#### Meteorologist and pioneer of chaos theory who coined the expression 'the butterfly effect' to explain his ideas

Professor Edward Lorenz, a meteorologist and mathematician, was best known as a pioneer in the field of chaos theory. He developed a mathematical model of the way in which air moves around in the atmosphere. Trying to predict the weather with a computer, his analyses of weather patterns led him to realise that they did not always change as predicted.

Very small variations in the initial values of the 12 variables he used in his computer to model the weather would, he discovered, result in very divergent weather patterns. The variables were numerical rules or equations expressing the relationships between temperature and pressure, between pressure and wind speed and so on.

One day at the end of 1961, Lorenz wanted to re-examine a run of results he had obtained on his ancient Royal McBee computer but, instead of starting the whole run from the beginning, he decided to take a shortcut and started midway through. To give the computer the initial conditions he typed in the numbers from the earlier printout.

The programme had not been changed and so the new run should have duplicated the old one. When he compared the new printout with the other one he discovered to his amazement that there was no resemblance. It was, in the words of James Gleick, the author of the book

*Chaos*, as if he had chosen "two random weathers out of a hat".

The great difference between Lorenz's printouts arose because the numbers he had entered for the rerun were very slightly different from the numbers stored in the computer for the first run. In the computer memory, six decimal places were stored but on the printout, to save space, just three decimal places appeared. The difference -- one part in a thousand -- was, Lorenz assumed, of no consequence.

From this accidental discovery, a scientific revolution was launched and a new science -- chaos theory -- born. Lorenz published his conclusions in 1963 in a paper described by another scientist as "a masterpiece of clarity of exposition about why weather is unpredictable".

In a talk he gave to the American Association for the Advancement of Science in 1972 entitled:

*Predictability: Does the Flap of a Butterfly's Wings in Brazil Set off a Tornado in Texas?*he coined the brilliant term "butterfly effect" to describe elegantly how a very small disturbance, such as the movement of a butterfly's wings, in one place can give rise to a series of events that induce enormous consequences in another, far distant, place. Put simply, small deviations in a system can result in large and often unsuspected results.

Lorenz investigated the basic mathematics behind the phenomenon and published his conclusions in a famous paper entitled

*Deterministic Nonperiodic Flow*. This describes a relatively simple set of equations that resulted in a pattern of infinite complexity called the

*Lorenz attractor*.

Chaos theory has had a profound effect not only in the field of mathematics but in almost every area of science, biological, physical and social, bringing "about one of the most dramatic changes in mankind's view of nature since Sir Isaac Newton".

In meteorology, chaos theory implies that it may be fundamentally impossible to forecast weather for more than two or three weeks with a reasonable degree of accuracy. Chaos theory has been ranked with relativity and quantum mechanics as the third scientific revolution of the 20th century.

Edward Norton Lorenz was born in 1917 in West Hartford, Connecticut. He received his bachelors degree in mathematics from Dartmouth College, New Hampshire, in 1938 and his masters degree in mathematics from Harvard in 1940.

After the war, during which he served as a weather forecaster for the US Army Air Corps, he studied meteorology at the Massachusetts Institute of Technology (MIT), earning his doctorate in 1948.

His interest in meteorology was longstanding. In an autobiography he wrote: "As a boy I was always interested in doing things with numbers, and was also fascinated by changes in the weather."

In 1948 Lorenz was appointed a member of the staff of what was then MIT's Department of Meteorology. In 1955 he was appointed an assistant professor and in 1962 he was promoted to professor. Between 1977 and 1981 he was head of the Department of Earth, Atmospheric and Planetary Sciences.In 1987 he became emeritus professor. He kept up his academic work for most of the rest of his life, publishing his last scientific paper shortly before his death.

While on leaves of absence from MIT, he held research or teaching positions at the Lowell Observatory in Flagstaff, Arizona, and visiting professorships at the Department of Meteorology at the University of California, Los Angeles; the Norske Meteorologiske Institutt in Oslo; and the National Centre for Atmospheric Research, Boulder, Colorado.

Lorenz received many honours, awards and honorary degrees. In 1975 he was elected Fellow of the US National Academy of Sciences. In 1983 he and Henry M. Stommel were jointly awarded the $50,000 Crafoord Prize by the Royal Swedish Academy of Sciences, a prize set up to recognize fields not eligible for Nobel prizes. In 1991 he was awarded the respected Kyoto Prize for basic sciences in the field of earth and planetary sciences for establishing "the theoretical basis of weather and climate predictability, as well as the basis for computer-aided atmospheric physics and meteorology".

In 1969 he received the Carl Gustaf Rossby Research Medal from the American Meteorological Society; in 1973 the Royal Meteorological Society awarded him the Symons Memorial Gold Medal; and in 2004 he received the Buys Ballot medal. In 1981 he became a member of the Norwegian Academy of Science and Letters and in 1984 he was made an honorary member of the Royal Meteorological Society.

A man known for his gentlemanliness and humility, Lorenz was a very keen outdoorsman who enjoyed hiking and cross-country skiing until well into old age.

Lorenz's wife died in 2001, and he is survived by his two daughters and son.

**Professor Edward Lorenz, meteorologist and mathematician, was born on May 23, 1917. He died on April 16, 2008, aged 90**

The Times, April 18, 2008 © The Times, 2008