Several years ago, the theoretical physicist Geoffrey West decided to investigate whether Kleiber’s law applied to one of life’s largest creations: the superorganisms of human-built cities. Did the “metabolism” of urban life slow down as cities grew in size? Was there an underlying pattern to the growth and pace of life of metropolitan systems? 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 household 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 database 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 130 times more innovative.
From Johnson’s Where Good Ideas Come From: