Speaking math

I wrote this as part of the writing workshop at Ferry Beach, the Unitarian Universalist family camp in Saco, Maine, our family has been going to for several years.

Kate has done the workshop every year she's been there. I did it this year for the first time.

One of the prompts provided by the workshop leader, Bill Trippe, was to write about something you're good at. Late in the week I helped a high-school student with some summer math homework she had as part of her prep for taking calculus in the fall. Reflecting on that experience led me to this.

Have you ever had to do arithmetic in Roman numerals?

Quick! What’s XXXVIII multiplied by XCIV?

If you take a moment to translate that into familiar terms – 38 times 94 – it’s not so bad. A few people can do it in their heads. Put out pencil and paper, and it’s a skill we expect of our grade-school students.

But what if you didn’t have Arabic numerals and place value, and you had to actually solve the thing using those damn letters?

It’s the rare person who has the ability to work with numbers under a system as clumsy as that. It would be a pretty valuable skill in a society that faced the logistical tasks of conquering and ruling an empire as large as Rome’s. And it must have looked like wizardry to most people.

Our number system makes arithmetic accessible to everyone, but actual math remains in the realm of magic for many people, which is a sad commentary on how poorly we teach math.

How do you know that a³ + a⁴ can’t be simplified down into a⁷? If you’re currently in an algebra class, you might be able to call up some rule of exponents to tell you it’s wrong. But if you speak math, you call up the rule after you get the feeling that you can’t combine those terms.

It’s the same way anyone relates to their native language. If you were raised speaking something close to Standard English, you don’t need a conscious memory of a rule to keep you from saying “I saw they.” It just feels wrong.

I like language as a metaphor, because it’s something almost everyone uses, and even at a basic level it’s a surprisingly complex task.

I used to think it was a miracle that birds could navigate through a tangle of branches while flying at high speed. I still marvel at it, but now realize it’s no more difficult than what we do to understand speech. We have to find our way through a thicket of sounds, sorting those sounds into words, mapping the words onto concepts, and stringing the concepts together, until a reality perceived by someone else and given shape in their brain has been transferred, as if by magic, into ours. Where there are ambiguities, we hold multiple possibilities in our mental buffers until we have enough information to choose the right path. When it works, you can cause an action in me out of all physical proportion to the slight air vibrations you sent my way.

And we do all this while flying through conversation in real time, occasionally managing to crap out a decent pun in mid-flight.

Watch and learn, birds.

That’s what it feels like to speak math, except that it has a universality that doesn’t exist in language. There are varieties of English where “He don’t know” is good grammar, but there’s no version of math where you can properly say a³ + a⁴ = a⁷. (*)

Music is another whole set of languages—not a universal language, but a family of closer and more distant relatives arranged in a genealogical tree, much like biological species—or, for that matter, like our spoken languages. I am fluent in classical music, as in English. I speak jazz awkwardly, and with many opportunities for misunderstanding, much like how I speak German.

Then there are idioms in which I am entirely at sea. A colleague in our art department asked me to observe his painting class. I could tell there was a visual grammar that moved easily through him and which his students were learning to use, but it was opaque to me. I saw that everyone else in the room was perceiving things in those paintings that my mind didn’t know how to read.

I am a halting speaker of other people’s emotions. On occasion, I see right past someone’s veneer to an inner state that they’re not trying to reveal, and there it is, laid out like the mechanism of a dodgy Swiss watch with the face pried off. Yet too often I seem deaf to cues that others pick up, as if, for me alone, they were spoken in Japanese.

On the other hand, I do speak math passably well.

(* I probably shouldn't state that so definitively. There are non-Euclidian geometries where peculiar things happen, like parallel lines meeting. Perhaps there's an algebra where a³ + a⁴ = a⁷. But I would guess that would be a far more specialized "language" than the math we learn in grade school and high school.)