7 ms·

I Rewired My Brain to Become Fluent in Math (2014)

262 points by paublyrne 10y ago

closed 10y ago
> By interleaving my learning—in other words, practicing so that I knew not only when to use that word, but when not to use it, or to use a different variant of it—I was actually using the same approaches that expert practitioners use to learn in math and science. This is huge! Even if you learn something so that you can use it without fail today, if you interleave your practice of using it (today) with other things, you'll do much better a week from now.
- Jugurtha 10y ago
  Interleaving has served me very well during my second year of Engineering. I hadn't attended that much and had a grade of 3/20. There were the final exams where the materials of the whole year was fair game. I buckled down for a month with a friend at my sister's house which was empty. I eliminated the modules with diminishing returns that I had passed or where I was close (easier to go from 0/20 to 12/20 than it is to go from 8/20 to 20/20 for the same amount of points). I was left with five modules I hadn't attended: Numerical Analysis (ANAI), Rational Mechanics(MECA), Strength of Materials(RDM), Vibrations-Waves-and-Propagation(VOP), and Atomic and Nuclear Physics(PAN). I drew a pentagon and organized the modules. Starting at the top, going counter-clockwise: VOP, ANAI, PAN, MECA, RDM. Each day, I'd do two modules: Day1: VOP-ANAI Day2: PAN-MECA Day3: RDM-VOP Day4: ANAI-PAN Day5: MECA-RDM Day6: Restart cycle. Many benefits: - You only do a module for half a day. Intensely. Then switch to another module and you sort of hustle your brain for a fresh start. It's not tired because you're doing something else now. "It's not like you've been studying all day" is the impression. - Mixing modules gives new insights. Especially in second year, there's a bootstrapping phenomenon: to understand a module of Physics, you had to understand a module in Maths. - You study a module hard. You don't see it the next day, but the day after. Not too soon to be sick of it and burn out, but not too far in the future not to remember any of it. The problem with the methods most other students followed was that it violated their brains and common sense: they'd do one module exclusively for a week (all chapters, all exercises). Then go on to the next one and do the same. By the time the exam comes: they're sick of the modules, and they remember nothing for the most part because it's been 3 weeks since they've last done the first module they started with. I, on the other hand, have seen any given module at most 3 days before. This allowed me to study 13 hours per day during a month without burnout (reading the course material for the first time, going over the exercises and exams, etc). The key was keeping a schedule. Up at 0500. 0500 - 0700: Study. 0700 - 0800: Breakfast. 0800 - 1200: Study. 1200 - 1300: Lunch and nap. 1300 - 1700: Study. 1700 - 1800: Afternoon snack and chill. 1800 - 2100: Study. 2100 - 2200: Dinner. 2200 lights out, going to sleep.
  - deleted 10y ago
    [deleted]
imjk 10y ago
I've realized lately that I often fool myself into thinking I'm proficient in some subject by picking up on concepts quickly. I think I "get" it because I can understand something on a conceptual level, but when it comes to practice, my deficiencies become apparent. I guess the tricky part is to push myself past those initial concepts to delve deeper into the subjects with practice. I need to slow down and remind myself that I don't really "get" it just because I can understand the concepts in a very broad sense.
- Waterluvian 10y ago
  Binary trees was that for me. I listened to lectures and understood them very well from a conceptual point of view. But once I started writing them from scratch as an exercise did I learn that understanding the theory alone was woefully insufficient.
  - trentmb 10y ago
    Maybe you just didn't understand the "theory" as well as you thought you did. I fell into the "it makes sense when we go over it in class, but not when I do it at home" trap often.
- stephengillie 10y ago
  When you're feeling proficient and confident in something, move your goalposts, and force yourself to take the next step: * Become proficient not just the concept or task, but good enough to where you can teach it to someone else, or write a clear and concise KB article. * Implement it (perform the task) repeatedly, with consistent outcomes. * Automate the process. * Use this as one part of a much more complex system.
- chrismealy 10y ago
  I've often had the experience of thinking I understood something well up until the point I tried to explain it to somebody. Teaching is the best way the learn. I think the "smart" person in a study group often gets the most out of it.
