Some months before his death, Duchamp produced a series of nine etchings dedicated to the theme of Lovers (Figs. 1 and 2) Aside from their erotic content, these nine etchings are alike in that they mark a return to "figurative" art, they are directly linked to Étant Donnés (through at least one among them, Le Bec Auer), and finally, they are copies in the style of older masters.

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Figure 3

Auguste Rodin Drawing for The Torture Garden, 1899.

The chosen models, Cranach, Ingres, Courbet, Rodin, are clearly artists to whom women and eroticism, as with Duchamp, played an crucial, if not determinant, role. A singular, intoxicating, cerebral eroticism, at times obsessive. To treat only the example of Rodin, it could be said that many of his sculptures--particularly Iris, Messenger of the Gods--are built around female genitals, or are sculptures of female genitals, just as Étant Donnés, with its perspectivist game and its illumination, is organized entirely around the genitals of a supine woman. What is more, in consulting certain Rodin drawings, one cannot help but notice their direct resemblance to the preparatory drawing of the Étant Donnés nude. Another pertinent example is drawing MR 5714 from the illustrations for Pierre Louÿs' Bilitis or, more precisely still, drawing MR 4967 from the illustrations for Octave Mirbeau's The Torture Garden (Fig. 3). Of the same illustrations, the drawings of these various titles merit further mention: "Buisson ardent," "Flamme," "Feu follet" (MR 4034)…

Stranger still is the case of Courbet. The engraving is a "selected detail," done in the style of Woman with White Stockings, which now belongs to the Barnes Foundation in Merion/Pennsylvania. Duchamp, playing on words, adds a faucon ⁽¹⁾ to it to trick us, his frustrated viewers, in keeping with Apollinaire's address to the absent Lou:
Il me faudrait un petit noc
Car j'ai faim d'amour comme un ogre
Et je ne trouve qu'un faucon. ⁽²⁾

Arturo Schwartz is equally justified in directly relating this engraving to the highly provocative pose of the Étant Donnés nude. Guided by this interpretation, we should not hesitate to see in Étant Donnés a "collage" of two references drawn from two of Courbet's works (Fig. 4) - just as the etching Selected Details after Ingres, # 1, is a combination of references drawn from two Ingres paintings. For one thing, the raised pose of the left arm recalls that of Woman Holding a Parrot (Fig. 5), a painting Duchamp could not have missed seeing in New York at the Metropolitan Museum. In addition and more importantly, the overall position of the body, the spread legs, cropped and separated from the head-the sort we tend to see, like pornographic graffiti, as sexual symbols, merely genitals and breasts, all the more provocative because they are anonymous-recall very distinctly the Courbet painting entitled The Origin of the World (Fig. 6).

It is possible here that Duchamp mocks Courbet's penchant for painting feathers, hair, and fleece, both by the wig that he had wanted "from a dirty blond" ⁽³⁾ and by the hairless genitals. One may wonder why Duchamp, at the end of his life, felt the need to pay this sort of homage, albeit ironically, to the "retinal" painter par excellance, and who, it is said, was no great intellect, and could be included in the category of painters who were paragons of the stupidity that Duchamp shunned.

Courbet gave many definitions to realism in art, such as "What my eyes see." Particularly relevant here is this declaration that confines painting to the domain of visible things: "An abstract, invisible object is not painting's domain." (from an 1861 letter) As it happens, precisely what Duchamp, from his youth, had endeavored to do was to turn away from such naturalism, leading the way toward what he once called "metarealism.⁽⁴⁾ "

The Large Glass, which for many years had been his attempt to attain this "metarealism," to portray this "abstract, invisible object," is the appearance in a three-dimensional world of a nude young woman belonging to the four-dimensional realm…

Étant Donnés, with the weighty signification of a geometry problem, seems ironically to lead us to the solid ground of visible reality.

It unfolds before the eye-or rather before both eyes - in the depth of the three-dimensional space that the realist Courbet was satisfied to offer on the two-dimensional surface of a canvas. Realism pushed to the limit? Realism pushed to the absurd? And does the assemblage in Philadelphia herald, finally, as other aspects of the work heralded Pop Art or conceptual Art, the hyperrealist sculpture of a De Andrea or a Duane Hanson? It is something else altogether. These visible things (resorting to the Courbetian designation of "What my eyes see") are affected by an additional, heightened visibility. The light is bit too intense, the flesh a bit too grainy.⁽⁵⁾ And this hint of abberation calls the "réalisme" of the entire scene into question.

