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Richardson, Lewis Fry

Richardson, Lewis Fry




Lewis Fry Richardson (1881–1953), British meteorologist and student of the causes of war, was born at Newcastle-on-Tyne, the youngest of seven children in a Quaker family. He attended the Newcastle Preparatory School, then Bootham School at York. His inclination toward science seems to have been inspired by J. Edmund Clark, a master at Bootham School, who was a meteorologist. However, while still in his teens, Richardson was convinced that “science ought to be subordinate to morals.” After leaving Bootham in 1898, he attended Durham College of Science at Newcastle, then King’s College at Cambridge.

Several appointments followed, each of short duration. Richardson worked as an assistant in the National Physics Laboratory, as chemist for a peat company, and as director of the physical and chemical laboratory of a lamp company. At the outbreak of World War I he was superintendent of Eskdalemuir Observatory of the Meteorology Office. Thenceforth, meteorology became one of his abiding scientific concerns, and he contributed some thirty papers and a book (1922) to that field. In 1926 his scientific achievements were recognized by his election as fellow of the Royal Society.

For Richardson, Quakerism is firmly identified with pacifism. Accordingly he declared himself a conscientious objector, a stand that subsequently barred him from university appointments. Nevertheless he participated directly in the war in a non-combatant capacity, as a member of the Friends’ Ambulance Unit, attached to the 16th French Infantry Division. After the armistice he returned to the Meteorology Office, but in 1920, when that office became part of the Air Ministry, Richardson resigned his position. He next took charge of the physics department at Westminster Training College and in 1929 became principal of Paisley Technical College and School of Art, his last post. Richardson retired in 1940 in order to devote all of his time to the study of war, searching both for its causes and for means to prevent it [seeWar, article onthe study of war].

It is with his work on war that Richardson’s name is most frequently associated. Although his pacifist convictions were surely a source of his dedication to this study, on which he spent at least 35 years, it is likely that his deep involvement with meteorology influenced his method of research. The prediction of weather is notoriously difficult, even though the determinants of weather are entirely understood. The principles governing the several variables—the motion of air masses, the changes of pressures and temperatures, the onset of precipitation—are all known, but the interactions among all these factors are so complex that even if the atmospheric conditions over the globe were precisely known at a given moment, the calculation of future states for even a short period would be a superhuman task. At one time Richardson estimated (1922) that it would take 60,000 human computers working at high speed to compute tomorrow’s world weather charts before tomorrow’s weather arrived. The vital lesson that Richardson therefore learned from the problems of meteorological prediction—one that has been confirmed by modern computing technology—is that events which seem to be governed by chance (as does the weather to one ignorant of the dynamics of air masses) are in fact governed by laws and can be predicted if enough information can be processed.

The link between this insight and Richardson’s approach to the phenomenon of war is in his rejection of the idea that war is a rational, or at least a purposeful, form of behavior, as is often assumed in the conventional political conception of international relations. Richardson viewed war instead in Tolstoyan fashion, as a massive phenomenon governed by forces akin to the forces of nature, over which individuals have little or no control. Accordingly, he ignored all those intricacies of diplomatic-strategic analysis usually pursued by political historians and turned his attention to quasi-mechanical and quantifiable processes which, he assumed, govern the dynamics of the international system of sovereign states. Neither the contents of memoranda and ultimatums nor dynastic claims, territorial ambitions, and networks of alliances play an explicit role in Richardson’s theory of war. Instead, one finds differential equations purporting to represent the interactions among states or the spread of attitudes and moods (like the spread of communicable diseases) among the populations of those states. The equations are quite similar to those representing physical or chemical systems, at times tending toward equilibria, at times moving away from equilibria at accelerated rates and culminating in explosions.

