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Proof you can do hard things

blog.nateliason.com

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Re: Proof you can do hard things

#111

Post by drewcoo »

m463 wrote: post #76
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…

I've found that some disciplines need calculus, others don't. I've found deeply understanding logic and binary/hex MUCH more important than calculus in my career.

> deeply understanding logic and binary/hex

So . . . logic and number bases? Do tell!

Re: Proof you can do hard things

#112

Post by rocqua »

cameldrv wrote: post #57
bee_rider wrote: post #53

Earlier quoted context omitted.

Calculus is needed to understand, like, basic sophomore and junior year engineering stuff. You can maybe pass the tests without understanding where the models came from if your professors are just really lazy and only give you canned problems, but that isn’t a goal we should strive for. And engineers should usually be using battle-tested models rather than coming up with their own derivations, so to some extent using…

I wonder if there’s a way to teach Calculus in a more practical way. I use the principles of Calculus constantly in many aspects of my job, but I don’t think I’ve ever done say, integration by parts professionally. Understanding deeply what an integral and a derivative are is a very useful skill though.

The valuable part of calculus to me was understanding the concepts of limits, differentiation, integration, and a tiny bit of differential equations.

Learning how to actually solve integrals or differential equations was useless other than it teaching me more about calculus and how it is useful. For calculations in practice I will turn to wolfram alpha, but it has some value to understand what wolfram alpha is doing under the hood.

I think a calculus course whose tests defocusses calculations might be very valuable for practically minded people. Knowing to think about derivatives is much more useful in practice than actually being able to calculate a derivative.

Re: Proof you can do hard things

#113

Post by rocqua »

bee_rider wrote: post #75
cameldrv wrote: post #57

Earlier quoted context omitted.

I wonder if there’s a way to teach Calculus in a more practical way. I use the principles of Calculus constantly in many aspects of my job, but I don’t think I’ve ever done say, integration by parts professionally. Understanding deeply what an integral and a derivative are is a very useful skill though.

As an undergrad I tutored folks in a sort of “calculus for non-STEM students” class that focused more on practical stuff and applications… and TBH I think trying to shield them from the complexity didn’t really do them any favors. I often found that they had some practical algorithm memorized step-by-step and some graphical or conceptual intuition, but when the steps and intuition betrayed them we’d end up spending a…

Isn't the actual calculations of e.g. integrals the least useful part of calculus for non-stem students? Instead the basic concepts are where the easily accessible value lies.

Teaching tricks without teaching the concepts not only fails in the way you describe (it prevents building ideas further). It also fails to teach anything useful at all. Because barely anyone outside of STEM wil ever have to solve any kind of integral or derivative in their life.

Re: Proof you can do hard things

#115

Post by gniv »

WesleyJohnson wrote: post #46

I lost interest in school around the 10th or 11th grade. I never took any math classes beyond what was required to graduate way back in '96 in Florida. I also didn't go to college. I've been a professional web developer since 2005 and a development manager (who still codes) since 2017. I don't understand the first thing about Calculus or even logarithms. I'm sure if I did, I'd probably be a better developer. I've had…

Just a meta comment: Don't think of calculus as hard in the same way learning a language or learning to paint is hard. Calculus is more of a gotcha moment. You fumble in the dark for a few focused hours (or minutes) and then you Get It. From then on it's relatively easy.

Re: Proof you can do hard things

#116

Post by meiji163 »

anon-3988 wrote: post #104
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…

>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. lol, typical HN answer. Mathematics is not "…

A better description is "simple", not "easy".

"If you do not believe that mathematics is simple, it is only because you do not realize how complicated life is." -von Neumann

Re: Proof you can do hard things

#117

Post by tjbiddle »

I like this approach as well.

My current explanation for this is more along the lines of being well-rounded. By being exposed to a number of different skills and learnings throughout your education, your more likely to be able to connect the dots in other areas - and just hold better conversations with people.

Don't need to ace all your classes for that, but put in the effort to try and structurally understand whatever it is you're coming across.

Re: Proof you can do hard things

#118

Post by newaccount74 »

"If you do weightlifting then sleep deprivation from a newborn is easy"

Right. Tell that to my partner, who has been nursing our newborn every two hours for the last 5 months. There is no way to wake up 2-4 times every night for months and not be tired.

Weight lifting would be zero help with that.

Re: Proof you can do hard things

#120

Post by selcuka »

fortenforge wrote: post #15

I don't want to be overly rude, but this is nonsense. The reason to learn calculus is that it's incredibly useful in several domains and never learning it prevents you from become a skilled practitioner in those domains which in turn reduces your future earning potential. Basically: https://www.smbc-comics.com/comic/why-i-couldn39t-be-a-math-...

Everything can be incredibly useful in several domains, but we don't teach everything. Instead, people learn what they need when they start working in that domain.

The point of the article is that calculus is not taught because it might be incredibly useful for a small percentage of students, but because it measures their ability to pick up a hard subject and ace it.

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