Modern microconomist Alfred Marshall explains that technology has greatly extended the power and reach of the planet's most gifted performers....He referenced a classical of the British opera singer Elizabeth Billington. She was a well-acclaimed soprano with a strong voice, that, naturally did not have access to a microphone or amplifier in 1798, let alone to MTV, CDs, iTunes, and Pandora. She could only reach a small audience. This limited her ability to dominate the market in the way that artists to do today. Marshall wrote, “so long as the number of persons who can be reached by a human voice is strictly limited, it is not very likely that any singer will make an advance on the £10,000 said to have been earned in a season by Mrs. Billington at the beginning of the last century, nearly as great [an increase] as that which the business leaders of the present generation have made on those of the last.” 

- Wikipedia

Technology has made it easy for us to reach large audiences. And to do so at no marginal cost. If a musician writes a song and puts it on iTunes, it doesn't cost him any money for one more person to download it.

The fact that technology has made it easy for us to reach large audiences has implications on the consumer side of things as well. As a consumer, I can go on iTunes and choose the best music to buy. To understand my point, consider a different world. In this world iTunes doesn't exist. In this world the best music is 200 miles away, but mediocre music is only 5 miles away. Because traveling 200 miles is inconvenient, I choose the mediocre music.

In today's world of iTunes, this doesn't happen. Technology exists that allows us to reach large audiences and to do so at little/no marginal cost. And so, the consumer can (and will) choose the best the market has to offer.

Now for the implications on the supply side. We've already seen that consumers can and will choose the best the market has to offer. "The best the market has to offer" is usually provided by a small number of talented people. Think about it: the best artists, performers, writers, athletes etc. These talented people end up serving a large proportion of the market, and are paid accordingly. This... is The Superstar Effect.

Because of these joint consumption economies, there is a unique opportunity to create and capture value. If you are the best, you capture insane amounts of value. Thus, there is a huge incentive to be the best.

So, should you invest in an attempt to outdo The Superstar and capture this value? Well, investment decisions are all about expected value. Balancing risk with reward. In this case, the potential reward is huge. Astronomical. These joint consumption economies allow you to reach tremendous markets. However, the question is "how big is the risk?".

Outdoing The Superstar is a large and complex task, and I won't pretend to have all the answers. However, I've had this nagging suspicion in the back of my mind for years. My suspicion is that people drastically overestimate this risk, and that with a good plan and enough resources, you could have an excellent chance at "outdoing The Superstar".

Before moving on, let me go through the logic one more time:

  • Today's joint consumption economies allow for firms to reach large amounts of people with little/no marginal costs.
  • Thus, consumers have tons of options to choose from.
  • Consumers often have similar enough tastes such that a large percentage of them end up choosing The Superstar.
  • In serving all of these people, The Superstar has created and captured a ton of value.
  • If another firm came along and outdid The Superstar, this new firm would replace The Superstar. It would now be the one to serve the large market, and would be compensated accordingly. There is a large reward for outdoing The Superstar.
  • Investment is all about balancing risk and reward. Investing in an attempt to outdo The Superstar has a very large potential reward. The question is, "what's the risk?".


Outdoing The Superstar

People seem to view large ventures like starting startups as a roll of the dice. They say things like, "9 out of 10 startups fail". I don't see things that way. I don't see it as "a roll of the dice". I see it as a deterministic puzzle that can be solved.

I should qualify that previous statement. I'm not trying to make a philosophical point, just a practical one. People seem to be afraid of what I'll call, Large Puzzles. Because of their size and complexity, people seem to be put off by them, and they fall back on outside view arguments like "9 in 10 startups fail".

I'll admit that Large Puzzles are complex, but I maintain that with enough resources and with a good plan, a lot of them are very solvable. I sense that a lot of these large joint consumption winner-take-all industries are ripe for the taking, and that with enough resources and a good plan, they can be taken.

My confidence isn't that high though. I don't understand these Large Puzzles well enough to really say. What I'm referring to are "relatively strong suspicions", not "beliefs" (my thoughts are cloudy enough such that I'm having trouble being more precise than this, sorry).


Investing

This is a bit of an aside and a rant, but here we go. Investors currently seem to be heavily biased towards investing in businesses that can be built incrementally. They want to...

