On 5/19/2021 9:42 PM, André G. Isaak wrote:
> On 2021-05-19 20:21, olcott wrote:
>> On 5/19/2021 8:57 PM, André G. Isaak wrote:
>>> On 2021-05-19 19:08, olcott wrote:
>>>> On 5/19/2021 7:56 PM, André G. Isaak wrote:
>>>>> On 2021-05-19 18:48, olcott wrote:
>>>>>> On 5/19/2021 7:35 PM, André G. Isaak wrote:
>>>>>>> On 2021-05-19 18:31, olcott wrote:
>>>>>>>> On 5/19/2021 7:19 PM, André G. Isaak wrote:
>>>>>>>>> On 2021-05-19 18:04, olcott wrote:
>>>>>>>>>> On 5/19/2021 6:50 PM, André G. Isaak wrote:
>>>>>>>>>>> On 2021-05-19 17:12, olcott wrote:
>>>>>>>>>>>> On 5/19/2021 6:04 PM, André G. Isaak wrote:
>>>>>>>>>>>>> On 2021-05-19 16:28, olcott wrote:
>>>>>>>>>>>>>> On 5/19/2021 5:16 PM, André G. Isaak wrote:
>>>>>>>>>>>>>>> On 2021-05-19 13:53, olcott wrote:
>>>>>>>>>>>>>>>> On 5/19/2021 2:47 PM, André G. Isaak wrote:
>>>>>>>>>>>>>>>>> On 2021-05-19 11:29, olcott wrote:
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> Truism(1)
>>>>>>>>>>>>>>>>>> Input: [Ĥ] to Ĥ([Ĥ]) would never halt unless is
>>>>>>>>>>>>>>>>>> simulation is aborted.
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> How is that a 'truism'?
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> Since we know that H_Hat(H_Hat) does in fact halt as
>>>>>>>>>>>>>>>>> evidenced by how it behaves when *not* run in a
>>>>>>>>>>>>>>>>> modified simulator, this would better be described as a
>>>>>>>>>>>>>>>>> 'falsism'.
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> Stopping at first big mistake.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> That wasn't a mistake.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> Do you agree that the definition of the Linz Ĥ on page 319
>>>>>>>>>>>>>>>> http://www.liarparadox.org/Peter_Linz_HP(Pages_315-320).pdf
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> Yes. I agree with the Linz definition.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> would specify infinitely nested simulation to the
>>>>>>>>>>>>>>>> internal halt
>>>>>>>>>>>>>>>> decider of Linz Ĥ @Ĥq0  wM  wM  (the second q0 start
>>>>>>>>>>>>>>>> state of Ĥ)
>>>>>>>>>>>>>>>> when this internal halt decider is based on simulating
>>>>>>>>>>>>>>>> its input?
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> No, I don't agree with the above because it makes no
>>>>>>>>>>>>>>> sense. Please rephrase it without using the word 'would'.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> André
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Ĥ.q0  wM  ⊢*  Ĥ.qx  wM  wM  ⊢*  Ĥ.qy  ∞
>>>>>>>>>>>>>> Ĥ.q0  wM  ⊢*  Ĥ.qx  wM  wM  ⊢*  Ĥ.qn
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> There are no conditions such that the input [Ĥ] to Ĥ([Ĥ])
>>>>>>>>>>>>>> halts besides the condition that the internal halt decider
>>>>>>>>>>>>>> @ Ĥ.qx terminates its simulation of [Ĥ].
>>>>>>>>>>>>>
>>>>>>>>>>>>> And so what?
>>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> Agreement or not?
>>>>>>>>>>>
>>>>>>>>>>> Why didn't you just read the remainder of my post where I
>>>>>>>>>>> explained my position. I said that if H_Hat(H_Hat) didn't
>>>>>>>>>>> terminate the simulation of its input, then it would be an
>>>>>>>>>>> _entirely different_ computation
>>>>>>>>>>
>>>>>>>>>> In the freaking hypothetical instance where the embedded copy
>>>>>>>>>> of H @ Ĥ.qx never terminates the simulation of its input [Ĥ]
>>>>>>>>>> would this simulation ever terminate?
>>>>>>>>>>
>>>>>>>>>> We can go at the 1,000 times if that what it takes.
>>>>>>>>>> We do not move forward until we have mutual agreement.
>>>>>>>>>
>>>>>>>>> I can't agree to something which is wrong.
>>>>>>>>>
>>>>>>>>> That 'hypothetical instance' doesn't exist unless we change H
>>>>>>>>> to an entirely different computation. It's no different from
>>>>>>>>> asking about the hypothetical instance where sqrt(9) returns 4.
>>>>>>>>>
>>>>>>>>> André
>>>>>>>>>
>>>>>>>>
>>>>>>>> It is not like this at all. It is mathematically projecting
>>>>>>>> execution trace of different encodings of an algorithm on the
>>>>>>>> same input.
>>>>>>>
>>>>>>> What does 'different encodings of an algorithm' mean in this
>>>>>>> context?
>>>>>>
>>>>>> The exact same algorithm, except non-halting inputs are not
>>>>>> aborted, that line-of-code is commented out.
>>>>>
>>>>> That's not a 'different encoding of an algorithm'. That is a
>>>>> different algorithm altogether.
>>>>
>>>> Do you agree that the definition of the Linz Ĥ on page 319
>>>> http://www.liarparadox.org/Peter_Linz_HP(Pages_315-320).pdf
>>>>
>>>> specifies infinitely nested simulation to the internal halt
>>>> decider of Linz Ĥ @Ĥq0 wM wM (the second q0 start state of Ĥ)
>>>> when this internal copy of H is based on simulating its input and it
>>>> does not abort the simulation of this input?
>>>
>>> Why exactly do you think that if you ask the same question over and
>>> over again that my answer is going to change?
>>>
>>> André
>>>
>>
>> I changed the question. If I have to change the words to get mutual
>> agreement I will and I did. We cannot move to any other steps of the
>> conversation until we have mutual agreement on the now changed wording.
>
> Linz's H_Hat is defined in relation to H. So if you consider a program
> where the 'internal H' does not abort the simulation of this input',
> then you are no longer talking about H_Hat, but about some other
> computation, in which case you can not call it H_Hat nor make inferences
> about H_Hat based on it.
>
> André
>

Truism(1a)
The simulation of [Ĥ] by its simulating halt decider Ĥ would never halt
unless this simulation is aborted.

Truism(1b)
(1a) is another way of saying that when the copy of H at Ĥ.qx only
simulates its input [Ĥ] its input never halts.

On 5/19/2021 9:43 PM, Ben Bacarisse wrote:
> olcott <NoOne@NoWhere.com> writes:
>
>> On 5/19/2021 7:56 PM, André G. Isaak wrote:
>>> On 2021-05-19 18:48, olcott wrote:
>>>> On 5/19/2021 7:35 PM, André G. Isaak wrote:
>
>>>>> What does 'different encodings of an algorithm' mean in this context?
>>>>
>>>> The exact same algorithm, except non-halting inputs are not aborted,
>>>> that line-of-code is commented out.
>>>
>>> That's not a 'different encoding of an algorithm'. That is a
>>> different algorithm altogether.
>>
>> Do you agree that the definition of the Linz Ĥ on page 319
>> http://www.liarparadox.org/Peter_Linz_HP(Pages_315-320).pdf
>>
>> specifies infinitely nested simulation to the internal halt
>> decider of Linz Ĥ @Ĥq0 wM wM (the second q0 start state of Ĥ)
>> when this internal copy of H is based on simulating its input and it
>> does not abort the simulation of this input?
>
> Part of the trouble is you don't know how to say what you mean. You may
> be asking for people to confirm something rather un-contentious, but you
> phrase it so badly, and so ambiguously, that they can't agree.
>
> The H^ you refer to should be called UTM^. It is a simulator (a perfect
> one) to which Linz's hat construction has been applied. That's what
> Halts with line 15 commented out is -- just a simulator. You want the
> world to confirm that UTM^([UTM^]) is a non-halting computation, which
> can be seen as having infinitely nested simulations.
>

You do seem to know the computer science of this the best and can
greatly improve the quality of my wording. (see 1b).

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

Truism(1a)
The simulation of: ([Ĥ][Ĥ]) by the simulating halt decider @ Ĥ.qx would
never halt unless Ĥ.qx aborts this simulation.

Truism(1b)
(1a) is another way of saying that simulation of: ([Ĥ][Ĥ]) by a UTM @
Ĥ.qx would never halt.

Unless and until people understand that (1a) is a paraphrase of (1b) we
cannot move to truism(2).

> This is obviously the case, but the clarity that comes from putting it
> like this is the last thing you want. You want to muddle together your
> two computations -- the one that really is non-halting (UTM^([UTM^]))
> with the one that halts and Halts gets wrong. That's why you talk about
> "the definition of the Linz H^" when you don't mean that at all. That's
> why you talk about "a different encoding of an algorithm" so it sounds
> like just the one.
>
> You should never, ever use H or H^ while talking about Linz unless you
> want to refer to a non-existent, hypothetical halt decider.
>
> Call your partial decider that simulates until the silly-non-halting
> pattern is detected P. P^([P^]) might have nested simulations, but you
> tell us that they are not infinite, because the silly-non-halting
> pattern is seen.
>
> P(<[P^], [P^]>) rejects which is obviously the wrong answer for the
> halting problem, but it's the right answer for the silly-non-halting
> problem because P is specified to report based on what UTM^([UTM^])
> does, not what P^([P^]) does.
>

--
Copyright 2021 Pete Olcott

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

On 5/20/2021 7:00 AM, Andy Walker wrote:
> On 20/05/2021 05:56, Jeff Barnett wrote:> [...] I assure you that
>> trying to say the same thing to him for the 579th time will have the
>> same effect as the first 578 tries. Saying something new wont do much
>> either.
>> PS this message is for all of us klutzes who have tried to improve
>> Pete. To tailor this message to your self, substitute your personal
>> version of 579 in the above paragraph.
>
>     Personally, I've tried very hard, and only occasionally failed,
> to say things to Pete only once.  It's a personal opinion, but I think
> this group would be much improved if "us klutzes" limited ourselves to
> one response each to Pete per day.  Ironically, such self-denial would
> probably even enable better progress to be made, as Pete would have
> some 40 fewer articles to "write" each day, and could use the extra 20
> minutes per day to improve his programs/experience/style/....
>

It is getting down to the point where at even one response per person
per day I will have unequivocally proved my point in less than 30 days
to everyone that would not dishonestly deny the truth.

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

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

Any high school student would be able to analyze the *basic logic of the
above* and know that it is correct very easily.

*Basic logic of the above*
If X is the only cause of Y and not X then not Y.

X = H stops simulating P
Y = The simulation of P stops

~X = H never stops simulating P
~Y = The simulation of P never stops

Denying the truth of the above would certainly look quite foolish.

