Clausewitz, Nonlinearity, and the Unpredictability of War
Favorite Excerpt (Via Clausewitz & Amol)
It is impossible “to construct a model for the art of war that can serve as a scaffolding on which the commander can rely on for support at any time.” Since the opponent is a reacting, animate entity, “it is clear that continual striving after laws analogous to those appropriate to the realm of inanimate matter was bound to lead to one mistake after another.” The notion of law does not apply to actions in war, “since no prescriptive formulation universal enough to deserve the name of law can be applied to the constant change and diversity of the phenomena of war.”
What is “Nonlinearity”? (Via Clausewitz)
“Nonlinearity” refers to something that is “not linear.” This is obvious, but since the implicit structure of our works often reveals hidden habits of mind, it is useful to reflect briefly on some tacit assumptions. Like other members of a large class of terms, “nonlinear” indicates that the norm is what it negates. Words such as periodic or asymmetrical, disequilibrium or nonequilibrium are deeply rooted in a cultural heritage that stems from the classical Greeks. The underlying notion is that “truth” resides in the simple (and thus the stable, regular, and consistent) rather than in the complex (and therefore the unstable, irregular, and inconsistent). (6)
The result has been an authoritative guide for our Western intuition, but one that is idealized and liable to mislead us when the surrounding world and its messy realities do not fit this notion. An important basis for confusion is association of the norm not only with simplicity, but with obedience to rules and thus with expected behavior—which places blinders on our ability to see the world around us. Nonlinear phenomena are thus usually regarded as recalcitrant misfits in our catalog of norms, although they are actually more prevalent than phenomena that conform to the rules of linearity. This can seriously distort perceptions of what is central and what is marginal—a distortion that Clausewitz as a realist understands in On War.
“Linear” applies in mathematics to a system of equations whose variables can be plotted against each other as a straight line. For a system to be linear it must meet two simple conditions. The first is proportionality, indicating that changes in system output are proportional to changes in system input. Such systems display what in economics is called “constant returns to scale,” implying that small causes produce small effects, and that large causes generate large effects. The second condition of linearity, called additivity or superposition, underlies the process of analysis. The central concept is that the whole is equal to the sum of its parts. This allows the problem to be broken up into smaller pieces that, once solved, can be added back together to obtain the solution to the original problem. (7)
Nonlinear systems are those that disobey proportionality or additivity. They may exhibit erratic behavior through disproportionately large or disproportionately small outputs, or they may involve “synergistic” interactions in which the whole is not equal to the sum of the parts. (8) If the behavior of a system can appropriately be broken into parts that can be compartmentalized, it may be classified as linear, even if it is described by a complicated equation with many terms. If interactions are irreducible features of the system, however, it is nonlinear even if described by relatively simple equations.