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A New Look: Marcel Duchamp, his twine, and the 1942 First Papers of Surrealism Exhibition

The First Papers of Surrealism exhibition, which opened on October 14, 1942 at the Whitelaw Reid Mansion in midtown Manhattan, was both historic and peculiar. As heralded by Newsweek magazine, First Papers of Surrealism was the “biggest all-surrealist show ever seen in the United States.”⁽¹⁾ It announced the arrival of Surrealism’s most celebrated artists, many of whom had recently left Europe to avoid the war. The exhibition’s title, in fact, alluded to the documents some artists had needed during their travels. In addition, First Papers of Surrealism benefited the Coordinating Council of French Relief Societies, a wartime charity organization.⁽²⁾ In such ways, the show was a very serious event, a product of and a response to the tumultuous political environment of the early 1940s.

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Figure 1
Title page, First Papers
of Surrealism catalogue,
1942. Philadelphia Museum of Art.

But First Papers of Surrealism was an equally whimsical affair, a playful reordering of the gallery experience. At the show’s opening, as children ran around and played catch, several hundred feet of twine, hung by Marcel Duchamp, festooned the primary exhibition space.⁽³⁾ This installation—hereafter referred to as his twine, the original title given by the First Papers of Surrealism catalogue (Fig. 1)—acted as something of a veil.⁽⁴⁾ It partially masked the room’s ornate Gilded Age architecture, as well as some of the paintings on display.⁽⁵⁾ Though certainly unorthodox, this installation was not without precedent. At the 1938 Exposition Internationale du Surréalisme in Paris, a taxicab carrying snail-covered mannequins was parked near the gallery’s entrance, coal bags were suspended from the ceilings, and the lights were dimmed so that visitors needed flashlights to see.⁽⁶⁾

In the First Papers of Surrealism exhibition, Duchamp’s twine created an intriguing environment through an economy of means. Yet for all the simplicity of the installation’s material, visitors were left uncertain of his twine‘s significance. As perhaps expected, the installation elicited a variety of interpretations. For Elsa Schiaparelli, one of the exhibition’s coordinators, the twine was something of a guide, “directing visitors to this and that painting with a definite sense of contrast.”⁽⁷⁾ Edward Alden Jewell, the New York Times art critic, focused on the installation’s functional effects, reporting that, “[the twine] forever gets between you and the assembled art, and in so doing creates the most paradoxically clarifying barrier imaginable.”⁽⁸⁾ Some visitors, such as Harriet and Sidney Janis, on the other hand, opted for more metaphorical interpretations. They believed the installation represented the complexity of understanding contemporary art, writing that Duchamp’s use of twine “symbolized literally the difficulties to be circumvented by the uninitiate in order to see, to perceive and understand, the exhibitions.” ⁽⁹⁾

Duchamp himself never provided any explicit interpretation of his twine. Instead, he tended, like Jewell, to stress more his twine’s functional value than its symbolic meaning. He believed that the installation was more transparent than opaque, saying in a 1953 interview: “It was nothing. You can always see through a window, through a curtain, thick or not thick, you can see always through if you want to, same thing there.”⁽¹⁰⁾ In recalling the frustration some of the other participating artists felt for his twine, Duchamp was unsympathetic. He doubted why “Some painters were actually disgusted with the idea of having their paintings back of lines like that, thought nobody would see their paintings.”⁽¹¹⁾

That Duchamp was keen to downplay, even deny, the obstructing quality of his twine is especially interesting, because that aspect has been the one most emphasized since First Papers of Surrealism closed on November 7, 1942. The installation has generally been discussed in terms of separation and dislocation; the twine deemed a dividing barrier, or what T.J. Demos calls “the maximal obstacle between paintings and viewing space.”⁽¹²⁾ This approach to the exhibition sets into motion a series of conflicts—installation versus paintings, paintings versus viewers, viewers versus installation—and has provided further opportunity to contextualize the exhibition within the political, social, and economic tensions of World War II. As Duchamp’s statements suggest, however, conflict was not the intended product of his twine.

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Figure 2
John Schiff, his twine at
First Papers of Surrealism
(South view), 1942. Philadelphia
Museum of Art.

Figure 3
John Schiff, his twine
at First Papers of Surrealism
(North view), 1942.
Philadelphia Museum of Art.

Looking at a photograph of the First Papers of Surrealism installation taken by John Schiff (Fig. 2), it is easy to see why his twine might be interpreted as an obstacle between viewer and art. The twine crisscrosses back and forth across the photograph’s frame, making the gallery and the art on display appear inaccessible. This photograph, moreover, is the best known and most consistently cited record of First Papers of Surrealism, which might explain the prevalence of this interpretation. Photographs, however, can be misleading, and Schiff’s is no exception.⁽¹³⁾ Though the photograph suggests a separation between the viewer—in this case Schiff—and the art, Duchamp’s twine installation was more permeable and the art on display more accessible than many believe it to have been. The essay to follow will clarify these misconceptions through a detailed study of the First Papers of Surrealism photographs and of the architecture of the gallery space itself, with the ultimate goal being a more complete and accurate conception of the exhibition’s design.

The aforementioned photograph by Schiff is reproduced, along with another installation shot (Fig. 3), in Lewis Kachur’s book Displaying the Marvelous, the most comprehensive study of First Papers of Surrealism to date.⁽¹⁴⁾ The same two photographs are also reproduced in Robert Lebel’s Marcel Duchamp.⁽¹⁵⁾ These photographs constitute the most comprehensive visual record of the exhibition and of his twine. Combined, they show the gallery in its near-entirety by presenting the room from opposite ends; one photograph looks north, the other south. They do not show the gallery from a single vantage point, nor were they “taken from the center” of the room, as Kachur has described them.⁽¹⁶⁾

To determine where Schiff’s photographs were taken and what they represent, it is necessary to visualize the architecture of the gallery itself. For the sake of clarity, this essay is accompanied by an interactive floor plan of the space (Fig. 4).⁽¹⁷⁾ Approximately 54 feet long by 25 feet wide, the room sits on the second floor of the Reid Mansion’s southern wing (Fig. 5). On the gallery’s west side, situated directly above Madison Avenue, there are three windows. The north and south ends each have two windows, which overlook the mansion’s courtyard and Fiftieth Street, respectively. Even though the gallery windows were covered during the exhibition, their locations are betrayed by light reflecting off the floor and are thus easily discernable in Schiff’s photographs. These same photographs do not show the gallery’s entrance, which was located at the middle of the east wall. They instead show only the ornate molding around the doorway, the entrance itself being hidden by the temporary partitions set up for the exhibition.

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Figure 4
Figure 5

First Papers of Surrealism
gallery plan, 1942, Design
by the author, 2006.
New York Palace Hotel (formerly
the Whitelaw Reid Mansion), New York, 2006.
Photograph by the author.

These partitions, each situated perpendicular to the nearest wall, allowed the Surrealists to increase the hanging space. As illustrated in the floor plan, there were ten such partitions: five ran the course of the west wall; two were placed at the north end; and three sat along the east wall. At the south end was a small stage with a piano on it. (Though they did little to change the gallery’s layout, there were also six temporary partitions set parallel to and directly against the walls, presumably used to avoid putting holes in the room’s original wood paneling.) On the whole, his twine was restricted to the ceiling space and the gaps between neighboring partitions—the main exception to this rule being the space between the two partitions flanking the entrance. There, a lack of twine allowed visitors to enter. The interior of the gallery was also free of twine and thus open to ambulation. Carroll Janis, the son of Harriet and Sidney Janis and one of the children present at the First Papers of Surrealism opening, confirms these details, recalling that “there was free access down the center of the large room, with ‘partitioned niches’ on either side.”⁽¹⁸⁾

A close examination of Schiff’s photographs makes it is possible to recreate where he stood when shooting. These vantages, which are marked on the accompanying floor plan, have also been recreated in two included photographs (Figs. 6-7).⁽¹⁹⁾ Because the view of the room’s southern end shows the stage that was set up there, the view of the northern end must have been taken from somewhere in the vicinity of this platform. Duchamp used hardly any twine in that area, so the photograph taken from the south (the north view) is without foreground obstructions. This photograph in turn shows that its counterpart, the south view, was taken from between the partitions at the opposite end of the room. As twine was strung across these partitions, the photograph taken there (the south view) represents the gallery as an area closed-off by a web of intersecting lines. The photograph is therefore deceptive, as the space beyond the twine was actually open and easily accessible.

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Figure 6
Figure 7

L’Orangerie room at the
New York Palace Hotel (South view),
2006. Photograph by the author.
L’Orangerie room at the New York
Palace Hotel (North view), 2006.
Photograph by the author.

In addition to providing information regarding the layout of First Papers of Surrealism, these photographs highlight the artificiality, or perhaps theatricality, of Schiff’s process. Kachur has described the photographs as being “as straightforward as possible,” but while that claim might hold true for the north view, it is hardly the case with the south.⁽²⁰⁾ Because of the twine’s layout, photographing the north view would have required little more than standing near or atop the stage. Photographing the south view, however, would have entailed a more involved process. To get this shot, Schiff had to stand behind the twine running between the northernmost partitions. If Duchamp’s installation was indeed a physical barrier, then Schiff’s task would have been quite demanding. But regardless of how easy or difficult the twine was to circumvent, the photographs are nonetheless carefully orchestrated.

Specifically, Schiff’s photographs and the means by which they were taken emphasize and demonstrate the permeability of Duchamp’s installation at First Papers of Surrealism. Even the south view, the one mostly obscured by his twine, nonetheless provides a relatively clear view of the exhibition. Moreover, the photographs actually seem to encourage the practice of looking through his twine. They ask the viewer to acknowledge the installation, the gallery space, and art beyond. It is something of a looking game: focus on the twine; focus on the gallery; focus on the art. The game repeats as the viewer continues through the exhibition. Becoming more accustomed to the environment, the viewer may realize that the relationship between the three entities is more a fluid partnership than a one-sided competition. Schiff’s photographs suggest this sort of dynamic interaction with the twine; in their staging, they actually document that experience.

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Figure 8
Max Ernst’s Le Surrealism
et la Peinture behind
twine at First Papers of Surrealism
, 1942. Newsweek,
26 October 1942.

Throughout the rest of the First Papers of Surrealism records and materials, the concept of seeing through his twine, of allowing Duchamp’s installation to somehow mediate the viewing experience, is consistently reiterated. A photograph from Newsweek (Fig. 8), for instance, shows Max Ernst’s Le Surréalisme et la Peinture (1942) behind his twine. In this case, the photograph’s small field of view limits the ability to locate either the camera’s vantage point or the placement of Ernst’s painting (though the work does appear to hang on one of the six partitions set parallel to and directly against the gallery walls). More importantly, the Newsweek photograph demonstrates how easily one could have viewed the painting despite the presence of the twine. Arnold Newman, another photographer to take pictures of the First Papers of Surrealism installation, took at least two photographs of his twine, both of which include Duchamp. In one (Fig. 9), the artist looks out coyly from behind his twine; in the other (Fig. 10), he stands beside his 1913 Cimetière des Uniformes et Livrées (or Network of Stoppages, as it is known in English). In both photographs, his twine functions as a framing device, something to be recognized but not focused upon.

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Figure 9
Figure 10

Arnold Newman, Marcel Duchamp, 1942. Philadelphia Museum of Art.
Arnold Newman, Marcel Duchamp behind his installation of “sixteen miles of string,” 1942. Zabriskie Gallery website.

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Figure 11
Marcel Duchamp,” First Papers of
Surrealism catalogue, 1942.
Philadelphia Museum of Art.

Since the geometric painting to Duchamp’s right in the second photograph by Newnam also appears in Schiff’s south view, Cimetière des Uniformes et Livrées must have hung on the partition between the middle and northernmost windows of the west wall of the gallery. The vantage point of Newman’s photograph, in turn, would have been just north of the gallery’s center.⁽²¹⁾ This point is also marked on the included floor plan. That Duchamp was posed beside this particular painting is not a coincidence. Cimetière des Uniformes et Livrées, which was fully reproduced in the exhibition catalogue (Fig. 11), is a layering of imagery derived from other paintings and drawings, the top level being the synapse-like forms of 3 Standard Stoppages (1914), made by dropping meter-long threads from a height of one meter onto a horizontal surface.⁽²²⁾ In other words, Newman’s photograph shows a painting behind twine of a painting behind twine. A more reflexive image could hardly be imagined.

Duchamp may well have collaborated with Newman on setting up the photograph. Duchamp’s designs for the First Papers of Surrealism catalogue emphasize permeability and the process of looking through. On the front cover is an image of a wall pocked with bullet holes through which Duchamp punched five actual holes (Fig. 12), while on the page facing Sidney Janis’s foreword to the catalogue, the artists participating in the exhibition are listed so that their names collectively create the shape of a keyhole (Fig. 13), again referencing the process of looking through.⁽²³⁾ The back cover is a detailed image of Swiss cheese (Fig. 14).⁽²⁴⁾ By emphasizing the transparency of his twine, Newman’s photographs reiterate the iconography of the catalogue. If Duchamp did not actively collaborate with Newman in creating the compositions of the photographs, they are nonetheless very much in keeping with the central idea of the First Papers of Surrealism installation and catalogue.

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Figure 12
Figure 13
Figure 14

Front Cover, First Papers
of Surrealism catalogue, 1942.
Philadelphia Museum of Art.
Artists names in keyhole,
First Papers of Surrealism catalogue,
1942. Philadelphia Museum of Art.
Back Cover, First Papers
of Surrealism catalogue,
1942. Philadelphia Museum of Art.

The Newman photograph of Duchamp beside Cimetière des Uniformes et Livrées also shows that twine was strung only from the edges of each partition on the sides closest to the middle of the gallery. Each partition, moreover, was set not directly against the wall but out by two or three feet. Such a layout would have made possible a navigable corridor ringing parts of the gallery’s east, north, and west walls. The corridor would have allowed passage around the gallery’s perimeter and entrance into the niches between facing partitions. The existence of such channels, however, is somewhat speculative. When asked, Carroll Janis could not confirm their presence, but nor could he deny the possibility that they had been there, writing, “I do not recall any corridor running around the back of the niches – but I wasn’t looking for it either!”⁽²⁵⁾

If there was not a continuous walkway, some other means of passage through his twine must have been present. How else could Schiff’s and Newman’s photographs be explained? Janis claims to “[not] recall any real access into the niches,” though he counters that, “the string had a certain fragile character…one could have slipped under at certain points.”⁽²⁶⁾ Jewell, whose account may be more reliable given his age at the time and the nature of his job, provides a more convincing description. He reports that “intrepid” visitors could “reach closer proximity [to the paintings] by means of certain strategically placed apertures.”⁽²⁷⁾ This statement, beyond verifying the existence of openings in his twine, indicates that such “apertures” were intentionally created for the express purpose of accessing the partitioned niches. In Schiff’s north view of First Papers of Surrealism, such an opening appears to exist between the partitions perpendicular to one another at the gallery’s northwest corner. Close to the gallery’s north end and to the spot where Cimetière des Uniformes et Livrées hung, this opening was likely the one used by Schiff when he shot his south view of the exhibition and by Duchamp when he posed for Newman.

Just how many people actually chose to traverse the skeins of the First Papers of Surrealism installation is uncertain. Duchamp and Schiff count for at least two, and perhaps there were more. But even if only a few visitors were “intrepid” enough to pass through the installation, the possibility for such passage is a reminder that his twine was far less an impediment than commonly believed. Moreover, for those who did not physically navigate the installation, his twine arguably did more to enhance the paintings on display than it did to obscure them. “It was,” as Janis writes, “a fantastically interesting see-through construction, which transformed the gallery space into an unforgettable experience.” Contrary to his parents’ interpretation, Janis believes the twine actually “helped explicate the new art.”⁽²⁸⁾

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Figure 15
First Papers of Surrealism
catalogue, 1942. Philadelphia
Museum of Art.

That Duchamp’s installation at the First Papers of Surrealism exhibition would be concerned with new, intriguing, and even playful methods of looking at art is not surprising. Experimenting with sight was for Duchamp a lifelong preoccupation. A work like To Be Looked at (from the Other Side of the Glass), with One Eye, Close to, for Almost an Hour (1918) predates the exhibition and demonstrates an early example of how Duchamp chose to engage the practice of looking. Concurrent with First Papers of Surrealism—and less than nine blocks away—at Peggy Guggenheim’s Art of This Century gallery, Duchamp’s Boîte-en-valise (1935-41) was on display through the peephole of a web-like apparatus.⁽²⁹⁾ Some years later, Duchamp would begin work on Etant donnés: 1° la chute d’eau, 2° le gaz d’éclairage (1946-66), a piece that summarizes many of the artist’s diverse interests but is above all about the act of looking through. Since the First Papers of Surrealism catalogue includes a reproduction of Duchamp’s In the Manner of Delvaux (1942) (Fig. 15), a collage showing a fragmented view of a female nude, Etant donnés, may have already been on Duchamp’s mind.⁽³⁰⁾ The use of certain other imagery in the catalogue—bullet holes, Swiss cheese, a keyhole—only furthers the likelihood of that possibility.

To what extent Duchamp himself would have related these or other works to the First Papers of Surrealism installation is uncertain. From a material point of view, he may have considered his twine to be more akin to 3 Standard Stoppages or With Hidden Noise (1916), as both those works involve string. Compositionally, he may have found more in common with Sculpture for Traveling (1918), another temporary work, which involved stretching parts of a bathing cap to different walls of a room. In truth, different aspects of his twine might resonate equally with many different works by Duchamp, and likewise there may be many ways to interpret the installation beyond the artist’s oeuvre alone. But analysis of that variety has never been this essay’s goal. The primary concern has always been the reexamination of the First Papers of Surrealism texts, photographs, and space. As his twine no longer hangs, having existed for not even a month, this documentary material is of utmost importance. By synthesizing as much of this information as possible, the hope has been the achievement of a more concrete understanding of the exhibition’s design and of the role his twine played there.

Notes

1. “Agonized Humor,” Newsweek, 26 Oct 1942, 76.

2. Ticket prices were listed as $1.10 for the opening preview and $.50 thereafter, as noted by Edward Alden Jewell in “Surrealists Open Display Tonight,” New York Times, 14 Oct 1942, from ProQuest Historical Newspapers the New York Times (1851-2003) .

3. At the request of Duchamp, Carroll Janis, the son of Sidney and Harriet Janis, and friends ran around and played ball in the galleries. The performance tickled some of the adult visitors and frustrated others. In Lewis Kachur’s Displaying the Marvelous (Cambridge: MIT Press, 2001), Kachur explains the children’s activities in a section called “Vernissage Consacré aux Enfants Jouant, à l’Odeur du Cèdre,” 195-7.

4. André Breton and Marcel Duchamp, First Papers of Surrealism (New York: Coordinating Council of French Relief Societies, Inc., 1942). As news of the installation spread, Duchamp’s handiwork soon acquired the catchy name Sixteen Miles of String. See, for instance, Robert Coates, “The Art Galleries, Sixteen Miles of String,” New Yorker, October 31, 1942, 72; Alfred M. Frankfurter, “The Passing Shows,” Art News: November 1-14, 1942, 24. This moniker, however, is misleading, as no such length was ever used; moreover, it is unnecessary when compared to the simpler title originally given in the exhibition catalogue: “his twine.” This phrase appears on the catalogue’s title page, alongside other basic information regarding the show. The same page also credits the “hanging” to André Breton, who indeed helped coordinate the exhibition. Thus, although “his twine” may also be understood as wordplay on “his twin,” a reference to the friendship between Duchamp and Breton, that interpretation is certainly secondary to the phrase’s purpose as a title credit.

5. Built in 1884 by McKim, Mead & White, the mansion was originally intended for railroad tycoon Henry Villard. Bankruptcy forced Villard to give up possession of the property, selling it to Whitelaw Reid, then editor of the New York Tribune. Today, the estate is part of the New York Palace Hotel, which calls the wing where the 1942 exhibition was held the Villard Mansion. See Christopher Gray, “Streetscape/Madison Avenue Between 50th and 51st Street; A Landmark 6-Home Complex in Dark Brownstone,” New York Times, 21 Dec 2003, from ProQuest Historical Newspapers the New York Times (1851-2003).

6. This exhibition is addressed in Kachur’s Displaying the Marvelous and Alyce Mahon’s Surrealism and the Politics of Eros, 1938-1968 (London: Thames and Hudson, 2005), among others.

7. Kachur, 179.

8. Edward Alden Jewell, “‘Inner Vision’ and Out of Bounds,” New York Times, 18 Oct 1942, from ProQuest Historical Newspapers the New York Times (1851-2003).

9. Harriet and Sidney Janis, “Marcel Duchamp, Anti-Artist,” View 5, no. 1 (March 1945), 18. Arturo Schwarz makes a similar interpretation in his The Complete Works of Marcel Duchamp (New York: Harry N. Abrams, 1969), 515.

10. Duchamp quoted in Kachur, 183

11. Ibid., 189-90.

12. T. J. Demos, “Duchamp’s Labyrinth: First Papers of Surrealism, 1942,” October (Summer 2001), 94.

13. Interestingly, the reception of his twine is strikingly similar to that of Duchamp’s Fountain, 1917. In both cases, photographs have been the primary means for seeing the original work. That is of course true with his twine, a temporary installation seen only by gallery visitors. Fountain also no longer exists, although replicas are on display at several museums, in particular the Philadelphia Museum of Art. Even before the original was lost, however, Fountain was for years known largely through Alfred Stieglitz’s 1917 photograph of the work. Stieglitz’s photograph exaggerated the formal qualities of Fountain, prompting critics to respond with overly aesthetical interpretations of the readymade. Yet time has shown that Fountain is more an ironic and provocative critique of art than an objet d’art per se. As this study explains, Schiff’s photograph of his twine suggests a more imposing, impassible installation than in reality. For more on the reception of Fountain, see William Camfield, Marcel Duchamp: “Fountain” (Houston: Menil Foundation, 1989), particularly pages 13-60.

14. Kachur, 176, fig. 4.3; 180, fig. 4.5.

15. Robert Lebel, Marcel Duchamp (New York: Grove Press, Inc., 1959), plates 111a and 111b.

16. Kachur, 168.

17. The floor plan was drafted by the author according to measurements taken at the gallery. The placement of the partitions and the stage have been determined as best as possible according to the photographs by Schiff and Newman.

18. Carroll Janis, letter to the author, 31 January 2007.

19. The gallery, part of the New York Palace Hotel (see note 5), is now called L’Orangerie and is a meeting/banquet hall. I visited the L’Orangerie room on November 7, 2006, coincidentally the sixty-fourth anniversary of the First Papers of Surrealism closing. Despite some renovations to the ceiling and the installation of some modern fixtures, the room seems to have changed little since 1942. At the New York Palace Hotel, I took a series of digital photographs and videos to document my visit. In particular, I tried to recreate the photographs taken by Schiff and Newman, which have been included here along with an exterior shot of the mansion.

20. Kachur, 187.

21. Ibid., 176, image caption 4.3, indicates this work as one by Robert Motherwell. It is not, however, El Miedo de la Obscuridad (1942), the Motherwell work reproduced in the First Papers of Surrealism catalogue. That it is even by Motherwell seems questionable. Kachur also identifies in this photograph works by Paul Klee, Ernst, Marc Chagall, Alexander Calder, and Pablo Picasso. In the other photograph by Schiff, reproduced on page 176, Kachur identifies works by Picasso, Yves Tanguy, René Magritte, Giorgio de Chirico, and Jean Arp.

22. For an animated illustration of how the works combine into a single whole, see Greg Alvarez’s video at http://www.marcelduchamp.net/stoppages.php.

23. It was actually Duchamp himself who fired a gun at the wall. See Martica Sawin, Surrealism in Exile and the Beginning of the New York School (Cambridge: MIT Press, 1995), 222-6.

24. A debate has arisen regarding this cheese, particularly what exact type is shown. See Stephen E. Hauser, “Marcel Duchamp Chose Emmentaler Cheese (1942),” Tout-Fait: The Marcel Duchamp Studies Online Journal, Issue 3, 2003 (27 November 2006).

25. Janis letter.

26. Ibid.

27. “Surrealists Open Display Tonight.”

28. Janis letter.

29. Kachur, 202.

30. Thomas Singer claims in “In the Manner of Duchamp, 1942-47: The Years of the ‘Mirrorical Return,’” Art Bulletin 86, no. 2 (June 2004) 346-69 that the origins of Etant donnés can be traced to In the Manner of Delvaux. His analysis, however, does not closely consider the work’s reproduction in the First Papers of Surrealism catalogue. Furthermore, while the conclusion drawn by Singer is correct—that the collage relates to Etant donnés—his argument is confusing. His study overemphasizes the importance of infrathinness, forgery, and mirrors, but does not discuss the striking visual similarities between a peephole and the cropping of In the Manner of Delvaux as it is reproduced.

A Problem With No Solution

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Figure 1
Julien Levy Gallery’s Exhibition
Announcement for Through the Big End
of the Opera Glass, 1943 In 1943, Marcel Duchamp was asked by the gallery owner Julien Levy to design the announcement for an exhibition to be called “Through the Big End of the Opera Glass.”⁽¹⁾ As the title implies (adapted, as it was, from Lewis Carroll’s Through the Looking Glass), the show was to feature unusually small-scale work. Years later, Levy explained that the idea for the exhibition came from having seen an example of Duchamp’s valise, in which the artist had packed miniature reproductions of his work into a portable suitcase.⁽²⁾ The show was to include not only work by Duchamp, but by two other artists as well: the French Surrealist painter Yves Tanguy, and the American collage and assemblage artist, Joseph Cornell. Within the announcement (Fig. 1), Duchamp reproduced a black-and-white layout by Cornell featuring the titles of Cornell’s work printed in a variety of expressive type faces surrounded by a collage of images referring to them, while Tanguy was represented by a drawing of one of his characteristically biomorphic three-dimensional shapes, accompanied, in this particular instance, by an opaque black shadow that curiously overlaps it.

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Figure 2
Marcel Duchamp, Cupid, Collection of the
Honorable Joseph P. Carroll
For his own contribution, on the back cover of the announcement Duchamp provided the image of a cupid with a stretched bow and arrow in his hands, but the figure is inexplicably reproduced upside down, for the artist’s signature—which is oriented legibly—streams off to one side at the level of the cupid’s head. At first glance, knowing that Duchamp often appropriated imagery for whatever purpose was required—in the fashion of culling images readymade—one might easily conclude that the cupid was clipped from some printed source and collaged into this position. However, the original layout for this announcement was recently discovered among the effects of Julien Levy, and it is now known that Duchamp painstakingly drew the cupid himself in pen and ink (Fig. 2). It is likely that he took the time to render this image because he could not find the reproduction of a cupid fixing his arrow in this precise direction, a detail that, as we shall soon learn, is critical to his intent, for the significance of the cupid’s aim can only be understood when the announcement is unfolded and fully opened.

Figure 3
Detail of Julien Levy Gallery’s Exhibition Announcement for Through
the Big End of the Opera Glass, 1943The paper stock Duchamp selected for this ephemeral publication was a translucent sheet folded in quadrants, forming a booklet. The first thing the recipient would have seen upon removing the announcement from its envelope was the title page, providing the name of the exhibition, its dates and its location. Upon opening the booklet, he would find Cornell’s layout opposite Tanguy’s drawing, and, on the back cover, Duchamp’s cupid. Closer examination of the cupid would reveal that something is printed on the opposite side of the paper: below Duchamp’s signature, in red ink, one can faintly read the words: “White to Play and Win” (Fig. 3). To chess enthusiasts, this phrase can mean only one thing: one is being presented with a chess problem to solve in which white is instructed to move first and eventually go on to win the game. Indeed, just above it, one can discern the faint outline of a chess board with pieces in various positions, printed, like the writing below it, on the opposite side of the sheet. If, at this point, someone is compelled to unfold the sheet and examine the opposite side, Duchamp provided additional instructions: “Look through from other side against light.”

For those already familiar with Duchamp’s work, these words might well bring to mind the elaborate title that he gave to a work on glass from 1918: To Be Looked at (from the Other Side of the Glass) with One Eye, Close to, for Almost an Hour (The Museum of Modern Art, New York). The comparison may not have been a simple coincidence of wording, for if an attempt were made to solve the chess problem, even grand masters would likely need more than an hour to solve it. If we follow Duchamp’s instructions and “look through from the other side against light,” we will see the layout of a chessboard from the proper position (with a white square in the lower right corner), each player with a king, a pair of pawns, and a single rook. We will also see the cupid he drew on the other side, the arrow from its bow pointing down the white knight’s file (or “B” file in algebraic notation), suggesting that the next best possible move for White would be to advance its pawn. One who studies this endgame problem at any length, however, would determine that this move would not attain a win for white. Indeed, virtually any move by white seems to result in a draw, even though there are a few compelling scenarios that—until properly analyzed—give the false impression that white has a chance to win (see analysis in boxed insert).

AN ANALYSIS OF DUCHAMP’S ENDGAME PROBLEM
AN EXCHANGE WITH LARRY EVANS

Diagram A

Diagram BAt first glance, the endgame chess problem that Duchamp devised (see Diagram A) gives the impression that White could play and win, for White has a pawn on the seventh rank and a quick promotion would seem inevitable. Black has two isolated pawns that could also advance, but they are farther from promotion and look as though they could easily be attacked by White’s rook. The following scenario seems plausible, as was suggested to me thirty years ago by international grandmaster Larry Evans:^(I)

1.
White
Black
2.
Ke4!
h4
3.
Kd5
h3
4.
Kc6
h2
5.
Rg7+
Kf3
6.
Rh7
Kg2
7.
Kc7
Rxb7+
8.
Kxb7
h1=Q
9.
Rxh1
Kxh1
10.
Kc6
f5
Kd5 and wins
(see Diagram B)

Diagram C

Diagram D

Diagram E
This variation, however, misses a possible move for Black, one that would not only extend play, but would eventually result in a draw.^(II) After the white king moves to c7 (the sixth move), the pieces are in the position and shown in Diagram C.

