Complex Adaptive Systems

PRINCETON UNIVERSITY PRESS

Contents

Chapter One

The goal of science is to make the wonderful and complex understandable and simple—but not less wonderful. —Herb Simon, Sciences of the Artificial

The process of scientific discovery is, in effect, a continual flight from wonder. —Albert Einstein, Autobiographical Notes

Adaptive social systems are composed of interacting, thoughtful (but perhaps not brilliant) agents. It would be difficult to date the exact moment that such systems first arose on our planet—perhaps it was when early single-celled organisms began to compete with one another for resources or, more likely, much earlier when chemical interactions in the primordial soup began to self-replicate. Once these adaptive social systems emerged, the planet underwent a dramatic change where, as Charles Darwin noted, "from so simple a beginning endless forms most beautiful and most wonderful have been, and are being, evolved." Indeed, we find ourselves at the beginning of a new millennium being not only continually surprised, delighted, and confounded by the unfolding of social systems with which we are well acquainted, but also in the enviable position of creating and crafting novel adaptive social systems such as those arising in computer networks.

What it takes to move from an adaptive system to a complex adaptive system is an open question and one that can engender endless debate. At the most basic level, the field of complex systems challenges the notion that by perfectly understanding the behavior of each component part of a system we will then understand the system as a whole. One and one may well make two, but to really understand two we must know both about the nature of "one" and the meaning of "and."

The hope is that we can build a science of complexity (an obvious misnomer, given the quest for simplicity that drives the scientific enterprise, though alternative names are equally egregious). Rather than venturing further on the well-trodden but largely untracked morass that attempts to define complex systems, for the moment we will rely on Supreme Court Justice Stewart's words in his concurring decision on a case dealing with obscenity (Jacobellis v. Ohio, 1964): "I shall not today attempt further to define the kinds of material I understand to be embraced within that shorthand description; and perhaps I could never succeed in intelligibly doing so. But I know it when I see it."

The field of complex systems must direct its "flight from wonder" toward discoveries that "make the wonderful and complex understandable and simple." We hope that there is a complex systems equivalent of Newton's Laws of Motion that will one day make our current computer simulations appear to us as archaic as machines implementing Ptolemy's epicycles. Even when the fundamental laws of complex adaptive social systems are uncovered, however, it is unlikely that our flight from wonder will be complete. Knowing Newton's Laws of Motion reveals a key simplicity in the world around us, and while we may take delight in the power of so simple an idea to explain the motion of our universe, the thrill of the discovery quickly wanes with the mundaneness of the outcome. Laws emerging from complex adaptive systems have an entirely different character—knowing Darwin's theory of evolution in no way diminishes the wonder that ensues as we observe its implications.

Writings on complexity in the social sciences go back hundreds of years, with Adam Smith's The Wealth of Nations (1776) representing one of the earliest and most cohesive discussions of the topic (see figure 1.1). One of the prime drivers of economic theory over the past two centuries has been Smith's concept of an "invisible hand" leading collections of self-interested agents into well-formed structures that are no part of any single agent's intention. Although much theoretical progress has been made on this idea, for example, the elegant proofs of existence given by Arrow and Debreu or the various contributions based on fanciful mechanisms like Walrasian auctioneers, the actual mechanisms behind the invisible hand still remain largely, dare we say, invisible.

Indeed, the tools and ideas that have been developed over the past decade hint at a new world of scientific possibilities for understanding complex adaptive social systems. While our ability to theorize about social systems has always been vast, the set of tools available for pursuing these theories has often constrained our theoretical dreams either implicitly or explicitly. Smith faced few limits while writing about the complexity of the world around him, whereas Arrow and Debreu's existence proof required a much more constrained view of social behavior. Often, tools get mistaken for theories with unfortunate consequences; elaborate computer programs (perhaps with lovely graphics) or mathematical derivations are occasionally assumed to make a real scientific statement, regardless of their scientific underpinnings. Indeed, entire literatures have undergone successive refinements and scientific degradation, during each generation of which the original theoretical notions driving the investigation are crowded out by an increasing focus on tool adeptness. This often results in science that is "smart but not wise."

