OLPC MEMO-1
Marvin Minsky, Feb 16, 2008 (revised March 22)

This is the first of several memos about how OLPC could initiate useful projects that then could grow without our further support—if adopted by groups in our Diaspora.

What makes Mathematics hard to learn? Drawbacks of Age-Based Segregation
Role Models, Mentors, and Imprimers Why Projects are better than Subjects
Making Intellectual Communities Why Classics are better than Textbooks

What makes Mathematics hard to learn?

Why do some children find Math hard to learn? I suspect that this is often caused by starting with the practice and drill of a bunch of skills called Arithmetic—and instead of promoting inventiveness, we focus on preventing mistakes. I suspect that this negative emphasis leads many children not only to dislike Arithmetic, but also later to become averse to everything else that smells of technology. It might even lead to a long-term distaste for the use of symbolic representations.

Anecdote: A parent once asked me to tutor a student who was failing to learn the multiplication table. When the child complained that this was a big job, I tried to explain that because of diagonal symmetry, there are less than 50 facts to learn.

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However, that child had a larger-scale complaint:

“Last year I had to learn the addition table and it was really boring. This year I have to learn another, harder one, and I figure if I learn it then next year there will be another one and there’ll never be any end to this stupid nonsense. "

This child imagined ‘Math’ to be a continuous string of mechanical tasks—an unending prospect of practice and drill. It was hard to convince him that there would not be any more tables in subsequent years.

To deal with the immediate problem, I made a deck of “flash cards,” each of which showed two digits on the front and their product on the back. The process was to guess each answer and, if it was correct, then to remove that card from the deck. This made the task seem more like a game in which one can literally feel one’s progress as the size and weight of the deck diminishes. Shortly the child excitedly said, “This deck is a really smart teaching machine! It remembers which products I’ve learned, and then only asks for the ones I don’t know, so it saves me from wasting a lot of time!”

However, a more serious problem was that this child had no good image or “cognitive map” of what might result from learning this subject. What function might Math serve in later years? What goals and ambitions might it help to achieve?

Anecdote: I asked a certain 6-year-old child “how much is 15 and 15”and she quickly answered, “I think it’s 30.” I asked how she figured that out so fast and she replied, “Well, everyone knows that 16 and 16 is 32, so then I subtracted the extra two 1’s.”

Traditional teacher: “Your answer is right but your method was wrong: you should add the two 5’s to make a 10; then write down the 0 and carry the 1, and then add it to the other two 1’s.”

The traditional emphasis on accuracy leads to weakness of ability to make order-of-magnitude estimates—whereas this particular child already knew and could use enough powers of 2 to make approximations that rivaled some adult’s abilities. Why should children learn only “fixed-point” arithmetic, when “floating point” thinking is usually better for problems of everyday life!

More generally, we need to develop better ways to answer the questions that kids are afraid to ask, like “What am I doing here, and why? ”What can I expect to happen next?” or “Where and when could I find any use for this?

I’ll conclude with a perceptive remark from MIT’s Phil Sung: “Students are being led to think that they dislike math when they actually just dislike whatever it is that they're being taught in math classes.”

Students need Cognitive Maps of their Subjects

Until the 20th century, mathematics was mainly composed of Arithmetic, Geometry, Algebra, and Calculus. Then the fields of Logic and Topology started to rapidly grow, and in the 1950 we saw a great explosion of new ideas about the nature of information and computation. Today, these new concepts have become so useful and empowering that our math curriculum is out of date by a century. We need to find ways to introduce these ideas into our children’s earlier years.

In the traditional curriculum, Arithmetic was seen as so absolutely foundational that all other mathematical thinking depended on it. Accordingly, we sentenced all our children to two or three year terms of hard labor at doing addition, multiplication, and division! However, today it might be better to regard those tasks as little more than particular examples of algorithms—and this suggests that we could start, instead, with some simpler and more interesting ones!

For example, we could engage our children’s early minds with simple examples and ideas about Formal Languages and Finite State Machines. This would provide them with thoughtful and interesting ways to think about programs that they could create with the low-cost computers that they possess. Languages like Logo and Scratch can help children to experiment not only with simple arithmetic, but also with more interesting aspects of geometry, physics, math, and linguistics! What’s more, this would also empower them to apply those ideas to develop their own ideas about graphics, games, and languages—which in turn could lead them to contribute practical application that their communities can develop and share.

Similarly in the realm of Geometry, we can provide young children with interactive graphical programs that can lead them to observe and explore various sorts of symmetries—and thus begin to grasp the higher-level ideas that mathematicians call the “Theory of Groups”—which can be seen as a conceptual basis not only for Arithmetic, but for many aspects of other subjects. (To see examples of such things, type “Geometer's Sketchpad” to Google.)

Similarly in the realm of Physics, children can have access to programs that simulate the dynamics of structures, and thus become familiar with such important concepts as stress and strain, acceleration, momentum, energy—and vibration, damping, and dimensional scaling.

