  \'Elie Cartan's "g\'en\'eralisation de la notion de courbure" (1922) arose
from a creative evaluation of the geometrical structures underlying both,
Einstein's theory of gravity and the Cosserat brothers generalized theory of
elasticity. In both theories groups operating in the infinitesimal played a
crucial role. To judge from his publications in 1922--24, Cartan developed his
concept of generalized spaces with the dual context of general relativity and
non-standard elasticity in mind. In this context it seemed natural to express
the translational curvature of his new spaces by a rotational quantity (via a
kind of Grassmann dualization). So Cartan called his translational curvature
"torsion" and coupled it to a hypothetical rotational momentum of matter
several years before spin was encountered in quantum mechanics.
