Description

Scaling is a basic process that characterizes many forms of life.  It refers to the fact that key features of entities strongly depend upon their size, and that in many respects larger versions of life-forms are scaled up versions of smaller ones.  For example, while elephants and mice have very different heart rates, their hearts beat about the same number of times over the course of a lifetime.  Likewise, many features of cities — such as the number of gas stations or patents — can be reliably predicted simply based upon their population size.  According to this view,  developed by Geoffrey West, Luis Bettencourt, and colleagues, larger urban forms are scaled up versions of smaller ones.

This parallel between basic features of organic and urban life has spawned a robust yet recent research tradition devoted to the study of urban scaling laws.  Central to this research is the observation that entities may scale superlinearly, sublinearly, and linearly, often referred to as “scaling regimes.” This means that a feature may increase faster (super), slower (sub), or at the same pace of the city size.  Sub-linear scaling represents economies of scale, whereas super-linear scaling is associated with increasing returns to interaction (which may result in higher crime rates or greater innovation).  Some observers see scaling in terms of innovation cycles and the evolutionary theory of urban systems – superlinear regimes characterize innovative sectors, whereas sublinear regimes result from the diffusion of innovations throughout the system. 

Our research problematizes a key assumption of this tradition: that scaling regimes depend upon the definition of the city in question, in particular its geographic borders.  Rather than search for the ‘true’ definition of the city’s boundaries, however, we instead suggest viewing cities as operating simultaneously at multiple scopes and scales.  For example, New York’s financial services industry on Wall Street may have a much wider scope than a gas station on the same street.

Building on this insight, we develop a series of techniques to identify and understand the scope at which various local features scale.  In particular, we deploy a search algorithm that finds for any feature (e.g. business types) the geographic area in which it reliably scales with population.  These scopes vary widely.  Second, we use these measures of scope to propose a new way to differentiate cities, in terms of size and variety of the scope of experience they offer.  In some cities we exist in large and diverse scopes, in others most scopes are small and similar.  Third, we examine how scope varies across the urban system, and fourth how it has evolved over time.  Overall, this research develops a more complex notion of cities as complex systems of features operating and interacting at many different scales.