  • See some sort of promise/traction before investing at all (usually).
  • Invest 10s/100s of thousands of dollars in a seed round.
  • See some more traction before they invest a couple/10s of millions in a series A.
  • See some more traction before they invest 10s/100s in the next round.
  • etc. etc.
What about firms that are trying to replace The Superstar? Such a task usually requires very large amounts of upfront investment. Because of the winner-take-all nature of these industries, you usually need to exceed a certain threshold of "firepower" before you have a shot at showing some traction, let alone at replacing The Superstar.

However, the fact remains that investment decisions are all about expected value. Risk vs. reward. Risk isn't inherently bad, it just needs to be balanced by the reward. An in the case of superstar industries, the potential reward is huge.

In fact, the idea that the distribution of returns in an investment fund follows a power law seems to be well accepted. This means that it makes sense for an investor to seek huge exits. Replacing a Superstar seems like a great way to do that to me.

But in reality, it seems that investors don't actually understand the power law. It seems that they try desperately to "minimize risk", and look desperately for signs of traction, and end up investing mostly in companies that can be built incrementally. Unfortunate.



Education

The Large Puzzle that I understand best is Education (which causes my System I to care disproportionately about it). I'll indulge myself and say it: the education system today is shit.

I think that Elon Musk said it well. He said (paraphrasing):

Consider The Dark Knight. It's awesome! It has all the best actors, directors, special effects etc. Now imagine if you took the same script and asked the local middle school to reproduce it. It'd suck. That's education.

I think that this division of resources is really the core of the problem. Things you could do once you pool resources:

  • Put a lot of effort towards making each lesson great (in dath ilan, "One hour of instruction on a widely-used subject got the same kind of attention that an hour of prime-time TV gets on Earth"). Figure out how to word things properly. What examples to use. What analogies to give. Make lessons visual, animated, interactive. Gamify them and make them fun (when appropriate). Make them beautiful. Apply design thinking. Make them skimmable so students can refer back to them when they're studying. Include convenient references to things the student might have a question on.
  • Break lessons into chunks and organize them according to their dependencies (this is an important and difficult task). I'm a big believer that knowledge is hierarchical. That concepts have dependencies (to know A, you have to know B). I think it makes a lot of sense to have students learn things that they have the proper foundation for. I think this makes more sense in the negative: you shouldn't have students learn things that they don't have the proper foundation for. (This is a bit of an aside, but I think that mastery should be fixed, and time should be variable. Currently it's the opposite.)
  • Open up time for teachers to spend personal attention on their students. In today's system, they're usually too busy to do this. (Note: even with these great lessons, I still think that teachers will be useful. The lessons could be pretty good, so I'm not sure if they'd be necessary, but I suspect that they'd still be useful. I think using a human will still be the best way to diagnose and address the holes in a student's understanding.)
  • Come up with great practice problems, exercises, projects etc. 
  • Make tests way more accurate and effective. Make them smaller. And for gods sake, have them created by a separate financial entity than the entity that does the teaching!
  • This applies to a lot of what I said above, but iterate, iterate, iterate!! See what works and what doesn't work and change. Given the amount of "experimental subjects (students)" and "technicians (teachers)", there's a tremendous opportunity to do this. Effective collaboration and coordination might be tough, but I sense that it's doable.
Sorry, I may have mixed in a few opinions that aren't directly related to the idea of pooling resources and that should really be asides.

Anyway, I think that the Large Puzzle of Education is very solvable. I think that with enough resources, you could do a good enough job such that it becomes an industry where The Superstar Effect takes over. Where one Superstar addresses a large proportion of the market. And I think that this would have a huge and beneficial impact on the world.
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53 comments, sorted by Click to highlight new comments since: Today at 5:57 AM

In addition to my other comments, I'd like to ask what your overall goal is for grade-school education. (It seems to me that most of your arguments are about grade school and not college. This may be wrong.)

The current (public school) system, inasfar as it has a single consistent goal, tries to optimize the minimal level of education that almost all students attain. Therefore it invests more in students who are doing worse: a lesson advances at the pace of the slowest students. There are sometimes multiple classes for differently performing students, but these are limited to a few subjects in a few years and are still very coarse-grained. (Of course the system also has non-education-related goals, which makes things harder to analyze.)

If I wanted to change the system to optimize average academic achievement instead, I would first of all group students by ability, not by age cohort. And this grouping would be separate for separate subjects. In today's system, if a student fails one class but does well in others, she must either repeat that year for the sake of one class, or advance a year and continue to fail to keep up in that one subject.

