click to enlarge

Photograph
of Charles Henry
Ford by Penny Arcade,
early 1990s

Charles Henri Ford (1913-2002) was a 20th century Renaissance man, admired for his literary criticism, editing and publishing, poetry, photography, film making, and visual art. “Flag of Ecstasy”, written for Duchamp, was the title poem of his 1972 poetry collection for Black Sparrow Press.

Ford was at the epicenter of the art world co-authored and influenced by Duchamp. Nurtured and encouraged from a young age by the likes of Ezra Pound, Gertrude Stein and William Carlos Williams, Charles’s contemporaries and collaborators later included Djuna Barnes, Parker Tyler, Pavel Tchelitchew, Man Ray, Peggy Guggenheim, Andre Breton, Cecil Beaton, Salvadore Dali, Jean Cocteau, William Burroughs, Ned Rorem, Joseph Cornell… the list goes on.

Charles did not consent to recite his poetry often. This recording (2000) is one of the few that exist. When Charles agreed to record, I asked him to include “Flag of Ecstasy” because of my personal interest in Duchamp. I was fascinated by Charles’s words written specifically for the amusement of Duchamp, whom Charles greatly admired. At 92, his speech in the recording is slightly slurred, but his voice carries the dignity and depth that characterize all of his work, regardless of medium.

The music behind Charles’s recitation is an atonal soundscape, my impressionistic reaction to the poem. There is nothing “Duchampian” in the logic or construction of this piece; it is simply a contemporary reaction to Duchamp as an individual (Charles’s poem) accompanied by my abstract composition, which is designed to provoke but not distract the listener from the poem. To collaborate with Charles, a genuine living Surrealist, was an honor and a thrill indeed.

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Charles Henri Ford,
“Flag of Ecstasy,”
published in View, vol.
5, no. 1 (March
1945), p. 4

FLAG OF ECSTASY
(For Marcel Duchamp)
by Charles Henri Ford

Over the towers of autoerotic honey
Over the dungeons of homicidal drives

Over the pleasures of invading sleep
Over the sorrows of invading a woman

Over the voix celeste
Over vomito negro

Over the unendurable sensation of madness
Over the insatiable sense of sin

Over the spirit of uprisings
Over the bodies of tragediennes

Over tarantism: “melancholy stupor and an uncontrollable desire to dance”
Over all

Over ambivalent virginity
Over unfathomable succubi

Over the tormentors of Negresses
Over openhearted sans-culottes

Over a stactometer for the tears of France
Over unmanageable hermaphrodites

Over the rattlesnake sexlessness of art lovers
Over the shithouse enigmas of art haters

Over the sun’s lascivious serum
Over the sewage of the moon

Over the saints of debauchery
Over criminals made of gold

Over the princes of delirium
Over the paupers of peace

Over signs foretelling the end of the world
Over signs foretelling the beginning of a world

Like one of those tender strips of flesh
On either side of the vertebral column

Marcel, wave!

I.

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Figure 1
Front view of
Duchamp’s postcard
to Katherine Dreier, 1933

There is a Tout-Fait article, dated May 2000 by Hans de Wolf. He thinks Duchamp appears in a postcard sent from Duchamp to Katherine Dreier (Fig. 1). There are 2 men behind the Duchamp figure that look an awful lot like Man Ray and Andre Breton. At least in my opinion. Could this be possible?

II.

I was deeply saddened by the news of Prof. Goulds death. I consider him one of my favorite authors. I didn’t always completely understand him, but I always enjoyed his sense of humor and his constant quest to understand the universe.

I was pleasantly surprised to see that he and Dr. Shearer have been analyzing my favorite artist, Marcel Duchamp. His “Readymades” finally made sense. I had previously thought of these items as his most boring work, but now they are my favorite.

