DUCHAMP AND INFINITY

The art of Marcel Duchamp is notable for its thematic repetition. Duchamp’s primary theme was that of Eros, which he represented both abstractly (The Large Glass, 1915-23) and concretely (Given, 1946-66).[1]  The infinity symbol,∞ —a mathematical notation introduced by the seventeenth-century English mathematician John Wallis—is a more specific throughline, appearing in works by or associated with Duchamp from 1921 onwards. What was its significance, in the context of his art? As is often the case with Duchamp, the question is not easy to answer.

At the turn of the twentieth century the fourth dimension was a general signifier for realms beyond three-dimensional “reality.” Infinity was a common narrative theme at a time when the fourth dimension was construed as an infinite realm beyond everyday three-dimensional experience.[2]  A reliable source regarding early twentieth-century artistic understandings of the fourth dimension is the poet and art critic Guillaume Apollinaire, who in 1913 published The Cubist Painters—a collection of essays written between 1905 and 1912. In his introductory essay to the collection, Apollinaire wrote:

“Until now the three dimensions of Euclidian geometry were enough to answer the disquiet that a sense of infinity instills in the soul of great artists. … Nowadays, scientists have gone beyond the three dimensions of Euclidian geometry. Painters have been led, quite naturally and one might say intuitively, to take an interest in the new possibilities for measuring space which in the modern artist’s studio were simply and collectively referred to as the fourth dimension. … This utopian turn of phrase is now really only of historical interest, …”[3]

In addition to the artistic example of Paul Cézanne (1839-1906), what inspired artistic fourth-dimensional explorations by the early Cubists—Picasso, Gris, Gleizes, Metzinger, et al.—were developments in mathematics suggesting additional spatial dimensions beyond the three we normally experience.[4] But by the time Apollinaire was wrapping up The Cubist Painters in fall 2012, he observed that artists like Picabia and Duchamp (with whom he spent an intense week in the Jura mountains in late October[5]) were going even further, exploring realms of experience that had no perceivable limit. In contrast to Greek art, Apollinaire wrote, which “took man as its measure of perfection, the art of the new painters takes the infinite universe as its ideal.” The key word here is “infinite”: the fourth dimension now “represents the vastness of space stretching eternally in all directions at any given moment. It is space itself, the dimensions of infinity.”[6]

As far as Apollinaire was concerned, by late 1912 the fourth dimension was outdated terminology for the fullness of reality. As for Duchamp, he explicitly identified the fourth dimension with Eros: This “transcendental conception,” his friend and first biographer Robert Lebel wrote, “was reinforced by his very tactile idea of the fourth dimension, since he considers the sexual act the pre-eminent fourth-dimensional situation.”[7]

MAN RAY’S DUCHAMP: In the top left corner of his 1923 portrait Marcel Duchamp (Rose Cela Vit), Duchamp’s American photographer friend Man Ray included two vertical intertwined infinity symbols, balancing the image of a rose at bottom right (figure 1).

Figure 1. Man Ray painting, now lost, later issued as an etching: Rrose Sélavy (Cela vit) – portrait of Marcel Duchamp, 1923. © Man Ray 2015 Trust / Artists Rights Society (ARS), NY / ADAGP, Paris 2024. Photo: ©  Telimage, Paris.

Flowers, particularly the lotus (in Asia) and the rose (Euro-America), are traditional symbols for female genitalia.[8]  When Duchamp decided to create an artistic pseudonym for himself, he chose a feminine name that is also the name of a flower: Rose Sélavy, which in French sounds like éros c’est la vie, “eros is life.” He then added a second “r”—Rrose Sélavy—later claiming he had been inspired by the name “Lloyd.”[9]  Be that as it may, the extra “r” does encourage pronunciation of Rrose as “eros.”[10]

In Man Ray’s 1923 portrait, the conflation of an image of a rose with the phrase cela vit, “it lives,” reiterates the erotic implication of the name Rose while emphasizing continuity. The intertwined infinity symbols at upper left reinforce these apparently disparate concepts of Eros and Infinity. In South Asian tradition, the lotus is a symbol for the female generative organ precisely because it is a common symbol for representing the infinite.[11]  This same pairing of vertical infinity symbol (in the form of a mala) and flower (meto pema or “flower lotus”) is a common feature of traditional Tantric Buddhist depictions of the Bodhisattva of Compassion (figure 2):

Figure 2. Nepal, twentieth century. Avalokiteshvara, Bodhisattva of Compassion. Private collection.

Images such as this were available to artists in France thanks to the public collections of the Musée Guimet (founded 1889) and Musée Cernuschi, aka the Musée des arts de l’Asie de la Ville de Paris, which Duchamp is documented as having visited.[12]

Music frames Man Ray’s portrayal of Duchamp: in the top left corner, above the infinity symbols, is a short and simple musical phrase.

Figure 3. Detail, Man Ray, Rrose Sélavy (Cela vit) – portrait of Marcel Duchamp, 1923. © Man Ray 2015 Trust / Artists Rights Society (ARS), NY / ADAGP, Paris 2024. Photo: ©  Telimage, Paris.

