It's Crowded Out Here

Do you know that where I'm sitting right now, the population density is 2,787,840 people per square mile?

And here are two other numbers (from Wikipedia) that you shouldn't believe: The population density of Manhattan is 71,201/sq mi. And of Australia: 7.3/sq mi.

And now a number that might just be credible: Hong Kong has 2,346.1/sq mi.

My personal population density I got by allotting myself 10 square feet, and then extrapolating to a square mile. True, as far as it goes, but this must be what Mark Twain meant by "lies, damned lies, and statistics."

Population densities (PDs) have meaning only if averaged over some relevant space. The size of that space is a matter of geographical judgment, and cannot simply be left to the statistician's computer.

Australia's is easy to discredit: 90% of the country is empty desert. The habitable land (on which the population survives) is much smaller, and the relevant population density must therefore be (a still low) 70-80 people per square mile.

So let's consider some relevant spaces. We'll start in Indiana, come back to New York, and end up in Hong Kong.

Indiana is a state where the population is fairly evenly dispersed: there are no large uninhabited spaces, and likewise, no megacities of enormous density. The PD is 169.5/sq. mile.

In Table 1, I have taken 2000 census data and ranked Indiana counties by population, reporting also the land area and the density.

There are big differences from one part of the state to another. Marion County (Indianapolis) is the most populous, with PD = 2171. At the other extreme, Warren County has the smallest density (90 of 92 by population), with PD = 23.1, or 100-fold smaller. Does averaging these numbers make any sense?

I have calculated what I call the Cumulative Density (CD). For Marion County, being the most populous, the CD is simply the PD for that county. For Lake County (Gary-Hammond, and #2 in population), the CD is the sum of the populations of the two counties, divided by the sum of their land areas, and so on. For Ohio County (smallest by population) all populations and all land areas are added, and CD = PD for the state.

Similarly, I have calculated the Anti-cumulative density (aCD), which is the same thing, but now starting at the bottom of the table. The aCD for Ohio County equals the PD for Ohio County, whereas the aCD for Marion County equals that for the state as a whole.

So what does this mean in terms of observables? Consider the drive from Indianapolis to St. Louis, westbound on I-70. This is a heavily traveled road, with lots of truck traffic. The largest city along this stretch is Terre Haute, in Vigo County.

Now consider an alternate, parallel route: the four-lane highway - US 40 (known for much of its stretch as the National Road). This has very little traffic, and almost no truck traffic. Why?

The interstate connects metropolitan areas, and hence traffic on the interstate will reflect the cumulative density. The parallel side roads such as US 40 carry mostly local traffic, and thus traffic should be proportional to the anti-cumulative density.

So the cumulative density for Vigo County is 528/sq mile, a number that averages in Indianapolis and its collar counties. On the other hand, the anti-cumulative density is 91/sq mile, or approximately 6 times smaller. Indeed, a factor of six is probably a good estimate for the traffic difference between I-70 and US 40. So for a more relaxing trip to Indy – if somewhat slower – take US 40.

The population density of Manhattan is almost as absurd as my personal population density. Manhattan is not an appropriate average: one needs to include reasonable hinterland space from which the island draws its food, water and labor. The metropolitan area does just fine.

Table 2 shows census data for Downstate New York, defined as the metro area most generously understood. This includes much of the Catskill Park from which the City gets its water. This area has 12.9 million people spread over 5100 square miles, for a PD of 2,530. (Including relevant parts of NJ reduces this number to 2140.)

This isn't Indiana anymore! Metro New York City really is more densely populated than the Hoosier state – by about a factor of 10. The aCD where I live (Ulster County) is double that of Vigo County, and indeed, my local highways are at least twice as busy.

But it would be a mistake to average in all of New York State into a single PD number. The census tells us that NYS has 401/sq. mile, but that is Mark-Twain-land. Upstate New York – beyond the political – has only tenuous connections with the City.

Table 3 shows the census data for all upstate counties in New York - the PD is 145/sq mile, or sparser than Indiana. Indeed, Hamilton County, entirely within the Adirondack Park, only has 3/sq. mile! I once lived in Chautauqua County (aCD = 71), and can compare upstate NY, Indiana, and downstate NY; my car insurance rates have varied proportionally to the aCD.

And finally, a word on Hong Kong. I've never been there, and haven't looked up any statistics other than the Wikipedia number, but I tend to believe that. It seems remarkably close to the New York metro number, which I hypothesize is a reasonable density for any large mega-city in the world.

Do you know that where I'm sitting right now, the population density is 2,140 people per square mile?

Now that's a number you can believe in.

Daniel Jelski is Dean of Science & Engineering State University of New York at New Paltz.