The major thrust of this exploratory program was to investigate the possibility of developing a science of cities and companies based on underlying mathematizable principles for understanding their organization, dynamics, growth and mortality and which would lead to quantitative, testable predictions. Given the extraordinary complexity and diversity of cities and companies, which reflect individual historical and geographical uniqueness, it is not clear that a systematic general theory is possible rather than a more traditional qualitative approach. Does each city and company require its own model to understand its organization and growth, or are there general quantifiable principles constraining their dynamics and organization, independent of history and geography?

A major theme pervading our work is that of scaling, inspired by biology. An example is shown in Fig. 1A where the surprising regularity of metabolic rate (the energy needed per second to stay alive) is shown as a function of mass. This regularity is manifested across almost all physiological and life-history variables (lifespan, heart-rate, etc) for mammals, fish, birds and even cells and has its origins in generic mathematical properties of networks that sustain life at all scales. Likewise, cities and companies function at multiple scales and, remarkably, also show similar scaling in most economic, innovation and infrastructural metrics (Fig. 1B). Worldwide, socioeconomic metrics, such as wages, wealth, patents, AIDS cases, violent crime and educational institutions, all increase by about 15% with each doubling of city size (“superlinear” scaling), whereas infrastructural metrics, such as length of roads, electrical cables, and number of gas stations, decrease by about 15% (“sublinear” scaling). Superlinearity implies that, per capita, socioeconomic quantities, whether wages, crime or patents, systematically increase by the same degree as city size increases; similarly, to the same degree, there are increasing savings from economies of scale in all infrastructural quantities. The bigger the city, the more the average individual owns, produces and consumes, whether goods, resources or ideas but they can also expect an equivalent increase in crime and AIDS.

The approximate universality of these scaling laws across geography and seemingly independent urban metrics strongly suggests that there are underlying generic principles constraining cities and that a fundamental, mechanistic theory is possible. We hypothesize that this originates in the underlying dynamics of social network structures and group clustering of human interactions, manifested in the metropolitan buzz of productivity, speed, and ingenuity. The quantitative regularities expressed by scaling suggest that there are universal dynamics of agglomeration that are accelerated by bringing more people together. Cities provide natural mechanisms for reaping benefits of high social connectivity between very different people conceiving and solving problems in a diversity of ways.

Similar processes are at play in companies. Firms are dedicated to many different products, services, and markets, and their dynamics and organization reflect some of these contingencies and interdependencies. Our preliminary analyses establish scaling in publicly traded companies (Fig. 1C) for net income and total assets. A striking feature is how well these scale despite representing thousands of companies from diverse business sectors in different countries. In contrast to cities, companies scale sublinearly representing economies of scale, much like organisms.

Generically, sublinear scaling leads to finite growth, as in biology. Preliminary analyses confirm this (Figs. 2A,E,F), indicating that firms are more like organ...

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