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I agree with the sentiment of this. I think our obsession with innate mathematical skill and genius is so detrimental to the growth mindset that you need to hav

by gsabo 2y ago

I agree with the sentiment of this. I think our obsession with innate mathematical skill and genius is so detrimental to the growth mindset that you need to have in order to learn things. I've been working a lot on my math skills lately (as an adult). A mindset I've had in the past is that "if it's hard, then that means you've hit your ceiling and you're wasting your time." But really, the opposite is true. If it's easy, then it means you already know this material, and you're wasting your time.

junto 2y ago
> I agree with the sentiment of this. I think our obsession with innate ~~mathematical~~ skill and genius is so detrimental to the growth mindset that you need to have in order to learn things. I strongly believe that the average human being can be exceptional in any niche topic given enough time, dedication and focus. The author of the book has picked out mathematics because that was what he was interested in. The reality is that this rule applies to everything. The belief that some people have an innate skill that they are born with is deeply unhelpful. Whilst some people (mostly spectrum) do seem have an innate talent, I would argue that it is more an inbuilt ability to hyper focus on a topic, whether that topic be mathematics, Star Trek, dinosaurs or legacy console games from the 1980’s. I think we do our children a disservice by convincing them that some of their peers are just “born with it”, because it discourages them from continuing to try. What we should be teaching children is HOW to learn. At the moment it’s a by-product of learning about some topic. If we look at the old adage “feed a man a fish”, the same is true of learning. “Teach someone mathematics and they will learn mathematics. Teach someone to learn and they will learn anything”.
- ponderings 2y ago
  I've had some success converting people by telling them others had convinced them they were stupid. They usually have one or two things they are actually good at, like a domain they flee to. I simply point out how everything else is exactly like [say] playing the guitar. Eventually you will be good enough to sing at the same time. Clearly you already are a genius. I cant even remember the most basic cords or lyrics because I've never bothered with it. I met the guitar guy a few years later outside his house. He always had just one guitar but now owned something like 20, something like a hundred books about music. Quite the composer. It looked and sounded highly sophisticated. The dumb guy didn't exist anymore.
  - shrubhub 2y ago
    But also, some people are stupid, right?
    - ajuc 2y ago
      The inborn part is how quickly you get results (good or bad). Stupidity is the results. If we spent 50% of time thinking productively - inborn thinking speed would matter. But in my estimate even 5% is generous. So it matters far more what kind of feedback you have to filter out the wrong results, and how much time you spend thinking - than how quickly you can do it. Also practice helps with speed.
    - yawpitch 2y ago
      Intellect is like a gas, it will expand to fill its container. The container, in humans, is epigenetic and social — genetics only determines how hot or cold your gas is, ie how fast and how fluidly it expands, but you’re taught your limits — it’s best to see stupid as not how limited you are relative to other but what limits you have now and may abandon in the future. That said, some people received a smaller starting container, and might need some help cracking it. That’s the work of those who think they’ve found a bigger one.
    - deleted 2y ago
      [deleted]
- shrubhub 2y ago
  So you're saying success at maths isn't an inbuilt ability. Instead, it depends on an (inbuilt) ability to hyper focus... Which you are just born with?
  - elbear 2y ago
    Not even that. It depends on the learned ability to stop pushing yourself when your focus is wavering. That's how you develop aversion towards the topic. Let your natural curiosity draw you to particular topics (that's why you might have a winding road through the subject).
    - air7 2y ago
      parent comment was a bit tounge-in-cheek but I'll continue the sentiment: You're saying that the curiosity is "natural" hence one is either born with it or not. I think that there is no way around the fact that it will be hard and uncomfortable to mimic the progress of someone that has an innate inclination towards a subject (be it talent or focus or curiosity) artificially.
      - card_zero 2y ago
        Hey, that doesn't have to be what "natural curiosity" means. Besides which it makes no sense to say people are born with complex interests. I mean, OK, your genes might incline you a certain way, but that's not the same thing. Being interested in a subject is massively helpful to learning it. But interest arises circumstantially, it's an emotion. The grim reality that it would be really useful to you to learn a certain subject does not necessarily make you interested in the subject, unfortunately. (Perhaps "financially interested", but that's something else.)
        ericd 2y ago
        I think there is some natural inclination towards abstract thinking versus more grounded in reality, just judging based on kids I know. Some of them really enjoy playing with ideas in their heads, some enjoy playing with things they can touch more. It seems likely that those different attractions would express themselves in how much they practice different things as time goes on.
- diffeomorphism 2y ago
  Caveat here is that "talent" and "dedication" is linked to speed at least in the beginning. For instance, any student can learn calculus given enough time and advice even starting from scratch. However, the syllabus wants all this to happen in one semester. This gives you vicious and virtuous cycles: Students' learning speed increases with time and past success. So "talented" students learn quickly and have extra time to further explore and improve, leading to further success. Students who struggle with the time constraint are forced to take shortcuts like memorizing "magic formulas" without having time to really understand. Trying to close that gap is very hard work.
  - drbig 2y ago
    Thank you for the insight that academic (in a very broad sense) bulk-fixed-time approach does in fact produce both of the cycles, and the gap indeed only widens with time (speaking from personal experience, especially from my life as an undergrad student). Reminds me of my personal peeve that "studying" should not be "being taught", studying is pursuit of understanding, "being taught" is what happens in primary school (and I'm aware I'm simplifying here).
    - blackbear_ 2y ago
      I would say that you could generalize this even further outside of education. A few early successes in life can greatly accelerate one's trajectory, while early failures could set one many years back. And this happens independently of whether those events are due to skill or luck.
  - jvanderbot 2y ago
    Indeed, speed is often read as "smarts" whereas I would maintain it's much more often "preparation". We can't on one hand believe in the plasticity and retrainability of the mind, while simultaneously believing that speed is something only a few are born with. On the nature/nurture scale, I think it's 20/80 or so - but prodigies and geniuses have an interest that keeps them thinking and learning 10x or 100x more than other kids, and a little bump that lets them get started easier and therefore much earlier. This sets them up for fantastic success very quickly. [1] shows a great example of this. I'm fond of saying "You can do anything you want, but wanting is the hard part", because to truly be a grandmaster, genius-level mathematician, olympic athlete, etc, requires a dedication and amount of preparation that almost nobody can manage. Starting late, with emotional baggage, kids, and having to spend 5 years relearning how to learn? Forget it. 1. https://danielkarim.com/how-to-become-a-genius-the-polgar-experiment/ https://danielkarim.com/how-to-become-a-genius-the-polgar-ex...
- graemep 2y ago
  > The author of the book has picked out mathematics because that was what he was interested in. The reality is that this rule applies to everything. My first thought when the article got to the dialog between logic and intuition bit was that the same is true for school level physics.
- LoganDark 2y ago
  > Whilst some people (mostly spectrum) do seem have an innate talent I think the only thing in autism that I'd call an innate talent is detail-oriented thinking by default. It'd be the same type of "innate talent" as, say, synesthesia, or schizophrenia: a side effect of experiencing the world differently.
  - yawpitch 2y ago
    > a side effect of experiencing the world differently A side effect for which there is a substantial, lifelong, and most importantly wide cost, even if it occasionally confers usually small, usually fleeting, and most importantly narrow advantage.
    - sethammons 2y ago
      At such cost with such narrow advantage, why has it persisted so pervasively? I would counter that the advantage is wider and the cost narrower than your current value system is allowing you to accept.
      - LoganDark 2y ago
        Natural selection doesn't care about cost or advantage, only reproduction.
        sethammons 2y ago
        It is the sum of costs and advantages that lead to reproductive success. The trait is still here and still prevalent meaning people are still getting laid and starting families and presumably leading fulfilling lives. I'm not sure what you are trying to say.
        LoganDark 2y ago
        > I'm not sure what you are trying to say. I'm saying, if it doesn't ruin lives to the point of preventing reproduction, then it stays in the gene pool. Basically, I'm saying this: > The trait is still here and still prevalent meaning people are still getting laid and starting families and presumably leading fulfilling lives.
- Malidir 2y ago
  >The belief that some people have an innate skill that they are born with is deeply unhelpful. Whilst some people (mostly spectrum) do seem have an innate talent, I would argue that it is more an inbuilt ability to hyper focus on a topic, whether that topic be mathematics, Star Trek, dinosaurs or legacy console games from the 1980’s. Nonsense! The brain you are born with materially dictates the ceiling of your talent. A person with average ability can with dedication and focus over many years become reasonably good, but a genius can do the same in 1 year and at a young age. We have an education system which gives an A Grade if you pass the course, but 1 person may put on 5 hours a week and the other works day and night.
  - PittleyDunkin 2y ago
    What makes you think that "genius" is nature and not nurture? I'd love to see the evidence for this; i'm deeply skeptical. Edit: I don't mean to argue that there aren't genetics involved in determining aptitude on certain tasks, of course, but the assumption that genius is born and never made feels like a very shallow understanding of the capacity of man.
    - Malidir 2y ago
      > I'd love to see the evidence for this; i'm deeply skeptical. Cool, come and have a coffee with me :) I have older and younger siblings and was the one randomly blessed. Whereas most recognised talents are associated with hard work and so there is then this visible link, I am a good example as I did the bare minimum throughout education (and beyond...). The way my brain processes and selectively discards/stores the information it receives is very different to majority of the population. I have no control over it. I take zero credit for any of my achievments - I regularly meet intelligent people near to retirement who have been to a tier 1 university, may have PHDs, worked 60 hours a week since they were born, been on course and what not and cannot reach the levels I can. My nurturing was no different to siblings/peers (and was terrible!) Note: I have my weaknesses too, but as a whole, I am exceptional. Not through effort!! Completely random - neither of my parents are intelligent and nothing up the ancestary tree as far as I know.
- dennis_jeeves2 2y ago
  >I strongly believe that the average human being can be exceptional in any niche topic given enough time, dedication and focus. And this also gives the proponent (you in this case) an excuse to blame a person for not focusing hard enough or not being dedicated enough if they don't grasp the basics, let alone excel.
- InDubioProRubio 2y ago
  The boostrap skill is the ability to obsess over something. To focus and self-reward on anything is a heaven sent. Good thing we do not medicate that if we are unable to get that energy on the road, that base skill.
- sdeframond 2y ago
  > I strongly believe that the average human being can be exceptional in any niche topic given enough time, dedication and focus. I respectfully, but strongly, disagree. There's a reason most NBA players are over 2 meters tall, and one does not become taller with time, dedication nor focus. It might be different for intellectual skills but I am not that sure. Almost anyone can become decent at almost anything though. Which is good already!
  - wtetzner 2y ago
    > I respectfully, but strongly, disagree. There's a reason most NBA players are over 2 meters tall, and one does not become taller with time, dedication nor focus. Being tall isn't a skill. I suspect you could be skillful enough at basketball to overcome the hight disadvantage. However, I think most people who might become that skillful see the high disadvantage (plus the general difficulty of becoming a pro basketball player) and take a different path through life. It's also possible that the amount of time that would be needed to grow your skill past the height disadvantage is too long, so it's not feasible to do it to gain a position in the NBA.
    - rafaelero 2y ago
      Intelligence is also not a skill, but the thing that makes you skillful in all cognitive tasks. Just like what height does to basketball players.
      - nemo 2y ago
        >Intelligence is also not skill, but the thing that makes you skillful in all cognitive tasks. Careful with that "all", even the most highly intelligent humans still have peaks and deficits in different domains.
        samatman 2y ago
        It's a matter of the definition. The general factor of intelligence, which is measured through various somewhat lossy proxies like IQ tests, is exactly the degree to which someone exceeds expectation on all cognitive tasks (or vice versa). The interesting finding is that this universal correlation is strong, real, and durable. Of course people in general have cognitive domains where they function better or worse than their g factor indicates, and that's before we get into the fact that intellectual task performance is strongly predicated on knowledge and practice, which is difficult to control for outside of tests designed (successfully, I must add) to do so.
- hilbert42 2y ago
  "What we should be teaching children is HOW to learn." Absolutely correct. And that begins with getting their interest, thus their attention; and that's a whole subject in and of itself.
- Gimpei 2y ago
  I don’t know if I agree. Grad school was profoundly humbling to me because it really showed me that there are a LOT of people out there that are just much much better than me at math. There are different levels of innate talent.
- red75prime 2y ago
  > The belief that some people have an innate skill that they are born with is deeply unhelpful. In practice your views result in stinting access of non-existent (in your opinion) talented children to a faster education track. They don't exist therefore they don't need different treatment (finer points get lost when the idea disseminates). Quite a hot theme in American education two (or so) years ago.
