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From: dbush <dbush.mobile@gmail.com>
Newsgroups: comp.theory
Subject: Re: Functions computed by Turing Machines MUST apply finite string
 transformations to inputs
Date: Sat, 3 May 2025 17:28:23 -0400
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On 5/3/2025 3:45 PM, Richard Heathfield wrote:
> 
> I am conscious that you have already explained to me (twice!) that Mr 
> O's approach is aimed not at overturning the overarching indecidability 
> proof but a mere detail of Linz's proof. Unfortunately, your 
> explanations have not managed to establish a firm root in what passes 
> for my brain. This may be because I'm too dense to grok them, or 
> possibly it's because your explanations are TOAST (see above).
> 
> You have said, I think, that Olcott doesn't need a universal decider in 
> order to prove his point. But a less ambitious decider doesn't 
> contradict Linz's proof, surely? So once more for luck, what exactly 
> would PO be establishing with his non-universal and impatient simulator 
> if he could only get it to work?

The core issue is that PO, despise being nearly 70 and having worked as 
a programmer, fundamentally doesn't understand proof by contradiction.

He thinks that the H in the Linz proof *is* a halt decider, and 
therefore whatever result it comes up with *must* be correct.

He then concludes that whatever mapping that H is computing is the 
"correct" halting function and therefore the *actual* halting function 
is "wrong".  It is on this basis that he claims HHH(DD)==0 is correct, 
and therefore *any* halting problem proof is flawed.

His alternate halting criteria, in which he uses simulation, is that 
H(X,Y) determines what would happen if the code of H was replaced by a 
pure simulator and H(X,Y) is subsequently run to simulate X(Y).  In 
cases where X at some point calls H this results in an answer of 
non-halting but also changes the code being decided on.  This is 
obviously invalid, but PO then goes through a series of "justifications" 
(ex. H is the test code, not the code under test) based on the idea that 
H *must* be correct.