On the Infinite, Pt. 1: Borges’s “The Book of Sand”

Andrew David King
November 23, 2013
Comments 2

Borges’s “The Book of Sand” is just four pages long—or two, if you scan them onto letter-size pages—making it less of a short story and more of a photograph: a singular glimpse inward, a revealing sliver, a narrative to which we have only one frame’s worth of access. “The Book of Sand” would seem to offer the apex of some such narrative as opposed to just any mysterious moment pulled from an endless miscellany; how many people ever come across anything as “diabolical” and heart-stopping as a book with infinite pages, let alone get the chance to pocket it? The action is abrupt, less an arc than a spike; over the course of four pages our protagonist, perhaps a fictionalized Borges, encounters a peddler, buys from him a book procured in India, discovers the book’s horrifying properties, decides to dispose of it, and eventually does so by hiding it a library—because, after all, “the best place to hide a leaf is in the forest.” (I don’t have the Spanish text, but in English, at least, the pun on “leaf” as page is present, the same homonym Whitman used to mock the publishing industry by titling his masterwork Leaves of Grass.)

The story acknowledges its obsession with the infinite immediately; the first thing the narrator does is begin recapitulating a version of Zeno’s paradox:

The line consists of an infinite number of points; the plane, of an infinite number of lines; the volume, of an infinite number of planes; the hypervolume, of an infinite number of volumes… No—this, more geometrico, is decidedly not the best way to begin my tale. To say that the story is true is by now a convention of every fantastic tale; mine, nevertheless, is true.

The turn contained in this first paragraph is from the articulation of an abstruse mathematical and philosophical problem to an assertion—namely, that the story about to be delivered should be believed despite its resemblance to any number of dubious yarns. To decide that proceeding “more geometrico”—in the manner of geometry, a phrase Spinoza would use in his Ethics, with all its idiosyncratic mathematical tendencies—is not the right way to begin, but nonetheless leaving this beginning in the story, is an odd move, is it not? And tricky: the ellipsis invites one to represent to oneself the sound of a voice trailing off, in hesitation or perplexity. The series of fragments that precede this procedural shift are perplexing enough; abstractly-construed spaces are, on this speaker’s conception, like Russian nesting dolls. Beyond this, they’re deemed, at one point, fitting material for the beginning of a fable about a book that defies Euclidean geometry, not to mention sanity.

What might this invocation mean for the story, and for the story’s unnerving hypotheses about texts, stories, fictions, and speech—and even language? Maybe there are parallels between the disturbing quality of the Book of Sand and more straight-laced mathematical paradoxes, but they’re not apparent to me at first glance; there’s something bizarre about Zeno’s paradox, sure, but it seems a different sort of bizarre than that which Borges’s speaker comes up against. The infinity produced by Zeno’s paradox vanishes whenever we defy it: the paradox says, however flippantly, that there are an infinite number of points between any two given points, and that crossing an infinite number of points should take an infinite amount of time—crossing from point A to point B should, or so the paradox goes, be impossible. (Impossible, that is, until we get up from the bed and cross the room to the door, or whatever the case may be.)

In a 1970 interview with L.S. Dembo for Contemporary Literature, Borges recalled his father using a chessboard to try to explain Zeno’s paradox to him, something that substantiates, if this wasn’t already clear, the relevance of the paradox to “The Book of Sand.” Dembo brings up a telling quote by Borges wherein the infinite is invoked; in the essay, “Valéry as Symbol,” Borges writes that Paul Valéry was

the symbol of a man infinitely sensitive to every phenomenon and for whom every phenomenon is a stimulus capable of provoking an infinite series of thoughts. Of a man who transcends the differential traits of self and of whom we can say… he is nothing in himself.

A man who is nothing in himself; a book that is nothing in itself. Is this not what the Book of Sand is—or is it, rather, everything? (And is there a difference, really? Can the two ends of the spectrum really be differentiated, except verbally?) But infinity, in the above-quoted essay, is a productive quantity; it is that which speaks through a medium—a man, a person, a book—as a radio signal through an antenna. It is not that which terrifies and silences the speaker of “The Book of Sand” with its perforations of the real, of reality. No, that is something different: but what is it?

