Math Fun

If the guru said “I see 97 with blue eyes”, it would work.
If she said “I see 50 with blue eyes” it would work.
If she said “I see 01 with blue eyes” it would work.

If everyone just picked a number out of thin air, even if they all happened to pick the same number, it would not work.

Not without the Guru imparting information that would go against the logically deduced expected result when going only by what can be seen for definite about the eye colour of all others, and thereby revealing information about the one unknown to any one blue-eyed islander: their own eye colour. THAT is the key. They are the ONLY two possibilities.

As Carleas says, if the Guru said she can see 97 people who have blue eyes, and they can start their count from 97, if the Guru said she can see 50, they can start from 50, just like they can start from one if and only if the Guru says she can see someone who has blue eyes.

Really?
Is the number, the guru says, some secret code which allows them to skip days?

It’s a “secret code” in that it’s able to give extra information to the blue-eyed islanders under special key circumstances in the deductive process, even though at other points it just seems obvious to anyone.

And yes, the amount of islanders she refers to makes a difference that could skip days. Consider:
If she said she saw 100 blue eyed islanders, each blue would see 99 and deduce the 100th must be themselves. They all leave at the first opportunity. Each brown would already see 100 blues and think that no more information was added to what they could already see AND deduce.

If she said she saw 99 blues, and there were only 99 blues, they would leave by the same logic.
If she said she saw 99 blues, and there were 100 blues, each blue would be waiting for the 99 that they see to leave on the first day. They don’t because they’re all expecting others to leave and not themselves. They would each have deduced that there were either the 99 blues that they could see, or that there were 100 and each of them were the 100th after the 99 they each counted. Therefore since it’s not the former, known and tested after the first day, they all leave on the 2nd.
If she said 98 and there were 100, the same logic continues in the way we should be used to by now. She can say any number and make it solvable, just as long as the number is less than or equal to the actual total amount of islanders with the eye colour mentioned by the Guru, and as long as the number is 1 or more. The same logic goes, it just makes the process either faster or slower.

The critical things to note are that the Guru’s information conflicts with what is known just from looking at some point in the deductive process, and that the process MUST only consider what is definitely known for sure, and deductively exploring SOLELY within those confines in order to avoid risky assumptions like the alternative attempts mentioned so far, and that no information is taken out of context, such as the information known by 100 blues being used to deduce about what would happen if there were 1 blue knowing only what 1 blue would know. Once you get all these things, you should be home free to accepting the correct solution. Well done if you can, this is apparently very hard to do for some.

Really?
Then you should be able to give such an example (as requested pages ago).
Please tell us one number between 0 and 99 such that “even if everyone picked that same number”, it would still not work to allow them to discover their actual eye color.

James, I gave you an example (pages ago): any number between 0 and 99. Take 98 because it’s easy to work with: if every islander magicallyhad 98 in their head, they would be able to conclude exactly nothing about their eye color from it, no matter how many days elapsed.

There is no deductive process between “I have number 98 in my head” and “I have blue eyes”. The only way any deduction happens is if the number means something, and they know it means something.

So just like Eugene, you are going to continue to feign ignorance, avoid questions, deny the obvious, and play every kind of semantic and rhetoric game you can come up with in order to sell your story. You couldn’t care less what is or isn’t true. You are just hell bound to sell that story at all cost. And all under the guise of philosophy and in this case even “logic”.

And just what is your story? Well, “the truth is that 200 master logicians cannot know anything of truth until a guru, a woman no less, tells them what she thinks”.

It reminds me of the Catholic priest telling me how Jesus actually had very little to do with early Christianity until the first millennium when they, the Vatican, decided to prop up a male figure so as to gain more acceptance of Mary’s dominion. Before that Mary was the only significant figure. That is what they are teaching the nuns too (as reported by some nuns).

Yeah, you logical men are hopeless without the guidance of a woman and a guru.

Well, that is your story, like TEW is Eugene’s. But the truth is that the truth is greater than your stories. And I’m not buying your stories. As you discovered on that relativity thread, I let the logic of the lack of alternatives dictate the story of truth, not guru’s, wishful thinking, or women.

