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From: =?UTF-8?B?QW5kcsOpIEcuIElzYWFr?= <agisaak@gm.invalid>
Newsgroups: comp.theory,sci.logic
Subject: Re: We finally know exactly how H1(D,D) derives a different result
 than H(D,D)
Date: Thu, 7 Mar 2024 19:06:36 -0700
Organization: Christians and Atheists United Against Creeping Agnosticism
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On 2024-03-07 16:02, olcott wrote:

> That Olcott machines always know their own TMD is unconventional.
> 
> 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.

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.

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.

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.

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.

André

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