Not since I had to read D’Arcy Wentworth’s On Growth and Form for coursework have I read such a fascinating book that highlights the importance of mathematical laws in governing boundaries and patterns we observe in life. Geoffrey West is a polymath in the truest sense of the word: a theoretical physicist who, over the course of 20 years, applied complexity science to many questions in biology initially, and then extended his ideas to patterns seen in the organization and functioning of cities and companies. Scale is a wide-ranging intellectual foray with no equation in sight.
The science of complexity studies that wonderful phenomenon of emergence: when collections of individuals (molecules, cells, people etc.) aggregate and things start to happen that you did not or could not predict based on the properties of the individuals. It’s the whole being more than the sum of its parts. It’s simple rules giving rise to complex patterns. It’s hard to give an exact definition, says West, but, to paraphrase a certain US judge, “you know it when you see it”. The scaling and scalability West is interested in, then, is how things change with size. As it turns out, many properties don’t simply double when something doubles in size (i.e. in a linear fashion), but either increase slower or faster (sub- and superlinear scaling in jargon).
This is something we are all intuitively familiar with. The phrase “economy of scale” has crept into everyday speech with the rise of large corporations such as Amazon. And most of us will be aware that the Richter scale, telling us how strong earthquakes are, is a logarithmic scale (an increase of one unit corresponding to a tenfold increase in amplitude).
After the US government in 1993 cancelled plans to build the SSC, a huge particle accelerator to be used for physics experiments, West and many other physicists found themselves subjected to the sentiment that the era of physics was over: the 21st century was to be the age of biology. With feathers properly ruffled, West decided to apply the quantitative, analytical and predictive thinking typical of physics to open problems in biology. Already in his fifties at this time, age, death and mortality were subjects of particular appeal. But, to West’s surprise, there was no proper mechanistic theory of ageing. Why do humans live for about a hundred years? And why do smaller mammals live shorter lives?
“[…] complexity […]”you know it when you see it””
The first two chapters to delve into West’s research are, for a biologist, an absolute pleasure to read. The famous biologist Julian Huxley coined the term allometric scaling to describe how certain properties of organisms scale disproportionately with size (e.g. elephants have relatively thicker legs than mice once you correct for the difference in length). However, allometric scaling affects more than just morphology, it also affects physiological mechanisms such as metabolism. West’s findings that the underlying geometric properties of the networks that deliver energy, materials and information to cells (e.g. the system of blood vessels) dictates general properties and limits, is one of the many “aha” moments that this book delivers. I will not try to summarise his argument here, but suffice to say it makes beautiful sense and is well presented. It allows us to explain why mammals can’t get smaller than shrews or bigger than whales. Why we stop growing with age. Or why larger animals live longer.
But networks for distributing stuff (whether this is material goods or immaterial things such as knowledge) are everywhere. And West being the polymath he is, the book then branches out to describe how his subsequent research and collaborations have tried to apply these network principles to cities and companies. In his opinion, cities are one of the greatest human inventions, having afforded a stage for many of the social and economic developments of the last two centuries to play out on. Rapid urbanization is generating many challenges that apply to cities everywhere (water availability, environmental impacts etc.). So, can the network principles observed in biology be applied here to describe, understand and predict the growth, dynamics and evolution of cities and companies? West’s findings suggest yes: the urban pace of life, crime, income, and many other things scale in a non-linear fashion when size increases.
Similarly, though West admits this is still very much work in progress, more recent work has been applying these ideas to ask if we can formulate a science of companies. Whether looking at company income, profits, or age, non-linear scaling patterns are found when comparing large numbers of companies across the globe.
“[…] that the underlying geometric properties of networks […] dictates general properties and limits, is one of the many “aha” moments that this book delivers”
A final chapter then asks if and how the accelerating pace of life and socio-economic development is sustainable. He thinks not (and I agree with him), and he goes to some effort to stress that his reasoning is not just another rehash of Malthusian arguments (a topic on which I hope to write more at some point). Opponents have pointed out that Malthus and later thinkers were mistaken by not taking into account human ingenuity and innovation, which have repeatedly saved the day. For now. But West makes a great point that even this tempo of breakthrough innovations (or paradigm shifts) is not scaling linearly with time. How to avert societal collapse is not something he has an answer to, but it certainly doesn’t lie in persisting in continued, open-ended growth.
Despite being a biologist, I found these later chapters very interesting, and here, too, moments of great insights will occur while reading. I do feel that this is where the book starts to lose focus a bit. Given how far removed the topic is from what I normally read and what I know, West does a great job at not making me lose interest and at keeping me on board, making me understand what he is talking about. But he does wander a fair bit, throwing in regular preludes, interludes and other digressions. And that’s before I mention the many anecdotes and introductions to co-workers. It’s not that the digressions are not interesting, nor that the anecdotes are not amusing. By and large they are, but the cohesiveness and focus of the book suffer somewhat in my opinion. An 8-page postscript / acknowledgement section in small print seems symptomatic of this, and buried in there are kudos to the editors who have pared down an even bigger initial manuscript. A further niggle is that the reproduction of certain graphs (especially those containing data points for multiple categories) in greyscale doesn’t really work. Although they get across the general message, they were clearly designed with colour in mind and in my opinion should either have been reproduced in colour, modified to be comprehensible in greyscale, or just left out.
Nevertheless, Scale is a book of exceptional breadth that talks about some really big ideas in a comprehensible manner. It’s the kind of book that doesn’t come along often, written on the back of a long and rich career. If you don’t mind taking your time and being led around many ideas, then Scale is a great book to sit down with and will provide plenty of food for thought.
Disclosure: The publisher provided a review copy of this book. The opinion expressed here is my own, however.
The folks over at Kurzgesagt have just released a video on the phenomenon of emergence: https://www.youtube.com/watch?v=16W7c0mb-rE