Chaos: Making a New Science

James Gleick’s Chaos: Making a New Science (originally published in 1987) details the history and ideas of chaos theory, or chaos science. Many of these ideas have since become relatively mainstream; for example, a 2004 science fiction movie, The Butterfly Effect, was named for one of its key precepts. However, when Gleick was writing, in the mid-1980s, chaos was still a fairly revolutionary concept. Gleick, a renowned science historian, explores the breakthroughs that chaos science offers with regard to understanding how dynamic systems work in the material world, as well as the nascent understanding that fundamental, potentially universal laws of nature govern such systems. Chaos reveals that order lurks within seemingly disordered systems and that even the smallest parts within a system can impact the larger whole. In addition, chaos is an interdisciplinary science, connecting disparate fields such as physics and mathematics as well as ecology and biology. Chaos was a finalist for the Pulitzer Prize and the National Book Award.

This guide refers to the 1988 Penguin Books paperback edition.

Summary

Chaos begins by implicitly comparing the work of chaos scientists to that of the atomic bomb pioneers at Los Alamos National Laboratory in New Mexico during World War II. The implication is that this science, too, will reverberate with revolutionary impact. Each chapter discusses a particular development within the field of chaos science, while the book as a whole recounts the history of how the field came to exist. In addition, each chapter profiles a scientist, or group of scientists whose work contributes to this innovative discipline and its new ways of looking at and understanding the universe.

In Chapter 1, Gleick discusses one of the most well-known concepts within chaos theory, the butterfly effect. Growing out of Edward Lorenz’s early computer models of weather conditions, the butterfly effect describes how even very small events in one part of a system can impact the system as a whole—such as the impact of specific weather events on Earth’s overall climate. Of course, this effect is not limited to weather, and Lorenz’s work will continue to influence ideas about nonlinear systems and randomness for years to come.

Chapter 2 describes the ways in which scientific revolutions—like the discovery of chaos—developed amid controversy. Many of the scientists, like Stephen Smale, began to question the foundations of scientific understanding in various fields. Smale rethought the basic pendulum; instead of examining the parts of the pendulum’s trajectory, Smale studied the entire space within which a pendulum moves. This led to his vision of the horseshoe, wherein when space is stretched and folded, points that are far apart can end up quite close together (as the book illustrates on page 51). This changed the way that scientists in all disciplines understood geometry.

Chapters 3 and 4 explore this understanding via ecology and fractal geometry, respectively. Robert May’s work in tracking animal populations revealed the action of chaos within dynamic systems. Instead of simple exponential increases, as in a typical Malthusian model, biological populations showed both periods of stability and periods of chaos. However, May also saw within the moments of chaos clear “windows of order” (74). The paradox of chaos is that within apparent disorder are stability, pattern, and structure. The work of Benoit Mandelbrot broadened this understanding. His discovery of fractal geometry indicated that infinite variations exist within a finite space. For example, England’s coastline contains infinite twists and turns when viewed at the smallest scales yet encompasses a finite space.

In Chapter 5, the author describes how the discovery of strange attractors indicated that although nature displays constant disorder, it operates on an inherent sense of order. That is, within the randomness of many natural systems exists a strange attractor that follows an orderly and stable set of rules. Physicist Mitchell Fiegenbaum’s theories, discussed in Chapter 6, advanced these ideas, revealing that universality underpins the workings of nonlinear, dynamic systems, giving different systems identical behaviors. While Gleick does not explicitly state the connection, chaos scientists were working toward a unified theory of their own.

Another physicist, Albert Libchaber, wanted to show that physical experiments could prove the theories, as Gleick recounts in Chapter 7. His “Helium in a Small Box” experiment revealed that unpredictability was measurable; the disorder, or chaos, within a dynamic system follows a set of physically “reproducible” results. Thus, the material evidence confirmed Fiegenbaum’s theories. The use of computers to explore these newfound ideas in various fields expanded. Technology was instrumental to the continuing development of chaos science.

Chapters 8 and 9 describe how scientists began to explore new images of chaos: Mandelbrot sets became a standard way to illustrate how chaos theory explains the infinite variation within finite areas, as well as how boundaries—the places between phase transitions, for example, or from stability to turbulence—are complex sites rife with unpredictability. Scientists such as Michael Barnsley endeavored to reveal that even within infinite possibilities, nature organizes itself: Fundamental patterns repeat throughout various natural systems. The Dynamical Systems Collective, or Chaos Cabal, expanded on this understanding by researching information theory. The work of this group of young scientists from the University of California, Santa Cruz, suggested that chaos itself is information. Dynamic systems generate both information and, counterintuitively, repeated patterns within seemingly chaotic outputs.

Chaos theory eventually impacted the field of biology as well, as Chapter 10 outlines. The fractal geometry of Mandelbrot makes sense in describing the ever-branching network of systems, veins, and vessels within the human body. In addition, chaos suggests that accepting that the human structure embodies dynamism—because the body is in a constant state of motion—can be crucial to health. After all, a biological system in stasis predicates death.

In Chapter 11, the author discusses the impact of chaos theory on other fields, particularly physics and mathematics. By looking at old problems in new ways, chaos has increased the understanding of not only dynamic systems but also universal laws. The desire to examine and experiment on a holistic scale changes the definitions of specific scientific ideas, like entropy. Even within entropy are order, pattern, and stability. As the author notes in his Afterword, while the field of chaos theory has become accepted and well-established as a discipline in its own right, its discoveries continue to accumulate and challenge established notions of conventional science.