Sources

LFR’s stature as a scientific innovator is recognised widely. In the UK the Richardson Institute at University of Lancaster, where peace and conflict resolution are studied, is named after him. There is a Richardson Wing at the Meteorological Office, a Richardson Effect in measuring coastlines, Richardson Extrapolation, and Richardson Iteration for solving certain differential equations, a Richardson Number in air flow, a Richardson Model of the arms race, and a Richardson theory of war. There are LFR awards given for meteorological research and a Lifetime LFR award given for peace studies. All of these were named by others, which is to be expected, humility being a quality of LFR that is mentioned in several sources.

There are already several biographical monographs and essays about LFR. The most substantial is by a Quaker, Oliver Ashford³, who was his student and who had a significant collection of primary material and personal recollections available to him from LFR’s family and other sources. There are several biographical essays, most of which use, as I do, Ashford’s biography as the major source. The most accessible biography is a brief essay by Helen Holt⁴ who similarly draws from Ashford’s work.

I have relied on Ashford’s extensive access to private papers in my outline of LFR’s career, supplemented by appropriate archives at Friends House Library, and the archive of the Eugenics Society, and first-hand obituaries from learned societies, in particular, the detailed work of Ernest Gold for the Royal Society⁵.

Along with Ashford and others, Quincy Wright, an American Quaker political scientist who worked with LFR in the 1940s, began to collect, publish and republish his work on war and peace in suitable journals and books shortly after his death. I have used the two volumes of collected published works that cover most of his fields of interest and provide source material for those working in meteorology, numerical analysis and war studies⁶.

Successive generations have provided overviews of his contributions to various academic fields⁷.There are several scholarly critical syntheses of his war and peace studies, most notably by Anatol Rapoport⁸. In relatively recent times there have been publications focusing on specific aspects of his work from a modern perspective. For example, there is a 2020 collection edited by Nils Gleditsch⁹ in which not only are his social science findings reported, but also his innovative quantitative social science methods.

Numerous student essays online indicate that his work in both meteorology and war studies is taught in appropriate university courses world-wide. It is clear from the variety of these sources that his interdisciplinarity, motivation, innovation and creativity continue to fascinate those who come across his ideas and work

LFR’s scientific career

During his early work in the peat industry that used his knowledge of physics, he became frustrated with the length of time it took to do necessary calculations about flow and devised a quicker method that reached an appropriate level of approximation in far fewer steps. His method was graphical in nature and was dismissed by some Cambridge mathematicians as archaic and inaccurate compared with what had been achieved by analytical methods in some special cases. It was, however, sufficient in some contexts of a more engineering nature. Similar graphical methods continued to be used in some contexts into the 1960s when computers first became powerful enough to make purely numerical methods sufficiently rapid. His application for a fellowship at Cambridge appears to have been blocked by his commitment to this approach that could be seen either as too old-fashioned or too innovative depending on the reviewer. Hunt suggests that his academic isolation started here and could have led both to a lack of recognition of future work and also, fortuitously, to the originality that the freedom to work alone gave him¹⁰.

He then had a variety of jobs and interests. For example, a few days after the sinking of the Titanic in 1912, he patented two devices for locating large objects at sea, one that worked through fog and another through the water. Both predated the methods used now but anticipated them. He withdrew from that direction as he was interested in saving life, not in doing any work that might help others to develop weaponry. He also began to be interested in psychology during this period and his interest in human factors, supported in the 1920s by achieving two psychology degrees, played into his future thinking about causes of war.

Eventually he moved into meteorology as a superintendent of a unit in the Meteorological Office. He found that a mixture of physics and mathematics suited his approach to problems, as did also the combination of experimentation, observation and mathematisation that led to usable results. His iterative method of calculating and other simplifying approaches to modelling were useful in this work.

He was also known throughout his life for devising improvised physical demonstrations and measuring devices of phenomena. For example, ‘we have observed the relative motion of two floating pieces of parsnip’ is the opening for a co-authored seminal paper on eddy diffusion¹¹. His family and students were often engaged in building physical models and his reports as well as his methods could be amusing. One notable experiment involved a ‘cracker balloon’ which was designed to ascend, explode, and deliver a measurement of temperature. This was supposed to make a popping sound but this was not heard. However, the test was saved when ‘a group of children, whose assistance had not been welcomed, began to call out’¹².

While he found the work fulfilling, cracks began to show between his meteorological commitment and his pacifism at the start of WW1. He responded with avoidance tactics, rather than outright refusal, to requests to work out how tremors could indicate the location of guns. The director, Napier Shaw, reported that LFR ‘had conscientious objections to being concerned with the use of scientific apparatus for locating engines of destruction’¹³.

LFR wrote a letter to The Friend in 1915 suggesting that working alongside soldiers at the front and hence sharing their vulnerability and fraternity, rather than avoiding any engagement with military action, was an appropriate position for Quakers. He tried to get leave to join the new Friends Ambulance Unit but was refused (it was unusual to release non-combatants whose work was seen as critical). In 1917, he resigned to take up ambulance work.

During this time he turned his thoughts to how a scientific approach to understanding war might be an appropriate pathway towards informing leaders how to avoid war and achieve peace. He then began the work that continued for the rest of his life. He began making notes about possible factors to take into account, drafting an article Mathematical psychology of war¹⁴, but it was a long journey between these initial insights and his substantial and influential study of the causes of war that was published after World War 2.

One innovative direction of his study was to wonder whether the lengths of boundaries between countries had any bearing on the potential for hostility. This inquiry led to the discovery of a relationship between the size of the unit of measurement and the estimated length that gives rise to the concept of ‘fractal dimension’, sometimes called the Richardson Effect. This aspect of LFR’s work is recognised as one of the foundational ideas in fractals, a branch of mathematics that was later pursued by pure mathematicians like Benoit Mandelbrot¹⁵ unknown to LFR at the time.

During his ambulance years, LFR also drafted a book about the usefulness of numerical processes for weather prediction that would be important for food production and other human activities. What is now known as ‘Richardson’s forecast factory’ ¹⁶ suggested that 64000 parallel processors could cover the globe and be used to predict weather. At the time, the calculations would take so long that the predicted weather would have already happened long before they were finished. He tested this in principle by using past weather data from across Europe and although the results were far from accurate, his methods attracted interest. In our era when more is known about certain influential factors, and the observation data itself is more accurate, his approach generates remarkably rapid and accurate forecasts.¹⁷

He seems also to have attended to his actual ambulance work with similar care and detail. A colleague reported that ‘his simplicity and integrity transformed into acts of permanent worth the performance of the most menial of tasks’¹⁸.

After the war he was accepted back into the Meteorology Office, despite his earlier resignation, but in 1920 this Office was taken over by the Air Ministry. So he resigned again, experiencing distress because his work there at the time had, in his own mind, nothing to do with war and everything to do with the betterment of life¹⁹. Weather prediction, however, could be used for war purposes by informing the military about the conditions for particular tactics. Instead, he looked for academic work in which he could continue his research, even paying to upgrade his Cambridge first degree to MA to have access to academic resources. He had initially refused to do this, which was the usual method, because he believed that academic honours should be achieved through work and not merely purchased. He failed to find such work which is why he ended his working life as principal of Paisley Technical College, rather than as a paid researcher. His passion for studying wars continued and he took early retirement at 60 in 1940 so that he could concentrate on it, being content to live relatively frugally as a result. It was at this moment that he was offered a Chair in Meteorology, a job that would have fulfilled his earlier academic desires, but he refused this with regret as it would have distracted him from war studies – work that at that time he felt uniquely qualified and driven to do²⁰.

The statistical method he used in this project was to collect data about nearly 300 wars and other ‘deadly quarrels’, such as murders and riots from 1820 to 1945, and analyse the topographical, geopolitical and social conditions that surrounded them. Years of precise but tedious work followed, resulting in several papers and his seminal work, published posthumously as Statistics of Deadly Quarrels²¹. Among other findings, he was able to list factors that were either hostile or pacifying in wars and understand their frequency and magnitude. His data, mathematical models and analytical methods have been studied, critiqued and extended by many scholars, and his assumptions and conclusions about human behaviour reveal his care for the human costs of wars and how they come about. As an example, his method of counting the dead extended beyond the battlefield, including:

• Armed people dying in combat, at sea, dying later from weapon wounds, poison gas, starvation in siege, malicious acts of enemies;

• Civilians dying as above but as non-combatants;

• After-effect deaths from disease, exposure, hunger, lack of care etc. among the people at war.

He excluded:

• Deaths in neutral, non-belligerent communities, accidentally killed;

• Unintentional deaths by civilians by exposure or disease;

• Post war reduction in birth rates.

We might add new experiences since 1945 to these lists, or move groups into inclusion that he excluded. His data were mainly about land and air battles, and would have excluded the fallout from Hiroshima and Nagasaki, and possibly underestimated the ecological effects of scorched earth practices, next-generation radiation deaths, and forced migration. What is important is that he did not limit his data to deaths of combatants.

Anatol Rapoport²², in his respectful and extensive critique of LFR’s work from the point of view of a leader in Conflict Studies, identifies important threads throughout that are influenced by LFR’s underlying values. First, the motivation is peace rather than militarism, and this influences the construction of equations to contrast stability. such as through cooperation, with instability such as through threats and unlimited hostility. Secondly, LFR attends to how human behaviour and moods change and relate to each other between nations, rather than what political decisions are made, and these insights are supported by statistical generalisations of data across a wide range of quarrels. Thirdly, LFR uses the scientific methods of deduction, induction and a continual search for causality. Because LFR’s approach is empirical and continually searching, it uncovers many components to war beyond the military, political and historical and, hence, possible levers for peace. In his 1940s work, he also identified a statistical tail of deaths due to conflicts arising from apparent enjoyment of fighting, pride, lack of land for the size of population, and the need to fight for fair pay. Currently we might look at responses to climate change and extreme weather events as additional data.

It has been apparent in my summary of his career that his academic life was not a straightforward process of pursuing funded research, publishing and career progression. Instead it was a navigation through channels carved by his pacifism and ethics in a world of growing militarism. He might have had a conventionally distinguished career in meteorology if he had not been so keen to stay away from weapons and to spend time on his war and peace studies. Despite this, his meteorological legacy is substantial.

Evidence of LFR’s methods and academic values

LFR’s Quakerism is mentioned as a recognisable ingredient in his academic demeanour in most eulogies and biographical essays. For example, Julian Hunt²³ observes that:

Knowing about the lives and beliefs of creative people helps in the understanding and appreciation of their work. This is especially true in the case of Lewis Fry Richardson, much of whose scientific work changed and evolved as a direct result of and from his reaction as a Quaker to the political and technological changes that occurred during his lifetime. His life is an inspiration, showing how a mathematical scientist can respond to the problems of the world around him, while not necessarily being in accordance with the ways favored [sic] or promoted by the established organizations that direct and finance science.

Rapoport refers to a Christian principle of ‘returning good for evil’ as embodied in LFR’s approach to understanding conflicts and wars²⁴.

Academically, LFR was committed to the idea that scientific methods provide insights into how the world works, not only in material characteristics but also in the ways in which people behave, both as individual organisms reacting psychologically to events and as groups acting en masse socially and politically.

In a range of topics across fields (he also had some results in psychology) his method was to seek plausible relationships within phenomena, subject these to experimentation and statistical analysis, and from these to devise mathematical tools that might explain, and hence predict, the behaviour of the objects of study. The mathematical tools were usually differential equations that encapsulated how relatively small changes in one or more aspects could affect, and be affected by, changes in other aspects which might be small, large, positive, negative or even chaotic or catastrophic. In many of his studies these associated changes could be extremely small, and a reason why some of his results and methods only became useful after his death due to the need for modern computing power. Such changes can only be described as causal if there is also a scientific explanation for the relationship between the changes.

Michael Spagat and colleagues identify that in all of LFR’s research he was using mathematics to synthesise micro and macro elements of situations²⁵. In my perception, this accords with the Quaker tradition of improving life at micro levels through personal change and charity while also influencing at a macro level through advocacy and political and social action. The combining of micro and macro study has led some to claim that LFR was helping to found complexity science²⁶. This combination is reflected mathematically in the use of statistics and also in a field of numerical analysis, both areas which LFR used repeatedly and also, in the latter, made practical contributions. While statistics gather data and present generalities, ignoring outliers, numerical analysis deals with relationships in which a small change in one component might cause much bigger changes in a system. Both approaches are necessary to understand the workings of a system. The mathematics cannot do any work on its own: human agency has a role too. In the introduction to his booklet, ‘Arms and Security’, he wrote:

The equations are merely a description of what people would do if they did not stop to think, they follow their traditions and their instincts because they have not yet made a sufficiently strenuous intellectual and moral effort to control the situation. The process described by the ensuing equations is not to be thought of as inevitable. It is what would occur if instinct and tradition were allowed to act uncontrolled²⁷.

This sort of work involves seeking underlying truth, experimentation, doubt, open-mindedness and a willingness to be surprised by what is not immediately observable; thus it is thoroughly compatible with a Quaker approach to beliefs about life that are based on experience as well as satisfying the application of science to human problems²⁸.

