Complexity_ A Guided Tour - Melanie Mitchell [9]
These are key questions, but they have not yet been answered to anyone’s satisfaction and remain the source of many scientific arguments in the field. As I describe in chapter 7, many different measures of complexity have been proposed; however, none has been universally accepted by scientists. Several of these measures and their usefulness are described in various chapters of this book.
But how can there be a science of complexity when there is no agreed-on quantitative definition of complexity?
I have two answers to this question. First, neither a single science of complexity nor a single complexity theory exists yet, in spite of the many articles and books that have used these terms. Second, as I describe in many parts of this book, an essential feature of forming a new science is a struggle to define its central terms. Examples can be seen in the struggles to define such core concepts as information, computation, order, and life. In this book I detail these struggles, both historical and current, and tie them in with our struggles to understand the many facets of complexity. This book is about cutting-edge science, but it is also about the history of core concepts underlying this cutting-edge science. The next four chapters provide this history and background on the concepts that are used throughout the book.
CHAPTER 2
Dynamics, Chaos, and Prediction
It makes me so happy. To be at the beginning again, knowing almost nothing…. The ordinary-sized stuff which is our lives, the things people write poetry about—clouds—daffodils—waterfalls…. these things are full of mystery, as mysterious to us as the heavens were to the Greeks…It’s the best possible time to be alive, when almost everything you thought you knew is wrong.
—Tom Stoppard, Arcadia
DYNAMICAL SYSTEMS THEORY (or dynamics) concerns the description and prediction of systems that exhibit complex changing behavior at the macroscopic level, emerging from the collective actions of many interacting components. The word dynamic means changing, and dynamical systems are systems that change over time in some way. Some examples of dynamical systems are
The solar system (the planets change position over time)
The heart of a living creature (it beats in a periodic fashion rather than standing still)
The brain of a living creature (neurons are continually firing, neurotransmitters are propelled from one neuron to another, synapse strengths are changing, and generally the whole system is in a continual state of flux)
The stock market
The world’s population
The global climate
Dynamical systems include these and most other systems that you probably can think of. Even rocks change over geological time. Dynamical systems theory describes in general terms the ways in which systems can change, what types of macroscopic behavior are possible, and what kinds of predictions about that behavior can be made.
Dynamical systems theory has recently been in vogue in popular science because of the fascinating results coming from one of its intellectual offspring, the study of chaos. However, it has a long history, starting, as many sciences did, with the Greek philosopher Aristotle.
Early Roots of Dynamical Systems Theory
Aristotle was the author of one of the earliest recorded theories of motion, one that was accepted widely for over 1,500 years. His theory rested on two main principles, both of which turned out to be wrong. First, he believed that motion on Earth differs from motion in the heavens. He asserted that on Earth objects move in straight lines and only when something forces them to; when no forces are applied, an object comes to its natural resting state. In the heavens, however, planets and other celestial objects move continuously in perfect circles centered about