Using traditional tools, social scientists have often been constrained to model systems in odd ways. Thus, existing models focus on fairly static, homogeneous situations composed of either very few or infinitely many agents (each of whom is either extremely inept or remarkably prescient) that must confront a world in which time and space matter little. Of course, such simplicity in science is a virtue, as long as the simplifications are the right ones. Yet, it seems as though the world we wish to know lies somewhere in between these extremes.

One of the most powerful tools arising from complex systems research is a set of computational techniques that allow a much wider range of models to be explored. With these tools, any number of heterogeneous agents can interact in a dynamic environment subject to the limits of time and space. Having the ability to investigate new theoretical worlds obviously does not imply any kind of scientific necessity or validity—these must be earned by carefully considering the ability of the new models to help us understand and predict the questions that we hold most dear.

The science of complex systems is a rapidly evolving area, in terms of both domains and methods. The interest in this area, as well as its rapid subsequent diffusion, has been rather remarkable (especially in a field like economics, where, as Paul Samuelson (1999, xi) once remarked, "science advances funeral by funeral"). We intend for this book both to summarize some key past contributions as well as to lay out an agenda for the future. Any such agenda will require the efforts of many scientists, and we hope to provide sufficient insights and practical guidance so that others can productively join in this research effort.

The tools and ideas emerging from complex systems research complement existing approaches, and they should allow us to build much better theories about the world when they are carefully integrated with existing techniques. Some of the discussions in this book surround basic issues in good scientific modeling. Having a good understanding of these issues is certainly a prerequisite for anyone interested in pursuing work in this area, and unfortunately explicit discussions of modeling are rarely encountered by most scholars.

The book's central theme, "The Interest in Between," has two meanings. The first relates to the level and techniques we use to illustrate the core material in complex adaptive social systems. The second concerns the scientific space that this area occupies.

Complex systems has become both a darling of the popular press and a rapidly advancing scientific field. Unfortunately, this creates a gap between popular accounts that rely on amorphous metaphors and cutting-edge research that requires a technical background. Here we hope to provide a point of entry that lies between metaphor and technicalities. Our work focuses on simple examples that are accessible, yet also contain much deeper foundational insights. This approach is analogous to learning game theory by studying the Prisoner's Dilemma or the Centipede game. While game theory rests on a very abstract and technical foundation—fixed points, hemicontinuous correspondences, and the like—most of the core insights are contained in the analysis of these simple games. In a similar spirit, here we rely on simple models and examples to convey the key ideas. These illustrations will exist in between metaphor and abstract mathematics, in between the flowery language that has taken hold in the press and concrete computations. We view this "in-between" as a good point of entry into the material and hope that it gives readers the ability and interest to dig deeper into the field as they see fit.

We have strived to make this book accessible to both academics and the sophisticated lay reader. Whether you are a graduate student or faculty member in the social sciences trying to understand better what complex systems is about and how it could be used, an engineer hoping to improve your models of processes by using social agents, or someone interested in business, economics, or politics who wants a deeper understanding of the causes and implications of complexity, you should find this book useful and approachable.

Ultimately the study of complex systems illuminates the interest in between the usual scientific boundaries.

It is the interest in between various fields, like biology and economics and physics and computer science. Problems like organization, adaptation, and robustness transcend all of these fields. For example, issues of organization arise when biologists think about how cells form, economists study the origins of firms, physicists look at how atoms align, and computer scientists form networks of machines.

It is the interest in between the usual extremes we use in modeling. We want to study models with a few agents, rather than those with only one or two or infinitely many. We want to understand agents that are neither extremely brilliant nor extremely stupid, but rather live somewhere in the middle.

It is the interest in between stasis and utter chaos. The world tends not to be completely frozen or random, but rather it exists in between these two states. We want to know when and why productive systems emerge and how they can persist.

It is the interest in between control and anarchy. We find robust patterns of organization and activity in systems that have no central control or authority. We have corporations—or, for that matter, human bodies and beehives—that maintain a recognizable form and activity over long periods of time, even though their constituent parts exist on time scales that are orders of magnitude less long lived.

It is the interest in between the continuous and the discrete. The behavior of systems as we transition between the continuous and discrete is often surprising. Many systems do not smoothly move between these two realms, but instead exhibit quite different patterns of behavior, even though from the outside they seem so "close."

