On Wednesday, May 4, 2022 at 11:54:14 PM UTC-4, olcott wrote:
> On 5/4/2022 10:43 PM, Dennis Bush wrote:
> > On Wednesday, May 4, 2022 at 11:38:54 PM UTC-4, olcott wrote:
> >> On 5/4/2022 10:20 PM, Dennis Bush wrote:
> >>> On Wednesday, May 4, 2022 at 11:09:35 PM UTC-4, olcott wrote:
> >>>> On 5/4/2022 9:59 PM, Dennis Bush wrote:
> >>>>> On Wednesday, May 4, 2022 at 10:55:07 PM UTC-4, olcott wrote:
> >>>>>> On 5/4/2022 9:28 PM, Ben wrote:
> >>>>>>> olcott <polc...@gmail.com> writes:
> >>>>>>>
> >>>>>>>> On 5/4/2022 7:59 PM, Ben wrote:
> >>>>>>>>> olcott <polc...@gmail.com> writes:
> >>>>>>>>>
> >>>>>>>>>> On 5/4/2022 9:16 AM, Ben wrote:
> >>>>>>>>>>> olcott <polc...@gmail.com> writes:
> >>>>>>>>>>>
> >>>>>>>>>>>> On 5/2/2022 6:10 PM, Ben wrote:
> >>>>>>>>>>>>> olcott <polc...@gmail.com> writes:
> >>>>>>>>>>>>>
> >>>>>>>>>>>>>> On 5/2/2022 11:39 AM, Ben wrote:
> >>>>>>>>>>>>>>> olcott <polc...@gmail.com> writes:
> >>>>>>>>>>>>>>>
> >>>>>>>>>>>>>>>> It is clear that the input to H(P,P) specifies infinitely nested
> >>>>>>>>>>>>>>>> simulation to H.
> >>>>>>>>>>>>>>> What two pointers must be passed to H for H to tell up about the halting
> >>>>>>>>>>>>>>> of P(P)? If H can't report on the halting of the computation P(P) it is
> >>>>>>>>>>>>>>> not a halt decider, and you have already told use that H(P,P) == false
> >>>>>>>>>>>>>>> and that P(P) halts.
> >>>>>>>>>>>>>>
> >>>>>>>>>>>>>> If H can report on the halting of non-input P(P) then it is not a
> >>>>>>>>>>>>>> decider because deciders only compute the mapping from inputs to final
> >>>>>>>>>>>>>> states.
> >>>>>>>>>>>>> TM deciders compute mappings from inputs to final states /according to
> >>>>>>>>>>>>> some property of the inputs/
> >>>>>>>>>>>>
> >>>>>>>>>>>> That par is exactly correct.
> >>>>>>>>>>>>
> >>>>>>>>>>>>> -- whether the input represents, for
> >>>>>>>>>>>>
> >>>>>>>>>>>> That part has been the key error of everyone in that they all believe
> >>>>>>>>>>>> that is can represent something other than what it actually specifies.
> >>>>>>>>>>>
> >>>>>>>>>>> So now, after thinking otherwise for years, you claim that there is no
> >>>>>>>>>>> way to even specify the computation P(P) for you pseudo-C halt decider
> >>>>>>>>>>> H. At least that is a clear admission that the halting of function
> >>>>>>>>>>> calls like P(P) can not be decided because, apparently, passing P and P
> >>>>>>>>>>> to H does not specify that computation, and you can't say what two
> >>>>>>>>>>> arguments /would/ specify it.
> >>>>>>>>>>>
> >>>>>>>>>>> A clear and unambiguous statement that no D such that D(X,Y) == true if
> >>>>>>>>>>> and only if X(Y) halts and false otherwise is possible would be the
> >>>>>>>>>>> honest way to move things on. If you were clear about this, maybe
> >>>>>>>>>>> someone will talk to you about [whatever] it is that your H is
> >>>>>>>>>>> deciding.
> >>>>>>>>> So you won't admit that no algorithm can do what D is specified to do?
> >>>>>>>>> You are just going to pretend that no one cares about actual halting.
> >>>>>>>>> I hope you see that by ignoring this point you are confirming that you
> >>>>>>>>> know D can't exist. If you thought such a D was possible, you'd be
> >>>>>>>>> shouting that from the roof tops since it's what everyone else says is
> >>>>>>>>> impossible.
> >>>>>>>>>
> >>>>>>>>>> I adapted my system so that I could empirically test this:
> >>>>>>>>>> H1(P,P)==true is empirically proven to be correct
> >>>>>>>>>> H(P,P)==false is empirically proven to be correct
> >>>>>>>>>
> >>>>>>>>> But neither can tell us squat about the halting of P(P) -- the thing
> >>>>>>>>> that H was originally supposed to decide.
> >>>>>>>>
> >>>>>>>> Are you simply wired to ignore my words so that you can disagree with
> >>>>>>>> everything that I say?
> >>>>>>>>
> >>>>>>>> H1(P,P)==true reports on the behavior of P(P).
> >>>>>>>
> >>>>>>> I try to ignore that bits that are irrelevant. These two deciders
> >>>>>>> decide all halting instances between them:
> >>>>>>>
> >>>>>>> bool H1(X, Y) { return true; }
> >>>>>>> bool H2(X, Y) { return false; }
> >>>>>>>
> >>>>>>> Neither is interesting. For H1, the key case is H1(H1_hat, H1_hat) or
> >>>>>>> maybe you call it H1(P1,P1) now since P is what you used to call H_hat.
> >>>>>>
> >>>>>> H1(P,P)==true is empirically proven to be correct
> >>>>>> H(P,P)==false is empirically proven to be correct
> >>>>>
> >>>>> If that is so then H and H1 don't perform the same mapping. This means that one (or both) do not compute the halting function.
> >>>>>
> >>>>> So which one doesn't compute the halting function?
> >>>> *ALL THESE THINGS ARE EASILY VERIFIABLE FACTS*
> >>>> Both take the machine code of P as input parameters and are provably
> >>>> correct simulations of this same input yet one correctly determines that
> >>>> its input halts and the other correctly determines that its input does
> >>>> not halt.
> >>>
> >>> Which means at least one is not computing the halting function. So which one is it?
> >>>
> >> The above paragraph means that it makes no mistakes in computing the
> >> halting function. This is a verifiable fact, not any mere opinion. The
> >> reason that I did the HP in C/x86 was so that every detail can be shown
> >> thus gaps in reasoning revealed.

Just because a simulating halt decider aborts doesn't necessarily mean it was correct to do so. On the other hand, a simulating halt decider that simulates to a final state is always correct and proves that any mapping of the same input to non-halting is necessarily incorrect.

> >
> > Any decider that maps the halting function performs the *same* mapping of inputs to outputs.
> That is now proven to be factually incorrect.

FALSE. The mapping of the halting function is DEFINED (i.e. is immutable and fixed) as:

M w maps to true if and only if M(w) halts, and
M w maps to false if and only if M(w) does not halt

So any halt decider that does not compute this *exact* mapping is not computing the halting function.

>
> If the above paragraph is proven to be a fact then this proves that both
> H and H1 compute the halting function correctly. The above paragraph can
> be proven to be a fact.
> > Since H and H1 perform different mappings they can't possibly both map the halting function.
> >
> > So which one doesn't?
> --
> Copyright 2022 Pete Olcott "Talent hits a target no one else can hit;
> Genius hits a target no one else can see." Arthur Schopenhauer