In any case, we need to provide our children with better cognitive maps of the subjects we want them to learn. I asked several grade-school teachers how often they actually used long division. One of them said, "I use it each year to compute the average grade.” Another teacher claimed to have used it for filling out tax forms—but couldn’t recall a specific example. But none of them seemed to have clear images of mathematics as a potential lifetime activity. Here is a simple but striking example of a case in which a child lacked a cognitive map:

A child was sent to me for tutoring because of failing a geometry class, and gave this excuse: " I must have been absent on the day when they explained how to prove a theorem."

No wonder this child was confused—and seemed both amazed and relieved when I explained that there was no standard way to make proofs—and that “you have to figure it out for yourself”. One could say that this child simply wasn’t told the rules of the game he was asked to play. However, this is a very peculiar case in which the ‘rule’ is that there are no rules! (In fact, automatic theorem-provers do exist, but I would not recommend their use.)

Bringing Mathematics to Life

What is mathematics, anyway? I once was in a classroom where some children were writing LOGO programs. One program was making colored flowers grow on the screen, and someone asked if the program was using mathematics. The child replied, “Oh, mathematics isn’t anything special: it’s just the smart way to understand things.” Here are a few kinds of questions that pupils should ask about the mathematical concepts we ask them to learn:

Arithmetic: Why does “compound interest’ tend to add more digits at constant rates? How do populations grow? How does recursion lead to exponentiation? It is easy to understand such things when one experiments with computer programs, but not when a child is constrained to the tedious rate of boring numerical calculation,

Geometry: How many different ways can you paint 6 colors on the faces of a cube? Can you envision how to divide a cube into three identical five-sided objects? We know that gloves come in left- and right-hand forms—but why are there only two such versions of things? We all live in a 3-D world, but few people learn good ways to think about 3-D objects. Shouldn’t this be seen as a handicap?

Logic: If most A’s are B’s, and most B’s are C’s, does this imply that many A’s must also be C’s? Many adults will give the wrong answer to this! Is it possible that when John Smith moved from Apple to Microsoft, this raised the average IQ of both companies? We all try to use logical arguments, but we also need to learn about the most common mistakes!

Mechanics: What makes a physical structure stronger when one braces it with triangular struts? That’s because two triangles are congruent, when their corresponding sides are equal—which means that that there’s no way to change a triangle’s shape, once the lengths of its sides are constrained. Today most children grow into adults without ever having learned to use the basic concept of “degrees of freedom.”

Statistics: Few mathematical subjects rival Statistics in the range of its everyday applications. How do effects accumulate? What kinds of knowledge and experience could help children to make better generalizations? How should one evaluate evidence? What’s the difference between correlation and cause? Every child should learn about the most common forms of biases—and also about why one needs to be skeptical of anecdotes.

A very few fragments of knowledge about statistics can illuminate most other subjects. In particular, it seems to me, that we should try to get children to learn to use the “T-test” method, which is an extremely simple statistical test, yet, one that handles huge ranges of situations. (To use it, only needs to know enough about the powers of 2!) Also they should understand using square roots to assess variations. (You can estimate a square root simply by halving the number of digits!) Example: Basketball scores often turn out to be number pairs like 103 to 97—which are not statistically significant!

Combinatorics: Consider that, when we teach about democracy, few pupils ever recognize that, in an electoral-college voting system, a 26% minority can win an election—and if there are 2 tiers of this, then a mere 7% minority could win! How do cultural memes manage to propagate? How does economics work? At what point should we try to teach at least the simplest aspects of the modern Theory of Games?

Abstract Algebra and Topology: These are considered to be very advanced, even postgraduate. Yet there are many phenomena that are hard to describe if one lacks access to those ideas—such as fixed-points, symmetries, singularities, and other features of dynamic trajectories, all of which appear in many real-world phenomena. Every large society is a complex organization that can only be well described by using representations at many different levels of abstraction—e.g., in terms of person, family, village, town, city, country, and whole-world economy—and “higher mathematics” has many concepts that could help to better understand such structures.

How can we encourage children to invent and carry out more elaborate processes in their heads? Teachers often insist that pupils “show their work”—which means to make them “write down every step.” This is convenient for making grades, as well as for diagnosing mistakes, but I suspect that this focus on ‘writing things down’ could lead to mental slowness and awkwardness, by discouraging pupils from trying to learn to perform those processes inside their heads—so that they can use mathematical thinking in ‘real time’. It isn’t merely a matter of speed, but of being able to keep in mind an adequate set of alternative goals and being able to quickly switch among different strategies and representations. This suggests that OLPC should promote the development of programs that help pupils to improve their working memories, and to refine the ways that they represent things in their minds:
The Impoverished Language of School-Mathematics.

There’s something peculiar about how we teach math. If you look at each subject in elementary school—History, English, Social Studies, etc.— you'll see that each pupil learn hundreds of new words in every term. You learn the names of many organizations, leaders, and wars; the titles of many books and their authors; and terms for all sorts of ideas and concepts—thousands of new words every year.

