Mathematics and Modernism: Jorge Luis Borges, Samuel Beckett and J.M. Coetzee

摘要

This thesis contributes to the understanding of the intricate relation between number, narrative and modernity by analysing the connection between the late nineteenth-century revolution in the mathematics of the infinite and selected texts of twentieth century modernist fiction. This ‘revolution’ in the infinite refers to Georg Cantor’s discovery of the ‘transfinite’ numbers, which measure multiple infinities of different ‘sizes.’ I will focus on the significance of number in key works of three twentieth-century writers: Argentine miniaturist Jorge Luis Borges, Irish novelist and playwright Samuel Beckett, and South African novelist J.M. Coetzee. Each of these writers participate in a different instantiation of literary modernism in vastly different regional and linguistic contexts. What unites them is the centrality of number to the literary innovations that shape and define their work.Through an analysis of number and the transfinite in fiction, I will forge a formal and conceptual connection between two domains regularly understood to be antithetical, without allowing one domain to ‘cannibalise’ the other. Studies of mathematics in literature frequently render numbers as metaphors or symbols, which I argue removes from mathematics that disciplinary and representational difference that makes it appealing to modernist project of literary supervenience. Additionally, this thesis makes a contribution to the relation between literary form, most importantly allegorical form, and the conceptual, textual and epistemological status of the numeral. In these texts, at the end of the allegorical ‘rainbow’, we find not another text or transcendental meaning, but a number.This understanding of numerical allegory allows for an account of the way that numerical form undergirds narrative perspective, description and the undescribable, and the relationship between the efficacy of the symbol and the fictional world. Formally, this thesis maps the reciprocity between mathematics and literature along the lines of the lemniscate. This strategy maintains the autonomy of the tropological and semiotic domain of literature, and the presentational domain of mathematics, but allows the two domains meet at a certain point. This point is the ‘transfinite.’ Where this point touches the mathematical domain, it takes the form of Cantor’s transfinite numbers, where it faces the literary domain, it constitutes a type of formal allegory, which I will call ‘transfinite allegory.’