But it may be that neither approach is strictly better than the other; it depends on what you are optimizing for. The school system optimizes for socializing kids (even if their models of how to do so are wrong and harmful) and for pleasing their parents. Academic achievement isn't a top priority, and even if it were, there is no objectively "correct" choice between maximizing average achievement, top 10% achievement, or top 90% achievement.

In addition to my other comments, I'd like to ask what your overall goal is for grade-school education. (It seems to me that most of your arguments are about grade school and not college.

I'd like to amplify that point. Educating people who mostly want to be educated is very different to educating people who mostly don't want to be there.

This is one of the most important things in education. Sometimes a completely opposite strategy is required. For example, if students want to learn, you can give them necessary resources and let them study at their own speed. If students don't want to learn, using this strategy they would learn nothing. Similarly, if students want to learn, it is good to have a debate about the topic. If they don't want to learn, they will only use the debate to waste time.

We could separate the students who want to learn from those who don't, and use different strategies for these groups. Problem is, how to separate them. If you ask students, some students will mistakenly believe they want to learn (for example, they would say they want to learn about computer science, when in reality they only enjoy playing computer games). Some of them will lie to make a good impression; or their parents will make them lie.

A possible approach would be to use some costly signalling. For example, to offer "advanced lessons" for volunteers in the afternoon, and later separate the students who participated in these advanced lessons. But this will only work once; when your method becomes known, again, even people without interest in the topic will "volunteer" for the advanced lessons.

It seems your first paragraph outlines a solution for the second paragraph. First spend some time teaching students using a method that works well for motivated learners and poorly for unmotivated learners. Then give a placement test measuring how much they learned. Put the people who did well in the placement test into a group that teaches motivated students, and the people who did poorly into a group that teaches unmotivated students.

I think the arguments apply to grade school as well as college. I'm not sure what my overall goal is in terms of balancing the trade-offs between weak/average/strong students. However, I don't think it matters much. I think that if you pooled resources, you'd be able to cater to all types of students.

However, I don't think it matters much. I think that if you pooled resources, you'd be able to cater to all types of students.

I think you're sidestepping the problem about which goal to optimize for.

In private schools, the investment in a student is partly proportional to the money spent by the student's parents. If a student is worse than average, they can pay for better tuition, in a more intense school program or from a private tutor. Or they can switch to a better, more expensive school. So a given school or program can (in the simplest case) divide resources between students equally, demand equal tuition pay and approximately equal aptitude on tests, and let market forces sort out the rest.

In a public school, however, resources are apportioned to students based on political factors and goals are set on a population, not an individual level. Academically poor students can't just be failed out of public legally-mandated school, and they also can't be forced to repeat classes forever. So the system has a natural tendency to invest more resources in poor students, because the incentives are much greater than any reward there may be for supporting already-good students. And as long as some students aren't doing well enough, any additional marginal resources will be spent to help them rather than someone else. The whole system is satisficing more than it is optimizing, because it's incentivized to care more about graduation/diploma rates than about average scores among those who do graduate.

(Disclaimer: I have not researched the subject extensively, and I am not very certain of the above.)

My main claim is that we should pool resources and create great lessons/tools that everyone can use. Ie. I don't see how it'd be the case that these lessons/tools would benefit a certain group of students disproportionately. And thus I don't see where the question of catering to certain students comes into play here.

As for my opinions though. First off, I'd like to say that I'm a big believer in the idea that education should be self-paced and personalized. But to answer your question, if we're going to fix time instead of mastery, I think that we should cater to the strong students. I believe in the idea of giving people sufficient (not necessarily equal) opportunity, and rewarding those who work hard. I think that in most cases, the weaker students are weak largely because they don't care and don't work hard. I don't have strong opinions about this stuff at all though.

Personally, I agree with your goals and like most of your ideas. But:

I believe in the idea of giving people sufficient (not necessarily equal) opportunity, and rewarding those who work hard.

The public school system disagrees, which makes your proposal impractical no matter how technically good it might be. Your ideas would be much more suited to private, higher education - which is already moving in that direction on some counts. And this was my point: when you observe public and/or legally mandatory schools are very badly designed, you should keep in mind their goals are different from yours.

Ah, I see your point now - practicality. I haven't been addressing that. So far I've just argued for what I think it should be, not really taking practicality into account.

