I would pay ungodly sums of money to be able to send this essay backwards in time to 15-year-old me. Still finding many of these points useful today (eg around setting up your body)!
This was very enlightening to read as somebody who is entering their second half of high school soon.
Besides computer science, one of my main interests is in mathematics, and it seems that it is especially in pure mathematics. Lately I have been working through a calculus textbook, reading and working through exercises each day. However, this definitely doesn't seem to be a "real thing" as you describe, and I've been struggling to come up with ideas for a real thing to do that ends up with the same, or better, outcome; namely, a deep understanding and knowledge of the topic. So I am wondering if you had any suggestions for such a real thing?
You do suggest the idea of proving theorems in another comment, but I am not sure this would apply well to learning these earlier, often calculation based, subjects like calculus and introductory linear algebra (I think, but I don't know much about linear algebra.) Or maybe my perspective on this is wrong, and I don't need to gain the same knowledge a textbook would give? Either way, I would love to hear your thoughts!
Calculus looks like a calculation-based subject if all the problems you work on are calculations, but all the facts you use to do the computations with had to get discovered at some point. A fun thing to do is to try to rederive them. Like, see if you can figure out from first principles why the derivative of sine is cosine, why integration is the inverse of differentiation, etc. Or, see if you can guess the extensions of existing concepts before reading that part of the textbook: what happens in edge cases, higher dimensions, etc?
On some level, it's hard to do "real" things in math as deeply as you can in other subjects, because you basically have to be on a PhD or really advanced undergrad level to be discovering original results. You might just have to bite this bullet and be satisfied that you're doing kind of the same thing as they are, except they're trying to prove conjectures no one knows existing proofs of yet, and you're trying to prove conjectures that are already settled but that are new to you. I wouldn't worry too much, though – finding the subject inherently interesting and engaging in a non-passive way (by doing exercises) for its own sake are both good signs.
You might also try learning calculus alongside physics or economics, so you can start applying it right away. There are various neat economic concepts and innovations you can understand better (and play around with) if you understand calculus. Or you could try to build a simple physics engine.
The other suggestion I'd give is to try learning to use a software proof system, which lets you express math and write proofs in a formal language. It can also help you automate the generation of the proof, but the formalization part feels more educationally useful, and it can verify that your proof is correct as well. This is the thing I really wish I'd been told about before starting a math degree. ("Wait, you mean Real Math Proofs are just... a paragraph you write down in English? And you do this by just thinking really hard until a solution jumps into your mind? And you don't know if you're right until someone checks your work?") Lean is one popular example; Coq is another I've tried. There's a bit of a learning curve, but it's a fun one.
Really great read, especially for someone who's struggling with the pressure of grades and high school, thank you for posting this!
Here, the only thing school achieves is stifling the time, energy, and resources to do anything but study the narrow curriculum you're given. I really hope there's a complete rehaul of the system because anything shorter than that wouldn't do it justice
I was a teacher of burnt out 15-17 year olds and managed to help a few by pointing out that they were in the middle of a golden age where they had close to adult levels of willpower, and close to childhood levels of malleability. Formal schooling in its current form feels like the biggest waste of human potential possible. Wonderful essay. I will save it to share with people around this age in my life.
> When you’re a young child, you actually do get to achieve real accomplishments. You learn to walk and talk, then to throw a ball, to write, to draw, to build a sandcastle or a fort in the woods. Once the tasks of basic interaction with the world become too easy, though, you get assigned years of fake work in a sequestered environment: instead of getting progressively harder real tasks, you get switched over to made-up ones until you’re eighteen.
I really like this. Except learning math, chemistry, history etc is a real task, it just seems like high schoolers are expected to learn far more of these subjects through rote memorization than will serve them.
have you tried asserting this onto any 14 year olds yet and what were the results? I read Paul Graham's essays in high school and I'm not sure it did much, beyond temporary agitation and maybe fostering a counterproductive sense of superiority. I wish my education focused less of total quantity of material and more on motivating the process of discovery, but the teachers who can do that are really rare.
So I actually would go so far as to say that learning math, chemistry, and history are still fake tasks if the end goal is just learning. The real tasks would be
- proving a theorem, or on the applied side, modeling a real-life problem in order to solve it
- coming up with a chemistry question and devising and running an experiment to figure out the answer (school usually gives you the question and procedure, all you do yourself is carry out the steps; either that or they give you the question on a test and ask you to come up with an experiment, but you don't actually carry it out)
- publicly arguing for some hypothesis about anthropology, economics, development, politics, etc. based on historical analysis (what you do in school is make arguments that are read by your teacher and classmates at most, about questions you usually didn't choose, and which are almost always narrowed to a specific time and place – "what was the most critical factor driving the Industrial Revolution in Britain?" – leaving out the step where you try to draw conclusions about how technology drives economic changes in general.
