Cities are accelerators and there are solid numbers to demonstrate it
Among the most memorable features of Shanghai’s 2010 World Expo was the quintet of ‘Theme Pavilions’ designed to facilitate exploration of the city in general (in keeping with the urban-oriented theme of the event: ‘Better City, Better Life’). Whilst many international participants succumbed to facile populism in their national pavilions, these Theme Pavilions maintained an impressively high-minded tone.
Most remarkable of all for philosophical penetration was the Urban Being Pavilion, with its exhibition devoted to the question: what kind of thing is a city? Infrastructural networks received especially focused scrutiny. Pipes, cables, conduits, and transport arteries compose intuitively identifiable systems – higher-level wholes – that strongly indicate the existence of an individualized, complex being. The conclusion was starkly inescapable: a city is more than just an aggregated mass. It is a singular, coherent entity, deserving of its proper – even personal – name, and not unreasonably conceived as a composite ‘life-form’ (if not exactly an ‘organism’).
Such intuitions, however plausible, do not suffice in themselves to establish the city as a rigorously-defined scientific object. “[D]espite much historical evidence that cities are the principle engines of innovation and economic growth, a quantitative, predictive theory for understanding their dynamics and organization and estimating their future trajectory and stability remains elusive,” remark Luís M. A. Bettencourt, José Lobo, Dirk Helbing, Christian Kühnert, and Geoffrey B. West, in their prelude to a 2007 paper that has done more than any other to remedy the deficit: ‘Growth, innovation, scaling, and the pace of life in cities‘.
In this paper, the authors identify mathematical patterns that are at once distinctive to the urban phenomenon and generally applicable to it. They thus isolate the object of an emerging urban science, and outline its initial features, claiming that: “the social organization and dynamics relating urbanization to economic development and knowledge creation, among other social activities, are very general and appear as nontrivial quantitative regularities common to all cities, across urban systems.”
Noting that cities have often been analogized to biological systems, the paper extracts the principle supporting the comparison. “Remarkably, almost all physiological characteristics of biological organisms scale with body mass … as a power law whose exponent is typically a multiple of 1/4 (which generalizes to 1/(d +1) in d-dimensions).” These relatively stable scaling relations allow biological features, such as metabolic rates, life spans, and maturation periods, to be anticipated with a high-level of confidence given body mass alone. Furthermore, they conform to an elegant series of theoretical expectations that draw upon nothing beyond the abstract organizational constraints of n-dimensional space:
“Highly complex, self-sustaining structures, whether cells, organisms, or cities, require close integration of enormous numbers of constituent units that need efficient servicing. To accomplish this integration, life at all scales is sustained by optimized, space-filling, hierarchical branching networks, which grow with the size of the organism as uniquely specified approximately self-similar structures. Because these networks, e.g., the vascular systems of animals and plants, determine the rates at which energy is delivered to functional terminal units (cells), they set the pace of physiological processes as scaling functions of the size of the organism. Thus, the self-similar nature of resource distribution networks, common to all organisms, provides the basis for a quantitative, predictive theory of biological structure and dynamics, despite much external variation in appearance and form.”
If cities are in certain respects meta- or super-organisms, however, they are also the inverse. Metabolically, cities are anti-organisms. As biological systems scale up, they slow down, at a mathematically predictable rate. Cities, in contrast, accelerate as they grow. Something approximating to the fundamental law of urban reality is thus exposed: larger is faster.
The paper quantifies its findings, based on a substantial base of city data (with US cities over-represented), by specifying a ‘scaling exponent’ (or ‘ß‘, beta) that defines the regular correlation between urban scale and the factor under consideration.
A beta of one corresponds to linear correlation (of a variable to city size). For instance, housing supply, which remains constantly proportional to population across all urban scales, is found – unsurprisingly – to have ß = 1.00.
A beta of less than one indicates consistent economy to scale. Such economies are found systematically among urban resource networks, exemplified by gasoline stations (ß = 0.77), gasoline sales (ß = 0.79), length of electrical cables (ß = 0.87), and road surface (ß = 0.83). The sub-linear correlation of resource costs to urban scale makes city life increasingly efficient as metropolitan intensity soars.
A beta of greater than one indicates increasing returns to scale. Factors exhibiting this pattern include inventiveness (e.g. ‘new patents’ß = 1.27, ‘inventors’ ß = 1.25), wealth creation (e.g. ‘GDP’ ß = 1.15, wages ß = 1.12), but also disease (‘new AIDS cases’ ß = 1.23), and serious crimes (ß = 1.16). Urban growth is accompanied by a super-linear rise in opportunity for social interaction, whether productive, infectious, or malicious. More is not only better, it’s much better (and, in some respects, worse).
“Our analysis suggests uniquely human social dynamics that transcend biology and redefine metaphors of urban ‘metabolism’. Open-ended wealth and knowledge creation require the pace of life to increase with organization size and for individuals and institutions to adapt at a continually accelerating rate to avoid stagnation or potential crises. These conclusions very likely generalize to other social organizations, such as corporations and businesses, potentially explaining why continuous growth necessitates an accelerating treadmill of dynamical cycles of innovation.”
Bigger city, faster life.