The Lottery of Fascinations


Suppose I were to come out tomorrow as gay.

I have amazing and wonderful friends, and I certainly wouldn’t expect them to hate me forever or tell me to burn in Hell or anything like that.

But even more than that, I think they would understand and accept the decision. There would be a lot of not-so-obvious failure modes they could fall into, but wouldn’t.

For example, I don’t think any of them would say something like “Oh, obviously you just haven’t met the right woman. I know this really cute girl Alanna, a friend of my sister’s. I’ll introduce you next time she’s around.”

Or “You must have just had a bad experience with women growing up. Maybe you always got into fights with your mother as a child. But there’s no reason to let that control you now.”

Or “But…but…women are attractive! How could you not be attracted to people who are attractive? That’s just silly!”

Or “You know, I’ve hung out with you a long time. You’re not into drama, you don’t wear flamboyant clothing, and you don’t speak with a lisp. You really have all the signs of someone who should be heterosexual. Maybe you’re just wrong about this whole ‘gay’ thing?”

Or “Don’t you realize how important heterosexuality is? Heterosexuality is responsible for childbirth, for most of the love poems throughout history, and for the nuclear family. How can you not recognize that being straight is better than being gay?”

No, there are a lot of things my friends are far too sophisticated to ever even think about saying if I were to announce something as prosaic and socially acceptable as being gay.

But announce that I don’t like math, and suddenly the knives come out.


It’s not that I don’t recognize that math is awesome. If there were “Pray the lack-of-interest-in-math away” camps, I would totally go to one. But just as a gay guy may recognize the many ways his life would be easier if he were heterosexual but this recognition does not immediately lead to finding women attractive – so discoursing on the beauty and importance of math does not suddenly make math books any more readable to me.

Certainly I love the sort of math that doesn’t involve doing actual mathematics. I love reading about Moebius strips and Klein bottles, discussing the implications of Cantor’s discoveries about infinity, even playing around with fractals and tessellations and other forms of mathematical art. It’s just that when you put actual equations in front of me, with numbers and symbols and variables, my brain melts.

I mean, I’m not terrible at math. I managed to scrape together an A in Calculus II, the last math class I was required to take and not coincidentally the last math class I ever took. I did it by memorizing the algorithms involved and plugging things into them, all the while desperately praying that there weren’t any deviations, however minor, on the test. This isn’t normal for me. In every other field, concepts slide naturally into my mind and I can manipulate them however they want, like fitting a bunch of Lego blocks together to make limitless possibilities.

But math is like constructing a Lego set on a picnic table outside in the middle of a thunderstorm. I grope blindly in the pouring rain for the first piece, and finally put it in place, but by the time I’ve found the second piece and move to connect it to the first piece, the first piece has blown away and is nowhere to be found, and the instructions are sopping wet, and the picnic table has just been carried away by a tornado.

I don’t know if it’s that I’m bad at math, or that I just don’t enjoy math enough to be intrinsically motivated to pursue it. I do know that I have never become good at something – good good, not “scrape together an A in a mid-level college class on it good” – without having intrinsic motivation to pursue it. And my attempts to hack intrinsic motivation, which would be like a instant win condition for everything if I could achieve it, have been mostly unsuccessful and left me with severe doubt it is even possible. So I have pretty much given up on math.

When I try to explain this to people, the responses are eerily similar to the ones they would never give if I said I was gay.

“Oh, obviously you just haven’t learned the right kind of math. I know this really cute proof of the Pythagorean Theorem in my sister’s textbook. I’ll show it to you the next time we have pencil and paper.”

Or “You must have just had a bad experience with mathematics growing up. Maybe you always got yelled at by your math teacher as a child. But there’s no reason to let that control you now.”

Or “But…but…math is interesting! How could you not be interested in a subject that’s interesting? That’s just silly!”

Or “You know, I’ve hung out with you a long time. You like rationality, you’re good at science, and you like analyzing things. You really have all the signs of someone who should be into math. Maybe you’re just wrong about this whole ‘not a math person’ thing?”

Or “Don’t you realize how important math is? Math is essential for statistics, for engineering, for science, for cognition itself! It’s closely linked to art and music and poetry! How can you not recognize that being into math is better than not being into math?”

And yes! I recognize it! Being bad at math is one of my biggest regrets in life! If I were building myself as an RPG character, things would look a lot different, believe you me.

My contribution to the “Scumbag God” meme

But I’m pretty sure this is a skill point kind of thing. I think it’s totally possible for people, even smart people, not to be into math. And I am constantly surprised that people who claim to be experts in evolutionary psychology seem to think it’s entirely plausible that natural selection would evolve gay people with zero interest in procreative sex, but find it totally outlandish that anyone could end up without a math drive.

And if they don’t have the skill points, telling someone to just try a little harder at math is like telling Tyrion Lannister to just try a little harder at basketball. Not only is he never going to beat LeBron James, but he’s going to get upset and frustrated trying, and it’s not his comparative advantage anyway.


This whole “comparative advantage” thing took me kind of by surprise.

Some people have trouble believing in ‘g’, the idea that all intelligence is correlated. I’ve always had trouble believing in anything else. I would see people around me being able to solve complicated math problems effortlessly, and think “They are smarter than me. I am their strict intellectual inferior. There is nothing I could possibly contribute to their conversations.”

And when these people started going out of their way to include me in their conversations, when they started making friends with me and even admiring me, I was pretty confused. For a while I was suspicious. Maybe I just had a few talents that were impressive for someone who was bad at math, like a chimp that has no verbal thought but can still remember where it hid the banana days later?

The idea that intelligence wasn’t monolithic, that I could be much worse than them in proofs and theorems but still be their equal in other areas, was hugely liberating to me, but it took me a very long time to accept it, to believe that I really was as valuable a human being as they were.

And when I tried to analyzed my certainty that – even despite the whole multiple intelligences thing – I couldn’t possibly be as good as them, it boiled down to something like this: they were talented at hard things, but I was only talented at easy things.

It took me about ten years to figure out the flaw in this argument, by the way.


I remember gossiping about a friend who was really into the worst types of politics – the kind where you’re obsessed about whether the head of the Republican National Committee will cut funding to a representative who said something mildly contrary to what someone else wanted him to say – and somewhere in the middle of the conversation my tone switched from “Yeah, what a loser to be concerned about that kind of thing” to “Yeah, poor guy, apparently he drew the short straw in the Things To Be Fascinated About Lottery.”

Since then I have returned to the idea of this Things To Be Fascinated About Lottery a lot. There are some good draws you can get – people who are honestly fascinated with business and intrinsically motivated to pursue it only need high IQ and a few other subsidiary skills to get super rich. People who draw math can pursue perfect pure and philosophical truth or excel at pretty much any science they choose and advance human knowledge. People who draw science without math have a harder time – I think I’m one of those – but there are still places for them.

And then there are other people who get other straws. There are some people who are really into politics, and find science really boring. There others who couldn’t care less about politics or science, as long as their sportsball team wins the Sports Bowl. Ozy picked a straw and ended up fascinated with gender, which wouldn’t be so bad except that it means ze occasionally has to talk to the other people who are fascinated with gender.

But the thing is, I couldn’t choose to be interested in sports any more than I could choose to be interested in math or a huge sports fan could choose to be interested in psychology or a gay person could choose to be interested in women. I mean, there’s probably some wiggle room, maybe if I put a lot of effort into finding the most interesting sports and learning everything about them I could appreciate them a little. But would I have comparative advantage over the kid who memorized the stats of every pitcher in both leagues when he was 8? Barring getting hit by some kinda cosmic rays or something, I don’t think that’ll ever> happen.

I’d hate to turn this into a “rank which straws are best” contest, but some certainly earn you more money, some certainly help you contribute to the future of humankind more, and some certainly land you in healthy areas of study with nice people and mostly rational thought while others land you in diseased fields full of angry partisans. I wish I had landed in math.

But I no longer blame myself for not having done so. And when anyone starts telling me about how I’d love math if I only did it their way, I now only have a little twinge of guilt in telling them to go away.

170 thoughts on “The Lottery of Fascinations

  1. Kiboh

    I think that part of the problem might be reasonable but misguided reactions to seeing the kinds of math you CAN do. I read your thing about “Investment and Inefficient Charity”, and was surprised by the way you used math near the end. It honestly didn’t occur to me that there existed a modern human who, in that situation, would:
    1. Be mathy enough to realize that they needed to integrate an exponential function in order to get the right answer.
    2. Not be mathy enough to be able to integrate said exponential function (Integ[e^kx dx]==(1/k)e^kx, that’s LITERALLY THE DEFINITION of e).
    3. Be mathy enough to create a functional workaround by using averages to approximate it the way you did.
    From my point of view, that’s an uncanny kind of cleverness which screams “insufficiently well-taught natural who’ll be a math genius if you just give him the right textbooks and encouragement”. I guess it could be a function of the society you find yourself in, too: if most people in a community qualify as “can do math, but doesn’t GET it” or “can do math, and does get it”, and then you prove that you do, indeed, intuitively GET math . . . it might be hard for them to see that you have trouble with the actually-implementing-it part.

  2. Sniffnoy

    I don’t think I’ve ever had the listed reactions to someone saying they don’t like math. On the other hand, there certainly are cases of “I don’t like X” that I do have that reaction to. Typically X here is something where saying “I don’t like X” requires, like, a failure to abstract, because X should not be the important thing — the primary example I’m of here is when X is a medium; more generally, X is not really a coherent category to dislike.

    E.g., for an extreme (but real) example, “I don’t like animation.” But more common examples — well, Dave Lartigue on his blog sometimes makes fun of people trying to get others to try e.g. board games or comic books or anime, with attitude of “They said they don’t like it, why don’t you just listen to them?” The problem is that it barely seems like a coherent category to dislike in the first place! Comic books are just another medium. Board games — well, lots of people aren’t into games, but if you’ll play [certain sorts of] video games but not [similar sorts of] board games, that seems off. Anime is just animation from Japan — OK, yes, it has its own set of tropes and conventions, but that’s not really a huge obstacle.

    Now, to continue with the above examples, I, for one, have no particular interest in comic books or anime (don’t think I’ve read/watched any in… a long time), and I certainly make no claim that anyone else should be particularly interested in e.g. board games (hell I barely qualify as “particularly intersted” in those either). And from what I hear, most comic books really are terrible! (And apparently so is comic-book fandom.) But that doesn’t mean I would reject something because it’s in comic-book form, any more than I would because it’s animated. That would just be unreasonable.

    Now, OK, medium certainly does have a real effect — movies and books are quite different in what they can show! — and so it’s quite possible that someone might have a reason for disliking a particular medium but fail to articulate it; maybe a person says “I don’t like TV shows” when what’s really going on is that they don’t like serial fiction. (Or even, they don’t really like motion pictures, they don’t really like serial fiction, so in combination they find it awful.) But, I don’t know, people… should be clearer and say that? (Since that isn’t strictly speaking specific to the device that is the television.) I don’t know. I don’t really have an answer to that.