Incidentally, Austrian violinist Fritz Kriesler deceived his fans by performing “Recently Found” compositions of famous 17th and 18th century composers, which he had in fact wrote himself, but in their style. He admitted his deception and probably did it out of a sense of modesty, rather than trying to change the ideas of what is and is not music.

c’est la vie,
Keith Sacra

Historians of art like to believe that they can solve the riddles of interpretation posed by masterpieces of old painting. Firm in the conviction that a great painting is endowed by its creator with a unique, unambiguous message, we struggle to recover that meaning through the use of textual and visual evidence. And, up to a point, the historical method can recover the forgotten aspects of works of art created centuries ago.

Las Hilanderas is proof of this assertion; for over two centuries, the subject was mistakenly identified as a view of women at work in a tapestry factory. Velazquez had painted the picture around 1658, for a friend named Pedro de Arce, a funcionario in the royal palace. By the early eighteenth century, the picture was believed to represent a scene from everyday life, “mugeres que trabajan en tapizeria.” With this description it is listed in the inventory of Luis de la Cerda, IX Duke of Medinaceli, who in 1711 surrendered it to the royal collection. By the end of the century, this interpretation of the subject had metamorphosed into an incontrovertible fact, as demonstrated by entries in the royal inventories, where it is called by the enduringly popular title, “Las Hilanderas“.

It was only in the twentieth century that the original and accurate identification of the subject began to be recovered, a process that required forty-five years to unfold. In 1903, the English critic C.R. Ricketts observed that the composition depicted on the tapestry hung on the rear wall was a partial copy of Titian’s Rape of Europa, now in the Isabella Stewart Gardner Museum, Boston, but formerly owned by Velazquez’ patron, Philip IV. (It had been acquired for the Spanish royal collection by Philip II.) Some years later, in 1940, Enriqueta Harris, the great English velazquista, identified the helmeted figure in the background as Minerva, who was gesturing toward Arachne. However, Harris believed that these two mythological figures were woven into the tapestry, a misapprehension corrected in 1948 by the American scholar Elizabeth DuGue Trapier, who pointed out that all the figures in the small background space were standing in front of the wall hanging. As it happened, 1948 was the culminating year in the recovery of the original subject. Maria Luisa Caturla, the renowned archival researcher, published an inventory of the original owner, Pedro de Arce, which was dated 1664. In this inventory, the title of the painting is listed as the “fabula de aragne.” Articles by Diego Angulo Iniguez (1948) and Charles de Tolnay (1949) definitively confirmed the identification of the subject as an illustration (a highly-original illustration) of a passage from Book VI of Ovid’s Metamorphoses. According to this venerable literary source, Arachne was a Lydian weaver who claimed that her skill exceeded that of Minerva. She was punished for her pride by being converted by Minerva into a spider, the scene that is about to occur in the background of Velazquez’ painting.

Far from ending discussion of the painting, the retrieval of the subject opened a new chapter in the historiography of Las Hilanderas. Velazquez’ composition is highly allusive and ambiguous. By virtue of his original conception of the antique text, the artist raises questions which both demand and frustrate attempts to answer them. Who are the women in the foreground? Who are the elegantly-dressed females who accompany Minerva and Arachne? Why did Velazquez reverse the logic of the composition, placing the climactic moment of the story in the distance instead of in the foreground? And what is the purpose of the quotation from Titian’s Rape of Europa? By a cruel paradox, the correct identification of the subject only obfuscated the significance of this masterpiece.

It would be tedious to review and analyze in detail the myriad of intepretations that have been inflicted on Las Hilanderas over the last six decades. One proposes that the painting is a political allegory, another that it symbolizes the virtue of prudence, another that it is Velazquez’ claim that painting is a liberal art not a manual craft and that he, therefore, is entitled to noble status. Although they differ one from another, these interpretations do share a common trait. Their authors assert with the absolute conviction, on the basis of the assembled evidence, that they have unlocked the “secret” of this masterpiece. Unconsciously, however, they make the opposite point–that no single interpretation can possibly be sufficient. Although ambiguity is the sworn enemy of the historical sciences, it is a precious resource of artistic creation. Las Hilanderas is the validation of reception theory, which holds that the meaning of art works is altered as the expectations and presuppositions of viewers change over time and through circumstance. It also proves that multiple meanings need not be self-contradictory. Indeed, I would argue that a great work of art demands a multiplicity of responses if it is not to become mere illustration.