LFR included in his work clear narratives about thought processes, experimental actions, and elements of doubt and self-checking so that claims to truth could be subject to critique. He aptly summarized his in The Mathematical Psychology of War²⁹: ‘the definiteness may be spurious, the brevity may be due to the omission of the more important things. Against these faults we must constantly be on our guard, they ought to be realized and admitted’.

In academic life there is a fine line between recognition of limitations and self-deprecation. After LFR’s death, Gordon Rogers wrote³⁰: ‘his unimpeachable intellectual honesty led him to hedge round his main conclusions with so many qualifications that the conclusions lost some of their force. He frequently understated his own case seriously lest he be unfair to his opponents’.

Humility was especially present in his work on war which was breaking new ground, starting during WW1 and continuing to his death after WW2. Social and political scientists working in the same area tended to be dubious about treating war and peace mathematically, preferring to depend on intuitive theories about human nature, ideologies, historical generalisations or philosophical beliefs rather than numerical evidence.

LFR anticipated his being challenged on the basis of the unpredictability of acts of individual leaders. He tackled this in typical style by setting up a discussion between himself and an imaginary critic³¹:

CRITIC: A serious objection to your description is that it does not mention intelligent aggression planned by a leader as moves in a chess game.

AUTHOR: That is admitted; for a description of predictable tendencies cannot include anything so unpredictable as moves in a game of chess. Yet the acts of a leader are in part controlled by the great instinctive and traditional tendencies which are formulated in my description. It is somewhat as if the chessmen were connected by horizontal springs to heavy weights beyond the chessboard.

LFR’s sampling methods could be questioned due to his dependence on availability of data. Modern critics suggest exceptional cases that do not match LFR’s intentions towards generality, and also changes in the nature of war that challenge his findings. For example, William Eckhardt ³² points out several pacifying mechanisms that are omitted from LFR’s studies; diplomacy, third parties, and international and regional treaty organisations have become more significant since World War 2.

Critics at the time were more likely to be doubtful about his methods. In the early to mid-twentieth century statistical modelling in the social sciences was a new method to use to generalise behaviour of classes of people, and LFR was trying to publish in an arena which was subject to energetic philosophical, historical, and values-based debate. He was ahead of his time in studying causes of war statistically and could not get published alongside historical or philosophical theories. There were no appropriate learned journals and societies until after World War 2. His membership in the Royal Society, given in recognition of his contributions to meteorology, was no help in getting a statistical study of wars published. His chosen champions were also of little help. For example, Bertrand Russell reviewed a proposed book for Stanley Unwin, a publisher with strong connections to Quaker writers, praising it highly but pointing out that it would not sell many copies³³.

As a physicist, statistician, and mathematician, he developed the idea that the magnitude of a war could be expressed as the logarithm, to the base ten, of the number of persons who died. Such a starting place is hardly likely to attract a reader who is looking for abstract concepts such as hatred or poverty, nor someone who wants advice about military strategy, nor someone who wants a discussion about the roles of democracy versus autocracy in wars and in peace. Yet, this starting place, eventually published in Nature as ‘Frequency of Occurrence of Wars and other Fatal Quarrels’³⁴, is now foundational in studies of war and peace and led to findings about the causes of war, their frequency, and identification of pacifying influences.

He is now recognised as the first person to show how what we now call an ‘arms race’ works, in particular that arming for belligerence and arming for defence act similarly in the race. The accumulation of weapons can be taken to indicate the size of the threat to other nations, whether or not they are ostensibly for attack or defence³⁵. He modelled this mathematically, while understanding the psychological background to such accumulations, and also reductions, as ‘war moods’³⁶. As well as overt concerns about attack and defence, populations go through phases of friendliness and hostility towards each other in the war process, and a war might end not only because of defeat or submission but also of ‘war-weariness’. This might be manifested as anger towards a government that allowed or precipitated a war to happen, or that presided over disaster. The arms race model, although initially only published by LFR himself on microfilm, attracted the attention of political scientists such as Quincy Wright, a founder of American peace studies.

LFR’s analysis of the causes of conflicts of all sizes is work for which he is now respected and honoured, but he had never held an academic position that supported his studies in this direction, unlike his meteorology work that was published, recognised and rewarded during his working life. Indeed, his war research has been described as technically ‘amateur’ in the sense that he was not paid for it. But this characterisation risks belittling the sustained and informed effort over time that he spent on it³⁷. Joseph Smagorinsky³⁸ describes him as a ‘renaissance man’ and Spagat et al ³⁹ as ‘one of the greatest scientists of the 20^th century’.

