## Wednesday, May 20, 2009

### Math and the City

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.

The same pattern holds for other measures of infrastructure. Whether you measure miles of roadway or length of electrical cables, you find that all of these also decrease, per person, as city size increases. And all show an exponent between 0.7 and 0.9.

Other interesting observations about Zipf’s Law in the article.

via The Wild Side

Rebelfish said...

I would argue that part of the <1 exponent for gas stations and roadways is due to "economy of scale" (and that may be the entire reason for electrical cables) but in the very large cities (NYC, Chicago) a main reason is that a large portion of people take mass transit and so never use gas stations and the buses/trains use "transportationways" much more efficiently.

Fat Knowledge said...

Good point. I think though that also applies in smaller cities as well, as buses become a more viable option as things become denser. I guess I thought that greater use of public transportation was implied in the economies of scale argument, but I completely agree with your logic regardless.