Lewis Fry Richardson - Writings On Quantitative Studies Of Conflict

Lewis Fry Richardson - Quantitaive Psychology and studies of conflict
  • Collected Papers (vol 2; 2009). Those in red are the longest or otherwise seem most important to me. This is a 750+-page volume. It has no index. Not all Richardson's writings are included in the 2 volume set; however their dates and titles are listed. Statistics of Deadly Quarrels (1960; ed. Quincy Wright & C C Lienau) is one of these.   –Rae West. My website
  • Some internet review notes below by Brian Hayes.
  • A note on La Griffe du Lion who writes online in the style of L. F. Richardson. (Added 3rd July 2016)

The Collected Papers of volume 2. (Excluding volume 1 on meteorology and numerical analysis)

    1913:1 The measurement of mental 'nature' and the study of adopted children. Eugenics Review. 4, 391-4     49
    1918 International voting power. War & Peace 4, 193-6     55
    1919:1 Mathematical Psychology of War. Oxford: W. Hunt     61
    1926:2 Power in the League of Nations. The World Outlook no. 29, 38 (also The Friend NS66, 384).     101
    1928:3 Thresholds when sensation is regarded as quantitative. British Journal of Psychology. 19, 158-66     105
    1929:3 Imagery, conation and cerebral conductance. Journal of general Psychology. 2, 324-52     117
    1929:4 Quantitative mental estimates of light and colour. British Journal of Psychology. 20, 27-37     149
    1930:2 (with J. S. Ross) Loudness and telephone current. Journal of general Psychology. 3, 288-306     163
    1930:3 (with R. S. Maxwell) The quantitative mental estimation of hue, brightness or saturation. British Journal of Psychology. 20, 365-7     185
    1930:4 The analogy between mental images and sparks. Psychol. Rev. 37, 214-27; 364     191
    1932:2 Determinism. Nature, Land. 129, 316     207
    1932:4 The measurability of sensations of hue, brightness or saturation. Report of a joint discussion on vision held on June 3rd 1932 at the Imperial College of Science by the Physical and Optical Societies, pp. 112-14; 116. London: The Physical Society     211
    1933:4 A quantitative view of pain. British Journal of Psychology. 23, 401-3     217
    1933:5 The measurement of visual sensations. Proc. Phys. Soc. Lond. 45, 585-8     223
    1935:2 Mathematical psychology of war. Nature, London. 135, 830-1     229
    1935:3 Mathematical psychology of war. Nature, London. 136, 1025     233
    1937:1 Hints from physics and meteorology as to mental periodicities. British Journal of Psychology. 28, 212-15     237
    1938:2 Generalised foreign politics. Report of the British Association for the Advancement of Science, 488-9     243
    1938:3 The arms race of 1909-13. Nature, London. 142, 792-3     247
    1939:1 Generalized Foreign Politics. British Journal of Psychology. monograph Suppl. no. 23, 91 pp.     251
    1941:1 Frequency of occurrence of wars and other fatal quarrels. Nature, London. 148, 598     351
    1941:2 Mathematical theory of population movement. Nature, London. 148, 784     355
    1944:1 Stability after the war. Nature, London. 154, 240     359
    1944:2 The distribution of wars in time. Jl R. statist. Soc. 107, 242-50     363
    1945 Distribution of wars in time. Nature, London. 155, 610     375
    1946:1 The number of nations on each side of a war. Jl. R. statist. Soc. 109, 130-56     379
    1946:2 Chaos, international and inter-molecular. Nature, London. 158, 135     409
    1947:1 Social science in the gap between the Royal Society and the British Academy. Nature, London. 159, 269     413
    1947:2 Arms and Insecurity. (Notes on the book, which is not reproduced here.)     417
    1948:2 War-moods: I. Psychometrika 13, 147-74. II. Psychometrika 13, 197-232     423
    1948:4 Variation of the frequency of fatal quarrels with magnitude. J. Am. statist. Ass. 43, 523-46     489
    1949:4 The persistence of national hatred and the changeability of its objects. British Journal of Medical Psychology. 22, 166-8     515
    1950:2 War and eugenics. Eugenics Review. 42, 25-36     521
    1950:4 Statistics of Deadly Quarrels. (Notes on the book, which is not reproduced here.)     535
    1950:5 Psychological Factors of Peace and War (ed. T. H. Pear). Chapter X Threats and security and Chapter XI Statistics of fatal quarrels. London: Hutchinson     541
    1951:2 The problem of contiguity; an appendix to Statistics of Deadly Quarrels. General Systems Yearbook 6 (1961), 140-87     577
    1951:3 Hints concerning international organization. Unpublished MS     629
    1951:4 Could an arms-race end without fighting? Nature, London. 168, 567-8     645
    1951:5 Could an arms-race end without fighting? Nature, London. 168, 920     651
    1952:1 Is it possible to prove any general statements about historical fact? Br. J. Sociol. 3, 77-84     655
    1952:2 Contiguity and deadly quarrels. Journal of the Royal statistical Society A 115, 219-31     665
    1952:4 Dr S. J. F. Philpott's wave-theory. British Journal of Psychology. 43, 169-76, 192-4     681
    1953:1 Voting in an international organization. Unpublished MS     695
    1953:2 The submissiveness of nations. Br. J. statist. Psychol. 6, 77-90     715
    1953:3 Three arms-races and two disarmaments. Sankhya 12, 205-28     731
[These notes mostly made 1992, before Internet. The 'Fry' and Quaker link suggest Richardson was related to the Fry chocolate manufacturers]
    Some of the following is from 'Prophet or Professor?' (1985) by Oliver M Ashford.
    'Nullum quod tetigit non ornavit' Samuel Johnson, of Oliver Goldsmith: 'He touched nothing that he did not adorn'.

Note to the Reader: Differential Equations
The greatest mathematical discovery since geometry and arithmetic and number notation was made, apparently independently, by Newton and Leibniz, and other contributors to their worldviews. For the first time, a technique was able to trap changes. Unfortunately, their technique is algebraic, as it has to be to allow for one word, statement, or concept to cover many instances. This gives it a forbidding appearance, easily enough to deter many people from investigating it, and simultaneously allowing its users to be, or pose as, carriers of expertise.
    The very simplest formula of this sort is (keeping things only in English) the change stays the same, is constant. Something may grow at a fixed rate, travel at some fixed speed, or whatever. Stresses in metals vary more or less with loads (unless they break). Another such formula, or relationship. is simple acceleration, the only everyday example I can think of; and historically the earliest, where some object falling freely increases in speed with time. This leads to ellipses and parabolas—or perhaps someone can rename them more meaningfully. Now, there are only a small number of easily solved formulas of this type; about eight, I think. They can all be listed on a single sheet of paper. They model things like insulin levels in blood quite well. The fun begins with greater complications. Anyone who can clarify the simpler examples would be doing general education a huge favour.
    Richardson started his career with mathematics of this sort, so-called finite difference analysis, and did his best to apply it to weather forecasting, and other hard-to-trap examples in physics: wind, smoke, water currents. His move to studying war was triggered by 1914, and, later, again by 1939. His books and papers written on war and peace are listed, above, in red; I've left some black, where they seem to have been followed by much longer treatments.

1952 quotation: Richardson's reading: he alternated books on history with statistics. (p. 657)
'Is it Possible to Prove any General Statements about Historical Fact?'
During the past 11 years it has been my habit read alternately books on history and books on statistical method. The contrast between these two disciplines has provoked the following remarks. [.. Richardson mentions a 1948 radio discussion between Pieter Geyl and A J Toynbee]
Examples of generalizations concerning historical fact will be taken chiefly from four works: Pitrim [sic] Sorokin's Social and Cultural Dynamics [back to ancient Rome]; Quincy Wright's A Study of War [back to 1480]; my own ... Statistics of Deadly Quarrels [back to 1820]; and A J Toynbee's A Study of History, as abridged by D C Somervell. [back to 4000 BC] ..
    .. by "statistical methods" he means ... such books as Yule and Kendall's An Introduction to the Theory of Statistics, R A Fisher's Statistical Methods for Research Workers, Harold Jeffreys' Theory of Probability, and M G Kendall's Advanced Theory of Statistics.

Richardson's conclusion after looking at random sampling by tables, the Poisson distribution (of the number of wars ending between 1919 and 1945, and chi-squared analysis, is that history undergraduates should 'acquire a few simple notions about historical method'.

Richardson discusses the classification of wars, which is not as simple as it might appear. Wars can run into each other, for example. Quincy Wright on the American Civil War of 1861-6 'is stated to have involved only one participant, because the Confederate South had no legal status either before or after the fighting.' Sorokin and Richardson classified wars (and insurrections, disturbances etc) by the numbers of deaths, though of course these may not be easy to estimate. Poisson distribution of no of wars starting in any year. probability of war 'breaking out' constant at any time. ie small but non zero

Compiling Statistics of Wars and Conflicts
Richardson has three letters or articles on 'Distribution of Wars in Time': 1941 (letter in Nature), 1944 (Statistical Society Journal), 1945 (letter in Nature). These deal almost entirely in the Poisson distribution applied to recently-compiled figures for wars. This is suggestive stuff, but is weakened by doubts: for example, Britain literally never had a war-free time, suggesting that war may be permanent, but redirected as circumstances change. Another doubt: if events are arranged by magnitude, that very process forces the results to take some long-tailed shape, so that maybe the process is easily explained in other ways.

List of 'Wars of Modern Civilization, 1480-1940 AD' by Quincy Wright, published 1942, his methodology being the use of his card index, is summarised in short appendices on pages 371-373. This is what Richardson wrote (p 365):–

Quincy Wright ... states that his list "is intended to include all hostilities involving members of the family of nations, [sic] whether international, civil, colonial or imperial, which were recognised as states of war in the legal sense or which involved over 50,000 troops. Some other incidents are included in which hostilities of considerable but lesser magnitude, not recognised at the time as legal states of war led to important legal results, such as the creation or extinction of states, territorial transfers, or changes of government."
    As a preliminary ... a decision had to be made concerning four of the large ones, namely the Thirty Years war, the French Revolution, the Napoleonic Wars and the First World War, because Wright listed them both as wholes and as parts. In order to make the wars less unequal in size, I included all the parts and eliminated the wholes, except two wholes which are shown as beginning before any of their main parts. The First World War is thus reckoned as five wars.
    Each calendar year can be characterized by the number 0, 1, 2, 3, 4 wars which begin in it, as shown in appendix 1. .. the number of years of each character .. counted by M W, E D R, and L F R) fitted a Poisson distribution to it. .. gives mean number per year of 299/432. There is considerable agreement. ..


[Fry also does a chi-squared test on it, and also tests whether it deviates significantly in the direction of the negative binomial distribution.] .. also relation between G and Q^2 introduced by Lexis and variously interpreted by successors like Keynes in 1921, Ch 32... [His conclusion seems to be:] that if the observation is incredible for a sample n from a Poisson population, then the rule ought to be rejected, but conversely if it is credible all we can say is that so far there is no objection to that law, though a more searching test might still reject it.

Wright picked 432 years from 1500 to 1931.. because it has a lot of factors. (Page 367) And Richardson said Wright's list: indicates the absence of any steady drift towards war or fewer wars; in other words, the number of them is roughly speaking the same. [Of course, the seriousness can go up. He concludes there are not more wars by dividing the data up into two cells of 216 years each, getting 143 in the first one and 156 in the second, 1716-1931. He uses many other tests; e.g. a 'Buys-Ballot table' quoted by Kendall in 1945. Richardson discusses classification of events by deaths; which he says is defined more objectively; what one person might call a war, another might call a mutiny or even an incident. The great obstacle to any scientific study of causes is contradictory evidence from opposing sides. Wright's definition of wars involves the notion of its 'legality' and 'political importance' which are always matters of opinion and can be permanently controversial. By contrast, the number of persons who died because of a quarrel, though often deliberately misstated, is almost in all cases ascertainable by ten years after the end, within a factor of three times more or less, which is small in comparison with the whole range. War dead were taken to include all those on both sides whether armed or civilians who were killed fighting or drowned by enemy action, or who died of wounds or from poison gas or from starvation or siege or other malicious acts of their enemies. Moreover, deaths from disease or exposure of armed personnel during a campaign are included, but not civilian deaths by epidemic diseases in places far distant from the geographical location of the fighting. .. Wright almost completed a card index of fatal quarrels classified according to the number of war dead were of the order of 10^7, 6, 5, or 4. The last group, which is the most numerous, concerns us now. Its precise range is intended to be from 10^3.5 to 10^4.5 of war dead. In popular language it consists of small wars, revolts, insurrections, and incidents in any part of the world, regardless of their legality. ..

[Appendix 2, his own figures from 1820 - 1930, had dates of beginning and also of endings of wars, corrected in red ink in his own wobbly handwriting, initialled LFR. Quincy Wright's list starts at 1482. Summary: from x = 0 to x>7, frequencies 18, 39, 37, 29, 12, 5, 2, 2, 0, adds up to 144 separate sets, which are of 3-year intervals, in which for example 18 sets of 3 years had no wars starting, 39 had 1, and so on. Figures with separate years go from 0 to >4, with 223 with 0, 142 with 1, 48, 15, 4, and 0 more than 4. Also of course they could be anywhere in the world.]

Note on the above material
    Richardson certainly seems to have been doing his best to make the real world conform to his mathematical ideals—a natural peril facing any system of ideas. And his results mostly apply to technically advanced societies: there's nothing on the lines of Harry Turney-High in Primitive Warfare. Richardson has another problem, which is how abstract to make his analyses: should his approach include all conflicts in all societies? A general theory would be terrific, but may be simply too complicated, and also regarded as largely irrelevant by decision-makers. Another problem is dangerous armaments: if one bomb can kill 100 million people, would that situation count as 'war'? Richardson assumes wars are between nations; there's simply no other analysis for him. And yet it is possible, as the Jewish evidence shows, for nations to include opposing internal forces. In fact it's possible that wars may have no other purpose than make money, or kill off other societies.

Richardson on mathematics: To have to translate one's verbal statements into mathematical formulae compels one to carefully to scrutinise the ideas expressed therein. Next, the possession of formulae makes it easier to deduce the consequences. In this way, absurd implications which might have passed unnoticed in a verbal statement are brought clearly into view and stimulate one to amend the formula. An additional advantage of a mathematical mode of expression is its brevity, which greatly diminishes the labour of memorising the idea expressed. If the statement of an individual become the subject of a controversy, this definiteness and brevity will lead to a speeding up of discussions over disputable points, so that obscurities can be cleared away, errors refuted, and truth found and expressed more quickly than could have been done had a more cumbrous method of discussion been pursued. Mathematical expressions, however, have their special tendencies to pervert thought. The definiteness may be spurious, existing in the equations but not in the phenomena to be described. And the brevity may be due to the omission of the more important things, simply because they cannot be mathematised. Against these faults we must constantly be on our guard. ... Mathematics has been used in this book both inductively, to summarise facts, and deductively, to trace the consequences of hypotheses. By mistaking the intention, it is possible to complain that the inductions do not follow from the previous hypotheses, and that the deductions go beyond the known facts. Certainly that is so, but it is no cause for complaint, rather for rejoicing. Those who say 'you can prove anything by statistics' should instead say 'unfortunately, we do not understand statistical methods sufficiently well to enable us to distinguish arguments that are genuine from those that are false.' To anyone who believes that words are the proper medium of expression, I recommend the following exercise: translate into word ax^2 + bx + c = 0, remembering that x, a, b, and c are not words; proceed in words, not using any algebraic symbols, to find and prove the solution of the equation.

Richardson gives an example of mathematics in effect making a suggestion: if preparations for war are discussed, why not negative preparations for war, which might point out ways to peace. Richardson is very much the technology employee type: his unit 'warfinpersal' the war-finance per salary, applies to groups of technical employees making bombs, planes, etc. Richardson discusses 'war moods' and clearly takes these from the media: newspapers rather than radio. He is entirely unaware that forces behind the scenes may control propaganda, and prepare for war over many years. And they may change in mid-stream: the propaganda in the USA after the Balfour Agreement is well-known. Richardson's explanation for swings in war moods was that the subconscious and conscious moods came to differ.

Richardson makes two principal uses of economic data: the first is an attempt to get a significant measure of the amount of resources devoted to warlike preparations in an arms race or a disarmament process; this brings him up against the ancient problem of a measure of value, and the comparability of different measures. His solution, the ? of WarFinPerSal, a hideous word which he subsequently seems to have abandoned in favour of warlike wartime. This is the money value of arms expenditure divided by some average wage which gives the average labour value of arms expenditure. The use of labour as a measure by him has a long history stretching from Adam Smith to Keynes. It has defects which Richardson recognised, defects both theoretical and statistical. It is likely to be misleading where there are wide disparities in the productivity of labour. Wage statistics are also notoriously unreliable. Today, with our improved national income statistics, we could use a much better deflator, so the problem of how best to deflate a value total ? production or get a real measure still plagues the statisticians. Richardson's use can however be justified as a useful approximation, probably the best available at the period. It may result in an overestimate of bellicosity in countries like Russia, with low productivity, and underestimate countries like Britain with high productivity. The error is however not likely to be greater than other errors in the model.
    The second use of economic data is more dubious. This is the use of international trade data as a measure of co-operation among nations, and therefore as an offset to arms expenditure in measuring bellicosity. The basic difficulty is that trade is not really a reaction process.. like an arms race.. The total volume of trade especially in the direction of comparative advantage in the international division of labour rather than power and bellicosity relationships. In particular, the short-run fluctuations in international trade are much more a reflection of the international propagation of the business cycle than they are of international relations proper. As Richardson noted in relation to the brief depression of 1908 and the depressions of 1920 and the early 1930s, .. working for Richardson the processes of international economic relations were more likely to find trade restrictions, for instance retaliatory tariffs or quotas. It is hard to get any satisfactory measure of trade restrictions. ...
    In the US, on the whole, the Democrats have been a low-tariff, high armaments party, whereas the Republicans have been a high-tariff, low armaments party. There is a fascinating future field of study here. Richardson's contribution however is to the very early pioneering. Its value consists in what it points toward rather than the actual results.

More Mathematics of Richardson
• 1. As we've seen, first, statistics in the sense of compiling tables, totting up single wars, tabulating them to see if one period is more 'warlike' than another; in other words, significance tests using various hypotheses.
• 2. Another type: draw graphs of expenditure over a number of years and draw lines through, take log scales etc.
• 3, Another: use of differential equations, where he has one country as expressed as a function of itself and other countries and constants. Simultaneous differential equations which can then be solved. His last paper, published in 1953, on Arms Races illustrates this (and other) techniques, deriving interesting diagrams reminiscent of 'cobweb' and other economics diagrams.
• 4. Matrices; Richardson has tables of countries, along top and down the side, and puts 'hostility' of one against the other in each section, and the obverse down the other way. So typically they may more-or-less match, but they aren't necessarily the same. So for example: total for Russia with the greatest amount which shows that Russia was the most hated country; and a total across showing that Germany was the most hating country, and draws conclusions on that basis.
• 5. Geometry, with simplified diagrams of countries. His long 1952 paper on contiguity tries to examine wars between neighbouring countries.