JamilD 10y ago
I've realized exactly the same thing. A starting intuition is necessary, but not sufficient, for understanding. I can watch as many lectures as I want, but nothing beats sitting down with a pen and a piece of paper, playing around with equations and developing a true, intimate understanding.
- pm90 10y ago
  This is why a lot of the best mathematics books won't just state theorems, but will actually heavily encourage the reader to solve problems as well, as that is considered an indispensable part of the learning process.
chrismealy 10y ago
The author is not wrong to emphasize the fundamental necessity of drilling, but in her article it sounds like she, having memorized basic facts (in Russian and math), ultimately achieved fluency through play.
- meesterdude 10y ago
  That was my takeaway as well. The author played with the equation f=ma, and understood it inside and out in various scenarios.
nicolas_t 10y ago
This is related to the Curse of the Gifted. When I was a kid, I could grasp concepts easily and I understood maths very quickly so I didn't really bother doing things like homework or actually studying. I then went to a decent university (a French Grande Ecole) and for the first year, I was still doing okish but I went from being a student who always had good results to doing average. Then, the second year came, and just understanding the concepts without cultivating fluency by practicing wasn't enough anymore and I failed hard. I hadn't learned how to learn and while I understood the concepts and could easily follow when the teacher solved a problem together with us, I had difficulties doing it on my own. I worked doing exercises and was able to pass but time and time again in my professional life, I've had the same issue where I tend to rely too much on my intuitive understanding until it fails. I'm not sure how to help kids not to go down this path. As a kid, I would avoid any rote memorization and would probably not do any non graded exercise since I knew that I understood (and also since as a geek wanting to fit in, I tried to be more accepted by my peers by purposefully not doing my homework). In the end, I think the key is play and giving maybe challenging exercises that forces the kid to use his newly found understanding would be a way to get them used to not just rely on their intuition understanding.
- goodells 10y ago
  I'm a student in university now, and I can relate to your experience. What helped me a lot as a kid was being motivated to learn things when it didn't seem like "learning". For example, I was able to get the hang of programming by playing a game that incorporated it, and it succeeded because it got me excited about doing cool things. Maybe this kind of "gamification" could be more useful than just adding points and rules to things to make people compete.
- camerintinbun 10y ago
  I had a similar path as yours. Never had to work all that hard through school, did a degree at a university in the sciences which was somewhat the same (had to try a little harder after the reality settled in from freshman year...), but I had always just assumed that was the next step. This was just something I had to do to move on, so a high mark was the end result. I was thrilled to graduate, took a job out in a semi-related field for about 5-6 years, then slowly began to get this feeling of "being dumbed down". Day by day, doing the same or similar things, not having to learn new stuff; it took a toll. I started listening to podcasts, and learning about all of the advances in science was enough to get me back into school and apply for a graduate degree. Here is where I think this is something that people have to recognize they want for themselves. Starting my grad classes with other students, mostly fresh from undergrad, I could see a change in the value I took from the classes compared to undergrads. I saw my old mentality in them ("Ugh why do we have to learn this, it won't be useful, just have to get this out of the way to checkmark a box..."). Whereas I spent time in a career, and had to force myself to make a major life-altering decision. I wanted what they had to say, whether it was relevant or not, because these ideas could be weaved together in the future. The properties that dictate the science of one is not fully independent from the other. This really became infectious. Everything I see, I try to learn beyond just memorization, but to a solid understanding and application level. "I'm running this test, the process isn't working, where is the most likely error? How can I optmize?" Unfortunately, I don't think you can just teach this. It has to be something that someone actively decides they want to commit to.
theyoungestgun 10y ago
