Specifically with regards to the physical aspect of continuity, Clifford invoked the image of a continuous medium that pervades the entire universe ( i.e., an ether).ģThus, for Clifford, the techniques of calculus are conventional tools that describe phenomena in space. Continuous space implies that there are no gaps or moments of non-existence in the fabric of the universe continuous time implies that there are no gaps in the fabric of forward-moving time.
Its mathematical definition is an abstraction of the assumed existence of continuity in space and time. The aim of this paper is to show how one mathematician, namely William Kingdon Clifford (1845-1879), conceived of mathematical “continuity”, how he used it, and how he subtly redefined it as part of his grander philosophical project-to prove that scientific theories based on action-at-a-distance principles ( i.e., instantaneous action across excessively large or infinitesimally small expanses of space) constitute poor means of explaining physical phenomena.ĢAs a mid-19 th century empiricist-influenced as much by the ideas of Charles Darwin and Herbert Spencer as he was by the ideas of Bernhard Riemann, Sir William Rowan Hamilton and Hermann Grassmann-Clifford’s approach to continuity can be summarized as follows: continuity is a conventional mathematical tool based on empirical evidence. “Continuity” is one of the fundamental concepts in calculus, and its history is by no means simple or straightforward. 1 Likewise, histories of “continuity” can introduce historians to the broadest themes in eighteenth- and nineteenth-century mathematics. S Hodge write that, in presenting a volume composed of various case studies in the history of ether concepts, their book introduces readers “to the broadest themes in the scientific thought of the eighteenth and nineteenth centuries”. 1 In their account of ether histories, Cantor and Hodge identify five categories of “ether' concepts (.)ġIn the edited collection Conceptions of Ether: Studies in the history of ether theories, G.
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