The Unimaginable Mathematics of Borges' Library of Babel by Bloch William Goldbloom;

Author:Bloch, William Goldbloom;
Language: eng
Format: epub
Publisher: Oxford University Press
Published: 2008-04-10T04:00:00+00:00

FIVE

Geometry and Graph Theory

Ambiguity and Access

If one does not expect the unexpected one will not find it out.

—Heraclitus, Fragment 18

A library is a collection of possible futures.

—John Barth, Further Fridays

THE LIBRARY, AS EVOKED IN THE STORY, HAS inspired many artists and architects to provide a graphic or atmospheric rendition of the interior. These range from Stefano Imbert’s lean and elegant drawing adorning the cover of this book, to the deliberately alienated Piranesi-like drawings of Desmazières in the Godine Press edition of The Library of Babel, to Toca’s beautifully symmetric honeycombs in Architecture and Urbanism, to Packer’s bold expressionist frontispiece in the Folio edition of Labyrinths, to a host of illustrations easily found online. All of these illustrations sacrifice, to some degree, accuracy in favor of artistic effect. For example, even the cover illustration of this book locates the spiral staircase in the center of the hexagon, whereas Borges writes (emphases added):

The universe (which others call the Library) is composed of an indefinite, perhaps infinite number of hexagonal galleries. In the center of each gallery is a ventilation shaft, bounded by a low railing. From any hexagon one can see the floors above and below—one after another, endlessly. The arrangement of the galleries is always the same: Twenty bookshelves, five to each side, line four of the hexagon’s six sides; their height of the bookshelves, floor to ceiling, is hardly greater than the height of a normal librarian. One of the hexagon’s free sides opens onto a narrow sort of vestibule, which in turn opens onto another gallery, identical to the first—identical in fact to all. To the left and the right of the vestibule are two tiny compartments. One is for sleeping, upright; the other, for satisfying one’s physical necessities. Through this space, too, there passes a spiral staircase, which winds upward and downward into the remotest distance.

As we shall see, quite a lot pivots on the ambiguity arising from the italicized phrase “One of the hexagon’s free sides opens onto a narrow sort of vestibule, which in turn opens onto another gallery, identical to the first—identical in fact to all.” (This passage is equally uncertain in Spanish, “Una de las caras libres da a un angosto zaguán, que desemboca en otra galería, idéntica a la primera y a todas.”)

Now, each hexagon has six sides, two sides of which lead to another hexagon. If Borges meant that each one of the free sides gives upon a narrow entrance way with two miniature rooms, then it follows that in every doorway, there is a spiral staircase, rising and sinking beyond sight. Surprisingly, profound and prodigious consequences derive from this doubled staircase arrangement.

On the other hand, we may read the italicized phrase in a different way. If Borges meant that exactly one of the free sides gives upon a narrow entrance way with two miniature rooms, then it follows that the Library contains pairs of hexagons, joined by small rooms and spiral staircases. Although the difference may seem slight, in this variation

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