Complexity Theory And Airpower:
A New Paradigm for Airpower in the 21st Century

Steven M. Rinaldi

Military theorists and analysts have frequently turned to the sciences for insight into the nature of warfare. For the past several centuries, classical physics provided a paradigm that was extensively used to frame theories of warfare.1 Military theorists borrowed a number of concepts from classical or "Newtonian" physics and applied them metaphorically to operational art: friction, center of gravity, mass, and momentum, to name a few. In a very real sense, a large body of military art and theory came to rest upon analogies to principles of classical physics. The Newtonian paradigm thus provided a foundation for centuries of military thought, and continues to play a major role today.

Yet much as classical physics cannot describe many classes of natural phenomena, the Newtonian paradigm is limited in its application to warfare. Armed conflict has many facets that cannot be adequately addressed within this paradigm. As a consequence, theories of war built upon a Newtonian frame are restricted in scope and applicability. Military science is in need of a new framework that better describes the true nature of war.

During the past three decades, a number of new sciences have arisen and developed rapidly. Based upon nonlinear dynamics and far-from-equilibrium thermodynamics, these disciplines include catastrophe theory,2 chaos theory,3 and most recently complexity theory.4 These theories push beyond some of the limitations of classical physics, and explore classes of phenomena outside the traditional linear realm. Recently, military theorists have applied these theories metaphorically to studies of conflict.5 Complexity theory lends itself particularly well as a new paradigm for military science, promising to be a far more powerful framework than the traditional Newtonian paradigm. Although its application to military science has a short history, complexity theory already has yielded insights into military science that the Newtonian paradigm is incapable of providing. Indeed, modern military concepts such as OODA loops and parallel warfare that cannot be treated under the Newtonian paradigm (metaphorically or otherwise) fit very comfortably into the realm of complexity.

In this paper, we will explore the evolution of airpower theory in the context of the two paradigms. Airpower theory is undergoing a fundamental shift from the restrictive Newtonian to the broader complex paradigm. Theories in the post-World War I era were decidedly Newtonian in nature. Gradually, theorists proposed concepts that fit more nearly into the complex paradigm than the Newtonian framework. This trend appears to be accelerating today, as the concepts of complexity theory become more widely spread and studied. By and large, this shift has not been due to a conscious effort to develop airpower theory within the complex paradigm. Rather, complexity theory has been used principally to reinterpret existing tenets of airpower theory.

We will start by defining the two paradigms, focusing on their essential characteristics. Next, we will examine airpower theories from the post-World War I, World War II, and modern eras. In particular, we will observe how the underlying natures of the theories have shifted from the Newtonian to the complex framework. Finally, we will move from the theoretical to the practical, and examine an application of complexity theory to operational art.

Airpower theory has been transitioning to the complex framework for decades. We must complete the shift and employ the new framework in our operational thinking. For it is only in incorporating insights from complexity in practical applications that we fully exploit the power the new paradigm has to offer.

The Newtonian and Complexity Paradigms

The Newtonian paradigm has governed the way military theorists viewed warfare for many years. However, it suffers from a number of serious shortfalls. Its applicability as a framework for recent theories of airpower is increasingly questionable. As our understanding of the behaviors of complex adaptive systems increases, the complex framework becomes more relevant to studies of warfare than the Newtonian paradigm. The principle reason may be found in the concepts of linearity and nonlinearity: warfare is an inherently far-from-equilibrium, nonlinear phenomenon. The Newtonian paradigm rests firmly upon linear principles, whereas complexity theory embraces the nonlinear.

Linear systems played an important role in the development of science and engineering, as their behaviors are easily modeled, analyzed, and simulated. A linear system has two defining mathematical characteristics. First, it displays proportionality. If some input X to the system gives an output of Y, then multiplying the input by a constant factor A yields an output of AY. The second characteristic of linear systems is superposition. That is, if inputs X1 and X2 give outputs Y1 and Y2 respectively, then an input equal to X1 + X2 gives an output of Y1 + Y2. Systems that do not display these characteristics are called nonlinear. Importantly, linear systems of equations can be solved analytically or numerically. Given a set of linear equations and initial conditions, we can calculate the future values of the variables. Consequently, if we can describe a system by a linear mathematical model, we can determine its future states exactly from its given initial state. A large body of mathematics has grown up around linear systems and techniques for their solution.

