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

Part Two

The ACTS doctrine maintained that the destruction of the war materiel manufacturing base and the concomitant breakdown of the morale of enemy civilian population would cause the enemy to capitulate.

The industrial web concept incorporated two principle characteristics of complex adaptive systems. First, the web consisted of a large number of interacting, interdependent parts. However, many of the key attributes of the linkages were ignored or only superficially examined. The lectures discussed and gave many examples of first-order linkages, the direct ties between two agents in an economy. Generally, higher order linkages (indirect ties between two agents that use other agents as intermediaries) were not discussed, although they could be inferred from some of the examples. The lectures only obliquely referred to nonlinear linkages, and never by name. For example, one lecture made the points:

The instructors recognized that small inputs could lead to disproportionately large outputs. Yet it is not clear that they deeply understood or comprehensively analyzed the nonlinear nature of the linkages. Finally, the lectures rarely pointed out feedback loops, branching and serial processes, and the time-dependent nature of the linkages. In short, the ACTS theory recognized the existence of linkages, but did not fully appreciate neither the important characteristics of the linkages nor the types of complex adaptive behaviors the linkages could create.

Second, the ACTS faculty understood that economies were composed of hierarchical structures. At the lowest level of the hierarchy, different economic sectors were linked and interdependent. For example, certain manufacturing operations relied upon electrical power, and the food distribution system required the transportation network. Similarly, economic sectors were connected and interdependent across different geographical regions. Moving up to the national level, the instructors contended that a nation’s economic system was tightly interlaced with its social, political, and military structures. The dependencies became absolute during a war, and disturbances in any sector would have impacts of varying intensity in the other sectors.39 However, the hierarchical structure did not stop at national boundaries. Nations themselves were economically intertwined, with trade and money providing the linkages.40 The spread of the Great Depression illustrated the international interconnections. The ACTS instructors clearly appreciated the hierarchical, interconnected nature of economies and national structures.

Despite this appreciation, the ACTS faculty did not fully understand the complex, adaptive nature of economies nor its implications. Indeed, aspects of the industrial web theory were thoroughly Newtonian. First, the ACTS lectures repeatedly stressed the importance of efficiency. For example, while examining the principle of the objective, one lecture noted:

We must concern ourselves with the total efficiency of military operations, because that is our responsibility. . .The objective of the air force must contribute its maximum to attaining the national aim. Military effort of all sorts has as its ultimate aim the destruction of the enemy’s material and moral means of resistance. The method of obtaining this result is not important in itself but every effort should be directed toward that result in the most efficient manner.41

The drive for efficiency led to the search for bottlenecks. This emphasis carried the risk of creating checklists of "panacea" target sets—minimal lists of targets perceived to most efficiently accomplish the mission. However, efficient target sets are not necessarily effective target sets, especially when an economy behaves as a complex adaptive structure rather than a Newtonian machine. Some of the experiences in World War II (especially in light of German workarounds and repair efforts) would bear this out.

A second Newtonian aspect of the ACTS theory was the presumption that the effects of bombing would accumulate. While discussing the principle of mass, one lecture stated:

But how is air "mass" obtained? In one of two ways—either by the employment of numerically strong formations, one blow of which will destroy the objective, or by repeated blows by a relatively weaker formation, the net results of which will accomplish the desired results. Here again, is a striking difference between air and ground action . . . The significant point is: in air force action results are of sufficient permanency that they accumulate. So the application of the principle of mass to air force operations is a matter of providing sufficient force to accomplish each assigned mission, a sufficient rapidity of missions to prevent adequate repair between times, and sufficient missions all contributing toward the desired end....the effect of the action of a striking force against normal, permanent ground installations is cumulative, and while it may take a group of bombardment to destroy a particular objective, that same objective may be destroyed by a squadron operating against it for four different missions.42

Several years later, another lecture postulated:

The results that are achieved by attack of the national economic structure are also cumulative and lasting. They build up from day to day and from week to week so that the pressure that formerly has been imposed by military action over long periods of time, may, by this method, be concentrated into a short period, and still produce that intense suffering upon the civil populace that has been essential for the collapse of the national morale and the national will to continue with the war.43

ACTS clearly saw bombardment as a linear process. Although there was some allowance for repairs, the lectures emphasized the cumulative nature of the destruction caused by bombardment. In other words, superposition applied to aerial attacks.