He continued to study war and peace until his death in 1953. It would be right to admire his persistence, spanning his whole adult life, in the pursuit of scientific tools that could be used by politicians and diplomats to identify the levers that avoid and prevent wars. It would, however, be glib to claim that he did this because he was a Quaker, even though honesty, humility, pacifism and a persistent search for truth are qualities of his work, without looking at some of the Quaker influences in his life.

The background to his values

LFR was the seventh child of a prosperous Quaker family⁴⁰. Four boys, including Lewis, attended Bootham School, the Quaker boys’ school in York. One boy attended another school with Quaker values; one girl attended Mount school, the Quaker girls’ school in York; and one, who became a surgeon, attended Cheltenham Ladies’ College, which at the time had principles similar to those of Quaker schools. Two children became artists and two went into the family business. Two of the Bootham boys were deeply influenced by science teaching there: Hugh became a botanist as well as a teacher of natural history and Lewis became, at first, a physicist. All seven children as adults were involved in philanthropy, voluntary work, and engagement with health, politics, prisons, or education and discussions of various kinds about peacebuilding. For example, Hugh gave lectures on the flaws in setting up the League of Nations as a militaristic structure that presumed war rather than as a peace-seeking society. It is clear that Quaker values were embedded in their family life, schooling and expectations of their life choices. The records we have of their Quakerism demonstrate making their ‘lives speak’ (as Quakers say⁴¹). It is possible to see philanthropy, justice, integrity, peace, charity and several other active virtues writ large.

The scientific influences at Bootham were strong. Sylvanus P. Thompson, an internationally respected physicist and well-known Quaker thinker, had taught there, Francis Pollard’s history of Bootham school describes how Thompson had established a legacy of inspirational teaching⁴². This continued during LFR’s time there. J Edmund Clark, whose teaching included practical explorations, was secretary of a Committee in the Royal Meteorological Society for twenty-five years so it is likely that he influenced LFR’s interest in the subject. Near the time LFR was there, a visitor to Bootham pointed out as a criticism, that most learning seemed to be happening in extra-curricular activities rather than in the classroom⁴³. Science classrooms in other schools at the time, where there were any, tended to involve recitations of facts, but at Bootham experiment and hypothesis were frequent educational methods.

These are the backgrounds connecting science and Quakerism that LFR encountered. I doubt that he thought of being a Quaker as a choice of ideology. However; it is more likely that being a Quaker is an obvious way to live for a birthright Friend mixing with people from other Quaker families.

Of his underlying beliefs LFR wrote that religion is founded upon ‘an inner sense which all of us more or less possess. I personally believe in a spiritual universe and in a material universe which act on one another, but only through the brain’⁴⁴. In these words he alludes to the Quaker belief that we are all capable of a direct relationship with the Divine, but his words seem to hedge whether this capability is equal across everyone, or is potentially equal but not equally exercised. However, I may be over-interpreting. What this note shows strongly is the connection, for him, between science and belief in something beyond scientific understanding. Religious aspects to his questioning about events in the world can be seen in some notes made in 1914: ‘When things don’t fit we have three alternatives: (i) Christ didn’t mean that. (ii) Christ not God. (iii) we are wrong’.⁴⁵

And, in relation to his Quaker background and work methods, he writes in his personal preface to Statistics of Deadly Quarrels⁴⁶:

I have a prejudice that the moral evil in war outweighs the moral good, although the latter is conspicuous. This prejudice is derived from the Quakers, who brought me up. I am not ashamed of it; indeed it has been one of the two principal motives for writing this book. The other principal motive is my prejudice that scientific method is more trustworthy than rhetoric.

Throughout his life, he made several obvious attempts to avoid engaging in anything that might contribute to conflict or weaponry, or distract him from his chosen path of peace, or peaceful, research. Some of these are reported above. During the late 1920s, Graham Sutton contacted LFR to ask for help with work taking place at Porton Down, the UK chemical warfare research centre. Could he help them with understanding diffusion in the upper air? Sutton reports that he expected LFR would refuse due to him being a Quaker, but pointed out to LFR that the uses of original scientific work could never be protected from use in ways that the originator might condemn⁴⁷. LFR’s wife, Dorothy, has reported that when he realised that his work might be used to extend the use of poison gas he destroyed some of his unpublished research⁴⁸. Ironically, when Porton Down issued advice about the dangers of gas diffusion in World War II, LFR, who was then an air warden being taught about the use of gas masks, was annoyed that his results about the effects of windspeed and turbulence were not taken into account in the training. His consistent refusal to have anything to do with the military, weaponry, tactical and belligerent aspects of war had closed some pathways. But his promotion of the historic evidence of pacification, the causes of hostility, the air polluting effects of poison gas, and the spread of radiation could contribute to alleviating suffering and it is likely that his work in these relevant areas is now well-enough known to have a positive effect.

