Borges and Mathematics

Appendix A

A review of the most recent edition of Borges’ complete works (Borges: Obras Completas, Sudamericana, 2011) allowed me to discover a surprising number of mathematical citations, somewhat over one hundred eighty. The complete list that I have compiled can be found (although not in English translation) at www.guillermomartinezweb .blogspot.com. Mathematical references are also included in verses of Borges’ poetry, as well as in fictional tales, reviews, and even in mini-lessons embedded in his essays. Despite the quantity of citations, a few recurrent themes connected with philosophical traditions or logical paradoxes clearly emerge, appearing with slight variations in different contexts. For readers interested in mathematics, we offer the following list of those major themes (Titles for as yet untranslated material appear in Spanish ): The concept of infinity (from a philosophical point of view, the generation of the multiple from the singular): “Acerca de UnaAPPENDIX A Mathematical Themes in Borges’ Work| 131 | | 132 | BORGES AND MATHEMATICS muno, poeta”; El idioma de los argentinos; “The Perpetual Race of Achilles and the Tortoise”; “Avatars of the Tortoise”; “The Aleph”; “Pascal”; “El pudor de la historia”; “When Fiction Lives in Fiction”; Arthur Waley’s Three Ways of Thought in Ancient China (London: Allen and Unwin, 1939) Infinite regression (in particular a study of infinite regression traced through Aristotle, Zeno of Elea, Lewis Carroll, and Saint Augustine ): “Avatars of the Tortoise”; “Coleridge’s Flower”; “Time and J. W. Dunne” Fractions tending to zero: “A Defense of Basilides the False”; “The Marked Dyer, Hakim of Merv” Ascending progression: “Two Notes” Transfinite numbers and Cantor’s infinite sets: “Ramón Gómez de la Serna: La sagrada cripta de Pombo”; “Acotaciones”; “There Are More Things”; “Alguien sueña”; “The Total Library”; “The Perpetual Race of Achilles and the Tortoise”; “A History of Eternity”; “The Doctrine of Cycles”; “The Aleph”; “Nihon”; “El tiempo” Infinitely sub-divisible segments: “The Lottery in Babylon”; “The Perpetual Race of Achilles and the Tortoise”; “The Library of Babel ”; “The Book of Sand” Russell’s Paradox: (in the “Catalog of Catalogs” version): “The Library of Babel” Pascal’s Sphere: “The Library of Babel”; “The Aleph”; “Pascal’s Sphere” APPENDIX A | 133 | Royce’s Map: “Another Poem of Gifts”; “When Fiction Lives in Fiction” Line, plane, volume: “The Book of Sand”; “Descartes”; Review of Edward Kasner and James Newman’s Mathematics and the Imagination The fourth dimension: “La cuarta dimensión”; “Emanuel Swedenborg , Mystical Works”; “Ibn-Hakam al-Bokhari, Murdered in His Labyrinth”; “A New Refutation of Time” The Euclidean Circle: “The Disk”; “Epílogo” Numbering systems: “Tlön, Uqbar, Orbis Tertius”; “A Survey of the Works of Herbert Quain”; “Funes the Memorious”; “John Wilkins’ Analytical Language”; “Doctor Brodie’s Report”; Review of Men of Mathematics by E. T. Bell; “Homenaje a Xul Solar ”; “The Total Library”; “Duodecimal Arithmetic, Longmans” Artificial languages: “Delphos or the Future of International Language , de E. S. Pankhurst”; “The Total Library” Huxley’s monkeys: “The Total Library” Self-reference: “The Library of Babel”; “The Aleph”; “Partial Magic in the Quixote”; “Nathaniel Hawthorne”; “Metaphors of The Thousand and One Nights”; “When Fiction Lives in Fiction” The Laplace Formula: “Gilbert Waterhouse: A Short History of German Literature (London: Methuen, 1934)”; “Notas”; “M. Davidson : The Free Will Controversy (Watts, London, 1934)”; “The Creation and P. H. Gosse”; “Pragmatismo”; Prologue to Canto | 134 | BORGES AND MATHEMATICS a mí mismo (León Felipe’s translation of Walt Whitman’s Song of Myself, Editorial Losada, Buenos Aires, 1941) ;“Observación final” Computers and Llull’s Cycle: “Ars Magna” Occam’s Razor: “A Defense of Basilides the False”; “On Literary Description” ...