4. Scaling Laws: Insights and Limitations

This chapter revisits rudimentary concepts pertaining to power laws and self-similarities, to illustrate the insights and limitations of scaling laws applied to urban systems. As a first step, we look at the role of city boundaries and the definition of the urban system. We portray different ways to delineate cities and metropolitan areas and discuss the effects of this choice on the system of cities. In particular, we look at the different results obtained for the Zipf’s exponent, and we show that Zipf's law is a necessary but not a sufficient condition to define a system of cities. We sketch some of the statistical difficulties arising when measuring power laws, and we show how these can lead to contradictory results when looking at scaling laws if not addressed properly. We describe some of the more rigorous approaches aiming at tackling this, such as the methods developed by Clauset and colleagues at the SFI on the one hand, and Leitão and colleagues on the other. In addition, we show that the aggregated level at which scaling laws are analysed does not provide any information about the heterogeneities present in urban systems. We briefly touch on the role of hierarchies and unexplored self-similarities to better understand these.