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A growing number of writers have noted the interesting—and useful—congruence between Clausewitz's world-view and that of modern nonlinear mathematics and the science reflected in Complexity Theory. Because this way of approaching Clausewitz is so different from the traditional military and historical approach, The Clausewitz Homepage has created this separate section devoted to its pursuit. Many of the items linked are also part of the traditional section.

"Thus, when Clausewitz speaks of war as a "total phenomenon," he is not talking about war in the abstract (ideal or absolute war), nor about war "in theory." He is talking about real war, war as we actually experience it, and he is describing just why it is that war is so dynamic, so unpredictable, so kaleidoscopic in its appearance. The visual metaphor provided in Clausewitz's discussion of his famous "trinity" in On War is a nearly exact analogy: Clausewitz is saying that theory must be, as war is, "like an object suspended among three sources of attraction." He is referring to the observed scientific fact that such a pendulum, once set swinging among three centers of attraction, behaves in a nonlinear manner: it never establishes a reliably repeating pattern. As it enters a phase of its arc in which it is more strongly affected by one force than the others, it gains a momentum which carries it on into zones where the other forces can begin to exert their powers more strongly. The actual path of the suspended object is never determined by one force alone but by the interaction between them, which is forever and unavoidably shifting. It is a classic demonstration of "deterministic chaos." The essence of this trinity lies not its components but in their dynamic interaction. Attempts to render the trinity graphically as a static triangle, pyramid, or even pair of pyramids miss this point entirely."

Christopher Bassford
"Clausewitz and His Works"

Click above to watch a video of Clausewitz's powerful visual metaphor.


rotating star symbol Illustrations of Chaotic Systems: Some useful images, videos, animations, Java apps, and Flash demos.

An Introduction to Chaos — David M. Harrison, (Department of Physics, U. Toronto)
See also: The Three-Body Problem Illustrated.

Clausewitz, Nonlinearity and the Unpredictability of War — Alan D. Beyerchen (Department of History, Ohio State University), International Security, 17:3 (Winter, 1992). Probably the most important article on Clausewitz since 1976.

Fractals — Definitions and Links.
(See also NOVA video, "Hunting the Hidden Dimension: Mysteriously beautiful fractals are shaking up the world of mathematics and deepening our understanding of nature." Aired October 28, 2008 on PBS.

Clausewitz and Nonlinearity Bibliography — from The Clausewitz Homepage.

Nonlinearity and Military Affairs — A working bibliography put together by Tom Czerwinski, Information Resources Management College, National Defense University, in 1999.

Illustration: "The Butterfly Effect" 2

Illustration: A "Fitness Landscape"

Illustration: "The Butterfly Effect" 1

Mitchell M. Waldrop, Complexity: The Emerging Science At The Edge Of Order And Chaos (Simon & Schuster, 1992). Waldrop tells us the historical development of the birthing ground of Complexity science, the Santa Fe Institute. However, his main subject is complexity science itself and its implications. As one reviewer puts it, "He not only tells you what Complexity IS, but WHY you should care about it." As with James Gleick's Chaos, this is must reading for any 21st-century Clausewitzian wannabe. (See Alan D. Beyerchen's essay on the connection.) ISBN: 0671872346.

John Lewis Gaddis, The Landscape of History: How Historians Map the Past (New York: Oxford University Press, 2004).
Is history a science? Gaddis, perhaps the most prominent historian of the Cold War and often called the "dean of American diplomatic history"," answers these and other questions in this short, witty, searching look at the historian's craft. Historians combine the techniques of artists, geologists, paleontologists, and evolutionary biologists, paralleling in intriguing ways the "new sciences" of chaos and complexity, but not the social sciences, where the pursuit of independent variables functioning within static systems seems divorced from the world as we know it. ISBN: 0195171578.

James Gleick, Chaos: Making a New Science (New York: Viking, 1987). In the 20th-anniversary edition of this now-classic work, Gleick, formerly a science writer for the New York Times, depicts the beginnings of Chaos theory, which draws on the seemingly random patterns that characterize many natural phenomena. It explains the thought processes and investigative techniques of Chaos scientists, illustrating concepts like Julia sets, Lorenz attractors, and the Mandelbrot Set with  sketches, photographs, and wonderful descriptive prose. Must reading for any Clausewitzian. (See Alan D. Beyerchen's essay on the connection.) ISBN: 0143113453.

Michael Cross, Professor of Theoretical Physics, CalTech

Military Applications of Chaos Theory (Air University)

Journal coverEmergence: Complexity & Organization
An International Transdisciplinary Journal of Complex Social Systems.

Cliodynamics logo Cliodynamics: The Journal of Theoretical and Mathematical History
The 2011 special issue, the journal's second edition, leads with an editorial, "An Inquiry Into History, Big History, and Metahistory," by SFI Faculty Chair David Krakauer, John Gaddis (Yale University), and Kenneth Pomeranz (UC Irvine). The authors define "history" as the study of written records, "big history" as all reconstructions of the past that do not rely on written materials, and "metahistory" as the "patterns that emerge from both modes of inquiry that make generalization, and hence analysis, possible."

Santa Fe Institute Logo The Santa Fe Institute


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