    (There is also the problem of people saying “I don’t like X” when they actually mean “I don’t like X as it currently exists” or “I don’t like existing implementations of X” or “I don’t like most X that currently exists” etc., but that seems to be more of a problem in e.g. political discussions. Similarly there’s saying “I don’t like X” when they really seem to mean “I don’t like the community that exists around X”, which seems to be more relevant here; and though it’s in a different context, I’ve noticed Stephen Bond seems to make this mistake a bunch — or rather, a similar one, namely using the latter to infer the former.)

    Math, on the other hand, seems to be a pretty coherent category, or at least mostly, anyway.

  3. Joachim Schipper

    Honestly, you could have fooled me if you’d just stop talking about not liking math. A good chunk of your posts is “look at those interesting numbers I found”… yes, it’s not hard, pure math for the sake of hard, pure math, but pre-verbal chimps tend not to pay too much attention to statistics and the like either.

  4. Emily

    You say “scrape together an A in a mid-level college class on it” as if that’s not significant, but when it comes to math, that’s actually incredibly significant. If you look at, say, math standardized test questions that high school students struggle with, you’ll get a sense of what “bad at math” means. A lot of bright people have this intuitive response against the idea of g applying to them – “oh, but I’m so much worse in this area than in these other areas.” But if you actually push on it, what comes out tends to be your type of story, where even in the area that you consider yourself weak in you’re actually extremely strong relative to the rest of the population, you’re just comparing yourself to people who are extremely, extremely strong in it. Perception of how good we are at something (which definitely affects how much we like it and how likely we are to pursue it) happens relative to our peer groups.

  5. Berry

    The threads explored by the comments to this post really, very strongly remind me of this scene from Good Will Hunting. Will also seems to be a good example of (a) why winning the Fascination Lottery is not always a guarantee of success and (b) why the lottery is partially ‘rigged’ by environment and childhood.

      1. Berry

        Oh, obviously. It’s not meant to be conclusive or watertight, but it’s a good sketch of what such a person might look like, and I believe such people do exist, but that would require personal details I’m not willing to go into.

  6. anon

    These comments are incredibly encouraging to me. I dropped Calc 2 last semester and have been feeling horrible about that. Now I’m starting to feel much better.

  7. Rachael

    I like the concept of the lottery of fascinations.

    This is the third time since I’ve been reading your blog that you’ve said you’re not very good at something, then given some examples to pinpoint what level you are at, which seems quite similar to the level I’m at, and I considered myself good at it. (The previous time was linguistics, in the context of Raikoth. Can’t remember what the other one was.)

    I think you just have an absurdly high bar. I know you lived until recently, and still socialise, in a super-smart Berkeley bubble; but it’s not just that, because I live in a super-smart Cambridge bubble (although I have friends and family who are definitely outside the bubble; maybe that makes the difference? Did you grow up in it and spend all your life in it?)

    By the standards of most of the world, and even by the standards of most smart people, you are both good at maths and interested in maths. Go into work tomorrow and see how many of your colleagues know the first thing about Klein bottles, fractals, or Cantor’s ideas about infinity.

  8. Vanzetti

    Is it bad of me to think that in most cases of people thinking they have no talent for something, it’s actually their teacher(s) who had no talent?

    1. Berna

      I don’t know; I remember suddenly getting much worse at math when we got a new teacher, but maybe it was just that the subjects got more difficult in the next class. And other people seemed to learn from him just fine…

  9. Paul Crowley

    I think this is a bit unfair; I think it’s reasonable to suppose that those responses are rarely warranted when someone comes out as gay but very often warranted when someone says they don’t like maths. Not in your case, sure; I know enough about you to know you will have explored quite a few avenues before coming to this position. But that’s really not true of most people!

  10. Moshe Zadka

    Scott, if you ever visit here, you have an open invitation from me: I will happily drive to wherever you are, and try my best to introduce you to my sister’s friend…err….I mean, show you pretty, pretty math that I think will interest you. I’m pretty much as straight as they come, and I was never shocked at my gay friends’ lack of interest in women, much as I’m not shocked by my model-theory friends’ lack of interest in differential topology — but asexuality, and lack of interest in any math, still weirds me out a bit, I admit.

    1. Deiseach

      Let me assure you it’s perfectly possible to come to the conclusion “On the whole, I’d rather not bother” when it comes to both sex and mathematics 😉

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  14. Sarah

    There does seem to be a phenomenon of “shit your brain just won’t do.” For me, those things are all nonverbal. I get lost easily, can’t handle mechanical contraptions, can’t shoot, can’t drive.

    Some people clearly have that for the cluster of stuff around foreign languages, poetry, and music. Working harder doesn’t help. They’re just missing a brain piece.

    I’m not as sure that exists with regard to math because you can use different mental strategies. With enough intelligence you can work around poor quantity reasoning or whatever. But there might be a discrete ‘can’t do math’ deficit, I don’t know.

    1. David Gerard

      Dyscalculia is the extreme case. Intelligent and capable people who literally cannot add two numbers to a result in the twenties or thirties. I didn’t believe it was possible until I met examples.

      1. Deiseach

        Oooh, that list of symptoms of dyscalculia is fascinating, since I can pick out these ones that I do suffer from in some degree:

        Dyscalculia involves frequent difficulties with everyday arithmetic tasks like the following:

        – Difficulty with multiplication-tables, and subtraction-tables, addition tables, division tables, mental arithmetic, etc.
        (Oh hell yes; have to run through the times tables in my head to add up “What’s 9+4”? On that note, we had a great teacher in Fifth Class, Sr. Joseph, who used to drill us by firing questions at us like “What’s 8+5? What’s 9 x 12?” and so on, so that the answer would be automatic from learning the tables, but I am still poor at it).

        – Problems with differentiating between left and right
        (Again, yes; you would not believe the amount of times I told people directions like “Turn right up ahead” while indicating the left side and I sometimes still confuse left with right to the point where I go ‘your right hand is the one you bless yourself with’ – and they say religion has no practical use!).

        – Inability to visualize mentally

        – Difficulty reading musical notation

        – Difficulty navigating or mentally “turning” the map to face the current direction rather than the common North=Top usage
        (Yes; I was used to navigating my way around City X and City Y because in both cases, the rivers running through them went north to south and it was easy for me to think “Street W is downstream”; when I went to City Z and had to navigate by the river which ran west to east, it gave me a physical pain in my head trying not to turn the ‘wrong’ way)

        – Having particular difficulty mentally estimating the measurement of an object or distance (e.g., whether something is 10 or 20 feet (3 or 6 meters) away).
        (Yes! Can’t judge how many yards/metres a distance is to save my life. Eight feet? Ten? Six metres? How tall is he? What size is that thing?)

        -Often unable to grasp and remember mathematical concepts, rules, formulae, and sequences
        (Ha, ha, ha, ha, ha. Yes.)

        – Mistaken recollection of names. Poor name/face retrieval. May substitute names beginning with same letter.
        (Very much yes. I am hideously awful with names, to the point where I forget the names of people I’ve worked with for five years about six months after leaving a place. I can remember faces, but names I go “It’s yer wan, you know, Mrs. Thing – O’Brien? No, Flynn? Oh, it’s McGrath!”)

        1. David Gerard

          Odder yet – I’m now recalling a dyscalculic friend who was programming in Java when she was a kid. So apparently you don’t need one for the other.

        2. Anonymous

          Oh, I forgot the number flipping thing! As in, if a series of numbers is 962, I was just as likely to write it down as 926 or even 629, which didn’t help when you’re trying to figure out where you went wrong in your addition 🙁

          I think dyslexia has the same or similar with words/letters. So maybe your Java friend could ‘see’ symbols better than ‘seeing’ numbers as numbers?

  15. Gareth Rees

    The idea of an “interest lottery” is provocative but I think you’ve got hold of something important there. Mathematics, on the other hand, is a big fat red herring: math is just a hard subject requiring huge efforts of concentration and practice to master, so you have to have a pretty strong intrinsic motivation to put in that effort. And motivation seems to be such a personal thing that what works for one person rarely works for another. (For me, it’s figuring out how to turn abstract math into concrete computation, but that’s not going to work for you, is it?) I don’t think math is remotely special in this respect.

    So the puzzle is not what might motivate you to put in more effort learning math, but why motivations are so personal and idiosyncratic. Where do our motivations come from? What motivates one person to work hard at math and another at medicine? Why does one person put hundreds or thousands of hours into birdwatching and another into mountain climbing? Why can’t they persuade each other that their respective enthusiasms are endlessly fascinating? Upbringing; opportunity; peer pressure: but these don’t remotely explain the observed variation.

    When I used to teach programming, it was clear to me that students who could draw on an intrinsic motivation (something that they really wanted to make the computer do, like a video game, or a fractal demo, a music synthesizer, a networked chatroom) generally learned to program (because they could use their motivation to carry them through the painstaking and laborious efforts involved in describing anything complex to a computer), whereas those who just did the coursework generally did not. That was because the coursework problems were based on things that interested the lecturers (who were of course all interested in highly abstract computer-science-y problems). I tried to broaden the range of problems in order to “hook” more of the students, but I didn’t have much success. Motivation seems to be just too personal, and I couldn’t get to know the students well enough to reliably find exercises that would grab their imagination and so enable them to draw on their reserves of concentration.

  16. Joe from London

    Btw, “An argument functionally similar to this one to show people why they need not be homosexual is recognised as not being valid” totally proves too much. “I can’t believe a guy as nice as you could be a serial killer”, or “Have you tried not being an alcoholic? I’ll introduce you to this guy my sister knows. He totally cured my brother’s dipsomania.”

    (I mean, to a certain extent psychopaths and homosexuals and alcoholics don’t choose their cravings. But they all certainly choose to act on them and I think we would take the above seriously rather than just saying “Scott? Yeah, he’s an alcoholic mass-murderer. Nothing we can do about it. Also got that bad math gene, too. Sucks to be him)

    1. Scott Alexander Post author

      Alcoholism is a really hard problem, pretty genetically determined, and the best solutions to it seem to involve chemicals rather than just trying really hard. And even when you do try really hard, it’s by forcing it rather than by learning to love not drinking. I think I might be too determinist to accept your examples.

      1. Charlie

        Presumably you’re cool with some plasticity, though. For example, the way peoples’ tastes in food, beer, or music can change as they get used to old things and build up tolerance to new ones.

        Once we’ve established that multiple reference classes exist, we can play tennis 😀 Or not, if that sounds better.

  17. Randy M

    “I am constantly surprised that people who claim to be experts in evolutionary psychology seem to think it’s entirely plausible that natural selection would evolve gay people with zero interest in procreative sex, but find it totally outlandish that anyone could end up without a math drive.”

    You have friends you have never left Berkley? Or should that be “anyone that they find acceptable as friends” or some such? Because maybe you should suggest that they lack an understanding-most-people-are-like drive.

    (Myself, I think I’m agnostic. I took (and passed) more calculus than I needed in college, and admit there are probably many things in math that are quite interesting–fractals, proofs, what have you–but personally don’t have any sort of ‘drive’ to uncover them rather than any of several other interesting things).

  18. Grognor

    Hey, don’t forget programming! In my experience, “this community”, whatever that means, is only slightly more willing to tolerate the idea that a smart person doesn’t have the is-able-to-become-a-programmer module installed than the idea that a smart person doesn’t have the loves-math-and/or-is-good-at-math module installed.

