Everyone knows that green eyed-ness is just a social construct anyway.
‘Raise a people’s army and smash the state’ is the correct answer.
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I am not aware of making any incorrect statement, or of making any statement that contradicts your earlier statements, or of making any statement that contradicts any of the solutions you linked.
I was just disagreeing with how the concept of “common knowledge” was explained in the video.
I never disagreed with any of the inductive proofs; most people’s trouble with understanding the puzzle stems from not knowing what new information was added to the system and thus being unable to believe that the situation changed.
Three of your linked solutions explain the point (n-th order knowledge vs. common knowledge) quite nicely. The xckd solution gets by without mentioning the question of what new information is actually added. It thus leaves itself open to “but why” arguments, but it is nonetheless correct.
The problem I had with the video is that it doesn’t make a clear distinction between second-order knowledge (everyone knows that everyone knows that there are green-eyed people) and common knowledge. In fact, the phrasing used in the video is such that anyone who does not know the definition of “common knowledge” runs a high risk of confusing it with “second order knowledge”. And that’s what I consider a “bungled explanation”.
This is what, in my opinion made @Spencer75 say “No one ever leaves. The mathematical proof has an error somewhere”.
And just to prove my point, @jsroberts answered with the commonly given “synchronization” explanation, which I also consider to be wrong:
So… to answer the puzzle correctly, all you need is the induction; the fact that no one left before is given as a fact as part of the puzzle, we do not need to prove or explain it. But an explanation of the solution needs to point out why the induction did not work before, and that is because of the lack of common knowledge or n-th order knowledge, and not because of any lack of “synchronization”.
Ok, I think we’re on the same page then. My initial response was to Aidanh, who believed that the information wasn’t necessary. I explained why it was necessary, and when you replied with an explanation to me, it sounded like you were again telling me again why the information wasn’t necessary.
But I think maybe we were misunderstanding each other.
Just to be entirely clear then:
- With no information given by an outside person, it doesn’t matter how many green-eyed people there are, none of them can ever leave.
- Once the information is given, it doesn’t matter how many green-eyed people there are, eventually they will all be able to leave.
Fair enough. You replied to Spencer75 who said “The puzzle is famously difficult because the answer is incorrect,” and suggested that no one can ever leave, even with the external information.
You replied “That’s what I think too.” That’s what I was responding to.
But I see that maybe you may have been agreeing to a different thing that he was saying.
To be clear, regardless of whether or not the explanation in the video is accurate, Spencer75’s point is not correct: It is not the case than no one can leave after they are told the information. They can leave.
You are right, though, that the “synchronization” argument is wrong. After all, there are many ways the prisoners could be synchronized. They could all arrive at the island on the same day. But, as you say, this would not be sufficient for them to solve the puzzle.
Indeed. I was agreeing with his claim that there was something wrong about the answer, and directly contradicting his/her theories of what would be a correct answer. My agreement was strictly limited to the first few sentences.
And of course, I admit it’s an exaggeration that “the answer” is wrong, it’s just that half the people trying to explain it use incorrect or inaccurate language.
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