Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

Proof you can do hard things

blog.nateliason.com

Post reply on HN
Print view View original

31–40 of 330 posts

Re: Proof you can do hard things

#31

Post by wwarner »

I like the idea, but I’m gonna say that (a) calculus is more than a good challenge and (b) math is actually easy.

To understand how things actually work, you need math, especially calculus. Deep learning? Calculus. Statistics? Calculus. Finance? Calculus. Physics? Calculus. Mech E, robotics, earth science, econ? Calculus.

Second, calculus, like all math, is easy. Like that’s the point, it’s the science of simple things. That math is competitive and presented as a cryptic challenge is beside the point — it is designed to make it possible for anyone to reason for themselves and solve problems. The sense of impatience and criticism around math is totally unwarranted and isn’t good for anyone.

I get kind of bummed when I see schools spending so much creativity and enthusiasm on art and theater. There really is no reason why science should be thought of as judgmental, difficult and painful, while putting on a play is creative, inviting and fun.

Re: Proof you can do hard things

#32

Post by ssivark »

From that perspective, going through any kind of struggle (and building willpower/discipline) would be a good enough proxy for learning calculus.

It’s a little sad that the best value that the OP can impute for learning calculus is masochism — I cannot imagine saying that for anything in the school curriculum that I actually learned/understood. I wonder (in good faith) whether the OP actually even absorbed calculus at all… (i.e. can they solve calculus problems even today, for example?) — if not, they’re not the person who should be making authoritative comments on the usefulness of calculus.

Calculus (Taylor approximations, perturbation modeling, error propagation, significant figures in measurement precision, gradient descent, etc — just off the top of my head) is so deeply embedded in my thinking, that it strongly shapes how I think and amplifies my effectiveness!

I disagree with the OP’s claim so fundamentally — they might as well claim that schools/education focus on literacy for the same reasons.

Re: Proof you can do hard things

#33

Post by rollinDyno »

I raised the same questions as Nat, but I think he hasn't really discovered why we were asking that. The reason why I was looking for a good reason to study calculus is because I was lazy, and if I'm lazy enough then I can change the definition of what "hard" means. For instance, I could convince myself that if my could teach calculus, and him being just another dude, then surely I could learn calculus.

I would also be cautious about setting yourself up for a hard life. The takeaway resonates well with the HN crowd, myself included, because we like challenging ourselves. There's a lot of people out there who are simply looking to satisfice their lives, and you'll need another way to motivate them to learn calculus.

Re: Proof you can do hard things

#34

Post by jameshart »

abtinf wrote: post #14
fsmv wrote: post #6

You take calculus to understand the nature of change over time, which is the foundation of physics. The formulas to do integrals aren't important but the concept of integrals is. Honestly I think we should try to focus on differential equations instead but maybe it's necessary to do calculus first.

It’s the foundation of a lot more than just physics. It’s absolutely crucial to economics and business, and it is a travesty that it isn’t a required part of lower division curriculum. You cannot grasp micro/macro/applied/business economics without understanding relationships between changing variables.

Understanding calculus helps you understand much more deeply than you could have grasped form just learning algebra what kinds of numerical relationship problems it is possible to actually figure out. Ideally you also need some infinite series, some linear algebra, some combinatorics, and an appreciation of complex numbers as well, so the absence of deep coverage of those from a typical high school math curriculum in favor of putting calculus on a pedestal is more annoying.

But the idea that if you know how the rate of change of a thing changes over time, that that gives you enough information to understand it completely? That’s pretty important and deep.

Re: Proof you can do hard things

#35

Post by arsenide »

TheAceOfHearts wrote: post #18

I hate the framing of problems or domains as hard, since it kept me from pursuing them further for many years. And the years later when I tried my hand at those problems, I found that it wasn't nearly as hard as it was being made out to be. Historically many problems have also been hard until people figure them out, and then they stop being considered hard problems. In recent years this has been mostly true of AI-rel…

It is useful to use the words hard and easy. As you mention, changing perspective around these concepts is the crux.

Hard problems or domains are unknowns. Working towards solving hard problems involves thinking through unknowns, which may or may not lead to understanding. An aversion to hard problems is an aversion to the unknown.

Re: Proof you can do hard things

#36

Post by codersfocus »

There will come a time when you have enough money, enough of everything, and deeper questions will arise. What is the meaning of existence? Why is there anything instead of nothing?

You will see that math plays a very fundamental role in our reality, and once you start seeing it in such a manner it may begin to interest you.

Re: Proof you can do hard things

#37

Post by smfjaw »

codersfocus wrote: post #36

There will come a time when you have enough money, enough of everything, and deeper questions will arise. What is the meaning of existence? Why is there anything instead of nothing? You will see that math plays a very fundamental role in our reality, and once you start seeing it in such a manner it may begin to interest you.

I feel like math is taught from too high of a level initially. I did a second major in Logic along with CS at university, I was pretty crap at maths in HS and never really 'got it', I could manage but never had any intuition. After doing a bunch of logic papers and learning about axioms and peano arithmetic everything made a lot more sense from a foundational perspective and it really changes the way you look at numbers and the world around you

Re: Proof you can do hard things

#38

Post by bigger_cheese »

TheAceOfHearts wrote: post #18

I hate the framing of problems or domains as hard, since it kept me from pursuing them further for many years. And the years later when I tried my hand at those problems, I found that it wasn't nearly as hard as it was being made out to be. Historically many problems have also been hard until people figure them out, and then they stop being considered hard problems. In recent years this has been mostly true of AI-rel…

Rightly on Wrongly some areas of study have the reputation/stigma of being difficult attached to them.

Back when I was a high school student math (not just calculus - but the entire subject of mathematics) had this reputation as being a "hard" subject as a result scores of my fellow students just decided math is to difficult I'm not going to engage with this.

I suspect this is related to a fear of failure or kids being afraid of "looking dumb" in front of their friends - There was a definite "if I don't try then it doesn't matter if I can't do it." attitude, so they just switched off in those particular classes.

A lot of these attitudes carry forward into adulthood. I'm almost 40 and amongst my generation programming has a similar reputation. People I grew up with think if you can read or write code you are some kind of mystical wizard with powers beyond the understanding of mere mortals.

I see it today at my day job - I work as an engineer (the non software kind). I've seen my coworkers completely baulk at computer code I hear all the same things I heard back in high school. "This is too hard, I can't learn this stuff, I'm not going to bother attempting to understand it".

Fluid Dynamics was a hard subject (in my opinion), Solid Mechanics was challenging a dozen lines of python code is not on the same level.

Re: Proof you can do hard things

#40

Post by TexanFeller »

wwarner wrote: post #31

I like the idea, but I’m gonna say that (a) calculus is more than a good challenge and (b) math is actually easy. To understand how things actually work, you need math, especially calculus. Deep learning? Calculus. Statistics? Calculus. Finance? Calculus. Physics? Calculus. Mech E, robotics, earth science, econ? Calculus. Second, calculus, like all math, is easy. Like that’s the point, it’s the science of simple thin…

It will be amusing if we find out that all the things come in discrete quanta, even space-time, which I hear hasn't been ruled out. Calculus and real numbers might not be sitting as pretty.
Post reply on HN