At this point, Black is forced to move his rook (otherwise, the white king will capture it on its next move). If he captures the white pawn and checks white’s king at the same time, the result will be a win for White (as Evans demonstrated above). But if Black moves his rook to g8 (6. … Rg8), he is in a far better position. There, if White promotes on the next move, he can capture the promoted piece (as indicated in Diagram D).

On the very next move, the white king will capture the black rook. The white rook will then capture the black pawn when it promotes, and the black king will, in turn, take the white rook, leaving a pair of kings and isolated pawns on each side of the board, a position that results in a draw.

There is another scenario that would allow White to continue play even further. After 6. … Rg8, if White does not promote his pawn on the 7th move, but, rather, advances his other pawn one square forward (7. b6, in the direction indicated by the Cupid’s arrow), play would continue as follows:

7
…
h1=Q
8
Rxh1
Kxh1
9
b8=Q
Rxb8
10
Kxb8
f5 draws

Diagram F

Diagram G
In this position, it may appear that White will win, since his pawn seems closer to promotion. When played out, however, this leads to Diagram G (discussed below), resulting in another book draw. A number of other possible scenarios were later suggested by Larry Evans. In the initial position, he strongly encouraged investigation of moving the white king to e3, or advancing the trailing pawn to b6 (as suggested in Duchamp’s design by the direction of the Cupid’s arrow).^(III) This latter suggestion (1. b6) eventually transposes to Diagram E. Following the strategy that I had proposed—of Black moving his rook to g8—Evans also suggested that White promote right away on b8, followed by a black rook capture (thereby eliminating White’s pawn that was threatening to promote). White’s king would then capture the black rook on b8, followed by the promotion of Black’s pawn, which would, in turn, be captured by the white rook. The black king would then capture the white rook, leaving the position found in Diagram F. If we compare the final positions in Diagrams E and F, we discover that they are very similar and transpose into each other. They both lead to Diagram G, which ends in a classic draw (as explained below). In position F only, the white pawn would queen, leaving the black king protecting a pawn that is about to promote (see Diagram G). The position leads to perpetual check, or stalemate.

The way a stalemate is achieved (from Diagram G) is that White starts a series of checks leading to the following position: White Kc7, Qg4 (check); Black: Kg2, f2. Then after … Kh1, Qf3+ Kg1, Qg3+, Black does not protect his pawn with … Kf1 (because then the white King steps back up the board, followed by a series of checks and King moves again, leading to eventual mating position), but instead plays … Kh1! Then if the white Queen takes the pawn with Qxf2, it is a stalemate; but meanwhile, Black is threatening to promote. So White has to give perpetual check or allow stalemate.^(IV)
The way a stalemate is achieved (from Diagram G) is that White starts a series of checks leading to the following position: White Kc7, Qg4 (check); Black: Kg2, f2. Then after … Kh1, Qf3+ Kg1, Qg3+, Black does not protect his pawn with … Kf1 (because then the white King steps back up the board, followed by a series of checks and King moves again, leading to eventual mating position), but instead plays … Kh1! Then if the white Queen takes the pawn with Qxf2, it is a stalemate; but meanwhile, Black is threatening to promote. So White has to give perpetual check or allow stalemate

Figure 4
Black & White photograph of Larry Evans playing
chess with Marcel Duchamp (Larry Evans is on
the left and Marcel Duchamp is on the right)Larry Evans—who had played chess with Duchamp on more than one occasion (Fig. 4)—was sufficiently intrigued by this problem that he graciously accepted my request to publish it in his monthly column in Chess Life & Review.^(V) At the time, I offered a $15 reward for its solution, not realizing that I would be inundated with responses, a number of which came from prison inmates who demanded immediate payment of the reward. Phone calls from several of these individuals were all the intimidation I needed to send checks, even though none of their solutions were actually convincing. The most thoughtful and detailed responses came from regular readers of Chess Life & Review, specialists in endgame strategy who proposed a variety of intriguing possibilities, all hoping that theirs was the ultimate solution (although I do not believe that any of them actually were). I have since subjected this problem to the most powerful computer programs available to me, and no solution has yet been found. I am now all the more convinced that this is a problem that cannot be solved. Duchamp has given us, in effect, a problem with no solution.^(VI)

I. In an effort to solve this problem, I wrote to E. B. Edmondson, then executive director of the American Chess Federation. He passed on my inquiry to Larry Evans, who responded to me in a letter dated June 2, 1976.

II. I presented these alternatives to Mr. Evans in a letter dated June 4, 1976.

III. Letter from Evans to the author, June 5, 1976.

IV. The analysis of this final position was generously provided by Allan G. Savage, author of
Reconciling Chess: a Marcel Duchamp Sampler (Davenport: Thinkers’ Press, 1998), and who is in the process of writing the fourth volume of the series published by Moravian Chess, The Chess Biography of Marcel Duchamp (1887-1968), which is scheduled for publication in 2008.

V. “Larry Evans on Chess,” Chess Life & Review (October 1976), p. 580.

VI. I have provided copies of the present analysis to several experienced chess players: Jennifer Shahade, Ralph Kaminsky, Allen G. Savage and Malcolm H. Wiener. These individuals are familiar with standard chess analyses and, although they agree with my general conclusion (that the problem has no solution), they believe my analysis to be redundant and—in comparison to professional analyses— somewhat amateurish. Nevertheless, I am grateful to all of them for having taken the time to review my text, and for having provided various recommendations for its improvement.

The rigor and intensity of this endgame problem stands in sharp contrast to the means by which Duchamp presents us with a hint of its solution: a cupid aiming his arrow toward the ground (or into the sky, if we consider that the cupid is presented upside-down). Cupid is, of course, the mythological god of love, and his arrow is usually aimed in the direction of an amorous target; a direct hit can cause the recipient to fall deeply and blindly in love. Knowing this, and knowing that when Duchamp designed this brochure he had recently met and fallen in love with Maria Martins— a Brazilian sculptor, married with three children, and in almost every respect, unattainable—one is tempted to speculate that Duchamp might have had a personal situation in mind when he decided that a cupid should indicate the path to follow in pursuing a solution to this vexing problem. Duchamp was well known for having said: “There is no solution, because there is no problem.”⁽³⁾ In the end, the problem that he faced with Maria Martins was insurmountable, demonstrating that in both chess and life— and perhaps in art as well—there are, indeed, problems without solutions.

Notes

This article first appeared in The Sienese Shredder no. 1 (Winter 2006-2007), pp. 180-87. At the time when it appeared, I was unaware of the fact that Grandmaster Pal Benko had published an analysis of this same endgame problem, concluding—as I did—that there was no solution (see “Duchamp Solved!?,” Chess Life [August 2005], p.588). I am grateful to Ralph Kaminsky for having drawn this article to my attention.

1. The date of this exhibition has been given variously, as either 1943 or 1948. Julien Levy consistently gave the date as 1943 (see his autobiography, Memoir of an Art Gallery [New York: G.P. Putnam’s Sons, 1977], p. 309, as well as the reference contained in the following note). For reasons that are unclear, however, in all editions of his otherwise reliable catalogue raisonné of work by Marcel Duchamp, Arturo Schwarz gives the date as 1948 (see The Complete Works of Marcel Duchamp [New York: Harry N. Abrams, 1969], cat. no. 329, page 523; revised and expanded edition [New York: Delano Greenidge Editions, 1997], cat. no. 530, p. 793, and descriptive bibliography 71, page 904). The date of 1943 cannot be challenged, however, for the show was reviewed in The New York Times on December 12, 1943 (I am grateful to Ingrid Shaffner for bringing this citation to my attention).

2. See the statement provided by Julien Levy for a brochure published on the occasion of “Through the Big End of the Opera Glass II,” a recreation of the original 1943 show at the Joan Washburn Gallery, New York, February 15 -March 12, 1977 (the brochure contained a facsimile reprint of the original fold-out catalogue).

3. This comment seems to have been quoted for the first time in Harriet and Sidney Janis, “Marcel Duchamp: Anti-Artist,” View, series V, no. 1 (March 1945), p. 24; it is repeated again in Winthrop Sargeant, “Dada’s Daddy,” Life, vol. 32, no. 17 (April 28, 1952), p. 111.

Fig. 1-3, © 2008 Succession Marcel Duchamp, ARS, N.Y./ADAGP, Paris.
Authorization to publish this article was provided by the author, Francis M. Naumann and The Sienese Shredder.

Remembering Marcel and Duchamp

READYMADE/UNMADE,
Laurent Sauerwein 2007

He was a face from my childhood before I realized he was an art history icon.

My father had bought a small house in the Catalan village of Cadaqués, on the Mediterranean coast of Spain. We would go there in the summer, and I would often see an elderly gentleman slowly walking through the village. My father would say hello and exchange a few pleasantries. I would shake the smiling gentleman’s hand, and we would all continue our summer business. Then I would hear about various dinners to which my father and his wife were invited along with the elderly Marcel – that was his name – and his wife Teeny. And at those dinners, there were another dozen people, the usual international lot, some permanently settled in Cadaqués, others just passing through.

Marcel was the discreet center of a small world of familiar faces you would run into, toward the cooler part of the afternoon, after having spent the day out in the boat, along the rocky shores of the Costa Brava.

I’d been told that Marcel Duchamp was an artist, but there was nothing extraordinary about that, as a lot of artists of all kinds lived or spent the summer in Cadaqués, some famous, others obscure, some remarkable, some very bad. Most of the art that was shown in the local galleries was mediocre, except for the Galeria Cadaqués, run by the architect Franco Bombelli. The gallery was a vaulted white-washed space where contemporary art was shown and where, on opening nights, you just might catch a glimpse of Marcel.

Every summer day

click to enlarge

Figure 1
Marcel Duchamp’s daily
trip to play chess at Café Meliton

There was another place where you were absolutely sure to see Duchamp: at exactly 5:00 p.m. and at precisely the same spot, in the same chair, at the same table, every summer day.

The place was the café Meliton, at the northern end of the Paseo, the village’s main meeting place. The tiny café has a handful of tables inside and, across the road, a few more, practically on the beach. You would never catch Marcel sitting outside, however, at least I never did. At 5:00 p.m. sharp, every day, he would go inside, just to the right, and sit down on the wicker chair, his back to the wall, covered, salon-style, with framed pictures, autographed photographs, small oil canvases and watercolor landscapes, faded surrealist sketches and other souvenirs. Marcel would sit there, watching the waiter and waitress go about their business, going to the counter at the rear to fill their round trays with drinks ordered by people sitting outside. Somewhere in the back, a very striking gentleman was discreetly supervising the operation. His last name was Meliton, which had a proud ring to it. He had a very distinguished tanned face, the hands of a fisherman and elegant, totally white hair. He was younger than Marcel but had been around. He had been an anti-Franco, Republican hero in the Spanish Civil War. The waiter was his son, the waitress his daughter. Marcel wanted to be at that particular table, so Meliton kept it for him. It went without saying. With Marcel, everything went smoothly.

Then Marcel would order a drink and gracefully proceed to light a cigar. It was a ritual of sorts, with inframince differences from day to day.

click to enlarge

Figure 2
Marcel and Teeny
Duchamp’s apartment on
the top floor of a house on
Port d’Alguer, in Cadaqués

In the summer of 1965, I took advantage of Duchamp’s daily habit. By then, I had just turned 21 and was living in Cambridge, Mass., discovering contemporary art among other things. And so, in my youthful mind, he was no longer Marcel, the elderly friend of my parents, but Marcel Duchamp, discreetly carrying about him the aura of a century of art. So one day, I went to Meliton’s a bit ahead of time, and sat at the table next to the one which I knew he would soon occupy. When he appeared, I greeted him, and he kindly invited me to pull up a chair. I was full of questions, all of which he answered with patience and courtesy. I didn’t ask him about his work really, probably because I felt comfortable with its enigmatic nature. But what I longed to hear about in my youthful enthusiasm, were details about people I’d been reading about so recently: Picabia, Tzara, Eluard, Max Ernst, Breton, Varèse, Masson… They were all in the Pantheon, names I had only encountered in books or museums, and Marcel had known them all. Marcel who was a familiar face, a warm and witty presence, a part of my childhood before he became, for me, a figure, no longer Marcel but Marcel Duchamp. Of course, in Cadaqués, you’d see Dali’s name everywhere, on postcards, mugs and tacky souvenirs. And you would occasionally run into him, with his funny moustache and walking cane, followed by the ever-present, ghostly Gala, his wife. They were unavoidable, but they were not in my Pantheon, whereas Marcel had become something of a spiritual father, someone paradoxically brought closer by his mystery, and the fact that everyone thought (wrongly, as it turned out) that he had ceased all artistic activity.

Meanwhile, back at the Café Meliton, at 5:30 sharp, a fellow walked in and sat across from Marcel. It was often a tall Swede. A wooden chess board was immediately brought to them. Glasses and cups were removed. At that point, I knew I had to shut up. The serious business was about to begin. I didn’t know much about chess at the time, so I don’t remember what openings Duchamp favored, or anything about his style of play. All I can say is, however dramatic the confrontation might have been, Marcel kept focused, samurai-like, periodically puffing on his cigar. I don’t remember whether he usually won, but it felt like he did, regardless of the outcome. My feeling was that he was less an aggressive player than one who knew how to exploit his opponent’s moves. I didn’t stay until the very end actually, because I thought that would have been indiscreet. What was at stake on the chess board seemed too intimate to watch.

Attracting Dust in New Zealand Lost And Found: Betty’s Waistcoat and Other Duchampian Traces

In 1983, three works by Marcel Duchamp found their way into the collection of the Museum of New Zealand Te Papa Tongarewa (Te Papa, Wellington, New Zealand). The following account demonstrates how two New York-based friends of Duchamp, Judge Julius Isaacs, and Betty Isaacs (Fig. 1) are tied to this course of events.

click to enlarge

Figure 1
Betty Isaacs and Julius
Isaacs, Wellington New Zealand,
1966. Copyright Fairfax NZ
Ltd. Courtesy Dominion
Post and Te Papa Museum

Moreover this essay exposes how this process, despite the diligence of Duchamp scholarship, led to the virtual disappearance of these works from the record. This essay will also draw (preliminary) conclusions about the significance of this process, both in terms of the new light shed on the fate of Duchamp’s work, and of the reception of this work outside the centers of art practice.⁽¹⁾ These works are the BETTY waistcoat (1961, New York), The Box in a Valise, (Edition D. 1961, Paris) and The Chess Players (copperplate etching, artist’s proof, 1965, New York). In addition, five 1st edition publications on Marcel Duchamp signed with personal dedications accompany the works.⁽²⁾ All these form part of the bequest of Judge Julius Isaacs to the National Art Gallery of New Zealand (NAG) in 1983.

The Duchamp works are the most important items in a gift of over 200 artworks, publications, and articles donated to the museum by the estate of Mrs. Betty and Judge Julius Isaacs, who were New York-based friends of Marcel Duchamp. The bequest of Judge Julius Isaacs, as characterized by Betty Isaacs, born in Tasmania, Australia and a one-time New Zealand resident between 1886 and 1913, is an eclectic range of over 80 sculptures, of both carved and cast forms. These were made during Isaacs’ career as a sculptor after graduating from the Cooper Union Art School in 1928. The bequest also contains 45 amateur paintings by Julius Isaacs, a small grouping of artworks by the American artist Larry Rivers, and works by two important New Zealand expatriates Frances Hodgkins (NZ/London) and Billy Apple (NZ/London/New York). The bequest also originally contained a large number of books which found their way into the NAG or other Wellington libraries, or, deemed to be of little value, were otherwise thrown into the rubbish bin.

Duchamp’s works stand out in relation to the rest, as the entire Bequest was accepted on the basis of the Duchamp articles, as well as the biographical association Betty Isaacs has with New Zealand. This was a clear sign of the museum’s recognition of Marcel Duchamp’s significance and their desire to acquire such works for their collection. History would demonstrate that this was an astute and canny move, as unique works by Duchamp were rarely available or in art market circles.⁽³⁾ Such rarity has caused consternation for those wishing to collect works by the artist who has eclipsed other 20th Century figures as holding the central importance to the history of contemporary art.

click to enlarge

Figure 2
Marcel Duchamp,
Boîte-en-valise
series G, 1968

Of the various artworks by Duchamp in the bequest, the following can be recorded. The Box in a Valise (Fig. 2) contains 68 unnumbered items enclosed in a light-green cloth and signed by Marcel Duchamp in blue ball-point pen, characteristic of the edition of 30 boxes assembled by Jacqueline Matisse Monnier in Paris, 1961.⁽⁴⁾ While this may have been a gift directly from Duchamp, no dedication appears within it. However, the Chess Players (Fig. 3) is indeed a gift from Duchamp to the Isaacs. It is an unnumbered artist’s proof, inscribed on the lower left in pencil ‘epreuve d’artiste,’ dedicated ‘pour Betty and Jules Isaacs’ in pencil on the lower centre, and signed and dated in pencil on the lower right ‘Marcel Duchamp/1965.’ This print belongs to a series of etchings engraved after Duchamp’s charcoal drawing, Study for Portrait of Chess Players (1911) (Fig. 4). The first series of etchings were a limited edition of 50 proofs, printed in black on handmade paper and hand numbered 1/50-50/50; plus ten artist’s proofs (one of which was a gift to the Isaacs).⁽⁵⁾ A single print from this edition was given to each of the artists who had contributed to the group exhibition A Homage a Caïssa. This exhibition was arranged by Duchamp in which works by selected artists were sold for the benefit of the Marcel Duchamp Fund of American Chess.

click images to enlarge

Figure 3
Figure 4

Marcel Duchamp, The
Chess Players, 1965
Marcel Duchamp, Study
for Portrait of Chess
Players, 1911

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Figure 5
Marcel Duchamp, Betty
Waistcoat, 1961. Bequest
of Judge Julius Isaacs,
New York (1983). Collection
of the Museum of New
Zealand Te Papa Tongarewa

The BETTY waistcoat (Fig. 5) is signed ‘Marcel Duchamp/1961’ in blue ball-point pen on the inside lining. Belonging to the series “Made to Measure” (1957-1961), this modified readymade is catalogued by Arturo Schwarz in The Complete Works of Marcel Duchamp as ‘present location unknown’. Schwarz writes, “Duchamp designed this waistcoat for Isaacs, a New York jurist and close friend (The occasion of the gift is unknown)”.⁽⁶⁾ The BETTY waistcoat is another instance of Duchamp’s habit to sign works and then to send these works to his peers, friends, or family. Three out of the four waistcoats from the series, “Made to Measure,” were gifts: the TEENY waistcoat (Fig. 6) was a gift from Duchamp to his wife in 1957, and the SALLY waistcoat (Fig. 7) was a gift to his son-in-law Paul Matisse on the occasion of his marriage to Sarah “Sally” Barrett on December 27, 1958. The fourth, the PERET waistcoat (Fig. 8), was named after Duchamp’s friend Benjamin Péret.⁽⁷⁾ The BETTY waistcoat was in all likelihood presented as a gift to the Isaacs for their 40th wedding anniversary (celebrated on September 11 1961). In a 1st edition copy of Richard Hamilton’s typographic translation The Bride Stripped Bare and Her Bachelors, Even (1960), gifted to the Isaacs, Duchamp pens: “dear Betty, dear Jules en attendant le gilet, affectueusement Marcel et Teeny” (Fig. 9) – here is a short correspondence setting up an exchange in the production of the work of art, one that demonstrates the awareness Marcel and Teeny would have had of the Isaacs’ forthcoming wedding anniversary. This is backed in 1967 when Duchamp penned a dedication to the long union of the judge and the sculptress: theirs was “an amicable institution.” (Fig. 10)

click images to enlarge

Figure 6
Figure 7
Figure 8

Marcel Duchamp,
Teeny Waistcoat, 1957
Marcel Duchamp,
Sally Waistcoat, 1958
Marcel Duchamp, Peret
Waistcoat, 1958

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Figure 9
Figure 10

Page from The Bride Stripped Bare
by Her Bachelors, Even (1960),
Richard Hamilton. Collection of the
Museum of New Zealand Te Papa Tongawera
Page from The World of Marcel Duchamp,
187-, Calvin Tomkins inscribed by Marcel
Duchamp: “pour Betty et Judge Isaacs/an amicable
Institution/et affectueusement/Marcel Duchamp/1967.”
Collection of the Museum of New Zealand Te Papa Tongarewa.

click to enlarge

Figure 11
Marcel Duchamp, Couple
of Laundress’s
Aprons, 1959

A waistcoat, ‘made to measure’ through tailoring, recalls Duchamp’s earliest thought for the term ‘readymade’ as an article of clothing available and ready to wear. A waistcoat, when worn, constitutes a union of sorts to the body. Through linguistic ploy, the letters B. E. T. T. Y (spelled in a 24-point lead font) are individually affixed to the waistcoat as buttons, and spell the name of Julius Isaacs’ wife in mirror reverse. By threading buttons Isaacs joins with his wife, a union that evokes an erotic connotation – “considering the fact that Duchamp’s most celebrated work is based on the theme of a bride being stripped bare, any piece of wearing apparel used in his art could carry the potential for a more erotic meaning”.⁽⁸⁾ Waistcoats were not the only garments used by Duchamp at this time; during the same period that the waistcoats were made for the series “Made to Measure” (1957-61), Duchamp also made the Couple of Laundress’s Aprons (1959, Paris) (Fig. 11), which are erotic garments of clothing of another (gendered) sort: domestic, not suited attire.

* * *

Betty Isaacs, forming the first-hand link to New Zealand, is the principal connection behind the bequest of Judge Julius Isaacs and New Zealand’s National Art Gallery. Betty Isaacs was born Ettie Lewis on September 2, 1894 in Hobart, Tasmania, and died aged 76 on February 4, 1971 in New York. She was one of four children to Annie Lewis (nee Cohen) a New Zealander, and Henry Lewis an Australian, who were married in Hobart in 1882. Upon the death of Henry Lewis in 1886, the Lewis family (Annie and children Gabriel, Rachel, Ettie and Rosalie) were brought by Betty’s grandparents, Mr. and Mrs. Benjamin Cohen, to Wellington, New Zealand where Betty was educated. Betty’s mother married a second time to Maurice Ziman on January 27, 1896 and together began a new family, eventually producing three children. In 1902, the family traveled to London and New York, returned to Wellington in 1903, and soon thereafter suffered a tragic setback: the death of Betty’s youngest sister Rosalie in 1905, and Betty’s 49 year old mother Annie Lewis in 1906. Betty remained in New Zealand for seven years, completed her education, and then, at age 19, departed for New York in 1913.⁽⁹⁾

Upon arriving in New York, Betty Isaacs changed her name and reverted back to her original family name Lewis. She trained and then served as a librarian between the years of 1915 and 1918. She then, for a period, worked at the New York City Public library where she met Julius Isaacs. They married on September 11, 1921. Between the years of 1925 and 1928 Betty Isaacs trained at the Cooper Union Art School and emerged as a sculptor in the late 1930’s after working as a designer in the textiles industry. Betty Isaacs’ debut exhibition was in 1953 at the Hacker Gallery, New York, and included 38 items of sculpture, 5 ceramic pictures and 2 mosaic panel drawings. The exhibition drew varied reviews from the New York Times staff critics: “Betty Lewis Isaacs . . . devotes herself to portraying animals from fish to polar bears, and she has evolved a manner of representing them that is naturalistic without being photographic”.⁽¹⁰⁾ But one critic found that “her animals tend to be petty,” instead favoring: “an inscrutable, poetic “Girl’s Head” just a little in the Zorach vein”.⁽¹¹⁾ Isaacs worked with a range of materials including wood, stone, alabaster and bronze. She was an enthusiast of wood in particular, and on a 1966 return trip to New Zealand hoped to find examples of carvings in the native Totara and Kauri.⁽¹²⁾

It was Betty Isaacs’ fond remembrance of her time spent in New Zealand that drew her and Julius Isaacs back to visit between August 25 and September 15, 1966. These memories are evident in the poem written by John Cage that recalls Isaacs’ early pastimes living in the suburbs of Wellington. In Number 66 of his many one minute read aloud stories published in Silence (1961) and A Year to Remember (1968), Cage writes:

Betty Isaacs told me that when she was in New Zealand she was informed that none of the mushrooms growing wild there were poisonous.So one day when she noticed a hillside covered with fungi,she gathered a lot and made catsup.When she finished the catsup, she tasted it and it was awful.Nevertheless she bottled it and put it up on a high shelf.A year later she was housecleaning and discovered the catsup,which she had forgotten about.She was on the point of throwing it away.But before doing this she tasted it.It had changed color.Originally a dirty gray, it had become black, and, as she told me, it was divine, improving the flavor of whatever it touched.⁽¹³⁾

John Cage was a friend of Betty Isaacs who he would have met sometime after 1941 in the close neighborhood of Greenwich Village. Cage wrote about Betty Isaacs as a subject for the above story and one other, and forms the connection to the Duchamps during the period he built a closer friendship with Marcel and Teeny Duchamp in the early 1960s in Greenwich Village. He would have introduced the Isaacs who lived at 21 East 10th Street in the years between 1941 and Julius Isaacs’ death in 1979, near the Duchamp’s 28 West 10th Street apartment. Prior to Marcel and Teeny’s departure from New York in 1964, Cage often visited the Duchamps at their apartment. In an interview with Calvin Tomkins, John Cage commented, “I was living in the country then, and I would bring wild mushrooms I had gathered and a bottle of wine, and Teeny would cook dinner.”⁽¹⁴⁾ It is highly probable that Betty Isaacs would share stories of New Zealand over a dinner of mushrooms, in the company of her husband Julius, John Cage and Marcel and Teeny Duchamp. The relationship Marcel and Teeny Duchamp had with the Isaacs does not feature significantly in published literature. Judge Julius Isaacs was a patron of the arts, particularly of music and writing, and according to Arturo Schwarz, a “close friend” of Marcel Duchamp.⁽¹⁵⁾ Julius Isaacs was born in 1896 and died in New York on his 83rd birthday on December 31, 1979. After studying at the City College, City University of New York where he was valedictorian and class president in 1917, he trained in law and his public service began in 1934. During the 1940’s he became Acting Corporation Counsel of the City of New York and was appointed as a New York City Magistrate by Mayor Fiorello H. LaGuardia. Julius Isaacs may well have been acquainted to Duchamp through legal practice or through social circles of New York arts patrons. Little extant correspondence (if any) between the Isaacs and Duchamp’s still remains.⁽¹⁶⁾ Betty Isaacs and Judge Julius Isaacs did not have any children, and Betty’s surviving family members in New Zealand are found on Betty’s stepfather’s side, Maurice Ziman, who, while remembering meeting the Isaacs on their 1966 New Zealand visit, have no knowledge of the extent of their New York based lifestyle or their friendships that developed in the 1960s.

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Figure 12
Page from Marcel Duchamp
(1959), Robert Lebel
(translated by George Heard
Hamilton). Collection of
the Museum of New Zealand
Te Papa Tongarewa.

The nature of the Duchamp/Isaacs friendship is verified by four short personal inscriptions written by Duchamp in publications gifted to the Isaacs, now in Te Papa’s works on paper collection. Dating from 1959 with the publication of Robert Lebel’s Sur Marcel Duchamp in English (translated by George Heard Hamilton) these read: “pour Betty, pour Jules Isaacs le magician des portes qui, pour lui, ne sout jamais ni ourestes . . . en grande affection, Marcel Duchamp N.Y. Oct. 1959.”(Fig. 12) Secondly, the aforementioned dedication in Richard Hamilton’s The Bride Stripped Bare by Her Bachelors, Even (1960): “dear Betty, dear Jules en attendant le gilet, affectueusement Marcel et Teeny”. On the inside cover to the catalogue NOT SEEN and/or LESS SEEN of/by MARCEL DUCHAMP/RROSE SELAVY 1904-64 (Cordier & Ekstrom Gallery, N.Y., 1965) Duchamp scribed: “To the judge of all things, dear Jules and Betty. Marcel.” And, as also previously noted, in Calvin Tomkins’ The World of Marcel Duchamp 1887 – (1966): “pour Betty et Judge Isaacs, an amicable Institution, et affectueusement. Marcel Duchamp, 1967.” One can conclude that their friendship was based through contact in Greenwich Village after 1941, and that these were also strengthened by John Cage’s friendship with Betty Isaacs. The ‘BETTY’ waistcoat and the personal dedications stand as proof, and from these are gleaned certain insight into the nature of their friendship.

Fondness for New Zealand was shared by both Betty and Julius Isaacs. On occasion, they dined and entertained the Minister of New Zealand’s foreign affairs, and over the years entertained other notable New Zealanders at their New York home: including Paul Gabites and Richard Taylor (New Zealand Consular-Generals), Sir Thaddeus McCarthy (Judge and president of the New Zealand Court of Appeal), John Hopkins (symphony conductor and co-founder of the New Zealand National Youth Choir) and the New Zealand expatriate artist Douglas MacDiarmid.⁽¹⁷⁾ Their bequest contains works by two of New Zealand’s most significant expatriate artists, Frances Hodgkins (NZ/London) and Billy Apple (NZ/London/New York). In addition, on June 1966, Julius Isaacs managed an exhibition of an important New Zealand expatriate, the writer and novelist Katherine Mansfield, for the 34th annual International Congress of the P.E.N. Club entitled “The Writer as Independent Spirit”.⁽¹⁸⁾ Shortly after this congress, the Isaacs embarked on their New Zealand visit.

