Open Thread: July 2010

komponisto

This thread is for the discussion of Less Wrong topics that have not appeared in recent posts. If a discussion gets unwieldy, celebrate by turning it into a top-level post.

Part 2

This thread is for the discussion of Less Wrong topics that have not appeared in recent posts. If a discussion gets unwieldy, celebrate by turning it into a top-level post.

Part 2

This should be important to the finite case. The probability of being the first to see 25/100 is WAY higher (x 10^25 or so) if the lake is 3/4 full of big fish than if it is 1/4 full of big fish.

But in the infinite case the probability of being first is 0 either way...

utilitymonster:

The probability of being the first to see 25/100 is WAY higher (x 10^25 or so) if the lake is 3/4 full of big fish than if it is 1/4 full of big fish.

Maybe I'm misunderstanding your phrasing here, but it sounds fallacious. If there's a deck of cards and you're in a group of 52 people who are called out in random order and told to pick one card each from the deck, the probability of being the first person to draw an ace is exactly the same (1/52) regardless of whether it's a normal deck or a deck of 52 aces (or even a deck with 3 out of 4... (read more)

4JGWeissman16y

There is a reason we consider infinities only as limits of sequences of finite quantities. Suppose you tried to sum the log-odds evidence of the infinite scientist that the pond has more big fish. Well, some of them have positive evidence (summing to positive infinity), some have negative evidence (summing to negative infinity), and you can, by choosing the order of summation, get any result you want (up to some granularity) between negative and positive infinity. You don't need anthropomorphic tricks to make things weird if you have actual infinities in the problem.