Patterns in war dynamics, Part VI. Building blocks for a new theory (3): Degrees of freedom

(3) Abnormal war dynamics are caused by the ‘too’ intense rivalries between two Great Powers, resulting in a decrease in the number of degrees of freedom of the System that determine the nature of its dynamics. Analysis of the non-systemic war dynamics of the System during the period 1495-1945 indicates that normally non-systemic wars produce circular trajectories – orbits – in phase space, when phase space is defined by intensity (or severity) and size (in terms of fractions) of non-systemic wars.

During the periods 1657-1763 and 1945-1989, these trajectories in phase space were distorted. I refer to these periods as the first and second exceptional periods, respectively.

pnas-fig-7

Figure 7: This figure shows two sub-cycles that can be identified during the first exceptional period (1657-1763), providing additional support for the assumption that during that period the non-systemic war dynamics were periodic – instead of chaotic – in nature. Basic data from Levy.

The data indicate that during the first exceptional period, non-systemic war dynamics were more extreme but also much more regular; during the second exceptional period, in contrast, non-systemic war dynamics were highly subdued. During the period 1657-1763, two highly regular sub-cycles can be identified in the war dynamics of the System, with each sub-cycle defined by four non-systemic wars. The correlation coefficient of the severities of these two sets of wars is 1.00. The war frequencies of both sub-cycles were rather similar, 0.082 and 0.085 wars/year, respectively.

The resemblance between both exceptional periods (1657-1763 and 1945-1989) is – as historians also observe – that the war dynamics during these periods were determined by the intense rivalries between only two Great Powers, Britain and France (1657-1763) and the United States and the Soviet Union (1945-1989), respectively.

I assume that in both cases the number of degrees of freedom of the System – that is the number of states (variables) that determined the war decisions of states – were temporarily reduced to only two instead of (at least) three, as is normally the case.

I suggest that the circular trajectories in phase space point to the chaotic nature of non-systemic war dynamics. I argue that during the first exceptional period (1657-1763), non-systemic war dynamics were not chaotic but rather periodic in nature. As the dynamics of other systems also indicate, for dynamics to be chaotic, at least three degrees of freedom are required, while periodic dynamics only require two.

The normally unpredictable nature of non-systemic war dynamics – as we also experience – is also consistent with these assumptions. Although chaotic dynamics are deterministic, they are also intrinsically unpredictable because of their sensitivity to the ‘initial conditions’ of the System.

The resumption of the unpredictable nature of the war dynamics of the System since 1989, often noticed and discussed by social scientists, politicians and defense planners, is no ‘coincidence’ and is consistent with the resumption of circular trajectories of war dynamics in phase space at that point in time.

The lack of a third degree of freedom (variable) during the period 1657-1763 also explains why these non-systemic war dynamics were not only remarkably regular but also more extreme in size and severity. Because of the lack of a third degree of freedom, the System lacked intrinsic inhibition: during that period, tensions that were produced were ‘magnified’ and released on short notice. Furthermore (see Figure 6), the second cycle (1648-1792) during the period 1657-1763 had not yet reached the tipping point, and its war dynamics were not yet constrained by the connectivity of the network of issues.

I assume that these developments – resulting in inhibited war dynamics – impacted the development of the second cycle toward a critical condition: development of the issue network toward the tipping point; consequently, the accumulation of tensions – and a next systemic war and ‘upgrade’ of the international order – was delayed.

I argue that the disturbance in the release ratio, and the lengthening of the lifespan of the second relatively stable period, are related to the abnormal – non-chaotic – nature of non-systemic war dynamics during the period 1657-1763. As explained above, tensions were immediately released (by means of non-systemic wars), and accumulation of tensions (and ‘charging’ of the System) was not possible until the intense and overriding rivalries between Britain and France were resolved (1763) and the tipping point was reached.

As the trajectories in phase state indicate, the second cycle resumed chaotic war dynamics after 1673, and the second cycle reached its tipping point in 1774. It took until 1792 to charge the System and produce a systemic war.

The research suggests that chaotic war dynamics and ‘smooth’ development of the System could be related; a relationship between chaos, development and order is also believed to exist in other complex systems.

Whereas during the first exceptional period (1657-1763), non-systemic war dynamics became more extreme, during the second exceptional period (1945-1989), war dynamics became subdued instead. I attribute the suppression of war dynamics to ‘mutual assured destruction’ – a deadlock – that was accomplished by the United States and the Soviet Union, through their mutual targeting with nuclear capabilities (which could not be destroyed through a first strike). At least temporarily, war had lost its functionality.

To be continued.