This is mentioned in her bio at the end, but worth noting here, I think: Barbara runs a coursera course on learning how to learn (https://www.coursera.org/learn/learning-how-to-learn https://www.coursera.org/learn/learning-how-to-learn). It is interesting in that I find that Coursera courses highlight the flawed learning processes she mentions quite well. I often find myself watching the videos, thinking I get it, buzzing through the usually basic follow-up questions, and moving on. Likely that material won't last in my brain for very long in a quickly usable fashion.
- fny 10y ago
  Coursera simply mirrors collegiate pedagogy: a professor lectures you for an hour, you take a quiz here and there, and then there are some larger assessments that prove mastery. Study habits and methods are entirely left up to the student. You could employ Dr. Oakley's methods, whatever works for you, or just breeze by without truly internalizing anything. Coursera's missing one powerful dynamic of a traditional university, however: incentives to remember beyond a class. Say you coast your freshman year without internalizing: you'll pay the price the following year or when you take some cumulative assessment like the MCAT. With Coursera everything still feels very disjointed. Even in the specializations, knowledge doesn't need to compound for success. You can easily succeed in edutainment mode. Why take notes when you can use your hands for popcorn?
Rainymood 10y ago
Can highly recommend the book the Coursera course is based on [1]: A mind for numbers [2]. Have read it multiple times back to from and front to back. [1]- https://www.coursera.org/learn/learning-how-to-learn https://www.coursera.org/learn/learning-how-to-learn [2] https://www.amazon.com/Mind-Numbers-Science-Flunked-Algebra/dp/039916524X https://www.amazon.com/Mind-Numbers-Science-Flunked-Algebra/...
sigi45 10y ago
I read her book, watched her videos and i like her. But while i do already know a shit ton of how to learn, my level of knowledge is not caped by learning issues or by my iq. It is caped because my stamina is where it is. I have enough stamina to learn and understand a shit ton of stuff but not to sit down day/every second day after day to learn. To Exercise. To do it on a regular base.
- dualogy 10y ago
  Well that's an entirely different problem to attack. Exercise: I used to do all kinds of programs incl "45 mins a day, 6 days a week" but found "sufficiently enjoyable results" while keeping the process enjoyable and in full balance with the rest of my life with just 3 reps a day, no break days, cycling through 8 exercises. Good enough for both health and looks if no Mr. Olympia goals. For learning, the right balance is a lot harder to strike IME. Going too hard on oneself or too soft is a real danger. The motivating goals for learning something or other will have to be consistently and sustainedly present to settle into the right balance over time. Whether (perceived) low stamina is merely due to "the undertrained stamina muscle", mismatch of expectations and results, or some deeper real physiological/psychological factor is also the the likeliest found out by yourself. Not reason not to go meta on this roadblock!
meesterdude 10y ago
> Gradually, neuroscientists came to realize that experts such as chess grand masters are experts because they have stored thousands of chunks of knowledge about their area of expertise in their long-term memory. Chess masters, for example, can recall tens of thousands of different chess patterns. Whatever the discipline, experts can call up to consciousness one or several of these well-knit-together, chunked neural subroutines to analyze and react to a new learning situation. This level of true understanding, and ability to use that understanding in new situations, comes only with the kind of rigor and familiarity that repetition, memorization, and practice can foster. This made a lot of sense to me. A pianist plays through these chunks of knowledge - and learns through them as well. These "chunked neural subroutines" can be built, and clearly are. I think a lot of resistance for me comes from learned helplessness (aka baby elephant syndrome). For me, growing up my inner narrative was one of failure and rejection. But as i've grown and changed this narrative to be more nurturing, I do see more and more, my capacity for a great many things. Am I crazy? A genius? An idiot? Nope. I just figured out that with a lot of curiosity, play and patience, you can become proficient or even a domain expert. That's easy to see, at a certain level. But I think for a lot of us, we have a concept of who we are, what we are and what we are not. And this, at least for me, this definition of I, has held me back more than anything. Change the definition, challenge assumptions, push boundaries. See who you are.