In the end, the ACTS theories were the first to incorporate some concepts from the complex paradigm. More precisely, the industrial web theory was based on the notion of economies composed of many interlaced, interacting parts. Economies exhibited hierarchies at local, national, and international levels. However, the doctrine did not extend much further into the complex paradigm. Furthermore, it contained principles from the Newtonian paradigm, most notably the search for efficiency and the presumption that bombing effects would accumulate. The result was a doctrine that had one foot in the complex paradigm and the other in the Newtonian paradigm.

The industrial web doctrine carried over into the air plans and operations of WWII. In 1940, General Henry H. Arnold established the Strategic Air Intelligence Section, A-2, to provide intelligence data and analyses for the Air Corps. Major Haywood S. Hansell, Jr., led the section’s strategic air intelligence and analysis effort. A former student and instructor at ACTS, Hansell applied the industrial web doctrine to economic-industrial-social analyses of the Axis powers. Not surprisingly, the analyses closely paralleled ACTS lectures. With regard to the German economy, the section focused on electrical power, steel, petroleum products, the aircraft industry, transportation, nonferrous metal supplies, machine tools, and food processing and distribution. Their studies led to target folders with aimpoints and bomb sizes.44

In July 1941, General Arnold created the Air War Plans Division. The division consisted of Colonel Harold L. George, Lieutenant Colonel Kenneth N. Walker, Major Laurence S. Kuter, and Major Hansell, all of whom had previously taught at ACTS. They were tasked with determining the forces and munitions required by the Air Corps for a potential war with the Axis. The division made the key assumption that the German economy was drawn taut and under extreme stress due to the war. The division produced its first plan, AWPD/1: Munitions Requirements of the Army Air Forces to Defeat Our Potential Enemies, in August 1941. The target sets in priority order were (1) the German Air Force, including aircraft factories, aluminum plants, magnesium plants, and engine factories; (2) electric power, including power plants and switching stations; (3) transportation, with a focus on rail and water; (4) petroleum, including refineries and synthetic plants; and (5) the morale of the German people. The web linkages were important to the planners:

Many factors formed vital links in Germany’s industrial and military might. The overriding question was, which were the most vital links? And among these, which were the most vulnerable to air attack? And from among that category, which would be most difficult to replace, or to "harden" by dispersal or by going underground? Each link in the chain had its own interconnecting links and the search had to be for the one or more keys to the entire structure.45

The "one or more keys to the entire structure" were, of course, bottlenecks. It is important to note the implied search for the most efficient bottlenecks in Hansell’s comment. From the target sets, to the concern about the interconnectivities, to the search for bottlenecks, the influence of ACTS doctrine upon AWPD-1 is clear.

A year later, President Roosevelt asked the military for another estimate of future military requirements. Hansell directed the air estimate. The result was AWPD/42: Requirements for Air Ascendancy, 1942. There was no change in strategic objective, and the approach followed closely that used for AWPD-1. The list of targets changed slightly between AWPD-1 and AWPD-42, taking into account the current strategic situation and lessons learned from combat. Like its predecessor, AWPD-42 was accepted as strategic guidance even though it was a munitions plan. And once again, the heritage of ACTS doctrine was evident.

Following the Casablanca Conference in January 1943, a directive for a new combined strategic air plan was issued. The new air plan drew heavily upon the analyses of the Committee of Operations Analysts (COA), established two months earlier. The COA was composed of civilian industrialists and economists who examined in detail enemy economic and industrial structures. The committee used several guidelines to determine target priorities:

In the determination of target priorities, there should be considered (a) the indis-pensability of the product to the enemy war economy; (b) the enemy position as to current production, capacity for production and stocks on hand; (c) the enemy requirements for the product for various degrees of activity; (d) the possibilities of substitution for the product; (e) the number, distribution and vulnerability of vital installations; (f) the recuperative possibilities of the industry; (g) the time lag between the destruction of installations and the desired effect upon the enemy war effort.46

The Committee looked for weaknesses and bottlenecks in the Axis economies that could be exploited. The analyses included the effects of substitution, industrial recuperation, and time criticality of the product on the war effort. Their prioritized target lists bore close resemblance to both AWPD-1 and AWPD-42. Not surprisingly, the ensuing strategic air plan for the Combined Bomber Offensive was similar to its two predecessors.

Due to the influence of the industrial web doctrine, the air campaign plans of World War II contained elements from the complex paradigm. The planners considered economies to be composed of many linked, interdependent sectors. As Hansell noted, the Air War Plans Division was concerned with linkages and their effects. Linkages figured in COA analyses as well. The Enemy Objectives Unit (EOU), a separate advisory panel on target selection and intelligence in the 8th Air Force, examined the nature of linkages in some detail. In particular, the EOU developed a measure of the "depth" of a good or service.47 Depth was roughly equivalent to the amount of time that would elapse between the cessation of production of some item and the appearance of its shortage on the battlefield. It is analogous to the notion of time criticality in tight and weak couplings.48 The analysts applied this measure to items with direct military utility such as petroleum as well as items with indirect utility such as electric power. The various planning groups recognized the existence of higher order linkages and hierarchies. All of these concepts played into planning considerations.

Nevertheless, aspects of the planning were Newtonian. Two particular examples stand out. First, to a certain degree, targeting was reductionist. The planners selected target systems that were considered vital to the Axis war effort, such as electricity or petroleum. The linkages between these systems and other sectors of the economic-industrial-social fabric of the nation were important. Once the target systems were selected, the analysts often proceeded in a reductionist fashion: they considered the systems in isolation from one another, and selected aimpoints within the isolated systems. Thus, the targeteers generated "efficient" aim points for individual systems without detailed consideration of cross-system effects. A close examination of AWPD-1 and AWPD-42 shows little consideration of the effects of aimpoints in one target system on the operation of another. In reality, economies are highly interconnected with multiple, important cross-system effects that must be taken into account. A Newtonian, reductionist methodology will miss these effects; consequently, what appear to be efficient aimpoints for an isolated target set might be neither efficient nor effective when the economy as a whole is considered.

A second example of Newtonian thought is found in the planners’ treatment of substitution. The EOU considered two types of substitution in their analyses.49 The first entailed replacing processes and equipment, such as using kilns from the ceramics industry in place of destroyed kilns used to dry grinding wheels. The second focused on replacing products or services, such as using aluminum in electrical lines rather than copper so that the copper could be used in radios and communication equipment. Hansell noted the importance of substitution and workarounds but conceded that they were difficult to anticipate and analyze. In general, the planners focused on bottlenecks for which substitution was very difficult if not impossible.

However, the planners missed a crucial aspect of substitution. They focused on what Olson terms the "tactical supply problem" rather than the more important "strategic supply problem."50 The tactical supply problem deals with depriving a military of specific items without which it cannot function. For example, if an airplane requires a certain part to operate properly (such as a variable pitch propeller spring), a lack of that part will ground it. No amount of other types of spares can make up for the missing part. Fundamentally, the tactical supply problem notes that a military cannot operate normally without an adequate supply of the right types of equipment and spares. The strategic supply question focuses on the ability of a nation as a whole to provide for the requirements of its military. In this case, Olson maintains that a nation can generally make up most of any shortages of required goods and services if it is willing and able to shift production from other items into production of the missing items. In essence, the strategic substitution question examines the adaptations an economy makes to fulfill the requirements of war.

Olson points out that the planners understood the tactical substitution problem, but failed to comprehend the implications of strategic substitution. By focusing on bottlenecks that would lead to tactical supply problems, the planners overlooked the ability of the German economy to perform strategic shifts. Consequently, they underestimated the ability of the Germany economy to absorb and adapt to the destruction wrought by the strategic air campaign. In a close analogy to complexity science, Olson states:

...a modern economy is not after all like a finely jeweled watch: it can lose a single part and continue to function. The modern economy is admittedly ‘intricate and interdependent,’ like an expensive watch, but the analogy stops there. For while the watch cannot replace one of its components, an economy a modern economy change is a law of life, and adjustment to change a commonplace, in peace and in war. It would be much better to compare an economy with a tree, which can grow a new branch when an old one is removed, than to a building, which will collapse if part of its foundation is destroyed.51

The air planners of World War II viewed the Axis economies and the substitution problem from the Newtonian perspective rather than the appropriate complex viewpoint. They thereby locked an important aspect of the air campaign planning into the Newtonian paradigm.

Airpower theory and application was clearly shifting from the Newtonian to the complex paradigm by World War II. The industrial web theory incorporated some characteristics of complex adaptive systems. The ACTS faculty recognized that economies were composed of linked and interdependent sectors with different hierarchical levels. The lectures had hints of nonlinearities and feedback loops, and some detail on the nature of linkages. However, Newtonian characteristics abounded: important behaviors such as adaptation and their implications for warfare were not fully understood, targeting was largely reductionist, and planners focused on efficiency. The result was an airpower theory that was part Newtonian and part complex. Decades would pass before airmen would propose theories that more fully rested upon the complex paradigm.

Modern Airpower Thought

Several current airpower concepts have significantly influenced modern operational and strategic art. We will examine three of these theories, specifically the Five Rings model of Colonel John A. Warden III, the OODA loop developed by Colonel John R. Boyd, and parallel warfare. These concepts largely rely upon ideas intrinsic to complexity. In fact, Boyd is among the first military theorists to directly state that his concepts represent far-from-equilibrium, complex adaptive systems.