--
Copyright 2021 Pete Olcott

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

On 5/20/2021 6:10 PM, Mike Terry wrote:
> On 20/05/2021 13:00, Andy Walker wrote:
>> On 20/05/2021 05:56, Jeff Barnett wrote:> [...] I assure you that
>>> trying to say the same thing to him for the 579th time will have the
>>> same effect as the first 578 tries. Saying something new wont do much
>>> either.
>>> PS this message is for all of us klutzes who have tried to improve
>>> Pete. To tailor this message to your self, substitute your personal
>>> version of 579 in the above paragraph.
>>
>>      Personally, I've tried very hard, and only occasionally failed,
>> to say things to Pete only once.  It's a personal opinion, but I think
>> this group would be much improved if "us klutzes" limited ourselves to
>> one response each to Pete per day.  Ironically, such self-denial would
>> probably even enable better progress to be made, as Pete would have
>> some 40 fewer articles to "write" each day, and could use the extra 20
>> minutes per day to improve his programs/experience/style/....
>>
>
> For me, the problem isn't so much the number of replies, it's more with
> the repetition of the same arguments over and over.
>
> PO will post something or other, and since November(ish) last year
> pretty much NOTHING he has posted has added anything!  Someone thinks
> "PO has said something wrong - I must correct it to protect the
> innocence of virgin newsgroup readers who could be corrupted.  Yes, I've
> said this before MANY times, but now I've no choice but to say it all
> again.  The innocent MUST be protected!"  [*]
>
> The problem with this is that if they do point out mistakes, PO WILL
> just respond with MORE WORDS - probably just some repetition of previous
> claims (sometimes not even related to OP).  And his reposted claims of
> course will repeat previous errors, so they will still feel obliged to
> post again.  ...And the cycle continues guaranteeing every PO thread
> will be a (potentially) infinite thread, with essentially zero content.
>
> I've wondered /why/ arguing with PO always goes like this?  Why doesn't
> PO see his mistakes, or see the simple correctness of other peoples
> reasoning?  I believe PO has some deficiency which renders him INCAPABLE
> of pretty much any form of higher ABSTRACT REASONING!  This sounds
> rather nasty, like I'm just insulting him, but I'm not interested in
> that.  If PO /really/ can't handle "abstract reasoning" that would be an
> awful life handicap, right?  Such a person would:
>
> a)  be incapable of (correctly) understanding the concepts underlying
>     most academic fields like CS, logic, mathematics, AI, and so on.
> b)  be incapable of following other people's reasoned arguments,
>     because those arguments have a starting point he lacks (concepts,
>     definitions, notations used) and proceed by /logical steps/
>     where correctness of conclusion genuinely follows from the
>     correctness of starting points.  Forget it - all waaaay too
>     abstract!
> c)  similarly be incapable of presenting their own /reasoned/
>     arguments [aka proofs].  Probably they just wouldn't understand
>     why academics write day-to-day proofs, or what one needed to look
>     like.  Perhaps they would genuinely see no difference between
>     their own repeated claims and other people's properly reasoned
>     arguments?
>
> So... such a person's claims aren't going to based on /reasoning/.  They
> will effectively be child-like /intuitions/ - first thoughts on a
> subject which they /believe/ should be true.  We all grow up with those,
> but then we go to school and learn abstract stuff which enables us to
> see the problems with our naive intuitions and we /learn/ new (better)
> stuff and make progress.  A person unable to engage with abstract ideas
> would be more or less stuck with those starting intuitions for life! And
> their arguments and proofs could only consist of statements and
> restatements of those intuitions, although for them that would probably
> be indistinguishable from what they see others doing when they "prove"
> stuff...
>
> Well, to my mind, everything above describes PO, harsh though that
> sounds.  "Arguing" with PO endlessly is (IMO) pointless, not only
> because it's all been said before many times and becomes time consuming
> and boring, but also because:
>
> -  He won't be able to follow any logical reasoning you present!  He
>    won't even understand the starting points.  It's all just
>    too abstract.
>
> -  His position is not based on /reasoning/, so will not be
>    changed by careful abstract reasoning, however thoroughly
>    people believe they are presenting those ideas.  The more
>    time spent on carefully arguing some subtle point and explaining
>    basic concepts underlying the ideas, the more likely PO will just
>    blank the whole thing.  (We've all seen that personally many
>    times, right?  Time thrown out the window!)
>
> -  PEOPLE HERE ALREADY UNDERSTANDS PO'S MISTAKES 'SUFFICIENTLY'.
>    I mean, sufficiently to understand why he has not proved his
>    claims (and never will), and sufficiently to satisfy natural
>    curiosity over where after all these years the
>    basic error will occur; the HP proof is after all not
>    complicated, and to start with everyone wants to know where
>    on earth PO has become confused!  I'd say those places became
>    clear by last Christmas, and nothing
>    significant has happened since!  :)
>
>
> CONCLUSION: I'm all behind your (Andy/Jeff's) suggestions, but I'd go
> further to suggest NEVER REPEATING THE SAME ARGUMENTS TO PO MORE THAN [A
> COUPLE] OF TIMES.  (Well, everyone will have their own threshold for
> that!  But 379 is too high.)
>
> But what to do when PO just repeats back previous claims with the same
> repeated errors, AS HE UNDOUBTABLY WILL?  This is tricky for someone
> believing it's their moral duty to protect the internet from untruth!
> :)  My suggestion would be to either
>
> a)  Ignore him.  [I suspect he will be more determined than you to
>     not be seen to be "defeated" by not replying - but that's an
>     illusion in the end - posting last doesn't mean you've "won",
>     anything, does it?]
>
> b)  I've tried replying, but with just a general notice rather than
>     repeating details of all PO errors - something like "Now you
>     are just repeating previous claims without actually addressing
>     any or my points.  Problems with those claims have been pointed
>     out many times by posters here - check the previous
>     posts if you're interested."
>
>     The point is this does not give a natural target for PO follow
>     up, and the subthread dies out.  Even if PO tries
>     his usual trick and responds with a generic repost of claims,
>     this way it lacks the illusion he aims for, namely that he's
>     engaged in an actual academic debate and is "dealing" with
>     all objections raised, so he must be right!  It comes across
>     more clearly as PO rehashing old stuff that has already been
>     dealt with, if PO could only understand that.
>
> I did actually try (b) for a while, and it worked in the local
> subthread, but it made little difference globally because it only takes
> one or two people to be in "always point out exactly what's wrong in the
> previous PO post" mode to send the thread into the PO
> potentially-infinite-thread pattern.
>
> [*]  Hey, eveyone can tell I don't hold with the "got to protect
> innocent Usenet virgins from untruths told on comp.theory" idea, right?
> I mean, who tells their children "go on the internet and hunt around in
> the unmoderated Usenet technical groups - for sure everything said there
> is true, you can stake your pensions on that!" ?   :)
>
>
> Mike.
>

Infinitely Recursive input on HP Proofs
peteolcott comp.theory Mar 11, 2017, 3:13:03 PM

Every time that I respond to any rebuttal people are so sure that I must
be wrong that they never notice that my response is subtly different
than the prior one. They merely spout off the same canned rebuttal.

The following is enormously different than its fundamental basis that I
posted more than four years ago (see above):

On 5/20/2021 8:29 PM, Kaz Kylheku wrote:
> On 2021-05-21, olcott <NoOne@NoWhere.com> wrote:
>> On 5/20/2021 6:52 PM, Kaz Kylheku wrote:
>>> On 2021-05-20, olcott <NoOne@NoWhere.com> wrote:
>>>> On 5/20/2021 11:54 AM, Kaz Kylheku wrote:
>>>>> On 2021-05-20, olcott <NoOne@NoWhere.com> wrote:
>>>>>> On 5/20/2021 7:13 AM, Ben Bacarisse wrote:
>>>>>>> olcott <NoOne@NoWhere.com> writes:
>>>>>>>
>>>>>>>> You do seem to know the computer science of this the best and can
>>>>>>>> greatly improve the quality of my wording. (see 1b).
>>>>>>>>
>>>>>>>> Ĥ.q0 wM ⊢* Ĥ.qx wM wM ⊢* Ĥ.qy ∞
>>>>>>>> Ĥ.q0 wM ⊢* Ĥ.qx wM wM ⊢* Ĥ.qn
>>>>>>>>
>>>>>>>> Truism(1a)
>>>>>>>> The simulation of: ([Ĥ][Ĥ]) by the simulating halt decider @ Ĥ.qx
>>>>>>>> would never halt unless Ĥ.qx aborts this simulation.
>>>>>>>>
>>>>>>>> Truism(1b)
>>>>>>>> (1a) is another way of saying that simulation of: ([Ĥ][Ĥ]) by a UTM @
>>>>>>>> Ĥ.qx would never halt.
>>>>>>>>
>>>>>>>> Unless and until people understand that (1a) is a paraphrase of (1b)
>>>>>>>> we cannot move to truism(2).
>>>>>>>
>>>>>>> You are abusing names and language. Use different names for different
>>>>>>> machines and you can be quite clear. Stop saying what would happen
>>>>>>> unless. TM's are what they are. I am inclined to stop future replies
>>>>>>> at the first "would .. unless".
>>>>>>>
>>>>>>
>>>>>> "Unless" of (1a) is merely the English word for a conditional statement
>>>>>> in a program.
>>>>>>
>>>>>> The above does not specify two machines. In the purely hypothetical case
>>>>>> where Ĥ.qx did not stop simulating its input then in this purely
>>>>>> hypothetical case the behavior of its input would be the same as if the
>>>>>> partial halt decider @ Ĥ.qx was replaced by a UTM.
>>>>>
>>>>> You must not replace anything but anything, unless you can prove they
>>>>> are absolutely equivalent.
>>>>>
>>>>> If you replace any component C of some entity E with something not
>>>>> equivalent to C, then you no longer have E. You have E2 or E'.
>>>>>
>>>>> If you use the same name for both objects, you're equivocating;
>>>>> you wrongly make arguments which say that properties that can be deduced
>>>>> about E2 are those of E.
>>>>>>
>>>>>> Any high school student would be able to analyze the basic logic of the
>>>>>> above and know that it is correct very easily.
>>>>>>
>>>>>> If X is the only cause of Y and not X then not Y.
>>>>>
>>>>> The probelm is that X does not happen.
>>>>
>>>> In other words you are disingenuously denying a tautology that is
>>>> obviously correct to any high school student by dancing around it with
>>>> with irrelevancies.
>>>
>>> No, you're too daft to understand that I'm mot deying it at all.
>>> I'm saying that it contains a vacuous truth that can just be
>>> removed. Since X does not happen for the given H, then "unless X" can
>>> (and should!) be exised from your tautology.
>>>
>>>> It is as if you are saying that it is utterly impossible to determine
>>>> the execution trace of any segment of code without actually running this
>>>> code.
>>>>
>>>>> If X is "detecting nested
>>>>> simulation" and Y is "discontinuing simulation", then this is
>>>>> is a vacuous truth, in the context of a decider which doesn't do any
>>>>> such detection.
>>>>>
>>>>> That's the problem; not that the logic is wrong, but that it's a
>>>>> useless, vacuous truth.
>>>>>
>>>>
>>>> If X is the only cause of Y and not X then not Y.
>>>
>>> Since we know what the value is of X, we can just substitute that
>>> value into the tautology, which then no longer mentions X.
>>>
>>
>> I have improved the wording of this since my prior reply to you.
>>
>>
>>
>> This halt deciding principle overcomes the pathological self-reference
>> error of the halting theorem:
>>
>> (A) Every simulation of input P that never halts unless simulating halt
>> decider H stops simulating it <is> a non-halting computation. This
>> remains true even after H stops simulating P.
>
> This is not an improvement. The specific decider H from the Linz
> context is one that /does not/ stop simulations (unless they terminate
> spontaneously).
>
> "unless H stops simulating, Y" is the same as "unless False, Y",
> which is just "Y".
>
> I think what you want is something like:
>
> for every possibl simulating decider D:
> for every machine I:
> - if the simulation of I will not stop unless D aborts it; and
> - if D's abort decision is correctly made;
> then:
> - I specifies a non-halting computation
>

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

> Now we need that "unless" part because we're generalizing over deciders,
> many of which can potentially identify various execution patterns and
> make abort decisions.
>
> In the specific case of H, this generalization is still true; however H
> does not recognize any execution patterns and does not abort anything;
> it just simulates. Therefore under H, a non-halting I is never
> identified as such.
>
> H cannot be altered in any way. Any decider decider that is not H is not
> called H.
>
> Ĥ embeds H, and also cannot be altered.
>
> In accordance with the above general "truism" that is universally
> quantified over deciders using the variable D, you can find another
> decider different from H, call it H2 such that H2(Ĥ, Ĥ) denotes a
> simulation which stops, and reports that Ĥ is non-halting.
>
> That doesn't refute any halting proof, though. The proof relies on the
> fact that H cannot do what H2 can do.
>

