On 2/16/2022 5:58 PM, Richard Damon wrote:
> On 2/16/22 8:35 AM, olcott wrote:
>> On 2/16/2022 6:55 AM, Richard Damon wrote:
>>> On 2/16/22 7:37 AM, olcott wrote:
>>>> On 2/15/2022 10:37 PM, Richard Damon wrote:
>>>>> On 2/15/22 10:39 PM, olcott wrote:
>>>>>> On 2/15/2022 9:14 PM, Richard Damon wrote:
>>>>>>> On 2/15/22 9:50 PM, olcott wrote:
>>>>>>>> On 2/15/2022 8:49 PM, olcott wrote:
>>>>>>>>> On 2/15/2022 8:07 PM, Richard Damon wrote:
>>>>>>>>>> On 2/15/22 8:17 PM, olcott wrote:
>>>>>>>>>>> On 2/15/2022 5:40 PM, Richard Damon wrote:
>>>>>>>>>>>>
>>>>>>>>>>>> On 2/15/22 11:49 AM, olcott wrote:
>>>>>>>>>>>>> On 2/14/2022 5:49 AM, Richard Damon wrote:
>>>>>>>>>>>>>> On 2/13/22 10:30 PM, olcott wrote:
>>>>>>>>>>>>>>> On 2/13/2022 7:27 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>> On 2/13/22 7:26 PM, olcott wrote:
>>>>>>>>>>>>>>>>> On 2/13/2022 6:24 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>> On 2/13/22 6:08 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>> On 2/13/2022 4:11 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>> On 2/13/22 5:04 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>> On 2/13/2022 3:40 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>>> On 2/13/22 4:24 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>> On 2/13/2022 3:12 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>> On 2/13/22 3:18 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>> On 2/13/2022 1:57 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/13/22 2:43 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/13/2022 11:19 AM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/13/22 9:38 AM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/13/2022 5:43 AM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/13/22 12:54 AM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/12/2022 8:22 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/12/22 9:02 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/12/2022 7:54 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/12/22 8:27 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/12/2022 6:57 PM, Richard Damon
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/12/22 7:37 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/12/2022 6:25 PM, Richard Damon
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/12/22 6:48 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/12/2022 5:39 PM, Richard
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/12/22 5:34 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/12/2022 8:41 AM, Richard
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/12/22 9:08 AM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/12/2022 6:49 AM, Richard
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/12/22 12:01 AM, olcott
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/11/2022 10:50 PM,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/11/22 11:36 PM,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/11/2022 6:58 PM,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/11/22 7:52 PM,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/11/2022 6:17 PM,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/11/22 7:10 PM,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/11/2022 5:36 PM,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/11/22 10:20 AM,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/11/2022 5:36
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> AM, Richard Damon
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/10/22 11:39
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/10/2022
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 10:20 PM, Richard
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/10/22 10:58
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/10/2022
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 6:02 PM,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Richard Damon
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/10/22
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 9:18 AM,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>   > I explain
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> how I am
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> necessarily
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> correct on the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> basis of the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> meaning of my
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> words and you
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> disagree on
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the basis of
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> your failure
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> to correctly
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the meaning
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of these words.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> No, you CLAIM
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> to explain
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> based on the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> meaning of the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> words, but use
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the wrong
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> meaning of the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> words.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> THIS IS
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> PROVEN TO BE
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> COMPLETELY
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> TRUE ENTIRELY
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> ON THE BASIS
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> OF THE
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> MEANING OF
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> ITS WORDS:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> When a
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> simulating
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> halt decider
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> correctly
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> determines in
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> a finite
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> number of
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> steps that
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the pure UTM
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> simulation of
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> its input
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> would never
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> reach the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> final state
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of this input
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> then it can
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> correctly
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> reject this
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> input as
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> non-halting.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> IF it
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> correctly
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> decided, then
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> yes.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> But it has
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> been shown, by
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the definition
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> construction
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> method of H^
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that if H <H^>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <H^> goes to
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> H.Qn then H^
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <H^> goes to
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> H^.Qn and
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Halts, and
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> thus by the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> definition of
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> a UTM, then we
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> also have that
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> UTM <H^> <H^>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> will halt.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢*
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢*
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Ĥ.qy ∞
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢*
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢*
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Ĥ.qn
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> You keep
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> getting
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> confused
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> between two
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> things:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> (1) The
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> execution of Ĥ
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> ⟨Ĥ⟩ versus
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> embedded_H ⟨Ĥ⟩
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> ⟨Ĥ⟩ (we only
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> look at the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> latter).
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> No, YOU qre
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> confused.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> By the definioon
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of how to build
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> H^, embedded_H
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> MUST be EXACTLY
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the same
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> algorithm as H,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> No it is
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> specifically not
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> allowed to be.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> embedded_H must
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> have an infinite
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> loop appended to
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> its Ĥ.qy state
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> and H is not
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> allowed to have
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> such a loop
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> appended to its
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> H.qy state.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Which is OUTSIDE
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the algorithm of H
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> itself, and
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> doesn't affect the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> behavior of H in
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> deciding to go
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> from Q0 to Qy/Qn.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> When the simulating
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> halt decider bases
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> it halt status
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> decision on whether
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> or not the same
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> function is being
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> called with the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> same inputs the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> difference between
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> H and embedded_H
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> can change the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> behavior. A string
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> comparison between
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the machine
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> description of H
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> and embedded_H
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> yields false.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> No, it can't, not
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> and be a COMPUTATION.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> You obviously don't
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> know the meaning of
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the words, so you
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> are just wrong.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Computation means
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> for ALL copoies,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Same input leads to
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Same Output.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> The fact that it is
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> not an exact copy
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> makes a difference.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> But it IS.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> H applied to ⟨Ĥ⟩ ⟨Ĥ⟩
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> does not determine that
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> itself is being called
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> multiple times with the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> same input. embedded_H
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> does determine that
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> itself is called
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> multiple times with the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> same input because
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> strcmp(H, embedded_H != 0.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Except that embedded_H
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> does't have a
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 'representation' of
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> itself to use to make
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that comparison, so that
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is just more of your
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Fairy Dust Powered
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Unicorn stuff.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> It can very easily have a
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> representation of itself,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that only requires that
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> it has access to its own
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> machine description.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> First, Turing Machines
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> DON'T have access to their
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> own machine description,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> unless it has been
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> provided as an input
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> You said that this was
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> impossible.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> So, you are agreeing that
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> they can't? Or do you just
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> not understand the logic.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I am agreeing that you
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> contradicted yourself.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> How, by saying that the only
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> way a Turing Machine can have
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> a copy of its representation
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is for it to be given (and H
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is defined in a way that it
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> can't be given as an extra
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> input)?
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> No appended infinite loop
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> making H and embedded_H the same
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Ḧ.q0 ⟨Ḧ⟩ ⊢* Ḧ.qx ⟨Ḧ⟩ ⟨Ḧ⟩ ⊢* Ḧ.qy
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Ḧ.q0 ⟨Ḧ⟩ ⊢* Ḧ.qx ⟨Ḧ⟩ ⟨Ḧ⟩ ⊢* Ḧ.qn
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> embedded_H ⟨Ḧ⟩ ⟨Ḧ⟩ ⊢* Ḧ.qn
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> H ⟨Ḧ⟩ ⟨Ḧ⟩ ⊢* H.qn
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Except that the infinite loop
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> isn't part of the copy of H in
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> H^, it is something ADD to it,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> which only has/affects behavior
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> AFTER H makes its decision.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> So another words hypothetical
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> examples get you so confused you
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> totally lose track of everything.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> What 'Hypothetical' are you
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> referencing.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> This is what I mean when I say that
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> you hardly pay any attention at all.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> This is the hypothetical that I am
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> referencing:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> No appended infinite loop making H
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> and embedded_H the same
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Ḧ.q0 ⟨Ḧ⟩ ⊢* Ḧ.qx ⟨Ḧ⟩ ⟨Ḧ⟩ ⊢* Ḧ.qy
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Ḧ.q0 ⟨Ḧ⟩ ⊢* Ḧ.qx ⟨Ḧ⟩ ⟨Ḧ⟩ ⊢* Ḧ.qn
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> And what do you mean by that?
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> When I redefine Ĥ to become Ḧ by
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> eliminating its infinite loop, I
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> probably mean: {I redefine Ĥ to
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> become Ḧ by eliminating its infinite
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> loop}.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Which does what? Since if you aren't
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> talking about Linz's H^, your results
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> don't mean anything for the Halting
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Problem.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> It provides a bridge of understanding
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> to my HP refutation.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> The key skill that I have applied
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> throughout my career is eliminating
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> "inessential complexity" (1999 Turing
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> award winner Fred Brooks) to make
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>   enormously difficult problems as
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> simple as possible.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> https://en.wikipedia.org/wiki/No_Silver_Bullet
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> But if you eliminate KEY ASPECTS then
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> you aren't talking about what you need to.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> It is just like learning arithmetic
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> before attacking algebra.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> It lays the foundation of prerequisites
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> for my actual rebuttal.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Just beware that if you make a statement
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that is only true for a limited case and
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> don't explicitly state so, pointing that
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> out is NOT a 'Dishonest Dodge'.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Since it is know that you are working on
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> trying to prove that a Unicorn exists,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> what you are saying WILL be looked at in a
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> light anticipating where you are going.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Also remember that showing a rule happens
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> to be correct for one case, doesn't prove
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that it will be for a different case.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> You have gone through all of this before,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> and it came for nothing, but if this is
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> how you want to spend your last days,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> knock yourself out.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I think that you already understand that
>>>>>>>>>>>>>>>>>>>>>>>>>>>>> With Ĥ ⟨Ĥ⟩
>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qy ∞ // this
>>>>>>>>>>>>>>>>>>>>>>>>>>>>> path is never taken
>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>> making Ḧ ⟨Ḧ⟩ an equivalent computation
>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Ḧ.q0 ⟨Ḧ⟩ ⊢* Ḧ.qx ⟨Ḧ⟩ ⟨Ḧ⟩ ⊢* Ḧ.qy
>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Ḧ.q0 ⟨Ḧ⟩ ⊢* Ḧ.qx ⟨Ḧ⟩ ⟨Ḧ⟩ ⊢* Ḧ.qn
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>> And, as seems common with your arguments,
>>>>>>>>>>>>>>>>>>>>>>>>>>>> you keep on forgetting the CONDITIONS on
>>>>>>>>>>>>>>>>>>>>>>>>>>>> each line.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>> H^ <H^> is
>>>>>>>>>>>>>>>>>>>>>>>>>>>> H^.q0 <H^> -> H^.Qx <H^> <H^>
>>>>>>>>>>>>>>>>>>>>>>>>>>>> Then
>>>>>>>>>>>>>>>>>>>>>>>>>>>> H^.Qx <H^> <H^> -> H^.Qy -> ∞ IF and only if
>>>>>>>>>>>>>>>>>>>>>>>>>>>> H <H^> <H^> -> H.Qy and
>>>>>>>>>>>>>>>>>>>>>>>>>>>> H^.Qx <H^> <H^> -> H^.Qn If and ohly if H
>>>>>>>>>>>>>>>>>>>>>>>>>>>> <H^> <H^> => H.Qn.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>> If you stipulate that H <H^> <H^> will never
>>>>>>>>>>>>>>>>>>>>>>>>>>>> go to H.Qy, then the behavior on that path
>>>>>>>>>>>>>>>>>>>>>>>>>>>> can be changed with no effect.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>> Without the If and only if clauses, the
>>>>>>>>>>>>>>>>>>>>>>>>>>>> initial description is incorrect because it
>>>>>>>>>>>>>>>>>>>>>>>>>>>> is incomplete.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>> So, WITH THE STIPULATION THAT H won't go to
>>>>>>>>>>>>>>>>>>>>>>>>>>>> H.Qy for either version, then changing H^ to
>>>>>>>>>>>>>>>>>>>>>>>>>>>> the H" that omits to loop is an equivalence,
>>>>>>>>>>>>>>>>>>>>>>>>>>>> but ONLY under that stipulation.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>> This of course shows that H will be wrong
>>>>>>>>>>>>>>>>>>>>>>>>>>>> about H", as H" will ALWAYS Halt if H
>>>>>>>>>>>>>>>>>>>>>>>>>>>> answers, and H not answering is always
>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrong. Thus H will either be wrong for not
>>>>>>>>>>>>>>>>>>>>>>>>>>>> answering or giving the wrong answer.
>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>> I am only making two versions of input to H:
>>>>>>>>>>>>>>>>>>>>>>>>>>> (1) Ĥ WITH an appended infinite loop
>>>>>>>>>>>>>>>>>>>>>>>>>>> (2) Ḧ WITHOUT an appended infinite loop
>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>> Only this is being examined:
>>>>>>>>>>>>>>>>>>>>>>>>>>> embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩
>>>>>>>>>>>>>>>>>>>>>>>>>>> embedded_H ⟨Ḧ⟩ ⟨Ḧ⟩
>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>> Right, but the conclusion that H" is
>>>>>>>>>>>>>>>>>>>>>>>>>> 'equivalent' to H^ is only true (if you mean
>>>>>>>>>>>>>>>>>>>>>>>>>> equivalent in the sense that they compute the
>>>>>>>>>>>>>>>>>>>>>>>>>> same function) if it is the case that neither
>>>>>>>>>>>>>>>>>>>>>>>>>> of H <H^> <H^> or H <H"> <H"> go to H.Qy.
>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>> Good.
>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>> Unless you want to indicate some other
>>>>>>>>>>>>>>>>>>>>>>>>>> definition of 'equivalent' you using (that
>>>>>>>>>>>>>>>>>>>>>>>>>> could be proper to do so here), you need to
>>>>>>>>>>>>>>>>>>>>>>>>>> include the conditions under which the
>>>>>>>>>>>>>>>>>>>>>>>>>> statement is true.
>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>> embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ḧ.qn
>>>>>>>>>>>>>>>>>>>>>>>>>    and
>>>>>>>>>>>>>>>>>>>>>>>>> embedded_H ⟨Ḧ⟩ ⟨Ḧ⟩ ⊢* Ḧ.qn
>>>>>>>>>>>>>>>>>>>>>>>>>    nd
>>>>>>>>>>>>>>>>>>>>>>>>> H ⟨Ḧ⟩ ⟨Ḧ⟩ ⊢* Ḧ.qn
>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>> Problem, embedded_H / H need to transition to a
>>>>>>>>>>>>>>>>>>>>>>>> state in H, not some other machine.
>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>> As soon as we append an infinite loop to H.y is
>>>>>>>>>>>>>>>>>>>>>>> it no longer H.
>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>> This is where you are showing your lack of
>>>>>>>>>>>>>>>>>>>>>> understanding of Turing Machines.
>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>> NO ONE has said that the machine where we added
>>>>>>>>>>>>>>>>>>>>>> the loop is still the machine H, in fact, Linz
>>>>>>>>>>>>>>>>>>>>>> calls that machine H', but H' CONTAINS a complete
>>>>>>>>>>>>>>>>>>>>>> copy of H, and that copy will still act exactly
>>>>>>>>>>>>>>>>>>>>>> like the original H to the point where it gets to
>>>>>>>>>>>>>>>>>>>>>> the stat Qy.
>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>> This ability to compose machines of copies of
>>>>>>>>>>>>>>>>>>>>>> other machines is basically like the concept of
>>>>>>>>>>>>>>>>>>>>>> calling subroutines (even if it is implemented
>>>>>>>>>>>>>>>>>>>>>> differently) and is fundamental to the design and
>>>>>>>>>>>>>>>>>>>>>> analysis of Turing Macines.
>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>> Would you have a problem saying the subroutine H
>>>>>>>>>>>>>>>>>>>>>> is no longer the subroutine H if one function just
>>>>>>>>>>>>>>>>>>>>>> calls H and returns while a second calls H and
>>>>>>>>>>>>>>>>>>>>>> conditionally loops? Yes, the whole program is not
>>>>>>>>>>>>>>>>>>>>>> H, but the subroutine H is still there and will
>>>>>>>>>>>>>>>>>>>>>> behave exactly like it used to in both of the cases.
>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>> One way to map a Turing Machine to ordinary
>>>>>>>>>>>>>>>>>>>>>> software is to think of the Q0 state (or whatever
>>>>>>>>>>>>>>>>>>>>>> is the 'starting' state of the Turing machine) as
>>>>>>>>>>>>>>>>>>>>>> the entry point for the function, and the Halting
>>>>>>>>>>>>>>>>>>>>>> States of the Turing Machine as retrun stateents
>>>>>>>>>>>>>>>>>>>>>> which return a value indicating what state the
>>>>>>>>>>>>>>>>>>>>>> machine ended in.
>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>> Thus the modifications Linz has done to H are
>>>>>>>>>>>>>>>>>>>>>> nothing more that building H^ as mostly a call to
>>>>>>>>>>>>>>>>>>>>>> H, with code before the call to manipulate the
>>>>>>>>>>>>>>>>>>>>>> tape to add the second copy, and code after the
>>>>>>>>>>>>>>>>>>>>>> return to loop forever if H returns the 'Halting'
>>>>>>>>>>>>>>>>>>>>>> answer.
>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>> The Machine/Subroutine H has not been touched at all.
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>> My point is that Ĥ ⟨Ĥ⟩ is equivalent to Ḧ ⟨Ḧ⟩
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>> And my point is that they are only equivalent in the
>>>>>>>>>>>>>>>>>>>> normal sense of the word if neither of H <H^> <H^>
>>>>>>>>>>>>>>>>>>>> and H <H"> <H"> go to H.Qy
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>> Without that qualification, it is a false statement.
>>>>>>>>>>>>>>>>>>>> PERIOD.
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>> They are equivalent in that neither can possibly go
>>>>>>>>>>>>>>>>>>> to their q.y state.
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> THAT is incorrect without the same
>>>>>>>>>>>>>>>>>> qualification/assumption/stipulation, the H doesn't go
>>>>>>>>>>>>>>>>>> to Qy.
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> If H was a white cat detector and you presented H with
>>>>>>>>>>>>>>>>> a black cat would it say "yes" ?
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> But we aren't talking about a 'detector'
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> Sure we are.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Then you don't know what you are talking about (and
>>>>>>>>>>>>>> showing your dishonesty by your clipping).
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> THe claim that H^ and H" are equivilent machines has
>>>>>>>>>>>>>> NOTHING to do with there being a 'Detector' but do they
>>>>>>>>>>>>>> behave exactly the same.
>>>>>>>>>>>>> So in other words you are disavowing that both ⟨Ĥ⟩ and ⟨Ḧ⟩
>>>>>>>>>>>>> have a copy of H embedded within them ?
>>>>>>>>>>>>>
>>>>>>>>>>>>> A halt detector is the same idea as a halt decider yet a
>>>>>>>>>>>>> halt detector need not get every input correctly. Every
>>>>>>>>>>>>> input that the halt detector gets correctly is in the
>>>>>>>>>>>>> domain of the computable function that it implements.
>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> Yes, they have a copy of the Halt Detector H in them, and
>>>>>>>>>>>> unless you are willing to stipulate that H will not go to
>>>>>>>>>>>> H.Qy when given H^ or H" as an input, then you can not show
>>>>>>>>>>>> that those machines are equivalent.
>>>>>>>>>>>
>>>>>>>>>>> If the simulating halt decider H cannot possibly go to H.qy
>>>>>>>>>>> on a specific input then any such stipulation would be
>>>>>>>>>>> redundant for this input.
