On 12/18/2021 3:04 PM, André G. Isaak wrote:
> On 2021-12-18 13:44, olcott wrote:
>> On 12/18/2021 2:07 PM, Richard Damon wrote:
>>>
>>> On 12/18/21 2:28 PM, olcott wrote:
>>>> On 12/18/2021 5:06 AM, Richard Damon wrote:
>>>>> On 12/17/21 11:29 PM, olcott wrote:
>>>>>> On 12/17/2021 10:18 PM, Richard Damon wrote:
>>>>>>> On 12/17/21 10:47 PM, olcott wrote:
>>>>>>>> On 12/17/2021 9:34 PM, Richard Damon wrote:
>>>>>>>>> On 12/17/21 9:59 PM, olcott wrote:
>>>>>>>>>> On 12/17/2021 8:44 PM, Richard Damon wrote:
>>>>>>>>>>> On 12/17/21 9:26 PM, olcott wrote:
>>>>>>>>>>>> On 12/17/2021 7:50 PM, Richard Damon wrote:
>>>>>>>>>>>>> On 12/17/21 7:54 PM, olcott wrote:
>>>>>>>>>>>>>> On 12/17/2021 6:43 PM, Ben Bacarisse wrote:
>>>>>>>>>>>>>>> olcott <NoOne@NoWhere.com> writes:
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> On 12/17/2021 3:25 PM, Ben Bacarisse wrote:
>>>>>>>>>>>>>>>>> olcott <NoOne@NoWhere.com> writes:
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> A function f with domain D is said to be
>>>>>>>>>>>>>>>>>> Turing-computable
>>>>>>>>>>>>>>>>>> or just computable if there exists some Turing machine
>>>>>>>>>>>>>>>>>> M = (Q, Σ, Γ, δ, q0, □, F) such that q0 w ⊢* Mqff(w),
>>>>>>>>>>>>>>>>>> qf ∈ F
>>>>>>>>>>>>>>>>>> for all w ∈ D (Linz:1990:243)
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> We all know your cut and paste skills are top notch.
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> Olcott paraphrase of above machine definition: Machine
>>>>>>>>>>>>>>>>>> M begins at
>>>>>>>>>>>>>>>>>> start state q0 on input w and transitions to qf as a
>>>>>>>>>>>>>>>>>> function of input
>>>>>>>>>>>>>>>>>> w.
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> But that's not a correct paraphrase.  As for the jumble
>>>>>>>>>>>>>>>>> of words that is
>>>>>>>>>>>>>>>>> "the computable function copy of H at Ĥ.qx", well, I
>>>>>>>>>>>>>>>>> despair.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> I take this to mean that you have no idea what the
>>>>>>>>>>>>>>>> behavior of Ĥ
>>>>>>>>>>>>>>>> applied to ⟨Ĥ⟩ would be:
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> You should, in general, take me to mean what I say, with
>>>>>>>>>>>>>>> as little
>>>>>>>>>>>>>>> interpretation as you can muster.  Your track record in
>>>>>>>>>>>>>>> paraphrasing me
>>>>>>>>>>>>>>> is abysmal.  Is my claim that I despair at your jumble of
>>>>>>>>>>>>>>> words in some
>>>>>>>>>>>>>>> way unclear?
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Since this is equivalent to Linz notation you can't say
>>>>>>>>>>>>>> that my question is not clear?
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>     Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qy
>>>>>>>>>>>>>>     Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> What would the behavior of Ĥ applied to ⟨Ĥ⟩ be if we
>>>>>>>>>>>>>> assume that Ĥ.qx acts exactly as if it was UTM(⟨Ĥ⟩, ⟨Ĥ⟩) ???
>>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> So, if you want to DEFINE that you H IS the same as UTM,
>>>>>>>>>>>>> then you have shown that H(<H^>,<H^>) nevers returns an
>>>>>>>>>>>>> answer, so while H^(<H^>) is FOR THIS H, non-halting, it
>>>>>>>>>>>>> doesn't matter as this H never answers, and so it wrong
>>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> Yes that it correct. I don't think that Ben understands
>>>>>>>>>>>> these things well enough to understand that.
>>>>>>>>>>>>
>>>>>>>>>>>>> Hypotheticals which change the contents of H^
>>>>>>>>>>>>
>>>>>>>>>>>> All hypotheticals are imaginary and have no effect on the
