Am I stupid? I can't fit these two concepts into any type of harmony.

[BillC]

How about this for a paradox (response to PairtheBoard or his evil twin):

You are offered the following set up. A fair coin is flipped until it first comes up heads, say on the nth flip (n=1,2,...), at which point you are paid 2^n dollars and the game ends. The instantaneous flips are timed as follows: the nth flip occurs exactly 1/2^n minutes after the previous flip for n>1 and the first flip (n=1) takes place 1/2 minute after the start of the game. The game is over in less than 2 minutes. Do you see why?

How much is this game worth to you?