Feels like many other comments here are trivial objections for the sake of sounding contrarian. Or even, humble bragging about how easy math was to the commenter. I found the article to be a great, new (to me), and widely applicable perspective on the matter.
Proof you can do hard things
81–90 of 330 posts
Re: Proof you can do hard things
#82Earlier quoted context omitted.
You don't use calc much when you use R, unless you're working on a problem that involves calculus, which isn't many problems, usually? R is usually used to do data stuffs in my experience. Like, "take in this data from this CSV, and do these manipulations" which may involve math but not often calculus.
using those "data stuffs" are usually based on calculus. Statistics and probability are both defined in terms of calculus. calculus is the most basic of mathematical machinery, that it is essentially a requirement to do anything else.
Sure thing, you may be calling a function that does some regression or something, but you aren't "doing calculus" when you are programming that in R.
Re: Proof you can do hard things
#83I hate the framing of problems or domains as hard, since it kept me from pursuing them further for many years. And the years later when I tried my hand at those problems, I found that it wasn't nearly as hard as it was being made out to be. Historically many problems have also been hard until people figure them out, and then they stop being considered hard problems. In recent years this has been mostly true of AI-rel…
I hate the framing of problems and domains as hard because I found it so confusing when they turned out to be easy for me. It gave me a false sense of competence and superiority. Because I found calculus (and everything else in school people said was hard) easy, I thought I was just exceptionally capable and other people were incompetent and/or stupid. I didn't find out until much later (and it still feels like much…
> I think learning how to learn things that are hard FOR YOU is quite possibly the most important skill in life.
I’d certainly agree it’s extremely valuable. There are some failure modes from taking it too far (like anything).
People tend to be happier when they’re very good at things. You also contribute more to the world. If you’re always doing things that are hard for you, you won’t do as much or as well, really by definition. It’s okay to do things that are easy for you. There are a lot of upsides!
Even if you choose an easy path, there will always be hard parts. So if you want to get anywhere, it’s essential to have practice navigating that. Just consider if that’s where you want to be all the time. I’ve done it myself and seen it in others, where you think you’re always challenging yourself, but you’ve actually just put yourself into a life that’s a bad fit.
Re: Proof you can do hard things
#84I like the idea, but I’m gonna say that (a) calculus is more than a good challenge and (b) math is actually easy. To understand how things actually work, you need math, especially calculus. Deep learning? Calculus. Statistics? Calculus. Finance? Calculus. Physics? Calculus. Mech E, robotics, earth science, econ? Calculus. Second, calculus, like all math, is easy. Like that’s the point, it’s the science of simple thin…
I saw an article where they asked a bunch of scientists and engineers if they actually used calculus in their professions. None of them did. They used Excel and the R programming language.
As an engineer calculus is pretty fundamental to my job. It underpins all sorts of stuff - Heat transfer, fluid flow, stress and strain rates, beam deflection, fracture mechanics etc.
I may not be solving differential equations by hand but I'm using knowledge about calculus everytime I reason about our industrial process.
The excel part is probably referring to solvers - where you plug in boundary conditions and spits out a solution. Edit - and excel or R (or Matlab) is what you use in lieu of needing to solve this stuff by hand.
Re: Proof you can do hard things
#85Feels like many other comments here are trivial objections for the sake of sounding contrarian. Or even, humble bragging about how easy math was to the commenter. I found the article to be a great, new (to me), and widely applicable perspective on the matter.
I am definitely not bragging — I’m saying the opposite, that all that pressure and elitism around math and science are unnecessary and counterproductive. I also liked the article just fine. The only controversial point I made is that science > art :)
Re: Proof you can do hard things
#86People (and employers) who can truly appreciate calculus wouldn't be impressed with a taken calculus course (thousands of students take calculus every year) or even a math BSc, and those who can't, how would they assess how hard your calculus course really was? There is no competition in a typical calculus course. Better ways of signaling the ability of doing hard things, especially for kids, in my opinion, are math/programming/etc contests. That's where you have a real competition and can show what you are capable of relatively to other people who participate and want to win. Also, it's important to note that passing a calculus course includes not only watching lectures or reading a textbook but also extensive problem solving. Typically "hard" college math courses are about memorization of abstract concepts, and taking any of them doesn't really prove you can do hard things (I'm not talking about PhD where you need to make novel contributions, thats crazy hard if you want your research to be competitive). Thats my experience and perspective but I'm living in my bubble.
Re: Proof you can do hard things
#87Calculus is important, because (among other things) the proper definition of limits teaches you how to manipulate logic quantifiers.
In any case, IMHO best advice to young people - try to learn hardest things you can. Later, there will be less time, less energy and more distractions.
Re: Proof you can do hard things
#88Learning difficult concepts is only one aspect of developing perseverance - which is probably the greater ability to master. Others are finishing what you start, developing habits to complete undesirable tasks (like regular exercise or doing the dishes) and overcoming fear.
The latter is something you see creep in as you get older and it's something that's always attracted me to hobbies that require you to keep your nerve like skiing, scuba diving and flying planes. There's nothing like having to land a plane solo with a bit of a crosswind to give you confidence in yourself.
Re: Proof you can do hard things
#89I mean, I found learning calculus to be fun and rewarding in its own right! It can be challenging at times, but also beautiful.
Re: Proof you can do hard things
#90What's it really mean to be hard?
Some things are vaguely impossible, like finding a solution to fluid mechanics, or finding a theory that combines quantum mechanics and general relativity.
Others are proven to be impossible under some conditions like the halting problem.
Others still require access to some amount of resources, or some amount of leverage, like buying a $100M yacht.
Lots of these hard things are quite unlikely for me to be able to do.
I think most people refer to the resource one? And that some people have more access to resources than they think, and the scales of resources needed are smaller than assumed?