### The Blue Islanders Puzzle - Real answer?

So I recently read about the Blue Islanders Puzzle:

There is an island upon which a tribe resides. The tribe consists of 1000 people, with various eye colours. Yet, their religion forbids them to know their own eye color, or even to discuss the topic; thus, each resident can (and does) see the eye colors of all other residents, but has no way of discovering his or her own (there are no reflective surfaces). If a tribesperson does discover his or her own eye color, then their religion compels them to commit ritual suicide at noon the following day in the village square for all to witness. All the tribespeople are highly logical and devout, and they all know that each other is also highly logical and devout (and they all know that they all know that each other is highly logical and devout, and so forth).Of the 1000 islanders, it turns out that 100 of them have blue eyes and 900 of them have brown eyes, although the islanders are not initially aware of these statistics (each of them can of course only see 999 of the 1000 tribespeople).

One day, a blue-eyed foreigner visits to the island and wins the complete trust of the tribe.

One evening, he addresses the entire tribe to thank them for their hospitality.

However, not knowing the customs, the foreigner makes the mistake of mentioning eye color in his address, remarking “how unusual it is to see another blue-eyed person like myself in this region of the world”.

What effect, if anything, does this faux pas have on the tribe?

This is a very interesting puzzle, and if you read the comments on the linked page, you'll see all sorts of fascinating arguments about what will happen. I pondered this puzzle on and off for a few days, it's a real noodle scratcher. I like how you must reason about people, who will also reason about other people. I see clear relationships to distributed computing and emergent behaviors, things I find really interesting.

But after a while something about this question really bugged me, and I think I finally figured out why. It's an flawed question.

The problem is it assumes the existence of someone or something that exhibits perfect logic. Though in this question, it phrases it as "highly logical", while different from "perfectly logical" the implication, I believe, is the same.

However, if the implication is not the same as perfectly logical, the question is meaningless until we quantifiably define what "highly" means in the phrase "highly logical". So as stated, the question is incomplete, we can't apply logic to how the islanders would act if all we know is they will be applying an indeterminate amount of logic to decide how to act.

But if the implication is that "highly logical" means "perfectly logical", then that too is nonsensical. Why? Because there is no such thing as perfect system of logic. Then we try to apply our various systems of logic and methods of proof to reason about something that is proved to not be possible, of course we come up with all sorts of conflicting answers.

I take the position the question has no correct answer, it's a flawed question.

Posted February 12, 2008 11:24 AM