The “when are we going to use this” question is about when “we” ourselves will directly use it - not when we will use something that uses it.

I don’t have to use any calculus to get a weather report, etc., because other people do that for me and give me their results - it’s part of their job.

Calculus is indispensable and is used in our everyday life - but most of us won’t use it ourselves, or need to know the specifics, or really even know the broader parts of it.

> The “when are we going to use this” question is about when “we” ourselves will directly use it - not when we will use something that uses it.

You don't have to use it directly for it to be useful.

Having some knowledge/experience with it means you can assume a level of trust in the result of a system that uses it, even if you don't touch it directly.

If you don't it's either blind trust (which requires quite a leap of faith) or, more probably, distrust.

By and large, there's very little of what we're taught (whether it's math, or logic, or science at large, or literature...) that we use directly in our everyday life. Nonetheless it helps build an internal compass that helps us eyeball/gut feel what we can trust or not trust.

The growing distrust in recent key events (climate change, covid...) is largely due to that compass being broken, and to me that's in good part due to a failing of education systems at large.

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.

You probably don't need to know how to compute a derivative, but there are tons of related concepts that are helpful for reasoning about systems in the world. You can always Google the chain rule, but having a general sense of the trend is often all you need.

For example, you don't have to remember how to derive it, but 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.

Learning is about concepts more than facts or algorithms.

>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.

positive and negative feedbacks happen in climate systems and economic systems.

if you want to have a chance of understand the economic news it is a good idea to have familiarity with them.

Oversimplifying leads to confidently wrong predictions based on superficial understanding. Basic intuition about differential equations doesn't meaningfully help you with the math of economic models, nor is math alone enough to understand what happens in a complex system made of people.

You may be better off not knowing anything and knowing that you don't.

Edit: Not to say it's good not to know things in general. Just that there's some minimum you need to know for it to practically help you, and sometimes it's a lot.

Zero knowledge doesn't prevent anyone from being confidently incorrect (in fact it seems to encourage it).

That's true. But if zero knowledge doesn't help, and a little more won't either, then why make people suffer to acquire that little bit more?

Which I guess just brings us back to the top of the question. My bad.

This is like saying we use quantum physics every day of our lives because physics. It's true, I guess, but you don't have to know anything about quantum physics and the vast majority of people don't need to know anything about calculus.

It's also clearly not the reason we are educating children in calculus. We can know this because we don't teach children to do weather calculations, we don't test them on statistical analysis, and so on.

The real reason public schools teach calculus is that they started doing it at some point for some reason and then never quit because they are bureaucracies resistant to change. All the people involved have a kind of status quo bias preventing them from saying "yeah, I guess that was useless, let's teach something else."

If I'm wrong, we could imagine a test. Take a comprehensive calculus exam from senior year of highschool or freshman year of college. What grade do you think the average adult would get on this test? How about top ten percentile adults for intelligence, wealth, or whatever? If, as I do, you think the average score would be F, can you explain why it's important to teach the general population of kids something that the general population of adults demonstrably do not know?

You can use all of these things without you personally knowing calculus. The point of the question is that it's posed by the people who aren't going to go on to create weather reports, credit card payment systems, video games, etc.

Except the kids taking high school calculus likely ARE going to do those things one day. Maybe not all of them, but some.

Heck, I don’t use calculus directly in my daily life. But I’m glad I took it because I recognize where it is used, and how, and that helps me understand my world better then without.

> The point of the question is that it's posed by the people who aren't going to go on to create weather reports, credit card payment systems, video games, etc.

I don't think so. If you're in high school and you ask this question, you surely do mean something like "what activity will I possibly doing in my future career that would require calculus" and in that case the answer that you may be a financial analyst, a meteorologist, an electrical engineer, etc. is right on. It's exactly what kids want to know.

But now there's this myth that "you won't ever use calculus in real life" which is totally wrong.

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.

> productive and generally useful, like learning to

to reason.

it would be great to teach people critical thinking. at every age, at every year.

applied epistemology, rationality, etc. of course no need for those fancy words.

