Newsgroups: comp.theory
References: <20210719214640.00000dfc@reddwarf.jmc>
<sd4pbc$f1b$1@gioia.aioe.org> <sd76r9$r63$3@dont-email.me>
<sd7cgs$1qmn$1@gioia.aioe.org> <uMGJI.28030$qk6.2244@fx36.iad>
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<sd8bim$1set$1@gioia.aioe.org> <87eebrlv2m.fsf@bsb.me.uk>
<sdckqo$cm8$1@gioia.aioe.org> <87a6mehx5q.fsf@bsb.me.uk>
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From: Rich...@Damon-Family.org (Richard Damon)
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 by: Richard Damon - Sun, 25 Jul 2021 18:31 UTC

On 7/25/21 11:10 AM, olcott wrote:
> On 7/25/2021 12:40 PM, Malcolm McLean wrote:
>> On Sunday, 25 July 2021 at 17:14:20 UTC+1, Mike Terry wrote:
>>>
>>> I think this is all a bit like Malcolm suggesting that PO is raising
>>> "interesting ideas" that might be useful with more study, or that some
>>> basic idea of PO's is "really quite clever...". It is NOT. PO has no
>>> incling of those possibilities and really no interest in them. He is
>>> simply saying things he naively thinks are true, without any logical
>>> reasoning going on. No cleverness at all. He is not "performing a
>>> magic trick", where he will pull a rabit out of a hat - he genuinely
>>> believes he is refuting the Linz proof, no tricks. Pretending otherwise
>>> may be being nice to PO, making him feel better, but is ultimately
>>> unhelpful IMO. I'd say it seems like "dishonest niceness" to me. (But
>>> maybe Malcolm really thinks PO is producing worthwhile results, or is on
>>> the path to that, in which case it's just being "actually nice"!)
>>>
>> I've always been very clear that I haven't yet seen from PO anything that
>> constitutes a refutation of Linz. However when we have, for example, the
>> "H is the operating system" ruse, I do tend to say "that's a clever
>> cheat"
>> rather than "how could you make such a simple and obvious error?".
>> Largely because it's a nicer way of conveying essentially the same
>> information.
>>
>> I did say recently that PO had constructed his own paradox. It's this. If
>> H is  simulating halt decider, and is called on H, it creates a series of
>> nested recursions. If it doesn't detect the situation, it never halts. If
>> it does detect the situation and terminates the simulations, it halts.
>> However if it halts, the nested recursions were not infinite.
>>
>> I do wonder if this could form the nucleus of an another proof that
>> halting is undecidable.
>>
>
> _P()
> [00000c25](01)  55          push ebp
> [00000c26](02)  8bec        mov ebp,esp
> [00000c28](03)  8b4508      mov eax,[ebp+08]
> [00000c2b](01)  50          push eax       // 2nd Param
> [00000c2c](03)  8b4d08      mov ecx,[ebp+08]
> [00000c2f](01)  51          push ecx       // 1st Param
> [00000c30](05)  e820fdffff  call 00000955  // call H
> ...
>
>  machine   stack     stack     machine    assembly
>  address   address   data      code       language
>  ========  ========  ========  =========  =============
> Begin Local Halt Decider Simulation at Machine Address:c25
> [00000c25][00211776][0021177a] 55         push ebp      // P1 begins
> [00000c26][00211776][0021177a] 8bec       mov ebp,esp
> [00000c28][00211776][0021177a] 8b4508     mov eax,[ebp+08]
> [00000c2b][00211772][00000c25] 50         push eax      // push P
> [00000c2c][00211772][00000c25] 8b4d08     mov ecx,[ebp+08]
> [00000c2f][0021176e][00000c25] 51         push ecx      // push P
> [00000c30][0021176a][00000c35] e820fdffff call 00000955 // call H1
>
> [00000c25][0025c19e][0025c1a2] 55         push ebp      // P2 begins
> [00000c26][0025c19e][0025c1a2] 8bec       mov ebp,esp
> [00000c28][0025c19e][0025c1a2] 8b4508     mov eax,[ebp+08]
> [00000c2b][0025c19a][00000c25] 50         push eax      // push P
> [00000c2c][0025c19a][00000c25] 8b4d08     mov ecx,[ebp+08]
> [00000c2f][0025c196][00000c25] 51         push ecx      // push P
> [00000c30][0025c192][00000c35] e820fdffff call 00000955 // call H2
> Local Halt Decider: Infinite Recursion Detected Simulation Stopped
>
> In the above computation (zero based addressing) H0 aborts P1
> No P(P) ever stops running unless H0 aborts its simulation of P1

So, why does that matter. The P derived from the H that does abort its
simulation of a copy of P does Halt, and thus shows that H was wrong.

The OTHER P, derived from an H that doesn't abort its simulaton of P
would be correctly decided as non-halting, but the H that is supposed to
make that decision never gives an answer.

Remember, H needs to give the right answer for the P that is derived
from it. That is why Linz called that P with the name H^, to show that
it was derived from that given H.

Yes Ha, the aborting H can correctly determine that Pn, derived from Hn,
the H that doesn't abort, but that is NOT the requirement of the Linz proof.

You just tried to proof that cats bark by looking at a dog. FAIL.

>
> (1) H does perform a pure simulation of its input until after it makes
> its halt status decision.

And thus is NOT a pure simulator. If I start to count to infinitiy, and
then stop, I didn't count to infinity.

>
> (2) It can be verified that this is a pure simulation on the basis that
> the execution trace does what the x86 source-code of P specifies.

And this is also wrong, as the Call instruction isn't traced correctly.

>
> (3) Because there are no control flow instructions in the execution
> trace that can possibly escape the infinite recursion the execution
> trace proves that a pure simulation of the above input cannot possibly
> ever reach its final state.

The is n control flow instructions only because the trace is incorrect.

UNSOUND LOGIC.

>
> (4) Therefore H was correct when it decided that its input never halts.
>

A conclusiion that is as UNSOUND as you are.

It is IMPOSSILBE for H to correctly answer non-halting for the H^
derived from it, since such a H^ is a Halting Computation.

At best, you can show that your logic system is inconsistent and can
show a 'proof' of anything.

Re: Black box halt decider is NOT a partial decider [ H(P,P)==0 is always correct ]

<sdkbc3$if8$1@dont-email.me>

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From: agis...@gm.invalid (André G. Isaak)
Newsgroups: comp.theory
Subject: Re: Black box halt decider is NOT a partial decider [ H(P,P)==0 is
always correct ]
Date: Sun, 25 Jul 2021 12:43:13 -0600
Organization: Christians and Atheists United Against Creeping Agnosticism
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 by: André G. Isaak - Sun, 25 Jul 2021 18:43 UTC

On 2021-07-25 12:22, olcott wrote:

> The key thing that must be understood is that [ H(P,P)==0 is always
> correct ] even though int main(){ P(P); } halts.

So why don't you try to somehow explain the above.

A halt decider H is, *by definition* a Turing Machine that accepts (P,
P) if P(P) reaches one of its final states in a finite number of steps
and which rejects it if it does not reach one of its final states in a
finite number of steps.

int main(){ P(P); } *is* simply the computation P(P), and it *does*
reach a final state in a finite number of steps.

So how can H(P, P) be "correct" if it rejects P(P), a computation which
*you acknowledge* reaches a final state in a finite number of steps?

André

--
To email remove 'invalid' & replace 'gm' with well known Google mail
service.

Re: Black box halt decider is NOT a partial decider [ H(P,P)==0 is always correct ]

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Subject: Re: Black box halt decider is NOT a partial decider [ H(P,P)==0 is
always correct ]
Newsgroups: comp.theory
References: <20210719214640.00000dfc@reddwarf.jmc>
<sd4pbc$f1b$1@gioia.aioe.org> <sd76r9$r63$3@dont-email.me>
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From: Rich...@Damon-Family.org (Richard Damon)
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 by: Richard Damon - Sun, 25 Jul 2021 19:25 UTC

On 7/25/21 11:22 AM, olcott wrote:

> I made my refutation of Linz a little more clear by changing all of the
> subscripts to be numeric. My refutation of Linz cannot be properly
> understood until after my refutation of simplified Linz / Strachey is
> first understood.
>
> https://www.researchgate.net/publication/351947980_Halting_problem_undecidability_and_infinitely_nested_simulation
>
>
> The key thing that must be understood is that [ H(P,P)==0 is always
> correct ] even though int main(){ P(P); } halts.
>

As Andre says, this last statement shows that either you you are
suffering from cognitive dissonance (and thus lack the ability to really
see what is true), or actively proclaiming something as true which you
know must be a lie (and thus are a liar).

Going over you latest paper.

First Error, from the first paragraph. The Halting Problem is NOT about
'C Functions' but about FULL COMPUTATION. That means that when you
examine the C function P, you MUST include in your analysis EVERYTHING
that this C function calls. You fail to do that later, when you ignore
what H does. The 'Function' P is NOT the Turing Equivalent to the Turing
Machines you later describe. This makes your WHOLE argument invalid, as
you have lost your equivalenc arguement that the whole thing is based on.

