Lewis Fry Richardson

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.


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 early working life reflected his eclectic interests:


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.

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, somewhat eccentrically, envisaged bands of messengers on motor-cycles cruising the Royal Albert Hall to communicate arithmetical results between banks of clerks in order to obtain the necessary numerical solutions. 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 the parody:

Big whorls have little whorls that feed on their velocity,
and little whorls have smaller whorls and so on to viscosity.

Mathematical analysis of war

Richardson also attempted to apply his mathematical skills in the service of his pacifist principles, in particular in understanding the roots of international conflict. As he had done with weather, he analyzed war using differential equations. 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."

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:

Missing image

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.

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.

Lewis Fry Richardson Medal

This is a medal awarded (since 1997) by the European Geophysical Society. http://www.copernicus.org/EGU/egs/award6s.htm


Richardson, Lewis Fry, "Generalized foreign politics," The British Journal of Psychology, monograph supplement #23, 1939.de:Lewis Fry Richardson


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