The Isaacs’ relationships with the New Zealand Consulate in New York underpin connections established for Betty Isaacs’ work in the NAG in New Zealand. Paul Gabites’ efforts (through photographs) to bring her work to the attention of the Selection Committee of the NAG in 1964, was met with “great interest.” However, the Selection Committee’s reply to Paul Gabites in 1964 also informed him that two purchases, a Barbara Hepworth and a Derain oil painting, had “more than absorbed our import collection for the next two years!” They added that “the members, however, have been made aware of the work of Betty Isaacs and we are that much ahead”.⁽¹⁹⁾ It was after Betty Isaacs’ death in 1971 that Julius Isaacs, with increased energies, offered her works to the NAG, which ultimately formed further origin for the later bequest. In 1972, nearly one year after Betty Isaacs’ death, Julius Isaacs wrote to Melvin Day, the director of the NAG, outlining brief biographical details of his wife Betty Isaacs. Two years later, the Selection Committee agreed to accept one work by Betty Isaacs, a gift sent from Julius Isaacs. In 1974, New Zealand’s Minister of Overseas Trade, Mr. Walding, accepted as ‘a gift to the Government and people of New Zealand’ the abstract sculpture “Torso in Bronze” (1962, New York). This transaction forms a definite trace to the bequest later confirmed in 1981 to the NAG by the executors of Judge Julius Isaacs’ estate.

Instruction left in Julius Isaac’s will asked the executors of his estate (representatives of the Chemical Bank Corporation, New York) to determine a suitable repository for the collection of his art works and related items either in the United States or abroad.⁽²⁰⁾ Isaacs’ will, dated August 29 1979, reads under paragraph (U) of Article Second: “I give and bequeath all my books and art objects, including paintings, sculpture and drawings to such museums and libraries in this country, Israel and New Zealand, as my executor shall select, to be kept as intact as possible or distributed separately to various such institutions, to be known as the BETTY LEWIS ISAACS and JULIUS ISAACS COLLECTION or COLLECTIONS . . . . I urge my executor to follow the advice of MEYER SHAPIRO and DOROTHY MILLAR as to the proper allocation of these works of art, especially of the sculpture of BETTY LEWIS ISAACS so that her reputation as an artist may best be preserved.”⁽²¹⁾

The initial offer of the estate’s collection was sent by L. David Clark (representative executor) to the Secretary of the Art Galleries and Museums Association of New Zealand (AGMANZ) on 13 November 1980. Luit Bieringa, who was the vice-president of AGMANZ and director of the NAG, does not recollect the broad possible scope of benefactors for the bequest. Bieringa’s opportunity to view objects, works and books in the estate became the opportunity “to not miss out on something unique” making sure that “the sequence from Betty Isaacs and the Judge Julius Isaacs bequest to the National Gallery was a natural one”.⁽²²⁾ Furthermore, the trace of origins outlined in this article certainly support Bieringa’s claim and would have determined the executor’s decision.

click to enlarge

Figure 13
Telegram from Chemical Bank
Corporation (N.Y) to the NAG.
Postmarked 06 June 1981,
Wellington, New Zealand.
Archives of the Museum of New
Zealand Te Papa Tongarewa.

It was Bieringa who secured the bequest for New Zealand. With AGMANZ support, Bieringa entered into a protracted process of disposition and scheduled a meeting with Paul F. Feilzer, the Senior Trust Officer of Chemical Bank Corporation, for February 8 and 9 1981 in New York, when he viewed selected works in the bequest. The collection of artworks and other related items in the Isaacs estate had been appraised by William Doyle Galleries, Inc., New York, who appraised (in U.S. dollars) the Betty Waistcoat at $20,000.00; the Chess Players at $2,000.00 and the Box in a Valise at $3,000.00. The bequest of Judge Julius Isaacs was confirmed via telegram to Luit Bieringa on June 6, 1981 from the Chemical Bank Corporation (Fig. 13), and the Board of Trustees of the National Art Gallery voted unanimously to approve acquisition on June 11, 1981. Although this approval was passed in June 1981, and Bieringa personally signed the receipt and release of the bequest in New York on November 9, 1981, it took until February 1983 before the works were formally accessioned into the national collection.

click to enlarge

Figure 14
Inventory of the Bequest
of Judge Julius Isaacs,
shipped by Day & Meyer,
Murray & Young Corp. –
Packers, Shippers and Movers of
High Grade Household Effects and
Art Objects (N.Y.) (23 November 1981).
Archives of the Museum of New
Zealand Te Papa Tongarewa.

Delays are not an uncommon occurrence a propos a peripheral location. The news of obtaining the bequest originally in June 1981 was in fact new news again by the time of its actual arrival in Wellington and its formal acquisition in 1983. The delay was due to the distance the freighted works had to travel across the Pacific Ocean (and also due in part to the large size of the entire bequest). The total freight was comparatively expensive (estimated at $5,700.00 US dollars), yet approval of the bequest was conditional on NAG’s meeting associated costs for its climate-controlled freight to New Zealand. The full inventory of the bequest of Judge Julius Isaacs was shipped by Day & Meyer, Murray & Young Corp. — Packers, Shippers and Movers of High Grade Household Effects and Art Objects (Fig. 14), and departed New York on the Malmros Monsoon on November 23, 1981, arriving in New Zealand on December 18, 1981 through Auckland. The shipment reached its final destination at the National Art Gallery in Wellington in February 1982. It took another full year for formal acquisition processes to be completed, but, finally, ‘Duchamp’ had arrived in New Zealand.⁽²³⁾

Bieringa, delighted by the acquisition of Duchamp’s works, writes: “As a young country New Zealand cannot, apart from its superb indigenous cultural assets, boast of rich assets reflecting the art historical developments of the Western world. As such several of the works contained in the Isaacs Estate, in particular the Duchamp items, will have a significant impact with the art museum collections in New Zealand, whereas their retention in Europe and America will only marginally affect the stature of any significant collection. Given the limited financial resources of our museums the impact of the Isaacs collection will be substantial.”⁽²⁴⁾

While the bequest was somewhat serendipitous, Bieringa exhibited a presence of mind in securing a small but significant collection of Duchampian works and articles for the NAG, especially at a time contemporaneous to a wider desire in collecting works by Duchamp. The bequest belongs to a limited transfer of his works to international museum collections after the artist’s death. Museums and curators arrived at the significance of Duchamp’s work much later than that of other 1960’s New York based artists, and so a period of institutional interest in Duchamp’s work grew belatedly.⁽²⁵⁾ Within a period in which very few Duchamp works might have actually been purchased or exchanged, the National Art Gallery of New Zealand succeeded in obtaining a small but unique collection.

Bieringa’s enthusiasm for the transaction made in 1983 has not been sustained by the institution that had facilitated the bequest. Indeed, The Box in a Valise, documented on its acquisition, has been shown on two occasions: at the Auckland Art Gallery, for the exhibition ‘Chance and Change’ in 1985, and more recently in 2003 at the Te Papa Museum, in ‘Past Presents’ an exhibition of works focusing on gifts to the collection. The BETTY waistcoat and The Chess Players were also documented upon their acquisition, but Te Papa museum art catalogue files have not recorded any further movement of these items for exhibition, either within the institution or beyond. In addition, the 80 sculptural works by Betty Isaacs have never had any comprehensive exhibition, and remain in their brown cardboard boxes in storage. Duchamp’s works have never formed a collective basis for any exhibition in New Zealand, though such an exhibition is long overdue. Therefore, akin to one of Duchamp’s time based pleasures (from his delayed work on the Large Glass) these three Duchamp works have, as in that figure of speech, attracted dust.

* * *

So what can be made of the fate of these Duchampian artworks? Firstly, their disappearance into a Museum Collection in a small city in an isolated country at the “bottom” of the South Pacific has effectively meant they were lost (until now) to Duchamp scholars. This fact starkly reminds us of New Zealand’s peripheral situation vis-à-vis the centres of culture and for which delays are a particular and peculiar circumstance. Yet, delay is also a favored operation and strategy of Marcel Duchamp and the sequential ‘delays’ to the uptake of Duchamp’s work in the 20th Century suggests that the marginal geographical location where these three Duchamp works are located is an affirmation of the ubiquity of their maker. These facts only impresses a stronger urge to make some sense out of these works within the cultural context in which they reside, in relation to the wider operations and strategies of Marcel Duchamp’s work. Rather than simply celebrate their re-discovery, I would argue the fate of these works actually tallies with aspects of Duchamp’s practice and this approach would stitch the works back into the picture.

click to enlarge

Figure 15
Marcel Duchamp as
Rrose Sélavy,
1921, photographed by Man
Ray, retouched by Duchamp

In attributing ubiquity one might think of Duchamp’s demeanor, his trans-gendered performance as Rrose Sélavy (Fig. 15), his employed translation and turns in meaning between French and English, his personal history and status as an expatriate between Paris and New York, travelling and slipping between varying reputations on both sides of the Atlantic. It is Duchamp’s ability to resist classification, at variance to other 20th century artists, that spawned a highly mobile legacy across historical periods and across generations of art makers. It is here that register is found with the Isaacs’ bequest: not for the first time material and visual artifacts by Duchamp’s hand slipped across national borders, arriving in a new context. The Isaacs’ bequest is part of a navigation of ‘Duchamp’ beyond the cultural centers within which he had historically operated. Marcel Duchamp’s legacy functions in the New Zealand context, as elsewhere, as an inescapable and indispensable example for local artists, but who have developed their distinctive practices not only as faint echoes of mainstream models but as canny adaptations within the limits of a local situation.

Returning to the dedications by Duchamp to the Isaacs, the earliest of which was signed by Duchamp in 1959, and the last in 1967, it is within this period that Duchamp was somewhat of a traveling inscriber: a (supposedly) retired artist, pen in hand, authorizing and laying claim to various reproductions of his work. “The sixties are notably the replica years – replicas of his own work, made by others and signed by Duchamp”.⁽²⁶⁾ Here the works in the bequest of Judge Julius Isaacs (1983) offer a vital model to a culture that has historically relied on the reproducibility of art and the beneficiates of “friends” to participate in wider culture. New Zealand’s position in the history of art is necessarily replete with (international) comings and goings: replete with networks formed overseas, of generating acquaintances, friendships and unions to serve as contacts and to sustain lines of communication upon returning. It is befitting that gifts from Duchamp are, in turn, gifts to New Zealand’s National Museum, made under the auspices of friends of this country.

Notes

1. This research is ongoing. I would like to acknowledge Christina Barton (Art History, Victoria University of Wellington, New Zealand) for considerable support in writing this article and her teachings.

2. A complete list and the Written dedications appear later in this article.

3. Francis M. Naumann discusses Duchamp’s relation to the art market at length in “Duchampiana II: Money Is No Object,” Art in America (March 2003): 67-73, and in “Marcel Duchamp: Money Is No Object. The Art of Defying the Art Market,” Tout-Fait: The Marcel Duchamp Studies Online Journal 2.5 (2003): News.

4. Arturo Schwarz, The Complete Works of Marcel Duchamp (New York: Delano Greenidge Editions, 2000) 764.

5. Ibid. 853.

6. Ibid. 808-9.

7. Ibid.

8. Francis M. Naumann and Hector Obalk, eds., Affectionately Marcel – The Selected Correspondence of Marcel Duchamp. (London: Thames and Hudson, 2000) 187.

9. Biographical details have been established through Julius Isaacs’ Letter to Melvin Day (10 Oct. 1972) and with descendents of Betty Isaacs: in email correspondence with Rob Golblatt “Betty Isaacs,” E-mail to the author (17 April 2005), and in personal interview with David Heinemann (30 May 2005).

10. “Isaacs Debut Show,” New York Times (12 Dec. 1953): 23.

11. “Women Sculptors at Galleries Here,” New York Times (12 Dec. 1953): 23.

12. “Sculptress Spent Childhood in New Zealand,” The Evening Star [Dunedin] (9 September 1966): page number unknown.

13. John Cage. “Untitled” poem, cited at http://www.lcdf.org/indeterminacy/s.cgi?66 (20 April 2005). Thanks to Rob Goldblatt who in an idle moment stumbled upon this poem whilst searching the web for Betty Lewis.

14. Calvin Tomkins, Duchamp – a Biography. (London: Pimlico, 1998) 411.

15. Julius Isaacs, Letter to Melvin Day (10 October 1972).

16. See “Historical Sketch,” P.E.N American Center Archives. Princeton University Library, http://libweb.princeton.edu/libraries/firestone/rbsc/aids/pen.html (04 June 2005).

17. Stuart MacClennan, Letter to Paul Gabites (24 September 1964).

18. Schwarz, op. cit. 809.

19. Francis M. Naumann, one authority on Duchamp’s personal correspondences, writes “I have never come across any references to Judge Julius Isaacs or to Betty Isaacs in my research through the extant Duchamp correspondence.” “Re: Duchamp correspondences- Betty and Judge Julius Isaacs/ New Zealand connections,” E-mail to the author (4 April 2005).

20. L. David Clark Jr., Letter to Cpt. J. Malcolm (13 November 1980).

21. Julius Isaacs, “Receipt and release of the bequest of Judge Julius Isaacs to the National Art Gallery of New Zealand” (November 9 1981).

22. Luit Bieringa, Personal interview with the author (17 May 2005).

23. However, this was not the first time works by Marcel Duchamp had arrived to New Zealand. 78 works from The Mary Sisler Collection toured the country in 1967.

24. Luit Bieringa, Letter to David Cark Jr (20 May 1981).

25. See Dieter Daniels, “Marcel Duchamp: The Most Influential Artist of the 20^th Century?,” Museum Jean Tinguely Basel. Ed. Marcel Duchamp. (Ostfildern: Hatje Cantz, 2002) 25-28.

26. Naumann and Obalk, op. cit. 15. For a history of signed replicas and editions in this period see Naumann’s “Proliferation of the Already Made: Copies, Replicas, and Works in Edition, 1960-64,” Marcel Duchamp: The Art of Making Art in the Age of Mechanical Reproduction (Amsterdam: Ludion Press, 1999) 208-254.

Bibliography

Bieringa, Luit. Personal Interview. 17 May. 2005

_____. Letter to L David Clark Jr. 20 May 1981. Archive file MU00000-4-23-2. Museum of New Zealand Te Papa Tongarewa. Wellington, New Zealand.

Cage, John. “Untitled” poem. 20 April 2005. http://www.lcdf.org/indeterminacy/s.cgi?66.

Clark Jr., L. David. Letter to the Art Galleries and Museums Association of New Zealand Inc. 13 November 1980. Archive file MU00000-4-23-2. Museum of New Zealand Te Papa Tongarewa. Wellington, New Zealand.

_____. Letter to Cpt. J. Malcolm. 13 November 1980. Archive file MU00000-4-23-2. Museum of New Zealand Te Papa Tongarewa. Wellington, New Zealand.

Daniels, Dieter. “Marcel Duchamp: The Most Influential Artist of the 20^th Century?” Marcel Duchamp. Ed. Museum Jean Tinguely Basel. Ostfildern: Hatje Cantz, 2002.

Goldblatt, Rob. “Re: Betty Isaacs”. E-mail to the author. 17 April. 2005.

Heinemann, David. Personal Interview. 30 May. 2005.

“Historical Sketch.” P.E.N American Center Archives. Princeton University Library. 04 June 2005. http://libweb.princeton.edu/libraries/firestone/rbsc/aids/pen.html

“Isaacs Debut Show”. New York Times 12 Dec. 1953: 23.

Isaacs, Julius. Letter to Melvin Day. 10 Oct. 1972. Archive file MU00000-4-23-2. Museum of New Zealand Te Papa Tongarewa. Wellington, New Zealand.

_____. Estate of Julius Isaacs. “Receipt and release of the Bequest of Judge Julius Isaacs to the National Art Gallery of New Zealand.” November 9 1981. Archive file MU00000-4-23-2. Museum of New Zealand Te Papa Tongarewa. Wellington, New Zealand.

Lensing, Mildred. “With Chisel or Spoon Mrs. Isaacs Creates.” Courier Journal

[Louisville] 8 Oct. 1955.

MacClennan, Stuart. Letter to Paul Gabites. 24 September 1964. Archive file MU00000-4-23-2. Museum of New Zealand Te Papa Tongarewa. Wellington, New Zealand.

Naumann, Francis M. “Proliferation of the Already Made: Copies, Replicas, and Works in Edition, 1960-64)”. Marcel Duchamp: The Art of Making Art in the Age of Mechanical Reproduction. Amsterdam: Ludion Press, 1999. 208-254.

_____. “Re: Duchamp correspondences- Betty and Judge Julius Isaacs/ New Zealand connections.” E-mail to the author. 4 April 2005.

_____. “Duchampiana II: Money Is No Object”. Art in America Mar. 2003: 67-73.

_____. “Marcel Duchamp: Money Is No Object. The Art of Defying the Art Market”. Tout-Fait: The Marcel Duchamp Studies Online Journal 2.5 (2003): News.

Naumann, Francis M and Obalk, Hector. Ed. Affect Marcel – The Selected Correspondence of

Marcel Duchamp. London: Thames and Hudson, 2000.

Schwarz, Arturo. The Complete Works of Marcel Duchamp. New York: Delano Greenidge Editions, 2000.

Taylor, Richard. Letter to Julius Isaacs. 21 July 1966. Archive file MU00000-4-23-2. Museum of New Zealand Te Papa Tongarewa. Wellington, New Zealand.

Te Papa Museum of New Zealand Te Papa Tongarewa Museum art catalogue references: Betty Waistcoat, Item No: 2810, Accession No: 1983-0032-229; The Chess Players Item No: 2330, Accession No: 1983-0032-179. Te Papa Museum of New Zealand Te Papa Tongarewa. Wellington, New Zealand.

Tomkins, Calvin. The World of Marcel Duchamp, 1887-. New York: Time Incorporated, 1966.

_____. Duchamp – a Biography. London: Pimlico, 1998.

William Doyle Galleries Inc. “Summary and appraisal of the Judge Julius Isaacs Bequest to the National Art Gallery of New Zealand.” 16 June 1980. Archive file MU00000-4-23-2. Museum of New Zealand Te Papa Tongarewa. Wellington, New Zealand.

“Women Sculptors at Galleries Here”. New York Times 12 Dec. 1953: 23.

Ziman, Vera. Letter to Luit Bieringa. 2 November 1981. Archive file MU00000-4-23-2. Museum of New Zealand Te Papa Tongarewa. Wellington, New Zealand.

The Bachelor Stripped Bare by Cabri Geometre, Even

1.1. The Bride stripped bare by her Bachelors, even

The Bride stripped bare by her Bachelors, even commonly known as The Large Glass (or simply The Glass) is the masterwork of Marcel Duchamp, and it is also one of the most representative and influential works of art of the 20th century. Duchamp spent several years completing his project, but the work was left unfinished in 1923. The actual execution of the work starts in 1915, but the first ideas date back to the Summer of 1912.

Duchamp planned each detail of this complex work, and left a huge corpus of notes, sketches, and blueprints, documenting not only his intentions and the desired final outcome, but also the different executive techniques for each single part of the Glass. These notes were published by Duchamp himself in three main collections.

The first one, edited in 1914, commonly known as The 1914 Box (Fig. 1) (because of the Kodak box containing the reproductions of the originals) contains sixteen notes and drawings; the second collection, dated 1934, is known as The Green Box (Fig. 2) (because of the green color of its binding) and contains a larger group of notes and sketches; finally, the third collection, named A l’infinitif but commonly known as The White Box, (Fig. 3) edited in 1966, contains for the most part a quantity of notes regarding mathematical
speculations on the fourth dimension, directly related to the Glass and other works. Duchamp asserted that this huge apparatus of notes must be considered an integral part of the Glass.
click to enlarge

Figure 1
Marcel Duchamp, The Box of 1914,
1913-14
Figure 2
Marcel Duchamp, The Green Box,
1934
Figure 3
Marcel Duchamp, The White Box,
1964

Figure 4
Marcel Duchamp, Bride’s Domain, in the
Large Glass(detail), 1915-23

Figure 5
Marcel Duchamp,Bachelors Apparatus, in the
Large Glass (detail), 1915-23

Two main parts constitute the Glass: the higher and the lower ones. The higher part is the realm of the Bride, (Fig. 4) and according to Duchamp’s intention, it depicts the 2D
projection of a 3D shadow of a 4D Bride. Thus, the realm of the Bride is intended to be a true 4D realm, which however cannot really be seen, since it is as depicted on a 2D support (the sheet of glass). The lower part is the realm of the Bachelors (Fig. 5) or the Bachelor apparatus (or utensil). In contrast with the Bride’s realm, the Bachelor’s realm is a 3D world. Thus it is imperfect in comparison with the 4D higher realm. In a note belonging to the White Box (but already issued with some minor variants in the Green Box), Duchamp wrote:

Principal forms, imperfect and freed
The principal forms of the bachelor apparatus or
utensil are imperfect:
Rectangle, circle, square, parallelepiped, symmetrical handle; demisphere.-i.e. these forms are mensurated (interrelation of their actual dimensions and relation of these dimensions to the destination of the forms in the bachelor utensil.)
In the Bride – the principal forms will be more or less large or small, no longer have mensurability in relation to their destination: a sphere in the Bride will have any radius (the radius given to represent it is “fictitious and dotted.”)

Likewise, or better still, in the Pendu Femelle parabolas, hyperbolas (or volumes deriving from them) will lose all connotation of men-surated position. ⁽¹⁾

Thus, the two parts of the Glass represent two distinct realities. The lower realm is imperfect and only tries to emulate the higher dimensionality of the Bride’s realm by means of expedients and tricks (very effective, as we shall see).

These tricks are largely based on perspective representations and on elementary geometric transformations. These transformations will gradually become more and more general, and, as we pass through the threshold of the horizon (the area which divides the two parts of the Glass) from the lower half into the 4D realm of the Bride (following the pathway described by Duchamp), we finally reach a world where, abandoning any metrical trait of the objects, only more general geometrical transformations take place: the topological ones. The subject is already thoroughly discussed by scholars ⁽²⁾.

Perspective is not only the drawing system used by Duchamp to compose the lower part of the work, but also (and better) perspective in itself is one of the most important themes of the Glass. Indeed, we have quite explicit statements by Duchamp, such as the following,
given during a famous interview with Pierre Cabanne, that supports this contention:

Duchamp: […] In addition, perspective was very important. The “Large Glass” constitutes a rehabilitation of perspective, which had then been completely ignored and disparaged. For me, perspective became absolutely scientific.

Cabanne: It was no longer realistic perspective.

Duchamp: No. It’s a mathematical, scientific perspective.

Cabanne: Was it based on calculations?

Duchamp: Yes, and on dimensions. These were the important elements. […] ⁽³⁾

Scholars largely speculated (and still speculate) on the meaning of such a rehabilitated perspective, no longer having a realistic purpose, being instead a mathematical and
scientific procedure.

Duchamp’s authoritative biographer Calvin Tomkins wrote for instance:

Vanishing-point perspective, which gave the illusion of three dimensions on a two dimensional surface, had been abandoned by modern artists who wanted their art to be a real thing rather than an imitation of reality. Why, then, did Duchamp, who certainly shared that ambition, choose to master such a discredited device? Was he looking for a mathematical formula through which he could actually evoke the presence of a fourth dimension? Whatever serious ambition he may have had along these lines he abandoned soon enough.⁽⁴⁾

Rhonda Roland Shearer suggests that Duchamp could have used a complex technique based on the overlapping of several different perspectives at once. According to her, such
a technique could explain both some strange features in the historical photos of the readymade and the difficulties one encounters as he or she tries to recreate the perspective of the lower half of the Glass, starting from its original blueprint (plan and elevation)⁽⁵⁾. She says for instance:

Most Duchamp scholars have either accepted or praised Duchamp’s perspective skills. The problem remains, however, that I and a few other scholars have actually made 3-D models from Duchamp’s plans
— and none of us can find any one perspective projection view that matches Duchamp’s perspective drawings! Moreover, the process of trying to recreate the Large Glass perspective drawing from what a viewer would see of the 3-D model via perspective (equivalent to what one eye or camera lens sees) quickly becomes maddening. When you fit one part of the Large Glass model to its projection in Duchamp’s perspective drawing (say; part A, the ellipse in one wheel of the Chocolate Grinder, for example — see illustration 49A), the rest (parts B through Z) immediately fall out of place. We lose the fit of part A, and all the other parts C through Z, once part B is matched — etc.⁽⁶⁾

A few lines above, we also read:

My discovery that the strangely distorted Chocolate Grinder uses the same systematic characteristic approach also found in the hatrack, coatrack and urinal (and a large set of other examples not discussed in this essay) returns us to Duchamp’s words that I used at the beginning of this essay — a quotation that now bears repeating. ⁽⁷⁾

Shearer shows a complete map of “at least” 43 different viewpoints which could have been used by Duchamp for the perspective of the Glass. Unfortunately, Shearer’s article is mainly focused on Duchamp’s readymades. The procedure used to inspect the Glass’s perspective is only briefly described, and only supported by means of 3D animations.

In the present paper, I will describe with some details the procedures I used to check the perspective of the Bachelor apparatus and will present and briefly discuss the outcomes reached.

In addition, considering some serendipitous discoveries I made by moving the elements of the Bachelor, as a further thesis, I would like to point out that the internal motions of the Bachelor apparatus (carefully planned and described in the Notes by Duchamp himself)
could be considered ways that permit the Bachelors to emulate the higher dimensionality of the Bride.

1.2. General procedures and remarks

Cabrì Géomètre II⁽⁸⁾ is the software I
used to reconstruct the perspective of the Glass. It is a world wide known pedagogical software, commonly used to teach geometry in high schools, thus it is not specifically oriented to graphic applications or to professional 3D rendering, but instead it is aimed at building geometric objects (even very complex) which can be dynamically transformed according to well defined geometric constructions and rules.

The basic objects that Cabri furnishes are the basic geometric elements of Euclidean geometry, as usually taught at school, such as points, straight lines, segments, angles, polygons, conics, and so on.

Cabri works essentially on the plane, but following the rules of projective geometry, it makes it possible to represent 3D objects in perspective (or even higher dimensional objects, such as a hypercube, for instance).

Just such a feature interested me, as I intended to verify Duchamp’s statement about his mathematical, scientific use of perspective. Indeed my concern was to reconstruct the correct perspective of the Glass, starting from the detailed and precise metric information we read in the autograph sketches of the elevation and plan of the Bachelor apparatus (Duchamp carefully gave us even the exact position of the vanishing point).

As a second step, I intended to compare the aseptic geometric drawings obtained with Cabri, with the reproductions of the actual Glass and of its parts. To do that, I used a second tool developed for using Cabri in Internet-like environments: CabriJava⁽⁹⁾.

This program allowed me to superimpose Cabri figures on the corresponding reproductions by Duchamp and to adjust them in a continuous way until the figures and the reproductions matched (or did not).

Here is the key question: Which kind of adjustment is allowed in order to state that Duchamp’s perspective matches the mathematical construction?

To answer that question, let us consider the perspective construction of a simple parallelepiped. Once we have the metric values for both the plan and the elevation of the parallelepiped (refer to Applet 1)and once we choose the vanishing point VP and the ground line (i.e. the elements given by Duchamp with the sketches of the plan and the elevation of the Bachelor apparatus), a degree of freedom still remains: following the standard perspective rules, we have to choose a couple of corresponding straight lines r and r’, for example the diagonal AC and the corresponding diagonal A’C’ ⁽¹⁰⁾.

Applet
1 depicts the situation. You can drag the straight line r’ to modify the figure, but always obtaining a perspective consistent with the given data, i.e., the metric of the parallelepiped, its position in the space, and the position of the vanishing point and the ground-line.

Perspective constructions and adaptations of Duchamp’s originals have been made for the overall view of the Bachelor apparatus and for each of its main elements. We shall discuss them later with some details.Fig. 6 shows how Duchamp’s elevation and plan sketches were inserted in Cabri.⁽¹¹⁾.

Fig. 7 and Fig. 8 illustrate the two basic steps followed to construct the perspective rendering of an A point in the plan sketch, passing through the A’ image of A on the ground-plane, and then elevating it at the A’’ position, according to the position of A in
the elevation sketch.

click to enlarge

Figure 6
Duchamp’s elevation and plan sketches
inserted in Cabri
Figure 7
Two basic steps illustrating the construction of the perspective rendering
of a single point, given its position in plan and elevation sketches
Figure 8

2.1. The overall view

Let us start with the perspective of the overall view.

To make pictures more suitable for the internet (therefore with not too heavy files) the elements of the Bachelor apparatus are inserted schematically, just to check the correctness of their mutual positions according to the rules of perspective. The corresponding details for each inserted element are checked in separate figures.

click to enlarge

Figure 9
Marcel Duchamp, The Bride stripped
bare by her Bachelors, Even, 1913

Figure 10
The straight line r’

The overall perspective is compared with both the Glass and the preparatory sketch of 1913 named The Bride Stripped Bare by Her Bachelors, Even, like the Glass itself. We shall refer to it simply as the 1913 Sketch (Fig. 9).For the lower part of the actual Glass, see below Applet 2 and Applet 3). This double superimposition is necessary because the important element called the Toboggan, one of the most difficult pieces to render in perspective, is actually absent in the Glass (remember that it was left unfinished by Duchamp) while it is present in the 1913 Sketch.

In both Applet 2 and Applet 3, CabriJava has some problems in displaying the ellipses of the Water Mill, which indeed are incomplete, and in addition an unexpected straight line is drawn starting from them. The same problems still remain for some curves of the Toboggan. However, despite these problems, I think that Applet 2 and Applet
3 will help understand the overall perspective.

Why? Look at the straight line r’ in Fig. 10

r’ is the perspective correspondent of the straight line r in the plan, which passes through the bottom-left point of the so called Chariot (the parallelepiped containing the Water Mill) and through the centre of the circle representing the Chassis of the Chocolate Grinder. The choice of line r’ is free, but according to that choice we obtain different perspectives. Thus, by dragging the blue line in Applet 2 and Applet 3, you will see how the perspective could change accordingly, always remaining consistent with Duchamp’s data ⁽¹²⁾.

Anyway, the problems of the applets are definitely overcome with Fig. 11 and Fig. 12 (which are static), where the geometrical perspective of Cabri is correctly displayed on the background of Duchamp’s originals.
click to enlarge

Figure 11
The geometrical perspective of
Cabri correctly displayed on
top of Duchamp’s original
1913 sketch and the lower half of the Large Glass
Figure 12
The geometrical perspective
of Cabri correctly displayed
on top of Duchamp’s original
1913 sketch and the lower half of the Large Glass

Look at Fig. 11. The major discrepancies between 1913 Sketch and the Cabri figure are on
the right side of the picture:

one of the blades of the Scissor (the lower on the right) doesn’t match perfectly with its counterpart⁽¹³⁾;

The right Sieve (the Sieves are the conical shapes just under the Scissor) is slightly in a lower position relative to the Cabri figure;

the Toboggan (the spiralling line on the right) is slightly shifted down.

