4 ms·
I find it bizarre that the author finds the use of the Axiom of Choice troubling here, but he is apparently okay with the requirement that each prisoner memoriz
by pavelrub 12y ago
I find it bizarre that the author finds the use of the Axiom of Choice troubling here, but he is apparently okay with the requirement that each prisoner memorizes an infinite amount of information, and will also be able to look and see infinitely many prisoners.
Our intuition fails here only if we see this whole scenario as something plausible. But the basic requirements here are ridiculous: this puzzle has nothing to do with reality, and we have no reason to rely on our finitistic intuitions when thinking about it.
- lisper 12y agoThe prisoners are metaphorical. What this is really about is a mathematical (not practical) strategy whose result seems to be at odds with probability theory.
- judk 12y agoBut if you remove the requirement that the algorithm be practical in any plausible Universe, there is no reason to reject it as countetintuitive.
- erichocean 12y agoOr hell, even correct! The result is basically a toy, metaphysically null. :)
- lisper 12y agoNothing infinite is practical or plausible in a finite universe.
- erichocean 12y agoIt's a pet peeve of mine in general when mathematicians use imperative proofs with impossible steps, for similar reasons. The world is indeed an "interesting" place when computation takes zero time, memory and storage are infinite, and you're allowed to give the reader step-by-step instructions that cannot be completed in any known universe. But yeah, if you're willing to accept all that, CHECK OUT WHAT I'VE PROVED!!1!!! (And hand me that Nobel—I've earned it.)