--
Copyright 2021 Pete Olcott

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

On 5/20/2021 10:21 PM, Kaz Kylheku wrote:
> On 2021-05-21, olcott <NoOne@NoWhere.com> wrote:
>> On 5/20/2021 8:29 PM, Kaz Kylheku wrote:
>>> On 2021-05-21, olcott <NoOne@NoWhere.com> wrote:
>>>> On 5/20/2021 6:52 PM, Kaz Kylheku wrote:
>>>>> On 2021-05-20, olcott <NoOne@NoWhere.com> wrote:
>>>>>> On 5/20/2021 11:54 AM, Kaz Kylheku wrote:
>>>>>>> On 2021-05-20, olcott <NoOne@NoWhere.com> wrote:
>>>>>>>> On 5/20/2021 7:13 AM, Ben Bacarisse wrote:
>>>>>>>>> olcott <NoOne@NoWhere.com> writes:
>>>>>>>>>
>>>>>>>>>> You do seem to know the computer science of this the best and can
>>>>>>>>>> greatly improve the quality of my wording. (see 1b).
>>>>>>>>>>
>>>>>>>>>> Ĥ.q0 wM ⊢* Ĥ.qx wM wM ⊢* Ĥ.qy ∞
>>>>>>>>>> Ĥ.q0 wM ⊢* Ĥ.qx wM wM ⊢* Ĥ.qn
>>>>>>>>>>
>>>>>>>>>> Truism(1a)
>>>>>>>>>> The simulation of: ([Ĥ][Ĥ]) by the simulating halt decider @ Ĥ.qx
>>>>>>>>>> would never halt unless Ĥ.qx aborts this simulation.
>>>>>>>>>>
>>>>>>>>>> Truism(1b)
>>>>>>>>>> (1a) is another way of saying that simulation of: ([Ĥ][Ĥ]) by a UTM @
>>>>>>>>>> Ĥ.qx would never halt.
>>>>>>>>>>
>>>>>>>>>> Unless and until people understand that (1a) is a paraphrase of (1b)
>>>>>>>>>> we cannot move to truism(2).
>>>>>>>>>
>>>>>>>>> You are abusing names and language. Use different names for different
>>>>>>>>> machines and you can be quite clear. Stop saying what would happen
>>>>>>>>> unless. TM's are what they are. I am inclined to stop future replies
>>>>>>>>> at the first "would .. unless".
>>>>>>>>>
>>>>>>>>
>>>>>>>> "Unless" of (1a) is merely the English word for a conditional statement
>>>>>>>> in a program.
>>>>>>>>
>>>>>>>> The above does not specify two machines. In the purely hypothetical case
>>>>>>>> where Ĥ.qx did not stop simulating its input then in this purely
>>>>>>>> hypothetical case the behavior of its input would be the same as if the
>>>>>>>> partial halt decider @ Ĥ.qx was replaced by a UTM.
>>>>>>>
>>>>>>> You must not replace anything but anything, unless you can prove they
>>>>>>> are absolutely equivalent.
>>>>>>>
>>>>>>> If you replace any component C of some entity E with something not
>>>>>>> equivalent to C, then you no longer have E. You have E2 or E'.
>>>>>>>
>>>>>>> If you use the same name for both objects, you're equivocating;
>>>>>>> you wrongly make arguments which say that properties that can be deduced
>>>>>>> about E2 are those of E.
>>>>>>>>
>>>>>>>> Any high school student would be able to analyze the basic logic of the
>>>>>>>> above and know that it is correct very easily.
>>>>>>>>
>>>>>>>> If X is the only cause of Y and not X then not Y.
>>>>>>>
>>>>>>> The probelm is that X does not happen.
>>>>>>
>>>>>> In other words you are disingenuously denying a tautology that is
>>>>>> obviously correct to any high school student by dancing around it with
>>>>>> with irrelevancies.
>>>>>
>>>>> No, you're too daft to understand that I'm mot deying it at all.
>>>>> I'm saying that it contains a vacuous truth that can just be
>>>>> removed. Since X does not happen for the given H, then "unless X" can
>>>>> (and should!) be exised from your tautology.
>>>>>
>>>>>> It is as if you are saying that it is utterly impossible to determine
>>>>>> the execution trace of any segment of code without actually running this
>>>>>> code.
>>>>>>
>>>>>>> If X is "detecting nested
>>>>>>> simulation" and Y is "discontinuing simulation", then this is
>>>>>>> is a vacuous truth, in the context of a decider which doesn't do any
>>>>>>> such detection.
>>>>>>>
>>>>>>> That's the problem; not that the logic is wrong, but that it's a
>>>>>>> useless, vacuous truth.
>>>>>>>
>>>>>>
>>>>>> If X is the only cause of Y and not X then not Y.
>>>>>
>>>>> Since we know what the value is of X, we can just substitute that
>>>>> value into the tautology, which then no longer mentions X.
>>>>>
>>>>
>>>> I have improved the wording of this since my prior reply to you.
>>>>
>>>>
>>>>
>>>> This halt deciding principle overcomes the pathological self-reference
>>>> error of the halting theorem:
>>>>
>>>> (A) Every simulation of input P that never halts unless simulating halt
>>>> decider H stops simulating it <is> a non-halting computation. This
>>>> remains true even after H stops simulating P.
>>>
>>> This is not an improvement.
>>
>> That is because you simply ignore rather than evaluate the rest of what
>> I say.
>
> Pardon me, let's look at it:
>
>>> Any high school student would be able to analyze the basic logic of the
>>> above and know that it is correct very easily.
>
> Insult attempt; next.
>
>> *Basic logic of the above*
>> If X is the only cause of Y and not X then not Y.
>
> I basically acknowleged the truth of the tautology.

I explained this better in my second reply to your post.
The second reply may wrap this part up.

I want to give Ben's example of clearer wording some credit for my
second reply to you.

I went back and studied all of what you said and found it to be quite
helpful after all.

--
Copyright 2021 Pete Olcott

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

On 5/21/2021 11:20 AM, Mike Terry wrote:
> On 21/05/2021 07:11, Jeff Barnett wrote:
>> On 5/20/2021 5:10 PM, Mike Terry wrote:
>>> On 20/05/2021 13:00, Andy Walker wrote:
>>>> On 20/05/2021 05:56, Jeff Barnett wrote:> [...] I assure you that
>>>>> trying to say the same thing to him for the 579th time will have the
>>>>> same effect as the first 578 tries. Saying something new wont do much
>>>>> either.
>>>>> PS this message is for all of us klutzes who have tried to improve
>>>>> Pete. To tailor this message to your self, substitute your personal
>>>>> version of 579 in the above paragraph.
>>>>
>>>>      Personally, I've tried very hard, and only occasionally failed,
>>>> to say things to Pete only once.  It's a personal opinion, but I think
>>>> this group would be much improved if "us klutzes" limited ourselves to
>>>> one response each to Pete per day.  Ironically, such self-denial would
>>>> probably even enable better progress to be made, as Pete would have
>>>> some 40 fewer articles to "write" each day, and could use the extra 20
>>>> minutes per day to improve his programs/experience/style/....
>>>>
>>>
>>> For me, the problem isn't so much the number of replies, it's more
>>> with the repetition of the same arguments over and over.
>>>
>>> PO will post something or other, and since November(ish) last year
>>> pretty much NOTHING he has posted has added anything!  Someone thinks
>>> "PO has said something wrong - I must correct it to protect the
>>> innocence of virgin newsgroup readers who could be corrupted.  Yes,
>>> I've said this before MANY times, but now I've no choice but to say
>>> it all again.  The innocent MUST be protected!"  [*]
>>>
>>> The problem with this is that if they do point out mistakes, PO WILL
>>> just respond with MORE WORDS - probably just some repetition of
>>> previous claims (sometimes not even related to OP).  And his reposted
>>> claims of course will repeat previous errors, so they will still feel
>>> obliged to post again.  ...And the cycle continues guaranteeing every
>>> PO thread will be a (potentially) infinite thread, with essentially
>>> zero content.
>>>
>>> I've wondered /why/ arguing with PO always goes like this?  Why
>>> doesn't PO see his mistakes, or see the simple correctness of other
>>> peoples reasoning?  I believe PO has some deficiency which renders
>>> him INCAPABLE of pretty much any form of higher ABSTRACT REASONING!
>>> This sounds rather nasty, like I'm just insulting him, but I'm not
>>> interested in that.  If PO /really/ can't handle "abstract reasoning"
>>> that would be an awful life handicap, right?  Such a person would:
>>>
>>> a)  be incapable of (correctly) understanding the concepts underlying
>>>      most academic fields like CS, logic, mathematics, AI, and so on.
>>> b)  be incapable of following other people's reasoned arguments,
>>>      because those arguments have a starting point he lacks (concepts,
>>>      definitions, notations used) and proceed by /logical steps/
>>>      where correctness of conclusion genuinely follows from the
>>>      correctness of starting points.  Forget it - all waaaay too
>>>      abstract!
>>> c)  similarly be incapable of presenting their own /reasoned/
>>>      arguments [aka proofs].  Probably they just wouldn't understand
>>>      why academics write day-to-day proofs, or what one needed to look
>>>      like.  Perhaps they would genuinely see no difference between
>>>      their own repeated claims and other people's properly reasoned
>>>      arguments?
>>>
>>> So... such a person's claims aren't going to based on /reasoning/.
>>> They will effectively be child-like /intuitions/ - first thoughts on
>>> a subject which they /believe/ should be true.  We all grow up with
>>> those, but then we go to school and learn abstract stuff which
>>> enables us to see the problems with our naive intuitions and we
>>> /learn/ new (better) stuff and make progress.  A person unable to
>>> engage with abstract ideas would be more or less stuck with those
>>> starting intuitions for life! And their arguments and proofs could
>>> only consist of statements and restatements of those intuitions,
>>> although for them that would probably be indistinguishable from what
>>> they see others doing when they "prove" stuff...
>>>
>>> Well, to my mind, everything above describes PO, harsh though that
>>> sounds.  "Arguing" with PO endlessly is (IMO) pointless, not only
>>> because it's all been said before many times and becomes time
>>> consuming and boring, but also because:
>>>
>>> -  He won't be able to follow any logical reasoning you present!  He
>>>     won't even understand the starting points.  It's all just
>>>     too abstract.
>>>
>>> -  His position is not based on /reasoning/, so will not be
>>>     changed by careful abstract reasoning, however thoroughly
>>>     people believe they are presenting those ideas.  The more
>>>     time spent on carefully arguing some subtle point and explaining
>>>     basic concepts underlying the ideas, the more likely PO will just
>>>     blank the whole thing.  (We've all seen that personally many
>>>     times, right?  Time thrown out the window!)
>>>
>>> -  PEOPLE HERE ALREADY UNDERSTANDS PO'S MISTAKES 'SUFFICIENTLY'.
>>>     I mean, sufficiently to understand why he has not proved his
>>>     claims (and never will), and sufficiently to satisfy natural
>>>     curiosity over where after all these years the
>>>     basic error will occur; the HP proof is after all not
>>>     complicated, and to start with everyone wants to know where
>>>     on earth PO has become confused!  I'd say those places became
>>>     clear by last Christmas, and nothing
>>>     significant has happened since!  :)
>>>
>>>
>>> CONCLUSION: I'm all behind your (Andy/Jeff's) suggestions, but I'd go
>>> further to suggest NEVER REPEATING THE SAME ARGUMENTS TO PO MORE THAN
>>> [A COUPLE] OF TIMES.  (Well, everyone will have their own threshold
>>> for that!  But 379 is too high.)
>>>
>>> But what to do when PO just repeats back previous claims with the
>>> same repeated errors, AS HE UNDOUBTABLY WILL?  This is tricky for
>>> someone believing it's their moral duty to protect the internet from
>>> untruth! :)  My suggestion would be to either
>>>
>>> a)  Ignore him.  [I suspect he will be more determined than you to
>>>      not be seen to be "defeated" by not replying - but that's an
>>>      illusion in the end - posting last doesn't mean you've "won",
>>>      anything, does it?]
>>>
>>> b)  I've tried replying, but with just a general notice rather than
>>>      repeating details of all PO errors - something like "Now you
>>>      are just repeating previous claims without actually addressing
>>>      any or my points.  Problems with those claims have been pointed
>>>      out many times by posters here - check the previous
>>>      posts if you're interested."
>>>
>>>      The point is this does not give a natural target for PO follow
>>>      up, and the subthread dies out.  Even if PO tries
>>>      his usual trick and responds with a generic repost of claims,
>>>      this way it lacks the illusion he aims for, namely that he's
>>>      engaged in an actual academic debate and is "dealing" with
>>>      all objections raised, so he must be right!  It comes across
>>>      more clearly as PO rehashing old stuff that has already been
>>>      dealt with, if PO could only understand that.
>>>
>>> I did actually try (b) for a while, and it worked in the local
>>> subthread, but it made little difference globally because it only
>>> takes one or two people to be in "always point out exactly what's
>>> wrong in the previous PO post" mode to send the thread into the PO
>>> potentially-infinite-thread pattern.
>>>
>>> [*]  Hey, eveyone can tell I don't hold with the "got to protect
>>> innocent Usenet virgins from untruths told on comp.theory" idea,
>>> right? I mean, who tells their children "go on the internet and hunt
>>> around in the unmoderated Usenet technical groups - for sure
>>> everything said there is true, you can stake your pensions on that!"
>>> ?   :)
>> Interesting and seemingly an accurate assessments of our favorite
>> troll. I note that since I posted my whimsy a few hours ago, he has
>> started seven new threads without an ounce of new content and on
>> second thought, without any real content at all. Given our
>> observations of his need to be in the middle of excitement, perhaps as
>> a cover for absolutely no social life or human contact, he's stirring
>> the pot again and again with the usual nonsense big time.
>>
>> I think he is like the commercial fisherman who wants increased
>> chances for bites so he throws multiple hooks in the water. He's
>> mutated from a hobby troll to a business class troll making me believe
>> that his social and mental states have simultaneously went kaput. I
>> think it would be interesting if the inmates here could resist the
>> urge, overpowering as it may be, to feed him so we can observe the
>> burst of schizoid activity and see where it takes him. All of this in
>> the interest of science of course.
>
> I don't think PO is a troll in the way that is usually taken - he's not
> simply stirring up trouble.  I'm sure he genuinely believes he's an
> unacknowledged genius, and that his claims have merit and would be
> accepted if only he could improve his wording a little!  You're probably
> right though, that PO has no other social contact and needs the
> interaction of these newsgroups.
>
> I think he knows he will never be given the job he's wanted with Cyc,
> which was (he's said) his initial motivation for posting here.  (Get his
> reputation points up, so Doug Lenat will admit his mistake and finally
> offer him that job.)  But he carries on posting here anyway, because
> that's all that's left him.
>
>
> Mike.
>