- scubbo 2y ago
  > an inbuilt ability to hyper focus on a topic, whether that topic be mathematics, Star Trek, dinosaurs or legacy console games from the 1980’s. I see you're familiar with Ryan North.
- myworkinisgood 2y ago
  Math is a stepping stone to critical thinking skills. And while one can probably learn those skills in any way, math forces you to learn those skills by learning the method of writing proofs. No other field forces you to push your critical thinking skills to the limit that math does.
solarized 2y ago
easy_things -> comfort_zone
cchi_co 2y ago
[dead]
faangguyindia 2y ago
[flagged]
- shrubhub 2y ago
  Most people don't try hard at the gym. Most people don't try hard at music. Most people aren't comedians. This reads like the foreword to the incel handbook.
  - theclansman 2y ago
    And that's obviously bad because incels are not real people with feelings.
    - shrubhub 2y ago
      It's bad because there's a strong whiff of being entitled to someone else's body.
    - sethammons 2y ago
      It is bad because it suffers from misattribution error, ultimately not leading to any solution and often making the situation worse. A downward spiral of misinterpreted signal
- lynx23 2y ago
  [dead]
- sureglymop 2y ago
  "A loser in societal view"... What does that objectively mean? That only reads like you had or have a low sense of self worth. It must've been your perceived definition of what society is because how could you have come to such a conclusion? I think I'd actually subconsciously tend more to viewing someone as "a loser" if they made such a statement because it comes off as self victimization (without an apparent explanation to an outside observer). And what's the shtick about girls? What are and were you looking for, love and a genuine relationship or attention to compensate for something? Personally I think your values and personality are what matter most and personality is usually what people fall in love with. Though charisma can help a lot to get the ball rolling. Most of what it takes is to treat people normally and nicely and you will have as much of a chance to find love as most people. Though respect from peers and attention from women ideally shouldn't be your driving force. I think curiosity and passion are much better driving forces that don't involve such external factors and possibilities for insecurities. Your post reads as if it expresses a frustration and a sense of entitlement. You may not be intrinsically entitled to the things you think you are. Think about that for a bit and try to be rational.
chipdart 2y ago
> I agree with the sentiment of this. I think our obsession with innate mathematical skill and genius is so detrimental to the growth mindset that you need to have in order to learn things. I would argue something different. The "skill" angle is just thinly veiled ladder-pulling. Sure, math is hard work, and there's a degree of prerequisites that need to be met to have things click, but to the mindset embodied by the cliche "X is left as an exercise for the reader" is just people rejoicing on the idea they can needlessly make life hard for the reader for no reason at all. Everyone is familiar with the "Ivory tower" cliche, but what is not immediately obvious is how the tower aspect originates as a self-promotion and self-defense mechanism to sell the idea their particular role is critical and everyone who wishes to know something is obligated to go through them to reach their goals. This mindset trickles down from the top towards lower levels. And that's what ultimately makes math hard. Case in point: linear algebra. The bulk of the material on the topic has been around for many decades, and the bulk of the course material,l used to teach that stuff, from beginner to advanced levels, is extraordinarily cryptic and mostly indecipherable. But then machine learning field started to take off and suddenly we started to see content addressing even advanced topics like dimensionality reduction using all kinds of subspace decomposition methods as someting clear and trivial. What changed? Only the type of people covering the topic.
- hehehheh 2y ago
  I think the ML people want to get (a narrow band) of stuff done and ivory towered people want to understand a prove things. ML is applied mathematic. Both are needed.
  - chipdart 2y ago
    > I think the ML people want to get (a narrow band) of stuff done and ivory towered people want to understand a prove things. ML is applied mathematic. Both are needed. I don't agree. First of all, ladder-pulling in math is observed at all levels, not only cutting-edge stuff. Secondly, it's in applied mathematics where pure math takes a queue onto where to focus effort. See how physics drives research into pure math.
- theclansman 2y ago
globalnode 2y ago
As a kid I was also terrible at maths, then later became obsessed with it as an adult because I didn't understand it, just like OP. It was the (second) best thing I've ever done! The world becomes a lot more interesting.
- doublerabbit 2y ago
  I haven't been able to grasp maths as a kid nor as an adult. I've tried night classes, tutors, activities. Nothing sticks. Even the standard 12x tables I struggle at. I want to understand it but my brain just can't understand the non-practicality side of things.
  - sethammons 2y ago
    My best friend was like that. Couldn't see the practicality until he got bit by a geology and water science bug. He went from calling me to get help figuring out percentages to doing chemistry equations in his head because he "got" the applicability. My brother's mom tutors math. One of her insights with a former student was that they were in need of forming some number sense. She started by walking them both out to the street: "how many tires are there on this street of parked cars?" The student, already flummoxed, started panic guessing. So she started with counting. For times tables, have you developed any intuition around it? For me, times tables are rectangles composed of unit squares and that helps with my intuition. Modern Common Core standards in the US focuses a lot on exposing different mental models to students. And after seeing the same 4x6 enough times your brain will automatically associate that with its solution. Instead of calculating, it is memorized. My brain doesn't require car tires, geology, or other practical needs: it likes puzzles. I struggle with medical stuff and I can feel my brain switching to meh-mode and hardly anything sticks. I don't know how many times I have been told about the different kinds of sugar and how your body uses that energy and I would still have to look it up.
    - doublerabbit 2y ago
      > For times tables, have you developed any intuition around it? I've tried different approaches. 4x3 being 3x4 But somehow I end up miscounting and giving the answer for 4x4 or be off a digit every-time. A good example was that I was at a brewery last night. They didn't do pint glasses but glasses of: 1/4, 1/2 and 2/3rd's. I thought 1/2 was more than 2/3rd's so I ordered a 1/2 rather than thinking I was getting more. However I was unable to visual how 2/3 is more than 1/2 when 1/2 is half a pint, or half a glass. My visual capabilities are great at others but just couldn't formulate the equation of 2/3 is more than 1/2. Very simple stuff, but it just doesn't meld.
khafra 2y ago
> If it's easy, then it means you already know this material, and you're wasting your time. One thing I'm anticipating from LLM-based tutoring is an adaptive test that locates someone's frontier of knowledge, and plots an efficient route toward any capability goal through the required intermediate skills. Trying to find the places where math starts getting difficult by skimming through textbooks takes too long; especially for those of us who were last in school decades ago.