The musical stave (five drawn lines on which the notes sit) extends around the entire perimeter of the page, joining up where it began to produce an infinite musical loop. Duchamp did produce music (Erratum Musical, 1913), but Man Ray’s reference may be to Kandinsky, who described as a “musical album” his 1912 collection of text and woodcuts, Klänge (“Sounds”), and who in his 1912 book On the Spiritual in Art wrote:

“In a mysterious, puzzling, and mystical way, the true work of art arises ‘from out of the artist.’ Once released from him, it assumes its own independent life, takes on a personality, and becomes a self-sufficient, spiritually breathing subject that also leads a real material life: it is a being … [and] possesses—like every living being—further creative, active forces.”[13]

In other words, creativity is infinite. In art and literature as in mysticism, the infinite points to the Absolute: perfection, wholeness, without beginning or end.[14]

THE MOBIUS MIND: The concept of Infinity has three primary applications: the mathematical, the physical, and the metaphysical.[15] Man Ray’s two intertwined infinity symbols suggest a Möbius loop—a continuous surface created by attaching the ends of a ribbon with a half-twist. When you trace a line along the surface of a Möbius loop, you eventually return to your starting point. Now visualize two ribbons. You twist one ribbon clockwise, the other counterclockwise, forming two opposing Möbius loops (figure 4).

Figure 4. Chiral Möbius loops. Photo: Paul Sharpe.

In mathematics, an object or a system is chiral if it cannot be superimposed onto its mirror image. Human hands are an example of chirality: the left hand is a non-superimposable mirror image of the right hand. This difference in symmetry becomes obvious if someone attempts to shake the right hand of a person using their left hand. What connects the Möbius loop with Eroticism is this quality of chirality, or “handedness.” Like Yin and Yang, like female and male, the two loops have chirality.

Möbius loops are two-dimensional surfaces in three-dimensional space. (figure 4). When you join two Möbius loops of opposing chirality together at their edges, you create a Klein bottle—a geometrical object with only one surface, as described by the German mathematician Felix Klein in 1882. A Klein bottle has no inside or outside. However, the Klein bottle can truly exist only in the fourth dimension because in the 3D of our everyday reality there needs to be a hole where the bottle penetrates itself, so the surface is not continuous (figure 5).

Figure 5. Klein Bottle. Photo: Kostsov for Shutterstock.

Add one more spatial dimension, however, and the two complementary loops can be unified to create a four-dimensional Klein bottle in which there is no hole, only an intersection of the surfaces. It is impossible to visualize this procedure because our imagination is limited to three spatial dimensions—an anomaly that opens the door to understanding the connection between Infinity and Eroticism. While a Möbius loop is a surface with a boundary, a Klein bottle, created by joining two loops of complementary chirality, has no boundary: it is infinite.

With his extensive thinking about dimensionality, Duchamp would surely have known about the Klein Bottle.[16]  One way of thinking about Erotism and Infinity is as a comparison: the Möbius loop is to the Klein bottle as physical sexual union is to metaphysical erotic union in which the mind is as engaged as the body. A contemporary example of regional art from Bhutan (figure 6) vividly illustrates this condition of psychosomatic union of male and female energies within the body/mind.

Figure 6. Sculpture in a gift shop, Paro Taktsang, upper Paro Valley, Bhutan, 2010. Photo: Jacquelynn Baas.

It is only in this expanded dimensionality where female and male chirality truly interpenetrate that one can reach a state of mental freedom like that occupied by the self-penetrating Klein bottle, with all its infinities and contradictions.

To Duchamp’s way of thinking, creativity is erotic energy, and the creative act is consummated in the fourth dimension. This is why, in Man Ray’s portrait of Marcel Duchamp, two intertwined infinity symbols accompany the erotic rose and the esoteric phrase, cela vit. The infinity symbol is horizontal in mathematical notation. Vertical infinity symbols like the ones in Man Ray’s portrait suggest the human figure. Intertwined, the two symbols suggest sexual union, while the vertical orientation encourages a metaphysical reading, linking heaven and earth in a creative embrace that, according to Chinese Daoist philosophy, generates “everything” in between.

DEPARTURES FROM LA BAGARRE D’AUSTERLITZ: Two years before Man Ray painted Rose Cela Vit (figure 1), Duchamp had featured two vertical infinity symbols in his sculpture La Bagarre d’Austerlitz (“The Brawl at Austerlitz,” figure 7). Duchamp placed these two infinity symbols (ostensibly glazier’s marks) side by side on the glass of two casement windows. La Bagarre d’Austerlitz is signed in white paint toward the bottom of its two edgewise sides: on one edge is “Marcel Duchamp”; on the other, beneath a brass plaque engraved with the title, is inscribed “Rrose Sélavy / Paris 1921.”

Figure 7. Marcel Duchamp. La Bagarre d’Austerlitz (The Brawl of Austerlitz), inside and outside, 1921. Casement windows marked with infinity signs, painted wood with glass, object : 24 ¾ x 11 5/16 x 2 ½ in. Staatsgalerie Stuttgart, acquired in 1980 with lottery funds, O360. © Association Marcel Duchamp / ADAGP, Paris / Artists Rights Society (ARS), New York 2024. Photo: © Staatsgalerie Stuttgart.

The use of glass as a field for notation calls to mind Duchamp’s Large Glass (1915-23), then still in process. Duchamp seems to have chosen glass as a support for that work primarily for its dual qualities of transparency and reflectivity, which he enhanced with mirroring (more chirality). Another precedent is a set of small, freestanding French windows made in New York in 1920. Duchamp titled this piece, Fresh Widow (figure 8).