    (My first instinct when I read this post was to recommend a book [a book I haven’t even read!]. Gee, I’m part of the problem.)

    1. St. Rev

      I can’t program. I mean, I can write down an algorithm no problem, but turning it into working code turns me into a bleeding, sobbing mess.

      1. Anonymous

        Man, this whole thread is killing me by aggravating my teacher bias. I can’t help but have flashbacks to all the hours I’ve spent sitting with students… making them painstakingly turn every operation they would perform into a line of code, until they finally realize, “WAIT A SECOND! These lines are all basically the same. I can use a loop!”

        From the perspective of my teacher bias, the longer the payoff takes, the sweeter it tastes.

        1. Anonymous

          That is really shocking, considering that your regular language skills are substantial. Have you learned any foreign languages? I imagine they would be more difficult than turning natural language sentences like, “I want to add 4 to 8 and then store the result in a box named [this],” into code.

        2. St. Rev

          Nope. I can read German with great difficulty if I have a dictionary handy.

          By ‘syntax’, though, I mean mostly that I can write code but I can’t read it. It’s very hard for me to decipher a man page, and it’s nearly impossible for me to debug, because I will start kicking holes in the office drywall before I notice that the comma in my code should be a semicolon, or that x should operate on y on the left rather than on the right. It’s a disability that you can work around in mathematics, but not in programming.

        3. Anonymous

          Interesting. I hear ya on the frustration factor, though. I remember freshman year, I was less sophisticated in my algorithm design, and I ended up copy/pasting a fair amount of stuff and then making small adjustments to handle some specific cases. Then, after my code didn’t work right and a long period of trying to debug, I realized that I had copy/pasted a whole bunch of zeros that were supposed to be O’s. The only way I could tell them apart in the editor we used for class was a tiny little dot in the middle of them. Oh how I wished I had something to throw as I tediously went through hundreds of instances, looking for zeros. About four years of debugging code for freshmen later… and I was able to spot those types of mistakes pretty darn quickly! 🙂

          I would think mathematics would actually make it easier. There’s not a whole lot that can make commas/semicolons easier (except maybe a good static code analyzer), but the whole left/right operation comes up pretty regularly in even linear and abstract algebra.

        4. Anonymous

          I think I’m even more confused, but more intrigued. You said you can write code but can’t read it. Was it easier for you to write math than read it? Or is there some axis that I’m completely missing (which is where the playing/writing music thing comes in)?

        5. St. Rev

          Yes. Mathematical thinking is mostly kinesthetic for me. Doing math is easy, translating it into symbols takes work but isn’t too hard, but reading symbols and trying to translate them back into terms I understand is very difficult for me.

          To overextend the musical analogy, it’s a bit like the difference between hearing music, singing it, and reading sheet music.

        6. Mary

          I remember once a programmer who had two enormous if and else clauses — because in the middle there was one line of code that differed.

        1. St. Rev

          “I know this really cute proof of the Pythagorean Theorem Ruby variant…”

          BASIC when I was young. Mostly I’ve worked with specialized symbolic environments, e.g. Maple, Cayley, GAP, Magma. Tried learning R recently, didn’t get far.

        2. Said Achmiz

          C isn’t cute, but if you don’t learn to program in C (or at least C++), you haven’t learned to program 😉

          (Based on looking at some R code, C/C++ is also syntactically much easier on one’s sanity.)

        3. Sniffnoy

          C++ is a monstrosity, I’d recommend avoiding it if possible.

          (Variants of C more recent than C89 are full of crap too. But that’s more avoidable.)

        4. Said Achmiz

          C++ is not a “monstrosity”. C++ is “inappropriate for some of the things people try to use it for, which is unsurprising given how widespread and well-known it is”.

          As far as the current discussion goes: C++ is an excellent language for developing an understanding of what, actually, is going on “behind the scenes”, while being syntactically straightforward, and conducive to experimentation and playing around with basic data and control structures.

          (As so often during these arguments, I feel I must point out that no one is standing next to you with a gun, forcing you to use this or that obscure C++ feature in every program you write.)

          Anyway, the reason I mentioned it is that in my comp-sci experience, understanding of basic concepts seems to be correlated with learning C or C++ first (I started with C, myself), and anticorrelated with learning Java first. (Java’s what a lot of people around here seem to start on, nowadays.)

    2. Sniffnoy

      Well, at a basic level, they’re kind of the same thing… maybe not so much when you’re programming something enormous like a web browser where getting the program truly entirely correct is not really doable…

  19. coffeespoons

    I’m a little surprised that so many of the replies tell you to do X, Y or Z to get yourself to like maths, after you made it very clear that you’ve tried lots of things.

    1. Said Achmiz

      I might write a post about how I’m really bad at even understanding the basics of music (being tone-deaf and all) despite numerous attempts to explain things to me; if the replies contained a lot “well, try so-and-so!”, some of them might be useful. You never know. Besides, comments on a post might be to the benefit of readers of said post, not just the blogger.

      1. Douglas Knight

        Quantity is over-rated. Did these numerous attempts come from people who had experience teaching beginners? I know people who took a class called “Singing for non-singers” and saw adults learn to sing from scratch. They took it 5 times and saw lots of adults learn, but the 5 times never did them any good.

        Asking for suggestions on a blog sounds like it will generate more examples of the same things that didn’t work for you. I am more optimistic about this Anonymous comment because it at least addresses the failure of most attempts, though it doesn’t really make any clear suggestions.

        1. Said Achmiz

          Sure. One was a “music appreciation” (taught basic concepts) class in high school, one was a similar thing but in college. Some others were music-theory-versed friends.

          Blog suggestions can be very diverse, especially in a crowd like this blog’s commenters.

        2. Anonymous

          Thanks for referencing me. I really like making people optimistic about success, so this is encouraging. You’re exactly right that having experience with beginners helps… a lot. It also helps if you’ve dedicated time specifically with students who are struggling. The most difficult time I had was with a program for struggling math students in 4th/5th grade. We’re talking the students who were doing poorly enough to possibly build a case for holding them back a year. There were so many challenges (at that age, some of them didn’t really want to be there), and I learned a ridiculous amount about what worked and didn’t work by trial/error.

          I’ve also worked with a lot of college-aged students during their first encounter with programming (in a course that was atrociously compressed). First encounters are nice in that all of the students’ gaps are your fault; first encounters are bad in that all of the students’ gaps are your fault. You also get lots of experiences with students who haven’t had feedback yet to inform them that this new field might be uniquely difficult for them and that they should be alright with sometimes going painfully slowly.

          Unfortunately, I haven’t done as much with music. I’ve never worked with someone who was proper tone deaf, so I’m not exactly sure how I’d go about it (or even if it’s something that requires serious qualification… though I would certainly give it my best shot!). As I alluded to in that other comment, I think it’s important to find a starting point, no matter how properly basic you both think it is… you need something that you can both agree on paired with a related basic challenge that is both a gap in the student’s ability and can be a stepping-off point for future work. Like I said, without experience with tone deaf people, I don’t really know the extent of the problem and am not sure I can give specific strategies. Honestly, I would try to ground my own understanding of their problem first. Play two seriously discordant notes. Can you tell them apart? If so, build on it, slowly. If not… look for literature on the subject? My teacher bias says that this is more a problem of my lack of education than your inability.

        3. Anonymous

          Another idea: depending on how rough things are with pitch (I’ll admit, I originally got very focused on the new problem I hadn’t encountered yet), I would probably try to concurrently win some battles in the rhythm/tempo arena. I might also ask questions about emotional responses to movie music. This could lead into some talk about dynamics.

      2. coffeespoons

        Right, but Yvain doesn”t seem to be asking for suggestions – he seems to be expressing frustration at the fact that so many people immediately suggest things!

  20. michael vassar

    It’s my impression that the track record for cute proofs of the Pythagorean Theory is better than that for cute friends of one’s sister. People have lots of experience with other people not liking math and then getting it and liking it.

  21. Said Achmiz

    Semi-serious comment:

    Ah! Now your decision to go into psychiatry makes all the sense.

    Real comment:

    Scott, have you ever tried doing the kind of math that shows up on math competitions? Not the really hard ones, like Putnam or the Math Olympiad, but the university-level ones. Here are some examples from the 2013 CUNY Math Challenge. (Keep in mind that on the competition, you have weeks to solve these.) Number 5 is especially elegant. Number 1 is interesting because a comp-sci person can solve it by writing a short program (which is what I did).

    While I did well in calculus class, this sort of math is a very different experience.

    1. Alex

      I love problem 5a but the solution is wrong, if A,B,C and D are co-linear then there is no circle passing through any three of those points.

      I agree that competition math is much more fun than high school or college math, and often has nothing to do with equations or numbers.

      1. St. Rev

        Solution needs a small patch: if A, B, C, D are collinear, then pick a third circle that doesn’t intersect the line, pick E and F on that circle, and proceed.

      2. Said Achmiz

        Yeah, I often don’t favor the given solution on these things. This was mine:

        “S must (at least) have 3 non-collinear points, because if it does not (if it has fewer than 3 points, or if all of its points are collinear) then it is trivial to construct a circle which does not intersect S. However, any 3 non-collinear points define a circle, and this circle would intersect S in 3 points.”

        No equations, no calculations, just reasoning and basic geometry. It’s about as far from “here is a list of disconnected techniques to try in order to integrate an expression” as you can get.

  22. Elizabeth

    The lottery model seems incomplete to me. I’m pretty sure that if I had friendly, dedicated teachers who knew how to plan interesting and effective lessons (not just idly interested friends who wanted to show me a pretty proof occasionally), I could get Math Love or Programming Love – I just don’t have access to that resource (or do but haven’t been able to flag it down in the last year and a half), and am too scared/burnt out/averse to learning those subjects to go seeking the resource out.

    I’m also pretty sure I could obtain Sports Love or Politics Minutiae Love if I spent enough time around people who were passionate and – importantly – good at introducing other people to the subject. I build a mental model of myself as being someone who’s NOT interested in those things, no way, because I don’t meta-want to be, or in other cases because they’re not a priority, not because I couldn’t be.

    (I totally might say that I couldn’t be interested in those things, if telling people I didn’t meta-want to be caused them to break out the knives/knifelike Helping Scripts.)

    Theory: the community of people who have Math Love/Programming Love/etc disproportionately includes people who do hardcore typical mind fallacy around Math Being Fun, because the world has told them it’s not so and they are currently overcompensating. (This makes them worse at introducing others to the topic.)

    (Context: I very recently got into scented oils/perfumes, an area I’ve had literally no interest in for eighteen years, and probably have a higher prior than usual about interests being obtainable because of that.)

    1. Scott Alexander Post author

      I think there’s lots of wiggle room for what kinds of things you like in the sense of “not totally genetically determined”, but I don’t think a lot of that wiggle room is in the form of “you can choose it just by wanting it”

  23. orthonormal

    Oh, obviously you just haven’t encountered sports in the right way. I know this really awesome football blog that I can link you to. Trust me, you’ll be excited to recognize the linebacker scrape against the inverted veer read option in no time!

    …I know it’s stressful for you to receive compliments, Scott, but I want to reiterate that your brain does things that I admire and wish I were as good at, especially your skill at writing clearly/incisively/hilariously about philosophy/psychology/etc and your creativity in fleshing out all aspects of alternate worlds. It would be awesome if we also had math in common, and if you ever get struck by lightning and start feeling really curious about math you should let me know ASAP, but your lack of fascination doesn’t in any way impede my friendcrush on you.