- llm_trw 2y ago
  >and plots an efficient route toward any capability goal through the required intermediate skills. LLMs currently can't find efficient paths longer than 5 hops when given a simple itinerary. Expecting them to do anything but a tactical explanation of issues they have seen in training is extremely naive with something as high dimensional as math.
- sn9 2y ago
  LLMs hallucinate and are completely the wrong tool for this. People need to learn about the history of AI. Expert-systems using techniques from the 80s are doing this right now [0]. [0] https://www.mathacademy.com/how-our-ai-works https://www.mathacademy.com/how-our-ai-works
bamboozled 2y ago
How have you been working on it? Asking for a friend ;)
- sn9 2y ago
  I'd strongly recommend Math Academy for at least 30 minutes per day.
bdjsiqoocwk 2y ago
It's funny because I've had the opposite heuristic most of my line: the things I want to do most are whatever is hardest. This worked great for building my maths and physics skills and knowledge. But when I started focusing on making money I've come to believe it's a bad heuristic for that purpose.
wslh 2y ago
Amazingly, I believe that today, with the myriad of tools available, anyone can advance in sciences like mathematics at their own pace by combining black-box and white-box approaches. Computers, in this context, could serve as your personal “Batcomputer” [1]. That said, I would always recommend engaging in social sciences with others, not working alone. Who knows? You might also contribute meaningfully to these fields as you embrace your own unique path. [1] https://dc.fandom.com/wiki/Batcomputer https://dc.fandom.com/wiki/Batcomputer
tgv 2y ago
I cannot agree. It's just "feel-good thinking." "Everybody can do everything." Well, that's simply not true. I'm fairly sure you (yes, you in particular) can't run the 100m in less than 10s, no matter how hard you trained. And the biological underpinning of our capabilities doesn't magically stop at the brain-blood barrier. We all do have different brains. I've taught math to psychology students, and they just don't get it. I remember the frustration of the section's head when a student asked "what's a square root?" We all know how many of our fellow pupils struggled with maths. I'm not saying they all lacked the capability to learn it, but it can't be the case they all were capable but "it was the teacher's fault". Even then, how do you explain the difference between those who struggled and those who breezed through the material? Or let's try other topics, e.g. music. Conservatory students study quite hard, but some are better than others, and a select few really shine. "Everyone is capable of playing Rachmaninov"? I don't think so. So no, unless you've placed the bar for "mathetical skill" pretty low, or can show me proper evidence, I'm not going to believe it. "Everyone is capable of..." reeks of bullshit.
- nestes 2y ago
  Not the original poster, but I want to push back on one thing -- being capable of something and being one of the best in the world at something are hugely different. Forgive me if I'm putting words in your math -- you mentioned "placing the bar for mathematical skill pretty" low but also mentioned running a sub-10s 100m. If, correspondingly, your notion of mathematical success is being Terence Tao, then I envy your ambition. I do broadly agree with your position that some people are going to excel where others fail. We know there trivially exist people with significant disabilities that will never excel in certain activities. What the variance is on "other people" (a crude distinction) I hesitate to say. And whatever the solution is, if there is even a solution, I'd at least like for the null hypothesis to be "this is possible, we just may need to change our approach or put more time in". On a slightly more philosophical note, I firmly believe that it is important to believe some things that are not necessarily true -- let's call this "feel-good thinking". If someone is truly putting significant dedicated effort in and not getting results, that is a tragedy. I would, however, greatly prefer that scenario to the one in which people are regularly told, "well, you could just be stupid." That is a self-fulfilling prophecy.
dghughes 2y ago
I took an online electronics tech course 15 years ago and what got me was my math skills were atrocious. Not shocking since like learning a new language or music use it or lose it is the obvious answer to why I sucked. I spent half my time re-learning math just so I could complete the course.
setopt 2y ago
> A mindset I've had in the past is that "if it's hard, then that means you've hit your ceiling and you're wasting your time." But really, the opposite is true. If it's easy, then it means you already know this material, and you're wasting your time. It’s a well-established effect in pedagogics that learning vs. difficulty has a non-monotonic relationship, where you don’t learn efficiently if the material is either too hard or too easy compared to your current level. There is an optimum learning point somewhere in-between where the material is “challenging” – but neither “trivial” nor “insurmountable” – to put it that way.
willtemperley 2y ago
> I think our obsession with innate mathematical skill and genius is so detrimental to the growth mindset that you need to have in order to learn things. Absolutely. There's also a pernicious idea that only young people can master complex maths or music. This is a self-fulfilling prophecy - why bother try if you're going to fail due to being old? Or perhaps it's an elitist psy-op, giving the children of wealthy parents further advantage because of course no-one can catch up.
User23 2y ago
I grow increasingly convinced that the difference in “verbal” and “mathematical” intelligence is in many ways a matter of presentation. While it’s indisputable that terse symbolic formalisms have great utility, one can capture all the same information verbally. This is perhaps most evident in formal logic. It’s not hard to imagine a restricted formalized subset of natural language that is amenable to mechanical manipulation that is isomorphic to say modal logic. And finally, for logic at least, there is something of a third way. Diagrammatic logical systems such as Existential Graphs capture the full power of propositional, predicate, and modal logic in a way that is neither verbal nor conventionally symbolic.
dkarl 2y ago
> If it's easy, then it means you already know this material, and you're wasting your time I think that's also a trap. Even professional athletes spend a little bit of their time doing simple drills: shooting free throws, fielding fly balls, hitting easy groundstrokes. Sometimes your daily work keeps up the "easy" skills, but if you haven't used a skill in a while, it's not a bad idea to do some easy reps before you try to combine it with other skills in difficult ways.
ericmcer 2y ago
I am trying to stress pushing through these barriers with my kid right now. The second her brain encounters something beyond its current sphere she just shuts down. I have heard it is the ego protecting itself by rejecting something outright rather than admitting you can't do it. It still happens to me all the time. My favorite technique was one I heard from a college professor. He starts reading while filling a notepad with sloppy notes, once a page is filled he just throws it away. He claimed it was the fastest way to "condition his brain to the problem space". More than the exercise I like the idea that your brain cannot even function in that space until it has been conditioned.
beezlewax 2y ago
I'd like to improve my mathematical knowledge (which has degraded to basically zero). Can you talk about the path or resources you are using to improve here?
- sn9 2y ago
  If you know how to multiply and divide, Math Academy will take you to college level math pretty quickly.