Figure 8. Marcel Duchamp, Fresh Widow, New York, 1920. Miniature French window, painted wood frame, and panes of glass covered with black leather, 30 1/2 x 17 5/8 in., on wood sill 3/4 x 21 x 4 in. The Museum of Modern Art, Katherine S. Dreier Bequest. © Association Marcel Duchamp / ADAGP, Paris / Artists Rights Society (ARS), New York 2024. Photo: © The Museum of Modern Art/Licensed by SCALA/Art Resource, NY.

Duchamp covered its glass panes with black leather, thereby extinguishing both transparency and reflectivity. He said of Fresh Widow: “This small model of a French window was made by a carpenter in New York in 1920. To complete it I replaced the glass panes by panes made of leather which I insisted should be shined every day like shoes. French window was called Fresh Widow, an obvious enough pun.”[17]  He may have used the same carpenter his friend Carrie Stettheimer had commissioned to build her twelve-room dollhouse in 1916, the year after Duchamp arrived in New York (figure 9).

Figure 9. Carrie Stettheimer, Stettheimer Dollhouse, ca. 1920. Painted wood, ca. 28 x 50 x 35 in.  Museum of the City of New York, gift of Miss Ettie Stettheimer, 1945. 45.125.1. Photo: Museum of the City of New York.

Soon after it was finished, Duchamp created for the art gallery at the back of the dollhouse a miniature version of his famous 1913 painting, Nude Descending a Staircase.[18]

Who is this fresh widow, whose black garb must be ritualistically attended to every day? Duchamp made Fresh Widow in New York after returning from Argentina, where he had gone in 1919 to escape the bellicose atmosphere of World War I. During the war years he had lost two people important to him: his close friend Guillaume Apollinaire and his brother, the talented sculptor Raymond Duchamp-Villon. Fresh Widow is the first piece Duchamp signed as his female artistic alter ego: ROSE SELAVY. It seems logical to conclude, therefore, that our widow is the saucy Rose herself, and that Fresh Widow was in part created as a hermetic altar to help her alleviate her grief.

Aside from the “obvious” pun, why a window? Over thirty years later, Duchamp explained his thinking at the time:

“I used the idea of the window to take a point of departure, as … I used a brush, or I used a form, a specific form of expression—the way oil paint is a very specific term, specific conception. See, in other words, I could have made twenty windows with a different idea in each one, the windows being called ‘my windows’ the way you say, ‘my etchings’.”[19]

Where might Duchamp have gotten this idea of deploying the window as a form of expression, a sort of language? For him, windows would seem to have been metaphors for apprehension leading to realization. Already in 1913, two years before he began fabricating The Large Glass, Duchamp wrote in one of his notes to himself:

“The question of shop windows

To undergo the interrogation of shop windows

The exigency of the shop window

The shop window proof of the existence of the outside world

When one undergoes the examination of the shop window, one also pronounces one’s own sentence. In fact, one’s choice is ‘round trip’…. No obstinacy, ad absurdum, of hiding the coition through a glass pane with one or many objects of the shop window. The penalty consists in cutting the pane and in feeling regret as soon as possession is consummated. Q.E.D.”[20]

Duchamp’s assertion that the shop window serves as “proof of the existence of the outside world” points to his understanding of consciousness, how we experience being-in-the-world—in our minds, via our sense organs. In French, Duchamp’s native language, window shopping is lèche-vitrine—literally, “lick shopwindow.” Sensual experience manifests in the mind; the shop window is mentally “interrogated.” To interrogate a window, according to Duchamp, is to embark on a journey; in his words, le choix est allé et retour—a round trip composed of perception followed by apprehension.

Duchamp is saying that to engage the sense of touch, we must destroy—cut the pane, break the glass. He compares this process with the act of coition, where regret follows consummation. Regret for what? La petite mort is a French expression for “the brief loss or weakening of consciousness”; in modern usage, it refers to “the sensation of post-orgasm as likened to death” (OED). The blackened windows of Fresh Widow imply loss of consciousness, death. What does La Bagarre d’Austerlitz (figure 7) add to Duchamp’s observations about the relationship between windows, Eros, and death? Here, the windows are clear, marked with infinity symbols. The message seems obvious enough: cela vit—to cite Man Ray’s portrait, Eros lives.

Duchamp associated Eros with creativity. Like the sexual act, the creative act implies a loss. In his essay, “The Creative Act,” he referred to the “gap representing the inability of the artist to express fully his intention, this difference between what he intended to realize and did realize.” To complicate this thought, he came up with a mathematical metaphor: the “personal ‘art coefficient’ is like an arithmetical relation between the unexpressed but intended and the unintentionally expressed.” Duchamp was clear that “the digit of this coefficient has no bearing whatsoever” on the “verdict” of the viewer.[21] This fact does not diminish the artist’s inevitable sense of loss. Yet at the same time, as we shall see, for Duchamp creativity is infinite; it is how we extend our life.

Unlike Fresh Widow, which was fabricated in New York, Bagarre was created in Paris where, two years before, Marcel and his surviving brother, Jacques Villon, had organized a memorial exhibition of their sculptor-brother’s work at the 1919 Salon d’Automne. Just back from Argentina, Marcel would have been reminded of Duchamp-Villon’s model for the façade of La Maison Cubiste—an architectural installation created for the Art Décoratif section of the 1912 Paris Salon d’Automne (figure 10). Duchamp’s late brother’s model facade seems relevant to the creation of Bagarre d’Austerlitz (figures 7a and 7b), which bears a strong resemblance to the right-hand window of Duchamp-Villon’s façade, which had also been shown at the New York Amory Show in 1913 along with Marcel’s work (figure 11).

