[HN Gopher] "When are we going to use this in our everyday life?"
___________________________________________________________________
"When are we going to use this in our everyday life?"
Author : susam
Score : 162 points
Date : 2022-10-04 19:31 UTC (3 hours ago)
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| _dain_ wrote:
| I suspect this exchange never happened, but at any rate:
|
| When the teacher justifies the subject not on its own merits, but
| for its alleged nootropic effects, that's how you know it's
| either a waste of time or the teacher himself doesn't know what
| it's for. Same for "it builds critical thinking" -- another 100%
| reliable hallmark for a bunch of BS meant to waste young people's
| lives on classroom exercises and homework. 21st century version
| of digging holes in the desert to build character.
|
| Calculus is useful for hundreds of things; if the teacher has to
| resort to this dodge he ought to be ashamed of himself. What a
| waste of an opportunity to tell them about its applications in
| civil engineering, in control theory, in statistics, in orbital
| mechanics, in 3D graphics, etc etc. If I had heard what that
| teacher said it would have killed my interest stone dead. Just
| another hoop I have to jump through, for my own good.
|
| And this isn't to say that everything must be justified on
| utilitarian grounds -- Shakespeare is not "useful" for anything
| but we have it in schools because it's inherently worthwhile,
| it's part of what makes life worth living.
| posharma wrote:
| Tumblr is still around?
| wizofaus wrote:
| It's hard not to wonder then whether it would be beneficial to
| keep solving differential equations on a weekly basis to keep our
| brains in shape even long after we've finished our formal
| education...
| NotYourLawyer wrote:
| Nobody solves differential equations by hand anymore. Almost
| without exception, the interesting ones have no closed-form
| solution.
| aaaaaaaaaaab wrote:
| But when there's a closed-form solution it's like God winking
| at you.
| 6gvONxR4sf7o wrote:
| Sure, but people manipulate them by hand plenty. The task is
| making them more amenable to solution by either A) converting
| it into one of the few closed form solutions, or B)
| converting it into a form more amenable to numerical
| solution.
| JackFr wrote:
| I had the experience of coming upon a differential equation,
| in the course of some research, which I could not solve
| explicitly. Mathematica choked on it and my boss and his
| office neighbor (both math PhD's) were unable to solve it
| explicitly. When I was about to give up set off to do it
| numerically my boss's neighbor suggested they call another
| fellow they both new. Two days later he delivered two neatly
| written sheets of paper with an explicit solution which
| featured a really novel (to all of us) substitution which
| facilitated the solution.
|
| Now in the grand scheme of things the differential equation
| we were looking at might not be 'interesting' in the sense of
| being representative of a class of problems in a rich branch
| of math, but it was sure interesting to us, as it modelled
| the behavior of the system we were studying. We all were
| pretty sure there wasn't a closed form solution (but
| certainly weren't going to spend time proving that) and were
| pleasantly surprised. The solver did not get a co-author
| credit in the eventual paper, but he did get a shout out in a
| footnote.
| seba_dos1 wrote:
| It absolutely would and I really wish I had done that. Starting
| again after many years is incredibly hard, I feel like I would
| need to start much lower than differential equations to get
| back in shape :)
| munificent wrote:
| I have had to answer this question to my kids (one of whom abhors
| math). The explanation I gave is this:
|
| For many subjects, most kids will end up never using them. But,
| we have no way to _predict_ which subjects will be useful for
| which kids. Without the ability to do that, our priority is
| maximize each child 's opportunity. We never want a kid to be in
| the situation where they _would_ have been interested in a
| subject and a career path but never ended up discovering that and
| using it because we didn 't expose it to them.
|
| So we teach some of every subject to every kid. That way no
| matter which path they end up following, they are as prepared for
| it as we can make them.
|
| (Also, yes, I agree that math is good general training for
| cognitive rigor. Also, numeric literacy is vital for all adults
| since we live in an ecomonic world and participate in a democracy
| where statistics are necessary to understand policies.)
| vlunkr wrote:
| I don't really agree with this. It seems to be based on the
| assumption that the entire purpose of school is to prepare you
| for a job. Obviously that's important, but education also
| simply enriches your life. Some of the electives I took in high
| school and college have had a great impact on the way view
| things, or the way I live my life, despite having nothing to do
| with my career.
|
| Also, lots of math is optional (depending on your school and
| career.) You may not use calc or trig regularly, but most
| people use some algebra and geometry.
| ethanbond wrote:
| Problem with this is that it's not very comforting to someone
| who feels extremely frustrated (not enriched at all) by the
| experience they're going through. That's true even if you
| know with certainty they'll feel enriched by it later on.
| agalunar wrote:
| > Obviously that's important, but education also simply
| enriches your life.
|
| You should read the Aims of Education speech given by Abbott;
| you might really enjoy it.
|
| https://college.uchicago.edu/student-life/aims-education-
| add...
| twelvechairs wrote:
| What we definitely should teach kids that isnt taught is
| discounted cash flow analysis as almost everyone has a loan at
| some point in life and few know how to calculate them
| habnds wrote:
| I definitely learned a present value calculation in high
| school at some point, it's not an actual DCF but does teach
| that fundamental principal about the time value of money.
| jakub_g wrote:
| Also, understanding basics of statistics.
| nicolashahn wrote:
| I agree with this. A less tactful way of explaining it:
|
| "When am I ever going to use calculus in my life??"
|
| You? Probably never. But we're teaching everyone on the off
| chance that one of you goes on to do something useful with it.
| Enabling that one person to find a way to make rockets more
| efficient or something is well worth the tradeoff of wasting
| the rest of the class's time, from a societal point of view.
| tshaddox wrote:
| Who will grow up to routinely do calculus mentally or on
| pencil and paper? I guess some people will be calculus
| instructors. Are there any other examples?
| michaelt wrote:
| Anyone who does a STEM degree?
|
| I mean, if you're an engineer and you don't know the
| relationship between position, velocity and acceleration -
| you're going to have a bad time.
| scarface74 wrote:
| Consider the number of people that go through a typical
| Calculus class and the debt people get into go to college.
| Are you sure that ROI makes sense?
|
| If you want to force everyone to learn Calculus for "the good
| of society", then don't force the onerous debt of student
| loans on private individuals.
| pydry wrote:
| Something like that did happen in one of my classes and the
| kids who didnt want to learn it said "why dont you just teach
| [ smart kid ] then? If anybody is gonna design rockets itll
| be him.
| bee_rider wrote:
| The problem with this way is that calculus is needed to get
| through, like, a basic engineering degree, I assume
| economics if you are doing it with any rigor. I suspect
| these aren't like careers for the top 1% braniac kids, they
| are normal B+ student fields (I mean I know everyone gets
| straight A's in highschool now, but you know what I mean).
| jjoonathan wrote:
| Do _you_ want to tell a parent that their kid has already
| decided not to design rockets?
| ackfoobar wrote:
| https://www.smbc-comics.com/comic/why-i-couldn39t-be-a-
| math-...
| edflsafoiewq wrote:
| Alternatively https://www.smbc-comics.com/comic/never
| tialaramex wrote:
| Funny as that comic is, it's very unclear at a young age,
| and even when they're a bit older it's far from obvious.
| Even at first degree stage, some of the apparently best
| qualified teenagers who turned up for their first classes
| this week are going to _flunk_ out anyway, and some of the
| kids who struggled and seemed like they 'd be lucky to get
| their degree will be potential Fields Medal winners in
| 10-15 years. Their prior record, even now they're adults,
| is at best _somewhat_ predictive and nowhere close to
| definitive.
| misterprime wrote:
| Perhaps also/instead:
|
| These lessons help bring you up to speed with foundational
| concepts and ways of thinking that took humanity a very long
| time to discover and develop. Learning these things while you
| are young will, at a minimum, help you keep up with others and
| avoid being scammed, or at best, help you quickly reach the
| current limit of our understanding and possibly expand our
| capabilities.
|
| You can also think of it like stretching and exercising your
| brain. You may not need to actually do that work, but it's
| still good for you and helps make other work easier.
