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“Bingo!!” said the teacher. “It’s the same thing with calculus. You’re not here because you’re going to use calculus in your everyday life. You’re here because

• otabdeveloper4 4y ago
  Seems like the grapes were very sour.
• behringer 4y ago
  Programmer here. I wish I knew more calculus. It's really tough to learn outside of school and much older.
  • tayo42 4y ago
    Why? There's so many resources now. I actually tried to relearn calculus recently. I ran into the same problem I had the first time in college, it felt like learning for learning sake and didn't have a strong enough motivation for it
  • danielvaughn 4y ago
    Yep. Even just linear algebra. I’m trying to get into graphics programming and it’s very difficult without a solid understanding of that stuff.
    • newhaus1994 4y ago
      “Just” linear alg, LOL. I made it through calculus 2/3 in high school but linear algebra gives me fits, especially since I only ever learned it in a data science context. Linear algebra is freakin’ tough!
    • askafriend 4y ago
      It's easy, just work through a book and do practice problems. The difficult part isn't the math, it's just finding time to do it.
    • dougabug 4y ago
      I would actually start with a first pass at elementary linear algebra, before taking a serious crack at even single variable Calculus. Then let the key ideas marinate in your brain; develop some facility and intuition / insight. Multivariable Calculus hardly makes any sense without a basic amount of linear algebra. It’s a bit of a historical accident that (Western) mathematics developed Calculus extensively prior to linear algebra taking shape as a significant subject. Don’t try to tackle Multivariable Calculus with a decent grip on matrices. Maybe do some computer graphics and learn how to build 2D & 3D shapes and animate them using matrices.
    • rramadass 4y ago
      You need this book: Practical Linear Algebra: A Geometry Toolbox by Gerald Farin and Dianne Hansford. You can get older editions for pennies. The 1st edition was actually called The Geometry Toolbox for Graphics and Modeling. You should also read Introduction to Applied Linear Algebra – Vectors, Matrices, and Least Squares by Stephen Boyd and Lieven Vandenberghe: https://web.stanford.edu/~boyd/vmls/ https://web.stanford.edu/~boyd/vmls/
      • rramadass 4y ago
  • tenebrisalietum 4y ago
    Basically it's two things: 1. answering the question "how do we get the next x" for a function x=y. If x=y, then if you increase x, you also increase y, so dx/dy=1. Figuring out dx/dy is fun when dealing with things like 3x^2+5x+7=y. But take the game of Pong, for example. A simple Pong game has a ball and the direction of the ball can be controlled by two variables - horizonal velocity (H) and vertical velocity (V). Each frame, you take the ball's X and Y and add H and V to it, to move the ball. When the ball collides with something, just multiply by -1 (to flip the sign) to reverse the ball. If you divide V by something like 0.0001 each frame, you will implement gravity. Want the ball to have a gravity or other "pull" that results in it hitting a point in a specific number of frames? Well ... someone who knew what they were doing would know what to do. That's all I got. 2. If you have a few points for x=y, you should be able to figure out dx/dy somehow. I think that's called integrals.
    • treis 4y ago
      >If you divide V by something like 0.0001 each frame, you will implement gravity. That'd be a wild ride.
    • itishappy 4y ago
      Minor correction: > If you divide V by something like 0.0001 each frame, you will implement gravity. You will implement air resistance. Air resistance is proportional to the velocity, gravity is a constant offset. V(n+1) = V(n) - drag * V(n) - gravity
    • behringer 4y ago
      Oh sure, that's simple enough. How about gravity over a sphere in 3 dimensions? How about a custom physics and collision engine? How about some portals? How about some non linear spaces? Games get incredibly complicated very quickly.
  • halikular 4y ago
    Sorry, but that's not any excuses for you not to start learning! Looks like your problem is procrastination which we all struggle with. Old age is also not as bad we're lead to believe for learning. It's all about getting into the habit of studying. That can come after an idea that turns into a goal and is kept in motion by brute force will. Alternatively the peer pressure from school or a course can keep you going and meeting goals effortlessly. There are now many easily accessible online resources like 3blue1brown's "essence of" series [1], Khan academy [2], or Brilliant.org's courses [3]. [1] https://www.youtube.com/playlist?list=PLZHQObOWTQDMsr9K-rj53DwVRMYO3t5Yr https://www.youtube.com/playlist?list=PLZHQObOWTQDMsr9K-rj53... [2] https://www.khanacademy.org/math/calculus-1 https://www.khanacademy.org/math/calculus-1 [3] https://brilliant.org/calculus/ https://brilliant.org/calculus/
  • WheelsAtLarge 4y ago
    "tough to learn outside of school and much older." Be very careful with this way of thinking. People around me have used it to justify not taking the time to learn something as far as I can remember. In short, giving up before they try. This attitude will hinder any possible growth. I guarantee it. What's tough is following thru, not the subject you are trying to learn. If you can't learn on your own take a class at a local college. It will force you to show up and try. But thinking that you can't learn because you are older is not true.
