Complexity versus chaos


Jason Collins


December 18, 2014

Another clip from David Colander and Roland Kupers’s Complexity and the Art of Public Policy: Solving Society’s Problems from the Bottom Up - a nice description of how two often confused terms, complexity and chaos, differ and interrelate:

Chaos theory is a field of applied mathematics whose roots date back to the nineteenth century, to French mathematician Henri Poincaré. Poincaré was a prolific scientist and philosopher who contributed to an extraordinary range of disciplines; among his many accomplishments is Poincaré’s conjecture that deals with a famous problem in physics first formulated by Newton in the eighteenth century: the three body problem. The goal is to calculate the trajectories of three bodies, planets for example, which interact through gravity. Although the problem is seemingly simple, it turns out that the paths of the bodies are extraordinarily difficult to calculate and highly sensitive to the initial conditions.

One of the contributions of chaos theory is demonstrating that many dynamical systems are highly sensitive to initial conditions. The behavior is sometimes referred to as the butterfly effect. This refers to the idea that a butterfly flapping its wings in Brazil might precipitate a tornado in Texas. This evocative—if unrealistic—image conveys the notion that small differences in the initial conditions can lead to a wide range of outcomes.

Sensitivity to initial conditions has a number of implications for thinking about policy in such systems. For one, such an effect makes forecasting difficult, if not impossible, as you can’t link cause and effect. For another it means that it will be very hard to backward engineer the system—understanding it precisely from its attributes because only a set of precise attributes would actually lead to the result. How much time is spent on debating the cause of a social situation, when the answer might be that it simply is, for all practical purposes, unknowable? These systems are still deterministic in the sense that they can be in principle specified by a set of equations, but one cannot rely on solving those equations to understand what the system will do. This is known as deterministic chaos, but is mostly just called chaos.

While chaos theory is not complexity theory, it is closely related. It was in chaos theory where some of the analytic tools used in complexity science were first explored. Chaos theory is concerned with the special case of complex systems, where the emergent state of the system has no order whatsoever—and is literally chaotic. Imagine birds on the power line being disrupted by a loud noise and fluttering off in all directions. You can think of a system as being in these three different kinds of states, linear, complex, or chaotic—sitting on the line, flying in formation, or scrambling in all directions.

Like chaos theory, complexity theory is about nonlinear dynamical systems, but instead of looking at nonlinear systems that become chaotic, it focuses on a subset of nonlinear systems that somehow transition spontaneously into an ordered state. So order comes out of what should be chaos. The complexity vision is that these systems represent many of the ordered states that we observe—they have no controller and are describable not by mechanical metaphors but rather by evolutionary metaphors. This vision is central to complexity science and complexity policy.