| striking wrote:
| I think a lot of the time it is just too abstract to grasp. I
| think the first time in my life where I was really happy to
| have learned calculus for my own intrinsic benefit was a few
| weeks ago, when I set up Home Assistant in an effort to
| automatically minimize heat in my apartment. It wasn't enough
| to tell the shade to come down at a certain temperature,
| because the apartment would already be too hot. So instead I
| could take the _derivative_ of the temperature of my apartment,
| allowing me to get out ahead of the worst part of the blast of
| sun. After all, if the temperature is increasing very quickly,
| we should act to stop it.
|
| I've used a decent amount of calculus in my life, but that was
| the first time I had been actually happy to have learned it.
| FatCatsClub wrote:
| tomjakubowski wrote:
| If you hadn't learned calculus or what a derivative is, do
| you suppose you would have eventually figured out to measure
| the change in temperature and respond to that?
|
| I wonder how much of the value of the course is just in the
| repeated observation that the rate of change (and so on) is
| useful to measure
| Jensson wrote:
| Humans has terrible intuition for these things, it was just
| 300 years ago humanity figured these things out but once we
| did we did all these things afterwards in just 300 years.
| Learning this one thing is the key to so many things.
|
| Basic math and physics education helps build intuition for
| it, but without people are really bad.
| hutzlibu wrote:
| "Basic math and physics education helps build intuition
| for it, but without people are really bad."
|
| Erm, in some abstract ways yes - but actually people are
| very good at extrapolating current physical events. "It
| is getting hot fast? Oh not, it might even get hotter,
| lets look for shade."
|
| Or throwing a ball. You would need calculus to correctly
| calculate the flight path of the ball, yet we can do so,
| without and very fast.
|
| Where our intuition fails often, is understanding the
| reason why things happen. For this physics and math
| should be taught from very early on.
| diceduckmonk wrote:
| It seems like this is a solution that should have been baked
| into the smart device. For example, the Nest thermostats
| preempts your arrival home and commences toward the desired
| temperature.
| ryukafalz wrote:
| The problem is, the automations you might want and the
| combination of devices you might want them to act on is
| large enough that manufacturers can't possibly foresee them
| all. When you want to do something ever so slightly outside
| the stock functionality, it's helpful to have a little
| knowledge.
|
| And let's not forget, it's helpful to be able to augment
| smart devices that already exist to do things like this
| rather than throwing them out and buying a newer one that
| can do it on its own.
| aaaaaaaaaaab wrote:
| You invented a PID controller!
| https://en.m.wikipedia.org/wiki/PID_controller
| arjvik wrote:
| Technically just the D component :)
| moffkalast wrote:
| The real way to motivate someone to learn a thing is to give
| them a project or something they actually want to achieve
| instead of trying to absorb some drivel without a reason why.
| That's where self learning shines. You give a great example
| there. A notable one of mine would be learning vector math
| and quaternions through trying to make games years ago, but
| the list is endless and not limited to math or physics.
|
| Most teachers and professors just parrot their subject
| material year after year after year without EVER giving a
| reason what any of that is used for or where should we apply
| it. It's just learning for learning's sake.
|
| I suppose it's no surprise that when people are finally given
| the option to learn in a practical way at the odd subject
| that allows for some project work most students can't seem to
| think of a damn thing they want to do. It's like a systematic
| suppression of creativity to make education more like a
| factory production line.
| imbusy111 wrote:
| It's called a PID controller.
| nickff wrote:
| > _" So we teach some of every subject to every kid. That way
| no matter which path they end up following, they are as
| prepared for it as we can make them."_
|
| We tend to waste a lot of time teaching subjects which they're
| unlikely to use, and fail to teach them about the ones that
| they would really benefit from. A basic understanding of
| criminal and civil law, along with accounting and statistics
| would be extremely useful to almost everyone as individuals and
| as citizens. Music, history, and calculus are useful to some
| people, but not nearly as many.
| leogout wrote:
| I would say that these subjects are more likely to turn into
| vocations than the teaching of how law and economy works.
|
| I see it like when I learned about programming, I was
| frustrated to learn about language theory, complexity,
| graphs, etc. I wanted to learn langages, frameworks,
| specifics for being ready to work right at the end of my
| degree but it would have made me more fragile and less
| versatile to future changes. Although law and economy are
| less likely to change as fast as the latest cool tech stack
| so this example is not the best.
| scarface74 wrote:
| We are subjected to the law everyday and we all need to
| know about money to support our addictions to food and
| shelter.
| MajimasEyepatch wrote:
| I've never liked how people say that statistics is useful but
| calculus is not. I do not believe that you can actually
| understand statistics without understanding at least some
| calculus. So much of statistics is about areas under curves!
| nickff wrote:
| The problem with this is that the first classes in calculus
| are usually focused on continuous functions, which don't
| really exist in statistical datasets. The math has a lot in
| common, but most people don't really see or use that to
| their advantage, as evidenced by the literature on
| "transfer of learning".
| galdosdi wrote:
| Have you actually studied calculus based
| probability/stayistics though? Your comment seems
| characteristic of my own former thinking from when I had
| only taken an algebra based intro stats course (AP
| statistics) and hadn't yet learn it the calculus based
| way a few years later.
|
| There is a lot of cool stuff you miss out on in the basic
| stats course because of having to dumb it down to avoid
| the calculus. Some I remember off hand:
|
| - proof of the central limit theorem, which gives the
| shocking result that if you sum several uniform
| distributions you get rapidly more precise approximations
| of the normal distribution, which looks similar to
| exp(-x^2) if I recall. This central result is the
| foundation of all statistical sampling. This is why in
| real life if you see something follow a normal
| distribution you can guess it is probably caused by a
| moderate to large number of somewhat independent factors,
| and vice versa. This is genuinely useful, but if you
| don't know it you won't miss it - poisson distribution
| which relates the mean time between events to the
| probability of failures. Obviously very applicable to a
| lot of real life tbings
| notacop31337 wrote:
| I feel that music and calculus are very different to history.
| I believe that history should be a fundamental course taught
| all the way through, we can't understand where we're going if
| we don't understand where we came from.
| Bayart wrote:
| > Music, history, and calculus are useful to some people, but
| not nearly as many.
|
| I couldn't imagine not introducing my kids to History, Music,
| the Classics and so on. I value them far higher than my
| experience with Computing, Finance, Law, what have you. What
| a pointless life to only have interest into things that are
| productive.
| geraldwhen wrote:
| I would rather analyze deep finance than listen to music. I
| just don't enjoy music, at all.
|
| Spreadsheets and algorithms on the other hand I find highly
| entertaining. I love many board games for this same reason:
| it's an opportunity to build novel algorithms in strange
| domains to achieve a specific purpose.
|
| And most can see that boardgames are more similar to
| "productive things" you find disdainful than music.
| deanCommie wrote:
| The problem is kids just don't know.
|
| I spent my entire university degree convinced that I was
| going to go into the video game industry. It took only a few
| months to realize that it's not what I wanted for a career,
| and I've spent the next 20 years loving my industry but doing
| anything but gaming.
|
| I was an arrogant teenager that thought I knew what I was
| doing. I disrespected the arts, music, history, and focused
| exclusively on stuff like Math and Calculus.
|
| Now I don't feel like a well-rounded adult, and I wish I
| spent more time when I was younger on music and humanities.
| winphone1974 wrote:
| Your experience is what I think of whenever someone
| discounts a liberal arts education. It seems like the
| perfect second degree!
| tshaddox wrote:
| It seems like what you're arguing for is to identify the most
| generalized, broadly applicable subjects possible. And that
| makes sense. Learning to read and write is probably the most
| obvious example, because it's about as broadly applicable a
| skill as one can imagine.
|
| The argument doesn't seem to apply very well to calculus
| though, does it?
| bee_rider wrote:
| I think this is a much more honest answer.
|
| We don't know who is going to be an electrical engineering
| student, and of those folks even many of them might manage to
| get through the degree without needing calc (you can memorize
| lots of answers and then get a career plugging in discrete
| components I guess), but we do know _somebody_ is going to have
| to design the antennas.
| psychlops wrote:
| Now, about how you use football in everyday life.....
| AnimalMuppet wrote:
| I'm 60. I learned things in high school football - about
| physical conditioning and discipline, and being able to push
| myself - that have been valuable over the last 40 years.
| abraxas wrote:
| Maybe I'm lucky. I'm on my fifth job (out of six) where calculus
| knowledge has been incredibly useful. I'm not even into ML or
| data analysis. Just a run of the mill software
| engineer/architect.