    P.S. I wasn’t faking about sports, by the way. In addition to math and other things I’m proud of, I did get Football on my list of fascinations (it helps to be born in Green Bay), and I can in fact wax eloquent about it (the amount of combinatorial brilliance that’s actually going on once you get past the surface level, as well as the tribal-religious experience of attending a football game live with passionate fans); but in the circles defined by my other interests, I’m not tempted in the least to push it on others, and indeed refer to it as my “intellectual vice”.

  24. Thomas Colthurst

    Thank you for this post. Well, thank you for all of your posts, but this post especially. I have a friend who desperately loves science and is deeply saddened by her professed inability at math and I’ve been saying all the stuff you list in section II and from now on I’m going to stop. So thank you for making me approximately 0.01% less of an asshole.

    I also have a shameful selfish reason for liking this post, which is that I’m insanely jealous of your ability to write so insightfully, so well, and so often. I know now that there is at least one dimension at which you are not just strictly better than me, which is surprisingly comforting.

    Which brings me to a comment with actual content: parallel to the Things To Be Fascinated About Lottery is the Lottery Of Things That You Find Rewarding and Meaningful. Some of us luck into receiving similar enough things in the two lotteries, some of us fight ourselves constantly because we didn’t, and some of us just give up and accept the empty feeling inside that comes from playing fascinating video games all day.

    P.S. Keep Darwin in mind; I believe he is the patron saint of being awesome at science without being awesome at math. Oh, and the kids are telling me that now-a-days, science is a team sport: outside of a few areas like theoretical physics, not being good at math doesn’t mean there’s no place for you at the table, it just means you need a co-author or two.

    1. Scott Alexander Post author

      I wonder whether there are two lotteries, Things You Like and Things You Find Meaningful, or whether there’s only a Things You Like lottery and the meaningfulness is determined solely by something like your self-esteem (that is, a great mathematician with good self esteem thinks math is important, a great mathematician with low self esteem thinks it isn’t)

  25. JRM

    I think the interest-as-ingrained thing is pretty sound. (And I think general intelligence is obviously true, but it’s not automatic that the guy with the best math skills has the best language skills or music skills or even logic skills.)

    Paula Poundstone used to do a bit where people told her why she would totally like sex if she did it right/had the right partner/whatever. She could not convince people that she did not like it. (I have had the same experience with pumpkin pie. My mother said, “You’ll like *this* pumpkin pie,” until I was 35. I don’t like pumpkin pie.)

    It’s surprising that SA’s not more mathy, because he profiles as a mathy dude. But yeah, it seems better to trust actual SA’s views than to trust our incomplete model of SA’s skills and wants. Failing to do so is error.

    –JRM, go Red Sox and Indians, because my math skills told me to bet on you at the start of this season.

  26. Sarah

    What nobody but me seems willing to admit:
    For seemingly almost everyone, yes, math is hard, and it hurts.
    I grew up on “Little Rudin.” That meant a lot of desperate weeping in the bathroom as a teenager.
    Luckily, I had parents who expected me to be decently good at math, and I expected myself to be good at math, and I kept plugging out of sheer pigheadedness until I found, rather to my surprise, that I was being considered ‘good at math.’ And it’s only then that I began to actually experience the ‘beauty’ people talk about.

    It’s a training period, though. Ballerinas talk about the ‘joy of dance’. But it’s the joy that lies on the other side of a training regimen that I never went through and have no interest in going through. I don’t have access to the joy of dance *now.*

      1. Anonymous

        And seriously… Rudin as a teenager is no joke. I might have to remember this as a technique when I have a teenager who has been misbehaving… give them the gift of desperate wee… errr… I mean “Little Rudin”.

    1. Earnest Peer

      Before I went to study math, a professor from our university (and a Leibniz prize laureate at that) once explained to me that math is very humbling, because no matter how good you are, there is always hard work ahead. Or as I heard someone else put it: “If math is easy for you, you’re not proceeding fast enough.”
      This is, of course, a framing issue: If it is too hard for you, you’re trying to proceed to fast. That might be the better way to put it, because the best people I’ve actually watched doing math were going lots of little steps rather than a few big ones.

  27. Joe from London

    You don’t find equations easy/enjoyable? I don’t see that that’s contradictory with being good at maths or finding it interesting. I definitely don’t have a comparative advantage with equations, but I find coffeetable maths fascinating.
    I’m curious to know whether you enjoyed the maths in, say, The Curious Incident of the Dog in the Night-Time, or in Godel, Escher, Bach, or even in Surely You’re Joking, Mr. Feynman (I didn’t enjoy Feynman’s description of the mental shortcuts he used for equations as much as I enjoyed the rest of it). The Man Who Loved Only Numbers doesn’t go into too much technical detail, but I really enjoyed the stuff that it did.

    My take is that I don’t enjoy changing the numbers in equations and I don’t think they’re where my main advantage lies, but I still enjoy mathsy stuff, and I studied maths for my undergrad degree (in England it’s normal that you pick one subject and study pretty much that one subject for your whole time at college, though I also audited a “History of Mathematics” course and could have taken “Philosophy of Mathematics” had I wanted to).

  28. Chris Hallquist

    People who know something about business, help me:

    This has never occurred to me to do before, but how do I find out if I would find business interesting? Specifically the parts needed to get rich?

    1. JRM

      You probably wouldn’t. If it hasn’t interested you yet, you might not be cut out for it.

      I attended Wharton, and I am reasonably sure this advice would not be well-received there, but FWIW, watch a few episodes of the American show Shark Tank. It’s kinda cheesy, but the sharks have good questions and (often) good reads. They also know failure modes.

    2. Kaj Sotala

      I suspect that “would I find business interesting” is too broad – after all, “business” covers everything from the start-up approach of “figure out a product that you think would provide people with a lot of value, and then build and sell it” (where you could in principle connect the business side of things to anything you found interesting, as long as you thought that the interesting thing would sell) to the big-company approach of “become the CEO of a huge firm” (which requires you to… actually, I don’t know what this requires you to do).

    3. Deiseach

      Are you willing to work eighteen to twenty hours a day, for seven days a week, for as long as it takes to get rich? Do you enjoy persuading people to buy things even if they don’t necessarily need or want them? Do you genuinely think that people’s lives are a morass of misery and deprivation if they don’t own your patented Carpet Edge Trimmer? Do you relish the idea of tax returns, making deals, cajoling the bank to lend you hundreds of thousands, and setting up shell companies owning other companies with your assets in the wife’s name all funnelled through a tax haven in the Pacific somewhere so you can shave 0.5% off your tax?

      Would you consider getting married just so you could have a wife in whose name to put your assets? Do you possess (in the Irish phrase) a neck like a jockey’s bollocks, so you have no difficulty in running up millions of euros worth of bank debt, decamping to America, declaring yourself bankrupt under the more lenient U.S. laws, and leaving your creditors go whistle while you shrug and say your luxury mansion means you are living on the pin of your collar?

      If you only want to get rich, then take up bank robbing instead. I realise I sound somewhat jaundiced about the wealth creators and entrepreneurs without whom we would all sink beneath the waves like Atlantis, but I’ve been listening for the past week to the (in)famous Anglo Irish Bank tapes.

        1. Deiseach

          True; it works better when the bank robs you 🙂

          More commentary on the Anglo Irish Bank affair, where they managed to screw the country to the tune of €34 billion. Seems like all the ex-executives and ex-debtors ended up in America, have filed for bankruptcy over there, and seem to be living there still. I extend my sympathies to your nation, having to host these types from my own. It’ll be interesting to see if extradition proceedings are taken; the current government investigation into the whole banking collapse has invited David Drumm, ex-CEO, to return to Ireland voluntarily to meet with investigators but that’s about as likely to happen as snowballs not melting in hell.

    4. Sarah

      I’m not rich, but I work in a business.
      “Interested in business” is not a natural category. Business is everything besides government, academia, and nonprofits. In other words, almost everything people do to earn a living.

      If ‘business’ seems like a big unknown to you, work at a small business (or make friends with someone who does — we blabber about it all the time.). You’ll find out what parts interest you. You’ll also learn that all these inchoate terms that refer to people in suits with good social skills are actually quite distinct; sales is not marketing is not business development is not operations.

    5. Earnest Peer

      I think this post might actually highlight one of the problems with “finding math interesting”, because, as the commenters above pointed out, business isn’t a monolith, and neither is math. Few things in math are actually interesting, and if you’re worried that you and only you are not particularly enjoying pages of epsilons and deltas or other bookkeeping equivalents, you might end up thinking you enjoy math less than someone who liked the exact same parts but didn’t think they had to enjoy the rest, too.

  29. Earnest Peer

    I have a bit of trouble ordering my thoughts right now, so this will be a bit jumbled together. Sorry.

    I don’t buy the “interest lottery” thing, at the very least not at the low level of abstraction you seem to be proposing here. What interests people is neither random nor fixed*. It’s very much subject to an internal cost & benefit analysis, and if doing math makes you feel stupid (this might be a simplification of the tornado metaphor) you will not be interested even if you are quite good – as was pointed out above, even a scrambled together A on calc 2 is very good for all people except maybe your particular choice in friends.
    I also feel like your friends are probably Not Helping. I can’t really put it in words, but your description sounds like you realize (or “realize”) that they’re setting you up to disappoint them, so you feel even less inclined to do math with their encouragement than without.
    A lot of mathy folks either don’t realize that non-mathy folks have their defenses of self-worth up, or they do realize, but they then think that knowing about those defenses means they won’t be a problem.

    *At least it’s not fixed at birth. If you do something for long enough, you might never be able to shake your interest in it.

  30. Deiseach

    Let me flip this around – how many of you have read the novel Shirley? Or would be interested in reading it?

    I read this when I was nine, and the only difficulty I had was with the pages of French dialogue because I didn’t speak French and didn’t know anyone who did (and hadn’t access to a French-English dictionary).

    I didn’t read this as part of a school assignment or enriched learning experience or the like; I picked it up in a neighbour’s house and borrowed it because it was a book. It feels like I’ve always been able to read; certainly I learned before starting ‘proper’ school (aged four and a half). I think I learned how to read when I was two, but it was at an age so early I don’t remember learning.

    This doesn’t mean I’m smart. It’s a flukey thing associated with the paternal side of my family (we are all early readers and gifted when it comes to English and languages). They also get the singing and music gene which I missed out on, and I rather imagine it’s associated with the mental problems gene which I didn’t.

    So I wouldn’t go around saying “You weren’t reading at an adult level when you were nine? You beef-witted dullard!” to people who were reading Matilda or whatever textbook was set at school. I know it’s a fluke talent, not a guarantee of being intelligent or competent. And contrariwise, people who don’t or can’t read those kinds of books are not stupid or lazy or uninterested.

    Same way – being great at maths? Good for you, and I’m glad you enjoy it. Long wear and great tear to you! But some of us can’t or don’t get it.