>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> So why do you resist it?
>>>>>>>>>>
>>>>>>>>>> What is wrong with stipulating as a requirement something you
>>>>>>>>>> 'know' to be true?
>>>>>>>>>>
>>>>>>>>>> The only reason I can see for you to object to listing that
>>>>>>>>>> requirement. is that at some point you are going to want to
>>>>>>>>>> violate that requirement.
>>>>>>>>>
>>>>>>>>> Specifically because it was redundant.
>>>>>>>>> embedded_H ⟨Ḧ⟩ ⟨Ḧ⟩ ⊢* Ḧ.qn
>>>>>>>>> embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
>>>>>>>>>
>>>>>>>>> It does not take a genius to know that when
>>>>>>>>> embedded_H transitions to H.qn it does not transition to H.qn
>>>>>>>>     embedded_H transitions to H.qn it does not transition to H.qy
>>>>>>>>
>>>>>>>
>>>>>>> So, are you stating as a fact that embedded_H <H^> <H^> and
>>>>>>> embedded_H <H"> <H"> both as a matter of DEFINITION go to H.Qn?
>>>>>>>
>>>>>>
>>>>>> For H to be correct then on the above specified inputs they must
>>>>>> both go to H.qn.
>>>>>>
>>>>>>
>>>>>
>>>>> But, by DEFINITION that is the WRONG answer.
>>>>>
>>>>> DEFINITION of a Correct Halt Decider:
>>>>>
>>>>> A) H <M> w goes to H.Qy if M w Halts, and to H.Qn if M w never Halts.
>>>> I am only talking about these two:
>>>> embedded_H ⟨Ḧ⟩ ⟨Ḧ⟩ ⊢* Ḧ.qn
>>>> embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
>>>>
>>>> Whenever any embedded_H must abort the simulation of its input to
>>>> prevent the infinitely nested simulation of this input the entire
>>>> nested simulation sequence specifies infinitely nested simulation.
>>>> This makes a transition to H.qn necessarily correct in this case.
>>>>
>>>
>>> Right, the NESTED simulation, but NOT the H^ / H" that is USING that
>>> embededeed_H, and it is THAT machine that defines the CORRECT answer
>>> for H.
>>>
>>
>> That problem is that you are flat out wrong about this.
>> embedded_H IS NOT REPORTING ON ITS OWN BEHAVIOR
>> THUS NOT REPORTING ON Ĥ ⟨Ĥ⟩
>>
>
> Then it is NOT a Halt Detector. PERIOD. BY DEFINITON.

On 2/16/22 7:12 PM, olcott wrote:
> On 2/16/2022 5:58 PM, Richard Damon wrote:
>> On 2/16/22 8:35 AM, olcott wrote:
>>> On 2/16/2022 6:55 AM, Richard Damon wrote:
>>>> On 2/16/22 7:37 AM, olcott wrote:
>>>>> On 2/15/2022 10:37 PM, Richard Damon wrote:
>>>>>> On 2/15/22 10:39 PM, olcott wrote:
>>>>>>> On 2/15/2022 9:14 PM, Richard Damon wrote:
>>>>>>>> On 2/15/22 9:50 PM, olcott wrote:
>>>>>>>>> On 2/15/2022 8:49 PM, olcott wrote:
>>>>>>>>>> On 2/15/2022 8:07 PM, Richard Damon wrote:
>>>>>>>>>>> On 2/15/22 8:17 PM, olcott wrote:
>>>>>>>>>>>> On 2/15/2022 5:40 PM, Richard Damon wrote:
>>>>>>>>>>>>>
>>>>>>>>>>>>> On 2/15/22 11:49 AM, olcott wrote:
>>>>>>>>>>>>>> On 2/14/2022 5:49 AM, Richard Damon wrote:
>>>>>>>>>>>>>>> On 2/13/22 10:30 PM, olcott wrote:
>>>>>>>>>>>>>>>> On 2/13/2022 7:27 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>> On 2/13/22 7:26 PM, olcott wrote:
>>>>>>>>>>>>>>>>>> On 2/13/2022 6:24 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>> On 2/13/22 6:08 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>> On 2/13/2022 4:11 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>> On 2/13/22 5:04 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>> On 2/13/2022 3:40 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>> On 2/13/22 4:24 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>> On 2/13/2022 3:12 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>>> On 2/13/22 3:18 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/13/2022 1:57 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/13/22 2:43 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/13/2022 11:19 AM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/13/22 9:38 AM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/13/2022 5:43 AM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/13/22 12:54 AM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/12/2022 8:22 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/12/22 9:02 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/12/2022 7:54 PM, Richard Damon
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/12/22 8:27 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/12/2022 6:57 PM, Richard Damon
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/12/22 7:37 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/12/2022 6:25 PM, Richard
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/12/22 6:48 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/12/2022 5:39 PM, Richard
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/12/22 5:34 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/12/2022 8:41 AM, Richard
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/12/22 9:08 AM, olcott
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/12/2022 6:49 AM,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/12/22 12:01 AM, olcott
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/11/2022 10:50 PM,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/11/22 11:36 PM,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/11/2022 6:58 PM,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/11/22 7:52 PM,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/11/2022 6:17 PM,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/11/22 7:10 PM,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/11/2022 5:36
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> PM, Richard Damon
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/11/22 10:20
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> AM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/11/2022 5:36
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> AM, Richard Damon
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/10/22 11:39
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/10/2022
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 10:20 PM,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Richard Damon
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/10/22
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 10:58 PM,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/10/2022
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 6:02 PM,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Richard Damon
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/10/22
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 9:18 AM,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>   > I explain
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> how I am
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> necessarily
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> correct on
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the basis of
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the meaning
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of my
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> words and
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> you disagree
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> on the basis
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of your
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> failure to
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> correctly
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the meaning
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of these words.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> No, you CLAIM
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> to explain
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> based on the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> meaning of
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the words,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> but use the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrong meaning
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of the words.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> THIS IS
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> PROVEN TO BE
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> COMPLETELY
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> TRUE
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> ENTIRELY ON
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> THE BASIS OF
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> THE MEANING
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> OF ITS WORDS:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> When a
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> simulating
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> halt decider
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> correctly
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> determines
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> in a finite
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> number of
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> steps that
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the pure UTM
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> simulation
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of its input
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> would never
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> reach the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> final state
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of this
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> input then
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> it can
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> correctly
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> reject this
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> input as
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> non-halting.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> IF it
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> correctly
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> decided, then
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> yes.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> But it has
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> been shown,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> by the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> definition of
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> construction
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> method of H^
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that if H
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <H^> <H^>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> goes to H.Qn
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> then H^ <H^>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> goes to H^.Qn
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> and Halts,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> and thus by
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> definition of
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> a UTM, then
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> we also have
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that UTM <H^>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <H^> will halt.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢*
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> ⊢* Ĥ.qy ∞
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢*
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> ⊢* Ĥ.qn
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> You keep
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> getting
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> confused
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> between two
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> things:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> (1) The
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> execution of Ĥ
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> ⟨Ĥ⟩ versus
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> embedded_H ⟨Ĥ⟩
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> ⟨Ĥ⟩ (we only
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> look at the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> latter).
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> No, YOU qre
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> confused.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> By the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> definioon of
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> how to build
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> H^, embedded_H
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> MUST be EXACTLY
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the same
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> algorithm as H,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> No it is
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> specifically not
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> allowed to be.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> embedded_H must
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> have an infinite
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> loop appended to
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> its Ĥ.qy state
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> and H is not
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> allowed to have
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> such a loop
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> appended to its
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> H.qy state.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Which is OUTSIDE
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the algorithm of
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> H itself, and
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> doesn't affect
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the behavior of H
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> in deciding to go
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> from Q0 to Qy/Qn.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> When the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> simulating halt
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> decider bases it
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> halt status
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> decision on
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> whether or not the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> same function is
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> being called with
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the same inputs
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the difference
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> between H and
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> embedded_H can
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> change the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> behavior. A string
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> comparison between
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the machine
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> description of H
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> and embedded_H
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> yields false.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> No, it can't, not
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> and be a COMPUTATION.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> You obviously don't
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> know the meaning of
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the words, so you
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> are just wrong.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Computation means
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> for ALL copoies,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Same input leads to
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Same Output.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> The fact that it is
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> not an exact copy
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> makes a difference.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> But it IS.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> H applied to ⟨Ĥ⟩ ⟨Ĥ⟩
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> does not determine
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that itself is being
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> called multiple times
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> with the same input.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> embedded_H does
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> determine that itself
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is called multiple
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> times with the same
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> input because
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> strcmp(H, embedded_H
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> != 0.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Except that embedded_H
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> does't have a
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 'representation' of
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> itself to use to make
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that comparison, so
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that is just more of
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> your Fairy Dust Powered
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Unicorn stuff.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> It can very easily have
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> a representation of
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> itself, that only
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> requires that it has
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> access to its own
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> machine description.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> First, Turing Machines
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> DON'T have access to
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> their own machine
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> description, unless it
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> has been provided as an
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> input
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> You said that this was
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> impossible.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> So, you are agreeing that
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> they can't? Or do you just
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> not understand the logic.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I am agreeing that you
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> contradicted yourself.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> How, by saying that the only
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> way a Turing Machine can have
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> a copy of its representation
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is for it to be given (and H
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is defined in a way that it
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> can't be given as an extra
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> input)?
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> No appended infinite loop
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> making H and embedded_H the same
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Ḧ.q0 ⟨Ḧ⟩ ⊢* Ḧ.qx ⟨Ḧ⟩ ⟨Ḧ⟩ ⊢* Ḧ.qy
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Ḧ.q0 ⟨Ḧ⟩ ⊢* Ḧ.qx ⟨Ḧ⟩ ⟨Ḧ⟩ ⊢* Ḧ.qn
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> embedded_H ⟨Ḧ⟩ ⟨Ḧ⟩ ⊢* Ḧ.qn
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> H ⟨Ḧ⟩ ⟨Ḧ⟩ ⊢* H.qn
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Except that the infinite loop
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> isn't part of the copy of H in
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> H^, it is something ADD to it,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> which only has/affects behavior
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> AFTER H makes its decision.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> So another words hypothetical
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> examples get you so confused you
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> totally lose track of everything.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> What 'Hypothetical' are you
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> referencing.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> This is what I mean when I say
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that you hardly pay any attention
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> at all.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> This is the hypothetical that I am
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> referencing:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> No appended infinite loop making H
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> and embedded_H the same
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Ḧ.q0 ⟨Ḧ⟩ ⊢* Ḧ.qx ⟨Ḧ⟩ ⟨Ḧ⟩ ⊢* Ḧ.qy
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Ḧ.q0 ⟨Ḧ⟩ ⊢* Ḧ.qx ⟨Ḧ⟩ ⟨Ḧ⟩ ⊢* Ḧ.qn
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> And what do you mean by that?
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> When I redefine Ĥ to become Ḧ by
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> eliminating its infinite loop, I
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> probably mean: {I redefine Ĥ to
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> become Ḧ by eliminating its infinite
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> loop}.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Which does what? Since if you aren't
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> talking about Linz's H^, your results
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> don't mean anything for the Halting
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Problem.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> It provides a bridge of understanding
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> to my HP refutation.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> The key skill that I have applied
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> throughout my career is eliminating
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> "inessential complexity" (1999 Turing
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> award winner Fred Brooks) to make
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>   enormously difficult problems as
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> simple as possible.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> https://en.wikipedia.org/wiki/No_Silver_Bullet
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> But if you eliminate KEY ASPECTS then
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> you aren't talking about what you need to.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> It is just like learning arithmetic
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> before attacking algebra.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> It lays the foundation of prerequisites
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> for my actual rebuttal.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Just beware that if you make a statement
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that is only true for a limited case and
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> don't explicitly state so, pointing that
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> out is NOT a 'Dishonest Dodge'.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Since it is know that you are working on
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> trying to prove that a Unicorn exists,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> what you are saying WILL be looked at in
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> a light anticipating where you are going.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Also remember that showing a rule happens
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> to be correct for one case, doesn't prove
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that it will be for a different case.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> You have gone through all of this before,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> and it came for nothing, but if this is
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> how you want to spend your last days,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> knock yourself out.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I think that you already understand that
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> With Ĥ ⟨Ĥ⟩
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qy ∞ // this
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> path is never taken
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> making Ḧ ⟨Ḧ⟩ an equivalent computation
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Ḧ.q0 ⟨Ḧ⟩ ⊢* Ḧ.qx ⟨Ḧ⟩ ⟨Ḧ⟩ ⊢* Ḧ.qy
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Ḧ.q0 ⟨Ḧ⟩ ⊢* Ḧ.qx ⟨Ḧ⟩ ⟨Ḧ⟩ ⊢* Ḧ.qn
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>> And, as seems common with your arguments,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>> you keep on forgetting the CONDITIONS on
>>>>>>>>>>>>>>>>>>>>>>>>>>>>> each line.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>> H^ <H^> is
>>>>>>>>>>>>>>>>>>>>>>>>>>>>> H^.q0 <H^> -> H^.Qx <H^> <H^>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Then
>>>>>>>>>>>>>>>>>>>>>>>>>>>>> H^.Qx <H^> <H^> -> H^.Qy -> ∞ IF and only
>>>>>>>>>>>>>>>>>>>>>>>>>>>>> if H <H^> <H^> -> H.Qy and
>>>>>>>>>>>>>>>>>>>>>>>>>>>>> H^.Qx <H^> <H^> -> H^.Qn If and ohly if H
>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <H^> <H^> => H.Qn.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>> If you stipulate that H <H^> <H^> will
>>>>>>>>>>>>>>>>>>>>>>>>>>>>> never go to H.Qy, then the behavior on that
>>>>>>>>>>>>>>>>>>>>>>>>>>>>> path can be changed with no effect.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Without the If and only if clauses, the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>> initial description is incorrect because it
>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is incomplete.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>> So, WITH THE STIPULATION THAT H won't go to
>>>>>>>>>>>>>>>>>>>>>>>>>>>>> H.Qy for either version, then changing H^
>>>>>>>>>>>>>>>>>>>>>>>>>>>>> to the H" that omits to loop is an
>>>>>>>>>>>>>>>>>>>>>>>>>>>>> equivalence, but ONLY under that stipulation.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>> This of course shows that H will be wrong
>>>>>>>>>>>>>>>>>>>>>>>>>>>>> about H", as H" will ALWAYS Halt if H
>>>>>>>>>>>>>>>>>>>>>>>>>>>>> answers, and H not answering is always
>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrong. Thus H will either be wrong for not
>>>>>>>>>>>>>>>>>>>>>>>>>>>>> answering or giving the wrong answer.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>> I am only making two versions of input to H:
>>>>>>>>>>>>>>>>>>>>>>>>>>>> (1) Ĥ WITH an appended infinite loop
>>>>>>>>>>>>>>>>>>>>>>>>>>>> (2) Ḧ WITHOUT an appended infinite loop
>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>> Only this is being examined:
>>>>>>>>>>>>>>>>>>>>>>>>>>>> embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩
>>>>>>>>>>>>>>>>>>>>>>>>>>>> embedded_H ⟨Ḧ⟩ ⟨Ḧ⟩
>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>> Right, but the conclusion that H" is
>>>>>>>>>>>>>>>>>>>>>>>>>>> 'equivalent' to H^ is only true (if you mean
>>>>>>>>>>>>>>>>>>>>>>>>>>> equivalent in the sense that they compute the
>>>>>>>>>>>>>>>>>>>>>>>>>>> same function) if it is the case that neither
>>>>>>>>>>>>>>>>>>>>>>>>>>> of H <H^> <H^> or H <H"> <H"> go to H.Qy.
>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>> Good.
>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>> Unless you want to indicate some other
>>>>>>>>>>>>>>>>>>>>>>>>>>> definition of 'equivalent' you using (that
>>>>>>>>>>>>>>>>>>>>>>>>>>> could be proper to do so here), you need to
>>>>>>>>>>>>>>>>>>>>>>>>>>> include the conditions under which the
>>>>>>>>>>>>>>>>>>>>>>>>>>> statement is true.
>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>> embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ḧ.qn
>>>>>>>>>>>>>>>>>>>>>>>>>>    and
>>>>>>>>>>>>>>>>>>>>>>>>>> embedded_H ⟨Ḧ⟩ ⟨Ḧ⟩ ⊢* Ḧ.qn
>>>>>>>>>>>>>>>>>>>>>>>>>>    nd
>>>>>>>>>>>>>>>>>>>>>>>>>> H ⟨Ḧ⟩ ⟨Ḧ⟩ ⊢* Ḧ.qn
>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>> Problem, embedded_H / H need to transition to a
>>>>>>>>>>>>>>>>>>>>>>>>> state in H, not some other machine.
>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>> As soon as we append an infinite loop to H.y is
>>>>>>>>>>>>>>>>>>>>>>>> it no longer H.
>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>> This is where you are showing your lack of
>>>>>>>>>>>>>>>>>>>>>>> understanding of Turing Machines.
>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>> NO ONE has said that the machine where we added
>>>>>>>>>>>>>>>>>>>>>>> the loop is still the machine H, in fact, Linz
>>>>>>>>>>>>>>>>>>>>>>> calls that machine H', but H' CONTAINS a complete
>>>>>>>>>>>>>>>>>>>>>>> copy of H, and that copy will still act exactly
>>>>>>>>>>>>>>>>>>>>>>> like the original H to the point where it gets to
>>>>>>>>>>>>>>>>>>>>>>> the stat Qy.
>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>> This ability to compose machines of copies of
>>>>>>>>>>>>>>>>>>>>>>> other machines is basically like the concept of
>>>>>>>>>>>>>>>>>>>>>>> calling subroutines (even if it is implemented
>>>>>>>>>>>>>>>>>>>>>>> differently) and is fundamental to the design and
>>>>>>>>>>>>>>>>>>>>>>> analysis of Turing Macines.
>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>> Would you have a problem saying the subroutine H
>>>>>>>>>>>>>>>>>>>>>>> is no longer the subroutine H if one function
>>>>>>>>>>>>>>>>>>>>>>> just calls H and returns while a second calls H
>>>>>>>>>>>>>>>>>>>>>>> and conditionally loops? Yes, the whole program
>>>>>>>>>>>>>>>>>>>>>>> is not H, but the subroutine H is still there and
>>>>>>>>>>>>>>>>>>>>>>> will behave exactly like it used to in both of
>>>>>>>>>>>>>>>>>>>>>>> the cases.
>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>> One way to map a Turing Machine to ordinary
>>>>>>>>>>>>>>>>>>>>>>> software is to think of the Q0 state (or whatever
>>>>>>>>>>>>>>>>>>>>>>> is the 'starting' state of the Turing machine) as
>>>>>>>>>>>>>>>>>>>>>>> the entry point for the function, and the Halting
>>>>>>>>>>>>>>>>>>>>>>> States of the Turing Machine as retrun stateents
>>>>>>>>>>>>>>>>>>>>>>> which return a value indicating what state the
>>>>>>>>>>>>>>>>>>>>>>> machine ended in.
>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>> Thus the modifications Linz has done to H are
>>>>>>>>>>>>>>>>>>>>>>> nothing more that building H^ as mostly a call to
>>>>>>>>>>>>>>>>>>>>>>> H, with code before the call to manipulate the
>>>>>>>>>>>>>>>>>>>>>>> tape to add the second copy, and code after the
>>>>>>>>>>>>>>>>>>>>>>> return to loop forever if H returns the 'Halting'
>>>>>>>>>>>>>>>>>>>>>>> answer.
