When physicists see a power law, they think in terms of phase transitions, and they smell Nobel prizes. They are like sharks with blood in the water

--- Steven Strogatz on the fuss about scaling laws, quoted in New Scientist, Ideas: the lifeblood of cities, 23 May 2007

In context, from New Scientist:

During the 20th century, many researchers studying urban growth focused on economies of scale and their effect on wages. In 1974, Vernon Henderson of Brown University in Rhode Island proposed that cities reach an optimal size by growing until their workers' per capita income reaches a maximum; when it starts to decline, workers leave for other cities. More recently, researchers including West have tried to identify deeper mechanisms behind these societal patterns. Though West is a physicist by training, his reputation stems mostly from his pioneering and controversial work on scaling laws in biology - how things change with size.

What is all the fuss about scaling laws? "Physicists are used to thinking about extremely large systems of identical particles," says Steven Strogatz, a mathematician at Cornell University in Ithaca, New York. Take a piece of iron: at high temperatures, the spins of the particles jiggle around in random directions. If you gradually lower the temperature, the spins stay random until you reach a critical point - then they suddenly line up, and you have a ferromagnet.

This switch from disorder to order is called a phase transition. In the 1960s, physicists noticed that phase transitions follow certain universal patterns, called power laws, even if they have nothing in common physically. Kenneth Wilson of Cornell showed in the 1970s that these power laws come about through the growth of fractal structures, work which won him the Nobel prize in 1982. Since then, Strogatz says, "When physicists see a power law, they think in terms of phase transitions, and they smell Nobel prizes. They are like sharks with blood in the water."