I Hate Coordinate Systems!

I hate coordinate systems! How do I wrap my head around these things?

Apply this three-part mental model of geospatial datasets. Many common problems happen when one of these parts is missing or out of sync. Attributes: the meanings or labels of a data point. Coordinates: numbers describing the data point's position in space. Coordinate (reference) system: metadata describing the space itself: origin, axes, units, etc.

I hate coordinate systems! What coordinate system should my dataset be in?

Look at the two things you do know: the attributes and the coordinates. A data point's attributes gives context to where on the Earth it is located. Most GIS software will display the minimum and maximum coordinates in the layer's properties as "extent" or "bounding box". From these, do some detective work on the coordinate system which you should use when redefining your dataset.

I hate coordinate systems! How do I redefine a dataset's coordinate system?

It depends on your software. Remember, redefining means the metadata about the coordinate system is modified but the coordinates are not. This contrasts with reprojections and transformations, which modify both the coordinate system and the coordinates.

I hate coordinate systems! Why is Mercator ever used if it's so distorted?

Mercator is the only conformal cylindrical map projection. Cylindrical map projections mean the whole Earth fits into a rectangle, which is very convenient for data processing algorithms that are used to working with rectangular images. Conformal means that angles and shapes are always preserved: north is always up, squares are always square, etc.

I hate coordinate systems! Why don't we always use longitude/latitude?

Good question. There are a bunch of reasons we use planar projected coordinate systems rather than just sticking with latitude,longitude geographic coordinate systems all the time: Planar measurements are ubiquitous. Common GIS features like property boundaries, road centerlines, forests, lakes, etc. are all reckoned in Euclidean distances, areas, and volumes - not in terms of angles.