One might understand “The Book of Sand” as an inquiry into the question of just what texts are. Are they infinite? Should they be? Does the idea of their autonomy bother us? The Book of Sand might be said to be autonomous; no one, if we’re to take the narrator and the peddler he meets seriously, ever sees the same page twice (whether by chance or by curse, we’re not told), and no one can ever get to the beginning or end of the book: one always finds more pages. Is it our inability to “master” this book, the book’s refusal to be so mastered, that makes the story so upsetting? As it stands, I think there’s something to be said for the brevity of the story, which I’ve commented on before. It comes and goes in the span of a few minutes. As far as its temporal form is concerned, it is entirely banal. And yet what happens within the space of its duration is anything but. Indeed, space and time conflate; just as the word “space” was used in Middle English and other pre-modern texts as a synonym for time, the Book of Sand comes to stand in for the object that surpasses, somehow, all the bounds of objecthood. It has infinite space; it has infinite time. In his interview with Dembo, Borges mentions his preoccupation, instilled by his parents, with philosophical idealism, a preoccupation that led to so many of the conundrums in his works:

Q. But you would say that you more or less were brought up on idealism?

A. Yes, and now when people tell me that they’re down-to-earth and they tell me that I should be down-to-earth and think of reality, I wonder why a dream or an idea should be less real than this table for example, or why Macbeth should be less real than today’s newspaper. I cannot quite understand this. I suppose if I had to define myself, I would define myself as an idealist, philosophically speaking. But I’m not sure I have to define myself. I’d rather go on wondering and puzzling about things, for I find that very enjoyable.

The Book of Sand, far from being an idea, seems quite real to the speaker. But maybe this is to miss the point; maybe the distinction between ideality and reality, in a world where such an infinite book can exist, is moot. In this way the influence of Kafka on Borges, which the latter has acknowledged, becomes clearer; what does The Metamorphosis do if not posit a world that is grotesque precisely because so much of its contents meet our standards for verisimilitude—that is, whose contents are intelligible, coherent, viable?

To risk moving into the muddy waters of symbolism, perhaps the Book of Sand might be understood not as an unlikely, common-sense-flouting thing floating out there among the rest of the matter in the plenum, waiting to be discovered. Maybe it is best understood through a more realistic (though it should be apparent, now, just how empty of meaning that word is) correlate, that of interpretive practice. This is, admittedly, to take a leap that might not be permissible—a move from the materiality of the book with which the speaker is so concerned to the interpretation of the text, with which he appears not to be concerned whatsoever. (His salesman’s treatment of the Bible he exchanges for the book, not to mention his quick haggling tactics, are just further evidence of this). But maybe this leap is productive, even justified. The Book of Sand, then, could be any book ever encountered by a conscious being; since every encounter is slightly different—if only in virtue of occurring at a different time—no one reading, even by the same being, will ever be the same. It will be impossible, as the peddler says, to find one’s page again. Any book could open a door up on the infinite, a realm about which we could say nothing, about which we could never be finished saying anything. And perhaps this is Borges’s horror.

A comment, in closing, on the story’s epigraph, clipped from George Herbert’s “The Collar.” A strange choice save for its reference to sand—the epigraph reads “…thy rope of sands…,” a phrase that quickly captures the paralysis, sensation of being bound up in the unbounded, that infinity induces. But a closer look at the relevant portion of the poem yields more insight:

Forsake thy cage,
Thy rope of sands,
Which petty thoughts have made, and made to thee
Good cable, to enforce and draw,
And be thy law,
While thou didst wink and wouldst not see.*

Herbert, speaking to himself, understandably frustrated with the duties and anxieties of a newly-minted member of the clergy. Blindness, here, is a refusal to see—a slightly prophetic refusal, given Borges’s late-life blindness, an ailment that itself recalls Milton and his blind composition of Paradise Lost. Even more important, though, is the insinuation that “petty thoughts” have made the cage, the rope of sands (it is “rope” and not the plural “ropes” in the version of the poem I have access to), and the implication that thought, also, might undo them.

