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Proof you can do hard things

blog.nateliason.com

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Re: Proof you can do hard things

#91

Post by nine_k »

smeej wrote: post #47
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…

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…

Ah, the trap of the gifted student! When everything other students find somehow hard is easy for you, you get a delusion that nothing is hard, and that putting in some effort is not necessary. A rude awakening may come at high school, or at college. Those who kept toiling just keep toiling, and overtake you, because.you're not used to pushing through.

I think it's important to learn early enough that things are usually hard when you get far enough into them, and that it's OK, it's not a brick wall, it just takes some effort to keep advancing.

Re: Proof you can do hard things

#92

Post by spot5010 »

Learn calculus because it is beautiful.

Newton had discovered the law of gravitation, but didn’t publish it for a long time because he couldn’t justify how the gravitational effect of a sphere could be the same as if all its mass was concentrated at a point in the center. He had to invent calculus to prove it. Isn’t that amazing?

I know the author is using calculus as an example of a hard thing, but if someone is genuinely following their curiosity, then things do not seem hard. Personally I wouldn’t want to work on hard things just to prove to myself that I can do hard things. I’m happy being lazy.

Re: Proof you can do hard things

#93

Post by kashunstva »

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…

> I hate the framing of problems or domains as hard

The easiness or difficulty of a domain or discipline is always in relation to some individual context; and that context includes variables that the learner controls. To the impatient, disinterested or undisciplined, I imagine calculus, learning the kanji, or playing the oboe all seem hard. But to the extent I can marshal patience, curiosity and discipline, the difficult domain becomes just a series of small steps integrated over time. I’m a musician and when a student complains about how hard a piece is, I ask if they can play the first note, then the second. If so, then it’s not hard. Because the process to acquire the whole thing is right there. Yes there are interpretive elements and techniques to be acquired along the way. But nothing is hard unless you are in a great hurry or you don’t really want to do the thing.

Re: Proof you can do hard things

#94

Post by BWStearns »

codeisawesome wrote: post #81

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.

It's almost like no one finished reading the post (emphasis added).

> I don’t particularly care what grades my kids get once they start school. But I do care that they consistently prove to themselves they can do hard things. If Calculus is how they want to do it, fine, but there are many, many more options.

Separately, as someone just recently learning calculus as an adult now I'm digging the obliviousness of the "math is just inherently easy" folks. I get where y'all are coming from but there's a deep lack of empathy there. Go teach some people something (anything) and learn that other people's brains don't necessarily contain your knowledge.

Re: Proof you can do hard things

#95

Post by gmadsen »

thfuran wrote: post #78
gmadsen wrote: post #67

Earlier quoted context omitted.

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.

You're kind of arguing that you can't walk without studying kinematics.

im not though. I don't think you need to know measure theory and understand how to formalize probability in terms of sigma algebras to do professional stats.

But I would be very skeptical of a professional data scientist that doesn't understand things like derivative, integral, limit on an intuitive level. I don't know how you would understand distributions without that knowledge

Re: Proof you can do hard things

#96

Post by wwarner »

m463 wrote: post #79
gmadsen wrote: post #67

Earlier quoted context omitted.

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.

Are probability and statistics really practically based on calculus? Most math curriculums do not have a calculus requirement to take statistics.

rho(x) is the probability density function, and it better sum up to 1 for all possible values of x.

Re: Proof you can do hard things

#97

Post by upxx »

As Hilbert put it, “Every boy in the streets of our mathematical Gottingen understands more about four-dimensional geometry than Einstein. Yet, despite that, Einstein did the work and not the mathematicians."

Re: Proof you can do hard things

#98

Post by XenophileJKO »

MaxBorsch228 wrote: post #86

People (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/…

I feel like you have missed the entire point. The point of the article was not to "signal" that you can do hard things. It was to build up the inner confidence. Competition is great, but largely orthogonal to the concept of having kids learn that they can do hard things.

Re: Proof you can do hard things

#100

Post by bruce511 »

nine_k wrote: post #91
smeej wrote: post #47

Earlier quoted context omitted.

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…

Ah, the trap of the gifted student! When everything other students find somehow hard is easy for you, you get a delusion that nothing is hard, and that putting in some effort is not necessary. A rude awakening may come at high school, or at college. Those who kept toiling just keep toiling, and overtake you, because.you're not used to pushing through. I think it's important to learn early enough that things are usual…

This extends into life as well. I play golf (for fun [2]), which cunningly has a scoring system that tells me I'm objectively rubbish, and getting (mostly) worse.

I've found this professionally useful in combating the seductive idea that "because I'm -really- good at one thing, I'm good at everything. "

I've seen the opposite in customers sometimes. Doctors who are very good doctors, have strong feelings about UI (that are objectively just wrong[1].) But because they operate in a culture which treats their word as law, they find it hard to accept that others may have skills in other areas they lack.

If you are an expert in something I recommend including something else in your life to keep you humble. That humility allows you to be a better spouse, parent, and human being. (And ironically a better expert who's able to recognise and adopt an idea or solution that'd better than yours even in your area of expertise.)

We choose to do these these things, not because they are easy, but because they are hard.

[1] think yellow comic sans italic text on blue background levels of wrong.

[2] golf is fun precisely because it is hard. Things that are easy are not fun. The pleasure of 1 perfect shot out of 100 tries is the dopamine that keeps us coming back.

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