CityReads│Scale: Simple Law of organisms, Cities and Companies

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Scale: Simple Law of organisms, Cities and Companies

Non-linear scaling explains everything from the productivity of cities to the safe dosage for LSD.

Geoffrey West, 2017. Scale: The Universal Laws of Growth, Innovation, Sustainability, and the Pace of Life, in Organisms, Cities, Economies, and Companies. Penguin Press.

Clémentine Cottineau, book review of Scale, 2017.

Source: http://journals.openedition.org/cybergeo/28543?lang=en

 At 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 urbanized 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. 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.

The 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 mice live for just two to three years whereas elephants live for up to seventy-five? And despite this difference, why is the number of heartbeats in a life span roughly the same for elephants, mice, and all mammals, namely about 1.5 billion?"

"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?" .

The book uses scaling relationships that quantitatively describe how almost any measurable characteristic of animals, plants, ecosystems, cities and companies scales with size.  These scaling laws provide us with a window onto underlying principles and concepts that can potentially lead to a quantitative predictive framework for addressing a host of critical questions across science and society.

The four figures below reveal something surprisingly simple, systematic, and regular.

These 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.

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. 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'.

Chapters 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."

The 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 introduces the sublinear scaling of the number of gas stations with city size.

"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".

Empirical 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.  A city that is twice as populous as another does not have twice as much infrastructure and twice as much productivity. It has a bit less infrastructure than you would expect, and a bit more productivity per head (as well as more crime).

The core argument of this book is that there is a simple law behind the complex systems from cells to cities, and companies: scaling.

There is a certain beauty in this simplicity and the derived predictions, 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 theoretically undefined.

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. 

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