The Bride is certainly there, surrounded by mechanisms now made visible. Finally, the appearance of what, in the Glass, remained hidden: the waterfall and the illuminating gas. She, herself, remains, with a sudden and strange reversal in appearance, something like the finger of a glove turned inside-out. In the Glass, she appears disembowelled, a mass of indistinct organs, an inside without an outside, entrails without skin-she conforms in this way to what theoreticians of the fourth dimension-Poincaré and Pawlowski-imagine in terms of the way our bodies would be seen by four-dimensional observers. On the other hand, in Étant Donnés, she appears as an exterior without an interior, an empty carcass, a hollow mold, a shell, an illusion.

Is this to say that she lacks insides? No, they exist. She has organs, organs that mark her as a sexual being: these are the four erotic sculptures, from Not a Shoe (Fig. 7) to Wedge of Chastity, which preceded her development, and which are, literally, the contents that correspond to her void (Fig. 8).

Figure 7	Figure 8
Marcel Duchamp Not a Shoe, 1950.	Marcel Duchamp Wedge of Chastity, 1954.

If the Female Fig Leaf (Fig. 9) is, as the evidence indicates, the imprint of a female groin, it is easy enough to imagine that Not a Shoe is a more limited but deeper imprint, literally stated, the impression of a vulva. And Dart-Object (Fig. 10), far from being a phallic extravagance, as Arturo Schwarz suggests, is an impression still more limited, intimate, and profound, of a decidedly feminine organ. ⁽⁶⁾

Figure 9	Figure 10
Marcel Duchamp Female Fig Leaf, 1950.	Marcel Duchamp Dart-Object, 1951.

There is a play here on the masculinity and the femininity of the mold: if the Malic Molds contained in their void the full form of the Bachelors, these molds that could be called "femalic," embody in full the hollowed out forms of the Bride's organs. ⁽⁷⁾

But still further: what is suggested is the reversibility of these organs. Dart-Object has an effectively phallic appearance, and its title adds to this evidence the aggressive behavior attributed to the male. Inversely, Female Fig Leaf, a blunt and massive object, photographed under a sort of illuminating gas that reverses values, turns the concave into the convex, becomes, like on the cover of Surréalisme, meme #1, a female figure imprinted with a strong, unusual "sex appeal."

The psychoanalyst, of course, has not failed to take an interest in this reversability of organs, the structure of a glove finger turned inside-out, that connotes sexuality. Sandor Ferenczi, in particular, in establishing his famous onto-and-phylogenetic parallel, had long meditated on the fact that the penis and vagina are a single organ, one and the same - a fanciful organ, a Mélusinian organ, developed here on the inside and there on the exterior, according to the needs of the species. ⁽⁸⁾ We will come back to this.

But let us go on further or rather elsewhere: into geometry. At the turn of the century, the principal studies on topology (analysis situs) began. Mathematicians then concentrated on such strange objects as the Mobius Strip and the Klein Bottle (Fig. 11). Let's also examine them. The strange particularities of the first are well-known. Take a strip of paper. It has two dimensions. Connect it by its shorter ends: you will get a ring with two surfaces, one internal and one external, and two sides. But if, instead of directly linking these two sides, you twist the strip before connecting it, you obtain a strange object that has no more than one surface and one side: paradoxical volume, unisurficial and unilateral (Fig. 12). Imagine, in a sort of Flatland à la Abott, a flat, two-dimensional being walking along this Mobius Strip: at no time would he be conscious of the third dimension that the torsion of the strip allowed him to cross (Fig. 13). Consequently, his consciousness could never grasp the exact form of this mathematical object.

Let us move on to the Klein Bottle. Broadly stated, it can be said that it is to the three dimensional world what the Mobius Strip is to the flat realm. Take up the same piece of paper, connecting it this time by its longer ends, as if you were rolling cigarette paper. You get a tube. Connect the two ends of this tube: you get a torus. Just as in the preceding example, it has two surfaces, one internal surface and one external surface, one outside and one within. But if, once again, before making the connection, you twist the tube, in an analogous twist to the one that brought the strip into the third dimension, this time crossing the fourth dimension, you get a paradoxical, unisurficial, and unilateral volume, possessing neither an inside nor an outside. As three-dimensional individuals, we are incapable of precisely conceiving the reality of such a volume. Only one "indigenous to the fourth dimension," to borrow the words of Duchamp himself in À l'infinitif, could grasp the torsion that creates such a volume that no longer has an outside nor an inside, and that makes of a solid mass a curious entity in which the notions of interior and exterior, of surface and depth, are annulled or exchanged.