In contrast, the left part of the 1913 Sketch matches quite well the remaining elements of the Cabri figure particularly the ellipses of the Chocolate Grinder. The left Sieve also matches perfectly the one in the Cabri figure.

In my opinion, some trivial explanations can be considered for the mismatches: maybe the reproduction of the 1913 Sketch used here is slightly rotated in the clockwise sense, around a centre located somewhere near the centre of the Chariot; this could explain why the
most evident discrepancies are on the right half of the picture, whereas the better matching is on the left. A second explanation could be that the sheet used by Duchamp for the 1913 Sketch could be somehow deformed. Indeed the squaring of the drawing (as I saw in all the photos I could examine, including the one used here) is not perfect.

Consider now the singular shape of the Toboggan. It is a strange mix of semicircles and semiellipses disposed on oblique planes: its correspondence with the Cabri figure, even though imperfect, is quite shocking; remember, indeed, that Duchamp drew it by hand;
it means that the drawing was made point per point. The exact placement of even just one of those points (starting from its position in plan and elevation) can be considered a very difficult task for anyone having only an intuitive knowledge of projective geometry.

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Figure 13
Possible construction lines of the Toboggan

To have the right idea of such difficulties look at Fig. 13 which displays the construction lines necessary for just one point for each of the four arcs forming the Toboggan (thus multiply these construction lines al least 4-5 times).

Consider now Applet 3 and the corresponding static Fig. 12, which superimposes the Cabri
figure on the lower part of the actual Glass.

Look at Fig. 12. The reproduction of the Bachelor apparatus matches quite well the Cabri
figure: look especially at the Scissor and the Sieve on the right, which fit a lot better with Cabri figure than the ones of 1913 Sketch. Also, the ellipses circumscribing the Water Mill seem to match it perfectly.

Consider finally the supports of the Chariot named the Runners with their four semicircular shapes. They scarcely match the Cabri figure. Note however that the Runners were not
yet present in the sketches of plan and elevation, thus we have no measures for them. I simply used four semi-circumferences without making any attempt to recreate the correct image.

In conclusion, the inspection of the overall perspective seems to suggest that the reciprocal positions of the main elements of the Glass are consistent with the hypothesis that Duchamp correctly used the rules of perspective. It is worth noting in particular his skill in managing very complex constructions such as the one for the Toboggan, especially considering that he was self-trained in perspective.

2.2. The Chariot with the Water Mill, the Capillary Tubes and the Cemetery of Uniforms and Liveries

The simplest solid to render with perspective is the parallelepiped with edges parallel and perpendicular to the horizon: it is the case of the Chariot. Not equally trivial is to draw the wheels of the Water Mill contained in the Chariot. Nonetheless the perspective rendering of this elements is almost perfect.

Applet 4 shows how the geometric construction fits the corresponding detail of the Glass. Because of some possible problems with CabriJava in displaying objects, we shall refer to Fig. 14, which is static, but displays the picture correctly.Here is a problem: the overall framework of the Chariot is made by rods which actually have thickness and width, whilst in Duchamp’s preparatory sketches of plan and elevation they are considered as pure linear elements without thickness and width. This implies a quite arbitrary superimposition of Cabri figure on the Glass picture (unless one considers a number of different possible assumptions regarding the passage from the sketches to the actual Glass, which I didn’t).

Apart from this problem, the perspective created with Cabri matches quite well the parallelepiped of the Chariot.

Observe now the wheels of the Water Mill.

click to enlarge

Figure 14
Static image
showing how the
geometric
construction fits
the
corresponding detail of the Glass

First, let us consider the ellipses circumscribing the Water Mill (in red in Fig. 14): they touch exactly the peripheral points of each paddle (as we already noticed in the overall perspective of the Bachelor apparatus), except for the paddle in the foreground. But there is no error here: indeed, Duchamp preferred to clip the parts of the paddles which fall beyond the limits of theChariot.

Look now at the ellipses (in blue) touching the internal points of each paddle. Duchamp didn’t insert them in the sketches of plan and elevation. Therefore, we don’t know the actual radius of such circles. Just for this reason, I inserted in Applet 4 the red large point. As the user drags it vertically, the radius of the internal Water Mill wheels varies accordingly. The match with the Glass is satisfactory.

Consider now the eight spokes of the Water Mill wheels. I drew them under the assumption that they formed a regular octagon, and placing two of them along a vertical line. They also perfectly match the originals.

Some minor mismatching are there with the paddles of the Water Mill, but they are not severe, in any case.
Let us finally consider the perspective of the nodes of the so called Capillary Tubes, from which the 9 Malic Moulds hang, forming the so called Cemetery of Uniforms and Liveries.

In the sketches of the elevation and plan, the positions of the 9 numbered nodes are present, but, unfortunately, some measures are missing, namely those necessary in the plan sketch. Therefore I deduced them by measuring and scaling the distances directly on the sketch. The outcome displayed in Applet 5 is quite unsatisfactory. In particular, the nodes (and accordingly the Uniforms) nos. 2, 3, and 7 are clearly misplaced, whereas the remaining ones are only approximately right. Even by dragging the red diagonal (which modifies the perspective viewpoint), the drawing remains wrong (at least with respect to the preparatory sketches).

In conclusion: the perspective of the Water Mill shows some minor mismatches with the Cabrifigure; namely: some paddles seem to be not properly drawn. For the rest, the geometric construction easily fits the corresponding parts of the Glass.

In contrast, the nodes of the Capillary Tubes are misplaced. We must consider however, that the sketches are quite reticent regarding this detail, and we cannot rule out the possibility that the Capillary Tubes were more carefully planned before the execution of the actual perspective of the Glass.

2.3. The Chocolate Grinder

The Chocolate Grinder is often said to have the most problematic perspective. Indeed, it seems “strangely distorted” according to Shearer⁽¹⁴⁾.In a second, stimulating essay, written in collaboration with Stephen Jay Gould, it is argued that:

Scholars have simply and uncritically accepted Duchamp’s claim that he rigorously used these principles in his major works. Ironically, however, no one who actually attempted the experiment has ever been able to render the bachelor machinery of the Large Glass under classical perspective, unless they alter Duchamp’s own drawings and therefore conclude that he was not, after all, a very accurate geometer. The Chocolate Grinder, especially, does not seem properly drawn, and no one has been able to show how the device might turn without the wheels interpenetrating and thus, to make the metaphor literal, grinding to a halt.⁽¹⁵⁾

click to enlarge

Figure 15
Marcel Duchamp, Chocolate Grinder, No. 2 ,
1914

Figure 16
Marcel Duchamp, Chocolate Grinder, No. 1 ,
1913

Figure 17
Geometric features of the Chassis and the
Rollers

The second and definitive painting of the Grinder (namedChocolate Grinder, No. 2 (Fig. 15), dated 1914) is quite different relative to the first one (dated 1913) (Fig. 16), not only because it openly shows its second important identity (connected with electromagnetism and wireless telegraphy), discussed by Linda Henderson⁽¹⁶⁾, but also because (as we shall see further on in this section) it acquires well-defined perspective construction, unlike the first version, whose perspective is quite problematic.

The first problem to solve in order to check the perspective of the Grinder, is to understand its geometry. Indeed, the sketches of plan and elevation are quite incomplete.

Essentially the Grinder is formed by three rollers (which seem to be frusta of a cone) placed on a Chassis (a cone with altitude much smaller than the radius of its base).

Duchamp’s sketches give us the complete measures necessary to reconstruct the Chassis, but for the roller, only two measures are given: the diameter of the circle of the major base and the length of the generatrix. No measures of angles are given. Reconstructing the rollers without additional assumptions is thus impossible.

At first I thought that the roller had to roll without sliding on the Chassis, and (of course) always rotating on theChassis itself, without leaving it. Geometrically speaking, this implies that the vertexes of the cones of each roller must coincide with the vertex of the cone of the Chassis; but looking at the actual Grinder we immediately understand that it is not the case: their vertexes clearly lay far beyond the vertex of the Chassis(Fig. 17). Thus the rollers grind the chocolate by sliding on the Chassis. Thus the assumption about the kind of friction of the rollers on the Chassis was wrong ⁽¹⁷⁾.

If we start from the measures of the roller given by Duchamp (radius of the major base and length of the generatrix), accepting their conical shape, and giving the angle the major base forms with a horizontal line, then the frustum of the cone is completely assigned (see Fig. 17).

In order to find the exact value for the measure of the unknown angle, I inserted in the Cabrifigure a corresponding further degree of freedom, allowing the user to drag the line corresponding to the major base of the roller in the elevation.

click to enlarge

Figure 18
Contact lines of the rollers with
the Chassis

Duchamp’s sketch of the plan doesn’t contain information about the mutual positions of the rollers and the exact positions of the contact points of the rollers with the Chassis. Thus, further assumptions must be made. Fig. 18 shows the simplest assumption (plan view of theChassis): the axes of the rollers form 120° angles, and one of them is parallel to the ground-line of the perspective. This hypothesis will prove exact (except for minor mismatches indicated below).

Finally let us examine Applet 6, which superimposes Cabri figure of the Grinder onto the 1914 picture Chocolate Grinder (No.2). I used the 1914 picture instead of the actual Grinder of the Glass, because we know that the latter was obtained by simply transferring on glass the former; thus using the 1914 picture I avoided considering those mismatches possibly derived from the transfer on glass, maintaining instead the focus on possible true perspective mismatches.

The outcome is once again unexpected, because the matching is almost perfect.

Applet 6 allows the user to see that:

The two ellipses corresponding to the Chassis and to the Necktie match well the Cabri figure (the ellipses of the Chassis are slightly smaller than the corresponding ones in the Cabri figure). The blue point on the top of the Grinder axis (or Bayonet) over the Necktie also matches well the point where the handle of the Necktie intersects the axis of the Grinder.

So good is the matching of the fixed parts of the Grinder with the Cabri figure that we see even the same very small portion of the Chassis visible in its higher part between the rollers!

Let us consider now the rollers. The grey line in the elevation, running along the major base of the roller allows the user, by dragging it, to choose the better unknown angle we talked about above (my best estimate is 81,9°).

The vertexes of the equilateral triangle (in the little circle under the Grinder) indicate the positions of the rollers (namely their contacts with the Chassis). The green point can be dragged in order to rotate the roller, and to test its matching with the original picture for each of the three positions.

In two cases (the two rollers in the background), the matching is almost perfect, whereas the roller in the foreground shows a minor mismatch, because the ellipse corresponding to its major base is slightly larger than in the Cabri figure.

In particular, note the blue points that indicate the center of the bases of the frustum of the cone. In the case of the roller to the right, the blue point coincides exactly with the insertion point of the roller on its axis. In the case of the roller in the foreground, one of the blue points matches perfectly the center of the major base of the roller.

click to enlarge

Figure 19
Tentative position
of the Louis XV legs
as vertex of an
equilateral triangle

Figure 20
One only visible leg
under the
assumption of
Fig. 19

Let us now consider the Louis XV legs of the Chassis. At first I thought that, because of the equilibrium of the whole device, the three legs had to be placed at the vertices of an equilateral triangle. Accordingly, the vertex corresponding to the leg in foreground is such that the exact position of the equilateral triangle must be as in Fig. 19.
Look now again at Applet 6. The three grey vertical segments and the corresponding cyan extremities indicate the position of the legs of the Chassisin case the legs were planned to be positioned as in Fig. 19. The background legs are clearly misplaced, whatever was their planned shape. The only visible leg in the perspective drawing would be that in foreground, whereas the others would be covered by the Chassis, as in Fig. 20.

Fig. 20 shows the Grinder with one only leg: even though appropriate for both the equilibrium and the perspective, it makes the whole Grinder seem to be supported by one only leg, which, of course, would be impossible.

The addition of the background legs makes the drawing acceptable for the eyes, but wrong for perspective. Indeed, in order to make the perspective we see in Chocolate Grinder (No.2), the background legs wouldn’t be placed according to Fig. 19 (the only disposition ensuring the equilibrium of the device): they have to be slightly shifted forward, which however makes the equilibrium impossible.

So far we have faced something paradoxical: if you pay the tribute required by the retina, you will obtain a thing which cannot stand up (a quite Duchampian statement, we have to acknowledge). Here I emphasize the Duchampian key concept of instability. Interestingly, a similar kind of paradox between retinal and mental data, with similar conflict between equilibrium and instability concepts, has been already discussed in terms of the Bicycle Wheelby Shearer⁽¹⁸⁾.

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Figure 21
A further investigation of the perspective project
in the 1913 Sketch

A further investigation of the sketches makes things clear. In both the 1913 Sketch and the elevation, we can see the legs actually drawn (see Fig. 21). In fact nothing tells us that they are disposed as an equilateral triangle; this misleading assumption was made because the visible legs are three, but very probably they actually are four, disposed as a square, like in Fig. 21. Indeed three of them are clearly visible in both of Duchamp’s sketches, whereas the fourth would-be leg (the posterior one) couldn’t be seen in neither of them: in the elevation because it is exactly behind that one in the foreground, and in 1913 Sketch because it is hidden by the Chassis. But this fourth leg is necessary for the equilibrium. According to this new assumption Duchamp’s perspective would turn out to be correct, and the equilibrium of the device would be safe. On the other hand, no actual datum contradicts this hypothesis of four legs, which in my opinion is thus confirmed. In conclusion: the perspective rendering of the legs is correct.

Consider now the threads sewn through canvas in the Chocolate Grinder, (No. 2) then carefully reproduced in the Glass.

Applet 7 shows the roller completed with similar threads, and helps check the correctness of their orientation. It proved to be consistent with the adopted perspective in two cases (the right and the foreground rollers) but also revealed some minor mismatching in the third case (the roller in background). In my opinion just the wrong perspective of the threads of the background roller makes the overall perspective of the Grinder difficult to be accepted for the eye.

To convince that what we said about the perspective of the Grinder No. 2 holds its validity in the passage to the Glass, look at Applet 8, which displays the Cabri figure superimposed on the actual Grinder of the Glass. Once again the matching is almost perfect.

Before concluding this section, I want to say a few words comparing the perspective rendering of both the first and the second version of the Grinder.

Applet 9 clearly shows that the perspective of the first Grinder is definitely wrong (at least accepting the measures of Duchamp’s sketches and the assumptions I declared above). The user can try to adapt the Cabri figure to the picture of the first Grinder, by dragging either the red diagonal or the green point (which have the same meaning as in Applet 6), but the outcome will be in any case unsatisfactory. Particularly the Necktie and the rollers seem to be totally wrong.Thus we can say that the passage from the first to the second version of the Grinder shows an extraordinary leap in Duchamp’s perspective skill.

In conclusion we can say that despite its strangely distorted view, and in spite of its intrinsic difficulty, the Grinder is one of the best executed elements in the perspective of the Glass. In any case the mismatches revealed above are consistent with the hypothesis that Duchamp drew the Glass according to the ordinary rules of perspective.

Recall Gould’s and Shearer’s statement that : «…no one has been able to show how the device might turn without the wheels interpenetrating…». Look now at Animation 1⁽¹⁹⁾. It shows theGrinder in action. Definitely, the rollers do not interpenetrate as the device is grinding.

Please refresh the page, if the animation stops

Animation 1
2.4. The Sieves or Parasols

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Figure 22
The Yport sketch, 1914

The Sieves (or Parasols) are the conical shapes that are disposed in semicircle behind the Scissor.

Unlike other elements of the Glass, we have detailed sketches which describe not only the measurements and the position of the cones, but also the detailed perspective procedures followed by Duchamp. We can see such perspective sketches and projects in the Green Box. ⁽²⁰⁾ But the most important sketch, drawn at Yport during the summer of 1914, is not published in any of the cited collection of notes. We shall refer to it as the Yport sketch. (Fig. 22)

Particularly, we note the following shortcut Duchamp used to speed his work.

Once the drawing of the base-circle of the first cone was executed by interpolating 8 reference points (clearly visible in the sketch), Duchamp exploited the semi-circumferences where the corresponding points of the other cones lay, and divided them with the vertices of the inscribed dodecagons (which is a quite simple and speedy procedure). As I worked with Cabri, I used the same procedure.

click to enlarge

Figure 23
The actual geometry of the Sieves

The Yport sketch also clearly shows a further detail: the declared altitude of each single cone (we read twelve cm in the elevation sketch) was probably modified by Duchamp on the basis of the geometry displayed in Fig. 23, in turn based on Yport sketch.

The shared altitude CH of the cones is such that the perpendicular to the base AB of the first cone intersects the base of the second one exactly at point C (and similarly for the others as well). Thus, the involved angle being of amplitude 30°, and being OH=23 cm, the measure actually used for the Sieves is CH=13.28 cm.For construction of the Sieves, I followed the geometry of Fig. 23, instead of using the measurements given in the elevation sketch.

Look finally at Applet 10. It shows that, once the best inclination of the diagonal (the red one) is chosen, the matching is perfect.

2.5. Some conclusion about the perspective of the Glass: the static viewpoint

Duchamp composed the Glass by hand and, above all, used absolutely unconventional media, which required him to invent ex novo appropriate techniques of execution. In general, we must suppose that drawing on glass is not as easy as drawing on paper or on canvas, especially if one of the main goals was precision, as in the case of the Glass.Just to have a correct idea of what this could mean, read the following description, regarding the execution of a preparatory study for the Chariot:

His first idea was to etch the design on the glass with fluoridic acid, a powerful corrosive used by commercial glass workers. “I bought paraffin to keep the acid from attacking the glass except where I wanted,” he said, “and for two or three months I struggled with that, but I made such a mess, plus the danger of breathing those fumes, that I gave it up. It was really dangerous. But I kept the glass. Then came the idea of making the drawing with the lead wire – very fine lead wire that you can stretch to make a perfect straight line, and you put a drop of varnish on it and it holds. It was very malleable material, lovely to work with.” (Duchamp used fuse wire, a coil of which was a staple in Paris apartments then.) ⁽²¹⁾.
We also already reminded that Duchamp was substantially self trained in perspective. In a note of the White Box we read:

Perspective.
See Catalogue of Bibliotèque St. Geneviève
The whole section on Perspective :
Niceron, (Father Fr., S.J.)
Thaumaturgus opticus ⁽²²⁾

The note suggests that while Duchamp was working at the library of Sainte Geneviève (1913-14) he read the whole section on perspective, and particularly (at least so we may assume from the note) the treatise on perspective and optics by mathematician Jean-François Niceron (1613-1646), titled Thaumaturgus opticus ⁽²³⁾.

Thus, in the years Duchamp was composing the first elements of the Glass, he also was concluding his education in perspective.

We can obtain the exact measure of his progress in perspective skill in those years by comparing the two versions of the Grinder (dated 1913 and 1914), as we did in section 2.3.

On the other hand, regarding now my reconstruction of the perspective, remember that procedures and tools I used are quite non-professional:

– the used software is perfect to study and teach geometry, but in general not for 3D rendering;

– the reproduction used are photos whose reliability is not certified (think for instance about possible parallax errors or perspective deformations);

– the photos were in addition reduced or enlarged to match the scaled measures I used withCabri, and such adaptations could be imperfect…

These considerations surely reduce each pretension of precision, but at the same time they also reduce the relevance of the minor mismatches revealed above.

Let us finally reconsider the perspective elements of the Glass that we have examined, in order to answer to the question: is the perspective of the Glass canonical (and/or correct)? Are there elements which permit us to hypothesize a non-canonical (and/or incorrect) use of perspective?In my opinion, the only mismatch one can consider a true error, or possibly as a non-canonical use of perspective, is the one regarding the nodes of the Capillary Tubes. For the rest the execution of perspective is quite stunning, especially for some elements such as the Grinderand the Toboggan.I believe that the matching between the geometrically reconstructed perspective and the actual perspective of the Glass is in general good or even perfect in some cases.Let us then reconsider Shearer’s argument. She describes the minor mismatches between computer aided designs and Duchamp’s originals

When you fit one part of the Large Glass model to its projection in Duchamp’s perspective drawing (say; part A, the ellipse in one wheel of the Chocolate Grinder, for example — see illustration 49A), the rest (parts B through Z) immediately fall out of place. We lose the fit of part A, and all the other parts C through Z, once part B is matched — etc.

Her statements can be discussed at two different levels.

At the level of single parts of the Glass, such as the Grinder, the Chariot, and so on (the micro level), I think that her statement is substantially wrong. With the exceptions of the nodes of theCapillary Tubes, the mismatches revealed by the inspection above are completely acceptable and consistent with the hypothesis that the Glass was drawn according to the usual rules of perspective, and must be considered as absolutely minor imprecisions due to Duchamp’s free-hand execution. I believe this conclusion holds unless a unitary theory can be formulated that explains all the mismatches at once.

Shearer proposes a unitary theory of this kind about the perspective of the historical photos of the readymade, but there are no explanations about the way that theory could be extended to theGlass.

Let us pass now to the higher level (the macro level), that of the overall view. Some further preliminary considerations are needed.

I executed Cabri figures in different sessions by separating the principal elements of the Glass.

This procedure risks creating a trivial error: choosing different and mutually inconsistent diagonals (possible diagonals are, for instance, the straight lines r and r’ in Fig. 10) for different figures can generate mistakes (remember that Duchamp’s measures allows such a degree of freedom). This implies the possibility of an overall perspective inconsistency, even if each individual element was rendered in correct perspective. In other words, choosing inconsistent diagonals would be equivalent to choosing different viewpoints. (This possibility agrees to some extent with Shearer’s proposal concerning the presence of several, different viewpoints in the perspective of the Glass).

The same considerations I did for the computer aided reconstruction of the perspective, could be applied to the execution of the actual Glass by Duchamp: remember indeed that the elements of the Glass were added by him one by one (even because each piece had to be executed with an appropriate technique) through successive and separate steps, which could expose Duchamp himself to the same risk of error I was exposed to.

Thus, it was very important to verify the mutual consistence of the details. In the contrary case, it would have been an important evidence for applying Shearer’s theory of multiple viewpoints to the perspective of the Glass (but, in such a case, there would be no evidences for an intentional choice by Duchamp, and consequently we couldn’t rule out the possibility of a simple mistake).

Now, in order to verify the perspective consistence of the single details with the overall view there were two possible ways:

either choosing every time the same couple of diagonal lines (which sometimes was very inconvenient), or choosing different couples of corresponding line, but verifying that they were consistent to each other.

I chose the second way. The check for consistency was done by comparing in each figure the position of the same straight line, namely r’ (refer to Fig. 10).

The check returned a positive response: each diagonal r passing trough the left lower point of the Chariot and the centre of the Chassis in the plan, corresponds to a straight line r’ in the ground plane of perspective, forming the same angle (16.3°) with the ground line. Hence, the details are perspectively consistent with each other and with the overall view.

Definitively, Duchamp used the canonical perspective rules, and mastered them at the highest level.

What is then the meaning of his mathematical, scientific perspective?

Often people think of mathematics as something which deals essentially with numbers. If there are no numbers there is no mathematics.

Remember for instance that after Duchamp’s claim about the mathematical use of perspective, Cabanne asked: «Was it based on calculations?» (we shall consider Duchamp’s interesting reply below), or even recall what Tomkins told about a possible formula.

Now, geometry is mathematics, and I think that Duchamp meant (among other things) that he used thoroughly projective geometry. Try to execute the perspective of the Toboggan to understand how much projective geometry he used.

Let us return to Cabanne and Duchamp dialogue.

Cabanne: Was it based on calculations?
Duchamp: Yes, and on dimensions. These were the important elements.

A few lines below we also read:

I almost never put any calculations into the “Large Glass” ⁽²⁴⁾

but again, a few lines below:

At the same time I was doing my calculations for the “Large Glass” ⁽²⁵⁾

I think that Duchamp used here the word calculations in the more general meaning of mathematical (namely geometrical) operation, construction, deduction: the only true calculations actually necessary for the drawing were the proportions possibly necessary for scaling the measures and a few minor operations ⁽²⁶⁾; for the rest there are only geometrical constructions.

Here, I want to emphasize the second element of Duchamp’s answer: that of dimensions, which of course refers to the fourth dimension.
Remember the already-cited Tomkins’ statement:

Was he looking for a mathematical formula through which he could actually evoke the presence of a fourth dimension? Whatever serious ambition he may have had along these lines he abandoned soon enough.

In other words Tomkins says that, even admitting the attempt to find the mathematical key which could open the door of the fourth dimension, Duchamp soon abandoned it, possibly (I’m hypothesizing) in favor of speculation on non-Euclidean geometry. I don’t agree with Tomkins. Not to diminish the importance of non-Euclidean geometry, but to emphasize the importance of the concept of higher dimensions in relation to perspective.

So far, we regarded Duchamp’s perspective from an eminently static viewpoint, and (consequently, I say) no reference to higher dimensions were highlighted.
The main goal of the remaining part of this article is just to establish a connection between the perspective of the Bachelor apparatus and the emancipated spatiality of the Bride realm, by introducing a new important element: that of motion.

3.1. The Chariot in the fourth dimension

In the introduction I argued that the Bachelor apparatus emulates the higher dimensionality and the topological properties of the Bride realm by coupling perspective with motion.

click to enlarge

Figure 24
Marcel Duchamp, Glider
Containing a Water Mill (in
Neighboring Metals), 1913-15

Let us start our course along this strand with the demonstration of a subject already widely discussed by scholars, regarding the Chariot ⁽²⁷⁾. In the years 1913-15 Duchamp worked at a preparatory study of the Chariot, named Glider Containing a Water Mill (in Neighboring Metals). (Fig. 24)It is the same element of the Glass, executed on a semicircular hinged panel of glass, which can rotate.

Applet 11 shows the situation. The red point on the bottom can be dragged to rotate about its hinge the plane where the Chariot is drawn. To simplify the drawing, the Water Mill is missing, to better focus the attention on the essential details.

The actual Chariot is drawn on a 2D support (the sheet of glass), and emulates its own status of 3D object by means of perspective. Accordingly, the 2D sheet of the glass emulates the ordinary 3D space. Hence the rotation of the Glider around its hinges suggests the rotation of a 3D object in a 4D hyperspace. Notice that just the sheet of glass used as support of the drawing allows to complete correctly the metaphoric turn in the fourth dimension: indeed just the transparency of the glass allows us to see the Chariot specularly reversed, as it reaches its final position. In fact we face an inverse congruence between two figures; just the exit from the 3D space and the rotation into the hyperspace allows two 3D figures inversely congruent to overlap on one another.

This idea is clearly presented by Duchamp in a note of the White Box and is widely discussed by Adcock ⁽²⁸⁾.Returning now to the applet, we can see a strong optical effect (also known as the Necker cube inversion), which can be described as if the Chariot would turn inside out as if it were a glove. Just this effect can be considered as a mental turn into the fourth dimension⁽²⁹⁾.

We can understand the variety and the subtlety of the game that Duchamp plays here, by comparing the rotation of the Glider with many other rotations of planes, everywhere present in the Bachelor apparatus. Consider for instance the rotation of the plane which ideally sustains the first Sieve (which we can actually see in the Yport sketch). Applet 12 allows the user to see this rotation by dragging the red point. Here we face a plane which rotates in a 3D space, giving rise to cones (which are 3D shapes) directly congruent with the starting one; on the contrary the glass plane of the Glider, which is 2D but perspectively simulates a 3D space, rotates in a true 3D space which accordingly simulates a 4D hyperspace, and gives rise to a second Chariot, inversely congruent to the starting one.

Now we can understand why Duchamp chose just the reproduction of the Glider as the cover of the White Box: remember indeed that the notes of this collection are mainly focused on the fourth dimension and its properties.

In short, with the Glider Duchamp suggests a rotary motion which allows the observer to look at two different Chariots, the one being the specular reversed image of the other, with the involvement of the fourth dimension concept we presented above.

Now, consider that the same thing can actually be done with the whole Glass, by simply walking around it. Once again the transparency of the glass permits the observer to look at two different Bachelor apparatuses, specular one to another, with analogous involvement of the fourth dimension concept. The motion of the observer around the Glass corresponds to the rotary motion of the Glider about its hinge as the observer stands still.

We shall exploit similar relative exchanges in motion (observed object rotating about its hinge and fixed observer vs. fixed object and observer moving around it) especially with the Sieves(in section 3.3.) and we shall consider the notes which carefully describe this inversion.

3.2. A new possible identity of the Grinder

One of the most important innovations of the 1914 painting Chocolate Grinder (No.2) are the threads directly sewn on the canvas; they obviously recall the coil-winding of an electromagnet.

Consider now a new possibility. The threads could also be related to the geometric concept ofruled surface.

A ruled surface is one which can be obtained by a straight line moving in the ordinary 3D space and leaving wherever it passes its trail: the ruled surface.