>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>> The Machine/Subroutine H has not been touched at
>>>>>>>>>>>>>>>>>>>>>>> all.
>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>> My point is that Ĥ ⟨Ĥ⟩ is equivalent to Ḧ ⟨Ḧ⟩
>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>> And my point is that they are only equivalent in
>>>>>>>>>>>>>>>>>>>>> the normal sense of the word if neither of H <H^>
>>>>>>>>>>>>>>>>>>>>> <H^> and H <H"> <H"> go to H.Qy
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>> Without that qualification, it is a false
>>>>>>>>>>>>>>>>>>>>> statement. PERIOD.
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>> They are equivalent in that neither can possibly go
>>>>>>>>>>>>>>>>>>>> to their q.y state.
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>> THAT is incorrect without the same
>>>>>>>>>>>>>>>>>>> qualification/assumption/stipulation, the H doesn't
>>>>>>>>>>>>>>>>>>> go to Qy.
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> If H was a white cat detector and you presented H with
>>>>>>>>>>>>>>>>>> a black cat would it say "yes" ?
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> But we aren't talking about a 'detector'
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> Sure we are.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> Then you don't know what you are talking about (and
>>>>>>>>>>>>>>> showing your dishonesty by your clipping).
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> THe claim that H^ and H" are equivilent machines has
>>>>>>>>>>>>>>> NOTHING to do with there being a 'Detector' but do they
>>>>>>>>>>>>>>> behave exactly the same.
>>>>>>>>>>>>>> So in other words you are disavowing that both ⟨Ĥ⟩ and ⟨Ḧ⟩
>>>>>>>>>>>>>> have a copy of H embedded within them ?
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> A halt detector is the same idea as a halt decider yet a
>>>>>>>>>>>>>> halt detector need not get every input correctly. Every
>>>>>>>>>>>>>> input that the halt detector gets correctly is in the
>>>>>>>>>>>>>> domain of the computable function that it implements.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> Yes, they have a copy of the Halt Detector H in them, and
>>>>>>>>>>>>> unless you are willing to stipulate that H will not go to
>>>>>>>>>>>>> H.Qy when given H^ or H" as an input, then you can not show
>>>>>>>>>>>>> that those machines are equivalent.
>>>>>>>>>>>>
>>>>>>>>>>>> If the simulating halt decider H cannot possibly go to H.qy
>>>>>>>>>>>> on a specific input then any such stipulation would be
>>>>>>>>>>>> redundant for this input.
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> So why do you resist it?
>>>>>>>>>>>
>>>>>>>>>>> What is wrong with stipulating as a requirement something you
>>>>>>>>>>> 'know' to be true?
>>>>>>>>>>>
>>>>>>>>>>> The only reason I can see for you to object to listing that
>>>>>>>>>>> requirement. is that at some point you are going to want to
>>>>>>>>>>> violate that requirement.
>>>>>>>>>>
>>>>>>>>>> Specifically because it was redundant.
>>>>>>>>>> embedded_H ⟨Ḧ⟩ ⟨Ḧ⟩ ⊢* Ḧ.qn
>>>>>>>>>> embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
>>>>>>>>>>
>>>>>>>>>> It does not take a genius to know that when
>>>>>>>>>> embedded_H transitions to H.qn it does not transition to H.qn
>>>>>>>>>     embedded_H transitions to H.qn it does not transition to H.qy
>>>>>>>>>
>>>>>>>>
>>>>>>>> So, are you stating as a fact that embedded_H <H^> <H^> and
>>>>>>>> embedded_H <H"> <H"> both as a matter of DEFINITION go to H.Qn?
>>>>>>>>
>>>>>>>
>>>>>>> For H to be correct then on the above specified inputs they must
>>>>>>> both go to H.qn.
>>>>>>>
>>>>>>>
>>>>>>
>>>>>> But, by DEFINITION that is the WRONG answer.
>>>>>>
>>>>>> DEFINITION of a Correct Halt Decider:
>>>>>>
>>>>>> A) H <M> w goes to H.Qy if M w Halts, and to H.Qn if M w never Halts.
>>>>> I am only talking about these two:
>>>>> embedded_H ⟨Ḧ⟩ ⟨Ḧ⟩ ⊢* Ḧ.qn
>>>>> embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
>>>>>
>>>>> Whenever any embedded_H must abort the simulation of its input to
>>>>> prevent the infinitely nested simulation of this input the entire
>>>>> nested simulation sequence specifies infinitely nested simulation.
>>>>> This makes a transition to H.qn necessarily correct in this case.
>>>>>
>>>>
>>>> Right, the NESTED simulation, but NOT the H^ / H" that is USING that
>>>> embededeed_H, and it is THAT machine that defines the CORRECT answer
>>>> for H.
>>>>
>>>
>>> That problem is that you are flat out wrong about this.
>>> embedded_H IS NOT REPORTING ON ITS OWN BEHAVIOR
>>> THUS NOT REPORTING ON Ĥ ⟨Ĥ⟩
>>>
>>
>> Then it is NOT a Halt Detector. PERIOD. BY DEFINITON.
>
> Not at all. The only thing that it proves is that you persistently fail
> to understand that all deciders are only accountable for their actual
> inputs. int Sum(3,5) is not accountable for Sum(7,3).
>

On 2/16/2022 6:47 PM, Richard Damon wrote:
> On 2/16/22 7:12 PM, olcott wrote:
>> On 2/16/2022 5:58 PM, Richard Damon wrote:
>>> On 2/16/22 8:35 AM, olcott wrote:
>>>> On 2/16/2022 6:55 AM, Richard Damon wrote:
>>>>> On 2/16/22 7:37 AM, olcott wrote:
>>>>>> On 2/15/2022 10:37 PM, Richard Damon wrote:
>>>>>>> On 2/15/22 10:39 PM, olcott wrote:
>>>>>>>> On 2/15/2022 9:14 PM, Richard Damon wrote:
>>>>>>>>> On 2/15/22 9:50 PM, olcott wrote:
>>>>>>>>>> On 2/15/2022 8:49 PM, olcott wrote:
>>>>>>>>>>> On 2/15/2022 8:07 PM, Richard Damon wrote:
>>>>>>>>>>>> On 2/15/22 8:17 PM, olcott wrote:
>>>>>>>>>>>>> On 2/15/2022 5:40 PM, Richard Damon wrote:
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> On 2/15/22 11:49 AM, olcott wrote:
>>>>>>>>>>>>>>> On 2/14/2022 5:49 AM, Richard Damon wrote:
>>>>>>>>>>>>>>>> On 2/13/22 10:30 PM, olcott wrote:
>>>>>>>>>>>>>>>>> On 2/13/2022 7:27 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>> On 2/13/22 7:26 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>> On 2/13/2022 6:24 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>> On 2/13/22 6:08 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>> On 2/13/2022 4:11 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>>> On 2/13/22 5:04 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>> On 2/13/2022 3:40 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>> On 2/13/22 4:24 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>> On 2/13/2022 3:12 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/13/22 3:18 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/13/2022 1:57 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/13/22 2:43 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/13/2022 11:19 AM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/13/22 9:38 AM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/13/2022 5:43 AM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/13/22 12:54 AM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/12/2022 8:22 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/12/22 9:02 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/12/2022 7:54 PM, Richard Damon
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/12/22 8:27 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/12/2022 6:57 PM, Richard Damon
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/12/22 7:37 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/12/2022 6:25 PM, Richard
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/12/22 6:48 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/12/2022 5:39 PM, Richard
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/12/22 5:34 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/12/2022 8:41 AM, Richard
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/12/22 9:08 AM, olcott
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/12/2022 6:49 AM,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/12/22 12:01 AM,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/11/2022 10:50 PM,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/11/22 11:36 PM,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/11/2022 6:58 PM,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/11/22 7:52 PM,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/11/2022 6:17 PM,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/11/22 7:10 PM,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/11/2022 5:36
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> PM, Richard Damon
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/11/22 10:20
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> AM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/11/2022 5:36
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> AM, Richard Damon
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/10/22 11:39
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/10/2022
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 10:20 PM,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Richard Damon
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/10/22
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 10:58 PM,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/10/2022
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 6:02 PM,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Richard Damon
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/10/22
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 9:18 AM,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>   > I
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> explain how
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I am
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> necessarily
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> correct on
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the basis of
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the meaning
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of my
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> words and
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> you
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> disagree on
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the basis
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of your
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> failure to
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> correctly
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the meaning
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of these
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> words.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> No, you
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> CLAIM to
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> explain
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> based on the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> meaning of
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the words,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> but use the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrong
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> meaning of
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the words.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> THIS IS
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> PROVEN TO
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> BE
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> COMPLETELY
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> TRUE
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> ENTIRELY ON
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> THE BASIS
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> OF THE
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> MEANING OF
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> ITS WORDS:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> When a
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> simulating
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> halt
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> decider
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> correctly
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> determines
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> in a finite
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> number of
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> steps that
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the pure
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> UTM
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> simulation
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of its
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> input would
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> never reach
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the final
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> state of
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> this input
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> then it can
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> correctly
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> reject this
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> input as
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> non-halting.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> IF it
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> correctly
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> decided,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> then yes.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> But it has
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> been shown,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> by the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> definition
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> construction
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> method of H^
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that if H
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <H^> <H^>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> goes to H.Qn
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> then H^ <H^>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> goes to
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> H^.Qn and
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Halts, and
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> thus by the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> definition
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of a UTM,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> then we also
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> have that
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> UTM <H^>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <H^> will halt.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢*
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> ⊢* Ĥ.qy ∞
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢*
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> ⊢* Ĥ.qn
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> You keep
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> getting
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> confused
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> between two
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> things:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> (1) The
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> execution of
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Ĥ ⟨Ĥ⟩ versus
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> embedded_H
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> ⟨Ĥ⟩ ⟨Ĥ⟩ (we
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> only look at
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the latter).
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> No, YOU qre
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> confused.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> By the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> definioon of
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> how to build
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> H^, embedded_H
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> MUST be
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> EXACTLY the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> same algorithm
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> as H,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> No it is
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> specifically
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> not allowed to be.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> embedded_H must
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> have an
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> infinite loop
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> appended to its
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Ĥ.qy state and
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> H is not
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> allowed to have
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> such a loop
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> appended to its
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> H.qy state.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Which is OUTSIDE
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the algorithm of
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> H itself, and
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> doesn't affect
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the behavior of
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> H in deciding to
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> go from Q0 to
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Qy/Qn.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> When the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> simulating halt
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> decider bases it
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> halt status
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> decision on
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> whether or not
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the same function
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is being called
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> with the same
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> inputs the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> difference
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> between H and
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> embedded_H can
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> change the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> behavior. A
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> string comparison
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> between the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> machine
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> description of H
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> and embedded_H
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> yields false.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> No, it can't, not
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> and be a COMPUTATION.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> You obviously
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> don't know the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> meaning of the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> words, so you are
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> just wrong.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Computation means
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> for ALL copoies,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Same input leads
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> to Same Output.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> The fact that it is
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> not an exact copy
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> makes a difference.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> But it IS.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> H applied to ⟨Ĥ⟩ ⟨Ĥ⟩
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> does not determine
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that itself is being
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> called multiple times
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> with the same input.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> embedded_H does
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> determine that itself
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is called multiple
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> times with the same
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> input because
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> strcmp(H, embedded_H
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> != 0.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Except that embedded_H
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> does't have a
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 'representation' of
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> itself to use to make
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that comparison, so
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that is just more of
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> your Fairy Dust
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Powered Unicorn stuff.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> It can very easily have
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> a representation of
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> itself, that only
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> requires that it has
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> access to its own
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> machine description.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> First, Turing Machines
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> DON'T have access to
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> their own machine
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> description, unless it
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> has been provided as an
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> input
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> You said that this was
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> impossible.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> So, you are agreeing that
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> they can't? Or do you just
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> not understand the logic.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I am agreeing that you
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> contradicted yourself.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> How, by saying that the only
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> way a Turing Machine can
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> have a copy of its
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> representation is for it to
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> be given (and H is defined
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> in a way that it can't be
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> given as an extra input)?
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> No appended infinite loop
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> making H and embedded_H the same
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Ḧ.q0 ⟨Ḧ⟩ ⊢* Ḧ.qx ⟨Ḧ⟩ ⟨Ḧ⟩ ⊢* Ḧ.qy
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Ḧ.q0 ⟨Ḧ⟩ ⊢* Ḧ.qx ⟨Ḧ⟩ ⟨Ḧ⟩ ⊢* Ḧ.qn
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> embedded_H ⟨Ḧ⟩ ⟨Ḧ⟩ ⊢* Ḧ.qn
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> H ⟨Ḧ⟩ ⟨Ḧ⟩ ⊢* H.qn
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Except that the infinite loop
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> isn't part of the copy of H in
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> H^, it is something ADD to it,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> which only has/affects
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> behavior AFTER H makes its
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> decision.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> So another words hypothetical
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> examples get you so confused
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> you totally lose track of
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> everything.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> What 'Hypothetical' are you
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> referencing.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> This is what I mean when I say
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that you hardly pay any attention
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> at all.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> This is the hypothetical that I
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> am referencing:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> No appended infinite loop making
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> H and embedded_H the same
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Ḧ.q0 ⟨Ḧ⟩ ⊢* Ḧ.qx ⟨Ḧ⟩ ⟨Ḧ⟩ ⊢* Ḧ.qy
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Ḧ.q0 ⟨Ḧ⟩ ⊢* Ḧ.qx ⟨Ḧ⟩ ⟨Ḧ⟩ ⊢* Ḧ.qn
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> And what do you mean by that?
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> When I redefine Ĥ to become Ḧ by
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> eliminating its infinite loop, I
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> probably mean: {I redefine Ĥ to
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> become Ḧ by eliminating its
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> infinite loop}.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Which does what? Since if you aren't
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> talking about Linz's H^, your
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> results don't mean anything for the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Halting Problem.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> It provides a bridge of understanding
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> to my HP refutation.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> The key skill that I have applied
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> throughout my career is eliminating
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> "inessential complexity" (1999 Turing
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> award winner Fred Brooks) to make
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>   enormously difficult problems as
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> simple as possible.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> https://en.wikipedia.org/wiki/No_Silver_Bullet
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> But if you eliminate KEY ASPECTS then
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> you aren't talking about what you need
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> to.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> It is just like learning arithmetic
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> before attacking algebra.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> It lays the foundation of prerequisites
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> for my actual rebuttal.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Just beware that if you make a statement
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that is only true for a limited case and
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> don't explicitly state so, pointing that
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> out is NOT a 'Dishonest Dodge'.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Since it is know that you are working on
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> trying to prove that a Unicorn exists,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> what you are saying WILL be looked at in
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> a light anticipating where you are going.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Also remember that showing a rule
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> happens to be correct for one case,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> doesn't prove that it will be for a
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> different case.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> You have gone through all of this
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> before, and it came for nothing, but if
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> this is how you want to spend your last
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> days, knock yourself out.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I think that you already understand that
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> With Ĥ ⟨Ĥ⟩
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qy ∞ //
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> this path is never taken
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> making Ḧ ⟨Ḧ⟩ an equivalent computation
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Ḧ.q0 ⟨Ḧ⟩ ⊢* Ḧ.qx ⟨Ḧ⟩ ⟨Ḧ⟩ ⊢* Ḧ.qy
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Ḧ.q0 ⟨Ḧ⟩ ⊢* Ḧ.qx ⟨Ḧ⟩ ⟨Ḧ⟩ ⊢* Ḧ.qn
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> And, as seems common with your arguments,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> you keep on forgetting the CONDITIONS on
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> each line.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> H^ <H^> is
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> H^.q0 <H^> -> H^.Qx <H^> <H^>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Then
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> H^.Qx <H^> <H^> -> H^.Qy -> ∞ IF and only
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> if H <H^> <H^> -> H.Qy and
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> H^.Qx <H^> <H^> -> H^.Qn If and ohly if H
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <H^> <H^> => H.Qn.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> If you stipulate that H <H^> <H^> will
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> never go to H.Qy, then the behavior on
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that path can be changed with no effect.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Without the If and only if clauses, the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> initial description is incorrect because
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> it is incomplete.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> So, WITH THE STIPULATION THAT H won't go
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> to H.Qy for either version, then changing
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> H^ to the H" that omits to loop is an
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> equivalence, but ONLY under that stipulation.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> This of course shows that H will be wrong
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> about H", as H" will ALWAYS Halt if H
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> answers, and H not answering is always
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrong. Thus H will either be wrong for not
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> answering or giving the wrong answer.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I am only making two versions of input to H:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>> (1) Ĥ WITH an appended infinite loop
>>>>>>>>>>>>>>>>>>>>>>>>>>>>> (2) Ḧ WITHOUT an appended infinite loop
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Only this is being examined:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>> embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩
>>>>>>>>>>>>>>>>>>>>>>>>>>>>> embedded_H ⟨Ḧ⟩ ⟨Ḧ⟩
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>> Right, but the conclusion that H" is
>>>>>>>>>>>>>>>>>>>>>>>>>>>> 'equivalent' to H^ is only true (if you mean
>>>>>>>>>>>>>>>>>>>>>>>>>>>> equivalent in the sense that they compute
>>>>>>>>>>>>>>>>>>>>>>>>>>>> the same function) if it is the case that
>>>>>>>>>>>>>>>>>>>>>>>>>>>> neither of H <H^> <H^> or H <H"> <H"> go to
>>>>>>>>>>>>>>>>>>>>>>>>>>>> H.Qy.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>> Good.
>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>> Unless you want to indicate some other
>>>>>>>>>>>>>>>>>>>>>>>>>>>> definition of 'equivalent' you using (that
>>>>>>>>>>>>>>>>>>>>>>>>>>>> could be proper to do so here), you need to
>>>>>>>>>>>>>>>>>>>>>>>>>>>> include the conditions under which the
>>>>>>>>>>>>>>>>>>>>>>>>>>>> statement is true.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>> embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ḧ.qn
>>>>>>>>>>>>>>>>>>>>>>>>>>>    and
>>>>>>>>>>>>>>>>>>>>>>>>>>> embedded_H ⟨Ḧ⟩ ⟨Ḧ⟩ ⊢* Ḧ.qn
>>>>>>>>>>>>>>>>>>>>>>>>>>>    nd
>>>>>>>>>>>>>>>>>>>>>>>>>>> H ⟨Ḧ⟩ ⟨Ḧ⟩ ⊢* Ḧ.qn
>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>> Problem, embedded_H / H need to transition to
>>>>>>>>>>>>>>>>>>>>>>>>>> a state in H, not some other machine.
>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>> As soon as we append an infinite loop to H.y is
>>>>>>>>>>>>>>>>>>>>>>>>> it no longer H.
>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>> This is where you are showing your lack of
>>>>>>>>>>>>>>>>>>>>>>>> understanding of Turing Machines.
>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>> NO ONE has said that the machine where we added
>>>>>>>>>>>>>>>>>>>>>>>> the loop is still the machine H, in fact, Linz
>>>>>>>>>>>>>>>>>>>>>>>> calls that machine H', but H' CONTAINS a
>>>>>>>>>>>>>>>>>>>>>>>> complete copy of H, and that copy will still act
>>>>>>>>>>>>>>>>>>>>>>>> exactly like the original H to the point where
>>>>>>>>>>>>>>>>>>>>>>>> it gets to the stat Qy.
