Proof you can do hard things • Hacker News Board

Re: Proof you can do hard things

#161

Post by nottorp » Wed, Jul 12, 2023, 9:38 AM UTC

bbbobbb wrote: post #157

jokethrowaway wrote: post #150

Earlier quoted context omitted.

I don't get why calculus is always brought as an example. It wasn't particularly hard, the entire class had to learn it in high school. We all had it (in a slightly harder shape) in every university course (no matter how detached from what we actually needed) I forgot all my calculus after high school, had to relearn it in uni and then I promptly forgot again. Exactly as the article says, it was more about proving we…

I think that it is a US specific obsession. I don't even know what "calculus" is really. I have had plenty of math classes both in high school and later at university but I don't recall any significant distinction that would leave me with some concrete idea of "algebra" vs. "calculus" vs. "whatever" years later.

I believe it was called "mathematical analysis" in my corner of the world. In high school and uni.

It's the continuity/limits/integrals stuff.

Also it was never optional. Either in high school or CS at uni.

Re: Proof you can do hard things

#162

Post by rcxdude » Wed, Jul 12, 2023, 9:40 AM UTC

jimmydddd wrote: post #42

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 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.

It depends on what the definition of 'using calculus' is, as well. I use the concepts of integration and differentiation all the time in my work: it's completely integral (hah) to a good chunk of what I do (as well as complex numbers, fourier transforms, and a bunch of other 'advanced' maths). What I don't do is grind through working out the analytic solutions to odd integrals or differentials. Firstly because it's rarely useful, and secondly because I have a machine to do that for me in the cases that it is. I think it's unfortunately common to have the attitude that the latter is the majority of what calculus actually is in practice, because it makes up a lot of calculus education, but it's not the case.

Re: Proof you can do hard things

#163

Post by hardware2win » Wed, Jul 12, 2023, 9:41 AM UTC

Etherlord87 wrote: post #159

hardware2win wrote: post #141

>You know they will never use it in adulthood, outside of certain career choices. If somebody says stuff like this, then they do not understand math, imo. Im a little bit sad whenever somebody argues for math by using "no phone available at the moment" argument. Math is insanely powerful world modeling tool. Starting from calculating right amount of fence for your garden, to estimation of 500km route arrival time whi…

I'm using math(s) a lot, trigonometry, matrices, algebra… But most of my friend, family, I couldn't convince to learn math just based on the argumentation they can use it in practice. Yes, calculating the right amount of fence is useful, but not only (as someone pointed out) you don't need a lot of math for that, people just take take a ruler on the plan, or count steps in field, going across the entire length, then…

>Who does this? How would you convince a friend to learn math in order to do this? What people do is they remember how long a 200 km route took and so they estimate the 2.5× longer path will take 2.5× more time.

Who does it? Navigation app in your phone. They modeled this problem using math. While you could probably model it somehow without math, but why would you want to do it other way, when you have reliable, mature and flexible tool

I didnt write that you shouldnt leverage tech.

Do it, yet be aware how it works and why. You can leverage math in other custom scenarios

Re: Proof you can do hard things

#164

Post by aleph_minus_one » Wed, Jul 12, 2023, 9:51 AM UTC

> But I recently realized there is a very good reason to take Calculus. It’s to prove you can do hard things.

While I do like mathematics (thus I clearly have no negative feelings about learning calculus), this argument is dubious: the longer I live, the more I realize that the capability to learn complicated scientific stuff (including mathematics) hardly does transfer to other areas of life.

Just consider this: if such skills transferred so well, one would expect that those people who make a steep career in companies have learned lots of insanely hard stuff, often hard mathematical and scientific stuff. The reality is that the people who have such a steep career are rather great "policitians" (in the negative sense), sycophants and self-promoters. On the other hand, learning hard scientific/mathematical stuff nurtures the personality trait of "no bullshitting" and developing less tolerance for claims that clearly cannot be abided by.

Thus: I really like learning hard things, but this personality trait is in my opinion often a career killer.

Re: Proof you can do hard things

#165

Post by Notatheist » Wed, Jul 12, 2023, 9:51 AM UTC

>But I recently realized there is a very good reason to take Calculus. It’s to prove you can do hard things

Doing hard things proves you can do hard things. Where does calculus enter into it?

>The more hard things you push yourself to do, the more competent you will see yourself to be

"The whole problem with the world is that fools and fanatics are always so certain of themselves, and wiser people so full of doubts."

>Most C students are not doing other hard things instead of school. They’re just goofing off, so they end up working for the A student.

This is ridiculous. Author goes on to imply these ("most C students") are on social media and using drugs. I'd put any money on them being much more likely to have been raised by the type of parent who believes their kid needs a reason to want to learn calculus.

Oh, and what is "hard" by the way? Is it doing something you're not good at until you're good at it? Does it need to be valuable from my perspective or that of my parent? Should it take a certain amount of time to become "good" at it? When am I good at it? Can it be a hobby I enjoy even while it's difficult, or must it be a chore? What if I'm forced to overcome some hurdle in my life for example growing up with a foolish parent with warped worldviews?

