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">

Is the wrong thing that you so stupidly repeat.

Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qy ∞
Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn

The simulation of ⟨Ĥ⟩ ⟨Ĥ⟩ at Ĥ.qx cannot possibly reach its final state
therefore it specifies a sequence of configurations that never halt.

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.

--
Copyright 2021 Pete Olcott

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