>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>> This ability to compose machines of copies of
>>>>>>>>>>>>>>>>>>>>>>>> other machines is basically like the concept of
>>>>>>>>>>>>>>>>>>>>>>>> calling subroutines (even if it is implemented
>>>>>>>>>>>>>>>>>>>>>>>> differently) and is fundamental to the design
>>>>>>>>>>>>>>>>>>>>>>>> and analysis of Turing Macines.
>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>> Would you have a problem saying the subroutine H
>>>>>>>>>>>>>>>>>>>>>>>> is no longer the subroutine H if one function
>>>>>>>>>>>>>>>>>>>>>>>> just calls H and returns while a second calls H
>>>>>>>>>>>>>>>>>>>>>>>> and conditionally loops? Yes, the whole program
>>>>>>>>>>>>>>>>>>>>>>>> is not H, but the subroutine H is still there
>>>>>>>>>>>>>>>>>>>>>>>> and will behave exactly like it used to in both
>>>>>>>>>>>>>>>>>>>>>>>> of the cases.
>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>> One way to map a Turing Machine to ordinary
>>>>>>>>>>>>>>>>>>>>>>>> software is to think of the Q0 state (or
>>>>>>>>>>>>>>>>>>>>>>>> whatever is the 'starting' state of the Turing
>>>>>>>>>>>>>>>>>>>>>>>> machine) as the entry point for the function,
>>>>>>>>>>>>>>>>>>>>>>>> and the Halting States of the Turing Machine as
>>>>>>>>>>>>>>>>>>>>>>>> retrun stateents which return a value indicating
>>>>>>>>>>>>>>>>>>>>>>>> what state the machine ended in.
>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>> Thus the modifications Linz has done to H are
>>>>>>>>>>>>>>>>>>>>>>>> nothing more that building H^ as mostly a call
>>>>>>>>>>>>>>>>>>>>>>>> to H, with code before the call to manipulate
>>>>>>>>>>>>>>>>>>>>>>>> the tape to add the second copy, and code after
>>>>>>>>>>>>>>>>>>>>>>>> the return to loop forever if H returns the
>>>>>>>>>>>>>>>>>>>>>>>> 'Halting' answer.
>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>> The Machine/Subroutine H has not been touched at
>>>>>>>>>>>>>>>>>>>>>>>> all.
>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>> My point is that Ĥ ⟨Ĥ⟩ is equivalent to Ḧ ⟨Ḧ⟩
>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>> And my point is that they are only equivalent in
>>>>>>>>>>>>>>>>>>>>>> the normal sense of the word if neither of H <H^>
>>>>>>>>>>>>>>>>>>>>>> <H^> and H <H"> <H"> go to H.Qy
>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>> Without that qualification, it is a false
>>>>>>>>>>>>>>>>>>>>>> statement. PERIOD.
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>> They are equivalent in that neither can possibly go
>>>>>>>>>>>>>>>>>>>>> to their q.y state.
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>> THAT is incorrect without the same
>>>>>>>>>>>>>>>>>>>> qualification/assumption/stipulation, the H doesn't
>>>>>>>>>>>>>>>>>>>> go to Qy.
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>> If H was a white cat detector and you presented H
>>>>>>>>>>>>>>>>>>> with a black cat would it say "yes" ?
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> But we aren't talking about a 'detector'
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> Sure we are.
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> Then you don't know what you are talking about (and
>>>>>>>>>>>>>>>> showing your dishonesty by your clipping).
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> THe claim that H^ and H" are equivilent machines has
>>>>>>>>>>>>>>>> NOTHING to do with there being a 'Detector' but do they
>>>>>>>>>>>>>>>> behave exactly the same.
>>>>>>>>>>>>>>> So in other words you are disavowing that both ⟨Ĥ⟩ and
>>>>>>>>>>>>>>> ⟨Ḧ⟩ have a copy of H embedded within them ?
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> A halt detector is the same idea as a halt decider yet a
>>>>>>>>>>>>>>> halt detector need not get every input correctly. Every
>>>>>>>>>>>>>>> input that the halt detector gets correctly is in the
>>>>>>>>>>>>>>> domain of the computable function that it implements.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Yes, they have a copy of the Halt Detector H in them, and
>>>>>>>>>>>>>> unless you are willing to stipulate that H will not go to
>>>>>>>>>>>>>> H.Qy when given H^ or H" as an input, then you can not
>>>>>>>>>>>>>> show that those machines are equivalent.
>>>>>>>>>>>>>
>>>>>>>>>>>>> If the simulating halt decider H cannot possibly go to H.qy
>>>>>>>>>>>>> on a specific input then any such stipulation would be
>>>>>>>>>>>>> redundant for this input.
>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> So why do you resist it?
>>>>>>>>>>>>
>>>>>>>>>>>> What is wrong with stipulating as a requirement something
>>>>>>>>>>>> you 'know' to be true?
>>>>>>>>>>>>
>>>>>>>>>>>> The only reason I can see for you to object to listing that
>>>>>>>>>>>> requirement. is that at some point you are going to want to
>>>>>>>>>>>> violate that requirement.
>>>>>>>>>>>
>>>>>>>>>>> Specifically because it was redundant.
>>>>>>>>>>> embedded_H ⟨Ḧ⟩ ⟨Ḧ⟩ ⊢* Ḧ.qn
>>>>>>>>>>> embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
>>>>>>>>>>>
>>>>>>>>>>> It does not take a genius to know that when
>>>>>>>>>>> embedded_H transitions to H.qn it does not transition to H.qn
>>>>>>>>>>     embedded_H transitions to H.qn it does not transition to H.qy
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> So, are you stating as a fact that embedded_H <H^> <H^> and
>>>>>>>>> embedded_H <H"> <H"> both as a matter of DEFINITION go to H.Qn?
>>>>>>>>>
>>>>>>>>
>>>>>>>> For H to be correct then on the above specified inputs they must
>>>>>>>> both go to H.qn.
>>>>>>>>
>>>>>>>>
>>>>>>>
>>>>>>> But, by DEFINITION that is the WRONG answer.
>>>>>>>
>>>>>>> DEFINITION of a Correct Halt Decider:
>>>>>>>
>>>>>>> A) H <M> w goes to H.Qy if M w Halts, and to H.Qn if M w never
>>>>>>> Halts.
>>>>>> I am only talking about these two:
>>>>>> embedded_H ⟨Ḧ⟩ ⟨Ḧ⟩ ⊢* Ḧ.qn
>>>>>> embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
>>>>>>
>>>>>> Whenever any embedded_H must abort the simulation of its input to
>>>>>> prevent the infinitely nested simulation of this input the entire
>>>>>> nested simulation sequence specifies infinitely nested simulation.
>>>>>> This makes a transition to H.qn necessarily correct in this case.
>>>>>>
>>>>>
>>>>> Right, the NESTED simulation, but NOT the H^ / H" that is USING
>>>>> that embededeed_H, and it is THAT machine that defines the CORRECT
>>>>> answer for H.
>>>>>
>>>>
>>>> That problem is that you are flat out wrong about this.
>>>> embedded_H IS NOT REPORTING ON ITS OWN BEHAVIOR
>>>> THUS NOT REPORTING ON Ĥ ⟨Ĥ⟩
>>>>
>>>
>>> Then it is NOT a Halt Detector. PERIOD. BY DEFINITON.
>>
>> Not at all. The only thing that it proves is that you persistently
>> fail to understand that all deciders are only accountable for their
>> actual inputs. int Sum(3,5) is not accountable for Sum(7,3).
>>
>
> And you don't understand that the 'behavior of its input' is what the
> machine its input represents would do with the input provided.

On 2/16/22 8:17 PM, olcott wrote:
> On 2/16/2022 6:47 PM, Richard Damon wrote:
>> On 2/16/22 7:12 PM, olcott wrote:
>>> On 2/16/2022 5:58 PM, Richard Damon wrote:
>>>> On 2/16/22 8:35 AM, olcott wrote:
>>>>> On 2/16/2022 6:55 AM, Richard Damon wrote:
>>>>>> On 2/16/22 7:37 AM, olcott wrote:
>>>>>>> On 2/15/2022 10:37 PM, Richard Damon wrote:
>>>>>>>> On 2/15/22 10:39 PM, olcott wrote:
>>>>>>>>> On 2/15/2022 9:14 PM, Richard Damon wrote:
>>>>>>>>>> On 2/15/22 9:50 PM, olcott wrote:
>>>>>>>>>>> On 2/15/2022 8:49 PM, olcott wrote:
>>>>>>>>>>>> On 2/15/2022 8:07 PM, Richard Damon wrote:
>>>>>>>>>>>>> On 2/15/22 8:17 PM, olcott wrote:
>>>>>>>>>>>>>> On 2/15/2022 5:40 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> On 2/15/22 11:49 AM, olcott wrote:
>>>>>>>>>>>>>>>> On 2/14/2022 5:49 AM, Richard Damon wrote:
>>>>>>>>>>>>>>>>> On 2/13/22 10:30 PM, olcott wrote:
>>>>>>>>>>>>>>>>>> On 2/13/2022 7:27 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>> On 2/13/22 7:26 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>> On 2/13/2022 6:24 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>> On 2/13/22 6:08 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>> On 2/13/2022 4:11 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>> On 2/13/22 5:04 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>> On 2/13/2022 3:40 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>>> On 2/13/22 4:24 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/13/2022 3:12 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/13/22 3:18 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/13/2022 1:57 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/13/22 2:43 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/13/2022 11:19 AM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/13/22 9:38 AM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/13/2022 5:43 AM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/13/22 12:54 AM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/12/2022 8:22 PM, Richard Damon
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/12/22 9:02 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/12/2022 7:54 PM, Richard Damon
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/12/22 8:27 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/12/2022 6:57 PM, Richard
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/12/22 7:37 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/12/2022 6:25 PM, Richard
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/12/22 6:48 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/12/2022 5:39 PM, Richard
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/12/22 5:34 PM, olcott
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/12/2022 8:41 AM,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/12/22 9:08 AM, olcott
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/12/2022 6:49 AM,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/12/22 12:01 AM,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/11/2022 10:50 PM,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/11/22 11:36 PM,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/11/2022 6:58 PM,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/11/22 7:52 PM,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/11/2022 6:17
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> PM, Richard Damon
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/11/22 7:10 PM,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/11/2022 5:36
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> PM, Richard Damon
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/11/22 10:20
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> AM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/11/2022
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 5:36 AM, Richard
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/10/22
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 11:39 PM,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/10/2022
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 10:20 PM,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Richard Damon
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/10/22
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 10:58 PM,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/10/2022
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 6:02 PM,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Richard
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/10/22
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 9:18 AM,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>   > I
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> explain how
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I am
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> necessarily
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> correct on
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the basis
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> meaning of my
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> words and
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> you
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> disagree
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> on the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> basis of
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> your
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> failure to
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> correctly
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> meaning of
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> these words.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> No, you
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> CLAIM to
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> explain
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> based on
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the meaning
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> words, but
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> use the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrong
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> meaning of
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the words.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> THIS IS
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> PROVEN TO
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> BE
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> COMPLETELY
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> TRUE
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> ENTIRELY
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> ON THE
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> BASIS OF
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> THE
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> MEANING OF
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> ITS WORDS:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> When a
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> simulating
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> halt
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> decider
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> correctly
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> determines
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> in a
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> finite
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> number of
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> steps that
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the pure
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> UTM
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> simulation
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of its
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> input
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> would
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> never
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> reach the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> final
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> state of
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> this input
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> then it
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> can
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> correctly
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> reject
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> this input
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> as
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> non-halting.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> IF it
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> correctly
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> decided,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> then yes.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> But it has
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> been shown,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> by the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> definition
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> construction method
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of H^ that
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> if H <H^>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <H^> goes
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> to H.Qn
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> then H^
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <H^> goes
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> to H^.Qn
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> and Halts,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> and thus by
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> definition
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of a UTM,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> then we
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> also have
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that UTM
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <H^> <H^>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> will halt.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢*
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> ⊢* Ĥ.qy ∞
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢*
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> ⊢* Ĥ.qn
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> You keep
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> getting
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> confused
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> between two
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> things:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> (1) The
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> execution of
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Ĥ ⟨Ĥ⟩ versus
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> embedded_H
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> ⟨Ĥ⟩ ⟨Ĥ⟩ (we
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> only look at
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the latter).
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> No, YOU qre
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> confused.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> By the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> definioon of
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> how to build
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> H^,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> embedded_H
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> MUST be
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> EXACTLY the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> same
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> algorithm as H,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> No it is
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> specifically
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> not allowed to
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> be.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> embedded_H
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> must have an
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> infinite loop
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> appended to
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> its Ĥ.qy state
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> and H is not
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> allowed to
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> have such a
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> loop appended
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> to its H.qy
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> state.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Which is
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> OUTSIDE the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> algorithm of H
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> itself, and
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> doesn't affect
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the behavior of
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> H in deciding
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> to go from Q0
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> to Qy/Qn.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> When the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> simulating halt
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> decider bases it
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> halt status
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> decision on
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> whether or not
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the same
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> function is
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> being called
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> with the same
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> inputs the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> difference
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> between H and
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> embedded_H can
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> change the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> behavior. A
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> string
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> comparison
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> between the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> machine
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> description of H
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> and embedded_H
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> yields false.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> No, it can't, not
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> and be a
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> COMPUTATION.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> You obviously
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> don't know the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> meaning of the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> words, so you are
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> just wrong.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Computation means
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> for ALL copoies,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Same input leads
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> to Same Output.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> The fact that it
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is not an exact
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> copy makes a
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> difference.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> But it IS.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> H applied to ⟨Ĥ⟩ ⟨Ĥ⟩
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> does not determine
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that itself is being
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> called multiple
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> times with the same
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> input. embedded_H
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> does determine that
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> itself is called
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> multiple times with
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the same input
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> because strcmp(H,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> embedded_H != 0.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Except that
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> embedded_H does't
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> have a
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 'representation' of
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> itself to use to make
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that comparison, so
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that is just more of
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> your Fairy Dust
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Powered Unicorn stuff.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> It can very easily
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> have a representation
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of itself, that only
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> requires that it has
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> access to its own
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> machine description.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> First, Turing Machines
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> DON'T have access to
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> their own machine
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> description, unless it
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> has been provided as an
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> input
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> You said that this was
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> impossible.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> So, you are agreeing that
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> they can't? Or do you
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> just not understand the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> logic.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I am agreeing that you
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> contradicted yourself.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> How, by saying that the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> only way a Turing Machine
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> can have a copy of its
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> representation is for it to
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> be given (and H is defined
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> in a way that it can't be
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> given as an extra input)?
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> No appended infinite loop
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> making H and embedded_H the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> same
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Ḧ.q0 ⟨Ḧ⟩ ⊢* Ḧ.qx ⟨Ḧ⟩ ⟨Ḧ⟩ ⊢*
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Ḧ.qy
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Ḧ.q0 ⟨Ḧ⟩ ⊢* Ḧ.qx ⟨Ḧ⟩ ⟨Ḧ⟩ ⊢*
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Ḧ.qn
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> embedded_H ⟨Ḧ⟩ ⟨Ḧ⟩ ⊢* Ḧ.qn
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> H ⟨Ḧ⟩ ⟨Ḧ⟩ ⊢* H.qn
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Except that the infinite loop
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> isn't part of the copy of H
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> in H^, it is something ADD to
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> it, which only has/affects
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> behavior AFTER H makes its
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> decision.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> So another words hypothetical
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> examples get you so confused
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> you totally lose track of
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> everything.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> What 'Hypothetical' are you
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> referencing.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> This is what I mean when I say
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that you hardly pay any
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> attention at all.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> This is the hypothetical that I
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> am referencing:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> No appended infinite loop making
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> H and embedded_H the same
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Ḧ.q0 ⟨Ḧ⟩ ⊢* Ḧ.qx ⟨Ḧ⟩ ⟨Ḧ⟩ ⊢* Ḧ.qy
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Ḧ.q0 ⟨Ḧ⟩ ⊢* Ḧ.qx ⟨Ḧ⟩ ⟨Ḧ⟩ ⊢* Ḧ.qn
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> And what do you mean by that?
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> When I redefine Ĥ to become Ḧ by
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> eliminating its infinite loop, I
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> probably mean: {I redefine Ĥ to
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> become Ḧ by eliminating its
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> infinite loop}.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Which does what? Since if you
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> aren't talking about Linz's H^,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> your results don't mean anything
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> for the Halting Problem.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> It provides a bridge of
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understanding to my HP refutation.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> The key skill that I have applied
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> throughout my career is eliminating
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> "inessential complexity" (1999
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Turing award winner Fred Brooks) to
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> make   enormously difficult problems
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> as simple as possible.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> https://en.wikipedia.org/wiki/No_Silver_Bullet
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> But if you eliminate KEY ASPECTS then
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> you aren't talking about what you
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> need to.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> It is just like learning arithmetic
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> before attacking algebra.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> It lays the foundation of
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> prerequisites for my actual rebuttal.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Just beware that if you make a
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> statement that is only true for a
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> limited case and don't explicitly state
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> so, pointing that out is NOT a
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 'Dishonest Dodge'.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Since it is know that you are working
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> on trying to prove that a Unicorn
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> exists, what you are saying WILL be
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> looked at in a light anticipating where
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> you are going.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Also remember that showing a rule
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> happens to be correct for one case,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> doesn't prove that it will be for a
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> different case.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> You have gone through all of this
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> before, and it came for nothing, but if
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> this is how you want to spend your last
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> days, knock yourself out.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I think that you already understand that
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> With Ĥ ⟨Ĥ⟩
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qy ∞ //
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> this path is never taken
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> making Ḧ ⟨Ḧ⟩ an equivalent computation
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Ḧ.q0 ⟨Ḧ⟩ ⊢* Ḧ.qx ⟨Ḧ⟩ ⟨Ḧ⟩ ⊢* Ḧ.qy
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Ḧ.q0 ⟨Ḧ⟩ ⊢* Ḧ.qx ⟨Ḧ⟩ ⟨Ḧ⟩ ⊢* Ḧ.qn
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> And, as seems common with your arguments,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> you keep on forgetting the CONDITIONS on
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> each line.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> H^ <H^> is
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> H^.q0 <H^> -> H^.Qx <H^> <H^>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Then
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> H^.Qx <H^> <H^> -> H^.Qy -> ∞ IF and only
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> if H <H^> <H^> -> H.Qy and
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> H^.Qx <H^> <H^> -> H^.Qn If and ohly if H
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <H^> <H^> => H.Qn.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> If you stipulate that H <H^> <H^> will
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> never go to H.Qy, then the behavior on
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that path can be changed with no effect.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Without the If and only if clauses, the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> initial description is incorrect because
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> it is incomplete.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> So, WITH THE STIPULATION THAT H won't go
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> to H.Qy for either version, then changing
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> H^ to the H" that omits to loop is an
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> equivalence, but ONLY under that
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> stipulation.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> This of course shows that H will be wrong
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> about H", as H" will ALWAYS Halt if H
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> answers, and H not answering is always
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrong. Thus H will either be wrong for
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> not answering or giving the wrong answer.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I am only making two versions of input to H:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> (1) Ĥ WITH an appended infinite loop
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> (2) Ḧ WITHOUT an appended infinite loop
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Only this is being examined:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> embedded_H ⟨Ḧ⟩ ⟨Ḧ⟩
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Right, but the conclusion that H" is
>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 'equivalent' to H^ is only true (if you
>>>>>>>>>>>>>>>>>>>>>>>>>>>>> mean equivalent in the sense that they
>>>>>>>>>>>>>>>>>>>>>>>>>>>>> compute the same function) if it is the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>> case that neither of H <H^> <H^> or H <H">
>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <H"> go to H.Qy.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>> Good.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Unless you want to indicate some other
>>>>>>>>>>>>>>>>>>>>>>>>>>>>> definition of 'equivalent' you using (that
>>>>>>>>>>>>>>>>>>>>>>>>>>>>> could be proper to do so here), you need to
>>>>>>>>>>>>>>>>>>>>>>>>>>>>> include the conditions under which the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>> statement is true.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>> embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ḧ.qn
>>>>>>>>>>>>>>>>>>>>>>>>>>>>    and
>>>>>>>>>>>>>>>>>>>>>>>>>>>> embedded_H ⟨Ḧ⟩ ⟨Ḧ⟩ ⊢* Ḧ.qn
>>>>>>>>>>>>>>>>>>>>>>>>>>>>    nd
>>>>>>>>>>>>>>>>>>>>>>>>>>>> H ⟨Ḧ⟩ ⟨Ḧ⟩ ⊢* Ḧ.qn
>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>> Problem, embedded_H / H need to transition to
>>>>>>>>>>>>>>>>>>>>>>>>>>> a state in H, not some other machine.
