| ITEC 122 |
| 2007fall |
| ibarland |
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On a tiny remote island lives a primitive tribe of philosophers, whose members all have a peculiar birthmark -- on their forehead is a dot which is either red or blue. The color of an individual's dot has assumed great social importance, and indeed the ultimate quest of any individual's life is to determine the color of their own dot. If anyone succeeds in doing so, that person has attained enlightenment, and with no reason left to live commits ritual suicide that very midnight (by doing a swan dive into the island's active volcano while yodeling, but the method is unimportant).
Of course, they don't have any mirrors, and there is a strict tabu against anybody giving information about other people's foreheads; consequently, nobody can actually determine the color of their own dot. Island life is very stable, everybody sitting around all day philosophizing and thinking; they have all become very accomplished logicians.
One balmy afternoon, an explorer from the outside world finds the island, and innocuously mentions "I see each of you have either a red dot or a blue dot on your forehead; how fascinating!"
Q: What happens?
Hint: Consider the explorer saying something even weaker: "I see at least one of you has a blue dot."
(If you want to reply to this to discuss, please label your subject-line with 'Spoiler' or 'Possible Spoiler?' or something like that. No fair if you've just heard the answer before from somewhere else! I'll post some mild hints after the break, or sooner if there is demand.)Real Q: If there were two or more people with red dots, the explorer gave no information that wasn't already known. So why did that change anything?
| ©2007, Ian Barland, Radford University Last modified 2007.Oct.30 (Tue) |
Please mail any suggestions (incl. typos, broken links) to iba�rland  rad�ford.edu |
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