Thing I wish I had understood in school: a wave is a periodic, differentiable system. A periodic system is a loop. Differentiable means the states are approximately continuous (you can fit a curve to them). A smooth wave has a differentiable derivative.
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Replying to @Plinz
my undergrad physics prof tried to hammer this into my skull in 10 different ways and I just couldn't see the forest for the trees at the time! I think more and more these days about doing some continuing education math courses now that I might be able to properly understand it
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Replying to @danlistensto
So depressing that we need to get THAT old before we begin to understand math.
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Replying to @Plinz
I think the distance and time need for me to think about it on my own, without the pressure of needing to pass a high stakes exam in a couple of days, is what did it. really questioning the model of cramming an entire uni edu into 4 years, and doing it with teenagers.
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For me, the problem was that I fundamentally did not understand that mathematics is about building and understanding mental operators. I only understood this for programming, because I learned programming by doing. I simply did not know how to learn math!
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