Maps are useful things, but it turns out that projecting a 3D object on a 2D map can cause a lot of unexpected problems. They even inspired an XKCD comic. This week we explore maps and map projections. We also chat about machine learning as part of #FunPaperFriday.
What’s the big problem?
- The Earth is a sphere, actually it’s an ellipsoid, actually it’s really bumpy and messy
- Taking 3D information and pushing in onto a 2D medium means that you must sacrifice something, you are losing a dimension with which you can express information.
- Projections are a well thought out as researched problem, even in pure mathematics.
- You have to pick a projection that will tell you want you need to know accurately, and know that you lose some other information.
- There is even a West Wing clip about this
A few examples of projection problems
- There are geographical properties that we care about: area, shape, direction, conformality, distance, scale… and you can’t get them all at once. In fact, some it’s hard to get more than approximately the right answer.
- Area: Maps that preserve area relationships between things on the globe are called equal area maps.
- Distance: Some maps (equidistant maps) show an accurate distance from the center of the projection to all points.
- Scale: The same scaling relation applied across the map will give accurate values for scale relations on the globe.
- Conformality: Scale in any direction at any point is identical. This means that parallels and meridians are at right angles. (Local shape preserved)
A few projections
- Projections can be generally classified as cylindrical, conic, azimuthal, or other. These are as you would think, projections onto cylinders, cones, planes, or with rules of “rectangular meridians” or something else. There are lots of sub-classes, you can view them here.
- Wikipedia lists over 60 different projections!
Fun Paper Friday
That’s what she said. Can we teach computers to better understand human speech patterns? This paper takes a humorous problem as a test case.
Shannon Dulin – @ShannonDulin