You then make arguements about a halt decider that is a 'pure simulator
until it makes its decision' and then you apply rules to this that only
apply to machines that are a TRUE PURE SIMULATOR.

This is unsound logic.

Yes, the act of H aborting its simulation of the input doesn't change
the behavor of the machine it is simulating, but DOES affect the machine
that is using the algorithm of H as part of its algorithm. Thus, when H
is simulating the copy for the machine that is using it, and it sees a
copy of itself in that machine, the behavior of that copy of itself
AFTER is does abort its simulation is important to that machine that is
the first machine was simulating.

In Symbols

We have P0(P) -> H0(P,P) simulates P1(P) -> H1(P,P) simulates P2(P)

H0 needs to take into account that H1 will abort its simulattion of
P2(P) when it gets to that part of its execution when deciding what
P1(P) is going to do.

You may think of this as removing 'pathological behavior' but it is
removing ACTUAL behavior, and not looking at the full behavior is why it
gets the WRONG answer.

You make the claim later on that No P(P) halts unless H0 aborts P1.

This is true, but that doesn't actually have any bearing.

We have two cases.

An Hn that doesn't abort, and then the Pn derived from this is proved to
be non-halting, but Hn never gives an answer to Hn(Pn,Pn) si this isn't
of any significance.

An Ha that DOES abort, in this case we have shown that when Ha returns
the non-halting answer to Pa that Pa does halt. SInce we have shown that
Pa0 halts, we KNOW that Pa1 would have reached its halting state if H0
had only simulated it longer, thus Ha0 was INCORRECT in deciding that
Pa1(Pa) was non-halting.

Yes, Ha can correct determine that Pn(Pn) is non-halting, but that isn't
the question it is required to get right.

This is where you first fatal flaw fully reveals itself. The Machine P
isn't just the code of the C function P, but machine P includes as part
of it the H that is calls, and thus changing that changes the P we are
looking at, and analysis of the wrong P can give us incorrect answers.

Re: Black box halt decider is NOT a partial decider [ H(P,P)==0 is always correct ]

<87wnpechf4.fsf@bsb.me.uk>

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From: ben.use...@bsb.me.uk (Ben Bacarisse)
Newsgroups: comp.theory
Subject: Re: Black box halt decider is NOT a partial decider [ H(P,P)==0 is always correct ]
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 by: Ben Bacarisse - Sun, 25 Jul 2021 19:38 UTC

olcott <NoOne@NoWhere.com> writes:

> I made my refutation of Linz a little more clear by changing all of
> the subscripts to be numeric.

You don't even accept Linz's definition of a halt decider. You have
nothing to say about hating, much less Linz's proof.

You once said:

"Everyone has claimed that H on input pair (Ĥ, Ĥ) meeting the Linz
specs does not exist. I now have a fully encoded pair of Turing
Machines H / Ĥ proving them wrong."

Linz's specs:

q0 [M] w ⊦ x1 qy x2 if M(w) halts, and
q0 [M] w ⊦ y1 qn y2 if M(w) does not halt.

You have no such TMs. You never did. The last two and a half years
have just been about your finding a way to avoid saying "sorry, I was
wrong about that".

The first sign that you knew you were wrong came when you refused to say
what the correct answer was for H(<[H^], [H^]>) (my notation). I asked:

|| (1) What is the decision -- halts, or does not halt?

and you said

| Yes it is one of those.

Could you have been more evasive? If you weren't lying, tell us now.
Which state, qy or qn does your H halt in (the actual Turing machine,
not the pile of X86 code) when given <[H^],[H^]>? Is it, like your junk
x86 code, the reject state? And is H^([H^]) a finite computation like
your pile of junk x86 code version? You won't tell us, because never
had such a pair of TMs, but I doubt you'll admit that either.

Then the Long Walk Back started, and after more than two and half years
of junk postings we arrive at this absurd claim:

> H(P,P)==0 is always correct ... even though int main(){ P(P); } halts.

From two actual Turing machines that everyone said were impossible, to a
pile of x86 junk code that no one cares about because it gets the answer
explicitly wrong.

--
Ben.

Re: Black box halt decider is NOT a partial decider [ H(P,P)==0 is always correct ]

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Subject: Re: Black box halt decider is NOT a partial decider [ H(P,P)==0 is
always correct ]
From: malcolm....@gmail.com (Malcolm McLean)
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 by: Malcolm McLean - Sun, 25 Jul 2021 19:46 UTC

On Sunday, 25 July 2021 at 20:25:38 UTC+1, Richard Damon wrote:
> On 7/25/21 11:22 AM, olcott wrote:
>
> > I made my refutation of Linz a little more clear by changing all of the
> > subscripts to be numeric. My refutation of Linz cannot be properly
> > understood until after my refutation of simplified Linz / Strachey is
> > first understood.
> >
> > https://www.researchgate.net/publication/351947980_Halting_problem_undecidability_and_infinitely_nested_simulation
> >
> >
> > The key thing that must be understood is that [ H(P,P)==0 is always
> > correct ] even though int main(){ P(P); } halts.
> >
> As Andre says, this last statement shows that either you you are
> suffering from cognitive dissonance (and thus lack the ability to really
> see what is true), or actively proclaiming something as true which you
> know must be a lie (and thus are a liar).
>
We simplifyL inz H_Hat by removing the invert loop. Now, obviously, we
can write a decider which categorises it correctly by just writing "return
true". But that's not what we're after.
Keep H as a "simulating halt decider". That is, it simulates its input,
until it either the input halts, or it detects that the input has got trapped
in a cycle. Now input P(P) {H(P, P)}.
The simulator simulates itself. Now either its cycle detector detects
the situation, or t doesn't. If it doesn't, H contexts pile up and the the
machine never halts until it runs out of tape. If it does detect the cycle,
it terminates the simulations and P(P) halts.
So whatever H() decides, it has to get the answer wrong. I'm not quite sure
where PO is getting confused. But it's probably the paradox - if H
detects the cycle as infinite, it is finite, and vice versa.

Re: Black box halt decider is NOT a partial decider

<87r1fmcgta.fsf@bsb.me.uk>

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From: ben.use...@bsb.me.uk (Ben Bacarisse)
Newsgroups: comp.theory
Subject: Re: Black box halt decider is NOT a partial decider
Date: Sun, 25 Jul 2021 20:52:01 +0100
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 by: Ben Bacarisse - Sun, 25 Jul 2021 19:52 UTC

Malcolm McLean <malcolm.arthur.mclean@gmail.com> writes:

> On Sunday, 25 July 2021 at 17:14:20 UTC+1, Mike Terry wrote:
>>
>> I think this is all a bit like Malcolm suggesting that PO is raising
>> "interesting ideas" that might be useful with more study, or that some
>> basic idea of PO's is "really quite clever...". It is NOT. PO has no
>> incling of those possibilities and really no interest in them. He is
>> simply saying things he naively thinks are true, without any logical
>> reasoning going on. No cleverness at all. He is not "performing a
>> magic trick", where he will pull a rabit out of a hat - he genuinely
>> believes he is refuting the Linz proof, no tricks. Pretending otherwise
>> may be being nice to PO, making him feel better, but is ultimately
>> unhelpful IMO. I'd say it seems like "dishonest niceness" to me. (But
>> maybe Malcolm really thinks PO is producing worthwhile results, or is on
>> the path to that, in which case it's just being "actually nice"!)
>>
> I've always been very clear that I haven't yet seen from PO anything that
> constitutes a refutation of Linz.

Unless I've misunderstood what you mean, that's an extraordinary thing
to say. What do you mean by a "a refutation of Linz"? PO won't say, so
you can't be using the term as he does. Do you mean a demonstration
that a TM halt decider does exist (as PO sometimes claims)? Do you mean
the production of a TM X such that X(<[X^][X^]> is correct about
X^([X^]) (as PO originally clamed)? Or do you mean the finding of
irreparable errors in the two proofs of the theorem in Linz?

In all cases your "yet" is a very odd word to use. What concept of such
a simple and well-established theorem do you have that using the word
"yet" is reasonable in this context?

--
Ben.

