Visitors to the area around Nature's London offices will be familiar with the scene: unending traffic and noise; the hurly-burly of the Underground; streets, concourses and platforms filled with people intent only on reaching their destination quickly. It's received wisdom that the bigger a city is, the faster life moves; Luis Bettencourt and colleagues supply some empirical evidence to back up that perception (Proc. Natl Acad. Sci. USA 104, 7301–7306; 2007).

The authors begin by examining how different indicators of cities' activity and infrastructure scale with their size. They use various sets of data from the United States, China and Germany, and characterize the scalings as power laws of the form (population)n. They find that indicators of economic activity — from personal income, to patent registrations, to total electricity consumption — vary with population with values of n in the range 1.1–1.3, regardless of where the data were collected. In other words, cities the world over become more hyperactive the larger they get. Perhaps as a corollary to that excess, the prevalence of crime and sexually transmitted disease grows similarly quickly.

Infrastructure indicators such as the lengths of the road and electricity networks, by contrast, scale to around (population)0.8. The larger the metropolis, the less of these things each citizen has at their disposal. Thus it seems that cities fulfill two basic needs of modern human society: they facilitate the exchange of ideas and, by extension, wealth creation; and they achieve economies of scale in the supply of a population's needs.

To look at how these very different dynamics affect city expansion over time, Bettencourt et al. construct a general equation that models the cost on resources of sustaining and increasing a population. Unsurprisingly, growth driven by the demands of efficiency, n < 1, stagnates after time: economies of scale eventually hit a bottom line.

City growth driven by wealth creation (n > 1), on the other hand, rapidly becomes hyperexponential. The only way to avoid collapse as a population outstrips the finite resources available to it is through constant waves of innovation. These effectively re-engineer the initial conditions of growth. But the greater the absolute population, the smaller the relative return on each such investment — so new ideas must come ever faster.

The city dweller looking for a quiet life is thus hit with a double whammy: the bigger the city, the faster life is; but the rate at which life gets faster must itself accelerate to maintain the city as a going concern.

In biological organisms, the authors note, the situation is completely different. Larger organisms have greater economies of scale, and slower-paced lives. Metabolic rates, for example, increase with (body mass)0.75. With the city, it seems, mankind has created an organism operating beyond the bounds of what is natural.