[HN Gopher] You are not dumb, you just lack the prerequisites
___________________________________________________________________
You are not dumb, you just lack the prerequisites
Author : JustinSkycak
Score : 642 points
Date : 2024-08-24 13:57 UTC (1 days ago)
(HTM) web link (lelouch.dev)
(TXT) w3m dump (lelouch.dev)
| bqc wrote:
| Would you like to recommend any resource?
| JustinSkycak wrote:
| Kind of depends what exactly you're trying to learn, but if
| you're working up to ML/AI, then there's _How to get from high
| school math to cutting-edge ML /AI_ from last week:
| https://news.ycombinator.com/item?id=41276675
| doctorpangloss wrote:
| This is really interesting but it seems too good to be true.
|
| You're going to reply that it's not for everyone, but you'll
| have nothing positive to say about the audience for whom this
| is a bad fit, which is also a suspicious form of
| generalization. It's kind of like how the chatbots and for
| that matter most online learning resources give the psychic
| feeling of learning.
| pests wrote:
| It seems impolite to make up your opponent's argument and
| then make commentary about it. Maybe let them respond?
| JustinSkycak wrote:
| What exactly is too good to be true? The idea that there's
| a path of knowledge leading from high school math to
| cutting-edge ML/AI?
| ydnaclementine wrote:
| I've been looking at this textbook for awhile. Very, very
| basics to calculus: https://www.amazon.com/Foundation-Maths-Dr-
| Anthony-Croft/dp/.... I wish there was a table of contents
| available
| bqc wrote:
| I'm interested in data structures and algorithms, particularly
| those related to mathematics. If you have any relevant
| materials or resources, I would greatly appreciate them.
| billconan wrote:
| but when I read a paper, it's difficult to know what the
| Prerequisites are.
| JustinSkycak wrote:
| This is one reason why it's helpful to learn bottom-up when
| possible as opposed to diving straight into the deep end and
| trying to fill in missing knowledge as you go.
| chrisweekly wrote:
| I think there are certain circumstances where getting in over
| your head and digging your way out is a better approach --
| but I don't know how to distinguish those cases from the
| rest.
| JustinSkycak wrote:
| I don't think there's anything wrong with trying to jump
| headfirst into things that interest you. I would just
| recommend that you need to be honest with yourself about
| whether you're making progress -- and if you're starting to
| flail (or, more subtly, doubt yourself and lose interest),
| then it's an indication you need to re-allocate your time
| into shoring up your foundations.
| carlmr wrote:
| Hm, I've always felt bottom up more difficult to learn. I
| always found it helpful to first have an overview, a mental
| map of sorts, of the high-level details, so that when I
| looked at the details later I could make connections and know
| where to "put" this knowledge relative to other things.
|
| With bottom up I always feel lost because I don't know what
| it's useful for, the relationships to other pieces of
| knowledge, etc.
| JustinSkycak wrote:
| It can definitely be helpful to take a top-down approach in
| planning out your overarching learning goals.
|
| However, the learning itself has to occur bottom-up.
| Especially in math. Math is a skill hierarchy, and if you
| cannot execute a lower-level skill consistently and
| accurately, you will not be able to build more advanced
| skills on top of it.
|
| I wrote about this recently here if you're interested:
| https://www.justinmath.com/how-to-learn-machine-learning-
| top...
| SoftTalker wrote:
| It's good to have a high level view of what your ultimate
| goals are, but if you are lacking too much foundational
| knowledge you can't even conceive of it. Especially in a
| subject like math, everything builds from the bottom up.
|
| We don't give first graders an overview of differential
| equations and their applications when we start teaching
| them addition and subtraction.
| ninetyninenine wrote:
| The higher your iq the more easier it is to go top down.
| JustinSkycak wrote:
| Yes, which is why most people struggle so much with the
| top-down approach ;)
| tombert wrote:
| My trick is to find the paper you want to read, but immediately
| skip to the references; recurse until you get to a paper that
| you more or less understand.
|
| It's a bit time consuming but it makes paper reading a lot more
| fun.
| JustinSkycak wrote:
| Reminds me of my colleague's recent post on his experience
| getting up to speed on his dissertation topic while doing a
| PhD in mathematics:
| https://x.com/ninja_maths/status/1820583797491925386
|
| I'll quote a snippet below:
|
| _"My biggest mistake when starting my doctoral research was
| taking a top-down approach. I focused my efforts on a handful
| of research papers on the frontier of my chosen field, even
| writing code to solve problems in these papers from day one.
| However, I soon realized I lacked many foundational
| prerequisites, making the first year exceptionally tough.
| What I should have done was spend 3-6 months dissecting the
| hell out of all the key research papers and books written on
| the subject, starting from the very basics (from my knowledge
| frontier) and working my way up (the bottom-up approach)."_
| findthewords wrote:
| Finding a path starting backwards... also known as dynamic
| programming.
| cultofmetatron wrote:
| I would legit PAY for an app that managed dependencies for
| understanding a paper so that I could see the path I need to
| take to understand what I'm reading. Could apply to books
| too.
| dataf3l wrote:
| some time ago I was thinking about this issue, maybe the
| concept of "parametric books" will become popular in the
| future.
|
| https://www.youtube.com/watch?v=VXktVbeWAeM
|
| https://www.youtube.com/watch?v=Tpb2rXtBos4
|
| perhaps, with the advent of AI, one will be able to convert
| a current book into a more detailed book, and also a
| current book into a smaller book, so maybe this idea is
| even easier to implement than 4 years or so ago, before
| chatgpt (but after summarizers, which prompted the idea in
| my head).
|
| I would humbly appreciate any feedback on the concept of
| parametric books, for now, it's just an idea, but it's a
| free one, anyone is free to implement it.
|
| thanks in advance, for your comments on it.
| sn9 wrote:
| I mean if you're regularly trying to read papers in a
| particular field, just follow the curricula for
| undergraduate degrees in that field.
| IshKebab wrote:
| Papers are a terrible way to learn unless you are already an
| expert in the field, because the prerequisites tend to be "the
| entire rest of the field". It's a rare paper that actually
| assumes you might not know everything the authors knew.
| fuzzfactor wrote:
| Prerequisites are so important, and math is one of the things
| where it makes more of a difference.
|
| >You Are Not Dumb, You Just Lack the Prerequisites
|
| I know what you mean, after years of study I now feel confident
| that I don't lack the prerequisites to be as dumb as I could
| possibly want to be ;)
| asdf6969 wrote:
| me except I'm socially dumb because I didn't learn how to have
| friends in middle school
| willismichael wrote:
| Umm... most people are really bad at relationships in middle
| school.
| hypeatei wrote:
| But people still had them. GP is saying they didn't have
| _any_.
| asdf6969 wrote:
| I did have friends lol. I was just a bit of an outsider
| from then through the end of high school. I didn't correct
| it until midway through uni and I think I missed out on a
| lot
| toast0 wrote:
| Having friends in middle school can be pretty tough.
|
| Learning how to have friends in elementary school and high
| school is a lot easier and mostly unconnected with middle
| school friendship.
|
| Hopefully your social life doesn't revolve around friendship
| with middle schoolers, so no big deal if you miss out on that
| skill.
| elzbardico wrote:
| Not always, but a lot of times not having friends in Middle
| School is class based. When I had this age I moved schools, in
| the first one I was objectively poorer than almost everyone
| else and the subject of bullying and loneliness. I would hide
| in the library during reccess not only because I liked reading,
| but to avoid the pain.
|
| Moved to another school were I was absolutely average socio-
| economically speaking, had some of the best years in my life.
| Rich kids are incredibly cruel.
| anubhavs wrote:
| Some courses in my university were restricted to students in
| their third year or above because of "mathematical maturity",
| which I thought was complete BS because some of the courses had
| no other prerequisites. But after taking some of them, I get it.
| There's a general sense of problem solving flow that takes time
| to develop.
| HPsquared wrote:
| In mathematics in particular, one abstraction is built on top
| of another. It's like trying to read without knowing the
| alphabet.
| H8crilA wrote:
| I often refer to this quite explicitly, something like "my
| skills include reading and writing modern math", as if it was
| a foreign language, or musical notation.
| Ekaros wrote:
| I wonder if part of this is also not wanting to list all of the
| pre-requisites that are at least partly needed.
| findthewords wrote:
| Most people are of average intelligence. Suppose that
|
| -a few IQ points here or there makes little difference in one's
| aptitude in real-world tasks
|
| -we then must accept that when most people think they are "dumb",
| there is some other effect going on such as:
|
| -lack of resources, hunger, mental distractions, illness, or
| motivating incentives.
| JustinSkycak wrote:
| Are you suggesting that when a student is struggling in
| calculus class due to not knowing their algebra, their issue
| can somehow be resolved without them having to learn algebra?
| danans wrote:
| I think they are suggesting that they might not have leaned
| algebra because of
|
| > lack of resources, hunger, mental distractions, illness, or
| motivating incentives
| Jensson wrote:
| Most people who are bad at math doesn't have those issues,
| lots of well off people are stupid.
|
| Edit: Also lots of people who lack many of those things
| still learn math very well. So it isn't a very good
| explanation. If you need optimal circumstances to learn
| then you have a problem.
| tjoff wrote:
| I'd argue motivation plays a much bigger role than
| intelligence.
| Jensson wrote:
| Everything I said is still right.
| tjoff wrote:
| Hardly.
|
| Yes, you can contort your definition of intelligence to
| be one where you have to be able to overcome whatever
| personal struggles one might have.
|
| But you wouldn't be actually measuring intelligence. And
| creating an environment that allows for more people to
| thrive isn't catering to the stupid either.
| Jensson wrote:
| Not sure what you are arguing, you didn't seem to read my
| post? I never said we shouldn't try to make more people
| succeed, or that everyone who fails are stupid.
| danaris wrote:
| The more I observe about people and how they learn and do
| things, the more I suspect that motivation plays a much
| bigger role than we think _in_ intelligence.
| Ekaros wrote:
| Looking at back to high school and then university. I
| fully believe I would have been capable of learning
| maths, electronics and so on... But I just did not care
| enough to put any actual work into the process. Still
| graduated. But well I really just did not care to put in
| effort. Thus lacked the motivation...
|
| Same can be said about any learning including languages.
| It really comes down to motivation, outside sufficient
| immersion.
| ozim wrote:
| I see it with people who "want to learn programming" but
| they fizzle out.
|
| That is not a single or 2 persons it is basically dozens
| of people whom I gave materials or tried to guide. It
| never is that they are too dumb to learn programming it
| is that they rather do something else than sitting in
| front of computer hunting down why their program doesn't
| compile.
|
| For math I got good enough to barely pass, for
| electronics I know basics, so I am "want to learn more
| math"/"want to learn more electronics" person but never
| get to really spend time on it.
|
| DevOps stuff, programming, databases, web frameworks is
| something I can fiddle with all day and not get bored, I
| can spend all day hunting that misconfig somewhere.
|
| On the face value all looks the same it is fiddling with
| stuff and solving puzzles, but somehow one type of
| puzzles is more interesting for me and since I do it a
| lot also much easier for me.
| hirvi74 wrote:
| I remember listening to a podcast where a psychiatrist
| was talking about something similar to what you are
| describing.
|
| Take something a person could desire like wanting to
| learn how to play the piano, for example. Often times,
| what people desire is not the learning part but the end
| result. People are fantasizing about drilling scales and
| chords for days on end. People are more likely to
| fantasize about creating music, playing music for the
| enjoyment of others, the praise, etc.. So, people tend to
| fizzle out when the reality does not meet the
| expectation.
|
| The brain tends to fantasize about all the good that
| something can bring, but the brain also tends to vastly
| underestimate the work required to achieve said goal.
| ozim wrote:
| I think for programming it is mostly idea of "easy job"
| like sit behind the keyboard and get paid loads of money,
| as soon it turns out it is not sitting but quite
| exhausting mental gymnastics they are out.
|
| I also heard that loads of times: "get a real job" (maybe
| not exactly in those words but hey, that was the gist)
| then I got people who would try out some basic things for
| an hour or two feeling mentally exhausted.
|
| Not saying they were not capable or stupid - just that
| they underestimate how much taxing it would be for them
| to do something like programming for couple hours.
|
| It is easy for me but I am doing it for 10+ years
| professionally and good couple years while I was a kid.
| danans wrote:
| > lots of well off people are stupid
|
| Sure, but being well-off can also cause mental
| distractions and suboptimal motivations.
|
| Having resources, well-off parents can pay for help in
| addressing those problems, but they have to first
| recognize the problems, which is something they might be
| resistant to.
|
| In the extreme form of this (in terms of wealth, learning
| problems, denial thereof, and poor academic performance),
| you get very wealthy people paying/bribing for elite
| credentials and access for their children.
| dleink wrote:
| "Most people are bad at math" doesn't matter, "When
| someone has those issues they are more likely to be bad
| at math" is what we're talking about.
| brigadier132 wrote:
| I think a few iq points is actually much more impactful than
| you realize. 1 iq point boosts lifetime earnings by $50k.
|
| https://www.sebjenseb.net/p/how-profitable-is-embryo-selecti...
| fuzzfactor wrote:
| I would say the most valuable benefits would not be measured
| in currency.
|
| not my downvote btw
| hnfong wrote:
| Right, and there is a well-known correlation between IQ and
| life expectancy/mortality rate....
| max_ wrote:
| If you used the same techniques used by IQ "research"
| peddlers to invest money in the stock market, choose startup
| founders or business managers -- you would go bankrupt with a
| probability of 1
| hnfong wrote:
| That's just wrong, because if it's true I could do the
| exact reverse and earn money with probability of 1....
| tgv wrote:
| > lack of resources, hunger, mental distractions, illness, or
| motivating incentives
|
| Sure, that's a factor, but people can also simply be dumb.
| There's no quality equal for all humans, whether it's length,
| strength, weight, hair color, or intelligence, regardless how
| you measure it. The (rather superficial) article looks at it
| from the first person stance, but individuals are bad at
| estimating their own cognitive capacities.
| ilrwbwrkhv wrote:
| That is why finding the right study materials for the
| fundamentals of a subject is so important. Take some time to find
| out the right method and material when learning something new
| till it speaks and inspires you. You will learn much better and
| faster.
| eesmith wrote:
| From Neal Stephenson's "Cryptonomicon", at
| https://archive.org/details/cryptonomicon0000step_b9v1/page/... :
|
| > "Shut up about Leibniz for a moment, Rudy, because look here:
| You--Rudy--and I are on a train, as it were, sitting in the
| dining car, having a nice conversation, and that train is being
| pulled along at a terrific clip by certain locomotives named The
| Bertrand Russell and Riemann and Euler and others. And our friend
| Lawrence is running alongside the train, trying to keep up with
| us--it's not that we're smarter than he is, necessarily, but that
| he's a farmer who didn't get a ticket. And I, Rudy, am simply
| reaching out through the open window here, trying to pull him
| onto the fucking train with us so that the three of us can have a
| nice little chat about mathematics without having to listen to
| him panting and gasping for breath the whole way."
| 65 wrote:
| The way I learned programming was to start with the absolute most
| basic thing I could think of - changing the color of a button on
| click in Javascript. With that I could start doing slightly more
| complicated things, until I could get a whole job as a
| professional software engineer.
|
| Learning is like climbing a staircase, and what you have to
| realize is you can't skip steps.
| ocean_moist wrote:
| I tend to slightly disagree. Some of my most valuable learning
| was taking on massive projects, and then just doing whatever I
| could to make it work. Of course, progress would be slow, and
| you'd need to chunk up the problem and take small steps, but it
| rarely felt like slowly building up or climbing a staircase.
|
| I think the trial by fire approach, just jumping into the deep
| end, is a much more effective way to learn. It's also more fun
| for me.
| pajeets wrote:
| I actually disagree with both of you. Programming is learning
| and the code is the side effect of what you have learned. If
| you jump at a large project but lack the fundamentals you are
| going to wasting energy on stuff you shouldn't be.
|
| Rather the best way to learn programming I find was to master
| the basics, memorize the most used routines and commands to
| avoid having to google it every time (ex. CSS)
|
| The problem now is we have LLM which kind of negate the need
| and we have lot of engineers who don't have good fundamental
| systems design.
|
| The other major issue is most of us engineers are scaling for
| a future that won't come. It's sufficient to squeeze ton of
| performance out of a single vertically scaled Postgres
| instance for example without the need to do exotic
| architectures.
|
| So prerequisites are important like in the article but less
| so now but the fundamentals and only learning what is needed
| is critical more than ever (ex. Kubernetes for a blog)
| akira2501 wrote:
| The best way to learn programming is to read and understand
| other programs.
|
| It's a really fun field, and you can isolate yourself and
| get very deep into thought, and then enter an exceptionally
| rewarding period of cycling between work and learning. I
| think a lot of programmers eschew more sensible things in
| favor of exclusively working in this mode.
| ocean_moist wrote:
| > If you jump at a large project but lack the fundamentals
| you are going to wasting energy on stuff you shouldn't be.
|
| "Wasting energy" in this case would be learning. This
| learning happens faster than following a tutorial and
| "mastering" the basics.
|
| > The problem now is we have LLM which kind of negate the
| need and we have lot of engineers who don't have good
| fundamental systems design.
|
| Yeah if you use LLMs for everything you are just going to
| struggle 10x harder when you encounter a problem. This does
| not discount my point.
|
| Also why is your name a slur.
| danaris wrote:
| > If you jump at a large project but lack the fundamentals
| you are going to wasting energy on stuff you shouldn't be.
|
| On the other hand, for many people (like me!) it can be
| hard to feel motivated to learn a new programming
| language/framework/etc just for the sake of it (especially
| when you've got plenty of stuff going on already). (Note
| that I use "motivation" here in the immediate, executive
| function sense, not in the broader desire to do a thing
| sense.)
|
| In such cases, I have found that the best way to learn how
| to do what a large project requires is to first define the
| project that you want to accomplish that uses them, and
| then break that down into all the parts you need to learn
| to make it happen.
|
| The outcome _is_ still "mastering the basics" before you
| actually take on the large project _as a whole_ , but it
| can still look very much like trying to tackle the large
| project from some angles.
| Jtsummers wrote:
| > I think the trial by fire approach, just jumping into the
| deep end, is a much more effective way to learn. It's also
| more fun for me.
|
| If people survive it this gets them past some substantial
| mental hurdles. People who take too long on the basics often
| get stuck in the beginner treadmill, not really progressing
| but getting better and better at those basics.
|
| Unfortunately, it's not perfect. Most of my colleagues who
| have taken this approach have deficient mental models of how
| computers work or are missing significant portions of
| background or fundamental knowledge.
|
| After the trial by fire, you have to go back and fill in the
| gaps, hopefully deliberately and not just by future trial by
| fire efforts.
| ocean_moist wrote:
| This isn't really my experience. I learnt ASM because I
| wanted to reverse engineer a C binary. I learnt kernel
| stuff because I needed to write a device driver. I learnt
| low level networking by writing an HTTP server in C. I
| learnt programming language design by writing my own
| programming language.
|
| This was, of course, before LLMs, but I don't see how I am
| missing "fundamentals." They generally come if you are
| building something non-trivial and are genuinely interested
| in technology.
| dns_snek wrote:
| From what I've observed there's different ways that
| people cope when they find themselves in the deep end.
| Some try to learn and understand everything they can
| about their new environment (this seems to describe your
| experience), while others just try to find a working
| solution for their immediate task.
|
| In my experience, the first approach is extremely
| effective, even if it can sometimes result in analysis
| paralysis. However workplaces almost always prefer the
| latter so it can be hard to fill in the gaps later.
| d0gsg0w00f wrote:
| Yes. I learned that about myself a long time ago. Sometimes it
| takes me a week to figure out "how to change the color of a
| button" but after that I can ramp up pretty fast. As I get
| older it just becomes a question of targeted time investment
| strategies. Where do I want to invest that week?
| HPsquared wrote:
| Books and courses usually list their prerequisites. Or good ones
| do, anyway.
| JustinSkycak wrote:
| One problem is that it's easy to _think_ you know the
| prerequisites when in fact you don 't.
|
| For instance, a student struggling in calculus may _think_ they
| know algebra because they got a decent grade in algebra class,
| even though they struggle to solve a quadratic equation and
| they 've forgotten how trig works.
|
| -- Maybe they got saved by grade inflation, or
|
| -- maybe they did learn these things but they've gotten so
| rusty that they need to effectively re-learn them again, or
|
| -- maybe they learned and still remember everything from their
| algebra class, but the class was watered-down and cherry-picked
| the simplest possible cases of problems within each topic
| (e.g., quadratic equation always has leading coefficient of 1
| and is solvable via factoring) ...
|
| There's a million different ways that a student can look at a
| list of prerequisites and mistakenly think that they have
| learned them, especially if the prerequisites are listed as a
| handful of high-level categories as opposed to hundreds of
| granular atomic topics.
| nicf wrote:
| I'm a tutor, mainly working with adults who want to learn proof-
| based math, and the message behind this post definitely lines up
| well with my experience! If you're the sort of person who's
| animated by the idea of learning math but finding it challenging,
| it's worth considering that you might be missing some knowledge
| or skills that you'd be able to develop just fine if you knew to
| focus on them.
|
| There definitely is such a thing as "mathematical talent", but
| (a) if you're really excited by math then there's a decent chance
| your limiting factor is knowledge rather than talent, and (b)
| there's plenty to appreciate in the subject regardless of how
| much of it you have. My students come to me at all different
| levels but if they have enough time and motivation to work on it
| they all learn a lot of math!
|
| There are also plenty of people in the world who just aren't that
| into this stuff, but that's not really the population I'm talking
| about --- unless they _have_ to learn it for some reason, it
| probably doesn 't bother them that much that they don't know a
| lot of math! And I imagine a good chunk (though probably not all)
| of this group could probably find something to like in the
| subject if it was presented in an appealing way.
| JustinSkycak wrote:
| 100% agree. What I typically tell people is "your mathematical
| potential has a limit but it's likely higher than you think."
|
| Not everybody can learn every level of math, but most people
| can learn the basics. In practice, however, few people actually
| reach their full mathematical potential because they get
| knocked off course early on by factors such as missing
| foundations, ineffective practice habits, inability or
| unwillingness to engage in additional practice, or lack of
| motivation.
|
| (My comment here is basically the intro to a detailed article I
| wrote on the topic: https://www.justinmath.com/your-
| mathematical-potential-has-a...)
| randcraw wrote:
| That's an excellent essay. I especially liked this part:
|
| " Active learning and deliberate practice will be covered in
| more depth in later posts, but below are some key points:
|
| - Effective learning is active, not passive. It is not
| effective to attempt to learn by passively watching videos,
| attending lectures, reading books, or re-reading notes.
|
| - Deliberate practice requires repeatedly practicing skills
| that are beyond one's repertoire. However, this tends to be
| more effortful and less enjoyable, which can mislead non-
| experts to practice within their level of comfort.
|
| - Classroom activities that are enjoyable, collaborative, and
| non-repetitive (such as group discussions and
| freeform/unstructured project-based or discovery learning)
| can sometimes be useful for increasing student motivation and
| softening the discomfort associated with deliberate practice
| -- but they are only supplements, not substitutes, for
| deliberate practice.
|
| - Deliberate practice must be a part of a consistent routine.
| The power of deliberate practice comes from compounding of
| incremental improvements over a longer period of time. It is
| not a "quick fix" like cramming before an exam. "
| JustinSkycak wrote:
| Thanks! Yeah, I guess I should probably link to some of
| those later posts about active learning and deliberate
| practice in the article. If you want to read more about
| that part you liked, here's the main one I'd follow up
| with: https://www.justinmath.com/deliberate-practice-the-
| most-effe...
| wonger_ wrote:
| And when they're knocked off course, they often develop math
| anxiety. It's a very real sense of dread that's been
| conditioned over time from test taking pressure, missing
| foundations, and underperforming.
|
| Then they're not just lacking motivation, they're motivated
| to avoid math, which makes remediation more difficult. So
| sad.
| JustinSkycak wrote:
| Totally. It's a vicious cycle. Once you get knocked off
| course, you fall into this current that's pulling you
| further off course. And the further off course you go, the
| stronger that current is.
| magicalhippo wrote:
| I've had similar experiences helping my SO, my sister and a
| good friend with post-high school math in various forms.
|
| My SO had a teacher at school who'd determined she couldn't
| do math, and had the worst passing grade as a result. She
| wanted to go to engineering college and lacking the
| prerequisites she had to take their pre-course, ie all the
| math and physics required compressed in a year. She struggled
| hard from the get-go, and I had to go back to elementary
| algebra and build up. Yet after a few hard weeks the efforts
| started paying off, and in the end she nearly aced the pre-
| course.
|
| My sister had never been into math, and had taken a
| vocational route working in a kitchen. After some time she
| wanted to go to college doing something else, and that
| involved taking college level math. While not as strong as my
| SO, again similar story where persistence and working the
| foundations helped a lot, and she aced her somewhat easier
| college math course on time.
|
| My friend was a bit different, in that he'd never been
| interested in math but had to take it to get the required
| points to get into some uni program he wanted. He's fairly
| smart but struggled with motivation. So for him it required
| finding the right way of forming the questions so he got some
| motivation to solve it.
|
| These are my most direct experiences, though I've also helped
| others here and there. It led me to believe _most_ people
| could do reasonably well at entry-level college math (ie
| basic calculus, statistics etc). For some it might require
| quite a lot of effort to get there, but still doable for
| someone with motivation.
| archagon wrote:
| Why do you think there is a limit at all? What is it about
| higher level math that is intrinsically incomprehensible to a
| subset of people?
|
| I suspect that the limit is actually in research and
| discovery, not comprehension. Calculus took some brilliant
| minds to develop but now it can be taught to most high
| schoolers.
| JustinSkycak wrote:
| As detailed in the article, my conclusion of there being a
| limit does not rest on the assumption that higher math is
| intrinsically incomprehensible to a subset of people
| (though, unrelatedly, I would expect that to be true in
| some cases).
|
| In the article, the key underlying assumption is that the
| further you go in math, the more energy it requires to
| learn the next level up -- and everyone's "energy vs level
| of abstraction" curve is shifted based on their cognitive
| ability and degree of motivation/interest.
|
| Here is a quote from the article that gets at the main
| argument:
|
| _" As Hofstadter describes, the abstraction ceiling is not
| a "hard" threshold, a level at which one is suddenly
| incapable of learning math, but rather a "soft" threshold,
| a level at which the amount of time and effort required to
| learn math begins to skyrocket until learning more advanced
| math is effectively no longer a productive use of one's
| time. That level is different for everyone. For Hofstadter,
| it was graduate-level math; for another person, it might be
| earlier or later (but almost certainly earlier)."_
|
| https://www.justinmath.com/your-mathematical-potential-
| has-a...
| SoftTalker wrote:
| > adults who want to learn proof-based math
|
| What is their usual motivation for this? Do they find they are
| running into regular work or life situations that require it?
|
| I think about all the math I took in high school and undergrad,
| and in my adult life I have not used anything more advanced
| than basic middle school algebra and occasionally some simple
| trigonometry. I don't even remember most of what I learned,
| other than very high-level concepts.
| nicf wrote:
| Motivations vary a bit, but most of them are just in it for
| personal enrichment, and the people who are in it for
| personal enrichment tend to be the most likely to stick with
| it. There are definitely jobs that require more math than the
| things you listed, but even if you have one of them the way I
| teach is usually more optimized for curiosity than
| professional goals.
| PartiallyTyped wrote:
| > What is their usual motivation for this? Do they find they
| are running into regular work or life situations that require
| it?
|
| I have a chip on my shoulder. In university I was depressed
| and didn't even bother attending lectures let alone doing the
| work in the first couple of years, couple that with
| professors who when contested were off by a 20-40% bc they
| cba to care for a secondary course in another department...
|
| When looking for thesis advisors, I found one interested in
| the things I was. They made a comment asking whether I had an
| issue with mathematics. Over the year I learned enough
| mathematics to get to what I was interested in and understand
| the bleeding-edge literature (calc, linalg, vec calc, prob
| theory, etc). I corrected some of his proofs in his classes
| by the end of the thesis.
|
| Still, my early grades haunt me, and parts of me wants to get
| a math degree just to prove that it is not a skill (read,
| intellect) issue.
| elawler24 wrote:
| I always thought I was bad at math. Then I decided to learn it
| again from the ground up when studying for the GMAT. I hired a
| tutor who completely re-taught me the basics and got me excited
| about it for the first time. I was amazed by how quickly I
| became comfortable with concepts as an adult, topics I assumed
| I was innately "bad" at. It made me realize how many things I
| could one day learn, given enough time and interest. Glad there
| are good tutors out there!
| scarmig wrote:
| Just wanted to chime in that Nic is an amazing tutor, and if
| you're someone who wishes they had studied math more
| rigorously, you should reach out! You'd be amazed how much you
| can learn in an hour every week or two that's focused entirely
| on your interests/strengths/weaknesses.
| fsckboy wrote:
| > _I 'm a tutor, mainly working with adults who want to learn
| proof-based math_
|
| are you calling college students adults? because otherwise,
| what adults are trying to learn proof based math?
| nicf wrote:
| Good question! No, I don't usually work with college
| students. Most of my students are actual grown-ups with jobs.
| I've found quite a few people who just wish they'd been able
| to study this stuff in college but didn't get the chance for
| whatever reason and still have some unresolved curiosity
| about it. It's a very fun group to work with; they're very
| motivated!
| KronisLV wrote:
| Lovely article, though honestly getting those prerequisites also
| takes a lot of time, effort and either motivation or discipline
| in ample amounts.
|
| As someone who was the "smart kid" growing up, going to the
| university without good work ethic was pretty eye opening, no
| longer being able to coast on intuitively getting subjects, but
| rather either having to put in a bunch of effort while feeling
| both humbled and dumb at times, or just having to sink
| academically.
|
| Even after getting through that more or less successfully and
| having an okay career so far, I still definitely struggle with
| both physical health and mental health, both of which make the
| process of learning new things harder and slower than just
| drinking a caffeinated beverage of choice and grokking a subject
| over a long weekend. Sometimes it feels like trying to push a
| rock up a muddy slope.
|
| And if I'm struggling, as someone who's not burdened by having
| children to take care of or even not having the most demanding
| job or hours to make ends meet, I have no idea how others manage
| to have a curious mind and succeed the way they do.
|
| Admittedly, some people just feel like they're built different.
| Even if I didn't have those things slowing me down as much
| (working on it), I'd still be nowhere near as cool as people who
| dive headfirst into low level programming, electrical
| engineering, write their own simulations, rendering or even whole
| game engines and such. Maybe I'm just exposed to what some
| brilliant people can do thanks to the Internet, but some just
| manage to do amazing things.
| vundercind wrote:
| > As someone who was the "smart kid" growing up, going to the
| university without good work ethic was pretty eye opening, no
| longer being able to coast on intuitively getting subjects, but
| rather either having to put in a bunch of effort while feeling
| both humbled and dumb at times, or just having to sink
| academically.
|
| Modern gifted education is very aware of this and is working on
| fixing that. How effectively, I dunno, probably not very, but
| at least it's a hot topic in the field this century.
|
| Damn near every person I've know who was "gifted" has a similar
| story, myself included. There's a lot of lost potential because
| we badly mis-handle those kids for years and years on end.
| dsign wrote:
| I thought that I was gifted, but in retrospect, maybe I
| wasn't. I couldn't play any games well; not the physical
| ones, not computer games, not card or board games. The other
| kids would get them fast, while I was always dumbfounded and
| it took me a long time to grasp the rules. Once, it became
| popular to play Warcraft in my circle of friends and, try
| hard as I may, I was the rag they mopped the floor with :-) .
| But math, physics and computer sciences were another story,
| because growing up I didn't have anything more interesting to
| do than reading and solving exercises from old soviet
| textbooks. So, I think I wasn't gifted, or just gifted by
| serendipity.
| Jensson wrote:
| Symbolic manipulation and intuitive understanding doesn't
| seem to be very correlated to me. I've met people who are
| very good at manipulating symbols, but they aren't very
| good at understanding less formal things like strategy
| games well, they tend to invent way too rigid rules for
| themselves and lose since they are bad at adapting.
|
| So maybe you are very smart with symbols, but less so with
| intuitive understanding? There is nothing wrong with that,
| makes it easier to decide what to work on, focus on your
| strengths and let others cover for your weaknesses.
| lamontcg wrote:
| My memory is kinda shit.
|
| So when I was in the gifted program, they got real
| concerned about how I didn't know my times tables and was
| super slow at a few of them. This was the 1970s, and
| before I knew binary, so 7s and 8s caused me issues. So
| I'd figure out 8x8 by going from 6x6=36 (real easy to
| memorize) and then adding +6+6 to mentally fill out the
| 8x6 block and then adding +8+8 to fill it out to a 8x8
| block (I'm visual/geometrical).
|
| I was the first kid in school to pass the AHSME to get
| invited to take the AIME though. Being before the
| internet, and being stuck on an island in Alaska, didn't
| get me enough exposure to higher math through my own
| self-direction to get anywhere on the AIME. If you don't
| live anywhere near a University library and/or don't know
| you can use it, that'll set you behind (at least back
| then, these days there's YouTube and sci-hub and
| friends).
|
| I still think I would have hit a wall anyway with Math,
| even with perfect exposure, because I'm visual and higher
| Math seems to require being very good with symbols and
| memory as well.
|
| I suspect lots of people still underestimate me because
| my memory is ass, and we associate memory with
| intelligence so much (e.g. Jeopardy).
| Viliam1234 wrote:
| I used to believe that I was good at math _because_ my
| memory was shit. So I had to actually _understand_
| everything, because I couldn 't rely on memorizing it.
|
| But some random facts were easy to memorize, for example
| that the chessboard has 64 fields. I had problems with
| 6x9 and 7x8 though, always confused about which one was
| 54 and which one was 56.
| eastbound wrote:
| Oh! So that's why my teachers made us memorize row by
| row: For me 54 and 56 are in an entirely different
| category (resp the 6 and 8 categories), didn't even
| realize they landed in the same dozen when learning my
| tables!
|
| And I don't have a good memory either.
| tharkun__ wrote:
| I can't tell you what 6x9 is. But I can tell you what 9x6
| is. I always turn that one around. My mind immediately
| jumps to a visual 60 coz 10x6 is super easy of course and
| subtracting 6 from it is easily 54.
|
| Similarly 8x7 I can't tell you but 7x8=56 in my brain
| feels like a little "rhyme" I just need to repeat and I
| have the answer.
|
| That's also how I remember (somewhat) arbitrary
| passwords. If it "flows" well almost like a rhyme and can
| be typed fluently I'll remember. Actual arbitrary ones
| don't work as well.
| novok wrote:
| You might have certain targeted deficiencies that make
| processing those things well difficult. Like I have a hard
| time finding things in visual space, so I'm not good at
| jigsaw puzzles. I have slower reaction times & processing
| speeds also which makes me not as good at video games as I
| should be combined with the visual space deficiencies. When
| a shit ton of stuff is happening on screen I lose my place,
| while others might be able to manage it.
|
| But I also show an ability to think and learn deeply and
| score very well on symbolic and verbal intelligence, I also
| connect the dots very well and show a lot of skip thinking
| behavior. I call my brain a high torque, low RPM engine.
|
| Also you might not like anything that is 'competitive', so
| your brain shuts down in avoidance / disinterest. Or you
| might think deeply about everything, so it always takes you
| a while at first, but once you grasp it you grasp it at a
| deep level unlike others.
| dleink wrote:
| Hmm, this rings some bells for some people I know. Did
| you learn about those deficiencies and proficiencies in a
| systematic way or through experience? Any resources you'd
| suggest for thinking more deeply about these things?
| novok wrote:
| A neuropsychological assesment figured it out for me,
| helped me connect some dots also.
| grugagag wrote:
| Things improve with practice though, at least they did
| for me. I largely sucked at action video games as a kid,
| I also didn't have interest probably because I wasn't
| good. I took to learning musical instruments and now in
| my 40s I accidentally found Im pretty good at videogames,
| much much better than when I was young. Coincidentally I
| got better at sports as well.
| odo1242 wrote:
| This reminds me of how a lot of top video game
| speedrunners (e.g. Portal) are professional musicians
| because they are very good with accurate timings lol
| vonunov wrote:
| There's also some anecdata floating around in the -- what
| would you call it, the "competitive speed typing"
| community? Or "people who play TypeRacer a _lot_ ". Some
| seemingly significant correlation between skill in typing
| and piano. Or at least the appearance of skilled typists
| having some interest or experience in piano. This could
| probably be generalized to being good at fingering or
| timing, or maybe even further, to having effective
| mindsets or attitudes regarding performance of skills
| (like the need for a presumptive confidence of sorts), or
| being aware of good practice methods.
| lelanthran wrote:
| I accept your hypothesis, but allow me to suggest an
| alternative hypothesis for you to consider (and maybe
| reject after consideration).
|
| I am in my late 40s. Modern videogames are a great deal
| easier than games I played as a child. I tried playing a
| few games from my mispent youth recently, and was
| absolutely amazed at just how much harder they were.
|
| FWIW, I also play music, mostly guitar.
| NegativeK wrote:
| Gifted/high IQ/whatever is not a blanket pass to excel.
| We'll suck at a lot of things, we're subject to plenty of
| the same mental illnesses and struggles, etc.
|
| Gifted education is intended to address the needs of the
| students beyond what can be provided in a standard
| classroom. That's not just more worksheets or harder
| textbooks; it should also cover students who are able to
| coast through the advanced classes and make sure they know
| that they, like every other human, won't have everything
| easy. A lot of school programs have missed the mark and a
| lot will, but education is a process of improvement. Many
| of the teachers today are doing better for the kids because
| of the lessons learned from our teachers.
|
| Special education (including gifted education) isn't
| legally mandated in schools to make the students prove
| they're eligible for the label. If you got value out of the
| program, it was meant for you.
| nothercastle wrote:
| Why do you think that after "no child left behind" the
| situation is better for talented kids? IMO the situation
| is much much worse. Many gifted programs are being
| eliminated and all classes are being slowed down to
| accommodate the bottom 33%. Even slightly above average
| kids are going to feel like 2 standard deviation genius
| doing basic school work because compared to the
| curriculum they are.
| matheusmoreira wrote:
| > Even slightly above average kids are going to feel like
| 2 standard deviation genius doing basic school work
| because compared to the curriculum they are.
|
| They'll be treated like geniuses too. I used to get
| treated like one because of my incredible ability to plug
| numbers into formulas and write down the answers that
| came out in a piece of paper. I simply did not understand
| how people could possibly have any problem with it. I
| found it so dull I ended up in a computers course where I
| learned to automate that kind of human computer nonsense
| away forever.
|
| They treated me like a genius for working out some basic
| math, and the truth is I _suck_ at math. I actually like
| math, but I suck at it. I used to get away with never
| needing to do homework as a kid. As a result I never
| developed the discipline necessary to hone math skills.
| Now I want to learn something interesting like queueing
| theory but I barely understand the papers and articles
| because I 'm missing numerous prerequisites.
| IOT_Apprentice wrote:
| Your post seems contradictory in that you could plug
| numbers into formulas and get answers. Isn't that a
| fundamental skill? Is there an implied value in
| understanding the formula and how to apply it via math to
| obtain a correct answer?
|
| The question then is how did you develop the ability.
| anthk wrote:
| Roguelikes like Nethack/Slashem/Dungeon Crawl Stone Stoup
| and strategy/RPG games such as Liberal Crime Squad or
| Battle for Wesnoth would be easier for you.
| Viliam1234 wrote:
| As a gifted kid, when you get to university, you are supposed
| to learn work ethics practically overnight. Until then,
| between your 6 and 18 years, the school kept telling you that
| you should slow down and wait until the average kids also get
| it.
|
| That's like failing at a sprinting competition, when your
| entire training consisted of walking really really slowly.
| ChrisMarshallNY wrote:
| My wife has a nephew that is _insanely_ smart. Like, aced
| the SATs at 15 smart.
|
| His mother insisted that he have a fairly normal-paced
| education, and it seems to have paid off.
|
| He's a really decent chap, who teaches at a university, is
| married, and has a kid. His college career was at top
| schools, though. They pretty much threw scholarships at
| him.
|
| I like the article. Very humble and encouraging.
| noduerme wrote:
| There are gifted schools that don't force kids to slow down
| to the lowest common denominator. I went to one. In theory,
| they also enforce a work ethic. My problem was the reverse:
| I started working after school when I was 15, and when I
| got to university I found my peers had absolutely slovenly
| work ethics and no experience, and I was being taught
| things that were laughable in a real work environment, by
| professors who hadn't had a real job in decades (if ever).
| And I was supposed to be paying $30k a year for the
| privilege. I realized at 19 that I was better off at any
| pay rate in the private sector ;)
| yial wrote:
| I had a similar experience perhaps in some ways. I
| graduated high school and initially started university at
| 14. (I was tall, which is probably good in this case, as
| it let me pass for a very young looking maaaaybe 18, in
| the setting).
|
| My "work history"
|
| Has been 8 ish, doing yard work around town with 2 other
| kids (nothing crazy, weeding, push mowing, leaves,
| clearing brush, etc), and then working at a stables for a
| bit when 12.
|
| I ended up getting an hourly part time position at
| campus, at 16 ish I took a break for 2 years, worked in
| grocery, and then in pharmacy.
|
| 18, I ended up back at school. Embarrassingly it took me
| 3 more years to finish my undergrad. But I worked full
| time or nearly full time the entire time. (Floater
| pharmacy tech, part time backup event photographer, and
| then as a store manager at a hobby store).
|
| I found it very hard to make friends with people my own
| age, but found it incredibly easy to make friends with
| returning students - either they had worked a career and
| came back to school, or had done some time in the
| military etc., I also made some great friends who had
| moved to the U.S., usually as late teens, from developing
| countries.
|
| Knowledge, perspectives, etc I learned from these people
| ... and from some people I ended up being very lucky to
| work with, honestly proved in hindsight to be much more
| impactful and valuable to my life and career then I could
| have ever imagined.
|
| I will say, tongue in cheek, but also some truth:
|
| You could probably apply the anna karenina principle to
| all of the people I can think of who were impactful in
| some way... either through the lens of trauma/ struggle /
| or dysfunctional family. (This would also apply to
| myself!)
| noduerme wrote:
| I believe real world friends or colleagues are your
| alternative family. (Online friends, not so much). In any
| case, its so critical to have your eyes open to other
| traditions and creeds and ways people live their lives.
| Without that, we would just judge without knowing why
| people did things.
|
| The person you need to show mercy to most is yourself.
| And to do that you have to understad how everyone else
| lives.
| axus wrote:
| Which school did you go to, and are you aware if it's
| kept the same high standards? I believe there are
| interesting challenges for any mind, the hard part is the
| match-making customized for each person. It'd be cool if
| there was an equivalent Facebook/Netflix algorithm for
| learning.
|
| I always thought the alternative to "gifted programs" is
| not having a program which is even worse. At some point
| optimizing teaching becomes unaffordable.
| noduerme wrote:
| The elementary school I went to operated somewhat as a
| petri dish for psychiatric experiments, as I realized
| later, with class sizes around 15 students and extremely
| personalized teaching. My 8-12 grades were at a private
| prep school. Both could be scalable models, but it would
| require a moonshot level of public funding to go into
| hiring potential teachers away from more lucrative jobs.
| (Personally, I'd love it if my taxes went to that).
|
| But I don't credit those schools for my success. Nor do I
| credit native intelligence. My two elder brothers are
| lawyers whose names you likely know; think of the largest
| case in recent history. One is severely dyslexic and the
| other I'd wager is mildly autistic. I'm a college
| dropout. Oddly, I earn more per hour designing databases
| than the famous one does taking down large companies.
| What we had in common was a pattern of learning _how_ to
| think, how to be curious and ask questions, and how to
| separate wheat from chaff. All of which came from our
| grandfather, who was forced to leave a yeshiva at 12
| years old, and his father, and his grandfather.
|
| I truly believe that almost all formal education is bunk.
| It's a useless plaster on a gaping social wound, namely
| that parents don't have the toolset to teach children a
| love of learning throughout their lives, along with the
| methods and skills to do so for themselves. All the
| information taught in K-12 schools is readily available,
| yet most adults can't remember a thing about the most
| basic aspects of history, math or science. The reason
| being, they weren't interested when they learned it the
| first time, and they weren't raised to be curious enough
| to answer their own questions or (re)fill holes in their
| own knowledge. This is why most people can't utter the
| words, "I don't know, let's look it up." Moreover, most
| people don't believe it's their obligation as a person to
| be as well-rounded as they can make themselves, because
| no one ever told them that was important, even crucial to
| their survival.
|
| Learning itself should be taught. And it can be taught at
| home. The major obstacle would be how to overcome,
| obliterate and shame the intellectual laziness of most
| people that's built into most cultures - including those
| of most who go to college. Everything else, all concepts
| and facts, can be learned later, and are ephemeral.
| madaxe_again wrote:
| My university experience was very much "submit! work!" - I
| was on "keeping of term" almost permanently and had the
| threat of rustication hanging over my head for the duration
| of my time there as I flat out refused to attend lectures,
| tutorials, or labs - I was having way too much fun running
| a bar and the debating society.
|
| Anyway. What I learned was that people rarely make good on
| their threats, that charm and doing the absolute bare
| minimum to not "get fired" will get you through - and that
| I can cram a three year physics course into a month of
| intense study and still pass with a 2:1, which they demoted
| to a Desmond as they didn't feel they could in good
| conscience reward me with a 2:1 - which also taught me that
| institutions can't be trusted and are ultimately run by
| opinion.
|
| This lead to a career path of opportunistic system-hacking
| and an early retirement to a cabin in the woods. I never
| had a work ethic, apart from in that which interests me. If
| something bores me, it's for the birds.
|
| I'm not quite sure what I'm trying to say here, other than
| that at _no_ point in my education was I given any useful
| guidance or advice, just expectations of prodigy, and was
| left to figure things out for myself - which I did, but not
| as I think others would have hoped. I now, in my forties,
| know that I have raging ADHD - it wasn't even a
| consideration as a kid - just that I was "brilliant but
| bone-idle".
| lr4444lr wrote:
| Do you think yours is a life well spent for anything or
| anyone other than your own enjoyment, even if you were
| clever enough to save yourself the stress suffered by
| many?
| madaxe_again wrote:
| I would say that it has not provided as much utility
| value to mankind as it could have. Sure, I've created
| jobs, generated wealth, given to philanthropic causes -
| and in excess of the lives lived by most - but I would
| say with confidence that had I perhaps had some guidance
| other than the eternal threat of punishment, I would have
| developed something other than a frankly criminal
| instinct, and might have been more able to give more to
| society and fulfil my potential.
|
| Instead, I learned to avoid the consequences, not to
| avoid the crime, and can't deny that I have chosen a
| selfish path as a result.
| biorach wrote:
| You could have phrased that in a much less judgemental
| way.
| mgaunard wrote:
| School is easy, the point of it is more to learn social
| skills.
| whiterknight wrote:
| We must spend 30-50% of state budgets, monopolize
| children's time, and expose them to violence and drugs so
| they can learn to socialize.
| mgaunard wrote:
| We don't spend 50% of state budgets on primary/secondary
| education.
| whiterknight wrote:
| It does if you consider the part going to your county:
|
| "In 2022, the federal government spent ... This is 13.6%
| of the total spent on elementary and secondary education
| in 2022. The remaining funding comes from state and local
| governments, which contribute 43.7% and 42.7%,
| respectively."
| feoren wrote:
| You've misread that. It is not saying that 43.7% of the
| state budget goes to elementary and secondary education.
| It is saying that 43.7% of the funding for education
| comes from the state. Those are completely different.
| whiterknight wrote:
| No. If 20% of the state budget is then that amount is
| matched by an equal part local. So state + local
| education would be 40% of the state budget.
|
| education (property tax) dominates local spend. So yes we
| do tax and spend extraordinary amounts on education.
| Loughla wrote:
| The most recent number I could find is from 2021, and on
| average, states spent 21.5% of their budget on k-12
| education.
| whiterknight wrote:
| The state and local pay about equal portions. But do you
| have anything to say about the argument in my comment?
| ricardobeat wrote:
| Was there an argument? Lots of places in the world have
| state-backed top-notch free education, without the guns
| and violence.
| avemg wrote:
| Believe it or not, it's not easy for many people. Be
| careful about making such sweeping generalizations based
| on your personal experience.
| sien wrote:
| It's funny, I was good at basketball as a kid. I played
| 'representative' and went to country championships.
|
| Doing that made it clear to you that you might be good in
| your city but there were still kids who were way, way better
| than you were likely to be.
|
| In contrast, smart kids often don't hit a 'bigger pool' until
| they get to university.
|
| In some ways many places are better at handling kids who are
| good at a sport than they are kids who are good at school.
| Terr_ wrote:
| > In some ways many places are better at handling kids who
| are good at a sport than they are kids who are good at
| school.
|
| An abrupt cynical thought: Could it be related to how
| sports are closer to being a revenue-source?
| ElevenLathe wrote:
| What high school makes money from their sports programs?
| Even in basketball or football-obsessed towns, I doubt
| the ticket sales and concessions revenue from home games
| would even cover the coaches' salaries, transportation to
| away games, and uniforms. Most schools near me have
| players sell candy or coupon books to pay for their
| teams' expenses.
| firesteelrain wrote:
| Schools in some parts of Texas, Florida and Ohio
|
| https://www.latimes.com/nation/la-na-stadium-arms-race-
| snap-...
| kjkjadksj wrote:
| Those are rare and usually heavily alumni donor
| subsidized.
| ElevenLathe wrote:
| The cost of these mega stadiums seems even less likely to
| be covered by revenue from the teams.
| uncanneyvalley wrote:
| It's not revenue, it's prestige. Except in Texas, where
| it's both.
| sien wrote:
| It's not revenue. I wasn't in the US. People sink money
| into high performance athletes. They lose money. In
| Australia only the AFL and Rugby League make much money.
| That is also only at the high levels.
|
| There are places in Australia, such as Sydney, that have
| a network of selective high schools for kids who do well.
| But outside of Sydney it's much weaker.
|
| There is more effort put into kids who are not doing well
| at school to improve their performance than in getting
| the most from kids who can do well. Perhaps it makes
| sense.
| throwaway2037 wrote:
| Wait, professional cricket doesn't make money?
| walthamstow wrote:
| You can make a decent living playing cricket in Aus (or
| England) but for the big bucks you have to go to the
| Indian Premier League
| cvwright wrote:
| Probably more that lots of kids will try super hard to be
| good at sports. Being good at school carries a certain
| level of stigma and lots of kids who could be "smart"
| choose to slack instead.
| cratermoon wrote:
| Nah. It's been painfully clear to nerds for a long time
| that sportsball players are much more highly respected
| and like than eggheads.
| kjkjadksj wrote:
| Sports only make money at the point of the most elite
| college programs, usually mainly its the football or
| basketball program that subsidizes the rest of the
| athletic program.
|
| I think its more you become aware of where you stand
| fast. You go to meets or games of a bunch of different
| schools and see who is literally the best in the area.
| You go to state competitions and see who is best in the
| entire state. And then there are nationals where you see
| who is best in the entire nation. Throughout this your
| stats are posted online where you and college scouts can
| see them.
|
| Academics have no comparison. We struggle to even compare
| grades because of grade inflation.
| BeFlatXIII wrote:
| There's "gifted" and there's gifted. The truly gifted often
| think they _have_ learned how to work hard because their
| classmates in the "gifted" classes got praised for their hard
| work. There's a top echelon of kid who is both common enough
| that every school district has 1-10 in each cohort but
| notably more advanced than what district standard gifted
| education is designed to handle.
| dheera wrote:
| Same here.
|
| I used to be one of the math/science wiz in grade school. I
| also got hammered on the work ethic part, multiple times.
| Unfortunately studying/working 12+ hours a day in the name of
| "work ethic" impacts my body beyond what I can handle, and
| mental health as well. That's not the way I operated growing
| up, and my body isn't going to handle it all of a sudden now.
|
| Here I am, 3 cardiac arrests later, trying to figure out how
| to fit into a society where everyone seems to be hellbent on
| working every waking hour and eating UberEats while I'm
| trying to stay alive with immense amounts of self-care in my
| off-work hours (cooking healthy, hiking, actually
| disconnecting from the internet, etc.).
| throwaway2037 wrote:
| > Unfortunately studying/working 12+ hours a day
|
| I am confused. Why didn't you reduce your hours to find
| mental happiness?
| paganel wrote:
| Not the OP, but there's another poster in this whole
| thread who says that he studied "16 hours per day" and
| that his former college mates, much gifted than him but
| who hadn't studied as much, now live "mediocre" lives.
|
| Which is to say that this is the competition that lots of
| people who study in a professional environment (i.e. not
| for fun) have to grapple with, I feel sorry for them
| because I don't see an easy solution for all this madness
| (because it is definitely madness to study 12-16 hours
| per day).
| dheera wrote:
| In high school I could sleep well AND ace everything. I
| didn't have to study that much to ace honors and AP
| courses.
|
| Partially because I aced everything, I got into one of
| the universities considered "top". Although I was excited
| about the research part, I quickly found out that many
| courses were hard af. I had to study 12+ hours a day to
| get good grades there. I did get good grades after the
| initial shock, but it was hard, I slept very little, and
| I fucked up my health doing it, without realizing it at
| first.
|
| Tech companies I have worked at, including the one I just
| left, routinely don't give you the option to work 8
| hours. It's either you work 12+ hours to meet performance
| expectations or they ask you to leave. My body,
| unfortunately, cannot tolerate that and "needing to work
| normal hours" isn't generally one of the available
| disability accommodations.
| brianf0 wrote:
| I was an inner city "gifted kid" - although I'm proud of what
| I have accomplished so far, I feel like my potential was
| stifled, as you said mis-handled. I'm very interested in
| helping inner city gifted kids today unlock their full
| potential. How could I start?
| noduerme wrote:
| Hey, screw modern education. Particularly if you went to a
| "gifted school". I was stupid for going to college for a
| year. At least I dropped out and saved myself a lifetime of
| debt.
|
| Think of the time you waste with that garbage versus how much
| you can "grok over a weekend" and the math is definitely in
| favor of the latter.
|
| The major flaw in the educational system in the US is that
| it's run for profit and it wrongly informs people they need
| to stay in it, rather than gaining real world experience.
| Coding, in particular, but also design and web are _trades_.
| Like bartending, plumbing, or fixing cars. They 're really
| only learned on the job, and every school that promises to
| place you in them is a racket. (I also wasted $500 on two
| weeks of "bartending school" when I was 21, just to see a
| roster of horrifically shitty bars that were supposedly
| hiring. All lessons in who's scamming you should be that
| cheap. What does higher ed cost these days?)
| FranzFerdiNaN wrote:
| Yes those people who went to school for dentistry or
| medicine or law or engineering are all idiots who just
| should have spend a weekend reading a Wikipedia page.
| darkwater wrote:
| Dentists and doctors in general is complicated because
| it's impossible to train "on your own", but law
| school...come on, you just need a good brain, patience
| and reading a lot.
| firesteelrain wrote:
| You have some valid points like college won't necessarily
| teach you what your job needs you to do. There have been
| some partnerships with companies where they have asked
| colleges to step in a build out degreed training programs.
|
| People with degrees regardless of degree do tend to make
| more money in the long run.
| noduerme wrote:
| >> People with degrees regardless of degree do tend to
| make more money in the long run.
|
| In aggregate. But that's wildly skewed by people who end
| up with higher degrees. If you look at bachelors, for
| every 2 people with a degree who make $20/hr bartending
| or selling used cars, there may be one person with no
| degree earning $150/hr coding or plumbing or fixing
| machines.
| matheusmoreira wrote:
| I'm not sure being "gifted" has anything to do with it. High
| school is easy, and they keep dumbing it down over time.
| Little to zero effort is required to pass. This can fool
| people with a minimal amount of intelligence into thinking
| they're Very Smart. Especially since everybody keeps telling
| you that you're the smartest kid around and treating you like
| a nerd. I was able to get near max grades with little study
| in the subjects I cared about, and passable grades with zero
| effort in the ones I didn't. It can seriously warp one's
| perception of reality.
|
| When I got into medical school I straight up failed a class
| for the first time in my life right in my first semester. I
| got my ass kicked so hard it's not even funny. I had to put
| in actual effort into learning stuff for the very first time
| in my life. I had to spend all of my waking hours in the
| laboratories to learn this stuff. I met people who had zero
| issues studying 5-10 times as much as I did. In the middle of
| it all I got diagnosed with ADHD by the neurologist I was
| shadowing.
|
| This is when I finally understood the point of school. One of
| the most bitter complaints from students is the fact most
| people don't use the knowledge they learn. That's not really
| the point of school. The point is to just show that you can
| learn. The point is teaching you how to study and apply
| yourself so that you don't get your ass kicked later in life
| when the really difficult stuff starts. Perseverance and
| mental resillience.
|
| I'm not really a "gifted" person but people treated me like
| one and in retrospect it was quite detrimental to me. If
| anything they probably need to identify the "smart" kids and
| kick their asses harder because the existing classes aren't
| getting the job done. But if teachers do that people accuse
| them of tracking...
| hnfong wrote:
| I wonder how many of these "work ethic" stories are just
| undiagnosed ADHD stories in disguise...
|
| I mean, this is the second time I see ADHD mentioned in
| this thread, and the story of somebody who just can't keep
| focus study for long hours kind of fits textbook symptoms.
|
| To be clear, I'm _not_ saying everyone commenting here with
| similar stories have ADHD, but uh... if it rings a bell,
| maybe think about it.
|
| (FWIW, I suspect I'm also an undiagnosed case...)
| matheusmoreira wrote:
| Oh lots. Not all but lots. It's not like I have a study
| to point to but I still have no doubt about that. You'll
| see lots of ADHD types here and in similar forums. For
| some reason, ADHD people seem to be really attracted to
| technology. They have "attention deficit" and yet don't
| have any trouble at all concentrating for 10 hours
| straight on things they care about and I often find that
| technology in general is in that list. Remember that
| "bipolar lisp programmer" article? It's more like ADHD
| lisp programmer. Actual bipolar patients I've seen
| weren't like that.
|
| When I talk to an ADHD patient, I end up getting this
| distinct feeling they're talking about me instead. I run
| them through the diagnostic criteria and they match. I
| still refer them to a trusted psychiatrist regardless so
| that a proper differential diagnosis can be made, which
| does include bipolar disorder. Psychiatry is hard and I'm
| not about to underestimate the difficulty of it,
| especially since I could kill the patient if I'm wrong.
| So far getting this feeling seems to be virtually
| pathognomonic though.
| hnfong wrote:
| Maybe because tech is responsive. In most cases the time
| required to compile, run and test code is a couple
| minutes. A couple hours at worst. The immediate
| gratification is really attractive for ADHD people.
|
| ^ This was what I intended to comment, and then I thought
| I should look up the "bipolar lisp programmer" article
| since I haven't read it before.
|
| And I'll just note that, while the article doesn't
| mention it, a major feature touted by Lisp enthusiasts is
| the REPL :) Talk about immediate gratification...
|
| By the way, the story sounds like mine too. Except I went
| to law school (law is undergrad in where I live).
| Everyone assumed I did poorly because I wasn't interested
| in the subject (a reasonable assumption since I was
| clearly oriented towards programming), but I think the
| real problem was the "artifice" mentioned in the article.
| Today, I still read legal cases/materials with interest
| from time to time, but if I were put back in that
| artificial law school environment I don't think I'd
| survive.
| varjag wrote:
| It's strange, smart kids in my uni absolutely aced it.
|
| Hate to be that guy but did you ever consider that you
| weren't much above average? It could be the weaksauce school
| curriculum issue.
| IOT_Apprentice wrote:
| Aced what? I'm missing context it seems.
| nsagent wrote:
| This rings so true to me. In fifth grade after being given an
| IQ test, I took Algebra I early, only to retake it when I
| moved to junior high the next year. Then I had to retake trig
| because I did no homework, but aced the tests. Luckily the
| teacher recognized my ability and allowed me to take pre-calc
| while I retook trig.
|
| By the time I was in undergrad I had no motivation to study.
| I'd skip classes and cram the night before for any class that
| was memorization based. I didn't even buy the books, just
| went to the library and checked the book out for a couple
| hours.
|
| Fast forward a bit and I ended up dropping some classes
| because I was paying so little attention, I didn't even know
| when the tests were supposed to be. Came in one day and the
| prof said, "You missed the test last week, I presume you want
| to retake it?"
|
| That said, I've done well enough having gone back later in
| life to get a PhD, but I do wonder sometimes if I would have
| accomplished more if I was forced to push the boundaries of
| my ability, thus leading me to develop a work ethic earlier
| on.
| Log_out_ wrote:
| Somewhere sits a autistic gamedev, mulling over a beer:
| "everyone i know can easily dive headfirst into low level
| programming, electrical engineering, write their own
| simulations, rendering or even whole game engines, but talking
| to people or women ,some people are just built differently
| .Wish i was born on the side with the greener grass..
| veunes wrote:
| But it's important to remember that everyone has their own
| set of challenges
| veunes wrote:
| In university the environment changes dramatically
| vaylian wrote:
| Yes. This is mainly because of 2 reasons:
|
| 1. Things actually get more complicated
|
| 2. Most of your "teachers" know a lot less about teaching
| than your school teachers, because they never had formal
| training in teaching. However, there are some lecturers who
| are natural talents.
|
| The second point is why you have to do more work to actually
| learn a topic. Your lecturer won't meet you halfway, but you
| have to get a lot closer to them to grasp their explanations.
| whiterknight wrote:
| Formal teaching training never made a bad teacher good.
| sn9 wrote:
| https://en.wikipedia.org/wiki/Direct_instruction
| necovek wrote:
| From that article:
|
| > however, when qualified by IQ and reading levels,
| Strategy Instruction (SI) had better effects for the high
| IQ group.
|
| Which only goes to show that being a great teacher is an
| impossible mission, and it's wonderful how many succees
| at it despite the difficulty.
| lr4444lr wrote:
| DI is rarely used to train teachers, unfortunately, and
| even if it were, the education-government complex designs
| school procedures and discipline rules that would make it
| very hard to implement.
| BlackFly wrote:
| I always thought the real reason was that the cadence of
| the lessons more closely matched what is possible for a
| person of average or above intelligence who was motivated
| to learn. The rate at which information is taught to
| children in school is kept at a low level because most of
| the students are not motivated to learn the subjects and
| instead need to be guided to learn those specific subjects.
|
| The example I was always given for this was the rate at
| which those same "non-gifted" students would learn subjects
| they actually care about--like dinosaurs or sports facts.
| Kids will soak that information up and spend tons of time
| learning more, but it just isn't useful. Instead we force
| them to spend less times on those subjects they love and
| guide them into things society views as more important.
| ziofill wrote:
| For me things got much better when I got to uni. In high
| school I didn't care about most of the subjects, but at uni I
| was studying what I had chosen for myself.
| wenc wrote:
| Also gifted child here, but grew up with parents who drilled
| into me that "effort matters, you might not be the best, but
| with effort you can be better than who you were yesterday and
| that is a worthy endeavor" It's just a slight switch of
| mindset, but that small switch carried me through times when
| subjects got too hard and when I wanted to give up because I
| felt I wasn't talented enough.
|
| I knew so many gifted kids who got perfect scores in college
| freshman year (engineering) but started giving up when things
| didn't come as easily to them. They all ended up leading
| mediocre lives after.
|
| I wasn't as smart as them but I knew I could always do better
| if I tried harder (even though the ROI wasn't great at first).
| So I just kept grinding (16 hour days studying). My GPA rose
| very gradually until eventually I finished with a not-great but
| respectable 3.6 (the 3.4-3.7 range is typically attained by
| folks who maybe didn't have natural talent but worked hard).
| That GPA got me into grad school where I got to study what I
| loved (way fewer exams, more research).
|
| Carol Dweck wrote a book on "growth mindset" that talks about
| this. You don't have to read the book, but the idea of growth
| mindset, though simple, has been really transformative in my
| life.
| novok wrote:
| Sometimes the greatest gift you can give a gifted kid is
| failing early at something they want, so they learn the grit
| to achieve it.
| wenc wrote:
| Absolutely. No matter how gifted a person is, there is
| going to be some point in their lives or some domain where
| pure talent will be insufficient.
|
| Even super geniuses like Terence Tao struggled (he nearly
| did not pass his generals).
|
| https://terrytao.wordpress.com/2019/06/27/living-proof-
| stori...
|
| https://web.math.princeton.edu/generals/tao_terence
|
| The American Mathematical Society has a PDF of essays of
| brilliant mathematicians (including Terence Tao) who
| despite their abilities, faced obstacles and difficulties
| that their sheer talents were inadequate to overcome, and
| they had to persevere.
|
| https://blogs.ams.org/inclusionexclusion/2019/06/26/living-
| p...
| ikr678 wrote:
| > Absolutely. No matter how gifted a person is, there is
| going to be some point in their lives or some domain
| where pure talent will be insufficient.
|
| Unfortunately, for some this comes in university where we
| see peers with worse grades getting access to better
| graduate roles and work placements because of who they
| are related to, and you can't study your way to having
| the right surname.
| JoshTriplett wrote:
| > Also gifted child here, but grew up with parents who
| drilled into me that "effort matters, you might not be the
| best, but with effort you can be better than who you were
| yesterday and that is a worthy endeavor"
|
| Can confirm that getting lauded for effort encouraged doing
| hard things and pushing the limits of my abilities, rather
| than focusing on things that came easily.
| Jensson wrote:
| Being lauded for effort when you didn't put in any effort
| doesn't help though, just makes you think grownups are
| dumb.
| JoshTriplett wrote:
| Being lauded for effort you _did_ put in can be quite
| effective, as confirmed both by numerous studies _and_ by
| the personal experiences of myriad people.
| Clubber wrote:
| >parents who drilled into me that "effort matters, you might
| not be the best, but with effort you can be better than who
| you were yesterday and that is a worthy endeavor"
|
| This is also taught heavily in middle/high school sports;
| it's a great life lesson.
| nuancebydefault wrote:
| This seems to be a story of a kind that shows up regularly at
| HN. People who are smart in several ways but because they
| cannot do what some other (1 out of 10000) people-with-or-
| without-children can, they don't feel smart and are a bit
| frustrated by it.
|
| Those others make a 'tutorial for creating a raytracer from
| scratch in a weekend', invent a format for a binary that runs
| as-is on several processor architectures, or are maintaining
| parts of the linux kernel.
|
| I easily recognize such stories, perhaps because that story
| might apply to myself as well. This unfulfillment treat applies
| to this post as well as the writer of the article (the writer
| indicated that before his 150 day submersion he felt a bit dumb
| at mathematics).
|
| The thing I want to bring across is now... we should not strive
| for such capability. There are many things to learn and ways to
| grow as a person, why beat ourselves up for not being very good
| at this or that particular thing?
| nsxwolf wrote:
| Well, we let kids believe they're just not good at math, and
| tell them that's ok I'm sure you're good at other things, and
| they believe it, and wish we'd stop doing that.
| nuancebydefault wrote:
| While they are not studying maths, they can grow and
| improve themselves in other ways, not?
| dwaltrip wrote:
| There's a world of difference between that and beating
| yourself up for not being in the top 0.01% of performance.
| MichaelZuo wrote:
| To coast through a serious program (physics, engineering
| physics, pure math, etc...) at a major university while
| barely doing any work and also simultaneously getting
| high marks takes a lot more than 0.01% performance.
|
| More like 0.001%, at the very least, with some extra luck
| needed too.
| pxc wrote:
| Worse still, we lead kids to believe that 'doing math' is
| performing computations. And so even many kids that can
| calculate passably grow up thinking that 'math' is boring
| and they hate it.
| nuancebydefault wrote:
| Pretty early after kids learn about numbers and
| computations, they learn about sets, units, lengths,
| surfaces, weights etc.
|
| Where i live, mathematical formulas are already thought
| to 7-8 year olds. Also real world questions are asked for
| which they need to find a solution, and where they need
| to explain how they found it.
|
| > grow up thinking that 'math' is boring
|
| How can it be thought in a less boring way, i do not
| immediately see it.
| pxc wrote:
| [delayed]
| IOT_Apprentice wrote:
| We have not acknowledged an approach that teaches the
| majority math properly. Find approaches that do and also
| have some problems that resonate to children in an age
| appropriate way set for their environment.
| KronisLV wrote:
| > There are many things to learn and ways to grow as a
| person, why beat ourselves up for not being very good at this
| or that particular thing?
|
| I'd say that this takes a lot of work to unlearn, be it
| social media or whatever else seems to teach us to compare
| ourselves against others. Even though there are people way
| more brilliant than me out there (maybe they're naturally
| gifted, maybe they have a better work ethic, or different
| circumstances), it is definitely possible to be happy for
| their success, rather than lean into being jealous or what
| have you.
|
| Of course, they will often achieve more than I will and will
| lead better lives as a result of that, but that's also
| something to accept and take in stride, rather than for
| example believing that I'm some temporarily embarrassed soon-
| to-be millionaire who's one good idea away from a lavish
| lifestyle. Not that it should discourage me from being
| curious about new ideas, even if writing my own particle
| simulation quite quickly ran into the n-body problem and also
| the issues with floating point numbers when the particles get
| close and the forces between them great.
| MichaelZuo wrote:
| What made you believe you were in the 99.999th percentile
| when going into university? (As opposed to something more
| realistic like the 99th percentile)
|
| Unless you were literally outsmarting your teachers every
| day at age 16, it seems difficult to successfully fool
| yourself in this way.
| biotinker wrote:
| There are a lot of things that one can be in the absolute
| top of, and overall academic achievement need not be one
| of them.
|
| Speaking personally, when these articles come out, there
| are always a lot of comments about "I didn't really try
| super hard in high school, but college was a huge wakeup
| call for me and I had to learn to learn."
|
| That wasn't me at all. I somewhat lazily skated through
| high school, and got a mix of 4s and 5s on AP exams. I
| did the exact same thing in college, with no change to my
| work/learning ethic, and lazily skated my way to
| finishing my 4-year molecular bio degree in 3 years, with
| a GPA of like 3.5 or so. Then I went to grad school, did
| more of the same for two years, and won an award for
| having the 2nd best masters thesis produced by the
| university that year.
|
| Then I got a great job in my field doing cancer research,
| did that for 5 years, then jumped careers entirely and
| now work in robotics.
|
| But you know what? I feel like I'm constantly surrounded
| by people smarter than me. I'm not some brilliant person,
| I'm just some dude that when presented with some problem,
| things just seem to make sense for a path forwards, and
| maybe my special thing is that I just always go explore
| that path and learn that either I was right or why I was
| wrong and that just pays dividends. When I see people
| around me who work hard at things, who study and memorize
| and read papers, they impress the heck out of me, because
| I really struggle to do the same thing. And when I do, I
| really struggle to absorb any information; if something
| doesn't make sense to me, it's like it just passes out of
| my head. I have to do/build/try it to make it make sense
| a lot of the time, or at least have things framed in a
| way that just intuitively makes sense for me.
|
| Anyway, my point is that maybe I was the top 99.99% of
| _something_ , because, clearly I was/am pretty good at
| some things that apparently most "gifted" people struggle
| with. But I never got a 4.0, I never aced all my classes,
| and I never really cared to as long as I felt I was
| getting what I needed to out of the classes. I did the
| work I needed to do to gain the information and skills I
| felt I was there for, and as long as the number assigned
| to me by the professor for doing so was at least an 80, I
| was happy.
| KronisLV wrote:
| > What made you believe you were in the 99.999th
| percentile when going into university?
|
| Oh, nothing at all. I'm just a case of suddenly
| discovering in university that you also need good work
| ethic and that showing up alone is no longer enough (as a
| sibling comment points out) and you can't always cram all
| of the topics for exams in your head in a single night
| before the exam. In my case, calculus introducing new
| concepts (for which I didn't have a practical use, so it
| was even more confusing) and probability theory get less
| intuitive was that wake-up call. Well, that alongside an
| ASM course with a toolchain that I couldn't easily get
| working on my computer, or working with Prolog in similar
| circumstances, or understanding that I've underestimated
| how long making a 2D simulation project in C++ for extra
| credit would take, if I need to have collision detection
| and some physics for a soccer example.
|
| That said, in my Master's studies, once I got to
| specialize in the things that were of more interest to
| me, I ended up graduating with a 10/10 evaluation for the
| thesis and 9.87/10 weighted average grade across the
| subjects. That's not like a super big achievement from a
| small regional university, but definitely goes to show
| that learning some things was easier for me than others.
| I probably need to venture outside of my comfort zone
| occasionally though and not just do the things that are
| comfortable.
| vasco wrote:
| The difference is that math is the only field of study of
| things that are 100% true about the universe. It's the most
| pure knowledge that humanity has, so it's normal people
| recognize it. You can read 100 philosophy books and maybe you
| will learn a few things that are correct among all the
| rambling, but everything you learn from the basics of math
| proof by proof all the way "up", you can be assured
| everything is true. There's something special about this
| field of knowledge that nothing else has.
| badpun wrote:
| Math is not about the universe, it would be true even if
| the universe didn't exist at all.
| riwsky wrote:
| It is, however, about turtles.
| tsurba wrote:
| In a sense even this is not true, as in any sufficiently
| complex (which turns out to be quite simple) formal system
| you can create proofs that are true and untrue at the same
| time creating a contradiction. In other words, mathematics
| works by setting up useful axioms and following up on the
| logical consequences, but they usually can be used to
| create contradictory proofs even if useful in many
| problems.
|
| I recommend learning about Godel's incompleteness theorem
| behind it all.
|
| For a pop science book that explains it nicely I recommend
| "I am a strange loop". The wiki intro is also quite good
|
| https://en.m.wikipedia.org/wiki/G%C3%B6del%27s_incompletene
| s...
| nuancebydefault wrote:
| Wait a minute, the universe as we know it, is a model of a
| universe, the way we humans understand it today.
|
| That model is flawed, this is in fact the basis of science.
|
| The latest scientific finding is considered true until... a
| more advanced model proves that there are cases where it is
| not true. A thrown object on earth follows a parabole? ...
| no it follows a straight line, the space around it is bent
| by a force that is known as the gravitational field.
|
| What about math itself, no universe considered?
|
| Math itself follows axioms which cannot be proven. Since we
| found no contradictions in the maths built upon those
| axioms, we consider those axioms to be true. You can think
| however of axioms on which you can build equations that are
| true and untrue at the same time.
|
| My point being, whether we like it or not, the Truth with a
| capital T does not exist or at least cannot be proven.
| jcpst wrote:
| > And if I'm struggling, as someone who's not burdened by
| having children to take care of or even not having the most
| demanding job or hours to make ends meet, I have no idea how
| others manage to have a curious mind and succeed the way they
| do.
|
| Paradoxically, I _feel_ like I have more time after I had kids
| than before. This is of course, after YOB (year of baby- first
| 12mo).
|
| You see, I experienced such small slices of free time during
| YOB, that I became way more efficient at a ton of stuff, and
| dropped things that were time wasters.
|
| Because I reproduced, I needed more dough. After working 3
| jobs, 90 hrs a week for long enough, I decided to study
| programming.
|
| Went to a code boot camp and walked out with a job. But the
| grinding didn't stop there. What followed that was years and
| years of grinding, and studying as much as possible outside of
| programming at work.
|
| Until finally, I got where I was going. I climbed up the ladder
| until I got tired of climbing, and avoided more stressful and
| time-demanding roles like management. I get senior dev
| compensation, don't work more than 40hr/week, and I don't
| commute. This is the life I built.
|
| For everything I pursue, there are others who can run circles
| around me. But I can still look down from that ladder and see
| how far I came.
|
| Wait, what am I talking about? Ok, the whole point is I became
| efficient and middle-class because I have mini-mes that deserve
| it.
|
| Also, you never know what's on the other side of that wizard
| level person you see. Everything I said sounds nice, but I
| wasn't taking care of myself. Last year I had a mental
| breakdown, and am just now getting out of it.
|
| So yeah, you're not alone, etc etc, you know. There's probably
| more people that can relate than you think.
| xyzzy_plugh wrote:
| It's wild how much kids teach you about yourself and your
| time on this earth, let alone your time available each day.
|
| It's hard work but I can't think of a better motivation to
| improve one's self. And the best part is you don't even
| necessarily realize that it's happening.
| jmatthews wrote:
| I was that kid, now I have 3 sons and I am homeschooling my
| oldest because he is similar. The hack is essentially to praise
| the work, not the outcome. On some level you have to be unfair
| to your kid to be fair with him.
| treflop wrote:
| I think one factor that people forget when they see someone
| else that dive headfirst into something like low level
| programming or electrical engineering and then wonder why they
| haven't is because maybe you just don't care.
|
| I did personally get a degree in EE and have worked on low
| level programming (and funnily enough I do a lot of frontend
| these days), but there are things that still wow me like people
| writing game engines. I tried working on game engines briefly
| and I never got anywhere.
|
| I eventually realized that I just _don't care_ about game
| engines or making games for that matter. I wasn't willing to
| put in the effort. Watching other people build game engines is
| more of a spectator sport for me. And that's fine.
|
| But when I do find something that makes me really happy, it
| keeps me up thinking all day and night about it.
| Aurornis wrote:
| > And if I'm struggling, as someone who's not burdened by
| having children to take care of or even not having the most
| demanding job or hours to make ends meet, I have no idea how
| others manage to have a curious mind and succeed the way they
| do.
|
| Parent here. Raising children has a way of making you more
| efficient. In my pre-child years there were days where I could
| putter around and relax because I knew I could make up the work
| later in the evening or even a weekend. Or at least that's the
| lie we tell ourselves in the moment.
|
| Post-kid, things come into focus. You learn how to do the work
| now whether you feel like it or not, because the price for
| doing it later becomes much higher.
|
| I also was misled by all of the internet comments about how
| parenting and raising kids is awful and everyone secretly hates
| it despite their fake happy social media posts. After having
| kids you realize you actually like your kids and want to spend
| more time playing with them. That alone is motivation to get
| work done now so you don't have to sacrifice the valuable kid
| time later.
|
| It's hard to explain until you get there, but I've talked to
| many other parents who went through the same growth phase. I've
| also caught up with some (not all, _some_ ) of my old friends
| from high school who were academic superstars but who did not
| have kids, and it's remarkable to observe how some (again,
| don't flame me, not all) of them are stuck in the low
| motivation/low effort loop and cite that as one of their
| reasons for not having kids. To each their own, but I for one
| am glad I ignored the internet/Reddit rhetoric about how kids
| are an impossible burden that will only make your life worse.
| sersi wrote:
| Also, having a kid is great to get you to learn new things. I
| want my son to learn to play an instrument, so I've finally
| been taking piano classes because I know that very few
| children of completely non-musical parents actually succeed
| in learning to play instruments. Learning piano has been a
| lot of fun, I have a blast playing simple things with him
| (he's still young) and learning some of my favorite music.
|
| Likewise, after reading "Math from Three to Seven: The Story
| of a Mathematical Circle for Preschoolers", I've been having
| a lot of fun getting back into Mathematics because it's fun
| doing things like this together.
| wvh wrote:
| The coasting until real work was required part sounds very
| familiar, and also the getting by in objective terms but being
| unhappy and struggling mentally part too.
|
| After embarrassingly many years I've learned that there's a
| little voice inside that says "you can't", "that won't work",
| "that was shit". Succeeding at anything, for anybody, is
| stacking a whole lot of little failures and frustration, but
| crucially, being able to ignore that little voice. I, and I
| assume many of us, have burned half of my energy and mental
| health fighting that little voice. To me, it seems that most of
| those manage-anything people are not just generally gifted
| intelligence-wise or physically, but have learned to silence
| that inner voice and just do things until they succeed, while
| still avoiding to do "stupid" things.
|
| As a distance runner, I've learned a bit of dopamine trickery,
| but managing that inner voice, and even being aware of it, is
| turning out to be a life-long project. It becomes a mission of
| figuring out what you're burning your energy on, and why. You
| can't strive for happiness or success, but it should be
| possible to get enough stuff done to find contentment and
| acceptance.
| detourdog wrote:
| I have just recently learned that the little voice can be
| amplified by people around you. Being removed from those re-
| enforcing that little voice is an amazingly freeing mentally.
| brailsafe wrote:
| Although I'm not on the super sweaty side of trying to grok
| some of those items in your list, I have been going back to
| square one from the perspective of having started with and
| followed the whole dependency tree of frontend but never
| understanding the really low level.
|
| Over time, I've learned to appreciate getting "reps" in
| whatever subject, and just sitting with it for ages and
| grinding your brain into dust trying. Something I've also been
| noticing now in my 30s, is that your and my ability to do that
| is something to be proud of--even if it won't come as fast as
| for someone innately faster or with more prereqs--because many
| people are truly not curious and don't push themselves. The
| amount of otherwise smart people even that won't or can't sit
| down to learn something for curiosity sake, and I'm not talking
| something very long-term like game engines, is... like next to
| zero people.
|
| And it not just true for learning hard or impractical subjects,
| but the overwhelming majority of the surprisingly high number
| of decent friends I have, do not have the patience for pushing
| themselves and will bail on hard physical activities as quick
| as possible, even if they're pretty fit. It's quite eye
| opening. They tell me they want to go do __, but not if they
| can't squeeze it in to an afternoon, even if they definitely
| have the time, and it really detracts from trying to share the
| experience or curiosity.
| bonoboTP wrote:
| Just accept that this is the case and meet people where they
| are. And collect some friends that share your curiosities and
| passions. People can be good and reliable friends even if
| they are content living a simple life in simple ways as it's
| always been, without pushing for abstract novelty and
| learning.
|
| People try to blame school for killing the natural curiosity
| of kids, but I've come to be very skeptical about this. It's
| an idealized romantic notion. Most mammals lose their
| playfulness in adulthood and most humans are like this too,
| even if not to the same extent (some say humans retain more
| neoteny, similar to domesticated animals like dogs that also
| remain more playful than wolves as adults).
|
| These two types of people often misunderstand each other. For
| you a job might become boring if it stays the same year upon
| year. But for most people the thought of having to keep up
| with ever changing knowledge requirements after school and
| even once they are settled in their jobs is utterly
| _terrifying_.
| brailsafe wrote:
| Ya, I'd actually agree with your whole comment, and for
| that reason I was somewhat hesitant to frame my last
| sentence as I did, because what you suggested is what I've
| come to learn to do anyway. Part of the reason I was
| hesitant is because it's not about me, so much as it is
| about reconciling that ambiguous difference in expectation
| when they express that they have an interest in something.
|
| Unfortunately, there's some amount of skepticism and doubt
| I have to embrace, being careful what I express an interest
| in, and letting them be as serious about whatever
| commitment as they're authentically prepared for. I
| typically only do things for myself now, and extend an
| invitation to people I think might want to join, but I
| don't bet on it, and only rarely plan more involved
| activities with people who've clearly put in some organic
| initiative. On the _extreme_ shallow end of this paradigm,
| I 'm sure as hell not going to agree to go on a hike
| "sometime" with anyone who's hopped up on coke or drunk at
| a party, obviously. But sometimes it's just less clear, and
| I have to ask myself "how likely is it that this person
| would plan this themselves and take the initiative, and do
| they even have appropriate footwear or baseline level of
| fitness?", and I might ask that explicitly and go from
| there. I also do the same for the them, such as if I'm
| asked if I want to "get into Tennis" or something. I just
| say "nah, not really, I might join if you have a spare
| racket but right now I couldn't give it the investment it
| might deserve" and we can spend time doing other things we
| already enjoy together.
|
| Otherwise though, I try to keep a small list of easy stuff
| in my back pocket to accommodate people with more rigid
| schedules and less innate drive for that specific outing;
| if after a few they want to take things further, I'll
| extend myself, and that's how good friendships last.
| bonoboTP wrote:
| Sometimes people are just bad at predicting their own
| level of commitment or disentangling desires and reality.
| Or they know they are "supposed to" do something so they
| promise it or even believe that this time it will work...
| This is often the case with diet and exercise and
| studying hard. Then sweets, sitting on the couch and
| procrastination happen. Then the cycle repeats.
|
| Also in some cultures it's rude to reject invitations so
| people always say yes but it's understood implicitly by
| both parties that it's just politeness. The US tends to
| be like this, always saying stuff like "you should come
| over for dinner sometime" etc and you must reply
| enthusiastically but both the invitation and the
| acceptance count only in reality if a date and time is
| attached. This is often baffling to continental Europeans
| for example who tend to be more direct and would follow
| up with a message next day, asking when they should come
| over. Which is awkward because it wasn't a real
| invitation.
| bonoboTP wrote:
| > Lovely article, though honestly getting those prerequisites
| also takes a lot of time, effort and either motivation or
| discipline in ample amounts.
|
| Exactly. It's like saying that winning a marathon is easy, you
| just need to run fast enough.
|
| The entire problem is that many people won't be able to learn
| the prerequisites of advanced math. There are always
| exceptional cases, like someone really smart who just totally
| slacked off during school because they spent all their time
| building apps or websites or tinkering with games or
| electronics. Or someone who was never given the opportunity to
| learn certain subjects because they had to work as a teen
| because their parents died etc. But the vast majority of people
| are presented with the prereq material they just can't absorb
| it.
| austin-cheney wrote:
| Math is hard but fortunately programming is easy. I am just a
| dumb soldier who taught themselves to program while traveling
| around Afghanistan.
|
| The down side of being a dumb soldier programmer is that it's
| really really hard to find sympathy when people complain about
| how hard life is when they are utterly reliant on a bunch of
| abstractions and clutter to do their jobs for them.
| brigadier132 wrote:
| Don't sell yourself short, programming is just as difficult as
| math. I'm confident saying if you are able to code you would
| also be able to learn pretty advanced math.
| jakeinspace wrote:
| It's a silly sort of comparison. Is reaching the programming
| competence necessary to hold an average software engineering
| job easier than attaining a PhD in mathematics? Yes, 100%. Is
| becoming a well-regarded software engineer by building large,
| complex systems or contributing significantly to projects
| like the Linux Kernel easier than getting to the top of your
| field in academic mathematics (tenured professor, high-impact
| papers)? I don't think so, or at least, it's not obvious to
| me that one is more "difficult" than the other. They take
| different skills and personalities, and I don't think that
| talent in one would necessarily translate to talent in the
| other.
| brigadier132 wrote:
| > average software engineering job easier than attaining a
| PhD in mathematics
|
| This isn't what I'm trying to say, I'm just saying that
| someone that can become good at programming could become
| good at advanced mathematics. If your criteria for good in
| advanced math is a phd then we disagree.
|
| > They take different skills and personalities
|
| I disagree, I think the skills are largely the same.
| Programming is literally encoding logic using a programming
| language which requires mathematical reasoning ability.
| Programming is more immediately practical, accessible and
| requires fewer credentials and that's why I think more
| people become good at it than math.
| austin-cheney wrote:
| That depends on what _being good_ means.
|
| I have absolutely no problem being a 10x developer. While
| I might be a better than average developer I am not more
| than 10x more talented than my peers.
|
| I have no problem achieving 10x status because I ask
| better questions and loathe doing repetitive work,
| especially out of social conformance. It completely blows
| my mind that most people strive first for emotional
| comfort, especially amongst a social reference group. Any
| effort moving in the opposite direction of that emotional
| comfort results in fear and possibly anxiety.
|
| That is why I abhor software as a career. As a dumb
| soldier I feel like I am the least educated in the room
| and my delivery is inversely proportional to that. That
| is because, as a dumb soldier, I focus first on delivery.
| Focusing on delivery first means knowing the end state
| and cutting out all the bullshit in the middle. Military
| people think like that because they are highly assertive.
| The average software developer is meek.
|
| Can you see the friction that follows? You have this dumb
| guy with less education that is a 10x developer but not
| because they are better at writing software. Nonetheless
| the output executes much faster with greater durability
| written in a fraction of the time only because of a
| difference in value system. That leaves the dumb soldier
| believing they are surrounded by a bunch of cowards.
| YZF wrote:
| I also taught myself how to program at a younger age.
|
| You'll be surprised how hard this is for many people. I was
| surprised by how many really struggled through the first
| introductory programming course in university.
|
| Math isn't that hard. But for almost everyone it requires a lot
| of work to get to the next level. Some of the same skills
| transfer. Something too removed from where you are feels very
| alien, partly because of language, symbols, conventions, etc.
| and also not having the building blocks/theories etc.
| bonoboTP wrote:
| Math/physics/engineering/programming rely on similar skills
| but need somewhat different attitudes. I know people who are
| great at advanced math (especially earlier generations) but
| don't think about it computationally at all, and their code
| is very messy. On the other hand I know great programmers who
| just don't like to think in terms of proofs and dislike the
| ambiguous and vague nature of math notation (yes, math is
| much more vague and handwavy in notation compared to its
| reputation, especially compared to programming). And there
| are people who love programming as a kind of puzzle and like
| prodding it for its own sake, pursuing elegance and will get
| nerdsniped for weeks if you teach them about quines, while
| others just love building things and whatever gets them there
| doesn't matter too much.
| cultofmetatron wrote:
| learned to code pretty easily. the rapid feedback was key vs
| math where you do a problem set and it might be days before the
| graded assignment is returned. I found mathacademy 2 months ago
| an its been a game changer for me. I just completed the first
| of their foundations course and it filled in a bunch of cracks
| in my foundational knowledge I didn't realize I had. the big
| advantage is that you do the problem and you get feedback
| immediately. They figured out how to close the loop on feedback
| to make learning it efficient.
| casebash wrote:
| Just thought I'd add a comment as someone who came top of the
| state in my grade in multiple olympiad competitions:
|
| I always felt that a large part of my advantage came from having
| a strong understanding of maths from the ground up.
|
| I felt that a lot more people could have gained the same level of
| understanding as I did if they had been willing to work hard
| enough, but I also felt that almost no-one would, because it'd be
| an incredibly hard sell to convince someone to engage in years-
| long project where they'd go all the way back to kindergarten and
| rebuild their knowledge from the ground up.
|
| In other words, excellence is often the accumulation of small
| advantages over time.
| ofrzeta wrote:
| I can only blame teachers. In primary school after four years
| they finally managed that there's only on kid per class left
| (that would be you I guess) has fun with math. At home I am
| fighting an uphill battle because I know it can be fun (my kid
| even likes logic puzzles). Living in Germany, for the record.
| TheRealPomax wrote:
| I'd rather blame the system that teaches the teachers. I'm
| certainly not going to blame someone for not knowing how to
| teach an onramp that they don't even know exists because they
| themselves were never taught properly.
| doubled112 wrote:
| Sometimes it's just the teacher.
|
| I loved reading until my grade 4 teacher decided we would
| all write a book report every week. Haven't read a story
| book since. It's been 20+ years.
|
| Forced fun is never fun. The other grade 4 class wrote
| three that year.
| pastage wrote:
| People react differently to task and teachers, there is
| no one way to do it. I got good grades because a teacher
| let us repeat a task like "write a report" seven-fourteen
| times. The feedback was given by him in class
| highlighting the important points of getting a good
| grades, and then 24 hours after handing in the report we
| got it back with notes mentioning which important parts
| we had missed.
|
| This thought me the rather simple lesson that getting it
| right on the first try is really hard.
|
| Writing a book report is completely different from
| reading a book. I have heard people doing literature in
| university being sick of books because of the same issue.
| dleink wrote:
| That sounds like a dream. I have a distinct memory of
| doing in class writing in 3rd grade where the teacher
| would force us to redo it if there were mistakes and give
| minimal feedback. As far as my 3rd grade memory can
| recall, I rewrote it several thousands times and never
| got it all the way right.
| veunes wrote:
| The idea of starting from scratch and rebuilding one's
| knowledge, especially when it means going back to the basics,
| is daunting
| randcraw wrote:
| I think much of that 'daunt' comes from the lack of
| instructional resources needed to support a solo journey
| through higher math. Yes, there are some great illuminating
| sources (like Kahn Academy and 3blue1brown), but if you're
| embarking on an epic quest (like recapping a BA in math), the
| essential guidance needed for coherent and graceful passage
| through all the requisite concepts simply does not exist --
| short of reading 20 HS and college textbooks, which will
| subject you to a maddening amount of redundancy while leaving
| many fundamental concepts underexplained.
|
| The day that large language models can capably tutor me
| through the many twisted turns of higher math -- that's when
| I'll believe that deep AI has achieved something truly
| useful.
| fragmede wrote:
| Can you link a chat and show specifically where one falls
| off explaining, eg complex numbers or integration by parts?
| it's been a while since my math minor, but ChatGPT seemed
| to be able to guide me through what I recall of those
| topics.
| laichzeit0 wrote:
| I always sucked at math, even though I did it in undergrad. I
| basically did this over the course of the last five years to
| try get better. It went something like this:
|
| Spivak - Calculus. This was a bad idea. Got maybe 30% of it.
| Gave up at Taylor series.
|
| Hammack - Book of Proof. Finally understood how to prove
| things, and induction arguments.
|
| Abbot - Understanding analysis. Got far, things fell apart
| around the Gamma function.
|
| Apostol - Volume I. Got better at calculus. Also
| trigonometry. Exercises were easy. Skipped differential
| equations. It was too hard.
|
| Hoffman/Kunze - Linear Algebra. Gave up after a few chapters,
| too hard.
|
| Friedman/Insel - Linear Algebra. Much better, got to the
| Spectral Theorem and gave up.
|
| Rudin - Principals of Mathematical Analysis. Absolutely
| brutal, probably got 30% of it.
|
| Abbot, round 2. Much easier this time, got through the whole
| book.
|
| Spivak, round 2. Much better, got through the whole book.
| Actually found it easy.
|
| Hubbard - Vector Calculus. Gave up early, it was too hard.
|
| Apostol - Volume 2. Much better. Stopped somewhere in the
| middle when it got too focused on differential equations and
| physics stuff.
|
| Back to Friedberg / Insel - Made it through the spectral
| theorem.
|
| In between I was doing a lot of mathematical statistics and
| probabilty stuff like Casell-Berger (I did this book twice,
| each time going back to the math where I floundered). I've
| worked through just about every exercise in the above books
| and watched YouTube video lectures where they exist (there is
| a good one for Rudin). Solution manuals sometimes exist,
| sometimes you have to find university courses based on the
| books and look for homework assignments where they have
| posted solutions, Quizlet has ok solutions, some are buggy.
| Apostol volume I some dude worked through and posted online.
|
| Anyway point is I refused to accept how stupid I am and I
| brutally forced myself to become better at math. My attitude
| was I don't give a fuck how long it takes, I will keep going
| until I get better.
|
| I think I'm better now, although I'm still shit. It's true
| what von Neumann said: In mathematics you don't understand
| things, you just get used to them.
| novok wrote:
| I think mathematics education is pretty horrible this way. You
| only start actually learning the foundations of math in your
| 3rd or 4th year of undergrad.
|
| At least nowadays there is a shit ton of youtube resources and
| more, so a self interested kid can learn it far easier. I tried
| and the books that were out there were... sparse and textbooks
| are written for other professors, not students.
| Viliam1234 wrote:
| It's not just working hard enough, but also doing the right
| kind of work. Many people make the mistake of trying to
| memorize things without understanding. Which may be easy at the
| beginning when you memorize a fact or two, but it gradually
| accumulates, especially in math when the old topics never go
| away as the new ones are introduced. And then the memorizers
| are actually working much harder, and even that is not enough,
| so they fail.
|
| So why the aversion to understanding? I suspect part of that is
| generational; if your parents sucked at math because they
| relied on memorization, they probably won't introduce you to
| math as an something worth understanding. It will either be
| "give up", or "work harder" but in the sense of memorizing
| harder. Not just your parents, but the entire culture around
| you will be like that. Another part is that most math teachers
| at elementary schools actually suck at math; because teachers
| are many, but people good at math are few and they have many
| better careers available. But another problem is the insistence
| of school system on everyone going forward at a predetermined
| speed -- sometimes understanding takes time, and when you don't
| have the time, you are forced to memorize; but once you start
| memorizing, you usually need to keep memorizing, because
| understanding can only be built on understanding the
| prerequisites.
|
| Properly taught elementary-school math should be fun, like
| this: https://www.matika.in/en/ Fun makes people think.
| madaxe_again wrote:
| Understanding is critical.
|
| I unfortunately spent the entire introduction to calculus in
| hospital, so missed it - when I came back to school, I was
| dropped straight into "differentiate this" and "integrate
| that". There was no explanation of what either operation was,
| just the rules that you followed to obtain the result. I had
| no idea that we were looking at rates of change or at areas
| under curves. For the first time in my life, I found myself
| bewildered, and struggling - until a month later I happened
| to find myself reading a biography of Newton which actually
| explained what the purpose of calculus/fluxions was - and
| then it became easy, as it was obvious if a result was
| nonsensical.
| synecdoche wrote:
| If passion, or own experience, is missing it may be a case of
| unknown unknowns for both parents and teachers.
|
| The Matika site looks really nice but I have difficulties
| comprehending the instructions. Even the very first one for
| first grade. "Children step by record." What does that mean?
| I tried the next one. "During addition we write addends below
| each other..." What? If all addends are below, no addend is
| on the top. It makes no sense. Then, "...and the sum below
| the line" with no line in sight. What, where, which line,
| how? That was frustrating.
| vonunov wrote:
| I feel the same way when I'm on hold and a recording tells
| me "your call will be answered in the order it was
| received". This isn't about grammatical pedantry -- I don't
| care that they didn't say _in which_ -- it 's about it not
| making sense. Which, as I said, isn't _grammatical_
| pedantry. But it probably is still a bit pedantic. Still,
| though, how can _one thing_ have an _order_? What order was
| my call received in? Is it before or after itself? I get
| the sense that whoever recorded that didn 't spend any time
| actually thinking about it, or they would have said "Calls
| are answered in the order [in which] they are received" or
| something.
| rendaw wrote:
| What are the fundamentals one should learn in kindergarten,
| elementary school, etc?
| casebash wrote:
| I'm not going to try to recap all of that, but, as an
| example, if you have a sufficiently strong understanding of
| arithmetic, learning basic modular arithmetic should be
| effortless, pigeonhole principle completely obvious.
|
| I was quite surprised when I tried applying for a Microsoft
| internship in uni and they gave me a question on the pigeon-
| hole principle.
| whatshisface wrote:
| Most kids don't build up knowledge over time, they forget it
| all over summer vacation.
| creesch wrote:
| Very well put. Many people are very blind for this, they forget
| that everything they can do they at some time had to learn as
| well. And not everyone learns everything at the same time.
|
| Anecdotally, something I can actually confirm from personal
| experience with math. As long as I could remember, I had
| trouble with a lot of it.
|
| Then during the last years of high school I had an excellent
| teacher and a lot of concepts actually did start to click on
| some level. Frustratingly, I still had a lot of trouble. While
| I understood the abstract concepts much better.
|
| In order to solve issues, I still had to apply a lot of
| concepts I was supposed to have learned in all the years
| previously.
| mewpmewp2 wrote:
| I just think for some people math is very fun since the very
| young age and so they of course practice it. For others it may
| not be, so it is hard work for them. E.g. I have always enjoyed
| ever since I can remember doing these exercises. When walking
| home I used to multiply different numbers as a past time in my
| head. Most people are not going to do those things, and it
| didn't feel hard work at all.
|
| In first grade I used to run through workbooks being addicted
| to solving those problems like some addictive mobile or video
| game and at that point teacher had to stop me and I was
| frustrated.
|
| I only had this addiction to math and physics - a bit to
| chemistry, and I couldn't really focus on other text /
| memorization based subjects.
|
| And it makes sense to me that genetically in a population you
| will have brains out of the box that are naturally optimized
| for different specialities, since having a specialized brain
| allows you to have more power in that specific area. Problem is
| when you force those specialised brains into the same way of
| studying.
| bonoboTP wrote:
| Exactly. We enjoy different activities. For math oriented
| kids it's not a grind, it's interesting and fun. For me,
| reading novels was much more of a grind, as I just wasn't
| that interested in people and their conflicts and condition.
|
| It took until my twenties that I could realize the value in
| humanities and "social" topics.
|
| Similarly most people will naturally learn about countless
| types of fashions and connotations of liking various music
| bands etc which is actually quite a lot of information to
| memorize. But it's fun and feels relevant while math feels
| disembodied and irrelevant to their social goals in life.
| tsurba wrote:
| Yet understanding is necessary but not sufficient when you read
| university math, especially advanced courses.
|
| Proofs assume you have the elusive thing referred to as
| "mathematical maturity", which means many algebraic
| manipulation steps are skipped because it's assumed you can
| just see the result straight away.
|
| This ability to see the connection is not understanding but
| learning by rote, having done the same tricks with similar
| equations a thousand times.
|
| This is what makes advanced math books/courses slow for me as a
| CS phd researcher. I can very slowly progress through, but it
| takes a massive amount of time to work through what just
| happened. If you take 60 instead of 20 courses on math the
| routine you have is just completely different. I guess you can
| call it fluency in the language.
|
| (For example now I'm reading optimal control & variational
| calculus along with the functional analysis it needs, its
| heavy.)
| det2x wrote:
| How would you approach rebuilding foundational knowledge from
| the kindergarten level? I have completed all the courses on
| Khan Academy from kindergarten through 6th grade and have also
| practiced with more challenging problems beyond those provided
| on Khan Academy. I'm trying to find the most effective
| strategies to solidify these fundamental skills.
| ocean_moist wrote:
| Some credit needs to be given for just jumping in. Just
| analytically breaking down complex problems into pieces that are
| understandable.
|
| It's often faster to work top-down and turn unknown unknowns ->
| known unknowns -> known knowns.
| JustinSkycak wrote:
| It can definitely be helpful to take a top-down approach in
| planning out your overarching learning goals.
|
| However, the learning itself has to occur bottom-up. Especially
| in math. Math is a skill hierarchy, and if you cannot execute a
| lower-level skill consistently and accurately, you will not be
| able to build more advanced skills on top of it.
| MichaelNolan wrote:
| I think these conversations of top down vs bottom up, are
| frequently a case where people are talking past each other
| due to using different definitions, and having different
| goals. And I think this is especially common when one of the
| people is a software engineer, and the other is not.
|
| For software, the tooling and the abstractions are so
| powerful that you can make incredible software without
| knowing what's really happening under the surface. Imagine an
| "abstraction ladder", with each level building on the
| previous level. Frequently in software development, you only
| need to understand a single level n, and maybe a little of
| n-1, to make great software. So the advice of "just jump in"
| is often great advice because you're jumping into a "shallow
| pool".
|
| (P.S, I love the work you're doing with MathAcademy, though I
| wish there was discounted price for "casual" learners that
| only have an hour or two a month)
| JustinSkycak wrote:
| Agree, it depends highly on goals. _Using_ off-the-shelf ML
| /AI models (to make great software) requires far less
| background knowledge than _implementing_ new models being
| introduced in papers, which in turn requires far less
| background knowledge than _producing_ new models that
| improve upon the state-of-the-art.
|
| Thanks for the kind words about Math Academy! It's true
| that we focus on students who are trying to acquire math
| skills to the highest degree possible -- we teach math as
| if we were training a professional athlete or musician. We
| maximize learning efficiency in the sense that we minimize
| the amount of work required to learn math to the fullest
| extent.
|
| I realize that there are many learners who only want to
| devote an hour or two per month, but, at least right now,
| such learners would be better served elsewhere. It's a
| totally different optimization problem -- maximize surface-
| level coverage subject to some fixed, miniscule amount of
| work -- and as a result it would require different
| different curriculum and possibly different training
| techniques (or at least, differently calibrated
| techniques).
|
| But it's definitely an idea to think about in the future.
| :)
| ocean_moist wrote:
| > Especially in math. Math is a skill hierarchy, and if you
| cannot execute a lower-level skill consistently and
| accurately, you will not be able to build more advanced
| skills on top of it.
|
| To be frank, I am only a math hobbyist and studying CS. I
| haven't taken any proof based courses (only calc 3, linear
| algebra).
|
| However, it is my experience that once you get the initial
| proof based stuff down and are familiar with common proof
| writing techniques, you can pretty much learn anything.
|
| I often start on an nLab page for a mathematical structure
| and just click on links in the definition till I see
| something I know. I then try and make sense of it and go back
| up the chain. I try to solve some problems and see some
| invariants. If I want to go more in depth I watch lectures on
| youtube and then read a book about it and do some more
| problems.
|
| I'm not really sure if this is a top down or bottom up
| process, but it seems more top down to me. Of course, if I
| encounter a whole field I don't know then I need to start
| from scratch and go bottom up. This is also for essentially a
| late-undergrad math major understanding of topics at most.
| danaris wrote:
| The top-down part is determining what skills you'll need,
| starting from the highest level and breaking them down as you
| go.
|
| Then the bottom-up part happens as you actually start
| learning them, methodically, building back up toward those
| high-level skills.
| photochemsyn wrote:
| Intelligence is far too complex to be meaningfully described with
| a single number like IQ. Measures of physical capability don't
| suffer from this issue - a person might be strong, or they might
| be fast, and everyone knows that the power lifter and the
| marathon runner use wildly different training regimens to improve
| their abilities.
|
| If physical capabilities are highly trainable, up to some genetic
| limit that the vast majority of people never even get close to,
| then it seems that intelligence must work the same way - e.g.
| prodigious feats of memorization can be achieved via training
| regimes (memory palaces etc.), as can one's three-dimensional
| visualization skills (e.g. a chessboard layout, or rotating a
| platonic solid, etc.) or the ability to rapidly construct
| arguments using logic and reason - but we don't seem to be able
| to classify different areas of mental ability as easily as with
| physical abilities.
|
| Sadly, this is one of those politically difficult topics as the
| blank slatists and the genetic determinists (Lysenko vs. Galton)
| have tried to use all kinds of pseudoscience to support their
| ideological arguments, when the underlying point is just that
| training your mind is as beneficial as training your body, and
| everyone should do it at least to some extent.
| ninetyninenine wrote:
| However iq is the most correlated number in psychology. It's a
| heavy predictor of many many things. It's the one thing in
| psychology that has the most scientific validation.
|
| Yes iq can't measure everything that intelligence represents.
| But it does measure something extremely important and
| meaningful to us.
| eesmith wrote:
| I think wealth might be more correlated, as it can be
| estimated without testing based on tax data. It's also a
| heavy predictor of many, many things, with scientific
| validation. Including IQ test scores.
| wenc wrote:
| If you're talking about IQ and wealth, they are not
| strongly correlated.
|
| IQ is correlated to income, but income is not wealth.
|
| https://www.sciencedirect.com/science/article/abs/pii/S0160
| 2...
| eesmith wrote:
| Then my main point is that wealth and/or income is likely
| more studied than IQ, because it is/they are easier
| information to acquire. Even in psychology, I suspect
| it's quicker to assess someone's "socioeconomic status"
| than IQ.
|
| The article you linked me to is paywalled. By "wealth" I
| mean family wealth even when one is 12 years old and have
| no income. The abstract says of another line of research:
| "Sibling comparisons ensure factors like the resources
| available during childhood, the impact of growing up in
| particular neighborhoods and genetic predispositions are
| all controlled, without explicitly adding these variables
| to the research."
|
| If they normalize for parental wealth, then the paper you
| linked to concerns a different topic.
| captainclam wrote:
| A really fascinating corollary I've observed since I've gotten
| into more advanced maths, or even doing actual research as a PhD
| student, is that there's nothing special going on at the higher
| levels. You're just working with different materials. Materials
| that require more time and effort to 'get', but once you get them
| they are just another tool at your disposal.
|
| I was similar to the author in that, throughout high school and
| undergrad, I presumed that the mind that could comprehend
| advanced math or do novel research (in any field) was truly
| unknowable. Like there was this x-factor they had that wasn't
| there for me.
|
| I've long enjoyed puzzle games (like The Witness or Stephen's
| Sausage Roll). It turns out that problem solving in non-trivial
| domains is never terribly different than problem solving in those
| games, or any other domain really. Like my brain isn't doing
| anything _different_ than the usual tree-search algorithm that
| any chess player performs when they are projecting moves ahead
| into the future.
|
| Its just iterating on concepts that seem abstruse to most people.
| But at the end of the day, deep problem solving in math or AI
| research tends to be the same moving-shapes-around-in-my head
| that I would do if I was trying to move an awkwardly shaped couch
| through a narrow doorway.
| dwaltrip wrote:
| That's a really cool observation, thanks for sharing
| almostgotcaught wrote:
| > Materials that require more time and effort to 'get'
|
| They really don't. Each rung in the ladder takes about as long
| to step through as the previous. The
| challenging/annoying/discouraging aspect is that a lot of
| research ( _especially_ in pure math) has so many rungs to step
| through.
|
| The truth is many of those aren't useful at all - distinctions
| invented purely for the sake of being able to say you invented
| something. Even when I was doing really "deep" research I could
| explain it to anyone by just dropping all the technical jargon
| and using goal oriented language instead. When I would do this
| most people would naturally try to reason about it in exactly
| the same way "researchers" would. The proof is they'd come up
| with the exact same solutions to the problems that were legit
| solutions, they had just already been discovered ie the low-
| hanging in fruit solutions.
| atomicnature wrote:
| The central thing to me is - "quality of efforts" more than
| "quality of results". For anything sufficiently complicated or
| "difficult" - one needs to persevere. There's nothing magically
| special in any place, like a university, except perhaps a few
| understanding people around to egg you on (that can make a big
| difference in the right conditions). But end of the day, it is
| the individual's effort that matters. Effort can make up for
| many, many deficiencies. More quality effort held steady over a
| long-enough time should produce at least tolerable results, if
| not exceptional results.
| atulatul wrote:
| But at higher you also learn how to solve problems. Suppose you
| see a problem which is quite unfamiliar, you have tools and you
| know how to use tools- combine tools, separate those and use
| for separate parts, invent tools, etc.
| otteromkram wrote:
| This is a good argument for, "why do I need to learn
| math/science? I'll never use it."
|
| Maybe you won't need to factor polynomials daily, but knowing
| how to solve that kind of problem can be applied to other
| scenarios outside of Algebra II.
|
| Great post!
| bonoboTP wrote:
| To see the brilliance of advanced ideas, you need to be quite
| advanced yourself.
|
| What you wrote is analogous to saying that playing football in
| the Premier League is nothing special compared to me and my
| weekend buddies playing in the yard, it's still human beings
| kicking a ball, just with better coordination and strategy.
| Yeah. Coming up with new math at a research level is also just
| manipulating conceptual objects in your mind. Except this
| insight doesn't make the average person capable of either.
|
| For some reason people have a big hangup around admitting that
| some people are more talented at abstract thought and advanced
| math than others, even though this is absolutely obvious even
| to a schoolkid. The existence of the Premier league in no way
| diminishes the value of kicking the ball with friends over the
| weekend. Math can be fun in the same way, but not everyone will
| reach the same levels.
| captainclam wrote:
| Hmmm...this wasn't at all my point, but I understand why I my
| comment could be read this way (the failure to communicate is
| mine).
|
| I am not suggesting an equivalency between all efforts at all
| levels, or that innate talent doesn't exist. I was not at all
| speculating about the nature of preternatural talent. The
| expertise-gap I was invoking was more like early undergrad to
| late grad school levels, not pick-up football to Premier
| League.
|
| The concept I'm getting at is that of a mental block I have
| observed in myself, and I suspect resides in others, which is
| really subtle but ultimately quite limiting. I'd have to
| think harder than I want to at the moment if I were to try to
| articulate it more clearly, but I do want to be clear that my
| comment wasn't about innate talent.
| bonoboTP wrote:
| Yes, maybe I have experienced something similar in my
| research area in machine learning. Fundamentally, the best
| people of the best labs use the same tools in roughly the
| same ways as I do, there's no set of magical secret tools
| on that tier. They also aren't really using any math I
| don't know about.
|
| They just comprehend papers quite fast, understand what's
| relevant and what is not with great intuition, have a lot
| of prior work in their memory, have gone through lots of
| projects so they know how to approach the new problem, they
| are aware of what actually are interesting open questions,
| they have refined "research taste", (and of course stuff
| like understanding the academic system and how to make the
| most of it etc). But the day to day activity is not
| fundamentally different than for lower tier researchers.
| They just have better ideas, better overview, and better
| execution. When they explain it all in hindsight it appears
| simple and as if you could have done it too. And of course
| they also run up against bugs and hardware issues and big
| messes but often just plow through and grind it out because
| they can see the light at the end of the tunnel well.
|
| It's kind of a bummer in a way. Life is just less magical
| than we imagine. When I was much poorer as a kid than now
| as an adult, I used to imagine that being rich must be so
| different. But actually people are just people, there is no
| discontinuity anywhere. I've flown business class and been
| to fancy dinners, it's not fundamentally different from
| taking a bus trip or throwing a student party at the dorm.
| The people talk about somewhat different subjects, or are
| more polite, but overall it's nothing that a poor person
| wouldnt be able to comprehend.
|
| It also reminds me how there's no "arrival" in life.
| There's alsays a next thing to do. But for example as a
| student you think graduation is "making it" but then you
| realize it continues in somewhat different form, but it's
| now about acing job interviews and you think landing a job
| will be the goal line, but then you see it goes on and now
| you chase promotions and good evaluations and so on.
| Similar things about private life.
| ninetyninenine wrote:
| No, this isn't universally true. Your intelligence does affect
| your ability to learn math. It is not always just a lack of
| prerequisites.
| JustinSkycak wrote:
| Sure, there is such a thing as mathematical talent. However,
| few people actually reach their full mathematical potential
| because they get knocked off course early on by factors such as
| missing foundations, ineffective practice habits, inability or
| unwillingness to engage in additional practice, or lack of
| motivation. Basically, your mathematical potential has a limit,
| but it's likely higher than you think.
| Barrin92 wrote:
| If you want to compete with Terence Tao, maybe. But everyone
| with a functioning brain can get to a high level of
| proficiency, I know because I've taught people who were
| convinced math is an alien language and they lack the math
| gene.
|
| It's the same with any skill, lots of people are convinced they
| can't make music, or learn Mandarin or what have you. 99% of it
| is preconceived notions that they don't belong into a certain
| club and because we keep telling people that if something's
| hard for you, you're untalented and you should focus on
| something else. But it's just effort, even if it's more effort
| for some in the beginning, there's no magic in any of it.
| ninetyninenine wrote:
| Sure but it absolutely matters heavily if not just as much
| prereqs.
|
| I met a girl who struggled with trig and another guy who
| basically trivially studied the subject and aced it. IQ
| matters a lot.
|
| We are talking in circles. Both matter but I'm saying with my
| example above that even at basic math, both still matter.
| It's not some thing where iq only matters for phd level math
| hnfong wrote:
| "Just effort" is a curious way to put it.
|
| Even for talented people, learning a skill to a high level
| takes years.
|
| Mere mortals don't really have that many years of free time.
| _Choosing_ a path that one seems talented at is usually the
| right path.
|
| It's one thing for the person to decide they want to take the
| risk knowing that they might not have the talent to learn the
| skill in a "reasonable" time, but it's another to thing to
| pretend there's no difference and cheer on a person chasing
| an improbable dream and waste a persons' life.
|
| To be or not to be. Basically.
|
| So basically the disagreement is to the approach to default
| to when the future is unclear. Taking the right action
| requires a degree of foresight that people generally don't
| have. (I'm not sure everyone has the same skill to intuit the
| future, but I'll grant you that it's just effort to learn it,
| even if it requires significantly more effort for some...)
| paretoer wrote:
| I suspect this is a feature of the modern world.
|
| I have heard of a few philosophers of their day years back
| being considered "the most learned man in Europe". Not the
| smartest, but the most learned. Learned implies agency, smart
| implies something innate.
|
| With the advent of IQ tests and the computer you get the
| brain as computer metaphor gone much too far.
|
| Terence Tao has a 64 core threadripper, so if you are just
| using a 4 core i5 don't even bother.
|
| Then of course if you believe an i5 is basically worthless it
| becomes a self fulfilling prophecy even though for most tasks
| both would be plenty fast enough.
| quacked wrote:
| A lot of people on HN just don't really know any stupid people.
| There are many adults in the US who struggle to work a grocery
| store self-checkout machine or remember a string of numbers
| longer than 5 or 6 digits. (I'm 70% sure the correct order of
| magnitude for this group is "millions" and 99% sure it's at
| least "hundreds of thousands").
|
| Maybe with better nutrition, childhood conditions, and
| healthcare a good portion of this group could have been
| promoted into a different group, but the idea that everyone
| just needs better prereqs and they'd learn math better isn't
| right. The article itself was written by someone who manages
| their own website.
| zvmaz wrote:
| I struggle with the self-checkout machine. I am a simpleton.
| I bow to your intelligence.
| karaterobot wrote:
| True, but then there's nothing wrong with being dumb. I know a
| lot of smart people, and they're all dumb about most things. Like
| the universe, we're mostly empty, with some hot, bright spots.
| What I mean is, don't think of yourself as fundamentally smart or
| dumb, think of yourself as having a lot to learn, no matter who
| you are or how others perceive you.
|
| But sure, this is a good reminder of how you go about learning
| new things. It's the Julie Andrews method of pedagogy: "start at
| the very beginning (a very good place to start)"
| password54321 wrote:
| The real truth: if you aren't good, there is nothing wrong with
| that and there are more than enough developers in the world and
| people who are good with math. What we need is more people
| creating real and interesting jobs for these skills.
|
| Also most people aren't great with spatial reasoning. Chess
| requires zero prerequisites yet the average level of chess on
| chess.com is constant one turn blunders. It took only a year of
| playing on and off to get to 98th percentile and up to maybe 70th
| percentile most of it is capitalising on basic mistakes. We need
| to stop deluding people with feels good content, that's how you
| get memes like imposter syndrome.
| pajeets wrote:
| Streams of tears roll down my cheek as I write this because this
| article perfectly highlighted that it wasn't the laziness but
| rather what was causing it , mainly the lack of prerequisite
| fundamentals needed to thrive in math field. Had I known this my
| life trajectory would've been different instead of self loathing
| and inferiority complex I built up around something so innocently
| simple.
|
| The rush of epiphany and self-forgiveness that overwhelms me
| after all these years. I realize now that learning grade school
| math in French and then started to learning algebra and calculus
| in Japanese abruptly moving to an English speaking institution to
| continue math degree (which i abandoned for reasons in the
| article i realize now ) screwed me up big time because neither
| French nor Japanese nor English is my first language.
|
| For instance I would store numbers in French in my head and
| perform arithmetic in French but to do any sort of additional
| algebraic or calculus I would need to switch to Japanese
| internally and finally write out response in English. Learning
| the advanced topics in English was never going to work out, it
| was like building a castle on sand and the stones are made out of
| mud. I always thought I was too "dumb" to
| understand math. During my school years, it was evident to me
| that for some kids math was easy, and for others like myself:
| painfully difficult. This belief shadowed me for
| years, a constant reminder that while believe I am smart... I'm
| not THAT smart. Recently, after 150 days immersed
| in learning math, I had a stark realization.
|
| The struggle wasn't because I wasn't capable, but rather, I was
| simply missing a shit-ton of pre-requisite knowledge.
|
| I wish I could show this article and translate it into other
| languages. There are lot of young kids in schools who tell
| themselves they are dumb or lazy because they can't do well in
| math and sciences.
|
| God knows how many of us are walking around feeling inadequate or
| frustrated at ourselves because we convinced ourselves we are not
| worth it or capable when in reality its the prerequisites both
| conscious and subconscious, overt and covert we fail to realize
| as fundamental stepping stones to success.
|
| It might as well be that failure in startups or business ventures
| or relationships even also stem from this principle: that the
| fundamental prerequisites were not taught or caught early on
| (either due to environment, upringing, socioeconomic constraints)
| have solidified into bad habits, bad model of world, bad model of
| others that ultimately transpire into bad thoughts, bad words,
| bad actions and opposite outcomes of what we set out to
| accomplish.
|
| Going forward I must make it my mission to realize what
| fundamentals and prerequisites I do not have and instead of brute
| forcing and letting my ego ignore it, I have to put aside time to
| build those basic building blocks.
|
| A cathartic angst feels deep in me. Might be too late for me due
| to my age and I fear I will ignore my own writing here and others
| will too. It's truly sad that we are all realizing it this late
| and will forget whatever lessons were learned. I wish society and
| people would stop pointing fingers at people and rather realize
| build tolerance from the fact that not everybody gets to build
| the same prerequisites as humans cannot be the same, some are
| innately inclined to better at certain things while others are
| not.
|
| Equal outcomes is a failure in the making and schools need to
| stop and focus on helping students build prerequisites on their
| own schedule and pace.
| whackyMax wrote:
| As a side note, the headline seemed a fun one, it seemed to me to
| say "you are not dumb, but you just lack a few prerequisites to
| be dumb".
| veunes wrote:
| > It's like trying to defeat a Elden Ring boss... at level 1.
| Just in love with this comparison
| GeoAtreides wrote:
| You know how there's a window for learning to speak?
|
| https://en.wikipedia.org/wiki/Critical_period_hypothesis
|
| I posit there's a similar window for highly abstract thinking,
| like math or logical thinking or, controversially, for learning
| how to learn.
| hervature wrote:
| Why are you stating a hypothesis as if it was fact? I'm 30 and
| started learning Spanish (1,000 hours so far) and think I'll be
| near-native level in another 1,000 hours and maybe actually
| native in 5,000 total hours which I might get to by the time
| I'm 40. As we age, we simply have other commitments that we
| cannot devote this much time to language learning. Kids
| "easily" learn language because they can easily put 1,000 hours
| of exercise each year for 5 years.
| GeoAtreides wrote:
| This is not about learning a second language, this is about
| learning to speak in the first place
|
| for example: https://en.wikipedia.org/wiki/Critical_period_hy
| pothesis#Dea...
| hervature wrote:
| The leading sentence is:
|
| > The critical period hypothesis[1] is a theory within the
| field of linguistics and second language acquisition that
| claims a person can only achieve native-like fluency[2] in
| a language before a certain age.
|
| Granted, I do admit I missed the subtlety that it applies
| to learning a first language as well.
| dranudin wrote:
| I have lived in a foreign country for about 3 years. My wife
| is from there and I speak with her in that language every
| day. I also took courses until the B2 level. My communication
| in that language amounts to easily more than 5000hrs. I am
| fluent, but no native speaker would call me native and that
| will never happen. My wife learned my language in school
| since elementary school up to graduation. She lives in my
| country since about 5 years. In her job she has to talk to
| people for basically 8hrs a day in the local language. She is
| fluent but nobody would call her native. Instead people
| wonder where she is from because they cannot match her accent
| to a particular country. Most likely we will never have
| native competency in the foreign language. So if you make it
| to native in 5000hrs, you are way above average.
| dleink wrote:
| I wonder if there's some kind of plateau you reach in a
| learning a language that way. Like, what if you started
| working with a hollywood dialect coach?
| sn9 wrote:
| Yeah there's definitely a gap between functionally fluent
| and being mistaken for a native that requires some
| intentionality and effective study that is unlikely to be
| crossed accidentally/passively or by focusing on the
| wrong things/methods.
|
| Some combination of learning the phonetics of the target
| language, 1000s of hours of comprehensible input, singing
| to music in the target language, and doing impressions of
| native speakers are all things that can help.
| laichzeit0 wrote:
| I'm bilingual since a child but didn't really use one of
| the languages much after age 12 to about 30. When I do
| speak the second language I can fool locals into thinking
| it's my first language, but it takes exactly 1 mistake or
| mispronunciation and they ask "oh are you actually
| English?". The bar is that that high for passing native
| fluency in another language, if you somehow could fake
| the accent perfectly as well (there is absolutely no
| way).
| naveen99 wrote:
| agree for most people. But what about comedians /
| impressionists that can copy accents at will with just a
| little practice...
| Dr_Birdbrain wrote:
| I would be curious to hear what "better learning methods" the
| author used. He calls them out but doesn't describe them.
| rod_o wrote:
| Pretty sure he means https://mathacademy.com/
| DantesKite wrote:
| According to this tweet, he used Math Academy.
|
| " Excited to see a @_MathAcademy_ student blowing up Hacker
| News with some insights they've realized about the process of
| learning math!"
|
| https://x.com/justinskycak/status/1827397012758917622?s=46&t...
| dr_kiszonka wrote:
| He nudges folks towards his product on HN too. (Which is why
| I would never subscribe to it.)
| j45 wrote:
| Math as taught by one of my teachers made a lot of sense.
|
| Some topics will come easier and click. Others will need to be
| brute forced by practicing examples.
|
| I can see how that generates pre-requisite knowledge one way or
| the other.
| atoav wrote:
| As an educator, this is the thing I always say. If you try to
| teach someone programming for example, try to make a honest list
| of all required prior knowledge. This is usually stuff that is
| totally _obvious_ to anybody in the field, but if you don 't know
| it it might give you a hard time. E.g. that programs run within
| the context of an operating system and the OS provides interfaces
| for interaction with hardware.
|
| Not all of that is needed upfront, but certain explanations just
| won't make any sense if required knowledge is missing.
| closetnerd wrote:
| The source of about 30% of the hits I took in homework and tests
| was, to this day, not having memorized the basic values of
| Sin/Cos(pi, pi/2, pi/4).
| YZF wrote:
| Instead of memorizing the values you can learn the shape of the
| graphs and/or learn the meaning of sin/cos on a right angle
| triangle.
|
| I think I got ok through a math/comp.sci. degree without
| memorizing values but I will say the "mechanical" aspects of
| math including trig functions and things like integrals and
| derivatives involve drilling those enough to make these things
| automatic (which is sort of memorizing but not exactly). I was
| always lazy so I never got really good at that (and my calculus
| related grades are evidence of that ;) ).
| philomath_mn wrote:
| Yeah I pretty much always think through the unit circle to
| get the value of sin(0) and cos(0) (unless I had been doing a
| lot of trig lately)
|
| I remember drawing everything out on trig exams though and
| making myself an on-demand cheatsheet.
| sn9 wrote:
| Here's an Anki deck for the unit circle:
| https://ankiweb.net/shared/info/1813562307
| digger495 wrote:
| The author's point about Elden Ring is especially on point..
|
| Because not only do you need to be level 50, but you need to try
| and fail five times before you see any kind of success.
|
| Failure is _inevitable_. Quitting is optional.
|
| You have to learn from each mistake.
| nsxwolf wrote:
| I wish someone had told me this in school.
| w10-1 wrote:
| For many practical applications, slow learners do just as well as
| fast ones, once they're up to speed.
|
| Math teaching is mostly playing hide-the-ball, which teachers
| justify by saying people learn more deeply when they figure it
| out for themselves. But really that just shifts the burden of
| backfilling prerequisites to the student.
| Jensson wrote:
| > But really that just shifts the burden of backfilling
| prerequisites to the student.
|
| Not if the students were taught that way from the start, learn
| for yourself at every step and you are never behind.
| whiterknight wrote:
| Are you suggesting that you don't learn as much when you figure
| our the puzzle as oppose to being told the answer?
| Viliam1234 wrote:
| This really depends on getting the details right.
|
| If you choose the right kind of problem that the children _can_
| figure out on their own -- it helps a lot. The will remember it
| better, and they will also feel better about their own skill at
| math.
|
| But if you incorrectly estimate the difficulty of the
| problem... and instead of noticing your mistake and fixing it,
| you just wait for a miracle to happen -- the kids will only
| waste time and get frustrated.
|
| The problem is teachers who believe they can do this trick, but
| fail to notice that they are doing it wrong, and then they
| blame the kids.
| neom wrote:
| Anyone here with developmental dyscalculia managed to overcome it
| and get into math? I have no clue how to deal with numbers, I
| know this is weird to say but it feels like they don't exist for
| me.
| bonoboTP wrote:
| Many branches of math aren't focused on numbers. One cool
| branch that has almost no prerequisites and isn't focused on
| numbers is graph theory. It can be a great subject to cut your
| teeth on, regarding formulating theorems and proving them.
| CM30 wrote:
| This tracks pretty well with my experiences learning programming,
| both when developing websites and making video game mods.
|
| The times I failed, I was looking at other people's work and
| trying to figure things out too quickly and in an unstructured
| way. I saw the complexities of a program that was in development
| for weeks/months/years, then basically panicked and thought I'd
| never be able to make something like that.
|
| When I learnt the basics, I then saw how these problems could be
| broken down into their simplest forms, and ended up learning a
| lot more efficiently as a result.
|
| Of course, having examples of what to do helps a lot, it's just
| your examples need to be merely a tad more complex than what you
| already know, not a masterpiece from some genius that spent the
| last decade working on it. Or if they are from that sort of
| person/company, you should try and break down sections of the
| work at a time to understand where they're coming from, not the
| whole thing at once.
|
| It's much more reasonable to try and figure out how someone like
| Facebook or Netflix implemented a profile page or edit button
| than say, how the whole system works on a greater level.
| gnarlouse wrote:
| This page needs to get reshared 8 billion times by 8 billion
| humans.
| throwaway25664 wrote:
| I'm enjoying going through your site, looking for inspiration and
| tactics. Btw, this page is missing: https://lelouch.dev/roadmap
| notjoemama wrote:
| Assessments are getting better in education and they help find
| missed skills. It's possible the author was smart enough to copy
| but not understand why they were doing what they were doing.
| Whether your local district focuses on skill acquisition versus
| graduation rate may determine the students success long term. I
| know little, but what I've seen from reading programs they're
| pretty much 'there' in discovering these blind spots. I don't
| know if there is comparable assessments or programs for
| mathematics.
| _benj wrote:
| I'm curious about what that "preliminary knowledge" is? I've read
| stuff like a mathematician delight and the Joy of X and it's such
| a beautiful, attractive but seemingly unattainable realm of
| knowledge.
|
| As an example, this is the math that I'm aware of and have been
| exposed to:
|
| Arithmetic Algebra Geometry Trigonometry Calculus
|
| I'm vaguely aware of linear algebra but haven't studied it (it
| also seemed unattainable)
|
| I'm also aware of discrete mathematics and even bought the book
| concrete mathematics by Knuth, only to be totally stuck in the
| very first example of recursion and the tower of Hanoi...
|
| So, what is that preliminary knowledge and how does one goes
| about acquiring it?
|
| From where I sit sometime it feels like I don't what I don't know
| and I don't even know how to ask how to learn what I don't know I
| don't know
| programjames wrote:
| Probably figuring out math paths. I've always been bad at
| remembering formulas or theorems, but that's because I remember
| how to get to that formula or prove the theorem instead. E.g.
| in grade school, I never memorized the sum of cubes formula,
| but I knew
|
| a^3 + b^3 = a^3 - (-b)^3
|
| and that the difference of cubes looks somewhat like the
| difference of squares, so I guessed
|
| a^3 + b^3 = (a - (-b))(<and figured out the rest.>)
|
| Having the whole path in your head makes it so you don't get
| stuck when you forget one step, and also makes it easier to
| make new connections.
| _benj wrote:
| I like this idea. I'm guessing that it might be trying to
| learn math from proofs? or from first principles? I'm trying
| to figure out how could I find where to learn math in this
| way?
| kgeist wrote:
| Same, I never could remember formulas at school. What I did
| during exams was to "reconstruct" them visually: I'd sketch a
| few graphs at various random points and try to derive a
| formula from there. I also remember successfully solving
| problems by sketching geometrical shapes (triangles, lines
| etc.) and just trying to reason with basic logic + trial and
| error.
|
| I realized back then that a lot of math (at least school-
| level math) can be grokked if you visualize it
| geometrically/spatially, as manipulatable objects in space. I
| don't know why our teachers rarely explained it like that.
| For most students, it was like strange symbol manipulation
| rules that you must remember by heart and can't derive from
| scratch.
|
| Currently I'm fascinated with the way neural networks can be
| understood as a problem of trying to untangle tangled
| manifolds (to make them linearly separable) by
| "folding"/distorting space, using basic matrix
| manipulations... That way it's not magic anymore, it's
| something which appears so straightforward.
| kavouras wrote:
| It really depends on what you're interested in, its like saying
| I really want to learn computers.
| dundercoder wrote:
| So many times the solution is to be kinder to yourself. I love
| this.
| meken wrote:
| I can relate - I was quite bad at math through high school.
|
| I eventually hit a wall in college then, like the author, decided
| to start from the complete basics: positive and negative numbers,
| fractions, arithmetic, algebra, then calculus.
|
| Khan academy made this possible for me (in 2010), I don't know
| where I would be without it.
| patrick451 wrote:
| This post biases way too hard into the nurture side of the
| equation. The difference between the author and someone who is
| genuinely smart is that the genuinely smart don't need to spend
| months carefully working through all those prerequisites in
| carefully arranged order. Until you meet somebody like this, it's
| easy to delude yourself into assigning yourself more brilliance
| than you posses and think that everybody struggles the same way.
| It turns out some people really are smarter than you,
| prerequisites or not.
| datagreed wrote:
| I am confused: how exactly did the author managed to lack
| prerequisites for math in school?
| ksec wrote:
| That is what I dislike about Computer Science course ( BSc ) and
| much prefer Computer Engineering ( BEng ). There are far too many
| abstraction involves that most people just remember or know the
| skills set of the abstraction layer without ever understanding
| how that abstraction comes into the field in the first place.
|
| Over the past 10 years the media has have popularised the term
| First Principle often spoke about by Elon Musk ( He didn't invent
| the term but media help to spread it ). And this is precisely it.
|
| And this isn't just computer but literally every single subject
| taught are now about the grade and not the "WHY". We just dont
| know how most things are derived from. We just memorise it and
| society will reward you with Certificate and a "Smart" status.
|
| In Maths Richard Feynman [1] explaining mathematics in 4 pages
| from algebra to calculus. As the saying goes, I dont have time to
| write you a short letter, So I wrote a long one. Getting
| something simple and concise in 4 pages is the work of genius and
| takes a lot of time. I only wish something like this exists for
| all other subject with video course, completely free of charge in
| dozens of languages to kids all around the world.
|
| [1] https://www.feynmanlectures.caltech.edu/I_22.html
| default-kramer wrote:
| When I think of "Computer Science" I definitely think that it
| respects "build great things from a small set of first
| principles" as much as any field. In fact, I might argue that
| CS is just a subset of pure math. It's those pesky Computer
| Engineering concerns, warts like memory locality and branch
| prediction, that make CS "less pure" than it could have been :)
| [no offense to CE, I personally love those warts]
|
| > most people just remember or know the skills set of the
| abstraction layer without ever understanding how that
| abstraction comes into the field in the first place
|
| This sounds like you're describing pragmatic software
| development, or "software engineering" if you insist on
| sounding fancy. My degree was in SE and in retrospect I would
| have enjoyed CS more, but it really didn't matter in the long
| run. But I digress... the point is: a course that focuses on
| using an abstraction is a programming/SE course, whereas a
| course that focuses on the principles one might use to build
| such an abstraction is a CS course.
| j7ake wrote:
| Prerequisite is a euphemism for practice. You lack practice.
|
| It's like saying you can improve your skills in
| basketball/swimming/piano/singing if you just practice better.
|
| But obviously you can still be dumb and know a lot of math.
| lovestory wrote:
| I have still not graduated and this is my sixth year at
| university (in Europe). I find math too difficult and I still
| have calculus, linear algebra and probability. Discrete
| structures is the only math class I managed to pass and it took
| me too long to realize it's because the other classes have a long
| list of prerequisites. I have passed all of my software/IT
| classes aside from the maths and it's because they virtually are
| built from the ground up. On the other hand, strong math
| foundations are required even for the introductory math in my
| college. What I did was get great algebra and precalculus
| textbooks and went through them with great detail. After that I
| found the classes were not that hard to grasp.
| locallost wrote:
| Smarter people will get the prerequisites faster. Nothing wrong
| with that, I'm more of a persistent person myself, which is a
| quality in itself. The really accomplished people are both smart
| and persistent.
|
| But otherwise I agree with the article. I have zero basics in
| physics because my first teacher was generally senile and there
| was noone else (small town), and it was always something where I
| automatically tried my best to just get a passing grade.
| LarsDu88 wrote:
| This is me diving into leetcode without majoring in CS in
| undergrad.
|
| There's are also a bunch of precalculus stuff that comes in handy
| that I completely forgot. Like how to compute arithmetic sums!
| markozivanovic wrote:
| Hehe, two years ago, I wrote a similarly titled article - "You're
| not dumb, the prerequisites are bullshit." :)
| https://news.ycombinator.com/item?id=30035456
| Jacky4Chan wrote:
| That's one of L. Ron Hubbard's barriers to learning, described in
| his "basic study manual" book.
|
| -Another one is not fully understanding the words or concepts
| being used.
|
| -Another is not having an appropriate example or visualization of
| what is being explained.
| ruph123 wrote:
| How to tackle it?
|
| To me there are either two ways: when you are trying to learn the
| thing XYZ you are seeking, drill down to the first thing you
| don't understand and consult a lower level resource. Continue
| until you reach a level you understand. And the second way is:
| Re-learning "all" of essential math and then going back to XYZ.
|
| I don't think the second step is feasible, as you cannot possibly
| learn everything in a breadth-first kind of way until you are
| deep enough to learn the (now level-adjacent) topic XYZ.
|
| But for strategy 1, the question is 1) how to identify the
| problem that you are lacking (e.g. how to isolate math gibberish
| into a concrete concept) and 2) how to find a good resource to
| learn and practice this concept at this level?
|
| I do struggle with this and sometimes randomly learn some lower
| concept again but notice later it did not help me in the end and
| just left me with a million untied knots that were infeasible for
| me to entangle.
| necovek wrote:
| I am not sure I entirely agree with the premise: eg. you maybe
| are "dumb" (lack mathematical talent, really), but with proper
| instruction, you can learn a lot of math.
|
| Let me dive deeper.
|
| Our school system teaches math in a pretty inflexible way: "this
| is how everyone can get it". But even math talents don't learn it
| that way: as one, I was usually ahead of the school with my own
| reasoning (sometimes by a couple of grades) and could backtrack
| to the school method to understand it and apply it.
|
| Second, if you are good at maths naturally, everything else at
| school becomes easier: people simply treat you as "smart" in
| whatever you do just because you have a natural leaning to
| mathematics (both if they do or don't themselves). Even rote
| memorization subjects like history and geography become easier
| since, well, you are "smart": teachers simply do not ask much of
| you.
|
| And finally, I've met many an extremelly intelligent
| mathematician (uni professors and math competitors) who simply
| are outright _dumb_ : they could not process a simple logic
| statement in human language, even if they were regularly working
| on advanced research calculus.
|
| So, anyone can learn a lot of math, and doing so requires
| internalizing the foundations. However, people talented for
| mathematics find it easy to internalize them in various ways (not
| always the textbook way), so it's not hard work for them (eg. I
| could coast through the entire undergrad math and CS program too,
| cramming for a weekend for all but a couple of exams: memorizing
| all the axioms and theorems was the struggle, operating with them
| and proving them once I knew them was comparatively easy and I
| finished with a GPA equivalent of 3.4 or so).
|
| But math instruction is hard because math is a formal language
| representing a very specific mindset that not everybody can
| _naturally_ get. And instruction is usually performed by people
| not having attained that internalized knowledge of the
| foundations, thus not being able to look at it and describe it
| from numerous viewpoints required for individual students.
|
| Finally, we need to fix the society not to equate "good at maths"
| with "being smart": plenty of smart people who have a hard time
| with maths, and plenty of math wizards who are outright dumb.
| Grustaf wrote:
| But how could some 7 year olds have vastly different "pre-
| requisites" than others?
|
| In my experience aptitude plays a far bigger role. Yes, you
| compensate for lack of aptitude with a lot of hard work, but
| that's a different matter.
| creesch wrote:
| Because at 7 you obviously also already have 7 years of
| experience behind you. Sure, it is not as much as an adult, but
| it still matters a lot. Different environments and stimuli make
| it so that also for 7-year-olds, they can have vastly different
| prerequisites for anything.
|
| Often aptitude is not aptitude at all, but all of the above.
|
| Then, during learning anything, the same thing also applies.
| How much support you get from teachers and parents. What sort
| of environment you have available to practice in. And a lot
| more.
|
| Finally, when all other factors are equal, aptitude can play a
| certain role. But one that in an educational setting is largely
| irrelevant. Because if everything else is perfectly in place to
| teach something, including learning any prerequisites, aptitude
| is only something that matters in hindsight.
|
| Which is extremely important as well. Labeling someone as
| lacking aptitude can be highly discouraging. Repeatedly hearing
| that they aren't "naturally" good at something can lead them to
| stop trying, even if it's not true.
| Grustaf wrote:
| I really don't understand this cope. It's scientifically
| established that intelligence is highly heritable, especially
| the analytical kind. It also agrees with experience, we all
| know people who have a very hard time understanding
| mathematics, while others sail through it.
|
| Of course it's not fair, life isn't fair. But the good news
| is that you can quite easily compensate for lack of aptitude
| with more work, and that is most definitely the case for
| mathematics, up to and including undergraduate level.
|
| I grew up in Sweden where everyone goes to the same kind of
| pre-school, that does very little math teaching. Still, the
| difference in aptitude when we started school was
| significant. But we all know this.
| creesch wrote:
| Oh boy, I don't even know where to start here. It isn't a
| cope, it is a more nuanced take.
|
| Your take is so black and white that it only holds up if
| you almost willfully ignore all other context. Obvious
| things like different kids having a different home
| experience, exposure to different things outside of school,
| exposure to different things in the years leading up to
| pre-school, etc. These are just a few factors that actually
| heavily influence where someone starts and how easily they
| pick up some subjects. Then there is the fact that
| following the same curriculum or even being in the same
| class doesn't mean getting the same attention from
| teachers. In fact, ironically those with "more aptitude"
| sometimes get more attention further increasing their
| headstart.
|
| I honestly want to invite you to go back, read my other
| comment again, _actually take the time to internalize it_
| then reply back again.
|
| Because you are very close to actually agreeing with me.
| Specifically because you mention the practice and extra
| work bit. You just don't realize it yet.