    • wink 4y ago
      Obviously I've not looked at all of them but my main problem (especially with language books) is that there are so few good materials to learn from in self-study. Everything is "supporting the class room", or has some ridiculous split into (bad) contents and (worse) exercises that more often than not are the classic "draw three circles.. draw the rest of the owl". And yes, people usually go on to recommend some vague resource that helped them understand just enough if they were starting from a decent problem already. (IMHO a good example here is vector math. If you do some stuff with 3d and games the problems are clear and most people will start from there and then learn enough to understand it. But just learning it in isolation is where people complain).
  • dougabug 4y ago
    You have the first prerequisite, the desire to learn! Try to find resources which nurture your interest, until it grows into the will to learn. I find the history of mathematics and how it came to be, its role in the rise of civilization, to be quite inspiring. Between YouTube, and maybe the right blogs or online classes, it seems like a motivated person could learn almost anything online. There’s also a social aspect, we learn by talking about things with others, sometimes as pupils, other times as peers, and even teachers. Try to teach concepts you’ve learned to other people. Finally, you can’t learn math just by reading or listening, any more than you can learn to play soccer just by watching matches. Math is a problem solving art, you have to resist the urge to peek at the answer until you’ve exerted serious effort and put in the time.
  • rramadass 4y ago
    It is not that tough if you approach it in the right manner. Here is my "guaranteed understanding" 5-step recipe for Calculus :-) a) Learn co-ordinate systems Geometry. b) Learn Functions and Graphs. c) Learn Derivatives. d) Learn Integrals. e) Learn Differential Equations. Focus on understanding single-variable only and ignore everything else in the beginning. You will find the following resources most helpful. 1) First refresh the basics from George Simmons' Precalculus Mathematics in a Nutshell : Geometry, Algebra, Trigonometry (it is less than 150 pages!) - https://archive.org/details/precalculusmathe00geor https://archive.org/details/precalculusmathe00geor (pdfs are available elsewhere on the web) In particular; read the Trigonometry section thoroughly. 2) Higher Math for Beginners (Mostly Physicists and Engineers) by Zeldovich and Yaglom - https://archive.org/details/HigherMathForBeginners/mode/2up https://archive.org/details/HigherMathForBeginners/mode/2up - Read everything from the beginning including Preface/Notes/etc. (which setup the Motivation) through chapter 1 (Functions and Graphs), chapter 2 (What is a Derivative) and chapter 3 (What is a Integral). That's it! You now "know" Calculus; the rest is mere elaboration on this basic edifice. You should be able to do this in a week by just studying an hour or two everyday. 3) For a more Pictorial/Graphical help in understanding the above, get the book: Who Is Fourier?: A Mathematical Adventure by Transnational College of Lex. This is a manga-style book which gives a very intuitive understanding of Calculus and more. Do not wait but get started today; You can thank me later :-)
    • duckmysick 4y ago
      I'd like to add to this list a series of lectures on YouTube by Professor Leonard: https://www.youtube.com/watch?v=fYyARMqiaag&list=PLF797E961509B4EB5 https://www.youtube.com/watch?v=fYyARMqiaag&list=PLF797E9615...
      • rramadass 4y ago
        Great! I should also add the famous 3Blue1Brown's videos on the "Essence of Calculus" - https://www.youtube.com/playlist?list=PLZHQObOWTQDMsr9K-rj53DwVRMYO3t5Yr https://www.youtube.com/playlist?list=PLZHQObOWTQDMsr9K-rj53...
• punnerud 4y ago
  “Training the brain to not give up”, also called “grit”, is a more precise way to say it. Programming, music, art ++ isn’t as good as calculus on this.
  • WheelsAtLarge 4y ago
    Learning to play a music instrument or learning to paint, well, is the definition on not giving up. So, no...
  • bibanez 4y ago
    Never heard it put that way! Still, it takes grit to graps any deep formal topic, and there are those in all the disciplines you mentioned. Harmony for music, Composition for Art and programming for systems are some examples
  • coldtea 4y ago
    Grit is useless without focus. Calculus, and math in general, provides focus: it cuts through the BS. We aren't living in an era of people suffering because they did too much calculus they don't need. We are, on the other hand, living in an era where people are lied to, fooled, prayed upon, and duped everyday, because they can't understand math. We also live in an era where people could do amazing things, even as amateur hobbyists with some math and science knowledge, but are drowned in BS doom-scrolling, binge-watching of crap, and the like...
  • bnralt 4y ago
    I was just reading Sir Walter Scott's Waverley where he suggest that this is the main reason for a classical education as well: > Edward would throw himself with spirit upon any classical author of which his preceptor proposed the perusal, make himself master of the style so far as to understand the story, and, if that pleased or interested him, he finished the volume. But it was in vain to attempt fixing his attention on critical distinctions of philology, upon the difference of idiom, the beauty of felicitous expression, or the artificial combinations of syntax. “I can read and understand a Latin author,” said young Edward, with the self-confidence and rash reasoning of fifteen, “and Scaliger or Bentley could not do much more.” Alas! while he was thus permitted to read only for the gratification of his amusement, he foresaw not that he was losing for ever the opportunity of acquiring habits of firm and assiduous application, of gaining the art of controlling, directing, and concentrating the powers of his mind for earnest investigation—an art far more essential than even that intimate acquaintance with classical learning which is the primary object of study. But I think the above poster has a decent point, in that there are many places where you can train your brain to focus that will also provide you with skills that are more useful for most people. For instance, I'd say statistics, combinatorics, and probability will be more useful to most people. Of course, if you're in a field where you need to learn calculus, then you need to learn calculus, just like if you're in a field that needs differential equations or topology, you need to learn that. But that's a small segment of the population. I've studied calculus for fun (and differential equations as well), and enjoy it, but have never once found myself running into a use for it in the real world.