- justifier 10y ago
  i agree, and i like your 'see who who are' i say the same when people cite the taxi cab number(o) story and suggest some kind of intuition or magic ramanujan simply had worked with cubes enough to recognise the number, still very impressive, but anyone could do it with the kind of interest ramanujan had for number theory (o) https://en.m.wikipedia.org/wiki/Taxicab_number https://en.m.wikipedia.org/wiki/Taxicab_number
  - number-sequence 10y ago
    a rather interesting aspect of the taxicab number story is that ramanujan had been looking at "near misses" to the fermat equation, and this was the first values of one of the infinite families of near misses he had constructed. The story is often dramatized to make it sound like Ramanujan just knew about all the cubes and their sums and he pulled this out of thin air on the spot, but the truth is probably that he had worked enough with these equations to recognize the number when Hardy mentioned it. check it out, super neat number thy stuff! https://arxiv.org/abs/1510.00735 https://arxiv.org/abs/1510.00735
scribu 10y ago
Previous discussion: https://news.ycombinator.com/item?id=8402859 https://news.ycombinator.com/item?id=8402859
gyrgtyn 10y ago
Check out the book Make It Stick. It's the recent research, summarized.
hive_mind 10y ago
Barbara Oakley's MOOC is great. I taught me to take Pomodoro seriously. Also taught me that taking breaks is important to help the brain integrate material.
EternalData 10y ago
Every time I see Barbara Oakley I feel the need to post her "Learning How to Learn Talk". https://www.youtube.com/watch?v=O96fE1E-rf8 https://www.youtube.com/watch?v=O96fE1E-rf8
notvaluable 10y ago
I seem to recall that this post was posted here previously, I don't remember when. Well googling 15 seconds,https://news.ycombinator.com/item?id=12508776 https://news.ycombinator.com/item?id=12508776
pmoriarty 10y ago
Lately I've been picking up the soroban[1], the Japanese abacus, and it's been tons of fun. It feels a little like solving a Rubik's cube with arithmetic, or maybe like working with a finite state machine. There are different algorithms to apply depending on the state of the soroban, and applying the right sequence of these algorithms will get you to the right result. I find it to be a little addictive, and sometimes find it a bit hard to stop. I always feel like wanting to improve my skills a little more, become a little faster at it, and increase the number of digits I can handle without making a mistake. The soroban is a great tool for developing concentration, a memory for numbers, a facility for performing a relatively complex series of steps in a certain sequence, and eventually for lightning fast mental arithmetic. In Japan, soroban use is taught to young kids[2], who after a while develop enough proficiency not to need the physical device any longer and can perform the calculations on an imaginary soroban, and eventually can achieve some really amazing feats of mental arithmetic, such as this example from their national competitions: [3] [1] - https://en.wikipedia.org/wiki/Soroban https://en.wikipedia.org/wiki/Soroban [2] - https://www.youtube.com/watch?v=Px_hvzYS3_Y https://www.youtube.com/watch?v=Px_hvzYS3_Y [3] - https://www.youtube.com/watch?v=7ktpme4xcoQ https://www.youtube.com/watch?v=7ktpme4xcoQ
equalunique 10y ago
``At some point, self-consciously “understanding” why you do what you do just slows you down and interrupts flow, resulting in worse decisions.`` I experienced this phenomena while learning the dvorak keyboard layout. The GNU Typist dvorak lesson can be completed in just one day. A mental map of where all the keys are in dvorak was developed very quickly. The problem I was faced with was the relatively slow thought process of envisioning the key layout, moving my typing finger to where it needed to be, and then continuing this thought process as I went on to type full words. Knowing I could type much faster in regular Qwerty layout, this was frustrating. After a month, I was thankful many words no longer required much thinking to write. Months later, I now very much prefer to turn on Dvorak layout on whatever computer I'm logged into. Great article. I'm also keen on brushing up on my math. Kahn Academy is an amazing learning resource and math is their biggest offering. Not taking advantage of it seems like a sin.
Chris2048 10y ago
> your mind constructed the patterns of meaning. Continually focusing on understanding itself actually gets in the way For an engineer, who only needs to use the math, maybe. But what if you need an understanding too? Once you have "intuition" it's easy to stick with that, rather than challenge your understanding.