However, in the case of school-mathematics, the vocabulary is remarkably small. The children do learn words for various objects and processes—such as addition, multiplication, fraction, quotient, divisor, rectangle, parallelogram, and cylinder, equation, variable, function, and graph. But they learn only a few such terms pr year—which means that in the realm of mathematics, our children are mentally starved, by having to live in a “linguistic desert.” It is hard to think about something until one learns enough terms to express the important ideas in that area.

Specifically, it isn’t enough just to learn nouns; one also needs adequate adjectives! What's the word for when you should use addition? It’s when a phenomenon is linear. What's the word for when you should use multiplication? That’s when something is quadratic or bilinear. How does one describe processes that change suddenly or gradually: one needs terms like discrete and continuous. To talk about similarities, one needs terms like isomorphic and homotopic. Our children all need better ways to talk about, not only Arithmetic and Geometry, but also vocabularies for the ideas one needs to think about statistics, logic, and topology. This suggests an opportunity for the OLPC children’s community: to try set up discussion groups that encourage the everyday use of mathematical terms—communities in which a child can say “nonlinear” and have others admire, and not discourage her.
Mentors and Communities:

If one tries to learn a substantial skill without a good conceptual map, one is likely to end up with several collections of scripts and facts, without good ways to know which of them to use, and when—or how to find good alternatives when what you tried has failed to work. But how can our children acquire such maps? In the times before our modern schools, most young children mainly learned by being forced to work on particular jobs, and ended up without very much ‘general’ competence. However, there always were children who somehow absorbed their supervisors’ knowledge and skills—and there always were people who knew how to teach the children who were apprenticed to them.’

I’ll come back to this in another Memo about the disadvantages of modern age-based classes. Today most education is broader, but apprenticeship itself now is rare, because few teachers ever have enough time to interact very much with each of their students: a modern teacher can only do so much. The result is that no one has time to deal thoroughly questions like “What am I doing here, and why? ”What can I expect to happen next?” or “Where and when am I likely to use this?

However, now we can open new networks through which every child can communicate. This means that we can begin to envision, for each of our children, a competent adult with enough “spare time” to serve as a mentor or friend to help them develop their projects and skills. From where will all those new mentors come? Perhaps that problem will solve itself, because our lifespans are rapidly growing. The current rate of increasing longevity today is one more year for every four, so; soon we may have more retired persons than active ones!

Of course, each child will be especially good at learning particular ways to think—so we’ll also need to develop ways to match up good “apprenticeship pairs.” In effect we’ll need to develop “intellectual dating services” for finding the right persons to emulate!

In any case, no small school r community can teach all possible subjects, or serve the needs of individuals who abilities are atypical. If a child develops a specialized interest, it is unlikely that any local person can be of much help in developing that child’s special talents and abilities. (Nor can any small community can offer the range of resources to serve children with limited abilities.) However, with more global connections, it will be easier to reach others with similar interests, so that each child can join (or help form) an interactive community that offers good opportunities.

(Some existing communities will find this hard to accept, because most cultures have evolved to reward those who thinking about the same subjects in the same ways as do the rest! This will pose difficult problems for children who want to acquire new ways to think and do things that their neighbors and companions don't do—and thus escape or break out of the cultures in which they were born. To deal with this, OLPC will need to develop great new skills of diplomacy.)

Emphasizing Novelty rather than Drudgery?

Actually, I loved arithmetic in school. You had to add up a column of numbers and this was fun because there were so many different ways to do it. You could look here and there and notice three 3's and think, “that's almost a 10 so I'll take a 1 off that 7 and make it a 6 and make that 9 into a 10." But how do you keep from counting some numbers twice? Well, you could think: “Now I won’t count any more 3's.” How many children did these things exactly as they were told to do? Surely not those who became engineers or mathematicians! For when you use the same procedure again, there’s little chance to learn anything new—whereas each new method that you invent will leave you with some new mental skill (—such as a new way to use your memory).

For example, when you add 6 and 7 and write down a 3, how do you remember to “carry” a 1? Sometimes I’d mentally put it on my shoulder. How do you remember a telephone number? Most people don’t have too much trouble with remembering a ‘local’ 7-digit number, but reach for a pen when there’s also an area code. However, you can easily learn to mentally put those three other digits into your pocket—or in your left ear, if you don’t have a pocket!

Why are so many people averse to Math? Perhaps this often happens because our usual ways to teach arithmetic only insist on using certain rigid skills, while discouraging each child from trying to invent new ways to do those things. Indeed, perhaps we should study this subject when we want to discover ways to teach aversions to things!

Negative Expertise

There is a popular idea that, in order to understand something well, it is best to begin by getting things right—because then you'll never make any mistakes. We tend to think of knowledge in positive terms—and of experts as people who know exactly what to do. But one could argue that much of an expert’s competence stems from having learned to avoid the most common bugs. How much of what each person learns has this negative character? It would be hard for scientists to measure this, because a person’s knowledge about what not to do doesn’t overtly show in that individual’s behavior.

