I’ve raved before about Robert Sapolsky’s fantastic Stanford course Human Behavioral Biology (iTunes), but I have to draw your attention to two stand-out lectures near the end of the course. In lectures 21 and 22, Sapolsky talks about how the mathematics of chaos helps answer the big questions in biology.
At the very beginning of the course, in lecture 1, Sapolsky tells his students to read James Gleick’s 1987 bestseller Chaos, a book that Sapolsky says changed his life. I was intrigued and I duly read the book, which is an introduction to the science and mathematics of chaos. I learned a lot about complex and unpredictable systems like weather, and how small perturbations can have huge consequences, the famous “butterfly effect.” But after reading the book I was puzzled. What did this chaos stuff have to do with human behavior?
In these two lectures, Sapolsky makes the connections. He starts out with a whirlwind history of scientific reductionism, the idea that we can understand a system if we break it down into its component parts. Reductionism, Sapolsky says, is the basis of most of modern science, but reductionism cannot explain everything. As an example he cites the complex branching systems in the body like the circulatory system. These systems have millions of branches, and we don’t have enough genes to code for all of these branching node if we had to have one gene per node. It turns out that the mathematics of fractals, which are part of chaos theory, can help explain how the branching can come about with a few simple rules that are relatively easy to code.
He goes on to talk about cellular automata, the intriguing patterns that emerge when a system has a few simple rules. (For a quick visual overview of cellular automata check out The Game of Life, and this nifty Java program that runs a number of cellular automata.) He also touches on neural networks, fractals, and how an ant colony can solve a problem that human mathematics cannot. It’s all great fun, and eminently understandable, even if you don’t want to make your way through all the other lectures in the course.