• dopidopHN 4y ago
  Calculus in itself yes. But the statistics / probability or optimisation stuff you can execute are nice ( eg : gradient descent ) Or even linear algebra. I think it made me better at grasping highly formal stuff.
  • Jensson 4y ago
    > But the statistics / probability or optimisation stuff you can execute are nice ( eg : gradient descent ) You learn gradient descent in calculus, it is based on derivatives...
    • deleted 4y ago
      [deleted]
    • dopidopHN 4y ago
      I learned it as part of "operational research", that was some algo-y math course. No idea if that translate. But yeah, definitely closer to calculus than stats or proba.
    • noobermin 4y ago
      There are a lot of people in these comments saying, "this thing is more important than calculus" and it turns out it's a concept that is fully fleshed out in analysis which is just calculus essentially. I feel like the problem is calculus as taught focuses too much on algrebraic manipulation which is only useful essentially if you become theoretical physicist and little else while the "why" behind calculus leads you to a lot of more useful results that are along the lines of approximation and optimization, which is closer to what a modern understand of analysis is.
    • Enginerrrd 4y ago
      I think the argument was that a calculus based approach to understanding those subjects dramatically improves and enriches the study of those subjects.
  • WheelsAtLarge 4y ago
    Yes, a statistics course is so much more useful. It's not emphasized in school but it will truly help through out your life if you understand it.
• itishappy 4y ago
  Strongly disagree. To extend the original metaphor, calculus is an exercise, not a whole workout. Sure, if you only do squats, you may not end up looking as good in a tank top as the guy who does arms all day. On the other hand, you're never going to reach peak physical performance if you skip leg day. Good luck trying to understand any modern ML paper without a solid understanding of calculus, for example.
  • WheelsAtLarge 4y ago
    Ok, given the number of people that take Calculus, how many will ever read an ML paper? For that matter, how many even know or care what ML is? This only adds to my point.
    • viscanti 4y ago
      Economics, Statistics, ML, Engineering all use calculus. You might be able to get by in some areas without it, but it's not as if it's useless. It's also really easy and straightforward. You would create calculus if it didn't exist.
      • louhike 4y ago
        I can’t help but feel like there’s far more people who do not need more than really simple calculus than people who do. Should we really disadvantage people by frustrating them with subjects almost useless for them just for the sake of the few who will need it? There could be other things to learn with as much or more interest for them. Calculus can be a good thing but we should stop to make mandatory for a lot of persons and refuse it to reconsider its use.
        • viscanti 4y ago
          Calculus is really simple. The part some people have trouble with is that they're forced to remember all the other math they've learned to that point. Others struggle with it because the concepts are new. There are successful studies teaching 12 year olds calculus, using software that helps them with the computational side (they don't have to remember all their trig rules or how to factor but they need to know when to apply the core ideas). These arguments that people shouldn't learn calculus (or should because they need some rigor) are all wrong. A small number of people should learn to do by hand, all the non-calculus computation they'll run into in calculus. Most people should probably just be taught the main concepts and how to apply them using readily available software that can help them with the calculation part.
• molticrystal 4y ago
  One use of class + 1 of what is needed is that it demonstrates mastery of the previous material when it integrates such. For example, calculus shows mastery and a decent understanding of algebra and trigonometry among other topics of the level taught previously.
• coldtea 4y ago
  >There are better ways to exercise your brain that will be many more times better than Calculus. This is HW so one that comes to mind is programming. And become a programmer who doesn't know calculus?
  • WheelsAtLarge 4y ago
    Some programmers will use Calculus but most, by far, will not.
    • aidenn0 4y ago
      And none of the programmers who don't learn calculus will use it. I am surprised by the places where calculus comes up. I certainly didn't thing e.g. a class titled "Discrete Math" would need it, but it did. And Discrete Math is to CS what Calculus is to Physics.
    • coldtea 4y ago
      They will all could have used calculus at many points, and even more so algebra, combinatorics, statistics, and geometry (in game dev, UI work in canvas an many other places). But many wont, because they don't know it, so they'll trust some random formulas handed over by others (perhaps in Stack Overflow) for some things, or constrain their work and output to what they know. Same way somebody who doesn't know about X technique (not even that something of the sort exists), wont know that there could be a great solution to the problem he works on based on that. So he'll use a subpar solution (in performance, memory wise, or even correctness), working around his limitation - or be beholden to this or that library that offers it as a black box. Take a simple example: scoring systems. It's funny how many websites use crappy scoring implemented by a developer that 'doesn't have a use for math', and e.g. naively averages scores, and ranks a movie with two 10/10 reviews above a movie with a thousands of 9.9/10 reviews...
