One of the earliest pioneers of chaos theory was Edward Lorenz. Lorenz was a meteorologist at the Maachussetts Institute of Technology. In 1960, Lorenz began a project to simulate weather patterns on a computer system called the Royal McBee. Lacking much memory, the computer was unable to create complex patterns, but it was able to show the interaction between major meteorological events such as tornados, hurricanes, easterlies and westerlies. A variety of factors was represented by a number, and Lorenz could use computer printouts to analyze the results. After watching his systems develop on the computer, Lorenz began to see patterns emerge, and was able to predict with some degree of accuracy what would happen next.
While carrying out an experiment, Lorenz made an accidental discovery. He had completed a run, and wanted to recreate the pattern. Using a printout, Lorenz entered some variables into the computer and expected the simulation to proceed the same as it had before. To his surprise, the pattern began to diverge from the previous run, and after a few "months" of simulated time, the pattern was completely different.
Lorenz eventually discovered why seemingly identical variables could produce such different results. When Lorenz entered the numbers to recreate the scenario, he the printout provided him with numbers to the thousandth position (such as .617). However, the computer's internal memory held numbers up to the millionth position (such as .617395); these numbers were used to create the scenario for the initial run. This small deviation resulted in a completely divergent weather pattern in just a few months. This discovery creates the groundwork of chaos theory: In a system, small deviations can result in large changes. This concept is now known as the "Sensitive dependence on initial conditions."
At this time, Lorenz was using a series of twelve mathematical equations to try accurately to model weather patterns. Experimenting with data collected from weather stations, he ran a series of computer programs to test his model. Occasionally he would repeat an experiment. On one such occasion, instead of re-entering all the data he truncated the number .506127 to .506 and ran his program using this approximate value. To his amazement the new results were totally different. A very small change in his input data could result in a major change to his predictions. In addition, these changes appeared to be random in nature.
Puzzled by these findings Lorenz simplified his original model to one involving only three equations. The reduced system still exhibited sensitivity to input data, but now he could view the results in 3 dimensional space.
Prior to Lorenz's experiments, mathematicians and physicists had observed two kinds of systems. There are those which settle into a steady state (a fixed point), just as the temperature of a cup of coffee tends to room temperature, and those which repeat their behavior after a specified time period, such as the motion of the earth around the sun. But Lorenz's solutions were much more complicated, never repeating themselves nor settling to a single point; they filled out a strange fractal-like set in 3 dimensions similar to a double spiral and were very sensitive to small changes in the starting values.
Lorenz's discovery shocked the scientific world. Chaotic systems soon began to be recognised in all branches of science. As mathematicians started to unravel its mysteries, science reeled before the implications of an uncertain world intricately bound up with chance. The human heartbeat is chaotic, the stock market, the solar system and of course the weather. In fact the more we learn about chaos the more closely it seems to be bound up with nature. Fractal structures seem to be everywhere we look: in ferns, cauliflowers, the coral reef, kidneys… Rather than turn its back on chaos, nature appears to use it and science is beginning to do the same.
Recently mathematicians have shown that you can control chaos. For instance here in the Mathematics and Physics Departments at The University of Queensland theoretical and experimental work with lasers shows that the rich structure inherent in chaos can be harnessed to expand the capabilities of lasers. Perhaps in the future single systems, which are capable of multi-tasking, such as the brain, will be modeled by chaotic systems. We still have a lot to learn about how nature uses chaos, but perhaps unpredictable behavior is not undesirable. As Henry Adams
said "Chaos often breeds life, when order breeds habit."
