When the last sentence of the following is fully understood it will be
known that I am correct:

WE ALL AGREE ON THIS:
A halt decider must compute the mapping from its input finite strings to
its own accept or reject state.

HERE IS WHERE WE DIVERGE:
A halt decider must compute the mapping from its input finite strings to
its own accept or reject state:

On the basis of the actual behavior actually specified by its input.

THIS IS EVERYONE'S MISTAKE
All of my reviewers (and Linz) always measure a different sequence of
configurations than the one that is actually specified by the actual input.

Halting problem undecidability and infinitely nested simulation (V4)

https://www.researchgate.net/publication/359349179_Halting_problem_undecidability_and_infinitely_nested_simulation_V4

--
Copyright 2022 Pete Olcott

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

On 4/5/2022 9:01 PM, Ben Bacarisse wrote:
> olcott <NoOne@NoWhere.com> writes:
>
>> When the last sentence of the following is fully understood it will be
>> known that I am correct:
>>
>> WE ALL AGREE ON THIS:
>> A halt decider must compute the mapping from its input finite strings
>> to its own accept or reject state.
>>
>> HERE IS WHERE WE DIVERGE:
>> A halt decider must compute the mapping from its input finite strings
>> to its own accept or reject state:
>>
>> On the basis of the actual behavior actually specified by its input.
>>
>> THIS IS EVERYONE'S MISTAKE
>> All of my reviewers (and Linz) always measure a different sequence of
>> configurations than the one that is actually specified by the actual
>> input.
>
> What string must be passed to H so that H can tell us whether or not Ĥ
> applied to ⟨Ĥ⟩ halts?
>

Do you understand that different sequences of configurations may have
different halting behavior from each other?

When one sequence of configurations seems intuitively identical to
another sequence then computer science says that their behavior must be
the same UNLESS INTUITION IS WRONG AND THEY ARE DIFFERENT SEQUENCES.

--
Copyright 2022 Pete Olcott

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

On 4/6/2022 3:42 AM, Mikko wrote:
> On 2022-04-05 21:57:37 +0000, olcott said:
>
>> When the last sentence of the following is fully understood it will be
>> known that I am correct:
>>
>> WE ALL AGREE ON THIS:
>> A halt decider must compute the mapping from its input finite strings
>> to its own accept or reject state.
>
> This tells that a halt decider must be a decider but does not tell
> how a halt decider differs from any other decider.
>
>> HERE IS WHERE WE DIVERGE:
>> A halt decider must compute the mapping from its input finite strings
>> to its own accept or reject state:
>>
>> On the basis of the actual behavior actually specified by its input.
>
> The last line is too vague, and there is no point in an agreement about
> words without an agreement about the meaning of those words.
> In particular, the word "specified" does not specify what interpretation
> of the input gives the "specified" behaviour.
>
>> THIS IS EVERYONE'S MISTAKE
>> All of my reviewers (and Linz) always measure a different sequence of
>> configurations than the one that is actually specified by the actual
>> input.
>
> No, it is not a mistake. The exact meaning of "specified" is left vague.
> Therefore there can be different correct interpretations.
>
> Mikko
>

The actual execution trace of the simulated input: ⟨Ĥ⟩ ⟨Ĥ⟩ to embedded_H
conclusively proves that it would never reach its own final state under
any condition what-so-ever thus must be rejected by embedded_H.

--
Copyright 2022 Pete Olcott

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

On 4/6/2022 6:57 AM, Ben Bacarisse wrote:
> olcott <NoOne@NoWhere.com> writes:
>
>> On 4/5/2022 10:42 PM, Ben Bacarisse wrote:
>>> olcott <NoOne@NoWhere.com> writes:
>>>
>>>> On 4/5/2022 9:01 PM, Ben Bacarisse wrote:
>>>>> olcott <NoOne@NoWhere.com> writes:
>>>>>
>>>>>> When the last sentence of the following is fully understood it will be
>>>>>> known that I am correct:
>>>>>>
>>>>>> WE ALL AGREE ON THIS:
>>>>>> A halt decider must compute the mapping from its input finite strings
>>>>>> to its own accept or reject state.
>>>>>>
>>>>>> HERE IS WHERE WE DIVERGE:
>>>>>> A halt decider must compute the mapping from its input finite strings
>>>>>> to its own accept or reject state:
>>>>>>
>>>>>> On the basis of the actual behavior actually specified by its input.
>>>>>>
>>>>>> THIS IS EVERYONE'S MISTAKE
>>>>>> All of my reviewers (and Linz) always measure a different sequence of
>>>>>> configurations than the one that is actually specified by the actual
>>>>>> input.
>>>>> What string must be passed to H so that H can tell us whether or not Ĥ
>>>>> applied to ⟨Ĥ⟩ halts?
>>>>
>>>> Do you understand that different sequences of configurations may have
>>>> different halting behavior from each other?
>>> No an answer.
>>
>> Prerequisite order is required.
>
> What do I need to order?
>
>>>> When one sequence of configurations seems intuitively identical to
>>>> another sequence then computer science says that their behavior must
>>>> be the same UNLESS INTUITION IS WRONG AND THEY ARE DIFFERENT
>>>> SEQUENCES.
>>> Your opinion is noted.
>>
>> It is an objectively verifiable fact, not a mere opinion.
>
> Then there is no reason for you fear answering these two basic but key
> questions:
>
> What string must be passed to H so that H can tell us whether or not Ĥ
> applied to ⟨Ĥ⟩ halts?