• ludston 4y ago
  Indeed. I'm pretty sure that the research shows practicing music is a much, much better workout for your brain than doing calculus. Not only that, but practice in music is supposed to directly correlate with increases in mathematical ability.
  • hdctambien 4y ago
    The existence of a calculus class doesn't stop a student from taking music courses or being in the school band. In fact, at the schools I went to/taught at most students that took Calculus were also in the band.
    • ludston 4y ago
      The really interesting question this brings up is, is there some causal relationship between students that study music and their likelihood of taking calculus? (e.g. Assuming we call all kids that take calculus "smart kids", are smart kids more likely to also study music, or does studying music make kids into smart kids) Or, is there just some selection bias where kids from a certain background are more likely to do both?
• karaterobot 4y ago
  > There are better ways to exercise your brain that will be many more times better than Calculus... fixing a car, understanding music and playing music, art appreciation, literature and understanding the human condition... daily exercise These are all things we used to teach in high school. Did we stop? It's been a few decades for me.
  • hdctambien 4y ago
    For the last couple decades, at least, you can take all of those classes as 4 year programs at my local, public high school. In fact, you can take most of them at the same time. As it turns out, students have more than 1 class on their schedules every year! We also have mechanical engineering, culinary, law enforcement & forensic science, marketing & business, computer science, game design, education, ROTC, printshop, photography, we even have a class that teaches students how to do their taxes! (it is literally 2 lessons) and this is in Texas where people assume the worst about our schools. Many people that comment here about education don't really know what happens in a school outside of their memories of going to school as a teenager. When I became a teacher and looked back at the school I went to, I was surprised at all the opportunities that were available that I either wasn't interested in, or didn't notice existed. Most things that people think "schools should teach" are actually being taught at schools.
  • Izkata 4y ago
    Mid-2000s: > fixing a car As far as I remember, working with machinery was restricted to the academy students at my highschool, which was something like 5% of the students. It only accepts freshmen, so if you didn't get in then you can't get in later. > understanding music and playing music, art appreciation We did have band, but I don't recall anything for the rest. > literature We had English classes where we did some lightweight books - I remember Animal Farm, The Great Gatsby, and The Scarlett Letter. Thicker books like Nineteen Eighty-Four and Brave New World were in the academy version of the English classes, but not ours. > understanding the human condition We did have one or two psychology classes. > daily exercise Gym was required for a year or two, after that almost all of us opted out. It was pretty terrible, and I wouldn't be surprised if it put most of us off exercise. I know I cared less afterwards (used to have fun biking and rollerblading, gym class took the fun out of it).
• xwolfi 4y ago
  And Algebra ? Cause there are few subjects that help you quite so much to think in the abstract and when it becomes automatic, you see yourself toying with concept from any level without needing to define everything below to anchor them in reality. My non-maths wife is so much more attached to these anchors it s hard for her sometimes to accept to discuss ideas from a high level by accepting for now not to explain how their parts came to be. Calculus I imagine is useful to calculate an interest rate at the bank to avoid maybe stupid surprises ? But I wonder if advanced calculus is necessary indeed.
• narag 4y ago
  There are better ways to exercise your brain that will be many more times better than Calculus. Maybe. And there are probably better ways to exercise your brain than memorizing cities, mountains, seas and rivers in countries you're never going to visit. But that doesn't make any of that useless. All that knowledge, calculus included, makes you know how the worls is structured, wether you're going to pull the levers yourself or not. You can't decide you're not interested in something if you have no idea how that something looks, even superficially.
• eternityforest 4y ago
  I think the point of math is to learn other more advanced math. Which is so useful to the few that will have jobs that need it, that they want to push it as hard as possible just to give them every possible advantage, because it's hard. They want as many people in advanced STEM as possible, because that's basically like being a billionaire in terms of the level of wealth and comfort, and things like chemistry might solve some really big problems. Also, a really large number of people still think math is something you actually use daily. These are people that still balance checkbooks and make budgets with paper and do woodworking with fractions instead of CAD apps. Math really is useful to anyone who isn't comfortable letting a computer do half their thinking. I might never even own a checkbook in my life, and I've never even used basic algebra IRL. But I can see why someone who never got comfortable with a "There's an app for that" mindset would think long division was a life skill. I highly doubt I have the talent needed to ever learn a useful amount of math (My idea of useful is enough to get an EE or CS degree), so I don't make it a super high priority to get better at it.
• Wowfunhappy 4y ago
  We should be teaching subjects which will (A) ultimately be useful to as many people as possible and (B) exercise the brain as much as possible. I'm inclined to think statistics and programming would fulfill these requirements better than calculus. ---------- > Here are a few, understanding and fixing a car, understanding music and playing music, art appreciation, literature and understanding the human condition and on and on. High schoolers already spend a lot of time analyzing literature. I do think they should spend more time with other forms of art as well—why teach only literature criticism, when literature is just one of many art forms? However, this work exercises your brain in a distinctly different way than mathematics, and I do think students should learn both.
