On 2/2/2022 10:42 PM, Richard Damon wrote:
> On 2/2/22 10:50 PM, olcott wrote:
>> On 2/2/2022 9:30 PM, Richard Damon wrote:
>>>
>>> On 2/2/22 10:12 PM, olcott wrote:
>>>> On 2/2/2022 8:57 PM, Richard Damon wrote:
>>>>> On 2/2/22 9:31 PM, olcott wrote:
>>>>>> On 2/2/2022 8:08 PM, Richard Damon wrote:
>>>>>>> On 2/2/22 8:41 PM, olcott wrote:
>>>>>>>> On 2/2/2022 6:22 PM, Richard Damon wrote:
>>>>>>>>> On 2/2/22 10:20 AM, olcott wrote:
>>>>>>>>>> On 2/1/2022 9:58 PM, André G. Isaak wrote:
>>>>>>>>>>> On 2022-02-01 20:44, olcott wrote:
>>>>>>>>>>>> On 2/1/2022 9:24 PM, André G. Isaak wrote:
>>>>>>>>>>>>> On 2022-02-01 19:57, olcott wrote:
>>>>>>>>>>>>>> On 2/1/2022 8:48 PM, André G. Isaak wrote:
>>>>>>>>>>>>>>> On 2022-02-01 19:37, olcott wrote:
>>>>>>>>>>>>>>>> On 2/1/2022 8:08 PM, André G. Isaak wrote:
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> ⟨Ĥ⟩ applied to ⟨Ĥ⟩ is completely meaningless.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> Sure and so is the "I am going to go to the" part of
>>>>>>>>>>>>>>>> "I am going to go to the store to buy some ice cream."
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> When you don't cut off what I said in the middle of the
>>>>>>>>>>>>>>>> sentence then it makes much more sense.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> Can ⟨Ĥ⟩ applied to ⟨Ĥ⟩ simulated by embedded_H possibly
>>>>>>>>>>>>>>>> transition to ⟨Ĥ⟩.qn ?
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> That's just as meaningless. You can simulate Ĥ applied to
>>>>>>>>>>>>>>> ⟨Ĥ⟩ or you can provide ⟨Ĥ⟩ ⟨Ĥ⟩ as the input to a
>>>>>>>>>>>>>>> simulator. You cannot simulate ⟨Ĥ⟩ applied to ⟨Ĥ⟩ anymore
>>>>>>>>>>>>>>> than you can apply ⟨Ĥ⟩ to ⟨Ĥ⟩.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> So you are simply being nit picky about my use of
>>>>>>>>>>>>>> terminology.
>>>>>>>>>>>>>
>>>>>>>>>>>>> Yes, I insist on terminology being used correctly. And any
>>>>>>>>>>>>> place where you attempt to publish your results will be
>>>>>>>>>>>>> equally, if not more, nit picky.
>>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> It is fine and good that you help correct my terminology.
>>>>>>>>>>>> What is not fine and good is for you to reject the essence
>>>>>>>>>>>> of the gist of what I am saying entirely on the basis that I
>>>>>>>>>>>> did not say it exactly according to conventions. The is what
>>>>>>>>>>>> Ben always did. He never paid any attention to the actual
>>>>>>>>>>>> substance of what I was saying.
>>>>>>>>>>>>
>>>>>>>>>>>>>> When ⟨Ĥ⟩ ⟨Ĥ⟩ is the input to simulating halt decider
>>>>>>>>>>>>>> embedded_H and embedded_H correctly determines that its
>>>>>>>>>>>>>> simulated input cannot possibly reach any final state then
>>>>>>>>>>>>>> embedded_H is necessarily correct to transition to Ĥ.qn
>>>>>>>>>>>>>> indicating that its simulated input never halts.
>>>>>>>>>>>>>
>>>>>>>>>>>>> But now you've just hidden your meaningless terminological
>>>>>>>>>>>>> abuse. "Its simulated input" is only meaningful when it is
>>>>>>>>>>>>> construed as meaning the simulation of the computation
>>>>>>>>>>>>> REPRESENTED by the input, i.e. the
>>>>>>>>>>>>
>>>>>>>>>>>> Not at all. A simulator simulates a finite string and the
>>>>>>>>>>>> actual behavior of this simulated finite string is the
>>>>>>>>>>>> ultimate basis of whether or not it specifies a finite
>>>>>>>>>>>> sequence of configurations.
