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

On 3/7/24 6:16 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.

 The problem is that a Turing Machine doesn't have *A* description, but an infinte number of them. It can assume one of them, but that is worthless for trying to find a copy of itself in the input, because it has no idea which of the infinte variations that will be.