Richard Heathfield <rjh@cpax.org.uk> writes:

On 21/05/2025 18:47, olcott wrote:

...

*PAY ATTENTION*
I am saying that a key element of the halting problem
proof cannot exist, thus the proof itself cannot exist.

Yes, it can, and it does.

You'd think that at some point in decades he's wasted on this he might
have considered looking at the proofs that are not by contradiction.
I've repeatedly suggested looking at Radó's Busy Bee problem and proof.

Watch.

Definition: a prime number is an integer >= 2 with no divisors >= 2 except itself.

Hypothesis: there is no largest prime number.

Proof:

Assume that a largest prime number Pn exists.

Itemise all the prime numbers from P1(=2) up to Pn :

P1 P2 P3 ... Pn

Insert x symbols all the way along.

P1 x P2 x P3 ... x Pn

Add 1.

The number thus calculated is not divisible by any prime in our list (there being a remainder of 1 in each case), so the number calculated is (a)
prime, and (b) larger than Pn. Thus Pn is not the largest prime. This contradicts the assumption made at the beginning, which must therefore be false. Proof by contradiction.

The proof that no largest prime exists despite its assumption that such a prime /does/ exist - an assumption that turns out to be false.

Interestingly (and not, I think, coincidentally) Euclid's proof is not a
proof by contradiction. It shows (by case analysis) that any finite
list of primes is incomplete. There is (in the way Euclid does it) no
need to assume anything (other than some basic axioms).

The same strategy can be used for the halting theorem. The more direct
proof essentially shows that the infinite list of Turing machines (there
is only one, once we agree a numbering) does not include a halt decider
(just like it does not include uncountably many other deciders that the
cranks are never interested in).

PO seems to like talking to you so you might consider avoiding any
arguments about contradictions by providing an outline of the direct
proof instead.

I've lost count of the times when the proof by contradiction leads
students astray. Even if they don't think it's invalid, every year one
has to counter the idea that all the decider has to do is "spot the
tricky input" and the decider will work on everything else.

I'm finding it hard to believe that you can really be this stupid. Perhaps you just get off yanking people's chains.

Hmm... Don't forget Hanlon's razor. As for data points, PO has
published a website whose purpose is to "bring new scripture to the
world" and he has claimed, in a court of law, to be God.

Incidentally, there is even a modern proof by construction of the
infinitude of the primes. The idea being that since n and (n+1) have no
prime factors in common, n(n+1) has more distinct prime factors that n.
This gives a chain of ever larger sets of primes: the unique prime
factors of 2x3, 6x7, 42x43 and so on.

--
Ben.

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

On 22/05/2025 06:41, Richard Heathfield wrote:

On 22/05/2025 06:23, Keith Thompson wrote:

Richard Heathfield <rjh@cpax.org.uk> writes:

On 22/05/2025 00:14, olcott wrote:

On 5/21/2025 6:11 PM, Richard Heathfield wrote:

[...]

Turing proved that what you're asking is impossible.

That is not what he proved.

Then you'll be able to write a universal termination analyser that can >>>> correctly report for any program and any input whether it halts. Good
luck with that.

Not necessarily.

Of course not. But I'm just reflecting. He seemed to think that my
inability to write the kind of program Turing envisaged (an inability
that I readily concede) is evidence for his argument. Well, what's sauce
for the goose is sauce for the gander.

Even if olcott had refuted the proofs of the
insolvability of the Halting Problem -- or even if he had proved
that a universal halt decider is possible

And we both know what we both think of that idea.

-- that doesn't imply
that he or anyone else would be able to write one.

Indeed.

I've never been entirely clear on what olcott is claiming.

Nor I. Mike Terry seems to have a pretty good handle on it, but no matter
how clearly he explains it to me my eyes glaze over and I start to snore.

Hey, it's the way I tell 'em!

Here's what the tabloids might have said about it, if it had made the
front pages when the story broke:

COMPUTER BOFFIN IS TURING IN HIS GRAVE!

An Internet crank claims to have refuted Linz HP proof by creating a
Halt Decider that CORRECTLY decides its own "impossible input"!
The computing world is underwhelmed.

Better? (Appologies for the headline, it's the best I could come up
with.)

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.

Or perhaps you prefer this explanation from 2023:

| (1) A return value of 1 from H(D,D) means the input to H(D,D) has halted
|
| (2) A return value of 0 from H(D,D) has been redefined to mean
| (a) D does not halt
| (b) D has been defined to do the opposite of whatever Boolean value
| that H returns.

All very clear. Of course (2)(b) is undeciable in general.

--
Ben.

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Keith Thompson <Keith.S.Thompson+u@gmail.com> writes:

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.

It would be a tautology but for the "unless..." part. It does not make
the determination that it does not halt. It determines that it would
not halt were it not for the fact that the decider (a simulation) in
fact halts it.

--
Ben.

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

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.

Maybe it makes less sense out of the context it was posted in. This was
when he was being less obtuse. The computation in question only halts
because it is halted by the decider on which it is built. It is a
halting computation, but according to PO it can reported as not halting
because of what would happen if it were not halted by the decider from
which it is derived.

