My write-up of the "Blue Eyes" solution (SPOILER A

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elwood
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Re: My write-up of the "Blue Eyes" solution (SPOILER A

Postby elwood » Thu Oct 30, 2014 3:15 pm UTC

Hello marzis. Welcome to the thread (and to the forum).

Very briefly, to me the main flow in your reasoning is that you seem to interpret "logical" as "making perfect sense, intuitively". This is wrong as it's not what formal logic is about.

Secondly, I believe that there are at least a few subtle hints on the way you expose you analysis indicating that you most probably don't, in fact, understand completely the "common knowledge" approach. For instance, this:

marzis wrote:... the inability to know for certain that anyone on the island other than one's self that anyone else on the island knows for certain that there is at least 1 person on the island with Blue eyes...


is just false. I don't mean this offensively, I appreciate the effort behind that lengthy post, so If you want we can go on about that. But perhaps that brief comment clears things up for you.

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Re: My write-up of the "Blue Eyes" solution (SPOILER A

Postby marzis » Thu Oct 30, 2014 3:28 pm UTC

Thanks for the welcome.

So my relaying of the common-knowledge was faulty there, included a doubling of the phrase "that anyone else on the island", but I wanted to very quickly get past the reliance upon a common-knowledge theory to get a solution. I don't think we should derail the rest of my theory just because I mis-typed the phrasing of the common-knowledge idea.

If you could instead show me how a perfect logician, using formal logic, can choose to make the statement "I can see at least one person with blue eyes" with the knowledge that this statement will only be applicable to a portion of the receiving population, I'd appreciate that.

Or if you could show me how something else in my answer is wrong, or actually relies upon a false assumption, or actually can't be made because the information relied upon assumes a common-knowledge X that can't be established, etc etc, i'd appreciate that just as much.

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Re: My write-up of the "Blue Eyes" solution (SPOILER A

Postby firechicago » Thu Oct 30, 2014 3:39 pm UTC

You seem to be imputing some sort of "fairness" or ethical requirement to our guru.

Logic has no necessary relationship with fairness or ethics. The guru can be perfectly logical and make whatever true statement she wants. She is not required to give information to everyone equally any more than a "perfect soccer player" would be required to be able to bake a perfect souffle.

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Re: My write-up of the "Blue Eyes" solution (SPOILER A

Postby marzis » Thu Oct 30, 2014 3:54 pm UTC

Sure, she can say anything she would like, but as a perfect logician, she can only come to conclusions that are logical, and do so by a series of logical steps. I'm having trouble seeing the logical series that leads to 'I can see at least one person with blue eyes' when it only applies only to the blue eyed members of the island, rather than being one that can be applicable to everyone on the island.

If the information came (as is detailed, for example, on the wikipedia page about common knowledge theory) from an outside who is not constrained by the limits of being a perfect logician (as it is detailed in the xkcd variant) then of course this issue of having a 'choice' be logical, does not apply.

Basically, I am currently not seeing how it can be logical to 'choose' any subset within a set. If it cannot, then the Guru cannot do it, as she is a perfect logician, and the interpretation of her statement cannot be one that only applies to a subset within the set.

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Re: My write-up of the "Blue Eyes" solution (SPOILER A

Postby Adam H » Thu Oct 30, 2014 4:10 pm UTC

That's a really weird problem to have...

If it helps you feel better about the riddle, you could just say that the Guru is not logical. I don't think that affects the solution.
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Re: My write-up of the "Blue Eyes" solution (SPOILER A

Postby elwood » Thu Oct 30, 2014 4:20 pm UTC

marzis wrote:So my relaying of the common-knowledge was faulty there, included a doubling of the phrase "that anyone else on the island", but I wanted to very quickly get past the reliance upon a common-knowledge theory to get a solution. I don't think we should derail the rest of my theory just because I mis-typed the phrasing of the common-knowledge idea.


In fact, the error is that you should have repeated "that anyone on the island knows" another 98 times in that sentence for it to be correct. But ok, let's not diverge into that further.

If you could instead show me how a perfect logician, using formal logic, can choose to make the statement "I can see at least one person with blue eyes" with the knowledge that this statement will only be applicable to a portion of the receiving population, I'd appreciate that.


Formal logic is the branch of mathematics dealing with deriving conclusions from axioms using well-defined rules. As long as your axioms are non contradictory (and assumed to be true), every conclusion you reach will also be true. The islanders, including the Guru, are "perfect logicians" in the sense that if a conclusion can be derived from what they already know, they reach that conclusion instantly. So: the Guru's announcement is neither "logical" or "illogical", it's an axiom, one of the things given in the puzzle, it can't be derived from the rest of what is known, and as long as it's not contradictory the perfectly logical islanders are happy to go by it.

I'm having trouble seeing the logical series that leads to 'I can see at least one person with blue eyes' when it only applies only to the blue eyed members of the island, rather than being one that can be applicable to everyone on the island.


