The Unimaginable Mathematics of Borges' Library of Babel

The Unimaginable Mathematics of Borges' Library of Babel

The Unimaginable Mathematics of Borges' Library of Babel

The Unimaginable Mathematics of Borges' Library of Babel


"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 Gödel, 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.


One feels right away that this is the kingdom of books. People working at the
library commune with books, with the life reflected in them, and so become
almost reflections of real-life human beings.

—Isaac Babel, “The Public Library”

“WHO is the intended audience for this work in progress?” This question, asked almost apologetically by a friend, stumped me for only a fraction of a second. With the clarity and explosiveness usually reserved for a rare mathematical insight, the answer burst from me: Umberto Eco! Polymath, brilliant semiotician, editor of the journal Variaciones Borges, interpreter of “The Library of Babel,” and a favorite author for many years—Eco struck me as the ideal reader of this writing. (And Umberto, I hope you do read and enjoy this, someday.)

Of the more than six billion people who are not Umberto Eco, I imagine that those who’d find this work appealing would share, to varying degrees, the following traits: a familiarity with and affinity for Borges’ works, especially “The Library of Babel”; a nodding, perhaps cautious, acquaintance with the thought that mathematics might not be the root of all evil; and the habit of rereading sentences, paragraphs, and stories for sheer delight, as well for playing with the superpositions of layers of available meanings.

While it’s possible to set up a straw man and use it to wonder which way of presenting information is “better,”

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