From “Where Good Ideas Come From: The Natural History of Innovation” by Steven Johnson
Working out of the legendary Santa Fe Institute, where he served as president until 2009, West assembled an international team of researchers and advisers to collect data on dozens of cities around the world, measuring everything from crime to house-hold electrical consumption, from new patents to gasoline sales.
When they finally crunched the numbers, West and his team were delighted to discover that Kleiber’s negative quarter-power scaling governed the energy and transportation growth of city living. The number of gasoline stations, gasoline sales, road surface area, the length of electrical cables: all these factors follow the exact same power law that governs the speed with which energy is expended in biological organisms. If an elephant was just a scaled up mouse, then from an energy perspective, a city was just a scaled-up elephant.
But the most fascinating discovery in West’s research came from the data that didn’t turn out to obey Kleiber’s law. West and his team discovered another power law lurking in their immense data-base of urban statistics. Every datapoint that involved creativity and innovation – patents, R&D budgets, “supercreative” professions, inventors – also followed a quarter-power law, in a way that was every bit as predictable as Kleiber’s law. But there was one fundamental difference: the quarter-power law governing innovation was positive, not negative. A city that was ten times larger than its neighbor wasn’t ten times more innovative; it was seventeen times more innovative. A metropolis fifty times bigger than a town was 150 times more innovative.
Kleiber’s law proved that as life gets bigger, it slows down. But West’s model demonstrated one crucial way in which human-built cities broke from the patterns of biological life: as cities get bigger, they generate ideas at a faster clip. This is what we call “superlinear scaling”: if creativity scaled with size in a straight, linear fashion, you would of course find more patents and inventions in a larger city, but the number of patents and inventions per capita would be stable. West’s power laws suggested something far more provocative: that despite all the noise and crowding and distraction, the average resident of a metropolis with a population of five million people was almost three times more creative than the average resident of a town of a hundred thousand. “Great cities are not like towns only larger,” Jane Jacobs wrote nearly fifty years ago. West’s positive quarter-power law gave that insight a mathematical foundation. Something about the environment of a big city was making its residents significantly more innovative than residents of smaller towns. But what was it?