Lewis Fry Richardson
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Lewis Fry Richardson, FRS (11 October 1881 – 30 September 1953) was an English
mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...
,
physicist A physicist is a scientist who specializes in the field of physics, which encompasses the interactions of matter and energy at all length and time scales in the physical universe. Physicists generally are interested in the root or ultimate cau ...
, meteorologist,
psychologist A psychologist is a professional who practices psychology and studies mental states, perceptual Perception () is the organization, identification, and interpretation of sensory information in order to represent and understand the pre ...
, and
pacifist Pacifism is the opposition or resistance to war, militarism (including conscription and mandatory military service) or violence. Pacifists generally reject theories of Just War. The word ''pacifism'' was coined by the French peace campai ...
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 concerning
fractal In mathematics, a fractal is a geometric shape containing detailed structure at arbitrarily small scales, usually having a fractal dimension strictly exceeding the topological dimension. Many fractals appear similar at various scales, as ill ...
s and a method for solving a system of linear equations known as
modified Richardson iteration Modified Richardson iteration is an iterative method for solving a system of linear equations. Richardson iteration was proposed by Lewis Fry Richardson in his work dated 1910. It is similar to the Jacobi and Gauss–Seidel method. We seek the so ...
.


Early life

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 Quakers are people who belong to a historically Protestant Christian set of denominations known formally as the Religious Society of Friends. Members of these movements ("theFriends") are generally united by a belief in each human's abili ...
family, David Richardson operating a successful tanning and leather-manufacturing business. At age 12 he was sent to a
Quaker Quakers are people who belong to a historically Protestant Christian set of denominations known formally as the Religious Society of Friends. Members of these movements ("theFriends") are generally united by a belief in each human's abili ...
boarding school A boarding school is a school where pupils live within premises while being given formal instruction. The word "boarding" is used in the sense of " room and board", i.e. lodging and meals. As they have existed for many centuries, and now exte ...
, Bootham School in
York York is a cathedral city with Roman origins, sited at the confluence of the rivers Ouse and Foss in North Yorkshire, England. It is the historic county town of Yorkshire. The city has many historic buildings and other structures, such as a ...
, where he received an 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 , mottoeng = Her foundations are upon the holy hills ( Psalm 87:1) , established = (university status) , type = Public , academic_staff = 1,830 (2020) , administrative_staff = 2,640 (2018/19) , chancellor = Sir Thomas Allen , vice_cha ...
) where he took courses in
mathematical physics Mathematical physics refers to the development of mathematical methods for application to problems in physics. The '' Journal of Mathematical Physics'' defines the field as "the application of mathematics to problems in physics and the developm ...
,
chemistry Chemistry is the scientific study of the properties and behavior of matter. It is a natural science that covers the elements that make up matter to the compounds made of atoms, molecules and ions: their composition, structure, proper ...
,
botany Botany, also called , plant biology or phytology, is the science of plant life and a branch of biology. A botanist, plant scientist or phytologist is a scientist who specialises in this field. The term "botany" comes from the Ancient Greek w ...
, and
zoology Zoology ()The pronunciation of zoology as is usually regarded as nonstandard, though it is not uncommon. is the branch of biology that studies the animal kingdom, including the structure, embryology, evolution, classification, habits, an ...
. He proceeded in 1900 to
King's College, Cambridge King's College is a constituent college of the University of Cambridge. Formally The King's College of Our Lady and Saint Nicholas in Cambridge, the college lies beside the River Cam and faces out onto King's Parade in the centre of the cit ...
, where he was taught physics in the natural sciences tripos by (among others) J. J. Thomson and graduated with a first-class degree in 1903. At age 47 he received a doctorate in mathematical psychology from the
University of London The University of London (UoL; abbreviated as Lond or more rarely Londin in post-nominals) is a federal public research university located in London, England, United Kingdom. The university was established by royal charter in 1836 as a degr ...
.


Career

Richardson's working life represented his eclectic interests: * National Physical Laboratory (1903–1904). * University College Aberystwyth (1905–1906). *
Chemist A chemist (from Greek ''chēm(ía)'' alchemy; replacing ''chymist'' from Medieval Latin ''alchemist'') is a scientist trained in the study of chemistry. Chemists study the composition of matter and its properties. Chemists carefully describe th ...
, 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 The Eskdalemuir Observatory is a UK national environmental observatory located near Eskdalemuir, Dumfries and Galloway, Scotland. Built in 1904, its remote location was chosen to minimise electrical interference with geomagnetic instruments, whic ...
(1913–1916). *
Friends Ambulance Unit The Friends' Ambulance Unit (FAU) was a volunteer ambulance service, founded by individual members of the British Religious Society of Friends (Quakers), in line with their Peace Testimony. The FAU operated from 1914–1919, 1939–1946 and 19 ...
in France (1916–1919). * Meteorological Office at
Benson, Oxfordshire Benson is a village and civil parish in South Oxfordshire, England. The 2011 Census gave the parish population as 4,754. It lies about a mile and a half (2.4 km) north of Wallingford at the foot of the Chiltern Hills, where a chalk stream, Ew ...
(1919–1920). * Head of the
Physics Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which ...
Department at
Westminster Training College Westminster College was a teacher training college and college of higher education in England. The college was founded in London in 1851 as a training institute for teachers for Wesleyan Methodist schools, but moved to Oxford in 1959. Before t ...
(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 The Royal Society, formally The Royal Society of London for Improving Natural Knowledge, is a learned society and the United Kingdom's national academy of sciences. The society fulfils a number of roles: promoting science and its benefits, re ...


Pacifism

Richardson's Quaker beliefs entailed an ardent
pacifism Pacifism is the opposition or resistance to war, militarism (including conscription and mandatory military service) or violence. Pacifists generally reject theories of Just War. The word ''pacifism'' was coined by the French peace camp ...
that exempted him from military service during
World War I World War I (28 July 1914 11 November 1918), often abbreviated as WWI, was List of wars and anthropogenic disasters by death toll, one of the deadliest global conflicts in history. Belligerents included much of Europe, the Russian Empire, ...
as a
conscientious objector A conscientious objector (often shortened to conchie) is an "individual who has claimed the right to refuse to perform military service" on the grounds of freedom of thought, conscience, or religion. The term has also been extended to objec ...
, though this subsequently disqualified him from having 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 The Air Ministry was a department of the Government of the United Kingdom with the responsibility of managing the affairs of the Royal Air Force, that existed from 1918 to 1964. It was under the political authority of the Secretary of Stat ...
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 Pacifism is the opposition or resistance to war, militarism (including conscription and mandatory military service) or violence. Pacifists generally reject theories of Just War. The word ''pacifism'' was coined by the French peace camp ...
had direct consequences on his research interests. According to Thomas Körner, the discovery that his meteorological work was of value to chemical weapons designers caused 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 Meteorology is a branch of the atmospheric sciences (which include atmospheric chemistry and physics) with a major focus on weather forecasting. The study of meteorology dates back millennia, though significant progress in meteorology did no ...
led him to propose a scheme for
weather forecasting Weather forecasting is the application of science and technology to predict the conditions of the atmosphere for a given location and time. People have attempted to predict the weather informally for millennia and formally since the 19th cen ...
by solution of
differential equation In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, ...
s, the method used nowadays, 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 A computer is a machine that can be programmed to carry out sequences of arithmetic or logical operations (computation) automatically. Modern digital electronic computers can perform generic sets of operations known as programs. These prog ...
eople who computeare 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 there 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)
When news of the first weather forecast by the first modern computer, ENIAC, was received by Richardson in 1950, he responded that the results were an "enormous scientific advance." The first calculations for a 24-hour forecast took ENIAC nearly 24 hours to produce. He was also interested in
atmospheric An atmosphere () is a layer of gas or layers of gases that envelop a planet, and is held in place by the gravity of the planetary body. A planet retains an atmosphere when the gravity is great and the temperature of the atmosphere is low. A ...
turbulence In fluid dynamics, turbulence or turbulent flow is fluid motion characterized by chaotic changes in pressure and flow velocity. It is in contrast to a laminar flow, which occurs when a fluid flows in parallel layers, with no disruption between ...
and performed many terrestrial experiments. The
Richardson number The Richardson number (Ri) is named after Lewis Fry Richardson (1881–1953). It is the dimensionless number that expresses the ratio of the buoyancy term to the flow shear term: : \mathrm = \frac = \frac \frac where g is gravity, \rho is den ...
, a dimensionless parameter of the theory of turbulence is named for him. He famously summarised turbulence 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.''
_play_on_two_lines_of_Augustus_De_Morgan's_poem_Siphonaptera_(poem).html" "title="Augustus_De_Morgan.html" ;"title=" play on two lines of Augustus De Morgan"> play on two lines of Augustus De Morgan's poem Siphonaptera (poem)">Siphonaptera Flea, the common name for the order Siphonaptera, includes 2,500 species of small flightless insects that live as external parasites of mammals and birds. Fleas live by ingesting the blood of their hosts. Adult fleas grow to about long, ar ...
, "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). De Morgan's lines themselves reword two lines of Jonathan Swift's satirical poem "On Poetry: A Rapsody" of 1733.]


Richardson's attempt at numerical forecast

One of Richardson's most celebrated achievements is his retroactive attempt to forecast the weather during a single day—20 May 1910—by direct computation. At the time, meteorologists performed forecasts principally by looking for similar weather patterns from 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 meteorologist
Peter Lynch Peter Lynch (born January 19, 1944) is an American investor, mutual fund manager, and philanthropist. As the manager of the Magellan Fund at Fidelity Investments between 1977 and 1990, Lynch averaged a 29.2% annual return, consistently more ...
makes clear, Richardson's forecast failed dramatically, predicting a huge rise in pressure over six hours when the pressure actually was 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 is revealed 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.


Mathematical analysis of war

Richardson also applied his mathematical skills in the service of his pacifist principles, in particular in understanding the basis of international conflict. For this reason, he is now considered the initiator, or co-initiator (with
Quincy Wright Philip Quincy Wright (December 28, 1890 – October 17, 1970) was an American political scientist based at the University of Chicago known for his pioneering work and expertise in international law, international relations, and security studies. ...
and
Pitirim Sorokin Pitirim Alexandrovich Sorokin (; russian: Питири́м Алекса́ндрович Соро́кин; – 10 February 1968) was a Russian American sociologist and political activist, who contributed to the social cycle theory. Background ...
as well as others such as Kenneth Boulding,
Anatol Rapaport Anatol Rapoport ( uk, Анатолій Борисович Рапопо́рт; russian: Анато́лий Бори́сович Рапопо́рт; May 22, 1911January 20, 2007) was an American mathematical psychologist. He contributed to general ...
and Adam Curle), of the scientific analysis of conflict—an interdisciplinary topic 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 analysed war using mainly differential equations and probability theory. Considering the armament of two nations, Richardson posited an idealised 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 made 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 ''Statistics of Deadly Quarrels'' is a 1960 book by English mathematician and physicist Lewis Fry Richardson 11 October 1881 - 30 September 1953 published by Boxwood Press. The book is a mathematical and social science study on the origins of wa ...
'' (1960), he sought to analyse the causes of war statistically. 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 A logarithmic scale (or log scale) is a way of displaying numerical data over a very wide range of values in a compact way—typically the largest numbers in the data are hundreds or even thousands of times larger than the smallest numbers. Such a ...
for conflicts. In other words, there are many 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 organisation (there are more small towns with grocery stores than big cities with superstores).


Research on the length of coastlines and borders

Richardson decided to search for a relation between the
probability Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, ...
of two countries going to war and the length of their common border. However, while collecting data, he found that there was considerable variation in the various published lengths of international borders. For example, that between Spain and Portugal was variously quoted as 987 or 1214 km, and that between the Netherlands and Belgium as 380 or 449 km. The reason for these inconsistencies is the " coastline paradox". 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: Notice that the smaller the ruler, the longer the resulting coastline. It might be supposed that these values would converge to a finite number representing the true length of the coastline. However, Richardson demonstrated that this is not the case: the measured length of coastlines, and other natural features, increases without limit as the unit of measurement is made smaller. This is known nowadays as the ''Richardson effect''. At the time, Richardson's research was ignored by the scientific community. Today, it is considered an element of the beginning of the modern study of
fractal In mathematics, a fractal is a geometric shape containing detailed structure at arbitrarily small scales, usually having a fractal dimension strictly exceeding the topological dimension. Many fractals appear similar at various scales, as ill ...
s. Richardson's research was quoted by mathematician Benoît Mandelbrot in his 1967 paper How Long Is the Coast of Britain? Richardson identified a value (between 1 and 2) that would describe the changes (with increasing measurement detail) in observed complexity for a particular coastline; this value served as a model for the concept of fractal dimension.


Patents for detection of icebergs

In April 1912, soon after the loss of the ship ''
Titanic RMS ''Titanic'' was a British passenger liner, operated by the White Star Line, which sank in the North Atlantic Ocean on 15 April 1912 after striking an iceberg during her maiden voyage from Southampton, England, to New York City, Unite ...
'', Richardson registered a patent for iceberg detection using acoustic echolocation in air. A month later he registered a similar patent for acoustic echolocation in water, anticipating the invention of
sonar Sonar (sound navigation and ranging or sonic navigation and ranging) is a technique that uses sound propagation (usually underwater, as in submarine navigation) to navigate, measure distances (ranging), communicate with or detect objects on o ...
by
Paul Langevin Paul Langevin (; ; 23 January 1872 – 19 December 1946) was a French physicist who developed Langevin dynamics and the Langevin equation. He was one of the founders of the ''Comité de vigilance des intellectuels antifascistes'', an ant ...
and
Robert Boyle Robert Boyle (; 25 January 1627 – 31 December 1691) was an Anglo-Irish natural philosopher, chemist, physicist, alchemist and inventor. Boyle is largely regarded today as the first modern chemist, and therefore one of the founders ...
6 years later.Michael A. Ainslie ''Principles of Sonar Performance Modelling'', Springer, 2010 , page 10


In popular culture

A fictional version of Richardson, named Wallace Ryman, plays a pivotal role in
Giles Foden Giles Foden (born 11 January 1967)George Stade and Karen Karbiener (eds), ''Encyclopaedia of British Writers, 1800 to the Present'', 2nd edn, Infobase Publishing, 2010, p. 176. is an English author, best known for his novel ''The Last King of S ...
's novel ''Turbulence''. Richardson is mentioned in
John Brunner John Brunner may refer to: * Sir John Brunner, 1st Baronet (1842–1919), British industrialist and Liberal Member of Parliament * John L. Brunner (1929–1980), Pennsylvania politician * Sir John Brunner, 2nd Baronet (1865–1929), British Libera ...
's work, '' Stand on Zanzibar'' where ''Statistics of Deadly Quarrels'' is used as an argument that wars are inevitable. Richardson's work is also mentioned in Poul Anderson's speculative fiction novelette, ''Kings Who Die''. Richardson is mentioned in
Charlie Kaufman Charles Stuart Kaufman (; born November 19, 1958) is an American filmmaker and novelist. He wrote the films '' Being John Malkovich'' (1999), '' Adaptation'' (2002), and '' Eternal Sunshine of the Spotless Mind'' (2004). He made his directorial ...
's 2020 novel ''
Antkind ''Antkind'' is the 2020 debut novel of American screenwriter and film director Charlie Kaufman. Kaufman said in 2016 that the novel was being written so as to be unfilmable, and is itself about "an impossible movie." Synopsis Neurotic failed ...
''. Richardson's famous quote, "Big whirls have little whirls that feed on their velocity; little whirls have lesser whirls & so on to viscosity" is mentioned in the song "Dots & Lines" written and performed by lyricist/rapper
Lupe Fiasco Wasalu Muhammad Jaco (born February 16, 1982), better known by his stage name Lupe Fiasco ( ), is an American rapper, singer, record producer, and entrepreneur. He rose to fame in 2006 following the success of his debut album, '' Lupe Fiasco's ...
.


Personal life

In 1909 he married Dorothy Garnett (1885–1956), daughter of the mathematician and physicist William Garnett. They were unable to have children due to an incompatibility of blood types, but they adopted two sons and a daughter between 1920 and 1927. Richardson's nephew
Ralph Richardson Sir Ralph David Richardson (19 December 1902 – 10 October 1983) was an English actor who, with John Gielgud and Laurence Olivier, was one of the trinity of male actors who dominated the British stage for much of the 20th century. He w ...
became a noted actor. His great-nephew (through his wife Dorothy's eldest brother, (James Clerk) Maxwell Garnett, C.B.E.), Julian Hunt, went on to become a meteorologist and director general and chief executive of the British Meteorological Office from 1992 to 1997. A great-niece – of the same line of descent – is the former politician Virginia Bottomley, now Baroness Bottomley.


Legacy

Since 1997, the Lewis Fry Richardson Medal has been awarded by the European Geosciences Union for "exceptional contributions to nonlinear geophysics in general" (by EGS until 2003 and by EGU since 2004). Winners have been: * 2020: Valerio Lucarini * 2019: Shaun Lovejoy * 2018: Timothy N. Palmer * 2017: Edward Ott * 2016: Peter L. Read * 2015: Daniel Schertzer * 2014: Olivier Talagrand * 2013: Jürgen Kurths * 2012: Harry Swinney * 2011: Catherine Nicolis * 2010: Klaus Fraedrich * 2009: Stéphan Fauve * 2008: Akiva Yaglom * 2007: Ulrich Schumann * 2006: Roberto Benzi * 2005: Henk A. Dijkstra * 2004: Michael Ghil * 2003: Uriel Frisch * 2002: * 2001: Julian Hunt * 2000:
Benoit Mandelbrot Benoit B. Mandelbrot (20 November 1924 – 14 October 2010) was a Polish-born French-American mathematician and polymath with broad interests in the practical sciences, especially regarding what he labeled as "the art of roughness" of p ...
* 1999: Raymond Hide * 1998: Vladimir Keilis-Borok Since 1959, there has been a Peace Studies centre at
Lancaster University , mottoeng = Truth lies open to all , established = , endowment = £13.9 million , budget = £317.9 million , type = Public , city = Bailrigg, City of Lancaster , country = England , coor = , campus = Bailrigg , faculty ...
named the Richardson Institute which carries out interdisciplinary research on peace and conflict in the spirit of Lewis Fry Richardson.