This issue is important because it is possible that our mental accumulations of counterexamples are larger and more powerful than our collections of instances and examples. If so, then it is also possible that people might learn more from negative rather than from positive reinforcement? Many educators have been taught that learning works best when it seems pleasant and enjoyable—but that discounts the value of experiencing frustrations, failures and disappointments. Besides, many feelings that we regard as positive (such as beauty, humor, pleasure, and decisiveness) may result from the censorship of other ideas, inhibition of competing activities, and the suppression of more ambitious goals (so that, instead of being positive, those feelings actually may reflect the workings of unconscious double negatives). See the longer discussions of this in Sections 1-1 and 9-4 of The Emotion Machine. Also see “Introduction to LogoWorks” at web.media.mit.edu/~minsky/papers/Logoworks.html

When we were in junior high school, my friend Rich and I made a map of the school lunch tables according to popularity. This was easy to do, because kids only ate lunch with others of about the same popularity. We graded them from A to E. A tables were full of football players and cheerleaders and so on. E tables contained the kids with mild cases of Down's Syndrome, what in the language of the time we called "retards."

We sat at a D table, as low as you could get without looking physically different. We were not being especially candid to grade ourselves as D. It would have taken a deliberate lie to say otherwise. Everyone in the school knew exactly how popular everyone else was, including us.

My stock gradually rose during high school. Puberty finally arrived; I became a decent soccer player; I started a scandalous underground newspaper. So I've seen a good part of the popularity landscape.

I know a lot of people who were nerds in school, and they all tell the same story: there is a strong correlation between being smart and being a nerd, and an even stronger inverse correlation between being a nerd and being popular. Being smart seems to make you unpopular.

Why? To someone in school now, that may seem an odd question to ask. The mere fact is so overwhelming that it may seem strange to imagine that it could be any other way. But it could. Being smart doesn't make you an outcast in elementary school. Nor does it harm you in the real world. Nor, as far as I can tell, is the problem so bad in most other countries. But in a typical American secondary school, being smart is likely to make your life difficult. Why?

The key to this mystery is to rephrase the question slightly. Why don't smart kids make themselves popular? If they're so smart, why don't they figure out how popularity works and beat the system, just as they do for standardized tests?

One argument says that this would be impossible, that the smart kids are unpopular because the other kids envy them for being smart, and nothing they could do could make them popular. I wish. If the other kids in junior high school envied me, they did a great job of concealing it. And in any case, if being smart were really an enviable quality, the girls would have broken ranks. The guys that guys envy, girls like.

In the schools I went to, being smart just didn't matter much. Kids didn't admire it or despise it. All other things being equal, they would have preferred to be on the smart side of average rather than the dumb side, but intelligence counted far less than, say, physical appearance, charisma, or athletic ability.

So if intelligence in itself is not a factor in popularity, why are smart kids so consistently unpopular? The answer, I think, is that they don't really want to be popular.

If someone had told me that at the time, I would have laughed at him. Being unpopular in school makes kids miserable, some of them so miserable that they commit suicide. Telling me that I didn't want to be popular would have seemed like telling someone dying of thirst in a desert that he didn't want a glass of water. Of course I wanted to be popular.

But in fact I didn't, not enough. There was something else I wanted more: to be smart. Not simply to do well in school, though that counted for something, but to design beautiful rockets, or to write well, or to understand how to program computers. In general, to make great things.

At the time I never tried to separate my wants and weigh them against one another. If I had, I would have seen that being smart was more important. If someone had offered me the chance to be the most popular kid in school, but only at the price of being of average intelligence (humor me here), I wouldn't have taken it.

Much as they suffer from their unpopularity, I don't think many nerds would. To them the thought of average intelligence is unbearable. But most kids would take that deal. For half of them, it would be a step up. Even for someone in the eightieth percentile (assuming, as everyone seemed to then, that intelligence is a scalar), who wouldn't drop thirty points in exchange for being loved and admired by everyone?

And that, I think, is the root of the problem. Nerds serve two masters. They want to be popular, certainly, but they want even more to be smart. And popularity is not something you can do in your spare time, not in the fiercely competitive environment of an American secondary school.

Alberti, arguably the archetype of the Renaissance Man, writes that "no art, however minor, demands less than total dedication if you want to excel in it." I wonder if anyone in the world works harder at anything than American school kids work at popularity. Navy SEALs and neurosurgery residents seem slackers by comparison. They occasionally take vacations; some even have hobbies. An American teenager may work at being popular every waking hour, 365 days a year.

I don't mean to suggest they do this consciously. Some of them truly are little Machiavellis, but what I really mean here is that teenagers are always on duty as conformists.

For example, teenage kids pay a great deal of attention to clothes. They don't consciously dress to be popular. They dress to look good. But to who? To the other kids. Other kids' opinions become their definition of right, not just for clothes, but for almost everything they do, right down to the way they walk. And so every effort they make to do things "right" is also, consciously or not, an effort to be more popular.

