On December 5, 2005, at the Max Planck Institute in Bonn, Germany, the British mathematician Marcus du Sautoy, specialized in the study of symmetries, had a revelation: the idea of building a new object that would allow him to demonstrate an unsuspected relationship between the world of symmetries and that of elliptic curves. It was not, of course, a physical object, since its materialization would require access to a nine-dimensional space. It was a mathematical object that he would construct through the language of group theory. In other words, he had discovered a new group of symmetries. The joy of the discovery was marred by a thought: “No one else could have created Bach’s Goldberg Variations. Bach couldn’t have been beaten to the composition by someone else. But the group I’ve discovered now looks a little like a new species of butterfly—it existed before it was discovered.”
This distinction between science and art, in which the former offers its treasures to the scientists who manage to discover them, while the latter demands the genius to create what did not exist before, is often not so clear to artists. In fact, it is common to feel that such a musical composition, poem, novel or painting pre-existed in some dimension and that the creative work has been that of the copyist or the midwife: reproducing or unraveling a world that, like the butterfly of mathematics, was already there.
This vision of artistic creation was defined, moreover, in years when the study of literature had scientific pretensions. It was the golden age of Russian formalism, whose approach to the literary event led one of its most notable members, Osip Brik, to assert that “Eugene Onegin, Pushkin’s poem, would have been written even if Pushkin had not existed.” Terry Eagleton, who quotes the phrase in his Introduction to Literary Theory (1983), calls it an airy remark.
The greatest criticism, however, came from Leon Trotsky. In the fifth chapter of Literature and Revolution, 1924, Trotsky labels the Russian Formalists “insolent abortion” and “desiccated abortion of idealism” and then dismantles formal poetics with these arguments:
In fact, the Formalists do not carry their idea of art to its logical conclusion. If one is to regard the process of poetic creation only as a combination of sounds or words, and to seek along these lines the solution of all the problems of poetry, then the only perfect formula of “poetics” will be this: Arm yourself with a dictionary and create by means of algebraic combinations and permutations of words, all the poetic works of the world which have been created and which have not yet been created. Reasoning “formally” one may produce Eugene Onegin in two ways: either by subordinating the selection of words to a preconceived artistic idea (as Pushkin himself did), or by solving the problem algebraically. From the “Formal” point of view, the second method is more correct, because it does not depend upon mood, inspiration, or other unsteady things, and has besides the advantage that while leading to Eugene Onegin it may bring one to an Incalculable number of other great works. All that one needs is infinity in time, called eternity.
Borges applied an analogous reasoning in a fateful moment of his life. It happened at the beginning of 1939, while he was recovering from an absurd accident that almost killed him. The anecdote is well known, so it is worth retelling. On Christmas Eve 1938, Borges went to visit a friend. Some versions say it was the Uruguayan Emma Risso Platero and others say it was the Chilean María Luisa Bombal. The truth is that Borges did not want to wait for the elevator and ran up the stairs. At some point, he felt something brush his forehead, but he ignored it. When the friend in question opened the door, she gasped in horror. Borges realized the corner of a window had done more than just graze him: his forehead and shirt were stained with blood. Days later, the wound developed into septicemia and he had to undergo emergency surgery.
When he finally recovered, Borges had a great concern: had the accident impaired his mental faculties? He decided to clear the x by taking two tests. A reading comprehension test and a writing test. For the first, her mother read him an excerpt from Out of the Silent Planet by C. S. Lewis. After two pages, the mother stopped. Borges was crying. “I cry because I understand,” he told him. For the second, the test was more difficult:
I had previously written quite a few poems and dozens of short reviews. I thought that if I tried to write a review now and failed, I’d be all through intellectually but that if I tried something I had never really done before and failed at that it wouldn’t be so bad and might even prepared me for the final revelation. I decided I would try to write a story. The result was “Pierre Menard, Author of the Quixote.”
This is how Borges recalled it in his “autobiographical notes” originally published in English in the September 11, 1970 edition of The New Yorker.
What is really interesting is that the anecdote of Borges’ story is the implementation of Osip Brik’s boutade about Eugene Onegin refuted by Leon Trotsky. It is the story of a 20th century Frenchman who set out to rewrite Don Quixote. Not to copy it, nor to reproduce it from memory, nor, much less, to believe himself to be Cervantes and repeat the feat. Rather, it was a matter of “continuing to be Pierre Menard and arriving at Don Quixote, through Pierre Menard’s experiences.”
Within the fiction of the story, the narrator reveals the texts that inspired his friend Menard: a philological fragment of Novalis and “one of those parasitic books that set Christ on a boulevard, Hamlet on La Cannabière, or don Quixote on Wall Street.” Without entirely ruling out these influences, I believe that this sentence by Menard himself in a letter to the narrator puts us on the right track: “The task I have undertaken is not in essence difficult […] If I could just be immortal, I could do it.” The same conclusion that, with irony, Trotsky had reached much earlier when he pointed out that to write Eugene Onegin, by means of the random combination of letters and words, all that is needed, besides a good dictionary, “is infinity in time, called eternity.”
