Mega-regions and supercreative growth

Number 11 on the HBR list  is the research of a Santa Fe Institute team on creativity, wealth-creation, and growth in mega-regions, which concludes that: "By almost any measure, the larger a city’s population, the greater the innovation and wealth creation per person."" The world, it seems, really is spiky after all.

Executives talk about their companies’ “DNA” and roles in “business ecosystems,” but the analogy to living organisms is more than metaphorical. Like the mathematical laws governing how organisms’ metabolism, growth, evolution, and mortality depend on size, there are rules that appear to govern the growth, performance, and even decline of cities and other social organizations. Although we can’t yet predict how specific cities or companies will evolve, we’ve found general mathematical relationships between population size, innovation, and wealth creation that may have important implications for growth strategy in organizations.

In biology, different species are in many ways scaled versions of one another. Bacteria, mice, elephants, sequoias, and blue whales may look different, but most of their fundamental characteristics, including energy and resource use, genome length, and life span, follow simple mathematical rules. These take the form of so-called power-law scaling relationships that determine how such characteristics change with size. For example, metabolic rate increases as the ¾ power of mass. Put simply, the scaling law says that if an organism’s mass increases by a factor of 10,000 (four orders of magnitude), its metabolic rate will increase by a factor of only 1,000 (three orders of magnitude). This represents an enormous economy of scale: the bigger the creature, the less energy per pound it requires to stay alive. This increase of efficiency with size—manifested by the scaling exponent ¾, which we say is “sublinear” because it’s less than one—permeates biology. These ubiquitous scaling laws have their origin in the universal properties of the networks that sustain life, such as the cardiovascular and respiratory systems.

Social organizations, like biological organisms, consume energy and resources, depend on networks for the flow of information and materials, and produce artifacts and waste. So it would not be surprising if they obeyed scaling laws governing their growth and evolution. Such laws would suggest that New York, Santa Fe, New Delhi, and ancient Rome are scaled versions of one another in fundamental ways—as, potentially, are Microsoft, Caterpillar, Tesco, and Pan Am.

To discover these scaling laws, Luís Bettencourt at Los Alamos National Laboratory, José Lobo at Arizona State University, Dirk Helbing at TU Dresden, and I gathered data across many urban systems in different countries and at different times, addressing a wide range of characteristics including energy consumption, economic activity, demographics, infrastructure, intellectual innovation, employment of “supercreative” people, and patterns of human behavior such as crime rates and rates of disease spread.

We did indeed find that cities manifest power-law scaling similar to the economy-of-scale relationships observed in biology: a doubling of population requires less than a doubling of certain resources. The material infrastructure that is analogous to biological transport networks—gas stations, lengths of electrical cable, miles of road surface—consistently exhibits sublinear scaling with population. However, to our surprise, a new scaling phenomenon appeared when we examined quantities that are essentially social in nature and have no simple analogue in biology—those associated with innovation and wealth creation. They include patent activity, number of supercreative people, wages, and GDP. For such quantities the exponent (the analogue of ¾ in metabolic rate) exceeds 1, clustering around a common value of 1.2. Thus, a doubling of population is accompanied by more than a doubling of creative and economic output. We call this phenomenon “superlinear” scaling: by almost any measure, the larger a city’s population, the greater the innovation and wealth creation per person.

Organismic growth, constrained by sublinear power-law scaling derived from the dynamics of biological networks, ultimately ceases, with the equations predicting what size organisms will reach. In contrast, our equations predict that growth associated with superlinear scaling processes observed in social organizations is theoretically unbounded. This would seem to bode well for organizations. Unfortunately, however, the equations also predict that in the absence of continual major innovations, organizations will stop growing and may even contract, leading to either stagnation or ultimate collapse. Furthermore, to prevent this, the time between innovations (the “innovation cycle”) must decrease as the system grows.

Though our research has focused on cities, the social and structural similarities between cities and firms suggest that our conclusions extend to companies and industries. If so, the existence of superlinear scaling that links size and creative output has two important consequences: First, it challenges the conventional wisdom that smaller innovation functions are more inventive, and perhaps explains why few organizations have ever matched the creativity of a giant like Bell Labs in its heyday. Second, it shows that because organizations and industries must apparently innovate at a continually accelerating rate to avoid stagnation, economizing by reflexively cutting R&D budgets and creative staffs may be a dangerous strategy over the long term.

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