It is the interest in between the usual details of the world. We need to find those features of the world where the details do not matter, where large equivalence classes of structure, action, and so on lead to a deep sameness of being.

The science of complex systems and its ability to explore the interest in between is especially relevant for some of the most pressing issues of our modern world. Many of the opportunities and challenges before us—globalization, sustainability, combating terrorism, preventing epidemics, and so on—are complex. Each of these domains consists of a set of diverse actors who dynamically interact with one another awash in a sea of feedbacks. To understand, and ultimately to harness, such complexity will require a sustained and imaginative effort on the part of researchers across the sciences.

Kenneth Boulding summarized science as consisting of "testable and partially tested fantasies about the real world." The science of complex systems is not a new way of doing science but rather one in which new fantasies can be indulged.

Chapter Two

I adore simple pleasures. They are the last refuge of the complex. —Oscar Wilde, The Picture of Dorian Gray

When a distinguished but elderly scientist states that something is possible, he is almost certainly right. When he states that something is impossible, he is very probably wrong. —Arthur C. Clarke, Report on Planet Three

We are surrounded by complicated social worlds. These worlds are composed of multitudes of incommensurate elements, which often make them hard to navigate and, ultimately, difficult to understand. We would, however, like to make a distinction between complicated worlds and complex ones. In a complicated world, the various elements that make up the system maintain a degree of independence from one another. Thus, removing one such element (which reduces the level of complication) does not fundamentally alter the system's behavior apart from that which directly resulted from the piece that was removed. Complexity arises when the dependencies among the elements become important. In such a system, removing one such element destroys system behavior to an extent that goes well beyond what is embodied by the particular element that is removed.

Complexity is a deep property of a system, whereas complication is not. A complex system dies when an element is removed, but complicated ones continue to live on, albeit slightly compromised. Removing a seat from a car makes it less complicated; removing the timing belt makes it less complex (and useless). Complicated worlds are reducible, whereas complex ones are not.

While complex systems can be fragile, they can also exhibit an unusual degree of robustness to less radical changes in their component parts. The behavior of many complex systems emerges from the activities of lower-level components. Typically, this emergence is the result of a very powerful organizing force that can overcome a variety of changes to the lower-level components. In a garden, if we eliminate an insect the vacated niche will often be filled by another species and the ecosystem will continue to function; in a market, we can introduce new kinds of traders and remove old traders, yet the system typically maintains its ability to set sensible prices. Of course, if we are too extreme in such changes, say, by eliminating a keystone species in the garden or all but one seller in the market, then the system's behavior as we know it collapses.

When a scientist faces a complicated world, traditional tools that rely on reducing the system to its atomic elements allow us to gain insight. Unfortunately, using these same tools to understand complex worlds fails, because it becomes impossible to reduce the system without killing it. The ability to collect and pin to a board all of the insects that live in the garden does little to lend insight into the ecosystem contained therein.

The innate features of many social systems tend to produce complexity. Social agents, whether they are bees or people or robots, find themselves enmeshed in a web of connections with one another and, through a variety of adaptive processes, they must successfully navigate through their world. Social agents interact with one another via connections. These connections can be relatively simple and stable, such as those that bind together a family, or complicated and ever changing, such as those that link traders in a marketplace. Social agents are also capable of change via thoughtful, but not necessarily brilliant, deliberations about the worlds they inhabit. Social agents must continually make choices, either by direct cognition or a reliance on stored (but not immutable) heuristics, about their actions. These themes of connections and change are ever present in all social worlds.

The remarkable thing about social worlds is how quickly such connections and change can lead to complexity. Social agents must predict and react to the actions and predictions of other agents. The various connections inherent in social systems exacerbate these actions as agents become closely coupled to one another. The result of such a system is that agent interactions become highly nonlinear, the system becomes difficult to decompose, and complexity ensues.

(Continues...)

Excerpted from Complex Adaptive Systemsby John H. Miller Scott E. Page Copyright © 2007 by John H. Miller and Scott E. Page. Excerpted by permission of PRINCETON UNIVERSITY PRESS. All rights reserved. No part of this excerpt may be reproduced or reprinted without permission in writing from the publisher.
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