Physicist Geoff West on why all organisms grow and die according to the same scaling laws, from bacteria to humans and big cities.
Prof. West, you argue that all organisms — from a small bacterium to a giant blue whale — follow the same universal law when it comes to growth.
It might sound crazy, but all organisms obey the same universal scaling laws, including systems created by man such as cities or companies. They grow fast in the beginning, then growth slows down, and in the end they all die. Energy is the fundamental concept and the fundamental quantity that drives everything in the universe. No matter whether we look at a bacterium or a company, there is no life without the constant flow and transposition of energy. If you plot metabolism vs. the size of an organism, you will find that all of them — from a single-cell organism up to a human — line up in an extremely simple way, according to a power law.
What’s your explanation for this distribution?
Linear growth means that the energy consumption of an organism will double when it doubles in size. But in fact, every time you double an organism you save 25% in energy, whether you double from 2 to 4 grams or from 2 to 4 kilos. So there is a mechanism that allows nature to be more efficient the bigger an organism becomes. The amazing thing is that every physiological variable that you measure reflects a similar kind of very systematic scaling. The reason is the network structure of life. It is very obvious for a tree, but it also holds true for elephants and humans. When you think of what’s inside us, we are a network of networks. These interconnected, highly integrated network systems determine where blood, oxygen, nutrients, hormones or neural impulses go. And this network is not arbitrary. Evolution has optimized networks to grow up to the point where they can minimize the amount of energy we have to use in order to stay alive. It thereby lets you maximize the energy you can allocate to having offspring.
Once a system has reached its optimal threshold it stops growing.
How did this preprogrammed limit on growth evolve?
A network’s purpose is to provide the optimum amount of energy to an organism so it can minimize its metabolism. A human being, for instance, only needs 2,000 food calories a day and not 10,000. Once a system has reached its optimal threshold it stops growing and goes into maintenance mode. That’s the reason why no organism can have arms that are two meters long or a tree trunk that’s 1,000 meters tall. Networks have a second characteristic. A network has to be what is technically called space filling to service every part, every cell of your body. Whatever the network of a city, it has to perform the same feat for survival: serve every building. That’s also true for a business. A company better serve all its customers and its product space in some way. Once you understand the mathematics behind these scaling laws, you can predict the characteristics of a system.
Don’t you risk simplifying things too much by comparing trees to animals and even humans?
The data we have gathered and analyzed show that we are looking at universal scaling laws. If you look at the equations that describe metabolism, you can say a mouse is a scaled down version of an elephant. If you give me the type and size of an organism, even if I have never seen it before, I can tell you with 80 to 90% accuracy almost everything about it. I can tell you how long it will live, how many offspring it will have, how many times its heart will beat over the course of its life, what the length of its aorta is, how many hours of sleep it needs. For the first time, we have a universal formula that describes the growth of all organisms. It is important to note that this growth or scaling is sublinear, meaning it’s not a straight line at a 90 degree angle but running slightly below. If you double an organism’s size, instead of delivering twice as much energy to a given cell or mass of tissue, you can only deliver 1.75 or just 75% more. The 25% savings are nature's efficiency gain.
Surprisingly, our formulas apply just as beautifully to urban life as to biology.
How did you come up with the idea to apply the scaling laws of biology to a modern city or enterprise?
Cities or companies are networks, too, but they are socio-economic networks. We wanted to test our theory and were wondering whether we can use it to predict certain metrics like the number of gas stations, depending on a city’s size. Surprisingly, our formulas apply just as beautifully to urban life as to biology. If a city doubles in size, I don’t need to double the infrastructure to keep its metabolism going. It also exhibits sublinear growth, although the number here is not 25% less than with biological organisms, but only 15%. In other words: A city that doubles in size doesn’t need 100 new gas stations but only 85. That’s true for all types of cities around the world and for any type of infrastructure: roads, gas and electricity networks, police stations. As we looked at the results, there were some I could not make sense of. Socio-economic factors such as patents per capita, mobile communications, crime and health statistics don’t scale in the usual sublinear fashion. They run 15 percent above the straight line, meaning they have superlinear growth.
Proving your grand theory wrong after all?
Quite the opposite. I hadn’t considered that the laws governing the growth of socio-economic networks are different. If cities and companies scale, some of that scaling is determined by something different as biology. By social networks made up of people not cells. Social networks thrive on feedback. The more people I am interacting with, the more ideas come out of it. This superlinear scaling is the key to urbanization’s success. You can observe the same superlinear scaling when you look at wages, wealth, the number of professional people, the number of restaurants. It’s also true for the negatives of urban life such as crime statistics, the amount of disease or AIDS cases. They all scale to the same degree, no matter where you look across the globe: cities in North and South America, Europe, Asia. Every time you double the size of a city, you can manage with only 85% of additional infrastructure, and at the same time you get 115% of the good, the bad, and the ugliness of social networks.
A city with millions of people is nothing else but a scaled up version of a small city, but it’s much more efficient.
Since 2015, more than half of humanity lives in cities, and that number is expected to reach three quarters by 2050. Is rampant urbanization on balance a good thing or reason to be concerned?
The more people move into a large city, the fewer additional resources we need per capita for infrastructure and energy. That’s why New York is the greenest city in the United States. A city with millions of people is strictly speaking nothing else but a scaled up version of a small city, but it’s much more efficient. Similar to how an elephant has a much more efficient metabolism than a mouse in spite of its size. We humans have invented this extraordinary machine called a city to facilitate what we’re doing best: producing ideas, wealth, and innovation.
But why do large cities not die off after a certain time like biological organisms do?
