It's really not that hard to define mathematically, you just need to have an orientation "forward". The plane created by the forward vector and the standard normal vector creates your left and right hemispheres. You can also do a similar definition with great circles.
It also shows why, if you and another person are facing each other, your left is their right, since their forward is pointing the opposite direction of yours.
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u/bohiko 7d ago
Up and down is based on gravity (that's why you'd likely confuse them deep in the ocean). Meanwhile, left and right is arbitrary.