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.

Proven and not refuted, so I consider you have accepted that you can't
refutte it.

H/embedded_H can not go to H.Qn except by aborting its simulation, which
means the pattern doesn't exist if your H claims the input is non-halting.

So, you argument FAILS.

You are beleiving in your Fairy Dust Powered Unicorns again.