Michael Batty is a British urban planner and geographer who has devoted a lengthy (48 years) academic career to understanding cities as processes on networks rather than simply as things at locations. His latest book draws together a wide range of mathematical and computational concepts, first to describe cities from this dynamic perspective, and then to suggest new approaches to urban design. His work will naturally be of interest to geographers and urban planners. In addition, as a concrete application of the growing field of network analysis and dynamics, it provides a rich array of examples to stimulate the development of new methods.

The first three chapters introduce the author’s basic thesis and the tools he uses to explore it. The thesis, shared with a growing community of geographers, is that a city’s shape and location are not nearly as important to understanding it as are the flows that characterize it and the networks that support them. Focusing on a city as a pattern of activity rather than a thing requires a new set of tools, with their roots more in physics and applied mathematics than in traditional sociological disciplines; he introduces the reader to these basic mathematical tools.

In the second section of the book, the author applies these tools descriptively, to develop the “science of cities.” Each of the six chapters in this section presents a distinct perspective. He begins by exploring the remarkably stable distribution of city sizes popularized by Zipf, showing how the distribution can emerge from simple models of growth. From this view of cities as indivisible atoms of various sizes, the second perspective moves to describing their hierarchical structure, and the third to predicting this structure using “space syntax,” a dual representation of a city’s road network inspired by the work of Hillier and Hanson. This approach moves back and forth between the graph of roads as locations linked by edges, and the graph of edges linked through common junctions. This shift in focus, from places to lines of unobstructed movement, opens up new approaches to modeling accessibility in cities. The fourth perspective shows the value of extending notions of distance, usually applied to the primal road network, to the dual representation. The fifth and sixth perspectives introduce two different methods for simulating growth and development: cellular automata for bottom-up hierarchical processes of growth, and flow-based models that look at movement over a city’s networks.

The third section of the book moves from modeling cities to modeling the design activities that seek to manipulate them deliberately. The author argues that the same network and flow idioms that dominate the city also govern processes of city planning. This section offers five successively more complex models. The first chapter, on hierarchical design, shows how different and sometimes incompatible criteria must be balanced against one another, and represents them as a network of constraints to which tools from the earlier chapters can be applied. Next, the process of averaging across this network of constraints is formalized as a Markovian design machine. So far, design has been viewed as an abstract process of manipulating constraints, but in the third step, actors are introduced, stakeholders who have interest or control (or both) over problems and policies that together influence the value of the different constraints. This model now captures the notion of collective action across this community of actors. The fourth refinement formalizes the interaction of these actors using Coleman’s social exchange theory. The final step is to model the dynamics of committee decision making in such a structure.

The book’s models are predominantly matrix formalisms, resting on mean-field assumptions that average across individual decision makers. The concluding chapter briefly acknowledges the value of extending these methods with more sophisticated agent-based tools. Such tools can preserve differences across individuals, sometimes yielding results that differ not just quantitatively, but also qualitatively, from those produced by closed-form analytic methods. Given the broad array of material that has been drawn together, it is perhaps not surprising that the notation is occasionally inconsistent. For example, the flow matrix is designated by T on page 62, but by F on page 96. An integrated table of notation would have been helpful. In addition, as pointed out in the acknowledgments, though the book’s graphics are all printed in grayscale, the explanations that accompany them sometimes call attention to color distinctions. The rank clocks tracing the evolution of city size through time, which appear as fairly tangled visual objects in the book, are much clearer in the colored versions available on the book’s website, and many other graphics in the book, which in their print form are somewhat obscure, must be viewed on the website to appreciate the insights that they convey.

In sum, this volume offers an ambitious synthesis of a dynamical approach to cities. It is an essential reference on this approach for geographers, and a solid example of innovative applications of computer modeling to a social domain that other model-oriented sociologists would do well to emulate.

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