On 5/21/2021 12:27 PM, Kaz Kylheku wrote:
> On 2021-05-21, olcott <NoOne@NoWhere.com> wrote:
>> I am correctly refuting the halting theorem on the basis that it is
>> entirely anchored in the pathological self-reference error.
>
> It's a fact that an algorithm which decides whether a Turing machine
> halts is also a Turing machine, when it is instantiated with a concrete
> piece of input.
>
> It is inescapable then, that if we ask the question "does the
> algorithm work on all Turing machines" that this set includes a machine
> based on that algorithm, which is deciding whether it itself terminates.
>
> All Turing machines means all Turing machines: not a single one is left
> out. A decider working on an input is a Turing machine. So ...
>
>> I have switched to the actual Linz machines now that my x86utm version
>> has provided such deep insight into the the actual mathematical
>> relationships.
>
> More like: your x86utm has produced execution traces that make you look
> like a fool, and so you have been shifting your interest away from it.
>

On the basis of the insights gained by my x86utm operating system halt
decider I can generalize its exact same halt deciding principle to
equally apply to the Peter Linz Ĥ configuration that copies its input
and has a copy of H embedded without it.

I need the help of my respondents on comp.theory so that I can put the
finishing touches on making my words clear enough that they are
obviously correct. It would have been impossible for me to ever complete
this proof without the feedback from respondents of comp.theory.

When my paper is published I will give the respondents of comp.theory
reviewer credit. It seems that your review has been the most helpful.
Ben may have been most helpful on the pure computer science side, I will
wait and see how this goes. Mike and Malcolm have also been very helpful
on the pure computer science side.

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

When we are answering the question:
Would the input P to the simulating halt decider H halt if its
simulation was never aborted?

This question <is> correctly answered by the proxy: Would the input P to
a simulator S halt?

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

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

The behavior of the proxy computation forms the halt deciding basis for
the inputs that would otherwise specify the pathological self-reference
error.

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

--
Copyright 2021 Pete Olcott

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

On 5/22/2021 9:56 AM, Kaz Kylheku wrote:
> On 2021-05-22, olcott <NoOne@NoWhere.com> wrote:
>> void H_Hat(u32 P)
>> {
>> u32 Input_Halts = Halts(P, P);
>> if (Input_Halts)
>> HERE: goto HERE;
>> }
>>
>> Halts decides the above case by using the behavior of the above code
>> when a simulator is substituted for the simulating halt decider to
>> correctly answer this question:
>
> For the thousandth time, "substitute" means to produce an entirely
> new S_Hat function /similar/ to the above H_Hat which calls Simulate
> instead of Halts.
>

Yes it does.

> // S_Hat is to Simulate what H_Hat is to Halts
>
> void S_Hat(u32 P)
> {
> u32 Input_Halts = Simulate(P, P);
> if (Input_Halts)
> HERE: goto HERE;
> }
>
> That creates a new test case which shows that the following decision is
> wrong or non-halting:
>
> Simulate(S_Hat, S_Hat)

It would not show that the decision is wrong because it never makes any
decision. It would also not directly show that it is not halting only
waiting an infinite amount of time would directly show this.

Its behavior could be examined and find the the same cycle repeats and
there is nothing in this cycle that could possibly break this cycle.

Simulating halt decider H would decide not halting on H(S_Hat, S_Hat).

> just like this is wrong or non-halting:
>
> Halts(H_Hat, H_Hat)
>

When you fully understand its foundational basis then you will fully
understand that it is not the wrong answer.

>> This question <is> correctly answered by the proxy: Would the input P to
>> a simulator S halt?
>
> You must stick to the diagonal of the test case / decider combination
> matrix.
>

Hell no. Although I never quite understood the diagonal argument it
really seems to me that it only tells you that incorrect questions have
no correct answer.

> Halts(S_Hat, S_Hat); // correct, but off the diagonal
>

I am not sure what off the diagonal means.
It is clear that Halts(S_Hat, S_Hat) == 0 is correct.

> The halting proof is a form of diagonal argument. It says that the
> diagonal entries all fail to decide.
>
> Cases F H G <---- deecciders
>
> F^ [ F(^F,^F) ] G(^F, ^F) H(^F, ^F)
> G^ F(^G,^G) [ G(^G, ^G) ] H(^G, ^G)
> H^ F(^H,^H) G(^H, ^H) [ H(^H, ^H) ]
>
> Only the diagonal [ ] entriess are relevant. When you substitute
> a decider in the test case, to obtain another test case, you
> move vertically through the table, which takes you off the diagonal.
>
> When you replacee the decider being applied to the test case,
> you move horizontally; again off the diagonal.
>
> To stick to the diagonal, you must make both substitutions
> in parallel. E.g. when yu change from the H^ case which "attacks" the H
> decider to the G^ test case which attacks the G decider,
> it is that attacked G decider which cannot decide that case.
> You must go from H(^H, ^H) to G(^G, ^G).
>
> Until you thoroughly internalize the above, you do not
> have a grasp on halting.
>

I understand where you are coming from. I am coming from somewhere else.
If you analyze what I am saying using conventional analysis then what I
am saying is incorrect.

To see that what I am saying <is> correct you must switch to
unconventional analysis.

Because we know that the only difference in the behavior of a simulating
halt decider and a simulator is that the simulating halt decider stops
simulating some of its inputs we can examine the behavior of these
inputs in a simulator to determine whether or not a simulating halt
decider would stop simulating these inputs.

If the simulation of input P to simulator S would never terminate then
we can know that simulating halt decider H must stop simulating input P.

>> The reason that the proxy can be used to answer the original question is
>> that the only difference between a simulating halt decider and a
>> simulator is that the simulating halt decider stops simulating some of
>> its inputs.
>
> Any difference whatsoever makes them different entities, which means
> that there cannot be a single H_Hat based on both of them.
> They are different columns in the table, corresponding to different
> rows via the diagonal.
>

--
Copyright 2021 Pete Olcott

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

On 5/21/2021 11:20 AM, Mike Terry wrote:
> On 21/05/2021 07:11, Jeff Barnett wrote:
>> On 5/20/2021 5:10 PM, Mike Terry wrote:
>>> On 20/05/2021 13:00, Andy Walker wrote:
>>>> On 20/05/2021 05:56, Jeff Barnett wrote:> [...] I assure you that
>>>>> trying to say the same thing to him for the 579th time will have the
>>>>> same effect as the first 578 tries. Saying something new wont do much
>>>>> either.
>>>>> PS this message is for all of us klutzes who have tried to improve
>>>>> Pete. To tailor this message to your self, substitute your personal
>>>>> version of 579 in the above paragraph.
>>>>
>>>>      Personally, I've tried very hard, and only occasionally failed,
>>>> to say things to Pete only once.  It's a personal opinion, but I think
>>>> this group would be much improved if "us klutzes" limited ourselves to
>>>> one response each to Pete per day.  Ironically, such self-denial would
>>>> probably even enable better progress to be made, as Pete would have
>>>> some 40 fewer articles to "write" each day, and could use the extra 20
>>>> minutes per day to improve his programs/experience/style/....
>>>>
>>>
>>> For me, the problem isn't so much the number of replies, it's more
>>> with the repetition of the same arguments over and over.
>>>
>>> PO will post something or other, and since November(ish) last year
>>> pretty much NOTHING he has posted has added anything!  Someone thinks
>>> "PO has said something wrong - I must correct it to protect the
>>> innocence of virgin newsgroup readers who could be corrupted.  Yes,
>>> I've said this before MANY times, but now I've no choice but to say
>>> it all again.  The innocent MUST be protected!"  [*]
>>>
>>> The problem with this is that if they do point out mistakes, PO WILL
>>> just respond with MORE WORDS - probably just some repetition of
>>> previous claims (sometimes not even related to OP).  And his reposted
>>> claims of course will repeat previous errors, so they will still feel
>>> obliged to post again.  ...And the cycle continues guaranteeing every
>>> PO thread will be a (potentially) infinite thread, with essentially
>>> zero content.
>>>
>>> I've wondered /why/ arguing with PO always goes like this?  Why
>>> doesn't PO see his mistakes, or see the simple correctness of other
>>> peoples reasoning?  I believe PO has some deficiency which renders
>>> him INCAPABLE of pretty much any form of higher ABSTRACT REASONING!
>>> This sounds rather nasty, like I'm just insulting him, but I'm not
>>> interested in that.  If PO /really/ can't handle "abstract reasoning"
>>> that would be an awful life handicap, right?  Such a person would:
>>>
>>> a)  be incapable of (correctly) understanding the concepts underlying
>>>      most academic fields like CS, logic, mathematics, AI, and so on.
>>> b)  be incapable of following other people's reasoned arguments,
>>>      because those arguments have a starting point he lacks (concepts,
>>>      definitions, notations used) and proceed by /logical steps/
>>>      where correctness of conclusion genuinely follows from the
>>>      correctness of starting points.  Forget it - all waaaay too
>>>      abstract!
>>> c)  similarly be incapable of presenting their own /reasoned/
>>>      arguments [aka proofs].  Probably they just wouldn't understand
>>>      why academics write day-to-day proofs, or what one needed to look
>>>      like.  Perhaps they would genuinely see no difference between
>>>      their own repeated claims and other people's properly reasoned
>>>      arguments?
>>>
>>> So... such a person's claims aren't going to based on /reasoning/.
>>> They will effectively be child-like /intuitions/ - first thoughts on
>>> a subject which they /believe/ should be true.  We all grow up with
>>> those, but then we go to school and learn abstract stuff which
>>> enables us to see the problems with our naive intuitions and we
>>> /learn/ new (better) stuff and make progress.  A person unable to
>>> engage with abstract ideas would be more or less stuck with those
>>> starting intuitions for life! And their arguments and proofs could
>>> only consist of statements and restatements of those intuitions,
>>> although for them that would probably be indistinguishable from what
>>> they see others doing when they "prove" stuff...
>>>
>>> Well, to my mind, everything above describes PO, harsh though that
>>> sounds.  "Arguing" with PO endlessly is (IMO) pointless, not only
>>> because it's all been said before many times and becomes time
>>> consuming and boring, but also because:
>>>
>>> -  He won't be able to follow any logical reasoning you present!  He
>>>     won't even understand the starting points.  It's all just
>>>     too abstract.
>>>
>>> -  His position is not based on /reasoning/, so will not be
>>>     changed by careful abstract reasoning, however thoroughly
>>>     people believe they are presenting those ideas.  The more
>>>     time spent on carefully arguing some subtle point and explaining
>>>     basic concepts underlying the ideas, the more likely PO will just
>>>     blank the whole thing.  (We've all seen that personally many
>>>     times, right?  Time thrown out the window!)
>>>
>>> -  PEOPLE HERE ALREADY UNDERSTANDS PO'S MISTAKES 'SUFFICIENTLY'.
>>>     I mean, sufficiently to understand why he has not proved his
>>>     claims (and never will), and sufficiently to satisfy natural
>>>     curiosity over where after all these years the
>>>     basic error will occur; the HP proof is after all not
>>>     complicated, and to start with everyone wants to know where
>>>     on earth PO has become confused!  I'd say those places became
>>>     clear by last Christmas, and nothing
>>>     significant has happened since!  :)
>>>
>>>
>>> CONCLUSION: I'm all behind your (Andy/Jeff's) suggestions, but I'd go
>>> further to suggest NEVER REPEATING THE SAME ARGUMENTS TO PO MORE THAN
>>> [A COUPLE] OF TIMES.  (Well, everyone will have their own threshold
>>> for that!  But 379 is too high.)
>>>
>>> But what to do when PO just repeats back previous claims with the
>>> same repeated errors, AS HE UNDOUBTABLY WILL?  This is tricky for
>>> someone believing it's their moral duty to protect the internet from
>>> untruth! :)  My suggestion would be to either
>>>
>>> a)  Ignore him.  [I suspect he will be more determined than you to
>>>      not be seen to be "defeated" by not replying - but that's an
>>>      illusion in the end - posting last doesn't mean you've "won",
>>>      anything, does it?]
>>>
>>> b)  I've tried replying, but with just a general notice rather than
>>>      repeating details of all PO errors - something like "Now you
>>>      are just repeating previous claims without actually addressing
>>>      any or my points.  Problems with those claims have been pointed
>>>      out many times by posters here - check the previous
>>>      posts if you're interested."
>>>
>>>      The point is this does not give a natural target for PO follow
>>>      up, and the subthread dies out.  Even if PO tries
>>>      his usual trick and responds with a generic repost of claims,
>>>      this way it lacks the illusion he aims for, namely that he's
>>>      engaged in an actual academic debate and is "dealing" with
>>>      all objections raised, so he must be right!  It comes across
>>>      more clearly as PO rehashing old stuff that has already been
>>>      dealt with, if PO could only understand that.
>>>
>>> I did actually try (b) for a while, and it worked in the local
>>> subthread, but it made little difference globally because it only
>>> takes one or two people to be in "always point out exactly what's
>>> wrong in the previous PO post" mode to send the thread into the PO
>>> potentially-infinite-thread pattern.
>>>
>>> [*]  Hey, eveyone can tell I don't hold with the "got to protect
>>> innocent Usenet virgins from untruths told on comp.theory" idea,
>>> right? I mean, who tells their children "go on the internet and hunt
>>> around in the unmoderated Usenet technical groups - for sure
>>> everything said there is true, you can stake your pensions on that!"
>>> ?   :)
>> Interesting and seemingly an accurate assessments of our favorite
>> troll. I note that since I posted my whimsy a few hours ago, he has
>> started seven new threads without an ounce of new content and on
>> second thought, without any real content at all. Given our
>> observations of his need to be in the middle of excitement, perhaps as
>> a cover for absolutely no social life or human contact, he's stirring
>> the pot again and again with the usual nonsense big time.
>>
>> I think he is like the commercial fisherman who wants increased
>> chances for bites so he throws multiple hooks in the water. He's
>> mutated from a hobby troll to a business class troll making me believe
>> that his social and mental states have simultaneously went kaput. I
>> think it would be interesting if the inmates here could resist the
>> urge, overpowering as it may be, to feed him so we can observe the
>> burst of schizoid activity and see where it takes him. All of this in
>> the interest of science of course.
>
> I don't think PO is a troll in the way that is usually taken - he's not
> simply stirring up trouble.  I'm sure he genuinely believes he's an
> unacknowledged genius, and that his claims have merit and would be
> accepted if only he could improve his wording a little!  You're probably
> right though, that PO has no other social contact and needs the
> interaction of these newsgroups.
>
> I think he knows he will never be given the job he's wanted with Cyc,
> which was (he's said) his initial motivation for posting here.  (Get his
> reputation points up, so Doug Lenat will admit his mistake and finally
> offer him that job.)  But he carries on posting here anyway, because
> that's all that's left him.
>
>
> Mike.
>

