The Discreet Charm of Abstraction: Hyperspace Worlds and Victorian Geometry

Abstract

Analytic or Cartesian-coordinate geometry, which describes space in terms of algebraic equations, was conceived by most Victorians as a translation of the “real-world” truths of Euclidean geometry. However, other commentators were concerned that once Euclid’s axioms were translated into a purely symbolic system, there would be no guarantee that that system corresponded to reality. The epistemological crisis intensified with mathematical advances in the later decades of the century, as algebraic equations began to yield problems that seemed to require additional spatial dimensions for their resolution. Charles Howard Hinton, an important popularizer of hyperspace philosophy, argued that imperceptible higher-dimensional worlds must actually exist, since they are conceivable mathematically. The algebraic system is no longer merely meant to represent an a priori truth (of Euclidean space); it also reveals something about that space that is not accessible through perceptual means. This paper examines the anxiety attendant upon the threat of an abstract hyperreal in the work of three imaginative hyperspace writers: Gustav Theodor Fechner, Charles Hinton, and H. G. Wells.