Humanities Seminar

One of the hallmarks of Einstein's theory of general relativity is the way in which it overturned our understanding of the connection between mathematical geometry and physical space. Although major figures of the nineteenth century were in general agreement that the only candidate physical geometries were constant curvature geometries, this idea was definitively undermined by the unprecedented use of variably curved geometry in general relativity. Even today there is still no agreement on the question of which geometrical objects represent spatio-temporal structure: although some argue that spacetime is best represented by a bare topological manifold, others argue that such a manifold must be equipped with a metric. In this talk I argue that Hermann Weyl's distinctive solution to the "Problem of Space" reveals a level of geometrical structure intermediate between the manifold and the metric, and that there are good reasons to regard this intermediate structure as the appropriate representative of spacetime in general relativity.