Lorenz , Edward Norton

(1917–) American meteorologist

Born in West Hartford, Connecticut, Lorenz was educated at Dartmouth College, New Hampshire, at Harvard, and at the Massachusetts Institute of Technology. He joined the MIT faculty in 1946 and served as professor of meteorology from 1962 until 1987.

Lorenz had trained initially as a mathematician, but after serving in the US Army Air Corps as a weather forecaster, he decided to continue as a meteorologist and work on the more theoretical aspects of the subject. Could forecasting, he asked, be significantly improved? If astronomers could predict the return of a comet decades ahead, it should surely be possible, given enough computing power, to forecast the state of the atmosphere for more than a few hours in advance. The pioneer of this method was the mathematician Von Neumann, who planned a program to predict, and even control, the weather. One day in 1961 Lorenz discovered that there were more than a few simple, practical obstacles to overcome.

In order to follow variations in weather conditions Lorenz set up a system in which he fed a set of initial conditions into the computer and allowed it to run on showing graphically the values taken by a single variable, such as temperature, over a long period of time. On one occasion he wished to examine part of one run in greater detail and fed in the initial conditions taken from an earlier run. To his surprise the computer produced a markedly different sequence from the original printout. Eventually Lorenz traced the source of the discrepancy. The initial conditions of the program, stored in the computer memory, had used the number 0.506127, correct to six decimal places; the printout, however, gave just three decimal places, 0.506. Lorenz, like everyone else, had assumed that so small a difference could have no significant effect. In fact, a small difference can, over a long period of time, build up to produce a large effect. Moreover, the way the difference affects the outcome is very sensitive to small changes. Technically, this is termed ‘sensitive dependence on initial conditions’. More graphically, it is called the ‘butterfly effect’, from the idea that a single butterfly flapping its wings in China might, weeks later, ‘cause’ a hurricane in New York.

The butterfly effect occurs because the weather depends on a number of factors – temperature, humidity, air flow, etc. – and these are to a certain extent interdependent. Thus the way the temperature changes depends on the humidity, but this depends on temperature. Consequently, equations relating these factors are nonlinear – a variable is a function of itself. And it is this nonlinearity that causes the sensitive dependence on initial conditions. The weather is a system that repeats itself, giving periods of dry weather and periods of wet, but it repeats itself in an unpredictable way. There are a number of similar nonlinear systems – for example, population cycles or economic cycles – that depend on nonlinear equations. The study of such systems has come to be known as ‘chaos theory.’

Lorenz went on to study behavior of this kind in a more rigorous and abstract manner. He considered some simple nonlinear equations describing fluid flow in a system with three degrees of freedom. He appeared to discover in the process a new kind of ‘attractor’. In broad terms an attractor is what the behavior of a system settles down to, or is attracted to. The simplest kind, a fixed-point attractor, is represented by a pendulum subject to friction. The pendulum, no matter how it starts swinging, will always come to rest in the same position. Its final state is predictable.

The Lorenz attractor, however, proved to be both chaotic and unpredictable. It was the first example of a ‘strange attractor’, a term introduced by David Ruelle in 1971. Lorenz discovered the attractor by examining the changing relationships between the three variables described by the equations. At any moment in time the variables will be defined by a point in three dimensional space. The point can be plotted. Lorenz found that the point never followed the same path, nor did the paths it followed ever intersect; instead it displayed a system of complex loops, something in fact like the wings of a butterfly.

Lorenz first published his work in 1963 in a paper entitledDeterministic Nonperiodic Flow. Although it received little early attention, it became one of the most cited papers of the 1980s.