    1. Anonymous

      I’m with you almost all the way. People who don’t get math are not “beef-witted dullards” (great phrase, btw… I wouldn’t have come up with anything that nice). I only have two objections: “uninterested” and “can’t”. Just strike those words out. Thankfully, they’re attached to conjunctions, so they’re not grammatically necessary. There’s an aspect of not able to floating around (just like certain body types allow a greater fulfillment of success in various sports, certain brain types allow a greater fulfillment of success in various academic disciplines), but I think there is also an aspect of Gladwell’s 10,000 hours.

      Time spent and teaching efficacy does mean something. I think we overestimate the variance of intrinsic capability compared to the variance of subject matter depth. This is linked to the question of how you define competency. As a society, we’ve made a big deal about basic literacy rates. This makes us subconsciously set the bar for literature at “can read”. Most people think, “Surely everyone has the capacity to learn how to parse basic sentences.” Why is this different from the thought, “Surely everyone has the capacity to learn how to parse basic mathematical sentences”? Being interested in and being capable of understanding Shirley is the same as being interested in and being capable of understanding the fundamental theorem of algebra (henceforth, FTA). It requires “mathematical maturity” or “literary maturity”… that weird-sounding requirement that upper-level maths profs will use to describe what you need for their course. It’s a combination of experience and innate ability. Furthermore, different readers of Shirley grasp different depths of understanding (just like FTA). Nobody says, “Well I can’t understand all the implications of Shirley in as deep a fashion as this other group of people. Therefore, I’m just innately unable to do literature.” Yet people would be just fine with saying the same thing about FTA and math.

      tl;dr I may not be interested or experienced enough to come up with the phrase “beef-witted dullards”, but that doesn’t mean I simply can’t do literacy.

      1. Deiseach

        I don’t know how best to describe this; the only time I have ever shed tears in school (and this is not a metaphor or a fanciful example or hyperbole; I mean real tears running down my face and dripping on my copybook) was when I was aged eight, in Second Class, and trying to understand the maths problem we had just been given – and failing miserably.

        The teacher was sympathetic but baffled; no matter how she tried to explain it, it Just. Did. Not. Click. With. Me.

        Other subjects, I could feel my mind “wrapping around” them (think of an enzyme binding to a substrate) – it was like my brain ‘reached out’ and took hold of the concept.

        Maths – no. It was like trying to jam a key into a lock where you couldn’t even get it in the hole, never mind force it to turn.

        It still functions like that – I get so far and then – jammed up. No shape. No way this will fit. You may as well tell me “Just flip your left hand over and you’ll have two right hands!” when it comes to getting my head round maths.

        1. Benquo

          The thing is, I’m conventionally “good at math” (just finished a Master’s in Math and Statistics), and sonething similar happens to me all the time. I’m going through the material, and all of a sudden I hit a wall.

          So I take a break, learn some related material, feel terrible that I don’t understand this thing that all these other things are built on, feel like I am an impostor and I’m going to fail at everything after that wall.

          Then a couple of later, when I review my notes, it seems obvious and I have no idea why I was stuck.

          Sometimes my brain is just tired, or I don’t know enough related stuff, or I need time for it to permeate my subconscious, or I’ve become stuck on trying to understand it one way and need to reset.

          I don’t know if any of this applies to you, of course. Do you still not understand the thing you were stuck on when you were eight?

        2. Anonymous

          I really like the direction Benquo has taken this. I, too, am conventionally good at math (I’m trying to finish up a PhD program in a math-heavy field). At a young age, I was skipping through concepts and tossing out answers that my elder sister and her friends had to sit down and churn a crank to compute. Yet still, I hit walls All. The. Time. The way I usually describe research is, “You bang your head against the wall for 3-4 months, then you have one week when everything seems so clear… then you go back to banging your head against the wall for 3-4 months.” I’ve never had a colleague disagree with this sentiment.

          And the funny part is… I’ve thought the exact same thing that people think about the more basic maths. I’ve literally thought, over and over again, “What I just can’t do this? What if I’ve just hit my hard stop?” Well, I’ve never been able to answer the question, because I’ve just kept on banging and haven’t yet had a defining hard stop moment. Still being a grad student, I’m fearful daily that this moment will come in fantastically awful fashion – my adviser or the department could just tell me, “Look. You’re not going to get a PhD.” But would that even be a hard stop moment? Could there be a qualifier, “You’re not going to get a PhD working on this problem,” or, “…working in this research group“? Maybe if I was in a different group, I would randomly be exposed to the idea that I need in order to make it all click? Who knows? All I know is that I keep telling myself the story, “Just keep working hard. You’ll have hard times. Hopefully, you’ll have enough good times to succeed.” Slow progress is socially acceptable enough in grad school that I can swallow it.

          One of my colleagues said about the prelim exam, “You’re going to be scared that you’ll fail, and you’ll work your tail off. But you have nothing to worry about. You’re going to pass. Probably in part because you were scared and worked your tail off. So maybe you should be worried while you’re not being worried.”

        3. Deiseach

          I know all about the ‘grit your teeth and keep slogging through” method, where you go ” I don’t get it, I don’t get it, I don’t get it, I – oh, I see now!”

          But maths is a language to which there is an intuitiveness that I do not possess. Same way as I would be hella awful at trying to learn a tone-based language because of my problems with differentiating pitch, I can’t get my head round the thingness of maths.

    2. Mary

      I read St. Augustine’s City of God at 12 for fun.

      I have a cousin who read All The President’s Men when he was six. Then he had spina bifada and was misdiagnosed. He taught himself to read out of a Sears catalog and could read fluently before he could walk.

  31. Harvey

    Scott, Scott.

    1) memorizing the puzzle pieces and snapping them together is how EVERYONE learns calc 2. There’s no magical peering into the source code of the universe, gaining a deep understanding of calculus, and deriving it on the spot. Calc 2 is literally only a set of problems that require different approaches to solve. While all of these approaches can be derived mathematically, there’s no way someone with only a few weeks of calc experience is going to grasp the significance of that, which brings me to my next point, that…

    2) … I think you’ve been in academia way, way too long, if you’ve stared equating “don’t have a pure and fundamental grasp of a concept that people spend their entire careers studying” with “bad at the subject.” This may come as news to you, but there are a LOT of people that could never, ever scrape together an A on calc 2. I’m an engineer, and I got a C+ in calc 2, and it was one of the hardest fought grades to avoid failing in my entire almost-a-decade of college experience. And some of my classmates fought no less hard and still failed. Maybe we had a poor teacher, but I’m willing to stake money on it being really actually extremely difficult material for most people, even people with an interest in this type of stuff. I realize it’s irritating to have to come to the conclusion that you’re not able to master every subject, but you’ve mastered quite a few, and seem well on your way to mastering a few more.

    3) The more I learn about people, the more I question concepts about IQ – there seems to be significantly stronger drivers in who is good or bad at things than some mysterious untapped potential. I would suggest that it’s less that you’re bad at math and more that you’re good at so many not-math things that you tend to see the world from the slant of these non-math things by default, and so having to think in a mathy way is foreign, strange, and difficult.

    4) Even though we barely talk, and I haven’t seen you in person in more than a decade, if you told me you were gay, I might come up with a few of those questions, or “failure modes,” as you call them, purely because you being gay doesn’t jive with anything I know. It wouldn’t be patronizing or anything; I’d simply be less confused about the whole matter if you explained in more detail, and your responses and thoughts to some of those types of questions would go a long way to clearing things up. Same with math, really. They’re not knives. People just want to help.

    1. Meredith L. Patterson

      Memorizing the puzzle pieces and snapping them together is how everyone teaches calc. I’m not at all convinced it’s how everyone learns calc, or indeed even a good way to learn calc.

      One of my CS colleagues swears that this whole limits approach is daft and that infinitesimals are a much saner logical grounding for calculus. Bell hasn’t made it to the top of my reading queue yet, so I can’t comment yet. But I’m one of those people who struggled through high school calculus, escaped with a D, and thought she was bad at math (though fascinated by it) — at least, until I tripped and fell into discrete math and realised as long as I can treat it as a language, it makes sense.
      Others’ mileage may, of course, vary.

      1. St. Rev

        Having taught calculus for years, I don’t think there is a way to do it right.

        –Limits as presented in introductory calculus are basically big fat lies.

        –Epsilon-delta methods work, and generate proofs that are usually not too bad…once you get used to ghastly multivariable logical sentences like ‘for all real ε > 0 there exists a real δ > 0 such that for all x with 0 < |x − c | < δ, we have |f(x) − L| < ε'. But that's a ridiculously high bar.

        –Nonstandard analysis (infinitesimal methods) can be a bit more intuitive to start out with, but putting it on a firm foundation requires some high-powered set-theoretic topology and resulting digressions into matters that are at least as arcane as epsilon-delta methods. Plus, hardly anyone actually uses nonstandard analysis, so you'll have serious translation problems if you want to discuss with others or pursue further study.

        Calculus is just a big mess from a pedagogical standpoint; it's become central to the college mathematical experience because physicists and engineers rely on it.

        1. Anonymous

          “Calculus is just a big mess from a pedagogical standpoint”

          So true. Most math departments already have distinctions like turn the crank linear algebra versus more rigorous linear algebra, but they don’t usually have a track for, “I’m not going to just turn the crank for calculus, so I’d like to learn this whole business the right-way-round.” The hard part would be packaging this for people outside the math department. It’s hard to say, “Hold on a couple years for the real payoff,” when they need to be able to turn the crank right now in order to solve problems in physics class, lest they fail to fit astrodynamics in their four year curriculum. Most math departments will tell you, “If you can’t package a class for some engineers or computer scientists, you can’t afford to offer the class.”

          I’m in dynamics/control, and basically everyone who wants to do real, relevant research needs to at some point say, “My calc education was worthless. I need to go back to the math department and sort out a lot of problems.”

        2. St. Rev

          Sometimes ‘calculus for math majors and other people who actually have to understand it’ is set aside formally or informally as an ‘honors’ section.

        3. Anonymous

          I took honors calc in undergrad. It was structured exactly the same way as the regular calc series. I think you would agree (purely inferring from your text (and text is a tough medium)) that the whole endeavor needs to be turned around.

        4. St. Rev

          Yeah. My first impulse would be to return to the classical liberal-arts standard, and make proof-centered geometry a la Euclid the capstone mathematical requirement for non-technical degrees. One big problem with calculus is that it corrupts the curriculum backwards in time: students take several years of mishmash classes like ‘college algebra’ and ‘pre-calculus’ that give students tools for taking calculus and little else. And a lot of those students never take calculus anyway! It’s absurd.

          In principle that might screw up students who start out in a liberal-arts major and decide to switch to something more technical–but that almost never happens anyway.

        5. Doug S.

          Most math departments already have distinctions like turn the crank linear algebra versus more rigorous linear algebra, but they don’t usually have a track for, “I’m not going to just turn the crank for calculus, so I’d like to learn this whole business the right-way-round.”

          At Rutgers, I took a proof-centric course called “Advanced Calculus I” that went into great detail about the foundations. Introducing derivatives was pretty much the last subject covered…

        6. Anonymous

          …was that the first course you took? Or was it assumed that everyone in the room had “the standard sequence”?

        7. Anatoly

          Epsilon-delta proofs are a tool to train the student to rigorously think about complicated math statements, by forcing them to process alternating quantifiers. I think this is why even pure mathematicians invariably go through them in their first year.

