This is a long post, not because there’s a lot to say about stereotypes (though there is), but because I’m going to try to make you better at thinking, and better at thinking about thinking. In order to do that, I’m going to walk you through several scenarios with thought-puzzle questions in them, and even stop and give you a test in the middle, and you should really not try to guess where I’m going with it all because the thought-puzzles will work better if you’re not trying to connect everything with what you think you know about stereotypes, even if I agree.

Also, if you just skip to the bottom, you won’t have learned to think any better, and it pretty much just says “in general, generalizations suck”, which you’ve probably heard me say anyway.

Disclaimer: I wrote the beginning of this post over a month ago, then just let it sit. Hopefully it still feels fairly cohesive and educational.


Let’s say I’ve got a suitcase full of socks. Socks are important, right? Today I pull out a pair of tan socks, and they’re quite elastic. I can just pull them straight over my feet in one motion.

Question 1: If I pull out another pair of tan socks, will they be elastic?

Now this is silly. Some socks are elastic and some are not so elastic. But it’s not unlikely that another pair of tan socks would be like the first pair.

Okay, so I pull out not one more pair of tan socks, but five more. All of them are about as stretchy as the first one, and I’m set for the rest of the week. And just for kicks, I hunt around in the suitcase for a pair of navy blue socks, and these aren’t elastic at all, to the point where I manage to rip one trying to get it on my foot.1

Question 2: If I pull out a seventh pair of tan socks, will they be elastic?

At this point it’s pretty likely, right? And indeed, my seventh pair of tan socks is pretty elastic. Maybe not quite as stretchy as the previous pairs, but still pretty good.

Uh-oh, my brother just came in and borrowed most of my socks. He’s going on a trip next week.2 Now what am I going to wear?

Question 3: If I go to the store to buy more elastic socks, what color should I buy?

Tan ones, right?

I mean, yeah, you know I’m going to trip you up sooner or later, but seriously, even the not-so-elastic tan socks were still stretchier than the navy blue socks. So you know now that tan socks are generally stretchy, and hey, all else being equal, you might as well go with the tan ones.

Congratulations, you’ve just made a generalization—an extrapolation from the samples you’ve been given to the rest of the world, or at least your part of it. Or in other words, a stereotype.

And that’s a bad thing. Right?

Why it’s a bad thing

There are a couple of reasons. The obvious one is that seeing seven pairs of stretchy tan socks doesn’t prove that all tan socks are stretchy. If I just go buy a pack of socks because they’re tan, they might not be stretchy. The kinds of socks they have in the store probably aren’t in the same stretchy/non-stretchy ratio as the socks in my suitcase.

The next one is that one pair of navy blue socks being inelastic does not mean they all are. It’s entirely possible socks are sold in packs by color and elasticity, and that if I wanted stretchy blue socks I could go buy a pack of stretchy blue socks.

(Or in other words, we know that “stretchy” and “tan” go together, but we don’t know if “stretchy” implies “tan”, or if “tan” implies “stretchy”, and we don’t know if “not tan” implies “not stretchy” or if “not stretchy” implies “not tan”. ALL of those things could be false!)

And in a different vein, deciding to go with tan socks again because of past experience means you’ll never try anything new. Maybe they make blue socks that are just as stretchy and come with a free iPod Touch.

Why it’s a good thing

New socks!

Seriously, it’s not unreasonable to say you’ve had favorable results before, and you’d like to have them again, so you’ll do the same thing again. Maybe they make amazing blue socks, but maybe they make really bad blue socks that wear holes in the sole after a single day of walking to work. You already know that there are good tan socks.

And there’s more than that: socks aren’t randomly created. Some company makes socks, and in general the same model of sock does stay pretty much the same. I probably bought all my tan socks in the same pack; it makes sense that they’d all be the same.

That may not apply to all socks at the store, but still. If the tan socks and the blue socks are from different companies, well then obviously you know this one company has gotten it right at least some of the time, while the other company may or may not have. (You do, in fact, know this; it’s a restatement of the information I gave you.) And from your prior knowledge about companies and commodity consumer goods, you can figure that the company’s not likely to radically change their sock design any time soon.

