Drawing on mathematical biology and, of course, history, this lecture offers what I believe to be a fundamental critique of the dominant approach, based on the equations of F. W. Lanchester. Lanchester Theory, by which I mean the original equations and their contemporary extensions, produces anomalous results, mathematically precluding important observed behaviors, like the trading of space for time. These deep problems arise because the belligerents, as idealized in the theory, are completely non-adaptive. War is, I argue, precisely a process of coadaptation, though the contestants bear a much closer resemblance to Ashby's cat than to Homo economicus . My own Adaptive Dynamic Model tries to capture this as simply as possible, in the process overcoming the anomalies of Lanchester Theory.
Sensitive dependence is bad news.
I think so. The general rule is simply that the odd man out instantly allocates all force to the attacked party . Now, many academic political scientists and statesmen dismiss any form of collective security because this perfect form is implausibly altruistic. The lecture shows that in arms race models sufficiently nonlinear to produce really volatile dynamics, highly diluted, or imperfect, collective security regimes can damp the explosive oscillations and induce convergence to stable equilibria below initial armament levels. Put differently, the injection of tiny degrees of altruism can profoundly calm the otherwise volatile dynamics.