Book Review | Scale - The Universal Laws Of Growth, Innovation And Sustainability In Organisms, Economies, Cities And Companies By Geoffrey West

Introduction: Scaling

What is common to living organisms, cities, and corporations? This book explores brilliantly the uniting link. The intuitive feel is that these three have chaotic, messy, and difficult-to-understand rules of growth and collapse. However, the author shows, by deep data and extensive research, that it is not so. The amazingly simple rules governing the growth and size of organisms, corporations, and cities allow extrapolation to answer questions like the maximum possible size of the organisms, or sustainability of cities.

What is “scaling”? It simply refers to how systems respond when their sizes change. If the size of the organism or the city doubles or halves, what happens to the system? In cities, would doubling the size of the city mean double the rate of employment, crime, and wealth creation? Does the heart rate and blood pressure double with the doubling of the size of the organism? If the size of an animal is one-fourth that of another animal, would its food requirement decrease by a factor of four? Similarly, if the size of the corporation doubled, do the profits double too?

Such seemingly innocuous questions about scaling in the last five decades have deeply impacted every single aspect of our lives. Scaling arguments have allowed a deeper understanding of a wide variety of issues: tipping points and phase transitions, chaotic phenomena, quarks as the building blocks of nature, the unification of the fundamental forces of nature, and the evolution of the Universe after the Big Bang. More practically, scaling plays an important role in designing buildings, ships, airplanes, and computers. Doubling the size of a ship or bridge to double its capacity would collapse the structure with its own weight, as some initial builders realised painfully.

Understanding scaling laws would allow extrapolation from small to large in an efficient and cost-effective manner.

SFI, or the Santa Fe Institute, is an amazing place that, in the words of the author, is an instantiation of the very thing it studies: a complex adaptive system. The science of scaling and the study of complex adaptive systems combine physics, mathematics, biology, economics, and social sciences in a unique blend. This book is the result of the efforts of the hundreds of scientists and scholars working at that institute. The institute is known internationally as the “formal birthplace of the interdisciplinary study of complex systems.”

Generic Properties of Complex Adaptive Systems

Living organisms, cities, and companies are complex adaptive systems. They are self-sustaining, and their networks have certain key general properties allowing their life histories. The study of living organisms initially established three general network properties, which later extended to cities and corporations. Such studies have led to the determination of mathematical scaling laws.

The first is “space-filling,” which implies that the tentacles of the network must extend everywhere throughout the system. The geometry and topology of the network must serve all locally active subunits. The networks fill the system in a manner that the “last in the line” would be able to access the services of the whole. For instance, a living organism’s cell receives adequate nutrition and disposes of waste effectively.

The second is the “invariance of terminal units,” which means that the terminal units of a given network design have approximately the same size and characteristics irrespective of the size of the organism. Terminal units—the cell, or the mitochondria in the cells powering respiration, the petioles, or the last branch of plants and trees—are of the same size irrespective of the size of the organism. The size of the cell, or mitochondria, is the same in humans, whales, mice, and elephants. The basic building blocks of living organisms remain the same size, explaining the parsimonious nature of natural selection.

The third and final postulate states that the continuous multiple feedback and fine-tuning mechanisms implicit in the ongoing processes of natural selection over enormous time have led to the “optimisation of network performance.” In living organisms, networks have evolved to minimise the energy for sustaining an average lifespan and performing mundane tasks to maximise the amount available for sex, reproduction, and raising of offspring.

Eventually, these ideas led to a predictive mathematical framework for deriving power scales and understanding many essential features of diverse biological systems and functions, including tumors, ageing, death, cell size, and evolutionary rates. The theory and observation showed that, from cells and whales to community structures, the pace of life systematically and predictably slows down with increasing size, and economies of scale accompany this. This is known as the “metabolic theory of ecology.”

Life Sciences

There is an important and powerful observation in biology called the ’quarter-power scaling law’ which states that almost all physiological variables and life-history events scale with the size of the organism in a simple and predictable fashion. What began as a ‘scaling program’ study of biological organisms at the Santa Fe Institute, where the author worked and was its president too, expanded beyond biological systems to human socioeconomic systems like cities and companies and finally led to evolving theories on global sustainability.

Despite the huge diversity and complexity of life, many fundamental parameters like metabolic rate, heart rate, and blood pressure scale in a simple and systematic fashion with respect to size. Metabolism scales as a power law with an exponent of ¾ over 27 orders of magnitude in mammals from the shrimp to a blue whale, the smallest to the largest. This implies that as the size of the organism doubles, the metabolic rate goes up not by 100% but by 75%. Hence, there is an ‘economy of scale’ operating here.

The ¾ power scaling says that, despite having 10,000 times as many cells to support, the metabolic rate of an elephant is only 1000 times larger than that of the rat. The metabolic rate of an elephant cell is less than that of a rat. Biology primarily relies on economies of scale. This is true for most physiological traits or events that happen during a person’s life, such as life spans, growth rates, DNA nucleotide substitution rates, genome lengths, tree heights, and the mass of cerebral grey matter.

Also, the corresponding exponents express a universality, invariably approximating simple multiples of ¼—a quarter-power allometric scaling. One of the amazing consequences of these scaling laws is that almost all mammals have a fixed heartbeat of 1.5 billion times during a lifetime! The author fascinatingly explains the maximum size attainable by an organism without collapsing under its own weight and the mechanisms for growing, plateauing, ageing, and then dying.

The evolution of living organisms has natural selection and randomness at its core. We would expect that each organism or living organism would have its own unique history where randomness, mutations, and interactions with environments come into play. Systemic rules and regularity are antithetical to the concept of randomness woven into natural selection. However, the regularity of scaling suggests that generic underlying mechanisms constrain evolutionary processes. Hence, there is a possibility of some basic quantifiable laws from which the gross behaviour of living organisms would emerge.

From Living Organisms to Cities and Corporations

These three principles are at the core of scaling laws, which have their analogous counterparts in cities and corporations. The “optimised,” “space-filling,” and “fractal-like branching networks” have dynamical and geometric constraints that are independent of specific evolved designs. Researchers at SFI extended the observations to evaluate the growth and evolution of cities and corporations.

Do some similar scaling laws apply to them too? Do the parameters related to a city, like the per capita income, crimes, and social networks, increase in a linear fashion or a sub-linear fashion? The surprising observations concluded were that indeed similar scaling laws, like for biological organisms, existed, and exhibited well-defined power laws. However, there were some essential differences.

“Zipf’s law” (originally for word usage in a language) stated that the frequency of any word in a corpus of text is inversely proportional to its rank in the frequency table. In plainer English, this means that the most frequent word is twice as frequent as the second most frequent, three times as the third most frequent, and so on. The mystifying aspect of this law is that it is applicable to a huge array of examples, like cities, corporations, ships, trees, particles, meteorites, sand particles, oil fields, file sizes of internet traffic, and many more. The largest city in the world is twice the size of the second largest city. So, at a fine level, there are common laws that unite physics, chemistry, mathematics, and social sciences.

The Growth of Cities

Infrastructural measures of a city scale sub-linearly with the population size with a power exponent of 0.85 instead of 0.75 seen in biology. This includes the number of roads, power cables, electricity lines, gas stations, and so on, which show an economy of scale. This means that as the population of a city doubles, the infrastructural costs go up by only 85%, leading to a 15% saving. However, a new phenomenon called superlinear scaling became evident for socio-economic activities involving human interaction, such as wages, patents, AIDS cases, and violent crime. These scale with a common exponent around 1.15.

Since this is the case, social interaction metrics like innovation and wealth creation always go up as a city gets bigger, while infrastructure metrics show that people are saving more. Hence, whether the city size doubles from 50,000 to 100,000 or from 400,000 to 800,000, there is infrastructural growth of 85%, leading to 15% savings, and socioeconomic quantities increase by 15%. Hence, income, patents, and standards of living rise in cities, but the bad news is that crime and disease rise too. All socioeconomic parameters experience an equal increase in good, bad, and ugly aspects. Since the good is generally more attractive, there is a tendency worldwide to gravitate to the cities.

More than 50% of the population will be living in cities in the next few decades. The surprising observation is that this urban scaling transcends geography and culture. Whether in the US, China, India, Japan, or Europe, the phenomenon of sublinear and superlinear scaling is evident. Something as random as human interactions and social networking leading to emergent behaviour and the predictable growth of cities with mathematical rules is indeed surprising.

The social networks and urban infrastructure that define a city have some predictable growth rates. Big Data analysis of cell phone data carried out by researchers has confirmed this. The cities grow at a ‘super-exponential’ rate, and they are open-ended, meaning that they never collapse like a biological organism or even a corporation, for that matter. Corporations and living organisms seem to have a finite lifespan; that does not seem to apply to cities.

Despite having the same growth equations, organisms and cities have different outcomes, according to the author. Biology uses sublinear scaling and economies of scale to keep growth stable and slow down the pace of life. On the other hand, socioeconomic activity uses superlinear scaling and increasing returns to scale to keep growth unlimited and speed up life in cities. People even walk faster to an extent of 15% in the cities. In the social networks that characterise a city, there is a continuous positive feedback mechanism leading to multiplicative enhancement and, hence, an increased pace of life. Cities, as per this theory and observation all over the world, are showing a super-exponential unbounded growth.

This has tremendous implications for long-term sustainability issues on a global scale. Urbanization and migration take place rapidly in the study of urban economics, but the infrastructure lags. This gives rise to slums and all the socio-economic issues related to that. The world needs to prepare itself for the challenges of an ever-growing urban population and the increasing movement of the population from the rural to the urban areas.

Continued Urbanization and Finite time singularity

Two hundred years back, the US was mainly agricultural, with just 4% living in the cities. Today, 80% live in the cities. This is the case for developed nations as well as developing nations. No country comes even close to 4% being urban; Burundi, the poorest and least developed nation, is 10% urbanised. In 2006, half the world’s population concentrated in the urban areas. It was 15% a hundred years back and 30% by 1950. By 2050, the urban population will constitute 75% of the world population, with more than 2 billion moving to the cities. To put the staggering number in perspective, the author estimates that over the next 35 years, a million and a half people will urbanise every week!