There is no such logical series! And there doesn't need to be one. The Guru providing information equally/fairly/whatever-way is not part of the island axioms.

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Re: My write-up of the "Blue Eyes" solution (SPOILER A

Postby rmsgrey » Thu Oct 30, 2014 7:05 pm UTC

An important question if you're using the fact the guru didn't make some other statement in your reasoning is what the guru's rules and goals are.

All we know about the guru's rules is that she is allowed to make exactly one statement, as the only communication between islanders other than observation of departures and eye-colours.

All we know about the guru's goals is... well, whatever we can deduce from the statement she makes, which, without knowing the statements she had to choose between, doesn't tell us much at all.

Without knowing what the guru wants to achieve, and what restrictions there are on the guru's statement, you can't really reason based on it...

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Re: My write-up of the "Blue Eyes" solution (SPOILER A

Postby marzis » Thu Oct 30, 2014 7:43 pm UTC

If the providing of the axiom, as you refer to it, of 'I can see at least one person with Blue eyes' wasn't relayed by a source that we had previously been identified as a perfect logician, then I absolutely agree that the common-knowledge route is the only way to go. This is because the islanders have no reason to believe the statement would be made with any reference to logic at all, they must, if you will, take it on faith (i.e., process it as an axiom).

But we know 3 things about the Guru. 1) She has Green eyes. 2) She is a perfect logician. 3) She is the only person on the island who can communicate at all, that she can only do so once, and that when she finally does, she says 'I can see at least one person with Blue eyes'.

The other 200 perfect logicians know that the Guru is a perfect logician, but how can they know that her statement is an axiom, and not some result of a logical deduction?

If I am reading your statement correctly, then the Guru being a perfect logician is irrelevant to the riddle. But I feel like that is just a decision to allow for her statement to be processed by the 200 as an axiom rather than as an internal result of logical reasoning (by the Guru). This could be stopped if I were shown how my analysis of the Guru's statement isn't logical (and therefore not something the 200 members would conceive of, and therefore, no longer presenting an issue of a 'choice' or 'decision' being made)

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Re: My write-up of the "Blue Eyes" solution (SPOILER A

Postby brenok » Thu Oct 30, 2014 8:25 pm UTC

marzis wrote:The other 200 perfect logicians know that the Guru is a perfect logician, but how can they know that her statement is an axiom, and not some result of a logical deduction?
Why would that matter? The guru has vision. Seeing a person with blue doesn't require any logic, and whether or not you would classify that as an "axiom" or "theorem" doesn't change the fact that it's true by definition on the terms of the problem.

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Re: My write-up of the "Blue Eyes" solution (SPOILER A

Postby rmsgrey » Thu Oct 30, 2014 9:15 pm UTC

marzis wrote:This could be stopped if I were shown how my analysis of the Guru's statement isn't logical (and therefore not something the 200 members would conceive of, and therefore, no longer presenting an issue of a 'choice' or 'decision' being made)


Your analysis is logical, but it includes assumptions about the Guru's choices and motives.

If you assume that the Guru has to make a statement which will enable at least one person to deduce their eye colour, and that they aren't allowed to identify any person or group of people other than by their eye colour, and assume that the Guru wants to maximise the number of person-days people spend on the island (so minimise the number of people who leave, and, subject to that constraint, maximise the length of time those who are leaving stay), then you conclude that she would say "I can see at least one person with X eyes" where X is the least common colour she observes. With these assumptions, assuming the Guru's rules and motives are common knowledge, everyone except the Guru leaves the island on Night 100.

If the islanders don't know both the Guru's rules and her motives, then they can't reason from her choice of statement.

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Re: My write-up of the "Blue Eyes" solution (SPOILER A

Postby phlip » Fri Oct 31, 2014 2:44 am UTC

One of the (often unstated) assumptions in this form of logical puzzles is that when it's a given in the puzzle that someone says something (like the guru's announcement in this puzzle), then you just take it as read that they said it, don't care about their motivation for saying it, and that the only information it carries is literally the content of the message.

For a simple example... say I have a deck of cards, and I draw a card at random. Now, say if I have this habit where if I draw an ace, I'll tell you "I have an ace", but otherwise I'll say what colour it is... so I draw my card, look at it, and say "It's a red card". Now, with that information, you'd know it's a red non-ace card. But without that information, if this were in a logical puzzle where all the puzzle says is "I draw a card and say it is a red card", then all you can take from it is the context of the message, and assume that all 26 red cards are equally likely.

For a more concrete example, take the Boy/Girl paradox, often worded as "A parent tells you they have two children, and at least one of the children is a boy. What is the chance that both are boys?"... Now, you can take the stance of "in what circumstances would they make that statement?"... if they have two boys, then they would make that statement, but if they had one boy and one girl, then they'd only make that statement half the time (the other half they'd instead make "... and at least one of the children is a girl"). This then changes the probability calculations by adding extra weight to the two-boys case. However, the standard logic-puzzle reading of that phrasing is that the message contains exactly the information in the actual message - that at least one of the two children is a boy.

