Mathmatics of Urban Infrastructure

Steven Strogatz, a professor of mathematics at Cornell University, just blogged about Math and the City in the NY Times. The article is fascinating because he describes mathematical relationships that seem to hold for city size and infrastructure, and how these are similar to those for living organisms. For example, large animals have a smaller circulation system (per unit volume) than small ones, just like large cities have fewer roads (per person) than smaller cities:

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.

In other words larger cities are more efficient than smaller ones.