If you do these things, you're still learning, but I think the distinction is that the learning is in service of the doing, rather than vice versa.
Nope, don't know enough fourteen-year-olds to have play-tested this on them, unfortunately :/ if you know any, feel free to give it a shot and report back!
Did you ever read anything by Alfie Kohn? I didn't discover Paul Graham until college alas, but Kohn was my PG in terms of radicalizing me early.
I sent this to my niece who just turned 15 and is, thankfully, doing a lot of this stuff already (releasing music, making animations, writing fiction, doing some version of independent/online high school). I'll let you know if she has any thoughts on it. I was really inspired by it. I managed to get out of high school early and do a lot of independent study, but I wish I had some of the more practical advice and a better understanding of what college was useful for. I will save it for my own kids in a few years. I've read Kohn's Punished by Rewards and it made a lot of sense to me, but I found it very hard as a parent to feel like I was living up to the standard. Sounds a little different from what you are talking about maybe. I wonder which book you found useful?
I think I might have read Punished by Rewards, but can't remember it very well since it was so long ago. The one I kept rereading when I was in school was The Homework Myth. What were the practical challenges you ran into trying to apply his ideas to parenting?
Crickets so far, but I'll see her later on in the summer and try to get her thoughts on it.
I had to go back and look at my order history on Amazon, but I think I misremembered and the Kohn book I actually read was Unconditional Parenting. I must have read it when my first kid was 1 or 2 (now 9). The anecdote that I remember most from the book was a parent being at an art class with their kid and the kid coming up to show them what they made, and instead of saying "that's great!" or "great job!", saying "what do you think?" and the kid looks at it and says, "I think I could improve it by doing such-and-such". The idea being that when you constantly praise a kid for the work they do, they start doing things for the praise, rather than the intrinsic value or enjoyment of it and, I guess they might be less likely to reflect on what they've done. I got a very "NEVER PRAISE YOUR KID OR YOU WILL RUIN THEM!!!" vibe, but it's possible that that was more my nervous new parent interpretation. I think there is something to be said for the approach though, and keeping an eye out for whether your kid is seeming to be overly praise-seeking, etc., but never praising your kid or their work is just not realistic (sometimes you really think it's great!). Again, it may not be that that's what he was really advocating, but that was what I came away with it feeling... and it's been a while so take with a grain of salt. Then there is also the gray area between praise and encouragement, the latter being unambiguously good I think, but often sounding like praise.
On the subject of Punished by Rewards, I think I generally agree and we mostly don't do rewards at home, but unless you homeschool or find a school that is 100% on board with that philosophy, your kids will be getting gold stars and pokemon cards for doing their work/behaving. Even the Montessori schools we've tried have done it to some degree.
I like <learning in service of the doing>, I wonder if it is a rule or rather a special case for long-term interests. I'd say most of my learning now is not in service of the immediate doing, but are in conversations with friends on politics, work, where we might want to live and how to buy a house, future work. i.e. prospective doing, or just developing as a person. High schoolers should have the same flexibility to understand the natural world and human-world without always contributing to it.
It seems like the student would still need a good teacher or personal tutor to help scope and provide feedback on the real tasks
No, I hadn't, I just checked out his post on feedback, interesting! He's got a friendly name
I actually disagree with the idea that you shouldn't try to form or participate in groups, because being a founder or someone who has to organise it does build skills above just participating - and best of all, you'll often get a budget!
I would say that joining a football team probably teaches very few things other than playing football and teamwork, as the coach usually handles all the real world interfaces. However, becoming the president or treasurer of a club (assuming that an adult doesn't just do that job, but try to convince adults to let you) can often be really educational. I picked these two roles because they tend to have "real jobs" compared to most other roles - president does the work management (or just the work, depending on club dysfunction), treasurer handles money. Secretary is a maybe - some clubs use their secretaries well, some badly, so it's a bit of a crapshoot.
President gets you a headstart on things like contacting real-world people and groups, whether to collaborate, or to buy stuff. You get comfortable with speaking to strangers on the phone (an unbelievable number of young people struggle with this). You learn what it takes to organise an event (estimate how many people are coming to things, book a venue, organise stuff and people to happen).
