Last week, over at the Gray Lady’s house, there was a story about something called Zipf’s Law, which supposedly predicts the relative populations of our cities. It’s named after a fellow named George Zipf who several decades ago “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.” So, if Country X’s largest city has 12 million people, the second largest would have 6 million, the third largest 4 million–anyway, you get the idea. The author noted that, even though Nobel laureates have looked into it, “no one knows” why Zipf’s law works. It just kind of does. (Bigger chart after the jump)

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It probably isn’t much of a surprise to learn that New York is about twice as big as LA and three times as big as Chicago. Less mundane though, is the fact that it would contravene some mysterious but very strong law of collective behavior if it were any other way. So while there’s no “logical” reason to think that a country like ours couldn’t have two or more big cities approximately tied for the title of the largest, that kind of thing apparently just doesn’t happen.

The mathematician Steven Strogatz wrote a fascinating item for the NY Times about this earlier in the week, explaining how various elements of urban organization tends to conform to specific mathematical patterns:

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.

Keep in mind that this pattern emerged on its own. No city planner imposed it, and no citizens conspired to make it happen. Something is enforcing this invisible law, but we’re still in the dark about what that something might be.

Wow, right? It’s like some sort of weird and arbitrary rule that you might set up in a Sims-style game. But it’s not just population — these laws also extend to infrastructure:

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Nate Silver, the precocious statistician who knew the final results of the 2008 election before it even happened, has taken on the tricky and high-stakes question of why Americans are driving less.

“High stakes” because the decades-long trend in increasing car usage has been a defining force in post-war America–shaping everything from our daily routines to our community structures to our natural landscape. But that trend line suddenly broke downward in 2007 and are now, month after month, U.S. motorists are logging fewer miles. So what brought about the reversal though and will it last? Was it higher gas prices? Or a tanking economy leading to fewer commuters? Or was something else at work — a slow-dawning realization that 50-mile commutes are madness and that life is bit better if we take a more balanced approach to transportation?

Writing for Esquire, Silver built a regression model to tease apart the various causes — and found that gas prices and unemployment alone don’t quite explain the current data:

The model predicts that given a somewhat higher unemployment rate but much lower gas prices, the lower gas prices should have won out: Americans should have driven slightly more in January 2009 than they had a year earlier. But instead, as we’ve described, they drove somewhat less. In fact, they drove about 8 percent less than the model predicted.

So–as we’ve speculated about on this site recently–maybe there is some kind of cultural shift at work here.

But the jury isn’t in yet:

There is strong statistical evidence, in fact, that Americans respond rather slowly to changes in fuel prices. The cost of gas twelve months ago, for example, has historically been a much better predictor of driving behavior than the cost of gas today.

The real test will come as the summer unfolds and Americans have had time to get “used to” lower gas prices.

Gas prices peaked in July of last year. So if Silver’s 12-month lag effect holds in this case, August and September will be telling months. We’ll be watching.