On 4/10/2022 7:44 PM, Dennis Bush wrote:
> On Sunday, April 10, 2022 at 8:40:34 PM UTC-4, olcott wrote:
>> On 4/10/2022 7:28 PM, Dennis Bush wrote:
>>> On Sunday, April 10, 2022 at 7:58:55 PM UTC-4, olcott wrote:
>>>> On 4/10/2022 6:26 PM, Dennis Bush wrote:
>>>>> On Sunday, April 10, 2022 at 7:20:44 PM UTC-4, olcott wrote:
>>>>>> On 4/10/2022 6:14 PM, André G. Isaak wrote:
>>>>>>> On 2022-04-10 17:08, olcott wrote:
>>>>>>>> On 4/10/2022 5:59 PM, André G. Isaak wrote:
>>>>>>>>> On 2022-04-10 16:40, olcott wrote:
>>>>>>>>>> On 4/10/2022 5:35 PM, André G. Isaak wrote:
>>>>>>>>>>> On 2022-04-10 15:56, olcott wrote:
>>>>>>>>>>>> On 4/10/2022 4:49 PM, André G. Isaak wrote:
>>>>>>>>>>>>> On 2022-04-10 15:00, olcott wrote:
>>>>>>>>>>>>>> On 4/10/2022 3:15 PM, olcott wrote:
>>>>>>>>>>>>>>> On 4/10/2022 3:07 PM, André G. Isaak wrote:
>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> I'm trying to get you to write using correct and coherent
>>>>>>>>>>>>>>>> notation. That's one of the things you'll need to be able to
>>>>>>>>>>>>>>>> do if you ever hope to publish. That involves remembering to
>>>>>>>>>>>>>>>> always include conditions and using the same terms in your
>>>>>>>>>>>>>>>> 'equations' as in your text.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> Not sure how that makes me a 'deceitful bastard'.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> André
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> THAT you pretended to not know what I mean by embedded_H so
>>>>>>>>>>>>>>> that you could artificially contrive a fake basis for rebuttal
>>>>>>>>>>>>>>> when no actual basis for rebuttal exists makes you a deceitful
>>>>>>>>>>>>>>> bastard.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> IT IS THE CASE THAT the correctly simulated input ⟨Ĥ0⟩ ⟨Ĥ1⟩ to
>>>>>>>>>>>>>> embedded_H never reaches its own final state of ⟨Ĥ0.qy⟩ or
>>>>>>>>>>>>>> ⟨Ĥ0.qn⟩ under any condition what-so-ever therefore ⟨Ĥ0⟩ ⟨Ĥ1⟩ is
>>>>>>>>>>>>>> proved to specify a non-halting sequence of configurations.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Ĥ.q0 ⟨Ĥ0⟩ ⊢* H ⟨Ĥ0⟩ ⟨Ĥ1⟩ ⊢* H.qy
>>>>>>>>>>>>>> Ĥ.q0 ⟨Ĥ0⟩ ⊢* H ⟨Ĥ0⟩ ⟨Ĥ2⟩ ⊢* H.qn
>>>>>>>>>>>>>
>>>>>>>>>>>>> This is now the third reply you've made to the same post.
>>>>>>>>>>>>>
>>>>>>>>>>>>> That post didn't make any arguments whatsoever about your claims.
>>>>>>>>>>>>> It simply pointed out that you are misusing your notation and
>>>>>>>>>>>>> urged you to correct it.
>>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> THE NOTATION IS A STIPULATIVE DEFINITION THUS DISAGREEMENT IS
>>>>>>>>>>>> INCORRECT.
>>>>>>>>>>>
>>>>>>>>>>> If the notation is junk, then the definition is also junk.
>>>>>>>>>>>
>>>>>>>>>>> That's like "stipulating" that
>>>>>>>>>>>
>>>>>>>>>>> +×yz÷² = ±z+³
>>>>>>>>>>>
>>>>>>>>>>> It's meaningless because the notation is meaningless, much like
>>>>>>>>>>> your notation above.
>>>>>>>>>>>
>>>>>>>>>>> This is meaningless:
>>>>>>>>>>>
>>>>>>>>>>> Ĥ.q0 ⟨Ĥ0⟩ ⊢* H ⟨Ĥ0⟩ ⟨Ĥ1⟩ ⊢* H.qy // what's the condition?
>>>>>>>>>>> Ĥ.q0 ⟨Ĥ0⟩ ⊢* H ⟨Ĥ0⟩ ⟨Ĥ1⟩ ⊢* H.qn // what's the condition?
>>>>>>>>>>>
>>>>>>>>>>> With no conditions specified, the above is just nonsense.