          Our brains find it really difficult to process more than one quantifier in a row. “For all x, something” or “there exists x such that something” is easy. “For all x there exists y such that something” is already very difficult for most people and must be trained. Add another level, as in your example, and it’s hopeless to make sense of without persistent training.

          Suppose you present calculus to freshmen without epsilon-delta proofs. That will also affect their ability to process (and of course construct) many other proofs that have nothing to do with calculus at all, just because epsilon-delta hammered into them this ability to calmly keep several interacting things in their minds. They will have trouble with induction proofs because they will find it more difficult to keep track of the inductive invariant. They will have trouble with reductio ad absurdum proofs that get rid of several different cases by nested applications of suppose-this -> contradiction. That also requires them to remember what we assumed at the beginning, what we just supposed, what we already ruled out.

          Maybe there’s a better way to conduct this sort of training in short-term mathematical memory and making sense of complicated statements, without epsilon-delta proofs, but I don’t know how to get there.

        8. Sniffnoy

          Considering the “alternating quantifiers as games” interpretation, perhaps it might help if that were taught more explicitly as intuition for helping to understand alternating quantifiers? Of course for all I know a lot of teachers already do this…

    2. Scott Alexander Post author

      I am thrilled that you didn’t stick to your threat not to read my blog anymore.

      It may help to understand this post if I mention I spent the last year mostly hanging out around math Ph. D type people who discussed very pure abstract math-y stuff pretty much 24-7.

  32. Kaj Sotala

    It took me about ten years to figure out the flaw in this argument, by the way.

    You know, I kinda know what the flaw is, but I’d still appreciate it if you could spell it out for me. Because I keep getting that “I’m not as good at maths as all these other intelligent people, thus I can’t really be as good as them” thing too. And although I know it’s incorrect, it’s still useful to hear other people spelling out why it’s incorrect.

    I think I have it somewhat better than you – I’ve got a bit of an actual interest in math, and I’ve taken optional university math courses every now and then, and even enjoyed some of them. But also failed some of them miserably. Mostly my problem is that while I enjoy the feeling of having figured out how some mathematical concept works, I don’t have a similar fascination with actually doing the exercises needed for properly figuring it out, so I might easily flunk if the exercises happen to be at all challenging, because I don’t have the intrinsic motivation for tackling those. (This is why I’ve really appreciated our university’s new approach for teaching maths, which among other things involves breaking down one big difficult assignment into multiple easier ones. I’ve found that to do wonders for my learning. If only all of our math courses would employ that strategy…)

    And then I go somewhere like Less Wrong where I see people writing long posts about decision theory and trying to figure out complex mathy concepts just for fun, or otherwise hear people discussing complicated math more-or-less recreationally, and then my brain goes “gaaah I’m so stupid and I doubt these people could ever really actually respect me”.

    Things To Be Fascinated About Lottery

    That’s a great term for it, and now that you bring it up, it’s actually also one of the reasons why I’ve been thinking about edugames lately. For a while, I have been worried about the fact that we seem to be living in a society where are a lot of people draw terrible straws in the Lottery – mainly picking up interests like “playing video games” and never having any interest in anything that could provide them a worthwhile occupation.

    With them being exposed to the right kinds of games, perhaps they could pick up an interest in math or science or whatever from early on. Part of the reason why I’ve always found probability maths interesting is that I read The Hitchhiker’s Guide to the Galaxy from an early age…

    Of course, you can also do badly in the lottery if you happen to draw too many interests. I kinda like math and I kinda like fiction-writing and I kinda like AI stuff and I kinda like psychology and the social sciences and even the humanities and I kinda like the idea of making edugames and… argh. It’s a constant struggle to even try to stay focused on just one thing.

    1. Deiseach

      My problem with the “Make maths fun!” model of teaching is that it conflates lack of motivation (this sounds dry and dull and boring so you’re not interested) with lack of ability (you could have cake and icecream and party hats and I’d still not be able to go much past ‘if x is 2, 2x=4’).

      I’m sure there are a large group who are turned off maths by how it’s taught, but I’m equally sure there are others like me who could no more advance past a certain point in the subject than they could fly to the moon by flapping their arms, and it certainly doesn’t help to be told by teachers “You’re not flapping hard enough!”!

      1. Kaj Sotala

        Sure, there is also that. But after having seen one 4-year-old and one 9-year-old solve something like a hundred equations within a few hours and having a lot of fun doing so (playing DragonBox), I strongly suspect that the amount of math that nearly everyone could learn is much more than is commonly believed.

        1. Kaj Sotala

          Well, we did frequently give her hints and reminders of what the rules were, but yeah. She liked it enough that when she couldn’t finish the game on one sitting, she begged for me to visit again soon so that she could finish it (playing it on my laptop).

          I’d say “go for it” with the 6yo, at least the 5+ version should work great. (I don’t know how the 4yo would’ve done on the more challenging 12+ version.)

      2. Mary

        It has more poisonous effects:

        In the schools, young children are no longer taught in whole classes but in little groups. It is hoped that they will learn by discovery and play. There is no blackboard and no rote learning. Perhaps the method of teaching by turning everything into a game can work when the teacher is talented and the children are already socialized to learn; but when, as is usually the case, neither of these conditions obtains, the results are disastrous, not just in the short term but probably forever.

        The children themselves eventually come to know that something is wrong, even if they are not able to articulate their knowledge. Of the generations of children who grew up with these pedagogical methods, it is striking how many of the more intelligent among them sense by their early twenties that something is missing from their lives. They don’t know what it is, and they ask me what it could be. I quote them Francis Bacon: “It is a poore Center of a Mans Actions, Himselfe.” They ask me what I mean, and I reply that they have no interests outside themselves, that their world is as small as the day they entered it, and that their horizons have not expanded in the least.

        “But how do we get interested in something?” they ask.

        This is where the baleful effect of education as mere entertainment makes itself felt. For to develop an interest requires powers of concentration and an ability to tolerate a degree of boredom while the elements of a skill are learned for the sake of a worthwhile end. Few people are attracted naturally by the vagaries of English spelling or by the rules of simple arithmetic, yet they must be mastered if everyday life in an increasingly complex world is to be negotiated successfully.

        full text here:

    2. Chris Hallquist

      I’m not Scott, but maybe it will help for you to hear this from me: the problem with the, “they were talented at hard things, but I was only talented at easy things” argument is that the things you think are “easy” only seem that way because you’re talented at them.

    3. cool rich guy

      Not being interested in sports is a pretty bad draw in the lottery of fascinations if you’re male – it’s a huge handicap when it comes to making friends with other males, as I know from experience. I think if I put in a little effort, I could become at least a little fascinated with most possible subjects, but not being interested in sports seems to be an overwhelming preference that is firmly hard-coded into my brain. I have nothing against anyone who is into sports, but I really don’t understand how so many people can find watching football on TV so exciting.

      1. Kaj Sotala

        I don’t think not having an interest in sports was ever a problem for me, but then males might be less sports-centric in my country.

        1. Deiseach

          Ahem! *clears throat meaningfully* Gentlemen, interest in sports is not gender-specific. The person in my life most interested in sports was my mother.

          From working for a woman who bred and raced greyhounds, to visiting the Cardiff Arms Rugby Park when she lived in Wales, to indoctrinating my brother with a love for Manchester United Football Club, to eagerly following the horse-racing from Ascot and Aintree, she was the sporty one in our family while my father (ex-Army, used to play handball in his youth) couldn’t care less about it 🙂

  33. Deiseach

    *falls on your neck sobbing* Brother! I feel your pain!

    Maths is a language I cannot speak. Never mind managing to scrape an A in college-course maths, I just about scraped a D in Pass level Leaving Certificate maths (this was a bad result, as demonstrated by the lecturers in my third level laboratory technician training course who spoke in appalled tones of people who ‘only scraped a pass in Leaving Cert maths’).

    And yes, I’ve been on the receiving end of the statements about “you must have been taught badly” (there is something to that, because the way we were taught the subject made no sense at all), “can’t you see the beauty of it?” (yes, I can, but I can’t emulate it), “how can you not be interested in such a fascinating and vital subject” (oh, very easily, I assure you) and the one that made my schooldays a living hell: “You’re just not trying hard enough”.

    If I had been equally bad at all subjects, the teachers would just have written me off as stupid and that would have been that, but because I was good at everything else, it was “You’re not trying! You’re lazy! How can you pretend you don’t understand this when everyone else in the class gets it? Your parents will hear about this in your end-of-term report!”. Oh yeah, that certainly made me love maths even more.

    Only way I ever passed a test was same as you said: blindly, mindlessly learn off the formulae and plug them in, and if anything needed comprehension of the basic underlying principles I was screwed.

  34. James

    Lockhart’s lament discusses the problem of lousy math tuition turning people off the subject. Like some of the commenters above he argues that math is a creative art, and therefore most of what is taught in schools scarcely deserves the name. I can believe that real math also bores someone though.

    To address the lottery of fascination, the reason why some people have abstruse and economically fruitless interests is not necessarily that they pulled the model train straw, but could be fun theoretic, i.e. the hobby provides them autonomy, complexity and a connection between reward and effort. I like to think that with age, people learn to gamify important things that don’t initially fascinate them, or discover the relationship to things that do. I thought probability theory was dull as ditch water until I learned that it’s fundamentally related to thermodynamics, AI and other fascinating things.

    1. JenniferRM

      After reading this there was one thing I wanted to say by way of a link to an essay, but first I tried “^f lockh” and found that someone had already beaten me to it.

      +1 on Lockhart. His Lament is worth reading!

    2. Anonymous

      Oh. My. This. Essay. There is so much truth. I always analogize math to literature. Sure, at some point you have to learn some of the finer details of spelling/grammar, but that’s not how we teach it. We read pleasing stories. In the process, we gradually pick up on more of the details. If you only grasp how the operations work, you find yourself bored and only chunking out details because you have to.

  35. Mark

    It took me about ten years to figure out the flaw in this argument, by the way.

    What was the flaw? That you deemed easy subjects you were talented at only because you were talented at them?

    1. David Gerard

      How it feels from the inside, I think. I’m a sysadmin. It feels like what I do is just repeatedly applied common sense, but the outside view is sufficiently obvious that even I can see it’s a talent rare and useful enough to be worth beer, chicks and dumptrucks full of money backed up to my house. *

      ( * beer, chicks, dumptrucks may not happen with 100% reliability)

      1. Deiseach

        I think there’s definitely a split between the arts type (very, very broadly speaking) and the maths/sciences type (again, very, very broadly speaking).

        Fr’instance, during lunch breaks in the clerical office I worked in, we used to do online crosswords. Myself and another woman worked through these in no time at all, but the women who were on the accounting/payroll/tax side struggled at times. To me, the word that fitted in with “—S—-” was obvious, given the particular clue. To them, no.

        Switch it around to equations, balance sheets or whatever, and the situation was reversed. For them, it was obvious what went where, while I struggled to find the error.

