“When are we going to use this in our everyday life?” (2017)

I struggled with trigonometry in high school, to the point that I had to repeat the class twice. Each time I took the class it was the exact same lesson, and I struggled.

During my senior year I was able to take a course through BOCES on audio production. That course related some of the trigonometry I was struggling with to a subject I was deeply interested in.

I don't expect Math teachers to start teaching audio production, but it would have been nice if the teacher had seen me struggling and at least attempted to approach the subject from a different angle ¯\_(ツ)_/¯

Humans has terrible intuition for these things, it was just 300 years ago humanity figured these things out but once we did we did all these things afterwards in just 300 years. Learning this one thing is the key to so many things.

Basic math and physics education helps build intuition for it, but without people are really bad.

The problem is, the automations you might want and the combination of devices you might want them to act on is large enough that manufacturers can’t possibly foresee them all. When you want to do something ever so slightly outside the stock functionality, it’s helpful to have a little knowledge.

And let’s not forget, it’s helpful to be able to augment smart devices that already exist to do things like this rather than throwing them out and buying a newer one that can do it on its own.

Technically just the D component :)

But that's part of the problem - not every school system lets you really choose a lot, and more importantly often does not let you choose to not take certain things, often with kinda arbitrary categories. (Speaking of the German school system here, the amount of bullshit I had to learn is astonishing, and I definitely didn't want to get rid of math or history)

The problem with this is that the first classes in calculus are usually focused on continuous functions, which don't really exist in statistical datasets. The math has a lot in common, but most people don't really see or use that to their advantage, as evidenced by the literature on "transfer of learning".

Your experience is what I think of whenever someone discounts a liberal arts education. It seems like the perfect second degree!

I think the kids are also misled to a great degree. They basically told us if we'd want to go to uni and go for a STEM degree we should absolutely, totally do the focused math courses etc.

When I arrived for my CompSci they basically said: "We'll leave what you already learned in math behind around christmas (so after half of the first semester), no matter what kind of math you learned before".

I can't 100% grade both judgments, but I did not take the advanced math thing, but if they hadn't said these (apparently) completely wrong thing, I 100% would've taken French at school. (Which is another problem I'll not go further into, some fixed tracks of what path you need to choose in which grade)

> Now I don't feel like a well-rounded adult, and I wish I spent more time when I was younger on music and humanities.

Easy remedy. Learn an instrument. Find someone local to take weekly lessons, and practice several hours a week. If you never did this before I think you will be overjoyed by how well you play with consistent practice.

Good luck convincing anyone here that they might be acting a little arrogantly.

I find teaching history essential. It helps understand the present, why things are as they are, and avoid repeating mistakes.

I had many different teachers with different approaches. Ones it was all about memorizing events and dates. Of course that is trash. But others is was about understanding why it went the way it went, why not other way. What were the key events that triggered another events, under which circumstances... alone the critical thinking that went into that, is every minute worth it.

Introducing kids to hobbies they might enjoy is good. But the fact that we teach them upper-class hobbies, and only upper-class hobbies, in school, suggests we're not doing it solely for their benefit.

How do you define "introduce"? When I went to school I'm pretty sure I had to take the music subject for around 10-11 years. First we had to learn the flute (no singing), then our third class teacher was shocked that no one could hit a not when singing. A little later it was a mix of good and bad, but mostly getting grades for singing, without ever properly being taught anything (not talking about the first 2 grades here, also ever onward, in a class of 30) and then some mix of tests on musical history.

The outcome? I still enjoy music despite this torture of lessons, but I never properly learned to play an instrument, and was mostly dissuaded instead of encouraged.

I would rather analyze deep finance than listen to music. I just don’t enjoy music, at all.

Spreadsheets and algorithms on the other hand I find highly entertaining. I love many board games for this same reason: it’s an opportunity to build novel algorithms in strange domains to achieve a specific purpose.

And most can see that boardgames are more similar to “productive things” you find disdainful than music.

You're welcome to introduce your kids to all kinds of things, but more people end up in prison than with record contracts.

History in Austria is 2 years about how Hitler was the bad guy and Austria had zero fault in WW2, was essentially forced into everything.

We all knew that's not the truth. The teacher knew, but that is what the text book said so we learned it.

My point is, while history is important it shouldn't be a marked lesson where you just have to remind right and wrong facts.

We are subjected to the law everyday and we all need to know about money to support our addictions to food and shelter.

That’s an interesting idea, but I’m not sure people who have leaned game theory in an academic setting actually apply it to their lives. This would be evidence of ‘transfer of learning’, which is alarmingly uncommon. If the students did manage to benefit from learning game theory, I’d support it being added to the curriculum.