  • Jensson 4y ago
    Have you people actually taken a basic statistics course that doesn't require calculus? They are all about memorizing formulas that you plug numbers in to calculate different statistical measures, they don't teach you to understand anything at all. We teach students calculus at that age since teaching them statistics is basically a dead end, we teach statistics to those poor students who will need to calculate statistical measures without understanding them but we should not force every kid to suffer through that boring thing. Calculus is way more interesting, since kids can easily understand it and you can derive all results on your own, statistics is just plug and chug, much worse than calculus ever could be since students aren't ready for it yet.
    • Wowfunhappy 4y ago
      > Have you people actually taken a basic statistics course that doesn't require calculus? They are all about memorizing formulas that you plug numbers in to calculate different statistical measures, they don't teach you to understand anything at all. Disclaimer I should have included: I personally took statistics in high school instead of calculus. I can't say what my experience would have been like if I'd known calculus, but loved learning statistics. I don't remember exactly what we did, but I recall it being quite conceptual. Certainly not just a ton of formulas.
    • analog31 4y ago
• Robotbeat 4y ago
  Mathematics is learned in a spiral process. It takes probably 3 classes or years before you become competent in it. You are introduced to calculus in high school, but only at the very end. Really, most of the work of calculus is becoming competent at algebra and pre-calculus, which teach you incredibly important concepts like exponential growth, etc (which fundamentally depend on calculus for their development and motivation, but not needed for basic calculations). Don't think algebra or exponential growth matter? I think these concepts are critical to basic citizenship. Real understanding of exponential growth helps you understand viscerally why, for instance, you should nip a viral outbreak in the bud, and reducing the spreadrate even slightly (R0) can make a huge impact later on, even if spread isn't totally stopped. This is all just gibberish if not learned in high school. Algebra is used in programming and is basically an introduction to many different programming concepts. Symbolic manipulation of variables, etc, needs to be understood at a basic level to competently program anything, or even use Excel spreadsheets effectively (which almost everyone who ever works a desk job--which is most people--will eventually come in contact with), which is a type of programming. If you learned 3 semesters of calculus, then you must have learned this in college. If your job is programming-related, then it's pretty relevant for you to understand concepts in calculus like limits, rates of change, total area under a curve, plus having a confident grasp of algebra (which is much of the actual work of calculus). Blue collar jobs like machinists, homebuilder/carpentry, plumbing, electrician, etc have tons of need for other areas of math that utilize concepts in algebra, pre-calculus, and geometry. As things become more automated, mechatronics and g-code programming are starting to become more relevant in a lot of trades that were previously highly manual. Tuning a PID loop is a fairly normal task for some of these. And you definitely benefit from pre-calc and calculus for things like this, being literally what the I and D stand for.
  • petesergeant 4y ago
    Like many, many people who understand exponential growth, I never took a calculus class.
    • Robotbeat 4y ago
      That's certainly possible, even without self-learning. The topic is explained in precalc, typically. But it's important enough that I think going further is helpful.
• JadeNB 4y ago
  > P.S. note: Many people disagree. Good, you should not take it as absolute truth. I guess my real point is that you should question whether you really need to take Calculus. Don't just take it blindly because you are told you should. You have other options. I agree, this should be questioned! Calculus is probably not the right choice for everyone, and I think most competent math departments are looking at how to make their curriculum more appropriate and relevant for today's world—certainly mine is. However, I think it is too easy to confuse "I don't see the relevance of this" with "this isn't relevant for me"; most students are not really in a position properly to evaluate whether a course of study is useful for them. Students shouldn't take whatever the university, or their professor, or anyone tells them as gospel—but neither should they think that their individual judgement will necessarily guide them towards the path that will best prepare them for whatever future it is that interests them, or the future that they don't yet know interests them. Perhaps most importantly, it is easy for a student to tell when they aren't using knowledge they have, but it is not so easy for a student to tell when they need knowledge they don't have! I'll also dare to venture the suggestion that a lot of people could benefit from a much less utilitarian approach to education. College for everyone is a wonderful opportunity, but I wish it were that, an opportunity, not a requirement—and, given that it is a de facto requirement, I understand students' frustration with it. But, while a student is here, I wish they would make the most of the experience, and treat as a chance to learn things just because learning is an enriching human experience, without subjecting every bit of knowledge to pure humanitarian experience. I don't program, but I am glad for the knowledge about programming I have; I don't use history directly in any professional historical sense, but I am glad that I know the history I do. I am a professional mathematician and use my knowledge as such—but I'd be glad I learned it even if it weren't my career.
  • JadeNB 4y ago
    Crucial and inexplicable error, now outside the edit window: "pure humanitarian experience" was supposed to be "pure utilitarian computation".
• cryptonector 4y ago
  > Total BS... Suppose for a minute that you had to do mental weight lifting, but you could choose which discipline to do it in. If you chose math as the discipline, then calculus would be perfectly fine as the mental weight lifting in high school. Are there other disciplines that you could choose? Certainly. Does you school give you such choices? If not, then that might be where the BS is. IDK about you, but there's a ton of stuff that I know only because I find it fun to know and not at all because it's useful to me in any other way. This must be true for many man many people.