Stepping back a bit, the “right” answer to all three questions is “I don’t know”. But in the real world, that just won’t cut it. You have to wear socks, you’d rather not rip your socks, you have to buy more socks when your brother borrows yours. Or something. At the heart of the thing, I gave you very limited information and asked you to make decisions based on that information. To not take that information into account would be foolish.

Shirts and Jackets

In addition to my suitcase of socks, I also have a number of black and white shirts and jackets. I can tell you that most of the jackets are black and most of the shirts are white.3 But what does that mean?

Well, it could mean this:

10 white shirts, 1 black shirt; 6 black jackets, 1 white jacket

Or it could mean this:

4 white shirts, 3 black shirts; 2 black jackets, 1 white jacket

Both of these cases fit the word “most”, but the latter combination makes it a lot more likely that I’ll end up having to wear a white jacket over a black shirt, arguably the hardest color combination to pull off.4 In other words, what I told you is a true fact about this wardrobe, but it does not really allow you to draw useful conclusions about what you’re likely to see me wearing.


All right, maybe you’re getting sick of clothes by now; I promise this is the last one. Anyone who’s met me probably noticed that I’m tall and fairly skinny, to the point where it is actually hard to find pants that fit well. In this final example, I’m trying to decide whether to buy more jeans or more khakis, and my number-one factor is going to be how much shorter they’re going to get if I wash them. Somehow I collect data and find out that, on average, jeans actually shrink more than khakis, lengthwise.

Question 4: When I go to the store, which pants should I buy?

Your answer to this probably depends on what you took away from the “Socks” section, but it’s actually “Shirts and Jackets” you should be thinking about right now. Maybe almost all jeans shrink more than even the “worst” khakis:

(two normal distributions; the one for jeans barely overlaps the one for khakis)

But maybe they are almost the same:

(two normal distributions again, but this time they are almost on top of one another)

In this graph, the mean, the median, and the mode—which happen to be the same here—all clearly show that “on average” jeans shrink more than khakis. It even shows that the worse jeans are worse than the worst khakis, and the best jeans are worse than the best khakis. These are true statements, but in this case they’re just not very useful. When the difference is this small, maybe I should be looking at some other factors instead (like, uh, price).

I’ll back that up with some numbers, too: if this is actually a standard normal distribution, the best 85% of jeans are no worse than (approximately) the best 90% of khakis. The best 50% of jeans are no worse than the best 85% of khakis. And the best 15% of jeans are clearly better than the worst 50% of khakis. If I have a way to estimate the shrinkage before I buy, I might get lucky and find an awesome pair of jeans, where before I might have naively given up before even trying.

Yes, along this one dimension jeans are still worse on average, but even for something like buying pants there’s more than one thing I should be considering. And we never went into how I collected the data, and how accurately it represents the pants available in the store.

Of course, maybe you thought of the idea of buying jeans that are one size too long and then letting them shrink. Troll.

A Test

Let’s try to apply this new-found knowledge, not with another similar example but with a totally different puzzle, and see if you can avoid the trap of irrelevant information.

This is called the 2-4-6 Puzzle, which appears in Harry Potter and the Methods of Rationality (though that’s not where I first heard it). I have a Rule—not a stereotype, an actual, fixed, always-true Law of Nature—that applies to triplets of three numbers. Your task is to use the boxes below to figure out the rule; type numbers in to find out which sequences satisfy the rule. You can make as many “experiments” as you want before trying to guess the answer.

  • 2, 4, 6
  • 3, 57, 3

Think you know? Let me repeat Harry’s warning, and tell you most people get this wrong when they first see it.

When you’re really sure you’re done, mouse over the blacked-out text below for the answer.

Three real numbers in increasing order, lowest to highest.

If you got it wrong, congratulations on discovering confirmation bias. People tend to seek out information that confirms their working theories, rather than disproving them. This makes it rather hard to discard beliefs even when there’s evidence against them, especially if you’ve had them for a long time.