>>>>>>>>>>>
>>>>>>>>>>> No. A simulator simulates a Turing Machine applied to an
>>>>>>>>>>> input. It takes as its input a finite string which represents
>>>>>>>>>>> that Turing Machine/Input pair. It's completely meaningless
>>>>>>>>>>> to talk about simulating a finite string.
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> It is possible for Turing machines to have blank tapes.
>>>>>>>>>>
>>>>>>>>>> The salient aspect for the Halting problem is whether or not
>>>>>>>>>> the finite string machine description specifies a finite or
>>>>>>>>>> infinite sequence of configurations. The ultimate basis for
>>>>>>>>>> determining this is the actual behavior of the simulated
>>>>>>>>>> finite string.
>>>>>>>>>>
>>>>>>>>>> Since this equally applies to machines having inputs and
>>>>>>>>>> machines not having inputs the distinction relative to inputs
>>>>>>>>>> is moot.
>>>>>>>>>>
>>>>>>>>>>>> If the correct simulation of ⟨Ĥ⟩ ⟨Ĥ⟩ by embedded_H cannot
>>>>>>>>>>>> possibly reach ⟨Ĥ⟩.qn then it is necessarily correct for
>>>>>>>>>>>> embedded_H to transition to Ĥ.qn and nothing else in the
>>>>>>>>>>>> universe can possibly refute this.
>>>>>>>>>>>
>>>>>>>>>>> Again, you're falling back on your belief that ⟨Ĥ⟩ applied to
>>>>>>>>>>> ⟨Ĥ⟩ is both meaningful (it isn't) and somehow distinct from H
>>>>>>>>>>> applied to ⟨Ĥ⟩.
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> The behavior of the simulated input when embedded_H applied to
>>>>>>>>>> ⟨Ĥ⟩ ⟨Ĥ⟩ is the ultimate measure of the halt status of this input.
>>>>>>>>>
>>>>>>>>> Which just proves you are not working on the Halting Problem,
>>>>>>>> No it only proves that you and André don't understand that a
>>>>>>>> halt decider computes the mapping from the inputs to an accept
>>>>>>>> or reject state (here is the part that you two don't understand):
>>>>>>>>
>>>>>>>> On the basis of the actual behavior specified by the actual input.
>>>>>>>> On the basis of the actual behavior specified by the actual input.
>>>>>>>> On the basis of the actual behavior specified by the actual input.
>>>>>>>>
>>>>>>>
>>>>>>> Which is DEFINED by what a the machine the input represents would
>>>>>>> do,
>>>>>>
>>>>>> These words prove themselves true on the basis of their meaning:
>>>>>> The actual behavior of the correct simulation of ⟨Ĥ⟩ ⟨Ĥ⟩ by
>>>>>> embedded_H is the ultimate measure of the behavior specified by
>>>>>> ⟨Ĥ⟩ ⟨Ĥ⟩.
>>>>>>
>>>>>
>>>>> WRONG, which shows you do not actually know the meaning of the words.
>>>> When you disagree that the correct simulation of a machine
>>>> description of a machine is the ultimate measure of the behavior
>>>> specified by this machine description it is just like saying that a
>>>> black cat is not a cat.
>>>>
>>>
>>> The problem is that 'Correct Simulation of a machine description' has
>>> an actual meaning, in that the simulation must match the actual
>>> behavior of the machine whose description it is simulating, RIGHT?
>> It must only do exactly what it actually does, if this does not meet
>> expectations then expectations must be incorrect.
>>
>> Here is what it actually does:
>> These steps would keep repeating:
>>    Ĥ1 copies its input ⟨Ĥ2⟩ to ⟨Ĥ3⟩ then embedded_H simulates ⟨Ĥ2⟩ ⟨Ĥ3⟩
>>    Ĥ2 copies its input ⟨Ĥ3⟩ to ⟨Ĥ4⟩ then embedded_H simulates ⟨Ĥ3⟩ ⟨Ĥ4⟩
>>    Ĥ3 copies its input ⟨Ĥ4⟩ to ⟨Ĥ5⟩ then embedded_H simulates ⟨Ĥ4⟩
>> ⟨Ĥ5⟩...
>
> And if that is what it actually does, then H NEVER aborts its simulation
> and thus never give an answer.
>

When embedded_H correctly matches the above infinite sequence this
conclusively proves that its correct simulation of ⟨Ĥ⟩ ⟨Ĥ⟩ cannot
possibly reach ⟨Ĥ⟩.qn. (We don't even need to mention any UTM).

--
Copyright 2021 Pete Olcott "Talent hits a target no one else can hit;
Genius hits a target no one else can see." Arthur Schopenhauer