Sometimes Stephen and I still get stuck doing the dishes together, and then he remembers he’s my brother. I wash, he dries, and he asks me benign, avuncular, maddening questions, such as how do I like Grade Nine. He is in Grade Eleven, stairways and stairways above me; he doesn’t have to rub it in. But on some of these dish-drying nights he reverts to what I consider to be his true self. He tells me the nicknames of the teachers at his school, all of which are rude, such as The Armpit or The Human Stool. Or we invent new swearwords together, words that suggest an unspecific dirtiness. “Frut,” he says. I counter with “pronk,” which I tell him is a verb. We lean against the kitchen counter, doubled over with laughter, until our mother comes into the kitchen and says, “What are you two kids up to?”
Sometimes he decides that it’s his duty to educate me. He has a low opinion of most girls, it seems, and doesn’t want me turning into one of the ordinary kind. He doesn’t want me to be a pin-headed fuzzbrain. He thinks I’m in danger of becoming vain. In the mornings he stands outside the bathroom door and asks if I can bear to unstick myself from the mirror.
He thinks I should develop my mind. In order to help me do this, he makes a Möbius strip for me by cutting out a long slip of paper, twisting it once and gluing the ends together. This Möbius strip has only one side, you can prove it by running your finger along the surface. According to Stephen, this is a way of visualizing infinity. He draws me a Klein bottle, which has no outside and no inside, or rather the outside and the inside are the same. I have more trouble with the Klein bottle than the Möbius strip, probably because it’s a bottle, and I can’t think of a bottle that isn’t intended to contain something. I can’t see the point of it.
Stephen says he’s interested in the problems of two-dimensional universes. He wants me to imagine what a three-dimensional universe would look like to someone who was perfectly flat. If you stood in a two-dimensional universe you would only be perceived at the point of intersection, you’d be perceived as two oblong discs, two two-dimensional cross sections of your own feet. Then there are five-dimensional universes, seven-dimensional ones. I try very hard to picture these but I can’t seem to get past three.
“Why three?” says Stephen. This is a favorite technique of his, asking me questions to which he knows the answers, or other answers.
“Because that’s how many there are,” I say.
“That’s how many we
eyes, through microscopes. “In facets,” I say. “But each facet would still have only three dimensions.”
“Point taken,” he says, which makes me feel grown-up, worthy of this conversation. “But actually we perceive four.”
“Four?” I say.
“Time is a dimension,” he says. “You can’t separate it from space. Space-time is what we live in.” He says there are no such things as discrete objects which remain unchanged, set apart from the flow of time. He says space-time is curved and that in curved space-time the shortest distance between two points is not a straight line but a line following the curve. He says that time can be stretched or shrunk, and that it runs faster in some places than in others. He says that if you put one identical twin in a high-speed rocket for a week, he’d come back to find his brother ten years older than he is himself. I say I think that would be sad.