Re: Flibble's Law

Richard Damon <richard@damon-family.org> writes:

On 4/18/25 5:16 PM, Mr Flibble wrote:

[...]

I'm not claiming we can build a decider with infinite resources.
I'm saying that if the problem permits infinite machines, then
infinite analyzers are fair game in theory.

>
No, you don't get to say that.

Well, actually ...

Sure, Mr. Flibble gets to say anything he likes.  Anyone can
define a mathematical system with any consistent rules they like,
and derive results that apply within that system.

The Flibble Reciprocity Principle:
In theoretical computation, every permitted infinity in problem
formulation implies a permitted infinity in problem analysis.
It's about playing the game by the rules of the game.

>
No, it is making up your own rules and admittion that you think
cheating is ok.
>
The "Rules" exist, and are defined, and they say that decider do NOT
get infinite time.

The "Rules" are fundamentally arbitrary (but ideally chosen for
their relevance to the real world).  Defining a new set of rules
is how we got useful and/or interesting things like non-Euclidean
geometry and complex numbers.

The flaw in Flibble's reasoning is that he claims that some kind of
"fair game" principle implies that he can make certain specific
rule changes.  I suggest that he doesn't need that excuse.

The rules under which most of us operate, and in which the Halting
Problem proof was constructed, are designed to correspond to
real-world computational models (with some simplifications like
not limiting storage size).

Mr. Flibble, I think, is inventing new rules because he doesn't like
the results from the existing rules.  I think he dislikes the fact
that the Halting Problem is not solvable, and is trying to define a
new system in which it's solvable in some sense.  And sure, he can
(try to) do that if he likes.  But it's worth spending time on that
*only* if the results of the new rules are interesting and/or useful.
It's also a good thing if the new rules are clearly defined, for
example rigorously defining what a "pathological input" is.

It would also be nice if Mr. Flibble acknowledged that the proof of
the unsolvability of the Halting Problem is valid within the usual
set of rules (and that he understands those rules), rather than
implying that the proof is invalid because the rules are "unfair"
or something.

--
Keith Thompson (The_Other_Keith) Keith.S.Thompson+u@gmail.com
void Void(void) { Void(); } /* The recursive call of the void */