Nevertheless, the vast majority of systems and phenomena in the real world are nonlinear. As their name implies, nonlinear systems do not display the linear characteristics of proportionality and superposition. Analytical solutions to nonlinear equations are generally the exception rather than the rule. Thus, the future states of nonlinear systems can often only be approximated. One method of approximating the behavior of nonlinear systems involves linearizing them, then employing linear systems analysis to the approximated system.6 Unfortunately, such techniques suppress or even eliminate many of the important dynamical characteristics of nonlinear systems; for example, chaos cannot exist without nonlinearities. However, the advent of modern digital computers has brought about a revolution in the study of nonlinear systems. Computers have made it possible to simulate their rich dynamical behaviors such as chaos that might otherwise not exist in linearized approximations.

Linearity is the cornerstone of the Newtonian paradigm. This has several important ramifications for military theory.7 First, warfare under the Newtonian paradigm is deterministically predictable, as effects are in principle calculable from their underlying causes. Given enough information about the current state of a conflict and armed with "laws" of combat, a commander should be able to precisely determine the outcome of the battle. The three-to-one rule of combat is a good example of a linear law. Determining the outcome of a war becomes a simple exercise if a sufficient amount of precise information is available, much as the future states of a linear system of equations can be exactly computed. A consequence of determinism in war, then, is the drive for greater quantities of ever-more-perfect intelligence from which the commander can make ever-more-precise predictions of the future. With intelligence and situational awareness approaching perfection, the Newtonian paradigm reduces fog and friction to a bare minimum just as chaos is banished from linear systems.

Reductionism is a second important consequence of the Newtonian paradigm. Reductionism is a methodology for solving problems. The analyst breaks the problem into its constituent pieces, solves each piece separately, then sums the results from the pieces to obtain the overall solution to the problem. This is a natural consequence of superposition. The history of warfare is replete with examples of reductionism. For example, targeting has largely been reductionist. Air planners generally break the enemy into a series of target systems, analyze each target system independently of all others to determine aimpoints, then sum the results to generate the overall air campaign.8 Historical analyses of wars are frequently reductionist—what is the isolated, independent cause (or causes) that led to the outcome of the conflict? As linearity allows and even encourages this mindset, reductionism is a principle characteristic of Newtonian warfare.

A third consequence of the Newtonian paradigm is the view of systems as closed entities, isolated from their environments. Outside events do not influence such a system; the only dynamics are those arising from its internal workings. The analyst thus has an inward focus, with a concentration on efficiency. The emphasis on efficiency is especially noteworthy for military operations. How can the commander obtain the desired objectives with the least cost? What targets must the planner select to most efficiently and economically accomplish the objectives? Numerical measures of merit, such as body counts, tank kills, and aircraft losses become paramount in analyzing the flow of the battle and determining strategy. Isolated, closed systems are perhaps easier to analyze, as outside forces and influences are of no consequence. However, isolated systems form only a small fraction of the physical universe. With the global information explosion, conflicts that are truly isolated from the outside world are increasingly rare, if they exist at all.

Warfare in the Newtonian paradigm has several defining characteristics. Schmitt lists several of the more important ones:

The Newtonian paradigm creates a simplified, idealized view of warfare. It is an appealing, comfortable framework as it offers simple means for analysis, methodical rules for planning and executing operations, and the illusion of predicting the future given enough information about the present. However, warfare is intrinsically more complicated than this simplistic framework allows. As Schmitt notes, the paradigm is in need of a serious tune-up, or better, a complete overhaul.

Complexity theory offers a broader, far more useful framework for military theory. This paradigm is based upon open, nonlinear systems in far-from-equilibrium conditions. A complex adaptive system has several defining characteristics.10 First, it is composed of a large number of interacting parts or "agents." The interactions between the agents are nonlinear.11 The interactions and behaviors of the agents influence the environment in which the system exists. Changes in the environment in turn influence the agents and their interactions. The agents and environment thus continuously affect and are affected by each other. Second, the agents characteristically organize into hierarchies. Agents at one level of the hierarchy cluster to form a "super agent" at the next higher level. A bureaucracy or military organization illustrates the concept: a number of aircraft form a squadron, several squadrons form a wing, and so forth. Third, there are intercommunicating layers within the hierarchy. Agents exchange information in given levels of the hierarchy, and different levels pass information between themselves as well. Finally, the complex system has a number of disparate time and space scales. For example, military operations at the squad level are highly localized and may occur very rapidly compared to events at the corps level. Complex adaptive systems in widely varying disciplines appear to share these four characteristics.

