The Simple Logical Puzzle That Shows How Illogical People Are
May 22, 2015 10:27 AM Subscribe
[Test spoilers]
I was correct, but I think this is less "logic" and more "how well can you parse deliberately misleading questions". Knowing it was a puzzle that most people get wrong was what put me on the track of really attacking the initial question.
The question is designed to lead people into making an assumption about non-even numbers and non-blue cards; it's deliberately constructed that way (as opposed to saying something like "any card can have a blue back, but even-numbered cards must have a blue back").
My main takeaway is either "Peter Watson was not very good at constructing clear questions," or "Peter Watson was kind of a dick," I guess.
posted by Shepherd at 10:44 AM on May 22, 2015 [20 favorites]
I was correct, but I think this is less "logic" and more "how well can you parse deliberately misleading questions". Knowing it was a puzzle that most people get wrong was what put me on the track of really attacking the initial question.
The question is designed to lead people into making an assumption about non-even numbers and non-blue cards; it's deliberately constructed that way (as opposed to saying something like "any card can have a blue back, but even-numbered cards must have a blue back").
My main takeaway is either "Peter Watson was not very good at constructing clear questions," or "Peter Watson was kind of a dick," I guess.
posted by Shepherd at 10:44 AM on May 22, 2015 [20 favorites]
Or hey, I could finish reading the article before coming here to shoot my mouth off after completing the test, that would also be a thing I could do.
posted by Shepherd at 10:46 AM on May 22, 2015 [8 favorites]
posted by Shepherd at 10:46 AM on May 22, 2015 [8 favorites]
What's the answer? The "interactive" video isn't interactive for me and doesn't tell what the answer is and I didn't see it anywhere else in the article.
posted by Mavri at 10:50 AM on May 22, 2015 [4 favorites]
posted by Mavri at 10:50 AM on May 22, 2015 [4 favorites]
8, green.
Since there's no actual statement about odd numbers in the question, you're led to believe that you need to flip the five (to make sure the other side is not-blue) and the blue card (to ensure it's an even number).
But since any card can have a blue back regardless of number type, you only need to flip the 8 (confirming blue) and the green (confirming an odd number).
posted by Shepherd at 10:53 AM on May 22, 2015 [1 favorite]
Since there's no actual statement about odd numbers in the question, you're led to believe that you need to flip the five (to make sure the other side is not-blue) and the blue card (to ensure it's an even number).
But since any card can have a blue back regardless of number type, you only need to flip the 8 (confirming blue) and the green (confirming an odd number).
posted by Shepherd at 10:53 AM on May 22, 2015 [1 favorite]
The "interactive" video isn't interactive for me and doesn't tell what the answer is and I didn't see it anywhere else in the article.
I had to reload the video to get it to work.
posted by Pater Aletheias at 10:56 AM on May 22, 2015
I had to reload the video to get it to work.
posted by Pater Aletheias at 10:56 AM on May 22, 2015
You have to turn on video annotations.
posted by Holy Zarquon's Singing Fish at 10:58 AM on May 22, 2015
posted by Holy Zarquon's Singing Fish at 10:58 AM on May 22, 2015
But wouldn't you have to turn over the 5 to ensure there is not an even number on the back? (thus disproving even number cards have blue backs) Or is that not valid since the instructions say that cards have a number on one side and a color on the other. Why is one statement subject for testing and not the other statement?
posted by ian1977 at 11:08 AM on May 22, 2015 [11 favorites]
posted by ian1977 at 11:08 AM on May 22, 2015 [11 favorites]
Shepherd: "The question is designed to lead people into making an assumption about non-even numbers and non-blue cards; it's deliberately constructed that way (as opposed to saying something like "any card can have a blue back, but even-numbered cards must have a blue back").
"
I tend to disagree with you. It's a formal proposition, and (at least in the US) we seem to be devaluing teaching reasoning, it's harder for people to reason their way to the phrasing you came up with, which is functionally equivalent to Wason's statement.
posted by boo_radley at 11:09 AM on May 22, 2015 [2 favorites]
"
I tend to disagree with you. It's a formal proposition, and (at least in the US) we seem to be devaluing teaching reasoning, it's harder for people to reason their way to the phrasing you came up with, which is functionally equivalent to Wason's statement.
posted by boo_radley at 11:09 AM on May 22, 2015 [2 favorites]
Also, if Wason's original question is misleading, the video -- with its emphasis on the "most efficient solution" -- is even more so. Searching for an efficient solution strongly implies that you need to get data on some cards which can be extrapolated to the rest. But the solution isn't about extrapolation, because turning over the other two cards isn't redundant -- it's just extraneous to the properly understood problem.
posted by Holy Zarquon's Singing Fish at 11:09 AM on May 22, 2015 [2 favorites]
posted by Holy Zarquon's Singing Fish at 11:09 AM on May 22, 2015 [2 favorites]
My first answer was to turn over the 8 alone, and when I was told that was wrong I realized I had to flip over the green as well.
posted by Faint of Butt at 11:15 AM on May 22, 2015 [4 favorites]
posted by Faint of Butt at 11:15 AM on May 22, 2015 [4 favorites]
The more I think about it the more I think you would have to turn over all 4 cards, to make sure the other side wasn't even.
posted by ian1977 at 11:17 AM on May 22, 2015 [4 favorites]
posted by ian1977 at 11:17 AM on May 22, 2015 [4 favorites]
And yet, this is very easy when the rule has social relevance -- Imagine you're a bartender at an all-ages party. Guests must wear wristbands that mark them as adult or under-age, and there are alcohol and soda drink tickets. Under-age guests are not allowed to have alcohol. (That is, if a guest is under-age, they can only have soda.) There are four people at the bar:
- alcoholic drink ticket, can't see wristband
- soda ticket, can't see wristband
- adult wristband, can't see drink ticket
- under-age wristband, can't see drink ticket
Whose tickets/wristbands do you need to check to make sure you don't serve alcohol to minors?
posted by zeptoweasel at 11:18 AM on May 22, 2015 [10 favorites]
- alcoholic drink ticket, can't see wristband
- soda ticket, can't see wristband
- adult wristband, can't see drink ticket
- under-age wristband, can't see drink ticket
Whose tickets/wristbands do you need to check to make sure you don't serve alcohol to minors?
posted by zeptoweasel at 11:18 AM on May 22, 2015 [10 favorites]
My main takeaway is either "Peter Watson was not very good at constructing clear questions," or "Peter Watson was kind of a dick," I guess.
The point of the question is to show how illogical human thinking is and it succeeds beautifully, not by asking an unclear question, but because humans are, in fact, illogical thinkers who go for the comfort of a first guess that appears to match their assumptions.
posted by Revvy at 11:28 AM on May 22, 2015
The point of the question is to show how illogical human thinking is and it succeeds beautifully, not by asking an unclear question, but because humans are, in fact, illogical thinkers who go for the comfort of a first guess that appears to match their assumptions.
posted by Revvy at 11:28 AM on May 22, 2015
If you look at the actual research paper (which is linked in the article), it does look like they explain to the subjects the detail about what is on the cards in addition to asking the question. Except color was not used in the expirements, as it talks only about cards with letters on one side and numbers on the other.
posted by achrise at 11:30 AM on May 22, 2015 [2 favorites]
posted by achrise at 11:30 AM on May 22, 2015 [2 favorites]
I'm confused. It doesn't matter what's on the other face of the blue card, but why don't you have to flip the 5 to make sure there isn't an even number on the back?
posted by charismatic megafauna at 11:30 AM on May 22, 2015 [4 favorites]
posted by charismatic megafauna at 11:30 AM on May 22, 2015 [4 favorites]
ian1977: “But wouldn't you have to turn over the 5 to ensure there is not an even number on the back? (thus disproving even number cards have blue backs) Or is that not valid since the instructions say that cards have a number on one side and a color on the other. Why is one statement subject for testing and not the other statement?”
The instructions are the givens. They are assumed to be correct. They are not being tested.
