THE ESSENCE OF CHAOS by Edward Lorenz

University of Washington Press 1993. ISBN 0-295 97514-8

Edward Lorenz is a professor of meteorology at MIT who wrote the first clear paper about what has come to be known as Chaos. The paper was called Deterministic Nonperiodic Flow and it was published in the Journal of Atmospheric Sciences in 1963.

Since then, or rather from about the mid 1970's there has been an explosion of interest in the subject with chaotic systems being identified and investigated in areas ranging from biology to economics. Lorenz himself of course first found the characteristics of chaos in weather patterns and in the book he recounts in a very interesting way how he made his discovery . He also puts forward his ideas as to what really constitutes the "essence" of chaos to free this from the mass of ideas and claims that have become associated with the word.

His definition is as follows; "The property that characterises a dynamical system in which most orbits exhibit sensitive dependence". Dynamical systems (like the weather) are all around us. They have recurrent behaviour (it's always hotter in summer than winter) but are very difficult to pin down and predict apart from the very short term. "What will the weather be tomorrow ? "can be anticipated but" What will the weather be in a months time?" is an impossible question to answer. (top)

 Lorenz showed that with a set of simple differential equations seemingly very complex turbulent behaviour could be created that would previously have been considered as random. He further showed that accurate longer range forecasts in any chaotic system were impossible, thereby overturning the previous orthodoxy. It had been believed that the more equations you add to describe a system, the more accurate will be the eventual forecast.

The book describes Lorenz's experimental proof of this as he aimed to restart a small simplified computer model of the world weather using virtually identical values for the variables. Common sense would suggest that the toy weather would develop in an identical way but the surprising (and essence of chaos) thing is that it doesn't. The weather pattern starts to diverge quite quickly with a measurable rate of divergence or doubling time showing conclusively that with high accuracy weather measurements, and even in the impossible case of every process being modelled correctly, the system still can't make a longer range prediction because of Lorenz's sensitive dependence on initial conditions (variables).

There are plenty of diagrams in this excellent book but he could have integrated them better with the text. It is frustrating to try to follow his ski slope example with its dimensions and compass directions.

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