Interesting article, but some of the comments posted below it indicate its flaws. In particular, there appear to be dimensional problems (of the usual "cgs" sort) in some of the arguments. About all I could conclude after reading both the article & all of the comments was the usual: "there are fractal sets with differing fractal dimensions". At 01:14 PM 5/20/2009, Dan Asimov wrote:
Interesting math column in today's NY Times about Zipf's law, which I'd thought applies only to word frequencies:
< http://judson.blogs.nytimes.com/2009/05/19/math-and-the-city/ >
One paragraph:
<< 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.