application kinematics physical cosmology introduced hermann minkowski minkowski introduced terms like worldline proper time mathematical physics realized submanifold events one moment proper time future could considered hyperbolic space three dimensions already alexander macfarlane charting submanifold algebra physics hyperbolic quaternions though macfarlane use cosmological language minkowski relevant structure called hyperboloid model hyperbolic geometry non euclidean planar algebras support kinematic geometries
Formal science Mathematics Pure mathematics Geometry Non-Euclidean geometry