Incompatibility: 2D and 3D

It’s been a while since I’ve done one of these, but Tom Leslie introduced me to the town of Correctionville, Iowa, and it was too good to pass up. The name of the town comes from a problem for which there is no ready solution: we treat plots of land as if they can be represented solely using two-dimensional surveys and maps when they are, of course, small pieces of the surface of a sphere.1 Sooner or later, that fiction runs up against reality.

Iowa, like pretty much all of the midwest, was surveyed in the first half of the nineteenth century into townships, each 36 square miles in area. Those 6-mile by 6-mile squares were then broken into 1-square-mile sections, which could then be further subdivided. If you imagine a large area being surveyed in this manner, you can see how the trouble arises: the north boundary is following a line of latitude that is a smaller circle (since we’re north of the equator) than the south boundary. String enough of those 6-mile-on-a-side squares together and eventually something has to give. The answer is a surveyor’s “correction line” where the fiction that the land is flat is adjusted by moving the north-south lines. If correction lines were not used, every “square” plot of land would actually have to be slightly trapezoidal, which would create a whole different set of problems.

Fifth Street in Correctionville is such a correction line, which is why the north-south streets all offset as they pass through it. I don’t know what happened with Fir Street, but note that Driftwood, Hackberry, and Birch Streets all offset by the same amount.

  1. Okay, not actually a sphere, an oblate spheroid. Okay, not actually an oblate spheroid, but an irregular shape close to an oblate spheroid.
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