        Also, we dealt with hiring teachers for secondary, continuing and adult education both full- and part-time, and it got where I could identify an art teacher by sight as soon as they walked in the door. It was very obvious who was there to interview for the history/science/English post and who was there for the art/music post 🙂

  36. Doug S.

    I wonder if one can develop an interest in something by looking at it sideways, in a way that makes it seem like something you already like? For example, I suspect I might become more interested in (American) football if I tried playing football video games. Sports has something of a bad reputation among intellectuals, but if I think about it, it doesn’t really seem any sillier to be interested in sports than to be interested in literature – you’re not going to affect the outcome of a novel any more than you’re going to affect the outcome of a sporting match you’re watching, after all. My father, for one, always found it silly when his English teacher asked “Why did Character X do this and not that?” about a story, when, as far has he was concerned, the real answer was always “Because the author wrote it that way.”

    As for math, well, one thing that I find fun is solving “interesting” puzzles. Sometimes I find mathematical puzzles interesting. Sometimes I don’t. If you don’t get that “you know, that’s kinda neat” feeling from seeing or doing clever math things, then, well, I guess you don’t.

    There’s a legend about Carl Friedrich Gauss. According to the legend, when he was a child, his teacher asked the students in the class to add up the numbers from 1 to 100, figuring that it would keep the students occupied for a while. Gauss, however, came up with the correct answer almost immediately, having come up with a clever trick to simplify the calculation:

    1+2+3+…+98+99+100 = X
    101 * 50

    5050 is indeed the right answer; Carl Friedrich Gauss had discovered that the sum of the first n positive integers is equal to n(n+1)/2. Seeing that kind of clever trick gives me the feeling “you know, that’s kind of neat” and makes me wish I had thought of it myself. 😉 If you don’t get that kind of feeling from this kind of thing, well, then you don’t, and I won’t force it on you any more.

    1. Berry

      Sports as Literature is exactly how I try to defend myself when my friends don’t understand why I follow it as a hobby.

      1. David Gerard

        Postmodernism as artistic criticism applied to everything in the human world, which is why it infuriates STEM types with its squishiness (and infinite capacity for BS).

    2. Deiseach

      My father would have loved you. He used to do maths problems out of our school textbooks for fun, and in his later years, when he wanted to sit down and relax, he’d work out acceleration and other vector questions for himself.

      Worst rows of my childhood were him trying to teach me how to do my maths homework and me being unable to get it. Inability to understand one another on both sides there.

      1. Mary

        Happens all the time. The person who has mastered something so deeply in his bones that he never has to think about it has a horrible time instructing someone still working with the basics.

  37. Jimmy

    Interests can be changed – deliberately even.

    I personally forced a switch in interest from tesla coils (which were useful for teaching me EE, but rather pointlessly awesome now) to hypnosis and psychology in general, which seemed to be a huge low hanging fruit. It was a very quick shift upon realizing this fact, and has every bit of the “intrinsic motivation” feel to it.

    Also, my little brother went from being a scrawny little kid with no interest in sports to being intrinsically motivated to do weightlifting, rugby and hockey – right after he got huge and athletic.

    I’m not saying that there isn’t a lottery aspect to it, but it would be a mistake to write it off as fundamentally unalterable.

  38. jooyous

    I feel like the “comparative advantage” remarks in this post are conflating fascination and comparisons to other people, which are really not the same thing? It matches up if you’re a person who doesn’t like math and isn’t really that good at it, which means it’s definitely better for you to go forth and do the things you like! However, there DO exist people that are bad at math and don’t realize they like it because they don’t realize that that’s a valuable thing to pay attention to! Those people need to hear that it’s okay to take math contests after school just for the cool, non-boring problems and not score top-in-their-school and Tyrion can play basketball in the park if he thinks it’s fun.

    Um, maybe perhaps possibly consider fixing plz?

    1. Deiseach

      I can’t sing. Never mind not being of the quality of Renee Fleming, I can’t even hold the tune to “Baa, baa, black sheep”.

      Now, if I demonstrate this, people will go “Okay, that’s a pity, but if you can’t do it you can’t do it” and it’s accepted that I don’t have the singing gene or talent or however this is distributed, even at the level of being able to sing like ordinary, average, non-professional, non-trained singers.

      But if I say “I can’t do maths”, then it becomes “Oh, you only think that. If you just try method X, Y or Z – read these books – examine this element of the subject – then you will find you can do it.” Not alone that, it becomes a Topic of National Importance (the whole future economy will collapse if schoolchildren do not, in sufficient numbers, take up STEM subjects).

      This makes inability not alone a personal misfortune but a national disgrace bordering on a crime. And nobody seems to believe that some people just do not have the gift.

      Perhaps it is because maths is associated with reasoning ability, so it’s treated as a practical, self-evident thing unlike arty subjects like language and music? A failure in maths means you’re lacking in human intelligence, and if you are otherwise competent as a human, then you must (despite what you may think) be able to understand mathematical principles if only you put in extra effort?

      1. Anonymous

        I tend toward believing that both singing and math can be taught. There’s variability in how far back a teacher needs to start (I’ve personally taken a college-aged person back to the four basic mathematical operations and have seen vocal teachers go back to very basic ear training to distinguish when notes are the same pitch). This process of going back to the first problem can be a tedious process that the tutor doesn’t want to engage in (they want to jump straight to the ‘cool’ stuff). The student is often happy to resolve something that they know is a gap in their ability (I heard a lot of “I’ve always wondered about that!!”)… but unless they’re very comfortable with their teacher, they may be embarrassed in being confused by something that even they think should be “basic”. This leads to a tough situation that incentivizes everyone telling a neat story about gifts.

        …either that, or it’s due to the whole synthetic a priori business (lolz).

        1. Deiseach

          Dear Anonymous, you almost tempt me to the cruelty of finding a microphone to rig up to the computer so I can attempt to sing “Baa, baa, black sheep” and prove to you that no, I really can’t sing 🙂

          From the age of four, when my father tried to teach me to play the melodeon, up all through music classes in school, I can’t pick up an instrument or learn to sing. It’s not that I’m tone-deaf, because I can tell the difference between tunes, but it’s very nearly that – to this day, I can’t pick out middle C on a piano keyboard (while everyone else was going “Oh yeah!”, I had to rely on counting from the side to find out which key it was to be struck).

          My sister can sing, play guitar and keyboards; three of my first cousins are professional singer-songwriters, my nephews are powering through the grade exams for piano and wind instrument no bother, everyone else in the family can play/sing. Me? No dice.

          Believe me, it’s not for lack of “you were never taught properly” that I can’t do it.

        2. Anonymous

          I would welcome it, because I really do have the teacher bias. I’ve wholeheartedly swallowed the fantasy that most anything can be learned (notwithstanding some physical facts like the sports maxim “you can’t teach size”) along with the outright myth that I’m capable of teaching it. It might be nice to have the whole paradigm shattered once-and-for-all.

          Your discussion of talent around your gene pool actually works in favor of my position rather than against it. Since your group has been habituated to quick success, it discourages slow success all the more. This is analogous to results we see in broad studies of educational systems: once behind, always behind… and increasingly so!

          As others around you progress quickly to playing simple melodies, you’re still counting out middle C. Are you going to want to continue counting out middle C over and over again until your brain decides, “Forget this! If I’m going to keep doing this, I’m going to find a shortcut.” Probably not. It doesn’t please your quick-success habituated teacher to see you counting out middle C yet again… and you’ve clearly already internalized this challenge as something properly basic enough to call the whole thing off. It’s much easier for everyone to just tell the story, “Forget this! I/she/he just can’t do this.” It short-circuits the earlier brain statement by denying the antecedent. You’re just not going to keep doing it.

          I think you can sum up my position as follows. Due to variation in gene magic, Gladwell’s 10,000 hours may vary, in any particular case, from 5 hours (total and complete prodigy/savant) to 100,000 hours. I’m completely cool with something being uniquely difficult or something that you’re currently unable to do. However, I think the “can’t” language is usually a convenient myth (and one that can have inconvenient consequences, as Gilbert points out). I’m also cool with, “100,000 hours? No thanks. I’d rather just read a good novel. This field will take me much less time to master.”

        3. Max

          I agree with this and (especially) the following comment of Anonymous with regards to math (mutatis mutandis). Yes, you can. Yes, you may have to start from 1st grade (ok, probably 4th or even 7th). Yes, it may take 100,000 hours. Yes, you may choose to so something else.

          I also think that curiosity is a bit like fire (though I know little about either 🙂 ) – it’s hard to kindle, but much easier to keep going once it’s started. Sure, some materials are more suitable for a fire than others, but once something is burning it will usually keep burning, unless you let it go out and then have to start it up again.

        4. naath

          The thing is that really, unless it’s a *useful* thing – why would anyone bother putting in 100,000 hours to scrape together a passable professional ability in something they suck at and hate when they could go and put in 10 hours at something they really love and achieve the same success?

          For instance I can’t write fiction (I can barely write anything) at present. Maybe I could be taught to. But it would be an agonising experience for both me and any teachers I might enlist into the experiment.

          I’ll put the effort in, but only if the effort is fun.

          Meanwhile I make my money doing things that I find easy.

          Sure, having basic maths skills is useful; especially for someone as interested in rationality as Scott. But if it’s not interesting and it’s not useful then… why not get on with what you *do* find interesting and useful and leave other people to do the maths.

          (as an aside my mother is a private maths tutor – I grew up listening to her teaching A level maths; I nearly have maths as my first language… and even with that sort of delight and fluency I’m nowhere close to being a *mathematician*)

      2. Gilbert

        Let me pour oil into the fire with some condescending mansplaining:

        The thing is, if people claim they suck at singing it’s usually true. But it is very, very common for woman to claim they are selectively dumb at math when they actually aren’t. And yes, this is a specifically female problem. For example, loads of high school girls talk about how they never could get math anyway so it’s not worth to put any effort in. This tends to turn into a self-fulfilling prophecy. Thing is many of them do math well and even happily if they can be tricked into not noticing it’s math. (By comparison boys tend to justify their teenage laziness by not needing to know this stuff in real life anyway. That delusion is not quite as harmful.) And adult woman still claim they never got some easy mathematical thing, then get it after like two sentences of explanation and go right on applying it. (That includes woman in happy monogamous relationships with other guys, so an alternative explanation one might entertain is unfortunately out.) So nowadays we don’t need to oppress woman any more, because they will do it all by themselves. And most people discount female claims of being bad at math because they are so much more often delusional than real.

        I think now I’ll run for the bunker.

        1. Sniffnoy

          Thing is many of them do math well and even happily if they can be tricked into not noticing it’s math.

          I just want to pick on this part of this comment: People in general seem to often exhibit this sort of failure to abstract. E.g. consider the Wason selection task.

        2. Deiseach

          *hunts in cupboard for good heavy cast-iron pan she hardly ever uses to throw at your head* 😉

          It’s not false modesty in my case, claiming I can’t do it because I’m a girl (I can’t do it because I can’t do it).

      3. Anatoly

        You probably heard the “no, but really, singing is something you _can_ be taught” line many times, and may be chagrined by it. But have you heard it from someone who can bear personal witness?

        Up until four months ago, I could not carry a tune exactly to the same basic degree you describe, “baa, baa, black sheep” and all. It’s always bothered me a little, but I’ve always assumed it just can’t be helped. Finally, when my piano teacher (I can’t play an instrument either, but am taking piano lessons as an adult beginner in my 30ies) remarked that it’d help my playing if I could sing the melody while practicing, I decided to take a free trial lesson from a voice teacher.

