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Comment by striking | Hacker News Reader

I think a lot of the time it is just too abstract to grasp. I think the first time in my life where I was really happy to have learned calculus for my own intrinsic benefit was a few weeks ago, when I set up Home Assistant in an effort to automatically minimize heat in my apartment. It wasn't enough to tell the shade to come down at a certain temperature, because the apartment would already be too hot. So instead I could take the derivative of the temperature of my apartment, allowing me to get out ahead of the worst part of the blast of sun. After all, if the temperature is increasing very quickly, we should act to stop it.

I've used a decent amount of calculus in my life, but that was the first time I had been actually happy to have learned it.

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The real way to motivate someone to learn a thing is to give them a project or something they actually want to achieve instead of trying to absorb some drivel without a reason why. That's where self learning shines. You give a great example there. A notable one of mine would be learning vector math and quaternions through trying to make games years ago, but the list is endless and not limited to math or physics.

Most teachers and professors just parrot their subject material year after year after year without EVER giving a reason what any of that is used for or where should we apply it. It's just learning for learning's sake.

I suppose it's no surprise that when people are finally given the option to learn in a practical way at the odd subject that allows for some project work most students can't seem to think of a damn thing they want to do. It's like a systematic suppression of creativity to make education more like a factory production line.

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)_/¯

Yeah I mean I don't really see how we could practically make this approach work in a standard classroom, but the idea that CGP Grey presents where each student would have a sort of AI-tailored personal curriculum (or "digital Aristotle" as he calls it) would potentially allow for it, since each student then gets their own interests turned into projects they can work towards (and still learning the same concepts) while the group teacher is mainly there as an observer and helper.

I think if you put together an entire class of completely different projects that all somehow end up teaching trigonometry it would also help show everyone all the possible applications for it when discussing afterwards. I never would've guessed trig is used in audio for example.

If you hadn't learned calculus or what a derivative is, do you suppose you would have eventually figured out to measure the change in temperature and respond to that?

I wonder how much of the value of the course is just in the repeated observation that the rate of change (and so on) is useful to measure

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.

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

Erm, in some abstract ways yes - but actually people are very good at extrapolating current physical events. "It is getting hot fast? Oh not, it might even get hotter, lets look for shade."

Or throwing a ball. You would need calculus to correctly calculate the flight path of the ball, yet we can do so, without and very fast.

Where our intuition fails often, is understanding the reason why things happen. For this physics and math should be taught from very early on.

We are (on average/intrinsically) terrible at predicting or even guessing how certain things will behave. A lot of times when you learn something like say skiing or diving, a major part of training is to untrain your brain from guessing incorrectly how things will unfold/what is the appropriate action. Try recovering a plane from a stall -- you might be able to guess why something happens, but you have to fight your brain to aim the nose of the plane down. (Again on average.)

We humans optimized for everything related to our body movement.

Of course we have no intuition for how planes behave.

And with Ski and co. I would argue it is somewhat intuitive, it is just a new tool that needs learning. But I do not remember learning ski or snowboard felt unintuitive. It was just hard coordinating it, but this is not unlearning to me.

> But I do not remember learning ski or snowboard felt unintuitive.

I struggled for years with 'keep your weight on the downhill ski'. When I realised that it sort of meant 'lean downhill' turning on steeps suddenly became a lot easier. This was counter intuitive in that when I turned on a bike, I was invariably leaning in to the turn, not out.

It was actually learning to skate on skis that helped me make the transition to better turning.

I only ever really got into calculus when I decided I wanted to know how AI worked—I'm a strong believer that academic learning needs to be motivated or it simply won't benefit most students.

It's called a PID controller.

It seems like this is a solution that should have been baked into the smart device. For example, the Nest thermostats preempts your arrival home and commences toward the desired temperature.

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.

You invented a PID controller! https://en.m.wikipedia.org/wiki/PID_controller

Technically just the D component :)

This is my favourite part of PID controllers, you can just arbitrarily not implement bits of them and still come out with something that approximates what you need. (Or endlessly oscillates around what you need ;) )

I bet that P is still in there too!

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