• raydiatian 4y ago
  The benefit of calculus isn’t about the ability to write things down on paper in a fancy code and playing a game to solve it. The benefit is that it paints your waking reality in a color you weren’t aware you could observe previously: curves, and expectation, and prediction. Based on your take here, I’m gonna guess that you’re in but haven’t yet graduated college. I’m not sure how you’re going to suggest “learning programming” rather than learning calculus, as calculus is a foundational element of all modern languages. For loops are a further generalization of Leibniz notation, in a rough but very real fashion. You can only understand a car so deeply without brushing up against physics, the study of which is classically explained by (you guessed it). Sure, you can argue that “you don’t need physics to understand a car well enough to fix it.” Okay, congrats on mastering the adult version of putting the right shaped block into the right shaped hole. Understanding music really doesn’t require a ton of calculus, unless you want to go into building instruments and music software. If you want to do sound design, you’re also fucked, because understanding Fourier transforms is an important aspect of being a good design engineer. To me, it sounds like you failed calculus twice and now are trying to prevent people from sharing in your grief. That’s less admirable than you think—-it’s not that calculus is fundamentally hard without reward or merit, it’s likely that somebody failed to indicate to you the importance of calculus.
  • pdonis 4y ago
    You are giving plenty of ways in which calculus can be useful. But the GP wasn't arguing against claims that calculus is useful. The GP was arguing against a claim that calculus was useless, but you should study it anyway as "weightlifting for your brain". Your arguments about how calculus is useful would be better directed at the teacher the GP was arguing against.
    • deleted 4y ago
      [deleted]
    • raydiatian 4y ago
      > But the GP wasn't arguing against claims that calculus is useful. So no clue who GP is. Grandparent is my best guess. And with respect to you, that would be the guy I was responding to, but that couldn’t possibly be correct because he said > rather than sitting on your butt learning a useless subject From context, inferred to be calculus, esp because > took me 3 semesters of Calculus to figure out that it was useless to me and 90+% of the people that take any of it Soooo… who is GP
• p1necone 4y ago
  If we don't teach calculus to kids in highschool then every (non software) engineering degree will have to be a year longer.
• deleted 4y ago
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• pizza 4y ago
  I agree that pedagogy should be flexible. Not be static/constant, but, rather, a relationship that reacts to inputs from students; changing dynamically to suit the student's needs. It'd be a great thing if people could build up a strong intuition about how their problems react to change over time, in order to maximize the value they get over time.. if only they had been taught a non-useless model for predicting how things change.. ;) More seriously: in an abstract sense, "when are we going to use this?" is a totally valid question - but most solutions are probably about changing the "this" in question, rather than getting the students to practice the act of recognizing in real life what they're being fed at school. Maybe recognizing applicability itself is a higher priority skill than whichever skill is being taught.
• raydiatian 4y ago
  > PS Note Many people disagree. Good, you should not take it as absolute truth. I don’t think anybody is concerned that what you’ve claimed could be misconstrued anywhere north of mostly false. The nonsense you’re boldly peddling here is absolutely false. Seriously, leave flat earth community if you want to be taken even remotely seriously in the working world somebody bud.
• Balgair 4y ago
  It depends. David Epstein's Range is a good way to look at outcome based learning. There are 'Kind Learning Environments'. Things like chess, golf, concert piano, etc. The goal is easy to define, you can rank yourself against others, and the feedback on effort is quick. In such scenarios, so argues Epstein, the 10,000 hour grind is a best way to achieve success. There are 'Unkind Leaning Environments'. Things like tennis, jazz, business, etc. The goal is difficult to define, you cannot easily rank yourself against others, and the feedback on effort is slow or nonexistent. In these environments, Epstein says that a 'browsing' approach is best. One where you learn as much as you can about as many disparate things as possible and to still deep degrees all the same. You want as many pegs to hang a hat on as you can get, curiosity is not wasted time. I would say that, in terms of education for the masses, learning Calculus is a great way to develop the 'browser' side of things. General/public education is inherently to be made for the 'unkind learning environment'. Specializing and 10,000 hour grind-fests obviously aren't suitable. Calc is especially useful as it gives the ideas of derivatives, rates, limits, and integrals for your mental toolset. These are powerfully broad ideas ripe for application. Additionally, as it is traditionally taught, it helps expand the mind to true higher math and lets pupils see how deep that logic/math rabbit hole can go. Lastly, the inescapable history behind it's development is another great dive and gives another avenue for the 'browser' mentality. I can scarce think of a better subject outside of religious texts that provides such great tutelage for the 'unkind' learning environment that is life.
  • aramadia 4y ago
    Tennis has got to be closer to a kind enviornment, a well defined set of strokes, immediate outcomes, a ranking system, and full information.
• civilized 4y ago
  I'm sorry, but "art appreciation is way better brain exercise than calculus" is just an extremely silly assertion. Not because the opposite is what's true, but because it's bizarre to compare them in the first place.
• PikachuEXE 4y ago
  While I can't comment on the example(s) you provided, I agree with much time is "wasted" on unnecessary stuff. Not even basic logic is taught! Nor any daily life useful skills like cooking...
• Loocid 4y ago
  >I guess my real point is that you should question whether you really need to take Calculus. There are very few classes in school that any student "really needs" yet for some reason Calculus, or math in general is the one that takes the brunt of this argument. Why? Whens the last time you needed to know that Hydrogen has 1 proton and 1 electron for instance?
