I'VE STARTED TEACHING MYSELF LINEAR ALGEBRA.
Oh Glob, let us pray. Hahahahaah.
Once, once, ONCE: over spring break this year I tried to truck through the MIT Open CourseWare once before in my life to try to learn it all in a week. A heedless youth was I! But half my students and half my friends are taking summer classes, so I wanted to try something with my brain. I'll try to take it more slowly this time.
Something I'm getting kind of excited about:
One thing I've noticed while tutoring is how many building blocks you need to understand physics and calculus and chemistry. And how a lot of abstract concepts like x- and y- components and infinitely-small increments really have to be internalized and thought about. It's a different way of thinking! Like if you could project someone's brain onto a screen, you'd get the same image over and over again if you asked for "George Washington" or something like that. If you asked for someone's image of a limit or a subspace or a whatever, you'd get all sorts of variably goopy, misshapen, forms. Everyone's real grasp of science is different, self-constructed. No one can really just "feed" you electric potential -- you have to digest it, cut it up, make it into a sandwich before it belonds to you and your brain.
I feel like I am not making my point clear enough because it's such a freaking cool experience to see it happening right in front of my eyes when I get to answer questions. So frustrating! Words are not enough for all the abstract ideas floating around out there, science or otherwise. The point of that whole blarb of words was just to say that being on the tutor's side so intensely this summer has made me way better at being a linear algebra student, because I'm alright with having to go over things three times over, looking at new sources, looking for metaphors but knowing when metaphors completely fall apart, and knowing that I have to, have to practice without looking at answers!
Hold up, I still have science rant bubbles forming -- burp: Humans went from barely grasping very, very basic ideas like what the heck a mole is to doing stoichiometry to doing electrochemistry to building nanotech solar panels. All just by taking these super basic ideas and putting them together and conjecturing and figuring and generalizing until they've built all of modern society and omygaaaad I love science. I love the way it works in your brain and forces you to make connections. It's like all you started off with was a stick. And then you saw that a stick could be stood up vertically. And from there you learned how to build a campfire. And somehow now we have rocket ships.
I was once silly enough to think that science is lonely, just a lot of problem sets in the corner of my room. So yeah it takes some private struggling to master it. But isn't that like music and writing and anything else that is beautiful? You have to work through it and evaluate it and make it your own before it can be shared as something wonderful to the rest of everybody. Also geek-out sessions about biochemicals are probably how I got my closest friends, so hollaaaa.
Good science also forces you to look at your own blind spots. We're so good at projecting our own expectations and fears on the world around us and thinking about the real world and how they work and really, really reasoning about what should happen if a and b are true -- putting yourself in nature's shoes instead of just dismissing things as impossible or accepted or bad for you -- makes you free. Makes you infinite.
Yes, I am getting a bit too poetic about this and will take my nerd hat and leave.