mathematics for psychonauts

            A blank white expanse sears your eyes, and you squint. The horizon is a razor-straight boundary between the brightest white and deepest dark you can imagine. As your eyes adjust to this strange polar world, shapes start to resolve on the white surface below you. First, you encounter a cluster of points, and find them completely textureless. There are enough that you don’t bother to count, they’re fixed to the white ground, and seem almost a part of it. You look into the black sky and notice directly above you a light smudge, which slowly focuses into the inverse of the points on the ground.

     Strange place this is, you think. You begin to move. The points on the ground fade into the distance behind you, but you can still see their inverse on the black above. This gives you some comfort. Eventually, something moving on the ground catches your eye. Again, it’s a cluster of points, but this time, scattered across a much larger area. Again, you poke at them, and again, they’re so textureless that you wonder if you’re seeing things. But, as you ponder this strange collection of points, they begin to move. They drift together, closer and closer, until they seem to be overlapping. You look closely and see that they’re not overlapping, but just perfectly touching one another, which each point touching two others. They fall into a line, one after another, and eventually the line stretches away into the horizon. You look up, and the line has appeared in stark white-on-black above you, and the two lines eventually meet at a point some indeterminate distance away.

      You wonder about the nature of that meeting point, so you make it your goal. Then, you know you’re moving because the cluster of points in the sky, which was previously nearly directly above you, has now fallen to a position just above the horizon behind you. Eventually they disappear below the horizon, but the view in front of you, bafflingly, stays exactly the same. Growing tired of the very sparse vista, you decide to turn around, and go back to where you at least had the variety of points with your line. Once you see the cluster of white points rising into the sky like a moon, you know you’re back where you started.
     You head towards them until they’re directly overhead, and you look below you for their black-on-white partners. And now they’re gone! What had seemed so thoroughly fixed to the ground earlier is now completely absent. You touch the white blankness where you expected the points to be, and find it feeling identical to the way it did before you began your journey. Confused, and maybe a little disconcerted, you realize that you wanted the points to be there. You didn’t know what you’d do once you arrived, but you wanted the points to be there when you did. Seemingly on cue, the points return again. At the precise moment when you specifically want them to be there, they appear. From then on, this black and white space acquires real meaning. The experience of blackness and whiteness are mere abstractions, convenient material from which to construct ideas, and watch them interact.

     Willing another line into existence, you notice that the new line does not necessarily follow the same path of the old one. From your current position, you can’t see where they intersect on the white plane, but you can see them intersect on the black plane, far above and towards the horizon. You continue to generate lines, one after another at random angles, until the area around you is filled with a random crisscrossing of lines, like a madman’s railyard. When you look up, you see all of your lines stretching away around you. You realize that even with all your activity, the black and white is still vast and mostly blank. If you only rode any one of those new lines, you’d find yourself in another utterly barren area.

            You ask yourself, what is this place? What place could be so featureless and empty, yet so ready to respond to your whim? My friends, the answer is simple.

            You are now exploring your own imagination.