20 ms·

You are not dumb, you just lack the prerequisites

• fuzzfactor 2y ago
  Prerequisites are so important, and math is one of the things where it makes more of a difference. >You Are Not Dumb, You Just Lack the Prerequisites I know what you mean, after years of study I now feel confident that I don't lack the prerequisites to be as dumb as I could possibly want to be ;)
• findthewords 2y ago
  Most people are of average intelligence. Suppose that -a few IQ points here or there makes little difference in one's aptitude in real-world tasks -we then must accept that when most people think they are "dumb", there is some other effect going on such as: -lack of resources, hunger, mental distractions, illness, or motivating incentives.
  • JustinSkycak 2y ago
    Are you suggesting that when a student is struggling in calculus class due to not knowing their algebra, their issue can somehow be resolved without them having to learn algebra?
    • danans 2y ago
      I think they are suggesting that they might not have leaned algebra because of > lack of resources, hunger, mental distractions, illness, or motivating incentives
      • Jensson 2y ago
        Most people who are bad at math doesn't have those issues, lots of well off people are stupid. Edit: Also lots of people who lack many of those things still learn math very well. So it isn't a very good explanation. If you need optimal circumstances to learn then you have a problem.
        • tjoff 2y ago
          I'd argue motivation plays a much bigger role than intelligence.
          • Jensson 2y ago
            Everything I said is still right.
            • tjoff 2y ago
              Hardly. Yes, you can contort your definition of intelligence to be one where you have to be able to overcome whatever personal struggles one might have. But you wouldn't be actually measuring intelligence. And creating an environment that allows for more people to thrive isn't catering to the stupid either.
              • Jensson 2y ago
                Not sure what you are arguing, you didn't seem to read my post? I never said we shouldn't try to make more people succeed, or that everyone who fails are stupid.
          • danaris 2y ago
            The more I observe about people and how they learn and do things, the more I suspect that motivation plays a much bigger role than we think in intelligence.
            • Ekaros 2y ago
              Looking at back to high school and then university. I fully believe I would have been capable of learning maths, electronics and so on... But I just did not care enough to put any actual work into the process. Still graduated. But well I really just did not care to put in effort. Thus lacked the motivation... Same can be said about any learning including languages. It really comes down to motivation, outside sufficient immersion.
          • 2y ago
  • brigadier132 2y ago
    I think a few iq points is actually much more impactful than you realize. 1 iq point boosts lifetime earnings by $50k. https://www.sebjenseb.net/p/how-profitable-is-embryo-selection https://www.sebjenseb.net/p/how-profitable-is-embryo-selecti...
    • fuzzfactor 2y ago
      I would say the most valuable benefits would not be measured in currency. not my downvote btw
      • hnfong 2y ago
        Right, and there is a well-known correlation between IQ and life expectancy/mortality rate....
    • max_ 2y ago
      If you used the same techniques used by IQ "research" peddlers to invest money in the stock market, choose startup founders or business managers — you would go bankrupt with a probability of 1
      • deleted 2y ago
        [deleted]
      • hnfong 2y ago
        That's just wrong, because if it's true I could do the exact reverse and earn money with probability of 1....
        • sudosysgen 2y ago
          Not really, you can't easily revert high volatility negative EV strategies, the transaction fees and interest will kill you.
  • tgv 2y ago
    > lack of resources, hunger, mental distractions, illness, or motivating incentives Sure, that's a factor, but people can also simply be dumb. There's no quality equal for all humans, whether it's length, strength, weight, hair color, or intelligence, regardless how you measure it. The (rather superficial) article looks at it from the first person stance, but individuals are bad at estimating their own cognitive capacities.
• asdf6969 2y ago
  me except I’m socially dumb because I didn’t learn how to have friends in middle school
  • willismichael 2y ago
    Umm... most people are really bad at relationships in middle school.
    • hypeatei 2y ago
      But people still had them. GP is saying they didn't have any.
      • asdf6969 2y ago
        I did have friends lol. I was just a bit of an outsider from then through the end of high school. I didn’t correct it until midway through uni and I think I missed out on a lot
  • toast0 2y ago
    Having friends in middle school can be pretty tough. Learning how to have friends in elementary school and high school is a lot easier and mostly unconnected with middle school friendship. Hopefully your social life doesn't revolve around friendship with middle schoolers, so no big deal if you miss out on that skill.
  • elzbardico 2y ago
    Not always, but a lot of times not having friends in Middle School is class based. When I had this age I moved schools, in the first one I was objectively poorer than almost everyone else and the subject of bullying and loneliness. I would hide in the library during reccess not only because I liked reading, but to avoid the pain. Moved to another school were I was absolutely average socio-economically speaking, had some of the best years in my life. Rich kids are incredibly cruel.
• anubhavs 2y ago
  Some courses in my university were restricted to students in their third year or above because of "mathematical maturity", which I thought was complete BS because some of the courses had no other prerequisites. But after taking some of them, I get it. There's a general sense of problem solving flow that takes time to develop.
  • HPsquared 2y ago
    In mathematics in particular, one abstraction is built on top of another. It's like trying to read without knowing the alphabet.
    • H8crilA 2y ago
      I often refer to this quite explicitly, something like "my skills include reading and writing modern math", as if it was a foreign language, or musical notation.
  • Ekaros 2y ago
    I wonder if part of this is also not wanting to list all of the pre-requisites that are at least partly needed.
• ilrwbwrkhv 2y ago
  That is why finding the right study materials for the fundamentals of a subject is so important. Take some time to find out the right method and material when learning something new till it speaks and inspires you. You will learn much better and faster.
• eesmith 2y ago
  From Neal Stephenson's "Cryptonomicon", at https://archive.org/details/cryptonomicon0000step_b9v1/page/12/mode/2up?q=train https://archive.org/details/cryptonomicon0000step_b9v1/page/... : > “Shut up about Leibniz for a moment, Rudy, because look here: You—Rudy—and I are on a train, as it were, sitting in the dining car, having a nice conversation, and that train is being pulled along at a terrific clip by certain locomotives named The Bertrand Russell and Riemann and Euler and others. And our friend Lawrence is running alongside the train, trying to keep up with us—it’s not that we’re smarter than he is, necessarily, but that he’s a farmer who didn’t get a ticket. And I, Rudy, am simply reaching out through the open window here, trying to pull him onto the fucking train with us so that the three of us can have a nice little chat about mathematics without having to listen to him panting and gasping for breath the whole way.”
• 65 2y ago
  The way I learned programming was to start with the absolute most basic thing I could think of - changing the color of a button on click in Javascript. With that I could start doing slightly more complicated things, until I could get a whole job as a professional software engineer. Learning is like climbing a staircase, and what you have to realize is you can't skip steps.
  • ocean_moist 2y ago
    I tend to slightly disagree. Some of my most valuable learning was taking on massive projects, and then just doing whatever I could to make it work. Of course, progress would be slow, and you'd need to chunk up the problem and take small steps, but it rarely felt like slowly building up or climbing a staircase. I think the trial by fire approach, just jumping into the deep end, is a much more effective way to learn. It's also more fun for me.
    • pajeets 2y ago
      I actually disagree with both of you. Programming is learning and the code is the side effect of what you have learned. If you jump at a large project but lack the fundamentals you are going to wasting energy on stuff you shouldn't be. Rather the best way to learn programming I find was to master the basics, memorize the most used routines and commands to avoid having to google it every time (ex. CSS) The problem now is we have LLM which kind of negate the need and we have lot of engineers who don't have good fundamental systems design. The other major issue is most of us engineers are scaling for a future that won't come. It's sufficient to squeeze ton of performance out of a single vertically scaled Postgres instance for example without the need to do exotic architectures. So prerequisites are important like in the article but less so now but the fundamentals and only learning what is needed is critical more than ever (ex. Kubernetes for a blog)
      • akira2501 2y ago
        The best way to learn programming is to read and understand other programs. It's a really fun field, and you can isolate yourself and get very deep into thought, and then enter an exceptionally rewarding period of cycling between work and learning. I think a lot of programmers eschew more sensible things in favor of exclusively working in this mode.
• HPsquared 2y ago
  Books and courses usually list their prerequisites. Or good ones do, anyway.
