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West G., 2017, Scale. The universal laws of growth, innovation, sustainability, and the pace of life in organisms, cities, economies, and companies, New York, Penguin Press, 479 p.

Clémentine Cottineau

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1At 76, the physicist and complexity scientist Geoffrey West has set himself the challenge to publish a book for the general public which summarizes his career's work on scaling and asks big questions about life, death, cities and companies, but also opens perspectives on sustainability in the urbanised world of today and tomorrow. This is a rather impressive challenge and the result is contained in the 479 pages of a volume concisely titled Scale, and extensively subtitled The universal laws of growth, innovation, sustainability, and the pace of life in organisms, cities, economies, and companies, published by Penguin Press, New York. Geoffrey West makes this book very readable by using a simple writing style, many examples from the animal and the urban world, repetitions of the main ideas and take-home messages, as well as many entertaining digressions about life in general and his own life in particular. For example, describing his 2-week long journey to reach California from London when he became a university student at Stanford in the 1960s, he illustrates the way travel time has shrunk over the past few decades and how the pace of life has not stopped accelerating since. Similarly, every scientific finding is contextualised and the protagonists introduced as characters in a novel. All this makes for a truly enjoyable read and a historical dive into the passionate theory of one of the most famous names in complexity science. What the urban geographer will make of it is a question I will turn to after the presentation of the content.

2The book starts with a chapter titled "the big picture" and indeed, West sets the scene with a series of (very) big questions:

"Why can we live for up to 120 years but not for a thousand or a million? Why, in fact, do we die and what sets this limit to our life spans? [...] Why do we stop growing? Why do we have to sleep for eight hours every day? [...] Why do almost all companies live for only a relatively few years whereas cities keep growing and manage to circumvent the apparently inevitable fate that befalls even the most powerful and seemingly invulnerable companies? [...] Is there a maximum size of cities? Or an optimum size? [...] Why does the pace of life continually increase and why does the rate of innovation have to continue to accelerate in order to sustain socioeconomic life?" (p.6-7).

3These questions have in common to be addressed in the book, thanks to the overarching theoretical framework of scaling. 'Scaling' here refers to the study of how the quantitative characteristics of an organism (or a system) change when the size of the organism is increased (or shrunk). In particular, there can be three regimes: either the system scales linearly, with all its characteristics increasing at the same rate g as the system itself; either it can scale sublinearly, which means that there are some 'economies of scale' and characteristics are multiplied by a factor smaller than g; either it can scale superlinearly, which means that there are some 'positive returns to scale' and characteristics are multiplied by a factor bigger than g.

The chapters 2 to 4 are centered on biology and present how West, Brown and Enquist's theory of scaling came about, what it can explain and through which processes and mechanisms. To summarize, West (the physicist) met Brown and Enquist (the ecologists), and together they worked with network properties and fractal geometry to model how energy flows in organisms so as to formulate quantified predictions about the metabolism of mammals of different sizes, in line with empirical observations. In particular, they constructed a model which results in the metabolic rate of organisms (i.e. the rate at which they process energy) scaling sublinearly with size, more specifically with an exponent of ¾, as empirically recorded since Kleiber in 1932. Their generative theory involves three assumptions: 1/ networks have to be space-filling, i.e. service all the units of the body in a single architecture; 2/ the terminal units are invariant in size, i.e. capillaries have the same radius for a shrew or an elephant; and 3/ the system has to be optimized.

From the scaling of metabolic rates derives the scaling of many other quantities in animals’ bodies: the total number of heartbeats they can expect throughout life, the radius of their aorta, the length of their life span, etc. This even allows for describing the full biology of a Godzilla as a scale up version of a whale, a human or an mouse (p.162). More seriously, every one of these scaled properties (for example, the minimum and the maximum size of mammal) is demonstrated using the network structure of the circulatory system, the underlying mechanism of energy diffusion through tissues from capillaries to cells and so on, embarking the reader into a passionate understanding of the scaling theory in biology. These chapters show that we as humans can live up to 120 years and not much more because, as for every mammal, our mass determines the rate at which we metabolise energy, and therefore the pace at which our cells get damaged. This metabolic rate scaling sublinearly with body mass, this constrains our life span to around 120 years, whereas mammals of bigger mass (elephant, whale) live slower but longer and animals of small mass (dog, mouse) live faster but shorter.