Nerds don't realize this. They don't realize that it takes work to be popular. In general, people outside some very demanding field don't realize the extent to which success depends on constant (though often unconscious) effort. For example, most people seem to consider the ability to draw as some kind of innate quality, like being tall. In fact, most people who "can draw" like drawing, and have spent many hours doing it; that's why they're good at it. Likewise, popular isn't just something you are or you aren't, but something you make yourself.

The main reason nerds are unpopular is that they have other things to think about. Their attention is drawn to books or the natural world, not fashions and parties. They're like someone trying to play soccer while balancing a glass of water on his head. Other players who can focus their whole attention on the game beat them effortlessly, and wonder why they seem so incapable.

Even if nerds cared as much as other kids about popularity, being popular would be more work for them. The popular kids learned to be popular, and to want to be popular, the same way the nerds learned to be smart, and to want to be smart: from their parents. While the nerds were being trained to get the right answers, the popular kids were being trained to please.

So far I've been finessing the relationship between smart and nerd, using them as if they were interchangeable. In fact it's only the context that makes them so. A nerd is someone who isn't socially adept enough. But "enough" depends on where you are. In a typical American school, standards for coolness are so high (or at least, so specific) that you don't have to be especially awkward to look awkward by comparison.

Few smart kids can spare the attention that popularity requires. Unless they also happen to be good-looking, natural athletes, or siblings of popular kids, they'll tend to become nerds. And that's why smart people's lives are worst between, say, the ages of eleven and seventeen. Life at that age revolves far more around popularity than before or after.

Before that, kids' lives are dominated by their parents, not by other kids. Kids do care what their peers think in elementary school, but this isn't their whole life, as it later becomes.

Around the age of eleven, though, kids seem to start treating their family as a day job. They create a new world among themselves, and standing in this world is what matters, not standing in their family. Indeed, being in trouble in their family can win them points in the world they care about.

The problem is, the world these kids create for themselves is at first a very crude one. If you leave a bunch of eleven-year-olds to their own devices, what you get is Lord of the Flies. Like a lot of American kids, I read this book in school. Presumably it was not a coincidence. Presumably someone wanted to point out to us that we were savages, and that we had made ourselves a cruel and stupid world. This was too subtle for me. While the book seemed entirely believable, I didn't get the additional message. I wish they had just told us outright that we were savages and our world was stupid.

Nerds would find their unpopularity more bearable if it merely caused them to be ignored. Unfortunately, to be unpopular in school is to be actively persecuted.

Why? Once again, anyone currently in school might think this a strange question to ask. How could things be any other way? But they could be. Adults don't normally persecute nerds. Why do teenage kids do it?

Partly because teenagers are still half children, and many children are just intrinsically cruel. Some torture nerds for the same reason they pull the legs off spiders. Before you develop a conscience, torture is amusing.

Another reason kids persecute nerds is to make themselves feel better. When you tread water, you lift yourself up by pushing water down. Likewise, in any social hierarchy, people unsure of their own position will try to emphasize it by maltreating those they think rank below. I've read that this is why poor whites in the United States are the group most hostile to blacks.

But I think the main reason other kids persecute nerds is that it's part of the mechanism of popularity. Popularity is only partially about individual attractiveness. It's much more about alliances. To become more popular, you need to be constantly doing things that bring you close to other popular people, and nothing brings people closer than a common enemy.

Like a politician who wants to distract voters from bad times at home, you can create an enemy if there isn't a real one. By singling out and persecuting a nerd, a group of kids from higher in the hierarchy create bonds between themselves. Attacking an outsider makes them all insiders. This is why the worst cases of bullying happen with groups. Ask any nerd: you get much worse treatment from a group of kids than from any individual bully, however sadistic.

If it's any consolation to the nerds, it's nothing personal. The group of kids who band together to pick on you are doing the same thing, and for the same reason, as a bunch of guys who get together to go hunting. They don't actually hate you. They just need something to chase.

Because they're at the bottom of the scale, nerds are a safe target for the entire school. If I remember correctly, the most popular kids don't persecute nerds; they don't need to stoop to such things. Most of the persecution comes from kids lower down, the nervous middle classes.

The trouble is, there are a lot of them. The distribution of popularity is not a pyramid, but tapers at the bottom like a pear. The least popular group is quite small. (I believe we were the only D table in our cafeteria map.) So there are more people who want to pick on nerds than there are nerds.

As well as gaining points by distancing oneself from unpopular kids, one loses points by being close to them. A woman I know says that in high school she liked nerds, but was afraid to be seen talking to them because the other girls would make fun of her. Unpopularity is a communicable disease; kids too nice to pick on nerds will still ostracize them in self-defense.

It's no wonder, then, that smart kids tend to be unhappy in middle school and high school. Their other interests leave them little attention to spare for popularity, and since popularity resembles a zero-sum game, this in turn makes them targets for the whole school. And the strange thing is, this nightmare scenario happens without any conscious malice, merely because of the shape of the situation.

For me the worst stretch was junior high, when kid culture was new and harsh, and the specialization that would later gradually separate the smarter kids had barely begun. Nearly everyone I've talked to agrees: the nadir is somewhere between eleven and fourteen.