See also

* Anomalous diffusion *
Arms race An arms race occurs when two or more groups compete in military superiority. It consists of a competition between two or more states to have superior armed forces; a competition concerning production of weapons, the growth of a military, and ...
* Coastline paradox * Energy cascade *
War cycles Edward Russel Dewey (1895–1978) was an economist who studied cycles in economics and other fields. Dewey's cycles work Dewey first became interested in cycles while Chief Economic Analyst of the Department of Commerce in 1930 or 1931 becaus ...
* Magnetic helicity *
Richardson extrapolation In numerical analysis, Richardson extrapolation is a sequence acceleration method used to improve the rate of convergence of a sequence of estimates of some value A^\ast = \lim_ A(h). In essence, given the value of A(h) for several values of h, ...
*
Richardson number The Richardson number (Ri) is named after Lewis Fry Richardson (1881–1953). It is the dimensionless number that expresses the ratio of the buoyancy term to the flow shear term: : \mathrm = \frac = \frac \frac where g is gravity, \rho is den ...
*
Modified Richardson iteration Modified Richardson iteration is an iterative method for solving a system of linear equations. Richardson iteration was proposed by Lewis Fry Richardson in his work dated 1910. It is similar to the Jacobi and Gauss–Seidel method. We seek the so ...
* Richards equation * Multiscale turbulence * Takebe Kenko *
Frederick W. Lanchester Frederick William Lanchester LLD, Hon FRAeS, FRS (23 October 1868 – 8 March 1946), was an English polymath and engineer who made important contributions to automotive engineering and to aerodynamics, and co-invented the topic of operations ...
*
List of peace activists This list of peace activists includes people who have proactively advocated diplomatic, philosophical, and non-military resolution of major territorial or ideological disputes through nonviolent means and methods. Peace activists usually work wi ...


Notes


References

* Wilkinson, David. ''Deadly Quarrels: Lewis F. Richardson and the Statistical Study of War'' (University of California Press, 2018
online review
* 320pp * * P.A. Davidson, Y. Kaneda, K. Moffatt, and K.R. Sreenivasan (eds, 2011). ''A Voyage Through Turbulence'', chapter 5, pp 187–208,
Cambridge University Press Cambridge University Press is the university press of the University of Cambridge. Granted letters patent by King Henry VIII in 1534, it is the oldest university press in the world. It is also the King's Printer. Cambridge University Pr ...
* * 544pp "A Quaker mathematician" (Ch 8) and "Richardson on war" (Ch 9) * * 290pp * Richardson, L.F. (1939). "Generalized foreign politics". ''The British Journal of Psychology'', monograph supplement No. 23. * Richardson, L.F. (1960). ''Statistics of deadly quarrels''. Pacific Grove, CA: Boxwood Press. * 1030pp; ''Volume 2: Quantitative psychology and studies of conflict.'' , 778pp * * 353pp * Angeletti Ferdinando (2021) ''Storicismo matematico e pacifismo scientifico: due esempi di determinismo storico della metà del XX secolo'' in ''Iconografie europee'' di Walter Montanari e Shirin Zakeri (a cura di), Roma, Nuova Cultura ISBN 978-8-833-65368-6;


External links

* {{DEFAULTSORT:Richardson, Lewis Fry 1881 births 1953 deaths 20th-century English mathematicians Academics of the University of Manchester Institute of Science and Technology Academics of Aberystwyth University Alumni of King's College, Cambridge People educated at Bootham School English cartographers British conscientious objectors English meteorologists English physicists English psychologists English Quakers Fellows of the Royal Society Lewis People associated with the University of the West of Scotland Scientists from Newcastle upon Tyne English Christian pacifists Fluid dynamicists People associated with the Friends' Ambulance Unit 20th-century psychologists Alumni of Armstrong College, Durham 20th-century English businesspeople