I have always wondered exactly how this works. Whenever there’s some maths area I’m struggling with, I only struggle with it while that area is the focus of study. Eigenvalues were a mildly unspeakable horror when I was learning specifically about Eigenvalues, but they suddenly became trivial when the I was asked to use them on a new unspeakable horror.
I don’t remember any progressive improvement. It’s as if I was asked to step up my game, and all the prerequisite knowledge just fell into line without any complaint. This pattern has existed throughout my maths education all the way back to basic algebra and I can’t really find a satisfactory explanation for it. No other subject of study behaves like this.
I wonder if that’s because you’re not trying to “understand” something, you’re just using it as part of a separate algorithm? You stop caring about what it means to find an eigenvalue, and just think about how to get what the number you need to solve the problem in front of you.
Also, oddly enough, when taking the math course that builds on something, you get a lot more practice at it than when you were taking the original course. In other words, you probably do a lot more algebra in calculus class than in algebra class.
I’m starting to wonder if, when first tackling a troublesome topic, I think of it as an enemy, but when given a different enemy I suddenly start treating it like a reluctant ally. The “falling into place” phenomenon also happens when the New Unspeakable Horror is a real-world issue I need to deal with, like a problem at work, or an exam.
I have always wondered exactly how this works. Whenever there’s some maths area I’m struggling with, I only struggle with it while that area is the focus of study. Eigenvalues were a mildly unspeakable horror when I was learning specifically about Eigenvalues, but they suddenly became trivial when the I was asked to use them on a new unspeakable horror.
I don’t remember any progressive improvement. It’s as if I was asked to step up my game, and all the prerequisite knowledge just fell into line without any complaint. This pattern has existed throughout my maths education all the way back to basic algebra and I can’t really find a satisfactory explanation for it. No other subject of study behaves like this.
I always said, “I’ve always been bad at math. I’m just bad at different math every year.”
Math divides into “way too hard” and “trivial”—the good news is that the “trivial” pile grows over time.
I wonder if that’s because you’re not trying to “understand” something, you’re just using it as part of a separate algorithm? You stop caring about what it means to find an eigenvalue, and just think about how to get what the number you need to solve the problem in front of you.
Also, oddly enough, when taking the math course that builds on something, you get a lot more practice at it than when you were taking the original course. In other words, you probably do a lot more algebra in calculus class than in algebra class.
I’m starting to wonder if, when first tackling a troublesome topic, I think of it as an enemy, but when given a different enemy I suddenly start treating it like a reluctant ally. The “falling into place” phenomenon also happens when the New Unspeakable Horror is a real-world issue I need to deal with, like a problem at work, or an exam.