A note of the Green box, usually considered as the only one of this collection directly related to the theme of the fourth dimension ⁽³⁰⁾, also describes rotational motions of lines considered as generatrix; in addition the note contains ubiquitous suggestions of moving lines which leave a sort of trail forming surfaces; also, the note connects such a practice with the idea of circularity:

The right and the left are obtained by letting trail behind you a tinge of persistence in the situation. […]
And on the other hand: the vertical axis considered separately turning on itself, a generating line at a right angle e.g., will always determine a circle in the 2 cases 1^stturning in the direction A, 2^nd direction B. –
[…]
As there is gradually less differentiation from axis to axis., i.e. as all the axes gradually disappear in a fading verticality the front and the back, the reverse and the obverse acquire a circular significance […] ⁽³¹⁾

Further examples possibly related to the idea of ruled surface can also be found in the White Box, such as the following:

On an infinite line let us take two points, A and B. Let us rotate AB about A as hinge. AB will generate some sort of surface, i.e. either curved, broken or plane ⁽³²⁾

or even this one:

Elemental parallelism: repetition of a line equivalent to an elemental line (in the sense of similar at any point) in order to generate the surface. ⁽³³⁾

click to enlarge

Figure 25
Marcel Duchamp, Sad Young Man on a
Train , 1911

Figure 26
Marcel Duchamp, Nude descending a Staircase no. 2, 1912

The formula of Elemental parallelism was not a sterile speculation, but one of the most important conceptual foundations of a whole creative period: we know that Duchamp used it for capital painting, such as Sad Young Man on a Train(1911) (Fig. 25) or Nude descending a Staircase (no. 2) (1912).(Fig. 26) He carefully explained it in the dialogue with Pierre Cabanne ⁽³⁴⁾.
As an example of how a ruled surface can be generated, imagine a luminescent straight thread moving about in the darkness; also imagine a camera with the shutter opened, to capture the luminous trail left on the film by the moving thread. This trail could be an example of ruled surface. The example is not chosen by chance: this explicative metaphor is used by E.J. Marey in one of his photography books ⁽³⁵⁾. Duchamp was interested in similar photographic experiments (chronophotography), and scholars already related the painting of 1912 Nude Descending a Staircase (No. 2) to chronophotography⁽³⁶⁾.
Thus, for a moment let us think of the threads of the Grinder as a suggestion of straight lines moving about, while the rollers are grinding, generating trails corresponding to several kind of ruled surfaces.

The connection between the glued threads of the Grinder and the duchampian concept of elemental parallelism has been already stressed by Craig Adcock, who also recalled that Duchamp spoke of the threads as generatrices⁽³⁷⁾

Let us start with the simpler example: what is the geometric locus of the diametric threads of the circular bases of the rollers, as they rotate around the axis of the Grinder, without rotating around their own axis? Animation 2⁽³⁸⁾ shows a rotating roller. The surfaces described by the diametric blue lines are one-sheeted hyperboloids.

Animation 3 : shows that as the diametric lines vary their inclination, the hyperboloids gradually change their shape, giving rise to the degenerate case.

Animation 2
Animation 3

The genesis of a single-sheeted hyperboloid by means of a rotating straight line is also displayed by Marey in his already cited photography book which Duchamp surely knew (Fig. 27).

click to enlarge

Figure 27
The genesis of a
single-sheeted
hyperboloid displayed
in Marey’s book

Figure 28
Two single-sheeted
hyperboloids forming a
special type of gearing

Figure 29
Marcel Duchamp,
Coffee Mill ,
1911

Look now at Fig. 28: being the single-sheeted hyperboloids (doubly) ruled surfaces, it is possible to use them to create a special type of gearing. The interest of Duchamp in similar devices is documented by a painting which can be considered as the most direct antecedent of the Grinder: the Coffee Mill (1911),(Fig. 29) which clearly displays the gearing machinery allowing the device to work.

We already recalled that Linda Henderson thoroughly documented that theChocolate Grinder is strongly related to electromagnetism and wireless telegraphy: it is its second identity, after the first one as both a true and metaphoric grinder (connected with the autoerotic activity of the Bachelor, resumed with the slogan: The bachelor grinds his chocolate himself⁽³⁹⁾). Now, I like the possibility of a third identity of the Grinder, as a geometric device to generate ruled surfaces.

Maybe it can be seen as a flight of fancy, but not so much, after all; read indeed once again the Green box note about the geometric properties of theBachelor apparatus:

Principal forms, imperfect and freed
The principal forms of the bachelor apparatus or utensil are imperfect:
Rectangle, circle, square, parallelepiped, symmetrical handle; demisphere.-i.e. these forms are mensurated (interrelation of their actual dimensions and relation of these dimensions to the destination of the forms in the bachelor utensil.)
In the Bride – the principal forms will be more or less large or small, no longer have mensurability in relation to their destination: a sphere in the Bride will have any radius (the radius given to represent it is “fictious and dotted.”)
Likewise, or better still, in the Pendu Femelle parabolas, hyperbolas (or volumes deriving from them) [emphasis mine] will lose all connotation of men-surated position.

The question is: where are those hyperbolas and volumes deriving from them (and the corresponding surfaces, we could add) which, once passed into theBride realm will lose their connotation? Are they maybe the ones generated by the Grinder? It is possible.

Accepting this hypothesis, let us take some further step.

What happens if, while rotating around the Grinder axis, the roller also rotates around its own axis? Applet 13 will help visualize the possible resulting surfaces for such a composition of motions.

The different possible outcomes depends on the different sliding component in the motion of the rollers (remember indeed that in their motion rollers also slide on the Chassis). It means that, once a complete turn around the Grinder axis is completed, the rollers also turn around their own axis by a certain variable angle ω, whose amplitude depends on the sliding component.

Look finally at Applet 13 ⁽⁴⁰⁾: at its opening, the parameters are fixed in order to have the roller making a half turn around its own axis, while making a complete turn around the axis of theGrinder.

The surface described by the diametric line of the major base of the roller is a Moebius band.
At the bottom of the figure you find two green points which can be dragged.

By dragging the upper one the roller will rotate and make a complete turn around the Grinderaxis: you can see that the diametric line actually rules the band. As you drag the lower green point you simply modify the ω parameter and accordingly the locus surface will gradually change its shape, giving rise to more complex bands.

A further step could be taken by observing the surfaces obtained by the longitudinal lines of the rollers as generatrices. Applet 14 visualizes them. Once again the two green points can be dragged, with the same meaning as before.

Now the question is: accepting the present hypothesis about the Grinder, what could be the meaning of the surfaces generated by it, in the general project of the Glass? In my opinion surfaces such as the Moebius band, with their topological properties, could be a means for theBachelor to emulate the higher and more complex space of the Bride; it could be a sort of bridge, between the Bachelor and the Bride realms: remember indeed that the Bride is characterized by topological properties where the metrical traits governing the lower half of theGlass lose their meaning. The same holds (all the more reason) for the more complex bands obtainable with the Grinder.
To be precise, I don’t mean that Duchamp thought exactly of the Moebius band (or of similar and possibly more complex surfaces), but it is possible that he could imagine similar figures, maybe knowing neither their name nor their status of well-defined and studied geometrical objects. Possibly he guessed some of their strange properties; after all we have a number of evidences of its astonishing geometric imagination. Jean Clair already discussed some works of Duchamp referring them to well defined topological objects (such as the Kleinian bottle). Also Clair informs us that in the 60’s Duchamp discussed the properties of such topological objects with the French mathematician Le Lionnais. Following this suggestion I discussed other possible examples, referable to the properties of both the Kleinian bottle and the Moebius band⁽⁴¹⁾.

In conclusion we could think of the Grinder as a ruled surfaces generator, or better, as a true surfaces grinder. The complex surfaces generated by Grinder’s motion could emulate the topological essence of the hyperspace of the Bride realm in the higher part of the Glass. The thesis is supported by some facts:

1. Notes from both the Green Box and the White Box (cited above) prove that Duchamp knew and used the concepts of ruled surface and quadric surfaces (at least on a qualitative level);
2. The idea of ruled surface is strictly connected with the practice of chronophotography which Duchamp praised and in a way used;
3. The surface of the rollers is carefully ruled by the threads sewn on the canvas, and as theGrinder is supposed to work, they rotate moving about in several complex ways; and, above all, the Grinder actually works as a surfaces generator;
4. It is proved that (at least) in the 60’s Duchamp knew at some qualitative level both the Moebius band and the Kleinian Bottle;

3.3. The Sieves’ perspective: a possible antecedent of Duchamp’s optical devices
Let us now consider the Sieves (or Parasols) and their function in the Bachelor apparatus. TheGreen Box notes describe the process which produces the so called Illuminating gas; as it leaves the Capillary tubes, it is then cut into bits, called spangles, which must run through the circular pathway of the Sieves:

As in a Derby, the spangles pass through the parasols A,C D.EF…B. and as they gradually arrive at D, E, F, … etc. they are straightened out, i.e. they lose their sense of up and down ([more precise term]). – The group of these parasols forms a sort of labyrinth of the three directions. –
The spangles dazed by this progressive turning. Imperceptibly lose [provisionallythey will find it again later] their designation of left, right, up, down, etc, lose their awareness of position.⁽⁴²⁾

By this way, the spangles, straighten out

[…] like a sheet of paper rolled up too much which one unrolls several times in the opposite direction ⁽⁴³⁾

lose their sense of space. The way it happens is described as a loss of distinction between left, right, up, down, etc. as they pass through a labyrinth of three directions.
The following note from the Green Box makes clear that in Duchamp’s thought the identifications left-right, front-back, hi-low and so on are connected with the suggestion of a higher dimension::

[…] the front and the back, the reverse and the obverse acquire a circular significance: the right and the left which are the four arms of the front and back. melt. along the verticals.
the interior and exterior (in a fourth dimension) can receive a similar identification.⁽⁴⁴⁾

Hence we can think that the circular pathway through the Sieves and the consequent loss of distinction between opposite orientations could be somehow connected with the suggestion of a higher dimension.
The pathway followed by the Spangles is strictly circular, because the seven Sieves (originally they were six and semi spherical) have nine holes (originally eight) which repeat exactly the shape of the polygon connecting the nine (originally eight) Malic moulds, where they come from.

The sieves (6 probably) are semispherical parasols, with holes. [The holes of the sieves parasols should give in the shape of a globe the figure of the 8 malic moulds, given schematic. by the summits (polygon concave plane). by subsidized symmetry]⁽⁴⁵⁾

Thus the Sieves convey the Spangles according to well defined circular trajectories.
Applet 15 shows the pathway of 5 possible Spangles, assuming for simplicity five arbitrary convenient positions of the holes. The blue point can be dragged to move the Spangles through the Sieves. The actual course of the Spangles is semicircular, but Applet 15 displays a complete turn, in order to emphasize some aspects we will discuss as we shall go along.
Applet 15 helps understand why the dazed spangles lose the sense of up-down and left-right (follow for instance the course of the blue one); in addition it displays a strong depth effect due to perspective rendering of the Spangles in motion.

click to enlarge

Figure 30
Five semcircumferences used by
Duchamp to perform the
perspective drawing of the cones

Figure 31
Because of the perspective,
the arcs are not concentric:
their centers are the points A, B, C.

Let us now return to the perspective of the Sieves. Particularly let us consider the Yport sketch of 1914. The following Fig. 30 summarizes those, among its features, relevant in this context.

We clearly see five semcircumferences used to perform the perspective drawing of the cones. Four of them were used to rotate four diametric points of the first ellipse, in order to easily obtain the corresponding transformed points of the remaining ellipses; the fifth arc was used to obtain the centers of each ellipse, starting from the first. Maybe other circumferences were used, also considering how perfectly the ellipses are drawn; however the sketch doesn’t show any trace of possible further arcs. Note that, because of the perspective, the arcs are not concentric: their centers are the points A, B, C, visible in Fig. 31, which also displays the complete circumferences.
I used for convenience just these circumferences as circular pathways of the spangles in Applet 15; according to the original project by Duchamp, nine similar circumferences must be used (one for each of the nine holes).
The White Box contains notes which specifically connect linear perspective with circular shapes, by means of the concept of gravity:

Gravity and center of gravity make for horizontal and vertical in space³In a plane² – the vanishing point correspond to the center of gravity, all these parallel lines meeting at the vanishing point just as the verticals all run toward the center of gravity.⁽⁴⁶⁾

This association between perspective and gravity (which interestingly and meaningfully was made in the same way by Klee⁽⁴⁷⁾) leads Duchamp to the following conclusion:

Resemblance –
Between a perspective view and a circle –
The vanishing point and the center –
To what in a perspective view would the
Circle itself correspond?

Horizon⁽⁴⁸⁾
Elsewhere in the White Box we also read:

Difference between “tactile exploration” or the wandering in a plane by a 2-dim’l eye around a circle, and of this very circle by the same 2-dim’l eye fixing itself at a point. Also: difference between “tactile exploration,” 3-dim’l wandering by an ordinary eye around a sphere and the vision of that sphere by the same eye fixing itself at a point (linear perspective).⁽⁴⁹⁾

Here Duchamp adds the motion as a further key ingredient in the perception of higher dimensions of space. Perspective representation and vision must be integrated by the motion of the eye in order to reach a better representation and understanding of higher dimensional objects:

A 3-dim’l tactile exploration, a wandering around, will perhaps permit an imaginative reconstruction of the numerous 4-dim’l bodies, allowing this perspective to be understood in a 3-dim’l medium.⁽⁵⁰⁾

Perhaps, the rotational motion of the Spangles through the Sieves may be intended as a suggestion of a wandering or tactile exploration of the space surrounding the Sieves, or, in general of the medium which the Glass is immersed in.
Following this course, the next step seems to be quite obvious: maybe the same effect could be reached if, instead of the wandering around an object, this very object could turn in front of the observer which remains in a fixed position.
In our case, what happens if the circumferences conveying the Spangles rotate around a fixed center (not necessarily one among points A, B, C in Fig. 31 in front of us?
Applet 16 illustrates the outcome: a set of seven eccentric circles (which I used before for the perspective construction) rotate around a center near to their own centers, which however doesn’t coincide with any of them. Use the blue point to fix the center of rotation into the desired position; drag the red point to shift the set of circumferences backward or forward; finally drag the green point to rotate the set of circles.
The depth effect is quite remarkable, and is further reinforced if the circles are colored, like in the following Animation 4.

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Animation 4

Thus we passed from a true 2D plane to the illusion of a 3D space. Hence, once again we have the emulation of the higher dimensionality of the Bride realm.
Only speculations? Possible, but it is exactly what Duchamp did a few years later with the filmAnemic Cinema (1925) (Fig. 32) and especially with the optical devices such as the Rotary demisphere (1925) (Fig. 33) and the Rotorelief (1935). (Fig. 34)

click to enlarge

Figure 32
Marcel Duchamp, Anemic Cinema, 1925
Figure 33
Marcel Duchamp, Rotary demisphere, 1925
Figure 34
Marcel Duchamp, Rotorelief, 1935

There Duchamp used once again sets of eccentric circumferences, which while rotating produce remarkable effects of depth (see for instance Animation 5, where a facsimile of the optical disc named Verre de Boheme, 1935 produces the effect of a three dimensional stemmed glass). The effect of depth produced by the Rotorelief has no relation with the stereoscopic vision; on the contrary it is even more surprising if seen with a single eye.

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Animation 5

Interestingly scholars generally don’t consider the connection of the Rotorelief with the previous efforts of Duchamp in perspective, but I think it is an important element to consider, as Adcock already carefully stressed⁽⁵¹⁾. Let us look once again at Animation 5. We see a 3D stemmed glass rotating in front of us, and it happens also because our mind perceives the set of circles as a Gestalt, and this can be possible all the more reason if the circles have some perspective consistence. Duchamp himself makes clear this point talking about his Rotorelief :

Thanks to an offhand perspective, that is, as seen from below or from the ceiling, you got a thing which, in concentric circles, forms the image of a real object⁽⁵²⁾

Thus, once again we have a strict correspondence between rotary motion, perspective, and suggestion of higher dimensions, with the optical illusion of depth, known as stereokineticeffect.
Indeed the rotating circles were drawn on the same sheet of paper (the Yport Sketch) and implicitly are present on the same sheet of glass; thus they actually belong to a plane; however in the perspective fiction they belong to different planes (parallel to each other) which determine a 3D space. Now, if the stereokinetic effect allows us to pass from the 2D plane to a 3D space, then according to the perspective fiction in the meantime we also pass from the ordinary space to a hyperspace.
Concluding this section, we shall consider an additional interesting feature of the Sieves which is to be stressed.
With their semicircular course, the circular bases of the conical Sieves ideally generate an half torus.

click to enlarge

Figure 35
If we identify the
diametrical points of a torus,
the surface we obtain
is a Kleinian
bottle.

With reference to Fig. 35, consider for a moment the whole torus, and its centre of symmetry C; also consider the couples of symmetric points of the torus, such as P and P’, or Q and Q’ and so on; call the points of such couples diametrical points. The loss of distinction (described above) between left-right, up down and so on, can be expressed in terms of identification of diametric points of our torus. Now, it is known that if one identifies the diametrical points of a torus for each possible couple, the outcome is a surface topologically equivalent to the Kleinian bottle. For those interested in the subject, it is clearly and simply presented in a classic text of David Hilbert ⁽⁵³⁾.
Thus let us reconsider the notes dealing with the Spangles and their run through the Sieves, which I reported at the beginning of this section. The loss of distinction (or identification) between left and right, up and down, interior and exterior already interpreted in terms of reference to higher dimensions, can also be interpreted in terms of possible reference to the topological properties of a Kleinian bottle.
The different possible interpretations are not in conflict; on the contrary, they are somehow related, if we think that only in the fourth dimension the Kleinian bottle could be properly built.
Hence we can think of the Sieves machinery of the Bachelor apparatus as a further emulation of the topological properties of the Bride realm.
In conclusion I suggest three things:
first, we have some further evidences that coupling perspective and rotary motion allows theBachelor apparatus to emulate the higher dimensionality of the Bride realm;
second, the perspective construction of the Sieves could be seen as the most direct and relevant antecedent of the successive optical devices;
third, the Sieves could be thought of as a sort of topological apparatus which returns objects with non ordinary properties (such as the Kleinian bottle); thus the Sieves could also be considered as an apparatus emulating the topological properties of the Bride realm.

3.4. Rotating the Water Mill: an unexpected further bridge toward the fourth dimension
The Water Mill perspective offers a further unexpected surprise.
Let me start with the description of the course which led me to the serendipitous discovery about the Water Mill that I will describe in this section; indeed I think this very course contains in itself some insight about the way one could possibly approach the Glass in particular and Duchamp in general.
Once the perspective of the Water Mill was obtained with Cabri, it was only a question of few additional contrivances, to allow the wheels to rotate, thus I did it.
In order to better appreciate the rotary motion of the Water Mill wheels, I filled the polygons corresponding to the eight paddles (which originally were transparent) with a solid grey color.
The unexpected outcome is displayed in Applet 17. What kind of motion was there? What happened to the Water Mill? Was it turning forward or backward?
Along with the widely explored category of the 3D impossible objects, do we deal here with a new category, that of the impossible motions?
After a few moments I realized what the problem was:
The grey filling color is opaque, and if there is overlapping of paddles, each new filling operation causes the covering of the previously filled paddle. As the animation is running, for each frame Cabri repaints the screen, and the paddles are repainted accordingly, following the same order used to fill them the first time. So, it happens that from time to time, the order followed by Cabri for filling the paddles can be the right or the wrong one. If it is right, the paddles are drawn consistently with their position and with the forward motion (the foreground upon the background ones). In the contrary case the filling order is wrong, so that paddles which actually must be in background, are filled as they were in foreground and vice versa, and the global outcome is the perception of a backward motion. In addition, consider that originally the paddles were filled by chance, without a precise order, so that the animation actually shows a continuing and unpredictable change of direction.

click to enlarge

Figure 36
Impossible Water
Mill wheel

Now look at the static picture of the Water Mill in Fig. 36 (it is a single frame captured from Applet 17). In spite of its correct perspective, we face an impossible 3D object, similar to that of Escher’s print Belvedere, based on the Necker cube. Indeed Fig. 36 shows a similar situation, namely the simultaneous presence of two different and inconsistent versions of the same object.
The first version is based on the perspective shortening of the background paddles compared with the major ones in foreground.
The second version of the Water Mill wheels is based on the reciprocal coverage of the elements: in our mind the element which covers another isover, and the covered element is under.
Thus our perception continuously oscillates between two different possible choices, each one corresponding to a different orientation of the Water Mill.
These two possible simultaneous orientations of the same object are specular: it means that no rigid motion inside the ordinary 3D space allows us to overlap these figures, which are inversely congruent. To physically obtain this result, we would have to rotate the figure in the forth dimension. Thus, once again the mental effort we make to invert the figure corresponds to a rotation in the fourth dimension.⁽⁵⁴⁾
The interesting thing is that the key element to achieve such a result is just the rotary motion, coupled with the perspective rendering of the wheels with their paddles, and not the coverage order of the paddles (which however propitiated the discovery) as we shall see.
Indeed, if you look at the static Fig. 20 and try to do the mental inversion of the object, is a lot harder than do that by observing the animated Applet 17.
The following applets are intended to enable the reader, step by step, to progressively lay aside the coverage order of the paddles, but always maintaining the optical effect of inversion.
Using Applet 18, you will learn to follow a single paddle (the red one, in this case) and to perform a stable mental inversion each time the paddle reaches its higher and lower positions.
Applet 19 will help you fix a single paddle (the one with the red border) but laying aside the coverage order, because the paddles are drawn transparent.
Finally Applet 20 shows a transparent Water Mill which you can invert without any help.
Use it to convince yourself that just the rotary motion of the paddles allows you to easily invert the object: stop it by passing with the mouse over its area and then leave it. Try now to invert the static frame. Once again it is a lot harder than with the moving picture.
With patience you will obtain a surprising result (even though only for a few instants at once):at the same time the wheels will rotate forward and backward, the paddles will be over and under, in front and back, the view point being both from the left and the right of the wheels.
This meaningfully agrees with some details of Duchamp’s speculations about the fourth dimension. Remember the already-cited note from the Green Box:

As a further detail consider the Green Box describing how the Water Mill works⁽⁵⁶⁾: one of its interesting features is that the rotation of the water wheels determines the onanistic left-right motion of the whole Chariot (which sustains the water wheels): this motion in fact could propitiate the left-right shifting of the viewpoint from where the wheels are viewed.
As a matter of fact, if you look at Applet 20 by shifting to the left and the right your head according to the rotation, it is a lot easier to make the required mental inversions than holding the same fixed position.
Now the question is: did Duchamp think of the Water Mill as a machinery allowing the observer to make possible these inversions, thus to make possible a turn into the fourth dimension? To be honest I don’t believe it, at least specifically for the Water Mill: we have no evidences that he thought of or planned what I said above.
However some objective data remain:
– the Water Mill wheels were planned to rotate;
– among other results, the infinite rotary motion of the water wheels was intended to enable the onanistic left-right motion of the Chariot (which sustains the wheels); the left-right motion of the Chariot with the Water Mill could be somehow connected with the specular inversions of the wheels, which accordingly seem to be viewed from the left or from the right;
– by means of the Glider (discussed in section 3.1.) Duchamp suggested us to specularly reverse just the Chariot and the Water Mill as a trick to make somehow visible the fourth dimension;
– and, especially, just a rotary motion (of either the observed object or the observer) makes possible such an inversion.
As a final objective datum to be added, consider now that using the water wheels and that mix of further ingredients, one obtains the outcome described by the applets above, which perfectly agrees with Duchamp’s speculation on fourth dimension.
By this way I don’t mean that Duchamp exactly thought about what the applets showed above, but simply that Duchamp’s recipe (that of mixing perspective and rotation in order to emancipate the spatiality of the Bachelor realm) does work effectively!

3.5. Further conclusion about the perspective of the Glass: the dynamic viewpoint
Let us return to Tomkins’ statement already cited:

We already said that Duchamp’s execution of the perspective drawing is absolutely canonical. As Tomkins suggests, no special mathematical formulas were used to carry out neither calculations nor geometrical constructions, but simply Duchamp carefully and thoroughly applied the rules of projective geometry.
However I think Duchamp didn’t abandon his ambition about evoking the presence of higher dimensions. Higher dimensionality being one of the declared (and most important) subjects of the Glass, he couldn’t abandon, because it meant to abandon the very project of the Glass, which he actually didn’t; the Glass was left unfinished, but after a period which covers more than ten years, not to consider Duchamp’s activity around the Glass in the years after his decision to leave it unfinished (thus he didn’t abandon soon enough).
I think that he behaved according to his claims: perspective effectively was one of the main ingredients in order to reach the illusion of the fourth dimension.
But, on the other hand we demonstrated that no special perspective tricks were used to modify what the canonical rules prescribe. And, of course, no special or magic effects are there inlooking at the Glass. The key is in thinking of the Glass, as Duchamp recommended, by stating the primacy of the grey matter over the retina.

Duchamp: I was mixing story, anecdote (in the good sense of the word), with visual representation, while giving less importance to visuality, to the visual element, that one generally gives in painting. Already I didn’t want to be preoccupied with visual language…
Cabanne: Retinal.
Duchamp: Consequently, retinal. Everything was becoming conceptual, that is, it depended on things other than the retina⁽⁵⁷⁾

In fact we have to consider the Glass as a continue and stimulating invitation to use the grey matter; this is one of the reasons for conceiving the notes as integral part of the Glass: they often are the starting point for successive mental activity, or even they are further integrations or suggestions to complete ideas born somewhere else.

I wanted that album [the Boxes] to go with the “Glass,” because, as I see it, it must not be “looked at” in the aesthetic sense of the word. One must consult the book, and see the two together. The conjunction of the two things entirely removes the retinal aspect that I don’t like. It was very logical.⁽⁵⁸⁾

We know that the range of speculations underlying Duchamp’s notes (and works) is wide enough to cover a plenty of different disciplinary fields. As an evidence of that, look at the monumental volume of Henderson⁽⁵⁹⁾ which however deals only with the scientific and technological humus from where the Glass took origin.
Why this digression on the disregard of Duchamp for the retinal, and consequently the accentuation of the importance of the notes? It is to stress that we have not to limit ourselves to the visual data we are facing. The Glass is not only the sheet of glass we can see at Philadelphia Museum but also that multilayered stratification of meanings that Duchamp himself suggested by means of the notes.
Thus, no surprise if I talk about a perspective which has to be moved to be fully understood, whereas the actual Glass is definitely static.
Indeed we already saw that the Glass was conceived in perpetual ubiquitous motion, with a particular inclination for circuital courses. We also have a number of claims about Duchamp’s attraction for circular motions:

Always there has been a necessity for circles in my life, for rotations. It is a kind of narcissism, this self-sufficiency, a kind of onanism. The machine goes around and by some miraculous process that I have always found fascinating, produces chocolate.⁽⁶⁰⁾

As a further reinforcement of the importance of rotary motions in Duchamp, I like also to remember here the extraordinary analysis which Stephen Jay Gould did of an historical photo representing (probably) Duchamp as a sort of ghost, surrounded by a myriad of suggestions of circular motions and shapes ⁽⁶¹⁾.

click to enlarge

Figure 37
Marcel Duchamp, Rotary Glass Plates (Precision
Optics) , 1925

If the Glass contains only suggested virtual motions, Duchamp also inserted actual rotary motions in the optical devices, starting from theRotary Glass Plates (Precision Optics) (1920, thus the execution of theGlass was still ongoing). (Fig. 37)
Thus I think that it is absolutely acceptable to consider the importance of mobile perspective in the Glass even though its exterior appearance is static.
After these necessary preliminary remarks, the thesis I presented in the third part of the present article can be resumed as it follows:
It is well known that the Bride belongs to an actual 4D realm (which we can see only by means of a 2D rendering of her 3D projected shadow). Also, her realm is characterized by the absence (or by the loss of meaning, which is the same) of the metric traits: the spatiality of the Bride realm is governed by more general topological (or even non-Euclidean) laws, where things no longer have mensurability (to use Duchamp’s word).
Also, it is known that the Bachelor realm is a true 3D domain, and its forms are imperfectobjects belonging to the standard Euclidean geometry (such as rectangles, parallelepipeds, circles…): the Bachelor can only try to emulate the higher dimensionality and the topological and non-Euclidean properties of the Bride realm⁽⁶²⁾, to make possible his (impossible) conjunction with the Bride.
Here the examples I presented in the third part of the article come into play. To emulate the emancipated spatiality of the Bride, the Bachelor can only use tricks and contrivances.
The key elements allowing such an emulation of higher dimensionality are:
perspective,
transparency,
and (rotary) motion.
Indeed just moving (rotating) the perspective elements of the apparatus, drawn on a transparent medium, we can reach the illusion (pay attention: just only the illusion) of a higher and emancipate spatiality.
Basically, the examples regarding the Chariot (see 3.1. and 3.4.) rise from a simple reasoning led by analogy: if two figures laying on the same plane (2D) are inversely congruent to one another (the one is specular to the other), no rigid plane motion allows to overlap them: to reach the result, a rotation into space (3D) is necessary to invert the congruence and allow the overlapping. By analogy, two spatial figures (3D) inversely congruent have to rotate in a 4D medium in order to overlap.
In the first example, the rotation of the Glider about its hinges allows the Chariot to turn inside out as if it were a glove (allowing, in fact, the identification left = right).
In the second example the rotation of the Water Mill wheels help us conceive (at least for a moment) the identification of both the specular version of the same 3D object and the contrary motions back and forth of the wheels.
Similarly, in the most part of the notes about the fourth dimension Duchamp led the reasoning by analogy: he observed what happens in the passage from 1D to 2D, or from 2D to 3D, and then extended the reasoning to the next passage from 3D to 4D.
But he clearly understood the limitations of such contrivances:

Will the passage from volume to 4-dim’l figure be produced through parallelism? Yes. But this elemental parallelism being a geometric process requires an intuitive knowledge of the 4-dim’l continuum [emphasis mine]. One can give the following definition for a 4-dim’l continuum. (By analogical reasoning, it is an enumeration of a few characteristic common to all the n-dimensional continuums rather than a definition): A representation of the 4-dim’l continuum will be realized by a multiplication of closed volumes evolving by elemental parallelism along the 4th dimension. Of course one has still to define by intuitive knowledge the “direction” of this 4th dimension [emphasis mine].⁽⁶³⁾

This note stresses Duchamp’s discontent, because, apart from giving a first possible key in guessing about higher dimensionality, it is sterile unless one has an intuitive knowledge of the“direction” of the fourth dimension.
Possibly Duchamp looked for other solutions.
The example regarding the Grinder (3.2.) could be seen as a possible alternative to analogical reasoning. The Grinder is based on a double rotary motion (around its own axis and around the axes of the rollers). On the one hand, the resulting ruled surfaces are connected with previous experiments concerning so-called elemental parallelism (thus, the Grinder looks backward). On the other hand those surfaces show interesting and unexpected topological properties, allowing the space of the Bachelor apparatus to expand (thus, at the same time, the Grinder looks forward).
The example regarding the stereokinetic effect applied to the Sieves (3.3) could be seen as a further different solution, involving perspective and rotary motion.
Also, the motion of the Spangles through the Sieves establishes a direct connection with the topological properties of a Kleinian bottle, which, in turn, is another way for the Bachelors to emulate the higher spatiality of the Bride.
In conclusion, we can say that the emancipation of the freed forms of the Bachelor apparatuspass through a dynamic perspective.
Duchamp did not abandon his ambition to make visible the presence of higher dimensions.