Normally when I tell the "Boy/Girl paradox" puzzle, I word it to take the "motivation" angle out... "I have a friend who has two children. I asked them 'do you have a son?' and they answered 'yes'"... which removes the motivation question by making it clear that the friend would respond identically in any situation where the answer to the question is "yes". The decision to ask about sons rather than daughters was made by me, rather than them, and couldn't be influenced by whether they actually have sons or daughters, because I don't know that.

I suppose you could do a similar rewording of this puzzle... instead of having the guru make their announcement spontaneously, say the guru decides that after a lifetime of silence, they will truthfully answer a single question. A blind traveller (who happens to also have green eyes, and, if it helps, is not necessarily a perfect logician) comes up to the guru and asks "is there anyone on the island with blue eyes", to which the guru answers "Yes".

Now the decision to ask about blue eyes rather than brown eyes is still arbitrary, but you can't make any inference from the choice, since the person who made the choice is blind anyway...

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Re: My write-up of the "Blue Eyes" solution (SPOILER A

Postby douglasm » Fri Oct 31, 2014 8:41 am UTC

marzis wrote:The other 200 perfect logicians know that the Guru is a perfect logician, but how can they know that her statement is an axiom, and not some result of a logical deduction?

They can't, and the only way this distinction would make any difference is if the islanders knew both that it is the result of a logical deduction and what that logical deduction is. The islanders do not know why the Guru said what he did. His motivations, ethics, sense of fairness, etc. are completely unrelated to the definition of "perfect logician".

The islanders can only use information they actually know to base their logical deductions on. They know that the contents of the Guru's announcement are true. They do not know why the Guru chose that particular statement. Thus, taking the Guru's statement as an axiom is the only choice available to them for performing logical deduction.

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Re: My write-up of the "Blue Eyes" solution (SPOILER A

Postby elwood » Fri Oct 31, 2014 2:45 pm UTC

Marzis, I believe I understand your point a lot better now.

The entire puzzle could be formulated in entirely mathematical terms, where an islander is a kind of abstract machine/automaton with properties like eye colour and being on/off the island, including an internal automatic theorem prover, an internal transition function, and a universal clock ticking days/nights as discrete intervals. It's not trivial to construct such a formulation, unless maybe you do that kind of stuff for a living (personally I don't) but it would be pretty straightforward.

So your objection is more or less: "well, if that's all there is to it, how does such an abstract machine decide to make the particular statement?"

And, well, I guess you are right, however the common interpretation of the puzzle is that the Guru's statement is something independent of the islander's hardwired internal theorem proving/state transition formulation (it is part of the basis used for inference, it would be something like included in the starting conditions of the mathematical formulation at t=0).

And you are also correct to observe that the Guru being a perfect logician is irrelevant to the problem. I guess it would be just kind of awkward wording to specify that in the puzzle description, and would also be unnecessary and confusing for no good reason.

Puzzles like this one are probably more appealing to our minds worded around situations involving people, I don't know, by triggering our "empathy reflex". So that you start thinking "well what would it look like from my perspective if I were on the island/in that prison/asking the question to the princess", and that's obviously easier to connect with than "what if I were a finite state automaton with the particular transition function". But it's got a certain kind of beauty being able to transform back and forth between these two perspectives.

(Damn, this thread is addictive)

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The "Blue Eyes" puzzle solution is invalid.

Postby Potatoberg » Thu Nov 06, 2014 12:53 am UTC

The problem starts at the 1st theorem:

[THEOREM 1] If there is one blue-eyed person, he leaves the first night.

If there are two blue-eyed people, they will each look at the other. They will each realize that "if I don't have blue eyes [HYPOTHESIS 1], then that guy is the only blue-eyed person. And if he's the only person, by THEOREM 1 he will leave tonight." They each wait and see, and when neither of them leave the first night, each realizes "My HYPOTHESIS 1 was incorrect. I must have blue eyes." And each leaves the second night.


Here is what the puzzle says:
Any islanders who have figured out the color of their own eyes then leave the island, and the rest stay.


How does that person know he has blue eyes and not red eyes or grey eyes or hazel eyes or black eyes? He doesn't. All he knows is that there is at least 1 person with blue eyes. Maybe he can see that person, but how would that person with the blue eyes know they have blue eyes and not red eyes? Quoting the puzzle again:
as far as he knows the totals could be 101 brown and 99 blue. Or 100 brown, 99 blue, and he could have red eyes.


Given that THEOREM 1 is wrong, all posterior inductions are also wrong.

Now add in people with one eye one color and the other a different color.

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Re: The "Blue Eyes" puzzle solution is invalid.

