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# Lewis Fry Richardson

Lewis Fry Richardson, FRS (11 October 1881 - 30 September 1953) was an English mathematician, physicist, meteorologist, psychologist and pacifist who pioneered modern mathematical techniques of weather forecasting, and the application of similar techniques to studying the causes of wars and how to prevent them. He is also noted for his pioneering work on fractals and a method for solving a system of linear equations known as modified Richardson iteration.

Family life and education

Lewis Fry Richardson was the youngest of seven children born to Catherine Fry (1838–1919) and David Richardson (1835–1913). They were a prosperous Quaker family, David Richardson running a successful tanning and leather manufacturing business.[1]

At age 12 he was sent to a Quaker boarding school, Bootham in York, where he received an excellent education in science, which stimulated an active interest in natural history. In 1898 he went on to Durham College of Science (a college of Durham University) where he took courses in mathematical physics, chemistry, botany, and zoology. Two years later, he gained a scholarship to King's College, Cambridge,[2] where he graduated with first-class honours in the natural sciences tripos in 1903.[3] At age 47 he received a doctorate in mathematical psychology from the University of London.[4]

In 1909 he married Dorothy Garnett (1885–1956), daughter of the mathematician and physicist William Garnett[5]. They were unable to have children due to an incompatibility in blood types, but they adopted two sons and a daughter between 1920 and 1927.[6]

Career

Richardson's working life reflected his eclectic interests:[7]

* National Physical Laboratory (1903–1904)

* University College Aberystwyth (1905–1906)

* chemist, National Peat Industries (1906–1907)

* National Physical Laboratory (1907–1909)

* manager of the physical and chemical laboratory, Sunbeam Lamp Company (1909–1912)

* Manchester College of Technology (1912–1913)

* Meteorological Office - as superintendent of Eskdalemuir Observatory (1913–1916)

* Friends Ambulance Unit in France (1916–1919)

* Meteorological Office at Benson, Oxfordshire (1919–1920)

* Head of the Physics Department at Westminster Training College (1920–1929)

* Principal, Paisley Technical College, now part of the University of the West of Scotland (1929–1940)

In 1926, he was elected to the Fellowship of the Royal Society[8]

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 Unit 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 Thomas Körner,[9] 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.

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 Augustus De Morgan's rewording of Jonathan Swift, "Great fleas have little fleas upon their backs to bite 'em, And little fleas have lesser fleas, and so ad infinitum." (A Budget of Paradoxes, 1915)].

Richardson's attempt at numerical forecast

One of Richardson's most celebrated achievements is his attempt in hind sight to forecast the weather during a single day — 20 May 1910 — by direct computation. At the time, meteorologists carried out forecasts principally by looking for similar weather patterns from past records, and then extrapolating forward. Richardson attempted to use a mathematical model of the principal features of the atmosphere, and use data taken at a specific time (7 AM) to calculate the weather six hours later Ab initio. As Lynch makes clear [10], Richardson's forecast failed dramatically, predicting a huge 145 mbar rise in pressure over 6 hours when the pressure actually stayed more or less static. However, detailed analysis by Lynch has shown that the cause was a failure to apply smoothing techniques to the data, which rule out unphysical surges in pressure. When these are applied, Richardson's forecast turns out to be essentially accurate — a remarkable achievement considering the calculations were done by hand, and while Richardson was serving with the Quaker ambulance unit in northern France.

[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 Pitirim Sorokin as well as others such as Kenneth Boulding, Anatol Rapaport and Adam Curle), 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."

In Statistics of Deadly Quarrels Richardson presented data on virtually every war from 1815 to 1945. As a result he hypothesized a base 10 logarithmic scale for conflicts. In other words, there are far more small fights, in which only a few people die, than large ones that kill many. While no conflict's size can be predicted beforehand—indeed, it is impossible to give an upper limit to the series—overall they do form a Poisson distribution. On a smaller scale he showed the same pattern for gang murders in Chicago and Shanghai. Others have noted that similar statistical patterns occur frequently, whether planned (lotteries, with many more small payoffs than large wins), or by natural organization (there are more small towns with grocery stores than big cities with superstores).

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[11] 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:

Britain-fractal-coastline-200km.png Britain-fractal-coastline-100km.png Britain-fractal-coastline-50km.png

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[12]. Today this is known as the Richardson effect.

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.

In popular culture

A fictional version of Richardson, called Wallace Ryman, plays a pivotal role in Giles Foden's novel Turbulence[13].

Richardson is mentioned in John Brunner's work, The Sheep Look Up where Statistics of Deadly Quarrels is used as an argument that wars are inevitable.

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:

2010 Klaus Fraedrich

2009 Stéphan Fauve

2008 Akiva M. Yaglom

2007 Ulrich Schumann[14]

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

See also

* War

* War cycles

* Richardson extrapolation

* Richardson number

* Modified Richardson iteration

* Takebe Kenko

* Frederick W. Lanchester

Notes

1. ^ Hunt, p. xiv

2. ^ Richardson, Lewis Fry in Venn, J. & J. A., Alumni Cantabrigienses, Cambridge University Press, 10 vols, 1922–1958.

3. ^ Hunt, p. xv

4. ^ Lewis Fry Richardson

5. ^ William Garnett (1850-1932) - Brief biography on the British Society for the History of Mathematics website (accessed 21 January 2008)

6. ^ Ashford (2004)

7. ^ Ashford 1985, Ch 3-7

8. ^ "Royal Society election citation EC/1926/21". The Royal Society. 1926. Retrieved 2008-01-21.

9. ^ Körner, T.W. (1996). "A Quaker mathematician" and "Richardson on war", Ch 8 and 9 in The Pleasures of Counting (Cambridge U.P.)

10. ^ Lynch, P. (2006) The Emergence of Numerical Weather Prediction (Cambridge U.P.)

11. ^ Lewis F. Richardson (1961). "The problem of contiguity: An appendix to Statistic of Deadly Quarrels". General systems: Yearbook of the Society for the Advancement of General Systems Theory. (Ann Arbor, Mich.: The Society, [1956-: Society for General Systems Research) 6 (139): 139–187. ISSN 0072-0798. OCLC 1429672. "In the previous section integrals were taken around simple geometrical figures, as a preliminary to taking them around frontiers shown on political maps. An embarrassing doubt arose as to whether actual frontiers were so intricate as to invalidate that otherwise promising theory. A special investigation was made to settle this question. Some strange features came to notice; nevertheless an over-all general correction was found possible. The results will now be reported. ... As an explanation of how chance can arise in a world which he regarded as strictly deterministic, Heri Poincare* (no date) drew attention to insignificant causes which produced very noticeable effects. Sea coasts provide an apt illustration.".

12. ^ Fractals and the Fractal Dimension (Vanderbilt University website, accessed 30 January 2008)

13. ^ Foden

14. ^ Text of lecture "From little whorls to the global atmosphere" given by 2007 prizewinner

References

* Ashford, Oliver M. (1985). Prophet or Professor?: Life and Work of Lewis Fry Richardson. Bristol: Adam Hilger. ISBN 978-0852747742. 320pp

* Ashford, Oliver M. (2004). "Richardson, Lewis Fry (1881–1953)". Oxford Dictionary of National Biography. doi:10.1093/ref:odnb/35739. http://www.oxforddnb.com/view/article/35739. Retrieved 2008-01-19.

* Hunt, J.C.R. (1998). "Lewis Fry Richardson and His Contributions to Mathematics, Meteorology, and Models of Conflict" (pdf). Annual Review of Fluid Mechanics 30: xiii-xxxvi. doi:10.1146/annurev.fluid.30.1.0. http://www.cpom.org/people/jcrh/AnnRevFluMech(30)LFR.pdf. Retrieved 2008-01-19.

* Körner, T. W. (1996). The Pleasures of Counting. Cambridge: Cambridge University Press. ISBN 978-0521568234. 544pp "A Quaker mathematician" (Ch 8) and "Richardson on war" (Ch 9)

* Lynch, Peter (June 2004). "Richardson's forecast: What went wrong?" (pdf). National Oceanic and Atmospheric Administration (NOAA). http://www.ncep.noaa.gov/nwp50/Presentations/Tue_06_15_04/Session_1/Lynch_NWP50.pdf. Retrieved 2007-04-19.

* Lynch, Peter (2006). The Emergence of Numerical Weather Prediction: Richardson's Dream. Cambridge: Cambridge University Press. ISBN 978-0521857291. 290pp

* O'Connor, John J.; Robertson, Edmund F., "Lewis Fry Richardson", MacTutor History of Mathematics archive, University of St Andrews, http://www-history.mcs.st-andrews.ac.uk/Biographies/Richardson.html .

* 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.

* Richardson, L F (1993). Ashford, Oliver M; Charnock H; Drazin, P G; Hunt, J C R; Smoker, P, Sutherland, Ian. ed. The Collected Papers of Lewis Fry Richardson, Volume 1: Meteorology and numerical analysis.. Cambridge: Cambridge University Press. ISBN 978-0521382977. 1030pp; Volume 2: Quantitative psychology and studies of conflict. ISBN 978-0521382984 778pp

* Richardson, L.F. (1910). "The approximate arithmetical solution by finite differences of physical problems involving differential equations, with an application to the stresses in a masonry dam". Philos. Trans. Roy. Soc. London Ser. A 210: 307–357.

* Foden, Giles (2009). Turbulence. London: faber and faber. ISBN 978-0-571-20522-6. 353pp

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