  • JustinSkycak 2y ago
    One problem is that it's easy to think you know the prerequisites when in fact you don't. For instance, a student struggling in calculus may think they know algebra because they got a decent grade in algebra class, even though they struggle to solve a quadratic equation and they've forgotten how trig works. -- Maybe they got saved by grade inflation, or -- maybe they did learn these things but they've gotten so rusty that they need to effectively re-learn them again, or -- maybe they learned and still remember everything from their algebra class, but the class was watered-down and cherry-picked the simplest possible cases of problems within each topic (e.g., quadratic equation always has leading coefficient of 1 and is solvable via factoring) ... There's a million different ways that a student can look at a list of prerequisites and mistakenly think that they have learned them, especially if the prerequisites are listed as a handful of high-level categories as opposed to hundreds of granular atomic topics.
• nicf 2y ago
  I'm a tutor, mainly working with adults who want to learn proof-based math, and the message behind this post definitely lines up well with my experience! If you're the sort of person who's animated by the idea of learning math but finding it challenging, it's worth considering that you might be missing some knowledge or skills that you'd be able to develop just fine if you knew to focus on them. There definitely is such a thing as "mathematical talent", but (a) if you're really excited by math then there's a decent chance your limiting factor is knowledge rather than talent, and (b) there's plenty to appreciate in the subject regardless of how much of it you have. My students come to me at all different levels but if they have enough time and motivation to work on it they all learn a lot of math! There are also plenty of people in the world who just aren't that into this stuff, but that's not really the population I'm talking about --- unless they have to learn it for some reason, it probably doesn't bother them that much that they don't know a lot of math! And I imagine a good chunk (though probably not all) of this group could probably find something to like in the subject if it was presented in an appealing way.
  • JustinSkycak 2y ago
    100% agree. What I typically tell people is "your mathematical potential has a limit but it's likely higher than you think." Not everybody can learn every level of math, but most people can learn the basics. In practice, however, few people actually reach their full mathematical potential because they get knocked off course early on by factors such as missing foundations, ineffective practice habits, inability or unwillingness to engage in additional practice, or lack of motivation. (My comment here is basically the intro to a detailed article I wrote on the topic: https://www.justinmath.com/your-mathematical-potential-has-a-limit-but-its-likely-higher-than-you-think/ https://www.justinmath.com/your-mathematical-potential-has-a...)
    • randcraw 2y ago
      That's an excellent essay. I especially liked this part: " Active learning and deliberate practice will be covered in more depth in later posts, but below are some key points: - Effective learning is active, not passive. It is not effective to attempt to learn by passively watching videos, attending lectures, reading books, or re-reading notes. - Deliberate practice requires repeatedly practicing skills that are beyond one's repertoire. However, this tends to be more effortful and less enjoyable, which can mislead non-experts to practice within their level of comfort. - Classroom activities that are enjoyable, collaborative, and non-repetitive (such as group discussions and freeform/unstructured project-based or discovery learning) can sometimes be useful for increasing student motivation and softening the discomfort associated with deliberate practice -- but they are only supplements, not substitutes, for deliberate practice. - Deliberate practice must be a part of a consistent routine. The power of deliberate practice comes from compounding of incremental improvements over a longer period of time. It is not a "quick fix" like cramming before an exam. "
• KronisLV 2y ago
  Lovely article, though honestly getting those prerequisites also takes a lot of time, effort and either motivation or discipline in ample amounts. As someone who was the “smart kid” growing up, going to the university without good work ethic was pretty eye opening, no longer being able to coast on intuitively getting subjects, but rather either having to put in a bunch of effort while feeling both humbled and dumb at times, or just having to sink academically. Even after getting through that more or less successfully and having an okay career so far, I still definitely struggle with both physical health and mental health, both of which make the process of learning new things harder and slower than just drinking a caffeinated beverage of choice and grokking a subject over a long weekend. Sometimes it feels like trying to push a rock up a muddy slope. And if I’m struggling, as someone who’s not burdened by having children to take care of or even not having the most demanding job or hours to make ends meet, I have no idea how others manage to have a curious mind and succeed the way they do. Admittedly, some people just feel like they’re built different. Even if I didn’t have those things slowing me down as much (working on it), I’d still be nowhere near as cool as people who dive headfirst into low level programming, electrical engineering, write their own simulations, rendering or even whole game engines and such. Maybe I’m just exposed to what some brilliant people can do thanks to the Internet, but some just manage to do amazing things.
  • vundercind 2y ago
    > As someone who was the “smart kid” growing up, going to the university without good work ethic was pretty eye opening, no longer being able to coast on intuitively getting subjects, but rather either having to put in a bunch of effort while feeling both humbled and dumb at times, or just having to sink academically. Modern gifted education is very aware of this and is working on fixing that. How effectively, I dunno, probably not very, but at least it’s a hot topic in the field this century. Damn near every person I’ve know who was “gifted” has a similar story, myself included. There’s a lot of lost potential because we badly mis-handle those kids for years and years on end.
    • dsign 2y ago
      I thought that I was gifted, but in retrospect, maybe I wasn't. I couldn't play any games well; not the physical ones, not computer games, not card or board games. The other kids would get them fast, while I was always dumbfounded and it took me a long time to grasp the rules. Once, it became popular to play Warcraft in my circle of friends and, try hard as I may, I was the rag they mopped the floor with :-) . But math, physics and computer sciences were another story, because growing up I didn't have anything more interesting to do than reading and solving exercises from old soviet textbooks. So, I think I wasn't gifted, or just gifted by serendipity.
• austin-cheney 2y ago
  Math is hard but fortunately programming is easy. I am just a dumb soldier who taught themselves to program while traveling around Afghanistan. The down side of being a dumb soldier programmer is that it’s really really hard to find sympathy when people complain about how hard life is when they are utterly reliant on a bunch of abstractions and clutter to do their jobs for them.
  • brigadier132 2y ago
    Don't sell yourself short, programming is just as difficult as math. I'm confident saying if you are able to code you would also be able to learn pretty advanced math.
    • jakeinspace 2y ago
      It's a silly sort of comparison. Is reaching the programming competence necessary to hold an average software engineering job easier than attaining a PhD in mathematics? Yes, 100%. Is becoming a well-regarded software engineer by building large, complex systems or contributing significantly to projects like the Linux Kernel easier than getting to the top of your field in academic mathematics (tenured professor, high-impact papers)? I don't think so, or at least, it's not obvious to me that one is more "difficult" than the other. They take different skills and personalities, and I don't think that talent in one would necessarily translate to talent in the other.
      • brigadier132 2y ago
        > average software engineering job easier than attaining a PhD in mathematics This isn't what I'm trying to say, I'm just saying that someone that can become good at programming could become good at advanced mathematics. If your criteria for good in advanced math is a phd then we disagree. > They take different skills and personalities I disagree, I think the skills are largely the same. Programming is literally encoding logic using a programming language which requires mathematical reasoning ability. Programming is more immediately practical, accessible and requires fewer credentials and that's why I think more people become good at it than math.
• casebash 2y ago
  Just thought I'd add a comment as someone who came top of the state in my grade in multiple olympiad competitions: I always felt that a large part of my advantage came from having a strong understanding of maths from the ground up. I felt that a lot more people could have gained the same level of understanding as I did if they had been willing to work hard enough, but I also felt that almost no-one would, because it'd be an incredibly hard sell to convince someone to engage in years-long project where they'd go all the way back to kindergarten and rebuild their knowledge from the ground up. In other words, excellence is often the accumulation of small advantages over time.
  • ofrzeta 2y ago
    I can only blame teachers. In primary school after four years they finally managed that there's only on kid per class left (that would be you I guess) has fun with math. At home I am fighting an uphill battle because I know it can be fun (my kid even likes logic puzzles). Living in Germany, for the record.
    • TheRealPomax 2y ago
      I'd rather blame the system that teaches the teachers. I'm certainly not going to blame someone for not knowing how to teach an onramp that they don't even know exists because they themselves were never taught properly.
      • doubled112 2y ago
        Sometimes it’s just the teacher. I loved reading until my grade 4 teacher decided we would all write a book report every week. Haven’t read a story book since. It’s been 20+ years. Forced fun is never fun. The other grade 4 class wrote three that year.