Richardson harbored no illusions concerning the adequacy of his mathematical theory in providing an “explanation” of war, much less a means of preventing it. In omitting strategic calculations, considerations of prudence, and other “rational” factors as determinants of war or peace, he was not asserting the irrelevance of these factors. Rather, he sought to build a viable theory of war in vacuo, as it were, an admittedly crude but tractable model upon which a more sophisticated theory could be developed. “The equations are merely a description of what people would do if they did not stop to think,” he wrote (1960a, p. 12). Some of his equations did fit what actually happened in the years preceding World War I, and Richardson concluded that the Great Powers in that instance were acting as if they were driven by mechanical forces.

In spite of the formal, mechanistic character of the equations that Richardson proposed as a model of international relations, he thought of the causes of war as primarily psychological. The underlying psychology was that of a mass, much simplified by the averaging out of the many opposing pressures, devoid of self-insight or foresight; it was not the psychology of an individual, with a large range of choices, moral convictions, and idiosyncratic preferences. Richardson’s first paper in this vein was entitled “Mathematical Psychology of War.” Written in 1919 and privately printed, it was not published until 1935. In the intervening years Richardson studied psychology as an external student of University College in London, receiving the special degree in 1929. His work in psychology is strongly oriented toward the quantitative approach, and some of it shows the same influence of the “meteorological orientation” as do his studies on war (1937).

Richardson published the complete version of his mathematical theory of war, Generalized Foreign Politics (1939), on the very eve of World War Ii. Its point of departure is a pair of differential equations representing a hypothetical interaction between two rival states. The components of interaction are (1) mutual stimulation of armaments buildup, assuming that each nation’s rate of increase of armaments expenditures is positively proportional to the other nation’s current expenditures; (2) self-inhibition of armaments, assuming that the rate of change of armaments expenditures is negatively proportional to the already existing armaments burden; and (3) constant stimulants to armaments buildup in the form of grievances or ambitions of states. These latter may also be negative, in which case they are interpreted as reservoirs of good will. Cooperation between the rival states, for example, in the form of trade, is interpreted as negative armaments expenditures.

Richardson then examined the dynamics of the postulated system. The solution of the equations (given the initial conditions and the parameters of interaction) determines the time course of the armaments expenditures. By substituting selected values for the parameters, Richardson was able to obtain a good fit of the predicted time course for the armaments buildup of the rival European blocs (the Central Powers and the Entente) in the years preceding World War i. However, the large number of free parameters and the small number of points representing the time course make this “corroboration” of the theory less than impressive.

Of considerably greater interest is the theoretical result deduced from the model, namely that depending on the relative magnitudes of the stimulation and inhibition parameters (but not of the grievance-good-will parameters), the system may be either stable or unstable. If the parameters are such that the system is stable, then an armaments balance is possible (this might also be interpreted as arms control). However, if the parameters are such that the system is unstable, then such a balance is not possible. The system must move one way or the other, depending on the initial conditions, either toward total disarmament and beyond to ever-increasing cooperation or into a runaway race, presumably followed by war.

By noting the rate of disarmament of Great Britain following World War I and the rate of rearmament of Germany prior to World War ii, Richardson was able to get rough estimates of the parameters in question. He concluded that the parameters were well within the region of instability and, moreover, that the initial conditions prior to World War i made it touch and go whether the system would move toward peace or war. Possibly just a slightly lower armaments level or just a little more interbloc trade would have pushed the system toward a united Europe instead of toward world war [seeDisarmament].

Following the analysis of the arms race of 1908–1914, Richardson attempted to analyze the similar process that started shortly after Hitler’s rise to power. The disappearance of the gold standard as a basis for the measure of expenditures and the scantiness of data from the U.S.S.R. made the analysis of the arms race preceding World War n extremely difficult, beyond anything that a lone investigator could accomplish in a lifetime. Still, Richardson’s theory of the mutually stimulating arms race did point to a second world war.

Whether or not these conclusions ought to be taken seriously is a difficult question. Certainly, controlled experiments on the scale of international relations cannot be brought to bear on the critical aspects of Richardson’s theory. Yet whatever the explanatory or predictive merits of the theory, one cannot deny that it invites us to see the phenomenon of war from an unusual point of view. This point of view may have been stated earlier (Richardson cites Thucydides as a proponent of the mutual stimulation theory of arms races and wars), but the quantitative implications of rigorously formulated models based on this view seem never to have been worked out.

Besides the two-nation problem of mutual stimulation in an arms race, Richardson also posed the N-nation problem. Again, the relevance of his results to real international dynamics is an open question because of the vastly simplified assumptions on which his models are based. Nevertheless, the results are interesting, not because of the answers they provide but because of the questions they raise. Thus, Richardson found, for example, that in an arms race involving three nations, the situation can be stable for each of the three pairs separately but unstable for all three taken together. This result may be relevant to the currently acute N-nation nuclear force problem [seeNuclear war].

Following his retirement in 1940, Richardson started extensive empirical investigations. He performed the monumental labor of gathering a vast variety of data related to all “deadly quarrels” that have been known to occur since the end of the Napoleonic Wars. Richardson’s treatment of the data again reveals his view of war and of violence in general as something with which the whole human race is afflicted. This view is diametrically opposed to that represented by strategic thinkers and most clearly expressed by Karl von Clausewitz, who saw war as an instrument of national policy and a normal form of intercourse among civilized states [seeClausewitz].

To Richardson, war is a particular case of a “deadly quarrel,” defined as a violent encounter among human beings resulting in one or more deaths. He placed all such encounters on a scale of magnitude (defined by the logarithm of the number of dead). Thus, single murders appear on this scale as deadly quarrels of magnitude 0 (log101 = 0), small riots with some ten victims as deadly quarrels of magnitude 1 (log1010 =1), and so on. The two world wars appear on this scale as deadly quarrels of magnitude 7.

Richardson sought to establish a relation between the magnitudes of deadly quarrels and the relative frequency of their occurrence, analogous to the relations established by George K. Zipf (1949) between ranks and sizes of a great variety of objects [seeRank-size relations]. But unlike Zipf, who singled out the rank-size relation as a unifying principle of fundamental importance, Richardson treated this relation as one of many to be examined in the search for regularities from which, he hoped, the laws governing human violence would emerge.

Richardson sought to relate the frequencies of wars not only to their magnitudes but to every other conceivable factor that could be extracted from the data. He examined the effect of the existence of common frontiers between the combatants and of the existence of a common language, of a common religion, and of a common government (as in civil wars). He made a list of all the “pacifiers” that have been supposed at one time or another to counteract the tendency to violent outbreaks, such as distraction by sports, diversion of hatred to other groups, the direction of hatred inward, armed strength as a deterrent, collective security, or intermarriage among potentially hostile groups. None of the indices related to these pacifiers shows up as a significant contributing factor either to the likelihood of a “deadly quarrel” or to its prevention. Possible exceptions are international trade and allegiance to a common government. Thus, hardly anything in the way of new knowledge as to the “causes” of wars has emerged from this monumental analysis, unless one views as new the refutation of established notions by negative results. In particular, neither armed might nor collective security measures (contrary to widespread opinion) emerge as significant war-preventing influences.

The failure of the “statistics of deadly quarrels” to generate a theory on the causes of wars was to be expected in view of the magnitude of the problem. Because Richardson worked alone and had no access to modern computing machinery, the bulk of his effort was absorbed in tedious data gathering and routine calculations. It is likely, of course, that any crudely empirical brute-force attack on the causes of wars is inherently doomed to failure. The nature of the primary contributing causes may be shifting rapidly and may be quite different in different cultural milieus, so that lumping together all the deadly quarrels in the world for a period of some 120 years may be statistically meaningless. Still, the pioneering significance of this work and Richardson’s gallantry in attacking the formidable problem singlehanded should not be underestimated. Whatever conclusions he drew or failed to draw, his work remains a rich collection of data.

Two of Richardson’s books were published in 1960, under the titles of Arms and Insecurity and Statistics of Deadly Quarrels (1960a; 1960b). The former, edited by Nicolas Rashevsky and Ernesto Trucco, contains Richardson’s mathematical theories of arms races, worked out in great detail, and the data relevant to those theories. The latter, edited by Quincy Wright and C. C. Lienau, contains the analysis of the voluminous data on violence ranging from murders to world wars. The two books were widely reviewed and helped establish Richardson’s reputation as the pioneer of research into the causes of war.

