icosahedron, bordered with cotton

While in Ottawa last week, I had a little peek at quilts in the curatorial wing of the Canadian Museum of History (formerly Museum of Civilization) in Gatineau — thank you, Forrest! — and my hands kept twitching. I wanted to make something! I wanted to work on my own quilt, which has been longer in the thinking stage than anything I’ve ever made. This is because of the long process of working out how to replicate the images I wanted to use. I’m much better at the doing than the planning. Strategies for this particular quilt have changed many times and so there hasn’t been much sewing — until yesterday, when I cut out and stitched the top and bottom borders on all the blocks. And this morning I’ve just finished the sides of the first block. It’s a model of Euclid’s icosahedron and I love how elegant it is. An icosahedron is a polyhedron with 20 equivalent equilateral triangle faces, 12 polyhedron vertices, and 30 polyhedron edges. In the Timaeus, Plato equated the polyhedra with elements and the icosahedron’s element is water. This block hasn’t been pressed so you can see the ruckles in this photograph. And the colours aren’t quite true. But I love the cotton, something from my quilter’s stash which I could never find the right use for, and I don’t have enough of it to line up the pattern at the corners perfectly. But every quilt is a a version of the Platonic ideal, I suppose, and maybe the next one will be better…

icosahedron block

skeins

I thought I’d missed the long farewell of the geese flying south over the coast — the snow geese passed overhead earlier in October apparently and the sight of them is one of joys of autumn. They stop on Westham Island for a few weeks and we’ve gone there to see them grazing in the shorn fields before they leave again for their winter refuge in the Great Central Valley of California. And the Canada geese, the Black Brants — looking at the maps of their flyways is like looking at a complicated knitting pattern, the lines passing and twisting and carrying one colour through the sky under or over another.

But the other day, driving with Angelica in Victoria, we saw a large skein flying high over Royal Oak where I spent my teen years. We both saw it at the same time and she said what I’ve always felt: “It makes me feel like crying when I see the geese flying south.” Our memories are knitted into the experience of seeing them. I remember riding over the vanished Broadmead meadows on my horse in autumn and seeing geese. I’d call to them, “Goodbye! Goodbye!”, and feel a kind of sorrow as I watched them disappear into cloud or distance. We often hear them when we are putting the garden to bed for winter, their calls bouncing off Mount Hallowell and echoing so that we can’t always tell where they are, and sometimes we miss seeing them completely, though we’ve heard the song of their passing. The other day, I couldn’t tell which geese we were seeing. They were too high and I was driving on the freeway. But I’m sure I could find out by looking at flyway maps and the annotations birders are famous for making.

Autumn brings with it all the ancient rituals, doesn’t it? The putting by of food, the stacking of cut logs in the woodshed, the airing of the winter quilts. Although I quilt (and am busy with the latest salmon quilt, stitching the spirals into the centre panel, and waiting for the moment when I can sew shell buttons onto the spines of the salmon I batiked, then dyed with indigo pigment), I find myself wanting to knit. I am hopeless with the patterns that look like math theorems: 2nd row P1A (5A, 1B, 9A, 6A) 4 times.

But I am slowly learning a little math, in part for an essay I’m working on called “Euclid’s Orchard”, which will have a quilt to accompany it, each piece — essay, quilt — documenting the other, and maybe it’s time to try to decode the knitting charts. I have the skeins to begin:

P1090168There might be a way to include the flyway maps in this essay, a way to bring geese into a discussion of genetics and orchards and Pascal’s triangles and a son who knows something about all these things.

patterns, ideas

I’m reading G.H. Hardy’s A Mathematician’s Apology, an elegant essay written towards the end of Hardy’s long and illustrious career in pure mathematics. I’m enjoying it very much. It allows me some insight (I hope) into the mind and work of my son, Brendan, who works in the field of optimal transportation as well as mathematical economics and physics.

This essay begins with a statement that locates its writer in age rather than youth. “It is a melancholy experience for a professional mathematician to find himself writing about mathematics. The function of a mathematician is to do something, to prove new theorems, to add to mathematics, and not to talk about what he or other mathematicians have done.” There are of course parallels with many other areas of human investigation and creative practice. Young writers write, don’t they? They tend not to think too much about exposition or justification. Painters, too.  They plunge into the work they are called to do and it’s only later, in retropect, that they attempt to figure out the patterns of this work, its context (if it’s lucky enough to have one — or many…), the connections between their work and that of their peers or predecessors.

But I’m thinking how lucky I am to have found this book which gives me some insights in the workings of an intelligence so mysterious to me. I’ve read about half of it and have some questions: all those theorems that I’m coming to, so beautiful in their abstract language, like Greek; when I look at a page of Greek, I can make out perhaps 1/8 of it but I know that using my lexicon, I can probably figure out more. Will this be the case with Euclid’s proof of the existence of an infinity of prime numbers? We’ll see.

There is much that I admire in this essay, even if I don’t necessarily agree with statements like this one: “A mathematician, like a painter or a poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas.”  I think of William Carlos Williams here and his poetic philosophy of intent:

 — Say it, no ideas but in things —

nothing but the blank faces of the houses

and cylindrical trees

bent, forked by preconception and accident —

split, furrowed, creased, mottled, stained —

secret — into the body of the light! (from Paterson)

Maybe we are all closer than we think we are, closer in our searching for meaning in those blank faces of houses, the cryptic notion of an infinity of prime numbers, and the beautiful patterns of the world that inspire one person to make equations and another to make poems or vast canvasses filled with angels or to translate one to another so that I can sit with a notebook, wondering how to work this illustration of Mendel’s law into both an essay on family history and a quilt.

Dominant and recessive phenotypes. (1) Parental generation. (2) F1 generation. (3) F2 generation.