Re: Black box halt decider is NOT a partial decider

<sdkfit$s2o$4@gioia.aioe.org>

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From: chris.m....@gmail.com (Chris M. Thomasson)
Newsgroups: comp.theory
Subject: Re: Black box halt decider is NOT a partial decider
Date: Sun, 25 Jul 2021 12:55:07 -0700
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 by: Chris M. Thomasson - Sun, 25 Jul 2021 19:55 UTC

On 7/24/2021 4:42 PM, Ben Bacarisse wrote:
> "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> writes:
>
>> On 7/23/2021 4:54 PM, Ben Bacarisse wrote:
>>> "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> writes:
>>>
>>>> On 7/23/2021 3:15 PM, Ben Bacarisse wrote:
>>>>> "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> writes:
>>>>>
>>>>>> On 7/22/2021 2:10 PM, Ben Bacarisse wrote:
>>>>>>> "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> writes:
>>>>>>>
>>>>>>>> On 7/21/2021 5:17 AM, Ben Bacarisse wrote:
>>>>>>>>> "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> writes:
>>>>>>>>>
>>>>>>>>>> For some stupid reason I always thought that the halting problem
>>>>>>>>>> extends to all problems, and all programs.
>>>>>>>>> It is a problem in mathematics and, like all mathematics, it is based on
>>>>>>>>> sound definitions. It says nothing about "all programs" unless "all
>>>>>>>>> programs" is a well-specified set. In that case, "all programs" might
>>>>>>>>> well have a halting problem, and might even have a halting theorem.
>>>>>>>>> The problem is always grounded to the context of some formal model of
>>>>>>>>> computation like Turing machines, recursive functions or the lambda
>>>>>>>>> calculus. I say "always" but that has to exclude comp.theory which is
>>>>>>>>> dominated by silly ideas coming from people who don't know much about
>>>>>>>>> such format models.
>>>>>>>>>
>>>>>>>>>> Well, here is some pure sarcasm:
>>>>>>>>>>
>>>>>>>>>> Every program halts because they will not get to run
>>>>>>>>>> forever... Eventually, Earth will die.
>>>>>>>>> This is not just sarcasm. It's a plain fact.
>>>>>>>>>
>>>>>>>>
>>>>>>>> Well, based on this fact, can we say everything on Earth halts because
>>>>>>>> the planet will eventually die?
>>>>>>>>
>>>>>>>> Humm... It should be "helpful" to think about infinity, where the
>>>>>>>> program is being executed on a system that never dies. Its output is
>>>>>>>> being observed by beings that never die.
>>>>>>>>
>>>>>>>> Does the program halt in the realm of the infinite?
>>>>>>> I don't know what this means. I can answer about the mathematics, but I
>>>>>>> don't know about these hypothetical computations that take time and are
>>>>>>> "observed" by mythical creatures.
>>>>>>
>>>>>> I was just wondering if the algorihtm might halt in a finite number of
>>>>>> steps, but the number of steps would take a very long time. The Earth
>>>>>> would be dead long before it gets a chance to halt.
>>>>> Would Sum[n=1..oo] 1/n^2 still be = (pi^2)/6 even if every addition took
>>>>> a year?
>>>>
>>>> Sure. It converges on that value. Gaining precision every step.
>>>>
>>>> Sum[n=1..oo] 1/n^24 converges on 1.
>>> Putting aside the value, the point is that the sum simply "is". It's
>>> just daft to talk about addition taking time.
>>
>> No problem. There in an instant. Makes me think of hyper
>> processes.
>
> It's not a view I like. 2 + 2 = 4 is simply a fact. It takes no time.

Agreed. I can see where it is as it is, no time involved for these truths.

>
>> However, I use a lot of math that takes intervals or steps
>> to reach a final result. Say, to draw a fractal.
>
> You certainly can take lots of time to find out which facts are the case
> in any given situation. And sometimes you can't be sure to find out in
> any finite time.

True. The fun part it we can draw things step-by-step during iteration.

>
>>> The problem with TMs is the language suggests action, but there is
>>> none. A TM computation is simply an iterated partial state-transition
>>> function. The sequence generated is either finite or it is not finite.
>>> That is fact about the function and the initial conditions just like a
>>> converging sum's value is a fact about limits.
>

Re: Black box halt decider is NOT a partial decider

<sdkflf$s2o$5@gioia.aioe.org>

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From: chris.m....@gmail.com (Chris M. Thomasson)
Newsgroups: comp.theory
Subject: Re: Black box halt decider is NOT a partial decider
Date: Sun, 25 Jul 2021 12:56:30 -0700
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 by: Chris M. Thomasson - Sun, 25 Jul 2021 19:56 UTC

On 7/24/2021 5:07 PM, André G. Isaak wrote:
> On 2021-07-23 17:54, Ben Bacarisse wrote:
>> "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> writes:
>
>>> Sum[n=1..oo] 1/n^24 converges on 1.
>>
>> Putting aside the value, the point is that the sum simply "is".  It's
>> just daft to talk about addition taking time.
>
> A problem with convergent series is that there is a common misconception
> that such series represent a procedure for calculating a value rather
> than the value itself.
>
> While infinite series certainly suggest an algorithm for calculating a
> decimal approximation of some value to arbitrary precision, that's not
> really what they are. They are simple expressions of a mathematical
> equality.
>
> I think the view of 'series as procedures' is one of the reasons why so
> many crackp^H^H^H^H^H^Hpeople have problems accepting, e.g., that
> 0.999... = 1.

..999... = 1 for sure. Its the limit, but it can be fun to break it down,
step-by-step and draw it, and/or alter the steps.

Re: Black box halt decider is NOT a partial decider [ H(P,P)==0 is always correct ]

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Subject: Re: Black box halt decider is NOT a partial decider [ H(P,P)==0 is
always correct ]
Newsgroups: comp.theory
References: <20210719214640.00000dfc@reddwarf.jmc>
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From: Rich...@Damon-Family.org (Richard Damon)
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 by: Richard Damon - Sun, 25 Jul 2021 20:04 UTC

On 7/25/21 12:46 PM, Malcolm McLean wrote:
> On Sunday, 25 July 2021 at 20:25:38 UTC+1, Richard Damon wrote:
>> On 7/25/21 11:22 AM, olcott wrote:
>>
>>> I made my refutation of Linz a little more clear by changing all of the
>>> subscripts to be numeric. My refutation of Linz cannot be properly
>>> understood until after my refutation of simplified Linz / Strachey is
>>> first understood.
>>>
>>> https://www.researchgate.net/publication/351947980_Halting_problem_undecidability_and_infinitely_nested_simulation
>>>
>>>
>>> The key thing that must be understood is that [ H(P,P)==0 is always
>>> correct ] even though int main(){ P(P); } halts.
>>>
>> As Andre says, this last statement shows that either you you are
>> suffering from cognitive dissonance (and thus lack the ability to really
>> see what is true), or actively proclaiming something as true which you
>> know must be a lie (and thus are a liar).
>>
> We simplifyL inz H_Hat by removing the invert loop. Now, obviously, we
> can write a decider which categorises it correctly by just writing "return
> true". But that's not what we're after.
> Keep H as a "simulating halt decider". That is, it simulates its input,
> until it either the input halts, or it detects that the input has got trapped
> in a cycle. Now input P(P) {H(P, P)}.
> The simulator simulates itself. Now either its cycle detector detects
> the situation, or t doesn't. If it doesn't, H contexts pile up and the the
> machine never halts until it runs out of tape. If it does detect the cycle,
> it terminates the simulations and P(P) halts.
> So whatever H() decides, it has to get the answer wrong. I'm not quite sure
> where PO is getting confused. But it's probably the paradox - if H
> detects the cycle as infinite, it is finite, and vice versa.
>

I think that fundamentally, PO is confusing different H^s built from
different Hs. This was shown by some of his recent instance that P is
JUST the code of his subroutine P, and that this machine doesn't include
the H that it calls. This allows him to make arguements over varing Hs
and show that Ha can correctly predict that Pn(Pn) is a non-halting
computation (but he omits the descriptive subscripts).

He conveniently ignores that Hn(Pa,Pa) also gets the right Halting answer.

(a subscirpt is a decider that aborts this nested simulation and decides
non-halting, the n subscirpt is a decider that doesn't abort this nested
simulaton).

This goes back to his long term issue of always wanting to reuse symbols
for different meanings in different cases, and then want to bring
results from one case into another.

Fundamentally we actually get the following cases:

Pn(Pn) is non-halting.
Pa(Pa) is Halting.

Hn(Pn,Pn) never return, and thus fails to be a decider.
Hn(Pa,Pa) will correctly answer that Pa(Pa) is Halting.

Ha(Pn,Pn) will correctly answer that Pn(Pn) is non-halting.
Ha(Pa,Pa) will incorrectly answer that Pa(Pa) is non-halting.
This last case happens as Ha aborts the simulation before it sees the
difference between Pn and Pa.

