There are two kinds of theories out there: ones that say "Hey, look I found something new! Look what we can do!" and then there are ones that say "Remember when we thought we might be able to do that thing, well it turns out we can't". Chaos theory is the latter - it turns out that we aren't as capable as we thought in predicting patterns, despite the recent revolutions in technology.

"Physicists like to think that all you have to do is say, these are the conditions, now what happens next?"
-Richard P. Feynman

The roots of Chaos theory comes from physics. 300 years ago Sir Isaac Newton saw the world as "deterministic". That is, from the same initial conditions the same sequence of events will happen. So if you rack up a set of billiard balls exactly the same way twice and hit it the same way twice, then the outcomes will be the same. Newton used this assumption to create laws which are now ubiquitous throughout physics. Determinism was the belief of the entire scientific community - it can even be traced back to the Ancient Greeks - until the 20th century with the birth of computers.

The key to grasping the concepts behind Chaos Theory is to understand the idea of uncertainty in measurement. In order to measure anything in the world truly, we must have infinite precision. How high is Mount Everest? Is it 29,035 feet? Or 29,035.2 feet? How precise is that measurement anyway? In order to know exactly how high Mount Everest really is we'll need to use an infinite amount of decimal points, something which is impossible even theoretically. There is, therefore, some uncertainty in the height of Mount Everest. Actually, there's uncertainty in everything we measure.

Scientists always knew about uncertainty, so why didn't they come up with Chaos until recently? Well they always figured that, since we knew the deterministic patterns, the closer we measured conditions, the closer our final answer will be to the true answer. So, if I were to add more thermometers and barometers around the world, then our meterologists will be able to predict our weather patterns with more accuracy and further in advance, right? Wrong. That's where Chaos comes in.

In 1963, Edward Lorenz wrote a computer program to simulate weather patterns. He measured what seemed to be the same initial conditions and came up with drastically different weather predictions. It turned out that his initial conditions (eg temperature, pressure, etc.) were only slightly different, yet their simulations completely diverged from each other after a short period of time. The world was intrigued. So in the 1970s, scientists like Poincaré studied the data from Lorenz along with other sources and came to the conclusion that deterministic solutions will always diverge no matter how similar the initial conditions are, all because of this uncertainty factor.

When you think about it, this makes sense on a superficial level because there's always going to be an error in our measurements. Those errors compile on each other the more time goes by. The more complicated a system happens to be, errors will combine to create so much uncertainty that the outcome is unpredictable. This is why Quantum Mechanics is so popular in physics today: if we study the smallest things we know of, then those will have the least amount of chaos in the end.

Now you usually see Fractals mentioned in the same vein as Chaos Theory, so how do those fit in? Well fractals came into the picture when Mandelbrot tried to measure the coastline of Great Britain. If you were to take a stick which was 1 kilometer long, you could approximate the length, but you'd be missing some bumps and bulges. Also, a 1 meter long measuring stick would only approximate the length. In fact, the shorter the stick you use, the longer the coastline becomes (in order to compensate for all the bumps and curves that occur in the sand and rock). So if the length of Britain's coastline is infinitely long, yet the area of the island is finite, something crazy must be going on here. That's how fractals began - with shapes with infinite perimeter but finite area (like the Van Koch snowflake). So the chaos involved in the imprecision of measurements birthed the idea of figures with fractional dimension.

Other than telling us that the 5-day forecast is a myth, what good is Chaos Theory? Some scientists tell us that our understanding of how predictions fall apart in the end points to a bigger picture. We must be a part of a vastly more complicated universe than we know of. It's possible that there are factors which we don't know of which affect our measurements. There's only question that still lingers: is our universe deterministic? Nobody knows.

Page last updated: February 04, 2008