Introduction to Urban Science: Evidence and Theory of Cities as Complex Systems

(4) the larger settlements are, the greater the distance between them, with villages found more closely together than larger cities; (5) the larger the size of settlements, the rarer they become (i.e., there are many small villages for every large city); (6) larger settlements have more functions; and (7) they have more “high-level functions” such

β is also a function of time, but we will see empirically in this chapter and in terms of statistical theory in chapter 4 that it is often time independent, a fact that when true carries great significance.

ingredients that may be useful for framing urbanization’s role in economic growth across time: (1) sustained economic growth is a system-level property (chapter 4), with the same average growth rates characterizing all cities; (2) higher growth rate volatilities σ reduce rates of economic growth; (3) very small rates of economic growth, below 1%, a

general mechanism for reducing urban land expansion by creating urban environments that have high value per connection but where this value is not invested proportionally in relatively cheaper transportation, such as cars. This will typically require mobility alternatives that are actually better than cars (that save time and money) and that have t

The prefactor, Y0(t), is independent of scale, N(t)

and urban environments. To these sociologists such changes included the dissolution of traditional social structures, the deep division of labor in cities

humans reached all other parts of the world (except Antarctica) well before they developed cities.

For example, farmers get a free lunch from the sun, and many forms of public support may be considered free lunches in cities, injecting money into the system.

We would now like to account for the behavior of collective growth in a system of cities and the pattern of relative fluctuations. Specifically, we would like to understand at a fundamental level the slowness and persistence of these deviations from scaling as well as get a handle on their typical magnitudes.

counts the number of yes/no questions (also known as bits) necessary to describe the distribution of types in the ecosystem.