262 points by paublyrne 10y ago

> By interleaving my learning—in other words, practicing so that I knew not only when to use that word, but when not to use it, or to use a different variant of it—I was actually using the same approaches that expert practitioners use to learn in math and science. This is huge! Even if you learn something so that you can use it without fail today, if you interleave your practice of using it (today) with other things, you'll do much better a week from now.

Jugurtha 10y ago
Interleaving has served me very well during my second year of Engineering. I hadn't attended that much and had a grade of 3/20. There were the final exams where the materials of the whole year was fair game. I buckled down for a month with a friend at my sister's house which was empty. I eliminated the modules with diminishing returns that I had passed or where I was close (easier to go from 0/20 to 12/20 than it is to go from 8/20 to 20/20 for the same amount of points). I was left with five modules I hadn't attended: Numerical Analysis (ANAI), Rational Mechanics(MECA), Strength of Materials(RDM), Vibrations-Waves-and-Propagation(VOP), and Atomic and Nuclear Physics(PAN). I drew a pentagon and organized the modules. Starting at the top, going counter-clockwise: VOP, ANAI, PAN, MECA, RDM. Each day, I'd do two modules: Day1: VOP-ANAI Day2: PAN-MECA Day3: RDM-VOP Day4: ANAI-PAN Day5: MECA-RDM Day6: Restart cycle. Many benefits: - You only do a module for half a day. Intensely. Then switch to another module and you sort of hustle your brain for a fresh start. It's not tired because you're doing something else now. "It's not like you've been studying all day" is the impression. - Mixing modules gives new insights. Especially in second year, there's a bootstrapping phenomenon: to understand a module of Physics, you had to understand a module in Maths. - You study a module hard. You don't see it the next day, but the day after. Not too soon to be sick of it and burn out, but not too far in the future not to remember any of it. The problem with the methods most other students followed was that it violated their brains and common sense: they'd do one module exclusively for a week (all chapters, all exercises). Then go on to the next one and do the same. By the time the exam comes: they're sick of the modules, and they remember nothing for the most part because it's been 3 weeks since they've last done the first module they started with. I, on the other hand, have seen any given module at most 3 days before. This allowed me to study 13 hours per day during a month without burnout (reading the course material for the first time, going over the exercises and exams, etc). The key was keeping a schedule. Up at 0500. 0500 - 0700: Study. 0700 - 0800: Breakfast. 0800 - 1200: Study. 1200 - 1300: Lunch and nap. 1300 - 1700: Study. 1700 - 1800: Afternoon snack and chill. 1800 - 2100: Study. 2100 - 2200: Dinner. 2200 lights out, going to sleep.
- deleted 10y ago
  [deleted]

imjk 10y ago

I've realized lately that I often fool myself into thinking I'm proficient in some subject by picking up on concepts quickly. I think I "get" it because I can understand something on a conceptual level, but when it comes to practice, my deficiencies become apparent. I guess the tricky part is to push myself past those initial concepts to delve deeper into the subjects with practice. I need to slow down and remind myself that I don't really "get" it just because I can understand the concepts in a very broad sense.

Waterluvian 10y ago
Binary trees was that for me. I listened to lectures and understood them very well from a conceptual point of view. But once I started writing them from scratch as an exercise did I learn that understanding the theory alone was woefully insufficient.
- trentmb 10y ago
  Maybe you just didn't understand the "theory" as well as you thought you did. I fell into the "it makes sense when we go over it in class, but not when I do it at home" trap often.
stephengillie 10y ago
When you're feeling proficient and confident in something, move your goalposts, and force yourself to take the next step: * Become proficient not just the concept or task, but good enough to where you can teach it to someone else, or write a clear and concise KB article. * Implement it (perform the task) repeatedly, with consistent outcomes. * Automate the process. * Use this as one part of a much more complex system.
chrismealy 10y ago
I've often had the experience of thinking I understood something well up until the point I tried to explain it to somebody. Teaching is the best way the learn. I think the "smart" person in a study group often gets the most out of it.

