Not to start a traditional puzzle flame war, but can someone clarify for me the situation where at least three people on the island have blue eyes? It seems that in this case everyone knows that everyone knows [...] that there is “at least one person with blue eyes”.
Blue-eyed person A: “Look at that poor sap over there with the blue eyes [B]. I bet he thinks there’s only one person with blue eyes [C] on this island. Little does he know!”
Help?
It gets interesting when the pebblesorters turn on a correctly functioning FAI, which starts telling them that they should build a pile of 108301 and legislative bodies spend the next decade debating whether or not it is in fact a correct pile. “How does this AI know better anyway? That looks new and strange.” “That doesn’t sound correct to me at all. You’d have to be crazy to build 108301. It’s so different from 2029! It’s a slippery slope to 256!” And so on.
This really is a fantastic parable—it shows off perhaps a dozen different aspects of the forrest we were missing for the trees.