What is space or space-time. Well one can look at this either as a physicist or a mathematician. Physicists tend to take a simplistic approach. space(-time) is where things happen. So space(-time) is all about locations. A location is a point in space(-time) where something happens. So we can say Osama-bin Laden was killed at a particular latitude and longitude, in the top story building, and at a particular time. A lot of physics is about locations, how things are measured and how they relate to one another.
So physics normally starts with a coordinate system ( which is slightly odd since space-time doesn't seem to come equipped with a natural coordinate system ), and GR is all about how one coordinate system relates to another.
Note that the coordinates given above are curvy. Both latitude and longitude both curve and if greenwich is the origin then that takes a complex curvy path as the earth rotates and orbits the sun.
So physics starts with coordinates. What about mathematices?
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