Geoffrey B West: The Universal Laws of Growth and Pace

## Why cities live forever **West focussed on cities** in his discussion of the newly discovered exponential scaling laws that govern everything alive. “We live,” he said, “in an exponentially expanding socio-economic universe.” Global urbanization has reached the point that there are a million new people arriving in cities every week, and that rate is expected to continue to midcentury. What is the attraction? One reason for constant urban growth is that the bigger the city, the more efficient it is, because of economies of scale. With each doubling of a city’s size, the numbers of gas stations and power lines and water lines, etc. increase at a rate a little less than double. In other words, with every size increase there is a 15% improvement in energy efficiency. “That‘s why New York is the greenest city in America,” West said. The same dynamics of networks explain how what is called “power-law scaling“ works in biology. The bigger the animal, the slower and more efficient its metabolism is, at a rate lower than 1-to-1 (“sublinear” in West’s terminology). This leads to some remarkable constants. Shrews weigh 2 grams, and in their 14-month life their heart beats a billion times. Blue whales weigh 200 million grams, and in their 100-year life, their heart beats the same billion times. Ditto for all mammals (except humans, who have achieved a lifetime average of 2 billion heartbeats, presumably for cultural reasons.) In _physical_ terms, cities are like organisms, enjoying sublinear economies of scale with each increase in size. But when you look at cities in terms of their _social-economic_ networks, an astonishing finding emerges. Once again there is power-law scaling if you count patents, wages, tax receipts, crimes, restaurants, even the pace of walking, but _instead of slowing down with increasing size, cities speed up with increasing size_. Their increase is greater that 1:1. It is superlinear. “Bigger cities are better,” said West. Each time they increase in size, they are 15% more innovative socio-economically at the same time they are 15% more efficient in terms of energy and materials. Furthermore, they apparently live forever. They create most of civilization’s problems, but they are capable of solving problems even faster than they create them. However, when you compare companies with cities, companies have similar metabolic efficiencies of scale as they grow, but their innovation rate, instead of increasing with size, _slows down_ as they get ever bigger. And they are mortal. The average lifespan of a publicly traded companies is 10 years. They can grow prodigiously, but their net income, sales, profits, and assets can’t quite keep up—they are sublinear. Successful new companies start off like cities, full of innovation, but over time the nature of corporate growth leads them to focus ever more solely on exploiting their success, and eventually they taper off and die like animals. The city feeds on their corpses and creates new companies.