The study of chaos, like the study of any performative genre, must begin by acknowledging the mutable properties of a process that evolves through space and time. As chaos theory tells us, a seemingly stable system may progress undisturbed indefinitely, until, at one moment, the system suddenly becomes "chaotic," or ceases to proceed in an orderly manner. Chaos theorists have routinely concentrated on these moments of transition from stability to chaos, illuminating the importance of what has previously been perceived of as systematic irregularities or statistical "dirt" (the elements that traditional scientific inquiry is unprepared to acknowledge and has generally pushed to the margins or completely ignored).

Like deconstruction, chaos theory focuses on the elements that don't quite fit within a system in an orderly, logical way. Both offer analytical techniques focused on the interrelationship of contrasting elements, but chaos theory is able to do so without the self-devouring impasse of non-communication. By examining such "natural" occurrences as the weather, the onset of turbulence, and the fluctuations of the stock market, chaos theorists have devised a methodology to approach systems that appear to move in completely random directions.

For example, take a simple dynamical system (a system in motion that varies with an inconsequential amount of randomness) like a pendulum. Given the correct energy boost at the proper time a pendulum will run indefinitely in a precise and orderly manner (nearly any clock can attest to this). The same is true for a double pendulum (essentially one pendulum hung underneath another). Given the proper periodic boost it will follow a smooth motion. However, give it just a slight extra amount of energy and that smooth motion will become a chaotic rhythm (or arrhythm).

To illustrate this transformation from an orderly to a chaotic system "chaotician" James Yorke stated (in a recent lecture) that most physics textbooks only cover the first type of regular rhythmic activity. "He then gave the double pendulum a hefty swing, which caused it to execute exquisitely complex chaotic motion, and remarked that, apparently, until twenty years ago no one ever swung that hard."⁵ Externally (from our vantage point) the chaotic movement of the double pendulum appears to be completely random, following a jerky, irregular pattern. What is fascinating about this example is that this irregular movement conforms to a logical structure that is completely internal to the system. What may be looked at as chaotic is in reality a complex dynamic system controlled by, and dependent upon, all of the factors involved. The movement of the double pendulum is determined by the relationship that each of the variables (the initial energy boost, the previous swing, the following swing, etc.) has to do with the system as a whole. So, while the tag "chaos theory" may seem to indicate a search for total randomness, the study of various chaotic systems has revealed underlying patterns of an unpredictable order.⁶

This discussion of the interaction of elements that comprise a chaotic system must be grounded in a philosophical position that is concerned, not with the final product (as a static entity), but with a system in motion (a dynamic process). As Stephen Kellert points out in his book in the Wake of Chaos, "Chaos theory shows us that the need for diachronic methods of understanding is much broader than previously thought."⁷ It is impossible to examine a system like the arrhythmic movement of the double pendulum with the traditional scientific tools of hypothesis, theorem, controlled experimentation, and proof. Dynamic systems simply do not conform to any predetermined (synchronic) conclusions, but exist in space and time and demand the evolution and application of diachronic methods of analysis.

As Kellert further explains, "chaos theory does not provide predictions of quantitative detail but of qualitative features; it does not reveal hidden causal processes but displays geometric mechanisms; and it does not yield law-like necessity [as does Newtonian physics with its emphasis on predictability] but reveals patterns."⁸ This statement is echoed by James Gleick in perhaps the most accessible book on the subject, Chaos: Making a New Science, "To some physicists chaos is a science of process rather than state, of becoming rather than being."⁹

One of the most popular motive images in chaos theory is derived from a paper delivered to the American Association for the Advancement of Science in 1972 by Edward Lorenz entitled, "Predictability: Does the Flap of a Butterfly's Wings in Brazil Set off a Tornado in Texas?" The image, while both playful and striking, encapsulates an extremely important element of the study of chaos. As Lorenz describes, the storm created by the flap of the butterfly's wings represents a system that is "sensitively dependent on initial conditions," that is to say, every element present at the creation of the system is an integral part of how that system moves and evolves.

Lorenz's paper, although focused on the unpredictability of the weather, is essentially an essay on the concept of iteration. By taking a seemingly insignificant occurrence, like the flap of a butterfly's wings, and multiplying it again and again and again it is possible to create a fiercely uncontrollable system like a tornado (iteration should not be unfamiliar to anyone who has placed a microphone too close to a speaker, thereby allowing the sound to be "fedback" into the system and creating a squealing din from a whisper). ¹⁰ As Gleick points out, this sensitive dependence on initial conditions is not a recent discovery, but has its place in folklore:

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 battle was lost;
For want of a battle, the kingdom was lost! ¹¹

To review, chaos theory looked at from a philosophical position, stresses process over product, the interaction of all elements of a dynamic system, the sensitive dependence on initial conditions, iteration, the revelation of previously hidden patterns, and the evolution of a system driven by its own internal logic. What then do these abstract thoughts have to do with the concrete process of theatrical performance? Suppose, for example, we juxtapose two entirely different types of drama, the ordered linearity of Henrik Ibsen and the chaotic dynamism of what Bonnie Marranca has termed "The Theatre of Images."¹²