Acknowledgements

I want to express my thanks to Prof. Silvia Pianta, for some clarifications about the hyperboloids, and to my friend Paolo Mazzoldi, who checked the article for the linguistic correctness.

Notes

1. Michel Sanouillet and Elmer Peterson (eds), The Writings of Marcel Duchamp (New York: Da Capo Press, 1989), 83.
For the corresponding note issued in the Green Box see also pp. 44-45.

2. See for instance:
Craig Adcock, Marcel Duchamp’s Notes from the « Large Glass » : An N-Dimensional Analysis, (Ann Arbour: UMI Research Press, 1983).
Jean Clair, Marcel Duchamp et la fin de l’art (Paris: Gallimard, 2000).
For some further details see also:
Roberto Giunti (a), “R. oS. E. Sel. A. Vy” in Tout-Fait, Vol. 2, Issue 4 (January 2002): Articles.
Roberto Giunti (b), “Complexity Art” in Tout-Fait, Vol. 2, Issue 5 (April 2003): Articles.

3. Pierre Cabanne, Dialogues with Marcel Duchamp, trans. Ron Padget, (New York: Viking Press, 1971), 38.

4. Calvin Tomkins, Duchamp, A Biography, (New York, Henry Holt and Company, 1996), 128.

5. Sanouillet and Peterson [1], 40, 41.

6. Rhonda Roland Shearer, et al., “Why the Hatrack is and/or is not Readymade: with Interactive Software, Animations, and Videos for Readers to Explore” in Tout-Fait, Vol. 1, Issue 3 (December 2000): 9.

7. Roland Shearer, [6], 9.

8. Cabrì Géomètre II, The Interactive Geometry Notebook, by Jean Marie Laborde and Franck Bellemain. Cabrì Géomètre II is a trademark of Université Joseph Fourier.

9. Information on CabriJava and free download of the software at this site:
http://www-cabri.imag.fr/cabrijava/

10. Of course the choice of such couple of corresponding lines determines the position of the viewpoint, or, equivalently, the distance of the observer from the picture. The matter was already known in the Renaissance. See for instance Tony Phillips, who carefully and simply explains it at

http://www.math.sunysb.edu/~tony/whatsnew/column/alberti-0102/alberti1.html

11. Note that the plan sketch is symmetrically reversed upside-down with respect to Duchamp’s original orientation. This was done to allow simpler prospective procedures with Cabri
12. Be patient with dragging, because the applet must recalculate the entire perspective; it requires up to tens of seconds, according to the speed of the used processor. Also, drag only by a little step at a time.

13. In addition, the blades of the Scissor in Cabri figure are shorter than the original; but in this case we cannot speak of mismatch, simply because Duchamp’s sketches don’t include the exact measure of the length of the blades.

14. Roland Shearer [6], 9.

15. Gould, Stephen Jay and Rhonda Roland Shearer “Drawing the Maxim from the Minim: The Unrecognized Source of Niceron’s Influence Upon Duchamp” in Tout-Fait, Vol. 1, Issue 3 (December 2000): News.

16. Linda Henderson, Duchamp in Context: Science and Technology in the Large Glass and Related Works(Princeton, Princeton University Press, 1998).
17. Anyway this wrong assumption could perhaps be useful, at least to clarify a minor detail about the Grinder. We know that Duchamp saw such a machine in the window of a confectionary shop in Rouen. See for instance the entry for March 8, 1915 in:
Jennifer Gough-Cooper and Jacques Caumont, and Pontus Hulten, ed. ‘Ephemerides on or about Marcel Duchamp and Rrose Sélavy, 1887-1968’, in P. Hulten, ed., Marcel Duchamp: Work and Life (Cambridge, Mass.: MIT Press, 1993).
We still have a hatching of that window, showing the very machine seen by Duchamp; we can clearly see the three rollers which are very elongated, and this shape could indicate that their vertexes coincided with that of the basement; thus maybe they rolled without sliding. However Henderson (in [16], 59) points out that similar grinders standardly have only two rollers, and shows a hatching of such a grinder (fig. 67 of her book): here the rollers slide on their basement, because their vertexes lay far beyond the centre of it. I’m not an expert in grinding chocolate, but maybe we could have an explanation for everything: if there is no sliding (as we could suppose for the Rouen grinder) a minor power is required to rotate; on the contrary, if there is sliding (which gives a better grinding) higher power is required to rotate, and in addition there is the risk to break the machine for the higher friction; the solution could be to remove one roller, to diminish both required power and risks of breaking.

18. Roland Shearer, Rhonda: “Why is Marcel Duchamp’s Bicycle wheel shaking on its stool” <http://asrlab.org/articles/why_bicycle_wheel.htm>

19. In general I inserted Animations instead of the usual Applets if (as in the present case) the visualization is too complex to be rendered correctly with CabiJava.

20. Sanouillet and Peterson [1], 55.

21. Tomkins [4], 137.

22. Sanouillet and Peterson [1], 86.

23. In the stimulating article cited in [15] Stephen Jay Gould and Rhonda Roland Shearer doubt that theTaumaturgus could have influenced Duchamp, and as a further support of their hypothesis they stated:
At least three scholars well versed in the science of Duchamp’s interests in optics and perspective (Jean Clair, Linda Henderson and Craig Adcock) have followed Duchamp’s literal instruction, and searched Thaumaturgus opticus to locate the influence of classical works upon Duchamp’s understanding of perspective. But they found nothing beyond the undoubted status of Thaumaturgus as a good and standard text for its time.
In short, Gould and Roland Shearer argue that the Thaumaturgus is a quite conventional book, which academically resumes the standard knowledge then available on geometric optics and perspective; it was written in highly formal Latin and with academic purpose. His spirit is quite far from Duchamp’s personal style. Thus the Authors suggest a possible different influence of Niceron upon Duchamp: La perspective curieuse, ou magie artificielle des effects merveilleux, published in 1638; it is a shorter and amusing handbook, written in French, in a very different style (“chatty and irreverent”, say Gould and Roland Shearer) than the opus maior. A number of tricks (based on optics and perspective) are presented, which undoubtedly could better match Duchamp’s interests. Particularly, some of them were in fact used (or projected to be used) by Duchamp, for instance the now called Wilson-Lincoln effect, present in the project of the Glass (see Sanouillet and Peterson [1], 65).

24. Cabanne [3], 40.

25. Cabanne [3], 41.

26. To have an example of similar necessary and very trivial calculations, consider the project of the Tobogganin the elevation sketch. Starting from the overall altitude of the Toboggan (26 cm), Duchamp divided it into four parts, three of them measuring 7,73 cm, and one of 2.78 cm. Notice however that 7,73X3+2.78 gives 25,97 instead of 26. Other similar minor mistakes in calculations can be found elsewhere in the project.
27. See for instance Henderson [16], 82-83; and Adcock [2], 176-77.

28. See Sanouillet and Peterson [1], 97 and Adcock [2], 164-65, 177.

29. On the Necker cube inversion, and its meaning with reference to the fourth dimension, see particularly:
Rudy Rucker, The Fourth Dimension. A Guided Tour of the Higher Universes, (Houghton Mifflin Company, Boston Massachusetts, 1984).
30. Henderson [16], 82.

31. Sanouillet and Peterson [1], 29.

32. Sanouillet and Peterson [1], 96.

33. Sanouillet and Peterson [1], 92.

34. Cabanne [3], 29, 34-35.

35. E. J. Marey, Le Mouvement (Paris: G.Masson, Editeur, 1894)

36. See Henderson [16], 9; See also Cabanne [3], 34:
Cabanne: Didn’t films influence the “Nude Descending a Staircase?”
Duchamp: Yes, of course. That thing of Marey…
Cabanne: Chronophotography.
Duchamp: Yes. In one of Marey’s books, I saw an illustration of how he indicated people who fence, or horses galloping, with a system of dots delineating the different mouvements. That’s how he explained the idea of elementary parallelism. As a formula it seems very pretentious but it’s amusing.
37. Adcock [2], 188-189.

38. The same remark of note [19] holds.

39. Sanouillet and Peterson [1], 68.

40. In general the red surfaces are displayed only for the first turn of the roller around the Grinder axis. The geometric loci displayed in Applet 11 are quite complex, and the same applet could work not perfectly and too slowly.

41. Clair [2]; Giunti [2a]

42. Sanouillet and Peterson [1], p. 49

43. Ibid., 50.

44. Ibid., 29.

45. Ibid., 49.

46. Ibid., 87.

47. Roberto Giunti, “Analysing Chess. Some deepening on the chaos concept by Klee”, VisMath, Vol. 4, No. 3 (2002), http://www.mi.sanu.ac.rs/vismath/pap.htm

48. Sanouillet and Peterson [1], 87.

49. Ibid., 88.

50. Ibid., 88.

51. Adcock [2], 183.

52. Cabanne [3], 72.

53. David Hilbert and S. Cohn-Vossen, Geometry and the Imagination (New York: Chelsea, 1999).

54. See once again Rucker [29]

55. Sanouillet and Peterson [1], 29.

56. Ibid., 57-59.

57. Cabanne [3], 38-39.

58. Cabanne [3], 42-43.

59. Henderson [16].

60. Tomkins [4], 125.

61. Gould’s analysis is contained as a separate box inside the already cited article of Roland Shearer [6]

62. It is well known that the Capillary Tubes (alias the Standard Stoppages, the starting point of the whole machinery of the Bachelor apparatus), sound like a non-Euclidean axiom, but they seem to be unable to generate something emancipated, maybe because of the mechanic gearing of the parts of the apparatus, which in turn recalls a too rigid (non-emancipated) logic.

63. Sanouillet and Peterson [1], 92.
Fig. 1-5, 9, 11-12, 14-16, 20-22, 24-29, 32-34, 37 © 2007 Succession Marcel Duchamp, ARS, N.Y./ADAGP, Paris.

Cinq petites choses à propos de L.H.O.O.Q.

1

click to enlarge

Figure 1
Marcel Duchamp, L.H.O.O.Q.

Tentant tardivement de préciser quand, en 1919, a été “fait” L.H.O.O.Q., Marcel Duchamp fournira deux dates: au début 1953, dans ses entretiens avec Sidney, Harriet et Carroll Janis, il dira décembre⁽¹⁾ ; en juin 1966, dans ses entretiens avec Pierre Cabanne, octobre⁽²⁾ .

Ceci, autant en regard des faits rapportés que de la lecture qu’on peut en faire, n’est pas sans conséquence.

Du début août au 27 décembre 1919, en effet, Duchamp habite, avenue Charles-Floquet (Paris 7e), chez Francis Picabia et Gabrielle Buffet (cette dernière enceinte d’un quatrième enfant de lui, qui naît le 15 septembre). Picabia, lui, a emménagé depuis quelques jours ou semaines déjà rue Émile-Augier (Paris 16e), chez Germaine Everling, sa maîtresse (également enceinte de lui, et dont l’enfant naîtra le 5 janvier 1920⁽³⁾). Il faut déduire de cette situation particulière que, durant ce séjour de presque cinq mois, les contacts Duchamp-Picabia n’ont été que très épisodiques, sinon inexistants (sauf, selon toute vraisemblance, vers la fin du séjour), cela permettant d’ “expliquer” pourquoi L.H.O.O.Q. n’est pas publié dans les n 9 (novembre 1919), 10 (décembre 1919) ou 11 (février 1920) de 391, la revue de Picabia, mais bien, dans une version Picabia intitulée Tableau dada par Marcel Duchamp⁽⁴⁾ , dans le n 12 (mars 1920). Michel Sanouillet ajoute sur ce point une précision: “Picabia lui demanda par lettre l’autorisation de “refaire” une Joconde pour 391, autorisation qui fut naturellement accordée. Mais Picabia, qui n’avait conservé de l’oeuvre de Duchamp qu’un souvenir imprécis, se borna à dessiner la moustache⁽⁵⁾.” Picabia, en effet, ne reprend sur le coup que “L.H.O.O.Q.”, l’inscription qui deviendra le titre du readymade⁽⁶⁾, l’inscrivant à son tour, verticalement et sans les points, sur l’une de ses toiles, Le double monde⁽⁷⁾, datée de [décembre] 1919 et exhibée sur scène par André Breton lors du Premier vendredi de (la revue) Littérature, le 23 janvier 1920, première manifestation de Dada à Paris.

À cause de son titre (Tableau dada par Marcel Duchamp), la version Picabia passera pour l’original pendant plusieurs années, cet original n’étant montré pour la première fois qu’en mars 1930 à Paris, en même temps qu’une réplique agrandie (faite fin janvier ou début février 1930⁽⁸⁾), lors de l’exposition intitulée La peinture au défi et préfacée par Aragon.

Pour un poète, romancier et critique comme Aragon, un readymade n’est pas, dès cette époque, qu’un objet industriel, déplacé de son contexte et détourné de sa fonction utilitaire.

3

Il faut préciser que la reproduction en couleur qui en est la base n’est pas une carte postale, malgré que tant de gens l’aient dit ou écrit⁽⁹⁾. Il n’y a qu’à regarder le verso, publié par Arturo Schwarz dès 1969 dans la 1re édition de son catalogue, pour constater qu’il n’y a pas le dispositif habituel de la carte postale avec la place pour l’adresse et le timbre (à droite), pour le “message” et la légende de l’illustration (à gauche), mais plutôt, par Duchamp, telle indication technique (au crayon) sur comment photographier le recto, et, plus tard, par dessus la précédente, telle déclaration officielle devant notaire (à l’encre) comme quoi il s’agit bien de l’original⁽¹⁰⁾. Ce petit palimpseste, au verso, n’ayant d’égal, au recto, que cette mine (de crayon ajoutant les moustaches et la barbiche⁽¹¹⁾) sur la mine (de la Joconde).

Mais où Duchamp s’est-il procuré cette reproduction en couleur? Le plus vraisemblable, comme il le raconte aux Janis en 1953, est qu’il l’a achetée dans quelque boutique installée près du Louvre, rue de Rivoli, afin de vendre à bon marché telle ou telles reproductions des grandes oeuvres de ce musée, façon de faire bien connue dans toutes les grandes villes où il y a d’importants musées. Faut-il rappeler qu’en avril 1911 le déjà très célèbre tableau de Léonard, peint au début du XVIe siècle, a été volé au Louvre et que, parce qu’on pouvait le croire disparu ou détruit (il ne sera retrouvé qu’en décembre 1913), on en a massivement diffusé, durant ces années ou immédiatement après, diverses reproductions couleur, photos retouchées ou non, dont certaines au format d’une carte postale⁽¹²⁾. Sans doute sait-on également qu’en 1919 c’est le 400e anniversaire de la mort du peintre. Il est fait allusion à ces deux événements (telle perte peut-être irrémédiable et tel anniversaire) dans le choix de Duchamp.

Quand Duchamp demande par lettre (New York, 9 mai 1949) à son ami Henri-Pierre Roché d’aller acheter une ampoule de sérum – devenue ampoule d’Air de Paris – pour remplacer celle, actuellement cassée, qu’il a rapportée de Paris, fin décembre 1919, à ses amis Louise et Walter Arensberg, il écrit:

Pourrais[-]tu aller dans la pharmacie qui est au coin de la rue Blomet et la rue de Vaugirard (si elle existe encore, c’est là que j’avais acheté la première ampoule) et acheter une ampoule comme celle-ci: 125c.c. et de la même dimension que le dessin […]
— Si pas rue Blomet ailleurs, mais autant que possible la même forme, merci.⁽¹³⁾

La simple consultation d’un plan de Paris nous indique tout de suite qu’il n’y a pas de coin Blomet-Vaugirard, ces deux rues (15e) étant parallèles! Je rappelle cet exemple pour indiquer qu’une indication précise, même venant de l’auteur, peut être tout simplement inexacte, voire erronée. Ainsi en est-il de L.H.O.O.Q., carte postale.

Et quand Duchamp, dans “Apropos of Myself” (1962-1964), décrit cette reproduction en couleur comme étant “a cheap chromo”, il faut préciser qu’en français comme en anglais chromo est l’abréviation de chromolithographie “image lithographique en couleur” (Petit Robert I), chromolithograph “a color print produced by chromolithography”(The American Heritage of the English Language). En français, cependant, chromo, maintenant au masculin (et non plus au féminin), a un sens péjoratif: “toute image en couleur de mauvais goût”. Ce sens supplémentaire, qui met en scène le goût, fait intervenir la question esthétique, voire artistique, ce qui n’est pas le cas en anglais, cheap signifiant dans cet exemple “of poor quality” (dont la reproduction est de mauvaise qualité), mais surtout “inexpensive” (qui est bon marché⁽¹⁴⁾).

4

Quand Duchamp, dans ses entretiens de 1966 avec Cabanne, parle de Picabia et de L.H.O.O.Q., il en profite, si je puis dire, pour ajouter:

Une autre fois Picabia a fait une couverture de 391 avec le portrait de [Georges] Carpentier; il me ressemblait comme deux gouttes d’eau, c’est pour cela que c’était amusant. C’était un portrait composite de Carpentier et de moi.⁽¹⁵⁾

Cette autre fois, c’est l’été 1923, quand Georges Carpentier, le boxeur, est venu chez Picabia, au Tremblay-sur-Mauldre, le petit village où il habite depuis 1922, et que ce dernier a fait son portrait de profil; le boxeur, alors, a même signé le portrait. Quand Picabia, plus d’un an plus tard, a décidé de mettre ce portrait en première page du dernier numéro de 391 (n 19, octobre 1924), il a barré incomplètement cette signature (qu’on peut lire sous la rature) et a ajouté “Rrose Sélavy / par Picabia”, frappé après coup par la ressemblance entre Carpentier et Duchamp (dont Sélavy est le pseudonyme depuis 1920)⁽¹⁶⁾. Duchamp ne faisant qu’entériner, en 1966, cette “interprétation” de Picabia.

De la même façon, si, par contiguïté, ce “portrait composite” désigne aussi L.H.O.O.Q., il faut en déduire que Duchamp rappelle, en 1966, sa déclaration de 1961 à propos de ce readymade:

La chose curieuse à propos de cette moustache et de ce bouc est que, lorsque vous regardez le sourire, Mona Lisa devient un homme. Ce n’est pas une femme déguisée en homme, c’est un vrai homme; voilà ma découverte, sans qu’à l’époque je le réalise.⁽¹⁷⁾

En 1919, une femme (La Joconde dans L.H.O.O.Q.) est aussi un homme comme, en 1920-1921, un homme (Marcel Duchamp en Rose, puis Rrose, Sélavy) est aussi une femme.

5

Sans vraiment entrer dans l’interprétation du célèbre readymade, il peut néanmoins être remarqué que ce 400e anniversaire a pu être non seulement un déclencheur (en tant qu’anniversaire), mais aussi une contrainte (en tant que chiffraison), le 4 disant qu’il ne faut utiliser que quatre lettres, les 00 suggérant que l’une d’elles, qui doit être un O, soit redoublée⁽¹⁸⁾. Ces quatre lettres, comme Duchamp le dit dans “Apropos of Myself”, étant, comme on peut ici aussi le constater après-coup, dans l’ordre alphabétique – H, L, O, Q – dans le nom de la rue (cHarLes-flOQuet) où il habite alors. Mais aussi dans le nom du procédé à la base de cette reproduction: elle est cHromoLithOgraphiQue.

Et il me plaît de constater qu’à New York la notaire choisie par Duchamp et qui, signant, certifie, le 22 décembre 1944, qu’il s’agit de l’original (“This is to certify that this is the original “ready made” L H O O Q Paris 1919”⁽¹⁹⁾ ), se nomme Elsie Jenriche⁽²⁰⁾: comment ne pas voir qu’elle est là aussi parce qu’elle a ce nom (qui, de ce fait, revient métatextuellement sur l’un des enjeux de l’oeuvre), mixte de “je” (I en anglais ou Ich en allemand) et d’”autre” (else), et qu’il y est question de “genre” (jenre), else rimant avec le féminin (elle: La Joconde, La Gioconda) qui rime avec le masculin (L: Léonard, Louvre), elle étant devenu il!

Enfin, si l’on trace une ligne verticale à angle droit avec le haut de l’oeuvre et qu’on passe par le centre des moustaches, on voit bien que, à cause de l’angle du visage, on longe le nez, à gauche, du personnage femelle et désormais aussi mâle et qu’on arrive, “down below” (comme dira Duchamp en 1961), exactement entre “L.H.” et “O.O.Q.”. Ce redoublement du O est alors, une fois de plus, désigné.

Notes

1. Toujours inédits, les entretiens avec la famille Janis (Sidney, le père, Harriet, la mère, et Carroll, le fils) ont été faits à l’occasion de la préparation, par Duchamp, du catalogue et de l’accrochage de l’exposition Dada 1916-1923 à la Sidney Janis Gallery, New York, 15 avril-9 mai 1953. Dans la chronologie intégrée du catalogue Joseph Cornell / Marcel Duchamp… in resonance Joseph Cornell / Marcel Duchamp… in resonance, Philadelphia Museum of Art, 8 octobre 1998-3 janvier 1999, et The Menil Collection, Houston, 22 janvier-16 mai 1999, Ostfildern-Ruit, Cantz Verlag, 1998, p. 277, Susan Davidson, sans dire d’où elle tire cette précision, retient également le mois de décembre.

2. Pierre Cabanne, Entretiens avec Marcel Duchamp, Paris, Belfond, 1967, p. 114.

3. C’est un jour après la rencontre d’André Breton, invité là, et douze jours avant que, le 17 janvier, Tristan Tzara n’arrive là pour y habiter, ce séjour coïncidant avec le début de ce que Michel Sanouillet a appelé “Dada à Paris”: voir sa somme, Dada à Paris, Paris, Pauvert, 1965. Le siège du “MoUvEmEnT DADA, Berlin, Genève, Madrid, New York, Zurich”, dit le papier à lettre qui arbore cet en-tête, est maintenant à Paris. Par ailleurs, je note la coïncidence (qui n’en était peut-être pas une en 1919, étant donné l’état des connaissances sur l’oeuvre de Léonard): lorsque Duchamp est à Paris cette année-là, les deux femmes (l’épouse et la maîtresse) de Picabia sont enceintes de garçons; lorsque Francesco del Giocondo, au printemps 1503, passe une commande à Léonard pour qu’il fasse un portrait de son épouse, celle-ci lui a déjà donné deux garçons (en mai 1496 et en décembre 1502). Voir, autre somme, Daniel Arasse, Léonard de Vinci. Le rythme du monde [1997], Paris, Hazan, 2003, p. 388-389. La rime, ici, dans les deux cas: Joconde / féconde.

4. À Cabanne, Duchamp dit Tableau dada de [sic] Marcel Duchamp.

5. Michel Sanouillet, Francis Picabia et “391”, tome II, Paris, Losfeld, 1966, p. 113. (Le tome I est, en fac-similé, la réédition de 391 [1917-1924] augmentée de divers documents inédits, Paris, Losfeld, 1960.) Duchamp étant à New York depuis le 6 janvier et le no 12 de 391 ne paraissant (précise Sanouillet) qu’à la fin mars, on peut penser que Duchamp, interviewé par Schwarz (The Complete Works of Marcel Duchamp, New York, Abrams, 2e édition, 1970, p. 476), se souvient erronément de ce qui s’est passé à l’époque (je retraduis): “Mon original n’est pas arrivé à temps et, afin de ne pas retarder indûment l’impression de 391, Picabia a dessiné lui-même la moustache sur la Mona Lisa mais a oublié la barbiche.”

6. Je dis “l’inscription qui deviendra le titre du readymade” car, dans le catalogue-affiche de l’exposition chez Sidney Janis, Duchamp écrit: “La Joconde, postcard with pencil”. Ce n’est qu’à partir du premier catalogue de l’oeuvre duchampienne, celui de Robert Lebel (Sur Marcel Duchamp, Paris, Trianon Press, 1959), que ce readymade a L.H.O.O.Q. comme titre. Et ce n’est qu’à partir du catalogue Schwarz (Arturo Schwarz, The Complete Works of Marcel Duchamp, New York, Abrams, 1re édition, 1969) qu’on a les dimensions exactes dudit readymade: 19.7 x 12.4 cm ou 7¾ x 4⅞ pouces.

7. Les deux O de “L H O O Q”, eux-mêmes au centre de deux autres O qui ont la forme de ficelles formant des 8 ou encore la forme des pales d’une hélice, mais d’une hélice sans axe et molle, courbée par le vent, sont également – et doublement – les O de “double” et de “monde”. Le petit manque, en haut à gauche, dans l’un de ces autres O n’a d’égal, en bas à droite, que le petit manque dans le À de “À DOMICILE”, une autre inscription, et que le petit supplément – la queue – du Q de “L H O O Q”. Façon de faire coïncider ironiquement spéculations mathématiques (topologie) et spéculations marchandes (livraison “à domicile”, c’est-à-dire au logis).

8. “J’ai fait juste avant de quitter Paris une Joconde pour Aragon […] / Man Ray a la 1ère Joconde” (lettre de Duchamp à Jean Crotti, Villefranche-sur-mer, 6 février 1930, dans Affectionately, Marcel. The Selected Correspondance of Marcel Duchamp, édition de Francis Naumann et Hector Obalk, traduction de Jill Taylor, Gand et Amsterdam, Ludion Press, 2000, p. 171).

9. Trois exemples: Duchamp lui-même en 1953 (voir note 6); Ecke Bonk, Marcel Duchamp, The Box in a Valise. Inventory of an Edition, New York, Rizzoli, 1989, p. 241; Calvin Tomkins, Duchamp. A Biography, New York, Henry Holt and Company, 1996, p. 221.

10. Faut-il ajouter que Duchamp, dans les répliques ultérieures, n’a jamais utilisé une carte postale.

11. J’utilise ici le pluriel, comme Duchamp en avril 1942 lorsqu’il indique à l’encre, au bas de la maquette de l’une des deux versions Picabia (celle qui est reproduite dans 391), “Moustaches par Picabia / barbiche par Marcel Duchamp”. En français, on dit indifféremment, par exemple, ciseau et ciseaux (car il y a deux lames), pantalon et pantalons (deux jambes), moustache et moustaches (deux joues ou, simplement, deux côtés au visage). Je note par ailleurs que l’indication technique, inscrite par Picabia sur deux lignes au crayon verticalement à droite de la reproduction, commence par deux liaisons – celle qui amorce le 1 de “1 cliché” sur la première ligne et celle qui amorce le s de “sans” sur la deuxième ligne – qui n’ont d’égal que l’extrémité des moustaches! Pour une reproduction et des commentaires, voir Francis Naumann, The Art of Making Art in the Age of Mechanical Reproduction, catalogue de l’exposition chez Achim Moeller Fine Art, New York, 2 octobre 1999-15 janvier 2000. Si le voyage à Paris fait par Arp en avril 1942 est bien celui durant lequel il entre en possession de ces deux versions, la rencontre Arp-Duchamp (qui se connaissent depuis 1926) ne peut avoir lieu qu’en zone inoccupée (à Grasse où habite Arp, à Sanary où habite Duchamp, avant le départ de ce dernier pour les États-Unis le 14 mai).

12. Voir les deux cartes postales, datées 1914, reproduites dans Roy McMullen, Les grands mystères de la Joconde [1975], traduction d’Antoine Berman, Paris, Éd. de Trévise, 1981, p. 223.

13. Affectionately, Marcel, ouvr. cité, p. 272.

14. C’est d’ailleurs la traduction, par Michel Sanouillet, de ce passage: “un chromo […] bon marché” (“À propos de moi-même”, dans Duchamp du signe, Paris, Flammarion, 1975, p. 227). Naumann emprunte exactement la même voie: “an inexpensive chromo-lithographic color reproduction” (The Art of Making Art in the Age of Mechanical Reproduction, ouvr. cité, p. 10).

15. Pierre Cabanne, Entretiens avec Marcel Duchamp, ouvr. cité, p. 115.

16. Voir Michel Sanouillet, Francis Picabia et “391”, ouvr. cité, p. 166. On peut voir (391, ouvr. cité, p. 127) la signature de Carpentier et l’ajout de Picabia sous quelques-unes des lignes imprimées en caractères typographiques au bas de la page.

17. Herbert Crehan, “Dada”, Evidence, Toronto, n 3, automne 1961. Je traduis.

18. Ces deux “O.” ne sont pas sans évoquer aussi, par la rime “O.” / eau, le lac de montagne et le lac de plaine dans le célèbre tableau, respectivement en haut à droite et un peu plus bas à gauche dans le paysage dominé par la loggia où est le modèle, Lisa. Et que dire du chemin sinueux venant du lac de plaine, répercuté dans la queue du “Q.” (calligraphié par Duchamp)?

19. Une phrase présentative dans une autre, le référent de “This” (Ceci, comme dans “Ceci est mon corps” ou dans “Ceci est une oeuvre d’art”) étant cataphorique (c’est-à-dire qu’il suit le pronom): dans le premier cas, c’est “the original “ready made””; dans le second cas, c’est l’ensemble de la proposition formant le premier cas.

20. Dans son bref article, ““Desperately Seeking Elsie”. Authenticating the Authenticity of L.H.O.O.Q.’s Back” (Tout-Fait, New York, vol. I, n 1, décembre 1999), Thomas Girst nous apprend que cette dame, installée à l’Hotel St. Regis, New York, de 1943 à 1945, est une sténographe publique.