On 5/22/2021 6:21 PM, Ben Bacarisse wrote:
> olcott <NoOne@NoWhere.com> writes:
>
>> On 5/21/2021 5:48 PM, Ben Bacarisse wrote:
>>> olcott <NoOne@NoWhere.com> writes:
>>>
>>>> On 5/20/2021 6:41 PM, Ben Bacarisse wrote:
>>>>> olcott <NoOne@NoWhere.com> writes:
>>>>>
>>>>>> On 5/20/2021 7:28 AM, Ben Bacarisse wrote:
>>>>>
>>>>>>> Peter, if there is one post you really, really want my reply to, please
>>>>>>> indicate which it is. I will look out for you indication later
>>>>>>> today.
>>>>>
>>>>> Given that you replied here, I'll take that as the indication that it is
>>>>> this reply you would like me to reply to.
>>>>>
>>>>>> Ĥ.q0 wM ⊢* Ĥ.qx wM wM ⊢* Ĥ.qy ∞
>>>>>> Ĥ.q0 wM ⊢* Ĥ.qx wM wM ⊢* Ĥ.qn
>>>>>
>>>>> This appears to relate to the famous lines from Linz. If that is what
>>>>> you wanted, then we know that there is no TM H^ that behaves as
>>>>> specified. Imagine that you started by saying 3 > x > 5.
>>>>>
>>>>>> Truism(1a)
>>>>>> The simulation of: ([Ĥ][Ĥ]) by the simulating halt decider @ Ĥ.qx
>>>>>> would never halt unless Ĥ.qx aborts this simulation.
>>>
>>> There is no TM H and therefore no H^ as specified above and therefore
>>> no strings [H^] or ([H^][H^]).
>>>
>>> If you want "the simulating halt decider @ Ĥ.qx" to suggest some other H
>>> (and H^) you need to delete the previous specification.
>>>
>>> I'd hoped this just one significant reply would improve the dialogue.
>>> It's certainly made it simpler.
>>>
>>>>>> In the purely hypothetical case where Ĥ.qx did not stop simulating its
>>>>>> input
>>>>>
>>>>> H^.qx is a state in a TM. It is literal nonsense to say that a state in
>>>>> a TM "did not stop simulating...".
>>>>>
>>>>> "It's input" is also literal nonsense because states don't "have" input.
>>>>
>>>> I am stopping at your first big mistake, Linz specifies the input to
>>>> the embedded halt decider at Ĥ.qx as wM wM.
>>>
>>> You stopped at a correct remark. States don't "have" input. Even your
>>> suggestion that there is an implied input is wrong since a state can
>>> entered when the tape is in lots of different configurations.
>
> You did not say which post you'd like me to reply to today, so I've
> picked this one.
>
>> I want to move on from that triviality to this:
>
> It would appear you don't really want a debate. I have no problem
> moving on from minor errors, but the post I replied to referred to a
> non-existent Turing machine, and discussed the properties of

My reasoning is plugged into this Linz proof at the point immediately
after page 319 and assumes every detail of the proof on pages 317-319.

> non-existent strings. Those are not trivialities. Are they also to be
> forgotten, now, just like we are supposed to forget the actual Turing
> machines you said you had back in Dec 2018?
>
>> Truism(A) Every simulation of input P that never halts unless
>> simulating halt decider H aborts this simulation <is> a non-halting
>> computation. This remains true even after H stops simulating P.
>
> If only you could use a formal notation you might be able to be clear.
>
>> When we are answering the question:
>> Would the input P to the simulating halt decider H halt if its
>> simulation was never aborted?
>
> That is a question you appear to think is interesting but you can't
> explain why. The world is interesting in the halting problem which is
> about whether a string represents a finite computation or not. There
> was a time when you claimed to be addressing that question.
>

For some inputs that question can only be correctly answered through a
proxy that is immune to the pathological self-reference error.

>> This question <is> correctly answered by the proxy: Would the input P
>> to a simulator S halt?
>
> No. This "proxy" is just the question "does the string P represent a
> finite computation?". A computation and it's simulation have the same
> halting status. In my notation UTM(<M, s>) = ⊥ iff M(s) = ⊥.
>

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

When we define a proxy computation Ĥ2 on the basis of replacing the copy
of H at state Ĥ.qx with a UTM will the UTM at state Ĥ2.qx halt on its
([Ĥ2], [Ĥ2]) input?

The answer is clearly no.

(a) The only difference between a simulating halt decider and a
UTM/simulator is that the former stops its simulation at some point.

(b) Where a computation P has an embedded simulating halt decider H we
create proxy computation P2 replacing every instance of H with simulator S.

The following two points are the key basis of my whole proof, so far
they have proved far too subtle for anyone here to begin to grasp.

(c) Because of (a) when P2 is a halting computation then H does not need
to stop P and H decides halting.

(d) Because of (a) when P2 is an infinite computation then H must stop P
and H decides not halting.

> Your uninteresting question is quite different. It asks about a
> property of P were it different. Mathematicians avoid that sort of daft
> language. The two strings would be given different names -- P that
> embeds the "decider" H, and P' the string representing the computation that
> embeds H', the other version of H. In your clearer wording from last
> year, the same code but with line 15 commented out.
>
>> ∃H ∈ Simulating_Halt_Deciders
>> ∀P ∈ Turing_Machine_Descriptions
>> ∀I ∈ Finite_Strings
>> (UTM(P,I) = ∞) ⊢ (H(P,I) = 0)
>>
>> In English it says that whenever the input (P,I) to UTM would never
>> halt then a simulating halt decider correctly decides not halting on
>> this input.
>
> It does not say that, but this time I don't think I can even get the
> poetic gist of what you are saying, because the only meaning I can
> squeeze from these symbols is something you know to be false or at least
> something that you could simply state unambiguously in words.
>
> You have an odd obsession with simulation. Writing UTM(<[M],I>) = ∞ is
> the same as writing M(I) = ∞ because a computation and its simulation
> have the same halting status.
>
> And there is no need to restrict H. If the above is true for the
> mysterious and undefined set Simulating_Halt_Deciders it is true that ∃H
> ∈ TM (the set of all Turing machines) with the stated property.
>
> And you don't know what ⊢ means. You are, I think, using it
> metaphorically for either "if ... then ...", or "if and only if". My
> guess is the latter, but do step in if that guess is wrong.
>
> So you appear to be saying that there is a Turing machine H such that
> for all TMs M and finite strings s
>
> ~(M(s) is finite) if and only if H(<[M], s>) = 0.
>
> I.e. you appear to be simply saying that there is a TM that decides
> halting.
>

--
Copyright 2021 Pete Olcott

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

On 5/23/2021 9:59 AM, Kaz Kylheku wrote:
> On 2021-05-22, olcott <NoOne@NoWhere.com> wrote:
>> On 5/22/2021 9:56 AM, Kaz Kylheku wrote:
>>> The halting proof is a form of diagonal argument. It says that the
>>> diagonal entries all fail to decide.
>>>
>>> Cases F H G <---- deecciders
>>>
>>> F^ [ F(^F,^F) ] G(^F, ^F) H(^F, ^F)
>>> G^ F(^G,^G) [ G(^G, ^G) ] H(^G, ^G)
>>> H^ F(^H,^H) G(^H, ^H) [ H(^H, ^H) ]
>>>
>>> Only the diagonal [ ] entriess are relevant. When you substitute
>>> a decider in the test case, to obtain another test case, you
>>> move vertically through the table, which takes you off the diagonal.
>>>
>>> When you replacee the decider being applied to the test case,
>>> you move horizontally; again off the diagonal.
>>>
>>> To stick to the diagonal, you must make both substitutions
>>> in parallel. E.g. when yu change from the H^ case which "attacks" the H
>>> decider to the G^ test case which attacks the G decider,
>>> it is that attacked G decider which cannot decide that case.
>>> You must go from H(^H, ^H) to G(^G, ^G).
>>>
>>> Until you thoroughly internalize the above, you do not
>>> have a grasp on halting.
>>>
>>
>> I understand where you are coming from. I am coming from somewhere else.
>> If you analyze what I am saying using conventional analysis then what I
>> am saying is incorrect.
>>
>> To see that what I am saying <is> correct you must switch to
>> unconventional analysis.
>
> The Turing model of computation, and the halting question and its
> proofs are entirely contained within "conventional analysis".
>
> You're using the language of conventional analysis to refer to
> its concepts and constructs, and to dispute its results.
>

As I recently explained to Ben My proof assumes the entire Peter Linz
proof on pages 317-319 and is inserted at the end of page 319, skipping
page 320.

