Re: Hypothetical possibilities --- Complete Proof

On 8/4/2024 9:33 PM, Ben Bacarisse wrote:

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

On 02/08/2024 23:42, Ben Bacarisse wrote:

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

Of course these traces don't support PO's overall case he is claiming,
because the (various) logs show that DDD halts, and that HHH(DDD) reports
DDD as non-halting, exactly as Linz/Sipser argue. Er, that's about it!

PO certainly used to claim that false (non-halting) is the correct
result "even though DDD halts" (I've edited the quote to reflect a name
change).  Unless he's changed this position, the traces do support his
claim that what everyone else calls the wrong answer is actually the
right one.

>
So, in your opinion, what do you believe is PO's criterion for "correct
result", exactly?  It would be handy if you can give a proper mathematical
definition so nobody will have any doubt what it is. Hey, I know you're
more than capable of getting a definition right, so let's have that
definition!

 You are joking right?
 PO has no idea what he's talking about.  I mean that more literally than
you might think.  The starting point is a gut feeling ("If God can not
solve the Halting Problem, then there is something wrong with the
problem") shored up by a basic axiom -- that PO is never wrong.  This
produces a endless sequence of nonsense statements, like
    "the fact that a computation halts does not entail that it is a
   halting computation" [May 2021]
    "The fact [that] a computation stops running does not prove that it
   halts" [Apr 2021]
 and
    "The same halt decider can have different behavior on the same input"
   [Jan 2021]
 

Definition:  A TM P given input I is said to "halt" iff ?????
              or whatever...

 Do you really think I can fathom what PO considers to be the "correct
result" in formal terms?  He certainly doesn't know (in general) and I
can't even hazard a guess.
 

It's easy enough to say "PO has his own criterion for halting, which is
materially different from the HP condition, and so we all agree PO is
correct by his own criterion, but that does not say anything about the HP
theorem because it is different from the HP definition".

 He's been very, very clear about this:
    "A non-halting computation is every computation that never halts
   unless its simulation is aborted.  This maps to every element of the
   conventional halting problem set of non-halting computations and a few
   more."
 There is something called the "conventional halting problem" and then
there is there is the PO-halting problem.
 He's even explained in detail at least one of these "few more" cases.
He sketched the simulator and explained that false (non-halting) is
correct because of what would happen if line 15 (the check for "needs to
be aborted") were commented out.  The "few more" cases are halting
computations that would not halt if the code where a bit different -- if
the "decider" did not stop the simulation.
 That was in 2020.  The last four years have all been about fleshing out
this sketch of a decider for this "other" halting condition.  I am
staggered that people are still talking about it.  Until he repudiates
the claim that false is the correct answer for some halting
computations, there is nothing more to discuss.
 

But is that /really/ something PO agrees with?

 Does he really agree with what he said?  Does he agree that there is
"the conventional halting problem" and also his own non-halting that
includes "a few more" computations?  Does he agree with himself when he
stated, in Oct 2021, that "Yes that is the correct answer even though
P(P) halts" when asked "do you still assert that H(P,P) == false is the
"correct" answer even though P(P) halts?"?
 

I don't think so somehow,
because I'm pretty sure PO believes his claim "refutes" the HP result.

 I am sure he still agrees with what he has said, and I am equally sure
he still thinks he has refuted a theorem about something else.  He,
literally, has no idea what he is talking about.
 

He
wouldn't say that if he freely acknowleded that he had invented a
completely different definition for halting.

 Why do you say that?  Are you assuming he is sane?  Remember he has
published a website intended to bring new scripture to the world
(https://the-pete.org/) and has asserted in a court of law (through
lawyers, maybe) that he is God.
 

Also, for what you're saying
to be the right way of looking at things, PO would have to admit that the
HP proof with its standard definition of halting is valid, and that there
is nothing wrong with the Linz proof, other than it not applying to his own
favourite PO-halting definition.

 Only if you assume his mind functions like yours or mine.  Take this
quote on the point you make example:
    "My current proof simply shows exactly how the exact Peter Linz H
   would correctly decide not halting on the exact Peter Linz Ĥ.
    This definition of halting circumvents the pathological self-reference
   error for every simulating halt decider:
    An input is decided to be halting only if its simulation never needs
   to be stopped by any simulating halt decider anywhere in its entire
   invocation chain."  [May 2021]
 He clearly thinks that having a different definition of halting
invalidates Linz's proof.
 

I.e. I think your way of looking at it is a bit "too easy" - but I'd be
happy to be convinced! Personally I suspect PO has no such "new and
different definition" and that anything along those lines PO is thinking of
will be quite incoherent.  No doubt you could make some definition that is
at least coherent but we have to ask ourselves - is that definition
/really/ what PO is thinking???

 There is no doubt that he has a different definition.  How could he have
been more clear?  There is the conventional halting problem and then
there is what he is considering that includes "a few more" cases.  He
clearly tells us that false is the correct answer for some halting
computations.  He gives a (flabby) definition of PO-halting and states
that it "circumvents" the proof.
 

Nowadays, I think PO's position is more that:
-  yes, DDD() halts when run directly
-  but DDD() when it runs inside HHH simulator /really/ does not halt, in some kind of
    sense that it /really/ has infinite recursion which would never end
    however far it was simulated (because it "exhibits" infinite recursion in some way)
-  and yes, DDD() /does/ halt when simulated within UTM(DDD),
-  but the behaviour of DDD depends on who is simulating it.  It terminates when
    UTM simulates it, but doesn't terminate when HHH simulates it, due to some
    kind of pathelogical relationship specifically with HHH.  This difference in
    simulation is /more/ than one simulator aborting earlier than the other...

 I fear you have got sucked into the PO tar-pit.  Until he categorically
repudiates the claim that H(P,P) == false is the correct answer even
though P(P) halts, I would say that there is nothing more to say.
 Obviously his position "evolves" because he has to keep people talking
to him (has is a narcissist and needs the attention).  But cranks are
never wrong so he is stuck with what he's said in the past.  All of the
last four years has been about layering piles of detail on the basic
notion that if the decider were not to halt the computation, the result
would be a non-halting computation so saying "does not halt" is correct
even though the computation halts.
 

The proof that I was correct all along for the last three years is
void DDD()
{
   HHH(DDD);
   return;
}
*Anyone that knows C should agree that*
DDD correctly emulated by any HHH that can possibly exist
cannot possibly reach its own "return" instruction.
That only gets people to accept the first half of the Sipser
approved criteria and see what Ben sees.
When we add the this "return" instruction is Jeff Barnett's
mentioned "halt state" things get much clearer. Then we might
begin to see:
HHH computes the mapping from its input finite string of x86
machine code... to the above behavior that does not halt.
Everyone persistently ignores that deciders only compute
the mapping from their input finite string. This is the
key mistake of the conventional halting problem proof that
even Linz makes. *The Linz proof is the greatest proof*
--
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer