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Proof you can do hard things

• User23 3y ago
  Same reason you should be able to do pullups or deadlift twice your body weight. To paraphrase Socrates: no one should live their life without learning what they are capable of.
• perlgeek 3y ago
  > But I recently realized there is a very good reason to take Calculus. It’s to prove you can do hard things. This doesn't explain why Calculus over any other number of hard things.
  • PartiallyTyped 3y ago
    They don’t have to. They said just do hard things. It could be anything, for the author it was calculus.
• LucasOe 3y ago
  I don't think this is the reason you learn calculus in school, but I do think it is a good reason to learn it.
• abtinf 3y ago
  The reason to learn calculus is because, as soon as you grasp it, you will start to see it everywhere.
  • kickaha 3y ago
    I’m old and we were poor: my family got our first microwave oven about the same time as I started to learn calculus in 12th grade. Both changed everything in an epistemologically qualitative manner. Life before calculus/microwave, and life after calculus/microwave. How did we warm up leftovers before the microwave? What did the world look like before I learned calculus?
  • hnfong 3y ago
    Once you get obsessed with something, you'll see it everywhere. For you, that's calculus. And no I'm not kidding, a couple years ago when I was studying distributed systems, I saw the CAP theorem everywhere. Why isn't distributed systems part of the high school curriculum? It's used in basically ALL computing devices (before cloud computing, distributed system theories were applied in multicore systems...)
• stkai 3y ago
  "My goal with our kids is to avoid lying to them as much as possible." ← Thank you. Why is that so difficult for parents to do?
  • hnthrowaway0315 3y ago
    Sometimes being absolutely honest is not the best option, I guess not only for kids but for all human interactions.
    • yCombLinks 3y ago
      Yeah, but lots of parents lie far more often than would be useful for a child. But more importantly, absolutely honest is not the same as absolutely open. You can be absolutely truthful in the things you say without causing harm. If you think the truth would cause a child harm, then direct them away from a topic or tell them they aren't ready, etc.
• ericsaf 3y ago
  I took calculus in High School just so I could make a comment here saying I did so. It almost cost me my diploma as I didn't want to do the homework. I paid attention in class though and learned just enough to pass the exams.
• fsmv 3y ago
  You take calculus to understand the nature of change over time, which is the foundation of physics. The formulas to do integrals aren't important but the concept of integrals is. Honestly I think we should try to focus on differential equations instead but maybe it's necessary to do calculus first.
  • abtinf 3y ago
    It’s the foundation of a lot more than just physics. It’s absolutely crucial to economics and business, and it is a travesty that it isn’t a required part of lower division curriculum. You cannot grasp micro/macro/applied/business economics without understanding relationships between changing variables.
    • jameshart 3y ago
      Understanding calculus helps you understand much more deeply than you could have grasped form just learning algebra what kinds of numerical relationship problems it is possible to actually figure out. Ideally you also need some infinite series, some linear algebra, some combinatorics, and an appreciation of complex numbers as well, so the absence of deep coverage of those from a typical high school math curriculum in favor of putting calculus on a pedestal is more annoying. But the idea that if you know how the rate of change of a thing changes over time, that that gives you enough information to understand it completely? That’s pretty important and deep.
  • fatnoah 3y ago
    When I studied Calculus in high school, it was taught via mathematical proofs and concepts. I didn't really "get it" and struggled to keep a C average...until that one day I was working on a problem in the library about water draining from a pool it hit me that "it's about rate of change!". That was it...that concept changed Calculus from some weird math thing to something I could understand and get my head around. It also underscored the poor teaching methods at my school. I was somewhat vindicated by being the only person in my class to get a 5 on the AP test. I also ended up in a major where I did almost nothing but calculus for undergrad and grad work.
• kickaha 3y ago
  Am I just hopelessly old fashioned? Or is this not most of the justification for bachelors degrees?
  • ethanbond 3y ago
    I think the justification for most bachelors degrees is to get an entry level job in white collar land, no?
  • jebarker 3y ago
    I suspect it's the justification for many PhDs. If you don't go into academia then chances are the content isn't that relevant, but the experience of having to problem solve in uncharted territory is a great confidence booster and skill to have.
    • aleph_minus_one 3y ago
      > but the experience of having to problem solve in uncharted territory is a great [...] skill to have. While I do love to solve such problems, in many business areas there are hardly any hard problems to solve as part of your job: either because they don't exist, or because hardly any boss would be willing to let you work focusedly for years to potentially solve one the hard problems that do exist (which is what a PhD in mathematics or physics is about).
      • jebarker 3y ago
        That's true. I am fortunate to work in an applied research team that exists to take on unsolved problems. Although I'd argue that just having the ability to press on in the face of challenges is a closely related and widely useful skill.
• andruc 3y ago
  Everyone commenting so far seems to be missing the forest for the trees. Doing hard things, and the proof that comes with it, is empowering.
  • vehementi 3y ago
    It's pretty uncanny!
  • quickthrower2 3y ago
    That is not all! Doing hard things builds your capability in general (not just for the thing you learned).
  • bee_rider 3y ago
    The issue is that one tree—calculus is pretty important and fundamental to lots of fields of study—is covered in tinsel and lights, and also for some unfortunate reason some folks have gotten it into their heads that they’ll never need it and might as well light it on fire.
  • bobwow396 3y ago
    Exactly this. The article isn't really at all about calculus, but rather the benefit of challenging yourself more generally. Doing challenging things that push you out of your comfort zone better prepare you to do the things you actually want to do later in life.
• ethanbond 3y ago
  Self-image really is important, especially on the dimension of self-efficacy. There are compounding effects in both the positive and negative direction though. I’ve used this same idea to dig myself out of ruts. When things are fucked up I’ll start paying attention to small things and deliberately “defer” progress on a few bigger things that are harder to do and more costly to fail. Each small win helps build momentum into the next-biggest challenge. I’ve found this super useful for avoiding “habit destruction” during major life events/travel/moving.
  • Medh_Suk 3y ago
    "It costs you nothing to believe in yourself. But it will cost you everything if you don't." Discipline is a muscle. Go Build it. Key is to understand different activities require different muscles. Be mindful of picking your activities, but dont keep on waiting.
    • roflyear 3y ago
      I've never gotten anything out of discipline itself.
      • ethanbond 3y ago
        IMO the most disciplined thing to do is build systems that don't depend on discipline.
        • kayodelycaon 3y ago
          This is exactly what I do. "Discipline" in the traditional sense isn't an option. I have a severe impairment with executive function and can't do specific things at specific times. So I gave up on that. I go with the flow of my brain. When I can, I build and shore up systems that will survive chaos and reduce my cognitive load. When I can't do plan A, hopefully I can manage plan B, C, or D. This seems to work pretty well. I'm more reliable long-term when I allow myself to be unreliable day-to-day. :)
    • 3y ago
• paddw 3y ago
  There are infinitely many hard things. It is hard to learn Japanese. We don't require that every high school student attain basic proficiency in it though. The reason we learn calculus in high school is because it is foundational for many advanced STEM fields, and we will yield better results during university for the small percentage of students who go into those fields by forcing everyone to learn it in high school. Or, moreso, that's a viable justification for learning it today. Had history taken a different shape maybe we would learn something else, or maybe not. But the point is that calculus is not an arbitrary hard thing we learn for arbitrary reasons.
  • abenga 3y ago
    How does a kid know that they definitely will/will not be going into a STEM field in the future? Is it better to have your school-going years slightly marred by calculus and not particularly need it after, or want to go into STEM later in life but not have the grounding necessary?
  • savingsPossible 3y ago
    > and we will yield better results during university for the small percentage of students who go into those fields by forcing everyone to learn it in high school I fear that you might be right about this
• markus_zhang 3y ago
  I think there is an similar argument for Greek and Latin in grammar schools. And the same for ancient Chinese in Chinese schools. Partly for cultural immersion and partly for brain gymnastics. Math, and proof based Math such as Number Theory and Analysis is definitely in the same league if not for a career in academics.
• fortenforge 3y ago
  I don't want to be overly rude, but this is nonsense. The reason to learn calculus is that it's incredibly useful in several domains and never learning it prevents you from become a skilled practitioner in those domains which in turn reduces your future earning potential. Basically: https://www.smbc-comics.com/comic/why-i-couldn39t-be-a-math-teacher https://www.smbc-comics.com/comic/why-i-couldn39t-be-a-math-...
  • quickthrower2 3y ago
    That is a good comic. But I am not sure "reduces your future earning potential" is really right. If you are going for future earning potential, then there are other things. Probably along the lines of - learn to code - find a way to migrate to the US - live in SF/NYC - learn algorithms and data structures - learn leet code - emotional control/resilience for putting up with those kinda jobs ... etc I reckon there are plenty of PhDs earning less than $100k around the world, who know calculus and matrix algebra like their ABCs.
  • selcuka 3y ago
    Everything can be incredibly useful in several domains, but we don't teach everything. Instead, people learn what they need when they start working in that domain. The point of the article is that calculus is not taught because it might be incredibly useful for a small percentage of students, but because it measures their ability to pick up a hard subject and ace it.
• TheCaptain4815 3y ago
  One of the dumbest things I’ve ever heard a math teacher tell me/the class is “you’ll probably never use this outside of this classroom”! And I’ve heard this story before, so it seems slightly common? I entered college without a rock solid foundation in mathematics and it made things much more difficult.
• TheAceOfHearts 3y ago
  I hate the framing of problems or domains as hard, since it kept me from pursuing them further for many years. And the years later when I tried my hand at those problems, I found that it wasn't nearly as hard as it was being made out to be. Historically many problems have also been hard until people figure them out, and then they stop being considered hard problems. In recent years this has been mostly true of AI-related topics. A lot of people have achieved mastery over really hard problems and synthesized their learnings over countless hours, making the information much more easily accessible for future generations. If you keep hearing someone talk about how some field is hard you should take that as an opportunity to challenge yourself rather than shy away from it. One field that has recently interested me is organic chemistry, which I'm interested in learning mostly because of how many people I've heard talking about how it's so challenging. May I find a worthy opponent. Edit: This is relevant to HN when talking about C and C++. People talk about these languages as if they're some magical beasts, but in reality you can get really far with them by treating it as a serious endeavor. People will talk about how they don't have full mastery over the language, but you don't need anything close to that in order to be effective. If you know how to program in other languages you can pick up C++ just as easily and start being effective very quickly. No mastery required. It's not that hard.
  • arsenide 3y ago
    It is useful to use the words hard and easy. As you mention, changing perspective around these concepts is the crux. Hard problems or domains are unknowns. Working towards solving hard problems involves thinking through unknowns, which may or may not lead to understanding. An aversion to hard problems is an aversion to the unknown.
  • bigger_cheese 3y ago
    Rightly on Wrongly some areas of study have the reputation/stigma of being difficult attached to them. Back when I was a high school student math (not just calculus - but the entire subject of mathematics) had this reputation as being a "hard" subject as a result scores of my fellow students just decided math is to difficult I'm not going to engage with this. I suspect this is related to a fear of failure or kids being afraid of "looking dumb" in front of their friends - There was a definite "if I don't try then it doesn't matter if I can't do it." attitude, so they just switched off in those particular classes. A lot of these attitudes carry forward into adulthood. I'm almost 40 and amongst my generation programming has a similar reputation. People I grew up with think if you can read or write code you are some kind of mystical wizard with powers beyond the understanding of mere mortals. I see it today at my day job - I work as an engineer (the non software kind). I've seen my coworkers completely baulk at computer code I hear all the same things I heard back in high school. "This is too hard, I can't learn this stuff, I'm not going to bother attempting to understand it". Fluid Dynamics was a hard subject (in my opinion), Solid Mechanics was challenging a dozen lines of python code is not on the same level.
• xivzgrev 3y ago
  I can do hard things but loss of sleep from a newborn is still hard. This guy prob didn’t do overnight feedings for his kids
  • steve_adams_86 3y ago
    One of the things about doing hard things out in the world is that people often recognize you for it. With parenting, it’s the hardest thing you’ll ever do at times and most people in your life really don’t care. It’s a thankless job.
• hgl 3y ago
  > ... teenager asks why they need to learn calculus > But if we avoid hard things I don't see how you can justify the former by arguing the latter. These two are orthogonal. If I were that teenager, I think what I really would want to ask is that why it has to be calculus instead of some other things that is also hard but with obvious real world application like writing a small 3D game engine. And my answer to that question is you probably shouldn't if your were in an ideal education system. You would be taught what interesting interactions you could have with the physical world, and be induced to discover calculus or some other math tools that helps you understand how the interactions really work and demonstrates you really need such tools. You're more likely to grasp them when you're driven by curiosity.
• yawnxyz 3y ago
  I like the idea that "If you can master these topics, imagine what other topics you could master if you put your mind to it" — again, for the empowerment. It's not about a thing being hard. Walking is hard to a paraplegic. It's about overcoming a thing and feeling good about it (instead of external rewards, like a piece of candy or good grades). The real problem with school is that it replaces empowerment with gamification externalized rewards. You're not learning calc for the sake of understanding the world, you're doing it for a line item on a checklist. That doesn't come with empowerment. With the mere framing of "you can do [hard thing] to prove you can do hard things" is a bad framing because it could be anything — from doing calc, to bungee jumping, to drinking a gallon of milk (please don't). This framing doesn't actually lead to empowerment (and then self-improvement).
• Barrin92 3y ago
  To me what's more important than Calculus being hard, and I think that's especially true for maths more broadly is that it's beautiful and one of the fundamental ways how we can make sense of the world. Everyone benefits from doing some maths. I studied maths in uni and while I've not used it much, even as a programmer, I still enjoy doing it. My dad never had much schooling but now that he's retired he actually picked up a few of my books and slowly worked through high school to now undergraduate courses. He's having a lot of fun with it.
• esafak 3y ago
  Don't do hard things that are unrelated to your actual goal; they're in unlimited supply, and you could be doing hard things that are relevant instead. This essay wouldn't have impressed me in middle school; I don't know why it's on our front page.
• wrs 3y ago
  Not to distract everyone from complaining about calculus, but this reminded me of something I heard from a person with a Ph.D. in astrophysics from Caltech. They were not working in astrophysics, but they said the degree was still quite valuable to them. Whenever they had trouble learning something, rather than feel stupid, they reminded themselves: “I have a Ph.D. in astrophysics from Caltech, so I am definitely not stupid. This is just hard.”
• wwarner 3y ago
  I like the idea, but I’m gonna say that (a) calculus is more than a good challenge and (b) math is actually easy. To understand how things actually work, you need math, especially calculus. Deep learning? Calculus. Statistics? Calculus. Finance? Calculus. Physics? Calculus. Mech E, robotics, earth science, econ? Calculus. Second, calculus, like all math, is easy. Like that’s the point, it’s the science of simple things. That math is competitive and presented as a cryptic challenge is beside the point — it is designed to make it possible for anyone to reason for themselves and solve problems. The sense of impatience and criticism around math is totally unwarranted and isn’t good for anyone. I get kind of bummed when I see schools spending so much creativity and enthusiasm on art and theater. There really is no reason why science should be thought of as judgmental, difficult and painful, while putting on a play is creative, inviting and fun.
  • TexanFeller 3y ago
    It will be amusing if we find out that all the things come in discrete quanta, even space-time, which I hear hasn't been ruled out. Calculus and real numbers might not be sitting as pretty.
    • wwarner 3y ago
      There isn’t that much difference btw an integral and a summation.
      • TexanFeller 3y ago
        There are lots of corner cases where the difference matters, like when integrals with finite bounds can go to infinity where a finite sum cannot. Boundary cases and surprise infinities seem to be a common problem problem the theoretical physicists have battled in their theories for the last century.
  • jimmydddd 3y ago
    I saw an article where they asked a bunch of scientists and engineers if they actually used calculus in their professions. None of them did. They used Excel and the R programming language.
• ssivark 3y ago
  From that perspective, going through any kind of struggle (and building willpower/discipline) would be a good enough proxy for learning calculus. It’s a little sad that the best value that the OP can impute for learning calculus is masochism — I cannot imagine saying that for anything in the school curriculum that I actually learned/understood. I wonder (in good faith) whether the OP actually even absorbed calculus at all… (i.e. can they solve calculus problems even today, for example?) — if not, they’re not the person who should be making authoritative comments on the usefulness of calculus. Calculus (Taylor approximations, perturbation modeling, error propagation, significant figures in measurement precision, gradient descent, etc — just off the top of my head) is so deeply embedded in my thinking, that it strongly shapes how I think and amplifies my effectiveness! I disagree with the OP’s claim so fundamentally — they might as well claim that schools/education focus on literacy for the same reasons.
  • smeej 3y ago
    I remember when the AP Calculus test questions were released only a month or so after I had taken and aced the exam. I had no idea whatsoever how to solve the problems I had solved easily in the very recent past. It's as you say. I didn't absorb it at all. I stuffed it in short-term memory and passed an exam. But that's all I learned. I learned how to stuff things in short-term memory. I didn't learn calculus.
• rollinDyno 3y ago
  I raised the same questions as Nat, but I think he hasn't really discovered why we were asking that. The reason why I was looking for a good reason to study calculus is because I was lazy, and if I'm lazy enough then I can change the definition of what "hard" means. For instance, I could convince myself that if my could teach calculus, and him being just another dude, then surely I could learn calculus. I would also be cautious about setting yourself up for a hard life. The takeaway resonates well with the HN crowd, myself included, because we like challenging ourselves. There's a lot of people out there who are simply looking to satisfice their lives, and you'll need another way to motivate them to learn calculus.
• codersfocus 3y ago
  There will come a time when you have enough money, enough of everything, and deeper questions will arise. What is the meaning of existence? Why is there anything instead of nothing? You will see that math plays a very fundamental role in our reality, and once you start seeing it in such a manner it may begin to interest you.
  • smfjaw 3y ago
    I feel like math is taught from too high of a level initially. I did a second major in Logic along with CS at university, I was pretty crap at maths in HS and never really 'got it', I could manage but never had any intuition. After doing a bunch of logic papers and learning about axioms and peano arithmetic everything made a lot more sense from a foundational perspective and it really changes the way you look at numbers and the world around you
  • jononor 3y ago
    There is no end to things one cab learn, to what one can (attempt) to master. Hmm... Perhaps I am addicted to learning to avoid thinking about existential issues.
• WesleyJohnson 3y ago
  I lost interest in school around the 10th or 11th grade. I never took any math classes beyond what was required to graduate way back in '96 in Florida. I also didn't go to college. I've been a professional web developer since 2005 and a development manager (who still codes) since 2017. I don't understand the first thing about Calculus or even logarithms. I'm sure if I did, I'd probably be a better developer. I've had employees try to explain to me fairly basic log notation and my eyes just glaze over. It's never impacted my abilities, nor the respect and admiration I get from them as a well-experienced and knowledgable developer, but I can't help but feel ignorant. I need to go back to the basics and work my way up; I've lost a lot of it. Where do I start? Kahn Academy?
  • yCombLinks 3y ago
    Khan Academy is great, but there are also an incredible number of great youtube videos. I would watch this 3blue1brown video to see if you like his style : https://www.youtube.com/watch?v=WUvTyaaNkzM https://www.youtube.com/watch?v=WUvTyaaNkzM
    • WesleyJohnson 3y ago
      Thanks for the recommendation. Bookmarked
  • Natsu 3y ago
    A lot of math is cumulative, i.e. built on top of the prior concepts/tools. There are some things that are effectively the start of their own branches, but a lot of them then go back into a tangle of general mathematics that's all deeply interrelated, and also a subject onto itself when you get into ways to convert problems into totally different representations to use other mathematical tools on them. In your case, follow something like Khan academy through the normal grade school programs to pick up where you left off and work backwards on picking up any concepts you're weak on then pursue whatever threads interest you. Wolfram can also help you look up specific things or find necessary formulas if, e.g. you just need the formula for a cone or to know how to integrate sin().
  • kalid 3y ago
• maxwin 3y ago
  I think the better way is to come out with a lot of interesting real world scenarios that require calculus or other math. Math doesn't get created out of a vacuum. It was created for a reason. I think if we can avoid diving into abstractions too quickly and focus on specific real world problems and lead the kids step by step to the solutions , that would be more interesting.
• batman-farts 3y ago
  It's a bit sad that calculus remains the stereotypical example of difficulty in most curriculums. Throughout childhood, I remember it seeming like some sort of complex, inscrutable, untouchable phantom hanging in the distance at the far end of the high school math course progression. If somebody had told me that calculus is how you transition between dimensions, or that techniques of integration would enable me to generate 3D shapes from 2D lines, I think I would have been much more motivated to progress rapidly in math, and much less discouraged when I hit the "hard parts." Those are the answers I tend to give today when somebody asks me, "why take calculus?" Demystifying it doesn't even have to be a wholly practical explanation, like deriving acceleration from velocity. Segregating out the "hard stuff" doesn't even necessarily lead to great learning outcomes, either. At my high school, and it seems many others, the honors kids were put on the track leading to calculus while everyone else ended up in a dedicated statistics class. The honors kids were expected to pick up statistics through supplementary assignments in their laboratory science classes, and this same approach carried over into lower-division undergrad. As an adult, I feel like that approach has only given me cause to go back and seek out a firmer grounding in statistics.
  • sanderjd 3y ago
    Motivating topics for students is so important and underrated. It's also super hard I think. For one thing, everyone responds to different motivation. Some people are motivated to learn basic algebra more by the possibility of extending it into applied math so they can get a good job as an engineer. Others don't have any interest in that, but rather would be motivated by the beauty of pure math. And students themselves have no idea what they like. But yeah, I can think of so many examples of things that I would have been way more into in school if I understood how they mapped onto the adult world. Statistics is probably at the top of that list though.
• chasing 3y ago
  > You know they will never use it in adulthood, outside of certain career choices. Just going to register my dislike of this particular trope. Mostly because "certain career choices" is doing a huge amount of work. "Certain career choices" can give you access to a very high income. They can give you access to a deeper understanding of some pretty interesting stuff and put you in a position to accomplish all sorts of amazing things. People use calculus in the sciences, of course, but also in business, the arts, music, politics, and beyond. We learn calculus when we're young as a part of expanding ourselves, casting the widest possible net to find that intersection of what we're good and and what we're excited by. And to fill our quiver with as many arrows as possible for when we hit the adult world. And, of course, to build our self-esteem by showing ourselves we can accomplish hard things. But I would highly recommend against taking the attitude that "you'll probably never use it." That's counter-productive. And the people who "don't use things" are boring...
• codeisawesome 3y ago
  Feels like many other comments here are trivial objections for the sake of sounding contrarian. Or even, humble bragging about how easy math was to the commenter. I found the article to be a great, new (to me), and widely applicable perspective on the matter.
  • wwarner 3y ago
    I am definitely not bragging — I’m saying the opposite, that all that pressure and elitism around math and science are unnecessary and counterproductive. I also liked the article just fine. The only controversial point I made is that science > art :)
  • BWStearns 3y ago
    It's almost like no one finished reading the post (emphasis added). > I don’t particularly care what grades my kids get once they start school. But I do care that they consistently prove to themselves they can do hard things. If Calculus is how they want to do it, fine, but there are many, many more options. Separately, as someone just recently learning calculus as an adult now I'm digging the obliviousness of the "math is just inherently easy" folks. I get where y'all are coming from but there's a deep lack of empathy there. Go teach some people something (anything) and learn that other people's brains don't necessarily contain your knowledge.
    • aleph_minus_one 3y ago
      > I get where y'all are coming from but there's a deep lack of empathy there. Go teach some people something (anything) and learn that other people's brains don't necessarily contain your knowledge. Concerning the empathy point: I do believe that to become good in mathematics, you seriously have to believe that everything in mathematics is actually easy, and you either don't work hard enough (so you fail understanding it; solution: work harder) or you are too stupid to understand the material (which means that you should better work even harder to understand the material to compensate for this weakness).
• MaxBorsch228 3y ago
  People (and employers) who can truly appreciate calculus wouldn't be impressed with a taken calculus course (thousands of students take calculus every year) or even a math BSc, and those who can't, how would they assess how hard your calculus course really was? There is no competition in a typical calculus course. Better ways of signaling the ability of doing hard things, especially for kids, in my opinion, are math/programming/etc contests. That's where you have a real competition and can show what you are capable of relatively to other people who participate and want to win. Also, it's important to note that passing a calculus course includes not only watching lectures or reading a textbook but also extensive problem solving. Typically "hard" college math courses are about memorization of abstract concepts, and taking any of them doesn't really prove you can do hard things (I'm not talking about PhD where you need to make novel contributions, thats crazy hard if you want your research to be competitive). Thats my experience and perspective but I'm living in my bubble.
  • XenophileJKO 3y ago
    I feel like you have missed the entire point. The point of the article was not to "signal" that you can do hard things. It was to build up the inner confidence. Competition is great, but largely orthogonal to the concept of having kids learn that they can do hard things.
• js8 3y ago
  Calculus is important, because (among other things) the proper definition of limits teaches you how to manipulate logic quantifiers. In any case, IMHO best advice to young people - try to learn hardest things you can. Later, there will be less time, less energy and more distractions.
• tjmc 3y ago
  Learning difficult concepts is only one aspect of developing perseverance - which is probably the greater ability to master. Others are finishing what you start, developing habits to complete undesirable tasks (like regular exercise or doing the dishes) and overcoming fear. The latter is something you see creep in as you get older and it's something that's always attracted me to hobbies that require you to keep your nerve like skiing, scuba diving and flying planes. There's nothing like having to land a plane solo with a bit of a crosswind to give you confidence in yourself.
• AnnikaL 3y ago
  I mean, I found learning calculus to be fun and rewarding in its own right! It can be challenging at times, but also beautiful.
• 8note 3y ago
  What's it really mean to be hard? Some things are vaguely impossible, like finding a solution to fluid mechanics, or finding a theory that combines quantum mechanics and general relativity. Others are proven to be impossible under some conditions like the halting problem. Others still require access to some amount of resources, or some amount of leverage, like buying a $100M yacht. Lots of these hard things are quite unlikely for me to be able to do. I think most people refer to the resource one? And that some people have more access to resources than they think, and the scales of resources needed are smaller than assumed?
• spot5010 3y ago
  Learn calculus because it is beautiful. Newton had discovered the law of gravitation, but didn’t publish it for a long time because he couldn’t justify how the gravitational effect of a sphere could be the same as if all its mass was concentrated at a point in the center. He had to invent calculus to prove it. Isn’t that amazing? I know the author is using calculus as an example of a hard thing, but if someone is genuinely following their curiosity, then things do not seem hard. Personally I wouldn’t want to work on hard things just to prove to myself that I can do hard things. I’m happy being lazy.
• upxx 3y ago
  As Hilbert put it, “Every boy in the streets of our mathematical Gottingen understands more about four-dimensional geometry than Einstein. Yet, despite that, Einstein did the work and not the mathematicians."
• deleted 3y ago
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• bruce511 3y ago
  This resonates a lot with me. At school I coasted, ignored all home work, never studied, and was a consistent C. I was continually told I could fo better by putting in some work (an objective viewpoint I agreed with.) But i had better things to do. I started programming in grade 7, from a book, with a Apple 2 (circa 1982). There were no forums, no Internet just me and a thin booket that came with the computer, plus later, the odd magazine. It was never "hard", but it was fun. It taught me how to build things, how to approach problems, how to throw something away and make things better. How to imagine. Ultimately I would study comp Sci- people would teach me the right way to program, and 40 years later it's still my career. As I predicted at the time (somewhat obnoxiously to my then teachers, sorry Mrs Hodge), I had better things to do than raise my Geography score from a C to an A. School is important, but finding something you enjoy, where "work" feels like "fun" is the truely "gifted child".
  • szundi 3y ago
    True when you happened to find just one of the soon best paying new activities. Catching butterflies would have worked out less awesome probably.
    • malikNF 3y ago
      Ackchyually.... [1][2] [1]https://en.wikipedia.org/wiki/Commercial_butterfly_breeding https://en.wikipedia.org/wiki/Commercial_butterfly_breeding [2]https://money.cnn.com/2014/08/14/smallbusiness/butterfly-farm-jobs/ https://money.cnn.com/2014/08/14/smallbusiness/butterfly-far...
    • bruce511 3y ago
      Yeah, it didn't hurt that my interest co-incided with history. But there are lots of professions that can start as teenage interest. A friend of mine was obsessed with birds, he went into nature conservation, started in a bird reserve, and has had a long career climbing the ladder in that space. And also tour-guides bird watchers. Sure, not everything works out, but if you can turn your fun into your job, then you're one off the lucky ones.
    • jokethrowaway 3y ago
• zerop 3y ago
  Some things which are hard for someone might be easy for someone else. Usually academic things like calculus are seen as hard, but there are many hard things in day to day life, like selling anything to unwilling buyer, handling a rude customer with calm and much more. They too are hard and calculus guys can not do them well.
• tayo42 3y ago
  Funny, First semester of calculus I got a C i think, second semester, I failed. I thought about going back to community college and taking a calc class just to see if I can actually pass it. No reason other then that I suspect I could have passed it with better teaching. I hated that I had to memorize things, which felt tedious, not hard in a good way. If you dont memorize cos,sin,tan stuff you can't take tests fast enough. The class was just how good can you memorize things. I also hated the proofs, pages of proof. No idea why, and the teacher didn't speak english well or communicate well in general
• mediumsmart 3y ago
  I can do hard things that I am interested in, that is true. But I also have this theory that nothing can be proven, but I can’t prove it.
• derelicta 3y ago
  My bf learnt how to do hard things soon enough (mostly against his own will I admit) and I wish I could find the strength to emulate him in a way.
• tjbiddle 3y ago
  I like this approach as well. My current explanation for this is more along the lines of being well-rounded. By being exposed to a number of different skills and learnings throughout your education, your more likely to be able to connect the dots in other areas - and just hold better conversations with people. Don't need to ace all your classes for that, but put in the effort to try and structurally understand whatever it is you're coming across.
• newaccount74 3y ago
  "If you do weightlifting then sleep deprivation from a newborn is easy" Right. Tell that to my partner, who has been nursing our newborn every two hours for the last 5 months. There is no way to wake up 2-4 times every night for months and not be tired. Weight lifting would be zero help with that.
• a-dub 3y ago
  lol. it tends to be pretty flimsy proof, especially in light of the expanded horizon.
• pcwelder 3y ago
  So you proved to yourself that you can do hard things, what then? You don't need to continue proving the same, doesn't then that stop being a fuel for motivation? That's what happened to me at least.
  • nurbl 3y ago
    Well, you may now be more likely to go out and actually do some "hard things". Life is not only about proving yourself.
  • jononor 3y ago
    Are you not hungry for more? Don't you want to find out what other hard things you can overcome?
• noduerme 3y ago
  I agree in principle that your personal story is made of the rough things you've overcome, and it's refreshing to hear it stated in a positive way (calculus) as opposed to the usual negative way (abuse, alcoholism, etc). It misses something, though: Many people will slack endlessly on doing the hard thing until it appears to us to be a challenge we've come up with for ourselves. Then and only then does doing it the hardest way possible seem not just worthy of our time, but essential to our personal growth. I'd argue that as long as someone reaches that attitude toward something that they choose, they have lived a good life. And that something doesn't need to be a high school math class. The hard thing could be trying to become a chef when you're 50, or deciding to write your next app in Assembly knowing none at all, or surviving a month in the woods, or going to a foreign country with the intention of learning the language. It has to be hard to make it worthwhile, but it has to be your own to make it valuable as an accomplishment to you, as opposed to something imposed on you which you merely endured. I think this is why a lot of people come out of incredibly hard ordeals in the military with much less personal sense of self-worth than they were sold they would get going in. [edit: removed a critique. I had misinterpreted the words "errant period" to allude to something other than punctuation. My mistake.]
  • chrfrasco 3y ago
    I believe Nat is referring to a full stop rather than menstruation in the sentence about crying into tiktok.
  • justsomeadvice0 3y ago
    It took me a while to understand what you were talking about at the end there. I think the author is referring to a grammatical period ('sorry' vs 'sorry.'), not the menstrual kind, lol.
    • noduerme 3y ago
      hahah. oops. I edited and removed that criticism. The exact line was: >> We’ll cry into TikTok over an errant period at the end of a text message. My brain read that as, "At the end of a text message, we'll cry into TikTok over an errant period." lol
• HellDunkel 3y ago
  I am not convinced „doing hard things“ should be a top priority for kids. For my own kids -or actually everyone- i hope they find a passion big enough to make a living. This takes time and lots of experimenting and cannot be forced into existance. Grinding through „hard things“ can leave you with a great deal of confusion. It is so much easier to do „hard things“ if you love doing them. The problem with math is: it is very hard to learn later on in life. Maybe even as hard as drawing. Schools should really focus on reading, drawing, writing and math- everything else should come secondary.
  • gjadi 3y ago
    I recommend reading So Good They Can’t Ignore You: Why Skills Trump Passion in the Quest for Work You Love from Cal Newport for a different perspective on this.
    • HellDunkel 3y ago
      Thanks. I am sure there are some valid points to be found in this book but my own experience is enough for me at this point. I have worked in jobs where i was doing great and received positiv feedback- even earned more than today. Still hated it and moved on- best decision i could have made.
• barrenko 3y ago
  Conversely, hard domains are the only ones where you can achieve mastery.
• bryanmgreen 3y ago
  The only things in life that are hard are the things you don’t want to do.
• bigpeopleareold 3y ago
  I am not good in calculus and that's something I wish I did pick up when it came to it. The harder thing was keeping the pressure up to pass the tests and in total, pass a course, while dealing with the severe discomforting exhaustion of coming in early in the morning for classes, having to understand rather complex abstract notions. I still cannot think when tired or even inebriated. But going through that was really to get that good pencil pushing job reserved for college graduates, no? :D Instead, in the end, I like what I do and if the spirit moves me or need it for something, I would sharpen those calculus skills.
• hardware2win 3y ago
  >You know they will never use it in adulthood, outside of certain career choices. If somebody says stuff like this, then they do not understand math, imo. Im a little bit sad whenever somebody argues for math by using "no phone available at the moment" argument. Math is insanely powerful world modeling tool. Starting from calculating right amount of fence for your garden, to estimation of 500km route arrival time while taking traffic statistics into the account, to data science, ML, whatever more complex. Since math modeling is everywhere in "modeling" industries like engineerings, financial-ish jobs and other Then you basically not only get better tools to operate (model) in real world, day2day life, but also it opens you doors to highly paid careers. But the goal is not to have fancy jobs, but being able to do real world modeling.
  • raincole 3y ago
    I don't think you need calculus to calculate right amount of fence for your garden. > Since math modeling is everywhere in "modeling" industries like engineerings, financial-ish jobs and othet In other words, certain career choices, as the OP says.
    • l__l 3y ago
      This makes the same mistake being called out in the comment you're replying to. The point isn't about the mechanics of solving a differential equation, it's about gathering the intuition about a way of approaching problems. (Also, while it might not be the tools needed for the average homeowner, there are plenty of optimisation problems similar to "how much fence do I need" which are most easily solved by solving the Euler-Lagrange equations)
      • DrScientist 3y ago
        Interesting I've seen the opposite in highly trained mathematicians - they can really struggle with taking an intuitive leap without the safety net of the working out the numbers. While it's always better to work out the numbers if possible, sometimes it isn't possible and people get trapped trying.
    • 3y ago
• beeforpork 3y ago
  This is similarly true for finishing a degree. Luckily, that occurred to me before finishing a degree, because that did feel futile. But finishing a degree proves that you can finish stuff. That's valuable proof for yourself and when you need to give an impression. The topic itself really doesn't matter that much -- which is also good, because then you can freely choose it to your liking, if possible. TL;DR: I think this is very helpful advice to people who question stuff.
• aleph_minus_one 3y ago
  > But I recently realized there is a very good reason to take Calculus. It’s to prove you can do hard things. While I do like mathematics (thus I clearly have no negative feelings about learning calculus), this argument is dubious: the longer I live, the more I realize that the capability to learn complicated scientific stuff (including mathematics) hardly does transfer to other areas of life. Just consider this: if such skills transferred so well, one would expect that those people who make a steep career in companies have learned lots of insanely hard stuff, often hard mathematical and scientific stuff. The reality is that the people who have such a steep career are rather great "policitians" (in the negative sense), sycophants and self-promoters. On the other hand, learning hard scientific/mathematical stuff nurtures the personality trait of "no bullshitting" and developing less tolerance for claims that clearly cannot be abided by. Thus: I really like learning hard things, but this personality trait is in my opinion often a career killer.
• Notatheist 3y ago
  >But I recently realized there is a very good reason to take Calculus. It’s to prove you can do hard things Doing hard things proves you can do hard things. Where does calculus enter into it? >The more hard things you push yourself to do, the more competent you will see yourself to be "The whole problem with the world is that fools and fanatics are always so certain of themselves, and wiser people so full of doubts." >Most C students are not doing other hard things instead of school. They’re just goofing off, so they end up working for the A student. This is ridiculous. Author goes on to imply these ("most C students") are on social media and using drugs. I'd put any money on them being much more likely to have been raised by the type of parent who believes their kid needs a reason to want to learn calculus. Oh, and what is "hard" by the way? Is it doing something you're not good at until you're good at it? Does it need to be valuable from my perspective or that of my parent? Should it take a certain amount of time to become "good" at it? When am I good at it? Can it be a hobby I enjoy even while it's difficult, or must it be a chore? What if I'm forced to overcome some hurdle in my life for example growing up with a foolish parent with warped worldviews?
• phforms 3y ago
  It’s really interesting how we shy away from some “hard” things, even though there is literally nothing at stake that could prevent us from doing them. Nothing life-threatening, no (or minimal) risk of physical or psychological damage, no social exclusion, no irreversable decisions about the future to make. Why can’t we just try/do it – what are we so afraid of? Many people (especially those in a lucky environment) can just try to draw realistically (which is actually not that hard, given a good teacher/instruction), study a “hard” topic in philosophy, get good at playing a “hard” song on an instrument or even learn how to prove mathematical statements or how to model and analyze complex systems. We can just try, there is nothing at stake except our time and energy. When something is really interesting to me, I try not to stop myself from pursuing it just because it is considered “hard”. I have many mental issues (executive dysfunction, bad memory, etc.) but I am also stubborn and curious enough to try anything, again and again if I have to, which I never regretted. It doesn’t hurt and it can be so much fun with a humble and relaxed attitude and especially if I don’t try to compare myself to others, which might be one of the main things that is holding most of us back.
  • throwawybb1 3y ago
    > It’s really interesting how we shy away from some “hard” things, even though there is literally nothing at stake that could prevent us from doing them. Nothing life-threatening, no (or minimal) risk of physical or psychological damage, no social exclusion, no irreversable decisions about the future to make. Why can’t we just try/do it – what are we so afraid of? Heh, I don't know about that. I got into motorcycles because of how dangerous they are. When I was just learning dirt riding I specifically picked out an old barely used logging road to do so. It's 2 hours from the nearest town, about 40 miles long winding road with a sheer drop on either side. Getting there is tiring in of itself. Every time I started it, I was already fatigued from the ride out and I just go straight in without a break. But there's very little room of error. There's no cellular service, traffic is almost non existent. I don't tell my family when I got out there or where I am exactly. If I overcook a corner, loose focus for more then a second, fail to spot where the road's been eroded out, make just one little fatigued induced mistake... that's it. There's no getting out. There's no help coming. They won't even have my body to bury. Finding the strength to crank the throttle wide open and hold it open right until the last millisecond before disaster is hard as hell when every instinct is screaming to slow down. But in many ways, it's easier then trying to make friends or ask a someone out on a date. If and when I do make that fatal mistake, I don't have live with the knowledge that I screwed up a relationship or have to live with the regret what may or may not have not have been. Or worse; disappointing those who's opinion has weight. Dying is easy. Living with the consequences is hard.
• lucideer 3y ago
  There's some nice seeds of ideas here, but it's all a bit lost in (a) brevity - it's a deep topic so the post length can't do it much justice & (b) naïvety - their extremely oversimplified explainer for the “C students hire A students” trope is that the C students are actually secret A students in other areas. This assumes a utopian world where academic-style assessment of study/effort maps to career progression. C students do well for a range of reasons including-but-not-limited-to: charisma, nepotism, unconscious-bias-hiring on the basis of race/gender/accent/height/hair/appearance, normative mental health characteristics. It's not because of their secret extracurricular study: that's in direct contradiction of the message behind the trope.
• constantcrying 3y ago
  I really despise all the "why you should care about math" takes. The question is never asked about any other school subject and only mathematics has to justify itself that way. I had to learn about categories of plants and animals, interpret 20th century literature, learn about events from a thousand years ago, I did presentations on the demographics of European countries, how certain chemicals react and much, much more. I never used any of that knowledge for anything, certainly not in my career or in university. But somehow mathematics is the one field which needs to justify its own existence? Mathematics needs to bend itself over and "be relevant" so that people will actually learn about it? Why? Why not ask the same of any other subject. Justifying mathematics is easy, especially such a universally applicable subject as calculus. But I see no reason why it should have to justify itself in any way.
  • golergka 3y ago
    People aren't doing it because they think they should. They are doing it because they want to.
  • BiteCode_dev 3y ago
    That's because math is harder for most people. There is no difference between learning a name in history or in biology, or some workflow. But math reasoning really filters out people in a way nothing else does. All other topics just require memory and basic reasoning. Even physics mostly is hard because of math. And philosophy, mostly because of jargon and references. Otherwise, if you break it down, it's not that complicated. But you can break down a math problem as much as you want, some of them are beyond what you can do comfortably. And a lot of students reach this limit early in their life. I see this when I play board games with people: there is a threshold of rules and calculation power above which I lose 90% of the players. They just can't enjoy it, because it requires too much effort to play. It's similar for me and sport. I've been doing exercise all my life, but my brother will always do more, and harder, because there is a barrier after which it's just too painful for me. Math and athleticism can be trained, but there is a hard ceiling. And even before you reach that ceiling, closing the gap gets more and more expensive for some people, so much the ROI is difficult to justify.
• uwagar 3y ago
  prove to who? i refuse to prove myself to them.
• dangoodmanUT 3y ago
  This echoes in my soul
• mianos 3y ago
  It's not the point, but a lot of people are going on and on about the lack of need for calculus as a programmer. If you even touch how any machine learning works it's all basic calculus and intermediate linear algebra under the hood. Sure most people can get a long way without understanding anything under the hood but I think I am better developer knowing assembly and architecture. The same for ML, you can get by most of the time. You can also make a whole career not doing hard things. That's not for everyone.
  • hnfong 3y ago
    > it's all basic calculus and intermediate linear algebra under the hood It's all bits and bytes under the hood, which in turn is just electric signals under the hood, and ultimately (hopefully) quantum mechanics under the hood. Are you an expert in all of these? Why arbitrarily stop at the calculus layer?
    • mianos 3y ago
      Yes I am trained in electronics but I don't think understanding that level of detail ever helped me find bugs or improve the performance and reliability as that level is fairly static so you have to play the cards you are dealt. The same with the underlying physics. I have never had any use for that and I am not sure why they taught it hat first up. Interesting all the same
• analog31 3y ago
  I liked calculus because it was hard things that you could prove.
• costanzaDynasty 3y ago
  I don't know anything about Calculus. My time is school was mostly spending a year in class studying to take a single test so that the school got more government money. But I will say that when a bunch of people online carry on about how hard something is, it makes me want to try it. Usually it turns out that what ever they were saying was hard or impossible is difficult and time consuming but not impossible. The hardest part is getting over how other people have built something up as impossible. But perhaps my FU-mode is stronger than other peoples. Someone on here said I'd never work for a FAANG company, so I guess that's something I'll have to do just because. Not impossible.
• igorzij 3y ago
  I always felt like linking education to direct use of the knowledge is missing the point. It is irrelevant whether or not you'll need the knowlege you learned in school or at uni. What matters is your learnability, and that's the muscle you train with education. Learning smth just to use it to get paid for it is the lowest form of learning; the whole point is to acquire ability to learn whatever quickly so that you can become proficient in whatever is needed in the future, which in turn gives you an edge in the talent pool. In that sense the central point of the article is 100% valid - it's all about track record
  • hnfong 3y ago
    You can choose which subjects to study in university, or even whether to spend time to get a degree. So it's optional. And these days, university departments that don't actually do something gets its funding slashed, so in that sense market forces are working well. It's a different story for education up to high school. School is pretty much mandatory these days, and basically everyone has to go through it. It's a worthy question to ask why learn X instead of Y, if X has little real application? Why glorify those who can do maths well, as opposed to those who can best remember the names of Pokemon? Or those who can play LoL the best? Who defines which areas of knowledge counts as "education", and which areas are frivolous trivia? In the case of maths, the mere fact that it has tonnes of applications in many technical subjects is sufficient justification for me, but if you reject that line of reasoning, I'm not sure you can convince me (or anyone with critical thinking) that it's more worthy to pursue knowledge in maths than knowledge in "Pokemon studies".
• carapace 3y ago
  It's better to avoid waste, waste of time, waste of calories. Most of the things that most people want you to do are wasteful, pointless, better to not be done. A very valuable skill is to be able to discern bullshit, and decline it. (As an aside, the idea that calculus is hard is a pedagogical failure. Calculus is easy to learn if it's taught well. Most of our education systems actually make learning much more difficult than it is.)
• blueyes 3y ago
  This comment is not for or against calculus. Doing random hard things in order to get into college or get a white-collar job is really no different than pointless test preparation that shows you can follow instructions, and it has produced strange hierarchies such as Qing-era mandarins. Much better to find something that intrinsically motivates you to do hard things that feel less hard to you. It'll take you further. Or you can prove to the world that you are capable of a yearlong mindless grind...
• satokema 3y ago
  You should do calculus because it translates to actual problem-solving. Not everything is nice and chunky in discrete - calculus allows you to model and calculate continuous kinds of problems. Even if its not the area under the curve or some infinite series thing, it's a really good intro to modeling things in terms of adding up many small steps.
• QuadmasterXLII 3y ago
  For some small percentage of high schoolers who can learn calculus, that knowledge will be worth ~100k a year for 40 years- and worth far more than that for their bosses. We can’t tell in advance who is in that percent, so we hedge by teaching it to all of them.
• sourcecodeplz 3y ago
  You take maths because it shapes your brain, it forces new neuron connections to be formed in the right side of your brain. Then you also have literature and arts for the left side. The brain is like a muscle, if you don't train it, it wont grow AND you will basically be STUPID. That is it.
• jameshart 3y ago
  Of course, one thing a solid mathematical education will also give you is an appreciation that while ‘having passed AP Calculus’ implies ‘can do hard things’, that does not mean ‘having failed to take or complete AP Calculus’ implies ‘can’t do hard things’.
• riialist 3y ago
  I thought "doing hard things" would be something like a running Marathon, studying or working while having toddlers, learning to be a pro coder as an adult, taking care of your close ones while they are sick.. But it was about doing basic math. Proving to yourself or anyone else that "you can do hard things" since you did more or less math in school/collage/university will leave you trainwreck at the first real hard thing that bumps your way. And why some people don't do the math? I guess, because they are told its boring and/or hard, but they should do it anyway. And people don't like to be told what to do.
• thenerdhead 3y ago
  There’s a difference of having to do and wanting to do hard things. Most people pass a class because they have to for their degree. Most people raise a child while being sleep deprived because they frankly have to. When people want to do something, they don’t need to prove to themselves that they can do hard things because difficulty hardly matters to one with their mind set on something. For example anyone who decides to run a marathon one day. Instead for the things you have to do, one could reframe the “have to” with a “get to”. Gratitude is empowering. Not everyone gets to go to college. Not everyone gets the opportunity of being a parent. Etc.
• yayitswei 3y ago
  Attending a good college is also useful in the same way. "I went to Stanford, I should be able to figure this out."