>>>>>>>>>>>
>>>>>>>>>>> André
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qy
>>>>>>>>>> If the pure simulation of ⟨Ĥ⟩ ⟨Ĥ⟩ by embedded_H would reach its
>>>>>>>>>> final state.
>>>>>>>>>>
>>>>>>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qn
>>>>>>>>>> If the pure simulation of ⟨Ĥ⟩ ⟨Ĥ⟩ by embedded_H would never reach
>>>>>>>>>> its final state.
>>>>>>>>>
>>>>>>>>>
>>>>>>>>> This is still nonsense.
>>>>>>>>>
>>>>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qy
>>>>>>>> If the correctly simulated input ⟨Ĥ⟩ ⟨Ĥ⟩ to embedded_H would reach its
>>>>>>>> own final state.
>>>>>>>>
>>>>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qn
>>>>>>>> If the correctly simulated input ⟨Ĥ⟩ ⟨Ĥ⟩ to embedded_H would never
>>>>>>>> reach its own final state.
>>>>>>>
>>>>>>> And again you're still being inconsistent. You can either use H or use
>>>>>>> embedded_H, but you can't mix the two.
>>>>>>>
>>>>>> Sure I can. I just did.
>>>>>>>> This means that H pretends that it is only a UTM to see what its
>>>>>>>> simulated input would do in this case. If it would never reach its own
>>>>>>>> final state then H correctly rejects this input.
>>>>>>>
>>>>>>> A Turing Machine cannot "pretend" to be some different Turing Machine.
>>>>>> It can perform a pure simulation of its input until this simulated input
>>>>>> matches a repeating behavior pattern that proves this input never
>>>>>> reaches its own final state.
>>>>>
>>>>> If that's the case, why does an actual UTM applied to the *same* input halt?
>>>>>
>>>>> Hint: Because the result of an actual UTM applied to the input defines the correct answer, so H answers wrong.
>>>> Intuitively that would seem to be true, this intuition is incorrect.
>>>>
>>>> The ultimate definition of correct is the computation of the mapping of
>>>> the inputs to an accept or reject state on the basis of the behavior
>>>> that these inputs specify.
>>>>
>>>> That simulated inputs to embedded_H would never reach their own final
>>>> state under any condition what-so-ever
>>>> IS THE ULTIMATE MEASURE OF THEIR HALTING BEHAVIOR
>>>> and conclusively proves they specify a non-halting sequence of
>>>> configurations.
>>>
>>> Since embedded_H is the same as H (as you have yet to provide any evidence to the contrary), then the above can be applied to any simulating halt decider.
>>>
>> The topic is the single point that the simulated input ⟨Ĥ0⟩ ⟨Ĥ1⟩ to
>> embedded_h cannot possibly reach its own final state of ⟨Ĥ0.qy⟩ or ⟨Ĥ0.qn⟩.
>
> And that same logic gives us this:
>
> That simulated inputs <N><5> to Ha3 would never reach their own final
> state under any condition what-so-ever
> IS THE ULTIMATE MEASURE OF THEIR HALTING BEHAVIOR
> and conclusively proves they specify a non-halting sequence of
> configurations.
>
> THE SIMULATED INPUT CANNOT POSSIBLY REACH ITS OWN FINAL STATE
> THIS SINGLE FACT BY ITSELF PROVES THAT THE INPUT IS CORRECTLY REJECTED
>
> Try to find an error in the above.

I will dumb it down for you a whole lot.
If the simulated input to embeded_H is non-halting then it never halts.

--
Copyright 2022 Pete Olcott

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