... and during those lessons at one point they could learn about the usefulness of models, and the usefulness of math, money, programming, etc.

but otherwise there's no point in ramming math/programming/finance directly into the heads of kids.

If the goal is to teach reasoning then I think most 101/102 level calculus fails at that. For most students (including mine when I took it), their experience is just getting through generalized homework problems or an exam than actually applying that calculus to test a scientific hypothesis. Reasoning is taught better in those sciences, such as physics, biology, chemistry, or statistics, where you are explicitly developing and testing a null hypothesis. Maybe replacing calculus with statistics in high school curricula would be a lot more useful, if the goal is to teach reasoning and critical thinking.

I think math in general fails at that. After all it's just one tool in the big ol' cognitive shed.

(This is why I think the recent brouhaha about California changing some requirements completely misses the point... but meh. Education is like healthcare, completely broken and fucked in all the ways it could be.)

I would argue that saving money and personal financial planning uses calculus concepts, and that they are enhanced by formally knowing calculus. It makes questions like "how much money will i have after x years given my mortgage, income, and assets?" approachable. It isn't feasible for most people to hire a human financial planner, and i wouldn't want to use automated tools without understanding enough to be able to perform sanity checks.

Maybe we can try, "you have to learn calculus so you can land a job that lets you pay for things & services that handle calculus for you, so you never have to think about it again".

... except most of those are cheap. So. Hm.

> I'm sad to see this because we literally do use calculus every day of our lives. We just don't often recognize it. The weather report is made using calculus.

This is like claiming David Beckham uses advanced physics to kick his free kick.

Calculus is important to the world, sure. But it's not important to regular people to spend time and money learning it. In some cases, these people take out student loan to learn calculus which doesn't help them pay back the loan.

> This is like claiming David Beckham uses advanced physics to kick his free kick

David Beckham is in a highly-specialized field (professional soccer player) and this is about things everyday people use, so I guess I don't follow the analogy.

The problem with this is that people don't really retain information like that. College is 15 years in the past for me and I'd bet that if you handed me every exam I took in college I'd flunk everyone of them. And probably quite badly too. I'd wager most people are the same. So how can it be so important if we all remember so little.

I would argue its an even bigger missed opportunity not replacing calculus with programming classes focused on using a cli and writing scripts to do work with the computer. Like it or not people get by fine in life with abstractions of more complicated things, but I think having knowledge of programming is akin to learning to read in terms of the potential it can unlock that can be relevant to every career there is. If programming became widely mandated into the curriculum, we would probably see a lot more interesting technologies and applications of existing technologies emerge in the coming decades in places you wouldn't even expect, than if we pressed forward with forcing calc down everyone's throat in high school and making them hate math for life.

The issue is that calculus in itself with symbolic algebra is next to useless for average person. However intuitive concepts, like area under a curve, are not.

I "solve for x" all the time, though, admittedly, outside of work, it rarely gets more complicated than a simple expression with a fraction or two.

However, what is aggressively useful is dimensional analysis. When I'm doing a calculation and need to quickly check that the formulation is right, checking the units works every time.

You don't use it in those cases, you get what you need from someone else using calculus. In the same way you don't use cooking when you go at a restaurant.

You also can't live in that world without knowing meteorology, computer graphics, animation, and, well, all of manufacturing. Yet, we aren't suggesting to teach all of those things to every people now are we?

You’re getting a lot of answers about how you don’t need calc to use things other people have made with calc. This turns the answer into “so that you can avoid weird mysticism about how the world works.”

If you don’t know how other people made the things you use, then 1) you’re pigeonholed into being totally dependent on them, and 2) you’re likely to get all sorts of weird beliefs about how the stuff you depend on works (like crystal healing/homeopathy/etc in the bio realm).

Totally! Reminds me of Foundation by Isaac Asimov where scientists turn into the equivalent of priests in some cultures.

That's like saying you use general relativity because you own a GPS. Understanding general relativity is only useful for the people making the device, not the people using it. You don't need to be a mechanical engineer to drive a car, a biologist to have children or a mathematician to use a credit card.