Elena del Rivero clearly has arrived at the same conclusion. Her appropriation of Las Hilanderas is incredibly witty and perverse. Interpretations of her deconstruction of the painting could go in many directions, for it is a richly evocative work. Allow me to speak of Elena’s work in purely personal terms. I confess that when I first saw it, I nearly fell off my chair. My intense reaction exemplifies how meaning escapes the control of the artist, at least when the artist has not attempted to reduce significance to boring certainty. As my eyes scanned the image, I saw that Elena had invited an improbable intruder into the magical world of Las Hilanderas, none other than the most engimatic, elusive artist of the twentieth century, Marcel Duchamp. Velazquez and Duchamp in the same imaginary space! They had, in fact, inhabited the space between my ears for decades.

I encountered Velazquez and Duchamp at approximately the same time, in the late 1950s, a formative moment in my life. I had the good fortune of belonging to a family in which art was an obsession. My parents, Jean and Leonard Brown, were pioneering collectors of Dada and Surrealism, and Marcel Duchamp was a household god. My parents talked about him incessantly and in reverential tones. They regarded Duchamp as the most original artist of the twentieth century, and this at a time before his all-pervasive influence had become an acknowledged fact. My mother baptized him as “Leonardo Duchamp,” which was her way of expressing the belief that Duchamp and Leonardo da Vinci were extraordinary polymaths endowed with an ability to look into the future. Furthermore, each had essentially abandoned the practice of painting to pursue interests which can only be called extra-artistic. My mother also discovered a parallel between Duchamp’s Green Box, a strange assortment of sketches and writings related to his greatest work, the Bride Stripped Bare by Her Bachelors, Even, and the notebooks of Leonardo da Vinci. In both cases, the workings of the artist’s mind were presented as pieces of something larger that was never fully revealed. Duchamp was very pleased with the compliment and signed his print, the Chessplayers, with a dedication to my father: “From Leonardo Duchamp to Leonardo Brown.” Chess was the obsession of Duchamp’s later life, and he appears in Elena’s version of Las Hilanderas in the midst of his most notorious game of chess, the one that took place in Pasadena on 18 October 1963, against his naked opponent, Eva Babitz. Marcel enters the world of Minerva and Arachne as a de-stabilizing presence. It is a move that Velazquez, the master of ambiguity, would have certainly approved.

Duchamp, of course, was still alive when his spirit possessed our household and my parents eventually came to know him in person. They would travel to New York from our home in the provincial city of Springfield, Massachusetts, and meet Duchamp at his gallery or in a restaurant. On one occasion sometime in the late fifites, I accompanied them and had the opportunity to shake his hand. I hardly knew what to say and therefore said nothing. This was a very impoverished response from someone who aspired to be a historian of art, and I have tried to do better in my innumerable encounters with Velazquez. The first of these occurred in 1958, when, as a young student in Madrid, that I started my regular visits to the Museo del Prado, that shrine to the art of Velazquez, which would soon lead me to a career as a student of the master and of the Spanish Golden Age.

As I have mentioned, Duchamp and Velazquez are a most unlikely couple but they have been beloved inhabitants of my mental world. I see them as reticent artists, as brilliant critics of accepted modes of art-making, as cryptic analysts of accepted systems of beliefs and as masters of ambiguity, too respectful of art to bind it with the shackles of certainty. With brilliant insight, Elena del Rivero has brought them together in a way that seems completely natural, although it is obviously highly artificial. By collapsing the twentieth century into the seventeenth or, if you like, propelling the seventeenth into the twentieth, Elena’s interpretation of Las Hilanderas invites us to ruminate on the art of two of the most subversive masters in the history of western art. As such, it claims a place of honor in the historiography of this masterpiece and the never-ending history of its reception.

* This essay was originally intended to serve as the second half of an article dealing with the general topic of Duchamp and money. The first part—which deals with the subject of how Duchamp used money in both his art and life—appeared in the April 2003 issue of Art in America.

