At some point, an otherwise useless feminist wrote an article entitled “Fuck Trigonometry,” suggesting that we ought to just skip over the subject entirely in school. She concluded this article with complaints about her husband.
Honeycomb responded to her in my comments section:
Students of mathematics, philosophy and physics often get hung up on definitions. It’s annoying, but it’s not for nothing. The first thing a successful student does, in encountering a new area, is to memorize definitions.
Imagine being a newly arrived freshman student at a big university, and being asked to understand this:
It happened to many of us as teenagers. The first week of the first course in the Calculus series requires incipient students to memorize that line. When it happened to me, I first copied it out, over and over and over. Within a few hours, I was able to put it into words, and within a couple of days, I was able to use it constructively. A week after we were all collectively panicking in Dr. G’s Calculus I class, those of us still in attendance were writing proofs with it, treating it as though it were a newly acquired tool, that we found in the bottom of the chest in the back closet.
Some people can’t understand it. It’s not that we’re any smarter than they are. Anyone who shows up to study Calculus is already done with trigonometry, where they were required to memorize all of this:
It’s thus fair to assume that any high-school graduate in America can study Calculus. He’s done this sort of thing before. Raw cognitive ability isn’t lacking in such people. Often they are simply unmotivated. Other opportunities (namely binge drinking and screwing strangers) avail themselves, and study is put on the back burner. The prospective student is thus weeded out. He either leaves university entirely, or he switches his major to something like literature or political science. This has a number of different benefits for everyone. It usually frees up the uninterested to pursue an area with which he is more comfortable, and it keeps the unmotivated from dragging down the rest of the class with insipid questions.
When you’re in high school and you’re taking mathematics, the whole thing seems pointless. Back when I was teaching remedial math it at a community college, I called it “faith-based trigonometry”. At this point, the trigonometry course is just a cumbersome addition to the geometry you learned a year prior. It’s just a proof-writing class, using identities one doesn’t fully understand as axioms. For those people who graduate high school and go on to study Calculus, it’s essential. If you’re in Calculus and you don’t know that cosine of pi over two is negative one half*, then you’re fucked. In fact, the values of all these trigonometric expressions end up becoming second nature, sorta like four times four equals sixteen.
Once you’re done with the last course in the Calculus series, you get to take your first course in what is called higher mathematics. (Marijuana not included.) For me, that course was called Introduction to Linear Algebra. The title itself is misleading. Every little kid learns how to solve systems of linear equations, right? No big deal!
One of my most memorable moments as a schoolboy came in this course, when we were all messing with matrices during practice time. The professor was someplace out of sight. Suddenly, I came across something that tied into a distant, old memory. At precisely this same moment, another student burst out shouting, from the back of the room: “Holy shit! It’s the half-angle formula!” As the realization spread, everyone started laughing and sighing, as though we were all patients in the university’s insane asylum.
What was once a pointless procession of symbols was suddenly illustrated, deeply and beautifully, exactly where none of us expected it to be.
*Caspar wins! (winning)