Comment by 1-more
11 hours ago
> We'll be fine, your children aren't you, they'll find their own passions.
There's an Unschooling group on Facebook I watch. If you search "calculus" you get threads where a parent asks how their kid is going to learn calculus and the answers are mostly "when did you need calculus after high school." Aside from needing it for college, my answer would be "why am I raising my kid to be a 1:1 clone of me and not someone with a lot of different options." So I dig this as an answer. The world has ended a billion times already. People who work hard pursuing a skilled passion have never been obsolete.
Calculus is entry level math for all the hard sciences, engineering, and finance. It's how to think about how things change over time. Understanding what integrals and derivatives look like, especially as graphs, is very practical knowledge. Being able to think about compound interest and acceleration under gravity as driven by the same rules gives an understanding of what's happening underneath.
Whether the infinite-series summation limits are worth knowing is questionable, though. That's more of historical interest.
(But then, I once did a game physics engine and have a patent in that area. I spent a lot of time in the hell which is integration of stiff systems of nonlinear differential equations. Turned out that was the wrong way to approach the problem. Works, but there are better approaches.)
My grad program had an advanced math sequence that was traditionally numerical methods for solving PDE’s and boundary value problems. Except my year, a visiting professor made it infinite series solutions using laplace transforms. Because why would you want an inexact numerical solution when you could have an exact solution to whatever degree of accuracy you need. Line integrals have their own special place in hell.
> Whether the infinite-series summation limits are worth knowing is questionable, though. That's more of historical interest.
A very common example is compound, continual interest accumulation. As a mathematician, I had trouble understanding how banks calculate it (as they would obviously not point me at the derivation of the formula), but it's actually a limit sum over infinitely small interest terms.
Similarly, these techniques work to explain and derive numerical methods for calculating many natural constants like e, pi etc.
The only intuitive definition of e I can remember is "how much $1 becomes after a year in a savings account with 100% interest compounded infinitely" funny enough.
1 reply →
Where I live, the banks say that they compound interest daily, but pay interest monthly. So, I think the small interest term is just limited to a day where the error is small enough for the average person to not care.
Right? Just because my professional career never took me in those directions doesn't mean I want to foreclose them for my kid! I did do electrical engineering classes in college wherein I needed calculus, I just never took a derivative/integral after graduation because I ended up on the coding side of a Computer Engineering degree.
i hope i don't get downvoted for this, but billions of people function just fine without the most rudimentary understanding of calculus. while i love maths, i am sympathetic to the view that it's not an essential life skill, and might even be less so in the future.
It's interesting to see different perspectives on this.
For me, calculus was the first math I learned, where symbols represented something other than pure numbers or tangible points on a plane, and we proved things about higher level abstractions. Of course many of the topics had tangible applications, but it was a launching point towards further abstraction in the higher level math courses.
A friend of mine in grad school was a student in medieval church history, but was assigned to teach a freshman course in modern history. For one class session, he asked a math teacher to give a guest lecture on calculus. Then he lectured on its impact on society.
It's true that most people, including managers and engineers, forget their school math not long after school. Their software tools, such as Excel and CAD, can do the math that they need. One can hope without proof that a little bit of mathematical thinking rubbed off on them.
Mathematics is fundamental as it shows you there in fact exists a way to spot bullshit with no concern for however much rhetoric is used. Many people would be really and truly shocked to know we can definitively prove things given certain axioms, and not just have "wishy washy" verbal arguments or slogans. Without exposure to mathematical training, nonsense like belief in gods or supernatural thinking tends to increase.
The one-dimensional mentality of anti-intellectualism is absurd. I have heard parents outside of our school but in my community talk down French Immersion programs (versus English schooling) saying that people put their children in for the wrong reasons. I don’t know what the explicit reasons were in this case, but I am assuming that the other parent means academic overachievement.
Learning calculus or French can be beneficial, especially when the glass ceiling in certain workplaces is whether or not you’re bilingual. However, the point that’s getting missed is the metaexperience that consciously or subconsciously shapes the way the child interacts with the world later on.
Somehow I feel like the workplaces with a glass ceiling over bilingual is so small as to be immaterial.
Where I live (Oregon, USA) there are very few jobs that require it but a lot of jobs where speaking a second language might get you hired over someone else.
Most jobs that are focused on interacting with people benefit from speaking a second language if it’s a common language in your community: nursing, teaching, customer service, social work, etc.
I’ve seen job listings mention it as a nice-to-have and know bilingual friends who have gotten those jobs.
I only speak one language well but I wish I spoke more. I hope my son (and future other kids) learn multiple languages. But not for job/economic reasons: it just seems good for your brain and interesting for how you think about the world.
One example: I worked for an Alphabet company with some very, very accomplished people. When the drawdown on the project came, the people who were bi- or multi-lingual all kept their jobs. They were more useful in more situations for a multinational project. The 36 people let go probably wish they'd spent a little more time studying Japanese, Spanish or Norwegian.
I wonder. In my world, almost everyone I know is bilingual and I would not have met them and worked with them otherwise. So many of my coworkers are from countries where English is not required but they were fortunate to pick it up as a 2nd language for one reason or another and now work in a high paying company that requires English.
