Complexity_ A Guided Tour - Melanie Mitchell [8]
The World Wide Web
The World Wide Web came on the world scene in the early 1990s and has experienced exponential growth ever since. Like the systems described above, the Web can be thought of as a self-organizing social system: individuals, with little or no central oversight, perform simple tasks: posting Web pages and linking to other Web pages. However, complex systems scientists have discovered that the network as a whole has many unexpected large-scale properties involving its overall structure, the way in which it grows, how information propagates over its links, and the coevolutionary relationships between the behavior of search engines and the Web’s link structure, all of which lead to what could be called “adaptive” behavior for the system as a whole. The complex behavior emerging from simple rules in the World Wide Web is currently a hot area of study in complex systems. Figure 1.5 illustrates the structure of one collection of Web pages and their links. It seems that much of the Web looks very similar; the question is, why?
FIGURE 1.4. Individual actions on a trading floor give rise to the hard-to-predict large-scale behavior of financial markets. Top: New York Stock Exchange (photograph from Milstein Division of US History, Local History and Genealogy, The New York Public Library, Astor, Lenox, and Tilden Foundations, used by permission). Bottom: Dow Jones Industrial Average closing price, plotted monthly 1970–2008.
FIGURE 1.5. Network structure of a section of the World Wide Web. (Reprinted with permission from M.E.J. Newman and M. Girvin, Physical Review Letters E, 69,026113, 2004. Copyright 2004 by the American Physical Society.)
Common Properties of Complex Systems
When looked at in detail, these various systems are quite different, but viewed at an abstract level they have some intriguing properties in common:
Complex collective behavior: All the systems I described above consist of large networks of individual components (ants, B cells, neurons, stock-buyers, Website creators), each typically following relatively simple rules with no central control or leader. It is the collective actions of vast numbers of components that give rise to the complex, hard-to-predict, and changing patterns of behavior that fascinate us.
Signaling and information processing: All these systems produce and use information and signals from both their internal and external environments.
Adaptation: All these systems adapt—that is, change their behavior to improve their chances of survival or success—through learning or evolutionary processes.
Now I can propose a definition of the term complex system: a system in which large networks of components with no central control and simple rules of operation give rise to complex collective behavior, sophisticated information processing, and adaptation via learning or evolution. (Sometimes a differentiation is made between complex adaptive systems, in which adaptation plays a large role, and nonadaptive complex systems, such as a hurricane or a turbulent rushing river. In this book, as most of the systems I do discuss are adaptive, I do not make this distinction.)
Systems in which organized behavior arises without an internal or external controller or leader are sometimes called self-organizing. Since simple rules produce complex behavior in hard-to-predict ways, the macroscopic behavior of such systems is sometimes called emergent. Here is an alternative definition of a complex system: a system that exhibits nontrivial emergent and self-organizing behaviors. The central question of the sciences of complexity is how this emergent self-organized behavior comes about. In this book I try to make sense of these hard-to-pin-down notions in different contexts.
How Can Complexity Be Measured?
In the paragraphs above I have