>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>> As soon as we append an infinite loop to H.y
>>>>>>>>>>>>>>>>>>>>>>>>>> is it no longer H.
>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>> This is where you are showing your lack of
>>>>>>>>>>>>>>>>>>>>>>>>> understanding of Turing Machines.
>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>> NO ONE has said that the machine where we added
>>>>>>>>>>>>>>>>>>>>>>>>> the loop is still the machine H, in fact, Linz
>>>>>>>>>>>>>>>>>>>>>>>>> calls that machine H', but H' CONTAINS a
>>>>>>>>>>>>>>>>>>>>>>>>> complete copy of H, and that copy will still
>>>>>>>>>>>>>>>>>>>>>>>>> act exactly like the original H to the point
>>>>>>>>>>>>>>>>>>>>>>>>> where it gets to the stat Qy.
>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>> This ability to compose machines of copies of
>>>>>>>>>>>>>>>>>>>>>>>>> other machines is basically like the concept of
>>>>>>>>>>>>>>>>>>>>>>>>> calling subroutines (even if it is implemented
>>>>>>>>>>>>>>>>>>>>>>>>> differently) and is fundamental to the design
>>>>>>>>>>>>>>>>>>>>>>>>> and analysis of Turing Macines.
>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>> Would you have a problem saying the subroutine
>>>>>>>>>>>>>>>>>>>>>>>>> H is no longer the subroutine H if one function
>>>>>>>>>>>>>>>>>>>>>>>>> just calls H and returns while a second calls H
>>>>>>>>>>>>>>>>>>>>>>>>> and conditionally loops? Yes, the whole program
>>>>>>>>>>>>>>>>>>>>>>>>> is not H, but the subroutine H is still there
>>>>>>>>>>>>>>>>>>>>>>>>> and will behave exactly like it used to in both
>>>>>>>>>>>>>>>>>>>>>>>>> of the cases.
>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>> One way to map a Turing Machine to ordinary
>>>>>>>>>>>>>>>>>>>>>>>>> software is to think of the Q0 state (or
>>>>>>>>>>>>>>>>>>>>>>>>> whatever is the 'starting' state of the Turing
>>>>>>>>>>>>>>>>>>>>>>>>> machine) as the entry point for the function,
>>>>>>>>>>>>>>>>>>>>>>>>> and the Halting States of the Turing Machine as
>>>>>>>>>>>>>>>>>>>>>>>>> retrun stateents which return a value
>>>>>>>>>>>>>>>>>>>>>>>>> indicating what state the machine ended in.
>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>> Thus the modifications Linz has done to H are
>>>>>>>>>>>>>>>>>>>>>>>>> nothing more that building H^ as mostly a call
>>>>>>>>>>>>>>>>>>>>>>>>> to H, with code before the call to manipulate
>>>>>>>>>>>>>>>>>>>>>>>>> the tape to add the second copy, and code after
>>>>>>>>>>>>>>>>>>>>>>>>> the return to loop forever if H returns the
>>>>>>>>>>>>>>>>>>>>>>>>> 'Halting' answer.
>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>> The Machine/Subroutine H has not been touched
>>>>>>>>>>>>>>>>>>>>>>>>> at all.
>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>> My point is that Ĥ ⟨Ĥ⟩ is equivalent to Ḧ ⟨Ḧ⟩
>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>> And my point is that they are only equivalent in
>>>>>>>>>>>>>>>>>>>>>>> the normal sense of the word if neither of H <H^>
>>>>>>>>>>>>>>>>>>>>>>> <H^> and H <H"> <H"> go to H.Qy
>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>> Without that qualification, it is a false
>>>>>>>>>>>>>>>>>>>>>>> statement. PERIOD.
>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>> They are equivalent in that neither can possibly
>>>>>>>>>>>>>>>>>>>>>> go to their q.y state.
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>> THAT is incorrect without the same
>>>>>>>>>>>>>>>>>>>>> qualification/assumption/stipulation, the H doesn't
>>>>>>>>>>>>>>>>>>>>> go to Qy.
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>> If H was a white cat detector and you presented H
>>>>>>>>>>>>>>>>>>>> with a black cat would it say "yes" ?
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>> But we aren't talking about a 'detector'
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> Sure we are.
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> Then you don't know what you are talking about (and
>>>>>>>>>>>>>>>>> showing your dishonesty by your clipping).
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> THe claim that H^ and H" are equivilent machines has
>>>>>>>>>>>>>>>>> NOTHING to do with there being a 'Detector' but do they
>>>>>>>>>>>>>>>>> behave exactly the same.
>>>>>>>>>>>>>>>> So in other words you are disavowing that both ⟨Ĥ⟩ and
>>>>>>>>>>>>>>>> ⟨Ḧ⟩ have a copy of H embedded within them ?
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> A halt detector is the same idea as a halt decider yet a
>>>>>>>>>>>>>>>> halt detector need not get every input correctly. Every
>>>>>>>>>>>>>>>> input that the halt detector gets correctly is in the
>>>>>>>>>>>>>>>> domain of the computable function that it implements.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> Yes, they have a copy of the Halt Detector H in them, and
>>>>>>>>>>>>>>> unless you are willing to stipulate that H will not go to
>>>>>>>>>>>>>>> H.Qy when given H^ or H" as an input, then you can not
>>>>>>>>>>>>>>> show that those machines are equivalent.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> If the simulating halt decider H cannot possibly go to
>>>>>>>>>>>>>> H.qy on a specific input then any such stipulation would
>>>>>>>>>>>>>> be redundant for this input.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> So why do you resist it?
>>>>>>>>>>>>>
>>>>>>>>>>>>> What is wrong with stipulating as a requirement something
>>>>>>>>>>>>> you 'know' to be true?
>>>>>>>>>>>>>
>>>>>>>>>>>>> The only reason I can see for you to object to listing that
>>>>>>>>>>>>> requirement. is that at some point you are going to want to
>>>>>>>>>>>>> violate that requirement.
>>>>>>>>>>>>
>>>>>>>>>>>> Specifically because it was redundant.
>>>>>>>>>>>> embedded_H ⟨Ḧ⟩ ⟨Ḧ⟩ ⊢* Ḧ.qn
>>>>>>>>>>>> embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
>>>>>>>>>>>>
>>>>>>>>>>>> It does not take a genius to know that when
>>>>>>>>>>>> embedded_H transitions to H.qn it does not transition to H.qn
>>>>>>>>>>>     embedded_H transitions to H.qn it does not transition to
>>>>>>>>>>> H.qy
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> So, are you stating as a fact that embedded_H <H^> <H^> and
>>>>>>>>>> embedded_H <H"> <H"> both as a matter of DEFINITION go to H.Qn?
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> For H to be correct then on the above specified inputs they
>>>>>>>>> must both go to H.qn.
>>>>>>>>>
>>>>>>>>>
>>>>>>>>
>>>>>>>> But, by DEFINITION that is the WRONG answer.
>>>>>>>>
>>>>>>>> DEFINITION of a Correct Halt Decider:
>>>>>>>>
>>>>>>>> A) H <M> w goes to H.Qy if M w Halts, and to H.Qn if M w never
>>>>>>>> Halts.
>>>>>>> I am only talking about these two:
>>>>>>> embedded_H ⟨Ḧ⟩ ⟨Ḧ⟩ ⊢* Ḧ.qn
>>>>>>> embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
>>>>>>>
>>>>>>> Whenever any embedded_H must abort the simulation of its input to
>>>>>>> prevent the infinitely nested simulation of this input the entire
>>>>>>> nested simulation sequence specifies infinitely nested
>>>>>>> simulation. This makes a transition to H.qn necessarily correct
>>>>>>> in this case.
>>>>>>>
>>>>>>
>>>>>> Right, the NESTED simulation, but NOT the H^ / H" that is USING
>>>>>> that embededeed_H, and it is THAT machine that defines the CORRECT
>>>>>> answer for H.
>>>>>>
>>>>>
>>>>> That problem is that you are flat out wrong about this.
>>>>> embedded_H IS NOT REPORTING ON ITS OWN BEHAVIOR
>>>>> THUS NOT REPORTING ON Ĥ ⟨Ĥ⟩
>>>>>
>>>>
>>>> Then it is NOT a Halt Detector. PERIOD. BY DEFINITON.
>>>
>>> Not at all. The only thing that it proves is that you persistently
>>> fail to understand that all deciders are only accountable for their
>>> actual inputs. int Sum(3,5) is not accountable for Sum(7,3).
>>>
>>
>> And you don't understand that the 'behavior of its input' is what the
>> machine its input represents would do with the input provided.
>
> There is not misdirection of any "represents" to it.
> It is what the input actually does, its actual behavior.
>
> Olcott's Theorem
> If a simulating halt decider H must abort the simulation of any input to
> prevent the infinite simulation of this input then it is always correct
> for H to transition to its reject state on this input.
>
>

On 2/16/2022 7:56 PM, Richard Damon wrote:
> On 2/16/22 8:17 PM, olcott wrote:
>> On 2/16/2022 6:47 PM, Richard Damon wrote:
>>> On 2/16/22 7:12 PM, olcott wrote:
>>>> On 2/16/2022 5:58 PM, Richard Damon wrote:
>>>>> On 2/16/22 8:35 AM, olcott wrote:
>>>>>> On 2/16/2022 6:55 AM, Richard Damon wrote:
>>>>>>> On 2/16/22 7:37 AM, olcott wrote:
>>>>>>>> On 2/15/2022 10:37 PM, Richard Damon wrote:
>>>>>>>>> On 2/15/22 10:39 PM, olcott wrote:
>>>>>>>>>> On 2/15/2022 9:14 PM, Richard Damon wrote:
>>>>>>>>>>> On 2/15/22 9:50 PM, olcott wrote:
>>>>>>>>>>>> On 2/15/2022 8:49 PM, olcott wrote:
>>>>>>>>>>>>> On 2/15/2022 8:07 PM, Richard Damon wrote:
>>>>>>>>>>>>>> On 2/15/22 8:17 PM, olcott wrote:
>>>>>>>>>>>>>>> On 2/15/2022 5:40 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> On 2/15/22 11:49 AM, olcott wrote:
>>>>>>>>>>>>>>>>> On 2/14/2022 5:49 AM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>> On 2/13/22 10:30 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>> On 2/13/2022 7:27 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>> On 2/13/22 7:26 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>> On 2/13/2022 6:24 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>>> On 2/13/22 6:08 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>> On 2/13/2022 4:11 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>> On 2/13/22 5:04 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>> On 2/13/2022 3:40 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/13/22 4:24 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/13/2022 3:12 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/13/22 3:18 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/13/2022 1:57 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/13/22 2:43 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/13/2022 11:19 AM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/13/22 9:38 AM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/13/2022 5:43 AM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/13/22 12:54 AM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/12/2022 8:22 PM, Richard Damon
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/12/22 9:02 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/12/2022 7:54 PM, Richard Damon
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/12/22 8:27 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/12/2022 6:57 PM, Richard
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/12/22 7:37 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/12/2022 6:25 PM, Richard
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/12/22 6:48 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/12/2022 5:39 PM, Richard
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/12/22 5:34 PM, olcott
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/12/2022 8:41 AM,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/12/22 9:08 AM, olcott
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/12/2022 6:49 AM,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/12/22 12:01 AM,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/11/2022 10:50 PM,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/11/22 11:36 PM,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/11/2022 6:58 PM,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/11/22 7:52 PM,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/11/2022 6:17
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> PM, Richard Damon
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/11/22 7:10
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/11/2022 5:36
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> PM, Richard Damon
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/11/22 10:20
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> AM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/11/2022
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 5:36 AM,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Richard Damon
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/10/22
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 11:39 PM,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/10/2022
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 10:20 PM,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Richard Damon
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/10/22
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 10:58 PM,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 2/10/2022
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 6:02 PM,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Richard
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/10/22
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 9:18 AM,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>   > I
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> explain
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> how I am
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> necessarily correct
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> on the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> basis of
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> meaning of my
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> words and
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> you
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> disagree
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> on the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> basis of
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> your
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> failure
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> to
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> correctly
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> meaning
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of these
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> words.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> No, you
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> CLAIM to
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> explain
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> based on
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> meaning of
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the words,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> but use
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the wrong
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> meaning of
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the words.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> THIS IS
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> PROVEN TO
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> BE
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> COMPLETELY TRUE
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> ENTIRELY
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> ON THE
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> BASIS OF
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> THE
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> MEANING
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> OF ITS
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> WORDS:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> When a
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> simulating halt
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> decider
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> correctly
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> determines in
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> a finite
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> number of
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> steps
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> pure UTM
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> simulation of
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> its input
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> would
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> never
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> reach the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> final
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> state of
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> this
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> input
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> then it
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> can
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> correctly
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> reject
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> this
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> input as
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> non-halting.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> IF it
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> correctly
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> decided,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> then yes.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> But it has
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> been
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> shown, by
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> definition
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> construction
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> method of
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> H^ that if
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> H <H^>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <H^> goes
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> to H.Qn
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> then H^
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <H^> goes
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> to H^.Qn
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> and Halts,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> and thus
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> by the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> definition
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of a UTM,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> then we
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> also have
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that UTM
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <H^> <H^>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> will halt.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢*
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Ĥ.qx ⟨Ĥ⟩
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> ⟨Ĥ⟩ ⊢* Ĥ.qy ∞
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢*
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Ĥ.qx ⟨Ĥ⟩
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> ⟨Ĥ⟩ ⊢* Ĥ.qn
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> You keep
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> getting
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> confused
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> between two
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> things:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> (1) The
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> execution
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of Ĥ ⟨Ĥ⟩
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> versus
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> embedded_H
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> ⟨Ĥ⟩ ⟨Ĥ⟩ (we
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> only look
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> at the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> latter).
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> No, YOU qre
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> confused.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> By the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> definioon of
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> how to build
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> H^,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> embedded_H
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> MUST be
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> EXACTLY the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> same
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> algorithm as H,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> No it is
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> specifically
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> not allowed
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> to be.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> embedded_H
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> must have an
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> infinite loop
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> appended to
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> its Ĥ.qy
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> state and H
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is not
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> allowed to
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> have such a
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> loop appended
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> to its H.qy
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> state.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Which is
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> OUTSIDE the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> algorithm of H
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> itself, and
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> doesn't affect
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the behavior
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of H in
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> deciding to go
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> from Q0 to Qy/Qn.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> When the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> simulating halt
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> decider bases
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> it halt status
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> decision on
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> whether or not
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the same
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> function is
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> being called
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> with the same
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> inputs the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> difference
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> between H and
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> embedded_H can
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> change the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> behavior. A
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> string
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> comparison
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> between the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> machine
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> description of
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> H and
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> embedded_H
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> yields false.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> No, it can't,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> not and be a
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> COMPUTATION.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> You obviously
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> don't know the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> meaning of the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> words, so you
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> are just wrong.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Computation
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> means for ALL
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> copoies, Same
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> input leads to
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Same Output.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> The fact that it
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is not an exact
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> copy makes a
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> difference.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> But it IS.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> H applied to ⟨Ĥ⟩
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> ⟨Ĥ⟩ does not
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> determine that
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> itself is being
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> called multiple
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> times with the same
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> input. embedded_H
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> does determine that
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> itself is called
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> multiple times with
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the same input
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> because strcmp(H,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> embedded_H != 0.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Except that
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> embedded_H does't
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> have a
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 'representation' of
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> itself to use to
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> make that
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> comparison, so that
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is just more of your
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Fairy Dust Powered
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Unicorn stuff.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> It can very easily
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> have a representation
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of itself, that only
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> requires that it has
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> access to its own
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> machine description.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> First, Turing Machines
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> DON'T have access to
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> their own machine
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> description, unless it
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> has been provided as
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> an input
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> You said that this was
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> impossible.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> So, you are agreeing
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that they can't? Or do
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> you just not understand
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the logic.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I am agreeing that you
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> contradicted yourself.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> How, by saying that the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> only way a Turing Machine
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> can have a copy of its
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> representation is for it
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> to be given (and H is
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> defined in a way that it
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> can't be given as an extra
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> input)?
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> No appended infinite loop
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> making H and embedded_H the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> same
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Ḧ.q0 ⟨Ḧ⟩ ⊢* Ḧ.qx ⟨Ḧ⟩ ⟨Ḧ⟩ ⊢*
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Ḧ.qy
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Ḧ.q0 ⟨Ḧ⟩ ⊢* Ḧ.qx ⟨Ḧ⟩ ⟨Ḧ⟩ ⊢*
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Ḧ.qn
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> embedded_H ⟨Ḧ⟩ ⟨Ḧ⟩ ⊢* Ḧ.qn
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> H ⟨Ḧ⟩ ⟨Ḧ⟩ ⊢* H.qn
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Except that the infinite
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> loop isn't part of the copy
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of H in H^, it is something
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> ADD to it, which only
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> has/affects behavior AFTER H
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> makes its decision.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> So another words hypothetical
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> examples get you so confused
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> you totally lose track of
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> everything.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> What 'Hypothetical' are you
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> referencing.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> This is what I mean when I say
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that you hardly pay any
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> attention at all.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> This is the hypothetical that I
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> am referencing:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> No appended infinite loop
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> making H and embedded_H the same
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Ḧ.q0 ⟨Ḧ⟩ ⊢* Ḧ.qx ⟨Ḧ⟩ ⟨Ḧ⟩ ⊢* Ḧ.qy
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Ḧ.q0 ⟨Ḧ⟩ ⊢* Ḧ.qx ⟨Ḧ⟩ ⟨Ḧ⟩ ⊢* Ḧ.qn
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> And what do you mean by that?