JamilD 10y ago

I've realized exactly the same thing. A starting intuition is necessary, but not sufficient, for understanding. I can watch as many lectures as I want, but nothing beats sitting down with a pen and a piece of paper, playing around with equations and developing a true, intimate understanding.

pm90 10y ago
This is why a lot of the best mathematics books won't just state theorems, but will actually heavily encourage the reader to solve problems as well, as that is considered an indispensable part of the learning process.

chrismealy 10y ago

The author is not wrong to emphasize the fundamental necessity of drilling, but in her article it sounds like she, having memorized basic facts (in Russian and math), ultimately achieved fluency through play.

meesterdude 10y ago
That was my takeaway as well. The author played with the equation f=ma, and understood it inside and out in various scenarios.

nicolas_t 10y ago

This is related to the Curse of the Gifted. When I was a kid, I could grasp concepts easily and I understood maths very quickly so I didn't really bother doing things like homework or actually studying. I then went to a decent university (a French Grande Ecole) and for the first year, I was still doing okish but I went from being a student who always had good results to doing average. Then, the second year came, and just understanding the concepts without cultivating fluency by practicing wasn't enough anymore and I failed hard. I hadn't learned how to learn and while I understood the concepts and could easily follow when the teacher solved a problem together with us, I had difficulties doing it on my own. I worked doing exercises and was able to pass but time and time again in my professional life, I've had the same issue where I tend to rely too much on my intuitive understanding until it fails. I'm not sure how to help kids not to go down this path. As a kid, I would avoid any rote memorization and would probably not do any non graded exercise since I knew that I understood (and also since as a geek wanting to fit in, I tried to be more accepted by my peers by purposefully not doing my homework). In the end, I think the key is play and giving maybe challenging exercises that forces the kid to use his newly found understanding would be a way to get them used to not just rely on their intuition understanding.

goodells 10y ago
I'm a student in university now, and I can relate to your experience. What helped me a lot as a kid was being motivated to learn things when it didn't seem like "learning". For example, I was able to get the hang of programming by playing a game that incorporated it, and it succeeded because it got me excited about doing cool things. Maybe this kind of "gamification" could be more useful than just adding points and rules to things to make people compete.
camerintinbun 10y ago
I had a similar path as yours. Never had to work all that hard through school, did a degree at a university in the sciences which was somewhat the same (had to try a little harder after the reality settled in from freshman year...), but I had always just assumed that was the next step. This was just something I had to do to move on, so a high mark was the end result. I was thrilled to graduate, took a job out in a semi-related field for about 5-6 years, then slowly began to get this feeling of "being dumbed down". Day by day, doing the same or similar things, not having to learn new stuff; it took a toll. I started listening to podcasts, and learning about all of the advances in science was enough to get me back into school and apply for a graduate degree. Here is where I think this is something that people have to recognize they want for themselves. Starting my grad classes with other students, mostly fresh from undergrad, I could see a change in the value I took from the classes compared to undergrads. I saw my old mentality in them ("Ugh why do we have to learn this, it won't be useful, just have to get this out of the way to checkmark a box..."). Whereas I spent time in a career, and had to force myself to make a major life-altering decision. I wanted what they had to say, whether it was relevant or not, because these ideas could be weaved together in the future. The properties that dictate the science of one is not fully independent from the other. This really became infectious. Everything I see, I try to learn beyond just memorization, but to a solid understanding and application level. "I'm running this test, the process isn't working, where is the most likely error? How can I optmize?" Unfortunately, I don't think you can just teach this. It has to be something that someone actively decides they want to commit to.

theyoungestgun 10y ago

This is mentioned in her bio at the end, but worth noting here, I think: Barbara runs a coursera course on learning how to learn (https://www.coursera.org/learn/learning-how-to-learn https://www.coursera.org/learn/learning-how-to-learn). It is interesting in that I find that Coursera courses highlight the flawed learning processes she mentions quite well. I often find myself watching the videos, thinking I get it, buzzing through the usually basic follow-up questions, and moving on. Likely that material won't last in my brain for very long in a quickly usable fashion.