Treasurer learns about how most organisations do finance. Most of these kinds of things which are funded by a school are audited - you learn how to record things to pass an audit. You have a very unique, low-stakes opportunity to learn how to manage funds for a non-profit organisation - to understand your income sources, sometimes to get creative about income sources within rules and real world regulations, and to understand the expenditure. (You'll learn more if the club members are ambitious, try new things types, because a lot of ventures cost money, and it'll be your job to figure out if you can afford it and if you can't, how much you have to raise).
It also looks good on resumes because people will figure if you haven't embezzled club funds as a teenager with low impulse control, you probably won't do something similar as an adult. Note: do not embezzle club funds. A lot of these kinds of organisations are registered non-profits (or parts of anothet registered non-profit) and that's one of the few ways you can actually get into real world trouble by embezzling funds from a non-profit.
That being said, I know adults end up doing a lot of these things for high school clubs. But if you happen to have clubs you can join where adults let you do the job, you should.
Good point, getting access to a budget is generally good, if only to learn how to handle one — money is nice and real. There's an interesting tension here between teams and clubs: in my experience, teams generally had more camaraderie and some kind of emotional depth that clubs lacked, but clubs tended to have more freedom and less externally-imposed structure.
I also think a lot about KC, because his story is a terrible and tragic argument against precisely what he argues in the book he wrote.
I keep thinking "someone should have told that kid he CAN'T". His death was entirely preventable. He couldn't swim, wasn't wearing a life jacket, wasn't supervised, and was roughhousing with his brother in a kayak, when it capsized and he drowned.
I helped supervise about 15 5-8 year olds in canoes yesterday. Of them, about half are already competent swimmers, and 100% of them (including the adults) were wearing life jackets. There is absolutely no good reason not to teach your children swim. There is absolutely no good reason for anyone to be in a canoe without life jacket. Full stop.
And neither of those things prevent you from writing a book! Think about how many more books we'd have from him if the adults in his life had told him, just once, he couldn't, and how many more people would have taken his book seriously if he hadn't demonstrated the frailty of its thesis. No parent wants to lose a child like that.
I would pay ungodly sums of money to be able to send this essay backwards in time to 15-year-old me. Still finding many of these points useful today (eg around setting up your body)!
if my teenage self had benched bodyweight and sent 20 emails it would've been OVER for y'all
Been binging your posts the last few days. Absolutely loving them keep it up
hell ya brother
This was very enlightening to read as somebody who is entering their second half of high school soon.
Besides computer science, one of my main interests is in mathematics, and it seems that it is especially in pure mathematics. Lately I have been working through a calculus textbook, reading and working through exercises each day. However, this definitely doesn't seem to be a "real thing" as you describe, and I've been struggling to come up with ideas for a real thing to do that ends up with the same, or better, outcome; namely, a deep understanding and knowledge of the topic. So I am wondering if you had any suggestions for such a real thing?
You do suggest the idea of proving theorems in another comment, but I am not sure this would apply well to learning these earlier, often calculation based, subjects like calculus and introductory linear algebra (I think, but I don't know much about linear algebra.) Or maybe my perspective on this is wrong, and I don't need to gain the same knowledge a textbook would give? Either way, I would love to hear your thoughts!
Oh yeah this is a really good question. Math's kind of a weird case of its own.
Maybe you've read this essay already, but if you haven't, definitely recommend, it's a classic: https://www.maa.org/external_archive/devlin/LockhartsLament.pdf
Calculus looks like a calculation-based subject if all the problems you work on are calculations, but all the facts you use to do the computations with had to get discovered at some point. A fun thing to do is to try to rederive them. Like, see if you can figure out from first principles why the derivative of sine is cosine, why integration is the inverse of differentiation, etc. Or, see if you can guess the extensions of existing concepts before reading that part of the textbook: what happens in edge cases, higher dimensions, etc?
On some level, it's hard to do "real" things in math as deeply as you can in other subjects, because you basically have to be on a PhD or really advanced undergrad level to be discovering original results. You might just have to bite this bullet and be satisfied that you're doing kind of the same thing as they are, except they're trying to prove conjectures no one knows existing proofs of yet, and you're trying to prove conjectures that are already settled but that are new to you. I wouldn't worry too much, though – finding the subject inherently interesting and engaging in a non-passive way (by doing exercises) for its own sake are both good signs.
You might also try learning calculus alongside physics or economics, so you can start applying it right away. There are various neat economic concepts and innovations you can understand better (and play around with) if you understand calculus. Or you could try to build a simple physics engine.