Although there have been critics of the theory in the biology literature (for example Whitfield, 2004) this theory is now highly famous and widely cited across biology, ecology and complexity science in general. Its very success led to the application of scaling to cities and companies by West's team at the Santa Fe institute over the past ten to fifteen years, to predict the level of economic diversity, of crime, and productivity, leading to a 'grand unifying theory of sustainability'.

4Chapters 5 to 8 are devoted to cities. These chapters are of more direct interest to Cybergeo readers, and where the urban geographer becomes more critical. Chapter 5 introduces the key facts of urbanization and Chapter 6 exposes basics concepts of planning and architecture, which look like a condensed version of Peter Hall's Cities of Tomorrow in only 22 pages from Ebenezer Howard to Jane Jacobs and Norman Foster. This chapter is intended as a "prelude to a science of cities", by which West means a transposition of the scaling framework to cities, which can be related to classic models of urban studies. Before going into quantified prediction, he has to show that cities and organism are not too different in their fundamental functioning:

"Cities are sustained by similar network systems such as roads, railways, and electrical lines that transport people, energy, and resources and whose flow is therefore a manifestation of the metabolism of the city. These flows are the physical lifeblood of all cities and, as with organisms, their structure and dynamics have tended to evolve by the continuous feedback mechanisms inherent in a selective process toward an approximate optimization by minimizing costs and time: regardless of the city, most people on average want to get from A to B in the shortest possible time at the cheapest cost, and most businesses want to do likewise with their supply and delivery systems. This suggests that despite appearances, cities might also be scaled versions of one another in much the same was that mammals are." (p.251).

5The biological metaphor and anthropomorphism applied to cities is nothing new (Plato, Da Vinci, etc.) and there is probably an assumed level of provocation in such statements. The aim of Chapter 7 is precisely to evaluate the common features and processes which justify the translation of the scaling theory to urban systems. West picks an improbably starting point for this bridging of social and biological theories, as he introduces the sublinear scaling of the number of gas stations with city size. The study of infrastructure scaling, including gas stations, was indeed the first to be performed by the Santa Fe team on the cities project (Künhert et al., 2006). The fact that this element might not be the central point of urban studies is anecdotal; more importantly, this first example seems to miss its point and sheds suspicion on the rest of the exercice. G. West states that

"the scaling is sublinear, indicating a systematic economy of scale, meaning that the bigger the city the fewer the number of gas stations needed on a per capita basis. Thus, on average, each gas station in a larger city serves more people and consequently sells more fuel per month than in a smaller one" (p.272).

6Firstly, it is very probable that the reduction of the number of gas stations is not entirely the result of optimization and economy of scale but rather that the change in size for cities introduces a change in the nature of transportation supply and modal split, with more people using public transport, especially in Europe (where the data comes from), and especially as the study covers the largest cities of each country. Secondly, the extrapolation of the monthly sales of each gas station is quite adventurous, as the data West works with says nothing about the distribution of population by gas station, let alone the relation between population serviced and corresponding sales. I must say that sort of unrealistic statements are the main disappointments with this part of the book, because they are much more reliant on a belief that the scaling theory constructed for biology applies to cities and companies on the demonstration that it does, i.e. similar mechanisms generating the observed results. For example, the translation from circulatory networks in organisms to infrastructural networks in cities seems plausible, but it is not demonstrated that the fractality of road networks matches the regular branching of blood vessels. The transposition to social networks requires an even bigger leap of faith:

"Our roads and transport networks have to be space filling so that every local region of the city is serviced, just as all of the various utility lines have to supply water, gas and electricity to all of its houses and buildings. It's also natural to extend this concept to social networks: averaged over time, each person interacts with a number of other people as well as with groups of people in the city in such a way that collectively their network of interactions fills the available 'socioeconomic space'". (p.284-5)

