Chaos Theory Simplified

Chaos theory is an interesting idea. The term implies disorder or lack of rules or randomness. As we commonly think of chaos, we might think of the behavior of a mob after a huge football win or loss. But this would not be true.

Chaos theory as a name comes from the fact that the systems the theory describes (non-linear systems) would seem to be disordered or random or at least unpredictable. Chaos theory tries to find some underlying order in what appears to be random events or data.

The weird scientist in the movie “Jurassic Park” was a chaos theorist. He spoke about the flapping of butterfly wings in Brazil and studying whether they would or could cause a tornado in Kansas. While this may seem a little out there, the term “butterfly effect” is widely used. Chaos theory does look for underlying unifying patterns in systems.

Essentially, the theory looks at something called sensitive dependence on initial conditions. This means that even a very minute change in the initial conditions of a system can have dramatic effects on that system over time. Weather is a system that is studied widely so as to be better able to predict what conditions will be like.

Edward Lorenz was an early pioneer of the theory. He was working on weather predictions in 1961 and was using a computer to help with the calculations. As an aside, the advent of the computer with its ability to do virtually simultaneous large scale calculations was invaluable to the promotion of the theory.

Lorenz had initiated a sequence of data based on twelve variables in his attempt to predict weather. He wanted to see the sequence again, so re-entered the data. To save time, he began the new simulation in the middle of the old, using a printout from the prior calculations.

The weather patterns the computer predicted from the new simulation was very different from what had been initially predicted. Working backward, Lorenz discovered that he had entered the data only out to the third decimal point, whereas in the initial simulation, he had used the same data out to the fifth decimal point. These differences are really very, very small and, according to the thinking of the day, should have had only a tiny impact, if any, on the resultant predictions.

Scientists of the day had focused their thinking on linear systems, where the whole is essentially the sum of the parts. However, there had been a number of instances where linear functions did not explain the behavior of the system, such as with Lorenz. Non-linear systems are much harder to describe since the mathematical equations cannot be added together to produce new systems as with linear systems.

This phenomenon has been observed in such diverse areas as fluid dynamics, the motion of planets, economic cycles, general relativity, and in broad psycho-social systems. However, it has only been since the middle of the 20th century that mathematical techniques have been developed to deal with them.

To put this in more simple terms, consider a football team. Each individual player has a certain set of quantifiable skills at their position, skills which can be given a score. Summing the scores of all persons on a team, then comparing one team with the scores from another team should give a clear sense of the difference and thus predict the winner of a game between them. This is the linear way of looking at a team, only as the sum of its parts.

However, there are many other sets of variables that come into play such as “team chemistry”, whether the game is played at home or away, experience playing with one another, the mood or attitude of an individual player or players, and on and on. These can and do lead to results that are different from those predicted by linear thinking. As a great many people have observed over the years “this is why they play the game!”

We know from chaos theory that even very minute changes can produce widely different outcomes. Chaos theory also suggests that, if you can understand all of the variables affecting a system, the underlying pattern will eventually emerge and it will be easier to predict outcomes. This seems like a huge undertaking, even in football. But in physics…

Quantum chaos as a field of study grew out of quantum mechanics. At the time that many of the theories driving quantum mechanics were formulated, set aside were the facts that certain systems exhibited chaos (randomness) in their classical limits.

In other words, where Quantum mechanics would predict that a given system is a sum of its parts and thus should behave as X or Y, these results did not obtain. Some of these areas include level repulsion in the spectrum, ionization rates of atoms, enhanced stationary wave intensities in space, and so on. Using the mathematics developed as the result of chaos theory (fractals being an example), physicists are expanding their inquiry into chaotic systems.

Other areas utilizing chaos theory principles to extend and better understand the systems they deal with include psychology, sociology, biology, economics and so on. This most interesting concept has even been applied to the movement of traffic on roads.