Math Fun

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.

OK, let me return to the course, and try to explain why the number by itself is not enough.

I’ll include the guru, but instead of her saying “I see X blue eyes”, she’ll say “X”. That way, there’s no uncertainty about what number everyone is using, nor debate about whether a group of perfect logicians can know which of 100 numbers it’s the most logical to start with.

For whatever number X is, suppose there are X+1 people with a certain eye color. Now, if they knew, “there are at least X people with blue eyes,” they would leave on day 2 because they would see that the X people with blues eyes that they see haven’t left, and would reason that theirs must be the other set of blue eyes.

But in this case, they don’t. They know that the guru said “X” and that everyone else heard her say “X”, but they don’t have any knowledge attached to X. There is no chain of reasoning that gets them anywhere on day 2. They might notice that X happens to be the number of blue eyes that they see, but is that because there are exactly X blue eyes? There’s no inconsistency in assuming that X is just the number that came up on the dice she rolled; coincidence is insufficient to support a logical inference. They might even assume that she meant that there were at least X blue eyes, but they wouldn’t arrive at knowledge simpliciter, but knowledge assuming A. The conclusion of any syllogism would be burdened with that assumption.

Since X+1 wouldn’t work, X+2 wouldn’t either. If X is given as the number of blue eyes, the blue eyed islanders would expect the X+1 islanders they can see with blue eyes to leave on day 2. Since they don’t know anything about X, only that it is the number the guru said for no stated reason, they can’t start the logical process that gets them to their eye color. So no one else can found any other logical process on the fact that they failed to deduce their eye color: there’s nothing to be deduced from what they can see and the number X, so there’s nothing to be deduced from what they can see, the number X, and the failure of others to deduce anything from what they can see and the number X.

The same is true for any Y, X+Y: nothing can be deduced from X that will lead X+Y people to their eye color.

Make a syllogism if you disagree. Label each given with a letter, add some number as a given, and show a deductive logical process that leads to a conclusion like “my eyes are [some color]”.

This all seems to be a pointless exercise, primarily because I can’t make sense out of what you have written and in addition to the fact that you seem to fear anything being right other than the canonical solution.

And why don’t you just state a specific number that wouldn’t work for them and show how it would fail??

Already a losing proposition, but…

The the guru is going to say an actual number, right? Not literally “X”?

Okay. So for example if there had been 100 and the guru said “I see 99”. After the 1st day the 100th would realize that he must be the 100th.

That’s where you lost me. “They don’t” - what??
And in what case??
What “knowledge attached to X”??

???
How can X be an actual number and them not be able to deduce from it in the same way as always?

Again, not seeming to make sense.
If X happens to be the total number of blues on the island, all of the blues instantly know it.
Each of the blues would see 1 less than the guru said and deduce themselves to be the last.
They leave the 1st day. The rest stay.

The rest seems to be contingent on the prior reasoning, so isn’t making any sense either.

This is a clowns show. Sil is clearly defeated, FJ never was seriously engaging, Carleas seems to think it’s not credible to have a position that he finds difficult to challenge. Phyllo seems to side with James, which means that he’s seeing the utter bullshit of the other arguments.

Carleas and FJ think that the intellect gains credibility by looking away, becoming frustrated, and ignoring whole strings of argumentation.

I’ve admitted being wrong thrice in this thread, never had certainly until I saw there was absolutely no other way of thinking about this problem except to step beyond to stupid guru-trick, which is a heinously clever fools-bait, nothing to do with logic whatsoever.

I first thought it produced a necessary bias. Now I see it’s unnecessary bias. The thing works easily with 4 blues and 4 browns, all get off the island without the guru. If we accept the wait-a-day scheme on which the canonical solution relies and which contradicts the puzzle’s explanation.

Since James was a couple of steps ahead of me all the time (which I didn’t admit until I tried the scheme with both blue and brown simultaneously) I trust he’s capable of continuing the puzzle without the handy wait-one-day agreement to which no one actually is known to agree, since all see each other at all times (as they (do not) leave for the ferry). I am not willing to go there until a reasonable number of posters has come to their senses and seen that the guru is for the birds.

What the fuck.
Seriously, what the fuck.

I have been the only person to offer sufficiently sane, clear and exhaustive presentations of the only deductions that deal with absolute certainty and nothing else in order to come up with the correct solution. And that makes me wrong…

Having no arguments and simply saying the other person is wrong is NOT philosophy.
So mad at you right now.

I’ve even irrefutably debunked all proposed attempts at alternative solutions thus far. You conveniently miss that or something?

Only in your own mind.

Since Carleas is avoiding the question, perhaps you can answer it…
If everyone on the island happens, for whatever reason, to start counting days with the exact same number would they deduce their proper eye color?” And since you are going to say, “no”, please give an example of a number between 0-99 where their deductions would fail?

No, real world too.
I suggest to you too, to provide an actual counter to my arguments rather than just saying “nah ur rong”.

You mean “given some precarious assumption that has zero logical basis upon which to even be likely… etc.” ?

I’ll be happy to answer any questions you have, using examples, once you formulate them in a clearer way.
“to start counting days”… from when and according to what?
“with the exact same number”… of what?
“please give an example of a number between 0-99”… of what? Deductions about what?

In other words, you haven’t been reading anything but your own posts for many pages now.
… I suspected that.

Isn’t it interesting that Sil, FJ, and Carleas all don’t understand the words, “start with”, “counting days”, and “pick”. :sunglasses:
“But I don’t understand”… “but I don’t see the evidence”… :icon-rolleyes:

Yeah, those words are way too complex. What the hell is counting?
If you don’t think we understand them then feel free to continue living in your bubble, but it won’t get you anywhere or prove anything to anyone else.

