[jdashg]

"Anything can happen in infinity" only holds if anything can indeed happen, but "doesn't" due to vanishingly small probabilities. Infinite trials still have bounded results. I'm not sure there's a theoretical mechanism that can randomly materialize whales, no matter the unlikelihood!

[yetihehe]

There is, it's called quantum fluctuation. It is VERY unlikely a whole whale could materialise this way in a volume of known universe, but not impossible.

[dandare]

That is what I heard as well, but I still don't grasp it. Infinities have different sizes too, right? I imagine something like this: the probability of subatomic particle of a functional whale appearing due to quantum fluctuation drops faster and faster with each additional particle, while the additional space of infinite universe increases only with d3. I am no mathematician or physicist though.

[petertodd]

I think the intuition you need here is that while the size of the whale is bounded, the size of the infinite universe is not.(1) Thus the argument doesn't work, because the "faster and faster with each additional particle" assumption isn't met.

OTOH, your argument is a good one if we're talking about things like the entire infinite universe undergoing some transformation, provided that the probability of that thing happening somehow diminishes over time.

1) This is by far the best sentence I've ever written on Hacker News. So thank you! :)

[kstrauser]

That was a very good sentence.