Problem in logic

[Yoda]

I don't see the distinction at all, but the poorly written riddle does actually say both:

she says the following:
"I can see someone who has blue eyes."
Who leaves the island, and on what night?
There are no mirrors or reflecting surfaces. It is not a trick question, and the answer is logical. It doesn't depend on tricky wording or anyone lying or guessing, and it doesn't involve people doing something silly like creating a sign language or doing genetics. The Guru is not making eye contact with anyone in particular; she's simply saying "I count at least one blue-eyed person on this island who isn't me."

But my problem with the I see "someone" with blue eyes thing is that.... it's still obvious from the initial conditions. You know she sees "someone" with blue eyes, because you see it too. It's only important in the base case where you know she sees blue and you don't see any blue therefore you're blue.

In the actual case the perfect logician would also see that she sees someone with brown eyes, which I guess in your terminology would introduce a conflicting probability tree.

 

[Scout101]

Agree that they can see people with blue eyes before the announcement, so that part isn't new information. What it DOES do, though, is take a ton of options and boil it down to a binary yes/no equation they can solve for.

Before the Guru talks, each person can see a ton of blue and brown, and one green. They can't make any decision about their own color. Could be blue, brown, green, purple, red, whatever. There's no information to deduce that from, and can't set up anything that gives you that.

They could probably just announce that they are going to solve for blue on their own, and figure it out the same way they end up doing, but without communicating their intent, no way to do it. By the guru setting up a condition to test for, they can sort out blue or not blue by the process mentioned. Otherwise, you can see the same people as before, but no one EVER leaves, because they have no information about their own eye color to move on.

The Guru does't impart any information they couldn't already see, but it allows them to start the sequence without having to communicate their intent.

 

[Yoda]

But the intent itself isn't based on logic... it's just based on what the Guru is emphasizing. There is no logical reason to do anything other than think to yourself "You can see someone with blue eyes? Well no shit, obviously, there's either 99/100 of them/us! (or 100/101 if said by a brown).

 

[Scout101]

But it reduces the conditions to a set that is solveable. otherwise, you can't get to an answer, because even if you were the only blue on the island, you still couldn't leave.

Without being given the blue/not blue condition to work from, how does looking at a bunch of blues and browns give you anything to work from? You can still be any color physically possible, and you can see at least 3 options (blue, brown, green). The Guru is just giving everyone the common basis to solve for blue. Otherwise, no one can do anything. They might as well assume they all have green eyes and try to leave.

The 'i see at least one set of blue eyes' isn't the information they receive, it's that they can now SOLVE for blue.

 

[Ha'kiv]

The act of leaving is based on the assumption of being blue. The actual blues will leave one turn earlier than the others, so the others will never leave because they will see the blues have already left, and thus they aren't blues.

But if, as you say, what Guru says is of no importance, why does this matter? It doesn't work without the Guru, yet it would seem the Guru is only being captain Obvious.

 

[boobatuba]

The act of leaving is based on the assumption of being blue. The actual blues will leave one turn earlier than the others, so the others will never leave because they will see the blues have already left, and thus they aren't blues.

But if, as you say, what Guru says is of no importance, why does this matter? It doesn't work without the Guru, yet it would seem the Guru is only being captain Obvious.

You have a perfectly valid point. The guru doesn't really impart any new information, just gives the people a binary condition to solve for (I'm the one she's talking about/I'm not the one she's talking about).

 

[Ha'kiv]

So the Guru does not give any new information, yet it is impossible to solve the problem without her not giving any new information.

 

[boobatuba]

So the Guru does not give any new information, yet it is impossible to solve the problem without her not giving any new information.

She introduces a solvable, binary situation. That doesn't have to be "new information."

 

[Yoda]

But it reduces the conditions to a set that is solveable. otherwise, you can't get to an answer, because even if you were the only blue on the island, you still couldn't leave.

Without being given the blue/not blue condition to work from, how does looking at a bunch of blues and browns give you anything to work from? You can still be any color physically possible, and you can see at least 3 options (blue, brown, green). The Guru is just giving everyone the common basis to solve for blue. Otherwise, no one can do anything. They might as well assume they all have green eyes and try to leave.