When I read what you quoted the first time, it made no more sense than it did when you quoted it. I’ve kept up with this thread as best as I can, but the stuff that makes no sense, or isn’t clear enough to me is just as much that way as I re-read it as it was the first time I read it.

I’m not the only one to have come up against this problem - which I know from having read the last many pages - Carleas has asked on many occasions for you to make clearer what you are saying, saying things like “communication is a two way street”.

You do need to learn how to communicate.

Please start now by clarifying what the hell you’re trying to get at, rather than pretending to want to engage, but running back off into the bushes of obscurity and self-proclaimed clarity at the first opportunity.

I have re-iterated my own presentations of the correct solution several times now, each time improved in clarity from the last. When people fail to understand you, I suggest you learn from this example.

Yeah picking a number between 0-99 is a really tough task to comprehend.
But somehow I managed it and gave it as an example displaying all possible combinations of results.
Yet somehow it magically escapes you?

Picking merely the number 97, we get this;

Now can you pick a number that would fail to work that way?

I “picked” out the flaws for you. And they go for each of your “only 3” colours that exist:

Consider first the incompatibility between (A) and (D).

If, as in (D), “there were only 97 blues”, (A) would not be true. How would knowing that they all know that there were at least 97 blues be known by anyone when each of them does not even know their own eye colour (they only even see 96, never mind know that anyone else knows this)? Contradiction there methinks.

Consider now, (E). If there were only 98 blues, all islanders would only see that there were at least 97 blues (no knowing of knowing of seeing as in (A)).
(F). If there were only 99 blues, the blues would only know that other blues saw at least 97 blues (and not, as in (A), know that they all know that at least 97 blues were seen). Any browns/reds/misc-non-blues would see the 99, know that others see 98 and know that others know that others see 97, so (A) is valid for them.
(G) - only seen in the case of the blues, this is the only other case where anyone knows that they all know that there are at least 97 blues. (A) is also valid for them.

So they just leave because they each know that everyone knows that everyone sees 97 in their own particular circumstance? No they don’t, because none of that fictitious progression you were attempting backs it up. They just notice something that tells them nothing about their own eye colour. Where’s a good Guru when you need one, eh?

Essentially all you’ve done is pick out a few patterns that are incompatible with one another, and stick 'em together with a meaningless progression of numbers (upon proper examination of them) to make it look like there’s a process of logic.
There is, in fact, a great deal of omissions in your logic that would only be noticeable if you actually worked it through thoroughly, rather than just trying to fit some numbers together that you can make look like they fit together.

Also, what does “I am a brown/red out of x blues” even mean? Are browns part of the set of blues?! (I know what you meant to say).

So basically:

Yeah.

All of them.

James, when you say “pick”, it seems like what you really mean “identify a number such that that number of blue eyed islanders know that there are that many blue eyed islanders”. The distinction is important. The statement “I see 10 pairs of blue eyes” and the statement “10” contain different information. The statement “10” doesn’t contain any information; it’s simply yelling out an abstract property unattached to anything else. There is no relationship expressed. The statement “I see 10 pairs of blue eyes” contains information. The abstract property “10” is applied to a group of things, “pairs of blue eyes”. “10” is related to “blue eyes the guru sees”.

When you use the vague terms “pick”, “start with”, and “use”, that is not clear. As you yourself said, clarity is vital. Be precise. When we’re talking about the distinction between knowing that someone knows that someone knows and knowing that someone knows that someone knows that someone knows, we need significantly more precision that those terms provide. Specify what the numbers refer to, what the people are counting.

Let’s be clear here: you’re asking me to disprove a syllogism that you have not provided. Your claim is that simply having a number in mind is enough to prove eye color. My evidence for rejecting that is that the canonical solution is rigorously logical (something that has not been refuted), which entails that if there’s another solution, the problem itself contains an inherent contradiction. You have not identified that contradiction, and you have not rigorously demonstrated your solution. As far as I’m concerned, I’m being charitable in trying to refute a solution that you refuse to expound in any detail, based on the scanty tidbits about it that I’ve gleaned over these few dozen pages.

Now, one thing I’m sure that you’re saying is that everyone having the same number in mind at the same time is sufficient. It isn’t.

FC, you say “the thing works easily with 4 blues and 4 browns,” could you show that? I believe the mistake you are making is substituting knowing that they know that they know for knowing that they know that they know that they know, which breaks the logic that allows the canonical solution to work, and which requires the guru’s statement. If you could spell out the syllogism, it would further the discussion whether we’re able to refute it or not.

Wow…
Ask a simple question that any 3rd grader could understand, and what do you get…

You two want to jump into your future objections, “how do they know what number to pick”.

Can’t you calm down and just go one step at a time?
The question is pretty damn simple. It doesn’t take a PhD in logic or mathematics.
If you can’t answer such a simple question, I am really not interested in your excuses.
If you can’t handle arithmetic because of your religion, I am not going to try to explain the calculus.

On the Physics Forum site, you get banned for even mentioning that there might be any alternate understanding.
So I still admire Carleas for being far more tolerant than many online, but honestly, how hard is it to temporarily (as in a hypothesis) accept a notion long enough to prove it wrong? Is it really that threatening?

James, I have answered that question. Repeatedly. Silhouette has answered it. The answer is that for no number does “that way” work. “That” is not a “way” to solve the problem. Why? Because there is no valid deductive process that gets you from “this is a number” to “my eye are blue.”