Sublime

and strategic investment underpinning economic growth. We used deductive reasoning to derive general properties of cities, such as scaling relations and the laws of geography, as averages of processes over populations and time. We have seen that such “laws” describe the system as a whole but, like any average, do not actually apply to any specific

the process of population growth in cities is also one of recapitulation of this hierarchical ecology of sectors.

as advanced health care and education—are typically only available in larger urban areas.

(a minimum “income”)

as cities grow and their networks evolve, the area or volume of the networks needed to keep them functionally connected tends to become smaller on a per capita basis. For example, in larger cities more people can share the same bus or segment of road or sewer pipe.

The geography of most modern urbanization can ultimately be traced back to navigable waterways and deep harbors, followed by hundreds or even thousands of years of network effects pertaining to industry (i.e., progressive integration of labor and capital) and the iteratively compounding Pareto distributions that naturally follow.

the key to new functional definitions was the measurement of commuting flows over space,

When a city doubles in size, every measure of economic activity increases by 15 per cent per person.