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I’m underneath New York City, a few blocks east of Times Square. I’ve entered through a manhole in the middle of the street and descended a few feet down a slippery ladder. At first glance, there’s not much to see: just a tangle of wires and sewer lines that carry our electricity, our conversations, our shit. It’s the landscape of rodents and repairmen, a world that we notice only when something goes wrong, when a water main bursts or a sinkhole appears. But once my eyes adjust to the dim light, I begin to sense the quiet pulse of the place. There is the slow swoosh of anonymous liquids, punctuated now and again by the rumble of a subway train. The mechanical pumps keep a steady beat, like some sort of rusted heart. The city seems alive, and I’m inside its insides.
Cities have long been compared to organisms—Plato talked about the city as a corporeal body—but being underneath the street makes the metaphor literal. These are the guts of the city, the metal intestines that allow suburbs to sprawl and skyscrapers to rise. The fiber-optic cables are nerves, and the subway tunnels are thick jugular veins. Energy is distributed, and waste is digested. All this generates a sort of animal heat, which escapes from the grates in the gutters. The foul steam is exhaled breath. But how true is this metaphor? Are cities really like living things? A team of physicists and economists led by Geoffrey West of the Santa Fe Institute recently set out to answer these questions. It turns out that, in many respects, cities act just like creatures. They obey the same metabolic laws that govern every organism. Their infrastructure follows a distinctly biological design, which helps explain why cities are able to grow. According to data the team published in April, the urban spaces we’ve created have come to resemble their creators. A city is just a body writ large.
And yet, the researchers also found that cities are an unprecedented phenomenon. When it comes to social variables—things like economic activity that don’t have any clear biological analogue—cities break every rule. They are free from the constraints of ordinary living things and are instead subject to an entirely new set of requirements. “Once men and women started to form themselves into stable communities,” West says, “they introduced a completely new dynamic to this planet, perhaps even the universe.” By analyzing the metropolis using mathematics, West and his colleagues are able to look beyond the superficial differences separating Manhattan from Mumbai, or Chicago from Shenzen. They can see the constants of city life.
This new science of cities wouldn’t exist without the work of a little-known Swiss-American biologist, Max Kleiber, who spent most of his career studying dairy cows. In the early 1930s, Kleiber began measuring the metabolic rate of a vast range of different animals. He discovered a striking pattern: In virtually every species, the metabolic rate is equal to the mass of the animal raised to the 3/4 power. (Or, the metabolic rate increases on a scale three-quarters that of mass.) This simple equation could describe cows and humans and elephants and mice. It didn’t matter what the creature looked like, or where it lived, or how it evolved. The formula always worked.
Kleiber’s equation has important implications. The key part of the equation is the exponent, which is less than 1. This means that animals with a bigger mass will consume less energy per pound than smaller animals. As life grows, it develops enormous economies of scale. The elephant is much more metabolically efficient than the mouse. Humans are more efficient than hummingbirds. Girth is a good thing, at least from the perspective of energy consumption.
Subsequent researchers discovered a series of related equations, all of which also revolved around quarter-power exponents. For example, an animal’s lifespan can be roughly calculated by raising its mass to the 1/4 power. Heartbeats scale in the opposite direction, so that bigger animals have a slower pulse. The end result is that every living creature gets about a billion heartbeats worth of life. Small animals just consume their lives faster. Scientists couldn’t explain these equations. And as the decades passed, and biology became increasingly molecular, these quarter-power scaling laws faded into obscurity. They were curious artifacts from a different time, inductive laws neglected by a reductive science.
Fast-forward to 1993. Geoffrey West, then a physicist at Los Alamos National Laboratory, was looking for a new subject to study. He’d spent most of his career exploring the esoteric branches of theoretical physics—“dark matter, quarks, string theory, that sort of stuff,” he says—but the dearth of funding left him disillusioned. He reasoned that biology was “the science of the 21st century” and set out to find a biological problem that needed the skills of a theoretical physicist.
That’s when West stumbled upon the work of Max Kleiber. He was enthralled by the existence of quarter-power scaling laws. “I couldn’t believe that biologists hadn’t thought more about this,” West says. “As a physicist, I knew that laws like this aren’t accidents. They are telling us something very deep about the order of things. Life is the most complex and diverse physical system in the universe, and yet it seems to obey these absurdly simple scaling laws.”
West wanted to figure out the physical mechanisms underlying these laws. What made diverse forms of life obey such minimalist formulas? Why were the equations so universal? He teamed up with two ecologists, Jim Brown and Brian Enquist of the University of New Mexico, who both studied scaling laws. (Enquist had previously discovered that the same scaling laws also fit many different plants.) Their key insight was that the supply networks of life could be described in the language of fractal geometry, since each section of the network shared the structure of the whole. “It doesn’t matter if you’re talking about the skeletal system or the nervous system or the cardiovascular system,” West says. “These systems all share the same underlying logic, which is independent of the particulars or species.” Because every living thing relies on these fractal networks—the only difference between a mouse and an elephant is the sheer scale of the network—the varieties of life could all be modeled as variations of the same design.
Since their first paper was published in 1997, West, Enquist, and Brown have continued to refine their model, adding variables and layers of complexity. “This work has engendered extraordinary praise and engendered a lot of hostility,” West says. “There isn’t a strong tradition of theory in biology—the field is still in its Copernican phase—so people always think that demonstrating a few exceptions somehow invalidates the whole theory. ‘What about the crayfish?’ they say. There will always be exceptions to the rule. Theories in physics have exceptions too. But that doesn’t make the theory invalid.”
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