A discussion of scaling theory in general, and its application in physics, biology and social science, as well as an elaboration urban scaling and its relation to the universality and self-similarity lurking in the urban systems. The universality and self-similarity of various urban phenomena seem both trivial and non-trivial. On one hand, the dynamics of cities are so complex that it seems impossible to explain them in a simple way. Urban characteristics, geographic factors and historical paths are so entangled that even a well-designed plan often results in unintended consequences. This high level of complexity contradicts the universality and self-similarity that we observe in almost every property of cities (population distribution, crime rate, productivity and even economic diversity) because they imply the underlying dynamics are reducible to a simple form. On the other hand, universality is a natural, and even trivial, consequence derived from a common set of functionalities of cities. People share reasons to move to cities: more interaction, greater opportunity, higher productivity and better infrastructure. These basic dynamics of urbanization are manifested as a strong signal of universality and self-similarity under a single scaling law.

Hyejin Youn is an assistant professor at Kellogg School of Management at Northwestern University, and Northwestern Institute on Complex Systems (NICO). She was a research fellow at Santa Fe Institute and Harvard Kennedy School, and visiting scientist at MIT Media Lab. Before that, she was a senior research fellow at Mathematical Institute at University of Oxford, and Institute for New Economic Thinking at the Oxford Martin School; and ran a National Science Foundation grant (USA) to study Technological Change from the Map of Capabilities.