Figure 10. Raymond Duchamp-Villon, model for the façade of La Maison Cubiste, architectural installation created for the Art Décoratif section of the 1912 Paris Salon d’Automne. Bibliothèque Kandinsky/Musée National d’Art Moderne/Centre Pompidou/Paris/France. Photo © CNAC/MNAM, Dist. RMN-Grand Palais / Art Resource, NY.

Figure 11. Installation shot of the Cubist Room, 1913 Armory Show. Left: Raymond-Duchamp-Villon, La Maison Cubiste (Projet d’Hotel); right: Marcel Duchamp, Nude Descending a Staircase No. 2. © Association Marcel Duchamp / ADAGP, Paris / Artists Rights Society (ARS), New York 2024.  Walt Kuhn scrapbook documenting the Armory Show, 1913. Walt Kuhn, Kuhn family papers, and Armory Show records, Archives of American Art, Smithsonian Institution. Published in New York Tribune, February 17, 1913, p. 7, image 7, Library of Congress, Chronicling America: Historic American Newspapers. Photo: Wikimedia Commons, PD.

Duchamp said of his second window, “I called it The Brawl at Austerlitz, which is a simple alliteration on Gare d’Austerlitz, an important railway station in Paris. … I used the idea of the window to take a point of departure.”[22]  Brawl at Austerlitz thus seems to have been a point of departure for an allé et retour: a departure into violent memory and a return to infinity, continuity: cela vit.

Unlike Fresh Widow, the windows of La Bagarre have two sides: interior and exterior. A view of the front, or “interior” of Bagarre puts us in the mind of the artist, looking out through paired infinity signs into, to quote Apollinaire, “a still-virgin universe.”[23] As seen from the “exterior,” painted-brick side, looking in, the spectator (a role played by Duchamp in figure 12) peers into the mind of the artist.

Figure 12. Man Ray, Marcel Duchamp derrière son oeuvre La Bagarre d’Austerlitz (1921), 1935–1936. Gelatin silver print, 4 13/16 x 3 7/16 in. © Man Ray 2015 Trust / Artists Rights Society (ARS), NY / ADAGP, Paris 2024. Musée National d’Art Moderne/Centre Georges Pompidou/Paris/France.  Photo by Guy Carrard © CNAC/MNAM, Dist. RMN-Grand Palais / Art Resource, NY.

In the window between artist and viewer, an emotional and intellectual battle occurs. This Bagarre presents us with an interpretive conundrum, a mental brawl. As with any battle, at the 1805 Battle of Austerlitz two sides entered the arena unscathed, emerging forever changed. So it is with art: the creative act is one of violence, and destruction is an integral part of the creative process.

Unlike Fresh Widow, La Bagarre has two signatures: Rrose’s and Marcel’s. “Rrose Sélavy” is associated with title and date, privileging the female. From their opposing sides, as in a battle, female and male aspects of the artist unite in the infinite space that joins them. Theirs is an act of creative engagement—opponents turned collaborators. The journey is between two lovers, Sélavy and Duchamp, their union recorded on two panes of glass marked with signs of Infinity.

Around the same time he was exploring the concept of Infinity with Bagarre d’Austerlitz, Duchamp began experimenting with how an experience of Infinity might be generated by playing with viewers’ perceptions of dimensionality. With Man Ray, he created mind-machines in the form of innovative kinetic works like Rotary Glass Plates (Precision Optics) (1920) and Anémic Cinéma)—a 35 mm black and white film of rotating disks that alternate between eccentric circles, which appear to move sensuously in and out, and spiraling word strings (1926; ignore the sound track: the film was originally silent).

“The solution to this artistic problem finally came,” Duchamp said, “with the Disks in which true three-dimensionality was achieved, not with a complicated machine and a complicated technique [as with Rotary Glass Plates], but in the eyes of the onlooker, by a psycho-physiological process.”^[24] Duchamp’s “Rotoreliefs”—undulating three-dimensional images generated when the two-dimensional disks are viewed on a rotating turntable—were designed to produce an experience in the mind of the viewer suggesting the in-and-out motion of sexual intercourse, interspersed with the tickly mental vibrations generated by alliterative, suggestive nonsense words spiraling into space. All of this assumes a receptive viewer, of course. Through the time and space inherent to the medium of motion picture film,[25] Duchamp’s two-dimensional images become three-dimensional in the mind of the viewer, while their subtle sexual undertones evoke dimensions beyond time and space.

BATAILLE AND THE CONTINUITY OF BEING: Marcel Duchamp’s most collaborative thinking on the subject of Infinity took the form of a small diagram developed with George Bataille for the last issue of the Mémento Universel Da Costa (figure 14). The diagram depicts Adam, the original human, as whole and complete in themself.  At separation into two beings, Eve acquired a positively charged intellect and received negatively charged genitals; Adam received a negatively charged intellect and acquired positively charged genitals. What they still share is a heart that is infinite. The potential for reunion remains, always, at the heart of every individual.

