In 1996 you extended those ideas about the patterns of life at the Santa Fe Institute, where you collaborated with biologists for 15 years. How did that come about and what did you find?
One day I got a call from Mike Simmons, the vice president at the Santa Fe Institute. He brought me together with Jim Brown, a well-known biologist at the University of New Mexico who, in a fantastic coincidence, was looking for a physicist to work with on biological scaling. Along with Brown’s student Brian Enquist, we met informally here at the institute at 9 a.m. every Friday, and talked about finding an underlying theory for the scale laws. Ultimately we built a mathematical model of the mammalian circulatory system from scratch, working from basic physical laws that described networks, flow, and so on. When we put all those rules together, we determined that the blood flow rate through any mammal’s aorta scales as mass to three-quarters. That allows us to predict the blood flow rate of a mammal just by knowing its size. And the blood flow rate through the aorta defines the metabolic rate, because it’s what carries the oxygen. In other words, our mathematical model gave us Kleiber’s law.
So what did your mathematical model tell you about how real mammals are constructed?
That the scaling laws they follow are the natural, emergent outgrowth of networks—in this case, a circulatory network—that are constructed according to basic sets of rules.
Do these laws work in other life forms besides animals?
Yes. For instance, we extended scaling laws to plants and trees. We found that the number of branches scales to the radius of the tree trunk, which tells us that even the generic geometry of trees obeys scaling laws. When you walk through a forest, you just see this mess. Trees look like random conglomerations of branches. But in fact there’s unbelievable structure there. And these equations describe it.
In 2003 you started studying cities. What led you there?
Cities are obvious metaphors for life. We call roads “arteries” and so forth. But more importantly, they are our unique creations. Santa Fe feels unique, New York City feels unique. They have their own culture, history, and geography. They have their own planners, politicians, and architects. Yet when my collaborators and I looked at tremendous amounts of data about cities, we found universal scaling laws again. Each city is not so unique after all. If you look at any infrastructural quantity—the number of gas stations, the surface area of the roads, the length of electric cables—it always scales as the population of the city raised to approximately the 0.85 power.
So even without planning it, every city’s infrastructure follows the same mathematical pattern? How can that be?
The bigger the city is, the less infrastructure you need per capita. That law seems to be the same in all of the data we can get at. It is a really interesting relationship, and it’s very reminiscent of scaling laws in biology. However, when we looked at socioeconomic quantities—quantities that have no analogue in biology, like wages, patents produced, crime, number of police, et cetera—we found that unlike everything we’d seen in biology, cities scale in a superlinear fashion: The exponent was bigger than 1, about 1.15. That means that when you double the size of the city, you get more than double the amount of both good and bad socioeconomic quantities—patents, aids cases, wages, crime, and so on.
Despite all the efforts of planners, architects, and politicians, cities somehow obey scaling laws.”
And those laws apply to all cities, regardless of location?
This scaling seems to be true across the globe, no matter where you are. I think that what’s responsible for it is the hierarchical nature of human relationships. First of all, you cluster in a family. On average, an individual doesn’t have a powerful connection with more than four to six people, and that’s just as true here in the U.S. as it is in China. Then there are clusters of families, and then larger clusters that form neighborhoods, and so on, all the way up. The structure of this network of relationships could be analogous to the behavior of the networks of blood vessels in the body. They could be the universal thing holding the city together.
Does your discovery have practical implications for urban planning?
You tell me the size of any city in the United States and I can tell you with 80 to 90 percent accuracy almost everything about it. The scaling laws tell you that despite all of the efforts of planners, geographers, economists, architects, and politicians, and all of the local history, geography, and culture, somehow cities end up having to obey these scaling laws. We need to be aware of those forces when we design and redesign cities.
Can your insights about the scaling laws of cities help us understand the impact of population growth and urban migration?
I believe that part of what has made life on Earth so unbelievably resilient—able to evolve and survive across billions of years—is the fact that its growth is generally sublinear, with the exponents smaller than 1. Because of that, organisms evolve over generations rather than within their own lifetimes, and such gradual change is incredibly stable. But human population growth and our use of resources are both growing superlinearly, and that is potentially unstable.
Meaning that our consumption of resources can’t keep growing forever?
Right. Our theory suggests we will face something mathematicians call a “finite time singularity.” Equations with superlinear behavior, rather than leveling out like the sublinear ones in biology, go to infinity in a finite time. But that’s impossible, because you’re going to run out of finite resources. The equations tell us that when you reach this point, the system stagnates and collapses.
If your interpretation of population growth is true, why haven’t cities already collapsed?
The growth equation was derived with certain conditions that are determined by the cultural innovation that dominates each historic period: iron, computers, whatever it is. An innovation that changes everything—like a new fuel—resets the clock, so you can avoid the singularity a bit longer. But the theory says that to avoid the singularity, these innovations have to keep coming faster and faster.
What are the issues most likely to push us toward collapse?
I think the biggest stresses are clearly going to be on energy, food, and clean water. A lot of people are going to be denied these basics across the globe. If there is a collapse—and I hope I’m wrong—it will almost certainly come from social unrest starting in the most deprived areas, which will spread to the developed world.
How can we prevent that kind of collapse from happening?
We need to seriously rethink our socioeconomic framework. It will be a huge social and political challenge, but we have to move to an economy based on no growth or limited growth. And we need to bring together economists, scientists, and politicians to devise a strategy for doing what has to be done. I think there is a way out of this, but I’m afraid we might not have time to find it.
That sounds similar to the dire warnings of economist Thomas Malthus in the 19th century and biologist Paul Ehrlich in the 1960s. Those predictions proved spectacularly wrong. How is yours different?
I’ve been called a neo-Malthusian as if it’s a horrible word, but I’m proud to be one. Ehrlich and Malthus were wrong because they didn’t take into account innovation and technological change. But the spirit was correct, and it is unfortunate that people dismiss their arguments outright. Even though innovations reset the clock, from the work that I’ve done, I think all they do is delay collapse.