    All these things have severe problems.. more a kind of obsessive thing than anything very useful? Impression is he was a Quaker, a pacifist; very careful to ignore things like raw materials and imperialism; he was basically a privileged person. All this work is a rationalisation or pseudo-science which gets almost nowhere; not unlike ordinary economics. It's significant he also did work in weather forecasting, using numerical approximations, and was involved in fractals, Mandelbrot sets etc; for example, in measuring the coastline, he noticed as a fact, without going any further, that the total length appears to vary with the size of the unit taken; for example, the border between Portugal and Spain is reported differently by the Portuguese and Spanish. .. Same thing with other features: Note in passing: imports from a country are taken as the important thing, because you can't always tell where exports go to. For example, he quotes figures of exports from say Germany to France, and imports from Germany into France, and the figures quoted by the two countries are 'quite widely different'.


Richardson's Life (1881-1953) .. Born 11 Oct 1881 at The Gables, Newcastle-upon-Tyne. Came from a Quaker family. .. they had prayers and Bible-reading every day at mealtimes.. regular attendance at meeting for worship on Sundays. .. Began life as a vigorous infant with keen senses, tasking notice very early. Died i 1953. Rapoport liked him. Professor Boulding: 'Lewis Richardson's work in politico-metrics if I may coin a word for it has all the marks of what may be called without any sense of disparagement amateur genius. He is a man inspired by a vision of orderly relations in a field where disorder is usually regarded as supreme. Not content with a vision only, he seeks to bend what empirical data he can lay his hands on into a quantitative verification of the relations which he postulates. He does with dash and courage, but naturally, in view of the grave deficiencies of the data, with only limited success. The important thing however is that it should have been tried. Future generations will be able to run where he stumbled.
        [Amusing article from 1913 when Richardson was a lecturer:] 'This day I was tired and overstrained; the air was cold and raw, and several students sneezed; then more sneezed. Then ?Clair sneezed ostentatiously. Now the distinction between a natural and a forced sneeze is rather a difficult one. Indeed, it is questionable if many people can force a sneeze; I think they must have taken snuff. So if only I had been sensible I should have smiled and said nothing; people get tired of sneezing. But like a fool I said Clair, if you do it on purpose you'll have to go out. The class, realizing that they could plead they couldn't help it, sneezed the more vigorously. I got on with my lecture punctuated by sneezes for about three quarters of an hour. Then ?MacKorrer, who was just in front, sneezed as loud as possible. I told him to go out. This was unjust, for Duguid, Leonido, Watts, etc had all been as bad. He said, I won't go out, I can't help it. In a moment of madness I seized him and began dragging him towards the door. He hung on to my desk, dragging it off the raised step with a loud bang. ... Looking at the class, I said I think I ought to apologise to Mr ?MacKorrer.. a lecturer ought not to do that. Kilmer said, Oh it doesn't matter. The rest sat quiet. ?MacKorrer complained I didn't do it on purpose. I can't sneeze on purpose if I try. .. I made two serious mistakes. The first to say anything about sneezing. It is remarkable that I am never troubled with stamping or humming now, although students usually employ these methods for annoying a lecturer. .. Also eating in class has gone out of fashion. I never said anything about that...'

        [Cartoons he designed: Visit to 'Moonbeam Lamp Company' about 1912: Four little sketches, made at Sunbeam Lamp Co: 'above photo was of lamp testing (mechanical tests dept) the M L Co believes in combining pleasure with duty. The vacuum in their lamps is so strong that should one burst the explosion is most violent. The batsman wears mail armour. The officer, 4, is employed to remove any which fail. Paste department: throwing a spider on the paste: if the spider dies, the paste is good. This process was patented by the company's cashier. Drawing tungsten wire: the wire itself is too fine to be seen; (joke of people tugging way, anvil, and so on). Manager's Office M L Co: circular diagram with what appears to be a desk right in the centre, things all round it; rather childish humour.]

    [Self-portrait:] 'Another temperamental peculiarity had a great influence on my career. Any individual, if left solitary, may or may not experience a distressing emotion called loneliness. I hardly know what loneliness feels like. When I am solitary I am usually serene. When in a crowd I am often embarrassed. As a child I played much alone. Four of my six brothers and sisters showed tendencies to solitary lives. ...

    For example, I met Rutherford at Manchester in 1912-13 at a time when many other young research workers seemed to be saying, Here is a great man. How I admire him! Let me try to ingratiate myself with him, Learn from him, move in his orbit, to shine with the reflection of his glory. On the contrary, I thought here is a powerful man. He is a wonderfully interesting psychological exhibit. But he despises me. His researches are doubtless important, but there is not the least risk of their being neglected. Moreover I do not share his enthusiasms. How could I attend to my inner programmes in the neighbourhood of anyone so domineering? Let me go where there are fewer people buzzing around.

    [During World War 1:] 'As early as October 1914 he applied for leave from the meteorological office to join the red cross unit of the ambulance corps but the permission was declined. He handed in his resignation on May 16th. As a married man he was not yet subject to conscription, and was able to join the F A U, and to continue in its service without ever having to face a military tribunal. Attached as a driver to the motor ambulance convoy he went to the 14th French Army, the Section Sanitaire, with the ?anglaises from the SSA 13, worked alongside the regular French military section sanitaire. Each section of 56 men, mainly drivers for a fleet of 22 ambulances. ... Apparently he was a bad driver.. He judged drivers by the work they brought in, particularly broken springs through careless driving into shell-holes. LFR was not one of these. When the French Army Medical Service Poste de Secours, [that's aid posts].. they were passed further back into a poste de triage [sorting post].. then to an Hôpital d'evacuation. ..

    [World War 1: Descriptions by Robert ?Sharnley and Laurence Binyon; Herbert Morell; George Hutchinson; Olaf Stapledon.] Richardson wrote his 10-page manuscript in March 1915, 'The condition of ?a lasting peace in Europe'. Also wrote 'The Mathematical Psychology of War' in 1919. Most influenced, I think, by Russell. ... Richardson's sense of humour: to the tune of Three Blind Mice: 'I want to go home/ I want to go home/ No more bloody war/ No more bloody war/ I've stood two years of this blasted strife/ I'm tired of going in fear of my life/ I want to go home to my children and wife/ I want to go home.' Robert Graves recalls two defeatist ditties in 'Goodbye to All That.' Russell's 'War, the Offspring of Fear', 1914, Union of Democratic Control, was quite likely the start of his work.

    Russell said: 'I have read the manuscript you sent me of Mr Richardson on the mathematical psychology of war. I had seen at an earlier stage the same MS. It is much improved on what it was then. With regard to publication, my opinion would depend on whether Richardson has time and opportunity for further work on the subject in the near future. If he has, I should say that he ought to make his work fuller, insert more illustrations, and eliminate dogmatic statements of his metaphysical opinions where they are irrelevant. ... I consider it highly desirable in the interest of science that it should be published, although I hardly think the sale would be large. All Mr Richardson's main ideas appear to be true, original and important. His mathematical formulae greatly help to clarify one's ideas and he himself is careful to point out that they give only approximations, the exact truth being probably too complicated for such a mode of compression. He has done a remarkable piece of work which deserves great respect.'

    [Letter to Quincy Wright dated Sept 27 1953 from Hillside House, ?Killmun, Dunoon, Argyle, Britain:] 'Dear Prof Quincy Wright, I have just read your chapter on Freedom and Authority in 'International Organization', 1953. You do well to point out that the individual, the state, and the United Nations cannot all have complete freedom and authority. There is nowadays such a lot of vague nonsense talked about freedom. Last year I tried to pay œ80 to my son Stephen in the USA, but found that such a transaction was contrary to the regulations of 'the free world'. I am very sad to see that you, with your great reputation in international relations, still cling to the 19th C notion about a balance of power, namely that there can only be one balance, and that it is necessarily stable. Kenneth W Thompson is no better. Whereas in a recent paper on Three Arms Races and Two Disarmaments, in which I sent you an offprint, to show that there usually have been two independent balances of power, either of which, or both simultaneously, may be stable or unstable. A vivid illustration is that of a ship, perfectly stable for pitching fore and aft, but unstable for rolling. In the same paper I bring together some rather inadequate evidence which suggests that the equilibrium of x + y which was stable in the 19th C has since become unstable. If I publish anything more about this, which I am reluctant to do, being very old, and tired, it will be my unpleasant duty to attack you for trying to slur over in words distinctions which need mathematical symbols. I regret this because our hopes are really much alike. Yours sincerely, Lewis F Richardson

    [Quotation from the Epilogue:] Richardson mentioned in some ways that his creative temperament was a nuisance, as when driving a car. Perhaps it was also responsible for his apparent difficulty in communicating his ideas to others. Nobody could pretend that his book on weather forecasting or his writings on the causes of war make easy reading. The narrative lacks continuity and the logical connection between one chapter and the next is not always evident. The trouble may have been that he could never allow himself sufficient time to organise the material into a coherent whole. Once he had solved one problem, his thoughts turned immediately to the next.