In the nearly thirty-five years that have passed since Duchamp’s death, there has been a steady increase in the attention devoted to his work, not only by art historians, but also within the world of contemporary art. Certainly the retrospective exhibitions that were held in Philadelphia and New York (1973), Paris (1977), and Venice (1993), contributed to the appreciation of his work, as did the numerous articles and books on the artist that have appeared with consistency over the years. But exactly how much this kind of attention affects the financial evaluation of his work is difficult to determine with any degree of accuracy. Historical importance and contemporary relevance are certainly factors that should be taken into consideration when one attempts to evaluate a given work of art, but, as we shall see, taste (a factor Duchamp’s work confronts by its very nature) and quantity (which he attempted to control) are even more relevant concerns in a fickle and continuously changing art market.

In the late 1960s and early 1970s, Arturo Schwarz, Duchamp’s dealer in Milan, continued to sell examples of the artist’s work, as did a number of galleries in other parts of Europe and the United States. Schwarz still had nearly all of the readymades that were produced in the 1964 edition. At the time they were issued, the complete set was priced at $25,000. So far as is known, there were only two takers: the National Gallery of Canada, and the Cordier & Ekstrom Gallery in New York. The Canadian purchase took place through the efforts of Brydon Smith, Curator of Contemporary Art at the museum. In 1970, Smith approached Schwarz with an interest in purchasing the entire set of readymades, but discovered that there was not enough money left in the museum’s purchase account for that particular year. The following year the museum experienced a surplus in their operating budget, and through a skillful reappropriation of these funds, they were able to make the acquisition. “It was rather in the spirit of Duchamp,” Smith later mused, for the readymades were purchased “from an account usually reserved for office supplies and other such useful materials.”⁽¹⁾

The second set of readymades ended up in an even more unlikely institution: the Art Museum of Indiana University in Bloomington, Indiana. In 1971, Thomas T. Solley, director of the museum, was approached by Arne Ekstrom, owner of the Cordier & Ekstrom Gallery, through which Solley had made various purchases over the years. Ekstrom wanted to know if he would be interested in acquiring the complete set of readymades (which Ekstrom had purchased from Schwarz in the mid-1960s for a Duchamp exhibition at his gallery, and which were then languishing in his storage facility). Through the museum, Solley contacted a donor who agreed to facilitate the purchase, and the readymades were shipped out to Bloomington, where, to this very day, they remain on public display in the University Art Museum. Even though the purchase price had risen to $35,000 (a considerable sum in those years), the expenditure was not challenged by members of the art faculty, but was, surprisingly, applauded.⁽²⁾In the end, it would prove to be a very wise investment, for, as we
shall see, within thirty years the entire set of Duchamp readymades would escalate in value to well over one hundred times that amount.

click images to enlarge

• Figure 1
• Figure 2

• A Collection of Dada Art, Sotheby’s London,
  December 4, 1985, catalogue (cover).
• Marcel Duchamp, Bicycle Wheel, 1916/68,
  lot no. 251 in A Collection of Dada Art.

In contrast to the success of these private sales, the first attempt to sell the readymades at public auction proved a surprising and unexpected disappointment. In 1985, Sotheby’s in London offered “A Collection of Dada Art,” which was identified in the catalogue as “property of a Swiss collection, formerly the collection of Arturo Schwarz, Milan” (Fig. 1). Schwarz had closed his gallery ten years earlier, and the 261 separate lots in this auction represented the remaining inventory from his commercial activities (he had kept the most important pieces for his own private collection). Included was work by some of the most notable of Dada artists: Hans Richter, Hanna Hoch, Max Ernst, George Grosz, Marcel Janco, Kurt Schwitters, Francis Picabia, Man Ray, and a selection of works by Duchamp. The sale concluded with the complete set of readymades issued by the Galleria Schwarz in 1964 (Fig. 2), offered, however, as separate lots. Bidding for these items was anything but brisk. In the end, six of the smaller readymades sold, but at prices that were only about half their pre-sale estimates. This would indicate that the auction house set the reserve (the lowest price at which a work can be sold) unusually low, far lower than the low of the estimate. Despite this strategy, seven of the more important readymades — Bicycle Wheel, Bottle Rack, In Advance of the Broken Arm, Fountain, among others — failed to sell. Nevertheless, within a few weeks after the sale, Sotheby’s managed to find buyers for all the readymades that still remained in their possession, but at prices that were a fraction of the pre-sale estimates.⁽³⁾

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Figure 3
“Art or Junk?,” The National Enquirer,
London edition, February 4, 1986.

