Friday, September 10, 2010

Shadows and Plane Geometry

The shadow of the huge jet we are travelling on unceremoniously separates from the great soaring bird and swiftly disappears below us, as we take off from Toronto on Wednesday morning. The Westjet passenger plane and its shadow have officially parted ways and the two will not meet up again until they are reunited upon arrival four and a half hours later in Victoria British Columbia. During the flight, as I look down and out onto the Canadian landscape I can catch glimpses of it occassionally. Sometimes it jumps onto the cloulds below. Most of the time it is just a tiny dark speck racing over the planes of our northern geography, riding the contours of the lakes and rocky islands, slicing its way across the miles of farm land and then tumbling up and down the mountains, over acres of forested terrain on to the ocean.

My own shadow usually stays connected to me. It stretches and distorts and sometimes hides from me but it rarely leaves for very long, the way it separates itself from things that fly. I can jump, and for a brief second we are parted, but we re-attach immediately. It's like we are attracted to each other. My shadow and I are magnetized.

I can throw a rock in the air and for a brief moment the rock's shadow (if I can see it) trails along the ground racing to catch up with it. They are reunited at impact. The further the shadow and object are separated the harder and faster they try to get back together and the more violent is the moment of their convergence.

A rock and its shadow do not like to be cast too far. If they can't be on the same plane, they settle for tangents rather than projective geometry. A solid well-built wall makes planes that rocks and their shadows can live in comfortably. At the extremes of the sun's orbit across the sky all the shadows of all the rocks in the wall may venture out together, but not too far. Collectively they cast small, uniform amounts of shade over the surface of the wall. None show off. The attraction is the that no stone's shadow draws attention to itself. This is plane geometry. And rocks and walls are very good at it.

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