Robert Lebel described the Da Costa Encyclopédique as: “a voluntary dissident, marginal, and very confidential enterprise devoted to anonymity and virulent humor. It was too much perhaps to ask of the participants who, mostly, soon scattered, Duchamp remaining the only one to support this ephemeral publication through its third and last fascicule.”^[26]  Lebel was exaggerating somewhat, but by the time the third issue of this post-war surrealist journal appeared in 1949, only Duchamp, with the assistance Isabelle Waldberg and the distracted participation of Georges Bataille, kept the subversive satirical journal alive.[27]

Artistic manipulations of the encyclopedia or dictionary format include Bataille’s “Critical Dictionary,” which played an increasingly subversive role in his journal Documents (1929–1930);^[28] and the Dictionnaire abrégé du surréalisme, published in connection with the 1938 surrealist exhibition. Le Da Costa Encyclopédique was similarly intended to accompany the catalogue Le Surréalisme en 1947, which featured random quotes from authors like Fourier and Pascal that, while typical of the 1938 Dictionnaire abrégé, were not appropriate for the anonymous Da Costa.

Le Da Costa Encyclopédique and two subsequent Mémentos Universel Da Costa (1947-49) have been exhaustively documented by Pierre-Henri Kleiber, who emphasized that “the experience of Da Costa is inseparable from war—the upheavals it introduces into individual existence, the demoralization it entails, the unexpected contacts it promotes, the demands it imposes on those who have long questioned the fate of civilization.” ^[29]  Along the lines of post-World War I Dada, Robert Lebel emphasized the inappropriateness of “sacred sentiment,” which in modern individuals “gets identified with a sense of their own importance.” Lebel contrasted Surrealism’s self-important values and rituals with the unifying—and very American—efficacy of humor: “To communion in bombast [he was no doubt referring to André Breton], we must oppose communion in what the Americans call ‘debunking’—the deflation of all that is bloated, even in ourselves.”^[30] Like Bataille’s secret society, Acéphale,[31] Da Costa would be occult, but unlike Acéphale it would not be encumbered by occult ritual. Le Da Costa Encyclopédique was esoteric thanks to its insider humor, the fact that its authors were anonymous, and because it was a hard-to-obtain underground publication.

The influence of Georges Bataille within the “Clan Da Costa” is confirmed by the Encyclopédique’s readymade illustrations sourced from the Fonderie Deberny et Peignot. “Peignot” was Georges Peignot, father of Bataille’s beloved companion Colette (Laure) Peignot, who had died in 1938.^[32]  Marcel Duchamp served as both designer and typographer for Le Da Costa Encyclopédique, which was modeled on Le Petit Larousse illustré—a favored source for him.^[33]  Like Larousse, the entries in Le Da Costa Encyclopédique were anonymous, a policy that would change only nominally with the advent of Le Mémento Universel Da Costa, where “the names mentioned … are almost all fictitious.”^[34]  Bataille’s name thus does not appear among the contributors to Mémento Da Costa, which remained essentially anonymous.

There is, however, one entry in the first fascicule of Mémento that is a strong candidate for having been contributed by Bataille: the entry for “EVE. Biblically, the first woman.” The entry for “Adam,” Eve’s male counterpart, would appear in the second and last fascicule. Both entries are signed “M.B.”,[35] but their style and content point to a partnership between M[arcel] and B[ataille]. Duchamp and Bataille were unlikely bedfellows. Their relationship was a kind of chirality, with Duchamp’s penetrating mind, energetic nature, and wit balancing Bataille’s saturnine, hell-bent temperament. Bataille linked Eros with death. For Marcel Duchamp, Eros was creativity.

Adam and Eve—more specifically, the episode of the Fall—was a favorite subject of Duchamp. This may have had to do with the fact that the Biblical Fall introduced dualism into the world—specifically the “knowledge” of good and evil leading to judgment and shame. For his part, Bataille would have been interested in the Fall as the cause of separation from and abandonment by God. There is a noticeable shift in tone from the long, scholarly, myth-obsessed “Eve,” which is more characteristic of Bataille’s writing, to the terse, scientific-philological-mathematical “Adam,” which reads more like Duchamp. Still, it is impossible to be definitive—both had studied philology at the École des Chartes, and their mutual interest in eroticism and freedom comes through clearly in “Eve” and the entry and accompanying chart for “Adam” (figure 13).

Figure 13. Marcel Duchamp with Georges Bataille, “Le mystère d’Adam,” in Le Mémento Universal Da Costa, fascicule II, 1949, page 1. © Association Marcel Duchamp / ADAGP, Paris / Artists Rights Society (ARS), New York 2024. Photo: Jacquelynn Baas.

“Eve” begins with a pseudo-kabalistic creation myth and ends in a Dionysian vision that is almost impossible to follow. From the last two paragraphs:

“…Eve, divine spirit of Iève [‘organizer’ of the world from chaos], and her daughters, had to find in themselves all the necessary artifices to tempt, excite, and, finally, to seduce the Serpent, their bad boy [‘leur mal et leur mâle’]. For a long time, this was their only means of attracting a husband. It was not until the twentieth century that, finally, conscious of their rights and wresting them from the ophidian [reptilian] vanity of Man, life and strength were returned to Iève, the spiritual part of the human couple—Woman, resuscitated in all the brilliance of her divine glory. Io Evohé.”^[36]

Io Evohé! was the cry emitted by ecstatic dancers during the ancient Dionysian mystery rites—a research interest of Bataille’s.^[37]  Only in the twentieth century, according to the Da Costa entry, did Woman finally free herself from the need to subjugate herself to satisfy Man.

The entry for “Adam” humorously parodies alchemically infused, Fourier-influenced postwar Surrealists like Breton. Very different in tone from “Eve,” “Adam” reads, in its entirety:

“According to the Bible, the world was created in six days. On the sixth day, the first man appeared. According to Da Costa (Origines cosmiques du Genre Humain, Amsterdam 1644), the Bible could be deciphered with the aid of Platonic geometry and the French phonetic Cabala.