Following the publication of these two books, a number of investigators in England and the United States undertook to combine Richardson’s methods of mathematical model construction and data analysis in the field of international relations. In particular, content analysis methods have been used in attempts to obtain indices of internation hostility; various attempts have been made to extend Richardson’s theory of arms races to cover the present period; and his methods of correlation analysis, designed as a search for the causative factors of wars, have been modified and refined. In Volume 8 of General Systems some of these investigations were published or reprinted under the heading “After Richardson” (Rummel 1963; Smoker 1963).

The principal value of Richardson’s contribution lies in the idea of bringing quantitative analysis to bear upon the possible massive system-dynamic determinants of war. His work stands at one end of a spectrum, the other end of which is represented by game-theoretic analysis, where it is supposed that international relations can be viewed as interplays of strategies calculated by “rational players.” This latter view is by far the more prevalent among political scientists. Richardson’s quasi-deterministic view of international relations is complementary to the strategic view, which assumes rationality in the pursuit of “interests” but leaves unanalyzed the genesis of the interests. The strategic view may inquire how nations conduct (or would conduct, if they were rational) a diplomatic-military game but says nothing about how the game got started, why enmities are built up between some states and not between others, or, of course, why states behave so frequently and so clearly against their own interests. Although Richardson did not shed much direct light on these matters, his approach raises important questions that are too often ignored in the purely diplomatic-military approach to international relations.

Anatol Rapoport

[See alsoDisarmament; Peace; War. Other relevant material may be found underInternational relations; Systems analysis.]


1922 Weather Prediction by Numerical Process. Cambridge Univ. Press.

1933 The Measurability of Sensations of Hue, Brightness or Saturation. Pages 112–114 in Physical Society, London, Report of a Joint Discussion on Vision. London: The Society.

1935 Mathematical Psychology of War. Nature 135: 830–831; 136:1025 only.

1937 Hints From Physics and Meteorology as to Mental Periodicities. British Journal of Psychology 28:213–215.

1939 Generalized Foreign Politics: A Study in Group Psychology. Cambridge Univ. Press.

1960a Arms and Insecurity: A Mathematical Study of the Causes and Origins of War. Edited by Nicolas Rashevsky and Ernesto Trucco. Pittsburgh: Boxwood; Chicago: Quadrangle.

1960b Statistics of Deadly Quarrels. Edited by Quincy Wright and C. C. Lienau. Pittsburgh: Boxwood; Chicago: Quadrangle.


Boyce, Anne O. 1889 Records of a Quaker Family: The Richardsons of Cleveland. London: Harris.

Gold, E. 1954 Lewis Fry Richardson 1881–1953. Royal Society of London, Obituary Notices of Fellows 9:216–235. → Includes 4 pages of bibliography.

Rapoport, Anatol 1957 Lewis F. Richardson’s Mathematical Theory of War. Journal of Conflict Resolution 1:249–299.

Sheppard, P. A. 1953 Dr. L. F. Richardson, F.R.S. Nature 172:1127–1128.


Horvath, William J.; and Foster, Caxton C. 1963 Stochastic Models of War Alliances. General Systems 8:77–81.

Rummel, Rudolph J. 1963 Dimensions of Conflict Behavior Within and Between Nations. General Systems 8:1–50.

Smoker, Paul 1963 A Mathematical Study of the Present Arms Race. General Systems 8:51–59.

Zipf, George K. 1949 Human Behavior and the Principle of Least Effort: An Introduction to Human Ecology. Reading, Mass.: Addison-Wesley.

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Richardson, Lewis Fry


(b. Newcastle upon Tyne, England, United Kingdom, 11 October 1881; d. Kilmun, Scotland, United Kingdom, 30 September 1953), mathematics, meteorology, psychology, peace research.