In other words, one statement is subject to investigation because the person testing you says it's subject to investigation. The other statement is not because they say it's not. It's true that they might be lying about everything, but if so then there's no point in not picking up all four cards and burning them in a Satanic ritual in order to demonstrate the futility of all tests.
posted by koeselitz at 11:31 AM on May 22, 2015 [9 favorites]
The instructions are the givens. They are assumed to be correct. They are not being tested.
In other words, one statement is subject to investigation because the person testing you says it's subject to investigation. The other statement is not because they say it's not. It's true that they might be lying about everything, but if so then there's no point in not picking up all four cards and burning them in a Satanic ritual in order to demonstrate the futility of all tests.
posted by koeselitz at 11:31 AM on May 22, 2015 [9 favorites]
The more I think about it the more I think you would have to turn over all 4 cards, to make sure the other side wasn't even.
You don't have to turn over the blue card, because the if/then statement only goes one way -- if one face is even then the other face is blue. That doesn't mean only even-numbered cards have blue backs.
But if we're being literal you do have to turn over the 5, because it could have an even number on the other side. The question doesn't specify that all cards have one number side and one color side.
posted by Holy Zarquon's Singing Fish at 11:32 AM on May 22, 2015
You don't have to turn over the blue card, because the if/then statement only goes one way -- if one face is even then the other face is blue. That doesn't mean only even-numbered cards have blue backs.
But if we're being literal you do have to turn over the 5, because it could have an even number on the other side. The question doesn't specify that all cards have one number side and one color side.
posted by Holy Zarquon's Singing Fish at 11:32 AM on May 22, 2015
...actually, wait, it does say that. Nevermind.
posted by Holy Zarquon's Singing Fish at 11:32 AM on May 22, 2015 [4 favorites]
posted by Holy Zarquon's Singing Fish at 11:32 AM on May 22, 2015 [4 favorites]
Oh. I should have read the instructions carefully.
posted by charismatic megafauna at 11:33 AM on May 22, 2015
posted by charismatic megafauna at 11:33 AM on May 22, 2015
I thought at first that it was a semantic trick involving the word "shows". Since the blue and green cards "show" no numbers, the statement is irrelevant to them.
posted by mr_roboto at 11:45 AM on May 22, 2015
posted by mr_roboto at 11:45 AM on May 22, 2015
(Prefacing my comment by saying I got the right answer!)
Part of the problem may be the idea of testing the hypothesis (that all even numbers have blue on the back). People may naturally gravitate towards finding inductive evidence for this hypothesis, whereas the correct answer assumes, following Popper and the problems with induction that Hume raised, that we can only seek to falsify the hypothesis.
Looking at this intuitively, it is similar to the Raven paradox, which points out that if you wanted to verify that all ravens are black, you could go about this, according to standard logic, by verifying that all green things weren't ravens, all red things weren't ravens, etc. You find a blade of grass and exclaim: "Just as I thought! More evidence that all ravens are black! This green thing could have been a raven, disproving the hypothesis, but in fact it is a blade of grass!"
Likewise, if you'd only seen a couple of ravens in your life, you might think it was hasty to jump to the conclusion that all ravens were black (no matter how many blades of grass you studied), but if you'd seen thousands upon thousands (and yet no green ravens), you'd feel more confident that all ravens were black. Turning over the blue card carries the possibility that it will reveal an even number, which provides intuitive inductive evidence that all even cards have blue on their reverse side.
posted by Schmucko at 11:48 AM on May 22, 2015 [3 favorites]
Part of the problem may be the idea of testing the hypothesis (that all even numbers have blue on the back). People may naturally gravitate towards finding inductive evidence for this hypothesis, whereas the correct answer assumes, following Popper and the problems with induction that Hume raised, that we can only seek to falsify the hypothesis.
Looking at this intuitively, it is similar to the Raven paradox, which points out that if you wanted to verify that all ravens are black, you could go about this, according to standard logic, by verifying that all green things weren't ravens, all red things weren't ravens, etc. You find a blade of grass and exclaim: "Just as I thought! More evidence that all ravens are black! This green thing could have been a raven, disproving the hypothesis, but in fact it is a blade of grass!"
Likewise, if you'd only seen a couple of ravens in your life, you might think it was hasty to jump to the conclusion that all ravens were black (no matter how many blades of grass you studied), but if you'd seen thousands upon thousands (and yet no green ravens), you'd feel more confident that all ravens were black. Turning over the blue card carries the possibility that it will reveal an even number, which provides intuitive inductive evidence that all even cards have blue on their reverse side.
posted by Schmucko at 11:48 AM on May 22, 2015 [3 favorites]
While the study says that "it will be appreciated that [cards will have only a letter on one side and only a letter on the other]" in the materials section, I'm missing any communication to the test subject that this is the case.
posted by a box and a stick and a string and a bear at 11:48 AM on May 22, 2015
posted by a box and a stick and a string and a bear at 11:48 AM on May 22, 2015
Whose tickets/wristbands do you need to check to make sure you don't serve alcohol to minors?
All of them to be safe. At least in Oregon, you must check the ID of anyone who appears under 30, and the policy of many venues that have a mix of drinking age and underage patrons is to check everybody's ID regardless. The penalties for serving someone underage are harsh for the business and the server, and trying to save 30 seconds by making it a logic problem is probably not great from a cost benefit perspective.
posted by OverlappingElvis at 11:49 AM on May 22, 2015 [5 favorites]
All of them to be safe. At least in Oregon, you must check the ID of anyone who appears under 30, and the policy of many venues that have a mix of drinking age and underage patrons is to check everybody's ID regardless. The penalties for serving someone underage are harsh for the business and the server, and trying to save 30 seconds by making it a logic problem is probably not great from a cost benefit perspective.
posted by OverlappingElvis at 11:49 AM on May 22, 2015 [5 favorites]
Whose tickets/wristbands do you need to check to make sure you don't serve alcohol to minors?
All of them to be safe. At least in Oregon...
Further proof of how illogical Oregon is.
posted by miguelcervantes at 11:52 AM on May 22, 2015
All of them to be safe. At least in Oregon...
Further proof of how illogical Oregon is.
posted by miguelcervantes at 11:52 AM on May 22, 2015
The wrist band essentially is the ID check in that case. If you want to get rid of the fraud element in the hypothetical, feel free to sub in an infallible doorman that checks all IDs and then dunks the guest in an ink that only the doorman has access to.
posted by a box and a stick and a string and a bear at 11:53 AM on May 22, 2015 [1 favorite]
posted by a box and a stick and a string and a bear at 11:53 AM on May 22, 2015 [1 favorite]
Further proof of how illogical Oregon is.
Well, the OLCC, anyway.
posted by bink at 12:04 PM on May 22, 2015
Well, the OLCC, anyway.
posted by bink at 12:04 PM on May 22, 2015
Page 275 "The subjects were told that cards with letters on their front had numbers on their back and vice versa. "
posted by achrise at 12:05 PM on May 22, 2015
posted by achrise at 12:05 PM on May 22, 2015
if a card shows an even number on one face, then its opposite face is blue. Which cards must you turn over in order to test the truth of his proposition, without turning over any unnecessary cards?
Lets say "8" is on the opposite face of every card from the YouTube image in the article. Now what. The proposition isn't true. For example, the first card shows an even number on one face, and its opposite face is a "5". But you can't know it, smarmy voiceover, because you were too stuck up to turn over the "5" card.
posted by cashman at 12:07 PM on May 22, 2015
Lets say "8" is on the opposite face of every card from the YouTube image in the article. Now what. The proposition isn't true. For example, the first card shows an even number on one face, and its opposite face is a "5". But you can't know it, smarmy voiceover, because you were too stuck up to turn over the "5" card.
posted by cashman at 12:07 PM on May 22, 2015
Page 275 "The subjects were told that cards with letters on their front had numbers on their back and vice versa. "
So it's just this shitty article that botched the instructions. Well that sucks.
posted by cashman at 12:07 PM on May 22, 2015 [3 favorites]
So it's just this shitty article that botched the instructions. Well that sucks.
posted by cashman at 12:07 PM on May 22, 2015 [3 favorites]
With the qualification that I have training in formal logic and philosophy of knowledge and science, but very little of the psychology that seems to be that actual scope of discussion in the article:
The idea that the underage drinking phrasing is easier has less to do with "social relevance" than that it's essentially stating the contrapositive of the implication. Stating the original problem "if a card has one face of a color that's not blue, its other face must not be an even number" would probably result in more correct answers.
