This is a great illustration of how a map projection can work. Imagine that you have a reference globe here of the earth and that the graticule is a wire mesh, if you want and you have a light bulb that's inside there that's shining outwards and you've taken a sheet of paper and you've wrapped it around the entire globe as a cylinder and so you're shining a light from inside that wire reference globe and you're projecting shadows onto the sheet of paper. Projecting shadows like a projection. Interesting. Yes. So, what you'll see is that the light is projecting a shadow from the equator right onto the sheet of paper here and in actual fact, that sheet of paper is touching the reference globe at that location. As you move farther North, those lines are actually getting farther apart and I have a PowerPoint version of that so you can see is what's happening is that even though the distances on the reference globe between those different lines of latitude are equal on the projected version, they're not equal. They're getting more and more distorted or stretched as you move farther and farther from the equator. This is a really nice way of visualizing what's happening with the Web Mercator map and that's why you have Greenland looking so much larger than Africa because Africa is at the equator and you have no distortion at the equator and Greenland is much farther North and so you're getting this stretching that's taking place because of the way that that particular map projection was created which is using this process. Now there's lots of other ways to do this. You can have the sheet of paper via cone or some other shape and you can have the light bulb outside the Earth and put it in different locations. We'll worry about some of that stuff later. But for now I just want you to get the idea conceptually of how a projection works. This is actually done mathematically, but conceptually this is what's happening. Let's take a closer look at this. If we draw a line from the equator to the North Pole, so imagine that that line is actually going up and curving over to the top of the Earth and we draw some points on that line, if we rotate this like so. So, here's our line with our points and we move this over a little bit, what we're going to do now is transfer those points from our 3D globe to our 2D map. So, here's our sheet of paper and we're looking at it sort of edge on and we can transfer those points like so. So, in this case the light bulb is actually on the other side of the Earth. If you want to think of it that way. There's lots of different ways to do this. But with this case what happens is that the distance here is equal to the distance there on the reference globe but on our projected 2D version on our sheet of paper, that distance is no longer the same. So, with this different method of creating a map projection as you go towards the pole we're having the opposite effect. Things aren't getting larger, they're actually getting smaller, they're getting squished in size instead of being exaggerated in size. So, this doesn't necessarily say that one's better or worse, it's just a fact or an artifact or something that happens depending on the method that we choose to make our projection. An example of the results using the method I just described is a cylindrical equal area map and you'll notice here that these should be equal but they're not so the distance between lines of latitude on a reference globe are equal but on our map they're not as they're getting closer together as we go towards the poles. You can see there and these should not be equal but they are equal. What I mean by that is that the meridians are supposed to converge towards the poles, but they're not. Here they don't converge at all, the meridians are parallel to each other. You can see it over here on the reference globe, you can see that they're supposed to be converging and they're not so you can imagine it like the meridians that are converging have actually been stretched out this way and so anything that's closer to the poles is going to be stretched or distorted horizontally as well as what's happening vertically. So, maybe we don't like that, maybe we want to try a different method. Let's go back to our points on our line, on our 3-dimensional globe. We'll take a sheet of paper again and we'll transfer them in a different way so that now the distances between the points on the reference globe are equal to the distances on the sheet of paper. So, that must be better. That must be a good way of doing things because that would be correct. Well, not really. We're maintaining those distances in this direction but as we'll see you're still going to get distortion, there will always be distortion. Here's what the version of that map would look like using that projection. Here you can see that the distances between lines of latitude are still equal, so that's good. That's what we were looking for, that's what we just saw, that's great. But we still have the same problem we had with the previous projection is that those distances are not the way they're supposed to be. We still have these parallel meridians, they're not converging and so we're still getting distortion. So, what's happening is you can have things be correct in one direction but not the other or vice versa. So, keep that in mind as we're looking at different projections is that you can try to have things correct in one way but not another and you'll see how all that works I hope. Just to illustrate this again we've adjusted points along a meridian That's what I was just doing in that version or that method I was just showing you, but you can do the same along a parallel and so you can adjust both but in different ways. So, that's what I was just showing you is that you can have some that are being adjusted horizontally in one way and vertically in another, so you can have things that are stretched or shrunk in one direction versus another. One tip when looking at map projections is to focus on the graticule. It will help you visualize what has happened when that 3-D world was turned into a two-dimensional map. If you look at this one here for example and you see that it's a rectangle, and this is a rectangle, then you can imagine that that was a cylinder of paper that was wrapped around our globe. With something like this though, that was actually a different shape as we'll see that's using a cone sorry, around the globe This is using some other shape which is a little bit more unusual or well, it's not a simple thing to visualize like a cylinder or a cone but what this will do is show you or make you think about the fact that well, if the lines are parallel and they're not parallel on the globe, then that's telling you something about distortion. If you have things being stretched this way, so Greenland looks like it's been squished, that tells you something. So, if the lines of latitude and longitude are not what they were on the globe, what's happened to them? What do they look like on the globe? What do they look like on my map and what does that tell me about what distortion may have taken place and where? So, is it at the equator? Is it at the poles? Is it at some other location and what does that really mean?