Let us look at Dart-Object: this pseudo-phallic tube curves and bends in a curious way; if you mentally extend its inflection up to the point of the root or stalk it issues from, you get a volume strangely similar to a Klein Bottle. ⁽⁹⁾

Can we be accused of over-interpretation? Recall these facts: on the Glass, the Bride, a three-dimensional projection of a four-dimensional entity, presents herself as a mass of organs without a surface, a sort of inside without an outside. In Étant Donnés, by contrast, she is a shell without an interior, an outside without an inside. Recall also this note from the Green Box: "The interior and exterior (in a fourth dimension) can receive a similar identification. ⁽¹⁰⁾ " Recall finally that topology was developing at the beginning of the century, at the very time that Duchamp read Henri Poincaré and became interested in Riemannian geometry… There is further evidence of his ceaseless fascination with topology: when he met François Le Lionnais in the early 1960s, the first questions he asked of him concerned the Mobius Strip and the Klein Bottle. ⁽¹¹⁾

What is more, Dart-Object suggests something else: the genitals, seen as truncated, like the division of the being from itself-like something is missing-is not merely the effect of three-dimensional space. That we are sometimes allocated a vagina-and that designates a "woman"-virgin, bride, etc.-and sometimes a penis-and that indicates a "man"-bachelor, groom, etc.-this chance physiological event was never anything more than the effect of an assuredly ironic causality: the laws of Euclidian geometry. In a four-dimensional study-the place of erotic fulfillment, according to Duchamp-in keeping with an anamorphic illusion, vagina and penis would lose all distinctive character. It is the same object that we would sometimes see as "male" and sometimes as "female," in this perfect mirrorical return of the body that presupposes, because it takes place, the existence of a fourth dimension.

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Figure 14

Marcel Duchamp Couple of Laundress' Aprons, 1959.

Schwarz is therefore right, in a sense, to insist on hermaphroditism as an essential theme in Duchamp's oeuvre. But he is wrong to look for an explanation in Jungian archetypes and primitive religions. The model comes from Non-Euclidean geometry and the issues raised around 1900 by analysis situs. Transexuality, with Duchamp-his play on the transvestite, which goes from Rrose Sélavy to (in a more minor but also significant way) Couple of Laundress's Aprons of 1959 (Fig. 14) (mittens that can reverse gender like the finger of a glove)-is a kind of naïve ontological experience of a mathematical ideal that abolishes sexual differentiation.

To those who wish to pursue this further, one will recall the analyses marked out by Jacques Lacan in his Séminaire concerning "la schize du sujet," "l'optique des aveugles," and "phallus dans le tableau." ⁽¹²⁾

Going back to the phenomenological studies of Merleau-Ponty in Le Visible et l'Invisible, he recalls that "ce qui nous fait conscience nous institue du meme coup comme Speculum mundi" and he develops these lines, in which one cannot help but see the emerging shadow of Étant Donnés: "Le spectacle du monde, en ce sens, nous apparaît comme omnivoyeur. C'est bien là le fantasme que nous trouvons dans la perspective platonicienne, d'une être absolu à qui est transférée la qualité de l'omnivoyant. Au niveau même de l'expérience phénoménale de la contemplation, ce côté omnivoyeur se pointe dans la satisfaction d'une femme à se savoir regardée, à condition qu'on ne le lui montre pas." ⁽¹³⁾

Such is this perfect circularity of glance that transforms the voyeur into the seen object and makes the voyeur of the seen object, that makes prey of the hunter and catches the hunter in a snare, traps him in the spokes of an open eye. ⁽¹⁴⁾ A reversal like the glove of a finger in which the consciousness, Lacan says once more, this time citing a poet more than a bit close to Duchamp, "dans son illusion de se voir se voir ⁽¹⁵⁾, trouve son fondement dans la structure retournee du regard.⁽¹⁶⁾ "

Figs. 1, 2, 4, 7-10, 14
©2003 Succession Marcel Duchamp, ARS, N.Y./ADAGP, Paris. All rights reserved.