Colonel John A. Warden III’s Five Rings model provides a conceptual framework for analyzing the physical aspects of an opponent.52 Warden makes a clear distinction between the physical and morale sides of an enemy; he completely decouples one from the other:

The advent of airpower and accurate weapons has made it possible to destroy the physical side of the enemy. This is not to say that morale, friction, and fog have all disappeared. It is to say, however, that we can now put them in a distinct category, separate from the physical. As a consequence, we can think broadly about war in the form of an equation:

(Physical) x (Morale) = Outcome

...Looking at this equation, we are struck by the fact that the physical side of the enemy is, in theory, perfectly knowable and predictable. Conversely, the morale side—the human side—is beyond the realm of the predictable in a particular situation because humans are so different from each other. Our war efforts, therefore, should be directed primarily at the physical side.53

The decoupling of the physical and morale aspects of the enemy is a critical assumption in the theory. Warden then proceeds to examine only the physical characteristics and means of the enemy.

Figure 1 is a schematic of the Five Rings model. As the name implies, the model portrays an enemy system as a set of five concentric rings. The innermost ring represents the central leadership or direction of the system. The ring contains not only the enemy leaders, but also command communications and leadership security. These are the most crucial functions for normal operation of the enemy. The next most critical ring, organic essentials, contains key production (military and nonmilitary) and energy sources. The third ring encompasses the infrastructure of the system--—its transportation networks, factories, and so forth. Generally, elements of this ring are more redundant and numerous than those of the innermost two rings. The fourth ring contains the population and the food sources of the enemy state. The number of targets in this ring are more numerous than those of the inner rings and often more difficult to attack, moral considerations notwithstanding. The outermost ring represents the fighting mechanism or fielded enemy forces. Targets in this ring are numerous and hard, compared to those in the other rings. Ideally, a strategic attack will focus on centers of gravity closest to the leadership or innermost rings. Warden maintains that the five rings model can be used to represent any type of organization that can operate autonomously, whether it be a human body, a drug cartel, an electrical grid, a guerrilla organization, or an enemy nation.

Warden ascribes a number of physical attributes to the enemy system that are characteristic of complex adaptive systems. First, the individual components-—agents—of the rings are intertwined in complicated manners. To give a few examples, electrical power grids (ring two) feed communications networks (ring one), transportation networks (ring 3) provide coal for electrical generators (ring 2), and petroleum distribution networks (ring 2) deliver fuel oil to heat the homes of the population (ring 4). In general, the interactions are nonlinear. They may be of first or higher order. The nonlinear linkages lead to dynamical, often unpredictable behaviors when the enemy system is attacked, such as cascading breakdowns or possibly chaos. In sum, the enemy system consists of many agents linked together in intricate, nonlinear manners.

The second important physical characteristic of the model is an intrinsic, hierarchical structure. Warden contends that each element of every ring can itself be decomposed into five subrings. For example, an electrical grid (ring two) is composed of a leadership function (central control), organic essentials (energy input, such as coal, oil, or hydro power), an infrastructure (transmission lines and transformers), a population (workers), and a fighting mechanism (repairmen). Furthermore, each subring can be decomposed to an even finer degree. The result is a set of nested rings—a hierarchical organizational structure.

The third characteristic of Warden’s model is the layered communications between and across hierarchical levels. Communications (linkages) may be horizontal between two agents in different rings, vertical between agents at different hierarchical levels, or some combination of the two. Like the industrial web, the myriad of communication paths creates an intricate fabric for information exchange, and opens the door to some complex behaviors.

Not only does the model have several of the physical characteristics of complex adaptive systems, it also may allow some of the nonlinear behaviors of such systems. It may be possible to drive the system to chaos or force a cascading breakdown of its normal operating state. In particular, attacks may render the enemy incapable of further resistance, a condition termed strategic paralysis. In this state, the enemy is no longer capable of adapting to changes in his environment. Metaphorically, the enemy system has been pushed away from the edge of chaos.

Despite the elements it shares with complex systems, the model has a definite Newtonian aspect. The key assumption that the physical and morale sides of warfare can be decoupled is reductionist and has significant implications. As Warden notes, it is in principle possible to know everything about the physical side of an enemy—the topology of his power grid, his communications systems, his transportation networks, and so forth, including interconnections. However, without the morale (human) side and the subsequent ability to adapt, the physical side reduces to a Newtonian machine much like Olson’s finely jeweled watch. The human element in warfare is precisely what enables combatants to constantly adapt to their changing environments. It is indeed possible to deprive an enemy of his ability to react, as the Gulf War demonstrated. However, stripping the model of the morale side artificially removes much of the opponent’s capacity to adapt from the onset. The assumption of separate morale and physical aspects has significant ramifications for the model, and gives it a decidedly Newtonian flavor.