It would thus be appropriate to consider that ADAM = a dame = who had a wife.

Adam was androgynous until the sixth day and possessed within himself the two sexes. The human being is polarized into three active parts: mind, heart, sex. Man has a negative mind, neutral heart, positive sex.

Woman has the positive mind, neutral heart, negative sex.

The mystery of Adam before and after his division can thus be schematized in the following fashion: [figure 13].

So it was not a rib [‘côte’] that was removed from Adam by the creation of Eve.

It was a side [‘côté,’ “aspect”].

A geometrically symbolic side.”^[38]

Da Costa’s interpretation of the Genesis account to mean creation of the first human as an androgynous being wrenched apart, spiritually as well as physically, into two polarized beings yearning for reunion, was hardly new: Precursors can be found in Daoism, Buddhism, Tantra, Plato, the Greek mysteries, alchemical theory, and Mysterium Magnum, Jacob Boehme’s account of the Fall (1623).^[39]  The Da Costa diagram is more detailed. The first human being is diagrammed as possessing a positive/negative sex and brain. Adam and Eve “after” separation have oppositely charged sexes and brains.

A likely source for Duchamp and Bataille’s diagram is Magia Sexualis by the American occultist, medical doctor, and writer, Paschal Beverly Randolph (1825-1875):

“The whole universe, all living beings, … are ruled by the principle of two contrary forces, the one exercising upon the other an unavoidable power of attraction. They are called the positive and negative forces, and one finds them in good and evil, emission and reception, life and death, idea and action, man and woman (positive and negative magnetic poles) on the material plane, and, just the opposite, woman (active pole) and man (negative pole) on the mental plane.

Now, while the phallus of the man is polarized positively and kteis of the woman negatively, the head of the man, the organ of his mental manifestations is, on the contrary, negative with respect to the head of the woman, which is positive. This explains why the man, full of initiative in what concerns the physical manifestations of love, waits for the invitation of the woman, her feeling and her mental passion, to climb the ladder of union on the higher planes.”[40]

Randolph’s scheme corresponds precisely with the Da Costa diagram, which shows male and female oppositely “polarized into three active parts”: mind, heart, sex.

Magia Sexualis, which was still in manuscript form at the time of Randolph’s untimely death, was translated and published in 1931 by the Russian occultist, mystic, and teacher of sexual magic, Maria de Naglowska (1883-1936).[41] André Breton and Man Ray, among others, attended Naglowska’s occult seminars, which included demonstrations of sexual magic. Her influence was noted in the “Lexique succinct de l’érotisme” in the catalogue for Breton and Duchamp’s 1959 L’Exposition inteRnatiOnale du Surréalisme.[42]

Unique to Da Costa is the neutral, “geometrically symbolic side”—an infinity symbol—representing the separate but identical hearts of Adam and Eve. Women and men are magnetically attracted to each other: mind to mind, sex to sex, with the disinterested, “neutral” heart as connector, the infinite knot that holds our deepest selves. The implication is that (re)union can be attained only at the heart.

Da Costa’s “Mystère d’Adam” pooh-poohs the traditional story in which Eve is created from Adam’s rib: “it was not a rib [‘côte’] that was removed from Adam by the creation of Eve. It was a side [‘côté’]. The accompanying diagram accordingly depicts asexual reproduction by one entity into two separate entities, as described by Bataille in his book L’Erotisme (1957):

“In asexual reproduction, the organism … divides. … from one single being two new beings are derived. … But at one stage of the reproductive process there was continuity. There is a point at which the original one becomes two. As soon as there are two, there is again discontinuity for each of the beings. But the process entails one instant of continuity between the two of them.”[43]

This instant of continuity, this momentary opening to Infinity, is the paradise lost by Adam and Eve and their descendants, according to Da Costa. It is the source of their ongoing search for wholeness. Bataille writes:

“We are discontinuous beings, individuals who perish in isolation in the midst of an incomprehensible adventure, but we yearn for our lost continuity. We find the state of affairs that binds us to our random and ephemeral individuality hard to bear. Along with our tormenting desire that this evanescent thing should last, there stands our obsession with a primal continuity linking us with everything that is.”

We discontinuous beings long for Infinity in the form of continuity and wholeness. “This nostalgia,” Bataille asserts, “is responsible for the three forms of eroticism in man: physical, emotional and religious.”[44]  To recover lost continuity requires violence. “The whole business of eroticism is to strike to the inmost core of the living being, so that the heart stands still,”[45] in one instant of continuity between two hearts.

Duchamp, in contrast, identified Bataille’s moment of violence with creativity. The penalty for “cutting the pane” of three-dimensional reality with the creative act? Regret, as soon as “possession” is consummated. Regret for a continuity that is always provisional, for that “gap representing the inability of the artist to express fully his intention, this difference between what he intended to realize and did realize.”[46]

DUCHAMP À L’INFINITIF: It is significant that Duchamp entitled his last published collection of notes À l’infinitif, “in the infinitive.”[47] The infinitive is the basic form of a verb. Without inflection or tense, it is untethered from both subject and time. Just as Eros is independent of the aim to reproduce, so is creativity free of the need to produce a work of art. For Marcel Duchamp creativity was Erotism, a psychological and spiritual quest for continuity of being, Infinity. The creative act is an erotic act that closes the gap between self and other, between present self and future others. The mystery within the merging of two hearts opens to expansive Infinity, endless and indestructible.

