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From: immibis <news@immibis.com>
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Subject: =?UTF-8?Q?Re=3A_Working_out_the_details_of_the_steps_of_=C4=A4=2EH_?=
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On 9/03/24 17:53, olcott wrote:
> On 3/9/2024 10:21 AM, immibis wrote:
>> On 9/03/24 17:00, olcott wrote:
>>> On 3/9/2024 1:05 AM, Richard Damon wrote:
>>>> On 3/8/24 10:40 PM, olcott wrote:
>>>>> On 3/9/2024 12:25 AM, Richard Damon wrote:
>>>>>> On 3/8/24 9:55 PM, olcott wrote:
>>>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* ⊢* Ĥ.Hqy ∞ // Ĥ applied to ⟨Ĥ⟩ halts
>>>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.Hq0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.Hqn   // Ĥ applied to ⟨Ĥ⟩ does not 
>>>>>>> halt
>>>>>>>
>>>>>>> Expecting Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ to correctly report on the behavior of
>>>>>>> Ĥ ⟨Ĥ⟩ is a little nuts because Ĥ contradicts Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩.
>>>>>>
>>>>>> But that is the job it signed up for when it tried to call itself 
>>>>>> a Halt Decider.
>>>>>>
>>>>>
>>>>> There is no correct answer that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ can possibly
>>>>> provide that corresponds to the behavior of this Ĥ ⟨Ĥ⟩.
>>>>> Therefore it must have a basis for its wrong answer.
>>>>>
>>>>>
>>>>
>>>> WHY?
>>>>
>>>> What is the actual grounds for that statement?
>>>
>>> Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ cannot just sit around scratching its head it
>>> must do something. As soon as we have the basis for what
>>> it will do, then H ⟨Ĥ⟩ ⟨Ĥ⟩ has its basis to correctly
>>> decide halting.
>>
>> H ⟨A⟩ ⟨B⟩ cannot just sit around scratching its head, it must do 
>> something. As soon as we have the basis for what H will do, then we 
>> have a basis to construct an Ĥ where H ⟨Ĥ⟩ ⟨Ĥ⟩ is wrong.
>>
> 
> Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ can fool itself yet cannot possibly fool an external H ⟨Ĥ⟩ ⟨Ĥ⟩.
> 

If H ⟨Ĥ⟩ ⟨Ĥ⟩ transitions to state qn then Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ also transitions 
to state H.qn. If it does not do this then you did not follow the 
instructions properly when you wrote Ĥ.