Chaos: Making a New Science

Part of the Second Law of Thermodynamics, entropy indicates that everything in the universe tends toward disorder. It has been interpreted to mean that “[t]he universe is a one-way street” (308) wherein all leads to chaos rather than to pattern. Chaos science calls this interpretation into question. With regard to entropy’s application to heat and energy, the Law holds; however, when used to describe other systems—economic, social, political, etc.—it breaks down: “Somehow, after all, as the universe ebbs toward its final equilibrium in the featureless heat bath of maximum entropy, it manages to create interesting structures” (308). Thus, using entropy as a metaphorical measure of the disorder within a given system is difficult at best and inappropriate at worst. Chaos science reveals how nature tends toward patterns within that disorder. Entropy is another concept about which chaos prompts new perspectives.

Coined by Benoit Mandelbrot, the term “fractals” initially described his insights based on geometry: Nature does not develop in smooth and easily measurable Euclidean shapes; rather, it resolves itself in rough and irregular ways. Thus, fractal geometry measures the potentially infinite crags and crannies that form around the boundary of finite area—as in the coast of Great Britain or the branching arms of a snowflake: “In the mind’s eye, a fractal is a way of seeing infinity” (98). Mandelbrot uses mathematics and models to demonstrate his innovative ideas, and “[f]ractional dimension becomes a way of measuring qualities that otherwise have no clear definition: the degree of roughness or brokenness or irregularity in an object” (98). This insight eventually led to the Mandelbrot set, which “seems more fractal than fractals, so rich is its complication across scales” (221). Using Julia sets—mathematical models that defy the rules of Euclidean geometry—the Mandelbrot set reveals that each island branching off of the original is distinct and unique.

In addition, fractals illuminate the “Humpty-Dumpty Effect”: Once something is broken, it can never quite be put back together because “surfaces in contact do not touch everywhere. The bumpiness at all scales prevents that” (106). Once a teacup is broken, even when glued back together, it will have gaps, whether visible or not. Thus, fractals also describe the chaotic nature of surfaces.

One of the most important contributions made by the Dynamical Systems Collective out of the University of California, Santa Cruz, was information theory. Information itself describes bits transmitted across electronic lines, which now include the internet; it does not necessarily imply meaning or factual knowledge. Information connects the small scales and the large within a system, and as a system tends toward chaos, it creates more information. When these scientists “spoke of systems generating information, they thought about the spontaneous generation of pattern in the world” (261)—that is, order within disorder.

In addition, information theory links to other ideas within chaos science: “[T]he channel transmitting the information upward is the strange attractor, magnifying the initial randomness just as the Butterfly Effect magnifies small uncertainties into large-scale weather patterns” (261). As the author emphasizes in both the original book and the Afterword added in 2008, chaos itself could be considered information.