The problem with this way is that calculus is needed to get through, like, a basic engineering degree, I assume economics if you are doing it with any rigor. I suspect these aren't like careers for the top 1% braniac kids, they are normal B+ student fields (I mean I know everyone gets straight A's in highschool now, but you know what I mean).

Do you want to tell a parent that their kid has already decided not to design rockets?

Funny as that comic is, it's very unclear at a young age, and even when they're a bit older it's far from obvious. Even at first degree stage, some of the apparently best qualified teenagers who turned up for their first classes this week are going to flunk out anyway, and some of the kids who struggled and seemed like they'd be lucky to get their degree will be potential Fields Medal winners in 10-15 years. Their prior record, even now they're adults, is at best somewhat predictive and nowhere close to definitive.

Anyone who does a STEM degree?

I mean, if you're an engineer and you don't know the relationship between position, velocity and acceleration - you're going to have a bad time.

Nobody, but can they do whatever math they actually will need without first learning that?

I have no idea. So I will gladly defer to those who do understand math, and be glad someone does, or my career wouldn't exist.

Fair enough, but language history certainly didn't make them any better at it. And memorizing details can be a lot harder and thus more demotivating. It surely can't get much worse if they actually tried teaching kids to write better non-prose.

Do you really think doctors don't understand, or never learned, exponential growth? I knew a bioengineering student at Cal that was pretty smart and barely made it into med school. They had to go to a DO school instead of MD. So unless the bar for doctors used to be much lower than it is today, every doctor 'knows' what exponential growth is.

Whether they apply it to the real world is another thing.

I know people that don't think raising the minimum wage basically just causes inflation. They're just wondering why apartments in undesirable areas became 3x more expensive when minimum wage went from $5 to $15.

My discrete math professor always made the problems involve food. Because college students are always interested in food, he said.

This assumes most people care about making optimal financial decisions. They don’t.

The many, many people, including those in government, who clearly didn’t, prove that you’re an outlier.

That's certainly possible, even without self-learning. The topic is explained in precalc, typically. But it's important enough that I think going further is helpful.

So, I don't mean to force you into something you don't want, but do you think people who don't understand exponential growth are missing something relative to you? That they could benefit from the knowledge you have?

That's what I know having understood calculus to those who have bits and pieces of the concepts (exponential growth included) but don't have a big picture. If you have the time and ability to learn more, why limit yourself? Why allow yourself to be put at a disadvantage? And worse (not saying you are, it's hard to gauge from your comment) why would you be in favor of stiffing other people from being better?

I hope you do realize "discrete simulations" is an application of calculus (analysis really). The "continuous" version of calculus is a special case. Sure though, this is a problem with the way calculus is taught (too much focus on symbolic differentiation and integration, although that becomes valuable somewhat if you become a physicist or engineer, primarily).

> But the GP wasn't arguing against claims that calculus is useful.

So no clue who GP is. Grandparent is my best guess. And with respect to you, that would be the guy I was responding to, but that couldn’t possibly be correct because he said

> rather than sitting on your butt learning a useless subject

From context, inferred to be calculus, esp because

> took me 3 semesters of Calculus to figure out that it was useless to me and 90+% of the people that take any of it

Soooo… who is GP

> I really don’t see the connection with programming

It may just be the stupid way my brain is wired. When I think about calculus I can’t help but also consider programming, and vice versa. Okay, Calculus is not a precursor to learning to code. But the DNA of calculus is definitely there.

First, how building blocks of programming and calculus are similar.

1) We can probably throw out the control flow concepts, although they vaguely map to the notion of intervals on evaluated integrals.

2) I said for loops are a generalization of Leibniz notation. I also said it’s a rough relation. You said you don’t see the parallel because you claim pure maths calculus deals with reals and computers are discrete. Yep. Real numbers are discrete at the infinitesimal limit (grab your torch and pitchforks). I hope this is enough explanation on that front. Loops roughly = integrals. It’s purely theoretical. I get that you can’t actually represent an infinite precision real using bytes.

Next, algorithms.

1) I think there’s another very loose but valuable perspective in which calculus and efficient algorithm implementation at least shop at the same grocery store, if not fool around on the down low. I can imagine every possible implementation for solving the knapsack problem as being distributed in a higher dimensional space. There are a ton of bad ones out there with dogshit runtimes. But somewhere near the middle is one that goes zoooooom. That’s an optimization problem—that’s calculus.

2) And then within solving a problem itself. The *good* solutions make use of derivative-like notions. Properties about the problem which you use to solve it efficiently are effective pseudo-derivatives. The way that you can use a derivative plus a point to approximate some next point forward, you can use problem topology plus current state to improve state a bit further until you converge upon an “answer”.

The list goes on.