Complex adaptive systems exhibit a number of common behaviors. The first is emergence: the interactions of agents may lead to emerging global properties that are strikingly different from the behaviors of individual agents.12 These properties cannot be predicted from prior knowledge of the agents. The global properties in turn affect the environment that each agent "sees," influencing the agents’ behaviors. A synergistic feedback loop is thus created—interactions between agents determine emerging global properties which in turn influence the agents. Consider a pilot and his wingman engaged in tactical operations during a conflict. The myriad of such tactical operations interact and define the courses of the operational and strategic levels of war. However, the characteristics of the strategic level of war cannot be extrapolated from individual tactical engagements. The strategic environment in turn shapes future tactical engagements for the pilots, thus completing the cycle. A key ramification of emergence is that reductionism does not apply to complex systems.13 Since emergent behaviors do not arise from simple superpositions of inputs and outputs, reductionism cannot be used to analyze the behaviors of complex systems. The emergence of coherent, global behavior in a large collection of agents is one of the hallmarks of complex systems.14

A second fundamental behavior of complex systems is adaptive self-organization. As Kauffman notes, "contrary to our deepest intuitions, massively disordered systems can spontaneously ‘crystallize’ a very high degree of order."15 This appears to be an innate property of complex systems. Self-organization arises as the system reacts and adapts to its externally imposed environment. Such order occurs in a wide variety of systems, including for example convective fluids, chemical reactions, certain animal species, and societies.16 In particular, economic systems are subject to self-organization. The adjustments economies make under the rigors of war are manifestations of the dynamics of adaptive self-organization.

A third important behavior of complex systems is evolution at the edge of chaos. Dynamical systems occupy a "universe" composed of three regions.17 The first is an ordered, stable region. Perturbations to the systems tend to die out rapidly, creating only local damage or changes to the system. Information does not flow readily between the agents. In the second region, chaotic behavior is the rule. Disturbances propagate rapidly throughout the system, often leading to destructive effects. The final region is the boundary between the stable and chaotic zones. Known as the complex region or the "edge of chaos," it is a phase transition zone between the stable and chaotic regions. According to Kauffman, systems poised in this boundary zone are optimized to evolve, adapt, and process information about their environments.18 As complex systems evolve, they appear to move toward this boundary between stability and chaos, and become increasingly more complex. There is a direct parallel between the adaptations and substitutions made by economies due to wartime destruction and the concept of evolution at the edge of chaos. Social and bureaucratic structures display similar evolutionary patterns as well.19 Metaphorically, we can envision the former Soviet Union existing in the stable region, Somalia in the chaotic, and the U.S. and Western European nations at the edge of chaos. Evolution toward the edge of chaos appears to be a natural property of complex systems.

The final key behavior of complex systems is their ability to process information.20 The systems sense their environments and collect information about surrounding conditions. They then respond to this information via a set of internal models that guide their actions. Systems may also encode data about new situations for use at a later date. This characteristic is closely related to adaptation near the edge of chaos. As we shall discuss in more detail below, Boyd’s OODA loop relies upon just such information processing.21 Information processing is a common characteristic of complex systems, and enables them to adapt to changing environments.

Complexity theory provides a powerful framework for analyzing military art and science. Indeed, warfare is a nonlinear, complex, adaptive phenomenon with two or more coevolving competitors. The actions of every agent in the conflict, from individual pilots and infantrymen to numbered air forces and corps, influence and shape the environment. Environmental changes in turn cause adaptations in all hierarchical levels of the warring parties. As both allied and enemy actions influence the environment, warfare involves the coevolution of all involved parties. When viewed from this vantage point, it is clear that the Newtonian paradigm is too limited to adequately cover the many aspects of armed conflict. Warfare is more appropriately analyzed under the complex framework than the Newtonian. It is time to shift paradigms.

Airpower Theories and Shifting Paradigms

Airpower theory is transitioning from the Newtonian to the complex paradigm. In the early years of military aviation, airpower theories fit entirely within the Newtonian paradigm. Aspects from complexity first appeared in American airpower doctrine in the 1930s. Planners incorporated these aspects in the air campaigns of World War II. Only during the past few years have any works appeared that specifically referred to or were based upon complexity theory. For the most part, this shift has not been a deliberate attempt to incorporate principles from complexity into airpower theory. Rather, airpower theorists have increasingly proposed ideas that fall more naturally under the complex paradigm than the Newtonian paradigm. We will trace this shift by examining airpower theories from the post-World War I , World War II, and modern eras.

Airpower Theory After World War I

The Great War provided the first major test of the new aerial weapon. Following the war, proponents of airpower began to publish their theories. Two of the most prominent early theorists were the Italian General Giulio Douhet and the American General William Mitchell.

