Terry Tao: The blue-eyed islanders puzzle
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Terry Tao: The blue-eyed islanders puzzle
1–10 of 21 posts
Re: Terry Tao: The blue-eyed islanders puzzle
#2Yay, I believe the narrative on that one was poor. It lacks some details and makes you ask yourself lots of questions that are not actually part of the enigma.
xkcd has the same enigma, with a better wording (with no ambiguities): http://xkcd.com/blue_eyes.html
Re: Terry Tao: The blue-eyed islanders puzzle
#3Yay, I believe the narrative on that one was poor. It lacks some details and makes you ask yourself lots of questions that are not actually part of the enigma. xkcd has the same enigma, with a better wording (with no ambiguities): http://xkcd.com/blue_eyes.html
Seriously, the author says there are 2 "plausible" arguments. Obviously, he got it wrong the first time and won't let it go!
Re: Terry Tao: The blue-eyed islanders puzzle
#4Yay, I believe the narrative on that one was poor. It lacks some details and makes you ask yourself lots of questions that are not actually part of the enigma. xkcd has the same enigma, with a better wording (with no ambiguities): http://xkcd.com/blue_eyes.html
Seriously, the author says there are 2 "plausible" arguments. Obviously, he got it wrong the first time and won't let it go!
Fine, they all decided to watch tv instead, since they logically know thinking could get them killed.
Re: Terry Tao: The blue-eyed islanders puzzle
#5Yay, I believe the narrative on that one was poor. It lacks some details and makes you ask yourself lots of questions that are not actually part of the enigma. xkcd has the same enigma, with a better wording (with no ambiguities): http://xkcd.com/blue_eyes.html
Seriously, the author says there are 2 "plausible" arguments. Obviously, he got it wrong the first time and won't let it go!
Well, the problem is fundamentally that the people should've been playing the game before anyone said anything, so there's some confusion as to why the game only starts when the guru mentions a fact that's already self-evident.
That's a problem in both the grandparent link and xkcd's story.
Re: Terry Tao: The blue-eyed islanders puzzle
#6Earlier quoted context omitted.
Seriously, the author says there are 2 "plausible" arguments. Obviously, he got it wrong the first time and won't let it go!
Well, the problem is fundamentally that the people should've been playing the game before anyone said anything, so there's some confusion as to why the game only starts when the guru mentions a fact that's already self-evident. That's a problem in both the grandparent link and xkcd's story.
You don't think the guru provides more information? I don't follow.
Re: Terry Tao: The blue-eyed islanders puzzle
#7Earlier quoted context omitted.
Seriously, the author says there are 2 "plausible" arguments. Obviously, he got it wrong the first time and won't let it go!
Well, the problem is fundamentally that the people should've been playing the game before anyone said anything, so there's some confusion as to why the game only starts when the guru mentions a fact that's already self-evident. That's a problem in both the grandparent link and xkcd's story.
That's exactly the interesting point here: the foreigner states something self-evident (there is someone who has blue eyes), and yet it will kill all blue-eyed people, who would otherwise have been fine. Without the foreigner, the inductive chain cannot start at n=1.
Re: Terry Tao: The blue-eyed islanders puzzle
#8Earlier quoted context omitted.
Well, the problem is fundamentally that the people should've been playing the game before anyone said anything, so there's some confusion as to why the game only starts when the guru mentions a fact that's already self-evident. That's a problem in both the grandparent link and xkcd's story.
That's exactly the interesting point here: the foreigner states something self-evident (there is someone who has blue eyes), and yet it will kill all blue-eyed people, who would otherwise have been fine. Without the foreigner, the inductive chain cannot start at n=1.
Sure it can. Take the 100 brown, 100 blue problem xkcd states. If they all kept their eyes closed and then starting today opened them, the end result would be what you claim the foreigner would've instigated: people remove themselves when they figure out their eye color, and after enough time passes, if a bunch of people are still there who you believe should be gone, you must be part of the cause of uncertainty.
Re: Terry Tao: The blue-eyed islanders puzzle
#9Earlier quoted context omitted.
Well, the problem is fundamentally that the people should've been playing the game before anyone said anything, so there's some confusion as to why the game only starts when the guru mentions a fact that's already self-evident. That's a problem in both the grandparent link and xkcd's story.
That's exactly the interesting point here: the foreigner states something self-evident (there is someone who has blue eyes), and yet it will kill all blue-eyed people, who would otherwise have been fine. Without the foreigner, the inductive chain cannot start at n=1.
Also, this problem isn't solved by induction. It's solved by recognizing the pattern. You don't need to establish the base case via the outside observer. All you need to know is that the day-based formula works for any number of islanders.
It'd be like proving x^2 - 1 = (x+1)(x-1) for all x by starting with 1 and walking up the integers... Which is to say, not a bad way to prove it, but not necessary when you can logic it out otherwise.
Re: Terry Tao: The blue-eyed islanders puzzle
#10Earlier quoted context omitted.
That's exactly the interesting point here: the foreigner states something self-evident (there is someone who has blue eyes), and yet it will kill all blue-eyed people, who would otherwise have been fine. Without the foreigner, the inductive chain cannot start at n=1.
Sure it can. Take the 100 brown, 100 blue problem xkcd states. If they all kept their eyes closed and then starting today opened them, the end result would be what you claim the foreigner would've instigated: people remove themselves when they figure out their eye color, and after enough time passes, if a bunch of people are still there who you believe should be gone, you must be part of the cause of uncertainty.
No.
Suppose there are only three people with blue eyes. A knows that B can see at least one blue-eyed person. And B knows that C can see at least one blue-eyed person. But A doesn't know that B knows that. A reasons: if I have brown eyes, B can only see one blue-eyed person, ie C. And if B can only see one blue-eyed person, he will reason "if I have brown eyes, C cannot see anybody with blue eyes". Thus, if I have brown eyes, B does not know whether C can see anybody with blue eyes.
Or when there are four blue-eyed people, A's reasoning will be: if I have brown eyes, then B will only be able to see two blue-eyed people. He will then reason according to the above case. So if I have brown eyes, B doesn't know that C knows that D can see at least one blue-eyed person.
By saying "I see a blue-eyed person", the foreigner removes this uncertainty.