Fucking Trigonometry

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.

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Honeycomb responded to her in my comments section:

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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:

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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:

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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.

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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)

Author: Boxer

Secret King of all Gamma Males, Member of Frankfurt School, Your Fave Contrarian!

18 thoughts on “Fucking Trigonometry”

  1. Ya’ know Boxer .. I still have to go back and re-learn or study-up on my math from time to time.

    Because I was taught math as an application. Not a language. The law of primacy and dis-use come into play for me. Maybe it@ affects more people than just me.

    With regards to Math being a language .. I missed the boat as a kid because of how I was taught. I now teach any math to people via graphical form, first, instead of new’mayor’eek’alley first. Instead of saying graph this equation .. I ask them to answer questions from the graph and then have them write the equation.

    But that’s not how I learned it as a kid. It would have made my physics and nuclear eng degree much easier.

    Actually the US Navy’s Nuclear power program taught math this way. First time in my life that math came alive to me .. post college .. sigh .. it would’ve been helpful back in my high school days .. anyway .. I still find it useful.

    Still .. rote learning (i.e. memorization) is the lowest form of learning .. and everyone needs to be able to do it if they expect to progress in any technical field.

    ..
    ..

    And to stay on-topic .. she’s still moon-bat crazy.

  2. Hey Boxer ..

    I just saw this over at Spawney’s Space .. posted by Farm Boy ..

    I snorted (i.e. what the kids like to abbreviate as LOL) a lil when I read it ..

    https://www.campusreform.org/?ID=10338

    Do I need to put the video up of the monkeys that picked toys based on their sex .. males picked trucks .. & famales picked dolls? Cuz even monkeys are smarter than these broads.

    1. ‘Cuz even monkeys are smarter than these broads.’

      These broads are disconnected from their Creator. Even animals in their instinctual state of life know what their sex role is.

  3. Ô My Host,

    In every story where training is part of the coming-of-age, the student never wants to learn the basics but to just get on to the advanced stuff. Karate Kid did nothing but complain about Miyagi-san-no Sand Floor/Paint Fence/Wax Car pedagogical methods. (“I’ll do ANYTHING to learn karate. Oh, except that.”) All Luke Skywalker did was whine until he got to go rescue his friends and couldn’t finish with Yoda. Anikin was the same. But in the movies, everything turns out OK in the end; the apprentice always gets to skip the training yet still ends up kicking ass of the best of the best.

    This is not to mention the Mary Sue, the chicky-wick who kicks ass just because she’s a chicky-wick, and everybody knows that don’t no chicky-wick need no training from nobody not nohow. Especially from some aging white male master and lifetime student of the art who probably invented it in the first place.

    Driving a car is similar. You have to master the motions to the point that they can be done unconsciously before you can put them together on the road. There is simply no room for the mistake of mixing up the brake from the gas.

    Math is the same. You have to learn the facts, the tables, and quit asking why until you prove that you are willing to be a student who will listen to the Master, and after you’ve mastered Sand Floor, after you can use it without thinking, we can work on how you can use it. Just shut up and do it. The ones who succeed at math and who eventually can think outside the box are the ones who will do what they’re told and take each step on its own merits. It’s the ones who insist on practical application on Day One that drop out.

    BTW, cosine of two pi over three is minus one half; cosine of pi over two is zero.

    Regards,
    Caspar

  4. Dear Caspar:

    Welcome, brother. WordPress spammed your comment. I have no idea why. I’ve been getting tons of false poz lately from the filter.

    BTW, cosine of two pi over three is minus one half; cosine of pi over two is zero.

    You spoiled my fun! I was playing the ambiguity game, hoping our dear “mathbabe” would follow the backlinks, and show up to show me up.

    [cos(π)=(-1)]/2
    cos (π/2)=0

    Hence my writing it out longhand, rather than compactly noting as much.

    This is a nerdy variation on all those viral puzzles that were going around facebook a while ago. Get you a case of beer for catching it. I hope you’ll stick around.

    Best,

    Boxer

  5. Ahhh, tricksy! wink wink nudge nudge. In this brainwashee’s 40-year experience, “n pi over m” is a standard argument to a trig function. I would have spoken the example above as “cos pi divided by two”. Sorry about that, Chief!

