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The Cutting Edge of Chaos

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The following joke is attributed to Hermann Göring as he stood trial in Nuremberg, charged with conspiracy to commit crimes against peace, specifically --planning, initiating and waging wars of aggression; war-crimes; and crimes against humanity:1
One Englishman --an idiot; two Englishmen a club; three Englishmen an empire!

One German: a fine man; two Germans; a Bund;. three Germans: a war!

A joke in bad taste but consider the source. But also a simple, if simple-minded, analysis of data. It even hints at the science of emergent properties but I seriously doubt Herr Göring had that in mind.

Across the English Channel before Herr Göring would have the opportunity to dazzle the world with his wit  theoretician and mathematician Lewis Fry Richardson would dare to ask: is war inevitable? Can it be predicted? Can it be prevented? Why do we go to war? Is war murder?

The answers to these questions resist reduction to number, though Richardson pioneered the science of fractals and inspired the field of war gaming. Richardson himself may have had William Butler Yeats in mind when he observed that wars merge and split, or have no clear beginning or end; he said of them: Thinginess fails.

Richardson reduced war to data concluding:

  • War and murder differ only in the scale of the killing.
  • War is murder raised to an exponent.
  • Wars may be categorized logarithmically like hurricanes and earthquakes.
  • Arms races leading to wars may be modeled with differential equations.The occurrences of war may be plotted in a Poisson distribution like cancer clusters and tornado touchdowns.
Richardson was not the first to explore these possibilities. Often, he went off in different directions. His work is still available in journal articles, pamphlets, two posthumous volumes from 1960, and a two-volume Collected Papers of 1993. His work on arms races may be found in Arms and Insecurity and his statistical studies are published in Statistics of Deadly Quarrels.

Richardson is often criticized for equating war and murder; deliberately provocative it is charged. Richardson's retort is barbed and prescient:

Another Richardson theme is called cascading chaos, a concept referred to in the film Jurassic Park. Unstable systems are described as existing in a critical state between order and chaos, literally poised on the edge of chaos.

In the film, the park itself was such a system; the slightest disturbance might trigger a cataclysmic event. In nature, sparks have ignited forest fires; the movement of a grain of sand can trigger a landslide. Is it really surprising that the U.S. attack against Iraq is in danger of destabilizing the Middle East? Has it already done so?

Richardson counted total deaths and categorized war logarithmically magnitude one, two, three and so forth. A single murder is magnitude zero; ten or so deaths is magnitude one. With deaths in the tens of millions, both World Wars exceeded magnitude seven. The number of wars is inversely proportional to the number of deaths; for example, there are some ten million conflicts of magnitude zero but only two 20th century conflicts reached magnitude 7. Similarly, the number of deaths by murder is roughly equal to the number of deaths by world war.

Richardson listed seven megadeath conflicts in tier two, i.e, magnitude six. They are, in chronological order:3

  • Taiping Rebellion (18511864)
  • North American Civil War (18611865
  • Great War in La Plata (18651870)
  • Sequel to the Bolshevik Revolution (19181920)
  • First Chinese-Communist War (19271936)
  • Spanish Civil War (19361939)
  • Communal riots in the Indian Peninsula (19461948)
  • Richardson had hoped that his work might help prevent war by increasing the understanding of it. Sadly, he concluded that war is not only random like cancer clusters, it is inevitable like hurricanes and tornadoes. Richardson modeled a "death spiral", an escalating arms-race in which each nation responds by adding still more armaments to its arsenal. If the world avoided a nuclear disaster between the Soviet Union and America it is only because the fatigue and expense proved greater than perceived threats.

    Even so, other developments are equally worrisome. Richardson found evidence of "contagion"; i.e. an ongoing war increases the probability that a new war will start. And because only 12 of 94 world conflicts studied were between nations which shared no border, he concluded that war is a neighborhood affair. He found that of 94 world conflicts, only 12 were between combatants which shared no border. The inevitable conclusion: war is a "neighborhood affair".

    Religion is also a factor. Nations of differing religion are more likely to fight than nations sharing a single religion although only in the case of Confucionism did similarity of religion seem to have contributed in any way toward peace. Christian nations, moreover, seem to be more bellicose and have engaged in a disproportionate number of wars.

    For a while, Richardson was all but ignored. Now others now carry on his work. Lars-Erik Cederman of Harvard Universitys John M. Olin Institute for Strategic Studies has replicated Richardsons results in a new computer model. Princeton University professor Robert Gilpin models the small events which "cascade" into chaos. Vanderbilt University professor John Vasquez, likewise, explains wars in terms of cascading system instability. 4

    It must be pointed out that statistics do not govern events; they merely describe them. A murderer is not likely to win acquittal by pleading that his behavior is within known statistical norms.

    Are nations, then, to be absolved for merely playing out a terrible fate? Are religious wars to be tolerated because God is on one side or the other? Will neighboring nations be given leave to attack across shared borders? Are we to make war lightly because we have been wronged? Are "leaders" to be excused in any way for having lied a nation into war? Perhaps those questions are unanswerable. Consider the consequences: by Richardson's scale, a war of magnitude 9.8 will leave no one behind to ask the questions.

    William Butler Yeats wrote the most appropriate conclusion in 1922 a year of great disillusionment with World War I:

    Things fall apart; the centre cannot hold;
    Mere anarchy is loosed upon the world,
    The blood-dimmed tide is loosed, and everywhere
    The ceremony of innocence is drowned;
    The best lack all conviction,
    While the worst are full of passionate intensity.

    William Butler Yeats, The Second Coming


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