Lewis Fry Richardson

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Lewis Fry Richardson (October 11, 1881 - September 30, 1953) was a mathematician, physicist and psychologist. One of seven children, he was born in Newcastle upon Tyne, England, into a well-off, merchant Quaker family, and was the son of Catherine Fry and David Richardson.

Contents 1 Education and early working life 2 Pacifism 3 Weather forecasting 4 Mathematical analysis of war 5 Research on the length of coastlines and borders 6 Lewis Fry Richardson Medal 7 See also 8 References 9 External links

[edit] Education and early working life

He entered Bootham School in York in 1894 and fell under the dual influences of pacifist Quaker beliefs and, under master J. Edmund Clark, science, in particular, meteorology. In 1898 he attended Durham College of Science, to study mathematics, physics, chemistry, zoology and botany, before graduating from King's College, Cambridge with a first-class degree in the Natural Science Tripos in 1903.

Richardson's working life reflected his eclectic interests:

• National Physical Laboratory (1903-1904, 1907-1909)
• University College Aberystwyth (1905-1906)
• National Peat Industries (1906-1907) - as a chemist
• Sunbeam Lamp Company (1909-1912) - as manager of the physical and chemical laboratory
• Manchester College of Technology (1912-1913)
• Meteorological Office (1913-1916) - as superintendent of Eskdalemuir Observatory
• Friends Ambulance Unit in France between 1916 and 1919
• Works at the Meteorological Office at Benson, Oxfordshire between 1919 and 1920.
• In 1920 is made Head of the Physics Department at Westminster Training College.
• Between 1929 and 1940 is principal of the Paisley Technical College, now the University of Paisley.

[edit] Pacifism

Richardson's Quaker beliefs entailed an ardent pacifism that exempted him from military service during World War I as a conscientious objector though this subsequently disqualified him from holding any academic post. Richardson worked from 1916 to 1919 for the Friends' Ambulance Service attached to the 16th French Infantry Division. After the war, he rejoined the Meteorological Office but was compelled to resign on grounds of conscience when it was amalgamated into the Air Ministry in 1920. He subsequently pursued a career on the fringes of the academic world before retiring in 1940 to research his own ideas. His pacifism had direct consequences on his research interests. According to Korner (see ref), the discovery that his meteorological work was of value to chemical weapons designers led him to abandon all his efforts in this field, and destroy findings that he had yet to publish

[edit] Weather forecasting

Richardson's interest in meteorology led him to propose a scheme for weather forecasting by solution of differential equations, the method used today, though, when he published Weather Prediction by Numerical Process in 1922, suitable fast computing was unavailable. He described his ideas thus :-

“After so much hard reasoning, may one play with a fantasy? Imagine a large hall like a theatre, except that the circles and galleries go right round through the space usually occupied by the stage. The walls of this chamber are painted to form a map of the globe. The ceiling represents the north polar regions, England is in the gallery, the tropics in the upper circle, Australia on the dress circle and the antarctic in the pit.

A myriad computers are at work upon the weather of the part of the map where each sits, but each computer attends only to one equation or part of an equation. The work of each region is coordinated by an official of higher rank. Numerous little "night signs" display the instantaneous values so that neighbouring computers can read them. Each number is thus displayed in three adjacent zones so as to maintain communication to the North and South on the map.

From the floor of the pit a tall pillar rises to half the height of the hall. It carries a large pulpit on its top. In this sits the man in charge of the whole theatre; he is surrounded by several assistants and messengers. One of his duties is to maintain a uniform speed of progress in all parts of the globe. In this respect he is like the conductor of an orchestra in which the instruments are slide-rules and calculating machines. But instead of waving a baton he turns a beam of rosy light upon any region that is running ahead of the rest, and a beam of blue light upon those who are behindhand.

Four senior clerks in the central pulpit are collecting the future weather as fast as it is being computed, and despatching it by pneumatic carrier to a quiet room. There it will be coded and telephoned to the radio transmitting station. Messengers carry piles of used computing forms down to a storehouse in the cellar.

In a neighbouring building there is a research department, where they invent improvements. But these is much experimenting on a small scale before any change is made in the complex routine of the computing theatre. In a basement an enthusiast is observing eddies in the liquid lining of a huge spinning bowl, but so far the arithmetic proves the better way. In another building are all the usual financial, correspondence and administrative offices. Outside are playing fields, houses, mountains and lakes, for it was thought that those who compute the weather should breathe of it freely.” (Richardson 1922)

(Note that the word computers is used here in its original sense - people who did computations, not machines. Calculator also referred to people at this time.) He was also interested in atmospheric turbulence and performed many terrestrial experiments. The Richardson number, a dimensionless parameter in the theory of turbulence is named after him. He famously summarised the field in rhyming verse in Weather Prediction by Numerical Process (p 66):

Big whirls have little whirls that feed on their velocity,

and little whirls have lesser whirls and so on to viscosity.

[A play on Jonathan Swift's "Great fleas have little fleas upon their backs to bite 'em, And little fleas have lesser fleas, and so ad infinitum." (1733)].

[edit] Mathematical analysis of war

Richardson also applied his mathematical skills in the service of his pacifist principles, in particular in understanding the roots of international conflict. For this reason, today he is considered the founder, or co-founder (with Quincy Wright and Pitrim Sorokin), of the scientific analysis of conflict; an interdisciplinary field of quantitative and mathematical social science dedicated to systematic investigation of the causes of war and conditions of peace. As he had done with weather, he analyzed war using mainly differential equations and probability theory. Considering the armament of two nations, Richardson posited an idealized system of equations whereby the rate of a nation's armament build-up is directly proportional to the amount of arms its rival has and also to the grievances felt toward the rival, and negatively proportional to the amount of arms it already has itself. Solution of this system of equations allows insightful conclusions to be drawn regarding the nature, and the stability or instability, of various hypothetical conditions which might obtain between nations.

He also originated the theory that the propensity for war between two nations was a function of the length of their common border. And in Arms and Insecurity (1949), and Statistics of Deadly Quarrels (1950), he sought to statistically analyze the causes of war. Factors he assessed included economics, language, and religion. In the preface of the latter, he wrote: "There is in the world a great deal of brilliant, witty political discussion which leads to no settled convictions. My aim has been different: namely to examine a few notions by quantitative techniques in the hope of reaching a reliable answer."

[edit] Research on the length of coastlines and borders

While studying the causes of war between two countries, Richardson decided to search for a relation between the probability of two countries going to war and the length of their common border. While collecting data, he realised that there was considerable variation in the various gazetted lengths of international borders. For example, that between Spain and Portugal was variously quoted as 987 or 1214 km while that between The Netherlands and Belgium as 380 or 449 km.

As part of his research, Richardson investigated how the measured length of a border changes as the unit of measurement is changed. He published empirical statistics which led to a conjectured relationship. This research was quoted by mathematician Benoît Mandelbrot in his 1967 paper How Long Is the Coast of Britain?

Suppose the coast of Britain is measured using a 200 km ruler, specifying that both ends of the ruler must touch the coast. Now cut the ruler in half and repeat the measurement, then repeat again:

Notice that the smaller the ruler, the bigger the result. It might be supposed that these values would converge to a finite number representing the "true" length of the coastline. However, Richardson demonstrated that the measured length of coastlines and other natural features appears to increase without limit as the unit of measurement is made smaller. Today this is known as the Richardson effect.

Note that Richardson's results do not mean that the coastline of Britain is actually infinitely long. This would require the ability to measure with infinitesimally small rulers, something which quantum physics says cannot be done, as there is a lower limit to the smallness of a measurement, the Planck length. What Richardson's results do show is that natural geographic features, when considered over a wide range of scales, do not behave in the same way as the objects of Euclidean geometry.

At the time, Richardson's research was ignored by the scientific community. Today, it is seen as one element in the birth of the modern study of fractals.

Richardson died in Kilmun, Argyll, Scotland.

[edit] Lewis Fry Richardson Medal

Since 1997, the Lewis Fry Richardson Medal has been awarded by the European Geophysical Society for "exceptional contributions to nonlinear geophysics in general" (by EGS until 2003 by EGU by 2004) .

Winners have been:

2006 Roberto Benzi

2005 Henk A.Dijkstra

2004 Michael Ghil

2003 Uriel Frisch

2002 F.H. Busse

2001 Julian Hunt

2000 Benoit Mandelbrot

1999 Raymond Hide

1998 Vladimir Keilis-Borok

[edit] See also

• War
• War cycles
• Richardson extrapolation

[edit] References

• Ashford, O. M. (1985). "Prophet - or Professor? The Life and Work of Lewis Fry Richardson", Bristol: Adam Hilger.
• Korner, T.W. (1996). "A Quaker mathematician" and "Richardson on war", Ch 8 and 9 in The Pleasures of Counting (Cambridge U.P.)
• Richardson, L.F. (1939). "Generalized foreign politics". The British Journal of Psychology, monograph supplement #23.
• Richardson, L.F. (1960). Statistics of deadly quarrels. Pacific Grove, CA: Boxwood Press.

[edit] External links

• O'Connor, John J., and Edmund F. Robertson. "Lewis Fry Richardson". MacTutor History of Mathematics archive.