Re: Black box halt decider is NOT a partial decider

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Subject: Re: Black box halt decider is NOT a partial decider
Newsgroups: comp.theory
References: <20210719214640.00000dfc@reddwarf.jmc>
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From: Rich...@Damon-Family.org (Richard Damon)
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 by: Richard Damon - Sun, 25 Jul 2021 20:13 UTC

On 7/25/21 12:55 PM, Chris M. Thomasson wrote:
> On 7/24/2021 4:42 PM, Ben Bacarisse wrote:
>> "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> writes:
>>
>>> On 7/23/2021 4:54 PM, Ben Bacarisse wrote:
>>>> "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> writes:
>>>>
>>>>> On 7/23/2021 3:15 PM, Ben Bacarisse wrote:
>>>>>> "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> writes:
>>>>>>
>>>>>>> On 7/22/2021 2:10 PM, Ben Bacarisse wrote:
>>>>>>>> "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> writes:
>>>>>>>>
>>>>>>>>> On 7/21/2021 5:17 AM, Ben Bacarisse wrote:
>>>>>>>>>> "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> writes:
>>>>>>>>>>
>>>>>>>>>>> For some stupid reason I always thought that the halting problem
>>>>>>>>>>> extends to all problems, and all programs.
>>>>>>>>>> It is a problem in mathematics and, like all mathematics, it
>>>>>>>>>> is based on
>>>>>>>>>> sound definitions.  It says nothing about "all programs"
>>>>>>>>>> unless "all
>>>>>>>>>> programs" is a well-specified set.  In that case, "all
>>>>>>>>>> programs" might
>>>>>>>>>> well have a halting problem, and might even have a halting
>>>>>>>>>> theorem.
>>>>>>>>>> The problem is always grounded to the context of some formal
>>>>>>>>>> model of
>>>>>>>>>> computation like Turing machines, recursive functions or the
>>>>>>>>>> lambda
>>>>>>>>>> calculus.  I say "always" but that has to exclude comp.theory
>>>>>>>>>> which is
>>>>>>>>>> dominated by silly ideas coming from people who don't know
>>>>>>>>>> much about
>>>>>>>>>> such format models.
>>>>>>>>>>
>>>>>>>>>>> Well, here is some pure sarcasm:
>>>>>>>>>>>
>>>>>>>>>>> Every program halts because they will not get to run
>>>>>>>>>>> forever... Eventually, Earth will die.
>>>>>>>>>> This is not just sarcasm.  It's a plain fact.
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> Well, based on this fact, can we say everything on Earth halts
>>>>>>>>> because
>>>>>>>>> the planet will eventually die?
>>>>>>>>>
>>>>>>>>> Humm... It should be "helpful" to think about infinity, where the
>>>>>>>>> program is being executed on a system that never dies. Its
>>>>>>>>> output is
>>>>>>>>> being observed by beings that never die.
>>>>>>>>>
>>>>>>>>> Does the program halt in the realm of the infinite?
>>>>>>>> I don't know what this means.  I can answer about the
>>>>>>>> mathematics, but I
>>>>>>>> don't know about these hypothetical computations that take time
>>>>>>>> and are
>>>>>>>> "observed" by mythical creatures.
>>>>>>>
>>>>>>> I was just wondering if the algorihtm might halt in a finite
>>>>>>> number of
>>>>>>> steps, but the number of steps would take a very long time. The
>>>>>>> Earth
>>>>>>> would be dead long before it gets a chance to halt.
>>>>>> Would Sum[n=1..oo] 1/n^2 still be = (pi^2)/6 even if every
>>>>>> addition took
>>>>>> a year?
>>>>>
>>>>> Sure. It converges on that value. Gaining precision every step.
>>>>>
>>>>> Sum[n=1..oo] 1/n^24 converges on 1.
>>>> Putting aside the value, the point is that the sum simply "is".  It's
>>>> just daft to talk about addition taking time.
>>>
>>> No problem. There in an instant. Makes me think of hyper
>>> processes.
>>
>> It's not a view I like.  2 + 2 = 4 is simply a fact.  It takes no time.
>
> Agreed. I can see where it is as it is, no time involved for these truths.
>
>>
>>> However, I use a lot of math that takes intervals or steps
>>> to reach a final result. Say, to draw a fractal.
>>
>> You certainly can take lots of time to find out which facts are the case
>> in any given situation.  And sometimes you can't be sure to find out in
>> any finite time.
>
> True. The fun part it we can draw things step-by-step during iteration.
>
>
>>
>>>> The problem with TMs is the language suggests action, but there is
>>>> none.  A TM computation is simply an iterated partial state-transition
>>>> function.  The sequence generated is either finite or it is not finite.
>>>> That is fact about the function and the initial conditions just like a
>>>> converging sum's value is a fact about limits.
>>
>

The key point is that FINITE sums don't matter how you do them, but some
infinite sums DO matter the order you add the terms (if you break the
infinite sum into multiple infinite series to add, how fast you progress
down the different sets can give you different finite results if some of
the sub-sequences do not have a finite sum.

This is part of the complexity of the infinite series.

Re: Black box halt decider is NOT a partial decider

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Subject: Re: Black box halt decider is NOT a partial decider
Newsgroups: comp.theory
References: <20210719214640.00000dfc@reddwarf.jmc>
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From: news.dea...@darjeeling.plus.com (Mike Terry)
Date: Sun, 25 Jul 2021 21:28:10 +0100
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 by: Mike Terry - Sun, 25 Jul 2021 20:28 UTC

On 25/07/2021 18:40, Malcolm McLean wrote:
> On Sunday, 25 July 2021 at 17:14:20 UTC+1, Mike Terry wrote:
>>
>> I think this is all a bit like Malcolm suggesting that PO is raising
>> "interesting ideas" that might be useful with more study, or that some
>> basic idea of PO's is "really quite clever...". It is NOT. PO has no
>> incling of those possibilities and really no interest in them. He is
>> simply saying things he naively thinks are true, without any logical
>> reasoning going on. No cleverness at all. He is not "performing a
>> magic trick", where he will pull a rabit out of a hat - he genuinely
>> believes he is refuting the Linz proof, no tricks. Pretending otherwise
>> may be being nice to PO, making him feel better, but is ultimately
>> unhelpful IMO. I'd say it seems like "dishonest niceness" to me. (But
>> maybe Malcolm really thinks PO is producing worthwhile results, or is on
>> the path to that, in which case it's just being "actually nice"!)
>>
> I've always been very clear that I haven't yet seen from PO anything that
> constitutes a refutation of Linz. However when we have, for example, the
> "H is the operating system" ruse, I do tend to say "that's a clever cheat"
> rather than "how could you make such a simple and obvious error?".
> Largely because it's a nicer way of conveying essentially the same
> information.
>
> I did say recently that PO had constructed his own paradox. It's this. If
> H is simulating halt decider, and is called on H, it creates a series of
> nested recursions. If it doesn't detect the situation, it never halts. If
> it does detect the situation and terminates the simulations, it halts.
> However if it halts, the nested recursions were not infinite.

Right, that's a bit like something I pointed out to PO last year. Such
an emulation-based (putative) decider may have a number of tests in its
stepping loop. Some may be /sound/, like a properly implemented
tight-loop test, or a test might be unsound in that it incorrectly
decides halting for a non-halting input or vice-versa. The sound tests
might match and make correct decisions when examining particular inputs,
BUT it's sort of weird that the when H examines (P,P), the /sound/ tests
"mysteriously" never ever match! The only tests that will ever match
are those that are unsound... If there are /only/ sound tests in the
loop, none of them will match and H(P,P) will never make its decision
and halt! Of course that would disqualify H as a decider.

This applies for PO and his "detecting infinite recursions" test,
however much he believes his test to be sound... I've told him that a
reviewer will

Mike.

>
> I do wonder if this could form the nucleus of an another proof that
> halting is undecidable.
>

Re: Black box halt decider is NOT a partial decider

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From: anw...@cuboid.co.uk (Andy Walker)
Newsgroups: comp.theory
Subject: Re: Black box halt decider is NOT a partial decider
Date: Sun, 25 Jul 2021 21:32:33 +0100
Organization: Not very much
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 by: Andy Walker - Sun, 25 Jul 2021 20:32 UTC

On 25/07/2021 17:14, Mike Terry wrote:
> You're undoubtably right about my over-optimism, but the Archimedian
> property is implicit in other results a maths student studying real
> analysis would have proved (probably still being too optimistic here,
> butI only have my own background to go by...!),

Yes, but your background very likely included a lot more maths
at school than the average outside Oxbridge, and even more than the
average today. [FTAOD, this is not a claim that modern students are
worse than they used to be (and debates about that are usually
ignorant and always fruitless); rather, it was recognised that UK
education was too specialised from age 16 onwards, resulting in the
introduction of an extra subject at school and corresponding "budging
up" in traditional courses, squeezing out a lot of material.]

> e.g. between any two
> real numbers there is a rational number.

Indeed, but the use of the Archimedean property is typically
not mentioned in that proof -- it's so implicit that it disappears!
The typical student doesn't even think about it in those terms --
it's an "obvious" result that barely needs mention let alone proof,
after all, the rationals are "everywhere dense".

>> [...] Meanwhile, it's worth noting that there are
>> [lots of] games "G" such that
>>    0.999...9 [any number of 9's] < G < 1.
>> This does not contradict "0.99... == 1" as "G" is not a real number;
>> but it does mean that it's a deeper result than we tend to assume.
> Sure. I enjoyed Conway's "On Numbers and Games" as a student, and the
> easier "Winning Ways" books later on, but I would say that with all
> that understood, people who think 0.999... < 1 aren't thinking at all
> about surreal numbers! They are, almost universally, just confused,
> having never had to rigorously think through all the consequences of
> their position. (And that's perfectly reasonable - why /should/
> someone spend time thinking through such issues? No reason at all.)