Per my caveat, I bet someone has done a study with this variation, but it's kind of annoying the Nautilus article heads off in the "people reason good about people stuff" angle.
posted by 7segment at 12:09 PM on May 22, 2015
The idea that the underage drinking phrasing is easier has less to do with "social relevance" than that it's essentially stating the contrapositive of the implication. Stating the original problem "if a card has one face of a color that's not blue, its other face must not be an even number" would probably result in more correct answers.
Per my caveat, I bet someone has done a study with this variation, but it's kind of annoying the Nautilus article heads off in the "people reason good about people stuff" angle.
posted by 7segment at 12:09 PM on May 22, 2015
Yeah I went through about three cycles of being confident in my answer, getting surprised by the comments here, and re-reading the article before I just looked up the damn thing on Wikipedia.
posted by Monochrome at 12:10 PM on May 22, 2015
posted by Monochrome at 12:10 PM on May 22, 2015
So it's just this shitty article that botched the instructions. Well that sucks.
Both the article and the video specify this.
" In one version of the task, one subject (always one—he spurned testing subjects in groups) is presented with four cards lying flat on a table, each with a single-digit number on one face and one of two colors on the other."
And, from the video:
"Each card has a number on one side and a color on the other side" (First 7 seconds).
posted by miguelcervantes at 12:10 PM on May 22, 2015 [3 favorites]
Both the article and the video specify this.
" In one version of the task, one subject (always one—he spurned testing subjects in groups) is presented with four cards lying flat on a table, each with a single-digit number on one face and one of two colors on the other."
And, from the video:
"Each card has a number on one side and a color on the other side" (First 7 seconds).
posted by miguelcervantes at 12:10 PM on May 22, 2015 [3 favorites]
I got it right on the first try without confusion. Maybe programming has made me take things like this very literally.
Whose tickets/wristbands do you need to check to make sure you don't serve alcohol to minors?
I think the way this is presented, people are likely to add an implicit rule -- bartenders must collect tickets, or at least verify they're not serving alcohol to adults with soda tickets. That changes the answer.
posted by Foosnark at 12:12 PM on May 22, 2015 [2 favorites]
Whose tickets/wristbands do you need to check to make sure you don't serve alcohol to minors?
I think the way this is presented, people are likely to add an implicit rule -- bartenders must collect tickets, or at least verify they're not serving alcohol to adults with soda tickets. That changes the answer.
posted by Foosnark at 12:12 PM on May 22, 2015 [2 favorites]
Both the article and the video specify this.
The article does - I went to actually try the puzzle first, so the initial part shoved in the banter and talk about him chatting with subjects, I missed. The way the article is formatted, they have a paragraph break and then instructions right above the puzzle, like that is the instruction set for it.
The video is embedded to start at the 31-second mark, so that's why people would never even see that.
posted by cashman at 12:15 PM on May 22, 2015
The article does - I went to actually try the puzzle first, so the initial part shoved in the banter and talk about him chatting with subjects, I missed. The way the article is formatted, they have a paragraph break and then instructions right above the puzzle, like that is the instruction set for it.
The video is embedded to start at the 31-second mark, so that's why people would never even see that.
posted by cashman at 12:15 PM on May 22, 2015
I think there's something to the "cheater detection module" hypothesis. If the problem is phrased as "disallowed: even and not blue" then the answer seems to be more obvious than when phrased in the "if then" way.
posted by Pyry at 12:38 PM on May 22, 2015 [1 favorite]
posted by Pyry at 12:38 PM on May 22, 2015 [1 favorite]
Looking at this intuitively, it is similar to the Raven paradox, which points out that if you wanted to verify that all ravens are black
Ahem.
posted by Faint of Butt at 12:47 PM on May 22, 2015 [3 favorites]
Ahem.
posted by Faint of Butt at 12:47 PM on May 22, 2015 [3 favorites]
I wish they were real cards, so I could get mad and toss them in the air. Every time she says "You're wrong," I swear at her, kind of like when my GPS gets uppity.
posted by theora55 at 1:04 PM on May 22, 2015
posted by theora55 at 1:04 PM on May 22, 2015
Foosnark: "I got it right on the first try without confusion. Maybe programming has made me take things like this very literally.
"
Same here. Careful reading is required, not nice-to-have.
posted by signal at 1:09 PM on May 22, 2015 [6 favorites]
"
Same here. Careful reading is required, not nice-to-have.
posted by signal at 1:09 PM on May 22, 2015 [6 favorites]
Nailed it!
posted by Mental Wimp at 1:17 PM on May 22, 2015
posted by Mental Wimp at 1:17 PM on May 22, 2015
In programming this is a very natural problem--whenever you have a piece of code with unbound variables and you need to predict the behavior of the code, I.e. check that it satisfies some property. The mathematics of model theory provides the framework for this general problem, and a major research problem is how to check properties efficiently (due to the exponential complexity of cases)--flipping the least number of cards in this case.
posted by polymodus at 1:26 PM on May 22, 2015
posted by polymodus at 1:26 PM on May 22, 2015
Yeah, I don't think this is in any way misleading. But I suppose if you're not used to formal logic or programming or anything where you have to think "what is _actually being said_, not _what is implied_" then it could be tricky. There is only one constraint, there is no "trick" to it --- but people either add their own rules (like thinking somehow that it says anything about odd numbers or blue backed cards, when it specifically only applies to cards that have or could have an even number) or suspect a real "gotcha" answer (those who missed the first part of the instructions and thought a card could have numbers on both sides).
posted by thefoxgod at 1:43 PM on May 22, 2015
posted by thefoxgod at 1:43 PM on May 22, 2015
“Perhaps I was drawn towards the topic of reasoning because most things in life seemed unreasonable" is a great way to end this article.
(While the OLCC is indeed insane, the upside of their legal monopoly is oregonliquorsearch.com, the greatest website since HayNet. It can tell you how many bottles of W.L. Weller Antique Reserve are on the shelf before you drive to the store.)
posted by fifteen schnitzengruben is my limit at 1:50 PM on May 22, 2015 [1 favorite]
(While the OLCC is indeed insane, the upside of their legal monopoly is oregonliquorsearch.com, the greatest website since HayNet. It can tell you how many bottles of W.L. Weller Antique Reserve are on the shelf before you drive to the store.)
posted by fifteen schnitzengruben is my limit at 1:50 PM on May 22, 2015 [1 favorite]
I feel like this test is unfair because it required me to read and understand the instructions before clicking.
posted by goatdog at 1:54 PM on May 22, 2015 [10 favorites]
posted by goatdog at 1:54 PM on May 22, 2015 [10 favorites]
Yeah, I don't think this is in any way misleading. But I suppose if you're not used to formal logic or programming or anything where you have to think "what is _actually being said_, not _what is implied_" then it could be tricky.
There's also the added benefit of there being something at stake in both programming and the "socially contextualized" form of the problem mentioned in the article. Granted there's some short-term ego damage if you get the problem wrong, but there are no concrete consequences nor any sense of task urgency.
posted by kewb at 2:07 PM on May 22, 2015
There's also the added benefit of there being something at stake in both programming and the "socially contextualized" form of the problem mentioned in the article. Granted there's some short-term ego damage if you get the problem wrong, but there are no concrete consequences nor any sense of task urgency.
posted by kewb at 2:07 PM on May 22, 2015
This stupid puzzle conflates formal logic and normal language usage.
