Tracks and Tales: Living on the Grid

Iowa is superbly organized. I have a colleague who claims that there?s a hundred and one ways to get to anywhere in Iowa. She?s probably rather close to being right.

Our roads are, for the most part, all nicely laid out on a grid system. They go either north-south or east-west. Miss a turn? Just take the next one.

Like any system, it?s not perfect. Every so often, you have these dog legs along the road, usually when heading north-south. It?s like when the road was built, they started at both ends, got to the middle, and realized they didn?t line up right. The simple correction, then, was just to join them in a straight east-west line, or dog leg.

Now, doing that once or twice is one thing, but many of our roads are like that. And, interestingly enough, they all seem to dog leg along the same line. I blame this on a quirk of the Earth ? the stupid thing isn?t flat.

I recall a program from childhood, around the time I was learning geometry: that the shortest distance between two points is a straight line. Well, this educational program replied, no, not on a sphere (as like on the surface of the Earth, you know, the part we live on). They took a globe, a map, and a piece of yarn.

They used the yarn and the map to measure the distance and the layout (as in if you were traveling) between a U.S. city and one in Europe. Naturally, they had a nice straight line and you could visualize the plane traveling above it.

But then they linked the same two cities on the globe with the same length of yarn. The yarn did not lie over the same landscape. Instead it curved north and the distance between shortened. This, they said, was how a plane would plan its trip.

The shortest distance between two points on a sphere is an arc.

The other point they made was to compare a map of the world with the globe. In order to make a map look nice and rectangular, parts of it need to be stretched out. These areas are the near polar regions.

They made a cut out of Greenland from the map and compared it to Brazil. Greenland was huge. Then, they did the same on the globe; Greenland was much, much smaller ? its actual size.

Laying out flat the surface of a sphere requires a distortion of the image upon it. Yet our minds easily accept the distorted view: we like things nice and neat, with straight lines.

And here we return back to those dog legs. They are corrections between our misrepresentation between the land being flat and the reality of its spherical nature.

The problem is we want to place a grid work of road lines down, all square. Because this is how we view the Earth. I mean, from our perspective, it looks flat. But those north-south lines (longitudinal lines) are not parallel. They all meet up at the poles.

If you have two north-south roads, side by side, laid out in the pattern of the spherical Earth, eventually they will get closer and closer together the further north you go (unless you?re in, say, Argentina - then it would be the more south you go).

To keep the illusion of a neat, two-dimensional landscape (like that we put on maps), and roads that lay out a nice grid, we need to correct this actual trapezoidal landscape. So we put the dog legs in, straightening those north-south curves.

Another way we see this correction is in buying land. Along the last row of a township, you?ll have properties that are a bit more or a bit less in size though they look square on the map.

It will be interesting to see, in the future, if we let technology give us a more accurate picture of our surroundings. Perhaps use those 3-D screens for mapmaking. Hmmm.