Calculus is in programming and programming is in calculus. They are cross-pollenated dialects of the mother tongue of the universe.

Economics, Statistics, ML, Engineering all use calculus. You might be able to get by in some areas without it, but it's not as if it's useless. It's also really easy and straightforward. You would create calculus if it didn't exist.

There are going to be people in the world that are capable of reading things like an ML paper and there are going to be people who are not. Calculus (or other advanced mathematics) is part of what you'll need to understand those papers.

If having the ability to read such papers and understand such concepts isn't something you want for yourself then you definitely shouldn't take advanced mathematics courses. However, many people see the ability to understand those types of things to be a useful skill in giving them opportunities in the future.

From the general population? Not that many.

From this site? I'd wager a significant percentage.

Here's maybe a more generally relevant example: Have you heard about this thing called inflation?

"understand any modern ML paper"

I believe 7 people read an academic paper on average. (1 of those is a mother).

The flipside is that all the well renumerated jobs are very mathematically intensive.

Finanance, technology, they all are.

How is having that knowledge any different to if you knew the mathematics involved in the building and launching of the rocket?

Knowing that didn't help you at all. If you didn't know about Hydrogen that rocket still would have launched. It's purely for your own interest.

Unless you're a SpaceX engineer of course but then the other 99.9% of the people on the planet don't "need" to know about the size of Hydrogen and we are back to the same argument.

Just above, you wrote:

>Ok, given the number of people that take Calculus, how many will ever read an ML paper? For that matter, how many even know or care what ML is?

..and now you, apparently without joking, assert that the physics info is different because it's necessary in rocket science, the one thing that is colloquially used to describe knowledge that normal people will never have to worry about?

Ah yes, I too design rockets on a daily basis.

> Here's an HW case about why knowing about Hydrogen will help in life.

*proceeds to give an example only applicable to rocket scientists ...

I think you accidentally disproved your own point.

There is a parallel in college physics. Typically, most colleges have two tracks: "Calc-based" and "non-calc-based" physics. Everybody finds the non-calc-based course to be an utterly bewildering exercise in memorizing formulas. Even the calc based students are baffled by it. The calc based course is widely regarded as easier and more intuitive -- if you also take calc.

Stats is the same way. I was a math major, and my college had two stats tracks: "Math stats" and "stats for scientists." The first track was 2 semesters, and we had to prove everything. Of course we used calc. The second track was 1 semester, and was an utterly bewildering exercise in memorizing formulas.

I took "math stats," but was then asked to run the discussion section for "stats for scientists." There were things that were utterly intuitive to me, but that I couldn't satisfactorily explain to the students, such as the need for different formulas and methods for discrete and continuous distributions.

Freshman economics. The professor bent over backwards to make sense of the formulas related to things like the supply and demand curves, because he couldn't use derivatives. Also, it was 1982, and yes, the professor showed us the Laffer Curve.

> Have you people actually taken a basic statistics course that doesn't require calculus? They are all about memorizing formulas that you plug numbers in to calculate different statistical measures, they don't teach you to understand anything at all.

Disclaimer I should have included: I personally took statistics in high school instead of calculus.

I can't say what my experience would have been like if I'd known calculus, but loved learning statistics. I don't remember exactly what we did, but I recall it being quite conceptual. Certainly not just a ton of formulas.

> since kids can easily understand it

Maybe with a good teacher. I took calculus courses in high school and college and came out clueless. I could manage the rote work to complete the course, but the big picture was left blank.

I revisited it later in life as an adult and gained a fuzzy picture, but it is still not well defined in my mind. According to many comments here some mathematical concepts I am well versed in and use regularly, if not daily, are calculus and that surprises me as they don't seem like anything that was presented in said classes.

I dare say that calculus has a marketing problem.

Probabilities under normal curves or any shape probability distribution function are measured as areas under the curve. It helps to have an integral calculus intuition for comparing p(0.1<x<0.5) to p(0.5<x<0.6). It helps to have a multi variate vector distance interpretation of length for error and variance magnitude.

> Yes, a statistics course is so much more useful. It's not emphasized in school but it will truly help through out your life if you understand it.

I think this may be based on an impression of what math coursework used to be. A statistics course is a very common, if not required, part of any modern mathematics major.

There are a lot of people in these comments saying, "this thing is more important than calculus" and it turns out it's a concept that is fully fleshed out in analysis which is just calculus essentially. I feel like the problem is calculus as taught focuses too much on algrebraic manipulation which is only useful essentially if you become theoretical physicist and little else while the "why" behind calculus leads you to a lot of more useful results that are along the lines of approximation and optimization, which is closer to what a modern understand of analysis is.

