Re: Flibble's Law

Mr Flibble <flibble@red-dwarf.jmc.corp> writes:
[...]

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.
>
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 seems to be about inventing new rules because you don't like
the results you get from the existing rules.

There is no "fair game" principle in mathematics.  The fact that
a Turing machine can have potentially unlimited resources (though
any terminating Turing machine can use only finite resources)
*does not imply* that "infinite analyzers are fair game".

A halt decider that can give a correct answer for any input using
only finite time and tape would be extremely interesting and useful,
but such a thing has been proven to be impossible.  A halt decider
that can give a correct answer only, in some cases, after consuming
infinite resources is neither interesting nor useful.

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