The 'i see at least one set of blue eyes' isn't the information they receive, it's that they can now SOLVE for blue.

I'm still not buying this. But I probably won't be able to post more on the subject for a while. "I see at least one set of blue eyes" is exactly the information they receive, and they already know that it's true. I don't see how they can now solve for blue where they couldn't before unless they are reading into that statement something which isn't there... The Guru didn't say something like "The blue people should go first." Taking that meaning as *wink wink* *nudge nudge* doesn't strike me as logical.

She introduces a solvable, binary situation. That doesn't have to be "new information."

Why can't you come up with that situation yourself? It's trivial. They said that these are people with perfect logic, not computers in desperate need of programming. It's not actually solvable because there's no reason for everyone to solve for blue. They could assume brown too. Or I suppose more logically solve for nothing, because there isn't enough information.

 

[boobatuba]

I'm still not buying this. But I probably won't be able to post more on the subject for a while. "I see at least one set of blue eyes" is exactly the information they receive, and they already know that it's true. I don't see how they can now solve for blue where they couldn't before unless they are reading into that statement something which isn't there... The Guru didn't say something like "The blue people should go first." Taking that meaning as *wink wink* *nudge nudge* doesn't strike me as logical.

Once again, the guru doesn't say "I see at least one set of blue eyes." She says "I see someone with blue eyes."

Can't you see the difference between the two and how it introduces a binary situation for everyone else on the island?

 

[Ha'kiv]

So, no guru. You have blue eyes, and you see another person with blue eyes and two more with brown. The blue-eyed person does not leave on day one so you assume that.. your eyes could be just about any color in the universe. The browns don't leave on day two so you assume that.. your eyes could be just about any color in the universe. Same for the rest of them. Am I wrong? Yet if the Guru says what she says.. it obviously works out.

 

[boobatuba]

So, no guru. You have blue eyes, and you see another person with blue eyes and two more with brown. The blue-eyed person does not leave on day one so you assume that.. your eyes could be just about any color in the universe. The browns don't leave on day two so you assume that.. your eyes could be just about any color in the universe. Same for the rest of them. Am I wrong? Yet if the Guru says what she says.. it obviously works out.

You're exactly right.

 

[Ha'kiv]

Well then.. would seem like a bit of a paradox.

 

[Ha'kiv]

Speaking of problems - should I name my kitten Jean-Luc or Spock?

 

[boobatuba]

Well then.. would seem like a bit of a paradox.

Not at all. The problem is unsolvable until the guru introduces the binary situation (she's talking about me/she's talking about someone else).

Very simple.

ETA: Also very simple is the edit feature of each post that I just used on this one.

 

[Ha'kiv]

But.. there's no new information being provided. Nevermind, nevermind. Lets all just agree on the fact that we're lucky we have mirrors.

*Referring to my double post, I assume?

 

[Lindley]

There's no direct new information being provided now. But there would be new information being provided if there were only one blue-eyed person on the island. And that's the indirect information which is the entire key to the logic.

There are two blue-eyed people, one of whom is "you". The guru speaks; they aren't giving anyone any new information, but you don't know that. For all you know, your eyes are not blue, and thus the guru's statement would have given the other blue enough information to leave. Because that is not the case, you now gain the information that you must also have blue eyes.

There are three blue-eyed people, and you can observe two of them. The guru speaks; she isn't giving any of you direct new information, since everyone can all see at least two blues. If you didn't have blue eyes, then you would expect the other two to behave as above, and leave on the second night. But since they don't, that gives you the additional information that you must have blue eyes.

It's tempting to wonder whether we're losing information by focusing on only one individual's thought process. However, since we've chosen the individual arbitrarily, that isn't the case. Everyone's thought process is symmetric.

There are four blue-eyed people......

 

[Ha'kiv]

But there's not.

 

[DimesDan]

*Referring to my double post, I assume?

Referring to your multiple double posts more like it.

Oh, as for the question at hand, I've got no idea, I'm not very good at riddles and logic questions.

 

[Ha'kiv]

I apologize for my posts.