You cannot possibly understand my answer to that question until after
you first understand this:

The actual execution trace of the simulated input: ⟨Ĥ⟩ ⟨Ĥ⟩ to embedded_H
conclusively proves that it would never reach its own final state under
any condition what-so-ever thus must be rejected by embedded_H.

--
Copyright 2022 Pete Olcott

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

On 4/6/2022 6:40 PM, Ben Bacarisse wrote:
> olcott <NoOne@NoWhere.com> writes:
>
>> On 4/6/2022 4:25 PM, Ben Bacarisse wrote:
>>> olcott <NoOne@NoWhere.com> writes:
>>>
>>>> On 4/6/2022 6:57 AM, Ben Bacarisse wrote:
>>>>> olcott <NoOne@NoWhere.com> writes:
>>>>>
>>>>>> On 4/5/2022 10:42 PM, Ben Bacarisse wrote:
>>>>>>> olcott <NoOne@NoWhere.com> writes:
>>>>>>>
>>>>>>>> On 4/5/2022 9:01 PM, Ben Bacarisse wrote:
>>>>>>>>> olcott <NoOne@NoWhere.com> writes:
>>>>>>>>>
>>>>>>>>>> When the last sentence of the following is fully understood it will be
>>>>>>>>>> known that I am correct:
>>>>>>>>>>
>>>>>>>>>> WE ALL AGREE ON THIS:
>>>>>>>>>> A halt decider must compute the mapping from its input finite strings
>>>>>>>>>> to its own accept or reject state.
>>>>>>>>>>
>>>>>>>>>> HERE IS WHERE WE DIVERGE:
>>>>>>>>>> A halt decider must compute the mapping from its input finite strings
>>>>>>>>>> to its own accept or reject state:
>>>>>>>>>>
>>>>>>>>>> On the basis of the actual behavior actually specified by its input.
>>>>>>>>>>
>>>>>>>>>> THIS IS EVERYONE'S MISTAKE
>>>>>>>>>> All of my reviewers (and Linz) always measure a different sequence of
>>>>>>>>>> configurations than the one that is actually specified by the actual
>>>>>>>>>> input.
>>>>>>>>> What string must be passed to H so that H can tell us whether or not Ĥ
>>>>>>>>> applied to ⟨Ĥ⟩ halts?
>>>>>>>>
>>>>>>>> Do you understand that different sequences of configurations may have
>>>>>>>> different halting behavior from each other?
>>>>>>> No an answer.
>>>>>>
>>>>>> Prerequisite order is required.
>>>>> What do I need to order?
>>>>>
>>>>>>>> When one sequence of configurations seems intuitively identical to
>>>>>>>> another sequence then computer science says that their behavior must
>>>>>>>> be the same UNLESS INTUITION IS WRONG AND THEY ARE DIFFERENT
>>>>>>>> SEQUENCES.
>>>>>>> Your opinion is noted.
>>>>>>
>>>>>> It is an objectively verifiable fact, not a mere opinion.
>>>>> Then there is no reason for you fear answering these two basic but key
>>>>> questions:
>>>>> What string must be passed to H so that H can tell us whether or not Ĥ
>>>>> applied to ⟨Ĥ⟩ halts?
>>>>
>>>> You cannot possibly understand my answer to that question until after
>>>> you first understand this:
>>> No, you can't post the answer because you know it will show you are
>>> wrong.
>>> And, seriously, what do you think could make me not understand the
>>> answer? It's a string. How complicated it is? What you mean is that I
>>> can't possibly understand /that your answer is correct/ until I take the
>>> blue pill.
>>
>> You cannot possibly understand my answer until after you first
>> understand that because the correctly simulated input to embedded_H
>> cannot possibly reach it own final state, that embedded_H is
>> necessarily correct to reject this input and nothing in the whole
>> universe can possibly correctly refute this.
>
> Thanks. Keep not saying what string must be passed to H so that H can
> tell us whether or not Ĥ applied to ⟨Ĥ⟩

The string passed to embedded_H that it correctly maps to its final
reject state is: ⟨Ĥ⟩ ⟨Ĥ⟩.

It is the case that the correctly simulated input to embedded_H can
never possibly reach its own final state under any condition at all.
Therefore embedded_H is necessarily correct to reject its input.

Maybe you should brush up on modal logic, you don't seem to be able to
grasp what {necessarily} means.

◊P ⟷ ¬□¬P;
Possibly(P) ⟷ Not(Necessarily(Not(P)))

□P ⟷ ¬◊¬P;
Necessarily(P) ⟷ Not(Possibly(Not(P)))

https://en.wikipedia.org/wiki/Modal_logic

--
Copyright 2022 Pete Olcott

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