That's not to say that I haven't thought about and don't care about practicality though. Just that this is a huge topic and I thought it'd be more productive to break it up.

Anyway, I really don't know too much about politics and "how the system works". It's something I definitely plan on learning about in order to someday get my ideas implemented though.

I doubt that governments can be convinced via sensible argument to do something like this. But I envision something like the following being plausible: invest some 10s/100s of millions of dollars to create a prototype for one topic that is sufficiently great. That is clearly The Superstar, and thus everyone learning this topic will want to use the prototype. Hopefully this would lead to people wanting to invest/donate more money, and the project could expand. And finally, if the project grows large enough and is good enough, there'll be pressure for governments to adopt it or to adapt.

I think that the key is getting a prototype that is sufficiently dominant. That is clearly The Superstar. I'm not really sure what it'd take to achieve that, but I sense that it's doable with 10s/100s of millions of dollars. As for how to get that money... personally I'm going to try and start a startup.

Note: even with these great lessons, I still think that teachers will be useful. The lessons could be pretty good, so I'm not sure if they'd be necessary, but I suspect that they'd still be useful.

It seems you're thinking of a system where teachers help students learn, and the students want to learn and apply some minimal effort towards doing so. And where really good lecture material is prerecorded and teachers don't have to spend the majority of their time reading from standardized lecture notes.

But the biggest problems in modern education seem to lie in mandatory grade school, not in elective college degrees. Many students strongly don't want to study (at least certain subjects); others simply don't care enough to put in a lot of effort. The task of the teacher in practice is often to force students to study (or encourage them, if possible). For those students who do want to study, being forced to sit in the same class as those who don't is often a problem in itself.

[-][anonymous]9y50

Man this brings back childhood memories. I just look back and wonder why I had to spend all that time with annoying morons. Really makes me wonder how differently things turned out but if we had the technology to contact the split universe where my other self is basically as best as it could be I wonder if I could still feel that it's me. Not just a person who looks identical.

School is a prison for children.

Man this brings back childhood memories. I just look back and wonder why I had to spend all that time [in school] with annoying morons.

It gets you used to working with annoying morons.

Maybe that lesson is overrated.

If you work with the annoying morons as one of them, you are probably doing something wrong. And if you are their boss... well, this is the part the school didn't teach you.

[-][anonymous]9y00

The neighbor's grass is always greener and better to smoke.

Good point. As for whether or not we'd need these babysitters, I don't know. Perhaps there'd be weekly/monthly tests that students would have to pass, and that would provide sufficient motivation. Perhaps the motivation to eventually get a job would be sufficient. Perhaps learning would actually be fun, and there would be sufficient intrinsic motivation. I really don't know.

Outdoing The Superstar is a large and complex task, and I won't pretend to have all the answers. However, I've had this nagging suspicion in the back of my mind for years. My suspicion is that people drastically overestimate this risk, and that with a good plan and enough resources, you could have an excellent chance at "outdoing The Superstar".

Music appears to be a straightforward counter-example to your claim. Loads and loads of artists and bands struggle in obscurity for their whole lives, without being close to superstar. As someone surrounded by highly trained classical musicians, I know that they are mostly not going to be famous, because I know lots that have spent their lives being exactly that. Daniel Kahneman did some work in hedonism, and I recall him saying that music was an industry you should get in to if you want to be reliably unhappy, and theorising that this was because you never get anywhere. I think that this argument misses out the behavioural economics side, that people not only want the best, but people are going to want to keep with the current superstar, because they are high status too. Also, have you spent time looking for theories about why nobody else is jumping onto this mahoosive gap in the market? Any bias theory?

If you feel that you have a way of beating the market in, say, the education industry, feel free to go out and actually do it. But saying that it appears to be easy, seems an obvious error. What you actually have done is noticed a number of problems and flaws with a current system. They are all valid, and you're not the first to notice them. The education system is hard to change, due to the political situation it is controlled by, and that may be part of the reason that it is not fixed; because the people in charge have no incentive to do so.

the education system today is shit.

Whose education system? Compared to what?

Compared to:

1) One-on-one tutoring, which is generally considered effective but doesn't scale very well
2) Video games, which are very effective at inspiring people to seek mastery of, and at teaching, difficult skills
3) Whatever we fantasize about having.

Everyones. Compared to what it would be if people had some very basic degree of rationality. Think along the lines of "all it'd take for the world to be like dath ilan would be a little bit of sense, nothing extraordinary".