| eterevsky wrote:
| The problem with this explanation is that it doesn't answer the
| question "why calculus in particular". Why not chess or video
| games or crossword puzzles? All of them improve your mental
| abilities.
|
| It's useful to understand calculus because it is a basis for
| science and engineering. Understanding calculus will bring you
| one step closer to understanding how things work.
| ActorNightly wrote:
| Yep. By the analogy of working out for the football game,
| people should be taught the following
|
| * computer skills * finance math * formal logic/critical
| thinking/rational philosophy/bias identification *
| electrical/plumbing/auto/construction repair skills * cooking *
| principles of fitness
| imgabe wrote:
| When are you ever going to have to explain a sonnet or tell
| someone the the date of the battle of Gettysburg or dissect a
| frog or know what a precipitate is or... basically any specific
| thing you learn in school?
|
| It's not that you have to do each thing every day, it's that they
| give you a broad understanding of the context of what humans know
| about the world and how it works so you can understand it.
| Calculus is part of that too.
|
| What would school look like if we only taught things that are
| used every day? I guess kids would learn how to drive a car and
| put on pants and sit in a chair and read emails and that's about
| it.
|
| You know how TV shows with long-running story arcs will have
| "Previously on..." before an episode to catch people up with
| what's happening? School should be a 12 year long "Previously
| on..." the whole of human history so people can go into the world
| knowing what's happening and how we got to where we are.
| DrewADesign wrote:
| I have a learning disability related to some incredibly common
| cognitive issues that impact symbol recognition. I can abstractly
| reason about the concepts vastly more easily than most and can do
| fairly complex problems in my head quite easily- speaking to a
| math PhD candidate a year or two ago, he said "you know, you
| think about math exactly like a mathmetician does. I can't
| believe you're not interested in pursuing math in school." My
| cognitive profile, however, makes doing calculations on paper
| painstakingly difficult- high school geometry (passed in summer
| school with a D) was about my limit before failure was
| guaranteed.
|
| This shut the door to every college opportunity I was aware of. I
| ended up graduating in a night school program while working full
| time. Only after two decades when SATs and high school grades
| were no longer relevant did I start a BFA program, and soon after
| I realized how abjectly the system had failed me. I always
| assumed I was a fuckup with no discipline (which is what I was
| told) and played the part accordingly. Cognitively, I tore my
| program to shreds. A solid 4.0 GPA while having the time of my
| life takes more than the responsibility gained during adulthood.
| I could have easily competed in a serious ivy league degree
| program given the opportunity.
|
| Sure, learning traditional math calculation can benefit many
| people- but not everybody is cut out for it, and that's _fine_.
| Student should certainly be encouraged to pursue it, but using it
| or any other individual skill as gatekeepers for an enormous
| number of educational paths that may perfectly suit slightly
| different cognitive profiles is fucking stupid.
| abetusk wrote:
| This is a weak argument and, taken to the extreme, could have bad
| results.
|
| We teach calculus because it's a prerequisite for many scientific
| and engineering careers. It's not a mental exercise, it has
| direct, practical use for many types of scientific and
| engineering disciplines.
|
| We can argue whether people actually use calculus in their
| everyday lives (I would argue so but it's maybe overly broad) but
| I think the best reason is because it teaches us how the world
| works and has direct, practical utility for a variety of fields.
|
| On the other end, if the best argument really was that it was
| good 'mental exercise' then why not teach sudoku in class? Or
| minesweeper? Why not have people do a crossword puzzle for their
| final exam?
|
| We want education that has enriches and enables students, not
| mental machinations for the sake of it.
| MrSqueezles wrote:
| Yeah, the idea sounds like a black-or-white fallacy. The choice
| isn't, "calculus or nothing". There may be things we could
| teach that would be equally important that people would be more
| likely to use.
| robswc wrote:
| I think the easiest answer to this is "does it hurt to learn it,
| though?"
|
| Many things you learn aren't directly applicable to everyday
| life... but learning how to think and _learn_ is priceless.
|
| I also assume there's more objective reasons... like teaching 100
| things, knowing full well most people will only remember 10...
| but that's still better than 0.
|
| Yea, there's a time cost associated with learning but its
| certainly not the worst price to pay.
| davnicwil wrote:
| A lot of the stuff you learn in school is basically just a peek
| under the hood of how something works. So in the best case you
| leave with kind of a shallow sample of quite a few really deep
| subjects.
|
| This shallow knowledge is fairly useless by itself, for sure,
| beyond the very practical basics, but it gives you a _bit_ of a
| hook into a variety of core disciplines that you can later -
| maybe much later - use to connect to other things you do go deep
| on, even and perhaps especially in completely unrelated fields.
|
| I think really this is the value of an education done right,
| almost making you aware of what you don't know and giving you
| _just_ enough context on it that it 's not a completely unknown
| unknown, or unapproachable or unknowable 'magic'.
|
| So by itself any one thing you learn might be pretty useless, all
| together as a big picture it starts to get a lot more useful. But
| to get to that big picture you just have to grind through the
| hard, small, useless seeming stuff piece by piece!
| adhesive_wombat wrote:
| I still remember the lecture when it all lined up, like the
| Omega molecule in that Star Trek episode.
|
| Everything from Newton's laws, the quantum mechanics of a
| single electron, bulk materials (Ohm's law), semiconductors
| devices, communications theory (esp. Shannon's limit, Nyquist
| etc), Norton and Thevenin models, logic gates, ALUs, frequency
| domain operations, state machines, coding theory, all of it.
|
| It was a lecture where we basically figured out the required
| ADC clock jitter upper limit to get a certain number of bits at
| a certain sample rate[1]. At some point something fundamental
| like conservation of energy was invoked and I had a holy-shit
| moment when it all made sense.
|
| However, I do question how much of the grinding away at the
| maths is necessary and how much is tradition that may have made
| sense in slide rule and table days. Perhaps a more holistic and
| intuitive method with an emphasis on "if you need to do this in
| detail, remember this is where you go". Personally, I can
| barely remember any domain equations at all, other than Ohm's
| law![2]
|
| [1] It popped out as something like femto or attosecond and the
| lecturer said something like "and consider this when buying
| expensive audio files" (this was back when they were hard to
| get).
|
| [2] as the same lecturer as above told us on the first day in
| campus: "honestly, all you need is Ohm's law, everything else
| we're going to teach you is just that in a dress, you just need
| to know how to get back to it".
| kazinator wrote:
| Misuse of _literally_ in first paragraph. Math concepts never
| exist figuratively or metaphorically in a curriculum. They are
| always there, spelled out in literal letters and everything.
|
| The goal of math is to show you how ideas can be precisely put
| into symbols, and then symbols can be shuffled around to bring
| about clear reasoning according to rules that we can objectively
| verify to be true or false.
|
| Just because you don't factor quadratic equations or divide
| polynomials in real life doesn't meant that math doesn't leave an
| imprint on your ability to reason.
|
| The use of variables comes from math. When people use sentences
| like "customer C ordered from a company P", that is familiar
| because of the math you took in school. Math warns you of edge
| cases like that C and P potentially being indistinct.
|
| What's next? Drop gym class because 99%+ people don't need to
| shoot a basketball through a hoop in their job of personal life?
| Some lunatic parents being opposed to gym is a thing.
|
| Math is needed by people who go into engineering, tech,
| scientific and business fields. Those fields have more math
| courses. When you end up working in those fields, you will not
| necessarily use _that_ math either, but the concepts relevant to
| your job couldn 't be transmitted in their most rigorous forms
| without the mathematics.
|
| Math education is like a booster rocket. You can't declare it
| having been unnecessary just because it's not there any more once
| you have reached orbit.
|
| Nine months into life, you don't need a placenta any more, so
| what was the use of clinging to that?
|
| What are toddler toys good for? The only grownups using a BusyBox
| are embedded engineers.
|
| The "you're not going to end up using it" argument is pseudo-
| intellectual and hollow, based on the idea that anything used at
| any stage of development having to be justified by its
| indefinitely continued presence and utility, rather than a needed
| temporary benefit or a boost to the next stage, or other
| scaffolding role.
| adhesive_wombat wrote:
| Kinda, yes.
