WHY SMART PEOPLE ARE STUPID

[Phil]

Here’s a simple arithmetic question: A bat and ball cost a dollar and ten cents. The bat costs a dollar more than the ball. How much does the ball cost?

 

The vast majority of people respond quickly and confidently, insisting the ball costs ten cents. This answer is both obvious and wrong. (The correct answer is five cents for the ball and a dollar and five cents for the bat.)

 

For more than five decades, Daniel Kahneman, a Nobel Laureate and professor of psychology at Princeton, has been asking questions like this and analyzing our answers. His disarmingly simple experiments have profoundly changed the way we think about thinking. While philosophers, economists, and social scientists had assumed for centuries that human beings are rational agents—reason was our Promethean gift—Kahneman, the late Amos Tversky, and others, including Shane Frederick (who developed the bat-and-ball question), demonstrated that we’re not nearly as rational as we like to believe.

When people face an uncertain situation, they don’t carefully evaluate the information or look up relevant statistics. Instead, their decisions depend on a long list of mental shortcuts, which often lead them to make foolish decisions. These shortcuts aren’t a faster way of doing the math; they’re a way of skipping the math altogether. Asked about the bat and the ball, we forget our arithmetic lessons and instead default to the answer that requires the least mental effort.

 

 

From http://www.newyorker.com/online/blogs/frontal-cortex/2012/06/daniel-kahneman-bias-studies.html#ixzz1yaFyxQck

[chasetb]

I have to admit, the first answer that came to my mind for the bat-and-ball question was the incorrect one. But since I hate being wrong and like to double-check, I stopped reading, quickly added it up, realized I was wrong, corrected myself, then read how the article mentioned that most people get it wrong. Same thing for the lake question.

 

The article brought a quote to my mind: "The more you know, the more you realize how little you actually know".

[Fluffy]

I am trained to not respond the obvious to tricky questions, but yes, 1$ and 10c passed through my mind and was discarded.

[barmar]

I consider myself really good at math, but I admit I was fooled by this as well.

 

I still haven't started reading my copy of "Thinking, Fast and Slow", but I expect it will address this type of mistake. And I think I know the explanation: in most critical situations, making a good decision quickly is more important than making the best decision if it takes too long. This is the evolutionary cause of our susceptibility to optical illusions, and this puzzle is basically an intellectual illusion.

 

No caveman ever had to solve this type of mathematical puzzle; we're lucky we can do algebra at all, but don't expect most people to do it intuitively.

[Elianna]

Humans are very good at pattern recognition. You can see it in bridge all the time. People look for patterns (that aren't necessarily there), and then use those patterns to make predictions that are not based on logic.

[TimG]

My first thought was: it's not $1 and 10c. A moment later, I had the correct answer. I think I would have gotten this right even without the warning that comes with the question being asked in the Water Cooler, but of course, can't be sure. I in no way think this makes me smarter than those who are tricked by this problem.

[mike777]

It looks like the answer is 1.10 for the bat and ten cents for the ball.

 

 

I think people get fooled into thinking they have to stick to the budget and cant spend more than they have.

 

It was interesting that no one tried to get the bat and ball for undercost.

[ArtK78]

Funny, I got this right almost immediately. Maybe it is because I went to Princeton. :)

[Vampyr]

Don't really see how someone could get this question wrong even if answering quickly, unless they had made an assumption at the beginning -- "a bat and a ball cost a dollar and ten cents could be subconsciously interpreted as "a bat and a ball cost, respectively, a dollar and ten cents." I suspect that this is what is going on.

 

Ha, just saw Art's reply. I went to Princeton too.

[Vampyr]

My first thought was: it's not $1 and 10c.

 

Yes, it's pretty obvious they are trying to trick you. Maybe having a lot of experience/being very good at solving logic problems is a factor here -- such a person is not going to be fooled.

[barmar]

Don't really see how someone could get this question wrong even if answering quickly, unless they had made an assumption at the beginning -- "a bat and a ball cost a dollar and ten cents could be subconsciously interpreted as "a bat and a ball cost, respectively, a dollar and ten cents." I suspect that this is what is going on.

I did have a little trouble parsing that sentence quickly. Without a word like "combined", it sounds like it means respectively. But then they ask for the respective prices, which contradicts that, but the first impression is still biasing your thinking.

Ha, just saw Art's reply. I went to Princeton too.

That must be it, I just went to a trade school called MIT. We skipped algebra and went straight into calculus.

[ArtK78]

I like the sample question that appears later in the New Yorker article.

 

In a lake, there is a patch of lily pads. Every day, the patch doubles in size. If it takes 48 days for the patch to cover the entire lake, how long would it take for the patch to cover half of the lake?

 

I got this one right, also, but the fact that the article warns the reader of inherent bias in thought may have created a reverse bias in the way I thought about the question.

[Vampyr]

I like the sample question that appears later in the New Yorker article.

 

In a lake, there is a patch of lily pads. Every day, the patch doubles in size. If it takes 48 days for the patch to cover the entire lake, how long would it take for the patch to cover half of the lake?

 

I got this one right, also, but the fact that the article warns the reader of inherent bias in thought may have created a reverse bias in the way I thought about the question.

 

Maybe... but in this one it is not obvious what other answer a person might come up with.

[barmar]

Another issue is context. When you know someone is asking you a trick question, you'll contemplate before answering. When researchers do these studies, they take measures to try to negate this effect. For instance, they may have the subjects perform some other task, with the questions thrown in periodically; they think they're being tested on how well they perform the first task with these interruptions. Or they may ask lots of questions where the intuitive answers are right, along with occasional trick questions; the subjects will get used to answering quickly, and won't think harder for the ones that need it.

