Chaos and Determinism: A Paradigm

Policy makers depend upon ability to predict the outcome of their policies. Increasingly, in the field of international security ? in matters of war and peace ? prediction is based upon quantitative models. The point made here is that just because a model is mathematical, it does not follow that it can be used to make predictions, that non-linear models allow both predictive and chaotic regimes. After illustrating these matters with physical models, the paper turns to the modeling of an arms race between two antagonistic nations (or groups of nations). After discussing static and dynamic arms race models which are predictive, we turn to a simple non-linear arms race model which allows a transition from predictabililty to chaos. We then postulate that such a transition describes the transition from peace to war in the two party hostile competitive system being modeled by the nonlinear equations, that peace is to war in reality as determinism is to chaos in a mathematical model of that reality. Thus, escalation from peace to war through various levels of hostility may not be controllable, the ``slipping' from peace to war may be as inadvertent as the slipping from laminar flow to turbulence as an aircraft stalls and loses control. The lessons to be learned are to stay away from critical transition points if at all possible and ? more importantly ? to be very wary of claims of controllability in any escalation of a crisis.