Re: We finally know exactly how H1(D,D) derives a different result than H(D,D)

On 3/7/24 7:49 PM, olcott wrote:

On 3/7/2024 9:36 PM, Richard Damon wrote:

On 3/7/24 7:10 PM, olcott wrote:

On 3/7/2024 8:16 PM, immibis wrote:

On 8/03/24 03:06, André G. Isaak wrote:

On 2024-03-07 16:02, olcott wrote:
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That Olcott machines always know their own TMD is unconventional.
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That their own TMD is correctly construed as an additional input
to their computation (whenever they don't ignore it) does provide
the reason why Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ <Ĥ> and H ⟨Ĥ⟩ ⟨Ĥ⟩ <H> can compute different
results and still be computations.

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It's also the reason why you approach is fundamentally flawed. Putting aside the question of whether your proposal is workable (or even sane), if your 'Olcott Machines' automatically supply the machines they emulate with a copy of their own machine descriptions, then you are no longer working on the halting problem.
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The halting problem asks, is it possible to construct a TM X that, given a description of a second TM Y and an input string Z *and* *only* *that* *input* *to* *work* *with*, is it possible for X to determine whether Y applied to Z halts.
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Asking whether it is possible to construct a TM X which, given a description of a second TM Y, and input string Z, *and* a description X, can X determine whether Y applied to Z halts, is an *entirely* different question.
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The answer to these two questions may well be entirely different, and the answer to the second question tells us absolutely nothing about the answer to the first, which is the only thing the halting problem is concerned with.
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André
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It turns out that they are the same answer, since a machine which doesn't need its own description can ignore it, and a machine which does need its own description can be modified to include the description it needs (which won't be "its own" description any more, but it's impossible that it would need to be). Olcott is just grasping at straws to explain why obvious facts are false.

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It is possible for Ĥ to screw itself up and write an English poem
to the place where its own TMD is supposed to be. It is impossible
for Ĥ to write <H> to this location because it has no access or
knowledge of the existence of any separate <H>.
>

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OF COURSE it has knowledge of the ONE SPECIAL H that it was written to confound, so can have a (the) description of it.
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Why wouldn't it.
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You wouldn't send out an assissin without giving it complete information about its target.
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Once Olcott Machines get a description of themselves added, then H^ will be defined to confound just a particular description of H, but one can be defined to confound ANY of the description of H, so we can prove that ALL are confounded, just as the proof generalizes from the specific H that this H^ was built on to any and all machines that might be consider as a Halt Decider.

 No Ĥ can possibly be defined to confound any H besides the one
that is embedded within it because Turing machines do not call
external functions.
 

Right, so whatever machine you want to claim to be an actual Halt Decider, can have a input built from IT via the tempate, and it will be confounded, and thus show NOT to be an actual Halt Decider.
What ever machine you want to try to claim to be a Halt Decider has an Achilles heal in the input machine built from it.
Thus, NO machine can ever be a correct Halt Decider for ALL inputs.
PERIOD.
Halting Theorem proven.
PERIOD.
Remember, claimed decider exists first, then confounder created to prove it wrong.
In this game, second to move wins.