Richardson developed an elegant way for solving differential equations by an approximate numerical method and later applied this to weather prediction. To psychologists he is regarded as a pioneer in the measurement of perception. As a pacifist, he devoted his final years to his seminal work on the objective study of arms races and the causes of war.

Preparation Both Richardson’s father, a successful leather manufacturer, and his mother were devout members of the Society of Friends (Quakers). He was accordingly brought up in the best Quaker traditions and completed his school education at Bootham, a Quaker boarding school in York. Here he was greatly influenced by his science masters, who encouraged him especially to pursue his interest in natural history. He proceeded to Durham College of Science (now part of Newcastle University) from where he was awarded a scholarship to King’s College, Cambridge. He graduated with a First in the Natural Sciences Tripos in 1903.

Over the next ten years Richardson held a series of research and teaching posts, twice at the National Physical Laboratory, twice in industry, and twice in university physics departments. During his spell with National Peat Industries from 1906 to 1907 he was asked how best to design drains in a peat moss, taking into account the annual rainfall. As the mathematical equations involved were not solvable by analytical methods, he was led to study approximate methods of solution, first graphical and then numerical. He considered two types of problems, boundary value problems and initial value problems, which he called “jury” and “marching” problems respectively. The results of his efforts were published in 1910 in Richardson’s first important paper “The Approximate Solution by Finite Differences of Physical Problems Involving Differential Equations.” In it he demonstrated how his methods could be used to obtain rapid and sufficiently accurate solutions to many practical problems by calculating the stresses in a masonry dam. A clear account of Richardson’s method of numerical analysis was given by Ernest Gold (1954).

Weather In the following year Richardson suggested to the director of the British Meteorological Office, Sir Napier Shaw, that his method might be applied to calculate weather forecasts. Shaw was favorably impressed and in 1913 he gave Richardson an opportunity to develop his ideas by appointing him superintendent of Eskdalemuir Observatory in Scotland, where the not too burdensome administrative duties would leave him adequate time for research. Shortly after beginning his study, Richardson came under the influence of the ideas of Vilhelm Bjerknes but continued to use numerical methods rather than graphs. At this stage he was apparently not aware of the work of Felix Exner. By 1916 he had almost completed the first draft of his book Weather Prediction by Numerical Process but it still remained to provide a practical example.

At this point Richardson resigned from the Meteorological Office to serve as an ambulance driver in the Friends’ Ambulance Unit in France. During his rest periods from his horrific task of transporting wounded soldiers, he calculated a weather forecast for central Europe over a six-hour period on 20 May 1910—the date for which he felt that the best set of weather observations was available. The results of the computation were greatly at variance with the observed changes, the most- glaring error being a calculated rise in surface pressure of 145 millibars whereas in fact there had been very little change. The calculations were nevertheless included in his book, which was finally published in 1922. An excellent account of the reasons for the failure of the forecast was given by Peter Lynch (2006).

Richardson’s book had no immediate impact on the current practices for weather forecasting, which at that time were largely based on subjective methods and on the experience of the forecasters. Quite apart from the disastrous results of his attempt at numerical weather prediction, the available observing and computing facilities would have been wholly inadequate for the routine application of numerical methods. (The agenda to use electronic computers to calculate the weather started in 1946.) To his contemporary meteorologists, Richardson appeared to be a brilliant theoretician with completely impractical ideas.

This attitude changed dramatically in the 1950s, thanks to better mathematics and understanding of atmospheric dynamics, to the development of electronic computers, and to the great improvements in weather observations, especially in the upper air. In 1965 his book, which in the original edition had sold but a few hundred copies, was reissued as a Dover paperback, recommended as a classroom text in dynamic meteorology. Numerical methods of weather forecasting, similar in many ways to those of Richardson, rapidly became routine all over the world.

