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Proof you can do hard things

blog.nateliason.com

171–180 of 330 posts

Re: Proof you can do hard things

#171

Earlier quoted context omitted.

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.

In the US we'd reserve "mathematical analysis" (or more specifically, Real analysis) to the college level classes which involve writing proofs about the continuity of functions between sets of real numbers. You'd probably end up with a lecture on the mean value theorem here, and leave with the ability to prove it, among other things

"Calculus" is the application of that theory without argument. It's an advanced high school class or an early college one. There you'll integrate or differentiate real valued functions for use in optimisation problems or for determining qualitative features of such a function (e.g. where is it flat, where is it defined, etc).

In the US, you can probably pass calculus without writing a proof, but you can't pass mathematical analysis without at least understanding epsilon/delta proofs.

Re: Proof you can do hard things

#172

Earlier quoted context omitted.

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.

In the US we'd reserve "mathematical analysis" (or more specifically, Real analysis) to the college level classes which involve writing proofs about the continuity of functions between sets of real numbers. You'd probably end up with a lecture on the mean value theorem here, and leave with the ability to prove it, among other things "Calculus" is the application of that theory without argument. It's an advanced high…

I'm pretty sure we did proofs in high school. But that was a while ago, don't know what they do now.

Hey now that I think of it, "mathematical analysis" had continuity, limits, some integrals. And then every mathematically inclined uni specialization had "integral and differential calculations (let's shorten it to calculus)" which was more advanced use of integrals :)

A rose by any other name would smell as sweet, but it may be called a thorn in a different locale.

Re: Proof you can do hard things

#173

>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-d…

There is no license required for using math. Yea, if you dont want, then you will not use math. But, if you dont have some mental block, then you may find ways to apply math to your problems.

Abstract thinking is really useful during arguments, even about politics, religion, etc.

Re: Proof you can do hard things

#174
post #170

Earlier quoted context omitted.

>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.

You didnt understand my message.

Math is not about calculators or computers.

It is about modeling (e.g real world)

It is useful whenever non-standard, already modeled in your calculator problem apprears.

Re: Proof you can do hard things

#175

Earlier quoted context omitted.

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 (th…

I've found that one of the best ways to dismantle an overblown ego is to play StarCraft (Brood War or SC2, the result will be the same) or really any other 1v1 game. The direct feeling of being beaten, potentially overrun completely, time and time again, especially after putting in hard work is very humbling. Fighting games are very good for this except they've always invited a certain mental block in people where th…

> I've found that one of the best ways to dismantle an overblown ego is to play StarCraft (Brood War or SC2, the result will be the same) or really any other 1v1 game.

Sadly no. Playing SC2 online weaned me off online competitive games. Because of all the kids calling me a stupid noob ... when I won. The ones beating me were polite.

Re: Proof you can do hard things

#176

Earlier quoted context omitted.

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-d…

There is no license required for using math. Yea, if you dont want, then you will not use math. But, if you dont have some mental block, then you may find ways to apply math to your problems. Abstract thinking is really useful during arguments, even about politics, religion, etc.

> If you dont have some mental block

The "mental block" you're referring to here is a combination of individual aptitude, capacity, access to educational resources & time-/effort-budgeting over a lifetime. This isn't some free casual object people are refusing to collect on their travels, it requires investment.

Re: Proof you can do hard things

#177
There's some nice seeds of ideas here, but it's all a bit lost in

(a) brevity - it's a deep topic so the post length can't do it much justice &

(b) naïvety - their extremely oversimplified explainer for the “C students hire A students” trope is that the C students are actually secret A students in other areas. This assumes a utopian world where academic-style assessment of study/effort maps to career progression. C students do well for a range of reasons including-but-not-limited-to: charisma, nepotism, unconscious-bias-hiring on the basis of race/gender/accent/height/hair/appearance, normative mental health characteristics. It's not because of their secret extracurricular study: that's in direct contradiction of the message behind the trope.

Re: Proof you can do hard things

#178

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 diffi…

> 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

> But nothing is hard unless you are in a great hurry or you don’t really want to do the thing.

I got told this many, many times in my life, and it was incredibly frustrating when it was something I really wanted to do. I discovered after 34 years that I have ADHD, which makes a lot of stuff that can eventually become easy/easier with patience and perseverance to in practice be extremely hard.

I'm bringing this up because a lifetime of guilt and shame for not being able to accomplish something when it was deemed easy, that it "just requires some discipline", said by someone else pushed me away from a lot of things I'm interested in but wasn't able to keep motivated to do them after shame set in. It can spiral if you feel inadequate, and if you live with this you feel inadequate and "catching up" a lot of times.

Specifically, one of those things was music. I tried learning instruments when I was younger but the motivation was not in learning the instrument itself, it was music as a whole. I wanted to understand how it worked and how I could create it, not plow through guitar strumming exercises for months and months, then fingering techniques, then be able to play a few songs, and maybe in some years actually start to create something. To me what worked, in my natural branching way of thinking/learning, was to start producing electronic music some 4 years ago. Just some stupidly cacophonic basic loops in the beginning, which pushed my interest to learn the basics of music theory, learning the basics cleared to me a map I could guide myself through skills I was missing: rhythms, harmony, active listening, etc. After I started understanding what skills I needed to achieve what I wanted then it pushed my motivation to learn an instrument, the piano, and then learning the mechanical skills of the instrument made sense.

I bring this up because since I was diagnosed I had multiple conversations with people that suffered through the same as myself: being called undisciplined, inpatient, disinterested when they couldn't muster the motivation to plow through a structured path when it got boring to them. And that is not under my control, ADHD is much more about lacking motivation control than being hyperactive or actually having an "attention deficit", I get obsessed by things I'm interested in (music is an example), it's just that most of the resources to educate oneself on a discipline/domain is not tailored for people who needs to branch out, find pockets of skills that are interesting and motivating to learn, and putting the puzzle back together after acquiring some skills in a haphazard way than the usual structured learning path.

Re: Proof you can do hard things

#179
I really despise all the "why you should care about math" takes.

The question is never asked about any other school subject and only mathematics has to justify itself that way. I had to learn about categories of plants and animals, interpret 20th century literature, learn about events from a thousand years ago, I did presentations on the demographics of European countries, how certain chemicals react and much, much more. I never used any of that knowledge for anything, certainly not in my career or in university.

But somehow mathematics is the one field which needs to justify its own existence? Mathematics needs to bend itself over and "be relevant" so that people will actually learn about it? Why? Why not ask the same of any other subject.

Justifying mathematics is easy, especially such a universally applicable subject as calculus. But I see no reason why it should have to justify itself in any way.

Re: Proof you can do hard things

#180

I really despise all the "why you should care about math" takes. The question is never asked about any other school subject and only mathematics has to justify itself that way. I had to learn about categories of plants and animals, interpret 20th century literature, learn about events from a thousand years ago, I did presentations on the demographics of European countries, how certain chemicals react and much, much m…

People aren't doing it because they think they should. They are doing it because they want to.
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