Edit: a key part of that statement was "I'll indulge myself: ". I don't know everything about how it works so I can't really be too confident, but I strongly suspect that what I said about "what it would be if people had some very basic degree of rationality" is true. And that frustrates me, so I indulged myself a bit and used strong language. Sometimes strong language is unproductive and uncivil, but I sensed that it was useful here to better communicate my point.

You know that dath ilan has been criticised, right?

Here's a thing: problems often seem easier to solve to non experts than to experts, because the experts are aware of all the gotchas.

You know that dath ilan has been criticised, right?

That would be difficult to know for most people reading the Tumblr version, inasmuch as most of the harshest criticism I saw was on the LW version, which has since been deleted: http://lesswrong.com/lw/jzr/my_april_fools_day_confession/ One would have to know there was a LW post (which is mentioned nowhere in the Tumblr version, and Tumblr chooses to show mostly just upvotes on stuff, so don't go looking there for criticism), pluck the URL out of the ether somehow (I had to pull it out of IRC logs), hope there's an IA capture (which luckily, there is), and look it up (after all that I'm not sure how complete that version is, since the next IA capture is days later when the page - and its comments - have been deleted).

The biggest obstacle here is that underground construction is orders of magnitude more expensive than above-ground construction.

And private educators can teach more effectively than public educators...because they can spend more money.

The people who run public education systems aren't irrational, just cash strapped.

Dath ilan is all about gold plating mousetraps...never mind the cost/benefit ratios, look how shiny it is.

If you want to design a new credential, how do you make people accept/respect it? One way is "convince the relevant government to make it illegal for people to perform a specific task without your credential", but are there others?

As an employer, why should I hire someone who learned to code at App Academy but never went to college instead of the guy with the Comp. Sci degree from NJIT?

It should be noted that many employers do hire the somebody who learned to code at App Academy but never went to college over the other person.

(After all, the somebody can signal agentiness about becoming a better programmer, unlike the person. And the somebody is actually more likely to be a good employee than the person.)

(I'm not sure if you were implying the opposite of this or not (it is ambiguous))

Agreed. I just graduated from a different coding bootcamp (Fullstack Academy) and know that the good bootcamps have job placement rates in the mid-high 90s.

How do I tell the difference between a good bootcamp and a bad one?

In this context I was using good to mean selective and prestigious. I'm not really sure where you'd find this information. My understanding is that App Academy, Hack Reactor, Fullstack and Dev Bootcamp are (part of) the top tier.

As for how much you learn, that's a whole different question.

I don't know. That' s a tough question. Ideally, the invisible hand would do it for you. Firms would start to realize that people with this credential are good, and the market would reach some sort of equilibrium. But in practice, I'm not sure if this would work. I don't know enough about how things work to really say. However, my suspicion is that although the market may not be perfectly rational, it's rational enough such that if the credential was a really really strong indicator of quality, it's value would rise to somewhere in the ballpark of where it should be.

[-][anonymous]9y30

The "superstar effect" happened "naturally" with books, music, and so on. If there is this potential gain in education, why hasn't it happened, and what are you going to do about that?

I am not sure how much the Elon Musk quote has to do with education as in schooling. There was undoubtedly a great deal of learning by doing and selecting the best that went into creating the team that created The Dark Knight. A classroom can only go so far in that regard.

I am not really sure I understand what you mean by "pooling resources." Do you mean spending more? Nor do I understand what "division of resources" is or what it has to do with education or the Elon Musk quote or education or schooling.

Is fun, interactive, flashy teaching really better than rote repetition and instruction for the mastery of many skills? E.g.

Of course the testing situation in American public schools is not ideal, but it is the product of the incentives of the people in control of the resources. What can you do about that?

Iteration and change probably requires market competition.

However, the fact remains that investment decisions are all about expected value. Risk vs. reward. Risk isn't inherently bad, it just needs to be balanced by the reward. An in the case of superstar industries, the potential reward is huge.

There are pitfalls to expected value. Volatility is a killer. A lot of risk management is devoted to reducing the impact of volatility on your position. Even Kelly bets, which maximize long-term expected return, are subject to wide swings. It's okay to take on a few long shots with a high reward, but the longer the shot the smaller the fraction of your bankroll you want to bet (note that by the Kelly criterion, this holds true even if the potential returns are huge).

