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From: Richard Damon <richard@damon-family.org>
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 19:31:25 -0800
Organization: i2pn2 (i2pn.org)
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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:
>>
>>> 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
>>
> 
> 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.