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Understanding Infinity

The Mathematical Architecture Behind Jorge Luis Borges’ “The Library of Babel”

By Omar Al-MahmeedPublished 2 years ago 8 min read
Understanding Infinity
Photo by Alfons Morales on Unsplash

One of the more prominent themes behind Jorge Luis Borges’ anthological series Labyrinths is the idea of infinity. In “The Circular Ruins” infinity is a dreamscape thought into existence by men who dream of other men’s reality, endlessly creating worlds and universes for each other, and idea also discussed in “The Garden of Forking Paths” also shows the existence of infinite number of realities. The short story “The Library of Babel” also flirts with the theme of endless possibilities in an infinite world, as does the protagonist state, but shows that “The Library of Babel” gives the reader an exact record of all things it calls infinite in its hollows, therein indicating a finite integer in the process quantifiable by its inhabitants, indicating in an end to the architectural design of the Library itself, but what does the structure itself look like? Many scholars, architects, artists, and mathematicians of “The Library of Babel” have produced many blueprints of the design of the hexagonal space filling the short tale’s universe but cannot seem to agree on a specific shape to this marvel of architecture. But what if one could infer, from the reading of the story, that the Library may be conceptualized as a tower that spirals upwards and downwards for an exceptionally long time, too long, in fact, for one person to traverse the entirety of the structure? Does such a design hold up with the language Borges uses in his own conceptualizing of the Library, also?

The entire known universe, as portrayed in Jorge Luis Borges’ “The Library of Babel,” lays suspended in time in complete and perfect order as a vast Library filled with all the language known to man, reflecting the image of God in its varied knowledge and history. The eponymous Library—aptly making a parallel to the Judeo-Christian mythos and its story of the Tower of Babel. The fist indicator to the Library’s tower-like structure may come from its own name—Babel. In the Christian Bible, Babel is said to be a city and a tower built by a united race of man in order to reach God and the heavens above, “And they said, go to, let us build us a city and a tower, whose top may reach unto heaven” (King James Version, Genesis 11: 4). The fact that Borges uses the name in his title is no coincidence, but the word could come also physically represent the structure as a tower, much like the mythical story which its name borrows from.

The Library must look infinite as it carries a copious quantity of books inside its architecture, yet by following the logic and language of Borges in the tale, these tomes do quantify a finite number. The number of books, shelves, bookcases, rooms, and spiraling staircases are all reasonably represented in the tale in a tallied total, even as vast as it is, but it does not seem to follow its own logic in the tale as it expresses itself as infinite, so it must be finite then. According to the text, the Library has identical hexagonal rooms, each equipped with an orderly and identical structure within, starting from the hexagonal rooms to the tomes carried within:

“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; the 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 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” (112).


“Each wall of each hexagon is furnished with five bookshelves; each bookshelf holds thirty-two books identical in format; each book contains four hundred ten pages; each page, forty lines; each line, approximately eighty black letters” (113).

Following this blueprint, each hexagon has four walls of books, each containing five bookshelves, thirty-two books each that contain a finite four-hundred-and-ten pages with forty lines, and eighty letters per line. The structure itself is composed of the room, a vestibule or hall with two anti-chambers, the bathroom and bedroom, which opens into the next gallery. All these numbers indicate that they represent an integer that is still smaller than infinity, which also means that the number of rooms in the Library should also be finite and end somewhere. Even if one were to try to comprehend the magnitude of these impossible numbers, one would still have to know how to fit all this into an architectural space.

The most prominent illustration of what the Library could look like comes courtesy of French illustrator Érik Desmazières’ Planets whose illustrations are found on the 1997 edition of the book. This illustration, which is a masterpiece of art, does not reflect the exact dimensions and ignore much of the description given by Borges in the prose. The image here shows cathedral ceiling that rise high above the librarians with multiple towering bookcases that line the walls. The bookcases tapper at the bottom into multiple patioed areas and a raised central terrace with a large spherical structure upon it. The image is beautifully detailed and does introduce a magical description into the illustration, but it does not reflect the story’s description at all.