All granted, but it does mean that [proper] mathematicians
should, in many/most cases, be a little less glib in talking about
this problem and others. Both school and undergraduate maths tend
to encourage the view that there is One True Mathematics, and students
often have a view that Nothing Has Changed in maths for hundreds of
years, as distinct from all the exciting things that have happened in
physics/biology/computing/medicine/astronomy within our own careers.
A module in "history of mathematics" should be a corrective, and we
[ie, maths teachers] could do a lot by explaining some of the things
that have changed in maths, eg because of the influence of computers,
calculators and symbolic algebra packages, or because of a switch in
emphasis from [eg] geometry and differential equations to algebra
and statistics.

> If we grant that they were "really" talking about surreal numbers (or
> similar) then what surreal number is 0.9999... actually supposed to
> represent? Calling this s, with d = 1-s > 0 then what is 1-2d?

OK, I started to write it all out, but it got too long, and
it's not really relevant. It's not difficult, just tedious.

> If any reply is forthcoming it will be something like "that's 0.9999...
> with an 8 on the end, which is just incoherent - at least it can't
> make any sense with decimal notation being used.

Well, it can, actually. If we represent recurring decimals
eg by "1/3 == 0.(3)", "3/7 == 0.(428571) == 0.428(571428) == ..."
rather than by using "..." or by dotting the recurring part, then
not only can you easily recover everything you already know about
rationals and about decimal/binary/surreal representations thereof,
but you can also manipulate these objects as strings rather than
as numbers. You can then ask what is meant by "0.(9)" [answer: as
a real number it's "1", but as a game it's a (non-real) number which
is infinitesimally less than "1"]. You can also then ask about the
string "0.(9)8"; viewed as a game, we have [eg] "0(9) < 0.(9)8 < 1".
You can regard "(abcd)" as meaning "an arbitrary (but not infinite)
number of repetitions of abcd"; a "move" is then to choose how many
repetitions there are, so moving to "abcd" or "abcdabcd" or ... at
your whim. In "0.(9)8", you can move to "0.(9)" and defer having to
make the choice, which is why it is better. Note that "(9)" is an
infinite number, equal to "9(9)" but strictly less than "(9)9" as
you can defer the choice of how many "9"s to have. It all works
more smoothly in binary ....

[Stuff about PO deleted. I don't dissent from most of the
views represented in these threads about him, but AFAIK no-one here
actually knows him, so we are all arguing (as is he, it seems) from
ignorance. All we have is speculation, which is fun, and keeps
PO and several regulars here occupied, but I'm happy to leave it
to others.]

--
Andy Walker, Nottingham.
Andy's music pages: www.cuboid.me.uk/andy/Music
Composer of the day: www.cuboid.me.uk/andy/Music/Composers/Chwatal

Re: Black box halt decider is NOT a partial decider

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Subject: Re: Black box halt decider is NOT a partial decider
Newsgroups: comp.theory
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From: news.dea...@darjeeling.plus.com (Mike Terry)
Date: Sun, 25 Jul 2021 21:46:58 +0100
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 by: Mike Terry - Sun, 25 Jul 2021 20:46 UTC

On 25/07/2021 21:28, Mike Terry wrote:
Pressed Send too soon. :(
> On 25/07/2021 18:40, Malcolm McLean wrote:
>> On Sunday, 25 July 2021 at 17:14:20 UTC+1, Mike Terry wrote:
>>>
>>> I think this is all a bit like Malcolm suggesting that PO is raising
>>> "interesting ideas" that might be useful with more study, or that some
>>> basic idea of PO's is "really quite clever...". It is NOT. PO has no
>>> incling of those possibilities and really no interest in them. He is
>>> simply saying things he naively thinks are true, without any logical
>>> reasoning going on. No cleverness at all. He is not "performing a
>>> magic trick", where he will pull a rabit out of a hat - he genuinely
>>> believes he is refuting the Linz proof, no tricks. Pretending otherwise
>>> may be being nice to PO, making him feel better, but is ultimately
>>> unhelpful IMO. I'd say it seems like "dishonest niceness" to me. (But
>>> maybe Malcolm really thinks PO is producing worthwhile results, or is on
>>> the path to that, in which case it's just being "actually nice"!)
>>>
>> I've always been very clear that I haven't yet seen from PO anything that
>> constitutes a refutation of Linz. However when we have, for example, the
>> "H is the operating system" ruse, I do tend to say "that's a clever
>> cheat"
>> rather than "how could you make such a simple and obvious error?".
>> Largely because it's a nicer way of conveying essentially the same
>> information.
>>
>> I did say recently that PO had constructed his own paradox. It's this. If
>> H is  simulating halt decider, and is called on H, it creates a series of
>> nested recursions. If it doesn't detect the situation, it never halts. If
>> it does detect the situation and terminates the simulations, it halts.
>> However if it halts, the nested recursions were not infinite.
>
> Right, that's a bit like something I pointed out to PO last year.  Such
> an emulation-based (putative) decider may have a number of tests in its
> stepping loop.  Some may be /sound/, like a properly implemented
> tight-loop test, or a test might be unsound in that it incorrectly
> decides halting for a non-halting input or vice-versa.  The sound tests
> might match and make correct decisions when examining particular inputs,
> BUT it's sort of weird that the when H examines (P,P), the /sound/ tests
> "mysteriously" never ever match!  The only tests that will ever match
> are those that are unsound...  If there are /only/ sound tests in the
> loop, none of them will match and H(P,P) will never make its decision
> and halt!  Of course that would disqualify H as a decider.
>
> This applies for PO and his "detecting infinite recursions" test,
> however much he believes his test to be sound...  I've told him that a
> reviewer will

....expect to see a /proof/ of the soundness of any test in his loop, if
he's going to expect them to take matching of the test as /evidence/ of
halting status. (Of course PO can't deliver such a proof.)

>
> Mike.
>
>>
>> I do wonder if this could form the nucleus of an another proof that
>> halting is undecidable.
>>

Re: Black box halt decider is NOT a partial decider

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Subject: Re: Black box halt decider is NOT a partial decider
From: malcolm....@gmail.com (Malcolm McLean)
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 by: Malcolm McLean - Sun, 25 Jul 2021 20:54 UTC

On Sunday, 25 July 2021 at 20:52:04 UTC+1, Ben Bacarisse wrote:
> Malcolm McLean <malcolm.ar...@gmail.com> writes:
>
> > On Sunday, 25 July 2021 at 17:14:20 UTC+1, Mike Terry wrote:
> >>
> >> I think this is all a bit like Malcolm suggesting that PO is raising
> >> "interesting ideas" that might be useful with more study, or that some
> >> basic idea of PO's is "really quite clever...". It is NOT. PO has no
> >> incling of those possibilities and really no interest in them. He is
> >> simply saying things he naively thinks are true, without any logical
> >> reasoning going on. No cleverness at all. He is not "performing a
> >> magic trick", where he will pull a rabit out of a hat - he genuinely
> >> believes he is refuting the Linz proof, no tricks. Pretending otherwise
> >> may be being nice to PO, making him feel better, but is ultimately
> >> unhelpful IMO. I'd say it seems like "dishonest niceness" to me. (But
> >> maybe Malcolm really thinks PO is producing worthwhile results, or is on
> >> the path to that, in which case it's just being "actually nice"!)
> >>
> > I've always been very clear that I haven't yet seen from PO anything that
> > constitutes a refutation of Linz.
> Unless I've misunderstood what you mean, that's an extraordinary thing
> to say. What do you mean by a "a refutation of Linz"? PO won't say, so
> you can't be using the term as he does. Do you mean a demonstration
> that a TM halt decider does exist (as PO sometimes claims)? Do you mean
> the production of a TM X such that X(<[X^][X^]> is correct about
> X^([X^]) (as PO originally clamed)? Or do you mean the finding of
> irreparable errors in the two proofs of the theorem in Linz?
>
What would you accept as proof that the Earth is flat? I had a very good
teacher who used to pretend to be a flat earther. His case was that light
didn't travel in straight lines. When you relax the requirement that light travels
in straight lines, all of the simple proofs you read in geography textbooks
become invalid, and as schoolboys we didn't have the intellectual equipment
to refute him. But of course we knew that he was kidding. No one for a
moment supposed seriously that the Earth wasn't round.

All the things you have mentioned would be extraordinary, and all have been
attempted by PO (he won't show the halt decider but he does show the
execution traces, he claims that Linz's roof is based on a "pathological
liar paradox"). I and plenty of others have pointed out why we don't accept
that he truly has an extraordinary result, much less a refutation.

Whilst on the face of it your question seems reasonable, I think really
it's a poor basis on which to proceed. If there's an argument from PO
that seems to make sense, and doesn't have an obvious hole in it, that's
the time to start worrying about what criteria we'll apply to accept that
Linz has been refuted.
>
> In all cases your "yet" is a very odd word to use. What concept of such
> a simple and well-established theorem do you have that using the word
> "yet" is reasonable in this context?
>
"Yet" is disingenuous.

