It's a non-trivial point though. As you'll learn eventually, when solving differential equations the obtained values are often positive, even when the "correct" answer could be positive or negative. Therefore, you have to phrase the whole thing in terms of absolute values. Learning high school arithmetic is painfully boring, but it becomes useful eventually. So far, no one has found a way to make it not boring from the start. FYI, what kb is referring to above in the text you quoted is the Harmonic Oscillator, which is the most important solution to Newton's second law (although you'll learn nothing of it until calc-based physics). It basically rules the world.See, this is what I'm talkin' about! Where the hell was this when I spent a month learning that absolute values can't be negative?
Arithmetic is interesting on its own if you look at it right, but you still have to learn it the boring way first. The same thing happens in college, where you get 4 semesters of mindnumbing calculus classes, then you get to take analysis and see all the cool stuff that got glossed over in favor of tables of antiderivatives and computational tricks.
I recently saw a video by a mathematician who earned the MacArthur Genius Grant. He said that the way math is currently taught can be related to how much is taught. Currently, 1st year math is like learning a C major scale. 2nd year, G major. 3rd year D major and so on and so forth. You get no where that way, there's no application. The man who won the award is working toward revamping how it's taught.
Of course, you're right. that's just my impatience talking. Not a great example either, but something like the concept of absolute values can be learned as it's being applied too. And with more memorable purpose at that. I'm speaking for the sake of haste, efficiency, I guess. Not that I or most people want to spend all day learning, either. That's an argument of it's own of course.Learning high school arithmetic is painfully boring, but it becomes useful eventually