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Land Warfare and Complexity Part 1

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CIM 461/July 1996

Land Warfare and Complexity, Part I: Mathematical Backgorund and Technical Sourcebook (U)

Andrew Ilachinski

Center for Naval Analyses4401 Ford Avenue $Alexandria, Virginia 22302-1498

"So a military force has no constant formation, water has no constant shape: the ability to gain victory by changing and adapting according to the opponent is called genius." -- The Art of War, Sun Tzu (4th century B. C.)

"Strategy is a system of expedients. It is more than a science: it is the application of knowledge to practical life, the development of thought capable of modifying the original guiding idea in the light of ever-changing situations; it is the art of acting under the pressure of the most difficult conditions." -- Helmuth von Moltke (1800-1891)

"Everything is very simple in war, but the simplest thing is difficult. These difficulties accumulate and produce a friction, which no man can imagine exactly who has not seen war...This enormous friction, which is not concentrated, as in mechanics, at a few points, is therefore everywhere brought into contact with chance, and thus facts take place upon which it was impossible to calculate, their chief origin being chance." -- Carl von Clausewitz (1780-1831)

"Like friction and uncertainty, fluidity is an integral attribute of the nature of war. Each episode in war is the temporary result of a unique combination of circumstances, requiring an original solution. But no episode can be viewed in isolation. Rather, each merges with those that precede and follow it -- shaped by the former and shaping the conditions of the latter -- creating a continuous, fluctuating fabric of activity replete with fleeting opportunities and unforeseen events. Success depends in large part on the ability to adapt to a constantly changing situation." "The occurrences of war will not unfold like clockwork. Thus, we cannot hope to impose precise, positive control over events. The best we can hope for is to impose a general framework of order on the disorder, to prescribe the general flow of action rather than to try to control each event." -- Warfighting, FMFM-1

Land Warfare and Complexity, Part I: Mathematical Background and Technical Sourcebook

OverviewThe purpose of this paper is to provide the theoretical framework and mathematical background necessary to understand and discuss the various ideas of nonlinear dynamics and complex systems theory and to plant seeds for a later, more detailed discussion (that will be provided in Part II of this report1) of how these ideas might apply to land warfare issues. This paper is also intended to be a general technical sourcebook of information.

Two Intriguing QuestionsQuestion 1: What does the behavior of the human brain have in common with what happens on a battlefield? The human brain is composed of about ten billion neurons, each of which, on average, is connected to about a thousand other neurons. What each neuron does is a complicated function of what it did before and what its thousand or so neighbors were doing. Somehow, mysteriously, for reasons that are still not quite clear and perhaps never will be fully, this cauldron of ceaseless neuro-chemical activity spawns something called "consciousness" that emerges on a much higher level than the one on which any of the brain's constituent parts themselves live. Nowhere is there a prescription for an "awareness of self." Nowhere is there a hard-wired rule that says this arrangement of neurons will prefer football to boxing and that arrangement will prefer soccer to both. Nowhere on the neuronal level is there a rule that assigns the personality that is uniquely mine. These are all emergent, higher-level phenomena that, while owing their existence to the myriad interactions of ten billion neurons, cannot be deduced directly from them. As such, the human brain is the prototypical example of a complex system, or a system composed of many nonlinearly interacting parts. Now, what happens on a battlefield? While no battlefield can possibly consist of as many combatants as there are neurons in a human brain, the analogy between what makes the human brain "interesting" and what makes that which happens on a battlefield "complicated" is not such a poor one. Both consist of a large number of nonlinearly interacting parts whose individual behavior depends on the action and pattern of behavior of other (nearby and not-so-nearby) parts, both obey a decentralized control, both appear to be locally "chaotic" but harbor long-range order, both tend not to dwell for long times near equilibrium, preferring instead to existLand Warfare and Complexity, Part II: An Assessment of the Applicability of Nonlinear Dynamics and Complex Systems Theory to the Representation of Land Warfare is scheduled to be delivered to sponsor for review 1 July, 1996.1