Postby Cauchy » Thu Nov 06, 2014 9:06 am UTC

Potatoberg wrote:How does that person know he has blue eyes and not red eyes or grey eyes or hazel eyes or black eyes? He doesn't. All he knows is that there is at least 1 person with blue eyes.


But if he's the only person with blue eyes (as is postulated in the theorem), then he won't see anyone else with blue eyes, so he'll figure out that he must be the person with blue eyes.

That argument proposes islands with other numbers of blue eyes than exactly 100, to help illustrate the logic going through the original residents' minds.
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Re: My write-up of the "Blue Eyes" solution (SPOILER A

Postby douglasm » Thu Nov 06, 2014 7:19 pm UTC

He knows there is at least one person with blue eyes. He can see the eye color of everyone on the island except himself. He does not see anyone with blue eyes. Therefore his eyes must be blue. QED.

The "If there's only one person with blue eyes" thing is a theorem about a hypothetical case that is used for logical deduction but is not the one specified in the puzzle. The "he could have red eyes" quote is about the actual case specified in the puzzle. They have nothing to do with each other because they are about different cases.

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Re: The "Blue Eyes" puzzle solution is invalid.

Postby Potatoberg » Sat Nov 08, 2014 7:03 am UTC

Cauchy wrote:
Potatoberg wrote:How does that person know he has blue eyes and not red eyes or grey eyes or hazel eyes or black eyes? He doesn't. All he knows is that there is at least 1 person with blue eyes.


But if he's the only person with blue eyes (as is postulated in the theorem), then he won't see anyone else with blue eyes, so he'll figure out that he must be the person with blue eyes.

That argument proposes islands with other numbers of blue eyes than exactly 100, to help illustrate the logic going through the original residents' minds.


But the only blue-eyed person would have to rely on an argument from authority if he accepts the words of the guru as fact. What if the Guru is color blind? Even if we assume the guru is not color blind and says the truth, that's not the same as saying that the people in the puzzle know that the Guru does not lie and is not color blind. If we assume that the Guru never lies and is not color blind and that the people in the puzzle know that the Guru never lies and is not color blind, then THEOREM 1 is correct.
Sorry to be pedantic, but we are talking about perfect logicians.

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Re: The "Blue Eyes" puzzle solution is invalid.

Postby jestingrabbit » Sat Nov 08, 2014 7:45 am UTC

Potatoberg wrote:
Cauchy wrote:
Potatoberg wrote:How does that person know he has blue eyes and not red eyes or grey eyes or hazel eyes or black eyes? He doesn't. All he knows is that there is at least 1 person with blue eyes.


But if he's the only person with blue eyes (as is postulated in the theorem), then he won't see anyone else with blue eyes, so he'll figure out that he must be the person with blue eyes.

That argument proposes islands with other numbers of blue eyes than exactly 100, to help illustrate the logic going through the original residents' minds.


But the only blue-eyed person would have to rely on an argument from authority if he accepts the words of the guru as fact. What if the Guru is color blind? Even if we assume the guru is not color blind and says the truth, that's not the same as saying that the people in the puzzle know that the Guru does not lie and is not color blind. If we assume that the Guru never lies and is not color blind and that the people in the puzzle know that the Guru never lies and is not color blind, then THEOREM 1 is correct.
Sorry to be pedantic, but we are talking about perfect logicians.


You're right that the solution does depend on the islanders believing the guru, and that it is not stated in the puzzle that the islanders believe the guru. It does state the the solution "doesn't depend on tricky wording or anyone lying or guessing", and I believe that we can extend that to the guru ie the the guru is telling the truth and has reliable enough eyes to determine the eye color of one of the islanders is blue.
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Re: My write-up of the "Blue Eyes" solution (SPOILER A

Postby Xias » Sat Nov 08, 2014 9:22 am UTC

I think it's fair to say that the puzzle could be worded better.

The only way we might get around it is to add something to the first paragraph describing the guru and that the guru is honest. Anything else would introduce more common knowledge issues, as how do you know that A knows that B knows that the guru is honest?

However, there is a limit to how many caveats should be added to avoid some reason that the puzzle would be unsolvable. The institution of puzzle solving sort of includes the assumption that certain things that would be required to solve the puzzle are taken as given. I don't think it's insignificant that it wasn't until the 31st page (that I'm aware) that someone suggested that the Guru lying is a possibility.

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Re: My write-up of the "Blue Eyes" solution (SPOILER A

Postby jestingrabbit » Sat Nov 08, 2014 11:14 am UTC

Xias wrote:I think it's fair to say that the puzzle could be worded better.


