Chaos: Making a New Science

On an early computer, meteorologist Edward Lorenz created a weather simulation that generated interest among his colleagues, though it did not quite capture the weather as it actually behaved. Most meteorologists considered the idea of forecasting the weather akin to mere guessing rather than measurable science. Lorenz himself understood the limitations of his model. It could chart only particular measurements over a finite period of time. And, like most scientists, Lorenz simplified his program by rounding off measurements, assuming that such an incremental change would have virtually no impact on the final model. However, he discovered that he was wrong: In fact, the smallest changes in numerical measurements had outsized impacts on results. He both determined that long-term weather forecasting was impossible and understood that dynamic systems, such as climate, did not follow a standardized pattern: “I realized that any physical system that behaved nonperiodically would be unpredictable” (18).

This led to the understanding that even the smallest detail can have a significant impact on the larger whole, an understanding that has come to be called the “butterfly effect” (See: Index of Terms) or, technically speaking, “sensitive dependence on initial conditions” (23). Lorenz realized that these small impacts are inextricable from complex, dynamic systems, like weather. Events at the smallest scales inevitably affect what occurs on a larger scale. Through experiments such as the Lorenzian Waterwheel, Lorenz and others began to notice that nonlinear systems contained elements both of unpredictability and pattern; that is, order existed within the apparent disorder of interactions between even the smallest parts and the whole. When Lorenz mapped this idea on a computer, it displayed an image “like a butterfly with its two wings,” wherein no point overlapped or intersected with another, ad infinitum (30). While this might seem like the disintegration of scientific stability—infinite and never-repeating loops—the discovery instead signaled the need for a different way of studying dynamic systems.

The author summarizes the ideas of science historian Thomas S. Kuhn, who noted that science progresses not just through the steady accumulation of ideas but also through remarkable disruptions to accepted ideas—that is, revolutionary discoveries. If scientists always work from established foundations, without questioning received notions, they eventually reach “a dead end” (37). Thus, scientific revolutions are necessary to create new understandings about old problems; usually, these revolutions involve interdisciplinary collaborations, as chaos theory has. Still, any new science encounters resistance to its revolutionary ideas, and chaos is no different. Part of the problem with its early acceptance was its reliance on graphic images and the new generation of computers pioneered in the 1960s and 1970s. Many traditional scientists were skeptical of the legitimacy of these tools.

The pendulum returns to prominence in the new science of chaos precisely because the theoretical understanding of the way in which a pendulum works contradicts the actual behavior of a pendulum. When measurements of speed and friction are applied in a vacuum, the results are predictable; however, when a pendulum is set in motion outside of a vacuum, the results are not always predictable or uniform. Computers are better suited to calculate the subtle variations in different conditions that simulate the actual behavior. What many scientists, including Lorenz, found in these scenarios is that not only can unpredictability of pattern—chaos—be found, but pattern itself also can be discerned. Chaos theory called into question the habit of looking closely or only at specific parts while neglecting to examine the whole system.

Another scientist, mathematician Stephen Smale, began to study differential equations in a new way. These equations traditionally were intended to “consider one set of possibilities at a time” (47), but Smale wanted to investigate the math on a more global scale. Traditional physics assumed that minute changes in conditions would generate only minute changes in the mathematics. However, Smale discovered that when looking at dynamic systems, such as topology, incremental changes in one part of the system often disproportionately affected the whole. Initially, he erroneously assumed that systems could not be simultaneously unpredictable and stable. In fact, as the science of chaos demonstrated, these two states are not mutually exclusive: “Chaos and instability, concepts only beginning to acquire formal definitions, were not the same at all” (48). That is, a system could be unpredictable when examining its parts, but stable when observing the interaction of the whole.

To illustrate this, Smale stretched and folded shapes, demonstrating that points could not be simply plotted in predictable ways within dynamic systems. His “horseshoe” shape revealed how points that started out far apart in a system can, through movement (such as stretching and folding), come very close together. A rectangle, when stretched upward and folded over, can become a horseshoe; the two points at either end of the rectangle are now directly next to each other. This broadened the ways in which scientists could conceive of geometrical shapes within the context of motion.

The author ends the chapter with a discussion about the debate over the Great Red Spot of Jupiter. When discovered via the pictures sent back from the Voyager 2 expedition, the Great Red Spot—a site of turbulent movement on the surface of Jupiter’s gaseous planet—was the subject of much scientific conjecture. Mathematician and astronomer Philip Marcus finally suggested that the Great Red Spot exists as a space of steadiness within the larger turbulence of the planet’s surface. The complexity of the dynamic system indicates both stability and unpredictability, the hallmark of chaos.