Re: My reviewers think that halt deciders must report on the behavior of their caller

On 7/4/2025 3:53 PM, Richard Damon wrote:

On 7/4/25 4:43 PM, olcott wrote:

On 6/3/2025 10:02 PM, dbush wrote:

On 6/3/2025 10:58 PM, olcott wrote:

On 6/3/2025 9:46 PM, dbush wrote:

On 6/3/2025 10:34 PM, olcott wrote:

On 6/3/2025 9:12 PM, dbush wrote:

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Given any algorithm (i.e. a fixed immutable sequence of instructions) X described as <X> with input Y:
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A solution to the halting problem is an algorithm H that computes the following mapping:
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(<X>,Y) maps to 1 if and only if X(Y) halts when executed directly
(<X>,Y) maps to 0 if and only if X(Y) does not halt when executed directly
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Yes there is no algorithm that does that

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Excellent!
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Let The Record Show
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That Peter Olcott
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Has *EXPLICITLY* admitted
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That no algorithm H exists that meets the above requirements, which is precisely the theorem that the halting problem proofs prove.

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In the exact same way that there is no set of all set
that contain themselves. ZFC did not solve Russell's
Paradox as much as it showed that Russell's Paradox
was anchored in an incoherent foundation, now called
naive set theory.

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Which arose because the axioms of naive set theory created a contradiction.
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Likewise with halt deciders that are required to report
on the behavior of directly executed Turing machines.

 And what is the CONTRADICTION?
 The result is just some things are not computable.
 

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Directly executed Turing machines are outside of the
domain of every Turing machine decider.

 Then so is mathematics, as "numbers" can't be given to Turing Machines, only representations of them.
 

Numbers always work the same way so it makes no difference.
*HHH(DDD)==0 and HHH1(DDD)==1 are both correct*
https://claude.ai/share/da9b8e3f-eb16-42ca-a9e8-913f4b88202c
When we compare DDD emulated by HHH and DDD emulated
by HHH1 SIDE-BY-SIDE. (Mike didn't do it this way).
*The difference is when*
HHH begins to simulate itself simulating DDD and
HHH1 NEVER begins to simulate itself simulating DDD.
HHH doesn't actually abort its simulation of DDD until
after has simulated many hundreds of simulated instructions
later. HHH simulates itself simulating DDD until DDD calls
HHH(DDD) again.

By the exact same idea that we can represent a number by a finite string, we can express the algorithm, and input, of a Turing Machine as a finite string, and thus can talk about what it will do.
 

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In contrast, the axioms of computation theory do *not* create a contradiction.  It simply follows from those axioms that no H exists the meets the above requirements, which is a completely valid conclusion.

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*Claude.ai seems to be the smartest bot about computation*
https://claude.ai/share/48aab578-aec3-44a5-8bb3-6851e0f8b02e
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 Which you just continue to lie to, so proving that you are just a pathological liar.

--
Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer