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Chaos: Good For More Than Absolutely Nothing

Originally Posted by Meridyth Mascio and Tom Plick

Chaos, War, and DisarmamentDebate has raged over whether wars are due mainly to long-term causes (oppression, economic depression, nationalistic zealotry) or whether they only find their genesis in freak events (the murder of a ruler, the sinking of a fleet). Many believe the former; among these people was Lewis Richardson, who, in the 1930s, developed a simple model of an arms race between two countries. He related the size of a nation’s stockpile to its willingness to go to war, for two reasons: Firstly, arms could be easily qualified, whereas the "feelings" of a nation were not easily transformed into numbers. Secondly, the larger a nation’s stockpile, the greater its chance of winning a war, and thus, the greater its chance of starting a war. (When each nation’s stockpile is sufficiently large, the system becomes crisis-unstable: each nation wants to attack the other(s) first, lest the other(s) make the first blow.)Richardson’s model was the first attempt at modeling an arms race mathematically. Many analysts point out the inapplicability of Richardson’s model to modern conflicts - the model mishandles many situations, because of its simplicity and the assumptions made to secure that simplicity.Others after him, including Alvin Saperstein, took Richardson’s idea and elaborated on it, in an attempt to model reality more accurately. Saperstein modeled an arms race between three nations under two systems - in one, the nations were allowed to ally as they saw fit, so that a superpower might find the other two nations allied against it. In the other system, the nations were not permitted to ally, and thus were at odds with both of the other nations. Saperstein’s model was complex, and non-linear; recall that non-linearity breeds chaos.Saperstein showed the system permitting alliances to be stable - in time, he says, each country’s stockpile will dwindle to zero. Saperstein uses this observation in support of encouraging cooperation between countries instead of competition.More interesting than the alliance system is the system that disallows alliances.In the independent-nations scenario, several outcomes are possible, depending on the initial stockpiles of the nations and the "fear and loathing" values between the nations, plus many other parameters defined by Saperstein.
  1. Strong stability: Each nation’s stockpile decreases to zero (that is, in the limit, not necessarily in any finite amount of time).
  2. Weak stability: Each nation’s stockpile decreases to some non-zero amount.
  3. Weak chaos: The system has a strange attractor, but its basin of attraction is small, and so the system is still largely crisis-stable.
  4. Strong chaos: The system has a strange attractor, whose basin encompasses the entire system.
According to Saperstein, the strange attractor signals crisis instability, since once on a strange attractor, what happens in the long-term is anyone’s guess. The way to maintain peace, he says, is to avoid the appearance of the strange attractor. To him, knowing chaos is useful for avoiding it in world affairs.You can see our Powerpoint presentation again here.