I mean, yes and no. You can pile on legalese atop of legalese, and its never going to satisfy everyone. There's a buy-in that one assumes of the solver, which is what you mention in your third paragraph. I think the problem is just fine as is, and we rely on assumptions of validity and good-faith to communicate what's going on.
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Re: My write-up of the "Blue Eyes" solution (SPOILER A

Postby phlip » Sat Nov 08, 2014 12:40 pm UTC

Eventually you get to the point where you're specifying "Everything in this puzzle is written in English, and to be interpreted as normal for that language. The previous sentence is also written in English, and definitely not my own conlang where 'English' means 'a toy language where "Blue" and "Brown" are synonyms for the same colour'"... you've probably gone too far. But even that won't really make the puzzle Perfectly Specified.

(I feel like we've already had this conversation recently...)

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Re: My write-up of the "Blue Eyes" solution (SPOILER A

Postby Potatoberg » Sat Nov 08, 2014 11:05 pm UTC

phlip wrote:Eventually you get to the point where you're specifying "Everything in this puzzle is written in English, and to be interpreted as normal for that language. The previous sentence is also written in English, and definitely not my own conlang where 'English' means 'a toy language where "Blue" and "Brown" are synonyms for the same colour'"... you've probably gone too far. But even that won't really make the puzzle Perfectly Specified.


Solution: Don't reword the puzzle, create a new puzzle. If we insist that the puzzle is solvable then we will always be specifying. It's like a communist trying to rationalize why communism didn't work by creating a new, more specific definition of what communism is.
Also, I think the puzzle can be specified in such a way that it produces the accepted solution.

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Re: My write-up of the "Blue Eyes" solution (SPOILER A

Postby jestingrabbit » Sun Nov 09, 2014 1:17 am UTC

Potatoberg wrote:Also, I think the puzzle can be specified in such a way that it produces the accepted solution.


And rewording to that version would be like communism how?

As I pointed out, the puzzle states that no one is lying or guessing. That covers your criticism just fine. It might (though I don't really see it) lack clarity, but its there just fine.
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Re: My write-up of the "Blue Eyes" solution (SPOILER A

Postby rmsgrey » Sun Nov 09, 2014 1:34 am UTC

The version I first encountered has red-eyed and brown-eyed monks who have taken a vow of silence, know each other's eye-colours, are required to depart if they know they have red eyes, and have these rules as common knowledge. To this monastery, a tourist comes, is shown around by a guide from a nearby village, and, when all the monks are gathered to watch him depart, is overheard to say, loudly "Gee, I thought you said the monks with red eyes had to leave! So how come I saw one of those guys with red eyes?" before the guide can shut him up. His statement is assumed to be common knowledge, to be completely convincing, and to convey no information about which monk's eyes he happened to notice.

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Re: My write-up of the "Blue Eyes" solution (SPOILER A

Postby Potatoberg » Mon Nov 10, 2014 3:25 am UTC

jestingrabbit wrote:
Potatoberg wrote:Also, I think the puzzle can be specified in such a way that it produces the accepted solution.


And rewording to that version would be like communism how?

As I pointed out, the puzzle states that no one is lying or guessing. That covers your criticism just fine. It might (though I don't really see it) lack clarity, but its there just fine.


Rewording it is not like communism, but like the defense communists resort to when told that communism was tested out during the 20th century and was proven to not work: they simply change the specifications needed to reach a communist society (in this case, to reach the claimed solution to the puzzle).

Lying or guessing does not cover the Guru being color blind and not knowing so. But of course, you could always add to the puzzle that the Guru is not color blind in an attempt to force the solution you reached without such specification. Whenever you change the original puzzle's wording you're implicitly accepting that your previous solution was reached through a number of assumptions and was therefore invalid.

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Re: My write-up of the "Blue Eyes" solution (SPOILER A

Postby jestingrabbit » Mon Nov 10, 2014 1:46 pm UTC

Potatoberg wrote:Rewording it is not like communism, but like the defense communists resort to when told that communism was tested out during the 20th century and was proven to not work: they simply change the specifications needed to reach a communist society (in this case, to reach the claimed solution to the puzzle).

Lying or guessing does not cover the Guru being color blind and not knowing so. But of course, you could always add to the puzzle that the Guru is not color blind in an attempt to force the solution you reached without such specification. Whenever you change the original puzzle's wording you're implicitly accepting that your previous solution was reached through a number of assumptions and was therefore invalid.


One of xkcd's early comics covers situations like this, imo.

http://xkcd.com/169/

Have a look, and a think. Logic puzzles, rather than lateral thinking puzzles, or stupid word games, assume that certain things are evident. I mean, are you going to start talking about aberrant lighting conditions that make blue and brown look the same next, or that we haven't defined blue and brown or etc etc etc.

I did reach the solution through a number of assumptions. I don't think that renders the solution invalid. If you want to go play with tricky edge cases, be a lawyer, they'll love you.
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Re: My write-up of the "Blue Eyes" solution (SPOILER A

Postby Cauchy » Mon Nov 10, 2014 2:41 pm UTC

Potatoberg wrote:Lying or guessing does not cover the Guru being color blind and not knowing so. But of course, you could always add to the puzzle that the Guru is not color blind in an attempt to force the solution you reached without such specification. Whenever you change the original puzzle's wording you're implicitly accepting that your previous solution was reached through a number of assumptions and was therefore invalid.


