Map projection is the process by which a three dimensional datum is "projected", or shown, on a two dimensional surface. There are three surfaces onto which a map can be projected: the cone, the cylinder and the plane. Each of these projections has a certain amount of (unique) distortion; to save certain relationships between area, distance or angles one must sacrifice other relationships. Here I will denote the significance, perils and potential of (the below) map projections. First I will explain them and discuss their significance. Then I will move into the perils of projections, finally ending on a positive note with their potential.
The two below Mercator maps are examples of conformal projection, which preserves angles locally. This is important if one is navigating by sea or air and needs to keep a standard bearing on the land. The two below equidistant projections preserve distance. That is, they preserve the integrity of distance from one standard point or line. Obviously, this is good for knowing exactly how far away places are. The reason Washington D.C. and Kabul are different distances apart in my two equidistant projections is because one measurement runs across the Atlantic while the other runs across the Pacific. My final two maps preserve area, that is, the map images are proportional to the area of the landforms which they represent.
The perils of map projection are great. As I mentioned earlier, no map is able to preserve every relationship and must instead sacrifice the integrity of some relationships for others. You'll notice that in the Mercator Projection, Greenland is huge. (It's even bigger than Australia.) If you then look at either of the two Equal Area projections, you'll notice that Greenland looks much smaller. This is because in the "equal area" projection, area is preserved. On the other hand, if one attempts to navigate angles with an equal area map, it will be very difficult to succeed. (The conformal projection should instead be used in this case.) When choosing a map projection, one has to take into account what the map will be used for, and choose the projection accordingly. Otherwise you could end up in Sudan when you really wanted to hit Kenya.
The potential of map projections is infinite. There are countless ways in which to represent the world datum, and if you know what you're doing, you could personalize a map projection to meet your specific needs. 50% distance, 25% angles, 25% area? There must be a projection for that. Navigating? Use this one. Making a topo? Use another one. Learning the countries in Africa? Use this one. Want to inflate the importance of Greenland? Use that one. Projection has the potential to enhance any set of research, or aid in any travel, or really accomplish any spatial goal. (One can even manipulate projections to show a specific point of view.) As we grow in our map knowledge, perhaps there will be some all-encompassing map, able to preserve every relationship phenomenally. In fact, I'm almost positive there will be a map like this some day. Until then, we need to choose a projection very carefully.
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