Is there an underlying structure governing all forms of life at all scales? What about social systems, say, cities? Are there commonalities across different cities of different sizes? Even more, is there any commonality between biological organisms and social organizations? This talk will provide a quick summary of scaling theory, a mathematical framework which asks those questions, and its implications and applications in physics, biology and social science. In particular, I will elaborate scaling law in urban systems 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 unthinkable to explain them in a simple way, and even a well-designed plan often results in unintended consequences. Every city, traditionally regarded, has a unique historical path built on geographic factors and contingent policies that are so entangled. And yet, we observe regularities in almost every property of cities (population distribution, crime rate, productivity and even economic diversity), which seems to contradict the high level of complexity 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 common micro foundations have to be manifested as universality and self-similarity under a single scaling law. Science of Cities is the scientific attempt to understand these empirical observations and theoretical results.

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