  • WheelsAtLarge 4y ago
    Here's an HW case about why knowing about Hydrogen will help in life. Question: Why does Space X use kerosene and liquid oxygen rather than liquid hydrogen and liquid oxygen a better power to weight fuel. Simply because of the size of the molecule. The Hydrogen molecule is such a small molecule that it's difficult an expensive to use vs kerosene. It's very easy for it to leak. As we have seen in the Artemis 1 rocket that uses hydrogen. There's my use case. I've used it at least once.
    • Loocid 4y ago
      How is having that knowledge any different to if you knew the mathematics involved in the building and launching of the rocket? Knowing that didn't help you at all. If you didn't know about Hydrogen that rocket still would have launched. It's purely for your own interest. Unless you're a SpaceX engineer of course but then the other 99.9% of the people on the planet don't "need" to know about the size of Hydrogen and we are back to the same argument.
    • presentation 4y ago
      Ah yes, I too design rockets on a daily basis.
    • kristiandupont 4y ago
      Just above, you wrote: >Ok, given the number of people that take Calculus, how many will ever read an ML paper? For that matter, how many even know or care what ML is? ..and now you, apparently without joking, assert that the physics info is different because it's necessary in rocket science, the one thing that is colloquially used to describe knowledge that normal people will never have to worry about?
• pen2l 4y ago
  Knuth is the poster child for the school of thought that just doing a _lot_ of math problems, especially calculus, is great mental weightlifting and we should make our young students do a lot of math homework. See this interview: https://ia600803.us.archive.org/29/items/conversation-with-knuth/Image072217150714.pdf https://ia600803.us.archive.org/29/items/conversation-with-k... I spent hours and hours studying the mathematics book we used -- Calculus and Analytic geometry by Thomas. We were assigned only the even-numbered problems, but I did every single one together with the extras in the back of the book because I felt so scared. I thought I should do all of them. I found at first that it was very slow going, and I worked late at night to do it. I think the only reason I did this was because I was worried about passing. But then I found out that after a few months I could do all of the problems in the same amount of time that it took the other kids to do just the odd-numbered ones. I had learned enough about problem solving by that time that I could gain speed, so it turned out to be very lucky that I crashed into it real hard at the beginning. It's important to get down a lot of hours solving problems for the express purpose of improving your mental faculties, improving working memory. So for the finite amount of time you have, what problems do you choose to work on? I think maths and calculus is a great bet. Though I'd rather suggest a young person do Spivak's Calculus as opposed to Thomas' Calculus as Knuth used. You'll notice that most of geniuses we know were spending long periods of time solving problems. I'm kind of scared that we will have less people like Knuth in our people, people who can just go and deepthink and solve _difficult_ problems. If we keep up with this meme of 'no homework' we are in danger.
  • tyre 4y ago
    The takeaway here is that calculus was good _for Donald Knuth_. But not every kid wants to go into math or engineering or STEM. And even the ones who do, is calculus the best use of that time?
    • hypertele-Xii 4y ago
      While it's true that crafts, arts, cleaning, farming, and other jobs exist, it's also worth considering that science, technology, engineering, and mathemathics are world-revolutionizing disciplines. Not everyone needs to change the world, but there's good argument for throwing all kids at STEM to see which ones stick, because any one of them could end up saving billions of lives.
• unity1001 4y ago
  Our education system wasn't able to get rid of its scholastic roots. Even scientific establishment itself. The patterns that were developed at the time when early scientific research and teaching were evolving in medieval monasteries still keep appearing in research and education.
  • hypertele-Xii 4y ago
    Something that managed to evolve in a medieval monastery, during an era of warring kingdoms, must've been significant, and we dismiss our roots at our own peril. Of course, we should actively seek to simplify, clarify, and forget the unnecessary. But Chesterton's fence, etc.
    • unity1001 4y ago
      > Something that managed to evolve in a medieval monastery, during an era of warring kingdoms, must've been significant, and we dismiss our roots at our own peril. Nope, in such 'warring kingdoms' environments science and education were not able to prosper. The middle to latter parts of the middle ages in Europe were rather stable times to allow the development of both of those. Even with that, its still a medieval institution. It must progress and adapt to the 21st century.
• xapata 4y ago
  Yeesh. The concept of marginal change (from Calculus) is valuable in all sorts of situations. It's a basic concept for business and social policy.
• matheusmoreira 4y ago
  I don't know. I never learned calculus but I'm aware of the concepts and what they mean. I've recognized integration problems in my life... Seems like a very useful skill to me. For example, in computer programming there's game development: the physics simulation is essentially integration.
• Shorel 4y ago
  It depends a lot more on how calculus is taught than it depends on calculus itself. If your calculus education is: learn these formulas by rote memory and apply them to this set of problems. Yes, calculus, and in fact any and all the mathematics, will be mostly useless for you. You don't need the formulas. But, if your calculus education is: OK, there is this limit. No, I will not tell you the proof. You will find a proof of it by yourself, and you will show it to the class. Or: this is the volume. Imagine a way to calculate the volume! How would you do it? Or thousands more ways to stress your creativity to the max. Writing proofs is the most intense workout of creativity I have experienced. And it feels like writing code, in a way. The difference is in a mathematical proof you are also the compiler, the syntax checker, the interpreter, and the person who writes the program. If that's the way you learn calculus, not as a formula applier, but as a solution finder, then yes, calculus will make you a much better software developer. I say this based on personal experience, I consider my proper mathematical education, having to think about proofs in linear algebra, to have a very positive impact in my capacity to write software later. And I had been a software developer for ten years before the linear algebra and calculus courses. So it's not related to acquiring experience as developer later.
