It's the first five words of Scripture – “In the beginning, God created ….” I'm not talking about a literal six-day view of creation. I'm not interested in the young-earth debate or proving there was an ark. I want to step back a little further and discuss simply the evidence that there is a God – the simple concept that used to be the foundation of the discussion on Intelligent Design. Are there scientifically observed things about our world that point to intelligence behind their origins? THAT is the question I wish Ham had debated. Ham could have won that debate without question, because the evidence is everywhere.
“Math is the language with which God wrote the Universe.” GalileoI shall now delve into a tutorial on Chaos Theory and Fractal Geometry. I am not an expert, but a long time ago at a National Council of Teachers of Mathematics convention, someone presented this topic to me, and I realized right then that this was where the heart of the discussion on the existence of God could be mathematically and scientifically founded. I was hooked, and I started doing my own study of the topic. I decided to teach what I could to my algebra students at the time. Before I could do that, I had to teach a lot to myself first. What follows is a simple discussion of a complex subject. If you'll hang with me for a bit, I promise to at least give you something to think about.
“Contrary to the connotations implied by its name, chaos theory does not eradicate the possibility of order. It does not serve to propagate notions of chaos. Chaos theory is really a science about finding organization in seemingly complex systems. It serves to find order in disorder.” Library.advanced.org/12170 Andrew Davenport, Shane Kraynak, Brian TimkoChaos theory is a branch of mathematics that did not take off until the advent of computers, for it involves millions of calculations that were simply too hard to do by hand. The idea behind chaos theory is finding mathematical order and meaning in seemingly random events. The first real life issue studied involved global weather patterns.
There are several hallmarks to chaos theory.
1. It studies unstable systems. Consider weather patterns. While we may note general tendencies that repeat regionally year by year, there is much that is fundamentally unstable in weather, as evidenced in particular by this year's multiple, unprecedented winter storms.
2. These systems are sensitive to initial conditions. A meteorologist named Edward Lorentz first identified this in 1961 as he attempted to find mathematical equations that would predict weather patterns. In the midst of a long set of calculations, he re-entered a number in the middle, rounding it as he entered it. Instead of entering 123.0699212, for example, he entered just 123.0699. That tiny difference in the two numbers played out with drastically different final results. Lorentz called this the Butterfly Effect – the idea being that a butterfly flapping its wings in Africa could result in a hurricane in the Caribbean.
For want of a nail the shoe was lost.
For want of a shoe the horse was lost.
For want of a horse the rider was lost.
For want of a rider the message was lost.
For want of a message the battle was lost.
For want of a battle the kingdom was lost.
3. These systems are aperiodic (meaning that they never repeat themselves). This is one of the fascinating things about a chaotic system, and it is the reason it appears chaotic. Can something that never repeats itself and doesn't show a discernible pattern actually have mathematical underpinnings? Absolutely!And all for the want of a horseshoe nail. http://en.wikipedia.org/wiki/For_Want_of_a_Nail
4. These systems are iterative (meaning that the next answer depends on the previous answer).
Now, I am faced with a dilemma. I could write out more mathematical explanations of the basics of chaos theory, but I think instead that I should skip the middle explanation and move straight to the implications for intelligent design. Normal Euclidean geometry involves points, lines, and planes. Most of us probably recognize the elements of Euclidean geometry from tortured memories of high school. The problem with high school geometry is that lines, planes, squares, and circles tend to be what we humans engineer in this world. But IF there is a God, His world doesn't much fit with Euclidean geometry. Chaos theory gives us a new geometry, Fractal Geometry, that reflects the seemingly random, arbitrary parts of God's vast creation.
“Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line.” Benoit MandelbrotPrior to Lorentz and Mandelbrot, there wasn't a lot of discussion about the mathematical design behind our seemingly random world. About the ordered, predictable parts of our world, yes. But the random parts like coastlines, weather patterns, mountain shapes, and patterns of erosion? Not so much. The evolutionary mindset was “out of chaos, order.” In that view, the Big Bang happened, and primordial soup formed. Eventually random stuff came together, and out of that soup, life began. Chaos Theory and Fractals give us a new paradigm. Mathematical order, appearing chaotic, results in order – this is a foundational concept in Intelligent Design.
I'll never forget the graph projected onto the screen at that NCTM meeting where I was first exposed to the concept. The speaker entered in an equation on the graphing calculator, gave it an initial seed value, and let it begin plotting its seemingly random points. After a few minutes, a very clear image began to emerge. It was a human face. I realized in that moment that math was indeed the language with which God had written His Universe. And my own personal face as well.
*For a basic demonstration of how mathematical order, appearing chaotic, results in order, check out this Chaos Game.
Fractal fern image found here.
See also Math and Theology.