> If you want to use "unconventional analysis", you must rigorously pin
> down what that is, before you even approach the halting problem,
> and present that framework upfront.
>
> Within that framework, you must construct that framework's own model of
> computation. Then pursue that framework's version of the halting
> problem within that framework, and not make any claims with regard to
> conventional Turing halting (which will automatically make you look
> wrong).
>
> You can use similar language like "machine", "halts", and so on, if you
> make it clear up front that these words are in your own framework and do
> not have their conventional meaning.
>
> You also face this problem: what good is your alternative analysis?
> Conventional analysis is reliable and powerful. Can we apply your
> alternative analysis to a broad area of problems and get good results?
>
>> Because we know that the only difference in the behavior of a simulating
>> halt decider and a simulator is that the simulating halt decider stops
>> simulating some of its inputs we can examine the behavior of these
>> inputs in a simulator to determine whether or not a simulating halt
>> decider would stop simulating these inputs.
>
> Sure, but the difference in behavior means we are jumping to a different
> column of the input-decider matrix and are no longer on the diagonal.
> To return to the diagonal while staying in the same column, we must
> switch to a different row: the row for the test case which is based on
> that column's decider. Where row and column match, we have an incorrect
> or nonterminating halting decision, according to this conventional analysis.
>

The whole diagonalization thing is gibberish to me unless it only shows
that incorrect questions do not have correct answers.

> Any reasoning that leads you, through substitutions, to discovering a
> good halting decision, but which is off the diagonal trace, has led you
> to an irrelevant configuration. The proof says only that the
> configurations on the diagonal are incorrect or non-halting. The
> proof does not make any assertions about non-diagonal configuations,
> therefore those configurations are not counterexamples to the proof's
> claims.
>
> The undecidability of halting is precisely the claim that the entire
> diagonal consists of incorrect answers or non-halting. Since for every
> decider there is a diagonal entry, every decider is associated with a
> test case it does not handle.
>
> If every decider has at least one test case it does not handle, then
> there does not exist a universal (= handles all cases) decider:
> there is no algorithm that decides all cases of halting.
>

Generic halt deciding principle for inputs having the pathological
self-reference error

(a) Halt deciding simulator H only affects the behavior of input P in
one way and only under one condition. In all other cases a halt deciding
simulator H has no effect what-so-ever on the behavior of input P and
acts exactly like pure simulator S on input P.

(b) When an infinite computation is specified as input P to a simulating
halt decider H the halt decider H must stop the simulation of this input
P. When this same input is simulated by simulator S, its simulation
never stops.

(c) When a finite computation is specified as input P to a simulating
halt decider H the halt decider H simulates its input exactly as if H
was simulator S.

Because of the above simulating halt decider H can decide input P having
the pathological self-reference error on the basis of the proxy input P2
having the pathological self-reference error removed.

When input P invokes embedded simulating halt decider H on itself it
creates proxy input P2 replacing H with simulator S. The embedded halt
decider H examines the execution trace of proxy input P2. The embedded
halt decider correctly decides its input P on the basis of how it
decides input P2.

When we apply the Generic halt deciding principle to the embedded
simulating halt decider at state Ĥ.qx to its input ([Ĥ],[Ĥ]) we find
that the simulation of this input must be aborted.

Because the necessity to abort the simulation of an input is equated
with this input specifying
an infinite computation the simulating halt decider Ĥ.qx correctly
transitions to its final Ĥ.qn state deciding not halting on its input.

--
Copyright 2021 Pete Olcott

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

On 5/24/2021 6:37 PM, Ben Bacarisse wrote:
> olcott <NoOne@NoWhere.com> writes:
>
>> On 5/23/2021 7:24 PM, Ben Bacarisse wrote:
>>> olcott <NoOne@NoWhere.com> writes:
>>>
>>>> On 5/22/2021 6:21 PM, Ben Bacarisse wrote:
>>>>> olcott <NoOne@NoWhere.com> writes:
>>>>>
>>>>>> On 5/21/2021 5:48 PM, Ben Bacarisse wrote:
>>>>>>> olcott <NoOne@NoWhere.com> writes:
>>>>>>>
>>>>>>>> On 5/20/2021 6:41 PM, Ben Bacarisse wrote:
>>>>>>>>> olcott <NoOne@NoWhere.com> writes:
>>>>>>>>>
>>>>>>>>>> On 5/20/2021 7:28 AM, Ben Bacarisse wrote:
>>>>>>>>>
>>>>>>>>>>> Peter, if there is one post you really, really want my reply to, please
>>>>>>>>>>> indicate which it is. I will look out for you indication later
>>>>>>>>>>> today.
>>>>>>>>>
>>>>>>>>> Given that you replied here, I'll take that as the indication that it is
>>>>>>>>> this reply you would like me to reply to.
>>>>>>>>>
>>>>>>>>>> Ĥ.q0 wM ⊢* Ĥ.qx wM wM ⊢* Ĥ.qy ∞
>>>>>>>>>> Ĥ.q0 wM ⊢* Ĥ.qx wM wM ⊢* Ĥ.qn
>>>>>>>>>
>>>>>>>>> This appears to relate to the famous lines from Linz. If that is what
>>>>>>>>> you wanted, then we know that there is no TM H^ that behaves as
>>>>>>>>> specified. Imagine that you started by saying 3 > x > 5.
>>>>>>>>>
>>>>>>>>>> Truism(1a)
>>>>>>>>>> The simulation of: ([Ĥ][Ĥ]) by the simulating halt decider @ Ĥ.qx
>>>>>>>>>> would never halt unless Ĥ.qx aborts this simulation.
>>>>>>>
>>>>>>> There is no TM H and therefore no H^ as specified above and therefore
>>>>>>> no strings [H^] or ([H^][H^]).
>>>>>>>
>>>>>>> If you want "the simulating halt decider @ Ĥ.qx" to suggest some other H
>>>>>>> (and H^) you need to delete the previous specification.
>>>>>>>
>>>>>>> I'd hoped this just one significant reply would improve the dialogue.
>>>>>>> It's certainly made it simpler.
>>>>>>>
>>>>>>>>>> In the purely hypothetical case where Ĥ.qx did not stop simulating its
>>>>>>>>>> input
>>>>>>>>>
>>>>>>>>> H^.qx is a state in a TM. It is literal nonsense to say that a state in
>>>>>>>>> a TM "did not stop simulating...".
>>>>>>>>>
>>>>>>>>> "It's input" is also literal nonsense because states don't "have" input.
>>>>>>>>
>>>>>>>> I am stopping at your first big mistake, Linz specifies the input to
>>>>>>>> the embedded halt decider at Ĥ.qx as wM wM.
>>>>>>>
>>>>>>> You stopped at a correct remark. States don't "have" input. Even your
>>>>>>> suggestion that there is an implied input is wrong since a state can
>>>>>>> entered when the tape is in lots of different configurations.
>>>>>
>>>>> You did not say which post you'd like me to reply to today, so I've
>>>>> picked this one.
>>>>>
>>>>>> I want to move on from that triviality to this:
>>>>>
>>>>> It would appear you don't really want a debate. I have no problem
>>>>> moving on from minor errors, but the post I replied to referred to a
>>>>> non-existent Turing machine, and discussed the properties of
>>>>
>>>> My reasoning is plugged into this Linz proof at the point immediately
>>>> after page 319 and assumes every detail of the proof on pages 317-319.
>>>
>>> Yes, I know. That's why I said are talking about non-existent TMs and
>>> strings.
>>
>> Proof: We assume the contrary, namely that there exists
>> an algorithm,and consequently some Turing machine H, that
>> solves the halting problem. (Linz:1990:317)
>>
>> According to your reasoning the Linz proof needs one more line:
>> Because everyone knows that there is no such thing we are done!
>
> No. You are free to assume that such a TM exists but I am free to
> assert the logical conclusion of that assumption. I will assert it even
> if you show that the four sentences that conclude the proof contain a
> fatal logical flaw. I will assert it because there are many proofs of
> the result (there's even another in Linz) that you have no concept of.
>

You will assert it even if everyone else in the world agrees that I
refuted the halting theorem.

>> When following the Linz proof the existence of H is stipulated until
>> after page 319 where it seems to be contradicted. My proof begins
>> before this contradiction occurs.
>
> You have no proof of anything. And nothing you write removes the
> contradiction.
>

You cannot correctly assert that I have no proof you can only correctly
assert that you cannot see that I have a proof.

Correctly asserting that I have no proof is equivalent to totally
understanding everything that I am saying with the corresponding ability
to point out every detail of every error.

> The extraordinary part is the you are not talking about a halt decider
> so there is no need to assume a logically impossible TM to start with.
> Your proposed decider decides another property altogether. I'd be happy
> to show why it, too, does not exist, but you'd first have to admit what
> it is supposed to decide.
>

My halt decider correctly decides halting on inputs with pathological
self-reference on the basis of proxy input that has the pathological
self-reference removed.

>>>>> non-existent strings. Those are not trivialities. Are they also to be
>>>>> forgotten, now, just like we are supposed to forget the actual Turing
>>>>> machines you said you had back in Dec 2018?
>>>>>
>>>>>> Truism(A) Every simulation of input P that never halts unless
>>>>>> simulating halt decider H aborts this simulation <is> a non-halting
>>>>>> computation. This remains true even after H stops simulating P.
>>>>>
>>>>> If only you could use a formal notation you might be able to be clear.
>>>>>
>>>>>> When we are answering the question:
>>>>>> Would the input P to the simulating halt decider H halt if its
>>>>>> simulation was never aborted?
>>>>>
>>>>> That is a question you appear to think is interesting but you can't
>>>>> explain why. The world is interesting in the halting problem which is
>>>>> about whether a string represents a finite computation or not. There
>>>>> was a time when you claimed to be addressing that question.
>>>>
>>>> For some inputs that question can only be correctly answered through a
>>>> proxy that is immune to the pathological self-reference error.
>>>
>>> You have not given any reason why your alternate question is of any
>>> interest to anyone but yourself. You've accepted that giving the correct
>>> answer is an impossible constraint
>>>
>>> "To limit the scope of a halt decider to only report whether or not
>>> its input actually halts is to artificially constrain an otherwise
>>> correct halt decider."
>>>
>>> but relaxing the requirement that the decider should "report whether or
>>> not its input actually halts" does not obviously produce a problem that
>>> anyone cares about.
>>
>> My reasoning is no longer based on anything like the above quote.
>
> I need to know if you withdraw that remark. I won't quote it if you
> don't stand by it anymore. Unless you withdraw it, I'll quote it
> because it shows you understand that halting is not decidable.
>

On 5/25/2021 11:14 AM, Mr Flibble wrote:
> On Tue, 25 May 2021 08:44:15 -0500
> olcott <NoOne@NoWhere.com> wrote:
>
>> On 5/24/2021 11:40 PM, dklei...@gmail.com wrote:
>>> On Monday, May 24, 2021 at 7:01:42 PM UTC-7, olcott wrote:
>>>> Halt deciders must be free to predict that computations would not
>>>> halt. If they are only allowed to report whether or not an input
>>>> actually halts this makes them to wait forever before reporting
>>>> not halting.
>>>
>>> Therefore halt deciders do not exist. QED.
>>>
>>
>> Not at all. This concrete partial halt decider does correctly decide
>> not halting on its Infinite_Loop() input on the basis of examining
>> some of its behavior and thus predicting all of its future behavior.
>
> A partial halt decider is not a halt decider, it is a partial halt
> decider. Until you address the issues of branching logic predicated on
> arbitrary program input you can only ever have a partial halt decider
> which is next to useless.
>
> [snip]
>
> /Flibble
>

The following only talks about halt deciders. It does not mention
partial halt deciders.

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

The following provides the means for the embedded simulating halt
decider at state Ĥ.qx to correctly decide not halting on its input in
the computation: Ĥ([Ĥ]). This is explained on page 6 of the full paper.

*Halting problem undecidability and infinitely nested simulation*

When input P to simulating halt decider H has the pathological
self-reference error (PSRE) simulating halt decider H decides this input
P on the basis of proxy input P2 that has the pathological
self-reference error removed.

void H_Hat(u32 P)
{ u32 Input_Halts = Halts(P, P);
if (Input_Halts)
HERE: goto HERE;
}

The pathological self-reference error arises in the halting theorem from
the fact that both return values: {0, 1} from Halts() to H_Hat() are
incorrect when H_Hat() is invoked with its own machine address as input.

When we define H_Hat2() by replacing the call to Halts() with a call to
Simulate()

u32 Simulate(u32 P, u32 I)
{ ((void(*)(int))P)(I);
return 1;
}

H_Hat2() never halts on its own machine address as input.
This key fact is leveraged to correctly decide halting:
Halts((u32)H_Hat, (u32)H_Hat);

We hypothesize that input P having the pathological self-reference error
(PSRE) can be substituted for equivalent proxy input P2 such that the
halting status of P2 derives the halting status of P. If this
hypothesis is correct it becomes the basis for refuting the halting
theorem.

To put this in concrete terms if Halts((u32)H_Hat2, (u32)H_Hat2);
provides the correct halting value for Halts((u32)H_Hat, (u32)H_Hat);
then H_Hat becomes a decidable input. The rest of the proof will attempt
to show this.