In contrast to Warden, Colonel John R. Boyd’s theories of warfare focus on processes and patterns of thought. He is perhaps best known for his Observe-Orient-Decide-Act (OODA) model of decision making.54 In this model, a system observes some event of interest, decides how to resolve a problem posed by the event, and finally acts upon its decision. The cycle is illustrated in Figure 2. This process frequently arises during military operations, where the commander’s objective is to "get inside the enemy’s OODA loop." He does this by simultaneously destroying the enemy’s capability to sense, process, and act on information while preserving his own ability to do so. Once reaching this point, the commander can force the enemy to constantly react rather than take the initiative. Both the friendly and enemy sides cycle through the OODA loop; the friendly objective is to do so more rapidly than the adversary. In doing so, the enemy’s actions lose coherence with the changing environment.

The OODA model has deep parallels to the manners by which complex adaptive systems process information and adapt to their environments. In an exceptionally close paraphrase of Boyd’s theory, Kauffman describes how complex biological systems interact with their environments:

But it is also plausible that systems poised at the boundary of chaos have the proper structure to interact with and internally represent other entities of their environment ...organisms sense, classify, and act upon their worlds. In a phrase, organisms have internal models of their worlds which compress information and allow action... Such action requires that the world be sufficiently stable that the organism is able to adapt to it. Were worlds chaotic on the time scale of practical action, organisms would be hard pressed to cope.55

By sensing, classifying, and acting upon their worlds, organisms cycle through Boyd’s OODA loop and adapt to changing conditions. Chaos on the time scale of practical action implies that some organisms are unable to assimilate environmental conditions fast enough. Here, the environmental conditions change within a single period of an organism’s OODA loop, precluding it from acting coherently. In essence, the environment has "gotten with the organism’s OODA loop." The correspondence between Boyd’s model and the adaptive and information processing capabilities of complex systems is striking.

Boyd recognizes that his model of warfare is rooted in the complex paradigm. He notes that the "OODA Loop Sketch and related Insights represent an evolving, open-ended, far-from-equilibrium process of self-organization, emergence and natural selection."56 The OODA loop itself is a complex adaptive process, employed in conflicts by competing complex adaptive systems. As Boyd implies, the model lies outside the boundaries of the Newtonian paradigm, and falls within the complex paradigm.

Closely related to both Boyd’s and Warden’s models is parallel warfare. Warden asserts that states have on the order of several hundred vital, strategic level targets with perhaps ten aimpoints per target.57 Furthermore, these targets are usually small, expensive, have few backups and are difficult to repair or replace. By attacking a large percentage of targets simultaneously, the damage to and effect upon the enemy can be overwhelming. The enemy will be incapable of reacting to and recovering from the damage. Strategic paralysis or collapse of the enemy may result from his inability to respond to a parallel attack. The opposite limit is serial warfare, in which only one or two targets are attacked at a time. Here, the opponent may have adequate time to recover from the attack, repair the damage, disperse his resources, and adapt. Parallel warfare is fundamentally different from serial warfare, in that force is no longer concentrated against one or two targets at a given moment of time. Rather, force is distributed widely throughout the enemy state, thus significantly complicating the problems for the defense and rendering an adequate response far more difficult.

Parallel warfare is metaphorically tied to adaptation of complex systems. The objective of parallel warfare is to so rapidly modify the environment that the enemy is incapable of reacting to the changes. Borrowing Boyd’s terminology, the attack creates environmental change on a time scale shorter than the enemy’s OODA cycle time. The opponent can no longer sense the changes, and consequently cannot react—adapt—appropriately. The attack has "gotten within the enemy’s OODA loop."

Parallel warfare is crucial to the Five Rings model. To a certain degree, it enables Warden to decouple the physical from the morale side of warfare. By depriving the enemy of a coherent response, he can no longer repair or adapt to the destruction of his physical resources. In the theoretical limit of attacking everything simultaneously, the physical side of the enemy may indeed decouple from the morale and reduce to the finely jeweled watch. In the opposite theoretical limit of prolonged serial warfare, the physical and morale sides are inseparable. Warden’s key assumption depends heavily upon the rapid environmental changes created by parallel warfare.