by gsabo 2y ago

junto 2y ago

> I agree with the sentiment of this. I think our obsession with innate ~~mathematical~~ skill and genius is so detrimental to the growth mindset that you need to have in order to learn things. I strongly believe that the average human being can be exceptional in any niche topic given enough time, dedication and focus. The author of the book has picked out mathematics because that was what he was interested in. The reality is that this rule applies to everything. The belief that some people have an innate skill that they are born with is deeply unhelpful. Whilst some people (mostly spectrum) do seem have an innate talent, I would argue that it is more an inbuilt ability to hyper focus on a topic, whether that topic be mathematics, Star Trek, dinosaurs or legacy console games from the 1980’s. I think we do our children a disservice by convincing them that some of their peers are just “born with it”, because it discourages them from continuing to try. What we should be teaching children is HOW to learn. At the moment it’s a by-product of learning about some topic. If we look at the old adage “feed a man a fish”, the same is true of learning. “Teach someone mathematics and they will learn mathematics. Teach someone to learn and they will learn anything”.

ponderings 2y ago
I've had some success converting people by telling them others had convinced them they were stupid. They usually have one or two things they are actually good at, like a domain they flee to. I simply point out how everything else is exactly like [say] playing the guitar. Eventually you will be good enough to sing at the same time. Clearly you already are a genius. I cant even remember the most basic cords or lyrics because I've never bothered with it. I met the guitar guy a few years later outside his house. He always had just one guitar but now owned something like 20, something like a hundred books about music. Quite the composer. It looked and sounded highly sophisticated. The dumb guy didn't exist anymore.
- shrubhub 2y ago
  But also, some people are stupid, right?
  - ajuc 2y ago
    The inborn part is how quickly you get results (good or bad). Stupidity is the results. If we spent 50% of time thinking productively - inborn thinking speed would matter. But in my estimate even 5% is generous. So it matters far more what kind of feedback you have to filter out the wrong results, and how much time you spend thinking - than how quickly you can do it. Also practice helps with speed.
  - yawpitch 2y ago
    Intellect is like a gas, it will expand to fill its container. The container, in humans, is epigenetic and social — genetics only determines how hot or cold your gas is, ie how fast and how fluidly it expands, but you’re taught your limits — it’s best to see stupid as not how limited you are relative to other but what limits you have now and may abandon in the future. That said, some people received a smaller starting container, and might need some help cracking it. That’s the work of those who think they’ve found a bigger one.
  - deleted 2y ago
    [deleted]
shrubhub 2y ago
So you're saying success at maths isn't an inbuilt ability. Instead, it depends on an (inbuilt) ability to hyper focus... Which you are just born with?
- elbear 2y ago
  Not even that. It depends on the learned ability to stop pushing yourself when your focus is wavering. That's how you develop aversion towards the topic. Let your natural curiosity draw you to particular topics (that's why you might have a winding road through the subject).
  - air7 2y ago
    parent comment was a bit tounge-in-cheek but I'll continue the sentiment: You're saying that the curiosity is "natural" hence one is either born with it or not. I think that there is no way around the fact that it will be hard and uncomfortable to mimic the progress of someone that has an innate inclination towards a subject (be it talent or focus or curiosity) artificially.
    - card_zero 2y ago
      Hey, that doesn't have to be what "natural curiosity" means. Besides which it makes no sense to say people are born with complex interests. I mean, OK, your genes might incline you a certain way, but that's not the same thing. Being interested in a subject is massively helpful to learning it. But interest arises circumstantially, it's an emotion. The grim reality that it would be really useful to you to learn a certain subject does not necessarily make you interested in the subject, unfortunately. (Perhaps "financially interested", but that's something else.)
      - ericd 2y ago
        I think there is some natural inclination towards abstract thinking versus more grounded in reality, just judging based on kids I know. Some of them really enjoy playing with ideas in their heads, some enjoy playing with things they can touch more. It seems likely that those different attractions would express themselves in how much they practice different things as time goes on.
diffeomorphism 2y ago
Caveat here is that "talent" and "dedication" is linked to speed at least in the beginning. For instance, any student can learn calculus given enough time and advice even starting from scratch. However, the syllabus wants all this to happen in one semester. This gives you vicious and virtuous cycles: Students' learning speed increases with time and past success. So "talented" students learn quickly and have extra time to further explore and improve, leading to further success. Students who struggle with the time constraint are forced to take shortcuts like memorizing "magic formulas" without having time to really understand. Trying to close that gap is very hard work.
- drbig 2y ago
  Thank you for the insight that academic (in a very broad sense) bulk-fixed-time approach does in fact produce both of the cycles, and the gap indeed only widens with time (speaking from personal experience, especially from my life as an undergrad student). Reminds me of my personal peeve that "studying" should not be "being taught", studying is pursuit of understanding, "being taught" is what happens in primary school (and I'm aware I'm simplifying here).
  - blackbear_ 2y ago
    I would say that you could generalize this even further outside of education. A few early successes in life can greatly accelerate one's trajectory, while early failures could set one many years back. And this happens independently of whether those events are due to skill or luck.
- jvanderbot 2y ago
  Indeed, speed is often read as "smarts" whereas I would maintain it's much more often "preparation". We can't on one hand believe in the plasticity and retrainability of the mind, while simultaneously believing that speed is something only a few are born with. On the nature/nurture scale, I think it's 20/80 or so - but prodigies and geniuses have an interest that keeps them thinking and learning 10x or 100x more than other kids, and a little bump that lets them get started easier and therefore much earlier. This sets them up for fantastic success very quickly. [1] shows a great example of this. I'm fond of saying "You can do anything you want, but wanting is the hard part", because to truly be a grandmaster, genius-level mathematician, olympic athlete, etc, requires a dedication and amount of preparation that almost nobody can manage. Starting late, with emotional baggage, kids, and having to spend 5 years relearning how to learn? Forget it. 1. https://danielkarim.com/how-to-become-a-genius-the-polgar-experiment/ https://danielkarim.com/how-to-become-a-genius-the-polgar-ex...
graemep 2y ago
> The author of the book has picked out mathematics because that was what he was interested in. The reality is that this rule applies to everything. My first thought when the article got to the dialog between logic and intuition bit was that the same is true for school level physics.
LoganDark 2y ago
