Additional Math Pages & Resources

Tuesday, September 15, 2009

The Map is not the Territory

A cartographer is a person who draws maps of the land, while a hydrographer creates nautical charts of the sea. What do you call a person who makes charts for pilots? An aeronographer. And finally, a person who makes space charts is an astronographer.

A map shows the terrain and where it goes up (mountains) and down (valleys). A nautical chart shows the same "up" features, only we call them rocks and shoals and islands. Plus we want to see currents, and tides and winds. And lighthouses. Aero- and Astro- maps each have unique features and show things of concern to navigators.

All these maps share some common characteristics:
  • A map is NOT the territory it portrays, but is a likeness or representation of the reality
  • Maps are NOT pictures of the territory either
  • Maps are drawn to scale, otherwise they would be too large to handle
  • Not all objects on a map are drawn to scale; some are shown with symbols (blue line = river)
On a small-scale map details are drawn smaller. Many streams, roads, and landmarks are left out. A larger scale map allows for more detail but covers less, so you need more maps.  A city engineer may need detailed map of sewers, power and water lines, and streets and so use a scale of 1 inch = 50 feet.

Here's 1883 Bloomington, IN at that scale. (Click the map to enlarge it.) Notice the Jail!

With a scale of 1 inch = 50 feet, or 1:600, a 20" x 20" map shows an area 1000 feet square.

If the scale is 1 inch = 1 mile, or 1:63,360 scale, a 20" x 20" map can show an area 20 miles square.

If the scale is 1 inch = 5 miles, the scale is 1:316,800 and a 20" x 20" map represents 100 miles on a side.

The US Geological Survey (USGS) publishes many maps. Local governments produce others. Here's a map of Salem, MA from 1893, thanks to the University of New Hampshire Library.

Most topographical maps are 1:24,000 scale, except for Alaska which was mapped at 1:63,360.

Maps at 1:24,000 scale can provide detailed information about local features, including many buildings, campgrounds, creeks, bridges, fence lines, and private roads.

Small-scale maps (1:250,000 and smaller) show very large areas on single map sheets, but details are limited to major features, such as state lines, parks, airports, highways and railroads.

What is the area that can be shown on a 20" x 20" map at 1:250,000 scale?

Let's see: 63,360 goes into 250,000 about 4 times. 63,360 inches = 1 mile, so the 1;250,000 scale is about 1 inch = 4 miles. So 20 inches x 4 = 80 miles each side. 80 x 80 = 6400 square miles!

Here's a aircraft pilot's chart at that scale for Bournemouth in England.

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