But as I raved and grew more fierce and wild
At every word,
Methought I heard one calling, Child!
And I replied My Lord.*

Uncomfortable, I think, how much this portrayal of spiritual connection between supplicant and deity mimics the call and response of the seekers and the lost in a Borgesian labyrinth—another kind of infinity, one brought on by our own perceptual limitations (there is a way in and a way out). Perhaps Herbert meant this to be comforting, but it continues no further; we have no way of knowing whether or not the real has been encountered or something else, and neither does the speaker. The seen-before or the never-seen-before: the difference is slight. But the recognition of the familiar, like that embedded in –Child! –My Lord., makes all the difference in the retaining of knowledge, of language, of anything expressible. Without it we would be left turning the pages of an infinite book, noting the page numbers, as Borges’s speaker does, of its infinite images, creating a reference book that will never be complete.

*The indentation in the original differs from how it is represented here.

2 thoughts on “On the Infinite, Pt. 1: Borges’s “The Book of Sand”

  1. The Book of Sand, when it was first published in English, in the New Yorker, was printed on two facing pages, making it all the more remarkable.

    You write, quite perceptively, that, “Maybe there are parallels between the disturbing quality of the Book of Sand and more strait-laced mathematical paradoxes, but they’re not apparent to me at first glance; there’s something bizarre about Zeno’s paradox, sure, but it seems a different sort of bizarre than that which Borges’s speaker comes up against.”

    You are correct in thinking that Borges was not trying to bring “strait-laced mathematical paradoxes” into his stories for their own sake. As I wrote elsewhere in the review mentioned below, discussing the (possibly) purely mathematical and combinatorial origin of the books in The Library of Babel, “To the contrary, Borges was keen on emphasizing the mystical and the fantastic. As he wrote in The Total Library [a precursor to The Library of Babel], ‘I have tried to rescue from oblivion a subaltern horror: the vast, contradictory Library, whose vertical wildernesses of books affirm, deny, and confuse everything like a delirious god.'”

    Furthermore, I don’t think that the book Borges describes in The Book of Sand has anything to do with Zeno’s paradox, nor, for example, that the book in the story has a page between any two given pages. Each page in the book quite clearly has a next page and a previous page, even though there are no first or last pages. Borges begins the story by quoting Cavalieri, who had an entirely different conception of the composition of Cartesian space, in terms of infinitesimals, than we get from the “real analysis” of modern mathematics. See the footnotes on pages 224 and 225 of my review of William Goldbloom Bloch’s book, in the journal Variaciones Borges, available at this link:


    On the other hand, Borges was very much interested in Zeno’s paradoxes, and wrote a couple of essays about them. He begins Avatars of the Tortoise this way: “There is one concept that corrupts and deranges the others. I speak not of Evil, whose limited domain is Ethics; I refer to the Infinite.”

    By the way, the word for leaf in Spanish, hoja, can mean either a leaf of a tree or a blade of grass or a sheet of paper. So the pun you point out in the English translation of The Book of Sand is already in the original story.


  2. Beautifully written.
    I suppose Hegel’s ‘bad infinity’ and Cantor’s scandalous results regarding Aleph- which were still bitterly opposed by the Intuitionists when Borges was young- was very much part of the zeitgeist back then.
    Interestingly, by the Reflection principle, Borges’s intuition that the Aleph he saw must be a false Aelph is highly probable.
    The irony is that the Bible given in exchange for the Book of Sand itself states that if all the miracles of the risen Christ were written down in books then the world would not be big enough to contain them all. This suggests that books are only valuable so long as they are scarce in a particular sense- the avaricious and puritanical Scotsman values Money and Scripture, while Borges, the snobbish bibliophile, agog for wonders, in the end proves yet more contemptible. Or so it at first appears. Actually, Borges had read Cantor and knew of his tragic fate.
    The author has done well to evoke the memory of Borges’s father in the context of Herbert’s poem.
    An oddly moving piece.

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