|
| But also, specifically for calculus, thinking of things of the
| areas or slopes of other things, and how incremental changes
| affect them, is a very simple and powerful lens for lots of
| things.
|
| Of course, lots of teachers just hammer the fiddly memorisables
| until the wonder is dead because they're easy to test and/or they
| don't have an intuitive feel of the underlying meaning
| themselves.
|
| And, for calculus, the fiddlies have never been so needless to
| know as everything non trivial is a computer job and no one is
| limiting things carefully to closed forms. Few people need the
| chain rule specifically, they'd be much better served with
| knowing that there's a thing called the chain rule and what that
| _means_ , rather than the exact painful calculations and lists of
| forms.
| nedsma wrote:
| Bravo!
| ozim wrote:
| I don't like this answer but I kind of see how it fits this
| specific scenario - answering bunch of high-schoolers and keeping
| them somewhat motivated.
|
| For me real answer is "if you manage to learn yourself calculus -
| you will learn how to learn anything".
|
| Most of the time when I just pushed through at university I
| noticed ways I retain knowledge - how after first repeating steps
| time after time without understanding I was starting to grasp
| things because I did something 10 times and somehow things fall
| in place, how trying different approaches helps to connect the
| dots, how building mechanical movements on basics help me speed
| up understanding of more complex stuff.
|
| Just like you have to grind multiplication table to later solve
| longer equations quickly.
|
| Now lets say you don't solve equations - but whole approach
| applied to filling in taxes, like first you fill in forms as an
| example 10 times, try to calculate all on your own 10 times - and
| yes you are wrong because you don't understand all fields and why
| you have to fill them in and with which value. If you do it 10
| times on your own you submit 11th that you know is most likely
| correct.
|
| You also learn how you feel when you are wrong - so you get
| intuition that "this is stupid" starts to be "I don't understand
| it yet - have to dig through a bit more". Well high-schoolers by
| default mark things "this is stupid" if they don't understand
| something which is also meta answer for such question - but
| telling them that they don't understand is not proper answer in
| class setting :).
| yamtaddle wrote:
| > I don't like this answer but I kind of see how it fits this
| specific scenario - answering bunch of high-schoolers and
| keeping them somewhat motivated.
|
| The great thing about kids is that they'll often accept shitty
| arguments as long as they seem legit at first glance. I mean,
| so will plenty of adults, but kids especially.
|
| Which is handy since, as an adult, shitty arguments are most of
| what I've got.
| didibus wrote:
| I think it begs the question, but is Calculus the best and only
| way to exercise your brain?
|
| What if you did programming instead? Or learned anything else?
| More practical math maybe even like Linear Algebra?
|
| It reminds me of how my teachers justified why we were learning
| Latin, it'll make you better at languages, it'll be easier for
| you to learn other languages after... But all this is true if you
| learn Spanish instead, and you also happen to have learned a
| practical skill while you're at it!
| [deleted]
| saint_fiasco wrote:
| Surely there are ways to exercise one's brain that also happen to
| be useful in everyday life.
|
| It's hard to pick something that everyone would find useful and
| engaging, so I understand why schools just pick an arbitrary
| subject and stick with it.
|
| It would be nice if they were honest about it. If they were, they
| might say something like "We could train your brains with
| something fun like chess practice, or something useful like
| programming classes and statistics. But we already have calculus
| teachers around because some kids will become engineers or
| whatever, and we don't want to hire a thousand teachers for a
| thousand niche subjects so we'll use the teachers we already
| have".
| weaksauce wrote:
| > We could train your brains with something fun like chess
| practice, or something useful like programming classes and
| statistics.
|
| except probability and stats does require calculus. maybe not
| at the high school level but if you are doing it in college
| it's almost certainly going to have some needing of calculus.
| eastbound wrote:
| How can one be a citizen if they don't understand stats, and
| how to cheat them? The citizenship should only be automatic
| if you pass that class.
|
| Which is what the majority at 18 intends to do.
| [deleted]
| tonymet wrote:
| Expecting immediate or predictable payoff with any activity will
| set you up for failure or at least mediocrity in life.
| NotTheDr01ds wrote:
| Quoted from some source or are you just extremely quotable.
| Serious question - That is a great viewpoint!
| m463 wrote:
| I remember reading "Surely You're Joking, Mr. Feynman!" and
| remembered the section where he was evaluating math textbooks.
|
| He was annoyed that kids would have to learn number bases that
| were not 10:
|
| "Translating from one base to another is an utterly useless
| thing."
|
| But honestly that is something from math class that I use EVERY
| day (ok, ok, maybe not weekends)
| macawfish wrote:
| You could easily use the reasoning from calculus in your everyday
| life. For example, understanding even just the basic gist of
| stokes' theorem could be useful just as a basic cognitive tool.
| But a lot of people are never challenged to think about this.
| Like imagine not having any intuition for flux. There are people
| who have none. That's cognitive impairment if you ask me.
| harrisonjackson wrote:
| The way I explain it to my kids is all about opportunities. I am
| not going to force them into a career path that uses calculus but
| I am going to make sure they have as many opportunities as
| possible to make their own choices later in life and that means
| right now they will do the math homework.
| magila wrote:
| Football players lift weights because it is known to be one of
| the more effective ways to build muscle strength. Do we have
| evidence to support the claim that learning calculus is
| particularly effective at improving general cognitive ability?
| passion__desire wrote:
| Good question. Maybe rigorous mathematical expositions should
| be replaced with visual metaphors or explanations that will get
| the idea across without children going through tiresome process
| of manipulating symbols and calculations.
| rileyphone wrote:
| "The power to understand and predict the quantities of the
| world should not be restricted to those with a freakish knack
| for manipulating abstract symbols."
|
| http://worrydream.com/KillMath/
| mr_toad wrote:
| Most people can't do more than the simplest derivations in
| their head, the symbols are just a notational placeholder,
| and also used to communicate with others.
|
| The abstraction is the what you have to have a knack for,
| not the symbols themselves.
| thraizz wrote:
| diet_jerome wrote:
| Can I get some evidence to show that practicing calculus will
| make you more intelligent?
| umanwizard wrote:
| I've never understand why people bitch about having to study
| math, but are seemingly fine studying history, literature, etc.,
| which are just as useless in everyday life.
| almenon wrote:
| Studying history is extremely important for doing your civic
| duty as a citizen and voting.
| yamtaddle wrote:
| Various forms of entertainment are typically much improved by
| significant history and higher-level literacy training. People
| like entertainment.
|
| High school math's only helpful for entertainment if you like
| recreational math puzzles or maybe Factorio or something.
|
| You'll notice it takes far less convincing to get kids to
| understand the value of addition and arithmetic and maybe even
| very basic algebra. This is because they can immediately use it
| for play and entertainment. You're locked out of a ton of board
| games, even, if you can't do simple arithmetic with small
| numbers. "How much more money do I need to buy that video game
| I want?" is a question they're motivated to answer.
|
| When it's common for people to encounter and eagerly choose to
| engage with entertainment the enjoyment of which is greatly
| enhanced by knowing how to find a second derivative, I expect
| math will stop being _particularly_ prone to this kind of
| scrutiny.
| pshc wrote:
| My take is that studying history and literature aids in
| understanding human behavior and connecting with different
| people, valuable in many situations, but not sufficient by
| itself as having hard skills/opportunity/leverage/etc are just
| as important.
| UniverseHacker wrote:
| because those don't take as much effort as math
| divbzero wrote:
| My teacher's answer to the same question was: "You will use it on
| your test next week."
| mkl95 wrote:
| > "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 calculus is weightlifting for your brain."
|
| There are many non calculus things that are weightlifting for
| your brain, including many math fields that high schoolers don't
| even know about. Calculus is taught to teenagers for historical
| reasons, do not overthink it.
| wvenable wrote:
| A great many things that humans depend on every day require
| some understanding of calculus. If we stop teaching teenagers
| the vast amount of knowledge that humans have accumulated over
| centuries then progress will stop.
| nightski wrote:
| I've only maybe used differentiation/integration a few times in
| my professional career (use it more on personal projects
| actually). That said, having a solid intuition about
| first/second order derivatives, rates of change, is incredibly
| valuable when thinking about the world. I probably use this
| intuition quite a bit in day to day life without even realizing
| it. I do wish more probability & statistics was taught earlier
| on though.
| mkl95 wrote:
| I agree on the intuition. But once the intuition and the
| fundamentals are there, should teenagers spend months
| crunching calculus heuristics? It's still the way it's taught
| in Europe and it's incredibly inefficient.
| sarchertech wrote:
| "Young man, in mathematics you don't understand things. You
| just get used to them."
|
| --John von Neumann
|
| I'm sure there's room for improvement, but intuition and
| understanding are usually the result of repetition.
| mkl95 wrote:
| Ironically, if von Neumann was alive today he would
| probably encourage kids to use some number crunching
| software rather than "getting used to it". In that sense
| civilization may actually have regressed since the von
| Neumann / Feynman days. Ditching pen and paper for
| sophisticated computing tools gave us nuclear power and
| moon landings within 20 years.
| sarchertech wrote:
| Would he? And no one is arguing that working engineers
| should be taking derivatives by hand.
| mr_toad wrote:
| Who's going to write the software if no one knows
| calculus?
| ajuc wrote:
| Calculus (and the rest of math) is taught because development
| of human civilization depends on some people knowing it and
| developing it further. And if you don't start early it's hard
| to catch up not to mention developing it further.
|
| And it's also training your brain (but that can be done by
| other things like puzzles or games).
| mkl95 wrote:
| I'd say this used to be true, but calculus has become a
| historical artifact even at some engineering fields. We have
| become very good at building abstractions. Matrix / linear
| algebra on the other hand is something we unconsciously do
| all the time for high level tasks such as rearranging UIs.
| hjkl0 wrote:
| The question includes this part:
|
| > There are literally math concepts taught in high school and
| middle school that are only used in extremely specialized fields
| or that are even so outdated they aren't used anymore!
|
| So a more appropriate analogy would be doing the wrong exercises
| for the type for the type of sport being played. It's still
| exercise, so probably increases the chances of winning somewhat?
| roflyear wrote:
| Yeah I like this better. If 99% of the people are not going to
| use 99% of the things taught in that class, certainly there are
| subjects that are equally beneficial on a problem-solving basis
| that are also useful.
| pshc wrote:
| Calculus is a workout for the brain, but closed form symbolic
| manipulation has few use-cases in normal life.
|
| Now take stats and probability? Also a great way to expand one's
| mind, and key to decoding truths and understanding the dynamics
| of the world.
| Waterluvian wrote:
| I used to be irritated about all the crap I suffered through.
| School was very difficult for me. University was a complete
| breeze, which shocked me.
|
| But as an adult I look back and am glad that I was exposed to all
| those subjects and concepts. I forgot most of them but I remember
| the broad concepts enough that I am at least literate when smart
| people are talking. This applies to the arts more than the
| sciences for me.
|
| I'm still angry that the website kidnaps me and ruins my back
| arrow.
| sbf501 wrote:
| I was trying to fix a curtain the other day and cursed myself for
| not paying attention in 6th-grade Home Economics class. And not a
| month goes by when I don't hear my 10th grade American History
| teacher's voice in my head. Or my 8th grade teacher's grammar
| class when I can remember how to reword passive voice in a
| document, or whether I used a dangling participle in it. :)
|
| I'm pretty sure the idea that "90% of what you learn is school is
| a waste" is just some bullshit spun by adults who got poor
| grades, various BS artists hawking something (or even their own
| persona), or people that want to restructure schooling in the US
| (which might not be a bad thing... in some cases).
| tibbon wrote:
| I wish my teachers had given me better answers to this question.
| As a teen I was definitely motivated by practicalities. No one
| could answer when I was going to use matrix math in life. The
| answer, which is glaringly obvious now is in machine learning. I
| really wish I had done better in math in particular, enabling
| more advanced programming, machine learning, 3d modeling
| concepts, DSP programming, etc.
|
| But also, things don't have to be practical to be worth learning.
| I just think some of the subjects I struggled with in retrospect
| had much better examples of when they'd be used, and a huge
| opportunity was missed.
| sergiotapia wrote:
| But even this answer is bullshit. The real answer is these are
| just hoops you need to jump through to get a good job. My
| daughter will most likely grow up to become a great artist, she
| has talent for it and she loves it. I can't see her ever doing
| algebra and beyond in her career or interests. Why do we continue
| to torture kids with this one size fits all? It's terrible
| aaaaaaaaaaab wrote:
| I was always good at art. Until the age of 14 I wanted to be an
| artist. I paid no attention to math - I spent most of those
| classes practicing graffiti lettering in my notebook. It was
| around this time that we got Internet in our household, and I
| wanted to create a custom website for my artworks, because I
| found deviantART lame. So I started looking into how websites
| are made, and ended up cobbling together a basic PHP page on a
| free hosting provider. I was fascinated by web programming, so
| I decided that I would go on to get a software engineering
| degree, but I still considered graphic design and illustration
| my main forte. The first class on the first day of university
| was Introduction to Linear Algebra, which started with
| matrices, determinants and Gauss-Jordan elimination. I vividly
| remember it was that first 2-hour lecture that made me realize
| math was actually awesome! It sounds stupid, but it was at that
| lecture that I realized for the first time that _vectors are
| just lists of numbers_. Like, what the hell? It all made sense,
| and it was beautiful!
|
| As the years went by, each new topic that I've learnt seemed
| like some kind of revelation: the fundamental theorem of
| calculus, Fourier- and Laplace transforms, Cauchy-Riemann
| equations, the central limiting theorem, Markov chains,
| quaternions, Galois theory, and the list goes on. I felt like I
| was living in Plato's cave before, being oblivious to this
| infinitely complex and fascinating world.
|
| I still love making all kinds of art, but it is mathematics and
| software engineering where I feel truly at home. (the pay is
| also nice)
|
| Anyway, my point is that you shouldn't assume someone with
| artistic talents wouldn't find math enjoyable, or that they
| wouldn't be talented in it if they gave it an honest try. It
| can "click" at any point in life, not just high school - but if
| it "clicks" it's going to be an awesome journey.
| theptip wrote:
| There is a good analogy to weight training here.
|
| A sports team doesn't use bodybuilding (maximum hypertrophy)
| techniques, or powerlifting (max strength) they use functional
| power training like Olympic lifts or power cleans. If you only
| had powerlifting it would be better than nothing, but it's not as
| good as the best.
|
| Similarly, perhaps it's beneficial to view calculus as "brain
| training", but that doesn't mean it's the best modality. For
| example I think Statistics could provide the same challenge,
| while also being more applicable to the real world.
| softwarebeware wrote:
| I'm sad to see this because we literally do use calculus every
| day of our lives. We just don't often recognize it. The weather
| report is made using calculus. The calculation of the minimum
| payment on your credit card bill is made with calculus. Calculus
| is used in computer animation and video games. It's part of
| statistical analyses that affect government and financial
| institution decisions. It's used in manufacturing.
|
| It's impossible to live a day in the modern world without
| calculus.
|
| It's a huge missed opportunity to liken it to working out.
| ergocoder wrote:
| > I'm sad to see this because we literally do use calculus
| every day of our lives. We just don't often recognize it. The
| weather report is made using calculus.
|
| This is like claiming David Beckham uses advanced physics to
| kick his free kick.
|
| Calculus is important to the world, sure. But it's not
| important to regular people to spend time and money learning
| it. In some cases, these people take out student loan to learn
| calculus which doesn't help them pay back the loan.
| ActorNightly wrote:
| The issue is that calculus in itself with symbolic algebra is
| next to useless for average person. However intuitive concepts,
| like area under a curve, are not.
| adhesive_wombat wrote:
| I "solve for x" all the time, though, admittedly, outside of
| work, it rarely gets more complicated than a simple
| expression with a fraction or two.
|
| However, what is aggressively useful is dimensional analysis.
| When I'm doing a calculation and need to quickly check that
| the formulation is right, checking the units works every
| time.
| 6gvONxR4sf7o wrote:
| You're getting a lot of answers about how you don't need calc
| to use things other people have made with calc. This turns the
| answer into "so that you can avoid weird mysticism about how
| the world works."
|
| If you don't know how other people made the things you use,
| then 1) you're pigeonholed into being totally dependent on
| them, and 2) you're likely to get all sorts of weird beliefs
| about how the stuff you depend on works (like crystal
| healing/homeopathy/etc in the bio realm).
