Scale: The Universal Laws of Growth, Innovation, Sustainability, and the Pace of Life, in Organisms, Cities, Economies, and Companies

by Geoffrey West

The existence of these remarkable regularities strongly suggests that there is a common conceptual framework underlying all of these very different highly complex phenomena and that the dynamics, growth, and organization of animals, plants, human social behavior, cities, and companies are, in fact, subject to similar generic “laws.”

Indeed, there is a fundamental law of nature that cannot be transgressed, called the Second Law of Thermodynamics, which says that whenever energy is transformed into a useful form, it also produces “useless” energy as a degraded by-product: “unintended consequences” in the form of inaccessible disorganized heat or unusable products are inevitable. There are no perpetual motion machines.

Whenever energy is used or processed in order to make or maintain order within a closed system, some degree of disorder is inevitable—entropy always increases. The word entropy, by the way, is the literal Greek translation of “transformation” or “evolution.” Lest you think there might be some loophole in this law, it is worth quoting Einstein on the subject: “It is the only physical theory of universal content which I am convinced will never be overthrown” . . . and he included his own laws of relativity in this.

To maintain order and structure in an evolving system requires the continual supply and use of energy whose by-product is disorder.

The battle to combat entropy by continually having to supply more energy for growth, innovation, maintenance, and repair, which becomes increasingly more challenging as the system ages, underlies any serious discussion of aging, mortality, resilience, and sustainability, whether for organisms, companies, or societies.

Scaling and scalability, that is, how things change with size, and the fundamental rules and principles they obey are central themes that run throughout the book

Scaling simply refers, in its most elemental form, to how a system responds when its size changes. What happens to a city or a company if its size is doubled? Or to a building, an airplane, an economy, or an animal if its size is halved? If the population of a city is doubled, does the resulting city have approximately twice as many roads, twice as much crime, and produce twice as many patents? Do the profits of a company double if its sales double, and does an animal require half as much food if its weight is halved?

Scaling arguments have led to a deep understanding of the dynamics of tipping points and phase transitions (how, for example, liquids freeze into solids or vaporize into gases), chaotic phenomena (the “butterfly effect” in which the mythical flapping of a butterfly’s wings in Brazil leads to a hurricane in Florida), the discovery of quarks (the building blocks of matter), the unification of the fundamental forces of nature, and the evolution of the universe after the Big Bang.

This systematic “value-added” bonus as size increases is called increasing returns to scale by economists and social scientists, whereas physicists prefer the more sexy term superlinear scaling.

sublinear scaling.

much of the book is devoted to explaining and understanding the origins of such nonlinear behavior and how it can be used to address a broad range of questions with examples drawn from across the entire spectrum of science, technology, economics, and business, as well as from daily life, science fiction, and sports.

U.S. Supreme Court justice Potter Stewart, who when discussing the concept of pornography and its relationship to free speech in a landmark decision of 1964 made the following marvelous comment:

A typical complex system is composed of myriad individual constituents or agents that once aggregated take on collective characteristics that are usually not manifested in, nor could easily be predicted from, the properties of the individual components themselves.

Ant colonies are built without forethought and without the aid of any single mind or any group discussion or consultation. There is no blueprint or master plan. Just thousands of ants working mindlessly in the dark moving millions of grains of earth and sand to create these impressive structures. This feat is accomplished by each individual ant obeying just a few simple rules mediated by chemical cues and other signals, resulting in an extraordinarily coherent collective output. It is almost as if they were programmed to be microscopic operations in a giant computer algorithm.

These computer investigations were very important in providing strong support for the idea that there might actually be a simplicity underlying the complexity that we observe in many such systems and that they might therefore be amenable to scientific analysis.

In general, then, a universal characteristic of a complex system is that the whole is greater than, and often significantly different from, the simple linear sum of its parts.

This collective outcome, in which a system manifests significantly different characteristics from those resulting from simply adding up all of the contributions of its individual constituent parts, is called an emergent behavior.

An important lesson from these investigations is that, while it is not generally possible to make detailed predictions about such systems, it is sometimes possible to derive a coarse-grained quantitative description for the average salient features of the system.

For example, although we will never be able to predict precisely when a particular person will die, we ought to be able to predict why the life span of human beings is on the order of one hundred years.

This scaling law for metabolic rate, known as Kleiber’s law after the biologist who first articulated it, is valid across almost all taxonomic groups, including mammals, birds, fish, crustacea, bacteria, plants, and cells. Even more impressive, however, is that similar scaling laws hold for essentially all physiological quantities and life-history events, including

growth rate, heart rate, evolutionary rate, genome length, mitochondrial density, gray matter in the brain, life span, the height of trees and even the number of their leaves.

0.75. So, for example, across the globe, fewer roads and electrical cables are needed per capita the bigger the city.

Despite their amazing diversity and complexity across the globe, and despite localized urban planning, cities manifest a surprising coarse-grained simplicity, regularity, and predictability.15

finite time singularity. In a nutshell, the problem is that the theory also predicts that unbounded growth cannot be sustained without having either infinite resources or inducing major paradigm shifts that “reset” the clock before potential collapse occurs.

like organisms and cities, companies also scale as simple power laws.

