Compression and Decompression in Mathematics1

Abstract

The mathematician Hermann Weyl (1952) explained that a body in the world incorporates its environment, or rather, its ancestors' environment of evolutionary adaptation. An unmoving minuscule organism that floats in the ocean at a depth where gravity and water pressure balance each other out is nearly spherical, because for such an organism all directions are functionally the same, and so selection produced a suitable body. Its experience has spherical symmetry and so does its body. A plant fixed to the ground-like a tree-is asymmetric top to bottom because gravity creates an environment where all directions are not the same. The tree's environment is characterized by a constant difference: the gravity vector points down; a tree's form must deal with that. On the other hand, trees have mostly equivalent environments in any direction perpendicular to the vertical gravity vector-"mostly equivalent" because there are variations in the relative path of the sun, the flow of water, a strong onshore wind, and so on. Accordingly, trees, ignoring these local differences, for the most part have bodies that are the same in all directions perpendicular to the vertical axis. An animal on the ground that moves has different experience in the direction it is headed than it has from the direction whence it came, and so has a body that is different front to back. We run into things we are moving toward, not things from which we are moving away. We experience gravity and we move. Accordingly, our bodies are, on the outside, anatomically , pretty much different up-down and front-back, but not so much left-right. What can happen from the left can happen from the right. What we can do to the right we can pretty much do to the left. We can mostly reverse our experience to the left versus right just by doing an about-face. We are set up for this: it would