To someone used to formal logic, the statement "even front implies blue back" means just that. And the 'correct' solution is obvious.
But in common usage, the converse is also implied: "odd front implies non-blue back." That is how statements are generally understood: when the law says "You must stop when the light is red", we do not ask "Must we also stop when the light is green?" No, go on green is implied, otherwise, there is no reason to mention color at all. The converse of a useful implication is true.
I also note, as mentioned about, that the '5' card must be checked, because it could have an even number on its other side. The statement of the puzzle does not require that all cards have a number on one side and a color on the back--there may be numbers on both sides. Or perhaps some of the cards have no other side.
This is the kind of error nearly-smart people make all the time. Smart people (like me) make the same errors too, be we know the errors are there, waiting to reveal us as the jerks we are.
In conclusion: NEVER implement your own clever encryption scheme. You are too stupid, for all values of 'you'.
posted by hexatron at 2:53 PM on May 22, 2015 [1 favorite]
To someone used to formal logic, the statement "even front implies blue back" means just that. And the 'correct' solution is obvious.
But in common usage, the converse is also implied: "odd front implies non-blue back." That is how statements are generally understood: when the law says "You must stop when the light is red", we do not ask "Must we also stop when the light is green?" No, go on green is implied, otherwise, there is no reason to mention color at all. The converse of a useful implication is true.
I also note, as mentioned about, that the '5' card must be checked, because it could have an even number on its other side. The statement of the puzzle does not require that all cards have a number on one side and a color on the back--there may be numbers on both sides. Or perhaps some of the cards have no other side.
This is the kind of error nearly-smart people make all the time. Smart people (like me) make the same errors too, be we know the errors are there, waiting to reveal us as the jerks we are.
In conclusion: NEVER implement your own clever encryption scheme. You are too stupid, for all values of 'you'.
posted by hexatron at 2:53 PM on May 22, 2015 [1 favorite]
This stupid puzzle conflates formal logic and normal language usage.
The correct answer to the puzzle is correct even given that ambiguity. You're only saying that there are answers that would be correct if you assume one kind of usage or the other.
The statement of the puzzle does not require that all cards have a number on one side and a color on the back--there may be numbers on both sides. Or perhaps some of the cards have no other side.
The statement of the puzzle includes this:
The correct answer to the puzzle is correct even given that ambiguity. You're only saying that there are answers that would be correct if you assume one kind of usage or the other.
The statement of the puzzle does not require that all cards have a number on one side and a color on the back--there may be numbers on both sides. Or perhaps some of the cards have no other side.
The statement of the puzzle includes this:
four cards lying flat on a table, each with a single-digit number on one face and one of two colors on the other.posted by straight at 3:20 PM on May 22, 2015 [3 favorites]
Calling it illogical seems an odd way of putting it. For example, I did 8/blue/green; I wasn't being illogical, I was extending the logic to assume symmetry. It's a useful way of demonstrating unconscious assumptions about the logical frame, sure, but it's not illogical, since that's how we tend to organize things.
posted by tavella at 3:22 PM on May 22, 2015
posted by tavella at 3:22 PM on May 22, 2015
hexatron: “This stupid puzzle conflates formal logic and normal language usage. To someone used to formal logic, the statement 'even front implies blue back' means just that. And the 'correct' solution is obvious. But in common usage, the converse is also implied: ‘odd front implies non-blue back.’ That is how statements are generally understood: when the law says ‘You must stop when the light is red’, we do not ask ‘Must we also stop when the light is green?’ No, go on green is implied, otherwise, there is no reason to mention color at all. The converse of a useful implication is true.”
This seems wrong to me. We constantly encounter normal, everyday situations, described by normal, everyday usage, wherein the converse of a correct statement is absolutely not accepted to be true.
Your example is sort of confusing, I think; "you must stop when the light is red" might seem to imply that you must go when the light is a different color (i.e. green) – but it absolutely does not, because the fact that you have to stop at a red light doesn't say anything whatsoever about what you should do at a green light, or when you should go, etc. You aren't allowed to just go when the light is not-red – what if the light is yellow, or there happens to be somebody who stumbled into the crosswalk, etc? – nor are you told if there might be other situations in which you really should go. "Red means stop / green means go" is itself an oversimplified binary, which is why the law doesn't say that; you are required to stop at a red light, but you are not necessarily required, in most situations, to go for a green light.
In short: the experiment is about the fact that, although it may be true that all cards with even numbers have blue backs, that doesn't necessarily mean that all cards with blue backs have even numbers on the other side. Similarly, in the real world, although it is true that when you see a red light you must stop, that doesn't necessarily mean that when you are stopped it is because of a red light; nor is it necessarily true that when the light is not-red you must go.
Even in "normal usage," we have to be able to distinguish situations in which "A, therefore B" does not imply "B, therefore A." That's not just an over-complicated situation that formal logic deals with. It's one that is quite common in the world, as your example shows.
posted by koeselitz at 3:23 PM on May 22, 2015 [3 favorites]
This seems wrong to me. We constantly encounter normal, everyday situations, described by normal, everyday usage, wherein the converse of a correct statement is absolutely not accepted to be true.
Your example is sort of confusing, I think; "you must stop when the light is red" might seem to imply that you must go when the light is a different color (i.e. green) – but it absolutely does not, because the fact that you have to stop at a red light doesn't say anything whatsoever about what you should do at a green light, or when you should go, etc. You aren't allowed to just go when the light is not-red – what if the light is yellow, or there happens to be somebody who stumbled into the crosswalk, etc? – nor are you told if there might be other situations in which you really should go. "Red means stop / green means go" is itself an oversimplified binary, which is why the law doesn't say that; you are required to stop at a red light, but you are not necessarily required, in most situations, to go for a green light.
In short: the experiment is about the fact that, although it may be true that all cards with even numbers have blue backs, that doesn't necessarily mean that all cards with blue backs have even numbers on the other side. Similarly, in the real world, although it is true that when you see a red light you must stop, that doesn't necessarily mean that when you are stopped it is because of a red light; nor is it necessarily true that when the light is not-red you must go.
Even in "normal usage," we have to be able to distinguish situations in which "A, therefore B" does not imply "B, therefore A." That's not just an over-complicated situation that formal logic deals with. It's one that is quite common in the world, as your example shows.
posted by koeselitz at 3:23 PM on May 22, 2015 [3 favorites]
It would have helped if they would have defined whether the universe was only the cards presented or all possible cards. If you start the test by saying "for only the cards in front of you," the test subject stops trying to solve for all possible future card sets. Then the problem becomes easy.
I agree with others that this is less of a test of innate human test subject nature and a test of some people thinking they are oh-so-cleaver when in fact they rig the game by being unclear. They don't mean to be unclear, but they are. No matter what, assumptions are required with a lack of clarity, and it's not that people are not logical, it's that they make assumptions in a given direction away from the test intentions.
I suppose if you are given enough time you could run the permutations on the various assumptions and reverse engineer that you can only perceive the test as against the 4 cards because that is the assumption needed to come to a presented solution. That seems to not really test the psychological thesis presented.
posted by Muddler at 3:26 PM on May 22, 2015
I agree with others that this is less of a test of innate human test subject nature and a test of some people thinking they are oh-so-cleaver when in fact they rig the game by being unclear. They don't mean to be unclear, but they are. No matter what, assumptions are required with a lack of clarity, and it's not that people are not logical, it's that they make assumptions in a given direction away from the test intentions.
I suppose if you are given enough time you could run the permutations on the various assumptions and reverse engineer that you can only perceive the test as against the 4 cards because that is the assumption needed to come to a presented solution. That seems to not really test the psychological thesis presented.
posted by Muddler at 3:26 PM on May 22, 2015
I like to think outside the box. My answer is to punch the researcher in the face.
posted by rankfreudlite at 3:26 PM on May 22, 2015 [2 favorites]
posted by rankfreudlite at 3:26 PM on May 22, 2015 [2 favorites]
Muddler: "It would have helped if they would have defined whether the universe was only the cards presented or all possible cards. "
The test is defined in terms of the four cards on the table. What do you mean by 'universe' and why would you care about 'all possible cards'?
