{"id":1723,"date":"2017-05-25T03:21:18","date_gmt":"2017-05-25T03:21:18","guid":{"rendered":"http:\/\/blogs.lincoln.ac.nz\/gis\/?p=1723"},"modified":"2023-05-07T03:45:08","modified_gmt":"2023-05-07T03:45:08","slug":"map-projections-part-2-the-allegory-of-the-cave","status":"publish","type":"post","link":"https:\/\/blogs.lincoln.ac.nz\/gis\/map-projections-part-2-the-allegory-of-the-cave\/","title":{"rendered":"Map Projections Part 2: The Allegory of the Cave"},"content":{"rendered":"

In this second post on map projections we cover the range of different types of projections.\u00a0 Part 1 gave us a broad overview of different map projections<\/a><\/em><\/p>\n

In thinking about map projections I’m reminded of an old story<\/a>.\u00a0 Now bear with me on this one: in this story, imagine some prisoners, chained in a cave all their lives, their heads unable to turn such that all they can see in front of them is the cave wall.\u00a0\u00a0 Behind them, a great fire burns, and in between prisoners and fire, puppetters march past with their puppets held high so that they cast shadows on the cave wall.\u00a0 It looks something like this:<\/p>\n

\"\"<\/a><\/p>\n

The idea here is that the prisoners, not knowing anything else, take the shadows to be reality.\u00a0 The shadows have become how they understand the world.\u00a0 In another part of the story, a prisoner breaks free and emerges from the cave, sees the sun for the first time and realises that things were not at all the way they seemed, and it’s all a bit frightening.\u00a0 (Sorry, there’s really not a happy ending to this story.\u00a0 Well, there is…sort of…but it’s not your typical Hollywood blockbuster ending.)<\/p>\n

Map Projections<\/strong><\/p>\n

Okay, so I’ll admit, I’ve got some issues with this story too, but what does it have to do with map projections?\u00a0\u00a0 Like the prisoners, what we see on maps is a bit like the shadows thrown on the cave wall.\u00a0 In fact, the reason they’re called projections is because map makers originally used shadows cast on a surface to translate the 3D earth onto a flat, 2D plane.\u00a0 Imagine (if you will) a spherical globe constructed with a metal frame of meridians of longitude, parallels of latitude and the land masses.\u00a0 Also imagine a light bulb at the center of this globe.\u00a0 Take a large piece of paper and shape it into a cylinder.\u00a0 Place that cylinder over the globe so it touches at the equator and turn the light on.\u00a0 Now trace the outline of the shadows on the cylinder, et voila!\u00a0 Unroll the paper and you’ve got a projected map.<\/p>\n

\"https:\/\/sciencedemonstrations.fas.harvard.edu\/presentations\/mercator-projection\"<\/a>
https:\/\/sciencedemonstrations.fas.harvard.edu\/presentations\/mercator-projection<\/a><\/em><\/figcaption><\/figure>\n

And like the prisoners, it’s the shadows that give us our reality. \u00a0 When the paper is unrolled,\u00a0 the technique outlined above gives us the tried and (I was going to say true, but…<\/a>) Mercator Projection.\u00a0 (Do check out this link\u00a0<\/a> where they actually show how this works.)\u00a0<\/em> In a very analog way, this is how map projections work.\u00a0 The main differences between different projections created this way are the kinds of surface the shadows are projection onto.\u00a0 Above, it’s a cylinder.\u00a0 But we can also use cones, or planes that touch the globe at a point.\u00a0 This gives us the three main types of projections: azimuthal (planar), conic and cylindrical:<\/p>\n

\"\"<\/a><\/p>\n

When unfolded, each lays flat and the traced shadows give us what’s where.\u00a0 Now we’re really only just beginning to look at the range of possible map projections (there are thousands built from these three simple approaches) especially when we realise (like our prisoners) that we can also work with mathematical projections that use equations to go from 3D to 2D.\u00a0 Here’ a small list of projections<\/a> (69 in total, a mere smattering).\u00a0 As noted earlier<\/a>, with any projection, it’s impossible to transfer the features on the surface of a sphere onto a flat plane without creating some sort of distortion.\u00a0 As soon as we turn the light on (metaphorically speaking) we sacrifice something: area, shape, bearing, or distance.<\/p>\n

Another way we can classify projections is what aspect of the surface they preserve.\u00a0 Here are the main categories:<\/p>\n