Re: Black box halt decider is NOT a partial decider

<sdkjsb$12g1$1@gioia.aioe.org>

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https://www.novabbs.com/devel/article-flat.php?id=18929&group=comp.theory#18929

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From: chris.m....@gmail.com (Chris M. Thomasson)
Newsgroups: comp.theory
Subject: Re: Black box halt decider is NOT a partial decider
Date: Sun, 25 Jul 2021 14:08:25 -0700
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 by: Chris M. Thomasson - Sun, 25 Jul 2021 21:08 UTC

On 7/25/2021 1:13 PM, Richard Damon wrote:
> On 7/25/21 12:55 PM, Chris M. Thomasson wrote:
>> On 7/24/2021 4:42 PM, Ben Bacarisse wrote:
>>> "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> writes:
>>>
>>>> On 7/23/2021 4:54 PM, Ben Bacarisse wrote:
>>>>> "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> writes:
>>>>>
>>>>>> On 7/23/2021 3:15 PM, Ben Bacarisse wrote:
>>>>>>> "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> writes:
>>>>>>>
>>>>>>>> On 7/22/2021 2:10 PM, Ben Bacarisse wrote:
>>>>>>>>> "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> writes:
>>>>>>>>>
>>>>>>>>>> On 7/21/2021 5:17 AM, Ben Bacarisse wrote:
>>>>>>>>>>> "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> writes:
>>>>>>>>>>>
>>>>>>>>>>>> For some stupid reason I always thought that the halting problem
>>>>>>>>>>>> extends to all problems, and all programs.
>>>>>>>>>>> It is a problem in mathematics and, like all mathematics, it
>>>>>>>>>>> is based on
>>>>>>>>>>> sound definitions.  It says nothing about "all programs"
>>>>>>>>>>> unless "all
>>>>>>>>>>> programs" is a well-specified set.  In that case, "all
>>>>>>>>>>> programs" might
>>>>>>>>>>> well have a halting problem, and might even have a halting
>>>>>>>>>>> theorem.
>>>>>>>>>>> The problem is always grounded to the context of some formal
>>>>>>>>>>> model of
>>>>>>>>>>> computation like Turing machines, recursive functions or the
>>>>>>>>>>> lambda
>>>>>>>>>>> calculus.  I say "always" but that has to exclude comp.theory
>>>>>>>>>>> which is
>>>>>>>>>>> dominated by silly ideas coming from people who don't know
>>>>>>>>>>> much about
>>>>>>>>>>> such format models.
>>>>>>>>>>>
>>>>>>>>>>>> Well, here is some pure sarcasm:
>>>>>>>>>>>>
>>>>>>>>>>>> Every program halts because they will not get to run
>>>>>>>>>>>> forever... Eventually, Earth will die.
>>>>>>>>>>> This is not just sarcasm.  It's a plain fact.
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> Well, based on this fact, can we say everything on Earth halts
>>>>>>>>>> because
>>>>>>>>>> the planet will eventually die?
>>>>>>>>>>
>>>>>>>>>> Humm... It should be "helpful" to think about infinity, where the
>>>>>>>>>> program is being executed on a system that never dies. Its
>>>>>>>>>> output is
>>>>>>>>>> being observed by beings that never die.
>>>>>>>>>>
>>>>>>>>>> Does the program halt in the realm of the infinite?
>>>>>>>>> I don't know what this means.  I can answer about the
>>>>>>>>> mathematics, but I
>>>>>>>>> don't know about these hypothetical computations that take time
>>>>>>>>> and are
>>>>>>>>> "observed" by mythical creatures.
>>>>>>>>
>>>>>>>> I was just wondering if the algorihtm might halt in a finite
>>>>>>>> number of
>>>>>>>> steps, but the number of steps would take a very long time. The
>>>>>>>> Earth
>>>>>>>> would be dead long before it gets a chance to halt.
>>>>>>> Would Sum[n=1..oo] 1/n^2 still be = (pi^2)/6 even if every
>>>>>>> addition took
>>>>>>> a year?
>>>>>>
>>>>>> Sure. It converges on that value. Gaining precision every step.
>>>>>>
>>>>>> Sum[n=1..oo] 1/n^24 converges on 1.
>>>>> Putting aside the value, the point is that the sum simply "is".  It's
>>>>> just daft to talk about addition taking time.
>>>>
>>>> No problem. There in an instant. Makes me think of hyper
>>>> processes.
>>>
>>> It's not a view I like.  2 + 2 = 4 is simply a fact.  It takes no time.
>>
>> Agreed. I can see where it is as it is, no time involved for these truths.
>>
>>>
>>>> However, I use a lot of math that takes intervals or steps
>>>> to reach a final result. Say, to draw a fractal.
>>>
>>> You certainly can take lots of time to find out which facts are the case
>>> in any given situation.  And sometimes you can't be sure to find out in
>>> any finite time.
>>
>> True. The fun part it we can draw things step-by-step during iteration.
>>
>>
>>>
>>>>> The problem with TMs is the language suggests action, but there is
>>>>> none.  A TM computation is simply an iterated partial state-transition
>>>>> function.  The sequence generated is either finite or it is not finite.
>>>>> That is fact about the function and the initial conditions just like a
>>>>> converging sum's value is a fact about limits.
>>>
>>
>
> The key point is that FINITE sums don't matter how you do them, but some
> infinite sums DO matter the order you add the terms (if you break the
> infinite sum into multiple infinite series to add, how fast you progress
> down the different sets can give you different finite results if some of
> the sub-sequences do not have a finite sum.
>
> This is part of the complexity of the infinite series.
>

True. Fwiw, I have great fun taking from the infinite pool and breaking
things apart into segments. For instance drawing a finite view of an
infinite field line on a segment-by-segment basis. Fwiw, here is an
example of some of my work treating iterations of escape time fractals,
like a Julia set in the following test, as a segment by segment process:

https://youtu.be/UpNDkOKdcjk

Also, this draws its lines on a segment-by-segment basis:

http://fractallife247.com/fdla/

Try clicking around to create new attractors in the field in real time.

Check this out, click on the Animation Testing 123 button:

http://fractallife247.com/test

Also, click around on the canvas. The lines are being constructed on a
step-by-step basis.

Re: Black box halt decider is NOT a partial decider

<pJGdnXgeu6JxQmD9nZ2dnUU78RXNnZ2d@brightview.co.uk>

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Subject: Re: Black box halt decider is NOT a partial decider
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From: news.dea...@darjeeling.plus.com (Mike Terry)
Date: Sun, 25 Jul 2021 23:04:28 +0100
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 by: Mike Terry - Sun, 25 Jul 2021 22:04 UTC

On 25/07/2021 19:15, Ben Bacarisse wrote:
> Mike Terry <news.dead.person.stones@darjeeling.plus.com> writes:
>
>> On 25/07/2021 15:26, Ben Bacarisse wrote:
>>> Mike Terry <news.dead.person.stones@darjeeling.plus.com> writes:
>>>
>>>> Anyway I would be with you on the "static" vs. operational (temporal)
>>>> process question, but we might both be outliers I guess. [Something
>>>> you said a few years back raised the possibility in my mind that
>>>> perhaps we had both studied at the same university, possibly even
>>>> around the same time. (Cambridge, 1979-1981.)]
>>> Blimey, yes. Peterhouse.
>>>
>> (Trinity Hall... (Probably I don't need to add my usual "not
>> Trinity"))
>
> Indeed not. Just up the road, and one of the loveliest colleges. I
> don't think we met.
>

No, probably not...

Re: Black box halt decider is NOT a partial decider

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Subject: Re: Black box halt decider is NOT a partial decider
Newsgroups: comp.theory
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From: news.dea...@darjeeling.plus.com (Mike Terry)
Date: Sun, 25 Jul 2021 23:21:59 +0100
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 by: Mike Terry - Sun, 25 Jul 2021 22:21 UTC

On 25/07/2021 16:56, Andy Walker wrote:
> On 25/07/2021 15:26, Ben Bacarisse wrote:
>> Mike Terry <news.dead.person.stones@darjeeling.plus.com> writes:
>>> [...] (Cambridge, 1979-1981.)]
>> Blimey, yes.  Peterhouse.
>
>     Bloomin' youngsters!  [Sidney, 1961-65.]
>

Wow, from the era before they (nearly) all went mixed! :)

Re: Black box halt decider is NOT a partial decider

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From: ben.use...@bsb.me.uk (Ben Bacarisse)
Newsgroups: comp.theory
Subject: Re: Black box halt decider is NOT a partial decider
Date: Sun, 25 Jul 2021 23:42:54 +0100
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 by: Ben Bacarisse - Sun, 25 Jul 2021 22:42 UTC

Mike Terry <news.dead.person.stones@darjeeling.plus.com> writes:

> On 25/07/2021 21:28, Mike Terry wrote:
> Pressed Send too soon. :(
>> On 25/07/2021 18:40, Malcolm McLean wrote:
>>> On Sunday, 25 July 2021 at 17:14:20 UTC+1, Mike Terry wrote:
>>>>
>>>> I think this is all a bit like Malcolm suggesting that PO is raising
>>>> "interesting ideas" that might be useful with more study, or that some
>>>> basic idea of PO's is "really quite clever...". It is NOT. PO has no
>>>> incling of those possibilities and really no interest in them. He is
>>>> simply saying things he naively thinks are true, without any logical
>>>> reasoning going on. No cleverness at all. He is not "performing a
>>>> magic trick", where he will pull a rabit out of a hat - he genuinely
>>>> believes he is refuting the Linz proof, no tricks. Pretending otherwise
>>>> may be being nice to PO, making him feel better, but is ultimately
>>>> unhelpful IMO. I'd say it seems like "dishonest niceness" to me. (But
>>>> maybe Malcolm really thinks PO is producing worthwhile results, or is on
>>>> the path to that, in which case it's just being "actually nice"!)
>>>>
>>> I've always been very clear that I haven't yet seen from PO anything that
>>> constitutes a refutation of Linz. However when we have, for example, the
>>> "H is the operating system" ruse, I do tend to say "that's a clever cheat"
>>> rather than "how could you make such a simple and obvious error?".
>>> Largely because it's a nicer way of conveying essentially the same
>>> information.
>>>
>>> I did say recently that PO had constructed his own paradox. It's this. If
>>> H is  simulating halt decider, and is called on H, it creates a series of
>>> nested recursions. If it doesn't detect the situation, it never halts. If
>>> it does detect the situation and terminates the simulations, it halts.
>>> However if it halts, the nested recursions were not infinite.
>> Right, that's a bit like something I pointed out to PO last year.  Such
>> an emulation-based (putative) decider may have a number of tests in its stepping loop.  Some may be /sound/, like a properly implemented
>> tight-loop test, or a test might be unsound in that it incorrectly decides halting for a non-halting input or vice-versa.  The sound tests
>> might match and make correct decisions when examining particular inputs, BUT it's sort of weird that the when H examines (P,P), the /sound/ tests
>> "mysteriously" never ever match!  The only tests that will ever match are those that are unsound...  If there are /only/ sound tests in the
>> loop, none of them will match and H(P,P) will never make its decision and halt!  Of course that would disqualify H as a decider.
>> This applies for PO and his "detecting infinite recursions" test,
>> however much he believes his test to be sound...  I've told him that a reviewer will
>
> ...expect to see a /proof/ of the soundness of any test in his loop,
> if he's going to expect them to take matching of the test as
> /evidence/ of halting status. (Of course PO can't deliver such a
> proof.)

Right. And very well put. But he's abandoned almost all pretence at
dealing with halting. What makes a sound test has been defined to be
what H does. This is the "adapted" criterion for halting. Not halting,
but whatever it is he chooses to put into H. When he says that its
"impossibly incorrect" (if that's the term, I try to forget such things)
this is what he means.

--
Ben.

Re: Black box halt decider is NOT a partial decider

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From: ben.use...@bsb.me.uk (Ben Bacarisse)
Newsgroups: comp.theory
Subject: Re: Black box halt decider is NOT a partial decider
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 by: Ben Bacarisse - Sun, 25 Jul 2021 22:44 UTC

Andy Walker <anw@cuboid.co.uk> writes:

> On 25/07/2021 15:26, Ben Bacarisse wrote:
>> Mike Terry <news.dead.person.stones@darjeeling.plus.com> writes:
>>> [...] (Cambridge, 1979-1981.)]
>> Blimey, yes. Peterhouse.
>
> Bloomin' youngsters! [Sidney, 1961-65.]

I was literally a babe in arms!

--
Ben.

Re: Black box halt decider is NOT a partial decider [ H(P,P)==0 is always correct ]

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From: jbb...@notatt.com (Jeff Barnett)
Newsgroups: comp.theory
Subject: Re: Black box halt decider is NOT a partial decider [ H(P,P)==0 is
always correct ]
Date: Sun, 25 Jul 2021 16:58:27 -0600
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 by: Jeff Barnett - Sun, 25 Jul 2021 22:58 UTC

On 7/25/2021 2:04 PM, Richard Damon wrote:
> On 7/25/21 12:46 PM, Malcolm McLean wrot
<SNIP>

> This goes back to his long term issue of always wanting to reuse symbols
> for different meanings in different cases, and then want to bring
> results from one case into another.
A long time ago I read Godel's dissertation retypeset in the exact
notation of the original. It was maddening because each and every little
theorem, lemma, etc. started out completely reassigning the meanings of
symbols for that result. It was the most difficult thing I ever tried to
read. I finally found a cleaned up proof and was able to scan through it
and catch the flavor. I'm curious whether PO ever saw the original and
adopted the style to impress us all!
--
Jeff Barnett

Re: Black box halt decider is NOT a partial decider

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Subject: Re: Black box halt decider is NOT a partial decider
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From: news.dea...@darjeeling.plus.com (Mike Terry)
Date: Mon, 26 Jul 2021 01:08:24 +0100
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 by: Mike Terry - Mon, 26 Jul 2021 00:08 UTC

On 25/07/2021 23:42, Ben Bacarisse wrote:
> Mike Terry <news.dead.person.stones@darjeeling.plus.com> writes:
>
>> On 25/07/2021 21:28, Mike Terry wrote:
>> Pressed Send too soon. :(
>>> On 25/07/2021 18:40, Malcolm McLean wrote:
>>>> On Sunday, 25 July 2021 at 17:14:20 UTC+1, Mike Terry wrote:
>>>>>
>>>>> I think this is all a bit like Malcolm suggesting that PO is raising
>>>>> "interesting ideas" that might be useful with more study, or that some
>>>>> basic idea of PO's is "really quite clever...". It is NOT. PO has no
>>>>> incling of those possibilities and really no interest in them. He is
>>>>> simply saying things he naively thinks are true, without any logical
>>>>> reasoning going on. No cleverness at all. He is not "performing a
>>>>> magic trick", where he will pull a rabit out of a hat - he genuinely
>>>>> believes he is refuting the Linz proof, no tricks. Pretending otherwise
>>>>> may be being nice to PO, making him feel better, but is ultimately
>>>>> unhelpful IMO. I'd say it seems like "dishonest niceness" to me. (But
>>>>> maybe Malcolm really thinks PO is producing worthwhile results, or is on
>>>>> the path to that, in which case it's just being "actually nice"!)
>>>>>
>>>> I've always been very clear that I haven't yet seen from PO anything that
>>>> constitutes a refutation of Linz. However when we have, for example, the
>>>> "H is the operating system" ruse, I do tend to say "that's a clever cheat"
>>>> rather than "how could you make such a simple and obvious error?".
>>>> Largely because it's a nicer way of conveying essentially the same
>>>> information.
>>>>
>>>> I did say recently that PO had constructed his own paradox. It's this. If
>>>> H is  simulating halt decider, and is called on H, it creates a series of
>>>> nested recursions. If it doesn't detect the situation, it never halts. If
>>>> it does detect the situation and terminates the simulations, it halts.
>>>> However if it halts, the nested recursions were not infinite.
>>> Right, that's a bit like something I pointed out to PO last year.  Such
>>> an emulation-based (putative) decider may have a number of tests in its stepping loop.  Some may be /sound/, like a properly implemented
>>> tight-loop test, or a test might be unsound in that it incorrectly decides halting for a non-halting input or vice-versa.  The sound tests
>>> might match and make correct decisions when examining particular inputs, BUT it's sort of weird that the when H examines (P,P), the /sound/ tests
>>> "mysteriously" never ever match!  The only tests that will ever match are those that are unsound...  If there are /only/ sound tests in the
>>> loop, none of them will match and H(P,P) will never make its decision and halt!  Of course that would disqualify H as a decider.
>>> This applies for PO and his "detecting infinite recursions" test,
>>> however much he believes his test to be sound...  I've told him that a reviewer will
>>
>> ...expect to see a /proof/ of the soundness of any test in his loop,
>> if he's going to expect them to take matching of the test as
>> /evidence/ of halting status. (Of course PO can't deliver such a
>> proof.)
>
> Right. And very well put. But he's abandoned almost all pretence at
> dealing with halting. What makes a sound test has been defined to be
> what H does. This is the "adapted" criterion for halting. Not halting,
> but whatever it is he chooses to put into H. When he says that its
> "impossibly incorrect" (if that's the term, I try to forget such things)
> this is what he means.

Perhaps the root problem is that PO REALLY REALLY REALLY believes his
"infinite recursive behaviour" test is sound, for whatever reason. I
mean that his intuition that it is sound is AS STRONG OR STRONGER than
his recent understanding that a machine which runs and transitions into
a halt state is a halting computation.

So he has an example where both
(a) the computation P(P) undeniably reaches a halt state (so is halting)
(b) his test in H(P,P) matches the computation when it runs!!!!!!! so it
is UNDENIABLY "exhibiting infinite recursion" (WTM)

Both principles are equally believed by PO, so both conclusions MUST be
correct! A "paradox"!!! P(P) halts, and yet it exhibits infinite
recursion and so "cannot halt", even though it does. What to do?!