In our school it was eighth grade, which was ages twelve and thirteen for me. There was a brief sensation that year when one of our teachers overheard a group of girls waiting for the school bus, and was so shocked that the next day she devoted the whole class to an eloquent plea not to be so cruel to one another.

It didn't have any noticeable effect. What struck me at the time was that she was surprised. You mean she doesn't know the kind of things they say to one another? You mean this isn't normal?

It's important to realize that, no, the adults don't know what the kids are doing to one another. They know, in the abstract, that kids are monstrously cruel to one another, just as we know in the abstract that people get tortured in poorer countries. But, like us, they don't like to dwell on this depressing fact, and they don't see evidence of specific abuses unless they go looking for it.

Public school teachers are in much the same position as prison wardens. Wardens' main concern is to keep the prisoners on the premises. They also need to keep them fed, and as far as possible prevent them from killing one another. Beyond that, they want to have as little to do with the prisoners as possible, so they leave them to create whatever social organization they want. From what I've read, the society that the prisoners create is warped, savage, and pervasive, and it is no fun to be at the bottom of it.

In outline, it was the same at the schools I went to. The most important thing was to stay on the premises. While there, the authorities fed you, prevented overt violence, and made some effort to teach you something. But beyond that they didn't want to have too much to do with the kids. Like prison wardens, the teachers mostly left us to ourselves. And, like prisoners, the culture we created was barbaric.

Why is the real world more hospitable to nerds? It might seem that the answer is simply that it's populated by adults, who are too mature to pick on one another. But I don't think this is true. Adults in prison certainly pick on one another. And so, apparently, do society wives; in some parts of Manhattan, life for women sounds like a continuation of high school, with all the same petty intrigues.

I think the important thing about the real world is not that it's populated by adults, but that it's very large, and the things you do have real effects. That's what school, prison, and ladies-who-lunch all lack. The inhabitants of all those worlds are trapped in little bubbles where nothing they do can have more than a local effect. Naturally these societies degenerate into savagery. They have no function for their form to follow.

When the things you do have real effects, it's no longer enough just to be pleasing. It starts to be important to get the right answers, and that's where nerds show to advantage. Bill Gates will of course come to mind. Though notoriously lacking in social skills, he gets the right answers, at least as measured in revenue.

The other thing that's different about the real world is that it's much larger. In a large enough pool, even the smallest minorities can achieve a critical mass if they clump together. Out in the real world, nerds collect in certain places and form their own societies where intelligence is the most important thing. Sometimes the current even starts to flow in the other direction: sometimes, particularly in university math and science departments, nerds deliberately exaggerate their awkwardness in order to seem smarter. John Nash so admired Norbert Wiener that he adopted his habit of touching the wall as he walked down a corridor.

As a thirteen-year-old kid, I didn't have much more experience of the world than what I saw immediately around me. The warped little world we lived in was, I thought, the world. The world seemed cruel and boring, and I'm not sure which was worse.

Because I didn't fit into this world, I thought that something must be wrong with me. I didn't realize that the reason we nerds didn't fit in was that in some ways we were a step ahead. We were already thinking about the kind of things that matter in the real world, instead of spending all our time playing an exacting but mostly pointless game like the others.

We were a bit like an adult would be if he were thrust back into middle school. He wouldn't know the right clothes to wear, the right music to like, the right slang to use. He'd seem to the kids a complete alien. The thing is, he'd know enough not to care what they thought. We had no such confidence.

A lot of people seem to think it's good for smart kids to be thrown together with "normal" kids at this stage of their lives. Perhaps. But in at least some cases the reason the nerds don't fit in really is that everyone else is crazy. I remember sitting in the audience at a "pep rally" at my high school, watching as the cheerleaders threw an effigy of an opposing player into the audience to be torn to pieces. I felt like an explorer witnessing some bizarre tribal ritual.

If I could go back and give my thirteen year old self some advice, the main thing I'd tell him would be to stick his head up and look around. I didn't really grasp it at the time, but the whole world we lived in was as fake as a Twinkie. Not just school, but the entire town. Why do people move to suburbia? To have kids! So no wonder it seemed boring and sterile. The whole place was a giant nursery, an artificial town created explicitly for the purpose of breeding children.

Where I grew up, it felt as if there was nowhere to go, and nothing to do. This was no accident. Suburbs are deliberately designed to exclude the outside world, because it contains things that could endanger children.

And as for the schools, they were just holding pens within this fake world. Officially the purpose of schools is to teach kids. In fact their primary purpose is to keep kids locked up in one place for a big chunk of the day so adults can get things done. And I have no problem with this: in a specialized industrial society, it would be a disaster to have kids running around loose.

What bothers me is not that the kids are kept in prisons, but that (a) they aren't told about it, and (b) the prisons are run mostly by the inmates. Kids are sent off to spend six years memorizing meaningless facts in a world ruled by a caste of giants who run after an oblong brown ball, as if this were the most natural thing in the world. And if they balk at this surreal cocktail, they're called misfits.

