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Reduce the problem to 2 blue-eyed people and it should be more clear. If Alice and Bob are the only people with blue eyes, then yes, Alice might think that the

Reduce the problem to 2 blue-eyed people and it should be more clear. If Alice and Bob are the only people with blue eyes, then yes, Alice might think that the speaker was only talking about Bob. But when Bob fails to sacrifice himself the next day, that must be because he also sees a person with blue eyes, and that can only be Alice.

vacri 11y ago
It's different with only two people than it is with multiple. When there's only one other person and they don't act the next day, then the logic works. But when there are numerous people and there is no reason to start counting, then it doesn't extrapolate out. Put more clearly: Foreigner says "blue eyes!". n is 2. If you have blue eyes and you don't see the other blue-eyed person top themselves, you conclude that you also have blue eyes as does the other person, and it's belly-opening time. But when n is 100, that initiation is missing. No-one tops themselves the next day? Hardly suprising - there are a hundred of the buggers. There is no reason to start counting, no "hang on, why didn't ol' blue eyes over there kick the bucket?". And, given that these are humans and not cronjobs, no-one is going to be patiently waiting day in, day out for 100 days to see when they'll all kill themselves. Drama can't even fester, since the tribesfolk are forbidden from talking about the issue. Life goes on, and over three months later, the foreigner's statement wouldn't cause a bloodbath :) TL;DR: if you want to make a fancy logic puzzle, don't use 'humans with bizarre rules' as your subjects. :)
- knughit 11y ago
  You aren't applying all possible logical reasoning about the situation (such as the characters recursive mental models of each other's mental models), unlike the hypothetical completely rational characters.
  - vacri 11y ago
    I think you've missed my point. At low n, yes, that recursion works. But once you get to the point where you can see that each [other] blue-eye can see multiple blue-eyes, there's no real reason to start counting. There's nothing to logically deduce if the people aren't mentally counting, as keeping that mental count is a fundamental part of the algorithm. If n is 7, for example, then a blue-eyed tribesperson would see that the other blue-eyes can see [at least] the remaining 5. And as such, there is no reason to start counting. There's no "hey, that guy didn't do anything!" to start the process going, as there would be with low n. The algorithm is separated from it's starting conditions. Also, the characters are definitively not 'completely rational', as they're also described as being 'devout' :)

vacri 11y ago

It's different with only two people than it is with multiple. When there's only one other person and they don't act the next day, then the logic works. But when there are numerous people and there is no reason to start counting, then it doesn't extrapolate out. Put more clearly: Foreigner says "blue eyes!". n is 2. If you have blue eyes and you don't see the other blue-eyed person top themselves, you conclude that you also have blue eyes as does the other person, and it's belly-opening time. But when n is 100, that initiation is missing. No-one tops themselves the next day? Hardly suprising - there are a hundred of the buggers. There is no reason to start counting, no "hang on, why didn't ol' blue eyes over there kick the bucket?". And, given that these are humans and not cronjobs, no-one is going to be patiently waiting day in, day out for 100 days to see when they'll all kill themselves. Drama can't even fester, since the tribesfolk are forbidden from talking about the issue. Life goes on, and over three months later, the foreigner's statement wouldn't cause a bloodbath :) TL;DR: if you want to make a fancy logic puzzle, don't use 'humans with bizarre rules' as your subjects. :)

knughit 11y ago
You aren't applying all possible logical reasoning about the situation (such as the characters recursive mental models of each other's mental models), unlike the hypothetical completely rational characters.
- vacri 11y ago
  I think you've missed my point. At low n, yes, that recursion works. But once you get to the point where you can see that each [other] blue-eye can see multiple blue-eyes, there's no real reason to start counting. There's nothing to logically deduce if the people aren't mentally counting, as keeping that mental count is a fundamental part of the algorithm. If n is 7, for example, then a blue-eyed tribesperson would see that the other blue-eyes can see [at least] the remaining 5. And as such, there is no reason to start counting. There's no "hey, that guy didn't do anything!" to start the process going, as there would be with low n. The algorithm is separated from it's starting conditions. Also, the characters are definitively not 'completely rational', as they're also described as being 'devout' :)