What do I remember of reading about chaos theory in the 1970s and ’80s? That everything is chaotic but there is order in the chaos. In 1972 a scientific paper entitled “Predictability: Does the Flap of a Butterfly’s Wings in Brazil set off a Tornado in Texas?” Following that, James Gleick published “Chaos: Making a New Science,” which became a best-seller because of its premise and because of its readability by a layperson (that would be me).

Somewhere around that time, Marin County philosopher Alan Watts sat on top of Mt. Tamalpais, let out a breath to the West and imaged it flowing around the earth to come around and touch him on the back of his head.

Prior to reading Chaos, I never liked killing anything . . . not an art, bug or moth. I had to excuse myself from frog-cutting-up in science classes. When the neighborhood boys tormented any creature, I cried. After reading Chaos, I can’t kill anything because of the effect it might have on our universe. Also, since that time, it has become very clear to me that everything is everything . . . we are all irrevocably connected. “We” meaning everything, not just people.

20th Century science introduced three main theories to the general public: quantum mechanics, relativity, and chaos. Chaos theory is a blanketing theory that covers all aspects of science, hence, it shows up everywhere in the world today: mathematics, physics, biology, finance, and even music.

The term chaos theory is used widely to describe an emerging scientific discipline whose boundries are not clearly defined.

From various Web sites:

Chaos theory is a developing scientific discipline which is focused on the study of nonlinear systems. To understand chaos theory, you must first have a grasp its roots: systems and the nonlinear.

System can be defined as the understanding of the relationship between things which interact. To better understand this idea, we will examine the example of a pile of stones. The pile is a system which interacts based upon how they were piled. If their initial piling is not in balance, the interaction results in their movement until they find a condition under which they are in balance. A group of stones which do not touch each other is not a system because the interaction between is so minute, it can be considered non-existant.

Systems can be modeled, meaning systems can be created which will theoretically replicate the behavior of the original system. Following the pile of stones example, one could take a second group of stones which are identical to the first group, pile them in exactly the same way as the first group, and predict that they will fall down into the exact same configuration as the first group. Similiarly, a mathematical model, based upon Newton’s law of gravity, could be used to predict how piles of same and different types will interact. Generally speaking, mathematical modeling is the key to modeling systems, although it is not the only way.

Nonlinear has to do with the type of mathematical model used to describe a system. Until the interest in chaos theory, hence nonlinear systems, most models were analyzed as though they were linear systems. In other words, when the mathematical models were draw in a graph format, the results appeared as a straight line. Calculus was Netwon’s mathematical method for showing change in systems within the context of a straight line and statistics.

Linear systems are easy to generate and simple to work with. That is because they are very predictable. For example, you could think of a factory as a linear system. We could predict that if we add a certain number of people, or a certain amount of inventory to the factory, that we will increase the number of pieces produced by the factory by a comparable amount.

As most managers know, factories don’t operate this way. Change the number of people, inventory, or any other variable in the factory and you receive widely differing results on a day to day basis from what would be predicted from a linear model. This is true because a factory is actually a nonlinear system, as are most systems found in life. When systems in nature are modeled mathematically, we find that their graphical representations are not straight lines and that the system’s behavior is not so easy to predict.

Prior to the devolepment of chaos theory, the majority of scientific study involved attempting to understand the world using linear models. Beginning with the work of Sir Isaac Newton, physics has been the has provided the processes for modeling nature, and the mathematics associated with them have been in a linear nature.