Life in this twisted world is stressful for the kids. And not just for the nerds. Like any war, it's damaging even to the winners.

Adults can't avoid seeing that teenage kids are tormented. So why don't they do something about it? Because they blame it on puberty. The reason kids are so unhappy, adults tell themselves, is that monstrous new chemicals, hormones, are now coursing through their bloodstream and messing up everything. There's nothing wrong with the system; it's just inevitable that kids will be miserable at that age.

This idea is so pervasive that even the kids believe it, which probably doesn't help. Someone who thinks his feet naturally hurt is not going to stop to consider the possibility that he is wearing the wrong size shoes.

I'm suspicious of this theory that thirteen-year-old kids are intrinsically messed up. If it's physiological, it should be universal. Are Mongol nomads all nihilists at thirteen? I've read a lot of history, and I have not seen a single reference to this supposedly universal fact before the twentieth century. Teenage apprentices in the Renaissance seem to have been cheerful and eager. They got in fights and played tricks on one another of course (Michelangelo had his nose broken by a bully), but they weren't crazy.

As far as I can tell, the concept of the hormone-crazed teenager is coeval with suburbia. I don't think this is a coincidence. I think teenagers are driven crazy by the life they're made to lead. Teenage apprentices in the Renaissance were working dogs. Teenagers now are neurotic lapdogs. Their craziness is the craziness of the idle everywhere.

When I was in school, suicide was a constant topic among the smarter kids. No one I knew did it, but several planned to, and some may have tried. Mostly this was just a pose. Like other teenagers, we loved the dramatic, and suicide seemed very dramatic. But partly it was because our lives were at times genuinely miserable.

Bullying was only part of the problem. Another problem, and possibly an even worse one, was that we never had anything real to work on. Humans like to work; in most of the world, your work is your identity. And all the work we did was pointless, or seemed so at the time.

At best it was practice for real work we might do far in the future, so far that we didn't even know at the time what we were practicing for. More often it was just an arbitrary series of hoops to jump through, words without content designed mainly for testability. (The three main causes of the Civil War were.... Test: List the three main causes of the Civil War.)

And there was no way to opt out. The adults had agreed among themselves that this was to be the route to college. The only way to escape this empty life was to submit to it.

Teenage kids used to have a more active role in society. In pre-industrial times, they were all apprentices of one sort or another, whether in shops or on farms or even on warships. They weren't left to create their own societies. They were junior members of adult societies.

Teenagers seem to have respected adults more then, because the adults were the visible experts in the skills they were trying to learn. Now most kids have little idea what their parents do in their distant offices, and see no connection (indeed, there is precious little) between schoolwork and the work they'll do as adults.

And if teenagers respected adults more, adults also had more use for teenagers. After a couple years' training, an apprentice could be a real help. Even the newest apprentice could be made to carry messages or sweep the workshop.

Now adults have no immediate use for teenagers. They would be in the way in an office. So they drop them off at school on their way to work, much as they might drop the dog off at a kennel if they were going away for the weekend.

What happened? We're up against a hard one here. The cause of this problem is the same as the cause of so many present ills: specialization. As jobs become more specialized, we have to train longer for them. Kids in pre-industrial times started working at about 14 at the latest; kids on farms, where most people lived, began far earlier. Now kids who go to college don't start working full-time till 21 or 22. With some degrees, like MDs and PhDs, you may not finish your training till 30.

Teenagers now are useless, except as cheap labor in industries like fast food, which evolved to exploit precisely this fact. In almost any other kind of work, they'd be a net loss. But they're also too young to be left unsupervised. Someone has to watch over them, and the most efficient way to do this is to collect them together in one place. Then a few adults can watch all of them.

If you stop there, what you're describing is literally a prison, albeit a part-time one. The problem is, many schools practically do stop there. The stated purpose of schools is to educate the kids. But there is no external pressure to do this well. And so most schools do such a bad job of teaching that the kids don't really take it seriously-- not even the smart kids. Much of the time we were all, students and teachers both, just going through the motions.

In my high school French class we were supposed to read Hugo's Les Miserables. I don't think any of us knew French well enough to make our way through this enormous book. Like the rest of the class, I just skimmed the Cliff's Notes. When we were given a test on the book, I noticed that the questions sounded odd. They were full of long words that our teacher wouldn't have used. Where had these questions come from? From the Cliff's Notes, it turned out. The teacher was using them too. We were all just pretending.

There are certainly great public school teachers. The energy and imagination of my fourth grade teacher, Mr. Mihalko, made that year something his students still talk about, thirty years later. But teachers like him were individuals swimming upstream. They couldn't fix the system.

In almost any group of people you'll find hierarchy. When groups of adults form in the real world, it's generally for some common purpose, and the leaders end up being those who are best at it. The problem with most schools is, they have no purpose. But hierarchy there must be. And so the kids make one out of nothing.

