You know that I know that you know that I know – information management and point of view

Many years ago, I heard about a famously difficult logical puzzle sometimes called the blue eyes problem.

The problem goes: there is an isolated island with 201 people—100 with blue eyes, 100 with brown eyes, and one green eyed guru. They’re each perfect logicians and can each see everyone else at all times, but they may not communicate in any way. Once per day, at midnight, a ferry visits the island, and every person who knows they have blue eyes must leave immediately. The only person who may speak is the guru, and one day, the guru says, “I see someone with blue eyes.”

The question: how many people leave, and when?

I’m going to set aside the solution to the problem for a moment and tell you what I think makes this a problem: point of view. This problem is told from an omniscient point of view, but the actual actors solving the problem (the clue to this being “all of them are perfect logicians”) are the individual islanders. So step one, change your point of view. If you were an islander who did not know your eye color, how would you figure it out?

The second part is that it’s just too complex. You have to simplify it to three islanders (the guru, one brown eyed person, and one blue eyed) to get a handle on how the information flow works. On day one, the blue-eyed person looks around, sees nobody with blue eyes, knows they’re it, and leaves. For two blue eyed people, both blue eyed people see another blue-eyed person, go to bed, and wake up with nobody having left. They have to conclude, then, there are two blue eyed people, and both will leave. This scales. A third blue eyed person, perfect logician, knows 2 blue eyed people will leave on day 2, so there must be a third and they’re it, and so on.

One of the most difficult parts to wrap your head around is why anyone would leave in the first place. The guru is giving people new information. But what? Everyone can already see there are people with blue eyes. By saying it aloud, everyone suddenly knows that everyone knows that someone has blue eyes.

I’ve heard a very surreal illustration of what new information is being shared. If 3 friends are sitting at a table and you, evil genius, pass friend A a note saying “There’s a giant spider above you, and B and C know it” then that’s one kind of knowing. But what isn’t communicated there is whether B and C KNOW that A has now been informed. Knowing a piece of information, knowing that others know it, and knowing that they know that you know is called “common knowledge” in formal logic. It’s the basis of so many of these super hard brain teaser puzzles that once you wrap your head around the concept, they become a lot easier.


Two things strike me: first, that point of view puzzles and their illustrations naturally skew toward the uncanny. Spiders and mysterious islands and gurus who may speak and others who may not. Murder mysteries as a genre also lean on who knows what and who knows who knows what, but it’s very interesting that a corpse really isn’t necessary to make me squirm.

Second, to me, this has implications on point of view that seem counter-intuitive. The omniscient gives you all the information, which is the problem. It’s exactly the wrong point of view. There’s too much information, presented without an organizing agency or physical limitation. It’s used to conceal. It’s no coincidence Agatha Christie wrapped up a few 3rd person mysteries with a 1st person written confession.

I’m not arguing for the relative merits of first or close third and against omniscient. Omniscient isn’t unclear and therefore bad here; the puzzle is the intended effect, and then the solution is also a good use. What I am arguing is that point of view isn’t just camera placement, close or far. It’s how information is managed in a story, and can be used for an intended effect.

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