Analogy and the Dimensional Menagerie

Abstract

The development and presentation of the ideas of n-dimensional geometry in the English language in the second half of the nineteenth century is explored. Reading arguments made by J. J. Sylvester, Herman von Helmholtz, W. K. Clifford, G. F. Rodwell and Karl Pearson, a series of examples of the dimensional analogy, the mode in which expansion beyond three dimensions was repeatedly explained to a general audience is examined in order to demonstrate the persistence of this rhetorical model and to study in detail its structure. The frequent recourse to examples of biological lifeforms presented as experiencing the world two-dimensionally, such as flatfish, worms and ‘tidal ascidians’ is highlighted, and how the perceptual experiences of such creatures were used to extrapolate a model of higher-dimensional perception is discussed. The resulting hybridization of the dimensional analogy with the structures of Darwinian argument is demonstrated along with the concomitant profligacy of the conclusions drawn from this bastardized rhetoric. Drawing closely on Gillian Beer’s reading of analogy with reference to Darwin, the argument is presented that this construction, which in its germinal, geometric form was so appropriate for the demonstration of dimensional expansion, becomes semantically catalytic as a rhetorical tool.