Hopefully you’ve figured out now what this all has to do with stereotype, but if not, let’s recap. For this post I’m going to use female/male stereotyping as the basis, but I’ll come back at the end and visit non-binary groupings (i.e. ethnicity).

  • Socks: It is pretty well established that on average men are stronger than women. This is something that has a biological basis and can’t really be argued, and it’s the most legitimate reason for why Olympic sports are segregated by gender. Therefore, if you’re in a room of strangers and you want help moving heavy boxes around, you’d probably get the most added physical force if you ask a man.

    BUT…anyone who knows me knows that I’m actually pretty weak, and plenty of my female friends are stronger than I am. Indeed, it was hard coming up with an example here where both sides of the sock lesson applied at all. In the real world, you almost always have to evaluate people individually – even if men are biologically disposed to be worse at taking care of children than women, men who choose to be nannies are probably better. Heck, someone who’s already raised a child is almost certainly a better choice to watch your kid than someone who hasn’t, even if the former is male and the latter is female. That’s information you can use.

  • Shirts and Jackets: In the real world, things don’t usually come in black and white; even though gender is binary is usually grouped in a binary way, pretty much everything else (strength, hair length, introversion) has a spectrum. So let’s use a different case study: women in the US Senate. I can tell you that there are more men than women in the Senate, actually many more. But does that mean 60-40 or 80-20?

    …well, actually, at the time of this writing it was 83-17. In a country that’s actually slightly more women than men, that’s not good.

  • Pants: Okay, here’s the big one. When it comes to strength, the distributions of men and women are probably not as close together as the second graph, though they’re almost certainly closer than the first graph. The thing is, most jobs don’t require strength. And most other supposed gender biases (a) have not been demonstrated across large populations, (b) are cultural rather than innate, and/or (c) do not apply to the decision at hand.

Let me give you an example of that last one. Say you’re at a company that does nanotechnology R&D, and you’re interviewing potential candidates. And just for the sake of argument, let’s say that it’s true that on average men are better than women at math, physics, and engineering. This statement is not relevant to your hiring process. Why? Because your applicants aren’t selected randomly from the population of the United States. They’re selected from the pool of currently unemployed nanotechnology engineers, all of whom know more about nanotech than I do.

Okay, let’s go even further and grant that on average, male nanoengineers are better than female engineers. Never mind how we’re measuring “better”, just go with it. Even then, this is still most likely not relevant to your hiring process. Why? Because you only see a few people out of that population of “currently unemployed nanotechnology engineers”. The best men and the best women are most likely already employed, so you’re dealing with people selected from the middle of each curve. Possibly the worst, too. Here’s the second jeans/khaki graph again:5

(two normal distributions, almost on top of one another)

In reality, the distributions for skills like this probably aren’t bell curves, either…they’d be more like log-normal, which means that once you’ve screened out the obviously unqualified applicants, it’s a real tossup. (And with the unpleasant gender bias in engineering, the obviously unqualified women have probably self-selected out a long time ago.) Given how hard it is to find good skilled workers, letting gender be a factor in your decision is like letting the color of remote affect which TV you buy.


Some stereotypes just seem to stick in peoples’ minds. Jews are penny-pinchers. Asians are good at academics. All black people can sing.6 Women can’t do math.

Some of these things are cultural — that is, it’s probably true that a higher percentage of Chinese-Americans have regular acupuncture than white Americans, simply because a higher percentage of Chinese-Americans have grown up in a culture where acupuncture is a fairly standard medical treatment.

But there was a lesson snuck into “Socks”. It got to the point where it seemed fairly obvious that every tan sock in my suitcase was going to be stretchy. I could always suddenly pull out a non-stretchy one, but it would seem fairly unusual, and since we were getting a pretty good sample size (how many pairs of socks do I own anyway?) it’s fair to assume that the rest of my tan socks are the same.

The kinds of socks they have in the store probably aren’t in the same stretchy/non-stretchy ratio as the socks in my suitcase.