7Empirical data indeed show sublinear scaling for the physical infrastructure in cities – which is analog to biological networks – and the main discovery of urban scaling is the superlinear scaling of income, crime and patents. According to West, the two observations are related: "the approximate 15 percent increase in social interactions and therefore in socioeconomic metrics such as income, patents, and crime generated with every doubling of city size can be interpreted as a bonus, or payoff, arising from the 15 percent savings in physical infrastructure and energy use." (p.322). As for why this is supposed to happen so regularly across such a diverse range of socioeconomic phenomena:

"There is a natural explanation for why social connectivity and therefore socioeconomic quantities scale superlinearly with population size. Socioeconomic quantities are the sum of interactions or links between people and therefore depend on how correlated they are. [...] the underlying reason we are limited in the number and rate of interactions we can sustain with other people in the city is rooted in the hidden constraints imposed by space and time. We simply can't be in all places at all times." (p.319)

8Therefore, by optimizing road length in cities of larger size, we simply encounter more people, ‘correlate’ with them and thus produce more, innovate more and commit more crime at exactly the same rate as the one with which physical networks are optimized… There is a certain beauty in this simplicity and the derived predictions West goes on with, but for the social scientist, there are two questions arising at this point of the book. Firstly, everything in the theory relies on 'infrastructure' and 'socioeconomic metrics' scaling symmetrically around 1, but this has been shown not to always be the case when other teams have reproduced the analysis on different case studies. For example, Arcaute et al. (2015) have found that income scales linearly with city size in England and Wales, and that the value of the exponent varies with city definition, which is never defined in West’s book. How the theory copes with these results remains a mystery. Secondly, even if it did, we haven't understood why we became more productive or criminal by simply invoking the 'sum of interactions'. In other words, the underlying mechanism (is it sharing, matching and learning as economists put it for explaining the income premium (Puga, 2010)? Does sharing and matching apply to crime?) is theoretically undefined and not too far from… magic! As West puts it:

"The integration and interplay of these two very different networks magically gives rise to a disproportionate increase in social activity, innovation, and economic output." (p.295)

9Similar arguments could be made on the last chapters about companies, but are not in my domain of expertise so I will leave it here. My point is that West’s scaling theory does provide a fascinating number of quantitative predictions about cities and companies, but it does not provide yet a convincing explanation as to why it does so for social systems. Regardless, the book is full of gems of reflections around sustainability, growth and resources. For example, West argues very strongly that economics and planning need to include concepts of energy and entropy into the equation, invoking the fact that ultimately, every idea is powered by energy, which should be provided externally (the sun) rather than internally (fossil fuels).

10I would thus recommend this book for its captivating journey across disciplines and scientific figures (from Galileo to Brunel and Strogatz), for the effort made at unifying the study of life from the cell to the city through scaling, for the reflection of a brilliant scientist on matters as important as death, sustainability and growth. However, I would advise readers outside of social sciences to take some messages with care, as the statements are not always recognised as universal truth by the rest of the community, and I would encourage social scientists to exercise their critical spirit on this important contribution, and to develop alternative models to this physics approach to cities and citizens. I am secretly convinced that some of the book was written exactly in this provocative purpose to foster constructive contradiction and theoretical innovation.

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Arcaute, E., Hatna, E., Ferguson, P., Youn, H., Johansson, A., & Batty, M., 2015, "Constructing cities, deconstructing scaling laws", Journal of the Royal Society Interface, Vol.12, No102, 20140745.

Kühnert, C., Helbing, D., & West, G. B., 2006, "Scaling laws in urban supply networks", Physica A: Statistical Mechanics and its Applications, Vol.363, No.1, 96-103.

Puga, D., 2010, "The magnitude and causes of agglomeration economies", Journal of Regional Science, Vol.50, No.1, 203-219.

Whitfield, J., 2004, "Ecology's big, hot idea", PLoS biology, Vol.2, No12, e440.

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Clémentine Cottineau, « West G., 2017, Scale. The universal laws of growth, innovation, sustainability, and the pace of life in organisms, cities, economies, and companies, New York, Penguin Press, 479 p. », Cybergeo : European Journal of Geography [En ligne], Revue de livres, mis en ligne le 24 août 2017, consulté le 09 décembre 2018. URL :

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