Urban Organization and Dynamics, Population and Economic Growth, Sustainability

Perhaps no other large scale human social organization is as ubiquitous and informal as cities. It is estimated that in late 2005 humanity crossed a historic threshold whereby now the majority of the population worldwide lives in urban agglomerations. The fast pace of urbanization, especially in developing countries is accompanied by profound changes in socio economic organization and patterns of human behavior.
Historically cities have been the prominent sites of human innovation and wealth creation as well as crime, disease and extreme poverty. In spite of overwhelming evidence for these characteristics, a theory of cities as human organizations is still lacking at present,
We are investigating to what extent cities are self-similar structures in their rates of change, including innovation, wealth creation and human behavior. Important consequences follow from these empirical "laws" for growth, prosperity and the sustainability of human societies:

Scaling and Self-Similarity of Cities

Cities belonging to a common urban system (usually a nation) are on everage self similar in terms of their rates of change.
Social quantities such as measures of innovation, wealth creation, but also crime rates, disease incidence and economic costs show increasing returns to scale, increasing with city population size as a scaling law with an exponent &beta>1 (per capita increase).
Individual needs such as number of housing units, jobs or water consumtion rates increase linearly (&beta=1) with city size.
Infrastructural quantities such as road surface or length of electrical cabling show expected economies of scale (&beta<1).
These scalings predict that the pace of individual human behavior associated with social quantities should increase with city size, as observed for e.g. walking speed.
The scaling laws observed for social quantities vs. city size run in the opposite direction to rates of change in biological organisms vs. body size. In this sense cities, as collective entities that consume resources and produce innovation, wealth and waste, are new kinds of organisms displaying dynamics unique to human societies.

Consequences for Growth and Sustainability

Superlinear scaling of wealth creation and innovation implies periods of superlinear economic and population growth, as observed e.g. for New York City.
Super exponential growth is characterized by finite time singularities (which are estimated to occur in the order of decades) and subsequent population and economic collapse.
These crises, ironically resulting from desirable increasing returns to scale, can be averted by social and economic changes, that reset each growth cycle.
The characteristic times between singularities is predicted to decrease with poulation size, thus sustainable growth requires accelerating rates of major innovation and adaptation events.

Wealth creation and employment in creative occupations are superlinear functions (&beta>1, denoting per capita increase) of city size. Superlinear scaling of rates of wealth creation, innovation, crime and disease incidence are properties of cities as self-similar human organizations, and imply a speed up of the pace of life with population.

Publications:

Growth, innovation, scaling, and the pace of life in cities
Invention in the city: Increasing returns to patenting as a scaling function of metropolitan size