A Mandelbrot Diagram of the Soul

Several months ago I saw an excellent PBS show about Benoit B. Mandelbrot, the discoverer of fractal geometry. For those of you not in the mathematical know, fractal geometry is based on mathematical calculations so minute that they can only be accomplished by computer. They explain everything from the shape of coastlines to the branching of trees and plants, and demonstrate that the geometry of nature is far more complex than that of traditional mathematics.

For years, people thought Dr. Mandelbrot was nuts. Now his work is the basis of many inventions, including the sort of antennas that make it possible for tiny phones to access broadband internet.

But what most interested me about the documentary was Mandelbrot himself. As a child, he wasn't considered gifted in mathematics. Somewhere in elementary school he discovered that he could "see" algebraic equations in his head as geometric shapes and immediately knew the answers to the problems posed by his teachers. While the ancient Greeks saw numbers as shapes -- which is one reason they invented geometry -- people today are not accustomed to envisioning algebra in three dimensions. But his mind worked that way all by itself.

Fast forward to a month ago, when I participated in the first meeting of a spiritual book club at our parish. We had read a book about four saints named Theresa and one of the participants asked how it was possible for St. Therese of Liseaux to know so much about God when she was four years old. Later, I thought of Dr. Mandelbrot and his remarkable ability to see what no one else saw.

Long before graduating elementary school Dr. Mandelbrot and St. Therese both saw, as clear reality, what was invisible to everyone else. Dr. Mandelbrot went on to see a whole new form of mathematics -- not in the form of visions or mathematical ecstacies, but as concrete and obvious and reflected in nature. St. Therese went on to experience God in a whole new way -- not in the form of visions or ecstacies, but as so obvious in the world around her that she only bothered to explain it when made to. What they saw and explained has made a huge difference in the world.

Looking the incredible variety of saints the Church has produced, I wondered what they would look like if you could somehow calculate and plot them: all those martyrs and kings and hermits, all those scholars and peasants, all those prickly curmudgeons and open-hearted givers, every type of person there is made holy. Upon reflection, I think they would look like one of Dr. Mandelbrot's famous diagrams, all whorls and curves, unexpectedly but harmoniously veering out and coming back -- a Mandelbrot diagram of the soul.