    140: Staff at Westminster Training College 1928. Cartoons: presumably by him; rather childish. Jock Mr J S ?Russell; Aubrey is Mr A Twyman; Boq is M Boquier; Pop is Dr P C Austin; Shep is Mr R T Sheperd; Dickie is Mr D K Parr; Colonel is Mr H Amon; Crookie is Mr G Cruikshank and so on

    [Appendix, of his published works. A lot is about weather prediction by numerical processes. A few things about foreign policy: Arms and Insecurity, and so on. Mathematical Models in Social and Life Sciences. Pioneers of Peace Research: a Computer Perspective. And that's about the lot of it, really.]

    [Appendix A: Approximate arithmetical solution by finite differences of physical problems involving differential equations in an application to stresses in a masonry dam [1910]/ A Freehand Graphic Way of Determining Streamlines [1908] graphs of streamlines and potentials, which he tried to attach to weaponry/ Detection of distant thunderstorms by clicks in a telephone/ National voting and international assembly 1918/ The supply of energy from and to atmospheric eddies 1920/ Some measurement of atmospheric turbulence 1920/ Demonstration of electromagnetic inductor 1923/ Time-marking on a cathode ray oscilloscope 1933/ A quantitative view of pain 1933/ The distribution of wars in time 1945/ Relaxation Methods [appears to be another word for numerical methods of some sort]/ Some work on psychometrics, eugenics, IQs, that kind of thing popular at the time/ Book quoted: Bias in Judgement, by E Christopher Poulton, which is supposed to be to do with psychological measurements and so on]

    He said of himself "I come from ancestry which the Nazis would call Aryan, and the Communists would call bourgeois, but which I am happy to call English. I am aware of national prejudices and of the manner in which they are usually supports by facts selected, not by random sampling, but by pride and hate. Such bias I would fain avoid."

    [1939:] 'In 1939, when the clouds of war were gathering over Europe, an American journal received for publication a paper from Lewis F Richardson. He urged it be published immediately, because its publication might avert an impending war. The editors not only didn't rush the paper, but rejected it. The story, whether true or not, illustrates Richardson's strong belief that scientific knowledge may prevent disasters to humanity. We think that in this basic belief he was right. But what he forgot is that even if the theory had been considerably more developed and immediately applicable, those individuals who are primarily responsible for decisions which precipitate wars would not have read his paper anyway, and even if they had attempted to read it they could not have understood the mathematics in it.'

    ['Arms and Insecurity': Impressive sources; for example, the League of Nations provided information about arms expenditure and national income, apparently quite useful figures.]

    [Ideals:] 'Ideal A, a world in which there is plenty of variety, excitement, and disorder; ideal B, a world where love, joy, peace, long-suffering, gentleness, goodness, faith, meekness, and temperance prevail everywhere; ideal C, a world in which there are plenty of opportunities for the able and energetic to become millionaires; ideal D, a world in which no-one suffers poverty; ideal E, a world designed to make the next generation better than this one, by selective breeding or otherwise; ideal F, a world where nearly everyone loyally follows a leader while dissident minorities are suppressed; ideal G, a world where friendly co-operation abounds, where competition .. permitted but fighting is forbidden. I go on to discuss the difficulties of attaining only one of them, namely G, the last. Allow me to take as a working model the British House of Commons. It has been said to be the best club in London. To dine occasionally with political opponents is regarded by some members as a duty, yet the House is also the scene of daily strenuous contention. In foreign policy and defence, the opposition have often supported the government. When there are problems, the opposition generally try to modify or delay or frustrate them. ..
    [Note added May 2015: interestingly, Richardson assumes 'universalism'. The Jewish ideal, of a small group ruling through secrecy and with a monopoly of power, wealth and violence, is not considered]

    Friends ask me for practical recommendations. I am reluctant for the following reasons: social science however much it might be developed could never tell us exactly what we ought to do. It could warn us off some actions, suggest others are harmless, but a wide range of free choice would always remain open. Similarly, dynamics does not specify the machines that ought to be made. Moreover dynamics has persisted as enduring truth while machines have been scrapped and replaced by new designs. Social science should persist, and in order that it may do so it should be kept distinct from ephemeral practical policy. However, with caution, what follows is intended to be practical: 1 If you have the affection and the courage which goes to make saints and heroes, try Gandhi's method. 2 If you find it impossible to love your enemies, try as next best to understand them. One good way to get under their skin is to read the novels and plays which they enjoy. 3 Don't object if your relatives wish to marry foreigners. Such bonds may help to hold the world together. 4 Don't ban goods merely because they are foreign. Trade is a mild pacifier. 5 Develop loyalty towards world government. 6 Always remember that some of the defence preparation which your nation might intend to be purely for defence is certain to appear to some other nations as a dangerous threat against which they must make counter-preparations. Nevertheless, some purely defensive preparations do exist, for example air-raid precautions do not alarm unaggressive foreigners. 7 Because research on the science of pacification is now in progress, look out for new and better techniques.

    My wife holds it is wrong to disturb anyone's fundamental beliefs unless one has something better to offer instead. On the contrary, I think that people do not bother to search for, or even attend to new truth, unless they have become somewhat dissatisfied with traditional statements. Domestic controversy was illustrated one day when my wife missed a train by relying upon a timetable which was placarded in the railway station. She complained about it and the station master said he was sorry, he knew the placard was out of date, but he had nothing better to put in its place. The time may come when statesmen will resemble that station master insofar they have personally ceased to believe in the Roman proverb Si vis pacem parabellum yet do not possess any alternative belief that could be offered to their peoples to guide their conduct.

    Chapter 4: Submission and Retaliation: A Collection of Facts:
    1. A threat from his headmaster has usually overawed a schoolboy, especially if the headmaster had school tradition on his side, and the boy saw some streak of justice among the demands.
    2. A threat from one English schoolboy to another of about equal size on the playground has commonly been interpreted as an invitation to a friendly struggle, and has seldom led to a bitter feud unless it was followed by action that was felt to be unfair and extreme, or too often repeated.
    3. The opening of Japan to foreigners is described by Sir Charles N E ?Elliott, apparently in 1929, thus: 'the government of Washington, however, determined not to drop the matter and on July 8 1853 Commodore Perry entered ?Uraka harbour with 4 ships and 560 men. He bore a letter from the President requesting the conclusion of a commercial treaty, but abstained from any attempt to coerce or threaten. He presented his letter, distributed many presents consisting chiefly of mechanical toys and instruments, and after staying ten days sailed away to China, saying that he would return in the spring. The Japanese, who since the days of the Mongol invasion had not seen more than a couple of foreign ships together, were panic-stricken at the appearance of the American squadron. The emperor at Kyoto was solemnly informed of the awful event, and his majesty ordered that prayers for the destruction of the barbarians should be offered at the seven principal shrines. At first the government of ?Yido seems to have thought of resistance. The prohibition against building sea-going ships was removed and feudal chiefs were ordered to build and arm large vessels. The Dutch at ?Deshima were asked to furnish a Man of War and modern military appliances, and the army was prepared for action. But the conviction soon prevailed that effective resistance was impossible. On December 2nd, instructions were issued that if the Americans returned they were to be given a pacific reception. It is noticeable that, although the American commodore abstained from any attempt to coerce or threaten, yet the Japanese felt themselves to be coerced.
    4 According to Lewin [1915], in 1885 a German squadron was sent to Zanzibar in order to show the Sultan the power of the German government. The Sultan, giving way before this visible sign of German power, promised the withdrawal of his troops and acknowledged the protectorate over the territories occupied by the German East Africa Company.
    5 On 3rd May 1906, the British government sent an ultimatum supported by a fleet, in refusal of the Sultan of Turkey's demand that Egyptian troops should be withdrawn from the Sinai peninsula. The Sultan acquiesced. [Grey, 1925]
    6 On 1st July 1911, the government of Germany informed those of Britain, France and Spain that it had sent a warship to Agadir to protect German subjects, proteges, and interests in the south of Morocco. The British foreign minister Sir Edward Grey regarded Agadir as a closed port, and doubted the existence of German subjects in its neighbourhood. Disagreeable negotiations followed, including the counter-threat in Lloyd George's speech of July 21. Eventually, France gave Germany a portion of French Equatorial Africa, and Germany agreed in exchange to allow France a free hand in Morocco. The official British attitude is described by Grey [1925]: Moderate French and German views at the Agadir incident is summarised by M P Renouvin and Herr Hermann Lutz: all three writers agree that the results of the mutual threats were unsatisfactory.
    7 In October 1925 the Greeks invaded Bulgaria. M Briand acting as President of Council of the League of Nations reminded both belligerents of the solemn obligations undertaken by them under article 12 of the covenant, not to resort to war, and of the grave consequences which had been laid down for breaches thereof. The council met, and sent military attach‚s to the scene to press for an armistice. This was achieved within a week of the outbreak. [See 10 Years of World Co-operation, League of Nations, 1930].
    8 Economic sanctions by about 50 nations under the direction of the League of Nations failed to restrain Italy from making war on Abyssinia in 1935-6. In explanation of this failure, it was said by some that economic restraint was too mild, that the supply of fuel oil to Italy should have been cut off, and that Italy should have been threatened with war.
    9 During the Sudeten crisis, in the autumn of 1938, the immediate consequence of severe mutual threats between France and Britain on one side, and Germany and Italy on the other, was a readiness of all four to negotiate at Munich.
    10 But during the next six weeks, the opposite effect appeared, for Britain, France, Italy, Germany, and even the United States, all increased their armaments.
    11 On 1st September 1939 Germany went to war with Poland. On the evening of that day, and again more emphatically on 3rd September, the British and French governments informed the German government that they would make war against Germany unless the German forces were withdrawn from Poland. The response of the German government to this mighty threat seemed almost like inattention [see Henderson, 1940; also French diplomatic documents, and Cmd 6106] In the phraseology of Weber's law, we may say that the threat of war with France and Britain was for Germany on 2nd September 1939 almost below the indifference threshold.
    12 After the defeat of France and the Franco-German armistice on 22nd June 1940, the British newspapers contained many complaints about the submissiveness of the French government in Vichy to German demands. But is this a case of threats? Yes, because the French presumably had ever-present anxieties about the treatment of occupied France, about French prisoners-of-war in Germany, and about the ultimate terms of peace.
    13 The tripartite pact of Sept 27 1940 between Germany, Italy and Japan was designed to deter the United States from entering the war on the side of Britain by threatening that if they did so, then Japan would come in on the other side. W L ?Shirer [1941] who was in Germany at the time as an American newspaper correspondent pointed out that the German people are told that the fact is of world-shaking importance and will shortly bring final world peace.
    14 At a time of tension between the United States and Japan, Mr Winston Churchill, the British Prime Minister, made a speech at the Mansion House, London on the 10th Nov 1941 containing the following passage as reported by the Times: 'The United States' time-honoured interests in the Far East are well-known. They are doing their utmost to find a way of preserving peace in the Pacific. We do not know whether their efforts will be successful, but if they fail I take this occasion to say, it is my duty to say, that should the United States become involved in war with Japan, the British declaration will follow within the hour." [Loud Cheers]. In spite of this formidable threat, the Japanese began war with the United States by attacking Pearl Harbor on 7 December 1941.
    [More quotes: War Moods:] Here are two translations of a speech made by Herr Hitler, the German Chancellor, on 24th February 1940. "I am determined to see this fight through. Many have said that it would have been better to wait, but I say that it is better to fight it out now, since they would have attacked us anyway." Second: "I am determined to bring this fight to a successful end. Some of you may think that we should have waited a few more years, but I am convinced it was better for us that the others had started." The first was the Times, the second the Manchester Guardian, 1 March. On the same day, Mr Neville Chamberlain, British Prime Minister, in a reply to a vote of thanks, said that, paradoxical as it might seem, we do not feel that the strain and anxiety was so much now as the strain before the war, when it seemed it might be averted. Glasgow Herald, 26th Feb 1940. 'The moods connected with the transition from an arms race to war are discussed in a paper, called 'War Moods', in Psychometrika, 13 147-174 and 197-232 of 1948.'

    [p 62: Arms Race and Athletic Races]: 'The arms race phrase possibly invented by the editor of the London Daily Mail in 1912, must have been thinking of competition and the idea of athletes running. According to a 1927 experiment, when men run over short distances as fast as they could, the motion is described by dv/dt = b - v/a, where b and a are positive constants. After 28 metres, the speed had attained 98% of its maximum value, whereas of course an arms race goes up and up... accelerates..'
    [p 180: Table from different sources, showing German arms build-ups, or what purport to be German arms build-ups. Example: Hitler in his speech to the Reichstag on 1st Sept 1939, after announcing that Germany was at war with Poland, said "For six years now I have been working on the building up of the German defences. Over 90 billions have in that time been spent on the building up of these defence forces." .. HMSO 1939 table: 1933-1934 3/ 6 10 15 24 33 figures in billions of Reichsmarks. [Seems ridiculous because obviously there was hyperinflation and so on]. First two years' figures are taken from the League of Nations book and from 'The Banker'; the third is from a quote by Churchill in 'The Banker'; the fourth is taken from banker and economist Balogh; the fifth from Balogh and Harold Macmillan, MP; final from somebody called 'Cato'. [Are these the figures that A J P Taylor queried?]
    [Japan: special Manchurian Incident Bonds to finance war against China]
    [Chapter 22: Analogies with Disease:] 'First, it's infectious, via newspapers, cinema shows, radio. Second, some people are immune. Third, there's something analogous to the rise of temperature in a fever. Fourth, a long and severe bout confers immunity; men no longer readily join in. Fifth, the acquired immunity fades out after a decade or two. Also, there is a new generation not rendered immune. Sixth, could there be a vaccine?
    [Quotations:] Donald Hankey, 1916 described the beginning of the war in 1914. 'Some of us enlisted for glory, some for fun, and a few for fear of starvation. In this matter of the war, all classes were at one, not only in sentiment, but in practical resolve. The crowd that surged outside the Central Recruiting Offices in Great Scotland Yard were proof of it. All classes were there, struggling for the privilege of enlisting in the new citizen army. Conscious of their unity, determined to give effect to it in the common life of service, men and boys of the working class formed it majority. They were in the element, shouting, singing, cheeking the coppers, with as much ribald good humour as if the Recruiting Officer had been a music hall.' Hitler in 1924 said: 'During the boisterous years of my youth, nothing used to damp my wild spirits so much as to think that I was born at a time when the world had manifestly decided not to erect any more temples of fame, except in honour of business people and state officials.' Describing the outbreak of the war, which occurred when he was 25, he wrote: 'For me these hours came as a deliverance from a distress that had weighed upon me during the days of my youth. I am not ashamed to acknowledge that I was so carried away by an enthusiasm of the moment that I sank down upon my knees and thanked heaven out of the fullness of my heart for the favour of having been permitted to live in such a time.'
    [Examples of Acquired Immunity:] 1 At a certain great English college, there was in 1919-20 a contrast of feeling: the old fellows who had been unable to fight still hated the Germans, whereas the young ones who had returned from fighting and felt that they had done to the Germans much the same as we had done to us.
    2 Holidaying on foot with a knapsack was out of fashion in England for about five years after 1918, perhaps because of its resemblance to infantry exercises.
    3 The weariness of the victors in the Great War in 1918 was shown in 1922 and 23 by their reluctance to resist a comparatively small aggression by the Turks. The threat of renewed war with Turkey was profoundly unpopular.
    4 I remember thinking about 1924 that England had almost been converted to Quaker principles.
    5 There was an interval in London about 1925 to 1928 when plays about the Great War were out of favour and books about it didn't sell.
    6 The British Legion, an organisation for ex-servicemen from which conscientious objectors were debarred, was conspicuously active in promoting friendly relations with the Germans whom they had fought against in 1914-18 by organising exchanges of visits. In the year 1935, the British Legion took part, with the corresponding French, Belgian, Italian and German organisations, in setting up a Comit‚ International Permanent des Ancients Combattants
    [Acquired immunity is seldom permanent:] 1 When one cannot find statistics, it may be permissible to quote a leading man. Mr Clement Attlee saw service at Gallipoli, commanding a covering party at Souvla, was severely wounded in the relief of Kut. He was wounded again fighting as a major in France and was in hospital when the armistice was signed. Peace found him disillusioned, and for a time he was a pacifist, and took a prominent part inn the 'no war' movement. He felt the men in the army had been cheated. By 1924 he was under-secretary of state for war.
    2 The British Legion maintained its friendly international contacts until 1938. But on 28th May 1939 Major General Sir Frederick Morris in his presidential address declared it is obviously impossible for us to renew the contact we have made, so long as the press of Germany and Italy are daily abusing our country.
    3 W K ?Pfiler in 1941 in the course of German writings about World War 1, reports, there was a hiatus in the production of war novels between the end of the war and 1927. Then, however, the war was revived at extreme intensity. The flood of German war novels extended all over the world. At first the war was seen from a pacifist, liberal and egocentric point of view, but as the political wave of nationalism rose higher and higher it was the ethnocentric nationalist war novel that conquered the field. With the advent of the Third Reich, it held the monopoly on the German literary stage.
    4 It is relevant to note the dates of two works of art in which the war was described with realistic detail and antipathy. R C Sheriff's Journey's End, first produced in London 9 December 1928. E M Remarque's Im Westen nichts Neues was first published in Germany in January 1929. .. in translation first published in March 1929.. had run to 129,000 copies before August. These dates seem to mark the stage at which the thought of war, though disagreeable and shocking, had become very interesting to large numbers of people. At that time, 1928-29, actual war was not threatening. States were arranged in the Kellogg-Briand pact for the renunciation of war. If people thought imaginary war to be disagreeable and shocking, why did they attend to it? The Freudian explanation might be like that of the prude who is shocked by his social judgment, but attracted by his instinct. Alternatively, one might say that the younger generation growing up wished to know what their elders had suffered. Conclusion: we must not mistake war-weariness for the permanent conviction that war is morally wrong.
    [Richardson liked little debates between AUTHOR, and people like MENTOR, PACIFIST, LECTOR and so on: Example: 'instability coefficient from 1928-1933 comes to about .8 per year':]
    MENTOR: That is puzzling, for Hitler is generally believed to have been the great disturber of the peace, and he did not come into power until January 1933. How do you account for the instability having been greater during the four years before, and less during the six years after, his arrival?
    AUTHOR: The greater instability must I think have been an effect of the world-wide trade depression of 1929-1932
    MENTOR: Hm. Well, supposing that were so. Which of your so-called constants did the trade depression alter? The instability coefficient is only a consequent of other effects.
    AUTHOR: We can rule out the grievances, Gi, anyway, for in theory they have no effect on the instability. The trade depression may have increased the defence coefficients by making nations irritable, or it may have decreased the fatigue and expense coefficients by making unemployed men eager to be drilled, and manufacturers eager for armament production.
    MENTOR: Are you not forgetting that you used to assert that x = threats - co-operation, or more specifically, x = warlike expenditure - a fraction of foreign trade?
    AUTHOR: Yes, I have been forgetting that, purposely, [sic] during all this discussion of ten nations, for really we have had enough to do without considering ten more variables for trade. ...'
    [Formation of the Russo-German Pact:] 'May be expressed in the language of the theory by saying that the defence co-efficients of Germany and the USSR against each other which had been large in 1935 suddenly in August 1939 fell to near-zero.'