So what you're saying is that the solution to every riddle ever is "we don't know, there are all sorts of things that could be the case that weren't covered in the set-up".
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Re: My write-up of the "Blue Eyes" solution (SPOILER A

Postby rmsgrey » Mon Nov 10, 2014 5:04 pm UTC

Cauchy wrote:
Potatoberg wrote:Lying or guessing does not cover the Guru being color blind and not knowing so. But of course, you could always add to the puzzle that the Guru is not color blind in an attempt to force the solution you reached without such specification. Whenever you change the original puzzle's wording you're implicitly accepting that your previous solution was reached through a number of assumptions and was therefore invalid.


So what you're saying is that the solution to every riddle ever is "we don't know, there are all sorts of things that could be the case that weren't covered in the set-up".


I don't know about that - there are all sorts of things that could be the case that weren't covered in the setup...

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Re: My write-up of the "Blue Eyes" solution (SPOILER A

Postby Potatoberg » Tue Nov 11, 2014 1:52 am UTC

One of xkcd's early comics covers situations like this, imo.

http://xkcd.com/169/

Have a look, and a think. Logic puzzles, rather than lateral thinking puzzles, or stupid word games, assume that certain things are evident. I mean, are you going to start talking about aberrant lighting conditions that make blue and brown look the same next, or that we haven't defined blue and brown or etc etc etc.

I did reach the solution through a number of assumptions. I don't think that renders the solution invalid. If you want to go play with tricky edge cases, be a lawyer, they'll love you.


It's ironic that you tell me to be a lawyer when you search the archives to find an early comic that you think covers this situation like a lawyer searches the law to find something useful. It's also a lack of debate etiquette to call your opponent names.

Your argument that a previous puzzle said something that covers this puzzle is invalid for the same reasons that an ad hominem is invalid, given that had I copied the blue eyed puzzle and given it to a friend to solve I could not use such a defense if he argued that the Guru could be color blind.
These assumptions do render your solution invalid; such an argument is known as Hasty generalization.

What you call playing with tricky edge cases I call being rigorous with logic.

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Re: My write-up of the "Blue Eyes" solution (SPOILER A

Postby phlip » Tue Nov 11, 2014 7:24 am UTC

Linking to #169 isn't "searching the archives"... it's a commonly-referenced comic that any regular of the Logic Puzzles forum is going to be familiar with (and probably just know by number alone).
Potatoberg wrote:What you call playing with tricky edge cases I call being rigorous with logic.

And what you call "rigorous" I call "impossible standards of proof". To go back to my previous post... can you prove, with mathematical certainty, that the puzzle is written in English, and not, say, a conlang designed to bear a superficial similarity to English, but with different word meanings? If not, by your standards, solving the puzzle is obviously impossible, as it could mean anything... so what extra clarification would be necessary to add to the puzzle to clear up this ambiguity?

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Re: My write-up of the "Blue Eyes" solution (SPOILER A

Postby Xias » Tue Nov 11, 2014 9:24 am UTC

Again, potatoberg, it may be helpful to note that in over 30 pages of comments, including many in objection to the solution, nobody had an issue assuming that the guru was reliable and that this fact was common knowledge. It's simply not an unreasonable assumption to make, especially since failing to do so would render the puzzle unsolvable.

If failing to make that assumption - not simply making a different one but failing to make an assumption at all - led to a different solution, then it would be a critical ambiguity. As it stands, it's not really useful to try to remove ambiguity that hasn't really been ambiguous to anyone.

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Re: My write-up of the "Blue Eyes" solution (SPOILER A

Postby jestingrabbit » Tue Nov 11, 2014 12:09 pm UTC

Potatoberg wrote:It's also a lack of debate etiquette to call your opponent names.


Where did I call you a name? Knowing a lot of fallacy names isn't the same as knowing what a reasonable argument is.

Ultimately, there are assumptions that you expect a reasonable reader to make. I think the "lying and guessing" clause intends that we accept the words of the guru as reliable. Indeed, if we consider the third definition of lie, presented here

http://dictionary.reference.com/browse/lie

we see that it excludes even the case of a color blind and unaware guru. If we take that as the definition of lie, it necessitates that the guru is reliable, regardless of whatever else you might assume.