The lack of success in selling these works did not prevent at least one newspaper— the anything-but-respected National Enquirer — from asking its readers if the readymades were “Art or Junk?” (Fig. 3). The tabloid reproduced a selection of the objects with their prices, alerting their readers to the fact that “folks are asking a fortune for this stuff.” When an expert at Sotheby’s was asked to explain the “outrageous amounts… these wacky ‘artworks’ are worth,” she wisely replied: “It requires a great deal of knowledge of twentieth-century art to understand these pieces.” Few would argue with that explanation; to understand the prices would have required a great deal of knowledge of twentieth-century art, but also a thorough knowledge of the market in twentieth-century art.

The ideas Duchamp introduced continue to represent an influential force in the world of contemporary art, a factor that — one would assume — affects the financial evaluation assigned his work. This point was dramatically demonstrated in 1997 when one of the examples of Fountain from the Schwarz edition was offer by Sotheby’s in New York as part of their autumn sale of Contemporary Art (Fig. 4). Fourteen years had passed since the Schwarz sale in London when this same work failed to sell, but times had changed. The work was considered so important that the auction house decided to reproduce it on the front cover of its catalogue, and, in a clever decision (since the two works seem to share a common theme), Robert Gober’s Drain was chosen to appear on the back cover. I was asked by the auction house to write an entry on

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Contemporary Art, Sotheby’s
New York, November 17, 1999,
catalogue(front cover).

Contemporary Art, Sotheby’s
New York, November 17, 1999,
catalogue (back cover: reproduced:
Robert Gober, Drain,
edition no. 2/8, cast pewter,
4 ¼ in. x 4 ¼ in. x 3 in., 1989).
Figure 4

Fountain, which turned out to be an essay of six pages that provided not only a history of the original urinal, but the making of subsequent replicas, including the Schwarz edition. The organizers of the auction decided upon a pre-auction estimate of $1,000,000 — 1,500,000, an unprecedented amount for a work like this at auction, but perfectly in keeping with their knowledge of private sales. A year earlier, it was generally known within the art world that under the directorship of David Ross, the San Francisco Museum of Modern Art purchased an example of Fountain from the collection of Charles Saatchi for $1,000,000. This information may very well have contributed to the success of the Sotheby’s sale, for in the end, Fountain was purchased by Dimitri Daskalopoulos, a Greek collector, for $1,762,500, a new record for a work by Duchamp at auction. When questioned after the sale, Daskalopoulos said that he had purchased the piece because “for me, it represents the origins of contemporary art.”⁽⁴⁾

A knowledge of prior sales may have contributed to the exceptionally high price paid for this work, but there were other factors as well. In the days immediately preceding the sale, Daskalopoulos’s advisor in art purchases called me several times from Athens to inquire exactly how this particular
example of Fountain differed from one owned by Dakis Joannou, another Greek collector of modern art. Dakis’s Fountain, I explained, came from the collection of Andy Warhol, but it did not bear the important brass plaque that identified the work as part of the edition of eight signed and numbered examples.⁽⁵⁾ So far as I could determine, the work being sold by Sotheby’s was the very last example of Fountain from the Schwarz edition that was ever likely going to be made available for sale (the location of the seven other examples of this work from the complete edition of eight accompanied my essay in the catalogue).⁽⁶⁾

It should also be noted that as a collector of contemporary art, Daskalopoulos was certainly familiar with the high prices that were usually paid to secure important work. In fact, the two lots that directly preceded the sale of Fountain in the Sotheby’s auction sold for prices that either equaled or exceeded the amount paid for this particular readymade: a Jasper Johns drawing of a Flag sold for $1,762,500, and one of Andy Warhol’s paintings of wanted men (which was compared in the catalogue to Duchamp’s Wanted Poster of 1923/63) sold for $1,982,500. Even these prices were not exceptional when compared with the record-breaking $11 million dollars that was paid for a painting by Mark Rothko that followed a few lots later in the same sale. When it came to assessing the success of this sale, however, few neglected to mention the record-breaking price for a work by Duchamp.

