Sunday, May 24, 2009

Power Laws, Cities, and Organisms

Steven Strogatz has a brief but interesting article in the New York Times about how the amount of infrastructure needed for a city of a particular size scales up as a 3/4 power law, and that this is akin to the scaling of metabolism in large and small organisms. In other words, the economies of scale mean that the efficiency bonus that large cities have compared to smaller cities is similar to the calorie consumption of an elephant vs. the calorie consumption of an equal mass of mice.


At Tuesday, May 26, 2009 at 12:36:00 AM PDT, Anonymous Joshua said...

The problem with that New York Times blog entry is that the author claimed that George Zipf found 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."

However, after hundreds of blog posts, nobody was able to find one country where the largest city was about twice as large as the second-largest and three times as large as the third-largest.

It was unclear whether the problem is with Zipf's law or with the blogger oversimplifying it to be inaccurate.

At Tuesday, May 26, 2009 at 11:30:00 AM PDT, Blogger Adam Villani said...

Ha! Good point. I suppose that if you're going to present a conjecture as a law, maybe it shouldn't be so easily-debunked by readily-available data.

Then there's the 2D vs. 3D problem on cities vs. organisms.

At Tuesday, May 26, 2009 at 11:45:00 AM PDT, Blogger Adam Villani said...

I took a look at the Gabaix article explaining Zipf's law, and basically it doesn't hold true at the higher rankings, only at the lower ones. So, like, you get past the first dozen or so metro areas and then the distribution starts fitting a log line. I guess this tells us *something*, but it's a lot less interesting than a law that works for the bigger cities


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