Chess Set Theory: The Fractal Realism of Bontempelli & Borges

Jorge Luis Borges's writing is regularly and explicitly concerned with concepts of infinity and it has been recognized, in limited scholarship, for fractal structures, which are associated in turn with postmodern literature as it opens itself up fractally to a sort of contained infinity of interpretations.¹ Scholarship around the themes of infinity and fractal structures focuses on the labyrinth and the mirror, however, and seems to overlook the author's preoccupation with and use of the chess set in certain stories. While the fractal infinity studied in the labyrinthine "El jardín de senderos que se bifurcan" feels highly postmodern in its chaotic openness, and indeed, is compared to postmodern stories like Italo Calvino's 1967 "Il conte di Montecristo" [The Count of Montecristo],² the fractal geometry presented by the chess set is more stable and can in some ways be more closely associated with Borges's beginnings as a young writer during the scientific discoveries and modernist movements of the early 20^th century. I see the use of the chess set by the Italian avant-garde author Massimo Bontempelli in his 1922 La scacchiera davanti allo specchio³ as similar to its use in some of Borges's works, in a tendency I call Fractal Realism.

Massimo Bontempelli's La scacchiera is widely considered the first exponent of European Magical Realism in literature, while Jorge Luis Borges's categorization as a Magical Realist has been contentious and most scholars agree today that he is not, and cannot be, considered a Latin American Magical Realist.⁴ It is useful, thus, to reconsider these authors out from under the umbrella of the fraught term, which perhaps is the very thing that has prohibited an examination of this sort to date. I argue here that that which links Bontempelli and Borges is not illustrated by any of the 20th-century definitions of magical realism, but by another sort of imagining that is, nonetheless, partially defined in Franz's Roh's 1925 treatise in which he coined the term magischer realismus. Namely, I see a tendency which relies on discoveries in math and science to open up, fantastic but crucially possible, realms. It is not 'magical' thinking, per say, but fantastic mathematical imagining.

Two correlated terms that are central to this argument are 'transfinity' and 'fractality.' 'Transfinity' refers to an aspect of 'set theory,' which is a branch of mathematical logic that deals with sets. Transfinite numbers in math are larger than all finite numbers and transfinite sets allow propositions about infinite sets. The aleph numbers, which will prove important later on, are a sequence of numbers represented by the Hebrew letter, aleph, and used to represent the size of infinite sets. As I use the concept, a transfinite object in literature is similarly a finite object that represents and allows propositions about the infinite. 'Fractality' refers to the theorized, and partially glimpsed, shape of the universe, in which it is self-similar at infinite magnitudes: the atom resembles the solar system, which resembles the galaxy, and so on, theoretically continuing forever at both increasing and decreasing orders of magnitude. In this article, I will define fractal realism and set up the chess set as a 'transfinite object,' or one that represents infinity within a finite space. I will then examine how Massimo Bontempelli and Jorge Luis Borges use the chess set, in a 'fractally real' way. That is, in the fictional works I have chosen, the chess set is not simply a symbol of infinity or of naturally occurring fractal forms, it has agency in the stories as a transfinite access point to infinite realms that exist within our own. The new realms in these stories have been seen by some as 'magical' but I argue that they are, rather, first opened up in mathematical and scientific terms, and introduced by these authors in figurative terms via the chess set. In a fascinating addition to the set of fiction presented, this article discusses a virtually unknown talk given by Bontempelli in 1938. In it, he makes the same argument about...