- By Joshua Keating
Joshua Keating was an associate editor at Foreign Policy
This year marks that 50th anniversary of the branch of mathematics known as chaos theory. Appropriately enough for a field of study premised on the idea that seemingly insignificant events can have large and unpredictable consequences, the eureka moment of chaos is generally considered to be a short dense paper titled "Deterministic Nonperiodic Flow" published on page 130 of volume 20 of the Journal of the Atmospheric Sciences in 1963.
As James Gleick writes in his very entertaining history, Chaos: Making of a New Science, "In the thousands of articles that made up the technical literature of chaos, few were cited more often than "Deterministic Nonperiodic Flow." For years, no single object would inspire more illustrations, even motion pictures, than the mysterious curve depicted at the end, the double spiral that became known as the Lorenz attractor."
The paper’s author, Edward Lorenz, was an MIT mathematician working on an early computer weather modeling simulation. One day in 1961, in an effort to save time waiting for his vacuum tube-powered Royal McBee computer to run the program, Lorenz started his simulation from the middle, manually entering in data from an earlier simulation, but crucially, rounding a six decimal point number to three decimal points in order to save space. What Lorenz found after returning from a coffee break was that these tiny, seemingly arbitrary changes in his initial inputs had led to vastly different outcomes in the weather models he created.
As Gleick writes, "Lorenz saw more than randomness embedded in his weather model. He saw a fine geometrical structure, order masquerading as randomness." Lorenz, who died in 2008, would later become best known for coining the metaphor of the "butterfly effect" to describe systems that are extremely sensitive to their initial conditions.
Most casual readers can’t understand much of the mathematics of chaos theory, but the basic principles were popularized thanks in part to Gleick’s bestselling book, not to mention the trippy Mandelbrot Set images that have graced countless screensavers and dorm room posters and, of course, Jeff Goldblum’s character in Jurassic Park.
Chaos doesn’t have quite the pop culture cachet that it used to, but the study of what Lorenz called nonlinear systems – those in which outputs are not necessarily proportional to inputs — has been highly influential in fields ranging from physics, to engineering, to astronomy, agriculture to economics. (One of the main themes of Gleick’s books is that researchers in different fields were often working along very similar lines without being aware of each other. Some of this work was actually going on years before Lorenz’s "discovery.")
The late mathematician Benoit Mandelbrot’s ideas about turbulence in financial markets have enjoyed something of a renaissance in recent years thanks the global financial crisis. I was lucky enough to get the chance to interview Mandelbrot for FP a year before his death.
But chaos has also had applications in some less obvious areas, such as politics and international relations. In fact, there’s an argument to be made that the ideas behind chaos are far more intuitive in the study of politics and armed conflict than in the natural sciences where it originated. Take, for example, the old English proverb that’s second only to the Butterfly Effect as a commonly used layman’s explanation for chaos:
For want of a nail the shoe was lost.
For want of a shoe the horse was lost.
For want of a horse the rider was lost.
For want of a rider the message was lost.
For want of a message the battle was lost.
For want of a battle the kingdom was lost.
And all for the want of a horseshoe nail.
What, after all, is a better example of chaos theory than the harassment of a street vendor in Tunisia leading to a civil war in Syria?
As Ohio State political scientist Alan Beyerchen has argued, Carl von Clausewitz seemed to have an intuitive grasp of the idea of nonlinear systems and chaos more than a century before anyone used those terms. Take, for example, this passage from On War:
[I]n war, as in life generally, all parts of the whole are interconnected and thus the effects produced, however small their cause, must influence all subsequent military operations and modify their final outcome to some degree, however slight. In the same way, every means must influence even the ultimate purpose.
In more recent times, ideas from chaos and its related subfield complexity theory influenced the writing of Columbia International Relations theorist Robert Jervis, who in his book System Effects¸ argues that many social scientists don’t adequately grapple with the fact that interconnected actors in a complex system can produce results that seem like vastly more or vastly less than the sum of the system’s parts. Our own Stephen Walt summarized the argument in a review for the Atlantic back in 1998:
Because system effects are everywhere, Jervis emphasizes, "we can never do merely one thing." Any step we take will have an infinite number of consequences, some that we intend and others that we neither intend nor foresee. A military buildup may deter a threatening adversary and help to preserve peace, for example, but it may also divert funds from other social needs, encourage one’s allies to free-ride, and cause formerly neutral states to become friendlier with one’s rivals. The more complex the system and the denser the interactions between the parts, the more difficult it is to anticipate the full effects of any action.
More recently, some political scientists have tried to apply chaos to international relations even more explicitly. The Dutch military analyst Ingo Piepers, for instance, sees relations between great powers over the last five centuries as a complex system moving toward "attractors" like those described by Lorenz in his weather model.
Political scientists Joan Pere Plaza i Font and Dandoy Regis put together a very good and readable overview of chaos theory’s applicability to political science in 2006. They write:
Chaos theory is particularly useful in the field of peace research. First, the more diverse possibilities are actualized in a given situation, in terms of both actors’ roles and interactions between actors, the greater the likelihood of peace. Peace will therefore occur in states with high entropy, meaning that increasing disorder, messiness, randomness and unpredictability will bring more peace than it could occur in predictable or excessive ordered cou
ntries. Second, chaos theory aims to model whole systems, looking at overall patterns rather than isolating the cause-and-effect relations of specific parts of a system. Through this approach, chaos theory has discovered that many social systems are not simply orderly or disorderly. Some are orderly at times and disorderly at other times. Others are in constant chaotic motion, yet display an overall stability.
In an ambitiously titled 2007 paper, "A Chaotic Theory of International Relations? The Possibility for Theoretical Revolution in International Politics" the IR theorist Dylan Kissane argues that a view of international relations derived from chaos theory provides an alternative to both the realist view of an international system defined by anarchy and the liberal view that highlights interdependence. Kissane writes that "chaos better reflects the reality of an international system where individuals and non-state actors can have a significant effect at the international or system level."
Much of Kissane’s analysis is concerned with the distrution of power between actors in a chaotic system. "Unlike the anarchy of neorealist theory, chaos does not favour one distribution of power or security to another in terms of bringing stability to the system," he writes.
Kissane also discusses one of the primary limitations of the "chaotic theory" by quoting the late Kenneth Waltz’s argument that "success in explaining, not in predicting, is the ultimate criterion for a good theory." Chaos may not fully pass this test:
"A theoretical approach to international relations that expects that anything can occur within the system and which simultaneously cannot fully explain why such an event occurred – outside some basic notions arising from the nature of the system – may not be much of a theory at all."
This may be where "Big Data" – a concept as trendy today as chaos was 20 years ago – comes into play. Back in the late 1950s and early 1960s – around the same time Lorenz was doing his research on weather – many believed that the power of computers would eventually allow social movements and political trends to be predicted with a great degree of accuracy.
Today, most theorists have more modest goals. Chaotic systems are extremely difficult to predict in the long run, but they’re also not entirely random – as Lorenz observed – and with enough detailed information, patterns emerge allowing short-term predictions to be made, though always with a degree of uncertainty. As Kalev Leetaru told me recently discussing the GDELT events database, "Most datasets that measure human society, when you plot them out, don’t follow these nice beautiful curves," he says. They’re very noisy because they reflect reality. So mathematical techniques now let us peer through that to say, what are the underlying patterns we see in all this."
In other words, we’re hopefully getting better at analyzing patterns in war, peace, and social movements the same way Lorenz did in the months and years following his fateful coffee break.