>>>>>>>>>>>> actual world.
>>>>>>>>>>>>
>>>>>>>>>>>>> (which include its copy of H) don't say anything about the
>>>>>>>>>>>>> original H^ that was built from a different H.
>>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qy ∞ // infinite loop added
>>>>>>>>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
>>>>>>>>>>>>
>>>>>>>>>>>> When we put the infinite loop back in Ĥ applied to ⟨Ĥ⟩ still
>>>>>>>>>>>> never stops running because it still specified infinitely
>>>>>>>>>>>> nested simulation. It never reaches the infinite loop.
>>>>>>>>>>>
>>>>>>>>>>> So, which H do you want to try to claim to be your H, that is
>>>>>>>>>>> supposedly correct?
>>>>>>>>>>>
>>>>>>>>>>> The one that gets stuck in the infinite loop, and thus
>>>>>>>>>>> doesn't answer, or the one that DOES abort the simulation,
>>>>>>>>>>> and thus return the answer to H^ which lets H^ be halting,
>>>>>>>>>>> and thus H was wrong?
>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>>> The fact that for the case that H is identical to UTM gives
>>>>>>>>>>>>> a non-halting H^ doesn't provide ANY evidence that H^ built
>>>>>>>>>>>>> from an H that answers is non-halting.
>>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> When we understand that the hypothetical pure simulation of
>>>>>>>>>>>> the input to any simulating halt decider does provide the
>>>>>>>>>>>> correct halt status criterion measure for every input then
>>>>>>>>>>>> we understand that this is correct: Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
>>>>>>>>>>>
>>>>>>>>>>> No, because H isn't supposed to answer about the
>>>>>>>>>>> 'Hypothetcial' input based on a different H than the one that
>>>>>>>>>>> H^ is actually built on, but the actual input that it was
>>>>>>>>>>> given which is an H^ built on the H that you claim to be the
>>>>>>>>>>> correct answering one.
>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> Any input that must have its simulation aborted to prevent
>>>>>>>>>>>> the infinite execution of this input is an input that never
>>>>>>>>>>>> halts.
>>>>>>>>>>>
>>>>>>>>>>> No. Pure LIE.
>>>>>>>>>>>
>>>>>>>>>>> Halting is based on what the computation ACTUALLY DOES.
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> No one ever thought this aspect through before. Linz rejects
>>>>>>>>>> simulation before ever fully examining it.
>>>>>>>>>
>>>>>>>>> No, he doesn't, he doesn't distinguish at all about how the
>>>>>>>>> halt decider works, as it just doesn't matter. All that matters
>>>>>>>>> is that H needs to be a DEFINED machine, and he looks at the
>>>>>>>>> answer it gives, by how ever it does it.
>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> Every input that never halts when its pure simulation by H
>>>>>>>>>> never halts is an input that never halts.
>>>>>>>>>>
>>>>>>>>>> The input to Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ cannot possibly reach its final
>>>>>>>>>> state when 0 to ∞ steps of this input are simulated by H.
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> But it does when given to a real UTM. UTM applied to <H^> <H^>
>>>>>>>>> will halt if H applied to <H^> <H^> goes to H.qn.
>>>>>>>>>
>>>>>>>>> You need to FIRST define your H, and once you do you are NOT
>>>>>>>>> allowed to change it in determining what H^ does.
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>>> Your definition is just how you seem to befine your POOP.
>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> The meaning of those words proves that those words are correct.
>>>>>>>>>>>
>>>>>>>>>>> LIE.
>>>>>>>>>>>
