XPost: comp.theory, sci.logic, sci.math
On 4/10/2022 6:26 PM, Dennis Bush wrote:
On Sunday, April 10, 2022 at 7:20:44 PM UTC-4, olcott wrote:
On 4/10/2022 6:14 PM, André G. Isaak wrote:
On 2022-04-10 17:08, olcott wrote:
On 4/10/2022 5:59 PM, André G. Isaak wrote:
On 2022-04-10 16:40, olcott wrote:
On 4/10/2022 5:35 PM, André G. Isaak wrote:
On 2022-04-10 15:56, olcott wrote:
On 4/10/2022 4:49 PM, André G. Isaak wrote:
On 2022-04-10 15:00, olcott wrote:
On 4/10/2022 3:15 PM, olcott wrote:
On 4/10/2022 3:07 PM, André G. Isaak wrote:
I'm trying to get you to write using correct and coherent >>>>>>>>>>>> notation. That's one of the things you'll need to be able to >>>>>>>>>>>> do if you ever hope to publish. That involves remembering to >>>>>>>>>>>> always include conditions and using the same terms in your >>>>>>>>>>>> 'equations' as in your text.
Not sure how that makes me a 'deceitful bastard'.
André
THAT you pretended to not know what I mean by embedded_H so >>>>>>>>>>> that you could artificially contrive a fake basis for rebuttal >>>>>>>>>>> when no actual basis for rebuttal exists makes you a deceitful >>>>>>>>>>> bastard.
IT IS THE CASE THAT the correctly simulated input ⟨Ĥ0⟩ ⟨Ĥ1⟩ to
embedded_H never reaches its own final state of ⟨Ĥ0.qy⟩ or >>>>>>>>>> ⟨Ĥ0.qn⟩ under any condition what-so-ever therefore ⟨Ĥ0⟩ ⟨Ĥ1⟩ is
proved to specify a non-halting sequence of configurations. >>>>>>>>>>
Ĥ.q0 ⟨Ĥ0⟩ ⊢* H ⟨Ĥ0⟩ ⟨Ĥ1⟩ ⊢* H.qy
Ĥ.q0 ⟨Ĥ0⟩ ⊢* H ⟨Ĥ0⟩ ⟨Ĥ2⟩ ⊢* H.qn
This is now the third reply you've made to the same post.
That post didn't make any arguments whatsoever about your claims. >>>>>>>>> It simply pointed out that you are misusing your notation and >>>>>>>>> urged you to correct it.
THE NOTATION IS A STIPULATIVE DEFINITION THUS DISAGREEMENT IS
INCORRECT.
If the notation is junk, then the definition is also junk.
That's like "stipulating" that
+×yz÷² = ±z+³
It's meaningless because the notation is meaningless, much like
your notation above.
This is meaningless:
Ĥ.q0 ⟨Ĥ0⟩ ⊢* H ⟨Ĥ0⟩ ⟨Ĥ1⟩ ⊢* H.qy // what's the condition?
Ĥ.q0 ⟨Ĥ0⟩ ⊢* H ⟨Ĥ0⟩ ⟨Ĥ1⟩ ⊢* H.qn // what's the condition?
With no conditions specified, the above is just nonsense.
André
Ĥ.q0 ⟨Ĥ⟩ ⊢* H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qy
If the pure simulation of ⟨Ĥ⟩ ⟨Ĥ⟩ by embedded_H would reach its
final state.
Ĥ.q0 ⟨Ĥ⟩ ⊢* H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qn
If the pure simulation of ⟨Ĥ⟩ ⟨Ĥ⟩ by embedded_H would never reach
its final state.
This is still nonsense.
Ĥ.q0 ⟨Ĥ⟩ ⊢* H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qy
If the correctly simulated input ⟨Ĥ⟩ ⟨Ĥ⟩ to embedded_H would reach its
own final state.
Ĥ.q0 ⟨Ĥ⟩ ⊢* H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qn
If the correctly simulated input ⟨Ĥ⟩ ⟨Ĥ⟩ to embedded_H would never
reach its own final state.
And again you're still being inconsistent. You can either use H or use
embedded_H, but you can't mix the two.
Sure I can. I just did.
This means that H pretends that it is only a UTM to see what its
simulated input would do in this case. If it would never reach its own >>>> final state then H correctly rejects this input.
A Turing Machine cannot "pretend" to be some different Turing Machine.
It can perform a pure simulation of its input until this simulated input
matches a repeating behavior pattern that proves this input never
reaches its own final state.
If that's the case, why does an actual UTM applied to the *same* input halt?
Hint: Because the result of an actual UTM applied to the input defines the correct answer, so H answers wrong.
Intuitively that would seem to be true, this intuition is incorrect.
The ultimate definition of correct is the computation of the mapping of
the inputs to an accept or reject state on the basis of the behavior
that these inputs specify.
That simulated inputs to embedded_H would never reach their own final
state under any condition what-so-ever
IS THE ULTIMATE MEASURE OF THEIR HALTING BEHAVIOR
and conclusively proves they specify a non-halting sequence of
configurations.
--
Copyright 2022 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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