The modern theories of airpower we examined are more closely tied to complexity theory than their predecessors. The Five Rings model shares characteristics of complex adaptive systems, yet still has Newtonian aspects. When coupled with parallel warfare, it moves more closely to the complex paradigm. Boyd uses the language and concepts of complexity, recognizing that his models are indeed part of new paradigm. The impact of the new sciences is more clearly felt in modern airpower theories than in their earlier relatives.


Airpower theory is indeed transitioning from the Newtonian to the complex paradigm. The early theories of Douhet and Mitchell went beyond existing military thought, taking into consideration the revolutionary capabilities the airplane brought to warfare. Yet their concepts fell within the Newtonian paradigm. By the mid-1930s, the industrial web model incorporated some of the characteristics of complex adaptive systems. However, the behavioral aspects of complex systems were not clearly recognized, especially with respect to strategic substitution and adaptation. The theories of the WWII era were thus a mixture of complex and Newtonian ideas. In modern times, theoreticians have moved more closely toward the new sciences. Warden’s Five Rings model coupled with parallel warfare incorporate many characteristics and behaviors of complex adaptive systems. Boyd’s theories have made the transition, as he identifies his insights and the OODA loop with complex systems and their behaviors.


The complex paradigm provides a powerful metaphor for airpower. We will only gain from its insights if we frame our theories within the new paradigm and apply those theories in combat. In the preceding section we examined existing theories for Newtonian or complex aspects, and categorized them accordingly. We will now take the next important step by applying concepts from complexity-based airpower theories to practice. As an example, we will examine targeting modern economic systems.

Economies are complex adaptive systems.58 ACTS took the first steps toward this realization with its industrial web theory. However, we can go far beyond the web by examining the nature of its interconnections further. The agents in an economy are very intricately interwoven. The linkages have a variety of characteristics, including:

The linkages lead to synergies and dependencies of various agents upon each other. Backup systems, workarounds, repairs, tactical and strategic substitution, and human ingenuity provide the economy with flexibility and adaptability in the face of disasters. An economic system is without doubt complex and adaptive, and must be targeted accordingly.

Given this nature of an economy, what insight can the complex paradigm provide the planner? Perhaps most important is that a reductionist targeting approach is limited and may overlook important emergent system behaviors. We saw that targeting frequently followed the reductionist methodology: the planner selects target sets, then chooses aimpoints in each set without considering the linkages between sets. These linkages are critical, as they give rise to cross-system effects such as cascading breakdowns. By ignoring the linkages, the planner suppresses these effects. At best, the result is a campaign plan that inaccurately portrays the system-wide effects of destroying the selected targets. At worst, the result is a plan that fails to accomplish its objectives. What is required is a holistic targeting methodology that incorporates the linkages and synergies—an approach that targets the economy as a whole.

Engineering analysis tools and computer simulation techniques may provide the key to holistic targeting. Industry regularly uses engineering analysis tools to plan, design, and operate many sectors of an economy. Electrical utilities use circuit analysis techniques to manage their grids, develop contingency plans, and design for future growth. Similarly, water utilities and petroleum pipeline companies employ hydraulic analyses in their daily operations. The same is true for other elements of an economy, including communications, transportation, and natural gas distribution, to name a few. Collectively, these engineering techniques are called nodal analyses. The important point is that nodal analyses can determine the effects of the loss of one or more elements in a network. By analogy, a military planner could use the same tools to determine the effects of destroying certain network elements. It may be possible to further extend this idea, by considering several sectors of an economy together and determining the cross-sector effects with coupled nodal analyses. Yet a further extension would couple complex adaptive computer optimization routines such as genetic algorithms to nodal analyses to "evolve" target sets inside a computer.59 In this case, the planner would be targeting a complex adaptive economy with a complex adaptive system. By incorporating the linkages between sectors in an economy, targeting moves from reductionist to holistic, taking into deeper consideration the nature of the economy and the way it will respond to an attack.

In this example, we have gone beyond simple metaphorical comparisons of complexity science to airpower. Starting from the complex paradigm, we theorized that modern economies are complex adaptive systems. We then applied a principle from complexity science to a practical problem by examining holistic targeting. The result was a proposed methodology for targeting that may provide greater insight into the manner by which the enemy economy will respond to an attack. It is only in applying theory developed within the complex paradigm to practical problems that we can take advantage of what complexity science has to offer, and that we put the complex rubber on the ramp.


