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:
Around 2006, scientists started discovering new mathematical laws about cities that are nearly as stunning as Zipf’s. If one city is 10 times as populous as another one, does it need 10 times as many gas stations? No. Bigger cities have more gas stations than smaller ones (of course), but not nearly in direct proportion to their size. The number of gas stations grows only in proportion to the 0.77 power of population. The crucial thing is that 0.77 is less than 1. This implies that the bigger a city is, the fewer gas stations it has per person. [...]
The same pattern holds for other measures of infrastructure. Whether you measure miles of roadway or length of electrical cables, you find that all of these also decrease, per person, as city size increases. And all show an exponent between 0.7 and 0.9.
The story–definitely read the whole thing–goes on to make an anology between residents of a city and the cells of an organism. Mouse and elephant cells have similar metabolic rates in a petri dish. But in situ in the animals, the mouse cell burns much more energy than the elephant cell. There is an analogous effect that takes place among urban residents, with someone in a small town tending to have a higher innate resource metabolism than someone in a big city.
The author draws a conslusion that is quite familiar by now: “Put simply, bigger cities enjoy economies of scale. In this sense, bigger is greener.” Right! But human beings also seem hardwired to have relative few huge cities. It’s too sunny-Friday-afternoon-outside to really think too deeply about the implications of that, but certainly there are some important ones.
May 22nd, 2009 at 6:44 pm
None of this surprises me. First of all, it seems logical that a bigger city needs less infrastructure (per capita of course). Cities have a much higher population density and thus have a greater land value. The cost of owning and operation a gas station increases as your move into higher density. Further, even though there are fewer gas stations per capita, there are still more gas stations -that means more competition, which means it’s harder to keep your station open.
On the city population question, we can look to our own country and see that it is not exactly true. Population density does not follow that path at all. Neither does the population of the entire metro area. Something is amiss. Further, the actual populations of the city don’t even follow very well after you get further towards the edge.
May 22nd, 2009 at 7:24 pm
Interesting — but if you followed the comments to that NYT piece you would see that the population rule really doesn’t apply. Consider South Korea, for example: Seoul is nearly three times the size of the next largest city. In other cases, the top two cities are close to equal in population.
The principle that infrastructure doesn’t scale at 1:1 with increased population is an entirely separate point, which the NYT comments did not address, if I recall.
May 22nd, 2009 at 7:58 pm
O/T somewhat, but this calls to mind another ineffable but mysterious principle — Why is the “east side” of a city almost always less affluent/salubrious than the “west side”? (Same with south vs. north, though less pronounced.) It seems to be true regardless of the actual geography of the urban area.
May 22nd, 2009 at 11:41 pm
I find this fascinating if true. But obviously NYC doesn’t work.
May 22nd, 2009 at 11:54 pm
Zipf’s work was just an extension of Walter Christallers, central place theory in 1933, http://www.csiss.org/classics/content/67
You might find http://www.ekistics.org/ (science of human settlements) an interesting read, its a little hard to find outside of a specialist library but tries to answer alot of interesting questions, its been running since about 1960?
May 23rd, 2009 at 3:04 am
The east side / west side issue may be due to prevailing winds (at least in the Northern hemisphere). Wind in most places usually blows west-to-east, which means that the west side of a city will be downwind of the countryside, and probably non-objectionable odors and pollution. The east side of a city will be downwind of the west side, and thus all of its air pollution, and odors (in pre-industrial and third-world cities, I imagine the odors are a very big issue).
May 23rd, 2009 at 8:47 pm
Dayton and Cincinnati are two exceptions to that rule. In fact, they turn the rule on its head. And cities with highly restrictive geography, such as New York, San Francisco, Boston and Baltimore, follow no pattern that even resembles this rule.
June 7th, 2009 at 10:55 pm
If you read the entire article he attempts to draw a conclusion which is far fetched and mathematically/scientifically unsound.
Mr. Stogatz states
“that the metabolic needs of a mammal grow in proportion to its body weight raised to the 0.74 power.
This 0.74 power is uncannily close to the 0.77 observed for the law governing gas stations in cities. Coincidence? ”
end quote.
You might as well say that x^2 is the same as x^3. They are not at all the same. When dealing with powers, a small change makes a large difference. To say that
“0.74 is uncannily close to the 0.77″ is innumerate. For a population of p = 100,000 and p = 8,300,000 taking p^0.74 verses p^0.77 would give 831,763 and 1,445,439 respectively. Computing the percent error for p = 100,000 I get a 29% error and for NY population equal 8,300,000 I get almost a 39% error.
Expressing the power to only two significant figures means that the certainty for 0.74 is really only between 0.735 and 0.745. As an exponent that give a percent error of 14%.