People seem to view large ventures like starting startups as a roll of the dice. They say things like, "9 out of 10 startups fail". I don't see things that way. I don't see it as "a roll of the dice". I see it as a deterministic puzzle that can be solved.

Any solution you can implement, a competitor can potentially implement as well. You can't deterministically beat such a competitor.

Also, the testing effect. There seems to be some sort of consensus among scientists who research in the relevant area that many, low-stakes quizzes is better than few high-stakes tests, because it reduces student anxiety, encourages a more spread out practice distribution, and leverages the testing effect more. (There exists proper empirical support which I'm too lazy to dig up, but will if asked to.)

Thank you for your article, I really liked the optimism I felt conveyed from the paragraph about beating the superstar.

(I have my own caveat here, it does not pertain to the level of the easiness of the necessary plans or their implementation - in my experience it's much more the coordination problems that throw a wrench into these schemes: You are going to invariably need more people on the set; and you're going to end up spending factorially more time on explaining what exactly on earth you want to do) I notice though that most superstars didn't optimise their abilities, when treated separately, their ideas are barely trivial, and the stuff that is heard a decade, hundred years later probably was not made by a superstar of that time. (Know Giacinto Scelsi? He invented the stuff that people today use in music that the superstars of tomorrow will make. ~10% confident about that, considering x-risk and everything)

On another note, do I read you well enough to say that you wish to optimise on the teaching side? What if you could get more mileage out of optimising on the learning side, for instance propagating the urge of really wanting to learn stuff?

I'd also be interested how you'd set your plan in motion. Given infinite resources, what particular thing you know about would you change first. (Describe it to my system 1, pretty please)

On another note, do I read you well enough to say that you wish to optimise on the teaching side? What if you could get more mileage out of optimising on the learning side, for instance propagating the urge of really wanting to learn stuff?

Yes, I have been talking about optimizing the teaching side. Optimizing the learning side would be great as well! I don't really have any insightful thoughts on that though.

I'd also be interested how you'd set your plan in motion. Given infinite resources, what particular thing you know about would you change first. (Describe it to my system 1, pretty please)

Given infinite resources? Dependency tree!!! I'd build an online resource that does the following. Each node is a micro-concept. The nodes are linked according to their dependencies (to know A, you need to know B). And each node has a lesson/explanation, a test to see if the student understands the corresponding concept, and some practice exercises and projects. It'd take a ton of resources to organize the information properly, produce all of the explanations, tests, exercises... do it well, iterate etc.

As for practicality - http://lesswrong.com/lw/lh6/the_superstar_effect/bt7d

in my experience it's much more the coordination problems

See the above comment about practicality (that's the best I've got).

the education system today is shit.

Whose education system? Compared to what?

you shouldn't have students learn things that they don't have the proper foundation for.

I think that in education the problem usually isn't students learning things they don't have the proper foundation for, but rather people disagreeing on the goal of the learning. You don't elaborate your point and so I'm unsure what you mean precisely, so what follows may be a tangent.

Almost all academic subjects - in math, computing, natural sciences, history, literature, economics - have 'foundations' one could learn. In math, these are axiomatic formulations and proofs (as opposed to results), and often complex underlying theories. In computing, these are enginnering artifacts - software and hardware designs, implementations, and algorithms. In the sciences, these are the more fundamental laws of nature (which may be described by a slightly different science), as well as a great deal of organized facts, especially in biology. In history and literature, these are even more history and literature which provide the necessary background context.

One can always point towards a lesson (which isn't at a graduate level) and claim students are missing some fundamental background. So does that mean we shouldn't teach calculus without the underlying proofs, or programming 101 before operating system design, or classical physics before modern theories? That depends on what you want to accomplish.

When I studied undergrad CS, most courses had several versions you could choose from. All freshmen in the sciences & engineering faculties had to take a course on real number calculus, but there were as many as 5 variations, billed as calculus for math, physics, CS, engineering, and biology/chemistry majors, respectively. The math majors spent most of their time (and were tested mostly on) proving theorems. The engineering students studied solving really hard instances of the equations. And the biology students did the minimum and skipped some of the hard proofs entirely.

Did the biology students not "learn the proper foundation" for calculus? That depends entirely on the use they expect to make of it. The tradeoffs of the harder courses are clear: more time and effort spent studying, and more students failing the course and not graduating. (Also, things one learns but never uses are usually forgotten after a few years.)