Re: Proof you can do hard things

#166

Post by phforms » Wed, Jul 12, 2023, 9:56 AM UTC

It’s really interesting how we shy away from some “hard” things, even though there is literally nothing at stake that could prevent us from doing them. Nothing life-threatening, no (or minimal) risk of physical or psychological damage, no social exclusion, no irreversable decisions about the future to make. Why can’t we just try/do it – what are we so afraid of?

Many people (especially those in a lucky environment) can just try to draw realistically (which is actually not that hard, given a good teacher/instruction), study a “hard” topic in philosophy, get good at playing a “hard” song on an instrument or even learn how to prove mathematical statements or how to model and analyze complex systems. We can just try, there is nothing at stake except our time and energy.

When something is really interesting to me, I try not to stop myself from pursuing it just because it is considered “hard”. I have many mental issues (executive dysfunction, bad memory, etc.) but I am also stubborn and curious enough to try anything, again and again if I have to, which I never regretted. It doesn’t hurt and it can be so much fun with a humble and relaxed attitude and especially if I don’t try to compare myself to others, which might be one of the main things that is holding most of us back.

Re: Proof you can do hard things

#167

Post by lucideer » Wed, Jul 12, 2023, 10:04 AM UTC

hardware2win wrote: post #141

>You know they will never use it in adulthood, outside of certain career choices. If somebody says stuff like this, then they do not understand math, imo. Im a little bit sad whenever somebody argues for math by using "no phone available at the moment" argument. Math is insanely powerful world modeling tool. Starting from calculating right amount of fence for your garden, to estimation of 500km route arrival time whi…

You've given one day-to-day example (garden fence) which requires only extremely elementary math, and then listed a bunch of stuff related to specialised career paths... which was the OP's original qualifier:

> outside of certain career choices.

As someone who did a lot of calculus in university, and definitely hit a eureka moment while integrating over vector fields that helped me conceptualise some general day-to-day stuff better in my head, would most people generally benefit from that same conceptual "grokking": of course. Would it be worth the time & effort investment for them if they're not using it in their career: no.

Re: Proof you can do hard things

#168

Post by [deleted] » Wed, Jul 12, 2023, 10:05 AM UTC

keerthiko wrote: post #149

hardware2win wrote: post #141

>You know they will never use it in adulthood, outside of certain career choices. If somebody says stuff like this, then they do not understand math, imo. Im a little bit sad whenever somebody argues for math by using "no phone available at the moment" argument. Math is insanely powerful world modeling tool. Starting from calculating right amount of fence for your garden, to estimation of 500km route arrival time whi…

IME a big part of this misdirection stems from school focusing on the mechanics of math, rather than the intuition of math. In the long run, the mechanics of math (how to do long division, or differentiate an expression, or expand a geometric series) are important only insofar as to help us model and predict and analyze the world, intuitively. However, students who do not intuitively see the power of mathematical int…

[deleted]

Re: Proof you can do hard things

#169

Post by [deleted] » Wed, Jul 12, 2023, 10:05 AM UTC

bbbobbb wrote: post #157

jokethrowaway wrote: post #150

Earlier quoted context omitted.

I don't get why calculus is always brought as an example. It wasn't particularly hard, the entire class had to learn it in high school. We all had it (in a slightly harder shape) in every university course (no matter how detached from what we actually needed) I forgot all my calculus after high school, had to relearn it in uni and then I promptly forgot again. Exactly as the article says, it was more about proving we…

I think that it is a US specific obsession. I don't even know what "calculus" is really. I have had plenty of math classes both in high school and later at university but I don't recall any significant distinction that would leave me with some concrete idea of "algebra" vs. "calculus" vs. "whatever" years later.

[deleted]

Re: Proof you can do hard things

#170

Post by toyg » Wed, Jul 12, 2023, 10:06 AM UTC

hardware2win wrote: post #163

Etherlord87 wrote: post #159

Earlier quoted context omitted.

I'm using math(s) a lot, trigonometry, matrices, algebra… But most of my friend, family, I couldn't convince to learn math just based on the argumentation they can use it in practice. Yes, calculating the right amount of fence is useful, but not only (as someone pointed out) you don't need a lot of math for that, people just take take a ruler on the plan, or count steps in field, going across the entire length, then…

>Who does this? How would you convince a friend to learn math in order to do this? What people do is they remember how long a 200 km route took and so they estimate the 2.5× longer path will take 2.5× more time. Who does it? Navigation app in your phone. They modeled this problem using math. While you could probably model it somehow without math, but why would you want to do it other way, when you have reliable, matu…

So what I'm hearing is that math is only good when there is no GPS / no phone.

Let's be honest: advanced math is useful in programming contexts. Everywhere else, in 2023 you're using computer programs that will do the hard math for you.