Requiring the logically impossible is always an invalid requirement

[PeteOlcott]

It is clear that the impossibility of creating a CAD system that can
correctly draw square circles places no limits on what computers can do.

It is less clear that requiring a program H to report on the behavior of
another program D that does the opposite of whatever H says is a
logical impossibility when we see that program H1 can correctly say what
D will do.

When we get back to the original {halting problem} we can see that no
program H can ever always say what every program D will do because
some D will do the opposite of whatever H says.

So the when the {halting problem} requires a program H to always say
whatever program D will do includes programs that do the opposite of
whatever H says this is requiring the logically impossible, thus the same
as requiring a CAD system to correctly draw square circles.

The {halting problem} as defined requires the logically impossible therefore
it places no actual limits on what can be computed.

Added later on as a clarication.
----

When the definition of the halting problem results in requirement that
cannot be met because this requirement is a logical impossibility it is
this definition that must be rejected.

The inability to do the logically impossible never derives any limitation
on anyone or anything. The logical impossibility of solving the halting
problem (within its current definition) is exactly the same as the logical
impossibility of creating a CAD system that correctly draws square circles.

When a problem definition requires a logical impossibility then it is the
problem definition that must be rejected.

[promethean75]

Noted.

[PeteOlcott]

Noted.

Do you agree that I just showed that the {halting problem}
places no actual limits on what computers can do?

[promethean75]

I have no idea what any of u computer guys are talking about. I'm a highschool dropout Pete and I swing a hammer for a living.

[promethean75]

That's a trip tho. You're such a cool laid back well mannered smart guy that u don't even recognize when somebody is being an asshole.

Like u would stare flatly at me like Spock if i told a joke. That's how inhumanly smart u are. Humor is characteristic that your species does not have.

[PeteOlcott]

I have no idea what any of u computer guys are talking about. I'm a highschool dropout Pete and I swing a hammer for a living.

That is fine. I finally got the words simple enough that 10% of everyone can understand
them up from one in a million.

[PeteOlcott]

That's a trip tho. You're such a cool laid back well mannered smart guy that u don't even recognize when somebody is being an asshole.

Like u would stare flatly at me like Spock if i told a joke. That's how inhumanly smart u are. Humor is characteristic that your species does not have.

I played Spock as a kid. I stay happy all the time. I like good jokes.

[Skepdick]

It is clear that the impossibility of creating a CAD system that can
correctly draw square circles places no limits on what computers can do.

https://en.wikipedia.org/wiki/Taxicab_geometry

It is less clear that requiring a program H to report on the behavior of
another program D that does the opposite of whatever H says is a
logical impossibility when we see that program H1 can correctly say what
D will do.

It's not a logical impossibility if you structure it as a turn-based game.

Who goes first? H; or D?

Lets suppose H goes first. H believes that D will halt (and that D is a contrarian).
Despite believing that D won't halt H says "D won't halt". H lies about its true belief.
D does the opposite of what H says -> D doesn't halts; and H smirks having figured out how to manipulate D.

When we get back to the original {halting problem} we can see that no
program H can ever always say what every program D will do because
some D will do the opposite of whatever H says.

Consider the scenario above. Suppose H "lies" to D. Suppose that H communicates its true belief to the human programmer P.

P and H now share a belief that D will halt; even though H told D that "it won't halt."
D pulls off its contrarian act and it halts.

P and H smirk about the accurate prediction.

The {halting problem} as defined requires the logically impossible therefore
it places no actual limits on what can be computed.

Consider the definition incomplete. What I say about D and what I believe about D need not correspond.

Especially if I know that D is a contrarian.

[PeteOlcott]

Consider the definition incomplete. What I say about D and what I believe about D need not correspond.

Especially if I know that D is a contrarian.

Now matter what H says D does the opposite.

[Skepdick]

Consider the definition incomplete. What I say about D and what I believe about D need not correspond.

Especially if I know that D is a contrarian.

Now matter what H says D does the opposite.

H believes D will halt.
H says D won't halt (the opposite of what H actually believes)
D does the opposite of what H says and it halts.
H's belief about D is confirmed.
H has correctly predicted what D will do.

H believes D won't halt.
H says D will halt (the opposite of what H actually believes)
D does the opoosite of what H says and doesn't halt.
H's belief about D is confirmed.
H has correctly predicted what D will do.

[PeteOlcott]

Consider the definition incomplete. What I say about D and what I believe about D need not correspond.

Especially if I know that D is a contrarian.

Now matter what H says D does the opposite.

H believes D will halt.
H says D won't halt (the opposite of what H actually believes)
D does the opposite of what H says and it halts.
H's belief about D is confirmed.
H has correctly predicted what D will do.

H believes D won't halt.
H says D will halt (the opposite of what H actually believes)
D does the opoosite of what H says and doesn't halt.
H's belief about D is confirmed.
H has correctly predicted what D will do.

H guesses that D halts and D does the opposite.
H guesses that D loops and D does the opposite.

[Skepdick]

Now matter what H says D does the opposite.

H believes D will halt.
H says D won't halt (the opposite of what H actually believes)
D does the opposite of what H says and it halts.
H's belief about D is confirmed.
H has correctly predicted what D will do.

H believes D won't halt.
H says D will halt (the opposite of what H actually believes)
D does the opoosite of what H says and doesn't halt.
H's belief about D is confirmed.
H has correctly predicted what D will do.

H guesses that D halts and D does the opposite.
H guesses that D loops and D does the opposite.

D is not a mind-reader and doesn't know what H guessed.
D only knows what H said.

H now has a valid theory of how D works.
It does the opposite of what you say.

[PeteOlcott]

D is not a mind-reader and doesn't know what H guessed.
D only knows what H said.

H now has a valid theory of how D works.
It does the opposite of what you say.

Whatever H says D does the opposite making it logical
impossible for H to correctly say what D will do.

[Skepdick]

D is not a mind-reader and doesn't know what H guessed.
D only knows what H said.

H now has a valid theory of how D works.
It does the opposite of what you say.

Whatever H says D does the opposite making it logical
impossible for H to correctly say what D will do.

Where's the impossibility?

D does EXACTLY what H guessed (but didn't say).

Of course, H can't SAY what D will do. Because D will do the opposite.
but H can correctly guess what D will do.

[PeteOlcott]

Whatever H says D does the opposite making it logical
impossible for H to correctly say what D will do.

Where's the impossibility?

D does EXACTLY what H guessed (but didn't say).

Of course, H can't SAY what D will do. Because D will do the opposite.
but H can correctly guess what D will do.

There are only two possible things H can do:
(1) H says D halts making D loop
(2) H says D loops making D halt