They shouldn't teach calculus like they taught it to me and my peers. Basically we just one day started "differentiating" equations. We learnt a completely mechanical process. Like how to chop an onion, except it doesn't actually feed you or taste delicious.
It took me a while to realise the point. It's all about rates of change. They should start with that. No need to bother with the maths, just look at graphs and be like "that's a steeper slope than that", and, ooh, that one's sloping in the opposite direction. This is a fundamental intuition that's so useful to have. Most people don't understand that braking is acceleration. They just don't have the mental model that lets them see fuel burn and braking as opposite things. The sooner this intuition is there the better. Then teach the maths.
> They shouldn't teach calculus like they taught it to me and my peers. Basically we just one day started "differentiating" equations. We learnt a completely mechanical process.
I had a similar experience and it did ruin the fun in Calculus for me. It took me a long time to derive a bare-minimum mental model that I was satisfied with. It was at this point that I could 'feel' (imagine) how the general second-order linear differential equation (of two variables) works, without the need to 'calculate' or derive anything. This equation is the fundamental model for countless phenomena in the universe. It's such a shame, because that equation is easy to explain in words, without doing a single step of derivation.
Don't get me wrong. Formalism and rigor do have very important roles in Mathematics. But ignoring intuition and emphasizing formalism doesn't get you anywhere. Intuition isn't always right, but it shows you the 1000ft view of the problem when it does get it right. Formalizing the solution gets easier from there.
I have noticed that even professionals are taken by surprise when I convey the descriptive explanation. It shows how badly these things are taught. (I don't know if this is the situation everywhere.)
> The sooner this intuition is there the better. Then teach the maths.
Yes, that is exactly what I was suggesting. However, that 'intuition' is also part of Mathematics. Many practitioners call it the 'Mathematical sense', as opposed to common sense. You might have seen a rare few gifted individuals who find the correct answers to unintuitive and confusing problems (like the infamous Monty Hall problem) in their first try. They're employing this mathematical sense while the others revert to common sense. Who knows? Even you may be using it and surprising others without realizing it.
Unfortunately, our educational systems have reinforced this misconception that Mathematics is all about manipulating numbers and symbols (for many, even the idea about symbols are missing). This is a very sad situation that just sucks the life out of mathematics. A long essay (book) by Paul Lockhart, named 'A Mathematician's Lament' explains this problem splendidly.
PS: Funnily enough, I always struggled in and hated mathematics! Others were so good at applying long sequences of operations to get to the answer, while it was Chinese to me! (No offense intended here). But I was good at science. I relied on countless diagrams, tables, concept graphs, signal flow graphs, etc in place of equations and formulae to achieve this. I just converted them to equations and formulae whenever I needed to reproduce those. I thought, "Who needs mathematics when you can reason your way to the answer?"
It was close to the end of my formal education that I realized that every reasoning that I had done in my life was proper Mathematics! I had strong autistic traits and following numerous steps in sequence and in parallel was near impossible for me. But where I made up for that was in spatial intelligence. I had created book after book of Mathematics described in a visual language that I could digest. I didn't really hate mathematics. What I hated was the way in which it was taught and represented.
Learning Mathematics has become a whole lot easier and enjoyable after realizing it and embracing the fact that I needed my own ways of doing it. But honestly, I wish that so much time wasn't wasted in needless frustration.
My partner and I share everything we eat. I think we have passed food between chopsticks before. What's the "proper" way to do this? Just reach in to the other bowl?
Also wondering how many of these apply in a Chinese setting or any other chopstick culture. Are there a different set of taboos?
You are essentially a child to them. A child is just someone who has not yet developed the power to survive in a world full of adults. This is why parents guard and protect children, and when that fails society steps in to do it instead.
You are just a child to them. Not powerful enough to stick up for yourself. Ripe for abuse. The difference is society has decided not to step in to protect you from your abusive parents.
I use this. I run it in a sandbox[0]. I run it inside Emacs vterm so it's really quick for me to jump back and forth between this and magit, which I use to review what it's done.
I really should look into more "native" Emacs options as I find using vterm a bit of a clunky hack. But I'm just not that excited about this stuff right now. I use it because I'm lazy, that's all. Right now I'm actually getting into woodwork.
I was always wary of uv being written in Rust. Even if we can make a community fork, how big is the intersection between great Rust developers and people really into Python packaging and infrastructure? Not big, I would assume.
I do wonder if we should just rewrite something in Python, but make sure it runs with pypy. Pypy should give at least similar performance as Rust but being still regular Python means there is a far bigger pool of devs able to maintain it.
Astral has shown us the way, but I think it's time to take control of our own destiny as Python devs.
It took me a while to realise the point. It's all about rates of change. They should start with that. No need to bother with the maths, just look at graphs and be like "that's a steeper slope than that", and, ooh, that one's sloping in the opposite direction. This is a fundamental intuition that's so useful to have. Most people don't understand that braking is acceleration. They just don't have the mental model that lets them see fuel burn and braking as opposite things. The sooner this intuition is there the better. Then teach the maths.
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