Stopped by a friend’s house a few days ago to do homework, which somehow devolved into me analyzing what programming language I should try to learn next in a corner, which is completely irrelevant to the rest of this post. Oops.

Anyway, in normal-math-curriculum-land, my classmates are now learning about matrices. How to add them, how to multiply them, how to calculate the determinant and stuff. Being a nice person, and feeling somewhat guilty for my grade stability despite the number of study hours I siphoned off to puzzles and the like, I was eager to help confront the monster. Said classmate basically asked me what they were for.

Well, what a hard question. But of course given the curriculum it’s the only interesting problem I think could be asked.

When I was hurrying through the high-school curriculum I remember having to learn the same thing and not having any idea what the heck was happening. Matrices appeared in that section as a messy, burdensome way to solve equations and never again, at least not in an interesting enough way to make me remember. I don’t have my precalc textbook, but a supplementary precalc book completely confirms my impressions and “matrix” doesn’t even appear in my calculus textbook index. They virtually failed to show up in olympiad training too. I learned that Po-Shen Loh knew how to kill a bunch of combinatorics problems with them (PDF), but not in the slightest how to do that myself.

Somewhere else, during what I’m guessing was random independent exploration, I happened upon the signed-permutation-rule (a.k.a. Leibniz formula) for evaluating determinants, which made a lot more sense for me and looked more beautiful and symmetric

\[\det(A) = \sum_{\sigma \in S_n} \text{sgn}(\sigma) \prod_{i=1}^n A_{i,\sigma_i}\]

and I was annoyed when both of my linear algebra textbooks defined it first with cofactor expansion. Even though they quickly proved you could expand along any row or column, and one also followed up with the permutation formula a few sections later, it still felt uglier to me. Yes, it’s impossible to understand that equation without knowledge of permutations and their signs, but I’m very much a permutations kind of guy. Sue me.

Every time I notice that I have hoarded a large number of strange assignments and essays from another school year of work I get all guilty. First there’s the knowledge about ancient Chinese dynasties and plant hormones that I only have shadows of recollections of, which makes me wonder whether all the time and effort invested by teachers, classmates, and myself have gone wasted.

I know, though, that given that I still sense these shadows, it shouldn’t be difficult to look up and relearn this stuff if I ever need to do so. This brings me to the non-factual parts of the learning, such as writing skills with all its variations. There’s persuasive writing, which I don’t use much because I can’t usually even persuade myself to take a side in anything, let alone others. There’s descriptive writing mode, which I don’t use much because the most vividly describable things I encounter are food, and the shallowness of piling flowery adjectives together to talk about food just makes me cringe nowadays. Previously, I wrote at least two such compositions in sixth grade. Blech.

So. It looks like I’ve officially graduated.

I have to wonder whether it really means anything. Taiwan’s system classifies the grades neatly into 6/3/3 sections, but then our bilingual department also uses the somewhat illogical and faintly sexist freshman-sophomore-junior-senior naming thing, in which the big jump happened last year.

Neither of these naming issues, of course, really matter. Shakespeare says, “A rose by any other name would smell as sweet.” Nor, I would think, do the different color of uniforms we have to wear (pink, if you didn’t know.) But AP classes probably count for something.

I am going to take AP Biology. Why did I pick AP Biology anyway? It seemed like a reasonable default choice. I guess I would like to know something more about the mysteries of life and consciousness to guide my philosophical side, and many of the other courses looked too murderously intense. The perfect stepping stones into the giant hamster wheel of overachievement that everybody is crazy about here. But then I learned I still received eight chapters to study by myself during summer vacation, alongside the English reading assignment. Oh well, so much for relaxation.

You know, I used to think of this issue, about all the academic work we students pile onto ourselves and all the ensuing stress and chaos, from a strange detached third-person viewpoint. Not everybody has a mind that is fit for all that brainwork. Some people have to do the artistic, imaginative things. Some people cannot function optimally in our intense learning environment. Somehow, imperceptibly, according to my apparently not-all-that-bad grades, I put myself in the crazy book-grinding category, and I am having second thoughts.

I don’t feel the energy for all this intense future yet… The past is still so close, so vivid, so attractive. Our graduation trip, for instance.

Yeah, okay, fine, I admit it, what follows is a rough record of our graduation trip that has been stuck in draft limbo for approximately forever, and I was trying to segue into it. I’m a perfectionist, what can I say?

Finally getting into geography honors. And surviving, somehow, with grades that still might count as ridiculous-in-a-good-way. The one big change I’m getting used to is the need to take actual hardcore notes.

For eight years, most classes I’ve gone to, both inside or outside school, have been straight from a book or handout, which would be so easily read and comprehended (…to me) that any notes would be a waste of energy. A couple science teachers would make us take notes and count them as a grade. All you had to do to get an A was write down most of the important bits, even if the chapter sections were written in exaggerated cursive that took up half the page and there were random teddy bears straddling the margins, as in my notes.

There was a stage in maybe seventh grade where I told myself I would make neat, doodle-free notes that actually summarized the stuff in biology (the easy seventh-grade kind (not that we still remember all of it)), and to get to that goal I would force myself to use only one page for each section, with a special way to mark the vocabulary words. It helped studying a little, but the stage didn’t last, and I ended up doodling again.

Even when the going finally got tough and understanding became a nontrivial task, I still had irrelevant embellishments and a bunch of artificial fonts for my “notes”. Even in the days when I was free to go to the Chiao-Tung University for classes twice a week (and still get consistently ridiculous grades, judging by the score breakdowns the prof gave us after every test), my notes looked like this.

So, as triggered by my confrontation with the Chinese book report (remember? whatever the answer is, it’s okay): a reflection on my incompetence at dealing with two languages, and why this matters, or not.

I can think in both languages. It’s a natural product of our school environment. The two languages often have to complement each other; most of the nerdy terms or globally relevant allusions are English-exclusive (I couldn’t talk coherently about SOPA in any language other than English!), but a lot of cultural and geographical staples around here are Chinese only. And sometimes there are unexpected holes where an innocuous-looking phrase simply has a few too many connotations to translate perfectly (the example I always get stuck on, and have yet to solve satisfactorily with anything short of a full sentence recasting, is “appreciate”.)