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> When I redefine Ĥ to become Ḧ by
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> eliminating its infinite loop, I
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> probably mean: {I redefine Ĥ to
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> become Ḧ by eliminating its
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> infinite loop}.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Which does what? Since if you
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> aren't talking about Linz's H^,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> your results don't mean anything
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> for the Halting Problem.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> It provides a bridge of
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understanding to my HP refutation.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> The key skill that I have applied
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> throughout my career is eliminating
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> "inessential complexity" (1999
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Turing award winner Fred Brooks) to
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> make   enormously difficult
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> problems as simple as possible.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> https://en.wikipedia.org/wiki/No_Silver_Bullet
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> But if you eliminate KEY ASPECTS
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> then you aren't talking about what
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> you need to.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> It is just like learning arithmetic
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> before attacking algebra.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> It lays the foundation of
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> prerequisites for my actual rebuttal.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Just beware that if you make a
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> statement that is only true for a
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> limited case and don't explicitly
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> state so, pointing that out is NOT a
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 'Dishonest Dodge'.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Since it is know that you are working
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> on trying to prove that a Unicorn
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> exists, what you are saying WILL be
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> looked at in a light anticipating
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> where you are going.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Also remember that showing a rule
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> happens to be correct for one case,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> doesn't prove that it will be for a
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> different case.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> You have gone through all of this
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> before, and it came for nothing, but
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> if this is how you want to spend your
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> last days, knock yourself out.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I think that you already understand that
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> With Ĥ ⟨Ĥ⟩
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qy ∞ //
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> this path is never taken
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> making Ḧ ⟨Ḧ⟩ an equivalent computation
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Ḧ.q0 ⟨Ḧ⟩ ⊢* Ḧ.qx ⟨Ḧ⟩ ⟨Ḧ⟩ ⊢* Ḧ.qy
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Ḧ.q0 ⟨Ḧ⟩ ⊢* Ḧ.qx ⟨Ḧ⟩ ⟨Ḧ⟩ ⊢* Ḧ.qn
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> And, as seems common with your
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> arguments, you keep on forgetting the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> CONDITIONS on each line.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> H^ <H^> is
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> H^.q0 <H^> -> H^.Qx <H^> <H^>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Then
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> H^.Qx <H^> <H^> -> H^.Qy -> ∞ IF and
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> only if H <H^> <H^> -> H.Qy and
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> H^.Qx <H^> <H^> -> H^.Qn If and ohly if
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> H <H^> <H^> => H.Qn.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> If you stipulate that H <H^> <H^> will
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> never go to H.Qy, then the behavior on
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that path can be changed with no effect.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Without the If and only if clauses, the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> initial description is incorrect because
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> it is incomplete.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> So, WITH THE STIPULATION THAT H won't go
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> to H.Qy for either version, then
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> changing H^ to the H" that omits to loop
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is an equivalence, but ONLY under that
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> stipulation.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> This of course shows that H will be
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrong about H", as H" will ALWAYS Halt
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> if H answers, and H not answering is
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> always wrong. Thus H will either be
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrong for not answering or giving the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrong answer.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I am only making two versions of input to H:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> (1) Ĥ WITH an appended infinite loop
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> (2) Ḧ WITHOUT an appended infinite loop
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Only this is being examined:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> embedded_H ⟨Ḧ⟩ ⟨Ḧ⟩
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Right, but the conclusion that H" is
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 'equivalent' to H^ is only true (if you
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> mean equivalent in the sense that they
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> compute the same function) if it is the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> case that neither of H <H^> <H^> or H <H">
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <H"> go to H.Qy.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Good.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Unless you want to indicate some other
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> definition of 'equivalent' you using (that
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> could be proper to do so here), you need
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> to include the conditions under which the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> statement is true.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>> embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ḧ.qn
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>    and
>>>>>>>>>>>>>>>>>>>>>>>>>>>>> embedded_H ⟨Ḧ⟩ ⟨Ḧ⟩ ⊢* Ḧ.qn
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>    nd
>>>>>>>>>>>>>>>>>>>>>>>>>>>>> H ⟨Ḧ⟩ ⟨Ḧ⟩ ⊢* Ḧ.qn
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>> Problem, embedded_H / H need to transition
>>>>>>>>>>>>>>>>>>>>>>>>>>>> to a state in H, not some other machine.
>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>> As soon as we append an infinite loop to H.y
>>>>>>>>>>>>>>>>>>>>>>>>>>> is it no longer H.
>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>> This is where you are showing your lack of
>>>>>>>>>>>>>>>>>>>>>>>>>> understanding of Turing Machines.
>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>> NO ONE has said that the machine where we
>>>>>>>>>>>>>>>>>>>>>>>>>> added the loop is still the machine H, in
>>>>>>>>>>>>>>>>>>>>>>>>>> fact, Linz calls that machine H', but H'
>>>>>>>>>>>>>>>>>>>>>>>>>> CONTAINS a complete copy of H, and that copy
>>>>>>>>>>>>>>>>>>>>>>>>>> will still act exactly like the original H to
>>>>>>>>>>>>>>>>>>>>>>>>>> the point where it gets to the stat Qy.
>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>> This ability to compose machines of copies of
>>>>>>>>>>>>>>>>>>>>>>>>>> other machines is basically like the concept
>>>>>>>>>>>>>>>>>>>>>>>>>> of calling subroutines (even if it is
>>>>>>>>>>>>>>>>>>>>>>>>>> implemented differently) and is fundamental to
>>>>>>>>>>>>>>>>>>>>>>>>>> the design and analysis of Turing Macines.
>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>> Would you have a problem saying the subroutine
>>>>>>>>>>>>>>>>>>>>>>>>>> H is no longer the subroutine H if one
>>>>>>>>>>>>>>>>>>>>>>>>>> function just calls H and returns while a
>>>>>>>>>>>>>>>>>>>>>>>>>> second calls H and conditionally loops? Yes,
>>>>>>>>>>>>>>>>>>>>>>>>>> the whole program is not H, but the subroutine
>>>>>>>>>>>>>>>>>>>>>>>>>> H is still there and will behave exactly like
>>>>>>>>>>>>>>>>>>>>>>>>>> it used to in both of the cases.
>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>> One way to map a Turing Machine to ordinary
>>>>>>>>>>>>>>>>>>>>>>>>>> software is to think of the Q0 state (or
>>>>>>>>>>>>>>>>>>>>>>>>>> whatever is the 'starting' state of the Turing
>>>>>>>>>>>>>>>>>>>>>>>>>> machine) as the entry point for the function,
>>>>>>>>>>>>>>>>>>>>>>>>>> and the Halting States of the Turing Machine
>>>>>>>>>>>>>>>>>>>>>>>>>> as retrun stateents which return a value
>>>>>>>>>>>>>>>>>>>>>>>>>> indicating what state the machine ended in.
>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>> Thus the modifications Linz has done to H are
>>>>>>>>>>>>>>>>>>>>>>>>>> nothing more that building H^ as mostly a call
>>>>>>>>>>>>>>>>>>>>>>>>>> to H, with code before the call to manipulate
>>>>>>>>>>>>>>>>>>>>>>>>>> the tape to add the second copy, and code
>>>>>>>>>>>>>>>>>>>>>>>>>> after the return to loop forever if H returns
>>>>>>>>>>>>>>>>>>>>>>>>>> the 'Halting' answer.
>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>> The Machine/Subroutine H has not been touched
>>>>>>>>>>>>>>>>>>>>>>>>>> at all.
>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>> My point is that Ĥ ⟨Ĥ⟩ is equivalent to Ḧ ⟨Ḧ⟩
>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>> And my point is that they are only equivalent in
>>>>>>>>>>>>>>>>>>>>>>>> the normal sense of the word if neither of H
>>>>>>>>>>>>>>>>>>>>>>>> <H^> <H^> and H <H"> <H"> go to H.Qy
>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>> Without that qualification, it is a false
>>>>>>>>>>>>>>>>>>>>>>>> statement. PERIOD.
>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>> They are equivalent in that neither can possibly
>>>>>>>>>>>>>>>>>>>>>>> go to their q.y state.
>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>> THAT is incorrect without the same
>>>>>>>>>>>>>>>>>>>>>> qualification/assumption/stipulation, the H
>>>>>>>>>>>>>>>>>>>>>> doesn't go to Qy.
>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>> If H was a white cat detector and you presented H
>>>>>>>>>>>>>>>>>>>>> with a black cat would it say "yes" ?
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>> But we aren't talking about a 'detector'
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>> Sure we are.
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> Then you don't know what you are talking about (and
>>>>>>>>>>>>>>>>>> showing your dishonesty by your clipping).
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> THe claim that H^ and H" are equivilent machines has
>>>>>>>>>>>>>>>>>> NOTHING to do with there being a 'Detector' but do
>>>>>>>>>>>>>>>>>> they behave exactly the same.
>>>>>>>>>>>>>>>>> So in other words you are disavowing that both ⟨Ĥ⟩ and
>>>>>>>>>>>>>>>>> ⟨Ḧ⟩ have a copy of H embedded within them ?
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> A halt detector is the same idea as a halt decider yet
>>>>>>>>>>>>>>>>> a halt detector need not get every input correctly.
>>>>>>>>>>>>>>>>> Every input that the halt detector gets correctly is in
>>>>>>>>>>>>>>>>> the domain of the computable function that it implements.
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> Yes, they have a copy of the Halt Detector H in them,
>>>>>>>>>>>>>>>> and unless you are willing to stipulate that H will not
>>>>>>>>>>>>>>>> go to H.Qy when given H^ or H" as an input, then you can
>>>>>>>>>>>>>>>> not show that those machines are equivalent.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> If the simulating halt decider H cannot possibly go to
>>>>>>>>>>>>>>> H.qy on a specific input then any such stipulation would
>>>>>>>>>>>>>>> be redundant for this input.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> So why do you resist it?
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> What is wrong with stipulating as a requirement something
>>>>>>>>>>>>>> you 'know' to be true?
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> The only reason I can see for you to object to listing
>>>>>>>>>>>>>> that requirement. is that at some point you are going to
>>>>>>>>>>>>>> want to violate that requirement.
>>>>>>>>>>>>>
>>>>>>>>>>>>> Specifically because it was redundant.
>>>>>>>>>>>>> embedded_H ⟨Ḧ⟩ ⟨Ḧ⟩ ⊢* Ḧ.qn
>>>>>>>>>>>>> embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
>>>>>>>>>>>>>
>>>>>>>>>>>>> It does not take a genius to know that when
>>>>>>>>>>>>> embedded_H transitions to H.qn it does not transition to H.qn
>>>>>>>>>>>>     embedded_H transitions to H.qn it does not transition to
>>>>>>>>>>>> H.qy
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> So, are you stating as a fact that embedded_H <H^> <H^> and
>>>>>>>>>>> embedded_H <H"> <H"> both as a matter of DEFINITION go to H.Qn?
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> For H to be correct then on the above specified inputs they
>>>>>>>>>> must both go to H.qn.
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> But, by DEFINITION that is the WRONG answer.
>>>>>>>>>
>>>>>>>>> DEFINITION of a Correct Halt Decider:
>>>>>>>>>
>>>>>>>>> A) H <M> w goes to H.Qy if M w Halts, and to H.Qn if M w never
>>>>>>>>> Halts.
>>>>>>>> I am only talking about these two:
>>>>>>>> embedded_H ⟨Ḧ⟩ ⟨Ḧ⟩ ⊢* Ḧ.qn
>>>>>>>> embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
>>>>>>>>
>>>>>>>> Whenever any embedded_H must abort the simulation of its input
>>>>>>>> to prevent the infinitely nested simulation of this input the
>>>>>>>> entire nested simulation sequence specifies infinitely nested
>>>>>>>> simulation. This makes a transition to H.qn necessarily correct
>>>>>>>> in this case.
>>>>>>>>
>>>>>>>
>>>>>>> Right, the NESTED simulation, but NOT the H^ / H" that is USING
>>>>>>> that embededeed_H, and it is THAT machine that defines the
>>>>>>> CORRECT answer for H.
>>>>>>>
>>>>>>
>>>>>> That problem is that you are flat out wrong about this.
>>>>>> embedded_H IS NOT REPORTING ON ITS OWN BEHAVIOR
>>>>>> THUS NOT REPORTING ON Ĥ ⟨Ĥ⟩
>>>>>>
>>>>>
>>>>> Then it is NOT a Halt Detector. PERIOD. BY DEFINITON.
>>>>
>>>> Not at all. The only thing that it proves is that you persistently
>>>> fail to understand that all deciders are only accountable for their
>>>> actual inputs. int Sum(3,5) is not accountable for Sum(7,3).
>>>>
>>>
>>> And you don't understand that the 'behavior of its input' is what the
>>> machine its input represents would do with the input provided.
>>
>> There is not misdirection of any "represents" to it.
>> It is what the input actually does, its actual behavior.
>>
>> Olcott's Theorem
>> If a simulating halt decider H must abort the simulation of any input
>> to prevent the infinite simulation of this input then it is always
>> correct for H to transition to its reject state on this input.
>>
>>
>
> If the 'behavior' of the input to "H <M> w" is NOT "M w" then, by
> DEFINITION, you are not working on the Halting Problem, so FAIL.
>

On 2/16/22 9:12 PM, olcott wrote:
> On 2/16/2022 7:56 PM, Richard Damon wrote:
>> On 2/16/22 8:17 PM, olcott wrote:
>>> On 2/16/2022 6:47 PM, Richard Damon wrote:
>>>> On 2/16/22 7:12 PM, olcott wrote:
>>>>> On 2/16/2022 5:58 PM, Richard Damon wrote:
>>>>>> On 2/16/22 8:35 AM, olcott wrote:
>>>>>>> On 2/16/2022 6:55 AM, Richard Damon wrote:
>>>>>>>> On 2/16/22 7:37 AM, olcott wrote:
>>>>>>>>> On 2/15/2022 10:37 PM, Richard Damon wrote:
>>>>>>>>>> On 2/15/22 10:39 PM, olcott wrote:
>>>>>>>>>>> On 2/15/2022 9:14 PM, Richard Damon wrote:
>>>>>>>>>>>> On 2/15/22 9:50 PM, olcott wrote:
>>>>>>>>>>>>> On 2/15/2022 8:49 PM, olcott wrote:
>>>>>>>>>>>>>> On 2/15/2022 8:07 PM, Richard Damon wrote:
>>>>>>>>>>>>>>> On 2/15/22 8:17 PM, olcott wrote:
>>>>>>>>>>>>>>>> On 2/15/2022 5:40 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> On 2/15/22 11:49 AM, olcott wrote:
>>>>>>>>>>>>>>>>>> On 2/14/2022 5:49 AM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>> On 2/13/22 10:30 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>> On 2/13/2022 7:27 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>> On 2/13/22 7:26 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>> On 2/13/2022 6:24 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>> On 2/13/22 6:08 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>> On 2/13/2022 4:11 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>>> On 2/13/22 5:04 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/13/2022 3:40 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/13/22 4:24 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/13/2022 3:12 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/13/22 3:18 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/13/2022 1:57 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/13/22 2:43 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/13/2022 11:19 AM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/13/22 9:38 AM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/13/2022 5:43 AM, Richard Damon
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/13/22 12:54 AM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/12/2022 8:22 PM, Richard Damon
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/12/22 9:02 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/12/2022 7:54 PM, Richard
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/12/22 8:27 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/12/2022 6:57 PM, Richard
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/12/22 7:37 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/12/2022 6:25 PM, Richard
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/12/22 6:48 PM, olcott
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/12/2022 5:39 PM,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/12/22 5:34 PM, olcott
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/12/2022 8:41 AM,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/12/22 9:08 AM,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/12/2022 6:49 AM,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/12/22 12:01 AM,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/11/2022 10:50 PM,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/11/22 11:36 PM,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/11/2022 6:58
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> PM, Richard Damon
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/11/22 7:52 PM,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/11/2022 6:17
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> PM, Richard Damon
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/11/22 7:10
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/11/2022
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 5:36 PM, Richard
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/11/22
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 10:20 AM,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/11/2022
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 5:36 AM,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Richard Damon
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/10/22
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 11:39 PM,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/10/2022
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 10:20 PM,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Richard
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/10/22
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 10:58 PM,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 2/10/2022
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 6:02 PM,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Richard
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 2/10/22
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 9:18 AM,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> olcott
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>   > I
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> explain
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> how I am
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> necessarily
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> correct
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> on the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> basis of
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> meaning
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of my
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> words
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> and you
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> disagree
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> on the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> basis of
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> your
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> failure
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> to
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> correctly understand
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> meaning
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of these
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> words.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> No, you
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> CLAIM to
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> explain
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> based on
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> meaning
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> words,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> but use
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the wrong
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> meaning
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> words.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> THIS IS
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> PROVEN
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> TO BE
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> COMPLETELY
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> TRUE
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> ENTIRELY
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> ON THE
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> BASIS OF
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> THE
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> MEANING
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> OF ITS
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> WORDS:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> When a
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> simulating
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> halt
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> decider
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> correctly determines
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> in a
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> finite
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> number
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of steps
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> pure UTM
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> simulation
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of its
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> input
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> would
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> never
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> reach
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> final
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> state of
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> this
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> input
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> then it
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> can
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> correctly reject
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> this
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> input as
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> non-halting.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> IF it
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> correctly
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> decided,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> then yes.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> But it
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> has been
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> shown, by
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> definition of
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> construction
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> method of
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> H^ that
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> if H <H^>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <H^> goes
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> to H.Qn
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> then H^
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <H^> goes
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> to H^.Qn
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> and
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Halts,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> and thus
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> by the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> definition of
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> a UTM,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> then we
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> also have
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that UTM
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <H^> <H^>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> will halt.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Ĥ.q0 ⟨Ĥ⟩
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> ⊢* Ĥ.qx
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢*
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Ĥ.qy ∞
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Ĥ.q0 ⟨Ĥ⟩
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> ⊢* Ĥ.qx
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢*
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Ĥ.qn
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> You keep
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> getting
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> confused
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> between
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> two things:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> (1) The
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> execution
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of Ĥ ⟨Ĥ⟩
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> versus
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> embedded_H
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> ⟨Ĥ⟩ ⟨Ĥ⟩
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> (we only
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> look at
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the latter).
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> No, YOU qre
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> confused.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> By the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> definioon
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of how to
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> build H^,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> embedded_H
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> MUST be
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> EXACTLY the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> same
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> algorithm
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> as H,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> No it is
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> specifically
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> not allowed
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> to be.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> embedded_H
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> must have an
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> infinite
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> loop
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> appended to
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> its Ĥ.qy
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> state and H
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is not
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> allowed to
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> have such a
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> loop
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> appended to
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> its H.qy state.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Which is
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> OUTSIDE the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> algorithm of
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> H itself, and
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> doesn't
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> affect the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> behavior of H
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> in deciding
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> to go from Q0
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> to Qy/Qn.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> When the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> simulating
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> halt decider
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> bases it halt
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> status
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> decision on
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> whether or not
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the same
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> function is
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> being called
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> with the same
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> inputs the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> difference
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> between H and
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> embedded_H can
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> change the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> behavior. A
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> string
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> comparison
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> between the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> machine
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> description of
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> H and
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> embedded_H
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> yields false.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> No, it can't,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> not and be a
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> COMPUTATION.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> You obviously
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> don't know the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> meaning of the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> words, so you
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> are just wrong.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Computation
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> means for ALL
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> copoies, Same
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> input leads to
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Same Output.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> The fact that it
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is not an exact
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> copy makes a
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> difference.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> But it IS.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> H applied to ⟨Ĥ⟩
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> ⟨Ĥ⟩ does not
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> determine that
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> itself is being
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> called multiple
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> times with the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> same input.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> embedded_H does
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> determine that
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> itself is called
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> multiple times
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> with the same
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> input because
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> strcmp(H,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> embedded_H != 0.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Except that
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> embedded_H does't
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> have a
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 'representation' of
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> itself to use to
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> make that
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> comparison, so that
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is just more of
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> your Fairy Dust
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Powered Unicorn stuff.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> It can very easily
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> have a
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> representation of
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> itself, that only
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> requires that it has
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> access to its own
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> machine description.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> First, Turing
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Machines DON'T have
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> access to their own
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> machine description,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> unless it has been
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> provided as an input
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> You said that this was
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> impossible.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> So, you are agreeing
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that they can't? Or do
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> you just not understand
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the logic.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I am agreeing that you
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> contradicted yourself.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> How, by saying that the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> only way a Turing Machine
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> can have a copy of its
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> representation is for it
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> to be given (and H is
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> defined in a way that it
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> can't be given as an
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> extra input)?