        Having now taken seven lessons or so, I’m… still pretty terrible, but also an order of magnitude or two better than I used to be! For example, I can actually sing along with a song on the radio or sung by someone properly, and as long as the melody doesn’t have large jumps, I’m doing alright. That is astonishing; to four-months-ago-me, this is pretty much a magical ability.

        What my teacher told me during the first lesson is that although almost everyone has adequate musical hearing, about a quarter of the population don’t have a singing voice because the way they hear pitches from outside and the way they hear their own voice are mismatched, they’re out of sync. This, she said, _can_ be fixed with a few lessons – and I bear witness that she was right, in my particular case. If you can distinguish “wrong” musical sounds – for example, suppose someone plays the baa-baa melody on a piano, and then plays again, and the second time one of the notes is wrong – if you hear _that_, without knowing the exact pitch of the wrong or right note, but just hearing “this is a mistake” – then you can _probably_ pick up carrying a tune. I’m hedging and not saying definitely, but, based on my own anecdote and stuff I read since then about it – very probably. Consider taking a lesson or two from a voice teacher who claims experience in just such cases (sad, hopeless adult cases) as yours or mine.

        The two things I now have and didn’t have before that let me sing along passably now (to the simpler melodies, etc. etc.), and that I didn’t even know I needed, are: 1) a rough awareness of where my singing range is, and approximate understanding, coming from it, which sounds I should try to reach in unison and which I should try to sing an octave apart; 2) a peculiar feeling, that I can’t verbalize except as perhaps a sort of _very_ faint, almost imperceptible, pleasant buzz, that I experience when I’m singing the same pitch (unison or octave apart) with someone else. I was never aware of this feeling before and didn’t know how to look for it – I do now.

      4. Kevin

        This makes inability not alone a personal misfortune but a national disgrace bordering on a crime. And nobody seems to believe that some people just do not have the gift.

        That kind of sentiment (and I agree it exists) certainly goes too far in its respective direction. However, it is also important not to go too far in the other direction. Sometimes, people really will do better at something by believing it’s possible to learn it by practicing harder, instead of believing that it’s just a matter of having the gift.

        Example: The Trouble with Bright Girls

        She found that Bright Girls, when given something to learn that was particularly foreign or complex, were quick to give up; the higher the girls’ IQ, the more likely they were to throw in the towel. In fact, the straight-A girls showed the most helpless responses. Bright boys, on the other hand, saw the difficult material as a challenge, and found it energizing. They were more likely to redouble their efforts rather than give up.

        Researchers have uncovered the reason for this difference in how difficulty is interpreted, and it is simply this: More often than not, Bright Girls believe that their abilities are innate and unchangeable, while bright boys believe that they can develop ability through effort and practice.

        (Preemptive clarification: I’m not trying to make a point about gender here, even though the example involves it.)

  39. St. Rev

    Separate from but related to previous comment:

    –I did actually have lousy math teachers through high school and university, who did successfully turn me off of math for years. Tenth grade, twelfth grade, 2nd year of college. The summer before my 4th year in college, I picked up a book (Birkhoff & Mac Lane’s A Survey of Modern Algebra and started teaching myself.

    — I think the last real math class most people ever take is geometry. High school algebra, introductory statistics, calculus, even differential equations and linear algebra aren’t math math, any more than learning to use Windows and Excel counts as programming. (I didn’t do very well in any of those classes, either.) They’re incoherent grab-bags of mathematical tools hastily assembled under the Sputnik-era assumption that the US needed to create a few million engineers, now running on inertia and bloody-mindedness.

    None of the above is intended to imply ‘no really I bet you like girls you just haven’t met one yet’. Most people’s experience of ‘math’ is horrible, and that’s a shame, but I don’t think most people would like real math either.

    1. Douglas Knight

      By that standard, would geometry not only be the last real math class most people take, but the first?

      1. St. Rev

        Pretty much! And that worked out pretty well for a few thousand years. The mathematical content of a standard medieval university curriculum was arithmetic and Euclid.

        1. Geirr

          What else could plausibly serve as “real math” classes accessible to high schoolers? I remember the short, small bit of probability done in high school as being a series of click click moments, but statistics in college was more “Here is the normal distribution and how to use it.” It hadn’t really occurred to me that I might have some small amount of the find math cool trait. Geometry and basic probability were it for math ad making sense rather than engineering preparation.

        2. St. Rev

          You can go a long way into basic probability, and some distance with statistics, without much advanced math. You need calculus to work with continuous probability distributions, and 20th century statistics in particular tended to treat the normal distribution as the, er, norm, but I hope most LW people realize by now that that emphasis was misplaced.

          Logic and discrete math are another direction to go in, and there’s been some push in that direction as support for computer science, but the results haven’t been great as far as I can tell.

        3. Douglas Knight

          David Kelly of Hampshire College advocates replacing high school geometry proofs with rigorous probability, but I don’t know of any materials elaborating on the proposal.

    2. Anonymous

      Are there any classes that count as real math beyond geometry? I don’t know much about math and I’m curious

      1. Steve

        You tend to get into real math again after Calculus II/III. The classes with “analytic” in their names tend to be amongst the beginning of a mathematician’s education.

      2. St. Rev

        For starters, there’s real analysis, which is the actual math underlying calculus; topology, which is like geometry but floppier; abstract algebra, which is almost unrecognizably different from the ‘algebra’ people take in high school. There’s a whole lot once you get past the gate of calculus, but few people do get that far.

      1. Max

        Yes, and the hight school math is totally math. The problem is – the user DOES NOT KNOW THAT. And most of the time nor does the teacher. Sure, the developer knows all the cool things that you can do with it and how they connect to ”
        higher programming”, and an experienced programmer can see it too. But for the user it’s a bunch of boring menues and procedures to memorize.

        School math is fascinating and incredibly difficult to teach right (for example, try explaining why lengths and areas are different, but measured by the same numbers; what IS a number anyway?). The “rigorous” answers, in a sense, come from analysis and all those “real math” classes people refer to. But the questions are there, and even, on the substantive level, the answers. It’s just that few people find them or even know to look. There is much beauty behind the ugliness.

        1. David Gerard

          Mmm … I’m thinking of the serious user case. The sort of people who e.g. run much of the high financial world. Billions of dollars and pounds and euros go through Excel. Running on someone’s PC. That’s what the financial world actually runs on. Spreadsheets, VBA. Sheets that run overnight. These are extreme users, but they make the product what it is.

          (I’ve been thinking on this subject for a bit, and how one would make LibreOffice into a better Excel than Excel, and what that would mean. 1. VBA and formula fidelity, such that a .xlsx dropped into LO will run the same. 2. Speed: give these people 25% faster calculation and they will come. 3. Usability for these extreme users, which is the hardest bit. 1. is programming slog, 2. has potential [it’s an interpreted environment, but then MS was a programming tools company first], 3. requires actual testing resources.)

    3. Mary

      “They’re incoherent grab-bags of mathematical tools hastily assembled under the Sputnik-era assumption that the US needed to create a few million engineers”

      Eh, did you ever hear of the mathematician and the engineer who were put in an enormous room with a beautiful woman? They were told that every ten minutes, they could close half the difference between her. So, every ten minutes, the engineer moved. After a few times, the mathematician shouted at him, “Don’t you realize you’ll never reach her?”

      The engineer shouted back, “Don’t you realize that I can get close enough for all practical purposes?”

  40. Benquo

    It’s not that I don’t recognize that math is awesome. If there were “Pray the lack-of-interest-in-math away” camps, I would totally go to one.

    I went to college with a lot of people who thought they hated math in high school – until they had the chance to work through Euclid’s Elements as if it actually meant something, with no problem sets or answers in the back of the book, no equations or numbers, just 15 people and a conceptual compass and straightedge. One of those people is now a math teacher, and I am 99% sure her love for math is genuine.

    St. John’s basically is, among other things, ‘“Pray the lack-of-interest-in-math away” camp’. It’s also unusual and weird and not a lot of people get that kind of mathematical education, so your base rate for that kind of thing may understandably be low.

    It’s just that when you put actual equations in front of me, with numbers and symbols and variables, my brain melts.

    A lot of people think they don’t like math, but they actually just don’t like computation (“numbers”), or solving algebraic equations by hand (“symbols”), or rushing through a bunch of equations without understanding how they work. Math is big, it has a lot of parts, and the most boring parts get the most exposure. Also sometimes things that feel like not getting a concept are just a matter of not having the vocabulary, or needing more practice with something so it doesn’t become a distraction.

    For example, if I tried to read Les Miserables in the original French, I would find it pretty tedious. But that’s not because I’m bad at reading novels – it’s because I would be consulting a dictionary and grammar a lot, because I don’t know French very well. So I would be constantly drawing a blank as to what words mean, or what it means when they go together in a certain way, and looking stuff up. But that’s something I could fix with practice.

    On the other hand, it’s also possible that you really just don’t like math. Or that you specifically dislike the parts of math that would be useful to you. Or that you could like math if you learned it from a different perspective, but that this would take more time than you’re willing to spend on it. Just like I don’t want to take the time right now to learn French well enough to enjoy Les Miserables.

    1. roystgnr

      Indeed, math-lovers disproportionately say that “just because you didn’t like the math you were exposed to doesn’t mean you won’t like *this* math”, not because loving math leads to the belief that everyone else must too, it’s because loving one form of math leads to exploration and discovery of many other forms of math and ways of learning it. I’ve personally met people who didn’t like math before they met the right teacher or right subtopic, with no “pray yourself straight” self-delusion involved in the change. Hypothesizing that other such people exist stuck in the “before” stage isn’t wishful thinking, just induction.

      Continuing with the analogy to sexuality, suppose you’ve never been attracted to females and you were being annoyed by “haven’t met the right woman yet” friends. Wouldn’t it make a difference if you’d only ever met little girls and your friends were offering to introduce you to adults? … This is now a ludicrous analogy, but why? Because “never encountered adult women” doesn’t really apply to anybody. “Never encountered most forms of mathematics” describes (nearly?) everyone in the world.

      1. Pawel Aleksander Fedorynski

        Scott’s analogy is optimized for making a point rather than illuminating the issue at hand, but so is yours. In real life, the attraction of school-math and calculus-without-proofs does have something in common with the attraction of real math. So to continue in the same vein, it’s as if you only ever interacted with very mean and ugly women: if you never felt attracted to any of them, chances are that friendly and pretty women won’t arouse you either.

        If Scott agreed to spend a year thoroughly learning some real math, I’d bet 60% : 40% that afterwards he’d still say “meh, not interested.”

        1. Benquo

          OK, those odds seem plausible – but it seems like Scott has much higher confidence that he really just doesn’t like math.

    2. Mary

      You offer a solution for the actually geometrically minded, who do not like algebra. Me, I’m algebraically minded and HATE, HATE, HATE geometry.

      One of my sister loves algebra because it gets away from all those numbers — none too fond of arithmetic.

  41. Joe

    Leah Liberesco had a post the other day on something called Tau Day. She had a clever video with a bunch of what seemed to me really hard math. I’m like you I just don’t understand the attraction. Your meme is awesome by the way!

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