Coloured lenses :-)

What I don't get: if they already knew that there were only brown- and blue-eyed people, why weren't they extinct a long time yet? In this case, the anthropologist only learns them that there were at least two of every colour, but even that can not have been news and can't have changed the problem.
If they all knew that there were people with brown and people with blue eyes, and one person saw only brown-eyers, then he would have known he had blue eyes, and committed suicide. As no one had committed suicide, they must have known that there were at least two of every colour.

Basically, they can't have known beforehand that there were only two colours, or they would have been long gone.

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Knowledge is a curse, but ignorance is worse

Probably wouldn't work, since they remember what they saw before. It is usually sufficient to test any solution against the case where there is only 2 blue-eyed people, so each know the other person who has blue eyes.

Go back to the special case of two blue-eyed people. Everyone in the tribe could always see that the tribe has brown and blue eyes, which is all that the visitor said. So it seems there is no new information. That's why part (2) is so curious. But as montebianco correctly surmised, in the case where there are two people with blue eyes, each of those people knows there are blue-eyed people, but they do not know that the other blue-eyed person knows this! It is knowledge about the other person's knowledge that is the crucial aspect, and this chain continues if there are 5 blue-eyed people. montebianco was exactly correct in his explanation, and I was surprised he got it so quickly.

Nice icon, haven't seen that one before!

Ah, got it (I think): they did all know that there were blue- and brown-eyed people, but they didn't know that they did all know (i.e. that the other ones knew as well).
But this only goes when there is a 18-2 distribution, not with the initial given 15-5 distribution. If they knew upfront that there were only two colours, then no new info is given by the anthropologist in this case.

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Knowledge is a curse, but ignorance is worse

Are they allowed to lie? How about if one bluie and one brownie announce that they weren't paying attention during the meeting, what's all the fuss about?

Edit - although now that I think about it, this raises a whole bunch of new problems...

Can they bash their heads with rocks until they forget?

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Quaeso quousque humi defixa tua mens erit? Nonne aspicis, quae in templa veneris?

It works with all distributions. In the case of a 17-3 distribution, there would be three blue eyed people, A, B, and C.

Guy A would know that guy B has blue eyes.
Guy A would know that guy B knows that guy C has blue eyes.
But, Guy A can't know whether guy B knows whether guy C knows that anyone has blue eyes.

Guy A cannot conclude that guy B knows that guy C knows that anyone in the tribe has blue eyes. When the anthropologist arrives, guy A can make this conclusion. He now knows that guy B knows that guy C knows that at least one person has blue eyes.

It works the same with a 16-4 distribution, and all distributions.

But is this correct? If all know that that there are at least four blue-eyed people. They all know that everone can see at three blue-eyed and everyone knows the last statement is just a subset of knowing that everone knows there are at least three blue-eyed.

Perhaps the information revealed by the anthropologist is not important for its information content - but rather it becomes a "focal point" in time to actually consider the logical ramifications regarding distribution of eye color. Essentially, they already did have all the same information provided by the visitor - they just had managed to avoid thinking about it as a group!

Listen to ZZ Top and get some cheap sunglasses...

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The ether of general relativity therefore differs from that of classical mechanics or the special theory of relativity respectively, in so far as it is not 'absolute', but is determined in its locally variable properties by ponderable matter.

Albert Einstein, "On the Ether", 1924

Bong

But that isn't permanent. Massive brain trauma generally is.

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Quaeso quousque humi defixa tua mens erit? Nonne aspicis, quae in templa veneris?

The chief declares a brown-eyed person must go first.

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Lighten up! This is a stellar board! Author: duh.

"The Sun, with all the planets revolving around it, and depending on it, can still ripen a bunch of grapes as though it had nothing else in the universe to do..." Author: Galileo supposedly.

Maybe one of the blue-eyed people can lie and say that they didn't hear the anthropologist.

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Quaeso quousque humi defixa tua mens erit? Nonne aspicis, quae in templa veneris?

The blue-eyed people don't know they're blue-eyed. Who tells one to lie?

Maybe I'm not understanding how the tribe progresses to mass suicide, then...

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Quaeso quousque humi defixa tua mens erit? Nonne aspicis, quae in templa veneris?

This raises an interesting point. Unless the villagers assume that everyone has heard and understood the anthropologist's remark, they can't draw conclusions from the other peoples' lack of action.

Now this person, call him W, would only "know" that he had blue eyes after the meeting on the fourth day. He would feel confident about his eye color as long as he believed that at least one other blue-eyed person, say X, had heard the anthropologist and that X believed that at least one other blue-eyed person, say Y had heard the anthropologist and that X also believed that Y believed that at least one other blue-eyed person, say Z, had heard the anthropologist. W would believe this because otherwise X would have committed suicide on the third day because of Y's lack of action on the second day which would have resulted from the lack of action by Z on the first day. W would still be morally compelled to commit suicide on the fifth day, however.

If W waits until he knows he has blue eyes, he cannot promulgate his lie until after the fourth day. This delay will certainly arouse the suspicion of the other members of the tribe. As the above argument indicates, to feel certain of his own eye color, another blue-eyed person does not have to believe that W heard the anthropologist, only that there exists a chain such as the one that W relied upon. The chain would not have to actually include W.

Furthermore, the others may not believe W's lie, even if they pass off his suicide as just the result of a bad hair day.

Of course, anyone could tell a similar lie at any time before knowing his own eye color. We'd call it a white lie because it couldn't do any harm in any case.

The idea of raising some kind of doubt is a good one. To invalidate an alleged proof, I don't need to disprove the proposition. I need merely show that we cannot be 100% certain of the conclusion. As long as there is the slightest doubt, the slghtest possible loophole, we can't really say we know. If a tribe member doesn't know his eye color, he doesn't have to commit suicide. Looked at this way, how could a tribesman really ever know that everyone had heard the anthropologist and made the appropriate deductions. There is always some modicum of doubt about what has actually transpired in the course of human affairs - who has heard, done, and thought what.

Well, eventually they learn, but all blue-eyed people learn at the same time.

I agree with this, but it goes even further. Not only do they all need to hear it, they all need to know everyone else heard it. But they also need to know that everyone else knows everyone else heard it, etc.

I think it must be something along these lines, but now we need Ken G to tell us if lying is allowed