Douhet was an outspoken proponent of the aerial arm. He viewed the airplane as an inherently offensive weapon with a strategic mission. According to Douhet, the principle objectives of aerial warfare were to first obtain command of the air, then direct offensives against surface targets to crush the material and moral resistance of the enemy.22 The airplane was unique in its ability to perform these missions. It could leap over fortified lines of defense, mass anywhere, and attack any objective in enemy territory. Consequently, the boundaries of future wars would be national boundaries, with civilians and military alike subjected to the effects of war. Douhet theorized that under a steady rain of bombs, the enemy civilian population would rise up in terror and force its government to sue for peace. He stated:

A complete breakdown of the social structure cannot but take place in a country subjected to this kind of merciless pounding from the air. The time would soon come when, to put an end to horror and suffering, the people themselves, driven by the instinct of self-preservation, would rise up and demand an end to the war—this before their army and navy had time to mobilize at all!23

The prerequisite for victory was to secure command of the air. He flatly stated that "to have command of the air is to have victory" and that "the command of the air is a necessary and sufficient condition of victory."24

Douhet was convinced that an independent air force was essential for national defense. Starting from the "axiom" that command of the air meant victory, he arrived at the conclusion that national defense could only be assured by a sufficiently powerful air force independent of the army and navy.25 Defense against enemy airpower was futile to Douhet, as enemy forces could fly virtually undetected to and mass over any target of their choosing. Possession of a more potent offense, capable of rendering greater destruction upon the enemy, was the only acceptable solution. Consequently, Douhet felt that the independent air force should be composed of the greatest number of bombers possible. He disdained auxiliary uses of airpower, arguing that it was "worthless, superfluous, harmful...consequently, aerial means set aside for auxiliary aviation are means diverted from their essential purpose, and worthless if that purpose is not pursued."26 With command of the air equated to victory, the independent air force had to be designed to ensure this objective could be obtained.

In the United States, Mitchell was probably the most ardent early proponent of airpower. He recognized that the airplane brought a revolutionary new capability to militaries that would fundamentally change the nature of future campaigns:

The advent of airpower which can go straight to the vital centers and entirely neutralize or destroy them has put a completely new complexion on the old system of making war. It is now realized that the hostile main army in the field is a false objective and the real objectives are the vital centers. The old theory, that victory meant the destruction of the hostile main army, is untenable.27

Mitchell envisioned total warfare that would affect all the citizens of a nation as the way of the future. The vital centers included civilian objectives (cities, areas where food and supplies were produced, transportation)28 and the hostile nation’s means of making war (aircraft factories, flight training schools, war materiel manufacturers, means of communications, fuel and oil production).29 Like Douhet, he believed that an air force would need control of the air. The battle for control of the air would be the prelude to any land or sea engagements. If the United States were to lose control of its airspace in a conflict, then the enemy would be able to dictate the terms of peace "at any place within the United States that he may desire."30

Mitchell devoted considerable thought to the structure of the nation’s future military services. The country needed a separate air force with a centralized command system to control all aspects of the employment of aircraft. The air force would have to organize its resources so that it could swiftly mobilize in event of war. This would allow the air force to strike first at any potential enemy, thus gaining a considerable strategic advantage. The army and navy would assume secondary roles. He particularly downplayed the role of the surface navy. Its large infrastructure, high cost, and the vulnerability of ships to aerial bombardment fueled his conviction that surface navies were rapidly losing their importance to national defense. Mitchell could only see prominent national defense roles for the air force, the army, and the submarine corps.31

Despite their visionary theories for airpower, Douhet and Mitchell were firmly grounded in the Newtonian paradigm. Both men grasped the revolutionary new capabilities of the airplane and saw the implications for the future: the ability to overfly surface forces and mass above any enemy objective, strategic attack, and total warfare. But they incorporated their airpower theories into the existing linear framework, thus expanding the body of military theory without discarding the Newtonian paradigm. In particular, Douhet exhibited a striking sense of linearity in his logic and supporting examples.

Douhet relied heavily upon linear calculations and arguments to support three important propositions. First, World War I demonstrated the defensive nature of firearms and trench warfare. Douhet asserted that improvements in firearms would favor the defense. Starting from a simplistic calculation of the number of infantrymen required to storm a trench for a given rate of defensive fire, he concluded:

With this increased power of firearms, the offensive must, in order to win, upset this equilibrium by a preponderance of forces... But to say that the increased power of new weapons favors the defensive is not to question the indisputable principle that wars can be won only by offensive action. It means simply that, by virtue of increased fire power, offensive operations demand a much larger force proportionately than defensive ones.32

Increases in defensive power though improved firearms required proportionally larger offensive forces for victory. In effect, Douhet employed linear mathematics and logic to demonstrate the defensive nature of rifles, machine guns, and artillery.