        • pastage 2y ago
          People react differently to task and teachers, there is no one way to do it. I got good grades because a teacher let us repeat a task like "write a report" seven-fourteen times. The feedback was given by him in class highlighting the important points of getting a good grades, and then 24 hours after handing in the report we got it back with notes mentioning which important parts we had missed. This thought me the rather simple lesson that getting it right on the first try is really hard. Writing a book report is completely different from reading a book. I have heard people doing literature in university being sick of books because of the same issue.
• ocean_moist 2y ago
  Some credit needs to be given for just jumping in. Just analytically breaking down complex problems into pieces that are understandable. It's often faster to work top-down and turn unknown unknowns -> known unknowns -> known knowns.
  • deleted 2y ago
    [deleted]
  • JustinSkycak 2y ago
    It can definitely be helpful to take a top-down approach in planning out your overarching learning goals. However, the learning itself has to occur bottom-up. Especially in math. Math is a skill hierarchy, and if you cannot execute a lower-level skill consistently and accurately, you will not be able to build more advanced skills on top of it.
    • MichaelNolan 2y ago
      I think these conversations of top down vs bottom up, are frequently a case where people are talking past each other due to using different definitions, and having different goals. And I think this is especially common when one of the people is a software engineer, and the other is not. For software, the tooling and the abstractions are so powerful that you can make incredible software without knowing what's really happening under the surface. Imagine an "abstraction ladder", with each level building on the previous level. Frequently in software development, you only need to understand a single level n, and maybe a little of n-1, to make great software. So the advice of "just jump in" is often great advice because you're jumping into a "shallow pool". (P.S, I love the work you're doing with MathAcademy, though I wish there was discounted price for "casual" learners that only have an hour or two a month)
      • JustinSkycak 2y ago
        Agree, it depends highly on goals. Using off-the-shelf ML/AI models (to make great software) requires far less background knowledge than implementing new models being introduced in papers, which in turn requires far less background knowledge than producing new models that improve upon the state-of-the-art. Thanks for the kind words about Math Academy! It's true that we focus on students who are trying to acquire math skills to the highest degree possible -- we teach math as if we were training a professional athlete or musician. We maximize learning efficiency in the sense that we minimize the amount of work required to learn math to the fullest extent. I realize that there are many learners who only want to devote an hour or two per month, but, at least right now, such learners would be better served elsewhere. It's a totally different optimization problem -- maximize surface-level coverage subject to some fixed, miniscule amount of work -- and as a result it would require different different curriculum and possibly different training techniques (or at least, differently calibrated techniques). But it's definitely an idea to think about in the future. :)
• photochemsyn 2y ago
  Intelligence is far too complex to be meaningfully described with a single number like IQ. Measures of physical capability don't suffer from this issue - a person might be strong, or they might be fast, and everyone knows that the power lifter and the marathon runner use wildly different training regimens to improve their abilities. If physical capabilities are highly trainable, up to some genetic limit that the vast majority of people never even get close to, then it seems that intelligence must work the same way - e.g. prodigious feats of memorization can be achieved via training regimes (memory palaces etc.), as can one's three-dimensional visualization skills (e.g. a chessboard layout, or rotating a platonic solid, etc.) or the ability to rapidly construct arguments using logic and reason - but we don't seem to be able to classify different areas of mental ability as easily as with physical abilities. Sadly, this is one of those politically difficult topics as the blank slatists and the genetic determinists (Lysenko vs. Galton) have tried to use all kinds of pseudoscience to support their ideological arguments, when the underlying point is just that training your mind is as beneficial as training your body, and everyone should do it at least to some extent.
  • ninetyninenine 2y ago
    However iq is the most correlated number in psychology. It’s a heavy predictor of many many things. It’s the one thing in psychology that has the most scientific validation. Yes iq can’t measure everything that intelligence represents. But it does measure something extremely important and meaningful to us.
    • eesmith 2y ago
      I think wealth might be more correlated, as it can be estimated without testing based on tax data. It's also a heavy predictor of many, many things, with scientific validation. Including IQ test scores.
      • wenc 2y ago
        If you're talking about IQ and wealth, they are not strongly correlated. IQ is correlated to income, but income is not wealth. https://www.sciencedirect.com/science/article/abs/pii/S0160289607000219 https://www.sciencedirect.com/science/article/abs/pii/S01602...
• captainclam 2y ago
  A really fascinating corollary I've observed since I've gotten into more advanced maths, or even doing actual research as a PhD student, is that there's nothing special going on at the higher levels. You're just working with different materials. Materials that require more time and effort to 'get', but once you get them they are just another tool at your disposal. I was similar to the author in that, throughout high school and undergrad, I presumed that the mind that could comprehend advanced math or do novel research (in any field) was truly unknowable. Like there was this x-factor they had that wasn't there for me. I've long enjoyed puzzle games (like The Witness or Stephen's Sausage Roll). It turns out that problem solving in non-trivial domains is never terribly different than problem solving in those games, or any other domain really. Like my brain isn't doing anything different than the usual tree-search algorithm that any chess player performs when they are projecting moves ahead into the future. Its just iterating on concepts that seem abstruse to most people. But at the end of the day, deep problem solving in math or AI research tends to be the same moving-shapes-around-in-my head that I would do if I was trying to move an awkwardly shaped couch through a narrow doorway.
  • dwaltrip 2y ago
    That’s a really cool observation, thanks for sharing
  • almostgotcaught 2y ago
    > Materials that require more time and effort to 'get' They really don't. Each rung in the ladder takes about as long to step through as the previous. The challenging/annoying/discouraging aspect is that a lot of research (especially in pure math) has so many rungs to step through. The truth is many of those aren't useful at all - distinctions invented purely for the sake of being able to say you invented something. Even when I was doing really "deep" research I could explain it to anyone by just dropping all the technical jargon and using goal oriented language instead. When I would do this most people would naturally try to reason about it in exactly the same way "researchers" would. The proof is they'd come up with the exact same solutions to the problems that were legit solutions, they had just already been discovered ie the low-hanging in fruit solutions.
  • 2y ago
• ninetyninenine 2y ago
  No, this isn’t universally true. Your intelligence does affect your ability to learn math. It is not always just a lack of prerequisites.
  • JustinSkycak 2y ago
    Sure, there is such a thing as mathematical talent. However, few people actually reach their full mathematical potential because they get knocked off course early on by factors such as missing foundations, ineffective practice habits, inability or unwillingness to engage in additional practice, or lack of motivation. Basically, your mathematical potential has a limit, but it's likely higher than you think.
  • Barrin92 2y ago
    If you want to compete with Terence Tao, maybe. But everyone with a functioning brain can get to a high level of proficiency, I know because I've taught people who were convinced math is an alien language and they lack the math gene. It's the same with any skill, lots of people are convinced they can't make music, or learn Mandarin or what have you. 99% of it is preconceived notions that they don't belong into a certain club and because we keep telling people that if something's hard for you, you're untalented and you should focus on something else. But it's just effort, even if it's more effort for some in the beginning, there's no magic in any of it.
    • ninetyninenine 2y ago
      Sure but it absolutely matters heavily if not just as much prereqs. I met a girl who struggled with trig and another guy who basically trivially studied the subject and aced it. IQ matters a lot. We are talking in circles. Both matter but I’m saying with my example above that even at basic math, both still matter. It’s not some thing where iq only matters for phd level math
    • hnfong 2y ago
      "Just effort" is a curious way to put it. Even for talented people, learning a skill to a high level takes years. Mere mortals don't really have that many years of free time. Choosing a path that one seems talented at is usually the right path. It's one thing for the person to decide they want to take the risk knowing that they might not have the talent to learn the skill in a "reasonable" time, but it's another to thing to pretend there's no difference and cheer on a person chasing an improbable dream and waste a persons' life. To be or not to be. Basically. So basically the disagreement is to the approach to default to when the future is unclear. Taking the right action requires a degree of foresight that people generally don't have. (I'm not sure everyone has the same skill to intuit the future, but I'll grant you that it's just effort to learn it, even if it requires significantly more effort for some...)
