Mine is just a fling, some kind of mad infatuation. What future can there for me and the maths together?But it does thrill me to understand what I never could before. I don’t mean never could as in never regurgitating correct answers, never plugging in the proper formulas – I eventually pulled adequately adequate grades, parrot-like repeating meaningless phrases to the resigned and bored acceptance of my math teachers.
I mean understanding like standing under the ideas of the maths (because it begins to appear that there are many paths of mathiness, snaking through the forest of knowledge) – understanding like standing under a redwood tree in a warm rain – catching the smell of it. Feeling it filling out the lungs.
It thrills me to have discovered, for example, that the words sine and cosine are mistranslations made by the Romans, those unwhimsical engineers.
Years ago I asked and have asked many times since – but what does sine mean?
It doesn’t mean anything . . . It means this kind of relationship between parts of a triangle drawn within a circle’s arc . . . It means this kind of wave . . . It’s a convention – we could as easily call sine and cosine, Bob and Alice . . . It’s just a word.
This is the answer math teachers give, neo-Roman and unwhimsical.And it is not true.
Nothing is ever just words. Everything has been named by blood and bone beings who walked a world you and I would not be utterly lost in.
I love it that somewhere along the Indus, or the Ganges, an astronomer once drew a circle and then wanted to look at just a part of that circle. What to call that arc of a circle, the part of the circle under consideration? Why it looks like a bow! A rainbow. A hunter’s bow. Cupid’s bow. Something seen in the sky, dreamed of, sung of, something grasped in the hand.
I love it that what we now call the chord (the line, the string drawn) from one end of the bow to the other is just the bowstring — jya— hanging slack, waiting for its arrow. I love it that Gupta-era geometers in ancient India played with the word jya (“bowstring”), seeing a poetic resemblance between the bowstring of a bow and the length of a life – full of intentions and desire, and so for jya sometimes they playfully substituted jiva (“life”).
And then to know that Arab mathematicians adopted the Sanskrit term whole-cloth, without translation, but wrote it down, as they had to in Arabic, without vowels as jv. So that Gerard of Cremona, in 12th century Italy, reasonably mistook Sanskrit jiva for Arabic jaib (“bosom”) and so translated it to Latin as sinus (“bosom,” or “bay”). From which, in the 1500s, we English-speakers took our sine.I love it that that’s what sine means.
This small and abstract poem on perilous desire: bowstring, life, bosom, bay.
By Emily Dickinson 1830–1886
Wild nights – Wild nights!Were I with theeWild nights should beOur luxury!.
Futile – the winds –To a Heart in port –Done with the Compass –Done with the Chart!.
Rowing in Eden –Ah – the Sea!Might I but moor – tonight –In thee!.
Though the point – there is always a point in the maths – is that the compass and chart are wild themselves – that the mooring in that moonlit bay of mathematica is a pleasure as wild as the sea.
Knowing the naming process tells me someting about the shape of the idea being named. It’s like going back to the childhood home of a friend – who trusts you enough to bring you into that primal place – and with a new clarity, understanding why they are the way they are.
It helps me to know that the sine is the bowstring to a bow that arcs along a circle’s edge. But it is not the full circle. And usually it’s not even a full quarter-circle. What to call the rest of the quarter-circle, the part that isn’t the bow that belongs to the sine, the jya? The cosine is the koti-jya, the co-jiva, the bowstring that would belong to the neighboring, corresponding bow that together with the first completes a full quarter of a circle.
I like knowing that. And now I remember the right relationship between sine and cosine far better than I did with any more arbitrary — that’s just the way it is — definition.
My mind (all minds?) needs stories, colors and scents, desire and music, to fully function. I get further thinking of sine as a multicolored bow, stretched by the strong and handsome arm of Desire than I did when I tried to repeat over and over that sine is just a grunt we’ve agreed means a something, though it doesn’t really. That sine is really oog and cosine is its corresponding other, the co-oog.
“I don’t see the difference,” says Fritz. “Either way, they’re both just words.”
But he likes to look at my homework. “Even when you do math you’re doing words,” he says, a finger pointing to the snatches of encouragement and confusion I’ve written to myself in the margin in the process of working out a problem:
Still the same answer as before and not the answer in back of book ~ why? Unit vector, I surmise, would have length of one unit . . . so? Let’s just play with this because I’m rather lost . . .
It is the permission to play that I never had before.
I thought Math was a citadel, a gate with a system of locks and keys. No one ever told me I could possibly pick the lock with a hairpin given the right twist and patience. That Math was no citadel but a wandering maze of interconnecting trails through a rainforest of trees and vines, fruits and flowers of different knowings. I should have known – mathematics is a plural, I always knew. And I know now it is from the Greek μάθημα (máthēma), which means learning, study, science. Mathematics = the sciences, the studies of, the learnings.
“And what’s this – a treatise?” Fritz reads over my shoulder, then laughs as he reads aloud, “Math-ity obsession with simplicity trumps again?”
“Do you disagree?”
“No, but usually math doesn’t look like this – all wordy and full of commentary.”
Mathematics is Fritz’ first and truest love – well, maybe second, or even third, depending on how you count his mother in there. How he counts me. But definitely, his love of math is his purest and simplest devotion – no ambivalence, no juggling, no shielding himself or defensiveness.
“I love your pictures,” he says, chuckling, chin over my shoulder.
When I ask myself, as I do frequently ask myself these days, why I am so getting it this time? what’s different? how is it all making such exquisite sense where before it was all wingless muddle? – I know a good part of it is Fritz.
As in so many things, Fritz is a good part of my pleasure in this pavilion of shapes and eternal quantities, this peaceful place we can come to play, a paper paradise untouched by the messy cross-currents we are otherwise caught in, the prow of our pleasure boat floating free of the slimy weed that usually clutches at the sides of the lifeboat in which we too often must paddle side-by-side.
We wake in the morning and (instead of discussing the broken dishwasher) we lie in bed, propped up with pillows, pencils in our hands, graph paper pad against our knees. Our two heads bent over the shared sketch and computation.
This is how geeks sing their aubades.But even Fritz is a little mystified at what I’m so loving about what I’m suddenly seeing.
I think, to his eyes, my awe is at such little and such obvious almost-nothings that it seems misplaced.
As if you were to overhear in the checkout line at Wal-Mart, behind a cart of pork rinds and Double-Stuff Oreos, an exultant voice going on about how amazing the little rhyming chimes that jingle at the end of alternating lines of a poem are – how do they do that?!
Or manic vaporings about the beauty of a certain font, exchanged between levels of Oil Can Henry’s, while they drain your car’s fluids and check the filters, waxing ecstatic over the deeper symbolism of the serif.
Does it matter that my epiphanies are so tiny? Should we be surprised to discover wonders so slight and small?