I don't know about the original experiment, but some of the comments in this thread really point out the strange contortions some people seem to get into when faced with simple logic puzzles.
posted by signal at 3:36 PM on May 22, 2015 [10 favorites]
The test is defined in terms of the four cards on the table. What do you mean by 'universe' and why would you care about 'all possible cards'?
I don't know about the original experiment, but some of the comments in this thread really point out the strange contortions some people seem to get into when faced with simple logic puzzles.
posted by signal at 3:36 PM on May 22, 2015 [10 favorites]
I feel like this test is unfair because it required me to read and understand the instructions before clicking.
Poor presentation. I/O psychology isn't just a river in Egypt. Yeah.
posted by cashman at 4:03 PM on May 22, 2015
Poor presentation. I/O psychology isn't just a river in Egypt. Yeah.
posted by cashman at 4:03 PM on May 22, 2015
Signal: You are using a myopic view and assuming that "If a card . . ." means only the cards show. If you watch the entire video and read nothing more as the video is the sum of the test, the transcript is:
You are shown a set of four cards. Each card has a number on one side and a color on the other side. We would like to test the truth of the following statement: "If a card shows an even number on one face, then its opposite face is blue." Which card or cards must you turn over to test the truth of this proposition. Of course you could turn over all four cards, but what is the most efficient way to do it. Click on your answer.
You said "The test is defined in terms of the four cards on the table."
Where? They never say that. You are making that assumption. The proposition is only "If a card shows an even number on one face, then its opposite face is blue." You must assume that "a card" means only the four on the table, not the universe of possible cards. Proofs try to look at the world as a whole, and when presented with a common item like a card, it is logical to consider this as a proof of a universe of cards beyond the four in front of you. It is no more logical to be myopic, except that you must be to solve the question. It is also odd to play games and not set out that bit of instruction at the beginning to clarify the test. If the test question is unclear, then the conclusions drawn from the test must factor in the confusion, otherwise the test consists of unintended variables and conclusions are incorrect.
What is disheartening is that so many on this thread are demeaning to those that criticize the test or assume some weird superiority for having gotten the answer quickly and correctly. For what it is worth, yes, I've taken logic puzzle tests under testing procedures for academic purposes and done well, and if you do enough logic puzzles, you start to recognize poorly worded ones. Interestingly, it sounds as though the actual researcher here may have used more complicated introductions and conversations during testing to clarify the ground rules and the question, so perhaps what is really happening is this is just a shitty video representation of much better research.
posted by Muddler at 4:27 PM on May 22, 2015 [1 favorite]
You are shown a set of four cards. Each card has a number on one side and a color on the other side. We would like to test the truth of the following statement: "If a card shows an even number on one face, then its opposite face is blue." Which card or cards must you turn over to test the truth of this proposition. Of course you could turn over all four cards, but what is the most efficient way to do it. Click on your answer.
You said "The test is defined in terms of the four cards on the table."
Where? They never say that. You are making that assumption. The proposition is only "If a card shows an even number on one face, then its opposite face is blue." You must assume that "a card" means only the four on the table, not the universe of possible cards. Proofs try to look at the world as a whole, and when presented with a common item like a card, it is logical to consider this as a proof of a universe of cards beyond the four in front of you. It is no more logical to be myopic, except that you must be to solve the question. It is also odd to play games and not set out that bit of instruction at the beginning to clarify the test. If the test question is unclear, then the conclusions drawn from the test must factor in the confusion, otherwise the test consists of unintended variables and conclusions are incorrect.
What is disheartening is that so many on this thread are demeaning to those that criticize the test or assume some weird superiority for having gotten the answer quickly and correctly. For what it is worth, yes, I've taken logic puzzle tests under testing procedures for academic purposes and done well, and if you do enough logic puzzles, you start to recognize poorly worded ones. Interestingly, it sounds as though the actual researcher here may have used more complicated introductions and conversations during testing to clarify the ground rules and the question, so perhaps what is really happening is this is just a shitty video representation of much better research.
posted by Muddler at 4:27 PM on May 22, 2015 [1 favorite]
I think the subjects know that the experimenter's communication and their own reasoning are imperfect, so they "irrationally" want to verify the truth of conditions already implied in what they've been told. The wristband/drink ticket analogy where everything is spelled out still made me think that it would be simpler to just check all wristbands AND tickets than to sort out the implied categories, at least on my first shift bartending.
posted by 3urypteris at 4:34 PM on May 22, 2015
posted by 3urypteris at 4:34 PM on May 22, 2015
My experience agrees with the researchers who assert humans are less 'illogical' than 'cognitively lazy'.
"Irrationality" is most often "I just don't feel like thinking about it, so I'm going with my visceral, emotional reaction instead," which, of course, feels great in the moment.
posted by LooseFilter at 4:53 PM on May 22, 2015 [4 favorites]
"Irrationality" is most often "I just don't feel like thinking about it, so I'm going with my visceral, emotional reaction instead," which, of course, feels great in the moment.
posted by LooseFilter at 4:53 PM on May 22, 2015 [4 favorites]
3urypteris, I think you make a good point.
There is value in efficient logic to solve for large data sets. However, once you narrow this test to four cards in front of you, taking even an extra second thinking through what is the most efficient way to the answer in terms of number of card flips is actually very inefficient in terms of time, wherein an answer could be derived almost immediately by flipping all the cards and not thinking through the logic.
Our minds are somewhat wired for simple answers obtainable quickly through brute force. You have to break out of that mold to make great things happen on large scale, but sometimes using our senses to survey small things in front of us is the "right" answer in terms of overall efficiency.
There is also an elegance in simple solutions even if sometimes they appear brutish or "lazy." If you tried to use pure math to find the volume of a human, you would encounter some very complex math to account all our bumps and lumps, and likely you would never quite get there and settle for an approximation. However, if you just dunk us in a tub of water and measure the displacement in a simplified geometric vessel, you get an exact measurement that is precise to the limits of the measurement tools. Is that lazy? Maybe.
posted by Muddler at 4:59 PM on May 22, 2015 [3 favorites]
There is value in efficient logic to solve for large data sets. However, once you narrow this test to four cards in front of you, taking even an extra second thinking through what is the most efficient way to the answer in terms of number of card flips is actually very inefficient in terms of time, wherein an answer could be derived almost immediately by flipping all the cards and not thinking through the logic.
Our minds are somewhat wired for simple answers obtainable quickly through brute force. You have to break out of that mold to make great things happen on large scale, but sometimes using our senses to survey small things in front of us is the "right" answer in terms of overall efficiency.
There is also an elegance in simple solutions even if sometimes they appear brutish or "lazy." If you tried to use pure math to find the volume of a human, you would encounter some very complex math to account all our bumps and lumps, and likely you would never quite get there and settle for an approximation. However, if you just dunk us in a tub of water and measure the displacement in a simplified geometric vessel, you get an exact measurement that is precise to the limits of the measurement tools. Is that lazy? Maybe.
posted by Muddler at 4:59 PM on May 22, 2015 [3 favorites]
This test also fails to account for the fourth dimension.
posted by goatdog at 5:19 PM on May 22, 2015
posted by goatdog at 5:19 PM on May 22, 2015
I'm a regulator. I reserve the right to check any card I want at any time whether it's necessary or not. And sometimes I will just to remind you that I can. (But I still got the right answer)
Or sometimes maybe I won't check any, just assert that you're in violation and make you do the work.
posted by ctmf at 5:21 PM on May 22, 2015 [1 favorite]
Or sometimes maybe I won't check any, just assert that you're in violation and make you do the work.
posted by ctmf at 5:21 PM on May 22, 2015 [1 favorite]
Muddler: "You are using a myopic view"
Nope. I'm using a view that solves the puzzle.
