“What are years?”

winged victory

If you read this blog now and then, you  know that time is something I think about a fair bit. How we are shaped by it, how we conceive it, where it comes from, where it goes. We say it passes but it doesn’t. We are always in its flow, carried with it, through it. It doesn’t always feel like a continuum but it is. I think.

One of our sons is in Paris with his family for part of the autumn. He is working in what I think of as deep math. It’s a world that has held him since he was a small boy, walking down our driveway with his grandfather, telling him that numbers exist below zero. He was 3 or 4. I’ve tried to take the measure of that world—if you’ve read the title essay of Euclid’s Orchard, you will recognize my effort and where it took me—and I learned enough to know that I will never understand that part of my son’s life. But we do have things in common, beyond the obvious (I am his mother after all), and he is wonderful company.

Some mornings I wake to photos and short videos from Paris. It is evening there when I look at what my grandchildren did that morning. I am in the moment and they are asleep. I watch them ride carousels in the shadow of the Eiffel Tower and time stands as still as it can while children laugh and fly through the air in a small metal plane. I watch them race through the Louvre, eager to see everything. In the halls of great art, they are children from the new world. The winged Nike of Samothrace was a particular pleasure for them. Created circa 190 BCE, possibly to commemorate a sea battle, she stands on the prow of a ship of Lartos marble, her clothing of translucent Parian marble so airy that you half-expect to hear it swish. My grandchildren rush to the winged Nike and I watch them, 8000 kms away, earlier on the same day that they went to the Louvre with their mum, a life-time away, the sound of my granddaughter’s voice so clear. “That statue is like a lot of years old,” she says, as her brother stands at the base, his shirt on backwards.

I think of Guy Davenport’s beautiful poem for Marianne Moore, “At Marathon”, and its stunning conclusion:

Two thousand, four hundred and fifty-five
years ago. There are things one must not
leave undone, such as coming from Brooklyn
in one’s old age to salute the army
at Marathon. What are years?

Such as coming from Edmonton as children to race down to the Winged Victory of Samothrace. What is time?

in the mail


In today’s mail, the most beautiful postcards for Euclid’s Orchard. I’ll be taking them to Word on the Lake later this month. If you’d like me to mail one to you—and who doesn’t like mail?—send me an email with your address! I sent back the edited manuscript today so we’re one step closer. How would that be expressed in mathematical terms? I have no idea.

“the heavy blossoms of fruit trees in May”

Euclid's Orchard_cover Final.jpg

From my forthcoming book, Euclid’s Orchard (Mother Tongue Publishing, September, 2017).

Twelve quilt blocks wait for me to find an ideal pattern for them. I arrange them on Moravian blueprint, somehow expecting to see logic at work. Do I begin with the first idea I had—the representation of Euclids orchard, the set of line segments like a trellis to hold the heavy blossoms of fruit trees in May? Or do I find a way to let the blocks tell a story all their own, dense with figurative language? Does it matter?

sleeping house, the last morning

For a week, our house has been full. Three children, their partners, a baby. Some mornings I woke, excited, and wondered why, having forgotten in my sleep that they were all here. And then joy, a universe restored, even temporarily, to its old form. Well, new-old, because who would have imagined the small children who grew up here would become such capable purposeful adults? Not me, not when I remember the diapers, the kitchen floor strewn with toys, the clamour for favourite meals, a swim, the old stories at bedtime. But wait — some things haven’t changed!

I finished a long essay this spring, one I’ve had in mind for some time, and I know I’ve written of it here. It’s called “Euclid’s Orchard” and it’s about math, love, horticulture, quilting, coyotes, and the patterns that unite all of these. Here’s the last section, an offering as I listen to Brendan, Cristen, and Kelly getting ready to leave in less than an hour:

I tried hard to understand the Joy of Mathematics and realized that I couldn’t, except in the broadest possible way. That at the heart of it is an attempt to relate concepts that might not readily suggest themselves to be connected. Number theory and harmonic analysis, for example. And I can only think of those by relating them to the figurative language I learned as a student of literature. Language departing from its logical usage to urge the reader to emotional and intellectual discovery. On that mid-summer night, listening to coyotes sing madrigals in our abandoned orchard, I should have remembered Theseus in A Midsummer Night’s Dream:

The poet’s eye, in a fine frenzy rolling,
Doth glance from heaven to earth, from earth to heaven;
And, as imagination bodies forth,
The forms of things unknown, the poet’s pen
Turns them to shapes, and gives to airy nothing
A local habitation and a name. (V. i. 12-17)

They were our names, our bodies under the heavens, all of us singing together in different voices to tell the story of our orchard, our time here in this place we have inhabited since – for John and me – 1981, and the only way to shape the story is through connotation, not ordinary discourse, though I praise the literal, the specific, but by reaching up into the starlight to parse what lies behind it. A mathematician might see the strong-weak duality this way:
weak duality
I’ve tried to puzzle through equations: the arrows, the lines and diacritics, the glyphs, the beautiful characters that look like Greek to me. Oh, wait, they are Greek, though not used to shape the yearnings of Sappho or the grand battles of the Iliad, but something else: a notation, a way of assigning symbolic value to constants, function, variables. A way of talking about equalities between variables. It’s the chicken and egg argument written in the ancient markings of Simonides in wax. Would math work in Chinese characters or the syllabics of the far north? Would flowers still smell sweet if their seed patterns were random? Was a baby ever born without the blue eyes or sturdy legs of a potato-farming ancestor near the Carpathian mountains? Would it matter?

Inside I am stitching a spiral into the layers of the orchard I have pieced together, a snail shell curled into itself. That’s what I’ll see when I’ve finished. I begin the spiral at its very heart, keeping my course as even as I can as it opens out and widens. Not the complicated pathways of the sunflower, some turning left, some right, so that an optimal number of seeds are packed in uniformly, or Romanesco broccoli, its arcs within radi resulting in something so intricately beautiful I wonder how anyone could cut into it to eat it. On windowsills, pinecones. The plump Ponderosas, brought home from the Nicola Valley, and a few long monticolas. They’re dry, open, but at the base, where their stalk connected them to their trees, two spirals are still visible, like a relaxed embrace, lovers asleep. My spirals are simple, my hands sewing to follow a path from its knotted source, around and around, until I’ve learned that my pleasure comes from the journey itself, a needle leading me outward, towards completion. A quilt elegant and sturdy, a sequence emptied of its numbers.

And listen: the coyotes are singing, the deep voice of the father, the rather more shrill voice of the mother – anxious that all her offspring eat well and learn to hunt, to care for their safety in the forest beyond the orchard – and the lilting joyous youngsters unaware that a life is anything other than the moment in moonlight, fresh meat in their stomachs, the old trees with a few apples and pears too small and green for any living thing to be interested in this early in the season.

convergent threads (an equation)

I’m (slowly) working on a long essay, “Euclid’s Orchard”, which hovers in and around mathematics, horticulture, family history, and memory. Part of the work of the essay is puzzling through some theories and planning a quilt to accompany this thinking. I’ve gathered many images from my reading about math and genetics and am struck over and over again by their beauty. My mind is always drawn to pattern so looking at some of the graphic representations of Mendelian inheritance, Pascal’s triangle (esp. his own drawing of this, with his beautiful handwriting), the elegant Hardy-Weinberg principle, and others has been a fascinating journey into design and method. Friends Joe and Solveigh gave me Edward Frenkel’s Love & Math: The Heart of Hidden Reality for my birthday in January and it’s been such a revelation to spend time in the company of this extraordinary mathematician. The book is part memoir, part explication of his introduction to, and life-long commitment to, the Langlands Program, essentially a grand unified theory of mathematics. I really enjoyed his joyous presentation of braid groups in Chapter Five (serendipitously titled “Threads of the Solution”); the illustrations are clear and nicely organized and I’ve been pondering how to translate one (or more) to a quilt block.

Sometimes a gift comes from an unexpected source. The other day an email friend, Andrea, sent a link to a Discover magazine feature on artists using math ideas to make art. http://discovermagazine.com/mathart 

A fashionable equation: the Yang Baxter scarf, by Robin Endelman, 2013. Manos del Uruguay’s Silk Blend (merino and silk, hand-dyed).

I’m not sure yet what my quilt block will look like but I was thrilled to see this scarf and am happy to know that others in the world experience math by translating its equations to thread and texture.