Subsequent wordings have all been about hiding this. Just prior to this wording was the even more explicit claim that non-halting is correct
because of what "would happen if line 15 were commented out". It's
always been about what would be the correct decision were the
computation not what it actually is.

I suppose Ben quoted PO saying this, because PO /uses/ it to justify that a particular /halting/ computation will never halt,

He may be doing that now, but he used to use this form of words to
justify why non-halting is the correct result for some halting
computations. Obviously, to keep people talking he has had to scramble
to get away from what he has said in the past without repudiating it.
No crank likes admit they were ever wrong.

--
Ben.

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

On 24/05/2025 01:26, Ben Bacarisse wrote:

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

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.

Maybe it makes less sense out of the context it was posted in. This was
when he was being less obtuse. The computation in question only halts
because it is halted by the decider on which it is built. It is a
halting computation, but according to PO it can reported as not halting
because of what would happen if it were not halted by the decider from
which it is derived.

"The computation in question only halts because it is halted by the
decider on which it is built."

That is presumably you speaking in PO's voice, but my first reading
was as you saying it!

It was paraphrase. He has evolved (deliberately) from being very clear:
false is correct for some halting computations; the set of halting
computation is expanded to include some others; right though to the
wording that he managed to trick Sipser with.

The intermediate stages involved turns of phrase like "some computations
only halt because the simulator halts them" and "it would not halt if
line 15 were commented out" and so on. But the basic plan has been the
same for years: some halting computations can be classed as non-halting
because they halt for a reason he considers special -- a closely related
but different computation would not halt.

If PO were a normal person, the key would be to go back and forth getting answers to direct questions that would illuminate what he thinks. But
cranks always duck and dive when asked direct questions because they
know that must avoid being clear. I have dozens of notes of direct
questions being evaded, time and time again. The only game (for me) is
to try to get a crank to actually say what they mean as clearly as
possible. That is, after all, what a proper exchange of view should be
based on.

...

As ever, pointing it out to PO, however explicitly and clearly, has no
effect on what PO believes.

Right, but it is possible to try to get as clear and concise an
expression of what he believes. There's no point in trying to change
his mind, but his nonsense can then be laid bare for all to see. At
that point, I would want to just repeat it back (every time he posts)
with an brief explanation that it's wrong rather than try to educate PO.

--
Ben.

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Keith Thompson <Keith.S.Thompson+u@gmail.com> writes:

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

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

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.

Maybe it makes less sense out of the context it was posted in. This was
when he was being less obtuse. The computation in question only halts
because it is halted by the decider on which it is built. It is a
halting computation, but according to PO it can reported as not halting
because of what would happen if it were not halted by the decider from
which it is derived.

I think you're misreading it (or, if you prefer, I have yet to be
convinced that I'm misreading it).

OK. This sub thread is an excellent example of how cranks keep it all
going without shining any light on what's going on.

If the remark is correct, then it misrepresents PO's intended meaning
because he is discussing one of the cases where false is the correct
result for a halting computation. If the remark does represent his
intended meaning then it is unclear because you think it is simply a
tautology.

That makes it a bad quote for me to have pulled out. I should have
stuck with this exchange:

Me: Here's the key question: do you still assert that H(P,P) == false is
the "correct" answer even though P(P) halts?

PO: Yes that is the correct answer even though P(P) halts.

Everything that followed this was, as far as I can tell, an attempt be
less clear. But as Richard Heathfield has pointed out, we should always attempt to address the strongest and clearest-made point that is
offered. (I think this advice was originally from Daniel Dennet.)

I see you have offered a very detailed interpretation of what you think
the words used by PO mean. Please forgive me for not going into it in
any more detail. I'll just take that to mean PO was unclear and should
not have quoted his ambiguous words. When PO is clear, he is very
explicitly wrong, and that's the main point that keeps getting lost.

--
Ben.

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Richard Heathfield <rjh@cpax.org.uk> writes:

On 28/05/2025 18:33, olcott wrote:

I am not solving the halting problem.

Clearly.

But once upon a time he was. For example, in this exchange:

Me: Recent posts have said that you really do claim to have a halting
decider. Have you extended your claim or was that a
misunderstanding?

PO: I really do have a halting decider.

I think it's useful to know that trying to have any discussion with the
OP will eventually feel like nailing jelly to a wall.

--
Ben.

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Keith Thompson <Keith.S.Thompson+u@gmail.com> writes:

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

Richard Heathfield <rjh@cpax.org.uk> writes:

On 28/05/2025 18:33, olcott wrote:

I am not solving the halting problem.

Clearly.

But once upon a time he was. For example, in this exchange:

Me: Recent posts have said that you really do claim to have a halting
decider. Have you extended your claim or was that a
misunderstanding?

PO: I really do have a halting decider.

I think it's useful to know that trying to have any discussion with the
OP will eventually feel like nailing jelly to a wall.

Aug 10, 2020 https://groups.google.com/g/comp.theory/c/XRw3WhADb8I/m/JOwRQyV6BQAJ

Thanks. I usually post citations myself, but I'm getting lazy.

--
Ben.

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