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> No appended infinite loop
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> making H and embedded_H
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the same
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Ḧ.q0 ⟨Ḧ⟩ ⊢* Ḧ.qx ⟨Ḧ⟩ ⟨Ḧ⟩
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> ⊢* Ḧ.qy
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Ḧ.q0 ⟨Ḧ⟩ ⊢* Ḧ.qx ⟨Ḧ⟩ ⟨Ḧ⟩
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> ⊢* Ḧ.qn
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> embedded_H ⟨Ḧ⟩ ⟨Ḧ⟩ ⊢* Ḧ.qn
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> H ⟨Ḧ⟩ ⟨Ḧ⟩ ⊢* H.qn
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Except that the infinite
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> loop isn't part of the copy
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of H in H^, it is something
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> ADD to it, which only
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> has/affects behavior AFTER
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> H makes its decision.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> So another words
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> hypothetical examples get
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> you so confused you totally
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> lose track of everything.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> What 'Hypothetical' are you
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> referencing.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> This is what I mean when I say
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that you hardly pay any
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> attention at all.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> This is the hypothetical that
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I am referencing:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> No appended infinite loop
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> making H and embedded_H the same
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Ḧ.q0 ⟨Ḧ⟩ ⊢* Ḧ.qx ⟨Ḧ⟩ ⟨Ḧ⟩ ⊢* Ḧ.qy
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Ḧ.q0 ⟨Ḧ⟩ ⊢* Ḧ.qx ⟨Ḧ⟩ ⟨Ḧ⟩ ⊢* Ḧ.qn
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> And what do you mean by that?
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> When I redefine Ĥ to become Ḧ by
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> eliminating its infinite loop, I
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> probably mean: {I redefine Ĥ to
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> become Ḧ by eliminating its
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> infinite loop}.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Which does what? Since if you
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> aren't talking about Linz's H^,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> your results don't mean anything
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> for the Halting Problem.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> It provides a bridge of
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understanding to my HP refutation.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> The key skill that I have applied
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> throughout my career is
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> eliminating "inessential
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> complexity" (1999 Turing award
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> winner Fred Brooks) to make
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>   enormously difficult problems as
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> simple as possible.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> https://en.wikipedia.org/wiki/No_Silver_Bullet
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> But if you eliminate KEY ASPECTS
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> then you aren't talking about what
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> you need to.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> It is just like learning arithmetic
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> before attacking algebra.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> It lays the foundation of
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> prerequisites for my actual rebuttal.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Just beware that if you make a
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> statement that is only true for a
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> limited case and don't explicitly
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> state so, pointing that out is NOT a
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 'Dishonest Dodge'.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Since it is know that you are working
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> on trying to prove that a Unicorn
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> exists, what you are saying WILL be
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> looked at in a light anticipating
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> where you are going.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Also remember that showing a rule
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> happens to be correct for one case,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> doesn't prove that it will be for a
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> different case.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> You have gone through all of this
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> before, and it came for nothing, but
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> if this is how you want to spend your
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> last days, knock yourself out.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I think that you already understand that
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> With Ĥ ⟨Ĥ⟩
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qy ∞ //
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> this path is never taken
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> making Ḧ ⟨Ḧ⟩ an equivalent computation
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Ḧ.q0 ⟨Ḧ⟩ ⊢* Ḧ.qx ⟨Ḧ⟩ ⟨Ḧ⟩ ⊢* Ḧ.qy
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Ḧ.q0 ⟨Ḧ⟩ ⊢* Ḧ.qx ⟨Ḧ⟩ ⟨Ḧ⟩ ⊢* Ḧ.qn
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> And, as seems common with your
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> arguments, you keep on forgetting the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> CONDITIONS on each line.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> H^ <H^> is
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> H^.q0 <H^> -> H^.Qx <H^> <H^>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Then
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> H^.Qx <H^> <H^> -> H^.Qy -> ∞ IF and
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> only if H <H^> <H^> -> H.Qy and
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> H^.Qx <H^> <H^> -> H^.Qn If and ohly if
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> H <H^> <H^> => H.Qn.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> If you stipulate that H <H^> <H^> will
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> never go to H.Qy, then the behavior on
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that path can be changed with no effect.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Without the If and only if clauses, the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> initial description is incorrect
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> because it is incomplete.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> So, WITH THE STIPULATION THAT H won't
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> go to H.Qy for either version, then
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> changing H^ to the H" that omits to
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> loop is an equivalence, but ONLY under
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that stipulation.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> This of course shows that H will be
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrong about H", as H" will ALWAYS Halt
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> if H answers, and H not answering is
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> always wrong. Thus H will either be
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrong for not answering or giving the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrong answer.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I am only making two versions of input
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> to H:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> (1) Ĥ WITH an appended infinite loop
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> (2) Ḧ WITHOUT an appended infinite loop
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Only this is being examined:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> embedded_H ⟨Ḧ⟩ ⟨Ḧ⟩
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Right, but the conclusion that H" is
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 'equivalent' to H^ is only true (if you
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> mean equivalent in the sense that they
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> compute the same function) if it is the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> case that neither of H <H^> <H^> or H
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <H"> <H"> go to H.Qy.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Good.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Unless you want to indicate some other
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> definition of 'equivalent' you using
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> (that could be proper to do so here), you
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> need to include the conditions under
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> which the statement is true.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ḧ.qn
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>    and
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> embedded_H ⟨Ḧ⟩ ⟨Ḧ⟩ ⊢* Ḧ.qn
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>    nd
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> H ⟨Ḧ⟩ ⟨Ḧ⟩ ⊢* Ḧ.qn
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Problem, embedded_H / H need to transition
>>>>>>>>>>>>>>>>>>>>>>>>>>>>> to a state in H, not some other machine.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>> As soon as we append an infinite loop to H.y
>>>>>>>>>>>>>>>>>>>>>>>>>>>> is it no longer H.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>> This is where you are showing your lack of
>>>>>>>>>>>>>>>>>>>>>>>>>>> understanding of Turing Machines.
>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>> NO ONE has said that the machine where we
>>>>>>>>>>>>>>>>>>>>>>>>>>> added the loop is still the machine H, in
>>>>>>>>>>>>>>>>>>>>>>>>>>> fact, Linz calls that machine H', but H'
>>>>>>>>>>>>>>>>>>>>>>>>>>> CONTAINS a complete copy of H, and that copy
>>>>>>>>>>>>>>>>>>>>>>>>>>> will still act exactly like the original H to
>>>>>>>>>>>>>>>>>>>>>>>>>>> the point where it gets to the stat Qy.
>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>> This ability to compose machines of copies of
>>>>>>>>>>>>>>>>>>>>>>>>>>> other machines is basically like the concept
>>>>>>>>>>>>>>>>>>>>>>>>>>> of calling subroutines (even if it is
>>>>>>>>>>>>>>>>>>>>>>>>>>> implemented differently) and is fundamental
>>>>>>>>>>>>>>>>>>>>>>>>>>> to the design and analysis of Turing Macines.
>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>> Would you have a problem saying the
>>>>>>>>>>>>>>>>>>>>>>>>>>> subroutine H is no longer the subroutine H if
>>>>>>>>>>>>>>>>>>>>>>>>>>> one function just calls H and returns while a
>>>>>>>>>>>>>>>>>>>>>>>>>>> second calls H and conditionally loops? Yes,
>>>>>>>>>>>>>>>>>>>>>>>>>>> the whole program is not H, but the
>>>>>>>>>>>>>>>>>>>>>>>>>>> subroutine H is still there and will behave
>>>>>>>>>>>>>>>>>>>>>>>>>>> exactly like it used to in both of the cases.
>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>> One way to map a Turing Machine to ordinary
>>>>>>>>>>>>>>>>>>>>>>>>>>> software is to think of the Q0 state (or
>>>>>>>>>>>>>>>>>>>>>>>>>>> whatever is the 'starting' state of the
>>>>>>>>>>>>>>>>>>>>>>>>>>> Turing machine) as the entry point for the
>>>>>>>>>>>>>>>>>>>>>>>>>>> function, and the Halting States of the
>>>>>>>>>>>>>>>>>>>>>>>>>>> Turing Machine as retrun stateents which
>>>>>>>>>>>>>>>>>>>>>>>>>>> return a value indicating what state the
>>>>>>>>>>>>>>>>>>>>>>>>>>> machine ended in.
>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>> Thus the modifications Linz has done to H are
>>>>>>>>>>>>>>>>>>>>>>>>>>> nothing more that building H^ as mostly a
>>>>>>>>>>>>>>>>>>>>>>>>>>> call to H, with code before the call to
>>>>>>>>>>>>>>>>>>>>>>>>>>> manipulate the tape to add the second copy,
>>>>>>>>>>>>>>>>>>>>>>>>>>> and code after the return to loop forever if
>>>>>>>>>>>>>>>>>>>>>>>>>>> H returns the 'Halting' answer.
>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>> The Machine/Subroutine H has not been touched
>>>>>>>>>>>>>>>>>>>>>>>>>>> at all.
>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>> My point is that Ĥ ⟨Ĥ⟩ is equivalent to Ḧ ⟨Ḧ⟩
>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>> And my point is that they are only equivalent
>>>>>>>>>>>>>>>>>>>>>>>>> in the normal sense of the word if neither of H
>>>>>>>>>>>>>>>>>>>>>>>>> <H^> <H^> and H <H"> <H"> go to H.Qy
>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>> Without that qualification, it is a false
>>>>>>>>>>>>>>>>>>>>>>>>> statement. PERIOD.
>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>> They are equivalent in that neither can possibly
>>>>>>>>>>>>>>>>>>>>>>>> go to their q.y state.
>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>> THAT is incorrect without the same
>>>>>>>>>>>>>>>>>>>>>>> qualification/assumption/stipulation, the H
>>>>>>>>>>>>>>>>>>>>>>> doesn't go to Qy.
>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>> If H was a white cat detector and you presented H
>>>>>>>>>>>>>>>>>>>>>> with a black cat would it say "yes" ?
>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>> But we aren't talking about a 'detector'
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>> Sure we are.
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>> Then you don't know what you are talking about (and
>>>>>>>>>>>>>>>>>>> showing your dishonesty by your clipping).
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>> THe claim that H^ and H" are equivilent machines has
>>>>>>>>>>>>>>>>>>> NOTHING to do with there being a 'Detector' but do
>>>>>>>>>>>>>>>>>>> they behave exactly the same.
>>>>>>>>>>>>>>>>>> So in other words you are disavowing that both ⟨Ĥ⟩ and
>>>>>>>>>>>>>>>>>> ⟨Ḧ⟩ have a copy of H embedded within them ?
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> A halt detector is the same idea as a halt decider yet
>>>>>>>>>>>>>>>>>> a halt detector need not get every input correctly.
>>>>>>>>>>>>>>>>>> Every input that the halt detector gets correctly is
>>>>>>>>>>>>>>>>>> in the domain of the computable function that it
>>>>>>>>>>>>>>>>>> implements.
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> Yes, they have a copy of the Halt Detector H in them,
>>>>>>>>>>>>>>>>> and unless you are willing to stipulate that H will not
>>>>>>>>>>>>>>>>> go to H.Qy when given H^ or H" as an input, then you
>>>>>>>>>>>>>>>>> can not show that those machines are equivalent.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> If the simulating halt decider H cannot possibly go to
>>>>>>>>>>>>>>>> H.qy on a specific input then any such stipulation would
>>>>>>>>>>>>>>>> be redundant for this input.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> So why do you resist it?
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> What is wrong with stipulating as a requirement something
>>>>>>>>>>>>>>> you 'know' to be true?
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> The only reason I can see for you to object to listing
>>>>>>>>>>>>>>> that requirement. is that at some point you are going to
>>>>>>>>>>>>>>> want to violate that requirement.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Specifically because it was redundant.
>>>>>>>>>>>>>> embedded_H ⟨Ḧ⟩ ⟨Ḧ⟩ ⊢* Ḧ.qn
>>>>>>>>>>>>>> embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> It does not take a genius to know that when
>>>>>>>>>>>>>> embedded_H transitions to H.qn it does not transition to H.qn
>>>>>>>>>>>>>     embedded_H transitions to H.qn it does not transition
>>>>>>>>>>>>> to H.qy
>>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> So, are you stating as a fact that embedded_H <H^> <H^> and
>>>>>>>>>>>> embedded_H <H"> <H"> both as a matter of DEFINITION go to H.Qn?
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> For H to be correct then on the above specified inputs they
>>>>>>>>>>> must both go to H.qn.
>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> But, by DEFINITION that is the WRONG answer.
>>>>>>>>>>
>>>>>>>>>> DEFINITION of a Correct Halt Decider:
>>>>>>>>>>
>>>>>>>>>> A) H <M> w goes to H.Qy if M w Halts, and to H.Qn if M w never
>>>>>>>>>> Halts.
>>>>>>>>> I am only talking about these two:
>>>>>>>>> embedded_H ⟨Ḧ⟩ ⟨Ḧ⟩ ⊢* Ḧ.qn
>>>>>>>>> embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
>>>>>>>>>
>>>>>>>>> Whenever any embedded_H must abort the simulation of its input
>>>>>>>>> to prevent the infinitely nested simulation of this input the
>>>>>>>>> entire nested simulation sequence specifies infinitely nested
>>>>>>>>> simulation. This makes a transition to H.qn necessarily correct
>>>>>>>>> in this case.
>>>>>>>>>
>>>>>>>>
>>>>>>>> Right, the NESTED simulation, but NOT the H^ / H" that is USING
>>>>>>>> that embededeed_H, and it is THAT machine that defines the
>>>>>>>> CORRECT answer for H.
>>>>>>>>
>>>>>>>
>>>>>>> That problem is that you are flat out wrong about this.
>>>>>>> embedded_H IS NOT REPORTING ON ITS OWN BEHAVIOR
>>>>>>> THUS NOT REPORTING ON Ĥ ⟨Ĥ⟩
>>>>>>>
>>>>>>
>>>>>> Then it is NOT a Halt Detector. PERIOD. BY DEFINITON.
>>>>>
>>>>> Not at all. The only thing that it proves is that you persistently
>>>>> fail to understand that all deciders are only accountable for their
>>>>> actual inputs. int Sum(3,5) is not accountable for Sum(7,3).
>>>>>
>>>>
>>>> And you don't understand that the 'behavior of its input' is what
>>>> the machine its input represents would do with the input provided.
>>>
>>> There is not misdirection of any "represents" to it.
>>> It is what the input actually does, its actual behavior.
>>>
>>> Olcott's Theorem
>>> If a simulating halt decider H must abort the simulation of any input
>>> to prevent the infinite simulation of this input then it is always
>>> correct for H to transition to its reject state on this input.
>>>
>>>
>>
>> If the 'behavior' of the input to "H <M> w" is NOT "M w" then, by
>> DEFINITION, you are not working on the Halting Problem, so FAIL.
>>
>
> The behavior of the simulation of a TM description is defined as the
> same as its direct execution. You don't seem to get this.
>
>

On 2/16/2022 8:36 PM, Richard Damon wrote:
>
> On 2/16/22 9:12 PM, olcott wrote:
>> On 2/16/2022 7:56 PM, Richard Damon wrote:
>>> On 2/16/22 8:17 PM, olcott wrote:
>>>> On 2/16/2022 6:47 PM, Richard Damon wrote:
>>>>> On 2/16/22 7:12 PM, olcott wrote:
>>>>>> On 2/16/2022 5:58 PM, Richard Damon wrote:
>>>>>>> On 2/16/22 8:35 AM, olcott wrote:
>>>>>>>> On 2/16/2022 6:55 AM, Richard Damon wrote:
>>>>>>>>> On 2/16/22 7:37 AM, olcott wrote:
>>>>>>>>>> On 2/15/2022 10:37 PM, Richard Damon wrote:
>>>>>>>>>>> On 2/15/22 10:39 PM, olcott wrote:
>>>>>>>>>>>> On 2/15/2022 9:14 PM, Richard Damon wrote:
>>>>>>>>>>>>> On 2/15/22 9:50 PM, olcott wrote:
>>>>>>>>>>>>>> On 2/15/2022 8:49 PM, olcott wrote:
>>>>>>>>>>>>>>> On 2/15/2022 8:07 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>> On 2/15/22 8:17 PM, olcott wrote:
>>>>>>>>>>>>>>>>> On 2/15/2022 5:40 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> On 2/15/22 11:49 AM, olcott wrote:
>>>>>>>>>>>>>>>>>>> On 2/14/2022 5:49 AM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>> On 2/13/22 10:30 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>> On 2/13/2022 7:27 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>>> On 2/13/22 7:26 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>> On 2/13/2022 6:24 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>> On 2/13/22 6:08 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>> On 2/13/2022 4:11 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/13/22 5:04 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/13/2022 3:40 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/13/22 4:24 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/13/2022 3:12 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/13/22 3:18 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/13/2022 1:57 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/13/22 2:43 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/13/2022 11:19 AM, Richard Damon
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/13/22 9:38 AM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/13/2022 5:43 AM, Richard Damon
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/13/22 12:54 AM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/12/2022 8:22 PM, Richard Damon
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/12/22 9:02 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/12/2022 7:54 PM, Richard
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/12/22 8:27 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/12/2022 6:57 PM, Richard
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/12/22 7:37 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/12/2022 6:25 PM, Richard
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/12/22 6:48 PM, olcott
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/12/2022 5:39 PM,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/12/22 5:34 PM, olcott
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/12/2022 8:41 AM,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/12/22 9:08 AM,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/12/2022 6:49 AM,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/12/22 12:01 AM,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/11/2022 10:50
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/11/22 11:36 PM,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/11/2022 6:58
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> PM, Richard Damon
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/11/22 7:52
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/11/2022 6:17
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> PM, Richard Damon
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/11/22 7:10
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/11/2022
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 5:36 PM,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Richard Damon
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/11/22
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 10:20 AM,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/11/2022
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 5:36 AM,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Richard Damon
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/10/22
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 11:39 PM,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 2/10/2022
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 10:20 PM,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Richard
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/10/22
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 10:58 PM,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 2/10/2022
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 6:02 PM,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Richard
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 2/10/22
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 9:18 AM,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> olcott
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>   > I
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> explain
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> how I am
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> necessarily
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> correct
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> on the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> basis of
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> meaning
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of my
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> words
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> and you
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> disagree on
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> basis
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of your
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> failure
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> to
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> correctly
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> meaning
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> these
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> words.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> No, you
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> CLAIM to
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> explain
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> based on
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> meaning
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> words,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> but use
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrong
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> meaning
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> words.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> THIS IS
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> PROVEN
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> TO BE
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> COMPLETELY
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> TRUE
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> ENTIRELY ON
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> THE
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> BASIS
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> OF THE
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> MEANING
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> OF ITS
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> WORDS:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> When a
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> simulating
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> halt
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> decider
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> correctly
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> determines
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> in a
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> finite
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> number
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> steps
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> pure
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> UTM
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> simulation
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of its
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> input
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> would
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> never
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> reach
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> final
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> state
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of this
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> input
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> then it
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> can
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> correctly
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> reject
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> this
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> input
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> as
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> non-halting.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> IF it
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> correctly decided,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> then yes.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> But it
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> has been
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> shown,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> by the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> definition
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> construction
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> method
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of H^
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that if
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> H <H^>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <H^>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> goes to
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> H.Qn
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> then H^
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <H^>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> goes to
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> H^.Qn
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> and
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Halts,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> and thus
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> by the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> definition
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of a
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> UTM,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> then we
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> also
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> have
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that UTM
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <H^>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <H^>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> will halt.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Ĥ.q0 ⟨Ĥ⟩
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> ⊢* Ĥ.qx
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> ⟨Ĥ⟩ ⟨Ĥ⟩
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> ⊢* Ĥ.qy ∞
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Ĥ.q0 ⟨Ĥ⟩
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> ⊢* Ĥ.qx
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> ⟨Ĥ⟩ ⟨Ĥ⟩
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> ⊢* Ĥ.qn
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> You keep
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> getting
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> confused
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> between
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> two things:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> (1) The
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> execution
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of Ĥ ⟨Ĥ⟩
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> versus
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> embedded_H ⟨Ĥ⟩
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> ⟨Ĥ⟩ (we
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> only look
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> at the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> latter).
