An interesting article from Smithsonian magazine, about the mathematical study of cities: “Life in the city is essentially one giant math problem”.
Here’s a passage quoting Geoffrey West, about the ways that different measures of a city exhibit allometry with population size:
Remarkably, this phenomenon applies to cities all over the world, of different sizes, regardless of their particular history, culture or geography. Mumbai is different from Shanghai is different from Houston, obviously, but in relation to their own pasts, and to other cities in India, China or the U.S., they follow these laws. Give me the size of a city in the United States and I can tell you how many police it has, how many patents, how many AIDS cases, says West, just as you can calculate the life span of a mammal from its body mass.
I’ve heard West speak about this population allometry. Obviously some of the most interesting cases are those where a city mismatches the expected relationships. But it is fascinating the way that so many aspects scale with a positive allometry – getting proportionally greater as city size increases.