Thursday, November 21, 2013

Canada and the Mercator Projection: Latitude and Attitude

This post owes its existence to the excellent online tool MAPfrappe, which allows you to draw on a map of the Earth and then move it around; you can save your drawings, such as my outline of Canada. It took me a while to do, please feel free to play around with it to validate the time I spent judging how close to the squiggly borders was close enough!

Google Maps is a truly wonderful invention, but there is one flaw: the Earth is a sphere, and in order to fit it on a rectangular surface (like a computer screen), adjustments must be made. Google uses the Mercator Projection, which dates all the way back to 1569. It's famous, it's familiar, but there are many better ones.

The main weakness of Mercator is its exaggeration of surface area the closer you get to the poles; and of course Canada gets pretty close to the north pole. Compare the Mercator projection of Canada with an image from a globe: Ellesmere Island, the northermost landmass, has over four times more area in the Mercator projection!


Mapfrappe allows us to see what happens to the outlines when we move them elsewhere in the map projection. Canada extends from latitudes 42.3°N (Windsor, Ontario) to 83°N (the northern tip of Ellsemere Island). So let's drag the map so that the northern tip of Ellesemere is now at 42.3°S:


Wait a minute, the sharp-eyed among you may now be objecting. Something's wrong with this map! Windsor projects below the South Pole! How can anything be below the South Pole? And Canada's longitudes, which Mercator is not supposed to affect, have been drastically increased: the country now spans over 90% of the globe! You're seeing an artifact of geometry: MAPfrappe does not recalculate the projection of every point of the outline (which would be a very computationally comlex thing to do for what is essentially a whimsical exercise), it trapezoidally skews the projection according to its center. (I may be using the wrong terms to describe this: I'm a biochemist, not a mathematician.)

Who cares if parts of the globe where few people live are distorted in the Mercator projection, you may ask. It's a valid question. I'll just leave you with this: a comparison of the size of Canada with that of Africa on the Mercator projection (even leaving out the most northerly part) and on the globe. I think it's plausible this illusion may affect opinion and policy.




 Next week: I take even more latitude with latitude.

3 comments:

  1. Just one note about the south pole and the Mercator projection. the bottom of the map you see here is not the south pole. The south pole is infinitely distant, and this view of the Mercator projection is necessarily truncated.

    ReplyDelete
  2. Just one note about the south pole and the Mercator projection. the bottom of the map you see here is not the south pole. The south pole is infinitely distant, and this view of the Mercator projection is necessarily truncated.

    ReplyDelete
  3. That's correct, of course; I was trying to get across the fact that the algorithm that redrew the Canadian outline was an oversimplification without having to get into asymptotes and such.

    ReplyDelete

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