Hence, the fate of the planet is inextricably linked to the fate of the cities. Cities generate the biggest global challenges: climate change, the availability of energy and resources, social unrest, and financial market disruptions, but they are also centres of innovation, wealth creation, and power. Cities are the problem and the solution. The author says,

This strongly suggests that there is a great urgency to develop a more quantitative, predictive, computational framework that can complement the traditional, more qualitative, narrative approaches to understanding cities — a framework that can help inform today’s and tomorrow’s practitioners and policymakers.

“Finite Time Singularity” is the term used when a certain parameter, like the population or GDP, becomes infinitely large at a finite time. At this point, things would obviously collapse as the output becomes more than the input, which would be the infrastructural or the ugly socio-economic parameters like crime and disease. How does one counter that? The author says that “innovation” comes into play here. The growth equation remains the same, but it is wrong to assume that its parameters do not change.

So long as social metabolism by way of wealth and knowledge creation remains active, an intervention, or “innovation,” happens, which resets the clock, allowing growth to continue and the impending singularity to be avoided. The Industrial Revolution, iron, steam, coal, fossil fuels, computation, and digital information technology have been the successive major innovations that have funded our continued growth. But the worrying aspect is that at one point even the pace of innovation needs acceleration. The discoveries and adaptations need to occur at a faster pace to catch up with an impending doom. Maybe a future innovation in waiting is the combination of the human brain with nanotechnology and artificial intelligence. Perhaps it could involve exploring and settling on distant planets or moons. We can only make ‘intelligent speculations’ on the nature of future innovations to prevent a collapse of the world.

Corporations

Finally, the researchers extended these scaling laws to businesses and corporations. Do they exist? The answer was a resounding yes. Can a predictive, quantitative science of companies based on scaling laws graph the trajectory of a company’s rise and fall? Is Walmart a scaled version of a smaller company?

The scaling phenomenon is in a sub-linear fashion like for organisms, but with an exponent of 0.9 compared to 0.85 for infrastructure in cities and 0.75 for organisms. However, there is a higher variation around the main graph for companies as compared to organisms and cities. This variation is higher for companies in the initial phase. The average growth and demise, however, follow general principles and constraints that transcend their size and business sector.

Companies grow rapidly in the initial years, taper off as they mature, and eventually stop growing relative to the GDP if they survive. Innovative ideas mark the initial phase. As they stabilise, product space inevitably narrows, and administrations and bureaucracies consume more energy. Finally, stagnation sets in, and the company dies. Half of all the companies in any given cohort of U.S. publicly traded companies disappear within ten years, and scant few make it to fifty years.

Lasting for a hundred years is a rare phenomenon, an outlier on the statistical charts. Change, adaptation, and reinventing are easy in the initial growing phase but increasingly difficult as the company grows to a middling size. The parallels to biological organisms are very striking. Deaths relative to live people are the same regardless of animal or company age. Publicly traded companies die through acquisitions, mergers, and bankruptcy at the same rate regardless of how well established they are and what they do. This contrasts with the ‘unbounded’ growth noted for cities.

Concluding Remarks

The author ends with a note on the future of science. Newton, Maxwell, Darwin, Einstein, quantum mechanics, quark theory, string theory, and so on represent classical science, looking at the unity underlying the diversity of nature. Parsimonious equations and explanations converging to a theory of everything have been the inspiration and goal of science. The present book shows that the search for some simplicity at the core of complex adaptive systems like cities, living organisms, economies, or companies may be the future of science in the 21st century.

However, he laments that Big Data is changing the method of science today. The number of networked devices in the world is more than double that of the global population, and the total screen area of all such devices is larger than one square foot per person. A deluge of huge data is hitting us, giving information like never before in the history of humankind. Big Data comes with its glorious cousins — machine learning and artificial intelligence — helping each other grow in unison. Data is good, and more data is better. This is a significant challenge to the traditional fields of hypothesis, modelling, and testing. Correlation has superseded causation. The why of any subject is becoming irrelevant as data accurately predicts the what and where. There is no place for models, as many science writers have lamented.

The author quotes Jim Gray, a computer scientist at Microsoft tragically lost at sea in 2007, who said that the data revolution is a major paradigm shift in how science would advance in the 21st century. The Big Data revolution was the fourth paradigm. The first three were:

1. Empirical observation (pre-Galileo)
2. Theory based on models and mathematics (post-Newtonian)
3. Computation and stimulation

Regardless, the world is rapidly approaching finite time singularities, putting pressure on innovations to speed up. Sustainability is an issue that the world must come to grips with as early and as effectively as possible. The book concludes with a hopeful tone, leaving the reader with a deep sense of satisfaction, having gained new and fascinating knowledge. Physics, chemistry, biology, mathematics, economics, and social sciences come together in a heady cocktail in this voluminous book. The complexity and importance of the concepts necessitate a methodical approach from the author. The book’s initial size should not deter anyone. Definitely, this book is worth adding to one’s personal shelf!