This volume is dedicated to Christopher Alexander's seminal paper published in 1965, "A City Is Not a Tree," which has greatly influenced many people in disciplines from architecture and urban planning to the science of cities and the science of networks.
Alexander's original article addresses the fundamental problem of artificial cities or modern buildings that fail to embrace the inner structure of natural cities, which is key to their being more livable. Artificial cities are designed with a "tree" structure in which one unit cannot connect to other units without connecting through a higher-level unit. Natural cities have a semilattice structure in which units can connect to each other more freely through functional overlap. The semilattice structure does not appear as orderly as a tree structure; however, it unearths the structure of the complex fabric of living things. The tree structure is a result of the human tendency to mentally reorganize complex organization into non-overlapping categories, and it is intuitively accessible and easy to deal with within the capacity of the human mind. However, artificial cities designed with a tree structure have extreme compartmentalization and dissociation of their internal elements, a sign of coming destruction.
Batty elaborated on the implications and challenges of Alexander's insight in studying cities and city systems. An important message from Alexander's article is that a city should not be designed as a strict hierarchy of independent parts but as an interconnected semilattice of the parts. This challenges the hierarchy concept that is embedded in the prominent theories of cities and city systems, such as central place theory and Zipf's law. The hierarchy is a result of the "paradigm of simplification," for easier summarizing and understanding, and it ignores the fundamental connection feature of the increasingly interconnected city. The semilattice structure resonates with the system approach in social science and complexity science.
Alexander's article is the beginning of the search for general principles, fundamental theories, and a unified science of cities as complex systems. Bettencourt elaborated on how ideas and concepts in Alexander's article inform studies on cities and other complex systems, with focus on three concepts: i.e., problems of mixing and interactions in cities, open-ended urban design, and evolution and adaptation of spatial forms to socioeconomic life and vice versa. Alexander's article is resonant with the mixing problem in network science, i.e., how the vertices are connected to form a network. A tree graph can connect all vertices using a small number of connections, but it has the poorest connectivity. A semilattice has better connectivity and it implies that the connections among parts of the city are from the bottom up and dynamic, and the urban design is open-ended. A city is not a strict tree structure but an adaptive and evolving connected system in which different configurations are possible, and diversity and heterogeneity are typical.
Jiang considered a city a complex network. Although a semilattice is a network structure, Alexander did not deliberately look at cities from the network perspective, especially in light of recent development in complex networks. In contrast to Euclidean geometry and Gaussian statistics, which deal with regular shapes and similar things, Jiang argued that the complex network perspective can be used to characterize irregular shapes and skewed distributions, which are fundamental to many urban theories, and fractal geometry, power-law statistics, and Alexander's geometry should be adopted to develop sustainable cities.
Mehaffy puts Alexander's article into the larger context of Alexander's prolific career, mainly evolving from his Ph.D. dissertation, "A City Is Not a Tree," to A Pattern Language, to The Nature of Order. He introduced the context and achievement of each work. At their core is an emphasis on holism that recognizes how parts form wholes with a systemic rather than combinatoric understanding of structure. Alexander's work throughout his career has focused on morphogenesis, and his aim might better...