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.

For the full NY Times column click here.

1 comment:

  1. Seems there are also significant diseconomies in scale in big cities, such as traffic that contradict the bigger = greener statement. Also there are myriad of possible explanations for the gas station example that do not necessarily imply economies of scale. For example, in bigger cities real estate is probably more expensive thereby increasing the cost of investment for gas stations and forcing some gas stations out of business or preventing them from ever opening. The result of less gas stations is not necessarily more efficiency, the lines at these gas stations could be longer, the prices higher (likely). The phenomenon he cites as an economy of scale could itself very well be a diseconomy of scale. While the negative results in this case might have some green friendly side effects (increased relative cost of driving), extrapolating the "bigger = greener" idea from this seems to be a bit of a reach. Also, although I am not an expert, my understanding is that high concentrations of pollutants, which are more likely to occur in big cities, are much more damaging to the environment than a small amount dispersed over a large area.