Gas Stations, Mice and Elephants

"It appears that Aristotle’s metaphor of a city as a living thing is more than merely poetic."

That about sums up this article but how the author got there is fascinating.

From the New York Times...

One of the pleasures of looking at the world through mathematical eyes is that you can see certain patterns that would otherwise be hidden. It reveals Manhattan and a mouse to be variations on a single structural theme.

The mathematics of cities was launched in 1949 when George Zipf, a linguist working at Harvard, reported a striking regularity in the size distribution of cities. He noticed that if you tabulate the biggest cities in a given country and rank them according to their populations, the largest city is always about twice as big as the second largest, and three times as big as the third largest, and so on. In other words, the population of a city is, to a good approximation, inversely proportional to its rank. Why this should be true, no one knows.

Even more amazingly, Zipf’s law has apparently held for at least 100 years.

To figure out what gas stations, elephants and mice have in common, click here to read the article, it's not long but it's a bit too complicated to summarize.