    Sometime commenter here and there; I’ve been lurking for a while. Keep it up.

  6. Good job Casper .. I sped-read rat past-it.

    I seem to be doin a lot of that these days .. sigh .. where’s my cheaters .. gonna have to be more faithful about use’in’em.

    1. Dear Fellas:

      In this brainwashee’s 40-year experience, “n pi over m” is a standard argument to a trig function. I would have spoken the example above as “cos pi divided by two”. Sorry about that, Chief!

      That’s a variation of what I did when I started teaching, only I paused and used the word ‘all’ to signify a bracketed quantity, when I was speaking aloud: Cosine of pi, all over two, as opposed to cosine of pi over two. Even so, there are no standard ways to communicate this stuff, and division is inherently ambiguous, anyway. Example:

      Even bright people who oughta know mess this up (it appeared, some months ago on facebook, and was truly amusing to watch the attendant squabbling). A disturbing number of people actually multiplied 3 and (1/3). Others suspended the order of operations entirely.

      Putting it into your TI-89 gives you a hint about how you should really think about it. The rational number is just a portion of the greater division problem.

      (my calculator is dirty, because I’m a mediocre mathematician)

      I seem to be doin a lot of that these days .. sigh .. where’s my cheaters .. gonna have to be more faithful about use’in’em.

      The next article I publish will tie into this one, so it’s a good segue. (I would speed-read that one, too; because I can guarantee it won’t be any more interesting than this one).

      Best,

      Boxer

      1. Order / High-arc-ee Operations .. I’ve seen a number of these recently ..

        And though I can see both sides .. I know the old way .. and with math .. there is only one correct answer.

        Example ..
        6÷2(1+2)=

        This is clearly 1 ..

        but they claim 9 ..

        I was not taught this new method .. my old ways clearly nows that is 1.

        ..
        ..

        And clearly your problems answer is 9.

        ..
        ..

        I’m old .. and there can only be one .. lol

      2. And I’ve had an adult beverage already .. everything seems much funnier in my mind .. it never types out quite that way after the beverage wears off.

        Hmmmmmmm

  7. Order / High-arc-ee Operations .. I’ve seen a number of these recently ..

    And though I can see both sides .. I know the old way .. and with math .. there is only one correct answer.

    Example ..
    6÷2(1+2)=

    This is clearly 1 ..

    but they claim 9 ..

    I was not taught this new method .. my old ways clearly nows that is 1.

    ..
    ..

    And clearly your problems answer is 9.

    ..
    ..

    I’m old .. and there can only be one .. lol

    The answer to all questions of arithmetic…

    …is 69

    1. lol ..

      Obviously my diss-lex-ee-uh got the better of me .. lol

      Okay .. more adult beverage and much less eye straining fun on my phone .. Gotta check-in at my favorite meeting place on Saturday Night. 18 year old scotch awaits me.

      Yenz have a good night.

      1. Okay .. more adult beverage and much less eye straining fun on my phone .. Gotta check-in at my favorite meeting place on Saturday Night. 18 year old scotch awaits me.

        And I’m about to walk into the chapel… investigating the mysteries of the Church of Rome, I am…

        Thanks for goofing off with Boxer!

  8. They teach math completely wrong in public schools – at least in America. You spend the first six years of your education – the years when you learn the easiest and are the most malleable – leaning how to do what a pocket calculator does; and over the next six years, they start dumping different math units on you in no sensible order, by the gambit of different teaching styles – some teachers being engaging and effective, some being the nazi teachers from “the Wall”, some being so brain-dead that they can’t even do the problems correctly themselves, but they go ahead and turn you loose anyway.

    How I think they should teach math is by going through all calculation through elementary school – arithmetic, exponents, nth root and logarithms – then move onto theorems, algebra, trig, etc. They shouldn’t waste time doing pointless drills and exercises that are little more than busy work – they need to make it less tedious, not more tedious. There is an old saying, that the best training is a wet blanket. Horseshit. Most people can’t do well at something when they’re being drug through by their heels.

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