The Map of the World

Boston Public Schools just caused a stir by adopting a new map of the world.

"Boston public schools map switch aims to amend 500 years of distortion"reads the headline in the The Guardian, and "amend" is a good choice of words, because BPS decided to replace one set of distortions with another.

Boston had been using the Mercator Projection (1569), a version that we're all pretty familiar with.

Mercator distorts by spreading out the world as it approaches the poles, so that by the time we get to Greenland or Alaska, the land masses are looking much larger than they actually are. Mercator was mostly trying to help with navigation, and this map was fine for that. And since his audience/customers were mostly starting from Europe, his map reinforces the idea that Europe is the center of the world. And it makes Africa and South America look relatively smaller.

This is many people's mental map of the world, complete with its built-in distortions.

BPS decided to switch to the Gall-Peters projection (1855/1967) a map that sets out to render each land mass equally, so that the relative sizes of the land masses are accurate.

But because the projection is still onto a rectangle, Gall-Peters combats one distortion with another distortion. The Marcator inflates land area by stretching it out at the bottom and the top; Gall-Peters fixes that by squishing the map in at the top and the bottom until the land areas are comparable and "correct."

This version is not necessarily very useful for navigation, but in the late 20th century it stirred up a bit of a mess. Arno Peters was actually duplicating the 100-year-old work of James Gall, and he promoted it as a more just and socially aware map than the Mercator, annoying the crap out of the cartographic community, which had been trying to downplay, improve upon, and replace Mercator for a couple of centuries. But Peters managed to build a cottage industry around his map (and even eventually acknowledged that Gall had gotten there a century earlier). The Brits use the map, and UNESCO has based some of its mappery on it, the argument in favor of it being that it shows nations in their proper relative size, even if shapes and distances are distorted.

Are there other options? You bet there are.

Try, for instance, the Cassini projection (1745), which keeps its distances somewhat standard and lets you see the poles.














Or how about the various Eckert projections (1906) that avoid lots of distortion by not trying to fit the surface of the globe on a rectangle.

And once we've chucked the whole rectangular map thing, we can get the equal-area maps right and show every land mass in proper proportion to the others. Here's the Goode homolosine projection (1923).

And cartographers haven't stopped playing. This Bottomley (that's the guy's name) equal-area projection from 2003:

We'll stop now, but there are even freakier versions of the earth in existence. There are many, many maps of the world out there-- some good for navigation, some good for figuring distances, some for showing proper relationships between land masses, some focused on ocean shaped and depths. But here's one thing we know about all of them--

They are all wrong. They are all incomplete. They are all distorted in some fairly major way.

This is to be expected. When you take something that is huge and complex and multidimensional and try to render it onto a small two-dimensional surface, you must sacrifice some major chunks of the truth. For that reason, you have to be fairly deliberate about and conscious of what parts of the truth you are sacrificing for whatever specific utility you wish to get from your map. And you have to keep trying, because every solution you come up with will be inadequate in some major way. And you must always remember that your map is inadequate in some major ways and not mistake the two-dimensional rendering for the real thing.

That's the lesson here, or rather the reminder, because we already knew all this but certain people prefer to pretend they don't, is that whenever you try to render, describe, display, or create a measured model of something complicated (like a school or a teacher or a student's mind or learning) you will absolutely fail in some major ways. Furthermore, if you get to thinking your map of that world is perfect, you will make terrible mistakes.

It is hard to make a map of the world. You will always fail, and if your goal is to achieve perfection, you are doomed to lose in a fool's game. If, on the other hand, you do the best you can, keep trying, and remain aware of your shortcomings so that you don't bet the farm or attach huge stakes to a map that's not True-- well, you might have a chance. If you think your Big Standardized Tests and data sets based on them and numbers kicked out by your fancy formulae are a perfect guide to what's going on in schools, you are doomed to be lost. And it would be really nice if you didn't drag the rest of us with you on your doomed journey.