Slight aside: I just grokked the blue-eyed islander riddle. Cribbing the following from Scott’s livejournal:
One hundred people live on a far-off island. Fifty people have blue eyes, and fifty people brown eyes. The islanders have a strange taboo that they may never talk about eye color with one another, and that if anyone ever learns eir own eye color, ey must commit suicide that night. There are no mirrors or other reflective surfaces on the island, and no one ever talks about it, so it is improbable that anyone will ever learn eir own eye color and violate the taboo.
One day an explorer comes to the island and says: “At least one person on this island has blue eyes.”
What, if anything, happens?
The answer to the riddle is that fifty days later, all the blue-eyed people on the island commit suicide.
This did not make initially make sense to me, because I didn’t see how it generalizes to N. The initial problem I had was that it appeared to me that as the number of blue-eyed people increased, we would encounter a day where the fact that nobody died would not tell us anything, and as a consequence the chain falls apart because this is the same as any other day.
The intuition I failed to grasp is the expectation that each blue-eyed person recurses all the way down simultaneously. I rediscover the fact that things happen at the same time periodically.
Slight aside: I just grokked the blue-eyed islander riddle. Cribbing the following from Scott’s livejournal:
This did not make initially make sense to me, because I didn’t see how it generalizes to N. The initial problem I had was that it appeared to me that as the number of blue-eyed people increased, we would encounter a day where the fact that nobody died would not tell us anything, and as a consequence the chain falls apart because this is the same as any other day.
The intuition I failed to grasp is the expectation that each blue-eyed person recurses all the way down simultaneously. I rediscover the fact that things happen at the same time periodically.