Muddler: "You said "The test is defined in terms of the four cards on the table."
Where? They never say that. You are making that assumption."
"You are shown a set of four cards."
Muddler: "when presented with a common item like a card, it is logical to consider this as a proof of a universe of cards beyond the four in front of you."
Not really. This is what I mean by 'strange contortions'.
posted by signal at 5:38 PM on May 22, 2015 [3 favorites]
Nope. I'm using a view that solves the puzzle.
Muddler: "You said "The test is defined in terms of the four cards on the table."
Where? They never say that. You are making that assumption."
"You are shown a set of four cards."
Muddler: "when presented with a common item like a card, it is logical to consider this as a proof of a universe of cards beyond the four in front of you."
Not really. This is what I mean by 'strange contortions'.
posted by signal at 5:38 PM on May 22, 2015 [3 favorites]
Hm! Well, to help people along, from paragraph 5:
posted by boo_radley at 6:26 PM on May 22, 2015 [1 favorite]
The reigning assumption was that humans naturally reasoned analytically, but here was Wason’s subject admitting that, if given the choice, he’d be irrational again. It made Wason wonder: Is it the logical structure of the rules that make the puzzle difficult, or are people tripped up merely by the words with which the puzzle is expressed?The article then goes on to explain two methods of analytical thinking. This might be interesting to read.
posted by boo_radley at 6:26 PM on May 22, 2015 [1 favorite]
Maybe programming has made me take things like this very literally
I think this is possibly true. I got this right and tend to solve trick questions and riddles like this, and I attribute it mostly to training in programming and mathematical proof writing.
Now WHOSE GUESSES HERE DO I HAVE TO CHECK TO PROVE THIS?!?!!!!
posted by easter queen at 7:29 PM on May 22, 2015
I think this is possibly true. I got this right and tend to solve trick questions and riddles like this, and I attribute it mostly to training in programming and mathematical proof writing.
Now WHOSE GUESSES HERE DO I HAVE TO CHECK TO PROVE THIS?!?!!!!
posted by easter queen at 7:29 PM on May 22, 2015
Of course you could turn over all four cards, but what is the most efficient way to do it. Click on your answer.
If turning over all the cards tells you all you needed to know to verify the rule, we have to be trying to verify the rule for only those four cards.
I'm totally not getting it. How does considering 4 cards or an infinite number of cards change which of the 4 cards you select to turn over to test the truth of the statement "All cards with even numbers have blue backs"?
If there are more cards than the four you are seen, you can hope at most to falsify the statement: you can't prove the statement is true for all cards just by looking at four. But, the cards you'd want to turn over to falsify the statement for all cards are the same two cards you'd want to turn over to falsify/verify the statement for the four cards you have.
posted by BungaDunga at 7:36 PM on May 22, 2015 [1 favorite]
If turning over all the cards tells you all you needed to know to verify the rule, we have to be trying to verify the rule for only those four cards.
I'm totally not getting it. How does considering 4 cards or an infinite number of cards change which of the 4 cards you select to turn over to test the truth of the statement "All cards with even numbers have blue backs"?
If there are more cards than the four you are seen, you can hope at most to falsify the statement: you can't prove the statement is true for all cards just by looking at four. But, the cards you'd want to turn over to falsify the statement for all cards are the same two cards you'd want to turn over to falsify/verify the statement for the four cards you have.
posted by BungaDunga at 7:36 PM on May 22, 2015 [1 favorite]
That's what I understood the puzzle to be. Assuming the four cards are a sample of an infinite number, it's testing my ability to recognize that there's no way to prove the statement true for all cards—the best I can do is check that it's not provably false. And I only need two of the four sample cards to do that.
posted by ctmf at 7:53 PM on May 22, 2015
posted by ctmf at 7:53 PM on May 22, 2015
the narrative hides itself. This is not a puzzle. Clever is not the same as smart. so as it ever was
posted by yesster at 7:58 PM on May 22, 2015
posted by yesster at 7:58 PM on May 22, 2015
I'm amazed at how butthurt most of you are about getting the puzzle wrong. Relax!
posted by adecusatis at 8:03 PM on May 22, 2015 [1 favorite]
posted by adecusatis at 8:03 PM on May 22, 2015 [1 favorite]
As I recall from a freshman class in logical programming analysis, none of my peers immediately understood implication. I'm not surprised your average psych study participant failed it. Fortunately I've seen presenters mention this particular puzzle a few times, even the bit about social contexts mattering.
posted by pwnguin at 8:10 PM on May 22, 2015
posted by pwnguin at 8:10 PM on May 22, 2015
It's not even deceptively simple. It's just simple. To put it in plainer terms:
1. You are shown 4 objects.
2. You are told a statement regarding them.
3. You are asked to determine if the statement is true.
4. In order to determine if the statement is true, you have to turn over all 4 objects, because the statement is about a condition common to all 4 objects.
posted by rankfreudlite at 8:27 PM on May 22, 2015
1. You are shown 4 objects.
2. You are told a statement regarding them.
3. You are asked to determine if the statement is true.
4. In order to determine if the statement is true, you have to turn over all 4 objects, because the statement is about a condition common to all 4 objects.
posted by rankfreudlite at 8:27 PM on May 22, 2015
And yet you just failed. If you know someone is over 21, you dont need to check the contents of their Solo cup.
posted by pwnguin at 8:52 PM on May 22, 2015 [1 favorite]
posted by pwnguin at 8:52 PM on May 22, 2015 [1 favorite]
It is however, simple to summarize if you sit down and analyze logically.
1. The rule is "if a card shows an even number, then its opposite face is blue"
2. If statements are logical implications: a implies b, or a -> b
3. Implications can be rewritten as (not a) OR B.
4. We can therefore rewrite the rule as "does not show an even number or blue, " simplified to "shows an odd number or blue"
5. An OR statement is true if either condition is true. I.e. If one of the two conditions is satisfied, you don't need to check the other condition to validate the claim.
6. The odd face up and the blue face up satisfy the or conditional immediately, and thus do not need to be flipped.
7. Thus, the green and even cards need to be checked.
posted by pwnguin at 9:10 PM on May 22, 2015 [1 favorite]
1. The rule is "if a card shows an even number, then its opposite face is blue"
2. If statements are logical implications: a implies b, or a -> b
3. Implications can be rewritten as (not a) OR B.
4. We can therefore rewrite the rule as "does not show an even number or blue, " simplified to "shows an odd number or blue"
5. An OR statement is true if either condition is true. I.e. If one of the two conditions is satisfied, you don't need to check the other condition to validate the claim.
6. The odd face up and the blue face up satisfy the or conditional immediately, and thus do not need to be flipped.
7. Thus, the green and even cards need to be checked.
posted by pwnguin at 9:10 PM on May 22, 2015 [1 favorite]
If you've been told "all women must have long hair", and want to enforce this:
You don't care about men at all (they could have short or long hair). You don't care about long-haired people (they could be men or women).
You just need to look at women (to make sure they have long hair) and short-haired people (to make sure they're not women).
In other words: men can't break the rule, and neither can people with long hair.
posted by BungaDunga at 9:27 PM on May 22, 2015 [1 favorite]
You don't care about men at all (they could have short or long hair). You don't care about long-haired people (they could be men or women).
You just need to look at women (to make sure they have long hair) and short-haired people (to make sure they're not women).
