Several years ago, I wrote a bit about fractals. I am revisiting that post here.
I am so in favour of the actual infinite that instead of admitting that Nature abhors it, as is commonly said, I hold that Nature makes frequent use of it everywhere, in order to show more effectively the perfections of its Author. Georg Cantor, 1845-1918
Fractals are awesome (too bad that adjective is so blunted by overuse and misuse). Sure, they are beautiful and, of course, the fact that math is involved is intriguing to me. But the real reason that I like fractals so much is because I can think of no better way to describe how I think about the universe and eternity. And as I was taking some time to just “contemplate,” I came to the conclusion that a fractal also best describes my understanding of scripture.
Most people have seen the lovely images of fractals, and many may even have some concept of the mathematical equations that generate the images. But some of you may still wonder, “What is a fractal, really?” OK, Fractals 101.
a rough or fragmented geometric shape that can be split into parts, each of which is (at least approximately) a reduced-size copy of the whole,” a property called self-similarity. Roots of mathematical interest on fractals can be traced back to the late 19th Century; however, the term “fractal” was coined by Benoît Mandelbrot in 1975 and was derived from the Latin fractus meaning “broken” or “fractured.” A mathematical fractal is based on an equation that undergoes iteration, a form of feedback based on recursion.”
[Note: If you have been reading along with my Gödel, Escher, Bach book discussion group (see here), this will really start to set off fireworks in your brain. Any time you see the word “recursion” again, you will definitely think of Hofstadter’s explanations.]
So what do fractals have to do with anything? For one thing, they are an easily accessible visual aid to the complex idea of infinity. One of the most amazing things to teach, I think, is astronomy. When you contemplate what you are really seeing when you look at the night sky it takes your breath away. With the naked eye you see the moon, constellations, planets. Zoom out… with binoculars or a telescope you can see more. And when you look at images from the Hubble telescope you are looking at stars and galaxies that are huge, old, distant, beautiful, and oh-so-numerous. A field of what looks like stars is really a field of entire galaxies. It kind of reminds me of the end of the movie Men in Black when the camera pans out from earth, to the solar system, to the galaxy, to a marble that contains the galaxy and is in the hands of some alien who is playing a game with it. I’m not interested in the alien aspect… I’ve just always been fascinated by the degrees of immensity.
Now go the other way… zoom in to the earth, to the rocks, the minerals, the elements, the molecules, the atoms, the sub-atomic particles. But it is so hard to see the “big” picture of the universe and the “small” picture of the details all at the same time… except in a fractal! Looking at that one image I can keep going deeper and deeper and pondering the immensity of the created universe.
[by the way, if you want to see the version of this video that explains the processes being animated, go here]
But just as amazing as that (or maybe even more so), is being able to look at scripture in the same way. For so long I looked at Scripture far too linearly. I saw the history and the stories and prophesies. I memorized the Gospel accounts and looked for the symbols and types in the Old Testament and fulfillment in the New. But now I see that there is so much more. Just as a fractal is one whole that beautifully communicates a single equation, so Scripture is one communication–a breaking into creation by God–with both a singleness and multiplicity. One story, unfolded in many iterations. Acted out over centuries, through many generations, cultures, languages, and individuals. Story upon story. But all part of the same one communication. God is breaking through to us to tell us about Himself. Using our own human context to speak to us, so that we can understand. It’s more beautiful and more amazing than a hundred thousand galaxies or the patterns repeated over and over in nature or the dancing movement of electrons and quarks and leptons.
Sometimes the beauty and majesty are hard to see in the black and white text, and so I keep a mental bookmark of a fractal image in my Bible to remind me of just how glorious and precious the book in my hands is.