Trotsky’s “algebraic” solution also presides over the story “The Library of Babel.” In this story, the universe is conceived in the form of an eternal library containing all books: “In order for a book to exist, it is sufficient that it be possible.” Here the boundary between the real and the imaginary is blurred. It is as if in our world the object devised by Marcus du Sautoy could exist both in its mathematical formulation and in its nine-dimensional material concreteness. “The Library is ‘total,’” explains the narrator, and “its bookshelves contain all possible combinations of the twenty-two orthographic symbols (a number which, though unimaginably vast, is not infinite).” This vastness, although numerically not infinite, is infinite for the human capacities of the Library’s only inhabitants: the librarians. The chance of any of them finding during their lifetime a single volume with a few legible lines, other than a random arrangement of signs, is close to zero. “Some five hundred years ago, the chief of one of the upper hexagons came across a book as jumbled as all the others, but containing almost two pages of homogeneous lines.” After a century of analysis, the anonymous librarian tells us, the contents of those two pages were established: they were “he rudiments of combinatory analysis, illustrated with examples of endlessly repeating variations.”
This cruel circumstance led the librarians to think that in this totality there must be one or more books that would justify the existence of the Library and, therefore, of their lives. Of course, they found nothing. The inaccessibility of these precious books provoked a desperate measure: “One blasphemous sect proposed that the searches be discontinued and that all men shuffle letters and symbols until those canonical books, through some improbable stroke of chance, had been constructed.” This sect was banned and then disappeared. The same happened with the Russian Formalists when Stalin succeeded Lenin in power.
What moves the librarian to tell his story is to solve “the fundamental mysteries of mankind—the origin of the Library and of time—.” It is a matter of reconciling two opposing principles: that of the infinity of the Library, of its hexagonal galleries, of its floors that rise and fall without limit, with that of the finite vastness of the books that can emerge from the combination of the twenty-five orthographic symbols. “I will be bold enough to suggest this solution to the ancient problem: The Library is unlimited but periodic,” says the librarian. All that is needed to corroborate this hypothesis is, again, unlimited time: “If an eternal traveler should journey in any direction, he would find after untold centuries that the same volumes are repeated in the same disorder—which, repeated, becomes order: the Order.”
Now, did Borges read Trotsky or is it an amazing, mathematical, coincidence?
Literature and Revolution was published as a book in 1924, but several of the texts included therein had previously circulated as prologues to other works and as loose articles. Those were also the years of Borges’ Soviet enthusiasm, when he lived in Switzerland with his family between 1914 and 1918 and when, as a typical idealistic adolescent, he celebrated the advent of the Russian Revolution. His enthusiasm even made him want to learn the language. He recalled this in one of his conversations with Osvaldo Ferrari:
I find the Russian language very beautiful, every time I have heard Russian, I have regretted not knowing it. And I tried to study Russian, around 1918, let’s say, at the end of the First War, when I was a communist. But, of course, communism then meant the friendship of all men, the forgetting of frontiers; and now I think it represents the new tsarism.
From that same period date Red Psalms, a book of poems that Borges would destroy before his return to Buenos Aires. Some texts survived because they had been published in Spanish magazines such as Grecia and Ultra in the intense period between 1919 and 1921, when he lived in Mallorca, Madrid and Seville. “Gesta maximalista,” “Rusia,” “Trinchera” are the titles of some of these poems that record the revolutionary faith of the young Borges. The poem “Guardia roja” is perhaps the one that would bring him closest to the figure of Trotsky, in view of the fact that it was Trotsky who created and presided over the famous working class combat units, which arose in the context of the 1905 Revolution and which would gain prominence after October 1917.
The return to his homeland, the reunion with his hometown and with its modes of expression will quickly lead him to lose interest in his European follies. From the publication of his first book, Fervor de Buenos Aires (1923), until the end of the twenties, Borges’ interests would swing towards the opposite pole of the avant-garde: orality, popular literature and criollismo. The writing and publication of articles will intensify and will give rise to three compilations he will disowned to the point of prohibiting their reprinting: Inquisiciones (1925), El tamaño de mi esperanza (1926) and El idioma de los argentinos (1928).
Considering this context, it would seem strange that Borges would have been interested in reading Trotsky. Either armed with a dictionary and his rudimentary command of Russian, which seems highly improbable, or through some translation of Literature and Revolution (several translations already existed since 1924). This would explain why there is not a single mention of Trotsky in Borges’ work. This silence, however, may be misleading. In the first place, because Borges’ work is very vast and that elusive mention could be found by someone more meticulous than me. And, secondly, because Borges did read Trotsky, although without knowing it. I am referring to the text “For an Independent Revolutionary Art,” the manifesto signed by André Breton and Diego Rivera that Borges reviewed with marked disdain for Hogar magazine on December 2, 1938 (a few weeks before the accident).
