On 2/3/2022 5:50 AM, Richard Damon wrote:
> On 2/3/22 12:24 AM, olcott wrote:
>> On 2/2/2022 11:09 PM, Richard Damon wrote:
>>> On 2/2/22 11:50 PM, olcott wrote:
>>>> 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).
>>>>
>>>>
>>>
>>> Excepts as previously said, that pattern only exists if H never aborts.
>>>
>> That is not true. The pattern exists for at least any finite number of
>> steps where it can be recognized. The three iterations shown above are
>> plenty enough for it to be recogized.
>>
>
> But if it only exists for a finite number of steps (till it is
> recognized)

At that point right there embedded_H has complete proof that the correct
simulation of ⟨Ĥ⟩ ⟨Ĥ⟩ cannot possibly reach ⟨Ĥ⟩.qn.

--
Copyright 2021 Pete Olcott

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