At the center of it all

An idealized, symmetrical territory

]1 An idealized, symmetrical territory

One way of thinking about whether or not a territory “makes sense” is to consider how evenly and symmetrically its population is distributed within its borders. A theoretically ideal territory, in this sense, would have a dense node of population at its geographic center, and population would smoothly and evenly radiate away from this center—something like von Thünen’s isolated state, Christaller’s hexagonal cells arrayed around central places, or Howard’s radial plan for a garden city.

Such a symmetrically elegant territory will have its geographical center and its center of population at the same point.1 By contrast, in a territory whose population is highly off-balance, these two points will be far apart form each other. The more a territory’s population is concentrated at one corner or edge of its spatial extent, the greater the distance between the two centers. We can therefore define a simple statistical index of “off-centeredness” as the distance between a territory’s geographic center and its center of population. (To account for the size differences of different areas, we can also create a weighted off-centeredness value which is the raw off-centeredness divided by the square root of area.)

A territory which is symmetrically balanced, but not centered

]5 A territory which is symmetrically balanced, but not centered

This off-centeredness is not a perfect statistical measure. For instance, imagine a square territory with a large city at its northeast corner and an equally large city at its southwest corner. These two population weights on opposite corners would cancel each other out, and this territory would therefore have a low off-centeredness index, even though its population distribution would be badly off-centered. Still, as a crude index to the “sensibility” of geographic areas, off-centeredness gives us a good place to start.

I was curious what I might find if I generated the off-centeredness index for every county (and county-equivalent unit) in the United States. Here’s the data set I created, and here’s an interactive visualization for exploring the data.

What begins to emerge from the data is an interesting typology of counties in the United States. The four most off-centered counties2 are all ones which have outlying island areas that skew their geographic weighting: Mayagüez, Puerto Rico; Monroe, Florida, and both St. Bernard and Plaquemines Parishes in Louisiana’s Mississippi Delta (Keewenaw, Michigan, which includes Isle Royale in the middle of Lake Superior, exhibits the same effect, as does Dare, North Carolina, which includes the Outer Banks). High on the list we also find a number of western counties that are off-centered because they include huge swathes of uninhabited land: places like Washoe and Nye in Nevada; Jefferson, Washington; and Juab, Utah; as well as similar thinly-settled areas outside of the west, like Lake, Minnesota and Somerset and Piscataquis in Maine.

More interesting are the counties which are off-centered because a huge city at their edge has pulled their population off to one side. Denver has distorted Adams and Arapahoe in Colorado in much the same way that Los Angeles is a center of gravity for Riverside and San Bernardino in California. In other highly off-centered counties, it’s not a major city but a corridor of population which pulls askew: places like Whatcom, Washington or Herkimer, New York. Because our weighted index takes into account the size of the area, we also find some smaller counties high in the off-balanced ranking, usually because they are periurban territories split between urban and rural halves, like Passaic, New Jersey; Osceola, Florida; or Dorchester, South Carolina.

On the other end of the spectrum, the great rationalist William Penn would be pleased to know that Philadelphia is the most symmetrical county in the nation, with less than 35 meters separating its geographical and population centers. The other highly-centered counties are an interesting mix. There are plenty of Midwestern rectangular counties evenly patterned on the North American Grid: Tipton, Indiana; Walworth, Wisconsin; or my favorite, Appanoose, Iowa, perfectly centered on Centerville. But we also find ones that seemed to be centered due to topography—like Adair, Kentucky and Lewis, New York—as well as ones which seemed to be balanced almost by chance—like Tattnall, Georgia.

I’d love to know what else you find exploring this map. Take a look, and drop me a line if you uncover any interesting patterns!

  1. The geographical center or centroid is the point where a territory would balance if it were a flat, uniform surface. The center of population is the point where it would balance if that flat surface were weighted by the population distribution. 

  2. Actually, the most off-centered territory is the Aleutians West area in Alaska, but I have left it out of this data set for now because it crosses the -180 line of longitude, which creates all sorts of errors for both computing its center and displaying it on a web map.