Edward Norton Lorenz

For more information on Edward Norton Lorenz, visit Britannica.com.

American meteorologist (1917–)

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 entitled Deterministic Nonperiodic Flow. Although it received little early attention, it became one of the most cited papers of the 1980s.

Not to be confused with Ludwig Lorenz or Hendrik Lorentz.

Edward Norton Lorenz
Edward Norton Lorenz
Born	May 23, 1917(1917-05-23) West Hartford, Connecticut, United States
Died	April 16, 2008 (aged 90) Cambridge, Massachusetts, United States
Residence	United States
Fields	Mathematics and Meteorology
Institutions	Massachusetts Institute of Technology
Alma mater	Dartmouth College (BA, 1938) Harvard University (Master's, 1940) Massachusetts Institute of Technology (SM, 1943; ScD, 1948)
Doctoral advisor	James Murdoch Austin
Doctoral students	Kevin E. Trenberth
Known for	Chaos theory Lorenz attractor Butterfly effect
Notable awards	Kyoto Prize (1991)

Edward Norton Lorenz (May 23, 1917 - April 16, 2008) was an American mathematician and meteorologist, and a pioneer of chaos theory.^[1] He discovered the strange attractor notion and coined the term butterfly effect.

Contents 1 Biography 2 Awards 3 Work 4 See also 5 Publications 6 References 7 External links

Biography

Lorenz was born in West Hartford, Connecticut.^[2] He studied mathematics at both Dartmouth College in New Hampshire and Harvard University in Cambridge, Massachusetts. From 1942 until 1946, he served as a weather forecaster for the United States Army Air Corps. After his return from the war, he decided to study meteorology.^[1] Lorenz earned two degrees in the area from the Massachusetts Institute of Technology where he later was a professor for many years. He was a Professor Emeritus at MIT from 1987 until his death.^[1]

During the 1950s, Lorenz became skeptical of the appropriateness of the linear statistical models in meteorology, as most atmospheric phenomena involved in weather forecasting are non-linear.^[1] His work on the topic culminated in the publication of his 1963 paper Deterministic Nonperiodic Flow in Journal of the Atmospheric Sciences, and with it, the foundation of Chaos theory.^[1][3] His description of the Butterfly effect followed in 1969, ^[1][4][5] Kyoto Prize for basic sciences, in the field of earth and planetary sciences, in 1991,^[6] the Buys Ballot Award in 2004, and the Tomassoni Award in 2008.^{[citation needed]} In his later years, he lived in Cambridge, Massachusetts. He was an avid outdoorsman, who enjoyed hiking, climbing, and cross-country skiing. He kept up with these pursuits until very late in his life, and managed to continue most of his regular activities until only a few weeks before his death. According to his daughter, Cheryl Lorenz, Lorenz had "finished a paper a week ago with a colleague."^[7] On April 16, 2008, Lorenz died at his home in Cambridge at the age of 90, having suffered from cancer. ^[8]

Awards

• 1969 Carl Gustaf Rossby Research Medal, American Meteorological Society.
• 1973 Symons Memorial Gold Medal, Royal Meteorological Society.
• 1975 Fellow, National Academy of Sciences (U.S.A.).
• 1981 Member, Norwegian Academy of Science and Letters.
• 1983 Crafoord Prize, Royal Swedish Academy of Sciences.
• 1984 Honorary Member, Royal Meteorological Society.
• 1991 Kyoto Prize for ‘… his boldest scientific achievement in discovering "deterministic chaos" .’.
• 2004 Buys Ballot medal.
• 2004 Lomonosov Gold Medal

Work

Lorenz built a mathematical model of the way air moves around in the atmosphere. As Lorenz studied weather patterns he began to realize that they did not always change as predicted. Minute variations in the initial values of variables in his twelve variable computer weather model (c. 1960) would result in grossly divergent weather patterns.^[1] This sensitive dependence on initial conditions came to be known as the butterfly effect.^[9]

Lorenz went on to explore the underlying mathematics and published his conclusions in a seminal work titled Deterministic Nonperiodic Flow, in which he described a relatively simple system of equations that resulted in a very complicated dynamical object now known as the Lorenz attractor.^[3]

See also

Systems science portal

• Attractor
• Butterfly effect
• Chaos theory
• Experimental mathematics
• Lorenz attractor
• Meteorology
• Numerical weather prediction

Publications

Lorenz published several books and articles. A selection:

• 1955 Available potential energy and the maintenance of the general circulation. Tellus. Vol.7
• 1963 Deterministic nonperiodic flow. Journal of Atmospheric Sciences. Vol.20 : 130—141 link ^[10].
• 1967 The nature and theory of the general circulation of atmosphere. World Meteorological Organization. No.218
• 1969 Three approaches to atmospheric predictability. American Meteorological Society. Vol.50
• 1972 Predictability: Does the Flap of a Butterfly's Wings in Brazil Set Off a Tornado in Texas?
• 1976 Nondeterministic theories of climate change. Quaternary Research. Vol.6
• 1990 Can chaos and intransitivity lead to interannual variability? Tellus. Vol.42A
• 2005 Designing Chaotic Models. Journal of the Atmospheric Sciences: Vol. 62, No. 5, pp. 1574–1587.

References

1. ^ ^{a b c d e f g} Tim Palmer (2008). "Edward Norton Lorenz". Physics Today 61 (9): 81–82. doi:10.1063/1.2982132. 
2. ^ "Lorenz Receives 1991 Kyoto Prize". MIT News Office. 1991. http://web.mit.edu/newsoffice/tt/1991/24996/24998.html. 
3. ^ ^{a b} Edward N. Lorenz (1963). "Deterministic Nonperiodic Flow". Journal of the Atmospheric Sciences 20: 130–141. doi:10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2. http://ams.allenpress.com/archive/1520-0469/20/2/pdf/i1520-0469-20-2-130.pdf. 
4. ^ Edward N. Lorenz (1969). "Atmospheric predictability as revealed by naturally occurring analogues". Journal of the Atmospheric Sciences 26: 636–646. doi:10.1175/1520-0469(1969)26<636:APARBN>2.0.CO;2. http://ams.allenpress.com/archive/1520-0469/26/4/pdf/i1520-0469-26-4-636.pdf. 
5. ^ Edward N. Lorenz (1969). "Three approaches to atmospheric predictability". Bulletin of the American Meteorological Society 50: 345–349. http://eapsweb.mit.edu/research/Lorenz/Three_approaches_1969.pdf. 
6. ^ , Maggie Fox, Eric Walsh (2008). Edward Lorenz, father of chaos theory, dead at 90. Reuters. http://www.reuters.com/article/newsOne/idUSN1632944820080416. 
7. ^ Kenneth Chang (2008). "Edward N. Lorenz, a Meteorologist and a Father of Chaos Theory, Dies at 90". New York Times. http://www.nytimes.com/2008/04/17/us/17lorenz.html?ref=us. 
8. ^ "Edward Lorenz, father of chaos theory, dies at age 90". CNN. http://edition.cnn.com/2008/TECH/04/16/lorenz.obit.ap/?iref=hpmostpop. 
9. ^ The term was first recorded from Lorenz's address at the annual meeting of the American Association for the Advancement of Science, on December 29, 1979.
10. ^ According to the Web of Science online academic database, this paper has received at least 4000 unique citations by subsequent authors, making it one of the most-cited papers of all time.

External links

• List of Lorenz's publications, including downloadable pdfs (MIT website)
• Video clip of Edward N. Lorenz speaking at the International Conference on Complex Systems, hosted by the New England Complex Systems Institute (NECSI)
• Obituary, Daily Telegraph, 18 April 2008.

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