Monday, August 5, 2013

Mercators Projection Map

Every map starts with the same lie: The earth is flat. The globe isn’t a portable, affordable, or even satisfying way to look at the world, so these exaggerations are necessary. However, mapmakers have challenged isolated the nature of these distortions, and have learned to use them as levers, flaws that can be weighed against each other in the pursuit of targeting different cartographic needs. Every map tells a lie, but good maps use the right projection to tell specific truths. This is “Get to Know a Projection,” a Map Lab series that shows you all the different ways to unround the Earth. We begin with the projection you are likely to be most familiar with.

The Mercator projection is everywhere. If you went to public school any time before 1991, this is the map projection that told you Greenland was the size of Africa, Alaska was bigger than Brazil, and Antarctica was an infinite, frozen nightmare.

Geraldus Mercator, surrounded by what appears to be the inscription for the One True Ring. Franz Hogenburg/Wikimedia commons

At some point since then, you’ve hopefully been informed that Greenland is only about the size of Mexico, Alaska’s a fifth of Brazil, and Antarctica is only slightly larger (and barely more of a frozen wasteland) than Canada. (If you need a refresher, this interactive map puzzle is a great illustration of how the projection distorts landmasses). Hopefully, you’ve also had time to get over your anger at Mercator, because it’s really not a bad map. It’s just been in the wrong place for a long time.

Like symphonies, map projections are named after their makers. Geraldus Mercator was an engraver and globe-maker in 1500s Flanders. Until he came along, most cartographers were using Ptolemy’s grid of latitudes and longitudes, but were mostly focused on producing world maps that were descriptive, rather than functional. Rectangular maps had quickly come and gone out of style with academic cartographers, who thought it was silly to stretch the planet into corners. Instead, most preferred elliptical projections, using progressively curved lines of longitude and latitude to create artificial rounding. These mathematic transformations kept the Earth’s features by close to their true sizes and shapes (At least, true at the time. It was the Middle Ages).

Staying true to size and shape is great if you are sitting in your study, looking at the world from afar. But if you’re trying to explore, an idealized map is next to useless. Those proper shapes and sizes come at the expense of angularity, which means a ship’s plotted course gets twisted unless it’s plotted directly east to west. If they used elliptical projections, navigators had to constantly recalculate their bearing. But the Age of Exploration was well underway. Leave the works of art to the Renaissance. These sailors needed a tool.

To imagine how a Mercator projection works, picture shining a light through a translucent glass globe onto a piece of paper. Depending on where you put your light and how you use the paper, the globe’s features will cast a range of distorted shadows. Mercator rolled this imaginary piece of paper into a cylinder and wrapped it around his imaginary globe so that it touched only along the equator. Projecting implies a light source, and Mercator placed his hypothetical lamp opposite from where the paper touched, also on the equator. The shapes nearest the point of contact were close to perfect. The cylinder, however, was perpendicular to this point, and as the globe curved in from the paper, the lines of longitude stayed straight rather than meeting at the poles. The further they moved from the equator, the greater the distance between them became.

If he hadn’t extended the distance between the parallels, Mercator’s map would have been a simple cylindrical, or plat-carree projection, also unsuitable for navigation. Strebe/Wikimedia commons

Of course, now this meant that all the meridians now intersected at perfect 90 degree angles with the lines of latitude. Alone, this would still skew a line of bearing. However, Mercator saw that if he also proportionally increased the distance between the parallels, he could match the rate of angular distortion. Straightening and stretching the grid meant a course plotted on the map stayed true on the water. This meant no more obsessive course correction, as long as the winds and tides stayed true.

That wasn’t all. Mercator published a simple geometric formula that corrected the distance distortion he’d introduced by making direction true. With a few calculations, sailors could convert their endpoints into equatorial degrees and subtract the distance between.

Though maps before and after have been better at showing us the whole earth, Mercator’s was the first that gave us a means for exploring it. If you have a beef with what your social studies teacher hung over the blackboard, better chalk it up to inertia. Mercator never meant for his map to teach geography. Mercator’s map was so useful to sailors that its popularity eventually caught on with landlubbers. Today, it’s still the most often used map projection in the world. If you’ve used Google, Bing, Yahoo, OpenStreetMaps, or MapQuest, then you’ve plotted a course using Mercator.

S: Wired

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