| softwarebeware wrote:
| Totally! Reminds me of Foundation by Isaac Asimov where
| scientists turn into the equivalent of priests in some
| cultures.
| kowbell wrote:
| The "when are we going to use this" question is about when "we"
| ourselves will directly use it - not when we will use something
| that uses it.
|
| I don't have to use any calculus to get a weather report, etc.,
| because other people do that for me and give me their results -
| it's part of their job.
|
| Calculus is indispensable and is used in our everyday life -
| but most of us won't use it ourselves, or need to know the
| specifics, or really even know the broader parts of it.
| MajimasEyepatch wrote:
| You probably don't need to know how to compute a derivative,
| but there are tons of related concepts that are helpful for
| reasoning about systems in the world. You can always Google
| the chain rule, but having a general sense of the trend is
| often all you need.
|
| For example, you don't have to remember how to derive it, but
| knowing that y'' = y is a positive feedback loop (exponential
| growth) but y'' = -y is a negative feedback loop
| (oscillating) is really useful in all sorts of common sense
| scenarios.
|
| Learning is about concepts more than facts or algorithms.
| thfuran wrote:
| >knowing that y'' = y is a positive feedback loop
| (exponential growth) but y'' = -y is a negative feedback
| loop (oscillating) is really useful in all sorts of common
| sense scenarios.
|
| I'm not sure what sorts of situations you keep finding
| yourself in, but I think they're pretty atypical.
| lamontcg wrote:
| positive and negative feedbacks happen in climate systems
| and economic systems.
|
| if you want to have a chance of understand the economic
| news it is a good idea to have familiarity with them.
| [deleted]
| treis wrote:
| The problem with this is that people don't really retain
| information like that. College is 15 years in the past for me
| and I'd bet that if you handed me every exam I took in college
| I'd flunk everyone of them. And probably quite badly too. I'd
| wager most people are the same. So how can it be so important
| if we all remember so little.
| ALittleLight wrote:
| This is like saying we use quantum physics every day of our
| lives because _physics_. It 's true, I guess, but you don't
| have to know anything about quantum physics and the vast
| majority of people don't need to know anything about calculus.
|
| It's also clearly not the reason we are educating children in
| calculus. We can know this because we don't teach children to
| do weather calculations, we don't test them on statistical
| analysis, and so on.
|
| The real reason public schools teach calculus is that they
| started doing it at some point for some reason and then never
| quit because they are bureaucracies resistant to change. All
| the people involved have a kind of status quo bias preventing
| them from saying "yeah, I guess that was useless, let's teach
| something else."
|
| If I'm wrong, we could imagine a test. Take a comprehensive
| calculus exam from senior year of highschool or freshman year
| of college. What grade do you think the average adult would get
| on this test? How about top ten percentile adults for
| intelligence, wealth, or whatever? If, as I do, you think the
| average score would be F, can you explain why it's important to
| teach the general population of kids something that the general
| population of adults demonstrably do not know?
| [deleted]
| nicolashahn wrote:
| You can use all of these things without you personally knowing
| calculus. The point of the question is that it's posed by the
| people who aren't going to go on to create weather reports,
| credit card payment systems, video games, etc.
| yamtaddle wrote:
| Maybe we can try, "you have to learn calculus so you can land
| a job that lets you pay for things & services that handle
| calculus for you, so you never have to think about it again".
|
| ... except most of those are cheap. So. Hm.
| alistairSH wrote:
| Except the kids taking high school calculus likely ARE going
| to do those things one day. Maybe not all of them, but some.
|
| Heck, I don't use calculus directly in my daily life. But I'm
| glad I took it because I recognize where it is used, and how,
| and that helps me understand my world better then without.
| softwarebeware wrote:
| > The point of the question is that it's posed by the people
| who aren't going to go on to create weather reports, credit
| card payment systems, video games, etc.
|
| I don't think so. If you're in high school and you ask this
| question, you surely do mean something like "what activity
| will I possibly doing in my future career that would require
| calculus" and in that case the answer that you may be a
| financial analyst, a meteorologist, an electrical engineer,
| etc. is right on. It's exactly what kids want to know.
|
| But now there's this myth that "you won't ever use calculus
| in real life" which is totally wrong.
| yummypaint wrote:
| I would argue that saving money and personal financial
| planning uses calculus concepts, and that they are enhanced
| by formally knowing calculus. It makes questions like "how
| much money will i have after x years given my mortgage,
| income, and assets?" approachable. It isn't feasible for most
| people to hire a human financial planner, and i wouldn't want
| to use automated tools without understanding enough to be
| able to perform sanity checks.
| sofixa wrote:
| You don't use it in those cases, you get what you need from
| someone else using calculus. In the same way you don't use
| cooking when you go at a restaurant.
| geuis wrote:
| I highly doubt it was worth the 20 seconds of my time it took to
| load that page, dismiss the egregious popup, read the article,
| then fight whatever javascript was overriding the back button
| just to get back here to leave this comment.
| Archelaos wrote:
| The main problem with teaching calculus at school is, that only a
| few pupils really come to understand it. For most pupils, the
| educational outcome is the opposite of a meaningful
| "weightlifting for the brain". In order to pass their tests, they
| try to memorise some recipes that they have made up from sample
| solutions. Instead of learning to think systematically, they are
| taught to somehow muddle through and feign understanding where
| they know nothing at all.
| nradov wrote:
| It would be better to change the required mathematics curriculum
| in high school and college to focus more on statistics and less
| on calculus. Sure it's useful to understand the basic principles
| underlying calculus. But even in engineering work, only a small
| fraction of engineers actually use calculus. Statistics is just
| as good for strengthening the mind, and is more broadly
| applicable to many real world fields.
| yamtaddle wrote:
| I've long held a notion that doing exactly the opposite of what
| lots of math PhDs think we should do in primary and secondary
| school would be the right path--take math education _much
| farther_ from "real math". Focus almost completely on math as
| a tool for solving real problems.
|
| I have a feeling the people who were going to become math
| majors would do so anyway, under such a system, and the rest of
| the kids would learn and retain more math than they _in fact_
| do with how we teach it today-- "here's 6 weeks on how you
| solve quadratic equations, without a hint of a reason for doing
| this, feeling motivated yet?"
| agentultra wrote:
| You need to learn how to think. How to solve problems. How to
| express your ideas clearly. Maths is excellent training.
|
| And it can be enjoyable for its own sake without being practical!
| seba_dos1 wrote:
| I never understood people asking those questions. High school
| stuff is so basic that it's less about learning a particular
| subject and rather more about getting to know some common
| language that can be used to discover the world around. I hated
| some of the subjects I wasn't interested in back then, like
| biology or history, but I'm still glad that something has
| remained in my head because now I can have at least some basic
| clue in conversations surrounding those subjects and have some
| reasonable starting point in case I actually decide to pursue
| some understanding of a given topic. I believe that's the whole
| point of high school education after all.
|
| And not even talking about the fact that if you don't know
| <SUBJECT_NAME_HERE/>, you're simply not going to notice all the
| places where applying it could be useful.
| munificent wrote:
| _> High school stuff is so basic_
|
| For many kids, that's not true of all subjects. Some find
| certain courses very difficult.
| seba_dos1 wrote:
| I said that it's basic, not that it's easy. Learning basic
| history wasn't easy for me either.
| ajsnigrutin wrote:
| The problem with a lot of high school subjects is, that you
| have to memorize a bunch of dates and years, random names of
| random plants and animals, that you then immediately forget
| after you pass the exam.
|
| For example, (for me), the "important things" about world war 2
| is, who, why and how... what was before, what made people make
| decisions they did, how did it start, what happened during, and
| why and how it ended... the exact date when some named general
| attacked some small city somewhere is pretty irrelevant
| (atleast not a thing you should keep memorized), but a lot of
| history classes focus on exactly that... on which date which
| unit/general took over which town where did they break through,
| etc... I'd prefer half less memorization data and a googling
| class for kids to find the dates needed, and more focus on the
| whys and hows, because history repeats itself, while dates and
| names don't.
| tsimionescu wrote:
| To be fair, rote memorization is one of the most improtant
| and transferable cognitive skills you can develop.