The information you’ve learned about my suitcase might not apply at all to the real world. I seem to prefer stretchy socks (or at least rip the non-stretchy ones sooner); isn’t it likely that in the real world there might be many more non-stretchy socks than in my suitcase? Isn’t it possible that most socks in the store are non-stretchy, and you have to go search out the stretchy ones, tan or otherwise?

The sticky stereotypes are ones that an individual happens to see repeated enough that their brain starts believing there’s a pattern, a correlation. But your sample size is ridiculously small compared to the population size; if you say Asian-Americans are generally more submissive, that may or may not be a true statement (with regards to the word “generally”) but you clearly haven’t met some of my friends. You really shouldn’t be assuming the next person to walk in your room is going to act like the last dozen or even hundred you’ve seen when you’re selecting from a population of…probably tens of thousands, at least. And I really doubt that you’ve actually seen a hundred people in a row who are “the same” in almost any meaningful way.

We get another cultural dirty word, “prejudice”, from “pre-judging”, and that’s exactly what you’re doing when you act on stereotypes instead of the actual person.

Good Advice

Americans tend to be concerned about punctuality. If you arrive late for a meeting, make sure to give an apology and perhaps some explanation.

Thai cooking is generally very spicy; be careful!

Preschoolers tend to put things in their mouths; make sure to give them non-toxic markers.

Not all Americans are particularly punctual, and not all of them will mind if you’re late to something. Not all Thai food is spicy (particularly in a restaurant with a predominantly non-Thai clientele). And not all preschoolers put things in their mouths. Nevertheless, all of these are fairly good advice because they let you prepare for situations that may not match your norm; then if things turn out to be more familiar, you can adjust accordingly.

I promised I would mention ethnicity again, but there’s really not much to say other than it’s correlated with useful characteristics even less than gender. Culture may be correlated with useful things (if you grew up in a household with lots of books, you’re probably more likely to read, which might mean you’re better at communication), but that’s still something you don’t have any real evidence for when you first meet someone.

(Personal anecdote: one of my stereotypes is that people who are strongly Christian are usually anti-homosexual. Obviously this is not true for all people who strongly believe in Christianity, but when I made a new friend who was Christian I had to find out that he was not anti-gay. It’s not like I assumed he was homophobic beforehand, but if I had had to guess, I would have been wrong, and I was a bit more cautious about the subject than I might have been.)

This “good advice”, along with the lessons from “Socks”, is why our brains are set up to stereotype. We can’t possibly have all the information about someone right when we meet them, but we have to start interacting with them right away. So we take one of our mental templates and start filling it in as we learn more about the person, and eventually they’ll be a bona fide individual in our mind. And for the people we won’t interact with that long (say, the man at the cash register), well, our stereotype is probably good enough in most cases to have a successful social interaction. If you know that it’s conventional to bring a bottle of wine to a dinner party, that gesture is usually still appreciated even if it turns out the host doesn’t drink. We didn’t have that information in advance; we use stereotypes because there is nothing else to go on.

But you wouldn’t hire an American based on a general American trend of punctuality; you really don’t know if that particular American fits the stereotype. “Nothing else to go on” just isn’t good enough for anything more than the bare minimum of social interaction. A stereotype really means “I don’t actually have information about this case, so I’m going to extrapolate from past experiences…or maybe just things I’ve heard on TV.”

If you can catch yourself stereotyping, take the time to stop and think whether you really have enough information to draw a conclusion that affects your actions. And remember all the lessons from this article that demonstrate how our brains really like to draw conclusions even when the evidence is quite scanty and the sample space is huge.

In general, generalizations suck. If you have the opportunity to do better in your life, please do so. Thank you.

  1. This is a true story, sadly. ↩︎

  2. This part is not true. ↩︎

  3. Also not true. ↩︎

  4. Okay, white-on-white might actually be harder unless you’re in all white, like for a performance or something. ↩︎

  5. …because I’m too lazy to make a second graph with everything relabeled just for this example. ↩︎

  6. This one is not so prevalent anymore? ↩︎