This is my first year learning physics in school. Ever. I've been on earth for 17 years, not so much without understanding physics, but without understanding how much I didn't know about physics. I know that what I'm learning in class, despite being quite intensive, is like 3rd-grade arithmetic relative to just how much more there is to know. Hell, this year isn't even calculus based! I signed up ASAP for AP Physics next year. God damn, it can change your perspective on everything around you.
The above is the best argument for humility. Or, to paraphrase the immortal words of Don Rumsfeld (a decidedly unhumble man), "It's the unknown unknowns that you worry about." Teenagers are pricks (present company excluded, obviously :), because they don't yet know how much there is to learn about the world. Once the light becomes strong enough to allow you to see that you're standing at the edge of the abyss, then you start to understand the depth of the world. Or at least understand that you don't understand it.
I spend a large part of my day, at school, slouching over a desk covering my english notebook with dickbutt. I spend a lot of time half-listening to my teacher thinking: "Oh my god, I knoooooow." That inevitable attitude sticks with us, unfortunately. So I'll apologize on behalf of today's teens, if you get where we're coming from with that. Like I said, this is my first year learning about physics for real. Yeah there was "physical science" and bullshit like that, but no intensive courses to challenge me, both with an interest in the subject– "Hey, this shit matters!"– and a course that will be pushing me to make an effort. Why the hell should I have to wait until a year before I leave our education system to learn about something like physics? Maybe if our teachers looked us in the eye day 1 of middle school and said, "Listen punk, you don't even know how much you don't know. Don't believe me? Bam. Isaac newton. In less than a decade you'll be as old as he was when he invented calculus. Now go burn a village in Minecraft you little shit."
Maybe that would do a lot of people a lot of good. Myself especially included.
Physics is dope, dude. What's really cool about physics is if you can't derive it mathematically, you don't get to use it. Purifies the approach. Even cooler is how much a solid understanding of physics helps a solid understanding of the world and the universe. Keep at it. When I got to Diff EQ and discovered I could use the same equations to design the rear suspension of a car as I could to develop an oscillator for a synth as to predict the ebb and flow of wolf populations in the Siberian tundra, my mind was pretty well blown. There will come a time when you can read this page and watch the numbers pop out of the universe in green, like Neo in the Matrix.
Whaaaaa :D 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?I could use the same equations to design the rear suspension of a car as I could to develop an oscillator for a synth as to predict the ebb and flow of wolf populations in the Siberian tundra.
Check out the rest of the video. The main purpose is to use tau instead of pi, showing how much more intuitive it is.
Of that I have no doubts. My whole point was that when it was shown to me that the basic, fundamental constants of mathematics were all related such that they could be thrown into one equation and have it balance, I truly appreciated the beauty of math.
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