Generic halt deciding principle for inputs having the pathological
self-reference error

Whenever input P has the pathological self-reference error such that a
simulating halt decider H must decide halting on an input that invokes
itself we define proxy input P2 copy of P such that the embedded
simulating halt decider is replaced with a simulator.

(a) Simulating halt decider H and simulator S are equivalent
computations for all inputs P that halt. This means that H correctly
decides halting on P if and only if P2 halts.

(b) Simulating halt decider H and simulator S are equivalent
computations for all inputs P that do not halt up to the point where H
stops simulating P. This means that H correctly decides not halting on P
if and only if P2 does not halt.

In other words: Halts correctly decides not halting on H_Hat on the
basis that H_Hat2 does not halt.

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

--
Copyright 2021 Pete Olcott

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

On 5/23/2021 9:59 AM, Kaz Kylheku wrote:
> On 2021-05-22, olcott <NoOne@NoWhere.com> wrote:
>> On 5/22/2021 9:56 AM, Kaz Kylheku wrote:
>>> The halting proof is a form of diagonal argument. It says that the
>>> diagonal entries all fail to decide.
>>>
>>> Cases F H G <---- deecciders
>>>
>>> F^ [ F(^F,^F) ] G(^F, ^F) H(^F, ^F)
>>> G^ F(^G,^G) [ G(^G, ^G) ] H(^G, ^G)
>>> H^ F(^H,^H) G(^H, ^H) [ H(^H, ^H) ]
>>>
>>> Only the diagonal [ ] entriess are relevant. When you substitute
>>> a decider in the test case, to obtain another test case, you
>>> move vertically through the table, which takes you off the diagonal.
>>>
>>> When you replacee the decider being applied to the test case,
>>> you move horizontally; again off the diagonal.
>>>
>>> To stick to the diagonal, you must make both substitutions
>>> in parallel. E.g. when yu change from the H^ case which "attacks" the H
>>> decider to the G^ test case which attacks the G decider,
>>> it is that attacked G decider which cannot decide that case.
>>> You must go from H(^H, ^H) to G(^G, ^G).
>>>
>>> Until you thoroughly internalize the above, you do not
>>> have a grasp on halting.
>>>
>>
>> I understand where you are coming from. I am coming from somewhere else.
>> If you analyze what I am saying using conventional analysis then what I
>> am saying is incorrect.
>>
>> To see that what I am saying <is> correct you must switch to
>> unconventional analysis.
>
> The Turing model of computation, and the halting question and its
> proofs are entirely contained within "conventional analysis".
>
> You're using the language of conventional analysis to refer to
> its concepts and constructs, and to dispute its results.
>
> If you want to use "unconventional analysis", you must rigorously pin
> down what that is, before you even approach the halting problem,
> and present that framework upfront.
>
> Within that framework, you must construct that framework's own model of
> computation. Then pursue that framework's version of the halting
> problem within that framework, and not make any claims with regard to
> conventional Turing halting (which will automatically make you look
> wrong).
>
> You can use similar language like "machine", "halts", and so on, if you
> make it clear up front that these words are in your own framework and do
> not have their conventional meaning.
>
> You also face this problem: what good is your alternative analysis?
> Conventional analysis is reliable and powerful. Can we apply your
> alternative analysis to a broad area of problems and get good results?
>
>> Because we know that the only difference in the behavior of a simulating
>> halt decider and a simulator is that the simulating halt decider stops
>> simulating some of its inputs we can examine the behavior of these
>> inputs in a simulator to determine whether or not a simulating halt
>> decider would stop simulating these inputs.
>
> Sure, but the difference in behavior means we are jumping to a different
> column of the input-decider matrix and are no longer on the diagonal.
> To return to the diagonal while staying in the same column, we must
> switch to a different row: the row for the test case which is based on
> that column's decider. Where row and column match, we have an incorrect
> or nonterminating halting decision, according to this conventional analysis.
>
> Any reasoning that leads you, through substitutions, to discovering a
> good halting decision, but which is off the diagonal trace, has led you
> to an irrelevant configuration. The proof says only that the
> configurations on the diagonal are incorrect or non-halting. The
> proof does not make any assertions about non-diagonal configuations,
> therefore those configurations are not counterexamples to the proof's
> claims.
>
> The undecidability of halting is precisely the claim that the entire
> diagonal consists of incorrect answers or non-halting. Since for every
> decider there is a diagonal entry, every decider is associated with a
> test case it does not handle.
>
> If every decider has at least one test case it does not handle, then
> there does not exist a universal (= handles all cases) decider:
> there is no algorithm that decides all cases of halting.
>

https://www.youtube.com/watch?v=jM6osxSX9GA

It is not at all the horribly convoluted mess of the diagonal lemma:
https://en.wikipedia.org/wiki/Diagonal_lemma

--
Copyright 2021 Pete Olcott

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

On 5/26/2021 1:17 PM, Malcolm McLean wrote:
> On Wednesday, 26 May 2021 at 16:31:10 UTC+1, Ben Bacarisse wrote:
>> Malcolm McLean <malcolm.ar...@gmail.com> writes:
>>
>>> On Wednesday, 26 May 2021 at 11:59:25 UTC+1, Ben Bacarisse wrote:
>>>> Malcolm McLean <malcolm.ar...@gmail.com> writes:
>>>>
>>>>> On Wednesday, 26 May 2021 at 02:58:28 UTC+1, Ben Bacarisse wrote:
>>>>>> olcott <No...@NoWhere.com> writes:
>>>>>>
>>>>>>> My halt decider correctly decides halting on inputs with pathological
>>>>>>> self-reference on the basis of proxy input that has the pathological
>>>>>>> self-reference removed.
>>>>>> No. Your decider is factually wrong about the halting of at least one
>>>>>> case. You accept the facts that
>>>>>>
>>>>>> (a) Halts(H_Hat, H_Hat) is false, and
>>>>>> (b) H_Hat(H_Hat) is a finite (AKA halting) computation.
>>>>>>
>>>>>> What you deny is that a halt decider is a TM that answers yes/true/1 for
>>>>>> all inputs representing halting computations and no/false/0 otherwise.
>>>>>>
>>>>>> I was going to say that the honest response at this point would be for
>>>>>> you to rename the property you claim to be deciding, but I read on and
>>>>>> it seems you might not even know what the halting problem even is.
>>>>>>> On 5/24/2021 6:37 PM, Ben Bacarisse wrote:
>>>>>>
>>>>>>>> Every instance of the halting problem is decidable, (but you don't know
>>>>>>>> what decidable means,
>>>>>>>
>>>>>>> Decidable means that a membership algorithm exists.
>>>>>> That sounds like rote learning to me. Can you use this definition to
>>>>>> make my remark sufficiently exact that's it is obviously true?
>>>>>>
>>>>> So what about, say, a machine which halts when it finds a counter-example
>>>>> to Fermat's last theorem? I believe that the theorem has now been proved,
>>>>> with a highly complex proof, so that machine is known to be
>>>>> non-halting.
>>>> Right.
>>>>> But what does it mean to say that it is "decidable?"
>>>> PO's rote answer gives the missing clue. Decidability is a property of
>>>> sets. A set is decidable if a TM exists that accepts all members and
>>>> rejects all non-members. As a result, all finite sets are decidable, so
>>>> if the second "it" in your question refers to the single string encoding
>>>> the computation you describe above (a FLT counter-example search TM) then "it is
>>>> decidable" because the only set we might be referring to is the
>>>> singleton set that contains it.
>>>>
>>>> I'm not 100% sure this is what you were asking, but it's my best shot at
>>>> an answer.
>>>>
>>> So by "decidable" we mean that one of the two trivial Turing machines
>>> "write true" or "write false" must decide it correctly. Not that it is
>>> possible to write a machine that decides it correctly if we don't know
>>> the answer.
>> I am pretty sure I misunderstood your question. First, let me clarify
>> what the term means in general:
>>
>> Technically neither of your examples decides the set in question. In
>> formal terms, the set being decided is always a subset of N, so the
>> decider for your example looks for the string encoding of the number of
>> that one single computation and accepts only that one string while
>> rejecting all others. (It's safe to be slightly less technical and
>> forget about subsets of N. The set being decided can then be just a
>> subset of the finite strings over some finite alphabet.)
>>
>> But I don't think you were asking what it means for a singleton set to
>> be decidable. You were asking, I think, about what it means for the
>> /halting/ of an particular instance to be "decidable". On that
>> question, I would suggest one tries to avoid that usage altogether. As
>> best as I can tell, PO uses it to mean that some TM gets the answer
>> right.
>>
>> Have I understood what you were asking this time?
>>
> Yes. WIth the interminable H_Hat(H_Hat) example, if the offered H is
> reasonably simple, it's easy to build a decider which is more than a
> simple stub, and gives the correct answer for H_Hat(H_Hat). So it's
> easy to see that H_Hat(H_Hat) is "decidable".

Yet correctly deciding H_Hat(H_Hat) inherently requires implementing the
generic proxy input basis that has now been elaborated on the first two
pages of my proof. (The rest of the proof can be ignored).

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

With this generic proxy input basis we can now see how the actual
halting status of Ĥ(<Ĥ>) can be correctly decided. This is shown on page 2.

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

I do not analyze the halting status of H(<Ĥ>,<Ĥ>) because this involves
the additional complexity of two halt deciders coordinating with each
other. I only examine how the embedded copy of H at state Ĥ.qx decides
its input.

> Less clear when the test function involves solving an open mathematical
> problem to see whether or not it halts.
> But basically what you are saying is that we should avoid that terminology.
>>
>> I've let a lot of very lax use of language go unremarked on. It's just
>> tedious trying to correct every misuse of terms from someone like PO who
>> has not read a single book on the topic. But it's a mistake. In fact,
>> if I had a do-over from all those years ago, I'd talk only in terms of
>> recursive and recursively enumerable languages. These terms can't be
>> abused so easily.
>>
>> In these terms, the halting theorem is then a trivial corollary of a
>> more general theorem: that for any non-empty alphabet there are
>> recursively enumerable languages that are not recursive. This is, in
>> fact, how Linz gives the proof. The old proof is given because of its
>> historical interest.
>>
> PO has modified his claims on several occasions, but usually he has claimed
> not to have a general halt decider, but to have found a flaw in the H_Hat(H_Hat)
> proof.
> But yes, it's high time we moved on to other proofs that halt deciders cannot
> be built.
>

That I have correctly refuted the halting theorem would seem to be
sufficiently "interesting" (AKA significant) by itself.

--
Copyright 2021 Pete Olcott

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

On 5/26/2021 5:41 PM, Ben Bacarisse wrote:
> Malcolm McLean <malcolm.arthur.mclean@gmail.com> writes:
>
>> On Wednesday, 26 May 2021 at 16:31:10 UTC+1, Ben Bacarisse wrote:
>>> Malcolm McLean <malcolm.ar...@gmail.com> writes:
>>>
>>>> On Wednesday, 26 May 2021 at 11:59:25 UTC+1, Ben Bacarisse wrote:
>>>>> Malcolm McLean <malcolm.ar...@gmail.com> writes:
>
>>>>>> So what about, say, a machine which halts when it finds a counter-example
>>>>>> to Fermat's last theorem? I believe that the theorem has now been proved,
>>>>>> with a highly complex proof, so that machine is known to be
>>>>>> non-halting.
>>>>> Right.
>>>>>> But what does it mean to say that it is "decidable?"
>>>>> PO's rote answer gives the missing clue. Decidability is a property of
>>>>> sets. A set is decidable if a TM exists that accepts all members and
>>>>> rejects all non-members. As a result, all finite sets are decidable, so
>>>>> if the second "it" in your question refers to the single string encoding
>>>>> the computation you describe above (a FLT counter-example search TM) then "it is
>>>>> decidable" because the only set we might be referring to is the
>>>>> singleton set that contains it.
>>>>>
>>>>> I'm not 100% sure this is what you were asking, but it's my best shot at
>>>>> an answer.
>>>>>
>>>> So by "decidable" we mean that one of the two trivial Turing machines
>>>> "write true" or "write false" must decide it correctly. Not that it is
>>>> possible to write a machine that decides it correctly if we don't know
>>>> the answer.
>>> I am pretty sure I misunderstood your question. First, let me clarify
>>> what the term means in general:
>>>
>>> Technically neither of your examples decides the set in question. In
>>> formal terms, the set being decided is always a subset of N, so the
>>> decider for your example looks for the string encoding of the number of
>>> that one single computation and accepts only that one string while
>>> rejecting all others. (It's safe to be slightly less technical and
>>> forget about subsets of N. The set being decided can then be just a
>>> subset of the finite strings over some finite alphabet.)
>>>
>>> But I don't think you were asking what it means for a singleton set to
>>> be decidable. You were asking, I think, about what it means for the
>>> /halting/ of an particular instance to be "decidable". On that
>>> question, I would suggest one tries to avoid that usage altogether. As
>>> best as I can tell, PO uses it to mean that some TM gets the answer
>>> right.
>>>
>>> Have I understood what you were asking this time?
>>>
>> Yes. WIth the interminable H_Hat(H_Hat) example, if the offered H is
>> reasonably simple, it's easy to build a decider which is more than a
>> simple stub, and gives the correct answer for H_Hat(H_Hat). So it's
>> easy to see that H_Hat(H_Hat) is "decidable".
>
> I can only urge you not to use the term in this way.
>

void H_Hat(u32 P)
{ u32 Input_Halts = Halts(P, P);
if (Input_Halts)
HERE: goto HERE;
}

What is the right way to say it?