In this sense, companies are much more like organisms than cities. The scaling exponent for companies is around 0.9, to be compared with 0.85 for the infrastructure of cities and 0.75 for organisms.

It is not surprising, therefore, that an alternative definition of the BMI has been suggested in which the BMI is defined as body weight divided by the cube of the height; it is known as the Ponderal index.

Clearly, the structure, whatever it is, will eventually collapse under its own weight if its size is arbitrarily increased. There are limits to size and growth. To which should have been added the critical phrase “unless something changes.” Change and, by implication, innovation, must occur in order to continue growing and avoid collapse. Growth and the continual need to be adapting to the challenges of new or changing environments, often in the form of “improvement” or increasing efficiency, are major drivers of innovation.

In all of these cases, the big question is how do you realistically and reliably scale up the results and observations of the model system to the real thing?

The Great Eastern ended up as a floating music hall and advertising billboard in Liverpool before being broken up in 1889. Such was the sad ending to a glorious vision. A bizarre footnote to this tale that is probably of interest only to ardent soccer fans is that in 1891 when the famous British football club Liverpool was being founded, they searched for a flagpole for their new stadium and purchased the top mast of the Great Eastern for that purpose. It still proudly stands there today.

One of the curious unintended consequences of these advances is that almost all automobiles, for example, now look alike because all manufacturers are solving the same equations to optimize similar performance parameters. Fifty years ago, before we had access to such high-powered computation and therefore less accuracy in predicting outcomes, and before we became so concerned about fuel performance and exhaust pollution, the diversity of car design was much more varied and consequently much more interesting. Compare a 1957 Studebaker Hawk or a 1927 Rolls-Royce to a relatively

boring-looking 2006 Honda Civic or a 2014 Tesla, even though these latter vehicles are far superior machines.

As emphasized in the opening chapter, living systems, from the smallest bacteria to the largest cities and ecosystems, are quintessential complex adaptive systems operating over an enormous range of multiple spatial, temporal, energy, and mass scales.

D’Arcy Wentworth Thompson

Isambard Kingdom Brunel,

A cartoon of this process is shown here.

principles. 7. PHYSICS MEETS BIOLOGY: ON THE NATURE OF THEORIES, MODELS, AND EXPLANATIONS As I was struggling to develop the

of ecology

the philosophy

“zeroth order”

Optimization principles

they are space filling, have invariant terminal units, and minimize the energy needed to pump fluid through the system.

Even though your lungs are only about the size of a football with a volume of about 5 to 6 liters (about one and a half gallons), the total surface area of the alveoli, which are the terminal units of the respiratory system where oxygen and carbon dioxide are exchanged with the blood, is almost the size of a tennis court and the total length of all the airways is about

the size of a football with a volume of about 5 to 6 liters (about one and a half gallons), the total surface area of the alveoli, which are the terminal units of the respiratory system where oxygen and carbon dioxide are exchanged with the blood, is almost the size of a tennis court and the total length of all the airways is about 2,500 kilometers, almost the distance from Los Angeles to Chicago, or London to Moscow. Even more striking is that if all the arteries, veins, and capillaries of your circulatory system were laid end to end, their total length would be about 100,000 kilometers, or nearly two and a half times around the Earth or over a third of the distance to the moon . . . and all of this neatly fits inside your five-to-six-foot-tall body. It’s quite fantastic and yet another amazing feature of your body where natural selection has exploited the wonders of physics, chemistry, and mathematics.

2,500 kilometers, almost the distance from Los Angeles to Chicago, or London to Moscow. Even more striking is that if all the arteries, veins, and capillaries of your circulatory system were laid end to end, their total length would be about 100,000 kilometers, or nearly two and a half times around the Earth or over a third of the distance to the moon . . . and all of this neatly fits inside your five-to-six-foot-tall body. It’s quite fantastic and yet anothe...

space filling can scale as if it’s an area.

Its fractality effectively endows it with an additional dimension.

So when the time comes you stuff in as much and as many as you possibly can to fill the entire volume of the tub. Now, recall that ordinary volumes scale faster than areas, so if you were to double the size of your washing machine by doubling all of its lengths while keeping its shape the same, its volume would increase by a factor of eight (23) whereas all of its surface areas would increase by a factor of four (22). Naively, you might therefore conclude that because sheets are essentially all area and consequently two-dimensional (their thickness being negligible), you could accommodate four times as many sheets by doubling the size of your washing machine. However, if we stuff all of the sheets into the tub so that they completely fill its entire volume and because this volume has increased by a factor of eight, then it’s clear that you can actually accommodate eight times as many sheets, rather than just four times. In other words, the total effective area of two-dimensional sheets filling three-dimensional washing machines scales like a volume rather than an area, so in this sense, we have turned an area into a volume.

There is, however, one human invention that has evolved via this process which is comparable to what traditional natural selection has thus far produced, and that is the city. Cities clearly have an organic nature and share much in common with traditional organisms. They metabolize, they grow, they evolve, they sleep, they age, they contract disease, suffer damage and repair themselves, and so on.

Baruch Spinoza. As Einstein wrote,10 “We followers of Spinoza see our God in the wonderful order and lawfulness of all that exists and in its soul as it reveals itself in man and animal.”