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Torsors are algebraic structures that basically answer the question "why can I subtract two points in space / dates in time, but not add them?". Sure, you can pick an origin (space/time), but that's exactly because they are an affine space, and hence act like torsors.

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I think C++'s (std::chrono::time_point, std::chrono::time_delta) together make a torsor. The group G is std::chrono::time_delta and the set is std::chrono::time_point. Both the group action (time_point + time_delta) and the group operation (time_delta + time_delta) are declared here https://en.cppreference.com/w/cpp/chrono/time_point/operator....

Quite likely - see this discussion on whether to reify an explicit torsor concept in the design of Haskell's time libraries: https://old.reddit.com/r/haskell/comments/j9hfnd/torsors_in_...

An example that really stuck with me is that you can draw an arrow on a blank piece of paper and measure its length and direction without needing to define an x/y coordinate system on the paper. There is something there (the manifold and the action?) that is independent from the ways we can choose to describe the space.

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