>>>>>>>>>>> The meaning of Halting is that the thing ACTUALLY being
>>>>>>>>>>> decided on reaches a final Halting state.
>>>>>>>>>>>
>>>>>>>>>>> Since the ACUTAL H^ applied to <H^> does reach its final
>>>>>>>>>>> haltibng state,
>>>>>>>>>>
>>>>>>>>>> Because you know that TM's cannot have TM's for inputs it
>>>>>>>>>> seems quite stupid that you say that Ĥ.qx is applied to Ĥ.
>>>>>>>>>
>>>>>>>>> Who said H^.qx is applied to H^. WHERE DID I SAY THAT?
>>>>>>>>>
>>>>>>>> When everyone says
>>>>>>>>
>>>>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
>>>>>>>> if Ĥ applied to ⟨Ĥ⟩ does not halt.
>>>>>>>>
>>>>>>>> Instead of saying
>>>>>>>> if simulated ⟨Ĥ⟩ applied to ⟨Ĥ⟩ does not halt.
>>>>>>>>
>>>>>>>> They are saying that Ĥ.qx is being applied to a TM and not a TM
>>>>>>>> description.
>>>>>>>
>>>>>>> No, they are appling the definition of a CORRECT Halt Decider.
>>>>>>>
>>>>>>>>
>>>>>>>> Ĥ.qx is NOT applied to Ĥ
>>>>>>>> Ĥ.qx is applied to ⟨Ĥ⟩
>>>>>>>
>>>>>>> Right, but if H is a correcg halt decider (as is your claim) than
>>>>>>> H (and just H^.qx) must go to qy if H^ applied to <H^> halts and
>>>>>>> to qn if it doesn't.
>>>>>>>
>>>>>> That is under the false assumption that the behavior of the input
>>>>>> is the same when executed inside the halt decider as when it is
>>>>>> executed outside the halt decider.
>>>>>>
>>>>>
>>>>> But if they are different, that says that either the decider is NOT
>>>>> being an accurate simulator or the input is not a representation of
>>>>> an actual Algorithm.
>>>>>
>>>>
>>>> When the input to H is intentionally defined to have different
>>>> behavior inside of H than outside of H then this behavior will
>>>> necessarily vary.
>>>
>>> But H^ DOESN'T have different behavior inside of H than outside, and
>>> thus neither does its representation.
>>>
>>> H^ ALWAYS does the opposite of what the copy of H says it will do,
>>> whether it is being decided by H or not.
>>>
>>
>> The actual behavior of UTM(⟨Ĥ⟩ ⟨Ĥ⟩) of the actual input to to Ĥ.qx is
>> the only thing that this computable function is accountable for.
>>
>> Actual computer scientists would know this.
>
> Actual computer scientists would know that the claim that there is a
> computable function at Ĥ.qx is incoherent nonsense.
>
> André
>

98% of them would simply assume that I must be wrong and dismiss what I
say out-of-hand without complete review.

Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qy // infinite loop removed
Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn

The infinite loop has been removed because the behavior of the input to
UTM(⟨Ĥ⟩ ⟨Ĥ⟩) applied to the input to Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ is the same with or
without this infinite loop.

Actual computer scientists would know that computable function deciders
are only accountable for mapping their actual inputs to an accept /
reject states.

They would consistently remember that no computable function can ever be
judged on the basis of the behavior of non-inputs.

They would have to carefully study that in the case of a halt decider
this means that the halt status decision must have the behavior of
UTM(⟨Ĥ⟩ ⟨Ĥ⟩) applied to the actual input of the halt decider as its
ultimate basis.

The above sentence is the crux of my whole proof. Paraphrase:

The actual behavior of the pure simulation of the input to every
simulating halt decider is the ultimate halt deciding basis of every
simulating halt decider applied to every input pair.

--
Copyright 2021 Pete Olcott

Talent hits a target no one else can hit;
Genius hits a target no one else can see.
Arthur Schopenhauer