• karaterobot 2y ago
  True, but then there's nothing wrong with being dumb. I know a lot of smart people, and they're all dumb about most things. Like the universe, we're mostly empty, with some hot, bright spots. What I mean is, don't think of yourself as fundamentally smart or dumb, think of yourself as having a lot to learn, no matter who you are or how others perceive you. But sure, this is a good reminder of how you go about learning new things. It's the Julie Andrews method of pedagogy: "start at the very beginning (a very good place to start)"
• password54321 2y ago
  The real truth: if you aren't good, there is nothing wrong with that and there are more than enough developers in the world and people who are good with math. What we need is more people creating real and interesting jobs for these skills. Also most people aren't great with spatial reasoning. Chess requires zero prerequisites yet the average level of chess on chess.com is constant one turn blunders. It took only a year of playing on and off to get to 98th percentile and up to maybe 70th percentile most of it is capitalising on basic mistakes. We need to stop deluding people with feels good content, that's how you get memes like imposter syndrome.
• pajeets 2y ago
  Streams of tears roll down my cheek as I write this because this article perfectly highlighted that it wasn't the laziness but rather what was causing it , mainly the lack of prerequisite fundamentals needed to thrive in math field. Had I known this my life trajectory would've been different instead of self loathing and inferiority complex I built up around something so innocently simple. The rush of epiphany and self-forgiveness that overwhelms me after all these years. I realize now that learning grade school math in French and then started to learning algebra and calculus in Japanese abruptly moving to an English speaking institution to continue math degree (which i abandoned for reasons in the article i realize now ) screwed me up big time because neither French nor Japanese nor English is my first language. For instance I would store numbers in French in my head and perform arithmetic in French but to do any sort of additional algebraic or calculus I would need to switch to Japanese internally and finally write out response in English. Learning the advanced topics in English was never going to work out, it was like building a castle on sand and the stones are made out of mud. I always thought I was too “dumb” to understand math. During my school years, it was evident to me that for some kids math was easy, and for others like myself: painfully difficult. This belief shadowed me for years, a constant reminder that while believe I am smart… I’m not THAT smart. Recently, after 150 days immersed in learning math, I had a stark realization. The struggle wasn’t because I wasn’t capable, but rather, I was simply missing a shit-ton of pre-requisite knowledge. I wish I could show this article and translate it into other languages. There are lot of young kids in schools who tell themselves they are dumb or lazy because they can't do well in math and sciences. God knows how many of us are walking around feeling inadequate or frustrated at ourselves because we convinced ourselves we are not worth it or capable when in reality its the prerequisites both conscious and subconscious, overt and covert we fail to realize as fundamental stepping stones to success. It might as well be that failure in startups or business ventures or relationships even also stem from this principle: that the fundamental prerequisites were not taught or caught early on (either due to environment, upringing, socioeconomic constraints) have solidified into bad habits, bad model of world, bad model of others that ultimately transpire into bad thoughts, bad words, bad actions and opposite outcomes of what we set out to accomplish. Going forward I must make it my mission to realize what fundamentals and prerequisites I do not have and instead of brute forcing and letting my ego ignore it, I have to put aside time to build those basic building blocks. A cathartic angst feels deep in me. Might be too late for me due to my age and I fear I will ignore my own writing here and others will too. It's truly sad that we are all realizing it this late and will forget whatever lessons were learned. I wish society and people would stop pointing fingers at people and rather realize build tolerance from the fact that not everybody gets to build the same prerequisites as humans cannot be the same, some are innately inclined to better at certain things while others are not. Equal outcomes is a failure in the making and schools need to stop and focus on helping students build prerequisites on their own schedule and pace.
• whackyMax 2y ago
  As a side note, the headline seemed a fun one, it seemed to me to say “you are not dumb, but you just lack a few prerequisites to be dumb”.
• deleted 2y ago
  [deleted]
• veunes 2y ago
  > It’s like trying to defeat a Elden Ring boss… at level 1. Just in love with this comparison
• GeoAtreides 2y ago
  You know how there's a window for learning to speak? https://en.wikipedia.org/wiki/Critical_period_hypothesis https://en.wikipedia.org/wiki/Critical_period_hypothesis I posit there's a similar window for highly abstract thinking, like math or logical thinking or, controversially, for learning how to learn.
  • hervature 2y ago
    Why are you stating a hypothesis as if it was fact? I'm 30 and started learning Spanish (1,000 hours so far) and think I'll be near-native level in another 1,000 hours and maybe actually native in 5,000 total hours which I might get to by the time I'm 40. As we age, we simply have other commitments that we cannot devote this much time to language learning. Kids "easily" learn language because they can easily put 1,000 hours of exercise each year for 5 years.
    • GeoAtreides 2y ago
      This is not about learning a second language, this is about learning to speak in the first place for example: https://en.wikipedia.org/wiki/Critical_period_hypothesis#Deaf_and_feral_children https://en.wikipedia.org/wiki/Critical_period_hypothesis#Dea...
      • hervature 2y ago
        The leading sentence is: > The critical period hypothesis[1] is a theory within the field of linguistics and second language acquisition that claims a person can only achieve native-like fluency[2] in a language before a certain age. Granted, I do admit I missed the subtlety that it applies to learning a first language as well.
    • dranudin 2y ago
      I have lived in a foreign country for about 3 years. My wife is from there and I speak with her in that language every day. I also took courses until the B2 level. My communication in that language amounts to easily more than 5000hrs. I am fluent, but no native speaker would call me native and that will never happen. My wife learned my language in school since elementary school up to graduation. She lives in my country since about 5 years. In her job she has to talk to people for basically 8hrs a day in the local language. She is fluent but nobody would call her native. Instead people wonder where she is from because they cannot match her accent to a particular country. Most likely we will never have native competency in the foreign language. So if you make it to native in 5000hrs, you are way above average.
• j45 2y ago
  Math as taught by one of my teachers made a lot of sense. Some topics will come easier and click. Others will need to be brute forced by practicing examples. I can see how that generates pre-requisite knowledge one way or the other.
• Dr_Birdbrain 2y ago
  I would be curious to hear what “better learning methods” the author used. He calls them out but doesn’t describe them.
  • rod_o 2y ago
    Pretty sure he means https://mathacademy.com/ https://mathacademy.com/
  • DantesKite 2y ago
    According to this tweet, he used Math Academy. “ Excited to see a @_MathAcademy_ student blowing up Hacker News with some insights they've realized about the process of learning math!” https://x.com/justinskycak/status/1827397012758917622?s=46&t=E3U2EI7EXIhlBQmxg6oZ2g https://x.com/justinskycak/status/1827397012758917622?s=46&t...
    • dr_kiszonka 2y ago
      He nudges folks towards his product on HN too. (Which is why I would never subscribe to it.)
• atoav 2y ago
  As an educator, this is the thing I always say. If you try to teach someone programming for example, try to make a honest list of all required prior knowledge. This is usually stuff that is totally obvious to anybody in the field, but if you don't know it it might give you a hard time. E.g. that programs run within the context of an operating system and the OS provides interfaces for interaction with hardware. Not all of that is needed upfront, but certain explanations just won't make any sense if required knowledge is missing.
• closetnerd 2y ago
  The source of about 30% of the hits I took in homework and tests was, to this day, not having memorized the basic values of Sin/Cos(pi, pi/2, pi/4).
  • YZF 2y ago
    Instead of memorizing the values you can learn the shape of the graphs and/or learn the meaning of sin/cos on a right angle triangle. I think I got ok through a math/comp.sci. degree without memorizing values but I will say the "mechanical" aspects of math including trig functions and things like integrals and derivatives involve drilling those enough to make these things automatic (which is sort of memorizing but not exactly). I was always lazy so I never got really good at that (and my calculus related grades are evidence of that ;) ).
    • philomath_mn 2y ago
      Yeah I pretty much always think through the unit circle to get the value of sin(0) and cos(0) (unless I had been doing a lot of trig lately) I remember drawing everything out on trig exams though and making myself an on-demand cheatsheet.
  • sn9 2y ago
    Here's an Anki deck for the unit circle: https://ankiweb.net/shared/info/1813562307 https://ankiweb.net/shared/info/1813562307
• digger495 2y ago
  The author's point about Elden Ring is especially on point.. Because not only do you need to be level 50, but you need to try and fail five times before you see any kind of success. Failure is _inevitable_. Quitting is optional. You have to learn from each mistake.
• nsxwolf 2y ago
  I wish someone had told me this in school.