fny 10y ago
Coursera simply mirrors collegiate pedagogy: a professor lectures you for an hour, you take a quiz here and there, and then there are some larger assessments that prove mastery. Study habits and methods are entirely left up to the student. You could employ Dr. Oakley's methods, whatever works for you, or just breeze by without truly internalizing anything. Coursera's missing one powerful dynamic of a traditional university, however: incentives to remember beyond a class. Say you coast your freshman year without internalizing: you'll pay the price the following year or when you take some cumulative assessment like the MCAT. With Coursera everything still feels very disjointed. Even in the specializations, knowledge doesn't need to compound for success. You can easily succeed in edutainment mode. Why take notes when you can use your hands for popcorn?

Rainymood 10y ago

Can highly recommend the book the Coursera course is based on [1]: A mind for numbers [2]. Have read it multiple times back to from and front to back. [1]- https://www.coursera.org/learn/learning-how-to-learn https://www.coursera.org/learn/learning-how-to-learn [2] https://www.amazon.com/Mind-Numbers-Science-Flunked-Algebra/dp/039916524X https://www.amazon.com/Mind-Numbers-Science-Flunked-Algebra/...

sigi45 10y ago

I read her book, watched her videos and i like her. But while i do already know a shit ton of how to learn, my level of knowledge is not caped by learning issues or by my iq. It is caped because my stamina is where it is. I have enough stamina to learn and understand a shit ton of stuff but not to sit down day/every second day after day to learn. To Exercise. To do it on a regular base.

dualogy 10y ago
Well that's an entirely different problem to attack. Exercise: I used to do all kinds of programs incl "45 mins a day, 6 days a week" but found "sufficiently enjoyable results" while keeping the process enjoyable and in full balance with the rest of my life with just 3 reps a day, no break days, cycling through 8 exercises. Good enough for both health and looks if no Mr. Olympia goals. For learning, the right balance is a lot harder to strike IME. Going too hard on oneself or too soft is a real danger. The motivating goals for learning something or other will have to be consistently and sustainedly present to settle into the right balance over time. Whether (perceived) low stamina is merely due to "the undertrained stamina muscle", mismatch of expectations and results, or some deeper real physiological/psychological factor is also the the likeliest found out by yourself. Not reason not to go meta on this roadblock!

meesterdude 10y ago

> Gradually, neuroscientists came to realize that experts such as chess grand masters are experts because they have stored thousands of chunks of knowledge about their area of expertise in their long-term memory. Chess masters, for example, can recall tens of thousands of different chess patterns. Whatever the discipline, experts can call up to consciousness one or several of these well-knit-together, chunked neural subroutines to analyze and react to a new learning situation. This level of true understanding, and ability to use that understanding in new situations, comes only with the kind of rigor and familiarity that repetition, memorization, and practice can foster. This made a lot of sense to me. A pianist plays through these chunks of knowledge - and learns through them as well. These "chunked neural subroutines" can be built, and clearly are. I think a lot of resistance for me comes from learned helplessness (aka baby elephant syndrome). For me, growing up my inner narrative was one of failure and rejection. But as i've grown and changed this narrative to be more nurturing, I do see more and more, my capacity for a great many things. Am I crazy? A genius? An idiot? Nope. I just figured out that with a lot of curiosity, play and patience, you can become proficient or even a domain expert. That's easy to see, at a certain level. But I think for a lot of us, we have a concept of who we are, what we are and what we are not. And this, at least for me, this definition of I, has held me back more than anything. Change the definition, challenge assumptions, push boundaries. See who you are.

