Can you go into further detail about the nth abstraction of "he knows that I know..." and what effect that has on the population? The way I see it is that as soon as everybody knows that there are blue-eyed ppl and everybody knows that everybody else knows there are blue-eyed ppl the countdown begins... additionally, at that point you can already get to an infinite number of abstractions of the "he knows that I know that he.." statement because you both know that the other knows blue-eyed ppl exist, so you both know that the other knows that you know that blue-eyed ppl exist, so you both know....