Because cities have what I call a social metabolism. Contrary to what you might think, cities are extraordinarily resilient. We can hardly think of a city that has truly died — and if they did, it was mostly due to environmental problems tied to their location. Many cities go through bad times, and many stagnate, but they all come back. Yet even a successful city cannot escape the laws of physics. There is no infinite growth. A network that grows in superlinear fashion will eventually reach its limit when it will either stagnate or collapse and die. That can happen in five, 10 or 100 years, but it’s unavoidable.
There is no infinite growth.
Growth until collapse — that’s a model described by Thomas Malthus at the end of the 18th century…
True, I have only updated it for the modern era. You reach a resource limitation, and the system collapses. Humans have repeatedly avoided this transition to collapse by reinventing themselves. You need a major innovation to cause a paradigm shift. It’s like resetting the clock. The discovery of iron was one such reset, later the shift to coal, and more recently the invention of the computer. If you demand open-ended growth, then you have to have this continuous sequence of innovations. But there is a catch. Because time is speeding up, you have to do this reset in shorter and shorter intervals.
The limits of superlinear growth dictate why progress is constantly speeding up?
Exactly. If it took 100 years to develop some innovation a thousand years ago, now it takes only 25 years to a new wave of develop IT. Somewhere over the next 20 years, we have to make another major innovation that rivals the impact of the IT revolution. And we have to do another reset in even less time, and so on. You can take this argument ad absurdum. Eventually, you need to come up with a revolution every six months. Which means, we somehow have to find a way to break the chains of superlinear growth.
Silicon Valley’s tech elite disagrees. They claim we will always come up with something new to launch us into the next golden age.
The standard mantra from futurists and economists is to innovate our way out. But I doubt that things like autonomous vehicles or big data can save us because we pay with ever faster and shorter innovation cycles. More recently, I have been thinking that the way out of this could be to go back to the source of it all: social networks. This amazing growth stems from the way we are interacting with each other. If that is true, a deep cultural change could also be a reset. We need to shift away from always wanting more and demanding better quarterly results.
In his book “Scale” (Penguin, 2017) Geoffrey West tries to formulate a universal law describing the growth of complex organisms. The 76-year-old UK native previously worked at Stanford University before joining the interdisciplinary Santa Fe Institute in New Mexico, which is considered the birthplace of complexity research. West also worked for many years at the nearby Los Alamos National Laboratory.
Delving into the question “how everything works” has motivated West since his childhood. “I happened to come from a family of short-lived males. Getting on in my 50s, I became more conscious of the meaning of life.” He also considers biology as the dominant science of the 21st century, replacing physics. “It won’t be the dominant science unless it becomes quantitative, mathematized and computable, and therefore predictive.”
Geoffrey West’s universal scaling law offers intriguing insights when it comes to designing for urban growth and mobility.
As the physicist discovered by working with colleagues at the Santa Fe Institute and the ETH in Zurich, larger cities around the world require less infrastructure per capita than smaller ones as they keep growing.
“Transport and supply networks, such as the number of gas stations, the total length of electrical lines, road, water and gas lines, all scale in much the same way around the world,” West says. “A city of 10 million people typically needs 15 percent less of the same infrastructure compared with two cities of five million each.”
People and their social connections are the hidden reason for this similarity among urban systems across the globe. “Cities provide a natural mechanism for reaping the benefits of high social connectivity between people.” West compares traffic flow to a living body: “The main road leaving the city acts like an aorta, the subsequent roads are its arteries, and the terminal roads leading to the various towns and cities are its capillaries.” If urban planners used such live and detailed data, the academic believes, it would give them key metrics for successfully developing new parts of town or deciding where to build a new mall or stadium.
Scaling also speeds up urban life. The Israeli transportation engineer Yakov Zahavi was one of the first to recognize this when he wrote reports on urban transportation in the 1970s. He discovered that the average person spends about an hour each day traveling, no matter what size a city is and what mode of transportation he or she uses — a finding supported by global studies of urban commuters.
As mobility options increased from walking to horses and then subways and cars, people have stuck to their one-hour travel budget and chosen to live further away and travel longer distances to get to work. “The increase in transportation speed resulting from marvelous innovations has not been used to reduce commuting time but instead to increase commuting distances,” explains West.
This behavior has affected the urban geography. The size of cities, says West, has “to some degree been determined by the efficiency of their transportation systems for delivering people to their workplaces in not much more than half an hour’s time. Whether people lived in ancient Rome, a medieval town, or modern New York, they spend about an hour on commuting.”
Italian nuclear physicist Cesare Marchetti analyzed this universal rule of transport in more detail in the 1990s and even gave the one-hour travel radius a name: the Marchetti Constant. It has wide-reaching consequences for urban planning. He calculated that because walking speed is about 5 km/h, the typical size of a “walking city” is about 5 km across or 20 square km. Take a tram, and the one-hour city has a diameter of 14 km. Drive a car and 1 Marchetti increases to 40 km, assuming constant speeds.
With the rise of autonomous, shared vehicles or air taxis, some transportation experts like U.S. technologist Paul Levin think that Marchetti’s formula is overdue for an update that incorporates the quality of mobility and people’s willingness to travel because an AV lets them work or watch a movie en route. Future models of transport, Levin argues, will cause more sprawl because they make it possible for more people to live further away from work and commute increasingly longer distances.
The old urban cores may be car-free, but Marchetti’s one-hour travel rule still holds and will shape urban growth. Urban planners designing for the future of mobility should take note, West adds: “As planners begin to design green carless communities and as more cities ban automobiles from their centers, understanding and implementing the implied constraints of Marchetti’s constant becomes an important consideration for maintaining the functionality of the city.”