> Whilst some people (mostly spectrum) do seem have an innate talent I think the only thing in autism that I'd call an innate talent is detail-oriented thinking by default. It'd be the same type of "innate talent" as, say, synesthesia, or schizophrenia: a side effect of experiencing the world differently.
- yawpitch 2y ago
  > a side effect of experiencing the world differently A side effect for which there is a substantial, lifelong, and most importantly wide cost, even if it occasionally confers usually small, usually fleeting, and most importantly narrow advantage.
  - sethammons 2y ago
    At such cost with such narrow advantage, why has it persisted so pervasively? I would counter that the advantage is wider and the cost narrower than your current value system is allowing you to accept.
    - LoganDark 2y ago
      Natural selection doesn't care about cost or advantage, only reproduction.
      - sethammons 2y ago
        It is the sum of costs and advantages that lead to reproductive success. The trait is still here and still prevalent meaning people are still getting laid and starting families and presumably leading fulfilling lives. I'm not sure what you are trying to say.
        LoganDark 2y ago
        > I'm not sure what you are trying to say. I'm saying, if it doesn't ruin lives to the point of preventing reproduction, then it stays in the gene pool. Basically, I'm saying this: > The trait is still here and still prevalent meaning people are still getting laid and starting families and presumably leading fulfilling lives.
Malidir 2y ago
>The belief that some people have an innate skill that they are born with is deeply unhelpful. Whilst some people (mostly spectrum) do seem have an innate talent, I would argue that it is more an inbuilt ability to hyper focus on a topic, whether that topic be mathematics, Star Trek, dinosaurs or legacy console games from the 1980’s. Nonsense! The brain you are born with materially dictates the ceiling of your talent. A person with average ability can with dedication and focus over many years become reasonably good, but a genius can do the same in 1 year and at a young age. We have an education system which gives an A Grade if you pass the course, but 1 person may put on 5 hours a week and the other works day and night.
- PittleyDunkin 2y ago
  What makes you think that "genius" is nature and not nurture? I'd love to see the evidence for this; i'm deeply skeptical. Edit: I don't mean to argue that there aren't genetics involved in determining aptitude on certain tasks, of course, but the assumption that genius is born and never made feels like a very shallow understanding of the capacity of man.
  - Malidir 2y ago
    > I'd love to see the evidence for this; i'm deeply skeptical. Cool, come and have a coffee with me :) I have older and younger siblings and was the one randomly blessed. Whereas most recognised talents are associated with hard work and so there is then this visible link, I am a good example as I did the bare minimum throughout education (and beyond...). The way my brain processes and selectively discards/stores the information it receives is very different to majority of the population. I have no control over it. I take zero credit for any of my achievments - I regularly meet intelligent people near to retirement who have been to a tier 1 university, may have PHDs, worked 60 hours a week since they were born, been on course and what not and cannot reach the levels I can. My nurturing was no different to siblings/peers (and was terrible!) Note: I have my weaknesses too, but as a whole, I am exceptional. Not through effort!! Completely random - neither of my parents are intelligent and nothing up the ancestary tree as far as I know.
dennis_jeeves2 2y ago
>I strongly believe that the average human being can be exceptional in any niche topic given enough time, dedication and focus. And this also gives the proponent (you in this case) an excuse to blame a person for not focusing hard enough or not being dedicated enough if they don't grasp the basics, let alone excel.
InDubioProRubio 2y ago
The boostrap skill is the ability to obsess over something. To focus and self-reward on anything is a heaven sent. Good thing we do not medicate that if we are unable to get that energy on the road, that base skill.
sdeframond 2y ago
> I strongly believe that the average human being can be exceptional in any niche topic given enough time, dedication and focus. I respectfully, but strongly, disagree. There's a reason most NBA players are over 2 meters tall, and one does not become taller with time, dedication nor focus. It might be different for intellectual skills but I am not that sure. Almost anyone can become decent at almost anything though. Which is good already!
- wtetzner 2y ago
  > I respectfully, but strongly, disagree. There's a reason most NBA players are over 2 meters tall, and one does not become taller with time, dedication nor focus. Being tall isn't a skill. I suspect you could be skillful enough at basketball to overcome the hight disadvantage. However, I think most people who might become that skillful see the high disadvantage (plus the general difficulty of becoming a pro basketball player) and take a different path through life. It's also possible that the amount of time that would be needed to grow your skill past the height disadvantage is too long, so it's not feasible to do it to gain a position in the NBA.
  - rafaelero 2y ago
    Intelligence is also not a skill, but the thing that makes you skillful in all cognitive tasks. Just like what height does to basketball players.
    - nemo 2y ago
      >Intelligence is also not skill, but the thing that makes you skillful in all cognitive tasks. Careful with that "all", even the most highly intelligent humans still have peaks and deficits in different domains.
      - samatman 2y ago
        It's a matter of the definition. The general factor of intelligence, which is measured through various somewhat lossy proxies like IQ tests, is exactly the degree to which someone exceeds expectation on all cognitive tasks (or vice versa). The interesting finding is that this universal correlation is strong, real, and durable. Of course people in general have cognitive domains where they function better or worse than their g factor indicates, and that's before we get into the fact that intellectual task performance is strongly predicated on knowledge and practice, which is difficult to control for outside of tests designed (successfully, I must add) to do so.
hilbert42 2y ago
"What we should be teaching children is HOW to learn." Absolutely correct. And that begins with getting their interest, thus their attention; and that's a whole subject in and of itself.
Gimpei 2y ago
I don’t know if I agree. Grad school was profoundly humbling to me because it really showed me that there are a LOT of people out there that are just much much better than me at math. There are different levels of innate talent.
red75prime 2y ago
> The belief that some people have an innate skill that they are born with is deeply unhelpful. In practice your views result in stinting access of non-existent (in your opinion) talented children to a faster education track. They don't exist therefore they don't need different treatment (finer points get lost when the idea disseminates). Quite a hot theme in American education two (or so) years ago.
scubbo 2y ago
> an inbuilt ability to hyper focus on a topic, whether that topic be mathematics, Star Trek, dinosaurs or legacy console games from the 1980’s. I see you're familiar with Ryan North.
myworkinisgood 2y ago
Math is a stepping stone to critical thinking skills. And while one can probably learn those skills in any way, math forces you to learn those skills by learning the method of writing proofs. No other field forces you to push your critical thinking skills to the limit that math does.