|
| Also, even if I agree that history classes often go
| overboard, having some notion of the years and even dates
| that some things happened is important to having a general
| understanding of history. If you know the who, what, why of
| WW II but have only a vague idea of when it started and when
| it ended, or when some of the major events within took place,
| you'll have a very hard time correlating with other events.
| It matters for example that WW II happened only 20 years
| after WW I, not 5 years after, not a century after. You won't
| get a decent picture of the sequence of events if you don't
| know some rough dates at least - especially for events
| happening in different parts of the world, with more indirect
| linking.
| sedawk wrote:
| > To be fair, rote memorization is one of the most
| improtant and transferable cognitive skills you can
| develop.
|
| To say so is missing the whole point parent comment is
| trying to make. Memorization is an important skill, that is
| one thing but saying memorizing random stuff to build that
| skill is entirely a different claim. I bet there are better
| ways so learn and hone memory skills than memorize history
| place/time/dates and kill a student's interesting in
| learning.
| [deleted]
| seba_dos1 wrote:
| There are certainly many ways in which education could be
| improved to be more effective, and the way math is often
| being taught isn't an exception there. Many people rely on
| memorization for learning math as well, which is as
| counterproductive as it gets.
| rv3392 wrote:
| FWIW, history teaching seems to have moved away from just
| looking at dates - at least where I am.
|
| I graduated high school <10 years ago and most of our history
| classes (including WW1 and 2) were spent on what, why and
| how. A significant amount of time was spent looking at the
| leadup and aftermath of both WW1 and WW2 as well as the ideas
| of the time. We pretty much didn't look at troop movements,
| generals, battles, etc. apart from mentioning the really
| significant ones. Same goes for pretty much every other unit
| of history (mediaeval Europe, colonialism in Asia and Africa,
| etc.).
|
| Maybe this is a reflection of differences in teaching styles
| in different parts of the world?
| conductr wrote:
| My teachers were moving away from date memorization back in
| the 90s. These things were mostly approached as a lecture
| that talked about exactly what you wrote about WW2. Is your
| experience outdated or did I just get lucky? I went to
| American public school if it matters.
| ajsnigrutin wrote:
| Former yugoslavia, then slovenia... I had to know every
| goddamn date and every goddamn village on the exams. And
| ok.. WWII was the start of the socialist yugoslavia... but
| I had to know the same for napoleon and the french
| revolution, and he barely passed here. Franco revolution,
| the same.. and soviet one too. Also a bunch of caesars too.
|
| Geography was the same... ok, countries and capitals..
| sure.. but a bunch of mountains and rivers and streams,
| where exactly the source is, and where and into which river
| it flows into... not just the major ones, even the crappy
| minor ones. Also stuff like, what is the greatest export of
| nigeria and other countries that are far enough, that I
| didnt need to know.
|
| Of course I forgot all of that data probably days after the
| exam, and never cared for 99% of it, and googled the last
| percent when needed.
| forgotusername6 wrote:
| The most use I ever got from my high school English literature
| class was at a bar in college. An older, much more
| sophisticated English major was talking to me about her
| favourite line from Macbeth and I was able to finish her
| sentence. It felt amazing. You never know when it might come in
| handy.
| skizm wrote:
| "You won't, but the smart kids might." -some smbc that I can't
| find
| dnissley wrote:
| I used to hate math up until about 8th grade when I had the
| realization that math problems are just puzzles and when looked
| at in that way can be fun and interesting. Eventually this lead
| to the realization that so many other things can be viewed in the
| same way, and that fostering this ability to change how I view
| things was pretty crucial to leading a happy life.
|
| School is terrible at helping foster such an attitude though,
| perhaps because it is incredibly difficult to do so at scale
| (even at classroom scale), but also because most teachers don't
| have this ability within themselves.
| gumby wrote:
| My kid hated maths in school. I told him that unfortunately he
| was just "learning the alphabet" and it would just take a long
| time. This didn't console him.
|
| Then in grade 11 he did physics and calculus and suddenly it
| all made sense! He was super excited.
|
| Years later he says "I guess this is just more learning the
| alphabet" but it sounds to me like he's trying to convince
| himself. :-/
| ergocoder wrote:
| > 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 calculus is weightlifting for your brain.
|
| I doubt that there is no other ways (e.g. lower cost, more
| effective) to weightlift for your brain than learning calculus.
|
| Also, the professor has a conflict of interest here (e.g. making
| calculus sound important because he teaches calculus). It's like
| me holding a shit coin and pumping it up, but yeah let's ignore
| that conflict of interest.
| wildrhythms wrote:
| The mitochondria is the powerhouse of the cell.
|
| https://knowyourmeme.com/memes/mitochondria-is-the-powerhous...
| didgetmaster wrote:
| I learned a lot in calculus and physics classes in high school
| and college that I have never used over my 35 year career. But
| learning those principles was tangentially beneficial in many
| ways. It taught me how to solve problems and think through
| several steps to come up with an answer. When I hear or read
| stories about outer space, power generation, or communication
| signals; I have a framework that I can build upon to understand
| the issue.
|
| I have kids now in high school and when I help them with some
| math problems some of it comes back to me, but many of the
| formulas I memorized so many years ago are long gone from my
| memory. But that is ok.
| deathanatos wrote:
| IDK if that's the reason I'd given for calculus. I might not
| literally solve integrals, but the base knowledge of what an
| integral is, what a derivative is, yes, I absolutely use those.
| I'm also a SWE/SRE, so ... there's that. But how often I see
| graphs _from products whose entire job is metrics_ that are just
| labelled wrong, e.g., w / the base unit instead of the rate, or
| what actually use the base unit instead of the rate, making for a
| difficult UX1. If the devs of those products understood ...
| calculus (let alone stats!) maybe the products would be less
| garbage? As it is, I still need to know that as a user.
|
| But yeah, I've not taking a literal integral in a while. Usually
| I'm doing some sort of very crude integration.
|
| Similar w/ the CS degree and everybody in this field going "it
| isn't needed" and then going "why isn't the database answering
| this query quickly, when there is an index on those fields?2" and
| follow that with a discussion of how B-trees work (or rather,
| don't)...
|
| And should I ever _need_ to solve an integral, I will _recognize
| that problem when I see it_ , and know what Wikipedia articles I
| need to page back into my brain.
|
| 1what I mean here is, e.g., like what Azure Metrics does. E.g.,
| there's a graph I use that measures throughput, but the unit is
| just "Bytes". But each point is "number of bytes transmitted
| during the window of time represented by that point" so it's
| really "bytes / 5 minutes" or something. But of course, then, you
| zoom, and now it is "bytes / 10 mintues" ... but the axis doesn't
| tell you that. This has the effect that as you zoom in or out ...
| _the numbers change!_ Which makes no sense (obviously the effect
| of zooming a graph does not go back in time and alter the
| readings) ... but only if you were properly measuring bytes /sec.
| (But as it is, there's a constant / divisor caught up in there.)
|
| (And that ignores harder problems with zooming metrics, like
| aliasing or resolution, or other metrics problems like
| percentiles on aggregates or efficient computation of calculated
| values and where to put windows, etc. ... but _pfft_ I 'm in the
| stone age over here.)
|
| 2and it's almost always a 2D range query or a range + exact value
| and the exact value is the second column in the index...
| xyzzy4747 wrote:
| They should just replace some of the math classes with finance
| classes.
| renewiltord wrote:
| At no point in my life have I ever related to people who can ask
| this question. The closest I got is thinking if the names and
| dates I was memorizing about the Wars were worth anything. In the
| end, it turned out that I either have a tremendous memory through
| either that training regimen or that I have a memory that gives
| me an advantage in that test protocol: either one is a winner.
| And either is worth it.
| pipeline_peak wrote:
| A lot of kids at least need to have the opportunity of being
| exposed to something before they can decide if it's for them or
| not.
|
| The amount of kids who purely decide to take Calculus is next to
| nothing. They need applied interests to see the usefulness of
| higher math. For a lot of us, that was software or programming.
| kylehotchkiss wrote:
| And I still will never forget that my school never taught me how
| to write a check, how to file taxes, how to find jobs, how to
| find community in life. All that stuff about photosynthesis sure
| helped though!!
| WheelsAtLarge wrote:
| "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 calculus is weightlifting for
| your brain."
