The lie couldn't introduce the uncertainty, merely magnify its credibility. If I had previously been certain (meaning logically certain as opposed to psychologically certain), then I would not believe the lie. If you lie to me by telling me that my name is George, I won't believe you because I am certain that it is not true. If you tell me that my (putative) wife is cheating on me, then I might believe you.

Nick,
You and Ken mention this every time I understate the extent of what the members of the tribe have learned. I state only as much as I need to state to make whatever point I am currently attempting to make. Nevertheless, the solution to the problem may lie in the difference between what I have been stating and your more complete statement.

Well, they could ask the anthropologist to select a bluey, walk up to that person, and say "your eyes are blue." If the anthropologist does it, it seems to me that saves everyone but one. If the anthropologist spends several days posting on BAUT, well then...

OK, sorry about that, not trying to nitpick, just not sure sometimes how much everyone knows

Colored lenses or blinding won't help because each member already knows the eye color of each of the other 19 members of the tribe. The only additional information he/she will need is the knowledge of who has or has not committed suicide at each meeting.

Becoming rabbits won't help because anyone who was not present at the meeting is out of the loop, as someone, I believe Ken, pointed out earler. For the same reason, there would be no point travelling to the mainland and attempting to make new converts.

Not implying that you were nitpicking, merely pointing to the possible location of the key to the solution. The problem is a real toughie. It seems to be withstanding coffee, everything. My greatest fear is that Ken will become impatient and start giving us hints.

This problem has made me a senior member.

I agree, it gives me a headache whenever I think about it It seems to me my last solution (which is pretty close to what some others have posted, the only difference is you don't actually murder someone, you give him/her information that results in suicide) saves all but one. If there is a way to save them all, I haven't found it. And the clock is ticking on this tribe

We may assert that everyone already knew there were only two colors, that would not cause a problem. The point is, just as there is a difference between knowing and knowing that someone else knows, so is there a difference between knowing someone else knows, and knowing someone else knows that someone else knows, and so on.

That's right, had there been a green-eyed person in the back that the visitor failed to notice, then this would save all but the blue-eyed minority. To fix this up, we must assert the visitor met each person and shook their hand, and in his statement he added 'after meeting you all and staring carefully into your eyes, I can see that you are a lot like my family, in that both brown and blue eyes are in evidence but no other possibility".

I would allow lying, but only if it were plausible. A weak lie such as "I was asleep and didn't hear all the commotion, what's going on?" wouldn't cut it, because everyone could see that the person was in fact awake and aghast at the eye-color reference. I don't know if a plausible lie can save them, I have something else in mind that is neither death nor lying, but in light of the strength of their commitment to their religious community, it would be a pretty significantly bad result. Completely disbanding the tribe or the religion is unthinkable, as is murder or telling anyone their eye color.

We cannot disrupt the first phase. It is a fait accompli. We could only attempt to raise questions about its interpretation.

In order to disrupt the second phase, we would need to raise doubt about who has or has not committed suicide or about their thought processes or what they knew. Any plan that involves saving most of the tribe at the expense of more than one member would be inferior to Atraxani's murder plan. I don't think we want to sacrifice even one person. Well, I'm relieved by that point.

We need to raise doubts about the reason why no one has committed suicide.

Of course, since I'm confused at this point, who knows?

Note the other problem with pretending you didn't hear-- what if everyone believed you, and your eyes were brown? Would this help the situation?

Or to prevent the non-occurrence of suicide, as per my solution. But as Ken G hasn't commented, I'm guessing that's not it...

Perhaps the solution to prevent the mass suicide is to break the logic chain that leads up to the correct number. Before the first day pases, tell everyone (as a group so all know that all know) that "there are not two people with blue eyes."

Can I have two aspirin now?

Do you mean the solution of telling a blue-eyed person their eye color? That would constitute murder, in effect! We can't ask anyone to do that, not even to save the tribe. But there is something we might be able to ask the tribe to do, without anyone knowing their eye color, or dying, though it is still not a happy conclusion for those involved.

Could they be skeptical? What evidence was given that the visitor is not lying about what eye-colors he saw.