• w10-1 2y ago
  For many practical applications, slow learners do just as well as fast ones, once they’re up to speed. Math teaching is mostly playing hide-the-ball, which teachers justify by saying people learn more deeply when they figure it out for themselves. But really that just shifts the burden of backfilling prerequisites to the student.
  • Jensson 2y ago
    > But really that just shifts the burden of backfilling prerequisites to the student. Not if the students were taught that way from the start, learn for yourself at every step and you are never behind.
  • whiterknight 2y ago
    Are you suggesting that you don’t learn as much when you figure our the puzzle as oppose to being told the answer?
  • Viliam1234 2y ago
    This really depends on getting the details right. If you choose the right kind of problem that the children can figure out on their own -- it helps a lot. The will remember it better, and they will also feel better about their own skill at math. But if you incorrectly estimate the difficulty of the problem... and instead of noticing your mistake and fixing it, you just wait for a miracle to happen -- the kids will only waste time and get frustrated. The problem is teachers who believe they can do this trick, but fail to notice that they are doing it wrong, and then they blame the kids.
• neom 2y ago
  Anyone here with developmental dyscalculia managed to overcome it and get into math? I have no clue how to deal with numbers, I know this is weird to say but it feels like they don't exist for me.
  • bonoboTP 2y ago
    Many branches of math aren't focused on numbers. One cool branch that has almost no prerequisites and isn't focused on numbers is graph theory. It can be a great subject to cut your teeth on, regarding formulating theorems and proving them.
• CM30 2y ago
  This tracks pretty well with my experiences learning programming, both when developing websites and making video game mods. The times I failed, I was looking at other people's work and trying to figure things out too quickly and in an unstructured way. I saw the complexities of a program that was in development for weeks/months/years, then basically panicked and thought I'd never be able to make something like that. When I learnt the basics, I then saw how these problems could be broken down into their simplest forms, and ended up learning a lot more efficiently as a result. Of course, having examples of what to do helps a lot, it's just your examples need to be merely a tad more complex than what you already know, not a masterpiece from some genius that spent the last decade working on it. Or if they are from that sort of person/company, you should try and break down sections of the work at a time to understand where they're coming from, not the whole thing at once. It's much more reasonable to try and figure out how someone like Facebook or Netflix implemented a profile page or edit button than say, how the whole system works on a greater level.
• gnarlouse 2y ago
  This page needs to get reshared 8 billion times by 8 billion humans.
• throwaway25664 2y ago
  I’m enjoying going through your site, looking for inspiration and tactics. Btw, this page is missing: https://lelouch.dev/roadmap https://lelouch.dev/roadmap
• notjoemama 2y ago
  Assessments are getting better in education and they help find missed skills. It's possible the author was smart enough to copy but not understand why they were doing what they were doing. Whether your local district focuses on skill acquisition versus graduation rate may determine the students success long term. I know little, but what I've seen from reading programs they're pretty much 'there' in discovering these blind spots. I don't know if there is comparable assessments or programs for mathematics.
• _benj 2y ago
  I’m curious about what that “preliminary knowledge” is? I’ve read stuff like a mathematician delight and the Joy of X and it’s such a beautiful, attractive but seemingly unattainable realm of knowledge. As an example, this is the math that I’m aware of and have been exposed to: Arithmetic Algebra Geometry Trigonometry Calculus I’m vaguely aware of linear algebra but haven’t studied it (it also seemed unattainable) I’m also aware of discrete mathematics and even bought the book concrete mathematics by Knuth, only to be totally stuck in the very first example of recursion and the tower of Hanoi… So, what is that preliminary knowledge and how does one goes about acquiring it? From where I sit sometime it feels like I don’t what I don’t know and I don’t even know how to ask how to learn what I don’t know I don’t know
  • programjames 2y ago
    Probably figuring out math paths. I've always been bad at remembering formulas or theorems, but that's because I remember how to get to that formula or prove the theorem instead. E.g. in grade school, I never memorized the sum of cubes formula, but I knew a^3 + b^3 = a^3 - (-b)^3 and that the difference of cubes looks somewhat like the difference of squares, so I guessed a^3 + b^3 = (a - (-b))(<and figured out the rest.>) Having the whole path in your head makes it so you don't get stuck when you forget one step, and also makes it easier to make new connections.
    • _benj 2y ago
      I like this idea. I'm guessing that it might be trying to learn math from proofs? or from first principles? I'm trying to figure out how could I find where to learn math in this way?
      • programjames 2y ago
        Yes, essentially proofs. I didn't use that word because people usually only write proofs for each other, so they end up being much more formal. When it's just yourself, chicken scratch in the margins is good enough. How you learn it this way is by always asking yourself how something came to be. Why is the area of a triangle base * height / 2? Why are you allowed to subtract two equations (but not inequalities)? What is this curly thing in Green's theorem? How did someone come up with that alternating sign formula for the determinant? And so on.
• dundercoder 2y ago
  So many times the solution is to be kinder to yourself. I love this.
• meken 2y ago
  I can relate - I was quite bad at math through high school. I eventually hit a wall in college then, like the author, decided to start from the complete basics: positive and negative numbers, fractions, arithmetic, algebra, then calculus. Khan academy made this possible for me (in 2010), I don’t know where I would be without it.
• patrick451 2y ago
  This post biases way too hard into the nurture side of the equation. The difference between the author and someone who is genuinely smart is that the genuinely smart don't need to spend months carefully working through all those prerequisites in carefully arranged order. Until you meet somebody like this, it's easy to delude yourself into assigning yourself more brilliance than you posses and think that everybody struggles the same way. It turns out some people really are smarter than you, prerequisites or not.
• datagreed 2y ago
  I am confused: how exactly did the author managed to lack prerequisites for math in school?
• ksec 2y ago
  That is what I dislike about Computer Science course ( BSc ) and much prefer Computer Engineering ( BEng ). There are far too many abstraction involves that most people just remember or know the skills set of the abstraction layer without ever understanding how that abstraction comes into the field in the first place. Over the past 10 years the media has have popularised the term First Principle often spoke about by Elon Musk ( He didn't invent the term but media help to spread it ). And this is precisely it. And this isn't just computer but literally every single subject taught are now about the grade and not the "WHY". We just dont know how most things are derived from. We just memorise it and society will reward you with Certificate and a "Smart" status. In Maths Richard Feynman [1] explaining mathematics in 4 pages from algebra to calculus. As the saying goes, I dont have time to write you a short letter, So I wrote a long one. Getting something simple and concise in 4 pages is the work of genius and takes a lot of time. I only wish something like this exists for all other subject with video course, completely free of charge in dozens of languages to kids all around the world. [1] https://www.feynmanlectures.caltech.edu/I_22.html https://www.feynmanlectures.caltech.edu/I_22.html
  • default-kramer 2y ago
    When I think of "Computer Science" I definitely think that it respects "build great things from a small set of first principles" as much as any field. In fact, I might argue that CS is just a subset of pure math. It's those pesky Computer Engineering concerns, warts like memory locality and branch prediction, that make CS "less pure" than it could have been :) [no offense to CE, I personally love those warts] > most people just remember or know the skills set of the abstraction layer without ever understanding how that abstraction comes into the field in the first place This sounds like you're describing pragmatic software development, or "software engineering" if you insist on sounding fancy. My degree was in SE and in retrospect I would have enjoyed CS more, but it really didn't matter in the long run. But I digress... the point is: a course that focuses on using an abstraction is a programming/SE course, whereas a course that focuses on the principles one might use to build such an abstraction is a CS course.
• j7ake 2y ago
  Prerequisite is a euphemism for practice. You lack practice. It’s like saying you can improve your skills in basketball/swimming/piano/singing if you just practice better. But obviously you can still be dumb and know a lot of math.
• lovestory 2y ago
  I have still not graduated and this is my sixth year at university (in Europe). I find math too difficult and I still have calculus, linear algebra and probability. Discrete structures is the only math class I managed to pass and it took me too long to realize it's because the other classes have a long list of prerequisites. I have passed all of my software/IT classes aside from the maths and it's because they virtually are built from the ground up. On the other hand, strong math foundations are required even for the introductory math in my college. What I did was get great algebra and precalculus textbooks and went through them with great detail. After that I found the classes were not that hard to grasp.