In many cases it's harder to match up the optimal lesson for the goal. In grade school we studied history. Which historical subjects should be taught? How should the available time be spread across them - studying a few eras in depth, or many on a shallow level? How useful is it, and against what goal should it be judged, to learn about any one historical setting without understanding its causes and effects - what came before and after, what was happening elsewhere at the same time, why people behaved as they did? But any mandatory education system must make centralized decisions about the accepted minimum that everyone should know.

You're right, I wasn't clear enough about what I mean. Sorry.

1) Dependencies often have the connotation of getting deep into theories and proofs, but in a strict sense that's only a subset of dependencies. Like you said, what's relevant is what you're trying to accomplish. I'm completely on board with the idea that a bio major may not need to know all the theory behind, say calculus. But for whatever it is that the bio major is learning, it still has dependencies.

2) Try thinking about it like this: say that the bio major doesn't understand something and is in office hours with the professor. The professor does something like this: "You don't know A? Ok, well do you know B? You do, good. What about C? You do, good. What about D? No, ok, well do you know E? You do, good. What about F? You don't? Ok, let me explain it to you." Teachers (good ones anyway) implicitly are traversing the dependency tree in order to diagnose the holes in students' knowledge. I think that you could use software to approximate this.

  1. Since you placed this in your list of problems with the current state of education, do you have concrete examples in mind of study programs missing important prerequisites? How prevalent do you feel this is? (Grade school and college probably should be evaluated separately here, since colleges have entrance exams and explicit requirements that are supposed to be pretty much exhaustive wrt. required prior knowledge.)

  2. It's not always clear, and people often disagree, on what students are supposed to be learning to accomplish. In practice, most of the time, they're learning to pass the graduation or college-entrance exam; most students don't practice most of the knowledge they were taught. Also, subjects in the humanities have no clear goal at all. How can you quantify the use of studying history, and compare the utility of different historical subjects, in young people who haven't even chosen a profession yet? Yet most people agree that learning history, arts, etc. is worthwhile. (And we know it's not simply for fun - otherwise you could just point people at the library and save a lot of money on history classes.)

1) I think it's very prevalent and I think that most lessons do a pretty bad job of addressing prerequisites. To be clear, I'm not talking prerequisites as "you need algebra before calculus". I'm talking on a much smaller level than that.

As for examples... unfortunately I don't really have great examples. I'm a student and am constantly reading and learning, and am constantly thinking to myself, "They're trying to explain X but X depends on me knowing Y. I don't know Y, and there isn't any reason for them to have assumed that I did know Y. At the very least they should recognize that Y is likely to be something that trips students up (they'd see this if they did 'user research' and iterated) and provide convenient reference to material explaining Y."

2) Right. The question of what students should be learning is another separate and huge topic. I don't think this is the right place to properly argue them, but rest assured, I've got my opinions :)

  • I believe strongly that rationality should be a big part of the curriculum.
  • I think a big question is "to what extent do you let kids choose what they want, and to what extent do you force them to learn certain things". I don't think kids are mature enough to make great decisions. I think that they should be forced to learn a lot of "fundamental" things. The reasons for this are a) it'll allow them to have a better basis for making a career choice and b) it'll make them "more well rounded people". But I think that there should be much less of a focus on details. Eg. don't make kids memorize things, just have them understand the fundamental concepts. Memorizing details doesn't help achieve goals a) or b).
  • I see a lot of things like languages and music and literature as hobbies. It's very unlikely you end up using these things in your career or life. They at least should largely be electives rather than requirements. In general, I have a bit of a disapproval for the humanities.
  • I think that the basics of computer science should be a requirement. Same with the core ideas of economics, psychology and design (and probably some other things I'm not thinking of).
  • I would emphasize writing. Students should be able to make logical arguments and to write clearly and concisely.

I don't think kids are mature enough to make great decisions.

Even most undergrad students are not informed enough to make great decisions. They may know what they want, but they often mistake how hard it will be to study something, or how fun it would be to work in a profession, or their chances of finding a good job.

On the other hand, the bureaucrats and politicians who do write school programs don't always have the students' best interest in mind. They may discount subjects they don't understand well or aren't interested in personally. They may make decisions for political reasons, like making school easier to raise graduation rates. And, of course, many fields of study are excellent indoctrination and covert political propaganda tools and are chosen mostly for these reasons.