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Land Warfare and Complexity, Part I: Mathematical Background and Technical Sourcebook

almost exclusively in a nonequilibrium state, and both must continually adapt to internal and external pressures and to the environment. On paper, at least, the human brain and the battlefield appear to have much in common. Question 2: Might there be higher-level processes that emerge on the battlefield, in the way consciousness emerges in a human brain? Both of these enormously difficult, yet intriguing, questions are clearly meant to be taken rhetorically (at least for the moment). However, the motivation behind asking these two questions is what lies at the heart of this report and the overall project of which it is a part. The goal of this paper is to provide the reader with a basic set of tools and concepts out of which a tentative real answer to this question might conceivably (some day) emerge. A hint that these questions are neither ill-posed nor simply foolish is provided by an emerging new field of research that can loosely be called complex systems theory. In recent years there has been a rapid growth in what has come to be popularly known as the New Sciences of Complexity. Despite being somewhat of a misnomer, because the science is arguably more a philosophy of looking at behaviors of complex systems than a rigorous well-defined methodology, this emerging field nonetheless has many potentially important new insights to offer into the understanding of the behaviors of complex systems. A complex system can be thought of, generically, as any dynamical system composed of many simple, and typically nonlinearly, interacting parts. A complex adaptive system is a complex system whose parts can evolve and adapt to a changing environment. Complex systems theory is then the study of the behavior of such systems, and is rooted in the fundamental belief that much of the overall behavior of diverse complex systems -- such as natural ecologies, fluid flow, the human brain, the Internet, perhaps even on the battlefield, etc -- in fact stems from the same basic set of underlying principles. While research in this still-developing field has yet to produce an all-encompassing theory of complexity, it has already introduced promising new analytical methodologies and has uncovered many provocative and useful organizing principles. The fundamental challenge of this study is to assess what insights into the understanding of land warfare can be gained by using the tools and methodologies developed for the general study of nonlinear dynamics and complex systems.

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Land Warfare and Complexity, Part I: Mathematical Background and Technical Sourcebook

Two Words of CautionBefore we begin the discussion in earnest, two important words of caution are in order. The two words are infancy and buzzwords.

InfancyRemember that, at the present time, complexity cannot be regarded as anything but an infant science! The Santa Fe Institute in New Mexico, for example, which is widely recognized as being a leading research center for complex systems, was founded just a decade ago in 1984. Moreover, many of the analytical tools and models developed for the study of complex systems, such as genetic algorithms and agent-based simulations, have been either developed or refined as part of the artificial-life research effort that itself sprang up only in 1987. Consequently, it would be premature -- and unfair to complex systems theory -- to expect to find a mature set of tools and methodologies at such an early stage of this burgeoning field's development. Indeed, it is fair to say that it is as difficult to predict the potentially deep and lasting implications of research in complex systems theory as it is understood and practiced today as it would have been difficult to predict the implications of the state-of-the-art in, say, thermodynamics as it was understood circa 1820. As was true of thermodynamics then, 60 or so years prior to its full maturation, it is true to say of complex systems theory now, that the "killer application" (as it is often called in commercial software circles) or the "killer insight" (as it is sometimes called in physics) has not yet been born. We stress that all speculations about possible applications of complex systems theory, whether they appear in this report or elsewhere, must be interpreted in this light.

BuzzwordsMany buzzwords have appeared in the popular literature in recent years, not all of which have been described accurately. Terms and concepts such as new sciences, chaos, complexity, complex systems theory, complex adaptive systems, and so on, are commonly used to denote the ostensibly same fundamental core of principles. In fact, there is no universally agreed upon definition of complex systems theory. Complex systems theory is a catch-all phrase that embodies a remarkably wide variety of disciplines ranging from biology, chemistry, and physics to anthropology to sociology to economics. Its many subfields include (but are not lim

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