• locallost 2y ago
  Smarter people will get the prerequisites faster. Nothing wrong with that, I'm more of a persistent person myself, which is a quality in itself. The really accomplished people are both smart and persistent. But otherwise I agree with the article. I have zero basics in physics because my first teacher was generally senile and there was noone else (small town), and it was always something where I automatically tried my best to just get a passing grade.
  • globular-toast 2y ago
    The point about persistence is really important. I've worked with a lot of smart people who aren't persistent and, frankly, quite often lazy and/or uninterested. They don't work through problems by themselves and are quick to seek help or quick answers at every hurdle. Needless to say they aren't going and filling in the gaps in the requisite knowledge to better themselves either.
• LarsDu88 2y ago
  This is me diving into leetcode without majoring in CS in undergrad. There's are also a bunch of precalculus stuff that comes in handy that I completely forgot. Like how to compute arithmetic sums!
• markozivanovic 2y ago
  Hehe, two years ago, I wrote a similarly titled article - "You're not dumb, the prerequisites are bullshit." :) https://news.ycombinator.com/item?id=30035456 https://news.ycombinator.com/item?id=30035456
• Jacky4Chan 2y ago
  That's one of L. Ron Hubbard's barriers to learning, described in his "basic study manual" book. -Another one is not fully understanding the words or concepts being used. -Another is not having an appropriate example or visualization of what is being explained.
• ruph123 2y ago
  How to tackle it? To me there are either two ways: when you are trying to learn the thing XYZ you are seeking, drill down to the first thing you don’t understand and consult a lower level resource. Continue until you reach a level you understand. And the second way is: Re-learning “all” of essential math and then going back to XYZ. I don’t think the second step is feasible, as you cannot possibly learn everything in a breadth-first kind of way until you are deep enough to learn the (now level-adjacent) topic XYZ. But for strategy 1, the question is 1) how to identify the problem that you are lacking (e.g. how to isolate math gibberish into a concrete concept) and 2) how to find a good resource to learn and practice this concept at this level? I do struggle with this and sometimes randomly learn some lower concept again but notice later it did not help me in the end and just left me with a million untied knots that were infeasible for me to entangle.
• necovek 2y ago
  I am not sure I entirely agree with the premise: eg. you maybe are "dumb" (lack mathematical talent, really), but with proper instruction, you can learn a lot of math. Let me dive deeper. Our school system teaches math in a pretty inflexible way: "this is how everyone can get it". But even math talents don't learn it that way: as one, I was usually ahead of the school with my own reasoning (sometimes by a couple of grades) and could backtrack to the school method to understand it and apply it. Second, if you are good at maths naturally, everything else at school becomes easier: people simply treat you as "smart" in whatever you do just because you have a natural leaning to mathematics (both if they do or don't themselves). Even rote memorization subjects like history and geography become easier since, well, you are "smart": teachers simply do not ask much of you. And finally, I've met many an extremelly intelligent mathematician (uni professors and math competitors) who simply are outright dumb: they could not process a simple logic statement in human language, even if they were regularly working on advanced research calculus. So, anyone can learn a lot of math, and doing so requires internalizing the foundations. However, people talented for mathematics find it easy to internalize them in various ways (not always the textbook way), so it's not hard work for them (eg. I could coast through the entire undergrad math and CS program too, cramming for a weekend for all but a couple of exams: memorizing all the axioms and theorems was the struggle, operating with them and proving them once I knew them was comparatively easy and I finished with a GPA equivalent of 3.4 or so). But math instruction is hard because math is a formal language representing a very specific mindset that not everybody can naturally get. And instruction is usually performed by people not having attained that internalized knowledge of the foundations, thus not being able to look at it and describe it from numerous viewpoints required for individual students. Finally, we need to fix the society not to equate "good at maths" with "being smart": plenty of smart people who have a hard time with maths, and plenty of math wizards who are outright dumb.
• Grustaf 2y ago
  But how could some 7 year olds have vastly different ”pre-requisites” than others? In my experience aptitude plays a far bigger role. Yes, you compensate for lack of aptitude with a lot of hard work, but that’s a different matter.
  • creesch 2y ago
    Because at 7 you obviously also already have 7 years of experience behind you. Sure, it is not as much as an adult, but it still matters a lot. Different environments and stimuli make it so that also for 7-year-olds, they can have vastly different prerequisites for anything. Often aptitude is not aptitude at all, but all of the above. Then, during learning anything, the same thing also applies. How much support you get from teachers and parents. What sort of environment you have available to practice in. And a lot more. Finally, when all other factors are equal, aptitude can play a certain role. But one that in an educational setting is largely irrelevant. Because if everything else is perfectly in place to teach something, including learning any prerequisites, aptitude is only something that matters in hindsight. Which is extremely important as well. Labeling someone as lacking aptitude can be highly discouraging. Repeatedly hearing that they aren't “naturally” good at something can lead them to stop trying, even if it's not true.
    • Grustaf 2y ago
      I really don’t understand this cope. It’s scientifically established that intelligence is highly heritable, especially the analytical kind. It also agrees with experience, we all know people who have a very hard time understanding mathematics, while others sail through it. Of course it’s not fair, life isn’t fair. But the good news is that you can quite easily compensate for lack of aptitude with more work, and that is most definitely the case for mathematics, up to and including undergraduate level. I grew up in Sweden where everyone goes to the same kind of pre-school, that does very little math teaching. Still, the difference in aptitude when we started school was significant. But we all know this.
      • creesch 2y ago
• creesch 2y ago
  Related to this, it is why when writing documentation for something, it can be extremely useful to also list the prerequisites someone needs to pick up the information in the document before them. Possibly with also linking to resources about them, depending on your audience. Not only that, writing out the list of prerequisites also helps the author write a better document. Because thinking about what knowledge is required serves the same function as thinking about a good unit test does. It makes you stop to consider "the obvious" and sometimes realize you have overlooked something. Because when you are thinking about these prerequisites, you are likely also thinking about why they are needed and what challenges come with them. This in turn might lead you to revise aspects of the documentation to make them clear as well.
• bloqs 2y ago
  This is a half truth. Part of the reason some people take a lot longer to grok the prerequisites and get left behind in class is because of cognitive ability. Working memory (WAIS) digit span, and broader performance IQ (as opposed to verbal IQ), generally indicates how many conceptual 'items' you can have in your head at once. With more advanced math, this becomes _critical_ to forming the coherent plumbing between concepts in your head, leading to understanding. Incidently, ADHD is largely an expression of specific personality traits and low working memory.
  • agumonkey 2y ago
    I felt that during college. Suddenly I couldn't hold enough abstract terms or variables at once to be able to reflect. It slowed me down near zero, but weirdly, if you keep trying, your brain may evolve some new abilities and maybe as important.. keep feeling joy about learning even if slowly. I wonder how one can raise this aspect of thinking.
  • bruce343434 2y ago
    ADHD is largely an expression of dopamine misregulation actually.
• bqc 2y ago
  Would you like to recommend any resource?
  • ydnaclementine 2y ago
    I've been looking at this textbook for awhile. Very, very basics to calculus: https://www.amazon.com/Foundation-Maths-Dr-Anthony-Croft/dp/1292289686 https://www.amazon.com/Foundation-Maths-Dr-Anthony-Croft/dp/.... I wish there was a table of contents available
  • bqc 2y ago
    I’m interested in data structures and algorithms, particularly those related to mathematics. If you have any relevant materials or resources, I would greatly appreciate them.
  • JustinSkycak 2y ago
    Kind of depends what exactly you're trying to learn, but if you're working up to ML/AI, then there's How to get from high school math to cutting-edge ML/AI from last week: https://news.ycombinator.com/item?id=41276675 https://news.ycombinator.com/item?id=41276675
    • doctorpangloss 2y ago
      This is really interesting but it seems too good to be true. You’re going to reply that it’s not for everyone, but you’ll have nothing positive to say about the audience for whom this is a bad fit, which is also a suspicious form of generalization. It’s kind of like how the chatbots and for that matter most online learning resources give the psychic feeling of learning.
      • pests 2y ago
        It seems impolite to make up your opponent's argument and then make commentary about it. Maybe let them respond?
      • JustinSkycak 2y ago
• billconan 2y ago
  but when I read a paper, it's difficult to know what the Prerequisites are.