To try and understand LFR from a Quaker viewpoint is, however, not complete when we move a little beyond his emphatic pacifism, his search for truth, and, though I have not reported it here, his generosity and hospitality to students, family and others, his ‘kind heart’ and his ‘stimulating opinions’⁴⁹.

LFR and eugenics⁵⁰

There is, however, an irony in offering nature and nurture as influences since LFR was, for over 30 years, a member of the Eugenics Education Society⁵¹. One of their major interests was the relationship between nature and nurture as formative influences on children.

Nature, in their terms, would be evidenced from his extended family tree of high-achieving Quakers. The eugenic assumption would be that he inherited his intelligence and other qualities genetically. Nurture, in their terms, came from families and schools with Quaker principles, Quaker academics he met while at Cambridge and through work, and presumably conversations at home among his older brothers and sisters. Nurture is also a feature of friends he made while serving in Friends Ambulance Unit, and by regular attendance at various Quaker meetings, local and national, over his lifetime.

LFR’s interest in eugenics seems to have started at Cambridge where students were influenced by the positivism of Karl Pearson’s Grammar of Science⁵². The idea that human characteristics could be described statistically, and that opinions should be subject to statistical scrutiny, appealed to LFR’s sense of the role of mathematics in revealing correlations and hence possible causes of behaviour. Pearson was a pioneer in such methods and had been strongly influenced by Francis Galton who founded the study of eugenics. Galton came from substantial Quaker heritage, although his branch of the family had left Quaker membership in the middle of the 19^th century. Galton, who also had familial connections to Darwin, had defined eugenics as:

the science of improving stock, which is by no means confined to questions of judicious mating, but which, especially in the case of man, takes cognizance of all influences that tend in however remote a degree to give the more suitable races or strains of blood a better chance of prevailing speedily over the less suitable than they otherwise would have had⁵³.

Galton was a founder in the emerging science of statistics, using it to describe generalities and differences within and between races and other groups of living things. The statistical concepts of correlation and regression towards a mean are attributed to him. The illustrative examples about humans that he used in his writings to illustrate inferiority or deficiency now often seem abhorrent since they are used to compare races based on physical measurements and other judgements that assume white, European, educated norms as superior⁵⁴.

Pearson also came from Quaker ‘stock’ ⁵⁵ although he himself was a staunch atheist. He continued the eugenics and statistics work started by Galton with a particular focus on heredity. In the discipline of statistics he contributed methods of comparing populations by tests of relationships and by ranking qualities. Methods developed by both Galton and Pearson are standard throughout biosciences, psychology and social science today.

Both of them, despite their rejection of Quaker faith, seem to have enjoyed claiming Quaker heritage. For example, a letter from Galton to Pearson includes a reference to how Basque orderliness tugs at ‘every Quaker fibre in my heart’⁵⁶. Pearson’s obituary for Galton states:

Not only did the Society of Friends [Quakers] unite men religiously, but it produced special temperaments genetically. Even to this day it is strange how men whose families have ceased to be Quakers, yet find that their common sympathies and temperaments arise from Quaker descent. Galton owed the evenness of his temper, his placid acceptance of criticism, but his power of steady persistence in his own work and his own views, very largely to his Quaker ancestry, to the Galton and Barclay blood⁵⁷.

In 1907 LFR sold his physics books to raise money to study with Pearson in Cambridge and applied to stay there to further explore heredity but was unsuccessful in getting a position (as reported above). In 1913 he published a paper in Eugenics Review suggesting the potential for studies of the development of adopted children to contribute to the nature versus nurture debate⁵⁸. Among his own siblings it is hard to separate how influences in the family, their social circle and schools might have interacted with any inborn tendencies. His assumptions about nurture, like Galton’s about nature, were heavily weighted towards middle class, well-resourced and educated family contexts⁵⁹.

For eugenicists it was a short step from a Darwinian idea of evolutionary ‘survival of the fittest’ to initiating investigations into the effects of ‘breeding’ between ‘inferior stock’ and ‘better stock’. In Galton’s paper about restricting marriage he says:

Eugenics deal with … the heritage of a high character, capable brains, fine physique, and vigour; in short, with all that is most desirable for a family to possess as a birthright. It aims at the evolution and preservation of high races of men, and it as well deserves to be strictly enforced as a religious duty⁶⁰.