Another beautiful concept comes from the mind of Andrew DeGaff in his own illustration of the Library in The Library of Babel, which is the most visually appealing to look at but has some minor errors, placement of too many doorways in the hexagon and omitting the two-offshoot bedroom and bathroom of the structure. The image does wonders at trying to conceptualize the scale of the Library, showing series of endless tightly packed hexagonal rooms craftily placed upon one another. The image includes spiraling staircases but seems to add too many bookshelves in the rooms, and the hallways/vestibules between the structures are more evocative of corridors than offshoots.

In another artistic attempt, Kate and Andrew Bernheimer also try their hand at a digital render of the Library in The Universe, conceptualizing the space as a series of circuit of hexagonal packs around an open void that is not reminiscent of the description either. The illustration shows a series of six hexagonal rooms connected in a circuit-like structure with vast voids between the circuits. This image would be the closest illustration of the Library, as it includes vestibules, bathrooms and bedrooms, staircases, and the correct number of shelving, but the vast voids in between would not allow for a librarian on the lower levels to be able to look up into the next level, since the walls would be built up around each hexagonal room and the ventilation shafts would not line up or allow for the same observations. This depiction of the Library is better suited for the theory of it being a tower, too, only if the hallways were also included in the final design. So, based on this design of the Library, one could infer that the Library can be in a circuit shape based on the one line in the story, “…which my father once saw in a hexagon in circuit 15-94, consisted of the letters M C V…” implies that the Library does run in a circuital design (113).

The first impression of the structure would be that the hexagons are positioned in a honeycomb-like structure, where one room opens up to the next adjacent room and so on, yet this design does not take into account that some hexagonal rooms will inevitably have more than two entrances, which cannot be since all the rooms must contain four walls of bookshelves. This honeycomb design may work when you add the vestibule-like hallway between the two, but then you run into the probability that some hexagonal rooms will inevitably create other hexagonal room of empty space, which already goes against the implication that every hexagon must contain the bookshelves, vestibules, staircases, shaft, and thirty-two books on each shelf.

So, what if the librarian that looks down the vestibule hallway is in fact looking either up or down in either direction? From this visual, the librarian is still able to see both the room before it and after it as indicated by the author, “From any hexagon one can see the floors above and below” (112) and does not block the perception of the librarian to other floors, seeing as they could look over either the shaft to the other levels or look onwards between the halls into the other room. The tower theory holds in that it allows for the reader to be able to visual the building while still managing to include all aspects that Borges added to its construction. The rooms would simply arrange themselves above one another, connected by a series of halls that allows the librarian to go from one level to the next. In each hall the two offshoot rooms would be on opposite sides and the hall would open into the next hexagon. The main problem with this theory is that, according to the protagonist, the universe that these rooms inhabit are always the center of the universe, with no visible circumference to the structure of its reality, “The Library is a sphere whose exact center is any hexagon and whose circumference is unattainable” (113). This would indicate that the structure must be flat enough for the librarians to be able to traverse it in an endless fashion, so a tower that extends upwards would not work in its this replication in space.

Perhaps the attempts at visualizing the Library as a structure in our own reality breaks away from inclusion of the magical in the story. As the tale is made to be an account of the magically realistic then this structure does include magical ideas of concepts. The library, in its most orderly state, represents the answers to all of humanities suffering, and in such could not be understood even with its own mathematical detail. The Library represents the idea of the completely incomplete in its totality, an idea always sought after by humanity.


Works Cited:

Bernheimer, Kate and Andrew. “The Universe.” Rice+Lipka Architects, Lyn Rice & Astrid Lipka,

Borges, Jorge Luis. "The Library of Babel." Collected Fictions. Trans. Andrew Hurley. NewYork: Penguin, 1998.

DeGaff, Andrew. “The Library of Babel.” Plotted: A Literary Atlas, Plup, Oct. 2015. Print.

Desmazières, Érik. “Planets.” Warnock Fine Arts,

The Holy Bible, King James Version. Cambridge Edition: 1769; King James Bible Online, 2019.

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About the Creator

Omar Al-Mahmeed

Omar Al-Mahmeed is a bi-cultural, dual national Bahraini-American currently living in Houston, Texas and a graduate of the University of Houston’s English Literature department. He enjoys writing fiction, playing D&D, and reading edits!

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Comments (1)

  • Guanli Yunabout a year ago

    The Library of Babel is one of my favorite novels. I love her story. In my mind, the adventure of people is endless, like

Omar Al-MahmeedWritten by Omar Al-Mahmeed

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