| Grustaf wrote:
| No, I am very far from agreeing with you. I am saying
| that if you keep all other conditions the same, you will
| still see vast differences in the ease of understanding
| mathematics. This is borne out both by science - there is
| strong consensus that intelligence is highly heritable,
| and everybody's experience.
|
| So even if we limit "aptitude" to a strictly genetic
| sense, it will still explain most of the difference in
| math ability at 7. All other factors related to growing
| up will add up to less than half of that.
|
| Regarding practice compensating for genetics, I am not
| talking about having more supportive parents or more
| demanding pre-school, I am talking about Asian level
| hardcore drilling. That can certainly make up for most of
| the difference, at least when it comes to basic
| mathematics. But that means that the concepts that a
| child with math aptitude will pick up in 5 minutes will
| take 5 hours of drilling for another child.
| creesch wrote:
| > This is borne out both by science - there is strong
| consensus that intelligence is highly heritable
|
| That is again a simplification of reality, leaving out a
| lot of context and nuance.
|
| 1. You are right that research seems to indicate that
| intelligence is heritable, meaning that genetic factors
| play a role in individual differences in intelligence.
| Estimates of the heritability of intelligence typically
| range from 50% to 80%, depending on the study, age of the
| participants, and the methods used. I am guessing that
| this is where your " _All other factors related to
| growing up will add up to less than half of that_ "
| remark comes from. _However_ , that 50%-80% is in
| relation to the inheriting intelligence from the parents.
| It does _not_ mean that it influence more than half of
| your intelligence. It also highly depends on the specific
| aspects of intelligence that is being measured.
|
| 2. If we are throwing in statements as _borne out by
| science_ then you can 't ignore that studies also show
| that factors such as education, nutrition, and
| socioeconomic status significantly impact cognitive
| development. In fact, some of the most critical periods
| for brain development occur in early childhood. Things
| like: a) Prenatal environment: Factors
| such as maternal nutrition, stress levels, and exposure
| to toxins can affect fetal brain development.
| b) Early childhood nutrition: Proper nutrition in the
| first few years of life is crucial for optimal brain
| development. c) Stimulating environment:
| Exposure to a variety of experiences, toys, and learning
| opportunities in early childhood can enhance cognitive
| development. d) Physical activity: Regular
| physical activity from an early age can promote brain
| health and cognitive function. e) Parental
| interaction: The quality and quantity of interactions
| with caregivers, including talking, reading, and
| responsive care, significantly impact cognitive
| development from infancy. f) I could go on for
| a while, but the picture should be clear enough.
|
| Again, aptitude can be a thing. But all things
| considered, it is really not all that relevant when we
| are talking about the development of people and them
| learning things. Anyway, at this point your use of
| phrases like "cope" and a somewhat fatalistic view ("life
| isn't fair") already suggests to me that you actually
| have no interest in actually expanding your view and
| scope on these matters. In fact, it could easily be seen
| as you arguing in bad faith. Which is ironic given we are
| talking about intelligence and aptitude to picking up
| things. So I suppose this reply is more for other people
| to read. I am certainly done with this conversation now.
| Regardless, have a good day :)
| 0xpgm wrote:
| I've read that in some families, especially from Asian
| cultures, you're started off with math tuition as soon as you
| can read.
|
| And some people are just lucky to have the right environment. I
| happened to have had access to some more advanced books from
| older relatives as a kid and I noticed that it gave me an edge
| over my peers in some areas.
| Grustaf wrote:
| Asian families, for sure. But that's doesn't explain that
| vast chasm we all observed between non-Asians in school
| growing up. Why not just accept that it's possible to be born
| with an aptitude for math?
| hnfong wrote:
| If We closely guard this secret instead of telling people
| on online forums, We could gaslight people into thinking
| they are at fault for not being good enough at math. Then
| We mathematize everything that can be mathematized in
| higher education and research, and gatekeep it by requiring
| math even when it's not strictly needed.
|
| (I mean, that's not my opinion, that's just how modern
| society has been running for... a century or two?)
| Grustaf wrote:
| It's not the "access" to those books that gave you an edge,
| 95% of children would be completely uninterested in those
| books. As you know, today 100% of Western children have free
| and instant access to the best math teaching material you
| could imagine, right from the phones, but math grades keep
| falling.
| creesch wrote:
| Related to this, it is why when writing documentation for
| something, it can be extremely useful to also list the
| prerequisites someone needs to pick up the information in the
| document before them. Possibly with also linking to resources
| about them, depending on your audience.
|
| Not only that, writing out the list of prerequisites also helps
| the author write a better document. Because thinking about what
| knowledge is required serves the same function as thinking about
| a good unit test does. It makes you stop to consider "the
| obvious" and sometimes realize you have overlooked something.
|
| Because when you are thinking about these prerequisites, you are
| likely also thinking about _why_ they are needed and what
| challenges come with them. This in turn might lead you to revise
| aspects of the documentation to make them clear as well.
| bloqs wrote:
| This is a half truth. Part of the reason some people take a lot
| longer to grok the prerequisites and get left behind in class is
| because of cognitive ability.
|
| Working memory (WAIS) digit span, and broader performance IQ (as
| opposed to verbal IQ), generally indicates how many conceptual
| 'items' you can have in your head at once. With more advanced
| math, this becomes _critical_ to forming the coherent plumbing
| between concepts in your head, leading to understanding.
|
| Incidently, ADHD is largely an expression of specific personality
| traits and low working memory.
| agumonkey wrote:
| I felt that during college. Suddenly I couldn't hold enough
| abstract terms or variables at once to be able to reflect.
|
| It slowed me down near zero, but weirdly, if you keep trying,
| your brain may evolve some new abilities and maybe as
| important.. keep feeling joy about learning even if slowly.
|
| I wonder how one can raise this aspect of thinking.
| bruce343434 wrote:
| ADHD is largely an expression of dopamine misregulation
| actually.
| ta8645 wrote:
| Many people are in fact dumb, and will never acquire the
| prerequisites. We're not all blank slates with equal potential.
| notepad0x90 wrote:
| Late to the thread, but my view on being "dumb" in general, even
| if you have the pre-req's knowledge and ability are different
| things. Most people, in my opinion, are smart enough to
| understand and apply just about any complex subject or topic.
| Being smarter just means you can "compute" and understand or
| apply the subject in question faster than others.
|
| In the end, what we prioritize and how much time is available for
| us to tackle different subjects is the biggest limitation, not
| genetics or luck. Art and entertainment heavily influence these
| things.
| pazimzadeh wrote:
| > A cage of 5 mice costs ~$1k upfront and ~$5k/yr recurring
|
| You can get mice a lot cheaper than that, I'm not sure what kind
| of mice he's referring to but the prices depend on the vendor and
| mouse type.
|
| Where I work it's about $2 a day to house a cage of 5 mice. It's
| about $30 a mouse if you get C57BL/6NJ's from Jackson:
| https://www.jax.org/strain/005304
|
| So more like $150 for 5 mice and $800 to house for a year.
|
| Another good one to know if the size of antibodies (10-12 nm).
| hamandcheese wrote:
| Wrong article?
| pazimzadeh wrote:
| whoops yeah wrong article. was trying to comment on this
| https://news.ycombinator.com/item?id=41344176
| rendall wrote:
| Is that in the article? I didn't see that. Where is that from?
| sublimefire wrote:
| This is an optimistic take on things. With years you understand
| there is a small cohort that is not capable of learning the
| basics even if they try, then there are folks who do not even
| know they are lacking.
| feldrim wrote:
| I discovered this myself when I attended a data science summer
| school, a 2-day bootcamp. I knew Python and Jupyter. I know
| basics of Operations Research, though I barely passed the class
| back in time. I took classes on optimization classes thanks to
| industrial engineering classes. But at the end of the boot camp,
| I was as illiterate on data science as I was at the beginning. I
| was just more confused. Then, I understood that I was missing the
| mathematical prerequisites for the understanding. I still felt
| dumb though.
| TrackerFF wrote:
| A lot of people hate rote learning - but elementary math classes,
| meaning all the way up to calculus (or prior to more rigorous
| proof based classes), do require a bunch of memorization. That's
| on top of getting an intuition...the "Aha!" moments.
|
| I've observed that many math students in those types of
| elementary classes struggle because they're unable to recognize
| identities. They get some problem which involves substituting
| hard parts with easier parts using identities, but don't
| recognize them. So they try to solve the problem directly, and
| end up writing pages upon pages, before either getting stuck or
| doing some error that follows them until they get stuck.
|
| Once they're showed what identities to use, they say "of course,
| I should have known that!" - but they never put in the time to
| solve all the problems.
|
| And I was like that, too. I always thought that math would be a
| nifty because you'd "only" need to learn the various theorems,
| and if you understood those, then that should have been enough.
| It didn't really hit me that I'd need to put in hard work solving
| problem sets until I started recognizing patterns and knowing
| what to use, and where to use it.
|
| Same goes for those that don't really understand the theory. Lots
| of math problems later will be of the type "Here's a difficult
| looking problem, is [statement x] true or false?" - and because
| they don't understand what math theorem to use, and all its
| properties, they'll try to brute force it by jumping into
| calculations.
|
| You see it all the time in calculus, where students are asked to
| solve some nasty looking integral problem, which is much simpler
| if you know and use properties regarding symmetry and stuff like
| that.
|
| I'd say for most people, there's no free lunch when learning
| math. You'll need to understand it, and you'll have to practice.
|
| There's always going to be some extremely high-IQ individuals
| that can do pretty advanced math purely by logical deduction -
| but for the vast majority, it comes down to hard work.
| trwhite wrote:
| > A lot of people hate rote learning - but elementary math
| classes, meaning all the way up to calculus (or prior to more
| rigorous proof based classes), do require a bunch of
| memorization
|
| A lot of people still think reading and re-reading textbooks is
| the way to memorise theorems but recall (attempting to remember
| them without the book) is much better.
|
| I cannot recommend the book "A Mind for Numbers" by Barbara
| Oakley enough - it put me on a journey to re-learning Maths as
| an adult.
| maxrecursion wrote:
| I learned this as a teenager when I went from great at math to
| terrible because I got stuck with crappy teachers. Then, in 11th
| grade, I got put in algebra 2 with a great teacher and was
| tutoring other kids.
|
| Math is completely different than other subjects. You can't catch
| up by cramming or reading a book over the weekend. You have to
| consistently learn and use it over the years. And have competent
| teachers to teach it to you.
|
| Once you get placed in the remedial math, where they are just
| corralling misbehaving teenagers, and slapping out worksheets so
| kids can pass, you are basically screwed, unless you can get out
| of that situation.
| firesteelrain wrote:
| I don't even have to read the entire article for the title to
| resonate with me.
|
| But when you are poor and really need a leg up in society, you
| will do anything to push yourself forward - including going into
| student loan debt.
|
| I certainly wasn't equipped nor ready for computer science. Well
| let's say my computer science classes I did well. It was the
| Calculus and Physics that I struggled because I didn't have a
| good background from High School.
|
| I didn't have the necessary pre requisites.
|
| When I recently completed my Masters in Systems Engineering,
| getting a 4.0 GPA was no problem.
| sethammons wrote:
| My step-mom tutors. A high schooler was having a terrible time in
| algebra. She quickly realized there was foundational numeracy
| missing. The next lesson they walked out to the residential
| street and asked: how many tires are there. The kid froze and
| guessed. Time to start counting. A couple months later, the kid
| was able to raise their grade to passing in algebra
| spencerchubb wrote:
| too many stories like this. we need to organize schools by
| knowledge, not by age. and only pass kids to the next level
| when they're ready
| selimnairb wrote:
| I have a corollary: people who are smarter than I am are mostly
| just less lazy than I am.
| mehulashah wrote:
| I wish we didn't think of understanding math as being smart or
| dumb. Like, it was a singular ability. Math is a subject deep,
| wide, and rich of ideas as well as results. For me, learning and
| understanding new concepts and results is like discovering new
| mountains and trying to ascend them. I won't be able to ascend
| most, but I can certainly sit back and appreciate and enjoy their
| magnificence.
| Astro-Domine wrote:
| It's heartwarming to read comments from clever people, focusing
| on their struggles. Too often I interact with people who lock
| conversations into their own sphere of competence with the
| outcome being that I feel incompetent.
| shiandow wrote:
| Lately I've begun thinking that the way maths is taught, with
| each new concept following on the previous and no real way to
| revisit older content, just might be why people think there is a
| sharp divide between people who seem to understand all maths
| immediately and people who don't get it at all. Of course it
| might be the case that maths people exist, but _maybe_ it 's
| mostly survivor bias.
| jacobsimon wrote:
| One thing I noticed going through school is that math concepts
| are usually taught first before physics and other subjects ---
| precisely because the math is viewed as a prerequisite for the
| other material. But this always seemed entirely backward to me,
| because much of the math was invented for and motivated by
| people trying to solve actual problems in these other
| disciplines. I think we should teach people in the same order
| of operations, rather than treating math as an abstraction to
| be learned by itself.
| talkingtab wrote:
| To generalize. When people fail they can blame themselves or can
| examine how to change. I saw one person try open a gate, fail and
| say they were no good with mechanical things. I said "Its not
| you, the gates broken" and the person immediately opened the
| gate. This is pervasive. "I'll see it when I believe it" as the
| saying goes.
| chrsw wrote:
| When machine learning went mainstream I realized I didn't
| _really_ understand linear algebra.
| mahdavipanah wrote:
| I think intelligence (however defined) is important. But the
| problem is often people misuse this metric to predict a binary
| conclusion of whether they can acquire a skill or not instead of
| just considering it as one variable involved in the learning
| curve.
| godber wrote:
| This article makes me think of the skill tree or roadmap posts
| we've seen here on HN or Reddit over the years. For example
| https://roadmap.sh/frontend ...
|
| I feel like we could do a better job of providing ourselves
| fundamental tools like this in helping ourselves and others
| learn. Not just in tech, but in life overall. The "dev" tree
| above is embedded in the life skill tree that should start in
| elementary school.
|
| Haha, even the life skill tree has "fictional" branches that
| intercept the game world skill tree ... you really do have to
| learn all of the dependencies necessary to case 5th level
| fireballs ... there are real rules to be learned in the games
| their usefulness is just siloed into the fictional realm.
|
| Edit: I forgot to point out that roadmap is open source here:
| https://github.com/kamranahmedse/developer-roadmap
| dev1ycan wrote:
| Yeah but good luck going through the entirety of khan academy as
| an adult, it's not impossible but it's also a task as hard as
| learning a new (or multiple) languages...
|
| If you can dol it though and complete everything up to precalc
| you can most definitely do well in university.
| jkmcf wrote:
| This was my takeaway from college. In HS, you don't have a lot of
| prerequisites, excepting the "II" level classes. I quickly found
| out how unstable my math and physics foundations were. Luckily,
| few realize that Bs are closer to failing than they are to
| mastery.
|
| Even the college gut courses have hidden dependencies. I still
| feel for the business majors in my entry level stats class when
| the prof, bragging about learning calculus at 10, required
| calculus proofs for all the things.
|
| Much like Civilization and Diablo games, and @godber's comment,
| those tech trees should be required for all course syllabuses.
| bonoboTP wrote:
| People often, but not always, lack the prerequisites because they
| weren't able to learn them when it was taught in school. And that
| was because they lacked the pre-pre-requisites because they in
| turn didn't pick _those_ up when that was the material being
| taught.
|
| In math, things build upon previous things to much greater degree
| than in other subjects. If you get off track once, it's hard to
| catch up.
|
| But if you lack prerequisites because it was never taught in high
| svhool etc, that's a failure of the curriculum.
| fargle wrote:
| not untrue, but only part of the story.
|
| certainly your math skill level neither makes you "smart" or
| "dumb" (which really aren't opposites, either).
|
| prerequisites are (ahem) _required_. not having them does imply
| having a bad time.
|
| what's missing is that different people's brains work differently
| and people have different talents.
|
| if you learn differently, that can factor into that lack of
| prerequisite knowledge - perhaps the way it was taught didn't
| work for you.
|
| but some people's brains just don't like math. other's are gifted
| at it. you can have all the prerequisite knowledge needed, be the
| best most diligent student, be wildly intelligent in general, and
| still not just "get" math.
|
| so this article was about someone who actually did have a decent
| proclivity to math, but was robbed of it because of some missing
| foundation. and then said "ah ha!" there's the problem! but that
| doesn't mean that's the case for everyone else - far from it.
|
| it smacks of the "affirming the consequent" fallacy:
| ("dumb" => !math) !=> (!math => "dumb") (!prereq =>
| !math) !=> (prereq => math)
| j2kun wrote:
| > some people's brains just don't like math
|
| Sounds like perverse socialization to me. What actually
| justifies this claim? Do some people's brains "just not like
| reading?" Do some people's brains "just not like music?"
| There's nothing special about math here.
| fargle wrote:
| > Do some people's brains "just not like reading?
|
| yes, certainly. pretty common - outside of a disability, we
| can all learn to read, but it's hard and not enjoyable for
| many.
|
| > Do some people's brains "just not like music?
|
| yes. (when i say "like" btw. i meant roughly "natural
| ability", not "enjoy") of course most people love to listen
| to music, but many people do not have much of a musical
| ability - and you can't work, learn, or practice your way
| into it beyond a certain point, either.
|
| > There's nothing special about math here
|
| yes.
|
| some people are terrible at dealing with socialization and
| others are brilliant. we are _NOT_ all wired the same way. we
| all have different abilities. what justifies that claim is
| several billion examples.
| gradus_ad wrote:
| This is where LLM's have been the most helpful for me. When I am
| engaging with an entirely new subject and have a bunch of
| questions I need to pepper someone with, I can ask as many
| clarifying follow ups as I need without getting self conscious or
| worry about annoying whoever I'm speaking with. The LLM is
| infinitely patient and able to easily handle beginner level
| prereq questions.
| gmd63 wrote:
| This is the best blessing the internet has given to worldwide
| curiosity and intelligence. The ability to ask "why" ad
| infinitum, without pissing off parents or taking up the entire
| class's time.
| ndarray wrote:
| > This belief shadowed me for years, a constant reminder that
| while believe I am smart... I'm not THAT smart.
|
| Sentence missing an I
|
| > It's like trying to defeat a Elden Ring boss... at level 1.
|
| an
|
| > In fact, I'm still pretty dumb.
|
| Contradicts the first sentence I'm quoting.
| solidsnack9000 wrote:
| I suspect this highlights are more serious issue which is that
| most of our training methods are not adaptive. They work well
| only if the students arrives at the right phase in their
| understanding and otherwise make poor use of everyone's time. Yet
| assuming the student has something to learn, and the teacher
| knows about it, this does not have to be the case.
|
| One discussion of training I found eye opening was Pat McNamara's
| thoughts on what I believe he said was called "skills-based
| training" versus "performance-based training". With skills-based
| training, instructor start out the training session with the idea
| in mind to cover certain skills. A lesson is successful if it
| covers the skills the instructor wanted to cover. Performance-
| based training is geared towards improving the students'
| performance, so skills are introduced based on the students'
| actual level of ability and the relevance of training in a
| particular skill for improving their performance.
|
| One motivation for adopting performance-based training is the
| lack of success of skills-based training in many contexts. Why is
| skills-based training sometimes unsuccessful? One reason is that
| the skills may be too hard -- the instructor chooses the skills
| with imperfect information on the students' level, and they
| choose the wrong skills. The students receive the training but
| their abilities do not actually improve; they don't know what's
| going on. Another reason can be that the skills are too easy --
| the students receive the training and actually meet all the
| standards, but it doesn't actually help them get better.
|
| Pat McNamara discusses these concepts in the context of being a
| shooting instructor for police departments and military units. It
| seems that one often doesn't know what these units know before
| one shows up, and the officers and soldiers in any one unit can
| be quite different individually, so the instructor has frequent
| occasion to think about the relationship between what they
| planned to teach and what they actually did when prompted by the
| students' questions and challenges.
| toshaga wrote:
| Reminded me of the Feynman's technique. I relate completely. One
| of my biggest challenges in returning to university after several
| years of work was exactly having lost the grasp of prerequisite
| knowledge. Unfortunately, from experience, more often than not
| lecturers just play the "you should know this from previous
| courses/high school" card and you are pretty much left alone in
| your struggles. Gets even worse if an exam problem relies on some
| borderline trick that wasn't practiced throughout the course. You
| could probably tell I haven't let go of some grudges.
___________________________________________________________________
(page generated 2024-08-25 23:02 UTC)