His second proposition that rested solidly upon linear mathematics was the futility of defense against aerial attack.33 Given N targets worth defending and an enemy air force with an offensive power of X, Douhet argued that a nation required a defensive air force of power NX to ward off an enemy attack. Following this logic, if a nation had twenty defensive positions requiring protection, it could only ensure its defense with twenty times the total number of enemy aircraft. He concluded that defense against aerial attack was absurd as a nation would be forced to tie up an enormous amount of resources in defensive forces alone. To Douhet, it was far less expensive and more prudent to focus on the offensive mission of the airplane.

A third important proposition of Douhet’s theory was the inherently offensive nature of the airplane. Again, Douhet turned to mathematics to prove his case. Starting from an explosive with a given destructive power, he used simple, linear calculations to determine the size of a bombing force required to completely destroy a target of 500 meters diameter. From this result, he extrapolated the offensive potential of an air force based on the number of aircraft in its inventory.34 His case for the offensive nature of the airplane was idealized and mechanically precise. But in a fundamental oversight, Douhet’s linear calculations ignored fog, friction, and chance—the nonlinear, chaotic phenomena that are inherent to any combat environment. His arguments overlooked the myriad of factors that combine to make aerial warfare results mathematically incalculable, such as imprecise bombing runs and accuracy, mechanical failures, weather, and morale. Warplanes are indeed offensive systems, but Douhet’s supporting logic for this proposition was thoroughly linear.

Douhet and Mitchell were two important airpower theorists of the post-World War I era. Both saw the airplane as a strategic, offensive weapon system that would profoundly change the nature of future conflicts. Nevertheless, their airpower theories were rooted in the Newtonian paradigm. In essence, both men proposed extensions and modifications to the existing body of military theory. But they remained within the bounds of the Newtonian paradigm and did not incorporate any ideas from the yet-undefined science of complexity.35 To the degree that Douhet and Mitchell represent the early school of airpower thought, we can assert that the initial theories of airpower were decidedly Newtonian in character.

Airpower Theory and World War II

American airpower theory began its transition from the Newtonian to the complex paradigm several years before World War II. We can trace the transition to the Air Corps Tactical School (ACTS). In particular, the "industrial web" theory developed at ACTS contained some characteristics of complex adaptive systems. ACTS doctrines profoundly influenced the air campaigns of World War II. As a result, concepts from complexity theory turned up in the planning and execution of the air campaigns during the war.

A large body of doctrine developed at ACTS was based upon the industrial web theory. The ACTS instructors viewed an economy as a number of interlocked, interdependent sectors. For example, the aluminum industry required electricity to produce aluminum from bauxite ore, and the steel industry received raw materials and shipped finished products via the transportation network. The linkages and dependencies created a web-like structure within the economy. In particular, the instructors emphasized that dependencies would often give rise to bottlenecks—specific parts of the web that were essential for the normal functioning of the economy. Bottlenecks had several characteristics: they were critical for the operation of other industries, their destruction could cause the complete collapse of or work stoppage in an industry, and they were generally difficult to replace or repair. The ACTS instructors considered bottlenecks to be ideal targets in the industrial web context. Importantly, many parts of the web essential for manufacturing war materiel were also tightly connected to civilian use. The instructors singled out electricity and transportation as two economic sectors that were required by everyday life, civil manufacturing, and war materiel production.

Under the stress of war, the instructors believed that the industrial web would be severely strained and highly vulnerable to attack. Disruption or destruction of parts of the web would cause it to unravel, with an impact on both the social welfare and war materiel manufacturing capabilities of the nation:

...modern warfare places an enormous load upon the economic system of a nation, which increases its sensitivity to attack manifold. Certainly a breakdown in any part of this complex interlocked organization, must seriously influence the conduct of war by that nation, and greatly interfere with the social welfare and morale of its nationals.36

Disruption of the enemy’s web was therefore a primary objective in war:

Hence it is maintained that modern industrial nations are susceptible to defeat by interruption of this web, which is built to permit the dependence of one section upon many or all other sections, and further that this interruption is the primary objective for an air force. It is possible that the moral collapse brought about by the breaking of this closely knit web will be sufficient, but closely connected therewith is the industrial fabric which is absolutely essential to modern war.37