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[Dec. 1st, 2010|01:13 pm]
Scott
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There is a certain very curious logic problem which goes as follows:
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 is a very strange riddle, because the explorer has said nothing that the islanders don't already know; each blue-eyed islander can see that forty-nine other people have blue eyes, so the explorer telling them that at least one person has blue eyes should be complete non-information. So why do they commit suicide? And why fifty days later?
Consider the counterfactual where ninety-nine people on the island have brown eyes and only one has blue eyes. Call the blue-eyed islander Bob. The explorer says "At least one person on this island has blue eyes." Bob looks around, sees no one else on the island has blue eyes, and realizes it is him. Bob kills himself that night.
Now, consider the counterfactual where ninety-eight people have brown eyes and only two have blue eyes - call them Bob and Jane. The explorer says "At least one person on this island has blue eyes". Jane knows that ninety-eight islanders have brown eyes and Bob has blue eyes, so she knows there are only two possibilities: either only Bob has blue eyes, or else she and Bob both have blue eyes. If only Bob has blue eyes, the problem reduces to the one above, where Bob kills himself on the first night. So when she wakes up the next morning and sees that Bob has not killed himself, she knows there must not be only one blue-eyed person - and therefore she must have blue eyes. Bob, for his part, is using the exact same reasoning when he sees Jane has not killed herself. So both Bob and Jane kill themselves on the second night.
This trend continues. For n people with blue eyes, when no one kills themselves on night one it reveals n is not equal to one, when no one kills themselves on night two it reveals n is not equal to two, and so on. But every person has an upper bound on n - it's the number of blue-eyed people they see around them, plus one in case they themselves have blue eyes. So when the lower bound for n equals the upper bound for n, all blue-eyed people realize the value of n, realize it means they themselves must have blue eyes, and kill themselves. So in general, all blue-eyed people will commit suicide on night n. The original problem is the special case where n = 50.
What this riddle teaches me is that information is a weird thing. "At least one person has blue eyes" doesn't seem like information to someone who already knows at least ninety-nine people have blue eyes, but knowing that it is officially known that it is known that it is known that...and so on can have profound consequences.
This is the only way I make sense of the WikiLeaks disaster. I read over some of the facts linked in those WikiLeaks cable. None of them were at all surprising. The Arabs wanted us to bomb Iran? That's been all over the Internet for months. China's been hacking international websites? Wow, who knew that Nobel Prize website congratulating Liu Xiabao didn't just get struck by lightning or something? The US Department of State thinks Robert Mugabe is a jerk? Everyone thinks Robert Mugabe is a jerk!
And yet apparently in diplomatic circles, knowing this is a big deal. A big enough deal that it will threaten American security and deal a major blow to our future diplomatic efforts. Maybe there's a big difference between extreme suspicion and proof, although I fail to see why national governments, which aren't bound by the same rules as a trial jury, would bother preserving this difference. Or maybe it just gives people a Schelling point for rage. The Iranians have probably been pretty sure the Saudis want them bombed for years now, but they were never able to get too worked up about it for the same reason people rarely get worked up about world hunger - why start holding rallies about it now of all times? Maybe this gives them the excuse to lodge all those protests they've been saving up.
I do have one other question about WikiLeaks for which I cannot think of an answer so easily, which is - why do people need it? What's so important about www.wikileaks.org and Julian Assange? If I am revealing secret classified information lots of people and media outlets will want to read, can't I just upload it anywhere on the Internet - heck, stick it on PasteBin? Is the only thing that's remotely interesting about WikiLeaks their ability to create PR about the newest disclosure?
And if so, why are people putting so much effort into arresting Assange and getting the site shut down? Now that people know there's a niche, the PR will take care of itself, and as soon as Assange's in prison someone else will create a new leaks site. gLeaks. The Facebook Leaks Bazaar (like). www.reddit.com/r/ClassifiedDocuments. Microsoft Leaks 2010 ("It looks like you're trying to reveal documents about US espionage activities. Would you like to open the Easy Redaction Wizard?").
Heck, if those don't show up, I still have like five gigabytes free space on www.raikoth.net. |
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