The other suggestion I'd give is to try learning to use a software proof system, which lets you express math and write proofs in a formal language. It can also help you automate the generation of the proof, but the formalization part feels more educationally useful, and it can verify that your proof is correct as well. This is the thing I really wish I'd been told about before starting a math degree. ("Wait, you mean Real Math Proofs are just... a paragraph you write down in English? And you do this by just thinking really hard until a solution jumps into your mind? And you don't know if you're right until someone checks your work?") Lean is one popular example; Coq is another I've tried. There's a bit of a learning curve, but it's a fun one.
This is sick - I run a program (lol) very philosophically similar to what you write about. Sharing with the team + some of my students.
neat! what kind of program?
Really great read, especially for someone who's struggling with the pressure of grades and high school, thank you for posting this!
Here, the only thing school achieves is stifling the time, energy, and resources to do anything but study the narrow curriculum you're given. I really hope there's a complete rehaul of the system because anything shorter than that wouldn't do it justice
I was a teacher of burnt out 15-17 year olds and managed to help a few by pointing out that they were in the middle of a golden age where they had close to adult levels of willpower, and close to childhood levels of malleability. Formal schooling in its current form feels like the biggest waste of human potential possible. Wonderful essay. I will save it to share with people around this age in my life.
Thanks – if you end up sending it to a kid, please do tell me their thoughts!
> When you’re a young child, you actually do get to achieve real accomplishments. You learn to walk and talk, then to throw a ball, to write, to draw, to build a sandcastle or a fort in the woods. Once the tasks of basic interaction with the world become too easy, though, you get assigned years of fake work in a sequestered environment: instead of getting progressively harder real tasks, you get switched over to made-up ones until you’re eighteen.
I really like this. Except learning math, chemistry, history etc is a real task, it just seems like high schoolers are expected to learn far more of these subjects through rote memorization than will serve them.
have you tried asserting this onto any 14 year olds yet and what were the results? I read Paul Graham's essays in high school and I'm not sure it did much, beyond temporary agitation and maybe fostering a counterproductive sense of superiority. I wish my education focused less of total quantity of material and more on motivating the process of discovery, but the teachers who can do that are really rare.
So I actually would go so far as to say that learning math, chemistry, and history are still fake tasks if the end goal is just learning. The real tasks would be
- proving a theorem, or on the applied side, modeling a real-life problem in order to solve it
- coming up with a chemistry question and devising and running an experiment to figure out the answer (school usually gives you the question and procedure, all you do yourself is carry out the steps; either that or they give you the question on a test and ask you to come up with an experiment, but you don't actually carry it out)
- publicly arguing for some hypothesis about anthropology, economics, development, politics, etc. based on historical analysis (what you do in school is make arguments that are read by your teacher and classmates at most, about questions you usually didn't choose, and which are almost always narrowed to a specific time and place – "what was the most critical factor driving the Industrial Revolution in Britain?" – leaving out the step where you try to draw conclusions about how technology drives economic changes in general.
If you do these things, you're still learning, but I think the distinction is that the learning is in service of the doing, rather than vice versa.
Nope, don't know enough fourteen-year-olds to have play-tested this on them, unfortunately :/ if you know any, feel free to give it a shot and report back!
Did you ever read anything by Alfie Kohn? I didn't discover Paul Graham until college alas, but Kohn was my PG in terms of radicalizing me early.
I sent this to my niece who just turned 15 and is, thankfully, doing a lot of this stuff already (releasing music, making animations, writing fiction, doing some version of independent/online high school). I'll let you know if she has any thoughts on it. I was really inspired by it. I managed to get out of high school early and do a lot of independent study, but I wish I had some of the more practical advice and a better understanding of what college was useful for. I will save it for my own kids in a few years. I've read Kohn's Punished by Rewards and it made a lot of sense to me, but I found it very hard as a parent to feel like I was living up to the standard. Sounds a little different from what you are talking about maybe. I wonder which book you found useful?
Yes, please do pass on any thoughts she has!
I think I might have read Punished by Rewards, but can't remember it very well since it was so long ago. The one I kept rereading when I was in school was The Homework Myth. What were the practical challenges you ran into trying to apply his ideas to parenting?
Crickets so far, but I'll see her later on in the summer and try to get her thoughts on it.
I had to go back and look at my order history on Amazon, but I think I misremembered and the Kohn book I actually read was Unconditional Parenting. I must have read it when my first kid was 1 or 2 (now 9). The anecdote that I remember most from the book was a parent being at an art class with their kid and the kid coming up to show them what they made, and instead of saying "that's great!" or "great job!", saying "what do you think?" and the kid looks at it and says, "I think I could improve it by doing such-and-such". The idea being that when you constantly praise a kid for the work they do, they start doing things for the praise, rather than the intrinsic value or enjoyment of it and, I guess they might be less likely to reflect on what they've done. I got a very "NEVER PRAISE YOUR KID OR YOU WILL RUIN THEM!!!" vibe, but it's possible that that was more my nervous new parent interpretation. I think there is something to be said for the approach though, and keeping an eye out for whether your kid is seeming to be overly praise-seeking, etc., but never praising your kid or their work is just not realistic (sometimes you really think it's great!). Again, it may not be that that's what he was really advocating, but that was what I came away with it feeling... and it's been a while so take with a grain of salt. Then there is also the gray area between praise and encouragement, the latter being unambiguously good I think, but often sounding like praise.
On the subject of Punished by Rewards, I think I generally agree and we mostly don't do rewards at home, but unless you homeschool or find a school that is 100% on board with that philosophy, your kids will be getting gold stars and pokemon cards for doing their work/behaving. Even the Montessori schools we've tried have done it to some degree.
I like <learning in service of the doing>, I wonder if it is a rule or rather a special case for long-term interests. I'd say most of my learning now is not in service of the immediate doing, but are in conversations with friends on politics, work, where we might want to live and how to buy a house, future work. i.e. prospective doing, or just developing as a person. High schoolers should have the same flexibility to understand the natural world and human-world without always contributing to it.
It seems like the student would still need a good teacher or personal tutor to help scope and provide feedback on the real tasks
No, I hadn't, I just checked out his post on feedback, interesting! He's got a friendly name
I actually disagree with the idea that you shouldn't try to form or participate in groups, because being a founder or someone who has to organise it does build skills above just participating - and best of all, you'll often get a budget!
I would say that joining a football team probably teaches very few things other than playing football and teamwork, as the coach usually handles all the real world interfaces. However, becoming the president or treasurer of a club (assuming that an adult doesn't just do that job, but try to convince adults to let you) can often be really educational. I picked these two roles because they tend to have "real jobs" compared to most other roles - president does the work management (or just the work, depending on club dysfunction), treasurer handles money. Secretary is a maybe - some clubs use their secretaries well, some badly, so it's a bit of a crapshoot.
President gets you a headstart on things like contacting real-world people and groups, whether to collaborate, or to buy stuff. You get comfortable with speaking to strangers on the phone (an unbelievable number of young people struggle with this). You learn what it takes to organise an event (estimate how many people are coming to things, book a venue, organise stuff and people to happen).
Treasurer learns about how most organisations do finance. Most of these kinds of things which are funded by a school are audited - you learn how to record things to pass an audit. You have a very unique, low-stakes opportunity to learn how to manage funds for a non-profit organisation - to understand your income sources, sometimes to get creative about income sources within rules and real world regulations, and to understand the expenditure. (You'll learn more if the club members are ambitious, try new things types, because a lot of ventures cost money, and it'll be your job to figure out if you can afford it and if you can't, how much you have to raise).
It also looks good on resumes because people will figure if you haven't embezzled club funds as a teenager with low impulse control, you probably won't do something similar as an adult. Note: do not embezzle club funds. A lot of these kinds of organisations are registered non-profits (or parts of anothet registered non-profit) and that's one of the few ways you can actually get into real world trouble by embezzling funds from a non-profit.
That being said, I know adults end up doing a lot of these things for high school clubs. But if you happen to have clubs you can join where adults let you do the job, you should.
Good point, getting access to a budget is generally good, if only to learn how to handle one — money is nice and real. There's an interesting tension here between teams and clubs: in my experience, teams generally had more camaraderie and some kind of emotional depth that clubs lacked, but clubs tended to have more freedom and less externally-imposed structure.
I also think a lot about KC, because his story is a terrible and tragic argument against precisely what he argues in the book he wrote.
I keep thinking "someone should have told that kid he CAN'T". His death was entirely preventable. He couldn't swim, wasn't wearing a life jacket, wasn't supervised, and was roughhousing with his brother in a kayak, when it capsized and he drowned.
I helped supervise about 15 5-8 year olds in canoes yesterday. Of them, about half are already competent swimmers, and 100% of them (including the adults) were wearing life jackets. There is absolutely no good reason not to teach your children swim. There is absolutely no good reason for anyone to be in a canoe without life jacket. Full stop.
And neither of those things prevent you from writing a book! Think about how many more books we'd have from him if the adults in his life had told him, just once, he couldn't, and how many more people would have taken his book seriously if he hadn't demonstrated the frailty of its thesis. No parent wants to lose a child like that.
💚