In other words: men can't break the rule, and neither can people with long hair.
posted by BungaDunga at 9:27 PM on May 22, 2015 [1 favorite]
Makes sense, though my first thought was, what if 'opposite' means 'across from' in the line up of four cards, and then, what if they have fake ids? The problem I have with this sort of blind test for people, is that I think people are great at catching onto to logic games, and logic, period, but there is something to be said for presenting parameters like familiarity with if-then absolutes, and what not.
posted by branravenraven at 1:05 AM on May 23, 2015 [1 favorite]
posted by branravenraven at 1:05 AM on May 23, 2015 [1 favorite]
The correct answer is obviously 8 and blue and waiting for the end of the video or reading the comments here is only a waste of precious time.
posted by sour cream at 1:32 AM on May 23, 2015 [1 favorite]
posted by sour cream at 1:32 AM on May 23, 2015 [1 favorite]
1. You are shown 4 objects.The trick is that you are shown four objects but told a statement regarding only two of them.
2. You are told a statement regarding them.
3. You are asked to determine if the statement is true.
4. In order to determine if the statement is true, you have to turn over all 4 objects, because the statement is about a condition common to all 4 objects.
posted by Holy Zarquon's Singing Fish at 5:13 AM on May 23, 2015 [4 favorites]
The trick is that you are shown four objects but told a statement regarding only two of them.
I must have missed that. Where is that stated?
posted by rankfreudlite at 10:18 AM on May 23, 2015
I got the right answer. I'm a programmer, so I grok this sort of logic.
But why do researchers expect ordinary people to follow this very narrow sort of reasoning? Take pwnguin's post— his logic is impeccable, logical implication is indeed equivalent to "(not A) OR B". Besides programmers and logicians, who the heck knows or cares about that rule?
Logic problems always have to be cooked to be as abstract and hole-free as possible. Everyday problems (you can find a huge collection here) tend to be open-ended and require a large array of probabilistic heuristics to solve, rather than a strict algorithm.
This thread is full of approaches that are technically wrong for the logic problem, but interesting and clever in general. We have evolved to deal with tricky and untrustworthy adversaries (namely, other people), so a generalized wariness and curiosity pay off. "What if the card has numbers on both sides?" or "What if the ID is fake?" or "How do other sets of cards work?" or even "Is the experimenter giving me all the facts?" are all pretty good questions, even if the interactive video doesn't reward them.
posted by zompist at 1:44 PM on May 23, 2015
But why do researchers expect ordinary people to follow this very narrow sort of reasoning? Take pwnguin's post— his logic is impeccable, logical implication is indeed equivalent to "(not A) OR B". Besides programmers and logicians, who the heck knows or cares about that rule?
Logic problems always have to be cooked to be as abstract and hole-free as possible. Everyday problems (you can find a huge collection here) tend to be open-ended and require a large array of probabilistic heuristics to solve, rather than a strict algorithm.
This thread is full of approaches that are technically wrong for the logic problem, but interesting and clever in general. We have evolved to deal with tricky and untrustworthy adversaries (namely, other people), so a generalized wariness and curiosity pay off. "What if the card has numbers on both sides?" or "What if the ID is fake?" or "How do other sets of cards work?" or even "Is the experimenter giving me all the facts?" are all pretty good questions, even if the interactive video doesn't reward them.
posted by zompist at 1:44 PM on May 23, 2015
This thread is full of approaches that are technically wrong for the logic problem, but interesting and clever in general. We have evolved to deal with tricky and untrustworthy adversaries (namely, other people), so a generalized wariness and curiosity pay off. "What if the card has numbers on both sides?" or "What if the ID is fake?" or "How do other sets of cards work?" or even "Is the experimenter giving me all the facts?" are all pretty good questions, even if the interactive video doesn't reward them.
Good points, zompist. I think the aim of Peter Wason was to answer the question "What is the simplest research experiment that can be devised to prove that people are stupid?"
posted by rankfreudlite at 2:11 PM on May 23, 2015
Good points, zompist. I think the aim of Peter Wason was to answer the question "What is the simplest research experiment that can be devised to prove that people are stupid?"
posted by rankfreudlite at 2:11 PM on May 23, 2015
But why do researchers expect ordinary people to follow this very narrow sort of reasoning? Take pwnguin's post— his logic is impeccable, logical implication is indeed equivalent to "(not A) OR B". Besides programmers and logicians, who the heck knows or cares about that rule?
Because stupid illogical reasoning causes real harm. "All the 911 terrorists were Muslims therefore all terrorists are Muslims therefore all Muslims are terrorists."
posted by straight at 2:31 PM on May 23, 2015 [3 favorites]
Because stupid illogical reasoning causes real harm. "All the 911 terrorists were Muslims therefore all terrorists are Muslims therefore all Muslims are terrorists."
posted by straight at 2:31 PM on May 23, 2015 [3 favorites]
Seriously, straight? Prejudice is caused by an inability to solve logic problems? So, are logicians better people? Are smart people never prejudiced? Are stupid people always prejudiced? [citation needed], pal.
posted by zompist at 2:58 PM on May 23, 2015 [1 favorite]
posted by zompist at 2:58 PM on May 23, 2015 [1 favorite]
Besides programmers and logicians, who the heck knows or cares about that rule?
In the programming context, it's useful for understanding / proving what's true after an if-then statement. There's a lot of tools like PROMELA that could be used to improve software quality, but the number of programmers who understand formal logic is quite low, let alone programmers who understand LTL.
Putting aside the fact that programmers are a well paid and growing section of the population, I imagine lawyers and judges may also find principles of deduction useful. I'm sure other fields can chime in as well.
Personally, I enjoy reading up on research in behavioral economics, though I still haven't found the time to sit down and read Danny Kahneman's work, it's been repeated and summarized enough that I'll venture forward an answer for the more general population. It's one of many tools in the general System II category you can use to put your System I brain to work effectively. The population may not know or care about the rule, but solving that particular puzzle is difficult without it, and the common intuitive approach works only in specific contexts.
Of course, even if you do understand short-circuits and implication, the next challenge is deciding to use System II thinking in the first place. It's slower, and generally aided by tools like computers or pen & paper. It's exhausting and unrewarding, compared to System I thinking. When your intuition says '8 and blue', it's all to easy to go along. I imagine the best you can hope for is learning to doubt or ignore intuition. Which is a good skill for an academic or any other number of white collar workers to hone.
posted by pwnguin at 3:48 PM on May 23, 2015
In the programming context, it's useful for understanding / proving what's true after an if-then statement. There's a lot of tools like PROMELA that could be used to improve software quality, but the number of programmers who understand formal logic is quite low, let alone programmers who understand LTL.
Putting aside the fact that programmers are a well paid and growing section of the population, I imagine lawyers and judges may also find principles of deduction useful. I'm sure other fields can chime in as well.
Personally, I enjoy reading up on research in behavioral economics, though I still haven't found the time to sit down and read Danny Kahneman's work, it's been repeated and summarized enough that I'll venture forward an answer for the more general population. It's one of many tools in the general System II category you can use to put your System I brain to work effectively. The population may not know or care about the rule, but solving that particular puzzle is difficult without it, and the common intuitive approach works only in specific contexts.
Of course, even if you do understand short-circuits and implication, the next challenge is deciding to use System II thinking in the first place. It's slower, and generally aided by tools like computers or pen & paper. It's exhausting and unrewarding, compared to System I thinking. When your intuition says '8 and blue', it's all to easy to go along. I imagine the best you can hope for is learning to doubt or ignore intuition. Which is a good skill for an academic or any other number of white collar workers to hone.
posted by pwnguin at 3:48 PM on May 23, 2015
Seriously, straight? Prejudice is caused by an inability to solve logic problems? So, are logicians better people? Are smart people never prejudiced? Are stupid people always prejudiced?
I don't know. Prejudice sure looks like some sort of cognitive error. Obviously in many cases it seems to be a rationalization for some sort of self-serving motivation. But I think sometimes people of goodwill can be prejudiced because of sloppy thinking. And I think it can be rhetorically useful to call out sloppy thinking even when it's a politically-motivated rationalization.
You don't need training in formal logic to develop the kind of careful thinking illustrated in this puzzle, and this puzzle really is equivalent to the "terrorists are Muslims therefore Muslims are terrorists" error.
posted by straight at 5:09 PM on May 23, 2015 [2 favorites]
I don't know. Prejudice sure looks like some sort of cognitive error. Obviously in many cases it seems to be a rationalization for some sort of self-serving motivation. But I think sometimes people of goodwill can be prejudiced because of sloppy thinking. And I think it can be rhetorically useful to call out sloppy thinking even when it's a politically-motivated rationalization.