I learned it as part of "operational research", that was some algo-y math course. No idea if that translate. But yeah, definitely closer to calculus than stats or proba.

I think the argument was that a calculus based approach to understanding those subjects dramatically improves and enriches the study of those subjects.

> In primary school for example, we learn maths by memorising times tables and solving thousands of basic arithmetic problems. This was important in a time before calculators...

I used to think like you on this point, until I taught students who were brought up using calculators instead of memorizing multiplication tables, etc. It turns out that many of them could not figure out how to use calculators when needed--they didn't know what to enter because they were rarely required to do any mental math. It's really important for elementary school students to count out loud (including by 2's, 3's, etc.), and count backwards, and memorize multiplication tables, etc., so they are comfortable and confident doing basic arithmetic. Calculators are for people who already understand how to do arithmetic.

Be careful, it sounds like you're describing Common Core Math and several states made that illegal

Reminds me of a sci-fi short story where the military leaders against an alien (?) invasion keep demanding "harder and sharper" human tools for the war. Finally they need a poet and find they don't have any any more.[1]

Though I think that the way classical literature is taught is probably enough to sicken all but the most die-hard readers. Endless dissection of things on a word-by-word basis. Shakespeare (say) wasn't a godlike superhuman imbuing every single word with dozens of layers of meaning. Sometimes it's just a fart joke.

Exactly the same as maths teachers drilling integration rules to death and having everyone conclude, not unreasonably, "this is pointless bullshit". Or history teachers listing dates and names.

[1]: edit: not aliens, and it's by Alfred Bester: https://archive.org/details/New_Worlds_029v10_1954-11/page/n...

You're welcome to explain why you disagree with the OP and what true value can, in your view, be derived from studying classical literature.

I likely agree with you, but if you're just going to make a vaguely disparaging statement in the negative without elaborating or contributing to the discussion then you really might as well not comment at all.

But for these things they are often really quite uncontroversial. Are you calculating the weather by hand to confirm NOAAs numbers? Definitely not. In the end you have to put trust in things you don't understand, because you can't learn the exact underpinnings of each and everything you face in life within the span of one human lifetime.

I agree with this 100%. The insight into Calculus that we get in high school is pretty fleeting, but you do at least get to see the ingredients that go into things like weather reports. Otherwise it just becomes a magic black box. Maybe it doesn't work for a lot of people, but it just has to stick for enough people that we can continue to tell magic apart from science at the society level.

>knowing that y'' = y is a positive feedback loop (exponential growth) but y'' = -y is a negative feedback loop (oscillating) is really useful in all sorts of common sense scenarios.

I'm not sure what sorts of situations you keep finding yourself in, but I think they're pretty atypical.

But then why not just take these things in college, when you major in electrical engineering and are taking all the other highly specific classes for your field of interest? It makes no sense to make someone bound for e.g. a career in the arts to suffer through calculus. You could replace that time sink with something more productive and generally useful, like learning to program. Now you can make a website for your art portfolio without having to pay a webdev.

> To be fair, rote memorization is one of the most improtant and transferable cognitive skills you can develop.

To say so is missing the whole point parent comment is trying to make. Memorization is an important skill, that is one thing but saying memorizing random stuff to build that skill is entirely a different claim. I bet there are better ways so learn and hone memory skills than memorize history place/time/dates and kill a student's interesting in learning.

Former yugoslavia, then slovenia... I had to know every goddamn date and every goddamn village on the exams. And ok.. WWII was the start of the socialist yugoslavia... but I had to know the same for napoleon and the french revolution, and he barely passed here. Franco revolution, the same.. and soviet one too. Also a bunch of caesars too.

Geography was the same... ok, countries and capitals.. sure.. but a bunch of mountains and rivers and streams, where exactly the source is, and where and into which river it flows into... not just the major ones, even the crappy minor ones. Also stuff like, what is the greatest export of nigeria and other countries that are far enough, that I didnt need to know.

Of course I forgot all of that data probably days after the exam, and never cared for 99% of it, and googled the last percent when needed.

I graduated HS >20 years ago and did not have to memorize a single date in HS history. We did need to know the general ordering of events though. For example, we had to know that the Munich Agreement was before Pearl Harbor, and that the Korean War was after WWII, but it's hard to know anything about these events without knowing that.

OTOH I know people my age who went to different schools that had to memorize things like the exact date that Lincoln was assassinated, so there's definitely disparate pedagogy.

Most people can’t do more than the simplest derivations in their head, the symbols are just a notational placeholder, and also used to communicate with others.

The abstraction is the what you have to have a knack for, not the symbols themselves.

“Young man, in mathematics you don't understand things. You just get used to them.”

—John von Neumann

I’m sure there’s room for improvement, but intuition and understanding are usually the result of repetition.