Wednesday, May 20, 2009

Urban Mathematics = Cities are Alive

A rap scholar once said, "You wanna know how to rhyme you better learn how to add." Steven Strogatz, professor of applied mathematics, makes the persuasive argument that if you want to understand cities, it might help to learn some math too.

Strogatz illustrates, among other things, that larger (more populous) cities need less infrastructure than small ones. He attributes this to economies of scale:

For instance, if one city is 10 times as populous as another one, does it need 10 times as many gas stations? No. Bigger cities have more gas stations than smaller ones (of course), but not nearly in direct proportion to their size. The number of gas stations grows only in proportion to the 0.77 power of population. The crucial thing is that 0.77 is less than 1. This implies that the bigger a city is, the fewer gas stations it has per person. Put simply, bigger cities enjoy economies of scale. In this sense, bigger is greener.

Strogatz ultimately argues that this same ratio is applicable to other living organisms: proof that cities are living, breathing things. Makes sense to me.