Borges and Mathematics: los juegos con el tiempo y con lo infinito

Abstract

This thesis considers Jorge Luis Borges’ fascinations with mathematics, between 1929 and 1952. In the first chapter, I argue that Borges sees notions of the infinite, and the mathematics of ‘endlessness’, as means to understand philosophical variations on the self in “tiempo vivo.”[“living time.”] Unreality and paradox occur in the stories in Ficciones because the terms of their narrative worlds are figured totally by some mathematical-philosophical system. In the second chapter, I show how Borges’ idea of tiempo vivo is mathematically and philosophically derived, and how these ideas are linked to reading and perceptual experience in his first fiction. I examine his fiction in relation to his lesser-known nonfiction, arguing that Borges saw mathematical thinking in philosophy as a way of understanding perceptual experience in time, and thereby ‘the reader.’ The experience of reading, the recognition of similarity and difference between texts, is the central problem motivating Borges’ earliest fictional works. Borges understands language in literature, I argue, as mediating the importation of a writer’s past into the reader’s present—perceptual experience coded in one ‘present’ and decoded, differently, in another—evoking some composite perceptual experience, which he analyzes using mathematical series as analogy. Finally, I use these ideas to offer a reading of “A New Refutation of Time.” I suggest that the essay’s summary negation of time is sophistical, but that the reasoning it draws on is not. I think the real purpose of the essay is to argue against understanding time perceptually, the self temporally, perception itself as a mathematical series of percepts, and, ultimately, against conceiving of the self as the sum of what is experienced over time. In closing, I argue that the “refutation of time” refers instead to the power of the written word to evoke in the reader its own ‘present,’ and suspend all others—the tiempo vivo Borges refers to throughout his works.