We have a phrase to describe what happens when rankings have to be created without any meaningful criteria. We say that the situation degenerates into a popularity contest. And that's exactly what happens in most American schools. Instead of depending on some real test, one's rank depends mostly on one's ability to increase one's rank. It's like the court of Louis XIV. There is no external opponent, so the kids become one another's opponents.

When there is some real external test of skill, it isn't painful to be at the bottom of the hierarchy. A rookie on a football team doesn't resent the skill of the veteran; he hopes to be like him one day and is happy to have the chance to learn from him. The veteran may in turn feel a sense of noblesse oblige. And most importantly, their status depends on how well they do against opponents, not on whether they can push the other down.

Court hierarchies are another thing entirely. This type of society debases anyone who enters it. There is neither admiration at the bottom, nor noblesse oblige at the top. It's kill or be killed.

This is the sort of society that gets created in American secondary schools. And it happens because these schools have no real purpose beyond keeping the kids all in one place for a certain number of hours each day. What I didn't realize at the time, and in fact didn't realize till very recently, is that the twin horrors of school life, the cruelty and the boredom, both have the same cause.

The mediocrity of American public schools has worse consequences than just making kids unhappy for six years. It breeds a rebelliousness that actively drives kids away from the things they're supposed to be learning.

Like many nerds, probably, it was years after high school before I could bring myself to read anything we'd been assigned then. And I lost more than books. I mistrusted words like "character" and "integrity" because they had been so debased by adults. As they were used then, these words all seemed to mean the same thing: obedience. The kids who got praised for these qualities tended to be at best dull-witted prize bulls, and at worst facile schmoozers. If that was what character and integrity were, I wanted no part of them.

The word I most misunderstood was "tact." As used by adults, it seemed to mean keeping your mouth shut. I assumed it was derived from the same root as "tacit" and "taciturn," and that it literally meant being quiet. I vowed that I would never be tactful; they were never going to shut me up. In fact, it's derived from the same root as "tactile," and what it means is to have a deft touch. Tactful is the opposite of clumsy. I don't think I learned this until college.

Nerds aren't the only losers in the popularity rat race. Nerds are unpopular because they're distracted. There are other kids who deliberately opt out because they're so disgusted with the whole process.

Teenage kids, even rebels, don't like to be alone, so when kids opt out of the system, they tend to do it as a group. At the schools I went to, the focus of rebellion was drug use, specifically marijuana. The kids in this tribe wore black concert t-shirts and were called "freaks."

Freaks and nerds were allies, and there was a good deal of overlap between them. Freaks were on the whole smarter than other kids, though never studying (or at least never appearing to) was an important tribal value. I was more in the nerd camp, but I was friends with a lot of freaks.

They used drugs, at least at first, for the social bonds they created. It was something to do together, and because the drugs were illegal, it was a shared badge of rebellion.

I'm not claiming that bad schools are the whole reason kids get into trouble with drugs. After a while, drugs have their own momentum. No doubt some of the freaks ultimately used drugs to escape from other problems-- trouble at home, for example. But, in my school at least, the reason most kids started using drugs was rebellion. Fourteen-year-olds didn't start smoking pot because they'd heard it would help them forget their problems. They started because they wanted to join a different tribe.

Misrule breeds rebellion; this is not a new idea. And yet the authorities still for the most part act as if drugs were themselves the cause of the problem.

The real problem is the emptiness of school life. We won't see solutions till adults realize that. The adults who may realize it first are the ones who were themselves nerds in school. Do you want your kids to be as unhappy in eighth grade as you were? I wouldn't. Well, then, is there anything we can do to fix things? Almost certainly. There is nothing inevitable about the current system. It has come about mostly by default.

Adults, though, are busy. Showing up for school plays is one thing. Taking on the educational bureaucracy is another. Perhaps a few will have the energy to try to change things. I suspect the hardest part is realizing that you can.

Nerds still in school should not hold their breath. Maybe one day a heavily armed force of adults will show up in helicopters to rescue you, but they probably won't be coming this month. Any immediate improvement in nerds' lives is probably going to have to come from the nerds themselves.

Merely understanding the situation they're in should make it less painful. Nerds aren't losers. They're just playing a different game, and a game much closer to the one played in the real world. Adults know this. It's hard to find successful adults now who don't claim to have been nerds in high school.

It's important for nerds to realize, too, that school is not life. School is a strange, artificial thing, half sterile and half feral. It's all-encompassing, like life, but it isn't the real thing. It's only temporary, and if you look, you can see beyond it even while you're still in it.

If life seems awful to kids, it's neither because hormones are turning you all into monsters (as your parents believe), nor because life actually is awful (as you believe). It's because the adults, who no longer have any economic use for you, have abandoned you to spend years cooped up together with nothing real to do. Any society of that type is awful to live in. You don't have to look any further to explain why teenage kids are unhappy.

I've said some harsh things in this essay, but really the thesis is an optimistic one-- that several problems we take for granted are in fact not insoluble after all. Teenage kids are not inherently unhappy monsters. That should be encouraging news to kids and adults both.

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