30 CHAPTER THIRTY Life is full of Chaos

Most of us tend to assume that results change proportionally with inputs—that if we leave a little later we will get where we are going a little later, or if we study a little harder we will do a little better on the test. While that is often true, there are many situations in which it is not—situations in which a small difference at the beginning can result in a huge difference at the end. The study of such situations has developed into a new branch of science and mathematics over the past fifty years and is called Chaos Theory—aptly named for the havoc such “sensitive dependence on initial conditions” can create in your life. There is an amazing book that explains the development and uses of Chaos Theory, which I highly recommend: Chaos: The Making of a New Science, by James Gleick.

Some examples might help. I leave for work at five o’clock in the morning. I do this not because I am naturally an early riser, but because I know that if I leave then I will beat the traffic in which I will get caught if I wait and leave at six o’clock—if I leave at five o’clock I reliably get there by six thirty (one-and-a-half hours of travel), but if I leave at six o’clock I will not get there until eight o’clock (two hours of travel) and maybe not until nine o’clock (three hours of travel) if there is an accident, which is more likely with more traffic. If, on the other hand, I could wait until ten a.m. to leave, traffic would likely have dropped back off, and the trip would likely be back to an hour and a half.

Sometimes the impact of small changes is even more extreme, with small quantitative changes (a few more or less of something) resulting in important qualitative changes (whether something happens at all or not). Think of what happens if you miss a train or bus or plane by just a few minutes or even seconds. That small difference in your arrival time at the depot or gate will result in a large, and probably inconvenient, difference in how your day develops—you may end up not making the trip at all! The last five minutes of studying may lock the information in your brain in ways the first ten hours did not (you may finally “get it”), ensuring success on the test. This idea that small changes can beget disproportionally large changes is sometimes called the “butterfly effect,” and is captured in an old nursery rhyme:

For want of a nail, the shoe was lost,

For want of the shoe, the horse was lost,

For want of the horse, the rider was lost,

For want of the rider, the message was lost.

For want of the message, the battle was lost,

For want of the battle, the kingdom was lost,

And all for the want of a horseshoe nail!

Once you understand the idea, you will come to realize that we all experience the butterfly effect many times every day.

But there’s more. It turns out that situations or systems that are sensitive to initial conditions can display very complex behavior—and there are many, many natural systems that display that sensitivity. Consider, for instance, weather, which was one of the first things to which Chaos theory was understood to apply. A very small change in temperature or pressure (even the beating of a butterfly’s wings—thus the name, butterfly effect) can cause not just a large change in temperature or pressure, but a thunderstorm experienced a few weeks later: change in a chaotic system often happens not through a gradual, smooth process, but through turbulence. Thus it is expected that the most important short term manifestation of global warming (whatever its cause) is not the very slight increase in average temperatures around the world, but a very significant increase in the number of storms, hurricanes, and weather-related disasters—an increase in turbulence. This will likely have huge economic impact as property along coasts is repeatedly damaged, fruit crops are destroyed by late-winter temperature swings, and other consequences develop. We are already seeing that and should expect to see more.

The thing I love most about chaos theory is the way it helps us understand the complexity and beauty of the world. Simple equations can generate the endless variety of snowflakes, the placement of leaves on a tree (in fact, the shapes of the leaves themselves), the behavior of insects, and even “random” numbers—the “random” numbers generated by a computer are, in fact, not random, but generated by equations. Indeed, contemplating chaos theory makes me wonder whether anything in life is really random—perhaps everything is just an endless array of interacting chaotic systems, meaning, to quote Einstein, that “God doesn’t play dice with the world.” In the end, chaos theory gives me a sense of how small differences in the world (such as made or missed stoplights, the way the football bounced, information people remembered or forgot to tell us, a tool or instrument that just happened to break at the right or wrong time, etc.) might indiscernibly reflect the hand of God in my life, helping explain why it is written that, “We can make our plans, but the Lord determines our steps.” In any case, chaos theory makes me aware that everything I do may have more wide-ranging impact than I ever realized.