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I understand the logic behind the solution and it makes full sense to me. What I still struggle with is: what specific piece of information is being passed by t
by po 16y ago
I understand the logic behind the solution and it makes full sense to me. What I still struggle with is: what specific piece of information is being passed by the foreigner. I get that it is "everyone knows everything" but for n > 1 everyone already knew the specific fact that was being communicated. What is special about the announcement that drives it? It seems like it is actually "the timer starts now!"
- lkozma 16y agoThe specific information which was not known and is known after the foreigner's speech is that "everyone knows that everyone knows that everyone knows that (repeated n or more times) there are people with blue eyes." This was known only up to n-1 repetitions. To infer this new statement, the islanders have to be aware that the others are listening, they understand, they know that everyone understands, etc. etc.
- po 16y agoTo infer this new statement, the islanders have to be aware that the others are listening, they understand, they know that everyone understands, etc. etc. That's deeply unsatisfying because we are told that everyone is capable of making the observation that is communicated right from the beginning for n > 1. What prevents the group from acting as soon as the situation starts but before the foreigner speaks? The message adds information to the system but it is not that there is one person with blue eyes, i.e. what was explicitly stated. I think it adds information about the time at which an action will or will not occur. The information passed is "you can expect something to happen to the people with blue eyes tomorrow."