    [Arms races:] 'To the present writer it seems credible, though hardly definitely proved, that the modern instability of balances of power is a consequence of the application of science to war material, for because of the many kinds of complicated material required in peacetime by the fighting services many people are employed in their manufacture and their cost is a conspicuous item in the national budget. These activities becoming known to other nations are interpreted by them as threats. One of the lessons drawn by Viscount Gort from the campaign of the British expeditionary force which he commanded in 1939 is: 'The days are past when armies can be hurriedly raised, equipped, and placed in the field, for modern war demands ever-increasing use of complicated material. Indeed, the scientific side of warfare has been evolving at a very rapid rate, even since the end of the war of 1914-18, and is continuing to do so. Modern equipment requires time to design and produce, and once it is produced, further time is required to train troops in its technical and tactical uses.'

    [More about how people suspect defence to be concealed aggression:] 'Sir Neville Henderson, 1939, describing his experience as British Ambassador in Berlin in the two years preceding World War Two, gives many examples of defence suspected to be aggression. In February 1939, at a banquet of the German-English Society in Berlin, I took as my theme the fact that British rearmament was not only compatible with, but the necessary adjunct of, a passionate love of peace. I had just finished speaking when the head of the press bureau at the Ministry for Foreign Affairs entered the room, with a news telegram in his hand, reporting the vote in the House of Commons for a further 150 million for rearmament. He asked me somewhat indignantly how I reconciled my pacific utterances with this evidence of our aggressive attentions. I wrote across the telegram in German and signed it: Peace can only be assured if Britain is in a position to defend herself. In April 1939, the British and French governments began negotiations to persuade the USSR to join a peace front against German aggression. Our negotiators in Moscow gave meanwhile magnificent ammunition to Goebbels' propaganda to represent Germany once more as being encircled by the western powers. Britain, the chief architect of this alleged encirclement, was again proclaimed to be Germany's public enemy number one. Clearly, the Russian negotiations were a form of encirclement, but in no offensive sense, and solely as a means to resist aggression. Sir Neville Henderson, July 1939, says: 'there were three parties in Germany at this time. One, far removed from Hitler's entourage and representing the mass of the people, was all for peace and still hopeful that Hitler's wizardry would enable him to achieve his aims without war. The second was equally all for war at any price. It was confident in the might of Germany's army and air force, and in their invulnerability to attack from the west. It was the party in the closest touch with Hitler and was constantly pressing him to go ahead regardless of the consequences and arguing that in any case Britain either would not or could not fight. There was a third party which appeared really to believe that Britain's military preparations were being deliberately undertaken with a view to a preventive war, and which consequently argued that war in 1939 was better for Germany than war in 1940 or later. I was repeatedly told by those in closest touch with him that Hitler himself professed to share this view. Those who have base motives themselves tend to attribute similar motives to others. It was not conviction in this case, but empiricism which induced Hitler to represent to his army leaders that England was prepared for a preventive war. No other argument was more calculated to make them whole-hearted partisans of the immediate war, upon which, as the event proved, he was now and probably always had been bent.

    [Foreign Trade:] 'Von Blow who was German Chancellor from 1900-1909 seems to have thought he maintained a nice balance between threats and co-operation. This is what he said: "A conflict between Germany and England would be a great misfortune for both countries, for Europe, and for mankind in general. Ever since the day when I undertook the affairs of the Foreign Office, I have been convinced that such a conflict would never come to pass, 1 If we built a fleet that could not be attacked without very grave risk to the attacking party, 2 If we did not, beyond that, indulge in undue and unlimited shipbuilding and armaments, and did not overheat our marine boiler, 3 If we allowed no power to injure our reputation or our dignity, 4 If we allowed nothing to make an irremediable breach between us and England. That is why I always repelled any impertinent attack which was likely to hurt our feelings as a nation, whatever quarter it came from, but resisted all temptations to interfere in the Boer War, as that would have dealt English self-esteem a wound that would not heal. 5 If we kept calm and cool and neither injured England nor ran after her." ...'

    [Arms races from 1820 to 1908:] 'Historians mention arms races for only 10 out of 84 wars that ended between 1820 and 1929. These are 1914 World War, 1865 La Plata, 1892 Armenia, 1829 Caucasus, 1845 Punjab, 1859 Italy, 1878 Tekke Turkomans, 1892 Central Africa, 1894 Madagascar, 1926 China. ... We can definitely assert there were some wars for which one belligerent had made no special preparations. An example is the Indian mutiny of 1857. .. France vs the North German Confederation 1868-70, Russia vs Turkey 1872-77, [the war was in 1877; that seems to have been an arms race], ... 7 weeks war between Austria and Prussia in Summer 1866. By September of that year the North German Confederation had been formed. Prussia had made an offensive and defensive alliance with Bavaria, Wurttemberg, and Baden.. Russia vs Japan from 1901-1904.. that war began in 1904.. This was in fact an eventuality which had been foreseen, on which the naval and military policy of Japan had been based for ten years. .. [Gives the impression that the unstable arms races of the modern time first appeared between 1877 and 1900, for the reasons quoted by Viscount Gort before. (NB: Nothing about imperialism and conflicts over foreign territories, although obviously if there's no arms race it must mean presumably that the people fighting had enough arms to comfortably work with.)] .. Triple alliance between Italy, Austria-Hungary and Germany persisted since 1882.. the Franco-Russian alliance was confirmed in 1894.. the Entente between Britain and France took shape in April, 1904.. the Russo-Japanese war was ended by the Treaty of Portsmouth, in the USA, 23rd August 1905. In March 1906 Britain and Russia had become more friendly. In 31st August 1907 there was a convention, and from that date onwards for seven years there was peaceful opposition between the Triple Alliance .. and the Triple Entente of France, Russia, and Britain. ...'

    'Sir Edward Grey also named in retrospect 5 crises: Algeciras 1906, Bosnia-Herzegovina Oct 1908, Agadir July 1911, the Balkan Wars in 1912-13, and the final crisis of July and August 1914. The history books are so full of alarms and pacifications that the regularity of the[se] statistics seems surprising. .. the last decisions of peace were as follows: The Austro-Hungarian Law Budgets 14 June 1914, 2 weeks before the murder of the Archduke; the French Law of 15th July 1914; German Law of 27th May 1914; British Estimates of Spring 1914; the Italian Budget for the 12 months ended 30 June 1914 was decided by Royal decree on 17th July of the previous year.'

    [Arms races, point of balance, 'appeasement' pursued by Neville Chamberlain's government in Britain from June 1937 to August 1939:] '.. open up conversations with likely enemies about matters in dispute, taking care not to give them any valuable satisfaction at the expense of your own country. At the same time, increase your armaments both for defence and attack' [Ironic?]

    [Practical Politics, p 230:]
    CRITIC: Hello. Here we are again.. both alive. What have you been doing since we last met?
    AUTHOR: Recently, I have been studying an explosive
    CRITIC: Really? I am glad to hear that you took so useful a part in the war effort. No pacifist nonsense about that! By now I believe we've got something far more powerful than the old-fashioned picric acid or TNT. What's it called? Damitall? No?
    AUTHOR: I have indeed been studying an explosive so powerful that apart from it none of the others will do any harm. I refer to the human temper
    CRITIC: You are a naughty joker. But seriously now, I suppose the war will have considerably changed your views? When we last met you said that bombing airplanes were a danger to the nation that owned them
    AUTHOR: In a roundabout way, in peacetime
    CRITIC: Surely you have now abandoned that outrageous statement. What would have happened to Britain had it not been for the heroic airmen of her bombers and fighters?
    AUTHOR: Which nation had the most bombing airplanes just before the war?
    CRITIC: Germany, of course. That was the cause of all the trouble. Fools and pacifists hindered our rearmament. Their criminal folly has been vividly described by Cato in his book called 'Guilty Men'
    AUTHOR: But did you expect Germany to be beaten?
    CRITIC: Definitely
    AUTHOR: Well then from your statements it follows that the possession of bombing airplanes in times of peace will ultimately prove in a roundabout way to have been a danger to the nation that owned most of them. Indeed, without foretelling the future, it may be said that the damage already done to many German cities is an indirect consequence of the pre-war Luftwaffe
    CRITIC: But think of the long and terrible struggle that we have been let in for by our initial inferiority in the air. ...
    [Worth noting that he assumes Britain won the war; the fact that Germany outnumbered Britain in terms of aeroplanes is only a minor factor in the total war effort, which included the later entry of USA, admittedly after the Battle of Britain, and the USSR. So he's talking nonsense, isn't he, influenced by his Anglo-centric view of the world.]



[Return to top]

AMERICAN SCIENTIST JanFeb 2002 - review from Internet. Brian Hayes on Lewis Fry Richardson.

Statistics of Deadly Quarrels

    Brian Hayes

    Look upon the phenomenon of war with dispassion and detachment, as if observing the follies of another species on a distant planet: From such an elevated view, war seems a puny enough pastime. Demographically, it hardly matters. War deaths amount to something like 1 percent of all deaths; in many places, more die by suicide, and still more in accidents. If saving human lives is the great desideratum, then there is more to be gained by prevention of drowning and auto wrecks than by the abolition of war.

    But no one on this planet sees war from such a height of austere equanimity. Even the gods on Olympus could not keep from meddling in earthly conflicts. Something about the clash of arms has a special power to rouse the stronger emotions-pity and love as well as fear and hatred-and so our response to battlefield killing and dying is out of all proportion to its rank in tables of vital statistics. When war comes, it muscles aside the calmer aspects of life; no one is unmoved. Most of us choose one side or the other, but even among those who merely want to stop the fighting, feelings run high. ("Antiwar militant" is no oxymoron.)
    Figure 1. The Great War in La Plata (1865-1870) . . .Click to Enlarge Image

    The same inflamed passions that give war its urgent human interest also stand in the way of scholarly or scientific understanding. Reaching impartial judgment about rights and wrongs seems all but impossible. Stepping outside the bounds of one's own culture and ideology is also a challenge-not to mention the bounds of one's time and place. We tend to see all wars through the lens of the current conflict, and we mine history for lessons convenient to the present purpose.

    One defense against such distortions is the statistical method of gathering data about many wars from many sources, in the hope that at least some of the biases will balance out and true patterns will emerge. It's a dumb, brute-force approach and not foolproof, but nothing else looks more promising. A pioneer of this quantitative study of war was Lewis Fry Richardson, the British meteorologist whose ambitious but premature foray into numerical weather forecasting I described in this space a year ago. Now seems a good time to consider the other half of Richardson's lifework, on the mathematics of armed conflict.
Statistics of Deadly Quarrels

    Brian Hayes
    Wars and Peaces

    Richardson was born in 1881 to a prosperous Quaker family in the north of England. He studied physics with J. J. Thomson at Cambridge, where he developed expertise in the numerical solution of differential equations. Such approximate methods are a major mathematical industry today, but at that time they were not a popular subject or a shrewd career choice. After a series of short-term appointments-well off the tenure track-Richardson found a professional home in weather research, making notable contributions to the theory of atmospheric turbulence. Then, in 1916, he resigned his post to serve in France as a driver with the Friends' Ambulance Unit. Between tours of duty at the front, he did most of the calculations for his trial weather forecast. (The forecast was not a success, but the basic idea was sound, and all modern weather prediction relies on similar methods.)

    After the war, Richardson gradually shifted his attention from meteorology to questions of war and international relations. He found some of the same mathematical tools still useful. In particular, he modeled arms races with differential equations. The death spiral of escalation-where one country's arsenal provokes another to increase its own armament, whereupon the first nation responds by adding still more weapons-has a ready representation in a pair of linked differential equations. Richardson showed that an arms race can be stabilized only if the "fatigue and expense" of preparing for war are greater than the perceived threats from enemies. This result is hardly profound or surprising, and yet Richardson's analysis nonetheless attracted much comment (mainly skeptical), because the equations offered the prospect of a quantitative measure of war risks. If Richardson's equations could be trusted, then observers would merely need to track expenditures on armaments to produce a war forecast analogous to a weather forecast.

    Mathematical models of arms races have been further refined since Richardson's era, and they had a place in policy deliberations during the "mutually assured destruction" phase of the Cold War. But Richardson's own investigations turned in a somewhat different direction. A focus on armaments presupposes that the accumulation of weaponry is a major cause of war, or at least has a strong correlation with it. Other theories of the origin of war would emphasize different factors-the economic status of nations, say, or differences of culture and language, or the effectiveness of diplomacy and mediation. There is no shortage of such theories; the problem is choosing among them. Richardson argued that theories of war could and should be evaluated on a scientific basis, by testing them against data on actual wars. So he set out to collect such data.

    Others had the same idea at roughly the same time. The Russian-born sociologist Pitirim A. Sorokin published a long list of wars in 1937, and Quincy Wright of the University of Chicago issued another compilation in 1942. Richardson began his own collection in about 1940 and continued work on it until his death in 1953. Of the three contemporaneous lists, Richardson's covers the narrowest interval of time but seems to be best adapted to the needs of statistical analysis.

    Richardson published some of his writings on war in journal articles and pamphlets, but his ideas became widely known only after two posthumous volumes appeared in 1960. The work on arms races is collected in Arms and Insecurity; the statistical studies are in Statistics of Deadly Quarrels. In addition, a two-volume Collected Papers was published in 1993. Most of what follows in this article comes from Statistics of Deadly Quarrels. I have also leaned heavily on a 1980 study by David Wilkinson of the University of California, Los Angeles, which presents Richardson's data in a rationalized and more readable format.

Statistics of Deadly Quarrels

    Brian Hayes
    "Thinginess Fails"

    The catalogue of conflicts in Statistics of Deadly Quarrels covers the period from about 1820 until 1950. Richardson's aim was to count all deaths during this interval caused by a deliberate act of another person. Thus he includes individual murders and other lesser episodes of violence in addition to warfare, but he excludes accidents and negligence and natural disasters. He also decided not to count deaths from famine and disease associated with war, on the grounds that multiple causes are too hard to disentangle. (Did World War I "cause" the influenza epidemic of 1918-1919?)
    Figure 2. Magnitude of a war . . .Click to Enlarge Image

    The decision to lump together murder and war was meant to be provocative. To those who hold that "murder is an abominable selfish crime, but war is a heroic and patriotic adventure," Richardson replies: "One can find cases of homicide which one large group of people condemned as murder, while another large group condoned or praised them as legitimate war. Such things went on in Ireland in 1921 and are going on now in Palestine." (It's depressing that his examples, 50 years later, remain so apt.) But if Richardson dismissed moral distinctions between various kinds of killing, he acknowledged methodological difficulties. Wars are the province of historians, whereas murders belong to criminologists; statistics from the two groups are hard to reconcile. And the range of deadly quarrels lying between murder and war is even more problematic. Riots, raids and insurrections have been too small and too frequent to attract the notice of historians, but they are too political for criminologists.

    For larger wars, Richardson compiled his list by reading histories, starting with the Encyclopaedia Britannica and going on to more diverse and specialized sources. Murder data came from national crime reports. To fill in the gap between wars and murders he tried interpolating and extrapolating and other means of estimating, but he acknowledged that his results in this area were weak and incomplete. He mixed together civil and international wars in a single list, arguing that the distinction is often unclear.
    Figure 3. Frequency of outbreaks of war . . .Click to Enlarge Image

    An interesting lesson of Richardson's exercise is just how difficult it can be to extract consistent and reliable quantitative information from the historical record. It seems easier to count inaccessible galaxies or invisible neutrinos than to count wars that swept through whole nations just a century ago. Of course some aspects of military history are always contentious; you can't expect all historians to agree on who started a war, or who won it. But it turns out that even more basic facts-Who were the combatants? When did the fighting begin and end? How many died?-can be remarkably hard to pin down. Lots of wars merge and split, or have no clear beginning or end. As Richardson remarks, "Thinginess fails."

    In organizing his data, Richardson borrowed a crucial idea from astronomy: He classified wars and other quarrels according to their magnitude, the base-10 logarithm of the total number of deaths. Thus a terror campaign that kills 100 has a magnitude of 2, and a war with a million casualties is a magnitude-6 conflict. A murder with a single victim is magnitude 0 (since 100=1). The logarithmic scale was chosen in large part to cope with shortcomings of available data; although casualty totals are seldom known precisely, it is usually possible to estimate the logarithm within ±0.5. (A war of magnitude 6±0.5 could have anywhere from 316,228 to 3,162,278 deaths.) But the use of logarithmic magnitudes has a psychological benefit as well: One can survey the entire spectrum of human violence on a single scale.

Statistics of Deadly Quarrels

    Brian Hayes
    Random Violence

    Richardson's war list (as refined by Wilkinson) includes 315 conflicts of magnitude 2.5 or greater (or in other words with at least about 300 deaths). It's no surprise that the two World Wars of the 20th century are at the top of this list; they are the only magnitude-7 conflicts in human history. What is surprising is the extent to which the World Wars dominate the overall death toll. Together they account for some 36 million deaths, which is about 60 percent of all the quarrel deaths in the 130-year period. The next largest category is at the other end of the spectrum: The magnitude-0 events (quarrels in which one to three people died) were responsible for 9.7 million deaths. Thus the remainder of the 315 recorded wars, along with all the thousands of quarrels of intermediate size, produced less than a fourth of all the deaths.

    The list of magnitude-6 wars also yields surprises, although of a different kind. Richardson identified seven of these conflicts, the smallest causing half a million deaths and the largest about 2 million. Clearly these are major upheavals in world history; you might think that every educated person could name most of them. Try it before you read on. The seven megadeath conflicts listed by Richardson are, in chronological order, and using the names he adopted: the Taiping Rebellion (1851-1864), the North American Civil War (1861-1865), the Great War in La Plata (1865-1870), the sequel to the Bolshevik Revolution (1918-1920), the first Chinese-Communist War (1927-1936), the Spanish Civil War (1936-1939) and the communal riots in the Indian Peninsula (1946-1948).

    Looking at the list of 315 wars as a time series, Richardson asked what patterns or regularities could be discerned. Is war becoming more frequent, or less? Is the typical magnitude increasing? Are there any periodicities in the record, or other tendencies for the events to form clusters?