The implications for a range of social issues were of interest to many among the intellectual left of British politics, such as George Bernard Shaw, John Maynard Keynes, Bertrand Russell. A focus on nurture can support a need for social action for relief of poverty, improved education, nutrition, housing and health care, and many other strands of work that could impact upon the lives and longevity of the whole population. But during LFR’s membership there was also extensive discussion about how to prevent ‘deficient’ people from reproducing, since poverty, alcoholism, mental illness, and reluctance to work were assumed to be hereditary. Eugenics supported studies and campaigns in birth control, sterilisation, artificial insemination and other ideas that pointed towards limiting ‘breeding’ to those were deemed to be ‘fit’⁶¹. There was a well-intentioned strand of work about care for those who are ‘feeble-minded’, but this also included preventing procreation, sometimes on dubious grounds such as measuring physical characteristics. Pearson was particularly vocal about limiting ‘breeding’ and was also openly antisemitic, supporting this with tests of the mental powers of various races ⁶².

LFR had these ideas, and perhaps felt comfortable with them, because of the Quaker heritage of Galton and Pearson and also because of his stated commitment to mathematics as a tool for understanding the world. His own studies about war were beginning to suggest intermarriage (along with common languages such as Esperanto, common religion and contiguity of borders) might have a pacifying effect on relationships between nationalities. He wondered if children from two mixed races would carry with them the harmful remains of hostility and hatred, or have a calming effect and the end of hostility. Many eugenic papers involved comparing races and their mixed-race offspring. LFR was interested in people’s attempts to measure Galton’s notion of ’inherited general ability’ and accepted Pearson’s suggestion that there is a limit to what can be achieved by nurture given innate nature.

The tests used in such studies were supposed to test general cognitive capacity. In many studies the intelligence quotients (IQs) of mixed-race children tended to be averages of the average IQs of the parent races⁶³. Measures of general intelligence favoured disembodied logical responses to visual or verbal images on paper as the indicator of educability; hence they downplayed creativity, practical and social aspects of life. It is now known that such tests tend to reflect what the test-developers understood to be culturally valuable qualities, mirroring their own cultural and educational backgrounds and usually being linguistically biased⁶⁴. LFR used the results from such tests, like those of his colleague, Russell Munday⁶⁵, to support intermarriage between races that had similar IQs. In doing so he accepted studies that suggested mixing IQs from different races might reduce ‘fitness’ of the ‘stock’ but hoped to ameliorate concern about intermarriage as a useful pacifying influence, by publishing his war studies in Eugenics Review⁶⁶. Munday’s study of intermarriage between European colonials in Buenos Aires (which had been undertaken at LFR’s suggestion) led to LFR’s belief that the travelling ’managerial classes’, whom he assumed would have similar IQs, could be encouraged to intermarry to improve prospects for peace. He went further, saying that it should be those whose intelligence is ‘superior to the averages of their countries’ who could be so encouraged⁶⁷. In other words, only selective intermarrying was likely to be pacific as it would retain overall ‘fitness’. In so doing and standing too close to the eugenics that fuelled Naziism, LFR had made two fundamental scientific errors and a possible error of faith.

The first scientific error is to assume that the distinctions that are used to design tests of innate intelligence are free from cultural bias, but among people doing similar work they were the standard tests of ‘fitness’ and were used uncritically. The second scientific error is to assume that a correlation between races and IQ test results is the same as causation, the kind of error that he had determinedly not made in his war or weather studies. Such an assumption ignores the effects of different, or similar, national norms of nurture and culture.

That LFR accepted the idea that ‘superiority’ and ‘inferiority’ could be defined and measured seems to be an error of a faith that all humans are fundamentally equal, as Quaker historic testimony would offer. In 1922, London Yearly Meeting reminded Quakers that ‘God hath given to everyone a measure of grace’⁶⁸ and that George Fox, one of the founders of the faith, urged answering ‘that of God in everyone’⁶⁹. Quaker guidance during the period of LFR’s eugenic interests was emphatic about equality of all, and as an active Quaker in Yearly Meeting he would have heard relevant words. For example, the Epistle of Yearly Meeting 1918 states that the ‘Fatherhood of God … knows no restrictions of race, sex or social class’⁷⁰.

We know why he chose Eugenics Review to publish an overview of his theories about war because he says: ‘The Eugenics Society is notable for having had the intellectual courage to attend to emotionally embarrassing problems. I shall rely on that courage here. My results are offered as Truth’⁷¹. Yet his ‘Truth’ appears to include the possibility that humans can distinguish between superior and inferior people by using statistical reasoning.