For 99.99999% of people, there would be no dilemma here. Presented with
(a), which is /the definition/ of halting as used in HP proofs, and
given that (b) was an intuition for which they had /no proof/ of its
correctness, the conclusion would be: (a) is correct, so the test in (b)
hasn't worked for some reason. It is unsound.

And 99.3% of those people would be capable of resolving this - they'd
track through the computation in (a), using it to pin down where they
went astray in intuition (b). End of story.

All his recent posts seem to focus on a mixture of one or two totally
banal claims (along the lines of "a computation which never reaches one
of its halt states is a non-halting computation" (LOL), followed by a
bogus claim like "my trace UNDENIABLY proves that the test in (b)
MATCHED!!!!!! and any software engineer who understands x86 will confirm
this - THEREFORE non-halting behaviour HAS been detected so non-halting
is the right answer." (Well, that's what you said with "halting is what
H does", and I've rephrased it for you in 200 words for no real benefit
hehe.)

I don't see any more than that going on - an absolute faith in the
correctness of his unsound (b) test, although he must realise he can't
prove it is sound. I guess he really thinks reviewers will accept it as
obvious, and everybody here is just stupid or deliberately lying due to
being "in rebuttal mode".

Mike.

Re: Black box halt decider is NOT a partial decider

<H5oLI.18251$Ei1.16627@fx07.iad>

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https://www.novabbs.com/devel/article-flat.php?id=18936&group=comp.theory#18936

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Subject: Re: Black box halt decider is NOT a partial decider
Newsgroups: comp.theory
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From: Rich...@Damon-Family.org (Richard Damon)
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Date: Sun, 25 Jul 2021 18:20:39 -0700
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 by: Richard Damon - Mon, 26 Jul 2021 01:20 UTC

On 7/25/21 5:08 PM, Mike Terry wrote:
> On 25/07/2021 23:42, Ben Bacarisse wrote:
>> Mike Terry <news.dead.person.stones@darjeeling.plus.com> writes:
>>
>>> On 25/07/2021 21:28, Mike Terry wrote:
>>> Pressed Send too soon. :(
>>>> On 25/07/2021 18:40, Malcolm McLean wrote:
>>>>> On Sunday, 25 July 2021 at 17:14:20 UTC+1, Mike Terry wrote:
>>>>>>
>>>>>> I think this is all a bit like Malcolm suggesting that PO is raising
>>>>>> "interesting ideas" that might be useful with more study, or that
>>>>>> some
>>>>>> basic idea of PO's is "really quite clever...". It is NOT. PO has no
>>>>>> incling of those possibilities and really no interest in them. He is
>>>>>> simply saying things he naively thinks are true, without any logical
>>>>>> reasoning going on. No cleverness at all. He is not "performing a
>>>>>> magic trick", where he will pull a rabit out of a hat - he genuinely
>>>>>> believes he is refuting the Linz proof, no tricks. Pretending
>>>>>> otherwise
>>>>>> may be being nice to PO, making him feel better, but is ultimately
>>>>>> unhelpful IMO. I'd say it seems like "dishonest niceness" to me. (But
>>>>>> maybe Malcolm really thinks PO is producing worthwhile results, or
>>>>>> is on
>>>>>> the path to that, in which case it's just being "actually nice"!)
>>>>>>
>>>>> I've always been very clear that I haven't yet seen from PO
>>>>> anything that
>>>>> constitutes a refutation of Linz. However when we have, for
>>>>> example, the
>>>>> "H is the operating system" ruse, I do tend to say "that's a clever
>>>>> cheat"
>>>>> rather than "how could you make such a simple and obvious error?".
>>>>> Largely because it's a nicer way of conveying essentially the same
>>>>> information.
>>>>>
>>>>> I did say recently that PO had constructed his own paradox. It's
>>>>> this. If
>>>>> H is  simulating halt decider, and is called on H, it creates a
>>>>> series of
>>>>> nested recursions. If it doesn't detect the situation, it never
>>>>> halts. If
>>>>> it does detect the situation and terminates the simulations, it halts.
>>>>> However if it halts, the nested recursions were not infinite.
>>>> Right, that's a bit like something I pointed out to PO last year.  Such
>>>> an emulation-based (putative) decider may have a number of tests in
>>>> its stepping loop.  Some may be /sound/, like a properly implemented
>>>> tight-loop test, or a test might be unsound in that it incorrectly
>>>> decides halting for a non-halting input or vice-versa.  The sound tests
>>>> might match and make correct decisions when examining particular
>>>> inputs, BUT it's sort of weird that the when H examines (P,P), the
>>>> /sound/ tests
>>>> "mysteriously" never ever match!  The only tests that will ever
>>>> match are those that are unsound...  If there are /only/ sound tests
>>>> in the
>>>> loop, none of them will match and H(P,P) will never make its
>>>> decision and halt!  Of course that would disqualify H as a decider.
>>>> This applies for PO and his "detecting infinite recursions" test,
>>>> however much he believes his test to be sound...  I've told him that
>>>> a reviewer will
>>>
>>> ...expect to see a /proof/ of the soundness of any test in his loop,
>>> if he's going to expect them to take matching of the test as
>>> /evidence/ of halting status.  (Of course PO can't deliver such a
>>> proof.)
>>
>> Right.  And very well put.  But he's abandoned almost all pretence at
>> dealing with halting.  What makes a sound test has been defined to be
>> what H does.  This is the "adapted" criterion for halting.  Not halting,
>> but whatever it is he chooses to put into H.  When he says that its
>> "impossibly incorrect" (if that's the term, I try to forget such things)
>> this is what he means.
>
> Perhaps the root problem is that PO REALLY REALLY REALLY believes his
> "infinite recursive behaviour" test is sound, for whatever reason.  I
> mean that his intuition that it is sound is AS STRONG OR STRONGER than
> his recent understanding that a machine which runs and transitions into
> a halt state is a halting computation.
>
> So he has an example where both
> (a) the computation P(P) undeniably reaches a halt state (so is halting)
> (b) his test in H(P,P) matches the computation when it runs!!!!!!! so it
>     is UNDENIABLY "exhibiting infinite recursion" (WTM)
>
> Both principles are equally believed by PO, so both conclusions MUST be
> correct!  A "paradox"!!!  P(P) halts, and yet it exhibits infinite
> recursion and so "cannot halt", even though it does.  What to do?!
>
> For 99.99999% of people, there would be no dilemma here.  Presented with
> (a), which is /the definition/ of halting as used in HP proofs, and
> given that (b) was an intuition for which they had /no proof/ of its
> correctness, the conclusion would be: (a) is correct, so the test in (b)
> hasn't worked for some reason.  It is unsound.
>
> And 99.3% of those people would be capable of resolving this - they'd
> track through the computation in (a), using it to pin down where they
> went astray in intuition (b).  End of story.
>
> All his recent posts seem to focus on a mixture of one or two totally
> banal claims (along the lines of "a computation which never reaches one
> of its halt states is a non-halting computation" (LOL), followed by a
> bogus claim like "my trace UNDENIABLY proves that the test in (b)
> MATCHED!!!!!! and any software engineer who understands x86 will confirm
> this - THEREFORE non-halting behaviour HAS been detected so non-halting
> is the right answer."  (Well, that's what you said with "halting is what
> H does", and I've rephrased it for you in 200 words for no real benefit
> hehe.)
>
> I don't see any more than that going on - an absolute faith in the
> correctness of his unsound (b) test, although he must realise he can't
> prove it is sound.  I guess he really thinks reviewers will accept it as
> obvious, and everybody here is just stupid or deliberately lying due to
> being "in rebuttal mode".
>
> Mike.
>

My impression is that PO doesn't REALLY care about the Halting Problem
per se, only what it is used for in other proofs.

His REAL conviction it the concept that ALL Truth is Provable, and not
just as a form of logic system, but as an absolute truth.

He has probably seen too many simple proofs that show that because it
can be proved simply that we can't always prove if a given machine halts
or not, but it definitely does, so we have an unprovavle truth, so he
wants to damage the proof of this enough that he can argue that we can
call anything not provable as not really true or false.

He doesn't seem capable of forming a real proof, so he just falls back
to rhetorical arguments. Not understanding the real nature of proofs, he
seem to think that by showing an argument that something HAS to be wrong
with the wording of the actual halting problem, it allows him to propose
his alternate definition, that somehow no one else has ever thought to
do (maybe because this method of argument is unsound).

I think he honestly thinks that he has established that because we can't
come up with an answer that H can give, that because all Truth is
provalble, we MUST be allowed to cha
nge the question to something sort of the same that it can answer.

I don't think he has anywhere near enough of a basis in real logic
theory to be able to understand the implications of what he is saying,
remember he PRIDES himself for not being 'book learned' and thus
'brainwashed' into knowing that what he thinks is impossible.

He as basically condemended himself into committing all the errors of
the pass, and for any of them, he doesn't know enough that he has
actually ran into a problem.

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