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⟩...

--
Copyright 2021 Pete Olcott

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