  • tombert 2y ago
    My trick is to find the paper you want to read, but immediately skip to the references; recurse until you get to a paper that you more or less understand. It’s a bit time consuming but it makes paper reading a lot more fun.
    • JustinSkycak 2y ago
      Reminds me of my colleague's recent post on his experience getting up to speed on his dissertation topic while doing a PhD in mathematics: https://x.com/ninja_maths/status/1820583797491925386 https://x.com/ninja_maths/status/1820583797491925386 I'll quote a snippet below: “My biggest mistake when starting my doctoral research was taking a top-down approach. I focused my efforts on a handful of research papers on the frontier of my chosen field, even writing code to solve problems in these papers from day one. However, I soon realized I lacked many foundational prerequisites, making the first year exceptionally tough. What I should have done was spend 3-6 months dissecting the hell out of all the key research papers and books written on the subject, starting from the very basics (from my knowledge frontier) and working my way up (the bottom-up approach).”
    • findthewords 2y ago
      Finding a path starting backwards... also known as dynamic programming.
    • cultofmetatron 2y ago
      I would legit PAY for an app that managed dependencies for understanding a paper so that I could see the path I need to take to understand what I'm reading. Could apply to books too.
      • dataf3l 2y ago
        some time ago I was thinking about this issue, maybe the concept of "parametric books" will become popular in the future. https://www.youtube.com/watch?v=VXktVbeWAeM https://www.youtube.com/watch?v=VXktVbeWAeM https://www.youtube.com/watch?v=Tpb2rXtBos4 https://www.youtube.com/watch?v=Tpb2rXtBos4 perhaps, with the advent of AI, one will be able to convert a current book into a more detailed book, and also a current book into a smaller book, so maybe this idea is even easier to implement than 4 years or so ago, before chatgpt (but after summarizers, which prompted the idea in my head). I would humbly appreciate any feedback on the concept of parametric books, for now, it's just an idea, but it's a free one, anyone is free to implement it. thanks in advance, for your comments on it.
• ta8645 2y ago
  Many people are in fact dumb, and will never acquire the prerequisites. We're not all blank slates with equal potential.
• notepad0x90 2y ago
  Late to the thread, but my view on being "dumb" in general, even if you have the pre-req's knowledge and ability are different things. Most people, in my opinion, are smart enough to understand and apply just about any complex subject or topic. Being smarter just means you can "compute" and understand or apply the subject in question faster than others. In the end, what we prioritize and how much time is available for us to tackle different subjects is the biggest limitation, not genetics or luck. Art and entertainment heavily influence these things.
• pazimzadeh 2y ago
  > A cage of 5 mice costs ~$1k upfront and ~$5k/yr recurring You can get mice a lot cheaper than that, I'm not sure what kind of mice he's referring to but the prices depend on the vendor and mouse type. Where I work it's about $2 a day to house a cage of 5 mice. It's about $30 a mouse if you get C57BL/6NJ's from Jackson: https://www.jax.org/strain/005304 https://www.jax.org/strain/005304 So more like $150 for 5 mice and $800 to house for a year. Another good one to know if the size of antibodies (10-12 nm).
  • hamandcheese 2y ago
    Wrong article?
    • pazimzadeh 2y ago
      whoops yeah wrong article. was trying to comment on this https://news.ycombinator.com/item?id=41344176 https://news.ycombinator.com/item?id=41344176
  • rendall 2y ago
    Is that in the article? I didn't see that. Where is that from?
• sublimefire 2y ago
  This is an optimistic take on things. With years you understand there is a small cohort that is not capable of learning the basics even if they try, then there are folks who do not even know they are lacking.
• feldrim 2y ago
  I discovered this myself when I attended a data science summer school, a 2-day bootcamp. I knew Python and Jupyter. I know basics of Operations Research, though I barely passed the class back in time. I took classes on optimization classes thanks to industrial engineering classes. But at the end of the boot camp, I was as illiterate on data science as I was at the beginning. I was just more confused. Then, I understood that I was missing the mathematical prerequisites for the understanding. I still felt dumb though.
• TrackerFF 2y ago
  A lot of people hate rote learning - but elementary math classes, meaning all the way up to calculus (or prior to more rigorous proof based classes), do require a bunch of memorization. That's on top of getting an intuition...the "Aha!" moments. I've observed that many math students in those types of elementary classes struggle because they're unable to recognize identities. They get some problem which involves substituting hard parts with easier parts using identities, but don't recognize them. So they try to solve the problem directly, and end up writing pages upon pages, before either getting stuck or doing some error that follows them until they get stuck. Once they're showed what identities to use, they say "of course, I should have known that!" - but they never put in the time to solve all the problems. And I was like that, too. I always thought that math would be a nifty because you'd "only" need to learn the various theorems, and if you understood those, then that should have been enough. It didn't really hit me that I'd need to put in hard work solving problem sets until I started recognizing patterns and knowing what to use, and where to use it. Same goes for those that don't really understand the theory. Lots of math problems later will be of the type "Here's a difficult looking problem, is [statement x] true or false?" - and because they don't understand what math theorem to use, and all its properties, they'll try to brute force it by jumping into calculations. You see it all the time in calculus, where students are asked to solve some nasty looking integral problem, which is much simpler if you know and use properties regarding symmetry and stuff like that. I'd say for most people, there's no free lunch when learning math. You'll need to understand it, and you'll have to practice. There's always going to be some extremely high-IQ individuals that can do pretty advanced math purely by logical deduction - but for the vast majority, it comes down to hard work.
  • trwhite 2y ago
    > A lot of people hate rote learning - but elementary math classes, meaning all the way up to calculus (or prior to more rigorous proof based classes), do require a bunch of memorization A lot of people still think reading and re-reading textbooks is the way to memorise theorems but recall (attempting to remember them without the book) is much better. I cannot recommend the book "A Mind for Numbers" by Barbara Oakley enough - it put me on a journey to re-learning Maths as an adult.
• maxrecursion 2y ago
  I learned this as a teenager when I went from great at math to terrible because I got stuck with crappy teachers. Then, in 11th grade, I got put in algebra 2 with a great teacher and was tutoring other kids. Math is completely different than other subjects. You can't catch up by cramming or reading a book over the weekend. You have to consistently learn and use it over the years. And have competent teachers to teach it to you. Once you get placed in the remedial math, where they are just corralling misbehaving teenagers, and slapping out worksheets so kids can pass, you are basically screwed, unless you can get out of that situation.
• firesteelrain 2y ago
  I don’t even have to read the entire article for the title to resonate with me. But when you are poor and really need a leg up in society, you will do anything to push yourself forward - including going into student loan debt. I certainly wasn’t equipped nor ready for computer science. Well let’s say my computer science classes I did well. It was the Calculus and Physics that I struggled because I didn’t have a good background from High School. I didn’t have the necessary pre requisites. When I recently completed my Masters in Systems Engineering, getting a 4.0 GPA was no problem.
• sethammons 2y ago
  My step-mom tutors. A high schooler was having a terrible time in algebra. She quickly realized there was foundational numeracy missing. The next lesson they walked out to the residential street and asked: how many tires are there. The kid froze and guessed. Time to start counting. A couple months later, the kid was able to raise their grade to passing in algebra
  • spencerchubb 2y ago
    too many stories like this. we need to organize schools by knowledge, not by age. and only pass kids to the next level when they're ready
• avidphantasm 2y ago
  I have a corollary: people who are smarter than I am are mostly just less lazy than I am.
• mehulashah 2y ago
  I wish we didn’t think of understanding math as being smart or dumb. Like, it was a singular ability. Math is a subject deep, wide, and rich of ideas as well as results. For me, learning and understanding new concepts and results is like discovering new mountains and trying to ascend them. I won’t be able to ascend most, but I can certainly sit back and appreciate and enjoy their magnificence.
• Astro-Domine 2y ago
  It’s heartwarming to read comments from clever people, focusing on their struggles. Too often I interact with people who lock conversations into their own sphere of competence with the outcome being that I feel incompetent.
• shiandow 2y ago
  Lately I've begun thinking that the way maths is taught, with each new concept following on the previous and no real way to revisit older content, just might be why people think there is a sharp divide between people who seem to understand all maths immediately and people who don't get it at all. Of course it might be the case that maths people exist, but maybe it's mostly survivor bias.
