21–30 of 94 posts
Earlier quoted context omitted.
They are perfect logicians. It is not especially generous to think they can count (that is, if there are 100 blue eyed members, they can each count the other 99). If each blue eye can see 99 others and nothing happens on day 99, then they know what has to happen on day 100.
But why will a non-blue eyed person not think the same then?
Earlier quoted context omitted.
They are perfect logicians. It is not especially generous to think they can count (that is, if there are 100 blue eyed members, they can each count the other 99). If each blue eye can see 99 others and nothing happens on day 99, then they know what has to happen on day 100.
But why will a non-blue eyed person not think the same then?
Earlier quoted context omitted.
They are perfect logicians. It is not especially generous to think they can count (that is, if there are 100 blue eyed members, they can each count the other 99). If each blue eye can see 99 others and nothing happens on day 99, then they know what has to happen on day 100.
But why will a non-blue eyed person not think the same then?
Earlier quoted context omitted.
They are perfect logicians. It is not especially generous to think they can count (that is, if there are 100 blue eyed members, they can each count the other 99). If each blue eye can see 99 others and nothing happens on day 99, then they know what has to happen on day 100.
But why will a non-blue eyed person not think the same then?
So, what the visitor is providing is really the coordination, the point at which you can measure 100 or 99 days. But doesn't this setup require that there have always been 100 blue eyed people since forever? Any birth or death or all the islanders being crated at once would serve equally well as a timer. It seems like this problem only works because the blue-eyed islanders all know that there are 99 other islanders w…
No, the key is that the foreigner's statement establishes common knowledge at some point in time. What happened before that point in time is irrelevant. > the blue-eyed islanders all know that there are 99 other islanders with blue eyes That's true, but what they don't know (until the 2nd) day) is that all the other blue-eyed islanders know that all the other blue-eyed islanders know that there are 99 other blue-eyed…
Earlier quoted context omitted.
This is the missing element from most explanations I see of this problem. We all look at the n cases from the POV of a blue-eyed person. An outside observer with brown eyes has the same level of information available to him, so it seems to me just as likely that after the first day, each person, regardless of eye color, could reason that nobody left the previous day, so the visitor must have been referring to me. So…
Each blue-eyed person observes 99 other blue-eyed people in the tribe, thus reasoning that he/she has blue eyes on the 100th day. However, each brown-eyed person observes 100 blue-eyed people in the tribe, thus reasoning that he/she has blue eyes on the 101st day (however this does not happen because on the 100th day all the blue-eyed people commit ritual suicide.)
If they knew the color counts, they would know their eye color and all would have to commit suicide. The fact that the tribe still existed means, they didn't know the totals.
For example, if I know there are 100 people with blue eyes and I can count as many without including myself, then I must have brown eyes and must kill myself.
So again, there is no possible way the tribe had any idea what the exact counts where.
As a brown eyed person, there are either 100 blue eyed people meaning I have brown eyes, or there are a 101 blue eyed people and I have blue eyes. If a census was ever taken and the exact number known everyone would have to commit suicide.
Since the visitor didn't mention an exact number then there is still no way to know if you have blue or brown eyes.
However, the tribe now knows that the visitor knows he himself has blue eyes. Will they make him follow their ritual?
Update: OK, after reading the link in the first comment, I get it.
Earlier quoted context omitted.
They are perfect logicians. It is not especially generous to think they can count (that is, if there are 100 blue eyed members, they can each count the other 99). If each blue eye can see 99 others and nothing happens on day 99, then they know what has to happen on day 100.
But why will a non-blue eyed person not think the same then?
Randall Munroe has a much more thorough write-up on (a variation on) this puzzle: http://xkcd.com/solution.html (Though you might want to click his link to the problem description first since his is a variation.)
And for an even more detailed examination of the underlying philosophical issues: http://en.wikipedia.org/wiki/Common_knowledge_(logic) http://plato.stanford.edu/entries/common-knowledge/
What's most interesting about this scenario is that, for k > 1, the outsider
is only telling the island citizens what they already know: that there
are blue-eyed people among them. However, before this fact is announced,
the fact is not common knowledge.
I mean, what bit of information is added here?
Earlier quoted context omitted.
But why will a non-blue eyed person not think the same then?
A non blue eyed person will see that there are 100 blue eyed people and observe them killing themselves on the 100th day. For the blue eyes, if the 99 blue eyes they can see were all of the blue eyes, they would kill themselves on day 99. So the different eye colors have different information. As far as I can see, the brown eyes all kill themselves the next day.