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jkaufman comments on What false beliefs have you held and why were you wrong? - Less Wrong Discussion
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I'm not sure what you mean. You're saying it's not possible to make a coherent mathematical description of a physics system where something rotates around multiple axes? It wouldn't correspond to our world very well, but why are the mathematics impossible?
Yikes! Yes, even the model I ended up with sounds like it didn't represent rotations properly.
This was about a decade ago, so I'm not confident I remember what I did properly. But I think you can represent orientation as a one-time rotation from an initial position. So (ox, oy, oz) are a vector representing an axis with the magnitude indicating how far around that axis it rotates. Does that not work? (It's also possible that I kept orientation as a matrix.)
Rotation is a mathematical concept, not a physical one.
In 4d, an object can rotate about two axes at once. Say the 4 coordinates are w x y z. The w and x coordinates can do the usual rotation, while the y and z coordinates rotate together, perhaps at a different rate. Or instead of 4 real coordinates, take 2 complex coordinates a and b, and have them evolve by (a,b) → (exp(i.r.t).a, exp(i.s.t).b), where t is the time and r and s are speeds.
Not in 3 dimensions.
Come to think about it, yes it can.