You don't need training in formal logic to develop the kind of careful thinking illustrated in this puzzle, and this puzzle really is equivalent to the "terrorists are Muslims therefore Muslims are terrorists" error.
posted by straight at 5:09 PM on May 23, 2015 [2 favorites]
Except it's not a remote formal logic problem. The Wason test is about efficient reasoning of implicative logic. But science has plenty of that, from reasoning about health issue to economic issues, whenever models and variables are involved. And as more people are exposed to computational technology in different ways, algorithmic literacy could be a socially relevant form of numeracy. Etc.
posted by polymodus at 6:12 PM on May 23, 2015
posted by polymodus at 6:12 PM on May 23, 2015
In a certain sense, yes, this question is framed as a "trap" - in the same way that every single logic test that has ever existed is a "trap." It's okay to be against that; you just have to accept that, if you are, that means you're against all logic tests whatsoever. Which seems like a mistake.
Also, again, this question, really, really doesn't rely on so-called "formal logic." Normal people can and should see the difference between "a implies b" and "b implies a." If not, the world would fall apart. Seriously.
posted by koeselitz at 8:18 PM on May 23, 2015 [6 favorites]
Also, again, this question, really, really doesn't rely on so-called "formal logic." Normal people can and should see the difference between "a implies b" and "b implies a." If not, the world would fall apart. Seriously.
posted by koeselitz at 8:18 PM on May 23, 2015 [6 favorites]
Probably, yeah. If people hear "all ISIS supporters are Muslims" and think that means "all Muslims are ISIS supporters," then yes - we're probably fucked. I don't think this is an arcane formal logic puzzle safely beyond the ken of most people; and the misunderstandings people have with it have real-world consequences.
posted by koeselitz at 10:39 PM on May 23, 2015 [3 favorites]
posted by koeselitz at 10:39 PM on May 23, 2015 [3 favorites]
OK, how did the go-to example for the bad consequences of failing Wason's experiment become Islamophobia? This is getting offensive. No, turning over three cards instead of two does not make you into Ted Cruz.
If you're proud of yourself for getting the experiment right, good for you. This does not however make you a morally superior human being.
At least, perhaps read the article and note that 75% of people get the logic right when it's about a recognizable social situation (the underage drinking bit). Not everyone is good about reasoning about cards with numbers printed on them. If you really think that that means they're all bigots, it's not them that's failing logic.
posted by zompist at 10:57 PM on May 23, 2015 [1 favorite]
If you're proud of yourself for getting the experiment right, good for you. This does not however make you a morally superior human being.
At least, perhaps read the article and note that 75% of people get the logic right when it's about a recognizable social situation (the underage drinking bit). Not everyone is good about reasoning about cards with numbers printed on them. If you really think that that means they're all bigots, it's not them that's failing logic.
posted by zompist at 10:57 PM on May 23, 2015 [1 favorite]
It comes across as, "Ha ha! You lose, because you didn't know that we were playing by secret rules and strict definitions which don't adhere to conversational English!" My beef isn't with the puzzle, but with its framing as a trap exposing people's supposed irrationality. In the real world, it's irrational to adhere to strict rationality.
One of the interesting findings is that this isn't if vs if-and-only-if. If it were a matter of ambiguity between those two options, people would treat it more or less as rankfreudlite did. Instead people given unfamiliar 'p implies q' tasks tend to select cards P and Q. Even in the youtube video puzzle, there are twice as many hits for 'even and blue' than 'all cards'.
posted by pwnguin at 12:15 AM on May 24, 2015
One of the interesting findings is that this isn't if vs if-and-only-if. If it were a matter of ambiguity between those two options, people would treat it more or less as rankfreudlite did. Instead people given unfamiliar 'p implies q' tasks tend to select cards P and Q. Even in the youtube video puzzle, there are twice as many hits for 'even and blue' than 'all cards'.
posted by pwnguin at 12:15 AM on May 24, 2015
Probably, yeah. If people hear "all ISIS supporters are Muslims" and think that means "all Muslims are ISIS supporters," then yes - we're probably fucked. I don't think this is an arcane formal logic puzzle safely beyond the ken of most people; and the misunderstandings people have with it have real-world consequences.
The example I've used in conversation was, "Suppose a doctor claims, If a patient has TB, then their X-ray test will have little dots", and then asking "What would you need to do check if the claim was right." Another nice one similar to the beer example in the article: "If the diner is underage, then they may only be served apple juice."
My intuition, though, is that people who work with abstract systems and models—statisticians, computer chip designers, aircraft engineers, physicists, etc. etc.: lots of people—would all pass the card version of the task. But the article does not address this demographic issue.
Anthropology tells us there have existed cultures where people cannot count more than a certain number. Some context to keep in mind.
posted by polymodus at 2:24 AM on May 24, 2015
The example I've used in conversation was, "Suppose a doctor claims, If a patient has TB, then their X-ray test will have little dots", and then asking "What would you need to do check if the claim was right." Another nice one similar to the beer example in the article: "If the diner is underage, then they may only be served apple juice."
My intuition, though, is that people who work with abstract systems and models—statisticians, computer chip designers, aircraft engineers, physicists, etc. etc.: lots of people—would all pass the card version of the task. But the article does not address this demographic issue.
Anthropology tells us there have existed cultures where people cannot count more than a certain number. Some context to keep in mind.
posted by polymodus at 2:24 AM on May 24, 2015
Question: You have 1 apple. Somebody gives you another apple. How many apples do you have?
Answer: It's a trick question, confusing the everyday, man-on-the-street meaning of 'apple' with the logician's usage, plus you have to take into account an infinite amount of possible apples and how this question applies to them, also what exactly does 'give' mean? Is it a present, is it a sale, or simply showing them an apple? Finally, it's much more efficient to throw the apples in a blender and make an appletini than actually waste the time necessary to solve the puzzle.
posted by signal at 2:33 PM on May 24, 2015 [2 favorites]
Answer: It's a trick question, confusing the everyday, man-on-the-street meaning of 'apple' with the logician's usage, plus you have to take into account an infinite amount of possible apples and how this question applies to them, also what exactly does 'give' mean? Is it a present, is it a sale, or simply showing them an apple? Finally, it's much more efficient to throw the apples in a blender and make an appletini than actually waste the time necessary to solve the puzzle.
posted by signal at 2:33 PM on May 24, 2015 [2 favorites]
You are either Ted Cruz or Gregory Craig.
posted by boo_radley at 3:05 PM on May 24, 2015
posted by boo_radley at 3:05 PM on May 24, 2015
polymodus: "OK, how did the go-to example for the bad consequences of failing Wason's experiment become Islamophobia?"
Good lord - nobody said anything about moral superiority. It's just that some people are insisting, counter to all reality, that conversational human beings do not distinguish between these two distinct logical things. But they do. Every day. It is demonstrably false that this is solely the rea of logicians.
And, yeah, that's the counterpoint. Some have suggested above that most humans are too dumb or too simple or too irrational to know the difference between two logical modes. That's nonsense. This test is not about showing anyone's superiority - it's about asking how we can help people access what we know they can access.
posted by koeselitz at 11:47 PM on May 24, 2015 [1 favorite]
Good lord - nobody said anything about moral superiority. It's just that some people are insisting, counter to all reality, that conversational human beings do not distinguish between these two distinct logical things. But they do. Every day. It is demonstrably false that this is solely the rea of logicians.
And, yeah, that's the counterpoint. Some have suggested above that most humans are too dumb or too simple or too irrational to know the difference between two logical modes. That's nonsense. This test is not about showing anyone's superiority - it's about asking how we can help people access what we know they can access.
posted by koeselitz at 11:47 PM on May 24, 2015 [1 favorite]
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posted by Space Coyote at 10:43 AM on May 22, 2015 [6 favorites]