Towards a science of cities

The future of humanity and the long-term sustainability of the planet are inextricably linked to the fate of our cities. Cities are the crucible of civilisation, the hubs of innovation and entrepreneurship, the engines of wealth creation and centres of power, the magnets that attract creative individuals, and the stimulant for ideas, growth and innovation.

Geoffrey West

Geoffrey West is a theoretical physicist whose multiple award-winning research aims to develop a quantitative ‘universal’ theory to explain the structure and dynamic of cities, companies and social networks. In addition to being Distinguished Professor and Former President at the Santa Fe Institute, West also currently serves as Associate Fellow of the Said Business School, Oxford University and as visiting Professor of Mathematics at Imperial College London.

But they also have a dark side: they are the prime locus of crime, pollution, poverty, disease and the consumption of energy and resources. Rapid urbanisation and accelerating socio-economic development have generated multiple global challenges ranging from climate change and its environmental impacts to incipient crises in food, energy and water availability, public health, financial markets and the global economy.
By the second half of this century, the overwhelming majority of human beings will be urban dwellers, many in megacities of unprecedented size. Averaged over the next 30 to 40 years, about a million and a half people are being urbanised each week. This is equivalent to adding a Finland every month, a New York metropolitan area every two months or a Germany every year! It is in the very nature of a super-exponential expansion that the immediate future comes upon us increasingly more rapidly, potentially presenting us with unforeseen challenges we only recognise after it’s too late.
Given this, it is becoming increasingly urgent to ask whether we can develop a principled Science of Cities for understanding urbanisation and the dynamics, growth and evolution of cities in a quantitatively predictable integrated framework. This is needed as a complement to traditional methodologies to help inform policy addressing the challenges of a sustainable planet where all citizens can have a high quality and standard of living and lead meaningful lives.
Given the extraordinary complexity, diversity and apparent individuality of cities, and their need to continually adapt and grow, this would appear to be a daunting, if not impossible, task. However, a comprehensive analysis of data representing key characteristics of cities reveals a remarkable and extremely surprising simplicity underlying their extraordinary complexity: regardless of the metric, cities are to a large degree scaled versions of one another. Socio-economic metrics such as wages, patents, assets, sales, diversity, crime, police and disease, as well as infrastructural ones such as roads, petrol stations, electrical and water lines, and volumes of buildings scale systematically and predictably with population size, suggesting that universal principles that transcend history, geography and culture underlie their dynamics, organisation and structure.
Systematically across the globe, whether in Europe, the Americas or Asia, and regardless of the indicator, the larger the city the more innovative ‘social capital’ is produced; to put it in simple quantitative terms, if city size is doubled, then, for example, wages, wealth, patents, GDP and educational and research institutions all increase by approximately the same degree, namely, by about 15% per capita. This surprisingly systematic phenomenon is called superlinear scaling: the bigger the city, the more the average individual citizen owns, produces and consumes, whether it is goods, resources or ideas, all by about 15% with each doubling. This is the good news about cities and why they are so attractive and seductive.
Now to the bad news: to approximately the same degree, doubling city size also increases the amount of crime, pollution and disease by the same 15% per capita. The good, the bad and the ugly come along hand-in-glove as an integrated, predictable package. A person may move to a bigger city drawn by more innovation, more opportunity, more culture, higher wages, a greater buzz and sense of ‘action’, but they can also expect to confront an equivalent increase in garbage, theft, stomach flu and AIDS.
In contrast to the superlinearity of socio-economic activity, infrastructure scales sublinearly, meaning that with every doubling of size, cities need about 15% less infrastructure per capita, whether roads, electrical cables or water lines. Since the number of houses (real estate) and businesses increases linearly with size, these require less infrastructure per unit to support them. Cities manifest a surprisingly systematic economy of scale.
This inextricable linkage between benefits and costs of community structure originates in the ‘universal’ dynamic and generic mathematical properties of social networks and their integration with infrastructural networks. Despite cultural and ethnic differences, the modular clustering of human interactions in family, community, work and business are pretty much the same the world over. As urban creatures, we all participate in the multiple networks in which information is exchanged, as exhibited by the intensity of human interaction manifested in the metropolitan buzz of productivity, speed and ingenuity.  Superlinearity originates from the positive feedback mechanisms embodied in human social networks: each interaction builds on and multiplicatively reinforces previous ones ultimately leading to new ideas and greater wealth: the more you have, the more you get!
The resource and energy networks that sustain biological organisms and ecosystems (such as our circulatory system) are dominated by economies of scale (sublinear scaling) – the bigger the organism, the less energy is required per second to support each cell. The physics and mathematics of such networks constrain the pace of biological life to decrease systematically with increasing size. Consequently, big mammals live longer, take longer to mature, have slower heart rates and cells that work less hard than small mammals, all to the same degree: each doubling of mass increases timescales by about 25%. Small animals live life in the fast lane while big ones move ponderously, though more efficiently, through life (think of a mouse versus an elephant!)
Although the mathematics underlying superlinear scaling is very similar to that in biology, the positive feedback mechanisms in social networks lead to life speeding up rather than slowing down. The bigger the city, the faster the pace of life: diseases spread more quickly, business is transacted more rapidly and people walk faster… all approximately to the same predictable degree (the same ~ 15% rule).
In biology, a further consequence of sublinear scaling is that organisms typically stop growing, reaching a stable size at maturity. In contrast, this same mathematical framework predicts that socio-economic superlinear scaling leads to unbounded super-exponential growth, consistent with what is observed in open-ended economies. This is very satisfying, but there’s a big catch, which goes under the forbidding technical name of a finite time singularity.
In a nutshell, the problem is that the theory also predicts that unbounded growth cannot be sustained without either infinite resources or inducing major paradigm shifts or innovations that ‘reset’ the clock before potential collapse occurs. At all scales, open-ended socio-economic growth requires continuous cycles of reinvention via paradigm-shifting innovations. On the big scale of human history, these are associated with major discoveries such as those of iron, steam, coal, computation and, most recently, digital information technology. Indeed, the litany of such discoveries, both large and small, is a testament to the extraordinary ingenuity of the collective human mind.
Unfortunately, however, there is another serious catch. Theory dictates that to sustain continuous growth such discoveries must be made at an increasingly accelerating pace; the time between successive innovations must systematically and inextricably get shorter and shorter. For instance, the time between the most recent major shift from the ‘Computer Age’ to the ‘Information and Digital Age’ was perhaps 20 years, to be compared to the thousands of years between the Stone, Bronze and Iron Ages. And the time to the next significant innovation, whatever it is, is destined to be even shorter.
We are all too familiar with the short-term manifestations of the increasingly faster pace that new gadgets and models appear. It’s as if we are on a succession of accelerating treadmills and have to jump from one to another at an ever-increasing rate. We need to incorporate these ideas into our thinking about how our future plays out and how we got here.
Although a scientific understanding of how cities work may not be explicitly prescriptive for policy-makers and practitioners, it should be a major ingredient into how positive urban development is conceived. For instance, the job of policy-makers is to enhance the performance of their city relative to baselines for their size defined by the scaling laws. Cities are remarkably robust: success, once achieved, is sustained for several decades or longer, thereby setting a city on a long run of creativity and prosperity. A great example is metropolitan San Jose, home to the Silicon Valley, which has been consistently overperforming relative to expectations for its size for over 50 years, well before the advent of modern hi-tech industry. Unfortunately, the reverse is also true: it is very hard to turn around urban decay swiftly. Ineffective policy and unrealistic short-term expectations can condemn a city to decades of under-performance.