I recall white card stock on an easel. On the card stock was a thick, black circle with “God’s Love” imprinted in the center in a Stranger Things font. As the pastor’s kid, I was expected to sing loudest of all,
God’s love is like a circle
A circle big and round.
For when you see a circle,
No ending can be found.
As a nine-year-old in Sunday school, I drew the line. The lyrics were absurd. I complained to my mother. A circle has to be drawn, right? And doesn’t this mean it has to start from somewhere, and, also, end somewhere else? My mother told me I was missing the point.
Among Ivan Karamazov’s monologues in The Brothers Karamazov is his conviction that that the world “stands on absurdities.” But Ivan finds himself ill equipped to the task of questioning foundational beliefs. So he rejects people who do not think God “created [the world] according to the geometry of Euclid,” who believe in a God that “let parallel lines meet.” I may have been missing Ivan’s point, but this led me to question the absurdity of hypostatic union.
Hypostatic union is a theological term that describes how the fully God and fully human natures of Christ could be combined. The church fathers labored over how this was possible for centuries. A hair’s breadth too much divinity or too much humanity and you were spun off as a heretic. It’s an impossibly abstract concept that doesn’t render itself any more theologically understandable with linguistic concision. Note the fifth-century Definition of Chalcedon: “unconfusedly, unchangeably, indivisibly, inseparably”—as catchy as a praise and worship chorus and, for me, just as lacking. I’m not faulting the early church fathers. The math just wasn’t there. Jesus is a fractal.
You may remember that, back in math class, you were taught that interior angles of triangles add up to a fixed amount; parallel lines never meet. Remember lengths, areas, and volumes? Remember theorems and proofs? This is Euclidean geometry. And it is widely useful on a practical level; from arranging living room furniture to building a shed in the backyard, we use it all the time.
Another aspect of Euclidean geometry worth understanding involves the arc of a circle. When we examine this arc at smaller and smaller scales, it will eventually come to a fixed point. What was once warped straightens itself out if we adopt a Euclidean worldview.
But the more our world has been probed, the more questions have arisen of nature, the cosmos, the cell, the human body, morality. The Euclidean applications of area and length are unable to explain the chaotic branching of trees or the puffs of clouds or the zigzagging of a coastline. Phenomena exhibit more and more disorder the closer we look. The world doesn’t straighten itself out.
If we are to understand how Jesus is a fractal, we need to be better than Ivan Karamazov. We live in a non-Euclidean world. This requires new understandings of geometry to explain it. Fractals are particularly interesting because it’s a field of study that wrestles with observable disorder. Benoit Mandelbrot first utilized outlying, nearly forgotten mathematical concepts to explain the lack of order appearing at smaller and smaller scales. He figured out a way to make the increasing chaos and disorder predictable.
In his classic thought experiment, Mandelbrot presents a view of the coastline of Great Britain. From one distance, high above, we can measure the coastline in kilometers all the way around and record the length, the perimeter. But as we zoom in to the point we can measure our coastline in meters, we notice more zigs and zags we couldn’t see higher up. We measure it and this increases the overall length of the coastline. Not by much, but more than we had at the higher viewpoint. Zoom in again to measure it in centimeters and there is more zigging and zagging that also yields an even greater length. Zoom in to measure it at millimeters, another increase in length. And so on and so on and so on down to a view of the coastline at the quantum level where the scale supposedly can’t get any smaller. (Though every year, it seems to grow smaller and smaller.) In the pure mathematics realm of fractal geometry, though, fractals are infinite.
Mandelbrot proved that the chaotic, repetitive zigging and zagging is self-similar. Self-similarity is when an object displays the same properties, regardless of the scales of comparison. Much of the natural world exhibits this characteristic: one leaf of a fern resembles the entire plant; the florets of broccoli mimic the larger head. This geometric breakthrough was suddenly able to explain nature—the furcating of trees, clouds, snowflakes, coastlines; and the inside of our bodies—the bronchial branching in the lungs, ducts in the liver, the heart, blood vessels. Fractals make a deepening complexity and perceived disorder comprehensible.
According to science writer James Gleick, author of the book Chaos: Making a New Science, self-similarity also “helped scientists who study the way things meld together.” Like the infinite and the finite. Go back to Britain’s coastline and draw a circle around it. In the pure mathematics of Mandelbrot’s theory, the coastline increases to an infinitude of length as the scale continuously diminishes. And this occurs while the area of the circle remains constant, infinity within the finite.
Self-similarity has theological import. The Definition of Chalcedon uses the phrase “self-same” to understand Christ in relation to our human nature and in relation to the divine nature. Fully God and fully man, all the way down, regardless of scale. Infinity within the finite.
I may be missing the point, but fractals bring Christ a little closer to me. Christ and his two natures, grace upon grace, couldn’t have come into a Euclidean world. As God’s example of love, Christ is analogous, mimicked by the tree branches we can climb up and the coastlines where he spoke of fishing for people, like the organization of our capillary beds that bleed into our sweat. I live in a world desperate, to quote Jacques Maritain, for an “infinity that wounds the finite.” And, absurdly, maybe what it needs, you can draw a circle around.