While Rapoport has shown how LFR’s fundamental devotion to peace had shaped the design of his war research ⁷²; in eugenics research the fundamental ideas of human superiority shape the work. Galton and his followers had founded a tradition of measuring a subset of the capabilities of the mind, assuming that would indicate the whole of an individual’s educability and worth to society. Those who found differences between races or social classes tended to think about the group characteristics as the cause of the difference in the test outcome rather than a correlation that needed to be understood in terms of the people and the test itself. Above there are examples of how Galton and Pearson appear to have used Quaker heritage to explain some of their observed positive characteristics about each other, and perhaps LFR was also of this mind. But Quaker heritage is not the same as Quaker faith.

Despite the EES being committed to seeing innate differences of worth between people, LFR remained an involved member of it. He persuaded Carlos Blacker, the General Secretary of EES and proponent of controlling reproduction, to support a request to a publisher for his work in war and peace because it contained the finding that intermarriage could be pacifying. The tone of Blacker’s replies suggested mutual respect, and he did make repeated efforts on LFR’s behalf⁷³.

From a modern perspective it is surprising that LFR took the arguments of the EES and these interracial test findings seriously from a scientific point of view, let alone a moral view, and it is even more surprising that he was still using that idea after World War 2 when the extremes of eugenics had been displayed. Quakers such as Lionel Penrose, Lancelot Hogben⁷⁴ and George Newman had been dismantling eugenic beliefs and particularly the desire to interfere with population control⁷⁵. It may, of course, be true that intermarriage is a pacifying influence on the causes of wars, but the underlying reasons for that might be better found in Quaker beliefs in spiritual equality than in statistical measurement of characteristics assumed to indicate superiority. It is noticeable that LFR was using the idea of controlling human characteristics by the ‘nature’ argument of managing breeding while other eugenicists, including many Quakers, were already rejecting this and making the ’nurture’ argument for welfare⁷⁶. Historically, a continuous line can be drawn joining eugenic concerns about the overall quality of a population and universal health care, sanitation, universal education, good housing, and other social reforms. We also have hindsight about the dangers of eugenics to help us question why eugenics arguments about engineering superior populations through birth continued to attract not only some British Quakers but also some in the US⁷⁷.

The influence of LFR’s work

Lewis Fry Richardson’s analytical approach to the history of wars and other deadly quarrels remains foundational. Some of the causes and pacifying influences that LFR found may seem obvious to us with hindsight, with more general knowledge of psychology and the behaviour and attitudes of population, and with more than century of the use of mathematical modelling in the social sciences. The existence of statistically-analysed evidence to back up, or challenge, general knowledge, ideological theory and opinion was what LFR tried to provide and, arguably, did so.

Lewis Fry Richardson’s vast posthumous influence also includes:

• results and techniques in meteorology and weather forecasting that are sound, and lasting, and recognised both within and beyond his lifetime and still used;

• measurement of human reactions to sound, contributing to acoustic science;

• measurement of borders and coastlines contributing to the pure mathematics of fractals;

• a method of efficient solution of some differential equations that is still used;

• examples of the use of mathematical modelling in social science;

• attention to correlation of factual information, including social and cultural information, that was innovative and augmented war and peace studies that were beginning elsewhere.

All of these threads are today enhanced by computing power.

The situations he chose to focus on were about understanding aspects of peace, climate, psychology and improving life in various ways. Throughout their history, members of the Society of Friends have been known for their opposition to war and their belief that all people have equal value, all having the capacity to have a direct relationship with God. LFR would have been aware of these beliefs throughout his childhood and also aware of the typical Quaker commitment to standing up for truth. Alongside this, his involvement in the eugenics movement can be difficult to understand, especially given his reputation for kindness in his social, academic and family life, including nurturing adopted children. Seen through the lenses of the science of the time, and the ubiquitous influence of eugenic thinking among the statistical thinkers and the social reformers of the time perhaps it is more understandable. It does not, in my view, invalidate those contributions to science which carry strong moral commitments to pacifism, usefulness and service. It is a reminder of the need for care about judgements whose outcomes label and separate people in ways that exacerbate inequality of esteem. Finally, Dorothy Richardson provided the following quotation from LFR, in a letter in The Friend⁷⁸ that puts his work into the perspective of his whole life: ‘Our job in life is to make things better and easier for those who come after us here’ and, from his own notes a few months before he died: ‘A persistent influence in my life has been that of the Society of Friends (Quakers) with its solemn emphasis on private and public duty’⁷⁹.