Russell, Clifford, Whitehead and Differential Geometry
When Russell was ﬁfteen, he was given a copy of W.K. Cliﬀord’s The Common Sense of the Exact Sciences (1886). Russell later recalled reading it immediately “with passionate interest and with an intoxicating delight in intellectual clariﬁcation”. Why then, when Russell wrote An Essay on the Foundations of Geometry (1897), did he choose to defend spaces of homogeneous curvature as a priori? Why was he almost completely silent thereafter on the subject of Cliﬀord, and his writings on geometry and space? We suggest that Russell may have avoided Cliﬀord’s hypothesis that space had heterogeneous curvature because it seemed impossible to reconcile a coherent theory of measurement with a space of variable curvature. Whitehead objected to Einstein’s general theory of relativity on this basis, formulating an alternate theory that preserved the constant curvature of space and, therefore, a familiar sense of measurement. After Einstein’s general theory, Russell chose to distance himself from the position he argued in the Essay.