solarized 2y ago

easy_things -> comfort_zone

cchi_co 2y ago

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faangguyindia 2y ago

[flagged]

shrubhub 2y ago
Most people don't try hard at the gym. Most people don't try hard at music. Most people aren't comedians. This reads like the foreword to the incel handbook.
- theclansman 2y ago
  And that's obviously bad because incels are not real people with feelings.
  - shrubhub 2y ago
    It's bad because there's a strong whiff of being entitled to someone else's body.
  - sethammons 2y ago
    It is bad because it suffers from misattribution error, ultimately not leading to any solution and often making the situation worse. A downward spiral of misinterpreted signal
lynx23 2y ago
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sureglymop 2y ago
"A loser in societal view"... What does that objectively mean? That only reads like you had or have a low sense of self worth. It must've been your perceived definition of what society is because how could you have come to such a conclusion? I think I'd actually subconsciously tend more to viewing someone as "a loser" if they made such a statement because it comes off as self victimization (without an apparent explanation to an outside observer). And what's the shtick about girls? What are and were you looking for, love and a genuine relationship or attention to compensate for something? Personally I think your values and personality are what matter most and personality is usually what people fall in love with. Though charisma can help a lot to get the ball rolling. Most of what it takes is to treat people normally and nicely and you will have as much of a chance to find love as most people. Though respect from peers and attention from women ideally shouldn't be your driving force. I think curiosity and passion are much better driving forces that don't involve such external factors and possibilities for insecurities. Your post reads as if it expresses a frustration and a sense of entitlement. You may not be intrinsically entitled to the things you think you are. Think about that for a bit and try to be rational.

chipdart 2y ago

> I agree with the sentiment of this. I think our obsession with innate mathematical skill and genius is so detrimental to the growth mindset that you need to have in order to learn things. I would argue something different. The "skill" angle is just thinly veiled ladder-pulling. Sure, math is hard work, and there's a degree of prerequisites that need to be met to have things click, but to the mindset embodied by the cliche "X is left as an exercise for the reader" is just people rejoicing on the idea they can needlessly make life hard for the reader for no reason at all. Everyone is familiar with the "Ivory tower" cliche, but what is not immediately obvious is how the tower aspect originates as a self-promotion and self-defense mechanism to sell the idea their particular role is critical and everyone who wishes to know something is obligated to go through them to reach their goals. This mindset trickles down from the top towards lower levels. And that's what ultimately makes math hard. Case in point: linear algebra. The bulk of the material on the topic has been around for many decades, and the bulk of the course material,l used to teach that stuff, from beginner to advanced levels, is extraordinarily cryptic and mostly indecipherable. But then machine learning field started to take off and suddenly we started to see content addressing even advanced topics like dimensionality reduction using all kinds of subspace decomposition methods as someting clear and trivial. What changed? Only the type of people covering the topic.

hehehheh 2y ago
I think the ML people want to get (a narrow band) of stuff done and ivory towered people want to understand a prove things. ML is applied mathematic. Both are needed.
- chipdart 2y ago
  > I think the ML people want to get (a narrow band) of stuff done and ivory towered people want to understand a prove things. ML is applied mathematic. Both are needed. I don't agree. First of all, ladder-pulling in math is observed at all levels, not only cutting-edge stuff. Secondly, it's in applied mathematics where pure math takes a queue onto where to focus effort. See how physics drives research into pure math.
theclansman 2y ago

globalnode 2y ago

As a kid I was also terrible at maths, then later became obsessed with it as an adult because I didn't understand it, just like OP. It was the (second) best thing I've ever done! The world becomes a lot more interesting.

doublerabbit 2y ago
I haven't been able to grasp maths as a kid nor as an adult. I've tried night classes, tutors, activities. Nothing sticks. Even the standard 12x tables I struggle at. I want to understand it but my brain just can't understand the non-practicality side of things.
- sethammons 2y ago
  My best friend was like that. Couldn't see the practicality until he got bit by a geology and water science bug. He went from calling me to get help figuring out percentages to doing chemistry equations in his head because he "got" the applicability. My brother's mom tutors math. One of her insights with a former student was that they were in need of forming some number sense. She started by walking them both out to the street: "how many tires are there on this street of parked cars?" The student, already flummoxed, started panic guessing. So she started with counting. For times tables, have you developed any intuition around it? For me, times tables are rectangles composed of unit squares and that helps with my intuition. Modern Common Core standards in the US focuses a lot on exposing different mental models to students. And after seeing the same 4x6 enough times your brain will automatically associate that with its solution. Instead of calculating, it is memorized. My brain doesn't require car tires, geology, or other practical needs: it likes puzzles. I struggle with medical stuff and I can feel my brain switching to meh-mode and hardly anything sticks. I don't know how many times I have been told about the different kinds of sugar and how your body uses that energy and I would still have to look it up.
  - doublerabbit 2y ago
    > For times tables, have you developed any intuition around it? I've tried different approaches. 4x3 being 3x4 But somehow I end up miscounting and giving the answer for 4x4 or be off a digit every-time. A good example was that I was at a brewery last night. They didn't do pint glasses but glasses of: 1/4, 1/2 and 2/3rd's. I thought 1/2 was more than 2/3rd's so I ordered a 1/2 rather than thinking I was getting more. However I was unable to visual how 2/3 is more than 1/2 when 1/2 is half a pint, or half a glass. My visual capabilities are great at others but just couldn't formulate the equation of 2/3 is more than 1/2. Very simple stuff, but it just doesn't meld.

khafra 2y ago

> If it's easy, then it means you already know this material, and you're wasting your time. One thing I'm anticipating from LLM-based tutoring is an adaptive test that locates someone's frontier of knowledge, and plots an efficient route toward any capability goal through the required intermediate skills. Trying to find the places where math starts getting difficult by skimming through textbooks takes too long; especially for those of us who were last in school decades ago.