………………………………….

NOTES

[1] See Jacquelynn Baas, Marcel Duchamp and the Art of Life (Cambridge, MA: MIT Pres, 2019) and “The Bride Stripped Bare: Esoteric Origins for Duchamp’s Large Glass,” Interalia Magazine, September 2022 (https://www.interaliamag.org/articles/jacquelynn-baas-the-bride-stripped-bare-esoteric-origins-for-duchamps-large-glass/).

[2] See Linda Dalrymple Henderson, The Fourth Dimension and Non-Euclidean Geometry in Modern Art (Princeton, NJ: Princeton University Press, 1983; revised edition, Cambridge, MA: MIT Press, 2013).

[3] Guillaume Apollinaire, The Cubist Painters, ed. and trans. Peter Read (Berkeley: University of California Press, 2004), 15, 17.

[4] It took a while for artists to integrate Einstein’s 1905 theory of special relativity—time moves relative to the observer—into their work (see Henderson, 1). Aside from the Italian Futurists, Duchamp may have been one of the first, with his Sad Young Man on a Train (1911).

[5] See Calvin Tompkins, “The Jura-Paris Road,” in Duchamp: A Biography (New York: Museum of Modern Art, 2014), 100-112.

[6] Apollinaire, 16.

[7] Robert Lebel, Marcel Duchamp, transl. George Heard Hamilton (New York: Grove Press, 1959), 28.

[8] Michael Juul Holm, Ernst Jonas Bencard, Poul Erik Tøjner, The Flower as Image (Humlebæk, Denmark, Louisiana Museum of Modern Art, 2004).

[9] Katherine Kuh, “Marcel Duchamp,” 20th-Century Art from the Louise and Walter Arensberg Collection (Chicago: The Art Institute of Chicago, 1949), 17.

[10] Her name first appeared this way in 1921, inscribed on Picabia’s collaborative painting, Cacodylatic Eye. See Baas, MDAL, 151.

[11] https://pragyata.com/the-infinite-lotus/ (accessed 2 March 2024).

[12] Baas, MDAL, 85.

[13] Kandinsky: Complete Writings on Art, edited by Kenneth C. Lindsay and Peter Vergo (Boston: Da Capo press, 1994), 210. According to Marc Décimo (La Bibliothèque de Marcel Duchamp, peut-être [les presses du reel, 2002], 7), a copy of On the Spiritual in Art, annotated by Duchamp, was in the library of Duchamp’s brother Jacques Villon. Duchamp’s 1918 painting Tu m’ incorporates a hand pointing towards spiral infinity signed “A. Klang.” Duchamp later claimed “Klang” was the name of the sign painter who executed it, but this was also surely a reference to the Kandinskian concept, Klang, “sound.”

[14] Other symbols in the background of Man Ray’s painting reference technology at the end of the first two decades of the twentieth century: The two antennas would have been of the moment, as large antennas for radio broadcasts were just beginning to be installed in 1920 (https://www.fasttrackteaching.com/ffap/Unit_8_Early_1900s/U8_Radio_Pics.html). Radio would have seemed like magic at the time: invisible voice transmission over the air is almost mediumistic. Here we have two antennas, a transmitter (the artist) and receiver (the viewer). Moreover, radio waves are vibration, a form of “light,” the very thing Einstein had described as four dimensional in 1905. Below Duchamp’s neck are inscribed what look to be atomic orbitals, also very new at the time—Bohr’s “solar system” model of the atom was first developed in 1913 (https://www.scmp.com/lifestyle/technology/article/1251477/bohrs-atomic-model-100-years-old). The spider web behind Duchamp’s head suggests interconnectivity. (It foreshadowed Duchamp’s Mile of String that crisscrossed the exhibition spaces of the New York Surrealist exhibition of 1942.) Even today, AI is based on the concept of a neural network, or interconnected points of perception and understanding. Together, these images portray the life of Marcel: Cela Vit.

[15] Regarding infinity, see David Foster Wallace, Everything and More: A Compact History of  ∞ (New York & London: W.W. Norton, 2003) and David Deutsch, The Beginning of Infinity (London: Penguin, 2011).

[16] See Duchamp’s last published collection of notes, À l’infinitif (1966). See also Jean Clair, “Duchamp at The Turn of the Centuries,” Toutfait (published online 1 December 2000, updated 13 May 2019), figure 14 and related text: https://www.toutfait.com/duchamp-at-the-turn-of-the-centuries/ (accessed 14 March 2024).

[17] Anne d’Harnoncourt and Kynaston McShine, Marcel Duchamp (New York: Museum of Modern Art, 1973), 291.

[18] Sheila W. Clark, ed., The Stettheimer Dollhouse (New York and Petaluma: Museum of the City of New York with Pomegranate Press, 2009), 8-9, 48. It may have been Duchamp who suggested to Carrie the idea of a model house complete with art gallery. He was close to and admired by all three Stettheimer sisters. Florine Stettheimer was a painter and Ettie was a writer. It fell to Carrie, the eldest, to run the household, which left her little time for creativity. Marcel may have suggested she follow his brother Raymond Duchamp-Villon’s example and create a model house that she could decorate with works by artist-friends like himself (see figure 11).

[19] D’Harnoncourt and McShine, Marcel Duchamp, 295. (Punctuation modified slightly for readability.)