Re-evaluating the Art & Chess of Marcel Duchamp

Duchamp the Chess “Idiot”
Damisch: You remember Duchamp’s famous print of two chess players . . . [I was furious] that idiot, Duchamp! He just managed to get $2,000 off me for his Chess Association and in exchange he gave me this horrible etching of chess players. . . . [And he] said that Art no longer had any internal necessity; it was now a pure convention!⁽¹⁾

In 1961 Marcel Duchamp organized an auction of artworks to raise funds for the American Chess Foundation and asked many of his contemporaries to contribute works. The ‘horrible etching’ which Damish purchased, a reproduction of his 1911 cubist painting The Portrait of Chess players (Fig.1), is part of a largely incommensurate aspect of Duchamp’s historical and artistic legacy: Chess. Damisch’s response to this work is like that of other art historians to his entire involvement in the game. Most commonly, Duchamp’s involvement in chess is expressed as incomprehensible, or simply ignored.⁽²⁾Click to EnlargeFigure 1
Marcel Duchamp,
The Portrait of Chess Players, 1911

Popular historical representations tell that in 1923, after the completion of The Large Glass (Fig.2), he quit art to play chess.⁽³⁾
Nevertheless the connection between chess and Duchamp’s greater artistic agenda is fundamental to understanding him as an historical figure.

Damisch begins a critique on Duchamp as chess player, The Duchamp Defense, with an outline of his chess career, primarily to construct a ‘narrative’ of his achievements in the realm of chess.⁽⁴⁾
The reading of this is impressive. However, Damisch then poses the questions, how does such a narrative serve in attempting to understand Marcel Duchamp? What is the purpose of such a narrative? In developing an understanding of Duchamp, the artist, what is the purpose of understanding Duchamp the chess player? Damisch says that this narrative should not just be told for the love of a story but to establish the value chess was held by Duchamp.figure 2
Marcel Duchamp, Bride Stripped Bare by Her Bachelors, Even [a.k.a. The Large Glass], 1915-23, Philadelphia Museum of Art.

Above all is his belief that [Duchamp] was never more interested in chess than after he had ceased being interested in painting.⁽⁵⁾

This narrative shows that Duchamp’s involvement in chess was not a side-line interest but rather Duchamp’s dedication to chess was with “all the ambition and single minded passion of a professional.”⁽⁶⁾
Yet, as Damisch states, this passion that would dominate his time and intellect for over twenty years of his life “was no more than a game.”⁽⁷⁾
Thus if the aim is to understand his art work it has been common practice to dismiss such an investigation in Duchampian chess as an incongruous aspect of his life. Tomkins, who has written extensively on Duchamp, offers that,

Although chess claimed a great deal of the energy that had been formerly devoted to his Large Glass, the usual statement that he abandoned art for chess is misleading. In fact, one of the essential facts about it is that while he has successfully avoided playing the role of artist since 1923, he has never left the art world.⁽⁸⁾

Tomkins points out that the art world has used a blunt instrument to separate aspects of Duchamp’s life. The ‘quitting’ one activity and taking up of another is symptomatic of the way historical figures are commonly represented. Furthermore, historical methodology has placed restrictions upon how Duchamp has been investigated and subsequently represented. It is these assumptions of art historians that have led to the creation of a coherent art narrative of Duchamp’s life and work that has not allowed chess to disrupt or to inform it. Duchamp’s engagement in a variety of intellectual disciplines disrupts such a clear cut understanding of Duchamp as an artist. Such an approach restricts the historical and critical understanding of Duchamp by considering his activities outside the paradigm of art, as peculiar, inconsistent and irrelevant. As ‘an-Artist’ Duchamp allowed diverse and distinctly different institutions to converge, to interrelate, informing a complex philosophical understanding of art and the intellectual milieu in which he was living.

The Histories of Marcel Duchamp as Chess Player

. . . comparatively little has been written about Duchamp’s chess as a form of artistic activity, how it relates to his other artistic interests, and what it reveals about his attitude to art in general. A few writers have commented on these matters, but their views tend to be underdeveloped and are often highly speculative. Roger Cardinal summed it up when he remarked that “nobody has entirely assessed the significance of chess in Duchamp’s career.”⁽⁹⁾

When attempting to address the nature of chess in the life of Marcel Duchamp one is met with many contradictions. Even from within chess there is debate over Duchamp’s approach to the game and has also failed to bridge the theoretical distance in an attempt to reflect upon his art. Theorists have attempted to determine Duchamp’s playing style through a comparison of the complexities in conservative Classical chess play and Avant-garde Hypermodernism. Yet, due to misunderstandings concerning Hypermodernism in chess and of Dada in art, we will see how some, like Keene, Humble & Le Lionnais, have drawn various conclusions about Duchamp the chess player.

It is tempting for the art historians, like Arturo Schwarz, to adopt a systematic approach when writing about Marcel Duchamp and to create a theory through which all of his work can be seen. However one must be wary of theories that claim to unlock the system or pattern behind Duchamp’s work. For such dominant or meta theories have greatly affected how aspects of Duchamp’s life and works are understood. Francis Naumann in his article titled “Marcel Duchamp: A Reconciliation of Opposites,” warns that any attempt to formulate Duchamp “would be – in the humble opinion of the present author – an entirely futile endeavor .“⁽¹⁰⁾Francis Naumann suggests that Duchamp gave his response to those attempting to unlock the mystery when he said “There is no solution, because there is no problem.” In understanding the nature, role and significance of Duchampian chess, one needs to see beyond the problem / solution dilemma and operate at a different cognitive level involving multiplicity and complexity. This thesis aims to demonstrate a multiplicity of the complex relationships between Duchamp as artist and as chess player. The importance for this approach, as Naumann states, is that Duchamp himself moved through a number of contemporary artistic styles and each time developed a unique approach of self consciously “defying convenient categorization.”⁽¹¹⁾To support this claim Naumann offers a collection of quotations by Duchamp from a 1956 interview with James Sweeney emphasizing the importance of change and the defiance in his work to any tradition or “taste.”

‘It was always the idea of changing,’ he later explained, of ‘not repeating myself.’ ‘Repeat the same thing long enough,’ he told an interviewer, ‘and it becomes taste,’ a qualitative judgment he had repeatedly identified as ‘the enemy of Art,’ that is, as he put it, art with a capital A. ⁽¹²⁾

Humble asserts that published views on Duchamp’s chess as art are “underdeveloped and often highly speculative is, he suggests, due to the reason that nobody is entirely sure how to understand or to define chess itself. Humble muses that chess players themselves debate whether chess is a game, sport, science, or art.

With this being said, the mystery of chess in the life of Marcel Duchamp is a subject that has often been approached in a formulaic manner. Questions like; “What type of player was Duchamp?,” “What was the role of chess in his life?,” and “What is the relationship between chess and art?” have been presented in a simplistic and minimalistic fashion. One example of this is an article by grand master and chess theoretician Raymond Keene titled Marcel Duchamp: The Chess Mind. In this article Keene discusses Duchamp’s achievements, his associations, his theoretical positions, and attempts to establish a relationship between art and chess. Primarily his analysis focuses upon the nature of Hypermodernist chess praxis and the dada art movement. Keene seeks to show that Duchamp as well as being a Dadaist, was also a hypermodernist chess player and thereby establish that the relationship between chess and art is dada. In this way, Hypermodernism is often equated with dada, yet the similarities have more to do with the look and feel of the game rather than theory. In comparison to Classical or Modern games hypermodernism seems absurd and illogical.⁽¹³⁾

Keene’s theoretical analysis of Duchamp’s chess play dismissed comments made by a chess player and dadaist contemporary of Duchamp’s, Francis Le Lionnais. Le Lionnais defeated Duchamp in 1932 in Paris, and later stated that Duchamp was not a dada chess player, but a player who adopted a conventional, conformist, or classical style of play.⁽¹⁴⁾
To counter this claim, Keene looks closely at the influence and the similarities between Duchamp and the founder of hypermodernism, Grand master Aaron Nimzowitsch. Keene asserts that Duchamp borrowed a Nimzowitsch opening for the 1927 world Championship. Keene’s theories concerning the relationship between chess and art are convincing. Keene argues that the tactical talent displayed in his love for “paradoxical hidden points” is fundamentally Dada. Keene mirrors Duchamp’s comments that chess was a “violent sport” with that of Nimzowitsch who said “chess was a struggle like that of life.”⁽¹⁵⁾
Further, Keene shows Duchamp’s continuing dedication to Nimzowitsch. In the course of his research Keene visited Teene Duchamp, Marcel Duchamp’s wife, and found a copy of Nimzowitsch’s Chess Praxis that Duchamp had hand written (over 200 pages).

Keene demonstrates the associations between Duchamp and Nimzowitsch and dispels the comments made by Le Lionnais. Keene establishes a close association between Duchamp and Nimzowitsch, arguing that Nimzowitsch was a hypermodernist and therefore that Marcel Duchamp was one also. Keene’s conclusion is not far off, yet, it maintains an understanding of Hypermodernism that is misleading. Keene adopts a very clear theoretical methodology of forming binary opposites. His use of opposites, or opposition, is essential for the creation of a distinction between classical and hypermodern chess. Yet this position implies a conflict between the two styles of chess play that is not necessarily true. One of the intrinsic characteristics of Hypermodernism is its connectedness with the movement it surpassed.

The relationship does lie in the realms of Hypermodernism and Dada and yet it goes much further, as Duchamp goes further than Dada. Thus, Keene’s whole approach to find the solution to the problem of Duchampian chess is mistaken.

An interview between Ralph Rumney and Francois Le Lionnais was the catalyst for this thesis and investigation. I set out to determine which one of the theorists was correct, and it was not until I reconsidered my methodology that an alternative conclusion could be reached. Ralph Rumney has just asked Le Lionnais to describe Duchamp’s qualities as a player,

FRANCOIS LE LIONNAIS I don’t know how well I can do that . . . in his style of play I saw no trace of . . . a Dada or anarchist style though this is perfectly possible. To bring Dada ideas to chess one would have to be a chess genius rather than a Dada genius. In my opinion Nimzowitsch, a great chess player was a Dadaist before Dada. But he knew nothing of Dada. He introduced an anticonformism of apparently stupid ideas which won. For me that’s real Dada. I don’t see this Dada aspect in Duchamp’s style. . . .

RALPH RUMNEY You say he was not a Dadaist as a chess player. . . but was he an innovator?

FRANCOIS LE LIONNAIS Absolutely not. He applied absolutely classic principles, he was strong on theory – he’d studied chess theory in books. He was very conformist which is an excellent way of playing. In chess conformism is much better than anarchy unless you are Nimzowitsch, a genius.

This exchange ends with Rumney posing a question:

It seems to me that the extremely conformist style of Duchamp’s chess which you describe has parallels in everything he did, and that perhaps instead of looking for evidence of Dada in the way he played chess we should be looking for aspects of this conformism in his most anti-conformist action? ⁽¹⁶⁾

Le Lionnais, it would seem, contradicts Keene’s understanding of Duchamp’s chess. Instead of looking for conformity within Duchamp’s art, Keene refutes the very grounds for such an inquiry by stating that Duchamp was a Dadaist chess player and did not adopt a conformist or classical style. Yet even the investigation suggested by Rumney will bring us to a binary end. Lionnais claims to have seen no evidence of Duchamp’s Dadaist or hypermodernist chess play but instead a classical approach. Duchamp is either a conformist or a non- conformist artist, and Duchamp is either a conformist or non-conformist chess player. In the end this will not bring us to an understanding of Duchampian chess, but a series of binary oppositions. Keene reached this conclusion even though the original question was what sort of player was Duchamp? This investigation into Duchamp’s chess is met with two opposing views; he is either a Hypermodernist or a Classicist. The historian is being asked to determine whether Keene or Lionnais is correct.

The comparison between the chronological order of [my] paintings and a game of chess is absolutely right . . . But when will I administer checkmate – or will I be mated? ⁽¹⁷⁾

Click to Enlargefigure 3
Marcel Duchamp, The Green Box, 1934
Duchamp dropped clues along his way as to how we are to understand chess. When Duchamp co-wrote a chess book on end-game with chess theorist Vitaly Halberstadt, he collected all of the notes that he made in preparation for the book’s publication and placed them all in a ‘box’. He titled this ‘box’ The box of 1932. What is significant about the act of Duchamp ‘boxing’ his proofs and diagrams, is that it identically reflects his act of ‘boxing’ all of the notes he made in preparation for his Large Glass. Duchamp titled this box The Green Box (Fig. 3), and used it to take the viewer into the world of the ‘bride’ and the ‘bachelors’ the two major aspects of the Large Glass. Thus the Box of 1932 is to L’Opposition et les cases conjuguees sont reconciliees as The Green Box is to the Large Glass. Duchamp did not make any indication that his theoretical work on chess was to be understood through the shattered glass of his Bride. It is through the multiple paradigms in which Duchamp was involved, that we are to understand and represent him as an historical figure. Duchamp as artist sharing the values of other paradigms and bringing what is seen as incommensurate into unity. Duchamp has offered an explanation as to how two apparently incommensurate elements are united through the concept of ‘inframince’ (Fig. 4).figure 4
Marcel Duchamp, front cover for View, vol. 5, no. 1 (March 1945)

WHEN
THE TABACCO SMOKE
SMELLS ALSO
OF THE MOUTH
THAT EXHALES IT THE TWO ODOURS
ARE MARRIED
INFRAMINCE.⁽¹⁸⁾

The smell of smoke and the mouth are distinct and separate entities, though through the act of smoking, the two odors are combined forming a ‘new thought.’⁽¹⁹⁾
Thus through inframince, art and chess are married in the life and work of Marcel Duchamp. The relationship between art and chess is very complex and multi layered, and is not able to be reduced to a meta theory or solved by dismissing Duchamp’s engagement with chess.

The many paradigms in which Duchamp ‘worked’ or ‘played’ need to be understood as blending within art, via this understanding of inframince, like that of the smoke mixing with another odor. This proposed historical methodology is not only relevant to Duchamp but to all historical figures. The various contradictory positions held by historians and theorists concerning Duchamp and his incommensurate activities can be understood by the history of art. Art is what is brought into existence via a series of established conventions and fulfils various criteria. Postmodernism offers a perspective that is able to bring together that which was an anomaly to modernist historical representation of Duchamp. It is through postmodernism that the ‘sub-systems’ that Duchamp was part of can be understood and can become part of his historical representations. Unity can be created through acknowledging the existence of these paradigms and the way in which Duchamp’s activities created ‘inframince’ with each other: art and chess, chess and art, chess and science, science and art. Duchamp is ‘found’ through an historical and theoretical methodology founded upon such postmodern multiplicity.

Chess and Art “reconciled”

It is important to make a connection between many of the theories of Nimzowitsch and that of Duchamp, in particular those of aesthetics and thought. Duchamp made many statements that his art was an intellectual activity and he was critical of what he termed ‘retinal’ art. This is similar to the criticism that the Hypermodern chess players had for the classical school: classical theories were based on (formalistic) aesthetics and not on the intellect or logic. Duchamp’s interest in the intellect went beyond the realms of chess and he wished for a similar intellectual direction to take place in art.

This is the direction in which art should turn: to an intellectual expression.⁽²⁰⁾

There is a mental end implied when you look at the formation of the pieces on the board. The transformation of the visual aspect to the gray matter is what always happens in chess and what should happen in art.⁽²¹⁾

The observation that the words of Duchamp mirror those of Nimzowitsch have been made by a number of theorists. Some even go so far as to suggest that Duchamp’s Large Glass mirrors diagrams that Nimzowitsch used in his 1925 publication, which divided the chess board in two.⁽²²⁾
This is not to suggest that the way to understand Duchamp’s art is through his chess, but it is helpful to break down the intellectual barriers that exist between art and chess thus forming a reconciliation of these two paradigms in the person Duchamp.

Click to Enlargefigure 5
Marcel Duchmap, Opposition and Sister Squares are Reconciled, 1932In 1932, Duchamp, in collaboration with Vitaly Halberstadt, wrote a study on a specific end game situation titled L’Opposition et les cases conjuguees sont reconciliees (Opposition and Sister Squares Are Reconciled) (Fig. 5). Duchamp spoke of it as purely an intellectual study with no real practical application, for the situations being presented rarely came about.⁽²³⁾
He said to Cabanne,

The endgames on which this fact turns are of no interest to any chess player: and that’s the funniest thing about it. Only three or four people in the world are interested in it, and they’re the ones who’ve tried the same lines of research as Halberstadt and myself. Since we wrote the book together, chess champions never read this book, because the problem it poses never really turns up more than once in a lifetime. These are possible endgame problems, but they’re so rare that they’re almost utopian.⁽²⁴⁾

Duchamp called his work a “linguistic study,” which Damisch claims the Duchamp / Halberstadt text is built around the notion of ‘opposition.’⁽²⁵⁾
Using the language from a number of paradigms, especially from aesthetics and philosophy, to explain scientific and mathematical foundations of his chess theories.

Duchamp’s and Halberstadt’s discussion in L’Opposition et les cases conjuguees sont reconciliees involve end-game problem, and their discussions are very much couched in geometrical language, involving ‘translation,’ ‘displacement,’ and ‘rotation’ around ‘charniere’ or ‘hinges.’ Charniere’ is the term that Duchamp used in his mathematical notes to mean an ‘axis o rotation.’⁽²⁶⁾

Saussure directly uses the model of chess to introduce his oppositional theories of language. Damisch quotes from a small section where Saussure explains that it is only through words opposing one another that meaning is created;

a given term having . . . no value except through difference and through its opposition to the other terms in the language.⁽²⁷⁾

And furthermore that the relationship between languages and chess is,

Just as the game of chess is entirely in the combination of the different chess pieces, language is characterized as a system based entirely on the opposition of its concrete units.⁽²⁸⁾

Click to EnlargeFigure 6
Marcel Duchamp, Trébuchet, 1917/1964The end game is fundamentally a stage of opposition, where the only pieces that remain are the two Kings and some pawns.⁽²⁹⁾
Opposition is defined during the end game when symmetry is presented by the position of the Kings and pawns. The aspect of the end game that Duchamp and Halberstadt were concerned about was when a symmetry or a formalist structure arise and each player is struggling to keep equilibrium for survival. For there is security in symmetry during such situations because a player is able to restrict or control the moves available to the opponent. At the same time, due to the symmetry, a player may be forced into making a move that will cause their own defeat, otherwise known as a Trap or Trebuchet (the title of his 1917 Readymade) (Fig. 6).⁽³⁰⁾ In opposition there is a paradoxical element that interested both Duchamp and Nimzowitsch. Duchamp and Halberstadt’s book attempted to reconcile the two components of symmetrical endgame situations; opposition and sister squares. The squares represent the squares on the chess board that remain relevant to the chess pieces in symmetry. Hence the title of Duchamp’s book Opposition and Sister Squares Are Reconciled. The way that Duchamp explained it is as such,

The “opposition” is a system that allows you to do such – and – such a thing. The “sister squares” are the same thing as opposition, but it’s a more recent invention, which was given a different name. Naturally, the defenders of the old system were always wrangling with the defenders of the new one. I added “reconciled” because I had found a system that did away with antithesis.⁽³¹⁾

It is important to notice that within Duchamp’s study of endgames there is not an attempt to create further opposition by Duchamp positioning himself with one side or the other. Duchamp separates himself from the debates between the Classical school or “old system” and the hypermoderns. He was able to see that with hypermodernism there was an opportunity to create a synthesis between these two opposing understandings of end game theory. In so doing he displays a typically Hypermodern paradoxical attitude to classical theory.

Click to EnlargeFigure 7
Marcel Duchamp, Poster for the Third French Chess Championship, 1925 Rhonda Roland Shearer CollectionLet us take this one step further towards Duchamp ‘reconciling’ art and chess. Damisch makes the point that Duchamp’s chess poster designed for the 1925 Third French Chess Championship (Fig. 7) mirrored his theory of reconciliation. Duchamp extended the checkers of the chess board until they became cubes with one white, black and a third grey side, grey being the side of reconciliation. In the game of chess it is the opposition between black and white that gives the game its meaning. However, the ‘binary’ opposition of chess is defeated by Duchamp in the presence of the grey surfaces.⁽³²⁾

Let us return to Naumann’s article and interview contained in De Duve’s The definitively unfinished Marcel Duchamp. Francis Naumann presents Duchamp’s involvement in philosophical ‘reconciliation’ in the context of the German philosopher Stirner and the philosophical beliefs of existentialism and nihilism: That each position or situation exists as a unique entity, thus unable to be located within specific systematic constraints. Naumann points out that reconciliation is not only found in the works of Stirner but has a philosophical tradition that goes back to Plato.⁽³³⁾
More than that, ‘reconciliation’ is present in contemporary theories of structuralist theory, molecular biology, metaphysical poetry, and French symbolist poets. Thus this theme of ‘reconciliation of opposites’ is present in a number of intellectual domains. The theme is similarly reflected in writings since medieval times up until the time of Carl Jung who specifically wrote on the subject in Mysterium Coniunctionis: An Inquiry into the Separation and Synthesis of Psychic Opposites in Alchemy.⁽³⁴⁾
Yet Naumann warns us that one must be careful in the creation of a theory about Duchamp, for he consciously set out never to repeat himself and thus be defined. Naumann says:

No matter what his sources may have been – if any – his exploration of opposites and their reconciliation seems to have been motivated more by his unwillingness to repeat himself than by any possible willingness to conform to the dictates of a previously established system – philosophical, literary – or otherwise. His working method involved a constant search for
alternatives – alternatives not only to accepted artistic practice, but also to his own earlier work.⁽³⁵⁾

Naumann states that Duchamp was familiar with many aspects of reconciliation in maths, science, linguistics and philosophy. Therefore the relationship between chess and art in the historical figure Duchamp is contained within a wide intellectual field.

Historian Calvin Tomkins makes the similar observation that Duchamp’s fascination with art and chess seems to be bound up in mathematics.⁽³⁶⁾
The importance of logic, rationalism and Cartesian thought are an integral part of Duchamp’s work coupled with an anti-rationalistic interest, as seen in the works of Raymond Roussel and Alfred Jarry. Also Duchamp’s use of the term Cartesian is implicit of Descartes idea of man as a thinking mind, and matter an extension of motion. In terms of chess this duality is clearly seen, the movements of chess pieces upon a board are the physical expression of the chess player’s cognition. In an interview with Tomkins, Duchamp says:

Chess is a marvelous piece of Cartesianism, and so imaginative that it doesn’t even look Cartesian at first. The beautiful combinations that chess players invent – you don’t see them coming, but afterward there is no mystery – it’s a pure logical conclusion.⁽³⁷⁾

When the life and actions of Duchamp are placed within the historical context of Postmodernity we find the merger or reconciliation of a variety of intellectual paradigms. Duchamp’s studies into chess drew upon the knowledge and language of science, mathematics, and linguistics. Thus in order to understand the life and actions of Marcel Duchamp we must strive to understand the nature of intellectual reconciliation.

Duchamp as Chess Artist

And why . . . isn’t my chess playing an art activity? A chess game is very plastic. You construct it. It’s mechanical sculpture and with chess one creates beautiful problems and that beauty is made with the head and hands.⁽³⁸⁾

“I play chess all the time,” he wrote to Walter Arensberg. “I have joined the club here where there are very strong players classed in categories. I still have not had the honor of being classified, and I play with various players of the second and third categories losing and winning from time to time.” He had a set of rubber stamps made up so that he could play correspondence chess with Walter Arensberg. He even designed a set of wooden chessmen that he carved himself, all except the knight, which he farmed out to a local craftsman. In May he wrote to the Stettheimers that painting interested him less and less: “I play [chess] day and night and nothing interests me more than to find the right move..⁽³⁹⁾

It is deep below the layers of chess symbolism that Duchamp is encountered as a chess player and an artist. Art theorist Hubert Damisch raised the question as to why we encounter Duchamp in the world of chess at all. Damisch asks: how could he have spent so much of his life involved in nothing but a game? He makes a point of comparison, that Duchamp spent more of his life within this realm than he spent painting, though Duchamp renounced “neither the notion of “artist” nor that of “art.”⁽⁴⁰⁾
How has Duchamp slipped so easily into the realm of chess and become so difficult to follow? I have suggested that it is the art world’s scorn and misunderstanding for the game. Yet it is not within the “game” that we encounter Duchamp. The artist moved into the world of chess and it is here that the art theorist and historian loses Duchamp. What is significant is that Duchamp was able to enter the world of chess only due to his entering as an artist. Duchamp understood chess via the language, values, history, and culture of art. Thus on entering the world of chess we need to find the artist Duchamp. He was not found in the realm of symbolism, though he has left his footprints there, to perhaps lead us astray. When Duchamp entered the chess world he entered as an artist and he proclaimed that art was to be found here. Damisch summarizes Duchamp’s interest for chess as an artistic activity, and that a game of chess is considered “beautiful” in its own right and is as close as possible to becoming a work of art.⁽⁴¹⁾

Damisch understands Duchamp’s involvement in chess as deeply connected with his agenda as an artist. Damisch asserts that he was not interested in the symbolism of the chess pieces, the layers of historical meaning, or the psycho-sexual elements, but the way that chess was able to evoke abstract and intellectual movement of objects upon a new space or reality. This point Duchamp directly made when he answered the specific question as to the importance of symbolism in chess. Duchamp said that it holds no importance in the game, although chess acts like a drug of addiction.⁽⁴²⁾
Duchamp later said that the “expression” of chess and the “competitive” nature made it too incongruent with art, and thus is no art form at all. However, for Duchamp, it was not important to understand chess as a fight, or “sport” but through artistic qualities. This he explicitly stated during a BBC radio interview, when saying that the “competitive aspect was of no importance.” ⁽⁴³⁾

Of course, one intriguing aspect of the game that does imply artistic connotations is the actual geometric patterns and variations of the actual set up of the pieces and in the combinative, tactical, strategical, and positional sense. It’s a sad expression though – somewhat like religious art – it is not very gay.⁽⁴⁴⁾

Here Duchamp is presenting three ‘artistic’ or aesthetic levels concerning the game. First, the immediate visual impression of the chess pieces upon the board. This includes the chequered board, the sculptural formation of the pieces, and the variety of visual patterns that they form upon the board. Second, the abstract movement of the pieces through the ‘intellectual’ space. Finally, the emotional expression of chess.

The first level of aesthetics were explored by Duchamp in designing (but never making) a chess set. Writing to his sister Suzanne Duchamp he explained,

I am about to launch on the market a new form of chess sets, the main features of which are as follow: The Queen is a combination of a Rook and of a Bishop – the Knight is the same as the one I had in South America. So is the Pawn. The King Too. 2nd they will be colored like this. The white Queen will be light green. The black Queen will be dark green. The Rooks will be blue, light and dark. The bishops will be yellow, light and dark. The knights, red, light and dark. The white King and Black King. White and Black Pawns. Please notice that the Queens’ colour is a combination of the Bishop and of the Rook (just as she is in her movements).⁽⁴⁵⁾

While the immediate visual impression of the chess set would be striking, its purpose is to direct our attention to the second aesthetic level; the intellectual movement of the pieces. This is directly indicated by the coloring of the Queen – its movement being a combination of a Bishop and a Rook. His engagement in chess is seen as profoundly relating to the intellectualized movement of the pieces, to which he has brought the inventiveness of an artist to the aesthetics of the game. It is the ‘artistic’ intellectual and abstract movement of pieces that Duchamp, the artist, values within chess.

Duchamp spoke most openly and comprehensively to Pierre Cabanne concerning this perspective on the game. This interview sheds light upon a vast array of Duchamp’s chess quotations and references commonly used by historians and theorists when speaking on the subject.

Cabanne: I also noted that this passion [for chess] was especially great when you weren’t painting. So, I wondered whether, during those periods, the gestures directing the movements of pawns in space didn’t give rise to imaginary creations – yes, I know, you don’t like that word – creations which, in your eyes, had as much value as the real creation of your pictures and, further, established a new plastic function in space.

Duchamp: In a certain sense, yes. A game of chess is a visual and plastic thing, and if it isn’t geometric in the static sense of the word, it is mechanical, since it moves; it’s a drawing, it’s a mechanical reality. The pieces aren’t pretty in themselves, any more than is the form of the game, but what is pretty – if the word ‘pretty’ can be used – is the movement. Well, it is mechanical, the way, for example, a Calder is mechanical. In chess there are some extremely beautiful things in the domain of movement, but not in the visual domain. It’s the imagining of the movement or of the gesture that makes the beauty, in this case. It’s completely in one’s grey matter.

Cabanne: In short, there is in chess a gratuitous play of forms, as opposed to the play of functional forms on the canvas.

Duchamp: Yes. Completely. Although chess play is not so gratuitous; there is choice ..

Cabanne: But no intended purpose?

Duchamp: No. There is no special purpose. That above all is important.

Cabanne: Chess is the ideal work of art?

Duchamp: That could be. Also, the milieu of chess players is far more sympathetic than that of artists. These people are completely cloudy, completely blind, wearing blinkers. Madmen of a certain quality, the way the artist is supposed to be, and isn’t, in general. That’s probably what interested me the most.⁽⁴⁶⁾

Cabanne poses a range of questions directly concerning the relationship between art and chess. Cabanne begins by establishing an opposition to, or a clear distinction between, chess and art. The term Cabanne actually uses is “painting” yet in its context the word “art” is clearly implicit. The question posed to Duchamp points directly to the relationship Cabanne saw existing between chess and art. Cabanne asked Duchamp when he was not in the paradigm of art whether the movements of chess pieces gave rise to anything that he would value as art; and whether Duchamp discovered a new realm or space for art within chess. In affirmation of this, Duchamp continues to present an explanation of this artistic encounter within chess. As in his chess set design, Duchamp draws our attention to the multiple levels operating within the aesthetics of chess, and directs us to the aspect which he holds in the highest regard. Duchamp’s interest in the movements of a machine, a mystical machine, as directly and simply illustrated in his 1911 Coffee Grinder, operate also in the realm of chess, where the movements of the grinding mechanism is visible and the process or movement of the coffee through the machine is demonstrated. This is shown most clearly in Duchamp’s body of work that make up the King and Queen. There is a clear focus upon the movement of pieces upon the board in intellectual space.