llm_trw 2y ago
>and plots an efficient route toward any capability goal through the required intermediate skills. LLMs currently can't find efficient paths longer than 5 hops when given a simple itinerary. Expecting them to do anything but a tactical explanation of issues they have seen in training is extremely naive with something as high dimensional as math.
sn9 2y ago
LLMs hallucinate and are completely the wrong tool for this. People need to learn about the history of AI. Expert-systems using techniques from the 80s are doing this right now [0]. [0] https://www.mathacademy.com/how-our-ai-works https://www.mathacademy.com/how-our-ai-works

bamboozled 2y ago

How have you been working on it? Asking for a friend ;)

sn9 2y ago
I'd strongly recommend Math Academy for at least 30 minutes per day.

bdjsiqoocwk 2y ago

It's funny because I've had the opposite heuristic most of my line: the things I want to do most are whatever is hardest. This worked great for building my maths and physics skills and knowledge. But when I started focusing on making money I've come to believe it's a bad heuristic for that purpose.

wslh 2y ago

Amazingly, I believe that today, with the myriad of tools available, anyone can advance in sciences like mathematics at their own pace by combining black-box and white-box approaches. Computers, in this context, could serve as your personal “Batcomputer” [1]. That said, I would always recommend engaging in social sciences with others, not working alone. Who knows? You might also contribute meaningfully to these fields as you embrace your own unique path. [1] https://dc.fandom.com/wiki/Batcomputer https://dc.fandom.com/wiki/Batcomputer

tgv 2y ago

I cannot agree. It's just "feel-good thinking." "Everybody can do everything." Well, that's simply not true. I'm fairly sure you (yes, you in particular) can't run the 100m in less than 10s, no matter how hard you trained. And the biological underpinning of our capabilities doesn't magically stop at the brain-blood barrier. We all do have different brains. I've taught math to psychology students, and they just don't get it. I remember the frustration of the section's head when a student asked "what's a square root?" We all know how many of our fellow pupils struggled with maths. I'm not saying they all lacked the capability to learn it, but it can't be the case they all were capable but "it was the teacher's fault". Even then, how do you explain the difference between those who struggled and those who breezed through the material? Or let's try other topics, e.g. music. Conservatory students study quite hard, but some are better than others, and a select few really shine. "Everyone is capable of playing Rachmaninov"? I don't think so. So no, unless you've placed the bar for "mathetical skill" pretty low, or can show me proper evidence, I'm not going to believe it. "Everyone is capable of..." reeks of bullshit.

nestes 2y ago
Not the original poster, but I want to push back on one thing -- being capable of something and being one of the best in the world at something are hugely different. Forgive me if I'm putting words in your math -- you mentioned "placing the bar for mathematical skill pretty" low but also mentioned running a sub-10s 100m. If, correspondingly, your notion of mathematical success is being Terence Tao, then I envy your ambition. I do broadly agree with your position that some people are going to excel where others fail. We know there trivially exist people with significant disabilities that will never excel in certain activities. What the variance is on "other people" (a crude distinction) I hesitate to say. And whatever the solution is, if there is even a solution, I'd at least like for the null hypothesis to be "this is possible, we just may need to change our approach or put more time in". On a slightly more philosophical note, I firmly believe that it is important to believe some things that are not necessarily true -- let's call this "feel-good thinking". If someone is truly putting significant dedicated effort in and not getting results, that is a tragedy. I would, however, greatly prefer that scenario to the one in which people are regularly told, "well, you could just be stupid." That is a self-fulfilling prophecy.

dghughes 2y ago

I took an online electronics tech course 15 years ago and what got me was my math skills were atrocious. Not shocking since like learning a new language or music use it or lose it is the obvious answer to why I sucked. I spent half my time re-learning math just so I could complete the course.

setopt 2y ago

> A mindset I've had in the past is that "if it's hard, then that means you've hit your ceiling and you're wasting your time." But really, the opposite is true. If it's easy, then it means you already know this material, and you're wasting your time. It’s a well-established effect in pedagogics that learning vs. difficulty has a non-monotonic relationship, where you don’t learn efficiently if the material is either too hard or too easy compared to your current level. There is an optimum learning point somewhere in-between where the material is “challenging” – but neither “trivial” nor “insurmountable” – to put it that way.

willtemperley 2y ago

> I think our obsession with innate mathematical skill and genius is so detrimental to the growth mindset that you need to have in order to learn things. Absolutely. There's also a pernicious idea that only young people can master complex maths or music. This is a self-fulfilling prophecy - why bother try if you're going to fail due to being old? Or perhaps it's an elitist psy-op, giving the children of wealthy parents further advantage because of course no-one can catch up.

User23 2y ago

I grow increasingly convinced that the difference in “verbal” and “mathematical” intelligence is in many ways a matter of presentation. While it’s indisputable that terse symbolic formalisms have great utility, one can capture all the same information verbally. This is perhaps most evident in formal logic. It’s not hard to imagine a restricted formalized subset of natural language that is amenable to mechanical manipulation that is isomorphic to say modal logic. And finally, for logic at least, there is something of a third way. Diagrammatic logical systems such as Existential Graphs capture the full power of propositional, predicate, and modal logic in a way that is neither verbal nor conventionally symbolic.

dkarl 2y ago

> If it's easy, then it means you already know this material, and you're wasting your time I think that's also a trap. Even professional athletes spend a little bit of their time doing simple drills: shooting free throws, fielding fly balls, hitting easy groundstrokes. Sometimes your daily work keeps up the "easy" skills, but if you haven't used a skill in a while, it's not a bad idea to do some easy reps before you try to combine it with other skills in difficult ways.

ericmcer 2y ago

I am trying to stress pushing through these barriers with my kid right now. The second her brain encounters something beyond its current sphere she just shuts down. I have heard it is the ego protecting itself by rejecting something outright rather than admitting you can't do it. It still happens to me all the time. My favorite technique was one I heard from a college professor. He starts reading while filling a notepad with sloppy notes, once a page is filled he just throws it away. He claimed it was the fastest way to "condition his brain to the problem space". More than the exercise I like the idea that your brain cannot even function in that space until it has been conditioned.

beezlewax 2y ago

I'd like to improve my mathematical knowledge (which has degraded to basically zero). Can you talk about the path or resources you are using to improve here?

sn9 2y ago
If you know how to multiply and divide, Math Academy will take you to college level math pretty quickly.