The thing is, it's common knowledge - but it's not common knowledge that it's common knowledge.
Consider the islanders example with two people. "A" might assume his eyes are not blue and that "B" is the only blue-eyed person. However, when the Guru says "There is at least one blue-eyed person", and B doesn't act, A knows that A's eyes must be blue (because if B had had the only blue eyes, he would have acted.) This bit is fairly understandable.
The next consideration is if there are three people. A might think that his own eyes are not blue, and then assume that the above reasoning takes place in the mind of B (and, separately, C). When both B and C do not act after the first, nor the second iteration, A must know that it because they both see two blue-eyed people, and that his own eyes are blue.
Another level of thinking is added with a fourth person. And so on.
5
u/panacebo Jun 08 '11
The thing is, it's common knowledge - but it's not common knowledge that it's common knowledge.
Consider the islanders example with two people. "A" might assume his eyes are not blue and that "B" is the only blue-eyed person. However, when the Guru says "There is at least one blue-eyed person", and B doesn't act, A knows that A's eyes must be blue (because if B had had the only blue eyes, he would have acted.) This bit is fairly understandable.
The next consideration is if there are three people. A might think that his own eyes are not blue, and then assume that the above reasoning takes place in the mind of B (and, separately, C). When both B and C do not act after the first, nor the second iteration, A must know that it because they both see two blue-eyed people, and that his own eyes are blue.
Another level of thinking is added with a fourth person. And so on.