Developing this further, Duchamp reflects on the close relationship chess has to geometry and mechanical movement. The example he presents is the movement of Calder’s mobiles. But a mobile is aesthetic in the realm of the visual and Duchamp says that the aesthetics of chess are not in this domain. It is not even the physical sculptural pieces that are aesthetic or “pretty” – it is the movement of the pieces in intellectual space. The beauty of chess that Duchamp saw was the movement of the pieces within his mind. This is testament to what Duchamp said to Drot,

And further,

Mechanics in the sense that the pieces move, interact, destroy each other, they’re in constant motion and that’s what attracts me. Chess figures placed in a passive position have no visual or aesthetic appeal. It’s the possible movements that can be played from that position that makes it more or less beautiful.⁽⁴⁷⁾

Actually when you play a game of chess it is like designing something or constructing a mechanism of some kind by which you win or lose. The competitive side of it has no importance, but the thing itself is very, very plastic and it is probably what attracted me to the game.⁽⁴⁸⁾

Cabanne presents Duchamp with a summary of this understanding: The distinction between the aesthetics of chess and art (painting) is that in chess there is a free movement or “play of forms” whereas in art, forms are not considered to be free for they serve a functionally aesthetic purpose. Cabanne has made the battle ground for this debate the issue of values associated with aesthetic functionality. Duchamp corrects Cabanne by saying that the aesthetics of chess are concerned with the “play of forms” in intellectual space, however, the movement is restricted by choice, and each choice brings its own consequences just as the artist also faces the consequences of their actions. Chess is not free or “gratuitous” as crudely expressed by Cabanne.

Duchamp and David Antin wrote an article (in response to an interview they had conducted) in which they illustrate the choice and consequences within the intellectual realm of chess and the weight of meaning and significance placed upon a small sculptural object, the chess piece.

but I don’t want to talk about that now I would rather talk about chess since we’re talking about Duchamp its only right that we should talk about chess chessboards define the action in chess the action is usually on the board similarly if you use the word art you use a board as a perimeter and some where within the perimeter is the site of a action at least it would appear so to someone who knew how to play chess which is an action of a different sort for someone know how to play chess for if two people two chess masters are playing a game and somebody watches that game and he gasps ostensibly this is an act of little significance a man pushes a little piece of wood and moves it over here say and the other man gasps he watches the man next to him doesn’t know why he’s gasping the first man is gasping because the player whose move it was has just moved the bishop to a particular position on the board from which will ensure 15 alternative possibilities all of which are not very good.⁽⁴⁹⁾

This interest in intellectual movement was also Duchamp’s concern within painting, ‘intellectual expression’ was the direction that painting should take. Duchamp said;

I considered painting as . . . a means of expression, instead of a complete aim for life . . . the same as I considered that colour is only a means of expression in painting. It should not be the last aim of painting. In other words, painting should not be only retinal or visual; it should have to do with the gray matter of our understanding, not only the purely visual.⁽⁵⁰⁾

American Chess Master Edward Lasker saw that Duchamp’s interest in the aesthetics of chess had profound effects on Duchamp the chess player. Duchamp’s aesthetic concerns and insights influenced his style of play which had immediate implications on many of his tournament results. Duchamp was ever the artist within the world of chess. Schwarz also acknowledges that Duchamp’s aesthetic interest in chess, coupled with his “unorthodox” style led to many defeats at chess master levels.⁽⁵¹⁾

Duchamp’s interest in chess also revolves around the contradiction or paradox that exists between freedom and restriction. Within a strict framework of rules, there is great room for creative and imaginative thought. Duchamp’s Cartesian sentiments, also presented insights into the aesthetic realm of chess.

Chess is a marvelous piece of Cartesianism, and so imaginative that it doesn’t even look Cartesian at first. The beautiful combinations that chess players invent – you don’t see them coming, but afterward there is no mystery – it’s a pure logical conclusion.⁽⁵²⁾

Duchamp’s Hypermodernist chess praxis questioned all previously established styles and theoretical principals whilst maintaining a rigorous mathematical and scientific methodology. Duchamp as a chess player closely associated himself with Hypermodernism not only for its Dadaist position but also for its rigorous mathematical and logical approach. It was through a Cartesian approach that Duchamp wrote Opposition and Sister Squares Are Reconciled with chess theorist Halberstadt. This text has been observed to involve the “seemingly aimless maneuvers of the kings,” yet it shows his interest in the mathematic logic of chess.⁽⁵³⁾
His intellectual interest in both the acceptance and rejection of logical thought, or of freedom and restriction, became an interest in the middle ground. A middle ground of indifference, which he considered the “beauty of indifference,” and “an acceptance of all doubts.”⁽⁵⁴⁾
This “indifference” reflects Duchamp’s adoption of a Hypermodern chess style which is an interplay of romantic and modern forms. He explained his attitude of indifference to Andre Breton:

For me there is something else in addition to yes, no or indifferent – that is, for instance – the absence of investigations of that type. . . . I am against the word ‘anti’ because it’s a bit like atheist, as compared to believer. And the atheist is just as much of a religious man as the believer is, and an anti-artist is just as much of an artist as the other artist. Anartist would be much better, if I could change it, instead of anti-artist. Anartist, meaning no artist at all. That would be my conception. I don’t mind being an anartist . . . What I have in mind is that art may be bad, good or indifferent, but, whatever adjective is used, we must call it art, and bad art is still art in the same way as a bad emotion is still an emotion.⁽⁵⁵⁾

Duchamp was reluctant to draw a distinction between the artist and the anti-artist, which questions whether a theorist should make the distinction between art and chess. An indifference to the division between art and chess creating a free flow of ideas between the two. This free flow or traversal of paradigms existed not only between chess and art. Duchamp’s interest in this intellectual paradox flowed into his involvement in mathematics. Henri Poincare is believed to have presented Duchamp with a position that emphasized the resolution of the paradox. Poincare’s mathematical text Science et method has a chapter concerning mathematical invention, which suggests that by using the laws of mathematics one is able to be as inventive, imaginative and creative as a chess player. Poincare says that all mathematicians have “a very sure memory” or,

a power . . . like that of the chess player who can visualize a great number of combinations and hold them in his memory, . . . every good mathematician ought to be a good chess player, and inversely.⁽⁵⁶⁾

Poincare understood chess to be fundamentally associated with invention. An invention of pure elements of “harmony of number, and forms, of geometrical elegance.”⁽⁵⁷⁾
That strict rules and laws exists both within mathematics and chess. Within this framework, the practitioner is able to move and act freely and inventively. It has been suggested that chess operated for Duchamp as an arena of invention that he occupied after completing his conceptual and mathematical invention, the Large Glass.⁽⁵⁸⁾
Julien Levy said of Duchamp:

Marcel wanted to show that an artist’s mind, if it wasn’t corrupted by money or success, could equal the best in any field. He thought that, with its sensitivity to images and sensations, the artist’s mind could do as well as the scientific mind with its mathematical memory. He came damn close, too. But, of course, the memory boys were tougher, they had trained [for chess] from an early age. Marcel started too late in life.⁽⁵⁹⁾

Duchamp was seen by many of his chess opponents to be highly creative, and his use of inventive or “playful” mathematics within the Large Glass, demonstrates Duchamp’s freedom of movement between these paradigms. And perhaps it is within this context that we are to understand Duchamp’s statement that

From my close contact with artists and chess players, I have come to the personal conclusion that while all artists are not chess players, all chess players are artists.⁽⁶⁰⁾

Duchamp came to conduct chess as an artist and to conduct his art making as the chess player.

The theorist David Joselit also explores the way that chess and art relate in Marcel Duchamp’s life and art. Joselit sees chess as “living art” within Duchamp’s life. In which there is a traversal between art and chess as there is Duchamp’s traversal between art to life.

He took an ordinary article of life, placed it so that its useful significance disappeared under the new title and point of view – created a new thought for that object.⁽⁶¹⁾

Click to EnlargeFigure 8
Original Studio Photograph, 1916-17The photograph of Duchamp’s studio from 1917 presents the framework for this theory. Hanging vertically upon a wall is chess as a physical object, as opposed to the intellectual realms of chess, and upon the floor, chess as a conceptual reality via the readymade sculpture the Trap (Fig.8). It is well known that Duchamp played correspondence chess and these vertical boards were commonly used to illustrate his games in progress. The depth of logical methodology saw Duchamp thrive in correspondence chess and endgame studies. In these instances, the slow pace of the game creates little scope for oversights and incorrect moves, thus a purer logic is achieved. Joselit views this vertical chessboard through art stating that it has entered the arena of the painting. The chess board has entered or ‘colonized’ the paradigm of art via painting.

The rotated chess board suggests that the relationship between chess and art was not necessarily one of displacement but rather of the transformation or transposition of painterly themes into a realm that obviates “the intervention of the hand.” ⁽⁶²⁾

The flat vertical image upon a wall, yet the physical transient reality of chess, becomes an “erasable beauty” a painting that can be erased and begun over and over again.⁽⁶³⁾
Likewise Duchamp said:

At the end of the game you can cancel the painting you are making.⁽⁶⁴⁾

Duchamp wrote the following note that further expresses this:

Chess = a design on slate / that one erases, / the beauty of which / one can reproduce without the / intervention of the “hand.”⁽⁶⁵⁾

Click to EnlargeFigure 9
Marcel Duchamp, Coffee Mill, 1911 Thus Duchamp saw chess enlightening the paradigm of art. Chess is an “aesthetic idiom” to mathematically represent an “immobilized” movement as is seen in the Large Glass (1923) (Fig. 2) and Coffee Mill (1911) (Fig. 9). The artist chess player is able to “diagram it, to capture it within a grid of measurement.”⁽⁶⁶⁾

Joselit’s hypothesis is that chess is a projection into Duchamp’s world of the readymade as clearly displayed in the studio photograph. The readymade represents Duchamp’s traversal between art and everyday life and chess. Trebuchet or Trap draws directly from a theoretical movement within chess. This readymade sculpture is created by Duchamp by nailing a coat rack down upon his studio floor. Trebuchet is a tactical chess move that incites a player to make a move that will ultimately cause them to lose a positional advantage, a piece, or the game. The analogy of being tripped by the inverted coat rack is obvious, one Duchamp actually encountered when he brought the object home and never got around to mounting it to the wall. Duchamp becomes the chess piece tripped by the Trebuchet that was set by himself. Joselit sees a direct connection between the chess board tipped upon a wall and the coat rack that has been tipped down upon the floor. Each work has entered a new realm via its displacement. Duchamp the chess player in the realm of art and Duchamp the artist in the realm of chess, both in the realm of the everyday. Joselit understands that within this photograph, chess operates as a pivot for understanding the movement from the realm of painting to the realm of Duchamp’s readymades. Joselit says that these two works demonstrate the “discursive field that we might call ‘Duchampian chess.'”

To understand what is occurring within Duchamp’s art we need to understand the way chess operates as a theoretical and practical model. Within chess Duchamp enters the arena of the painting via the chess board hung upon a wall. The physical chess object can be aestheticised like that of a painting. Duchamp also enters the realm of the readymade object in his studio and the conceptual movement of correspondence chess through intellectual space via an arena of readymade rules and intellectual visualization. Through documentation and notation Duchamp geometrically charted the movement of the readymade upon the painterly plane. Then the entire chess object is placed within the context of the everyday. It is this nature of the everyday that prompted Duchamp in 1917 to publish a game of chess between the artists (both poor chess players) Roche and Picabia, in a regular chess column of a news paper. The readers were outraged! Duchamp wrote in response to this Richard Mutt Case of the chess world that;

It had been a game from everyday life: lyrical, heroic, romantic; with blunders, sudden panic reactions, flights of imagination and here and there even a correct move.⁽⁶⁷⁾

Joselit believes that Duchamp aimed to invent an art form that was equally as elegant and conceptually beautiful as chess and cites chess as being responsible for Duchamp’s low artistic production during the 1920’s. Joselit writes,

The game was no mere idle pastime for the artist, a smoke screen that could block the scrutiny of the art world. Rather, . . . chess, like the machine before it, provided Duchamp with a productive conceptual and aesthetic model that was unquietly capable of synthesizing the “spatial realism” or literalness of the readymade and the systemic complexity of the Large Glass. ⁽⁶⁸⁾

The systemic complexity concerning the Large Glass operates in a similar way to the game of chess. In this work, Duchamp established a conceptual mechanism which is understood to operate via the rules and laws referenced in the Green Box. The way to understand the workings of the Large Glass is via the Green Box. For example Duchamp’s use of colour must be understood via the associated notes. Duchamp wrote, “As in geographical maps, as in architects’ drawings; or diagrams with colour wash, need a colour key: substantive meaning of each colour used.”⁽⁶⁹⁾
Likewise, for chess, the conceptual workings and movements of the pieces operate via the established readymade rules of the game.⁽⁷⁰⁾

This comparison between the workings of the Large Glass and chess was also noted by Linda Dalrymple Henderson in her 1983 text entitled The Fourth Dimension and Non-Euclidean Geometry in Modern Art. She claims we see in the works of Duchamp a similarity of approach to chess and art, through the ‘geometrical theorizing’ in chess and in the notes for the Large Glass.⁽⁷¹⁾
Duchamp believed that language united his life with the Large Glass and with chess. Yet he maintained the belief that language was unable to communicate purely:

I don’t believe in language, which, instead of explaining subconscious thoughts, in reality creates thought by and after the word . . .⁽⁷²⁾

Duchamp was able to maintain the purity of the Large Glass by adopting and inventing a language of paradoxical referencing and operation, like the specialized chess.^*
Likewise the world of the Large Glass does not operate beyond its glass surface.⁽⁷³⁾

Duchamp was able to create a theoretical union whilst acknowledging the incommensurability of chess and art. A methodology that is not associated with hierarchy or dominance or comparison of criteria, but an approach that enters into the distinct paradigms of art and chess themselves. Marcel Duchamp enters chess holding onto the values of art: Not claiming that chess is art but valuing chess as he values art.

Notes

1. Bois, Hollier & Krauss, A conversation with Hubert Damisch, October #85 Summer, 1998, p.10.

2. Damisch, Hubert, The Duchamp Defense, 1979, October # 10, p.8

3. Hughes, Robert, Shock of the New, Thames & Hudson, London, 1991, p.52.

4. Damisch points out that Duchamp was interested in chess as a young man as shown by an etching by Jacques Villon (Marcel’s brother) showing Marcel playing chess with his sister at the age of seventeen. Duchamp played in the 1924 World Amateur Championship, four French championships from 1924 to 1928, and four Olympiads from 1928 to 1933. He tied for first place at Hyeres 1928 and won the Paris championship in 1932. He drew a game with Grand Master Tartakower in 1928. Several times he beat Belgian Champion Koltanowsky in 1929. He was awarded the chess title of Master in 1929. In 1931 Duchamp became a member of the Committee of French Chess Federation and the French delegate to the World Chess Federation. In 1931 Duchamp co-wrote a book on chess with Halberstadt titled L’Opposition et les cases conjures sont reconciliees. In 1935 Duchamp was Captain of the French Correspondence Olympic team.

5. Damisch, Hubert, The Duchamp Defense, 1979, October # 10, p.8. It is important not to read painting to mean art. Although Duchamp ceased painting his career as an artist continued.

6. Damisch, p.8.

7. Ibid, p.5-9.

8. Tomkins, Calvin, Ahead of the Game, Marmondsworth, Middlesex, Penguin, 1965, p.52-3.

9. Humble, Marcel Duchamp: Chess Aesthete and Anartist Unreconciled, Journal of Aesthetic Education, Vol.32 no.2, 1998, p.41.

10. Naumann, Francis, “Marcel Duchamp: A Reconciliation of Opposites,” de Duve, Thierry, ed., The Definitively Unfinished Marcel Duchamp. Cambridge, MIT Press (co-published with Nova Scotia School of art and Design). 1993, p.41.

11. Ibid, p.41.

12. ‘A Conversation with Marcel Duchamp’. A 30 minute film directed by Robert Graff incorporating an interview by James Sweeney, made at the Philadelphia Museum of Art in 1955 and broadcast by NBC in January 1956 in the program Elderly Wise Men.

13. Raymond Keene, Marcel Duchamp: The Chess Mind, Modern Painters, vol.2, no. 4, winter 1989, p.121

14. Rumney, R. “Marcel Duchamp as a Chess Player and One or Two Related Matters: Francois le Lionnais Interviewed by Ralph Rumney” Studio International 189 no.972 (January-February), 1975, p.127

15. Keene, p.123

16. Rumney 1975, p.128

17. Jones, A. Postmodernism and the Engendering of Marcel Duchamp. Cambridge, Cambridge University Press, 1994, p. 120.

18. View, ser. no.1, March 1945.

19. Duchamp (R.Mutt), The Blind Man, New York, 1917, found in Harrison/Wood, Art in Theory 1900 – 1990, Blackwell, 1992, p.248.

20. Sweeney, J. A Conversation with Marcel Duchamp, Wisdom: Conversation with the Elder Wise Men of Our Day, New York, W.W. Norton & Co., 1958, p.94-5.

21. Quoted in Damisch, Hubert, The Duchamp Defense, 1979, October # 10, p.10

22. Masheck, J., Marcel Duchamp in Perspective, New Jersey, Prentice-Hall, 1975, p.19.

23. Damisch, p.19-21.

24. Cabanne, Pierre, P. Dialogues with Marcel Duchamp. New York, Viking Press, 1971, p.77-8.

25. Damisch, p.22.

26. Adcock, Craig, Marcel Duchamp’s Notes for the Large Glass: An N-Dimensional Analysis, Ann Arbor, p.63.

27. Damisch, p.14. Quoting Ferdinand de Saussure, Course in General Linguistics, eds. Charles Bally and Albert Sechechaye, trans. Wade Baskin, New York McGraw-Hill, p.107.

28. Ibid, p.14

29. This work is concerned with that very special point of the endgame in chess when all the pieces have been lost, only the Kings and a few pawns remain on the board. And this special ‘lone-pawns’ situation is treated only from the even more particular situation in which the pawns have been blocked and only the Kings can play. This situation is called zugzwang, a German term of international use that indicates this blocked position in which only certain moves, and in a limited number, are possible. In this case (pawns blocked and only the Kings being able to move), even though they make use of conclusions already established by Abbe Durand, Drtina, Bianchette, etc., Duchamp and Halberstadt are the first to have noticed the synchronisation of the moves of the black King and the white King. This synchronisation is analysed at length and forms the basis of their system. In order to win, a white King cannot move indiscriminately without regard for the colour of the square on which he finds himself. Using the terminology of the authors of the book, he must choose a ‘heterodox opposition’ with respect to the colour of the square occupied by the black King. This ‘heterodox opposition,’ which represents the real contribution of Duchamp and Halberstadt to the theory of chess, would demand a technical explanation too lengthy to be given here. At any rate, for clarity I would add that the game of chess does contain the idea of ‘opposition,’ and that Duchamp and Halberstadt have renamed it ‘orthodox opposition’ in order to distinguish it form the ‘heterodox opposition’ that they have discovered. This ‘orthodox opposition’ is something that all chess players know about, and it is far form being a mystery. It is a sure means of winning in certain situations. In fact, ‘heterodox opposition’ is no more than an amplification of opposition. It is simply applied to a longer number of squares, and it adopts various forms that are missing in the rigid ‘orthodox opposition.

30. Trap or Le Trebuchet is a technical chess term, and is also the subject of a readymade by Duchamp.

31. Damisch, p.24.

32. Ibid, p.25-6.

33. de Duve, p.55.

34. Ibid, p.53-7.

35. Ibid, p.57.

36. Tomkins, Calvin, Duchamp: A Biography. London, Random House, 1998, p.211.

37. Ibid, p.211.

38. Marcel Duchamp, interview by Truman Capote in Richard Avedon, Observation, NY: Simon and Schuster, 1959, p.55.

39. Tomkins 1998, p.210-11.

40. Damisch 1979, p.8.

41. Ibid, p.9.

42. Documentary film by Drot, J. M. A game of chess with Marcel Duchamp, L’institut National de’Audiovisuael Direction des Archives: RM Associates/Public Media, 1987.

43. Kremer, M. The Chess Career of Marcel Duchamp. New in Chess, Alkmaar, Holland, 1989, p.34

44. Duchamp quoted by Brandy, Schwarz, Marcel Duchamp. New York, Harry N. Abrams, Incorporated, 1975, p.70.

45. Duchamp quoted by Naumann, Affectueusement, Marcel: ten Letters from Marcel Duchamp to Suzanne Duchamp and Jean Crotti. Archives of American Art Journal, 22, No. 4 1982, p.14.

46. Cabanne, 1971, p.18-19.

47. Drot, J. M., 1987.

48. Duchamp, Salt Seller: the Writings of Marcel Duchamp, New York, Oxford University Press, 1973, p.136

49. D’Harnoncourt & McShine ed. Marcel Duchamp, MoMA, Prestel, 1989 p.100 (original published format has been maintained)

50. Schwarz, Arturo, The Complete Works of Marcel Duchamp. London, Thames and Hudson, 1969, p.20.

51. Ibid, p.66.

52. Marcel Duchamp interview with Calvin Tomkins, undated, Tomkins, 1998, p.211.

53. Kremer, p.50.

54. Hamilton and Hamilton, BBC interview, London, 1959.

55. Duchamp quoted by Schwarz 1969, p.33.

56. Poincare, Science et methode, cited in Henderson, Duchamp in Context, Princeton, New Jersey, Princton University Press, 1998, p.186.

57. Ibid

58. Ibid

59. Schwarz 1969,p.70.

60. Archives of American Art, Smithsonian Institution, Washington, D.C. papers, August 30, 1952.

61. Duchamp, 1917, p.248.

62. Joselit, D., Infinite Regress: Marcel Duchamp 1910-1941. Cambridge, Massachusetts London, England, October, 1998, p.158

63. Joselit, D., Infinite Regress: Marcel Duchamp 1910-1941. Cambridge, Massachusetts London, England, October, 1998, p.160.

64. J. J. Tharrats, “Marcel Duchamp,” Art Actuel (Lausanne) 6 (1958): p.1

65. Marcel Duchamp, Notes, ed Paul Matisse, Boston: G.K.Hall, 1983, note 273, unpaginated.

66. Joselit, 1998, p.163.

67. Kremer, 1989, p.47.

68. Joselit, 1998, p.164.

69. Schwarz, 1969, p.27.

70. Joselit, 1998, p.173-4.

71. Henderson, Linda D., The Fourth Dimension and Non-Euclidian Geometry in Modern Art. Princeton, N.J., Princeton University Press, 1983, p.124.

72. Jones, p.133.

* The language of chess must be understood to go beyond the cliche of chess that are used in everyday speak like “checkmate” to the abstract world of piece movement, engagement, exchange, and combination.

73. M.D to Jehan Mayoux, March 8, 1956, Archives of Alexina Duchamp, Tomkins, 1998, p.394.

On Readymades by/of Marcel Duchamp

It is with great interest that I have been reading Rhonda Shearer’s investigative work on Duchamp’s readymades. Her analysis seems thorough and her approach scientific. But the “revelation” that some of the readymades may not have actually been ready-made, that is, ordinary commercial objects simply selected by the artist, does not seem like such a revelation to me. My background in not in science, rather I am a working artist who has always found Duchamp’s work to be full of humor, conceptual and visual (retinal – I know, I’m sorry Marcel) interest, and intellectual depth. Finding Duchamp’s work to resonate sympathetically within me, and with a small amount of biographical knowledge (I’m getting my chronology from Tomkins biography, with the grain of salt one must take with everything concerning Duchamp), I feel like I might offer some productive speculations on process that might shed some light for the more scientifically-minded in tout-fait’s audience.
Duchamp never showed much desire to repeat himself. After Nude he painted no more cubist paintings, after the large glass he made no more mechanosexual delays. He had ideas, executed some of them to his satisfaction, and moved on. When, later in life, he did not have ideas (or so he claimed) he spent his time at chess and breathing. If he clarified his thoughts on the idea Readymade around 1915, it stands to reason (mine at least) that he would execute his idea reasonably quickly and then move on. 1915 was the year of In Advance of the Broken Arm. Even before this was the bottle rack, which he never even signed and was not in his possession in New York. (As far as the “forgery” of the shovel goes, with its square handle, which Shearer uses to call it into doubt, I cannot say much — we are in a black swan predicament as far as proving anything goes.) But between these two early readymades (ignoring the earlier Stoppages and the bicycle wheel, which are commonly called readymades but clearly different in conception), and others we have heard of (Pulled at Four Pins) and can speculate he may have played with, Duchamp may have executed the “pure” (unmodified commercial object) readymade to his satisfaction. After all, once you have the idea, what’s interesting about repeating the simple (boring) act of buying an object and signing it? He had made a readymade (in the bottle rack) perhaps even before the idea was entirely clear to him. Why do any more? Even giving a snow shovel a humorous/poetical title shows a conceptual evolution beyond the simple core concept.

It seems to me that he moved on immediately to the more interesting (to the tinkerer’s mind, and Duchamp was certainly a tinkerer) project of modified readymades, such as With Hidden Noise of the following year. With Hidden Noise included the readymade aspect (buying or finding the components), assemblage, collaboration (he had Walter Arensberg put the mystery noisemaker inside), interactivity (you have to shake the thing to understand the title). Given that he had moved within months from the shovel (fall or winter 1915) to Noise (easter 1916), does it not make sense that by 1917-18 he had moved on to other ideas, which may or may not have included forgery, confusing modifications, and obfuscation of the idea that was initially (in the bottle rack) so simple and straightforward? The essential confusion, I think, is that Duchamp and, taking his lead, all his critics, lumped a bunch of disparate but related concepts under the umbrella term “readymade,” (compare the early readymades to 1921’s Why Not Sneeze Rrose Selavy) and while the shared classification did not bother Duchamp himself, it seems to put the taxonomists among us all in a tizzy.
As far as modification of the hatrack, bicycle wheel, trebuchet, etc. goes, all I can say is if they sat in my studio for years I’d have trouble refraining from playing with them. Duchamp had no qualms about modifying objects or documentation of objects, nor about commissioning others to physically create works for him, nor about giving misleading or false information in interviews, etc. If it gives you joy to sleuth out his “secrets,” good on you. The layers of confusion are one of the gifts he gave us.
Sincerely,

Evan Bender

Response to “Femalic Molds”

Chers Messieurs:

I wish to express my astonishment at reading the article you posted: “Femalic Molds” by Jean Clair (translation by Taylor M. Stapleton). Originally published in 2000, which translation you published in 2003.

Of course, I am aware of the interest in the fourth dimension of the Modernists, particularly with reference to Salvador Dali’s Christus Hypercubus, etc. and I have studied Duchamp’s Green Box since 1977.
I certainly recognize the influence of ideas on the fourth dimension in Cubism and of the cinema on Nude Descending a Staircase, but I had no idea of Duchamp’s ideas regarding the male and female figure and the fourth dimension.

I find, therefore, that I have created more of an homage to Duchamp than I had originally intended in my work, “Botty Shelly” (1999-2005). Here you see appropriated art and found mathematics. In 1999, when I
conceived of this work, I consciously placed it as though it was the Female Fig Leaf set atop Botticelli’s seashell. However, the Etruscan Venus is, itself a form of the Klein bottle. This aspect became increasingly important to me. I remembered a story I read in National Lampoon (of all places) in 1978 which described an IUD (Intra-Uterine Device) of the form of a Klein bottle.
It functioned by sending the male emission through the fourth dimension. I came to realize, therefore, that “Botty Shelly” was really the uterine opening — Annie Sprinkle’s “Public Cervix” — rendered as a vessel of
metaphysical transformation.

Incidentally, please see at: http://www.cs.unca.edu/~dickson/Klein/Klein.html; my models of the Moebius band and Klein bottle, which I believe really
shows how the latter is derived from the former. Now, to show how the Steiner Roman surface, and thus the Etruscan Venus are really forms of the Klein bottle — not obvious and quite another
matter for future visualization. And, also, accidental homage to Duchamp in my other work:
http://emsh.calarts.edu/~mathart/Zoetropes.html
http://emsh.calarts.edu/~mathart/Zoetrope1.html
http://emsh.calarts.edu/~mathart/portfolio/images/ZoeDismbl2_512.jpg
Note the inverted bicycle wheel in the construction, which is not apparent in the finished three-dimensional Zoetrope. [Natural Mathematical language directly converted to a four-dimensional object in physical space-time.]

Respectfully,

Stewart Dickson

Animated Reconstruction of Rotoreliefs

My relation to Marcel Duchamp is that of a chess player trying to win a game against someone who is dead but is determined to win in any case-no matter what I do. It is a hopeless game to get involved with the father of conceptual art who may laugh at art theory like Nam June Paik may laugh at a television screen. Duchamp beats the linguist into the critic and spits out absurd connections. He is someone who is specialized in breaking the rules. Maybe that’s why I like him.

The Flash piece is a reconstruction of Duchamp’s Rotoreliefs using text. They are meant as an homage to Duchamp. A linguistic analysis of any of the spirals will show various ambiguities in terms of meaning or phonetics. These sentences may really wring a scientific brain. There is no end.

My own work revolves around photography and short videos and animations. I am interested in feedback regarding problems and patterns and use the internet as a personal publishing space.

For more works, please visit:
www.lu-x.de

AN ANALYSIS OF DUCHAMP’S ENDGAME PROBLEM AN EXCHANGE WITH LARRY EVANS

Notes

1.1. The Bride stripped bare by her Bachelors, even

1.2. General procedures and remarks

2.1. The overall view

2.2. The Chariot with the Water Mill, the Capillary Tubes and the Cemetery of Uniforms and Liveries

2.3. The Chocolate Grinder

3.1. The Chariot in the fourth dimension

3.2. A new possible identity of the Grinder

Acknowledgements

Notes

1

3

4

5

Notes

AN ANALYSIS OF DUCHAMP’S ENDGAME PROBLEM
AN EXCHANGE WITH LARRY EVANS