Warfare is indeed a nonlinear, complex, adaptive phenomenon with two or more coevolving competitors. Airpower theory has gradually moved to this viewpoint, albeit without conscious effort until recently. Early airpower theories were firmly locked in the Newtonian paradigm. The transition to the complex paradigm began at ACTS, with the development of the industrial web theory. The transition has accelerated in the last few years, to the point where complexity has been explicitly called upon in several airpower theories and analyses. The shift away from the Newtonian paradigm must continue, as the paradigm is too limited to capture the essence of warfare. Only through the complex paradigm will theorists and strategists fully understand and capitalize upon the complex, nonlinear nature of warfare.

We must, however, move beyond simple metaphorical comparisons or analyses within the complex paradigm. The insights from complexity will have their greatest utility in practical applications. We saw this in the example of targeting modern economies. To employ Newtonian techniques to an inherently complex phenomenon hampers flexibility, inhibits creativity, and significantly limits our comprehension of the operational environment. We must formulate airpower theories within the complex framework and use the resulting insights in operational applications. To remain locked in the Newtonian paradigm will only deny airpower its full potential in future conflicts.

End Notes

1. John F. Schmitt, "Chaos, Complexity & War: What the New Nonlinear Dynamical Sciences May Tell Us About Armed Conflict" (Quantico, VA: Marine Corps Combat Development Command, 4 September 95), 16-25.

2. E. C. Zeeman, "Catastrophe Theory," Scientific American, vol. 234, no. 4 (April 1976), 65-83; E. C. Zeeman, Catastrophe Theory: Selected Papers, 1972-1977 (Reading, Mass: Addison-Wesley Publishing Company, 1977).

3. The chaos theory literature is vast. Excellent introductions include James Gleick, Chaos: Making a New Science (New York: Penguin Books, 1987); James P. Crutchfield et al, "Chaos," Scientific American, vol. 255, no. 6 (December 1986), 46-57; and Celso Grebogi et al, "Chaos, Strange Attractors, and Fractal Basin Boundaries in Nonlinear Dynamics," Science, vol. 238, no. 4827 (30 October 1987), 632-638.

4. A general introduction to complexity is M. Mitchell Waldrop, Complexity: The Emerging Science at the Edge of Order and Chaos (New York: Simon & Schuster, 1992). A more technical overview of the field is given in Grégoire Nicolis and Ilya Prigogine, Exploring Complexity: An Introduction (New York: W. H. Freeman and Company, 1989).

5. For applications of catastrophe theory to warfare, see Zeeman (1976), 76-77; Zeeman (1977), 16-17. Chaos and warfare are explored in Todor D. Tagarev et al., Chaos in War: Is It Present and What Does It Mean? (Maxwell AFB, AL: Air Command and Staff College, 1994); Pat A. Pentland, Center of Gravity Analysis and Chaos Theory or How Societies Form, Function, and Fail (Maxwell AFB, AL: Air War College, 1994). Applications of complexity theory to warfare are presented in Thomas J. Czerwinski, "Command and Control at the Crossroads," Marine Corps Gazette (October 1995), 13-15; Schmitt; and Steven M. Rinaldi, Beyond the Industrial Web: Economic Synergies and Targeting Methodologies (Maxwell AFB, AL: Air University Press, April 1995).

6. For example, we can expand the nonlinear system as a Taylor series, and keep only the constant and first-order (linear) terms. We then solve the linearized equations. This technique is frequently employed in the sciences and engineering.

7. Schmitt, 17-22.

8. The air campaigns in World War II generally followed this philosophy. See, for example, AWPD/1: Munitions Requirements of the Army Air Forces to Defeat Our Potential Enemies, 12 August 1941, USAF Historical Research Agency (hereafter HRA) file 145.82-1; and AWPD/42: Requirements for Air Ascendancy, 1942, HRA file 145.82-42.

9. Schmitt, 16-25.

10. Lee A. Segel, "Grappling with Complexity," Complexity, vol. 1, no. 2 (1995), 18-25.

11. The couplings between agents may be tight or loose, branching or sequential, and may contain feedback and/or feedforward paths. Rinaldi, 8-9.

12. Roger Lewin, Complexity: Life at the Edge of Chaos (New York: Macmillan Publishing Company, 1992), 12-13, 47.

13. P. W. Anderson, "More is Different," Science, vol. 177, no. 4047 (4 August 1972), 393-6.

14. Nicolis and Prigogine, 13.

15. Stuart A. Kauffman, The Origins of Order: Self-Organization and Selection in Evolution (New York: Oxford University Press, 1993), 173.

16. Nicolis and Prigogine, Chapter 1.

17. Kauffman, 173; Lewin, 48-55; Nicolis and Prigogine, 8.

18. Kauffman, 173.

19. Compare to the Organization Process Model II in Graham T. Allison, Essence of Decision: Explaining the Cuban Missile Crisis (HarperCollins Publishers, 1971), Chapter 3.