By the time of his discharge from the Friends’ Ambulance Unit in 1919 Richardson had become passionate about meteorology and he was happy to accept an offer from Shaw of a research post at Benson Observatory in Oxfordshire with William Henry Dines, a pioneer in making upper-air measurements with kites. Richardson devised several ingenious methods of conducting these measurements in such a way that the results would be available quickly, in time for use in weather forecasting, but none proved to be suitable for routine use. He also carried out a series of experiments on atmospheric turbulence, from which he derived a criterion, later to be called the Richardson number, for determining whether the turbulence would increase or decrease. This now ranks as a fundamental parameter in problems of the turbulent motion of the atmosphere.

Richardson’s stay at Benson was cut short in 1920 when the Meteorological Office became part of the Air Ministry. He regretfully resigned because his Quaker pacifist convictions made it unacceptable for him to work directly for the armed services. There being no university departments of meteorology in Britain at that time, Richardson accepted a position at Westminster Training College in London as lecturer in physics and mathematics (although he had no formal mathematical qualifications at this stage). He was destined to spend the rest of his career in the educational world, ending up from 1929 to 1940 as principal of Paisley Technical College (now the University of Paisley).

One of the conditions of Richardson’s appointment at Westminster was that he would have reasonable time for research work. His main achievement during the first part of his ten-year stay there was in the field of atmospheric diffusion. Hitherto, studies of diffusion had been based on measuring the distances of individual elements from a fixed point. Richardson’s novel idea was to measure the distance l between each of a pair of particles and its neighbor. From measurements involving parachuting dandelion seeds, the release of clusters of toy balloons, and puffs of tobacco smoke he determined empirically that the rate of diffusion was roughly proportional to 1 4/3. This same ratio was derived theoretically nearly twenty years later by Andrei N. Kolmogorov and Alexander M. Obukhov.

Psychology While still a student at Cambridge, Richardson had decided to spend the first half of his life under the strict discipline of physics and then to apply this training to researches on living things. To this end he started to study psychology in 1923 as an external student at University College in London. He obtained a pass degree in 1925 in psychology with pure and applied mathematics, and followed this up with an honor’s degree in psychology in 1929. In the meantime he had in 1926 been awarded a DSc for his work on physics, mathematics, and meteorology and had been elected as a Fellow of the Royal Society. In this same year he finally made a deliberate decision to abandon meteorology for psychology and immediately embarked on a series of experiments on the quantitative estimation of perception, the prevailing view at that time being that such estimates were meaningless.

His first paper on the subject, published in 1928, dealt with the threshold of sensation on the forearm. This was followed in 1929 by two papers on quantitative estimates of light and color. For the latter he invited a wide variety of people to assign a number between 0 (white) and 100 (scarlet) to a shade of pink. Most participants had no difficulty in providing a reasonable estimate. Richard-son’s most famous paper in this field related to loudness. Observers were asked to estimate the ratio of the loudness of a signal to that of a standard signal, the intensity of the signals being measured independently as a telephone voltage. In 1933 Richardson suffered from cellulitis of his right thumb and experienced various intensities of pain over a period of seven weeks. This led him to propose a quantitative scale for pain from A, a pain that can only be perceived by careful attention, up to E, a pain so intense that it arrests the movement of thought.

From all these experiments Richardson concluded that he had cleared the way toward a more scientific study of quantitativeness in sensations of various kinds but he found it difficult to convince other psychologists of the validity of his measurements. By the 1940s, however, the importance of the quantitative study of sensation had been widely recognized, not only in experimental psychology but also in many practical fields such as clinical psychology and the design of environments where people live.

On moving to Paisley Technical College in 1929, Richardson found that his administrative duties and heavy teaching load, which included giving evening classes in mathematics and physics up to degree level, meant that any serious research work was restricted to his limited spare time at home, mainly weekends and holidays. He soon converted a large room in his official residence into a workshop and laboratory and embarked on some experiments to study the analogies between the way thought occurs and the behavior of a neon lamp. When the voltage applied to the lamp is set just below that required for permanent illumination, the lamp behaves in a variable manner. Richardson found no less than sixteen analogies between this behavior and mental processes. He published several papers on this subject between 1930 and 1937 and urged physicists to develop the equations relating to the theory of sparking, in the belief that they would be of great interest both to physiologists and psychologists.

