"The Library of Babel" is arguably Jorge Luis Borges' best known story-memorialized along with Borges on an Argentine postage stamp. Now, in The Unimaginable Mathematics of Borges' Library of Babel, William Goldbloom Bloch takes readers on a fascinating tour of the mathematical ideas hidden within one of the classic works of modern literature. Written in the vein of Douglas R. Hofstadter's Pulitzer Prize-winning Godel, Escher, Bach, this original and imaginative book sheds light on one of Borges' most complex, richly layered works. Bloch begins each chapter with a mathematical idea-combinatorics, topology, geometry, information theory-followed by examples and illustrations that put flesh on the theoretical bones. In this way, he provides many fascinating insights into Borges' Library. He explains, for instance, a straightforward way to calculate how many books are in the Library-an easily notated but literally unimaginable number-and also shows that, if each book were the size of a grain of sand, the entire universe could only hold a fraction of the books in the Library.Indeed, if each book were the size of a proton, our universe would still not be big enough to hold anywhere near all the books. Given Borges' well-known affection for mathematics, this exploration of the story through the eyes of a humanistic mathematician makes a unique and important contribution to the body of Borgesian criticism. Bloch not only illuminates one of the great short stories of modern literature but also exposes the reader-including those more inclined to the literary world-to many intriguing and entrancing mathematical ideas.

Table of Contents

PREFACE; INTRODUCTION; COMBINATORICS: CONTEMPLATING VARIATIONS OF THE 23 LETTER; TOPOLOGY AND COSMOLOGY: THE UNIVERSE (WHICH OTHERS CALL THE LIBRARY); INFORMATION THEORY: CATALOGING THE COLLECTION; GEOMETRY AND GRAPH THEORY: AMBIGUITY AND ACCESS; REAL ANALYSIS: THE BOOK OF SAND; MORE COMBINATORICS: DISORDERINGS INTO ORDER; A HOMOMORPHISM: STRUCTURE INTO MEANING; CRITICAL POINTS; OPENINGS; ACKNOWLEDGEMENTS; APPENDIX ITHE LOGOS OF LOGARITHMS; APPENDIX IIFLAT-OUT DISORIENTED; APPENDIX IIIPEELING THE 3-SPHERE; APPENDIX IVA LABYRINTH, NOT A MAZE; APPENDIX VAN EXAMPLE OF THE ARS COMBINATORIA; BIBLIOGRAPHY

Reviews

"Mr. Bloch, professor of mathematics at Wheaton College, has woven an elegant, ingenious, scholarly interpretation of Borges's text that contradicts the disingenuous 'unimaginable' of his title."--New York Sun

"For the reader of Borges, some of Bloch's observations may offer a useful new way of engaging with the themes of the fiction." -- American Scientist

"You need no advanced mathematics to understand 'The Library of Babel' but chances are good that if you like the story, you'll enjoy Professor Bloch's excursions." -- Mathematical Association of America Review

"Given Borges' well-known affection for mathematics, this exploration of the story through the eyes of a humanistic mathematician makes a unique and important contribution to the body of Borgesian criticism. Bloch not only illuminates one of the great short stories of modern literature, but also exposes the reader - including those more inclined to the literary world - to many intriguing and entrancing ma