justifier 10y ago
i agree, and i like your 'see who who are' i say the same when people cite the taxi cab number(o) story and suggest some kind of intuition or magic ramanujan simply had worked with cubes enough to recognise the number, still very impressive, but anyone could do it with the kind of interest ramanujan had for number theory (o) https://en.m.wikipedia.org/wiki/Taxicab_number https://en.m.wikipedia.org/wiki/Taxicab_number
- number-sequence 10y ago
  a rather interesting aspect of the taxicab number story is that ramanujan had been looking at "near misses" to the fermat equation, and this was the first values of one of the infinite families of near misses he had constructed. The story is often dramatized to make it sound like Ramanujan just knew about all the cubes and their sums and he pulled this out of thin air on the spot, but the truth is probably that he had worked enough with these equations to recognize the number when Hardy mentioned it. check it out, super neat number thy stuff! https://arxiv.org/abs/1510.00735 https://arxiv.org/abs/1510.00735

scribu 10y ago

Previous discussion: https://news.ycombinator.com/item?id=8402859 https://news.ycombinator.com/item?id=8402859

gyrgtyn 10y ago

Check out the book Make It Stick. It's the recent research, summarized.

hive_mind 10y ago

Barbara Oakley's MOOC is great. I taught me to take Pomodoro seriously. Also taught me that taking breaks is important to help the brain integrate material.

EternalData 10y ago

Every time I see Barbara Oakley I feel the need to post her "Learning How to Learn Talk". https://www.youtube.com/watch?v=O96fE1E-rf8 https://www.youtube.com/watch?v=O96fE1E-rf8

notvaluable 10y ago

I seem to recall that this post was posted here previously, I don't remember when. Well googling 15 seconds,https://news.ycombinator.com/item?id=12508776 https://news.ycombinator.com/item?id=12508776

pmoriarty 10y ago

Lately I've been picking up the soroban[1], the Japanese abacus, and it's been tons of fun. It feels a little like solving a Rubik's cube with arithmetic, or maybe like working with a finite state machine. There are different algorithms to apply depending on the state of the soroban, and applying the right sequence of these algorithms will get you to the right result. I find it to be a little addictive, and sometimes find it a bit hard to stop. I always feel like wanting to improve my skills a little more, become a little faster at it, and increase the number of digits I can handle without making a mistake. The soroban is a great tool for developing concentration, a memory for numbers, a facility for performing a relatively complex series of steps in a certain sequence, and eventually for lightning fast mental arithmetic. In Japan, soroban use is taught to young kids[2], who after a while develop enough proficiency not to need the physical device any longer and can perform the calculations on an imaginary soroban, and eventually can achieve some really amazing feats of mental arithmetic, such as this example from their national competitions: [3] [1] - https://en.wikipedia.org/wiki/Soroban https://en.wikipedia.org/wiki/Soroban [2] - https://www.youtube.com/watch?v=Px_hvzYS3_Y https://www.youtube.com/watch?v=Px_hvzYS3_Y [3] - https://www.youtube.com/watch?v=7ktpme4xcoQ https://www.youtube.com/watch?v=7ktpme4xcoQ

equalunique 10y ago

``At some point, self-consciously “understanding” why you do what you do just slows you down and interrupts flow, resulting in worse decisions.`` I experienced this phenomena while learning the dvorak keyboard layout. The GNU Typist dvorak lesson can be completed in just one day. A mental map of where all the keys are in dvorak was developed very quickly. The problem I was faced with was the relatively slow thought process of envisioning the key layout, moving my typing finger to where it needed to be, and then continuing this thought process as I went on to type full words. Knowing I could type much faster in regular Qwerty layout, this was frustrating. After a month, I was thankful many words no longer required much thinking to write. Months later, I now very much prefer to turn on Dvorak layout on whatever computer I'm logged into. Great article. I'm also keen on brushing up on my math. Kahn Academy is an amazing learning resource and math is their biggest offering. Not taking advantage of it seems like a sin.

Chris2048 10y ago

> your mind constructed the patterns of meaning. Continually focusing on understanding itself actually gets in the way For an engineer, who only needs to use the math, maybe. But what if you need an understanding too? Once you have "intuition" it's easy to stick with that, rather than challenge your understanding.