• f1shy 4y ago
  It is a metaphor, and as such, has it limits. Of course there are better ways to exercise your brain than calculus. That is just a way. Is the best? I don't know honestly. I personally found algebra much more interesting as a brain opener. Basic ideas of calculus come up everyday in life: interest rates, credits, statistics. If you want to understand some physics, it is very useful. Can you understand physics without derivatives? Yes, but not as good as with them. Like everything is a compromise. One possibility would be that each person has a couple of teachers that go with him/her in a way or learning specifically tailored. The other extreme is to teach absolutely the same thing from 1st grade until graduate to everybody... the compromise is to separate it in primary/secondary/tertiary education and let choose paths. Everybody will have to learn things that will never be used "in life". We have to get over it.
• deleted 4y ago
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• eprparadox 4y ago
  " There are better ways to exercise your brain that will be many more times better than Calculus. " the ways that you list are great brain exercises but there's no good reason or research that suggests they are 'many more times better than Calculus'. and continuing to call it a 'useless subject' is also totally unjustified. if i just that art appreciation is a useless subject because 99% of people are not going to get a job writing movie reviews for a major publication or curating exhibits for museums is that sufficient justification to say 'art appreciation is useless. source: me'?
  • ludston 4y ago
    Nah you'll find that there actually is research done into which activities stimulate the brain the most. Some of the only things that stimulate all four hemispheres of the brain at the same time include sex or sight-reading and singing at the same time.
    • simonh 4y ago
      I'm not convinced that 'stimulating all four hemispheres of the brain' necessarily has anything whatever to do with improving learning ability and developing mental skills or critical thinking.
• asdff 4y ago
  People who claim its weightlifting for the brain probably forget that the stress you are putting yourself through cramming for the hellish calc final is probably a net harm
• robertlagrant 4y ago
  One thing that's eye-opening is how useful set theory could be to general reasoning. The number of basic category errors I see, even sometime on HN comments, but mostly in public discourse and political rhetoric and thinking, is astounding.
• BrandoElFollito 4y ago
  I think you are generally right. I used to teach physics at the university (and do research). The actual, practical use of anything you learn at school is close to zero. There are a few life-sustaining topics that should be addressed (of my head: what is electrical power and current (to be safe and understand your bills), percentages, some biology (reproduction, and generally - human body), geography (rather detailed for your own country, tahns more and more general), etc.) The problem is that many of these topics require at least a basic introduction that is not directly useful, but necessary to understand the rest. You also need to account for the maturity of the student, and would like to start early. All this means that by 15 you should have everything you need to be ready for everyday life. I guess 16 is an average age until which education is compulsory by law. Unfortunately the education provided by then is not they useful, per your (again - reasonable) criteria. The main obstacle I see is that except for a few brilliant students, you have a lot who start late. They are medium to say the least until 16 and then suddenly take off. A 14 yo doe snot have an idea about what to do later (and despite this we force them to make choices at 14 in France). So overall al lot of things could be improved, but that would mean fundamentally altering the way school works (everyone is equal and gets the same education)
• sainib 4y ago
  1 - World needs world class mathematicians to continue to evolve science for the betterment of humanity. 2 - Those world class mathematicians need to get started sooner in life to learn most of whats out there so they can work on extending the reach of collective human knowledge on Math. So, these mathematicians better get to calculus before they graduate high school. 3 - I wish there were two courses like "math for bright kids" and "math for not-so-bright kids". Since you feel you didnt need to learn calculus and, assuming you felt the same way when you were in school, you would be taking "math for not-so-bright kids" .. AND THAT would not have been acceptable to your parents back then. 4 - I wish teacher had magical powers to know who would go on to be a world class mathematicians but i dont think we are there yet but I feel if there are enough mathematicians in the world, we may get there some day. Case in point - Einstein did bad in school and showed his brilliance relatively late in life. In any case - lets stop the bickering because you had to study little bit more than what you are comfortable with, for the sake of overall evolution. Theres more good than bad here.
• solarmist 4y ago
  The mechanisms of calculus probably don't matter, but calculus is the study of change. In particular, how things change over time in non-linear ways. Calculus is the abstraction of multiplication in the same way that multiplication is the abstraction of addition. THIS is the real reason why calculus is important. Knowing how to study, describe, and understand changes that are not constant. If that isn't important in real life, then neither is counting or multiplication. Unfortunately, calculus is so deeply embedded in the vocabulary and forms of mathematics that even people with a "full education in calculus" often can't describe that. So they resort to stupid metaphors. They only unconsciously understand its value and fail to describe it.
• michaelcampbell 4y ago
  > There are better ways to exercise your brain They didn't assert it was the best way, but that it was _A_ way.