Source: ©2011 Reflections of a Rational Republican

The most recent issue of The Economist included a tantalizing article about the behavior of complex systems. The system in question was the interaction between coalition forces and insurgents in Afghanistan.

According to Professor Neil Johnson, the relationship between the coalition and insurgents exhibits a mathematical relationship much like that of the dynamic between a predator and its prey. This relationship models an arms race between an adaptive Red Queen (i.e., insurgents) and her counter-adapting Blue King opponent (i.e., coalition military).

Professor Johnson’s research shows that the formula (T_n = T₁n^-b) has been remarkably predictive in determining the course of an insurgency in several Afghan provinces. T_n represents the number of days between the nth fatal attack and its successor. T₁ represents the number of days between the first and second fatal attacks. The variable b is the single most important variable in the equation because it determines the course of the insurgency. A large positive b is ideal for the insurgency because it reduces the number of days between fatal attacks, while a negative b favors the coalition because it increases the number of days between fatal attacks.

This key insight could have a transformative effect on the future nature of warfare.

Here is a brief example of how the equation works. As the graph below shows, a higher b results in a much more rapid decrease in days between subsequent fatal attacks as an insurgent force conducts more attacks over time. In essence, the insurgents with b = 0.75 are learning more rapidly than the insurgents with b = 0.25. Therefore, the key for any future counterinsurgency campaign is to make every effort to maintain a very low or negative b.

Achieving this goal in practice is difficult. However, by using this mathematical relationship a priori in future counterinsurgency campaigns, the American military can better project which insurgent groups will likely become more persistent and allocate resources accordingly.