I think the intention of the puzzle statement is clear, and that the solutions are valid.
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Re: My write-up of the "Blue Eyes" solution (SPOILER A

Postby Yakk » Tue Nov 11, 2014 5:52 pm UTC

jestingrabbit wrote:
Potatoberg wrote:It's also a lack of debate etiquette to call your opponent names.
Where did I call you a name? Knowing a lot of fallacy names isn't the same as knowing what a reasonable argument is.

http://existentialcomics.com/comic/9
That is all.
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Re: My write-up of the "Blue Eyes" solution (SPOILER A

Postby Potatoberg » Wed Nov 12, 2014 1:38 am UTC

phlip wrote:... so what extra clarification would be necessary to add to the puzzle to clear up this ambiguity?

"The islanders know the guru is not color blind"

Xias wrote:Again, potatoberg, it may be helpful to note that in over 30 pages of comments, including many in objection to the solution, nobody had an issue assuming that the guru was reliable and that this fact was common knowledge. It's simply not an unreasonable assumption to make, especially since failing to do so would render the puzzle unsolvable.

If failing to make that assumption - not simply making a different one but failing to make an assumption at all - led to a different solution, then it would be a critical ambiguity. As it stands, it's not really useful to try to remove ambiguity that hasn't really been ambiguous to anyone.


For thousands of years of human history, nobody had an issue with assuming the world is flat, thus it's a reasonable assumption to make.

Sorry, but no.

jestingrabbit wrote:
Potatoberg wrote:It's also a lack of debate etiquette to call your opponent names.


Where did I call you a name? Knowing a lot of fallacy names isn't the same as knowing what a reasonable argument is.


You called me a Lawyer.
You're correct, knowing a lot of fallacy names isn't the same as knowing what a reasonable argument is. Is this supposed to be a refutation?

jestingrabbit wrote:Ultimately, there are assumptions that you expect a reasonable reader to make. I think the "lying and guessing" clause intends that we accept the words of the guru as reliable. Indeed, if we consider the third definition of lie, presented here

http://dictionary.reference.com/browse/lie

we see that it excludes even the case of a color blind and unaware guru. If we take that as the definition of lie, it necessitates that the guru is reliable, regardless of whatever else you might assume.

I think the intention of the puzzle statement is clear, and that the solutions are valid.


It doesn't matter because the puzzle does not state that the islanders know that the guru cannot lie or be mistaken. Why would they assume that a "guru dixit" argument is valid if they do not have this knowledge that the guru does not lie and is not mistaken?
"Nobody leaves" is the only valid solution to the puzzle as it's currently worded. Sure, the puzzle can be edited in an attempt to force that solution, but apart from implicitly admitting that the previously reached solution relied on unjustified assumptions, it's really just the story of the Texan sharpshooter.


Ridiculing your opponent is a lack of proper debate etiquette.

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Re: My write-up of the "Blue Eyes" solution (SPOILER A

Postby phlip » Wed Nov 12, 2014 1:48 am UTC

Potatoberg wrote:
phlip wrote:... so what extra clarification would be necessary to add to the puzzle to clear up this ambiguity?

"The islanders know the guru is not color blind"

... How would that prove the puzzle is written in English? (You did read the rest of that paragraph, right? And not just the half a sentence you quoted?)

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Re: My write-up of the "Blue Eyes" solution (SPOILER A

Postby Yakk » Wed Nov 12, 2014 2:40 am UTC

Potatoberg wrote:
phlip wrote:... so what extra clarification would be necessary to add to the puzzle to clear up this ambiguity?

"The islanders know the guru is not color blind"

But what if the guru thinks that the world for "blue" is "brown" and vice versa?
"The islanders know that the guru and they share a common word for blue and for brown".

But, what if the guru's eye pigments where swapped?

More clarification needed!

Or... maybe not?
For thousands of years of human history, nobody had an issue with assuming the world is flat, thus it's a reasonable assumption to make.
Many people had issues with assuming the world was flat. And despite the fact that "the world is flat" was rarely universally accepted in recorded history, it was often a reasonable assumption to make. And if "nobody had an issue with X for thousands of years, then assuming X is reasonable" is actually a relatively reasonable claim.

So, no, I'm not sure what you are getting at here?
It doesn't matter because the puzzle does not state that the islanders know that the guru cannot lie or be mistaken. Why would they assume that a "guru dixit" argument is valid if they do not have this knowledge that the guru does not lie and is not mistaken?
"Nobody leaves" is the only valid solution to the puzzle as it's currently worded. Sure, the puzzle can be edited in an attempt to force that solution, but apart from implicitly admitting that the previously reached solution relied on unjustified assumptions, it's really just the story of the Texan sharpshooter.
There is no foundation to human communication that is guaranteed to be solid. So no, there is no way to reword any such puzzle so that there is no ambiguity. Eliminating all ambiguity is not a possible act.
Ridiculing your opponent is a lack of proper debate etiquette.
The sky is sometimes a colour other than blue.

There are 3 bits of fluff in my pocket.

I think I want a brownie.

My nose itches.

You seem to think this is a debate. As in, the point of this thread is to have a debate.

