Counterintuitive Facts (13): 'Everyone Knows' and 'Everyone Knows That Everyone Knows' Are Completely Different Things

I. An island has 100 people, all with red eyes. The island has three rules:

1. No mirrors allowed
2. No telling anyone their eye color
3. If someone learns they have red eyes, they must commit suicide that night

II. Everyone can see the other 99 people's eyes. Everyone sees 99 pairs of red eyes. But because no one breaks the silence, everyone can wonder: "Maybe I'm the only one with blue eyes?" So, day after day, everyone is safe.

III. Until one day, a foreigner comes to the island. He stands in the central square and says one sentence: "There are red eyed people here."

IV. This sentence seems like stating the obvious. Everyone can see it. What new information is there?

V. But the result is: On the 100th night, all 100 people commit collective suicide.

VI. Why? Because the foreigner established C