    A null hypothesis useful in addressing these questions suggests that wars are independent, random events, and on any given day there is always the same probability that war will break out. This hypothesis implies that the average number of new wars per year ought to obey a Poisson distribution, which describes how events tend to arrange themselves when each occurrence of an event is unlikely but there are many opportunities for an event to occur. The Poisson distribution is the law suitable for tabulating radioactive decays, cancer clusters, tornado touchdowns, Web-server hits and, in a famous early example, deaths of cavalrymen by horse kicks. As applied to the statistics of deadly quarrels, the Poisson law says that if p is the probability of a war starting in the course of a year, then the probability of seeing n wars begin in any one year is e-ppn/n!. Plugging some numbers into the formula shows that when p is small, years with no onsets of war are the most likely, followed by years in which a single war begins; as n grows, the likelihood of seeing a year with n wars declines steeply.

    Figure 3 compares the Poisson distribution with Richardson's data for a group of magnitude- 4 wars. The match is very close. Richardson performed a similar analysis of the dates on which wars ended-the "outbreaks of peace"-with the same result. He checked the wars on Quincy Wright's list in the same way and again found good agreement. Thus the data offer no reason to believe that wars are anything other than randomly distributed accidents.

    Richardson also examined his data set for evidence of long-term trends in the incidence of war. Although certain patterns catch the eye when the data are plotted chronologically, Richardson concluded that the trends are not clear enough to rule out random fluctuations. "The collection as a whole does not indicate any trend towards more, nor towards fewer, fatal quarrels." He did find some slight hint of "contagion": The presence of an ongoing war may to some extent increase the probability of a new war starting.

Statistics of Deadly Quarrels

    Brian Hayes
    Love Thy Neighbor

    If the temporal dimension fails to explain much about war, what about spatial relations? Are neighboring countries less likely than average to wind up fighting one another, or more likely? Either hypothesis seems defensible. Close neighbors often have interests in common and so might be expected to become allies rather than enemies. On the other hand, neighbors could also be rivals contending for a share of the same resources-or maybe the people next door are just plain annoying. The existence of civil wars argues that living together is no guarantee of amity. (And at the low end of the magnitude scale, people often murder their own kin.)

    Richardson's approach to these questions had a topological flavor. Instead of measuring the distance between countries, he merely asked whether or not they share a boundary. Then, in later studies, he refined this notion by trying to measure the length of the common boundary-which led to a fascinating digression. Working with maps at various scales, Richardson paced off the lengths of boundaries and coastlines with dividers, and realized that the result depends on the setting of the dividers, or in other words on the unit of measurement. A coastline that measures 100 steps of 10 millimeters each will not necessarily measure 1,000 steps of 1 millimeter each; it is likely to be more, because the smaller units more closely follow the zigzag path of the coast. This result appeared in a somewhat out-of-the-way publication; when Benoit Mandelbrot came across it by chance, Richardson's observation became one of the ideas that inspired Mandelbrot's theory of fractals.

    During the period covered by Richardson's study there were about 60 stable nations and empires (the empires being counted for this purpose as single entities). The mean number of neighbors for these states was about six (and Richardson offered an elegant geometric argument, based on Euler's relation among the vertices, edges and faces of a polyhedron, that the number must be approximately six, for any plausible arrangement of nations). Hence if warring nations were to choose their foes entirely at random, there would be about a 10 percent chance that any pair of belligerents would turn out to be neighbors. The actual proportion of warring neighbors is far higher. Of 94 international wars with just two participants, Richardson found only 12 cases in which the two combatants had no shared boundary, suggesting that war is mostly a neighborhood affair.

    But extending this conclusion to larger and wider wars proved difficult, mainly because the "great powers" are effectively everyone's neighbor. Richardson was best able to fit the data with a rather complex model assigning different probabilities to conflicts between two great powers, between a great power and a smaller state, and between two lesser nations. But rigging up a model with three parameters for such a small data set is not very satisfying. Furthermore, Richardson concluded that "chaos" was still the predominant factor in explaining the world's larger wars: The same element of randomness seen in the time-series analysis is at work here, though "restricted by geography and modified by infectiousness."
    Figure 5. Web of wars is constructed from Richardson's data . . .Click to Enlarge Image

    What about other causative factors-social, economic, cultural? While compiling his war list, Richardson noted the various items that historians mentioned as possible irritants or pacifying influences, and then he looked for correlations between these factors and belligerence. The results were almost uniformly disappointing. Richardson's own suppositions about the importance of arms races were not confirmed; he found evidence of a preparatory arms race in only 13 out of 315 cases. Richardson was also a proponent of Esperanto, but his hope that a common language would reduce the chance of conflict failed to find support in the data. Economic indicators were equally unhelpful: The statistics ratify neither the idea that war is mainly a struggle between the rich and the poor nor the view that commerce between nations creates bonds that prevent war.

    The one social factor that does have some detectable correlation with war is religion. In the Richardson data set, nations that differ in religion are more likely to fight than those that share the same religion. Moreover, some sects seem generally to be more bellicose (Christian nations participated in a disproportionate number of conflicts). But these effects are not large.

   
Statistics of Deadly Quarrels

    Brian Hayes
    Mere Anarchy Loosed upon the World

    The residuum of all these noncauses of war is mere randomness-the notion that warring nations bang against one another with no more plan or principle than molecules in an overheated gas. In this respect, Richardson's data suggest that wars are like hurricanes or earthquakes: We can't know in advance when or where a specific event will strike, but we do know how many to expect in the long run. We can compute the number of victims; we just can't say who they'll be.

    This view of wars as random catastrophes is not a comforting thought. It seems to leave us no control over our own destiny, nor any room for individual virtue or villainy. If wars just happen, who's to blame? But this is a misreading of Richardson's findings. Statistical "laws" are not rules that govern the behavior either of nations or of individuals; they merely describe that behavior in the aggregate. A murderer might offer the defense that the crime rate is a known quantity, and so someone has to keep it up, but that plea is not likely to earn the sympathy of a jury. Conscience and personal responsibility are in no way diminished by taking a statistical view of war.
    Figure 6. Long-term catalogue of global conflicts . . .Click to Enlarge Image

    What is depressing is that the data suggest no clear plan of action for those who want to reduce the prevalence of violence. Richardson himself was disappointed that his studies pointed to no obvious remedy. Perhaps he was expecting too much. A retired physicist reading the Encyclopaedia Britannica can do just so much toward securing world peace. But with larger and more detailed data sets, and more powerful statistical machinery, some useful lessons might emerge.

    There is now a whole community of people working to gather war data, many of whom trace their intellectual heritage back to Richardson and Quincy Wright. The largest such undertaking is the Correlates of War project, begun in the 1960s by J. David Singer of the University of Michigan. The COW catalogues, like Richardson's, begin in the post-Napoleonic period, but they have been brought up close to the present day and now list thousands of militarized disputes. Offshoots and continuations of the project are being maintained by Russell J. Leng of Middlebury College and by Stuart A. Bremer of Pennsylvania State University.

    Peter Brecke of the Georgia Institute of Technology has begun another data collection. His catalogue extends down to magnitude 1.5 (about 30 deaths) and covers a much longer span of time, back as far as a.d. 1400. The catalogue is approaching completion for 5 of 12 global regions and includes more than 3,000 conflicts. The most intriguing finding so far is a dramatic, century-long lull in the 1700s.

    Even if Richardson's limited data were all we had to go on, one clear policy imperative emerges: At all costs avoid the clash of the titans. However painful a series of brushfire wars may seem to the participants, it is the great global conflagrations that threaten us most. As noted above, the two magnitude-7 wars of the 20th century were responsible for three-fifths of all the deaths that Richardson recorded. We now have it in our power to have a magnitude-8 or -9 war. In the aftermath of such an event, no one would say that war is demographically irrelevant. After a war of magnitude 9.8, no one would say anything at all.

© Brian Hayes


[Return to top]

A note on La Griffe du Lion, who writes online in the style of L. F. Richardson

The first time I heard of 'La Griffe du Lion' [anonymous Internet uploader; I presume the nickname is a reference to a fairly well-known quotation about Isaac Newton] in the Occidental Observer of 3rd July 2016. The link was to a piece on 'smart fraction theory'. 'La Griffe du Lion' immediately reminded me of Richardson's writing style, and methodology—most of Richardson's mathematical techniques are echoed in 'La Griffe du Lion'.

lagriffedulion.f2s.com is his site. [f2s.com seems to be freedom2support.net, owned by, or part of, talktalk.com. His site appears to be generated by Microsoft Front Page]. The Items are dated from 1999 to 2012, at present.

La Griffe du Lion's material has some errors, for example accepting the media lie that serial murders in the USA are mostly white. But here are some important issues which he may (or, I'd guess more likely, may not tackle):-
  1. Jews as a layer spread across many countries. As with L F Richardson, La Griffe assumes a world of nations and countries. There's no conceptual space for a layer, of if you like, a country spread among other countries.
  2. Therefore there is no analyses of the interests and behaviours of distinct separate group(s) spread across many countries. The effects on wars, conflicts, populations, are therefore not noted.
  3. Jewish paper money, considered as a power structure on its own, needs to be examined, and behaviours predicted, and counter-behaviours identified.

  4. Even more ambitiously, what about some technique to analyse alliances between groups?
  5. What about an analysis of lying as a strategy? Everyone has their own personal information, but everything else, in both space and time, is potentially untrue, or actually unknown. Perhaps there's a theory or overview of control of information?

Information Research, Scanning, HTML, site maintenance etc Rae West. Part of my big-lies.org website.   La Griffe du Lion added 3 July 2016