Peace and Other Studies While serving in the Friends’ Ambulance Unit during World War I, Richardson had turned his thoughts to the causes of war and how to prevent them. He developed two simple differential equations showing that the rate of increase in the warlike activity of one nation related to the current warlike activity of the enemy nation. He published these at his own expense in a fifty-page booklet titled Mathematical Psychology of War and sent copies to his colleagues in the Friends’ Ambulance Unit, most of whom were perplexed by the mathematics. He returned to this topic in 1934, appalled by the failure of the Geneva disarmament conference. To his great satisfaction he found that his equations showed remarkable success in describing the course of the arms races of 1909–1913 and 1933–1938. These results, together with a further elaboration of his ideas, were published in June 1939 in his substantial monograph Generalized Foreign Politics.

When World War II erupted in September 1939, Richardson decided that the time had come for him to retire from his post in Paisley so that he could have more time to devote to his war researches. He wanted to determine if any relationships of practical significance could be found from a statistical analysis of past wars. To this end he undertook the mammoth task of compiling quantitative data, such as the number of casualties, about wars which had occurred since 1820. From this he was able to analyze such features as the distribution of wars in time and the frequency of involvement of individual countries, of different languages, and of different religions. By 1945 Richardson had assembled the results of all this research, together with further material on arms races, in the form of a 500-page book, but no publisher could be found. With great difficulty he succeeded in having some of the main results published in a variety of academic journals. He also divided the book in two and published both parts at his own expense in microfilms.

Among the papers not published until after Richardson’s death was one on the problem of contiguity, in which he showed that there is a linear relationship between the logarithm of the measured length of a coastline and the length of the steps used in the measurements. The slope of the line gives a good indication of the wiggliness of the coastline. This result later proved to be important in the development of ideas about fractals.

The breadth of Richardson’s original thinking is demonstrated by some of his papers on other topics. For example, in 1913 he advocated a comparison of the development of intelligence of children of well-educated parents with that of children they have adopted from poor families. He also wrote three papers on voting methods in international assemblies, in the last of which he proposed a system whereby the voting strength of each country would be determined by its international importance, calculated on the basis of several readily ascertainable ingredients. Furthermore, after the sinking of the Titanic by an iceberg in 1912, he filed two patents for an echo-sounding system to warn ships of their approach to a large object in a fog. All these papers have been widely cited in the relevant literature.

At the time of their publication, Richardson’s papers about the causes of war had received little attention, but in the 1950s, when scientists were becoming more interested in the subject, they were brought to a wide audience in the social sciences largely by his son Stephen, especially in the United States. Edited versions of his two microfilms were published in 1960, under the titles Arms and Insecurity and Statistics of Deadly Quarrels. They were welcomed by economists, mathematicians, and physicists who had wanted to put the academic discipline of international relations onto a firmer and scientific footing. Richardson had become the founding father of peace research and within a few years more than two hundred institutes of peace research or equivalent had been established all over the world.

Throughout his life, Richardson conducted his varied researches almost entirely on his own. His main source of support and help was his wife Dorothy (daughter of the well-known educationalist William Garnett), whom he had married in 1909. Under his influence she left the Church of England and became an enthusiastic Quaker. As they were unable to have children of their own, they adopted two boys and a girl, Olaf and Stephen in 1920 and Elaine in 1922. Richardson died peacefully in his sleep on 30 September 1953 at their home in Kilmun, Argyll, to which they had moved from Paisley in 1943.


The most important archival collections are in Cambridge University (UK) Library and the Richardson Institute, University of Lancaster. The Ashford publication (cited below) contains a comprehensive bibliography.


Weather Prediction by Numerical Process. Cambridge, U.K.: Cambridge University Press, 1922. Reprinted by Dover Publications, New York, 1965, and by Cambridge University Press, 2006.

Arms and Insecurity. Pittsburgh: Boxwood; Chicago: Quadrangle, 1960.