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That is an interesting suggestion, and also cuts to the heart of what does "knowing" mean. But let us say that it is knowing like in a court of law, beyond reasonable doubt about the eye color. Here it is pretty clear beyond a reasonable doubt that the visitor would not lie, and it is pretty clear that no one in the tribe would perceive a reasonable doubt, or suspect anyone else of having reasonable doubt, etc. Remember, this tribe is much more logical than normal humans, and are well aware of their gift/curse. It is their highest value, along with the belief that one may not live with the knowledge of their own eye color. That doesn't seem like a very logical value, but this collision of logic and belief is an interesting subtext with no direct bearing on the intended puzzle. For example, trying to convince them that it is illogical to care what their eye color is would not be considered fair game, unless this were a Star Trek episode (in yet another example of Kirk's personal "interference directive")!

Could the chief declare that the anthropologist was some sort of demon spreading lies to destroy the tribe?

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It would be too obviously a disinformation campaign. Remember, this tribe is much more logical than standard human populations, even if they do have one particularly acute superstition! (Furthermore, the statement clearly wasn't a lie!)

Okay... if the requirement is that the suicide must be done in front of the whole tribe, could one person steal the anthropologist's boat and never come back? Not a full tribe = no suicide.

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Yes, that could indeed happen. Under what circumstances would this save the tribe?

Well, I'm expect you have another solution, but I'm not swayed by your argument. This is a matter of life and feath. To base a momentous decision on one offhand remark by an unkown visitor about a taboo subject, calls for the highest skepticism. No one cross-examined the visitor. The visitor didn't swear to tell the truth. He had no idea of the gravity of his staement. He could be lying. He could be mistaken.

There is only trust and no verification. You call these people logial? As is, the case doesn't hold water.

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I would argue this is skepticism taken to the level of self-denial. What reason would the person have to lie, and why would he not be considered authoritative to testify to the color of people's eyes? "Objection, your honor, this man is not an opthamologist" just doesn't cut it for me. But if it works for you, a logical person, then I suppose we cannot rule it out for the tribe to think this way. Like I said, there is a pretty deep issue of what does it mean to "know" something, and what do we know about how others like us will be thinking. But let me ask you this-- what happens if the 5 blue-eyed people think like me, instead of like you? What happens to the tribe?

This is probably the key to the solution. My stated interpretation of what they learned is like skim milk. montebianco's is like whole milk
just as it comes from the cow, including the layer of cream floating on top. I've been focusing on the underlying milk. I need to focus on the cream.

If any tribe member at all left the island permanently some time before the suicide was to take place, the suicide would become impossible. It needs to be done in front of the whole tribe. If a member is missing, the whole tribe isn't there, and the suicide cannot happen.

Also, even after the escaped person dies, there can be no suicide. No one can know if the person is dead or not, so they can never know if the entire tribe is present for a meeting where a suicide can occur.

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Oh, I see what you mean, I specified it had to be done in front of the whole tribe. I really just meant the whole tribe as it comprises the morning of the meeting, not counting anyone who has left the tribe. You are right by the letter of how I wrote it, but consider the new generalization. The rationale is, if you as an individual know your eye color, you are disgraced and may only recover your honor before your tribe and yourself by ritual suicide at the morning meeting.

A tribe member could only leave if he had not yet discovered the color of his own eyes. If he already knew his eye color, he would be duty-bound to stay and commit suicide. Each member of the tribe would know both the defector's eye color and the fact that he had not known his own eye color at the time he left. These facts would be sufficient (I think - I'm beginning to lose whatever wits I started with) for each bluey to eventually determine his or her own eye color. Each would then be morally bound to attempt to perform his/her grisly duty. They would have to attempt to track down the escapee, haul him back, and proceed - or else decide that by leaving he had forfeited his menbership in the tribe.

Ah, but the person doesn't know his eye colour until later. He needs to see people not killing themselves first. He can leave because he doesn't know his eye colour and is thus not duty-bound to stay. And if he isn't bound to stay, no one would track him down.

Anyway, this isn't the solution that Ken is looking for.

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

If the person left in time, he/her, himself/herself, would be saved. Maybe everyone should just split. They just need to be very careful in their new environments.