XPost: comp.theory, sci.logic, sci.math
On 12/26/2021 3:36 PM, Ben Bacarisse wrote:
olcott <NoOne@NoWhere.com> writes:
On 12/25/2021 7:27 PM, Ben Bacarisse wrote:
olcott <NoOne@NoWhere.com> writes:
On 12/25/2021 2:07 PM, Ben Bacarisse wrote:
olcott <NoOne@NoWhere.com> writes:
On 12/24/2021 8:50 PM, Ben Bacarisse wrote:
olcott <NoOne@NoWhere.com> writes:
On 12/24/2021 3:29 PM, Ben Bacarisse wrote:
olcott <NoOne@NoWhere.com> writes:
On 12/23/2021 7:18 PM, Ben Bacarisse wrote:
I will stick to symbols. So you think that one or both of >>>>>>>>>>>
Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qy but H.q0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊬* H.qy
or
Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn but H.q0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊬* H.qn
is possible?
And, much to my surprise, you are clear that you do indeed claim the >>>>>>> second of these to be true!
If so, you are wrong. If you don't, you agree with this: >>>>>>>>>>>
Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qy if, and only if, H.q0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qy
Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn if, and only if, H.q0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qn
Ĥ.qx maps ⟨Ĥ⟩ ⟨Ĥ⟩ to Ĥ.qn
corresponds to
H maps ⟨Ĥ⟩ ⟨Ĥ⟩ to H.qy
<cut>
The copy of H at Ĥ.qx
... which is applied to ⟨Ĥ⟩ ⟨Ĥ⟩ ...
correctly decides that its input never halts.
H applied to ⟨Ĥ⟩ ⟨Ĥ⟩ correctly decides that its input halts. >>>>>>> I.e.
Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn if, and only if, H.q0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qn
but
H.q0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qy
which is obviously absurd. It's logically absurd, but even if you >>>>>>> prevent logical deduction by removing the annotations (as you repeatedly
do), it's still patently absurd to claim that the same state transition >>>>>>> function and input results in different state transitions.
At least you are not trying to hide anything. You explicitly claim an >>>>>>> absurdity. No one can take this seriously.
<cut diversions>
H.q0 wM w ⊢* H.qy // iff UTM(wM, w) halts
H.q0 wM w ⊢* H.qn // iff UTM(wM, w) does not halt
You are frantically throwing up diversions. You claimed, above, that two identical sets of states and transitions can give rise to different configuration sequences:
"Ĥ.qx maps ⟨Ĥ⟩ ⟨Ĥ⟩ to Ĥ.qn
corresponds to
H maps ⟨Ĥ⟩ ⟨Ĥ⟩ to H.qy"
and, a little less vaguely:
"The copy of H at Ĥ.qx correctly decides that its input never halts.
H applied to ⟨Ĥ⟩ ⟨Ĥ⟩ correctly decides that its input halts."
Formally, in the context of Linz's H/Ĥ you assert that:
Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn but H.q0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qy
You don't want to address this mistake, but it's the elephant in the
room. If TMs don't act solely on the basis of their tape and state transition functions, then they are arbitrary and useless.
It would be dishonest to keep posting other stuff in an attempt to try t
get people to forget you ever said this. You must address it. But then
I think you'd have to accept the proof.
That you keep ignoring my explanation is not at all the same thing as my
not having provided an explanation.
The embedded copy of H at Ĥ.qx determines that the pure simulation of
its input never halts.
H at determines that the pure simulation of its input halts because the
copy of itself as Ĥ.qx aborts its input.
If you have no interest what-so-ever in the truth and you only care
about forming a rebuttal that gullible fools that are hardly paying
attention will accept then continue on your way.
--
Copyright 2021 Pete Olcott
Talent hits a target no one else can hit;
Genius hits a target no one else can see.
Arthur Schopenhauer
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