Statistics of Deadly Quarrels. Pittsburgh: Boxwood; Chicago: Quadrangle, 1960.

Collected Papers of Lewis Fry Richardson. Vol. 1, Meteorology and Numerical Analysis, edited by P. G. DRāzīn. Vol. 2, Quantitative Psychology and Studies of Conflict, edited by Ian Sutherland. Cambridge, U.K.: Cambridge University Press, 1993. Includes the titles mentioned in the text.


Ashford, Oliver Martin. Prophet or Professor?: The Life and Work of Lewis Fry Richardson. Bristol, U.K.: Adam Hilger, 1985. Contains a comprehensive bibliography of works by Richardson and of works about Richardson.

Gold, Ernest. “Lewis Fry Richardson: 1881–1953.” Obituary Notices of Fellows of the Royal Society 9 (1954): 217–235.

Lynch, Peter. The Emergence of Numerical Weather Prediction: Richardson’s Dream. Cambridge, U.K.: Cambridge University Press, 2006.

Platzman, George. “A Retrospective View of Richardson’s Book on Weather Prediction.” Bulletin of the American Meteorological Society 48 (1967): 514–550.

Rapoport, A. “Lewis F. Richardson’s Mathematical Theory of War.” Journal of Conflict Resolution 1 (1957): 249–299.

Oliver M. Ashford

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Richardson, Lewis Fry (1881-1953)

Richardson, Lewis Fry (1881-1953)

English physicist and meteorologist

Lewis Fry Richardson was an English physicist with a penchant for trying to solve a wide range of scientific problems using mathematics. During his career as a scientist and educator, Richardson explored mathematical solutions to predict weather , to explain the flow of water through peat, and to identify the origins of war.

Richardson was the youngest of seven children born to David Richardson, a tanner, and his wife, Catherine Fry, who came from a family of corn merchants. Richardson was born on October 11, 1881, in Newcastle upon Tyne. After completing his high school education in 1898, Richardson studied science at Durham College in Newcastle for two years before entering King's College at Cambridge, where he ultimately earned a doctorate in physics and then later returned to study and receive a degree in psychology. After graduating from King's College, Richardson held a number of positions in the years leading up to World War I. These included working as a scientist for a tungsten lamp factory, the National Peat Industries, Ltd., and serving four years as superintendent of the Eskdalemuir Observatory operated by the National Meteorological Office.

Richardson, who was born into a Quaker family, served with the French army as a member of the Friends'Ambulance Unit during the war from 1916 to 1919. Following the end of hostilities, Richardson returned to England, where he combined his scientific inquiry with teaching. In 1920, he accepted a position as director of the physics department at Westminster Training College. This was followed by an appointment as principal of Paisley Technical College in 1929, a post that he held until his retirement in 1940. Retirement allowed Richardson to continue his primary love, research.

Richardson began his research looking at practical problems, such as examining the flow of water through peat while he worked for the National Peat Industries, Ltd. Using differential equations, Richardson came up with ways to determine water flow that were far more accurate than other methods. His work eventually led to attempts at developing a system of weather prediction based on newly understood knowledge of the upper atmosphere and the roles played by radiation and eddies, or atmospheric currents which move contrary to main air flow. Richardson's work led to the publication of his book, Weather Prediction by Numerical Process, in 1922.

Richardson's experiences in France during the First World War also inspired him to probe the causes of human conflict using mathematics, and he published a paper in 1919 on the mathematical psychology of war. Eventually, he enlarged upon this early work in the book Arms and Insecurity and went on to complete a mathematical study of the world's wars. This work, which resulted in Statistics of Deadly Quarrels, examined the causes and magnitude of these conflicts. In his research, Richardson tried to define the relations between countries in terms of mathematical equations.

Richardson's pioneering use of mathematics resulted in him being elected a fellow in the Royal Society in 1926. Richardson died on September 30, 1953.

See also Atmospheric composition and structure; Weather forecasting methods; Weather forecasting

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