20. Lewin, 15, 138; Waldrop, 145-47.

21. John R. Boyd, "A Discourse on Winning and Losing," unpublished briefing and essays, Air University Library, document no. MU 43947 (August 1987). In particular, see p. 5 of Chapter 1, "Patterns of Conflict."

22. Giulio Douhet, The Command of the Air (Washington, D.C.: Office of Air Force History, new imprint, 1983), 142.

23. Ibid, 58.

24. Ibid, 25, 142.

25. Ibid, 28-32. Note that his arguments must be taken in the context of the geostrategic position of Italy.

26. Ibid, 99, emphasis in original.

27. William Mitchell, Skyways: A Book on Modern Aeronautics (Philadelphia: J. B. Lippincott Company, 1930), 255.

28. Ibid, 253.

29. William Mitchell, Winged Defense (New York: Dover Publications, Inc., 1988, reprint of 1928 original publication), 10, 126-7.

30. William Mitchell, Our Air Force: The Keystone of National Defense (New York: E. P. Dutton & Company, 1921), xix, xxi.

31. Mitchell (1988 reprint), 133.

32. Douhet, 11-12.

33. Ibid, 17, 55, 218-219, 239. His argument, of course, does not foresee the development of radar and modern defensive air control concepts.

34. Ibid, 20-22, 35-41, 50.

35. One may argue that it is unfair to mention that Douhet’s and Mitchell’s theories did not include any concepts from complexity, as the science would not arise for another 60 years. However, as Beyerchen has eloquently argued, Clausewitz’s theory of war included many concepts from nonlinear dynamics and chaos theory—two sciences developed some 130 years after his death. Alan Beyerchen, "Clausewitz, Nonlinearity, and the Unpredictability of War," International Security, vol. 17, no. 3 (Winter 1992/93), 59-90.

36. Major Muir S. Fairchild, "National Economic Structures" (Maxwell Field, AL: Air Corps Tactical School Lecture, 5 April 1939), 8-9.

37. "Principles of War Applied to Air Force Action" (Maxwell Field, AL: Air Corps Tactical School Lecture, 1934-1935), 3.

38. "Air Force Objectives" (Maxwell Field, AL: Air Corps Tactical School Lecture, 1934-1935), 5, 8.

39. Ibid, 2.

40. "Principles of War Applied to Air Force Action," 2-3.

41. Ibid, 5.

42. Ibid, 7-8. Emphasis in original.

43. Fairchild, 5.

44. Haywood S. Hansell, Jr., The Air Plan that Defeated Hitler (Atlanta: Higgins-McArthur/Longino & Porter, Inc., 1972), 49-51.

45. Ibid, 79.

46. Memorandum to Lieutenant General Arnold, 8 March 1943, Subject: Report of Committee of Operations Analysts with Respect to Economic Targets Within the Western Axis. Guido R. Perera, "History of the Organization and Operations of the Committee of Operations Analysts, 16 November 1942–10 October 1944," Vol. II, Tab 22, HRA file 118.01.

47. Carl Kaysen, "Note on Some Historic Principles of Target Selection," U.S. Air Force Project RAND Research Memorandum RM-189 (15 July 1949).

48. See footnote 11.

49. Kayson, 5.

50. Mancur Olson, Jr., "The Economics of Target Selection for the Combined Bomber Offensive," RUSI Journal, vol. CVII (November 1962), 308-314.

51. Ibid, 312.

52. John A. Warden III, "The Enemy as a System," Airpower Journal, vol. IX, no. 1 (Spring 1995), 40-55; John A. Warden III, "Employing Air Power in the Twenty-first Century," in The Future of Air Power in the Aftermath of the Gulf War, edited by Richard H. Shultz, Jr. and Robert L. Pfaltzgraff, Jr. (Maxwell Air Force Base: Air University Press, July 1992), 57-82.

53. Warden (1995), 43.

54. Boyd, 5. He introduces his concept on page 5 of Chapter 1, "Patterns of Conflict," and develops it with historical examples.

55. Kauffman, 232. Although Kauffman is discussing biological systems, complex systems in other domains process information in essentially the same manner.

56. John R. Boyd, "The Essence of Winning and Losing," unpublished notes (28 June 1995), 4, emphasis in original.

57. Warden (1995), 54.

58. For a detailed examination of economies as complex adaptive systems and the implications for targeting, see Rinaldi.

59. Ibid, Chapter 4.

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