On balance, I would trust students to influence their studies more than they do today, but I'm biased in favor of academically good students.

I see a lot of things like languages and music and literature as hobbies. It's very unlikely you end up using these things in your career or life. They at least should largely be electives rather than requirements. In general, I have a bit of a disapproval for the humanities.

Isn't that at odds with your desire to make students "more well rounded people"? If you think humanities aren't valuable, all I can say is that most people disagree (me included). It's a difference in values, and isn't eclectic learning according to different values necessary to make a person well-rounded?

Also, and perhaps more importantly, most technical and scientific (i.e. non-humanities) subjects taught in school are also unlikely to be used by most people in most careers. Going purely by how many people actually use something they learned in later life, most mathematics should be an elective (especially geometry and trigonometry), as should natural sciences (physics, chemistry, biology) and general subjects like history, geology, most of geography and economics, etc. Do away with the humanities too, and what's left for the core curriculum? You'd be back to the basics - reading, writing, and arithmetic.

Eg. don't make kids memorize things, just have them understand the fundamental concepts. Memorizing details doesn't help achieve goals a) or b).

I agree, understanding is much more important than memorizing. And memorized but poorly understood facts are usually forgotten later in life anyway.

However, most subjects do require memorization of a bunch of useful facts if they're to be taught at all. The precise date of a battle isn't important, but knowing who won and why it matters is.

I think that the basics of computer science should be a requirement. Same with the core ideas of economics, psychology and design (and probably some other things I'm not thinking of).

How many people do you think are going to use computer science (as opposed to programming), economics or psychology? I think very few are. Here too I feel this doesn't align well with your desire to make things few people use electives.

It may be that you are projecting your own love of e.g. compsci and dislike of e.g. literature to others. But forcing all students to learn compsci is very unlikely to make more of them like it. On the contrary, people sometimes report hating subjects like history because they're tainted by forced, badly conducted learning in school, even when they might have otherwise enjoyed them as adults.

I wonder. In this day and age, is film theory as relevant as literary theory? (As in, studying the techniques that filmmakers use to tell stories well that are unique to film, as opposed to those that are unique to prose or poetry.)

I would add computer/video game design theory.

I will now proceed to miss the point. ;)

Consider The Dark Knight. It's awesome! It has all the best actors, directors, special effects etc. Now imagine if you took the same script and asked the local middle school to reproduce it. It'd suck. That's education.

Oddly enough, sometimes you get the opposite effect. "Arsenic and Old Lace" is hilarious when performed by random high school students, but under no circumstances should professional actors ever be allowed to perform it. If the performances are too "good", the atmosphere goes from ridiculous and starts veering toward creepy (but not quite creepy enough to be genuine horror).

Disagree. The movie, which is a straightforward adaptation of the play, is creepy and hilarious; it's quite good.

There might be an uncanny valley effect involved, in which the play becomes good again if the actors are of superstar quality. I could see this happening if certain "amateur mistakes" are actually required for the play to succeed, and ordinary actors who aren't superstars wouldn't realize this.

I loved the version my local high school put on, but when my local community theater - which does hire professional actors - put it on, they played everything far too straight and it stopped being funny. I've never seen the movie, though, but my father reported the same experience as I did; he also loved Arsenic and Old Lace when his high school put it on, but he never cared for the movie very much.

Sorry, I don't think I'm understanding your point. Are you saying that education is analogous to "Arsenic and Old Lace"? That it's better when it's performed by incompetent people than when it's performed by competent ones?

There is no deep point, other than that throwing more resources at a production doesn't always make it better. (Consider the film adaptations of various stage musicals - many excellent stage musicals have made mediocre movies.) Mostly, though, I'm just a compulsive nitpicker. ;)

The Large Puzzle that I understand best is Education

Unless you are studying education, you don't know that much about education.

Would you say this about any topic? If not, how is education different?

I would say that lying in a hospital bed doesn't make you a doctor, and being incarcerated doesn't make you a criminologist.

Can you expand on what that has to do with your original comment? It seems that your original comment was substantially stronger than simply noting that being a student is not enough to understand education. If that's what you mean that seems like a different (and weaker) claim than your initial comment.

The original comment said understanding MUCH about education. It was implicit that understanding much about something is necessary to fixing it.

Yes, but they didn't say that their understanding came purely from being a student. So I'm not sure how the much is relevant.