 

I'm reminded of the reading puzzle where the word "the" is repeated across adjacent lines. If you know someone is giving you a puzzle, you'll read it slowly and see the repetition. But if this happened when reading an ordinary book, you'd almost certainly never notice unless you're a practiced proofreader.

[ArtK78]

Maybe... but in this one it is not obvious what other answer a person might come up with.

The "other" answer, which was the common answer, was 24 days.

[Phil]

Don't really see how someone could get this question wrong even if answering quickly, unless they had made an assumption at the beginning -- "a bat and a ball cost a dollar and ten cents could be subconsciously interpreted as "a bat and a ball cost, respectively, a dollar and ten cents." I suspect that this is what is going on.

 

Ha, just saw Art's reply. I went to Princeton too.

 

I agree. I think a better phrasing is a bat and a ball cost a total of $1.10, although the actual wording is sufficiently clear, especially because the 2nd condition (bat - ball = $1) clarifies the first.

[Vampyr]

The "other" answer, which was the common answer, was 24 days.

 

What seems to be indicated here is that the subjects didn't listen to the question properly (it is probably much easier for those of use who are reading it). If, as barmar suggested, they were being distracted with other tasks, it is no wonder their comprehension was impaired. The fact that we don't always listen or pay attention to others is not that surprising to me.

[blackshoe]

I know what you mean. Nobody ever listens to me. B-)

[gwnn]

What seems to be indicated here is that the subjects didn't listen to the question properly (it is probably much easier for those of use who are reading it). If, as barmar suggested, they were being distracted with other tasks, it is no wonder their comprehension was impaired. The fact that we don't always listen or pay attention to others is not that surprising to me.

To be fair, the stated condition is kind of ridiculous. In 48 days, just 1 square metre of lily pads could almost cover the entire land area of Earth (yea yea, actually they grow on water - then it would need less than 50). The first time I heard this my thought was "um ok, not 24, it must be between 24 and 48 ... close to 48 I guess..." etc. But the whole idea that it doubles every day is preposterous.

 

BTW another one for people here: you want to organise a knock-out tournament, no group stage/second chances. You have 79 teams. How many matches will you need?

 

This thread reminded me of this video (I believe it has been posted on BBF before), sorry for the title but it is still kind of nice:

[TimG]

BTW another one for people here: you want to organise a knock-out tournament, no group stage/second chances. You have 79 teams. How many matches will you need?

Will there be any three-way matches with two survivors or will there be byes?

 

78 teams will be eliminated, so 78 matches.

[kenberg]

Some friends visited over the weekend and the guy told this story about his school experience in Manhattan. The kids read some poem and the teacher asked, without any apparent intended humorous intent, if any of the kids in the class had ever been on an island.

 

Another story I heard. In a probability class of about 30 students, the prof asked the class to estimate the probability that at least two members of the class share a common birthday. A nice problem, except for the fact of identical twins sitting in the front row.

 

I would not want a record kept of all the really stupid things that I have said or done.

 

I don't really know how to eliminate these errors, but having a healthy respect for our own limitations is probably a good start. Many years back, working on my Ph.D. thesis, I proved this really nice result quite simply. Then I saw that the same technique would prove another really nice result. And then maybe another. And then I decided it would be a good idea to go back and find the flaw in my reasoning. Yep, there it was.

 

As to the bat and ball, one possibility is that the person answering the question doesn't much care what the answer is, and so does not give it serious and careful thought.

[Fluffy]

The "other" answer, which was the common answer, was 24 days.

 

humans only see arithemtic progressions on their world, and our mind is trained for them, need to study to understand geometric ones.

[barmar]

But the whole idea that it doubles every day is preposterous.

I think that's the point. In many math word problems, the stated conditions don't mirror real world situations. Common sense and intuition evolved to address problems that actually occur efficiently, not hypotheticals.

 

TV shows and movies often milk this for comedic effect. Someone is tutoring a "dumb" person in math, and gives them a word problem with a condition like "Two trains leave the station 15 minutes apart." The student then starts asking irrelevant questions, because his mind works intuitively by imagining the whole situation, he doesn't boil it down to just the mathematical aspects.

[ArtK78]

BTW another one for people here: you want to organise a knock-out tournament, no group stage/second chances. You have 79 teams. How many matches will you need?

The answer is a minimum of 78 matches, as every team but the ultimate winner must lose a match. But it could be more if a team may lose a match and continue in the event (such as in a three-way match with 2 survivors). You stated no second chances - I do not know if a three-way match with two survivors counts as a second chance. The only way to run a single-elimination event with 79 teams without multiple-way matches is to give byes - this could be accomplished easily by giving byes to 49 teams and having 15 head-to-head matches in the first round, leaving 64 teams for the second round. In that case, you would have 78 head-to-head matches before determining a winner.

 

The question sounds a lot like a story related by Jerry Machlin in his memoir. He was telling of an exchange between his uncle, Al Sobel, the famous tournament director of the early days of the ACBL, and Ozzie Jacoby. Jacoby was the youngest person to pass the actuary exam when he was 18.

 

Sobel asked Jacoby how many matches it would take to determine the winner of a single-elimination knock-out teams event if the original entry was 64 teams. Ozzie responded "32 and 16 and 8 and 4 and 2 and 1 - 63." Sobel said, "You are right, Ozzie, but it took you too long. You should realize that since every team but one must lose a match, it would take 63 matches to determine a winner." To which Ozzie replied, "Yes, but if you were running the event, it could take anywhere from 45 to 110 matches!"

[gwnn]

A three-way match is a group stage.