Geometry and topography in James Joyce's Ulysses and Finnegans Wake

Following the development of non-Euclidean geometries from the mid-nineteenth century onwards, Euclid’s system had come to be re-conceived as a language for describing reality rather than a set of transcendental laws. As Henri Poincaré famously put it, ‘[i]f several geometries are possible, is it certain that our geometry [...] is true?’. By examining Joyce’s linguistic play and conceptual engagement with ground-breaking geometric constructs in Ulysses and Finnegans Wake, this thesis explores how his topographical writing of place encapsulates a common crisis between geometric and linguistic modes of representation within the context of modernity. More specifically, it investigates how Joyce presents Euclidean geometry and its topographical applications as languages, rather than ideally objective systems, for describing visual reality; and how, conversely, he employs language figuratively to emulate the systems by which the world is commonly visualised. With reference to his early readings of Giordano Bruno, Henri Poincaré and other critics of the Euclidean tradition, it investigates how Joyce’s obsession with measuring and mapping space throughout his works enters into his more developed reflections on the codification of visual signs in Finnegans Wake. In particular, this thesis sheds new light on Joyce’s developing fascination with the ‘geometry of language’ practised by Bruno, whose massive influence on Joyce is often assumed to exist in Joyce studies yet is rarely explored in any great detail.