When we contemplate phenomena as diverse as electrochemical deposition or the spatial patterns of urban development, the natural assumption is that they have nothing in common. After all, there are many levels in the hierarchy that builds up from atoms to human society, and the rules that govern atoms are quite different from those that govern the geographical emergence of a city. The common view among many if not most biologists and social scientists is that the devil is entirely in the details. This school of thought asserts that social science and biology have little or nothing in common, and indeed, many biologists assert that even different fields of biology have little in common. If they are right, then science can only proceed by recording vast lists of details that no common principles will ever link together.
Physics, in contrast, has achieved a parsimonius description for a broad range of phenomena based on only a few general principles. The phenomena that physics addresses are unquestionably much simpler than those of biology or social science, and on the surface appear entirely dissimilar. A cell is far more complicated than a pendulum or an atom, and human society, being built out of a great many cells, is far more complicated still. Cells and societies have many layers of hierarchical organization, with complex functional and computational properties; they have identities, idiosyncracies stemming from an accumulation of historical contingency that makes them impossible to characterize in simple mathematical terms. Their complexity is far beyond that of the simple systems usually studied in physics. So, how can methods from physics conceivably be of any use?
The answer, as demonstrated by Frank Schweitzer in this book, lies in the fact that the essence of many phenomena do not depend on all their details. From the study of complex systems we have now accumulated a wealth of examples that demonstrate how simple components with simple interaction rules can give rise to complex emergent behaviors. This book shows this sometimes applies even when the components are themselves quite complicated. This is because, for some purposes, only a few of their features are relevant, and the complexity of the collective behavior emerges from the interactions of these few simple features alone. So although individual people are very complicated, and their decisions about where to live may be based on complicated, idiosyncratic factors, it may nonetheless be possible to understand certain statistical properties of the geographic layout of a city in terms of simple models based on a few simple rules. Furthermore, with only minor modifications of these rules, the same explanatory framework can be used to understand the dendritic patterns for zinc deposits in an electric field. It is particularly striking that such disparate phenomena can be explained using the same theoretical tools. We have long known in physics that many different phenomena can be explained with similar mathematics. For example, the equations that describe simple electric circuits consisting of resistors, inductors, and capacitors are precisely the same as those describing a system of masses and springs. This work shows that such mathematical analogies apply even more broadly than one might have suspected.
In the middle of the 20th century, John von Neumann said that "science and technology will shift from a past emphasis on motion, force, and energy to communication, organization, programming and control". This has already begun to happen, but as we enter the 21st century, the scientific program for understanding complex systems is still in its infancy. We are still experimenting to find the right theoretical tools. One of the obvious candidates for a starting point is statistical mechanics. This is a natural suggestion because statistical mechanics is the branch of physics that deals with organization and disorganization. One example where this has already succeeded is information theory. Claude Shannon showed how entropy, which was originally conceived for understanding the relationship between heat, work, and temperature, could be generalized to measure information in an abstract setting, and used for practical purposes such as the construction of an efficient communication channel. So perhaps there are other extensions of statistical mechanics that can be used to understand the remarkable range of emergent behaviors exhibited by many diverse complex systems.
But the reality is that classical statistical mechanics is mostly about disorganization. A typical model in statistical mechanics treats atoms as structureless ping pong balls. A classic example is Brownian motion: When a particle is suspended in a fluid, it is randomly kicked by the atoms of the fluid, and makes a random walk. This example played a pivotal role in proving that the world was made of atoms, and helped make it possible to quantitatively understand the relationship between macroscopic properties such as friction and microscopic properties such as molecular collisions. It led to the development of the theory of random processes, which has proved to be extremely useful in many other settings.
The framework that Schweitzer develops here extends that of Brownian motion by making the particles suspended in the fluid just a little more complicated. The particles become {\it Brownian agents}, with internal states. They can store energy and information and they can sense their environment and respond to it. They can change their internal states contingently depending on their environment, or based on their interactions with each other. These extra features endow them with simple computational capabilities. They are smarter than ping pong balls, but no smarter than they need to be. By adjusting parameters, the behavior can vary from purely stochastic at one extreme to purely deterministic at the other. Schweitzer shows that even when the Brownian agents are quite simple, through their direct and indirect interactions with each other they can exhibit quite complex behaviors.
Brownian agents can be used in many different contexts, ranging from atomic physics to macroeconomics. In this book, Schweitzer systematically develops the power of the Brownian agent model and shows how it can be applied to a wide range of problems, from molecule to mind. At the lowest level they can be simple atoms or molecules, with internal states such as excitation, and simple rules of interaction corresponding to chemical reactions. They can be used to describe the properties of molecular motors and ratchets. Or they can be cells or single-celled organisms responding to stimuli, such as electric fields, light, or chemical gradients. They can be used to study the group feeding properties of bark beetle larvae, or the trail formation of ants creating and responding to pheromone signals. With just a few changes in the model, they can be pedestrians forming trails based on visual queues, or automobile drivers stuck in traffic. Or they can be voters forming opinions by talking to their neighbors, or workers deciding where to work in a factory.
Agent based modeling is one of the basic tools that has emerged in recent years for the study of complex systems. The basic idea is to encapsulate the behavior of the interacting units of a complex system in simple programs that constitute self-contained interacting modules. Unfortunately, however, all too often agent based modelers lack self-restraint, and create agents that are excessively complicated. This results in models whose behavior can be as difficult to understand as the systems they are intended to study. One ends up not knowing what properties are generic, and which properties are unwanted side-effects.
This work takes just the opposite approach, by including only features that are absolutely necessary. It demonstrates that agent based modeling is not just for computer simulation. By keeping the agents sufficiently simple, it is also possible to develop a theoretical framework that sometimes gives rise to analytic results, and that provides a mental framework for modeling and interpreting the results of simulations when analytic methods fail. By insisting on parsimony, it adheres to the modeling style that has been the key to the success of physics (and that originally motivated the rational expectations equilibrium model in economics).
This book lays out a vision for a coherent framework for understanding complex systems. However, it should be viewed as a beginning rather than an end. There is still a great deal to be done in making more detailed connections to real problems, and in making quantitative, falsifiable predictions. Despite the wide range of problems discussed here, I suspect that this is only a small subset of the possibilities where the Brownian agent method can be applied. While I don't think that Brownian agents will gain a monopoly on theoretical modeling in complex systems, this book does a major service by introducing this new tool and demonstrating its generality and power in a wide range of diverse applications. This work will likely have an important influence on complex systems modeling in the future. And perhaps most important, it adds to the unity of knowledge by showing how phenomena in widely different areas can be addressed within a common mathematical framework, and showing that for some purposes, most of the details can be ignored.