As Horacio Tarcus tells in a documented essay on the aforementioned manifesto, it was written by Breton and Trotsky during their difficult coexistence in Mexico. However, as a result of a series of disagreements, Trotsky finally withdrew his signature and it was agreed that Rivera’s should be put instead.
That said, I could think of two possible solutions.
The first, more plausible because it is simple, is that Borges did read chapter V of Literature and Revolution, but had forgotten it. After the trauma of the accident and septicemia in the year 38 (a particularly difficult year since it was also the year of his father’s death), at the crossroads of putting his mental faculties to the test, his brain recovered Trotsky’s algebraic conjecture as if it were his own. In fact, something like this happened to him with the writing of “The Other,” an autobiographical story of 1969, whose structure he took from a story by Giovanni Papini he had read in his childhood and then forgotten.
The second solution is more surprising, but it would confirm what Trotsky denounced as madness: that, beyond personal experiences, inspiration or talent, a writer could formulate, by the pure combinatorial chance of words, the work written by another.
I believe, however, that Borges was able to find, like the librarian in his story, a third way. An alternative solution to the dilemma posed by Trotsky.
In the frontispiece of Fervor de Buenos Aires, Borges already warned: “To whoever reads: If the pages of this book contain any felicitous verse, forgive me, reader, for the discourtesy of having usurped it myself previously. Our nothingness barely differs; it is trivial and fortuitous the circumstance that you are the reader of these exercises, and I am their writer.”
This conviction will accompany him until the end of his life. In a beautiful lecture delivered on June 5, 1978, at the University of Belgrano, entitled “On Immortality,” Borges will insist on the essential triviality of the notion of author with respect to literature:
My opinion does not matter, nor my judgment; the names of the past do not matter if we are continually helping the future of the world, immortality, our immortality. That immortality need not be personal, it can do without the accident of names and surnames, it can do without our memory […] Perhaps the most important thing is what we do not remember in a precise way, perhaps the most important thing we remember in an unconscious way.
Trotsky said that the formalist conception of literary creation demanded the immortality of the “creator.” Borges agrees, but points out that this immortality need not be personal.
At the risk of deepening the triviality of these reflections, I would like to add something else. The book by Marcus du Sautoy with which this research began, Symmetry: A Journey into the Patterns of Nature, is from 2008. In The Creativity Code: Art and Innovation in the Age of AI, from 2019, Du Sautoy devotes himself to investigating “how AI is learning to write, paint, and think.”
In this book, in the chapter “The Songwriting Formula,” there is a section that immediately caught my attention: “Pushkin, Poetry and Probabilities.” There, Du Sautoy talks about François Pachet, a French scientist and composer responsible for having created “the AI first jazz.” To do so, Pachet used “a mathematical formula from probability theory known as the Markov chain.” Du Sautoy describes it as a series of events in which the probability of each event depends only on the previous event. It is named after its creator, the Russian mathematician Andrei Markov, and is considered a fundamental contribution to contemporary physics, biology, computer science and statistics.
Although he made his first formulations in 1906, it was not until 1913 that Markov presented his ideas in a work whose study material was quite exotic for mathematics: the verse novel Eugene Onegin, the Russian literary classic by Alexander Pushkin. “He had no hope of providing new literary insights into the poem: he simply wanted to use it as a data set to analyse the occurrence of vowels and consonants,” explains Du Sautoy.
However, although Markov was not looking for new ways to literary interpretation, his finding did provide new ways to literary production. Thanks to the Google search engine, whose operation has also been made possible in part by Markov’s chain, I find reference to two projects that combine poetry writing and artificial intelligence. One of them is Markomposition, created by Marie Chatfield Rivas, who defines it as “a poetry-generating Markov chain.” The other is called Markov, a Game of Poems, by Alexander Raichev, who proposes “a human-computer interaction for poetry writing based on basic texts and Markov processes.”
The eternity of the analogical era, which Trotsky opposed as an obstacle to the formalist method of creation, could be reduced to just a few seconds in the era of computers and algorithms. Perhaps we are approaching that Hegelian synthesis, that Spirit of literature postulated by Valéry, where authors will be dispensed with, once again and this time forever. It would seem that, thanks to technology, we will return to the pre-Homeric night when the ancient gods wove misfortunes so that future generations of men would not lack stories to tell. Only that by having an automatic and artificial supply of poems and stories guaranteed, misfortunes will no longer be necessary. We will be, at last, gods.
In any case, it is difficult to predict what will happen. We will have to be attentive, as Markov proposed, to the chain of events. Andrei Markov, who died a hundred years ago, in 1922, of septicemia.
Málaga, August 2022
 In these same terms, Trotsky described the formal method: “This school [the formalist] reduces its task to an analysis (essentially descriptive and semi-statistical) of the etymology and syntax of poems, to the counting of repetitive vowels and consonants, of syllables and epithets.”