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> No, YOU
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> qre confused.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> By the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> definioon
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of how to
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> build H^,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> embedded_H
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> MUST be
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> EXACTLY
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the same
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> algorithm
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> as H,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> No it is
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> specifically not
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> allowed to be.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> embedded_H
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> must have
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> an infinite
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> loop
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> appended to
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> its Ĥ.qy
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> state and H
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is not
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> allowed to
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> have such a
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> loop
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> appended to
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> its H.qy
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> state.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Which is
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> OUTSIDE the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> algorithm of
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> H itself,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> and doesn't
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> affect the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> behavior of
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> H in
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> deciding to
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> go from Q0
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> to Qy/Qn.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> When the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> simulating
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> halt decider
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> bases it halt
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> status
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> decision on
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> whether or
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> not the same
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> function is
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> being called
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> with the same
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> inputs the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> difference
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> between H and
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> embedded_H
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> can change
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the behavior.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> A string
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> comparison
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> between the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> machine
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> description
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of H and
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> embedded_H
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> yields false.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> No, it can't,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> not and be a
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> COMPUTATION.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> You obviously
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> don't know the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> meaning of the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> words, so you
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> are just wrong.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Computation
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> means for ALL
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> copoies, Same
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> input leads to
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Same Output.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> The fact that
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> it is not an
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> exact copy
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> makes a
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> difference.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> But it IS.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> H applied to ⟨Ĥ⟩
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> ⟨Ĥ⟩ does not
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> determine that
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> itself is being
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> called multiple
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> times with the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> same input.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> embedded_H does
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> determine that
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> itself is called
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> multiple times
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> with the same
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> input because
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> strcmp(H,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> embedded_H != 0.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Except that
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> embedded_H does't
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> have a
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 'representation'
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of itself to use
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> to make that
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> comparison, so
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that is just more
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of your Fairy Dust
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Powered Unicorn
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> stuff.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> It can very easily
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> have a
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> representation of
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> itself, that only
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> requires that it
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> has access to its
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> own machine
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> description.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> First, Turing
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Machines DON'T have
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> access to their own
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> machine description,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> unless it has been
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> provided as an input
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> You said that this
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> was impossible.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> So, you are agreeing
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that they can't? Or do
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> you just not
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand the logic.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I am agreeing that you
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> contradicted yourself.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> How, by saying that the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> only way a Turing
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Machine can have a copy
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of its representation is
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> for it to be given (and
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> H is defined in a way
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that it can't be given
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> as an extra input)?
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> No appended infinite loop
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> making H and embedded_H
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the same
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Ḧ.q0 ⟨Ḧ⟩ ⊢* Ḧ.qx ⟨Ḧ⟩ ⟨Ḧ⟩
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> ⊢* Ḧ.qy
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Ḧ.q0 ⟨Ḧ⟩ ⊢* Ḧ.qx ⟨Ḧ⟩ ⟨Ḧ⟩
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> ⊢* Ḧ.qn
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> embedded_H ⟨Ḧ⟩ ⟨Ḧ⟩ ⊢* Ḧ.qn
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> H ⟨Ḧ⟩ ⟨Ḧ⟩ ⊢* H.qn
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Except that the infinite
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> loop isn't part of the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> copy of H in H^, it is
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> something ADD to it, which
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> only has/affects behavior
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> AFTER H makes its decision.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> So another words
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> hypothetical examples get
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> you so confused you totally
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> lose track of everything.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> What 'Hypothetical' are you
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> referencing.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> This is what I mean when I
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> say that you hardly pay any
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> attention at all.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> This is the hypothetical that
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I am referencing:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> No appended infinite loop
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> making H and embedded_H the same
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Ḧ.q0 ⟨Ḧ⟩ ⊢* Ḧ.qx ⟨Ḧ⟩ ⟨Ḧ⟩ ⊢* Ḧ.qy
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Ḧ.q0 ⟨Ḧ⟩ ⊢* Ḧ.qx ⟨Ḧ⟩ ⟨Ḧ⟩ ⊢* Ḧ.qn
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> And what do you mean by that?
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> When I redefine Ĥ to become Ḧ
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> by eliminating its infinite
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> loop, I probably mean: {I
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> redefine Ĥ to become Ḧ by
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> eliminating its infinite loop}.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Which does what? Since if you
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> aren't talking about Linz's H^,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> your results don't mean anything
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> for the Halting Problem.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> It provides a bridge of
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understanding to my HP refutation.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> The key skill that I have applied
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> throughout my career is
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> eliminating "inessential
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> complexity" (1999 Turing award
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> winner Fred Brooks) to make
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>   enormously difficult problems
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> as simple as possible.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> https://en.wikipedia.org/wiki/No_Silver_Bullet
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> But if you eliminate KEY ASPECTS
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> then you aren't talking about what
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> you need to.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> It is just like learning arithmetic
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> before attacking algebra.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> It lays the foundation of
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> prerequisites for my actual rebuttal.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Just beware that if you make a
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> statement that is only true for a
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> limited case and don't explicitly
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> state so, pointing that out is NOT a
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 'Dishonest Dodge'.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Since it is know that you are
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> working on trying to prove that a
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Unicorn exists, what you are saying
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> WILL be looked at in a light
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> anticipating where you are going.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Also remember that showing a rule
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> happens to be correct for one case,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> doesn't prove that it will be for a
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> different case.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> You have gone through all of this
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> before, and it came for nothing, but
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> if this is how you want to spend
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> your last days, knock yourself out.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I think that you already understand that
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> With Ĥ ⟨Ĥ⟩
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qy ∞ //
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> this path is never taken
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> making Ḧ ⟨Ḧ⟩ an equivalent computation
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Ḧ.q0 ⟨Ḧ⟩ ⊢* Ḧ.qx ⟨Ḧ⟩ ⟨Ḧ⟩ ⊢* Ḧ.qy
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Ḧ.q0 ⟨Ḧ⟩ ⊢* Ḧ.qx ⟨Ḧ⟩ ⟨Ḧ⟩ ⊢* Ḧ.qn
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> And, as seems common with your
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> arguments, you keep on forgetting the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> CONDITIONS on each line.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> H^ <H^> is
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> H^.q0 <H^> -> H^.Qx <H^> <H^>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Then
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> H^.Qx <H^> <H^> -> H^.Qy -> ∞ IF and
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> only if H <H^> <H^> -> H.Qy and
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> H^.Qx <H^> <H^> -> H^.Qn If and ohly
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> if H <H^> <H^> => H.Qn.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> If you stipulate that H <H^> <H^> will
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> never go to H.Qy, then the behavior on
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that path can be changed with no effect.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Without the If and only if clauses,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the initial description is incorrect
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> because it is incomplete.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> So, WITH THE STIPULATION THAT H won't
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> go to H.Qy for either version, then
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> changing H^ to the H" that omits to
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> loop is an equivalence, but ONLY under
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that stipulation.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> This of course shows that H will be
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrong about H", as H" will ALWAYS Halt
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> if H answers, and H not answering is
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> always wrong. Thus H will either be
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrong for not answering or giving the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrong answer.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I am only making two versions of input
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> to H:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> (1) Ĥ WITH an appended infinite loop
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> (2) Ḧ WITHOUT an appended infinite loop
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Only this is being examined:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> embedded_H ⟨Ḧ⟩ ⟨Ḧ⟩
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Right, but the conclusion that H" is
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 'equivalent' to H^ is only true (if you
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> mean equivalent in the sense that they
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> compute the same function) if it is the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> case that neither of H <H^> <H^> or H
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <H"> <H"> go to H.Qy.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Good.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Unless you want to indicate some other
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> definition of 'equivalent' you using
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> (that could be proper to do so here),
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> you need to include the conditions under
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> which the statement is true.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ḧ.qn
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>    and
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> embedded_H ⟨Ḧ⟩ ⟨Ḧ⟩ ⊢* Ḧ.qn
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>    nd
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> H ⟨Ḧ⟩ ⟨Ḧ⟩ ⊢* Ḧ.qn
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Problem, embedded_H / H need to transition
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> to a state in H, not some other machine.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>> As soon as we append an infinite loop to
>>>>>>>>>>>>>>>>>>>>>>>>>>>>> H.y is it no longer H.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>> This is where you are showing your lack of
>>>>>>>>>>>>>>>>>>>>>>>>>>>> understanding of Turing Machines.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>> NO ONE has said that the machine where we
>>>>>>>>>>>>>>>>>>>>>>>>>>>> added the loop is still the machine H, in
>>>>>>>>>>>>>>>>>>>>>>>>>>>> fact, Linz calls that machine H', but H'
>>>>>>>>>>>>>>>>>>>>>>>>>>>> CONTAINS a complete copy of H, and that copy
>>>>>>>>>>>>>>>>>>>>>>>>>>>> will still act exactly like the original H
>>>>>>>>>>>>>>>>>>>>>>>>>>>> to the point where it gets to the stat Qy.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>> This ability to compose machines of copies
>>>>>>>>>>>>>>>>>>>>>>>>>>>> of other machines is basically like the
>>>>>>>>>>>>>>>>>>>>>>>>>>>> concept of calling subroutines (even if it
>>>>>>>>>>>>>>>>>>>>>>>>>>>> is implemented differently) and is
>>>>>>>>>>>>>>>>>>>>>>>>>>>> fundamental to the design and analysis of
>>>>>>>>>>>>>>>>>>>>>>>>>>>> Turing Macines.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>> Would you have a problem saying the
>>>>>>>>>>>>>>>>>>>>>>>>>>>> subroutine H is no longer the subroutine H
>>>>>>>>>>>>>>>>>>>>>>>>>>>> if one function just calls H and returns
>>>>>>>>>>>>>>>>>>>>>>>>>>>> while a second calls H and conditionally
>>>>>>>>>>>>>>>>>>>>>>>>>>>> loops? Yes, the whole program is not H, but
>>>>>>>>>>>>>>>>>>>>>>>>>>>> the subroutine H is still there and will
>>>>>>>>>>>>>>>>>>>>>>>>>>>> behave exactly like it used to in both of
>>>>>>>>>>>>>>>>>>>>>>>>>>>> the cases.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>> One way to map a Turing Machine to ordinary
>>>>>>>>>>>>>>>>>>>>>>>>>>>> software is to think of the Q0 state (or
>>>>>>>>>>>>>>>>>>>>>>>>>>>> whatever is the 'starting' state of the
>>>>>>>>>>>>>>>>>>>>>>>>>>>> Turing machine) as the entry point for the
>>>>>>>>>>>>>>>>>>>>>>>>>>>> function, and the Halting States of the
>>>>>>>>>>>>>>>>>>>>>>>>>>>> Turing Machine as retrun stateents which
>>>>>>>>>>>>>>>>>>>>>>>>>>>> return a value indicating what state the
>>>>>>>>>>>>>>>>>>>>>>>>>>>> machine ended in.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>> Thus the modifications Linz has done to H
>>>>>>>>>>>>>>>>>>>>>>>>>>>> are nothing more that building H^ as mostly
>>>>>>>>>>>>>>>>>>>>>>>>>>>> a call to H, with code before the call to
>>>>>>>>>>>>>>>>>>>>>>>>>>>> manipulate the tape to add the second copy,
>>>>>>>>>>>>>>>>>>>>>>>>>>>> and code after the return to loop forever if
>>>>>>>>>>>>>>>>>>>>>>>>>>>> H returns the 'Halting' answer.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>> The Machine/Subroutine H has not been
>>>>>>>>>>>>>>>>>>>>>>>>>>>> touched at all.
>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>> My point is that Ĥ ⟨Ĥ⟩ is equivalent to Ḧ ⟨Ḧ⟩
>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>> And my point is that they are only equivalent
>>>>>>>>>>>>>>>>>>>>>>>>>> in the normal sense of the word if neither of
>>>>>>>>>>>>>>>>>>>>>>>>>> H <H^> <H^> and H <H"> <H"> go to H.Qy
>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>> Without that qualification, it is a false
>>>>>>>>>>>>>>>>>>>>>>>>>> statement. PERIOD.
>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>> They are equivalent in that neither can
>>>>>>>>>>>>>>>>>>>>>>>>> possibly go to their q.y state.
>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>> THAT is incorrect without the same
>>>>>>>>>>>>>>>>>>>>>>>> qualification/assumption/stipulation, the H
>>>>>>>>>>>>>>>>>>>>>>>> doesn't go to Qy.
>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>> If H was a white cat detector and you presented H
>>>>>>>>>>>>>>>>>>>>>>> with a black cat would it say "yes" ?
>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>> But we aren't talking about a 'detector'
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>> Sure we are.
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>> Then you don't know what you are talking about (and
>>>>>>>>>>>>>>>>>>>> showing your dishonesty by your clipping).
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>> THe claim that H^ and H" are equivilent machines has
>>>>>>>>>>>>>>>>>>>> NOTHING to do with there being a 'Detector' but do
>>>>>>>>>>>>>>>>>>>> they behave exactly the same.
>>>>>>>>>>>>>>>>>>> So in other words you are disavowing that both ⟨Ĥ⟩
>>>>>>>>>>>>>>>>>>> and ⟨Ḧ⟩ have a copy of H embedded within them ?
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>> A halt detector is the same idea as a halt decider
>>>>>>>>>>>>>>>>>>> yet a halt detector need not get every input
>>>>>>>>>>>>>>>>>>> correctly. Every input that the halt detector gets
>>>>>>>>>>>>>>>>>>> correctly is in the domain of the computable function
>>>>>>>>>>>>>>>>>>> that it implements.
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> Yes, they have a copy of the Halt Detector H in them,
>>>>>>>>>>>>>>>>>> and unless you are willing to stipulate that H will
>>>>>>>>>>>>>>>>>> not go to H.Qy when given H^ or H" as an input, then
>>>>>>>>>>>>>>>>>> you can not show that those machines are equivalent.
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> If the simulating halt decider H cannot possibly go to
>>>>>>>>>>>>>>>>> H.qy on a specific input then any such stipulation
>>>>>>>>>>>>>>>>> would be redundant for this input.
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> So why do you resist it?
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> What is wrong with stipulating as a requirement
>>>>>>>>>>>>>>>> something you 'know' to be true?
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> The only reason I can see for you to object to listing
>>>>>>>>>>>>>>>> that requirement. is that at some point you are going to
>>>>>>>>>>>>>>>> want to violate that requirement.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> Specifically because it was redundant.
>>>>>>>>>>>>>>> embedded_H ⟨Ḧ⟩ ⟨Ḧ⟩ ⊢* Ḧ.qn
>>>>>>>>>>>>>>> embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> It does not take a genius to know that when
>>>>>>>>>>>>>>> embedded_H transitions to H.qn it does not transition to
>>>>>>>>>>>>>>> H.qn
>>>>>>>>>>>>>>     embedded_H transitions to H.qn it does not transition
>>>>>>>>>>>>>> to H.qy
>>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> So, are you stating as a fact that embedded_H <H^> <H^> and
>>>>>>>>>>>>> embedded_H <H"> <H"> both as a matter of DEFINITION go to
>>>>>>>>>>>>> H.Qn?
>>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> For H to be correct then on the above specified inputs they
>>>>>>>>>>>> must both go to H.qn.
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> But, by DEFINITION that is the WRONG answer.
>>>>>>>>>>>
>>>>>>>>>>> DEFINITION of a Correct Halt Decider:
>>>>>>>>>>>
>>>>>>>>>>> A) H <M> w goes to H.Qy if M w Halts, and to H.Qn if M w
>>>>>>>>>>> never Halts.
>>>>>>>>>> I am only talking about these two:
>>>>>>>>>> embedded_H ⟨Ḧ⟩ ⟨Ḧ⟩ ⊢* Ḧ.qn
>>>>>>>>>> embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
>>>>>>>>>>
>>>>>>>>>> Whenever any embedded_H must abort the simulation of its input
>>>>>>>>>> to prevent the infinitely nested simulation of this input the
>>>>>>>>>> entire nested simulation sequence specifies infinitely nested
>>>>>>>>>> simulation. This makes a transition to H.qn necessarily
>>>>>>>>>> correct in this case.
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> Right, the NESTED simulation, but NOT the H^ / H" that is USING
>>>>>>>>> that embededeed_H, and it is THAT machine that defines the
>>>>>>>>> CORRECT answer for H.
>>>>>>>>>
>>>>>>>>
>>>>>>>> That problem is that you are flat out wrong about this.
>>>>>>>> embedded_H IS NOT REPORTING ON ITS OWN BEHAVIOR
>>>>>>>> THUS NOT REPORTING ON Ĥ ⟨Ĥ⟩
>>>>>>>>
>>>>>>>
>>>>>>> Then it is NOT a Halt Detector. PERIOD. BY DEFINITON.
>>>>>>
>>>>>> Not at all. The only thing that it proves is that you persistently
>>>>>> fail to understand that all deciders are only accountable for
>>>>>> their actual inputs. int Sum(3,5) is not accountable for Sum(7,3).
>>>>>>
>>>>>
>>>>> And you don't understand that the 'behavior of its input' is what
>>>>> the machine its input represents would do with the input provided.
>>>>
>>>> There is not misdirection of any "represents" to it.
>>>> It is what the input actually does, its actual behavior.
>>>>
>>>> Olcott's Theorem
>>>> If a simulating halt decider H must abort the simulation of any
>>>> input to prevent the infinite simulation of this input then it is
>>>> always correct for H to transition to its reject state on this input.
>>>>
>>>>
>>>
>>> If the 'behavior' of the input to "H <M> w" is NOT "M w" then, by
>>> DEFINITION, you are not working on the Halting Problem, so FAIL.
>>>
>>
>> The behavior of the simulation of a TM description is defined as the
>> same as its direct execution. You don't seem to get this.
>>
>>
>
> Right. And the DIRECT EXECUTION of H" <H">