Re: Analysis of Flibble’s Latest: Detecting vs. Simulating Infinite Recursion ZFC

On 23/05/2025 19:37, Keith Thompson wrote:

Ben Bacarisse <ben@bsb.me.uk> writes:

Mike Terry <news.dead.person.stones@darjeeling.plus.com> writes:

[...]

And the big picture is that this can be done because false is the
correct halting decision for some halting computations.  He has said
this explicitly (as I have posted before) but he has also explained it
in words:
>
| When-so-ever a halt decider correctly determines that its input would
| never halt unless forced to halt by this halt decider this halt
| decider has made a correct not-halting determination.

 Hmm.  I don't read that the way you do.  Did I miss something?
 It assumes that the input is a non-halting computation ("its input
would never halt") and asserts that, in certain circumstances,
his mythical halt decider correctly determines that the input
is non-halting.
 When his mythical halt decider correctly determines that its input
doesn't halt, it has made a correct non-halting determination.
It's just a tautology.

You're reading it the way most people would, and in the way I said Sipser would be interpreting the oft-quoted "Sipser quote".  I don't think you've missed anything particularly.
I suppose Ben quoted PO saying this, because PO /uses/ it to justify that a particular /halting/ computation will never halt,  PO's HHH simulates DDD (which halts) but before DDD halts it spots a pattern in the simulation, and announces non-halting.  "Eh?" I hear you say!  PO claims HHH has "correctly determined that DDD would never halt" and so is correct to decide non-halting.  His "proof" that it is right to decide non-halting is his "when-so-ever.." quote, which broadly matches the Sipser quote.
So the problem is not so much the "when-so-ever.." words themselves [or the words of Sipser's quote], but understanding how PO is so thoroughly misinterpreting/misapplying them.  How can PO believe HHH has "correctly determined the DDD will never halt" when DDD demonstrably halts?
Rather that try to explain that, I'll suggest that it really doesn't matter exactly /why/ PO is confused.  It's enough that his claims are obvious nonsense, and readers of a certain level see this pretty much straight away.  People who post corrections and try to help PO /see/ his mistakes and change his mind are completely wasting their time, although of course it's entirely theirs to waste!
As to whether Ben's PO quote was helpful supporting material for his remark that PO believes it's right to decide non-halting for certain halting computations - you'll have to decide that.  [PO /does/ think it's right to decide non-halting for certain halting computations, although PO's conception of halting does not match yours or mine.]

 This kind of determination can be made in specific cases (but of
course not in general).  A simple program like `int main(void)
{ while (1); }` is non-halting.  If I run it, it will never halt
unless I force it to halt, e.g. by typing Control-C or pulling the
power plug.
 (I'm assuming that "when-so-ever" means the same as "when".)

Yeah, one of PO's affected wordings that he likes.  I read it as "whenever".
If you likewise ran PO's DDD(DDD) you would not have time to enter ^C because it would complete in short order.  His HHH which is simulating the computation can get its abort in, because the simulation is step-by-step, and after each step HHH gets to choose whether to continue or abort the simulation.
Mike.