  • jacobsimon 2y ago
    One thing I noticed going through school is that math concepts are usually taught first before physics and other subjects —- precisely because the math is viewed as a prerequisite for the other material. But this always seemed entirely backward to me, because much of the math was invented for and motivated by people trying to solve actual problems in these other disciplines. I think we should teach people in the same order of operations, rather than treating math as an abstraction to be learned by itself.
• talkingtab 2y ago
  To generalize. When people fail they can blame themselves or can examine how to change. I saw one person try open a gate, fail and say they were no good with mechanical things. I said "Its not you, the gates broken" and the person immediately opened the gate. This is pervasive. "I'll see it when I believe it" as the saying goes.
• chrsw 2y ago
  When machine learning went mainstream I realized I didn't _really_ understand linear algebra.
• mahdavipanah 2y ago
  I think intelligence (however defined) is important. But the problem is often people misuse this metric to predict a binary conclusion of whether they can acquire a skill or not instead of just considering it as one variable involved in the learning curve.
• perihelion_zero 2y ago
  [flagged]
• godber 2y ago
  This article makes me think of the skill tree or roadmap posts we’ve seen here on HN or Reddit over the years. For example https://roadmap.sh/frontend https://roadmap.sh/frontend … I feel like we could do a better job of providing ourselves fundamental tools like this in helping ourselves and others learn. Not just in tech, but in life overall. The “dev” tree above is embedded in the life skill tree that should start in elementary school. Haha, even the life skill tree has “fictional” branches that intercept the game world skill tree … you really do have to learn all of the dependencies necessary to case 5th level fireballs … there are real rules to be learned in the games their usefulness is just siloed into the fictional realm. Edit: I forgot to point out that roadmap is open source here: https://github.com/kamranahmedse/developer-roadmap https://github.com/kamranahmedse/developer-roadmap
  • deleted 2y ago
    [deleted]
• dev1ycan 2y ago
  Yeah but good luck going through the entirety of khan academy as an adult, it's not impossible but it's also a task as hard as learning a new (or multiple) languages... If you can dol it though and complete everything up to precalc you can most definitely do well in university.
• jkmcf 2y ago
  This was my takeaway from college. In HS, you don’t have a lot of prerequisites, excepting the “II” level classes. I quickly found out how unstable my math and physics foundations were. Luckily, few realize that Bs are closer to failing than they are to mastery. Even the college gut courses have hidden dependencies. I still feel for the business majors in my entry level stats class when the prof, bragging about learning calculus at 10, required calculus proofs for all the things. Much like Civilization and Diablo games, and @godber’s comment, those tech trees should be required for all course syllabuses.
• bonoboTP 2y ago
  People often, but not always, lack the prerequisites because they weren't able to learn them when it was taught in school. And that was because they lacked the pre-pre-requisites because they in turn didn't pick those up when that was the material being taught. In math, things build upon previous things to much greater degree than in other subjects. If you get off track once, it's hard to catch up. But if you lack prerequisites because it was never taught in high svhool etc, that's a failure of the curriculum.
• fargle 2y ago
  not untrue, but only part of the story. certainly your math skill level neither makes you "smart" or "dumb" (which really aren't opposites, either). prerequisites are (ahem) required. not having them does imply having a bad time. what's missing is that different people's brains work differently and people have different talents. if you learn differently, that can factor into that lack of prerequisite knowledge - perhaps the way it was taught didn't work for you. but some people's brains just don't like math. other's are gifted at it. you can have all the prerequisite knowledge needed, be the best most diligent student, be wildly intelligent in general, and still not just "get" math. so this article was about someone who actually did have a decent proclivity to math, but was robbed of it because of some missing foundation. and then said "ah ha!" there's the problem! but that doesn't mean that's the case for everyone else - far from it. it smacks of the "affirming the consequent" fallacy: ("dumb" => !math) !=> (!math => "dumb") (!prereq => !math) !=> (prereq => math)
  • j2kun 2y ago
    > some people's brains just don't like math Sounds like perverse socialization to me. What actually justifies this claim? Do some people's brains "just not like reading?" Do some people's brains "just not like music?" There's nothing special about math here.
    • fargle 2y ago
      > Do some people's brains "just not like reading? yes, certainly. pretty common - outside of a disability, we can all learn to read, but it's hard and not enjoyable for many. > Do some people's brains "just not like music? yes. (when i say "like" btw. i meant roughly "natural ability", not "enjoy") of course most people love to listen to music, but many people do not have much of a musical ability - and you can't work, learn, or practice your way into it beyond a certain point, either. > There's nothing special about math here yes. some people are terrible at dealing with socialization and others are brilliant. we are NOT all wired the same way. we all have different abilities. what justifies that claim is several billion examples.
• gradus_ad 2y ago
  This is where LLM's have been the most helpful for me. When I am engaging with an entirely new subject and have a bunch of questions I need to pepper someone with, I can ask as many clarifying follow ups as I need without getting self conscious or worry about annoying whoever I'm speaking with. The LLM is infinitely patient and able to easily handle beginner level prereq questions.
  • gmd63 2y ago
    This is the best blessing the internet has given to worldwide curiosity and intelligence. The ability to ask "why" ad infinitum, without pissing off parents or taking up the entire class's time.
• ndarray 2y ago
  > This belief shadowed me for years, a constant reminder that while believe I am smart… I’m not THAT smart. Sentence missing an I > It’s like trying to defeat a Elden Ring boss… at level 1. an > In fact, I’m still pretty dumb. Contradicts the first sentence I'm quoting.
• solidsnack9000 2y ago
  I suspect this highlights are more serious issue which is that most of our training methods are not adaptive. They work well only if the students arrives at the right phase in their understanding and otherwise make poor use of everyone's time. Yet assuming the student has something to learn, and the teacher knows about it, this does not have to be the case. One discussion of training I found eye opening was Pat McNamara's thoughts on what I believe he said was called "skills-based training" versus "performance-based training". With skills-based training, instructor start out the training session with the idea in mind to cover certain skills. A lesson is successful if it covers the skills the instructor wanted to cover. Performance-based training is geared towards improving the students' performance, so skills are introduced based on the students' actual level of ability and the relevance of training in a particular skill for improving their performance. One motivation for adopting performance-based training is the lack of success of skills-based training in many contexts. Why is skills-based training sometimes unsuccessful? One reason is that the skills may be too hard -- the instructor chooses the skills with imperfect information on the students' level, and they choose the wrong skills. The students receive the training but their abilities do not actually improve; they don't know what's going on. Another reason can be that the skills are too easy -- the students receive the training and actually meet all the standards, but it doesn't actually help them get better. Pat McNamara discusses these concepts in the context of being a shooting instructor for police departments and military units. It seems that one often doesn't know what these units know before one shows up, and the officers and soldiers in any one unit can be quite different individually, so the instructor has frequent occasion to think about the relationship between what they planned to teach and what they actually did when prompted by the students' questions and challenges.
• toshaga 2y ago
  Reminded me of the Feynman’s technique. I relate completely. One of my biggest challenges in returning to university after several years of work was exactly having lost the grasp of prerequisite knowledge. Unfortunately, from experience, more often than not lecturers just play the “you should know this from previous courses/high school” card and you are pretty much left alone in your struggles. Gets even worse if an exam problem relies on some borderline trick that wasn’t practiced throughout the course. You could probably tell I haven’t let go of some grudges.
• wtk 2y ago
  It's absolutely true. At work I keep a notepad open where I write down questions to get to the bottom of things. What occasionally stops me is shame that I might be asking my peers too silly questions as expected from my level. It's a daily struggle but there's no other way for me. Life's about learning and growing so you better get the right mindset for it.
• eichi 2y ago
  [dead]
• globular-toast 2y ago
  I often tell people they're not dumb (and therefore I'm not smart), they just lack the prerequisites. But they never go and acquire said prerequisites. I do. Maybe they are dumb.
• methods21 2y ago
  The fact that the push primary school students through to higher and higher levels of math, when they 'fail', is a sacrilege to the student and a stain on the education system. I see so many capable students that don't have the prerequisites for the current math level, and are now just completely lost with NO chance of finding the path in the current system. And completely demoralized and disenfranchised.... all for what? To meet some BS metrics? This really needs to change.