# Pronouns

My pronouns are "invariant / manifold". In topology, there is a very simple idea of an equivalence class. If you take a straight line (say from 0 to 1, and you say "one IS zero", then you've built yourself a circle. All of this is easiest in 2D, but you can build more complicated spaces this way. For example, if you take a square, and you identify the left side of the square with right side ("left IS right"), you've built a cylinder. Now if you take the circle on the top and the circle on the bottom and call them equivalent, you have a torus (a donut). A sphere is just the space built from a square, where you say "all the edges ARE a single point". Boom, you've built a sphere (or something topologically equivalent).

You probably already knows about the Mobius strip, too, but I'll remind you. If you take the square and you say that the top right edge IS the bottom left edge, and the bottom right edge IS the top left edge, you've built a Mobius strip. This one is weird, because you'll walk straight forward on it and end up upside down.

These are all "2-Manifolds", which means that you can really only travel in two "directions" (left = -right, and backward = -forward). They are "surfaces". In 3 dimensions, you might have something like a cube, where you say "the entire top face is equivalent to the entire bottom face" and you could proceed with all 6 faces identifying them with the opposite side. It's amazing how complicated things start to get already with only 3 directions, forget about the fact that you could do this with, for example any polyhedron with an even number of sides (a dodecahedron, say). In fact, the study of 3-manifolds and 4-manifolds is a very active area of cutting edge research in topology. Which is to say, non-trivial spaces with 3 or 4 directions are very complicated and hard to understand.

If the super-nerds have such a hard time grappling with complex spaces, I think we should give ourselves a little bit of a break for having trouble with social complexity, but I think we should also always strive to push our categories into more and more complex spaces. It's a good exercise. It keeps you fresh and light on your feet and it develops your empathy. I paint my toe-nails and wear a little shimmer on my eyelids in honor of this complexity. I try to cry when I am sad. But sometimes I still only have access to the 2 or 3 emotions we typically allow men to express. See if you can give the men in your life the space to be complex beings.