Apparently it's a controversial... area.

I'm a Canadian. I'm proud to be a Canadian. I'm proud of my fellow Canadians. But gee whiz, we can sure be sensitive sometimes.

In my post two weeks ago, I pointed out how the Mercator projection exaggerates the surface area of Canada. Map-lovers loved my post; Canadians hated it. Many seemed to think I was trying to cast aspersions on Canada's proud place as the world's second-largest country.

Far from it. But as big a fan of Canada as I am, I'm also a fan of the truth: it's a tight race for second place. If we lost Labrador, we'd drop to fourth. This fact is rather disguised by the Mercator projection:

Poor China, they really get the shaft: they drop a place and end up looking a third as big in relation to their Russian neighbours. The United States is partially buffered from this ignominious fate by Alaska.

I understand why Google Maps uses Mercator: having north, south, east and west perfectly correspond to the edges of the map is handy when you're giving directions. Plus equal-area projections (there are many different ones, because there are many different ways to do this) just look weird, with their elongated, phallic Africa:

There are hybrid projections that do a pretty good compromise, but most of the best ones aren't rectangular, and that can be inconvenient if you don't happen to have, say, a hexagonal iPhone screen.

There. Go Canada. You're big, but my favourite fact about you is that you share the world's largest undefended border. Well, that and the fact that we have the world's largest island inside a lake inside an island inside a lake.

Oh, one more thing: Relevant xkcd.

Read more

Canada: strong and free, but maybe not as north as you think

Canada is farther north than the United States: everybody knows this, and for the most part it's true. An article in Monitor on Psychology says people tend to take these geographical mental shortcuts too far: most Americans are surprised to find that all of Florida is farther south than the Mexican border, for example.

So let's see how much of the United States is below Canada's most southerly city, Windsor, Ontario (I won't cheat and count the little islands in Lake Erie that belong to Canada):

For the record, the red area comprises 22% of the surface area of the contiguous United States (38% if you include Alaska), and 15% of its population. Windsor is just 25 km further north than the California-Oregon border.

The paper also states that both Americans and Canadians tend to imagine Europe more southerly than it is in relation to them (they equate Spain's latitude with the southern states, for example). Let's have a look, without that pesky Atlantic Ocean in the way:

Once again using the online tool Mapfrappe, I've marked the Latitudes of Windsor and of the 60th parallel, which divides the Prairie provinces from Northern Canada. You'll notice Windsor, which has some cold winters, is even with northern Spain, which decidedly doesn't. That's another mental shortcut we all share: north = cold, but it's not that simple when you have a nice Gulf Stream warming your coastline.

The geographical comparison was less surprising to me than the demographic one. Six weeks ago, I posted a blog about Canadian population by latitude, whose data was a little coarse because Canada Post and Statistics Canada have copyrighted the most finely detailed geographical boundaries used in the census. A wonderful reader pointed me to the ISLCP II Project, which lists the population of the entire planet for every quarter-degree of latitude and longitude -- albeit from 1995, but I'll take it. Have a look at the relative* populations by latitude of the United States, Canada and Europe:

The most northerly Canadian city with over half a million population is Edmonton, Alberta: it's at about the same latitude as Dublin, Manchester and Hamburg, and 15% of Europeans live farther north than this. (The demarcation of Europe and Asia is fuzzily defined; I chose it as including Istanbul and Moscow, which is north of Edmonton.) And the median latitude of population in Europe is 7 degrees higher than in Canada -- that's over 800 kilometers.

Thanks to these histograms I realized I'm as susceptible to that misfiring geography heurism as anyone: in my mind, Hawai'i was about the same latitude as Sacramento, California, but it's over 500 kilometers farther south than the mainland United States.

Next week, I finish my latitudinal triptych with some sundry interesting tidbits I picked up while writing the last two.

*That means all the bars in each column add up to 100% of the population of the area; obviously, there are more people in Europe and the United States than in Canada.

Read more

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.

Read more