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 higherdimensional 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.keywords analogy, fourth dimension, worm, fl atfi sh, hybridization, DarwinIn his inaugural Presidential Address to the Mathematical and Physical Section of the British Association at Exeter in August 1869, James Joseph Sylvester presented an overview of the continental developments in geometric thought and how they related to space. He introduced the idea of n-dimensional space in an analogy borrowed from a recent biography of Carl Gauss: for as we can conceive beings (like infinitely attenuated bookworms in an infinitely thin sheet of paper) which possess only the notion of space of two dimensions, so we may imagine beings capable of realising space of four or a greater number of dimensions. (Sylvester, 1869, 237)
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.