|
| Total BS...
|
| 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. But there are so many more. 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. Recent research has shown that doing
| daily exercise is a great way to keep a healthy body and brain,
| rather than sitting on your butt learning a useless subject.
|
| Yes, there are professions where Calculus is needed and there are
| people that truly enjoy math. Cool, take all the math you need
| and want to learn. You should take it.
|
| Anyone that tells you that Calculus is a good way to exercise
| your brain is just trying to justify their job. Don't for a
| minute believe that it's the best way to use a limited resource
| like your time.
|
| Source: Me, it 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.
| behringer wrote:
| Programmer here. I wish I knew more calculus. It's really tough
| to learn outside of school and much older.
| WheelsAtLarge wrote:
| "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. 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.
| tayo42 wrote:
| 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 wrote:
| 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.
| halikular wrote:
| 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, from
| 3blue1brown's "essence of" series [1], Khan academy [2], or
| Brilliant.org's courses [3].
|
| [1] https://www.youtube.com/playlist?list=PLZHQObOWTQDMsr9K-r
| j53...
|
| [2] https://www.khanacademy.org/math/calculus-1
|
| [3] https://brilliant.org/calculus/
| tenebrisalietum wrote:
| 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.
| itishappy wrote:
| 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
| treis wrote:
| >If you divide V by something like 0.0001 each frame, you
| will implement gravity.
|
| That'd be a wild ride.
| ludston wrote:
| 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.
| punnerud wrote:
| "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 wrote:
| Learning to play a music instrument or learning to paint,
| well, is the definition on not giving up. So, no...
| bibanez wrote:
| 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 wrote:
| 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...
| itishappy wrote:
| 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.
| molticrystal wrote:
| 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 wrote:
| > _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?
| dopidopHN wrote:
| 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.
| WheelsAtLarge wrote:
| 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.
| Jensson wrote:
| > 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...
| Tade0 wrote:
| I think there a better argument to be made here and it's: you
| need to understand what's possible and what's not in a broad
| spectrum of fields.
|
| Case in point: a lot of bad cooking/cleaning advice comes from
| the lack of understanding of high-school level chemistry.
| Smoosh wrote:
| Just this week I have watched two videos on YouTube where the
| presenter is trying to address the comments on their previous
| videos where people are suggesting (something like) "connect an
| alternator to the wheels on an electric car to generate "free"
| energy to run the car".
|
| These comments show a thinking, inventive mind wishing to be
| useful and improve things, but such a basic lack of
| understanding of physics. I can only think that these people
| weren't paying attention at High School, were (poorly) home
| schooled, or have some sort of incapacity to understand/believe
| the established laws of science.
|
| Yet they think that they can invent simple solutions which have
| somehow eluded the experts in the field. Perhaps it is some
| form of Dunning-Kruger effect.
| lordnacho wrote:
| There's a number of angles to this.
|
| Want a fancy job? This is one of the hoops to jump through. Same
| as leetcode further down the line, you won't do it at work but
| you will do it to get work. But that's also a pretty tragic take
| on it.
|
| Practice for other things, sure, that is also a way to see it.
| You won't bench press the other team but you will make yourself
| stronger. But for what? A sport you'll never play? What are you
| preparing for?
|
| Here's another one. Math, especially pure math, is a thing that
| is totally separate from observation. It just sort of exists
| without being anywhere, and yet there's all this depth to it. You
| can get a puzzle that cannot be solved by any anything other than
| thoughts, and you can keep building on these puzzles that don't
| exist. Go nowhere and explore.
|
| Lastly I note that it's mostly math class that gets asked this
| "what's the point" question. But you may as well as this about
| everything else you do in school, and you will mostly find that
| you'll have spent years to learn French for 4 weeks of actual use
| in France, dissected frogs for no reason, and learned how to play
| the recorder. All things that I'm sure you can find positives for
| despite the superficial benefits being quite small.
| ergocoder wrote:
| > But you may as well as this about everything else you do in
| school
|
| And we should constantly question that...
|
| > Same as leetcode further down the line
|
| Leetcode is free and has proven sufficiently enough to get us a
| 6-figure job.
|
| > All things that I'm sure you can find positives for despite
| the superficial benefits being quite small.
|
| Except that the cost of going to school is expensive. Even if
| schools are free for you, it is paid by tax money. We should
| always aspire to teach useful subjects with decent ROIS in
| schools.
| jrumbut wrote:
| I would say that you don't really master the most advanced
| topic you learn.
|
| Attempting algebra is how you solify your knowledge of
| arithmetic, attempting calculus is how you learn algebra and
| finally master arithmetic.
| allturtles wrote:
| > Lastly I note that it's mostly math class that gets asked
| this "what's the point" question.
|
| I think it tends to come up as a way of resisting something
| hard and unpleasant, and math tends to be the subject that most
| often feels hard and unpleasant to a plurality of young people.
| Of course most of us, if we had been freed from HS math as
| teenagers and left to our own devices, would not have gone off
| to do something really useful. We would have instead spent that
| time on something far more useless, like browsing HN. :-)
| eastbound wrote:
| Also, we would be gullible to whatever new trend is invented
| by the people who do master those topics. I have interns
| upset because I don't want to pay them in bitcoins or give
| them shares in the company, while we're quietly churning 1m$
| ARR with just two engineers and myself (and others are doing
| orders of magnitude better). The same interns getting tired
| after 3 lines of documentation and suggesting that every
| documentation page should be a video, generated by those
| american SAAS for a hefty price. They are basically
| illiterate trying to cover their lack of skills.
|
| The divide between those who use and those who get used is
| getting wider. And I don't appreciate belonging to the first
| group, knowing how little my wisdom is.
| kcexn wrote:
| I think math feels hard and unpleasant to most students
| because the way it is taught is often extremely outdated.
|
| In primary school for example, we learn maths by memorising
| times tables and solving thousands of basic arithmetic
| problems. This was important in a time before calculators as
| being able to compute functions is a skill that students
| might need.
|
| Today though, arithmetic should be taught, not because it
| might be useful, but because from arithmetic we can discover
| interesting properties about numbers themselves. I think
| maths would have been more interesting if you showed students
| how properties of pure numbers have this nice association
| with any set of real world objects that can be ordered.
| chinchilla2020 wrote:
| There are also some counterpoints to it.
|
| I still cannot see a value in studying classical literature. At
| least not one that does not have 1000 better tradeoffs for
| other subjects.
|
| There are also aspects of studying that can 'nerdify' the brain
| and make you weaker at interpersonal skills. There are very few
| CEOs, influencers, actors, and musicians that are good at math.
| In fact, I think the artistic/athletic pathways in life can be
| damaged by beginning to condition someone for office work.
| JackFr wrote:
| > I still cannot see a value in studying classical
| literature.
|
| And that is the real tragedy of modern education.
| adhesive_wombat wrote:
| Reminds me of a sci-fi short story where the military
| leaders against an alien (?) invasion keep demanding
| "harder and sharper" human tools for the war. Finally they
| need a poet and find they don't have any any more.[1]
|
| Though I think that the way classical literature is taught
| is probably enough to sicken all but the most die-hard
| readers. Endless dissection of things on a word-by-word
| basis. Shakespeare (say) wasn't a godlike superhuman
| imbuing every single word with dozens of layers of meaning.
| Sometimes it's just a fart joke.
|
| Exactly the same as maths teachers drilling integration
| rules to death and having everyone conclude, not
| unreasonably, "this is pointless bullshit". Or history
| teachers listing dates and names.
|
| [1]: edit: not aliens, and it's by Alfred Bester: https://a
| rchive.org/details/New_Worlds_029v10_1954-11/page/n...
| CodeSgt wrote:
| You're welcome to explain why you disagree with the OP and
| what true value can, in your view, be derived from studying
| classical literature.
|
| I likely agree with you, but if you're just going to make a
| vaguely disparaging statement in the negative without
| elaborating or contributing to the discussion then you
| really might as well not comment at all.
| heavyset_go wrote:
| You'll better understand contemporary media and culture by
| being familiar with the foundations they're built upon. Much
| of modern media are either nods or homages to, or direct
| knockoffs of, classics. Creators weave allusions to other
| works in their own work all of the time, and you won't pick
| up on or appreciate them without familiarity with what
| they're alluding to.
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