We begin a discussion of the pluses and minuses, highs and lows of map projections in this post.  We’ll always have problems flattening out our spheroidal earth onto flat maps.

Not that I’m a huge basketball fan but I’d like to give Shaquille O’Neal the benefit of the doubt about claiming the earth is flat (he was joking…at least I hope he was).  And he is sort of right…one needs to visit the ISS to really get a sense of the curvature of the earth:

https://www.youtube.com/watch?v=UceRgEyfSsc (Fantastic video, by the way)

But curved it is.  In other, not unrelated news, the Boston public school system is rippling the geography world by adopting a different world map for its students:


In contrast to a more traditional world map:


So what’s all the fuss about this?  Well, both of these stories revolve (sorry) around the same point – we live on a spheroidal planet.  There’s a fundamental problem with trying to represent a 3D object (the surface of the earth) in a 2D space (a map), a topic we’ve alluded to in another post.  The classic example of this is trying to peel an orange into a flattened shape that accurately shows what’s on the surface:


In short – it’s impossible.  Or rather it’s impossible to do it in such as way that you retain all the relationships between what’s on the surface.  When flattening out the orange peel you have to make some choices about what you’re going to sacrifice.  Is it direction?  Is it area?  Is it proximity?  Any attempt to flatten the peel will mean sacrificing one or more of these relationships.

When making maps, it’s the same set of choices to make.  And this is where map projections come in.  Projections are methods that translate the three-dimensional surface of the earth (the globe) into flat, two-dimensional spaces (maps) and there are a multitude available.  The traditional world map that we saw above is called the Mercator projection, named for Gerardus Mercator, a Flemish geographer (amongst other things), who used a projection (soon to bear his name) that allowed colonial mariners to plot their trade route courses as straight lines, because the lines of longitude are parallel with this projection.  Of course on a globe, the lines of longitude converge and meet at the poles, so his projection does a sort of orange-peel-flattening thing that, in the process, takes two points (the poles) and stretches them out to a line, expanding the higher latitude land areas.  This is why Antarctica looks so huge on these maps; it’s nowhere near that big in reality but if you’re sailing from Scott Base to Lyttelton, using this chart makes life a lot easier.  Draw a straight line from point A to point B and use your compass to follow that line (taking variation into account, of course!).

But, like many things, the Mercator projection comes at a cost.  The cost here is area.  The Mercator projection distorts the size of land masses more and more as one moves closer to the poles but preserves direction as the diagram below shows:


On a globe the circles shown above would all be the same size.  The distortion required to make this map increases their size as one moves towards the poles.

The biggest complaint about Mercator has been that those distortions have contributed to a colonialist, Eurocentric view of the world and has supported the imperial leanings of the major colonisers.  By exageratting its size and placing it centrally on his map, Mercator literally (and figuratively) put Europe at the centre of the world.   Europe (Greenland especially), North America, and Antarctica are shown as much larger than they actually are.  South America and Africa, by contrast, are depicted as being much smaller. (There’s a great clip from The West Wing where this gets discussed better than I can)

The map that the Boston school system is now promoting uses the Gall-Peters projection.  With this one, the area of land masses is preserved, but the shape is distorted.  This allows us to make more accurate relative comparisons of areas but things certainly don’t look at all like what we’re used to.  Here’s how the scaled circles look on this one:


But it’s still not 100% correct.  No projection can be.  As soon as one tries to flatten out the orange peel, something gets distorted, be it size, shape, distance or direction (or combinations of these).  Cartographically, it’s not better, it’s just different.  Perhaps it’s better to say that it’s not better, it just makes different sacrifices.  Culturally, it may be “better” but others may argue that there are better projections than either of these.

So this opens the door for us to talk in more detail about map projections and how they affect GIS – we’ll get into that in the next couple of posts.  In the meantime, let’s leave off with two alternative world maps: Buckminster Fuller’s Dymaxion projection and the much more recent AuthaGraph map.

The Dymaxion Map

Fuller’s map involved projecting the globe surface onto a 20-sided polyhedron:

Which can then be unfolded in any configuration you like.  Here’s one possible unfolding:


And here is a figure showing the distortion of scaled circles – as you can see, there’s far less distortion than the Mercator projection above, thought it’s still not perfect:


Here’s an interesting use of it to map early human migrations (the colours show millennia before present day):


The AuthaGraph Map

Finally, by projecting to globe onto 96 tessellated surfaces, Japanese architect Hajime Narukawa created the AuthaGraph map:

Again, a very different look but it does preserve area (but not shape fully, or direction) and has been referred to as an “origami map” as it can be unfolded into different configurations like the Dymaxion map.  If you’d like to have a go with your own printed version, check here.

In all cases above, a map projection has been chosen to represent a 3-dimensional object in a 2-dimensional space.  In all cases above, distortions have been introduced based on that choice.  A globe will always be the best representation of the earth’s surface, but try circumnavigating the world using one of those, let alone adding a globe to your ArcMap map .  Certainly when it comes to GIS, we need projections so we can accurately map features and do analysis, and the good analyst will be aware of what projection is being used as well as what implications it brings.  Map projections and the coordinate systems that come with them sit underneath everything we do with GIS so it pays to have a good handle on what they’re all about.

In posts that follow we’ll go into some more gory depth on map projections and look specifically at the ones we mainly use in our little part of the world.  Stay tuned!