I'm sure you also noted that this week there was an entry in almost every news portal that Edward Norton Lorenz had passed away. He was an American mathematician and meteorologist, and a pioneer of Chaos Theory. By the way, he is the second person I write about in a short amount of time. If you remember the other one had been Arthur C. Clarke .

Why is Lorenz important to you?

Lorenz is one of those special people whose work tunneled mainstream to academics. Like Poincaré (1899), Birkhoff (1927) and others before him, Lorenz studied systems of non-linear equations. As a meteorologist he used these equations to predict the weather. Unlike others before him, he was able to incorporate in his research a new and exciting tool at the time - the computer. In 1963 he proved that systems of nonlinear equations could behave in an unpredictable way. When in 1976 he used a pocket calculator and the logistic equation to demonstrate how an equation of utter simplicity could have such complex behavior, he finally allowed the world to see the power of Chaos Theory!

What is the Logistic Equation?

I know you know this (these are for the other readers that have to a little catch up). The logistic function is an S-curve that represents the growth of a generic set P (imagine P as Google's stock price). The initial growth is exponential; then, as saturation begins, the growth slows, and at maturity, growth stops.

The formula is VERY simple, and yet different combinations of the variable factors lead to extremely different results.



The phenomenal thing about this equation is that for specific values of a, m, n, and t it actually depicts real phenomenon such as biology or economics. For instance, population growth follows the logistic equation. Initially when resources are plentiful the population can grow extremely fast, and has resource diminish, the population growth diminishes.

Why is Chaos Theory important to you?

In a nutshell Chaos Theory is a discipline that tries to bring order out of disorder. It tries to study how apparent random phenomenon actually have a deterministic behavior, or in other words, can be represented by a mathematical equation. It also studies how constantly changing events influence the balance of a system.

What can we really predict?

Mutual fund managers believe that the future price of stocks can be predicted using Chaos. Certain people in government believe that by analyzing patterns of phone calls, they can predict when a new attack is eminent. Google believes that they predict what interest you, by analyzing millions of clicks that are done over billions of session searches.