fractals

Examples of fractals are everywhere in nature. They can be found in the patterns of trees, branches, and ferns, in which each part appears to be a smaller image of the whole. They are found in the branch-like patterns of river systems, lightning, and blood vessels. They can be seen in snowflakes, seashells, crystals, and mountain ranges. We can even see the holographic and fractal-like nature of reality in the structure of the Universe itself, as the clusters of galaxies and dark matter resemble the neurons in our brain, the mycelium network of fungi, as well as the network of the man-made Internet.

The natural world is built upon common motifs and patterns. Recognizing patterns in nature creates a map for locating yourself in change, and anticipation what is yet to come.

Cocoa-buttered girls were stretched out on the public beach in apparently random alignments, but maybe if a weather satellite zoomed in on one of those bodies and then zoomed back out, the photos would show the curving beach itself was another woman, a fractal image made up of the particulate sunbathers. All the beaches pressed together might form female landmasses, female continents, female planets and galaxies. No wonder men felt tense.

While we think of the boundary between what is legal and what is not as a clear dividing line, it is far from being so. Rather, the boundary becomes further and further indented and folded over time, yielding a jagged and complicated border, rather than a clear straight line. In the end, the law turns out to look like a fractal: no matter how much you zoom in on such a shape, there is always more unevenness, more detail to observe. Any general rule must end up dealing with exceptions, which in turn split into further exceptions and rules, yielding an increasingly complicated, branching structure.

All high mathematics serves to do is to beget higher mathematics.