I see that saying she saw 100 blues would give them some useful information. But the idea that they would start counting from 10 (if she said she saw 10) seems even more weird than the original. :smiley:

James, I am arguing in good faith. When I believe that I am wrong, I admit it. I don’t believe that I am wrong here, and I have offered 10+ pages of argument in attempt to prove it.

Aren’t you sometimes wrong, James?

And now it’s women. In case anyone’s in doubt, the correct solution works just as well with a male Guru.

Are you contrasting the “weirdness” of starting counting from 10 with the “usefulness” of the Guru saying she saw 100 blues - as though the two must be incompatible?
Hopefully you are appreciating and enjoying the superficial “weirdness” as well as seeing the sense in it. If not, would you like me to extend the logic a bit further, that I initially began with only 100 and 99 as example numbers of blues that the Guru could say that she (or he!) sees in order to shorten the time period between her words and the exodus?

Carleas, did you forget to whom you are claiming that you admit when you’re wrong?
Am I supposed to compare your 3 post argument 5 years ago with your 800 post argument with me just 2 years ago, wherein, using these same tactics, you never once admitted that you were wrong about anything, but merely bailed out once nailed such that even you couldn’t wriggle out of it. You aren’t identical to FJ, but close… over focused on your own pitch.
…compared to me admitting that I was mistaken (even better than saying that the other guy is right) only a few posts and pages ago (which of course FJ took to the predicted false extreme).

I don’t believe your “good faith” story… either.

The weirdness is in the number of blues identified and how it seems to allow them to skip ahead. What is that information?
It seems possible for the guru to say that she sees no blues and they would start counting from zero. :smiley:

If the not so perfect logicians are focused on and only know of that one canonized solution, what the guru would be providing is the escape from their mental blindness by letting them complete the syllogism. The guru could pick any number and that is where the syllogism would begin the count… except “zero”. :sunglasses:

Why not zero? Can’t they figure out that she is lying?

Like I said, “not so perfect logicians”.

Because if it’s zero, they don’t learn anything when no one leaves. Take the example where there is 1 islander with blue eyes. Guru says “I see 0 islanders with blue eyes”. He doesn’t learn anything, and doesn’t leave. Now take the case of 2 islanders with blue eyes. Each sees the other, knows that the guru is lying, but doesn’t know that the blue eyed islander they can see knows that she’s lying. It is possible that they have brown eyes, and thus that the blue eyed islander they see sees no blue eyes and believes the guru. Even though they know the guru is lying, it doesn’t create the kind of common knowledge necessary to induce their own eye color.

The reason the guru can say any number greater than zero and it will work from that number is that, if there were only that number islanders with blue eyes, they would leave on the first day. If she said 10, 10 blue eyed islanders would leave the first day. 11 would learn when 10 didn’t leave that they too have blue eyes, and would leave on the second day. 12 would learn when 11 didn’t leave, etc.

It’s not just a matter of all agreeing on the same number and counting, but that the guru tells them something about the number: if there were only this many of you, they would leave on the first day, i.e. that they would know their eye color on the first day. That allows for the nested hypothetical of what the others know that the others know that the others know … to bottom out at the number the guru says. If it didn’t bottom out, it would get to zero and no one would leave. But it can bottom out at any number. If the guru says “I see 10 with blue eyes”, they know on day 1 what they wouldn’t learn until day 10 in the case where the guru says “I see 1 with blue eyes”: that there are at least 10 islanders with blue eyes.

The argument in which I defended the accepted understanding of special relativity against your attempt to disprove it? Of course the only explanation for why I refused to admit that I (and Einstein) were wrong about special relativity was that my fragile ego. What other explanation could there be…

That is exactly what it is.

The issue was that you were misusing the math and it was proven that you were (several times). It had nothing to do with Einstein. So yeah, that “fragile ego” thing is highly suspect… and even now still seems to be.

And btw, believe or not, this puzzle is directly related to all of the false flag terrorism (take over) going on throughout America.
It’s all about what any one person can do by expecting behavior from others… “nothing”.
And if he guesses wrong, he gets taken/voted off the “island”.

I contend that you do not understand the canonical solution.

And I contend that you understand nothing else.