The element of the set of computations specified by the input to
H_Hat(H_Hat) is a member of the set of non-halting computations.

>> Less clear when the test function involves solving an open mathematical
>> problem to see whether or not it halts.
>
> Well we know it's so hard that no algorithm can do it in general.
>

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

The element of the set of computations specified by the input to Ĥ(<Ĥ>)
is a member of the set of non-halting computations when Ĥ.qx specifies
the first state of a simulating halt decider.

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

>> But basically what you are saying is that we should avoid that
>> terminology.
>
> Yes. Sets are decidable. And referring to an instance as decidable
> makes me think the author is referring to the singleton set containing
> that instance.
>

--
Copyright 2021 Pete Olcott

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

On 5/26/2021 1:17 PM, Malcolm McLean wrote:
> On Wednesday, 26 May 2021 at 16:31:10 UTC+1, Ben Bacarisse wrote:
>> Malcolm McLean <malcolm.ar...@gmail.com> writes:

> Yes. With the interminable H_Hat(H_Hat) example, if the offered H is
> reasonably simple, it's easy to build a decider which is more than a
> simple stub, and gives the correct answer for H_Hat(H_Hat). So it's
> easy to see that H_Hat(H_Hat) is "decidable".

void H_Hat(u32 P)
{ u32 Input_Halts = Halts(P, P);
if (Input_Halts)
HERE: goto HERE;
}

int main()
{ u32 Input_Would_Halt = Halts((u32)H_Hat, (u32)H_Hat);
Output("Input_Would_Halt = ", Input_Would_Halt);
}

You are agreeing that H_Hat(H_Hat) is decidable,

I am taking this to mean that H_Hat(H_Hat) can be correctly determined
to be a member of the set of non halting computations.

> Less clear when the test function involves solving an open mathematical
> problem to see whether or not it halts.

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

Yet fail to see the equivalence of Ĥ(<Ĥ>) to Halts((u32)H_Hat,(u32)H_Hat);

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

--
Copyright 2021 Pete Olcott

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

On 5/27/2021 10:20 AM, Ben Bacarisse wrote:
> olcott <NoOne@NoWhere.com> writes:
>
>> On 5/26/2021 7:00 PM, Ben Bacarisse wrote:
>>> olcott <NoOne@NoWhere.com> writes:
>>>
>>>> On 5/25/2021 8:58 PM, Ben Bacarisse wrote:
>>>>> olcott <NoOne@NoWhere.com> writes:
>>>>>
>>>>>> My halt decider correctly decides halting on inputs with pathological
>>>>>> self-reference on the basis of proxy input that has the pathological
>>>>>> self-reference removed.
>>>>>
>>>>> No. Your decider is factually wrong about the halting of at least one
>>>>> case. You accept the facts that
>>>>>
>>>>> (a) Halts(H_Hat, H_Hat) is false, and
>>>>> (b) H_Hat(H_Hat) is a finite (AKA halting) computation.
>>>>
>>>> It turns out that (b) is a finite computation
>>>
>>> Yes, everyone knows this. That's why Halts is not a halt decider.
>>>
>>>> in the exactly same way that an infinite loop that has been aborted is
>>>> a finite computation. I explain this much better now.
>>>
>>> We don't need a better explanation of why Halts is not a halting
>>> decider. You need to give the problem that Halts /is/ deciding a proper
>>> name. It is not the halting problem.
>>>
>>>>> What you deny is that a halt decider is a TM that answers yes/true/1 for
>>>>> all inputs representing halting computations and no/false/0
>>>>> otherwise.
>>>
>>> Another opportunity for you to accept this basic fact about the problem
>>> you claim to be talking about goes un-taken.
>>>
>>>>> I was going to say that the honest response at this point would be for
>>>>> you to rename the property you claim to be deciding, but I read on and
>>>>> it seems you might not even know what the halting problem even is.
>>>>>
>>>>>> On 5/24/2021 6:37 PM, Ben Bacarisse wrote:
>>>>>
>>>>>>> Every instance of the halting problem is decidable, (but you don't know
>>>>>>> what decidable means,
>>>>>>
>>>>>> Decidable means that a membership algorithm exists.
>>>>>
>>>>> That sounds like rote learning to me. Can you use this definition to
>>>>> make my remark sufficiently exact that's it is obviously true?
>>>>
>>>> Your most recent post did teach me that I had been saying some things
>>>> somewhat incorrectly.
>>>>
>>>> void H_Hat(u32 P)
>>>> {
>>>> u32 Input_Halts = Halts(P, P);
>>>> if (Input_Halts)
>>>> HERE: goto HERE;
>>>> }
>>>>
>>>> The pathological self-reference error arises in the halting theorem
>>>> from the fact that both return values: {0, 1} from Halts() to H_Hat()
>>>> are incorrect when H_Hat() is invoked with its own machine address as
>>>> input.
>>>
>>> Why do you say that both 0 and 1 are incorrect?
>>
>> I am stopping at you first big mistake indicting that you are not
>> bothering to hardly pay any attention at all.
>
> Great. So my statements above that you are not talking about the
> halting problem is not a big mistake. Or were you not paying attention?
>

People in the dialogue seem to have a very short attention span so I
only focus on one point at a time. When I do this they quickly spout off
some unsupported dogmatic assertion or change the subject or both.

> And when I stated that you deny the basics facts about the halting
> problem, that too was not a big mistake. Or were you not paying
> attention then either?
>

You made too many mistakes to respond to. If we don't stay laser
focusing on a single mistake until it is resolved it never ever gets
resolved. It took you 4.5 years to finally acknowledge the infinitely
nested simulation of:

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

>> Even though H_Hat(H_Hat) either halts or fails to halt neither true
>> nor false are return values that Halts() can possibly correctly return
>> to H_Hat() in the computation Halts((u32)H_Hat, (u32)H_Hat);
>
> I explained why this is either incorrect reasoning or bad use or terms.

The problem for you is that it is an accurate use of terms and it lets
the hot air out of your attempt at rebuttal.

> And I answered your question assuming both interpretations. I can't
> make you pay attention to these problems. They remain quoted below if
> you want to address them.
>
> Also below is the really big question that you are avoiding. No doubt
> that is why you've pulled out the "I'll stop at the first thing I can
> legitimately object to" stunt. That big question is that you don't know
> what the instances of the halting problem are!
>

Yes you always focus on these tedious little things utterly ignoring
that the gist of what I said does correctly refute the halting theorem.

So I find an alternative correct way to say the things that I need to say.

For some simulating halt deciders H and some (Turing machine description
P / finite string I) pairs there is no Boolean value that H can return
to P that corresponds to the actual halting behavior of P(I) in the
computation H(P,I).

If anyone says is less precisely than this it is an intentionally
disingenuous misrepresentation.

>>> This is real code is it
>>> not? There really is (you tell us) a function Halts. It's a partial
>>> halt decider of your own design. You get to say what the correct answer
>>> is and, presumably, your code gives what you consider to be the correct
>>> answer. If you were not being so secretive, you'd publish Halts and we
>>> could all see what you consider to be the correct answer for every
>>> input.
>>>
>>>> If as you say all inputs halt or fail to halt then what is the proper
>>>> technical name for cases like the above case?
>>>
>>> If you are not talking about your actual code, and really meant to ask
>>> the hypothetical question "imagine that Halts is a perfect halt decider,
>>> what is the technical term for the call H_Hat(H_Hat)?" then the answer
>>> is "a contradiction" or maybe more correctly "an example that leads to a
>>> contradiction".
>>>
>>>>>> What I don't know is what an instance of the halting problem is.
>>>
>>>>>> It would seem to me that an instance of a decision problem would be a
>>>>>> Question/Input pair where the input is a specific finite string.
>>>>>
>>>>> So you've spent the last fifteen years talking about the halting problem
>>>>> without knowing what the problem instances are? No wonder you have
>>>>> spouted so much nonsense. And when I've told you (as I have on many
>>>>> occasions) the halting problem is, did you not understand me? If not,
>>>>> why didn't you ask for clarification?
>>>>>
>>>>> Would you like to know what the instances of the halting problem are?
>>>>
>>>> In computability theory and computational complexity theory, a
>>>> decision problem is a problem that can be posed as a yes–no question
>>>> of the input values. https://en.wikipedia.org/wiki/Decision_problem
>>>>
>>>> If we assume that a decision problem instance is a specific
>>>> Question/Input pair and the input is a specific finite string
>>>>
>>>> Then a halting problem instance would be does this Turing machine
>>>> Description P halt on its finite string I input?
>>>
>>> No. Would you like to know what the instances of the halting problem
>>> are? Just say no if you prefer to carry on pontificating in ignorance of
>>> the topic.
>>>
>>> You should write [P] for the encoding (description) of machine P and
>>> <x,y> for the encoding of the pair of strings x and y. P(I) is then a
>>> computation that either halts or fails to halt (I prefer "is finite or
>>> not") and <[P],I> is the string representing that computation.
>>>
>>> Can you use that notation to say what the instances of the halting
>>> problem are, and which instances should be accepted and which rejected?
>>>
>

On 5/23/2021 9:59 AM, Kaz Kylheku wrote:
> On 2021-05-22, olcott <NoOne@NoWhere.com> wrote:
>> On 5/22/2021 9:56 AM, Kaz Kylheku wrote:

>> Because we know that the only difference in the behavior of a simulating
>> halt decider and a simulator is that the simulating halt decider stops
>> simulating some of its inputs we can examine the behavior of these
>> inputs in a simulator to determine whether or not a simulating halt
>> decider would stop simulating these inputs.
>
> Sure, but the difference in behavior means we are jumping to a different
> column of the input-decider matrix and are no longer on the diagonal.
> To return to the diagonal while staying in the same column, we must
> switch to a different row: the row for the test case which is based on
> that column's decider. Where row and column match, we have an incorrect
> or nonterminating halting decision, according to this conventional analysis.
>
> Any reasoning that leads you, through substitutions, to discovering a
> good halting decision, but which is off the diagonal trace, has led you
> to an irrelevant configuration.

The substitutions are not actually made they are a teaching tool.

> The proof says only that the
> configurations on the diagonal are incorrect or non-halting. The
> proof does not make any assertions about non-diagonal configuations,
> therefore those configurations are not counterexamples to the proof's
> claims.

Now that I actually studied the very simple Sipser diagonalization proof
https://www.youtube.com/watch?v=jM6osxSX9GA

I can address this objection on the basis of adapting my H_Hat to become
a little closer to the Sipser D:

bool D(u32 P)
{ if ( H(P, P) )
HERE: goto HERE;
return false;
}

D correctly decides not halting on itself when H is based on simulating
its input.

On 5/27/2021 7:45 PM, Ben Bacarisse wrote:
> A halt decider is a TM that answers yes/true/1 for all instances
> representing halting computations and no/false/0 otherwise.

D(<D>) is decided to be a non-halting computation on the basis that an
aspect of this computation was aborted.

Its embedded halt decider H(<D>,<D>) aborts the simulation of its input,
which is an aspect of the complete D(<D>) computation.

> The undecidability of halting is precisely the claim that the entire
> diagonal consists of incorrect answers or non-halting. Since for every
> decider there is a diagonal entry, every decider is associated with a
> test case it does not handle.
>
> If every decider has at least one test case it does not handle, then
> there does not exist a universal (= handles all cases) decider:
> there is no algorithm that decides all cases of halting.
>

--
Copyright 2021 Pete Olcott

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