[20] = “therefore”. Q.E.D. is placed at the end of a mathematical proof to indicate its completion (from the Latin, quod erat demonstrandum, “that which was to be demonstrated”). Salt Seller: The Writings of Marcel Duchamp (Marchand du Sel), Michel Sanouillet, Elmer Peterson, eds. (New York: Oxford University Press, 1973), 74.

[21] See Jacquelynn Baas, “Marcel Duchamp’s ‘The Creative Act’,” Journal of Visual Art Practice, volume 22, no. 2-3 (Fall 2023), 140. (https://www.academia.edu/107702254/Marcel_Duchamps_The_Creative_Act, accessed 14 March 2024)

[22] D’Harnoncourt and McShine, 295.

[23] From Les Collines: “Le chauffeur [on the Jura-Paris road, 1912] se tient au volant / Et chaque fois que sur la route / Il corne en passant le tournant / Il paraît à perte de vue / Un univers encore vierge.” Here and elsewhere, translations from French in the text are by the authors.

^[24] Quoted in Hans Richter, Dada: Art and Anti-Art (New York: McGraw-Hill, 1965), 99. For more on Anémic Cinéma, see Jacquelynn Baas, “Meditations on the Medium of Time,” in Measure of Time, ed. Lucinda Barnes (Berkeley: University of California Berkeley Art Museum and Pacific Film Archive, 2007), 72–76.

[25] See https://www.alphavillejournal.com/Issue%202/HTML/2Editors%27Note.html (accessed 13 March 2024). Warm thanks to Nina Zurier for this reference and for her insightful queries and comments on this paper.

^[26] Robert Lebel, Marcel Duchamp (Paris: Belfond, 1985), 11–12.

[27] See Baas, MDAL, 264-266ff; also: Jacquelynn Baas, “Isabelle Waldberg,” Gagosian Quarterly (Spring 2020), 142-147. https://www.academia.edu/42195196/Isabelle_Waldberg (accessed 4 March 2020).

^[28] Bataille’s short essays on subjects such as “Absolute,” “Eye,” “Factory Chimney,” and “Keaton (Buster),” were accompanied by dark, erotic, violent photographs intended to counteract what Bataille viewed as Breton’s overly sanitized brand of Surrealism.

^[29] Pierre-Henri Kleiber, L’Encyclopédie “Da Costa” (1947–1949) (Lausanne: Éditions L’Àge d’Homme, 2014), 113. See also Pierre-Henri Kleiber, “Le Da Costa: histoire d’une obscure aventure encyclopédique,” Étant donné Marcel Duchamp, no. 7 (2006), 108–137; and Baas, MDAL, 259ff.

^[30] Lebel, letter in VVV, vol. 4 (February 1944), 41–44.

[31] For Acéphale, see Baas, MDAL, 205ff.

^[32] Kleiber, L’Encyclopédie “Da Costa,” 184–188.

^[33] As witnessed by a note in The Green Box: “take a Larousse dict. and copy all the so called ‘abstract’ words.” Salt Seller: The Writings of Marcel Duchamp, 31.

^[34] Encyclopédie des farces et attrapes et des mystifications, ed. François Caradec and Noël Arnaud (Paris: J. J. Pauvert, 1964), 229–230.

[35] Purportedly the artist Maurice Baskine (a favorite of Breton), who is not known to have written anything else; see Baas, MDAL, 265-266.

^[36] Le Mémento Universel Da Costa, fascicule I (1948), 5.

^[37] The penultimate issue of Bataille’s journal Acéphale was devoted to “Dionysos,” including an essay by Bataille on “Les Mystères Dionysiaques”: Acéphale, nos. 3–4 (July 1937), 22–23.

^[38] Le Mémento Universel Da Costa, fascicule II (1949), 1. There is no book with the title Origines cosmiques du Genre Humain by “Da Costa”—presumably Uriel Da Costa (1585–1640). The reference to “French phonetic Cabala” was a tongue-in-cheek poke at Breton, a fan of the French alchemist and esoteric author Fulcanelli (fl. 1920s), whose Phonetic Cabala—unrelated to the Hebrew Kabbalah—emphasized phonetic similarities between words for expressive purposes.

^[39] See Alex Wayman, “Male, Female, and Androgyne,” in Tantric and Taoist Studies, vol. 2, ed. Michel Strickmann (Brussels: Institut Belge des Hautes Etudes Chinoises, 1983), 593–631.

[40] Paschal Beverly Randolph and Maria de Naglowska, Magia Sexualis: Sexual Practices for Magical Power, translated and annotated by Donald Traxler (Rochester, Vermont: Inner Traditions, 2012), 16-17.

[41] Paschal Beverly Randolph, Magia Sexualis, French translation Marie de Naglowska (Paris: Robert Télin, 1931).

[42] André Breton and Marcel Duchamp, L’Exposition inteRnatiOnale du Surréalisme 1959–1960 (Paris: Galerie Daniel Cordier, 1959). See Sarane Alexandrian, Les libérateurs de l’amour (Paris: Éditions du Seuil, 1977), 185-206.

[43] Georges Bataille, Erotism: Death & Sensuality, transl. Mary Dalwood (San Francisco: City Lights Books, 1986), 13-14.

[44] Bataille, Erotism, 15.

[45] Bataille, Erotism, 17.

[46] See note 21.

[47] Marcel Duchamp, Á l’infinitif (New York: Cordier & Ekstrom, 1966).

Art, Creativity, Culture, Infinity, Philosophy, Sculpture