I believe the point of this thread is to discuss the correct answer, which has little to do with debate. Debate tends to be use to refer to a form of structured argument (usually for argument's sake), dominated by the arts of rhetoric. If your reason for being here is argument for arguments sake, maybe other people aren't here for that reason? And might find argument for argument's sake annoying?

Maybe?
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Re: My write-up of the "Blue Eyes" solution (SPOILER A

Postby jestingrabbit » Wed Nov 12, 2014 5:18 am UTC

Potatoberg wrote:
You called me a Lawyer.


No, I didn't. I suggested that

If you want to go play with tricky edge cases, be a lawyer, they'll love you.


That's not the same thing at all.


Potatoberg wrote:
jestingrabbit wrote:Ultimately, there are assumptions that you expect a reasonable reader to make. I think the "lying and guessing" clause intends that we accept the words of the guru as reliable. Indeed, if we consider the third definition of lie, presented here

http://dictionary.reference.com/browse/lie

we see that it excludes even the case of a color blind and unaware guru. If we take that as the definition of lie, it necessitates that the guru is reliable, regardless of whatever else you might assume.

I think the intention of the puzzle statement is clear, and that the solutions are valid.


It doesn't matter because the puzzle does not state that the islanders know that the guru cannot lie or be mistaken. Why would they assume that a "guru dixit" argument is valid if they do not have this knowledge that the guru does not lie and is not mistaken?


The puzzle has within it this paragraph, as a sort of clarifying addendum. Emphasis is mine.

There are no mirrors or reflecting surfaces, nothing dumb. 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."


She made that statement, and she is not lying or guessing. Therefore the puzzle states that the guru is reliable, using the third definition of lie at

http://dictionary.reference.com/browse/lie

It doesn't take a rewrite to make the previous solutions correct. It might take a rewrite to add more clarity. But right there in the puzzle statement, we see the statement that the guru makes, and the assertion that her words are true. That you can come up with scenarios where her word might be false is irrelevant, because the puzzle states that her word is true.

Regarding your allusion to the term "ipse dixit", meaning an unadorned dogmatic statement: this is the nature of these puzzles! The setup is dogmatically asserted, and the solutions are arrived at by accepting the setup and making arguments regarding it.
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Re: My write-up of the "Blue Eyes" solution (SPOILER A

Postby Potatoberg » Wed Nov 12, 2014 11:18 pm UTC

phlip wrote:
Potatoberg wrote:
phlip wrote:... so what extra clarification would be necessary to add to the puzzle to clear up this ambiguity?

"The islanders know the guru is not color blind"

... How would that prove the puzzle is written in English? (You did read the rest of that paragraph, right? And not just the half a sentence you quoted?)


The very use of English language in such hypothetical proof would be evidence that the language is English. You being able to comprehend this is proof that this is English. To say "this is not English" would be a performative contradiction.

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Re: My write-up of the "Blue Eyes" solution (SPOILER A

Postby phlip » Wed Nov 12, 2014 11:28 pm UTC

Potatoberg wrote:You being able to comprehend this is proof that this is English.

But how do I know I'm comprehending you? How do I know with mathematical certainty that you're not using a word I've never seen before that happens to be spelled the same as "comprehend" but actually means something totally different? How do I know you're not testing out a new conlang that has words that happen to be spelled the same as English words, but all of them mean different things? You could be telling us all about how cute your new pet cat is, and we just think you're talking about standards of proof, because we're making the assumption that you're using English. I just can't rule out that option with mathematical certainty.

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Re: My write-up of the "Blue Eyes" solution (SPOILER A

Postby Potatoberg » Wed Nov 12, 2014 11:43 pm UTC

jestingrabbit wrote:No, I didn't. I suggested that

Ok then, if you want to be like that then join assholes club united, they'll love you.

jestingrabbit wrote:
There are no mirrors or reflecting surfaces, nothing dumb. 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."


She made that statement, and she is not lying or guessing. Therefore the puzzle states that the guru is reliable, using the third definition of lie at

http://dictionary.reference.com/browse/lie

Something being a lie is not the same as the act of lying. I could say that something false is a lie, but when we say that a person lies we mean that the person deliberately withholds the truth, thus the first definition of lie should be applied: "a false statement made with deliberate intent to deceive; an intentional untruth; a falsehood." instead of definition 3: "an inaccurate or false statement; a falsehood." There is a reason we don't say a student lies in a mathematics exam if his calculations are incorrect.

jestingrabbit wrote:Regarding your allusion to the term "ipse dixit", meaning an unadorned dogmatic statement: this is the nature of these puzzles! The setup is dogmatically asserted, and the solutions are arrived at by accepting the setup and making arguments regarding it.

But the islanders do not know that they are in a puzzle of this nature, thus they have no reason to take the words of the Guru as unquestionable truths. They also don't have a sign saying "do not question the words of the guru". Not that it matters if they are all "perfect logicians".
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