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Edward Lorenz, Father of Chaos Theory, Dies at 90
An anonymous reader writes "Professor Edward N. Lorenz, who discovered in 1961 that subtle changes in the initial conditions of a weather simulation program could cause very large differences in its results, died of cancer Wednesday at the age of 90. The contributions of the father of chaos theory, who coined the term 'the butterfly effect' and also discovered the Lorenz Attractor, are best summarized by the wording of the Kyoto Prize in 1991 which noted that his discovery of chaos theory 'profoundly influenced a wide range of basic sciences and brought about one of the most dramatic changes in mankind's view of nature since Sir Isaac Newton.'"
Why aren't they reporting that his cancer was caused by a zebra sneezing in the UK last fall under a fig tree. It seems quite relevant.
...and also one that's fun to play with (needs java).
Its controversial that he was the first. A lot of people worked on this area. In fact, it is controversial that chaos will ever contribute to science in any way. The pure mathematical theory is very hard. See the work by Curt McMullen for example. Many people I know are very skeptical, and there are a lot of bad papers purporting to use chaos theory.
Back in my college days, I visited the library and looked up Lorenz's paper, "Deterministic Nonperiodic Flow." On the face of it, the presentation was not particularly striking, nor did it seem significant on a superficial reading. That it was buried in a meteorology journal, rather than a mathematics or physics journal, only further obscured its importance.
Lorenz's discovery was not so much about the specific nonlinear differential system (now named after him) that he discussed in the paper, nor was it about chaos theory as we now know it. The significance lay entirely in the notion that even simple dynamical systems can display sensitive dependence on initial conditions, and that when extrapolated to real-world phenomena, the intrinsic complexity of their behavior was all but inevitable.
A chaotic system is not merely disordered, or random. There is an underlying structure. Call it a kind of orderly disorder. Prior to (and indeed, for some time after) Lorenz's work, physicists largely dismissed this possibility as absurd. We can, in such a system, model its state at some infinitesimal time t+dt after some given state at time t. We can do this quite accurately. But as Lorenz showed, the deterministic property is insufficient to imply that one can know the state of the system at any arbitrary time in the future. There is a difference between knowing how the future is calculated from the past, versus knowing what the future will actually be.
Hence the chosen title. "Deterministic" = future states are well-defined from a known prior state. "Nonperiodic" = does not display cyclical behavior. "Flow" = fluid dynamics, in Lorenz's case, atmospheric convection.
He is truly missed.
Andy
Flow in the title of Lorentz paper is not a flow from fluid dynamics or physics. It's a purely mathematical term which mean a solution of differential equation (Lorentz equation in the case). In more general sense flow is a group action of R on the manifold - that is solution of the differential equation on the curved surface. It's studied by specific branches of mathematics - Differential (topological) dynamics, which in big parts owes its origination to the Lorentz paper. So the title of the paper really mean "Deterministic Nonperiodic Solutions"
Here's a simple chaos experiment you can do at home... Turn on a faucet slightly so that it drips regularly. Then increment the flow slightly, and pretty soon the drips will come out in a non-regular way. Understanding the transition from regular to irregular is part of what chaos theory is about.