Still, I get, over all, the number is small. They could have all had a different career in their native language.
You never know if learning calculus will make you discover new things that you might like to pursue. Also, you never know if you will need it or not apriori. By that logic, you shouldn't learn anything until you need it, wich I think would be a disaster.
> You never know if learning calculus will make you discover new things that you might like to pursue.
Just as you will never know what you might have discovered if you used the time you spent learning calculus learning something else instead, of course. There is no magic formula to life.
> you shouldn't learn anything until you need it
Impossible. Simply existing as a functioning human means you are going to be constantly learning something. Not everything you learn will be useful, but that's also true of calculus. Not everyone finds it useful in the end either. You never know what will end up being useful, but you also can't learn everything.
The great thing about the curious mind is that you tend to be naturally drawn towards the things that are most useful for you. Those born most likely to do something with calculus already voluntarily choose to learn about it. You don't have to make them. The stereotypical druggy who has no interest in anything but getting high, who suddenly has his life turned around because you force him to learn calculus, is little more than Hollywood fantasy.
This framing doesn't fit my experience. Most kids, left to their own devices, would not learn arithmetic.
I know few adults that were forced to learn something as kids that regret learning it. Conversely I know tons of adults that, as a kid talked their parents out of being forced to learn something and as an adult seriously regret it.
3 replies →
The classic SMBC: https://www.smbc-comics.com/comic/why-i-couldn39t-be-a-math-...
Thanks for highlighting that your children aren't you! Easy to forget.
Learning what infinitesimals were and how useful they were for understanding the rates of change was an actual eureka moment for me, and many people in my classes felt similarly. It fundamentally changes the way you view things as simple as a car accelerating or the way heat spreads through a system, the way fruits spoil faster in the winter if you have heat, why metals creak when they're cold and why they groan when they're heated.
The thing that really begets me in all of this is that what you describe, working hard pursuing a skilled passion, requires a foundation of knowledge that up until a year ago was considered a foregone conclusion for becoming someone of note. It doesn't matter whether someone learned it autodidactically or through structured schooling, the point is that the knowledge itself is fundamentally important. We never stopped teaching children basic arithmetic or mental math when slide rules, adding machines, and calculators became widespread. The reason why is pretty obvious.
And yet, the technofeudalists want us to stop teaching our children critical thinking, science, arts, technology, and everything else that encompasses the indomitable human spirit, and why? Because a machine can do those things too? Machines have been capable of or better at a great many things that humans are also capable of for the past hundred years or so and yet we have never stopped teaching humans those very things exactly because we used to recognize that those things had enormous utility in general in a sphere far beyond whatever is necessary for your calling or profession. It is absolute lunacy to me that someone could see LLMs and agentic flows do brute-force proofs and then somehow suggest that the entire field of mathematics is obsolete.
I urge you to read the piece "Complex Systems Won't Survive the Competency Crisis." If we lose all of our institutional knowledge of how the puzzle pieces all fit together there will be no one to save us when (when, not if) the systems we're creating now suffer a catastrophic failure. And they will. Model collapse has not happened yet because of luck. Synthetic data can only get you so far. And whenever we enter our Idiocracy/WALL-E stage of total compliance and deference to machines themselves, one day there will come a time when something breaks and no one knows how to fix it because they no longer understand the underlying principles.
You might say in an optimistic scenario you can just ask the LLM for the tools and resources and prior knowledge needed to fix it. Alas in many cases, this is barely enough, and most on this forum are technically knowledgeable enough to actually make use of that advice. It's hard to see a compliant, totally intellectually decrepit population doing the same. I'd also advise you that although unschooling has its benefits, it's a movement that is filled by those who are often cultists and other fringe hacks who have grievances with the school system for reasons unbeknownst to me and many others. I would not use them as any sort of advice forum or channel for meaning, and the fact that you seem to be taking them as gospel is extremely questionable and makes me uneasy about the future of this forum in general.
i mean even basic differentiation is useful for optimization problems.
Not to mention physics, which is useful for understanding why things are the way they are. Which, is an important skill lest you fall into anti intellectual traps like flat earthism.
Calculus is a shared language in the grand universal ocean of intellectual cultural. Rejecting calculus is rejecting part of that culture…
Yeah, for me the real click was in AP Physics where we derived an equation for some motion property rather than just being handed the formula as I had been in, say, 8th grade science. The meta lesson is that you can use math to get more information out of a model than you think you have, which, yeah, keeps you from becoming a 5G get the facts style individual.
1 reply →
I’m not sure there’s enough overlap between physics and calculus to justify calculus. That might mean you can’t derive physical equations yourself, but no one needs that who isn’t becoming a physicist.
3 replies →
I think their answer would be "why would I care how long it takes this ladder to slide down the wall?" Which STINKS don't get me wrong. This is not a group I take seriously.
Here is an example of a practical optimization problem:
A factory needs to produce 12,000 components per year. Each production run costs $300 to set up, and storing one component costs $4 per year. What production quantity Q minimizes the annual setup and storage costs?
1 reply →