One evening I was writing a video script about ice-melt. I had to take pause because I wasn't sure if water level goes up or down when a floating freshwater cube melts in saltwater. I did what any practiced scientist would do: I made a sketch, assigned some variables, did some algebra and got an answer in a few minutes: it goes up. I've done this in my career as a scientist more times than I can count, but because I was trying to communicate this to a general audience, something hit me:“I wanted this…” For years as a child I wanted to be able to do this very thing, wondering if it was real.
As a kindergartener falling madly in love with science and science fiction, the chalkboard had a symbolic mysticism to it. It was a place where brilliant people made discoveries and had eureka moments. A person could walk up to a chalkboard knowing only a little bit about something, and after writing some symbols down, “A-HA!”, walk away knowing a great deal more about that something. I wished that someday I too could wield the power of this symbolic magic, and that I too would have eureka moments. It took more than a decade for me to get my kindergartener’s wish… but it did come true.
I remember thinking when I was eight, even though I’d been doing math for as long as I could remember, it looked nothing like the kind that scientists used. First and foremost, my math didn't have any letters in it. The matter was simple; once my math had letters, I’d start having eureka moments. To this day I can recall my sheer disappointment when the first letters came in the form of “Line PQ” and “Triangle ABC”; ten-year-old me would have to wait a while longer. The next year my teacher let us in on a secret after a week of doing the sort of problem where you have 6 oranges on one side of a balance and 2 oranges and a mystery box on the other. “This is algebra,” she explained, “just label the box as x.” I remember being excited. To say this feeling was premature would be an understatement. The wait continued.
The start of middle school set the stage for more disappointment. Letters (variables, rather) were used in formulas like the area of a triangle, the period of the wave, the quadratic equation, etc. I felt cheated that formulas "seemed to be about more math” rather than the real world. Things like finding the heights of a tree with a protractor were neat, but hardly what I was after. The other source of constant torture was my calculator. Even though it was the kind the school had told me to buy, it had all these mysterious buttons on it. Nobody could tell me what the “cosh” or the “Σ” button was for. They looked science-y and there they were… taunting me. All I could get from teachers was "just wait." Mind you, this was before Google so I was on my own.
The chapter introductions to the school math book had these interviews with people who use that chapter’s math in their line of work. In one example a policeman explained a formula that used a square root to determine a car’s cruising speed from the length of skid marks. If I’d had the words to ask at the time, they’d been along the lines of “So, is there a real reason for using a square root, or did somebody just notice that the graphs for skid marks and square roots kinda match?” Other formulas would show up in science class (such as the period of a pendulum) but since nobody would show me where these formulas came from I began to suspect that scientists created formulas just by trying different arrangements of variables until some formula just happened to match data and/or units worked out. It did occur to me that the graph of a quadratic looks exactly like a ball flying through the air, but I didn't know how to ask if this was by coincidence or for a real reason.
With high school starting I began to believe the oracular chalkboard was a myth. I remember thinking that the chalkboard scenes from “The Day the Earth Stood Still” must have been glamorized. I continued to be unimpressed by the now common formulas in geometry, algebra, trigonometry and chemistry.
When I was 16 I placed into advanced physics. I went in not expecting much, but I was in for a surprise. Just in the first week it was clear just how wrong I’d had it; the oracular chalkboard was REAL. For the first time it was clear that math describes real-world phenomena for real reasons, and because of this, anyone who knows algebra can use math to learn about the real world. I remember feeling silly for suspecting otherwise, but considering how long I waited…
My last year of public school I took advanced chemistry and calculus. My experience was much the same as that in physics, and this would continue on as a college student of chemical engineering. It was plain as day now: because math describes the natural world in profoundly effective ways, to learn from the natural world we do math.
Here’s what kills me: Most people don’t take algebra-based physics in high school or college. Most people don’t get to see firsthand how someone can walk up to a chalkboard and teach herself something without doing an experiment. If I hadn't had this opportunity before leaving high school I could have easily went the rest of my life thinking the oracular chalkboard was a myth. If the average person isn't given the tools to experience this first hand, I think they should at least be able to consider the implications. I think most people understand that algebra is a tool that scientists use all the time, but they have no idea how or why it’s used.
In my experience, the average person has some vague notion that algebra is somehow powerful and that somewhere scientists use it for… something. The average person doesn't know it can be used for everyday musings such as freshwater cubes melting in salt water. It’s as if we’re showing children the various contraptions of a helicopter year after year, but most have no idea the blasted thing can fly. Only a select few students get to the point where they understand “Yes, I just saw a machine take off into the air. Yes, this is real. Yes, I can learn how to do this myself. Yes, I can use this tool to explore the world in a whole new way.” Without this perspective, it’s no wonder many opt to abandon the machine on some rooftop to rust.
There are plenty of skills that are by no means required to succeed in life: playing music, drawing, dancing, cooking, or speaking a foreign language. To respond to
xkcd’s question over why people are so proud to have not learned math: with these other skills it’s clear the sort of amazing things that can be accomplished with mastery of those skills. I think people who take pride in never having used algebra literally have no idea the kinds of amazing things that can be done with it.
My two cents. Thanks for reading.