####PAGES####

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Figure 5
Marcel Duchamp: Nine Works,
Sotheby’s London, December 7, 1999,catalogue (cover).

Figure 6
Marcel Duchamp, Study for
a Portrait of Chess Players,
1911, charcoal on paper, 19 ½ x 19 7/8 in.

Figure 7
Marcel Duchamp, L.H.O.O.Q.,
1920/42, rectified readymade
(made by Francis Picabia),
9 ¼ x 7 inches (23.8 x 18.8 cm).
Francis M. Naumann Fine Art, New York.

Three weeks after the sale took place in New York, an auction of Impressionist and Modern Art was held at Sotheby’s in London that included nine works by Duchamp ( Fig. 5). It was generally known that all nine of these works were owned by Georges Marci, a Swiss collector who had assembled the works over the course of the prior decade. These works were featured in a separate catalogue, for which I was again asked to write the introduction. Like the readymades, most of the items offered were produced in editions: the three erotic objects made in an edition of 8 to 10 examples, a reproduction of the L.H.O.O.Q.issued in an edition of 35, and a valise, produced in an edition of 150 examples. The only unique work was Study for a Portrait of Chess Players ( Fig. 6), a magnificent large Cubist drawing that Duchamp had made in 1911, but which he had given to Louise Varèse during his early years in New York (and which remained in her possession until her death in 1988). This drawing was given an estimate of 350,000-450,000 BP, and sold for an impressive 529,500 BP. It may have been the attraction of this single work that caused most of the other works by Duchamp to sell within or in excess of their pre-sale estimates. Only the valise — which was accompanied by five original letters from Duchamp to Poupard-Lieussou (the original owner of this item)—failed to sell. The pre-auction estimate was $165,000 – $206,000, far in excess of the amount that had ever been paid for a comparable work at auction, which was, apparently, the main factor that inhibited bidding.

The exceptionally high price paid for a work by Duchamp may have impressed many, but it is not a great deal of money when compared with the amount that would have been paid, for example, for an important drawing by Picasso from the height of his Cubist period. Indeed, when the prices of Duchamp’s work are compared with those paid for anything even remotely similar by Picasso, the differences can be astronomical. In a sale of Impressionist and Modern Art held at Christie’s New York in the fall of 2000, I wrote entries for two works by Duchamp: a replica by Francis Picabia of his famous L.H.O.O.Q. ( Fig. 7)(with an estimated value of $700,000-900,000), and a deluxe edition of the valise ( Fig. 8) (estimated at $800,000-1,200,000).The auction would also include a rare Blue Period painting by PicassoFemme aux bras croisés ( Fig. 9), a woman with arms crossed that—as a friend of mine recently observed—resembled (coincidentally) the positioning of La Jocconde in Duchamp’sL.H.O.O.Q..⁽⁷⁾When I found out about the Picasso, I requested that I be allowed to write entries on Duchamp that were at least as long as the one that was being written for this painting, though I was well that the Picasso would have a higher estimate (the catalogue stated “estimate upon request,” but the experts felt that the painting was worth between 30 to 40 million dollars). To my surprise, the auction house complied. Of course, I knew that the length of my entry would not affect the outcome of the sale, but I wanted Duchamp to be accorded the same historical respect as Picasso. On the night of the auction, the Picasso sold for over 55 million dollars, and, so far as I could tell, the two works by Duchamp did not receive even a single bid.

click images to enlarge

• Figure 8
• Figure 9

• Marcel Duchamp, The Box in a Valise, 1943, deluxe edition made
  for Kay Boyle (containing original Bachelor’s Domain,
  a hand-colored pochoir reproduction on celluloid of the lower
  section of the Large Glass).
• Pablo Picasso, Femme aux
  bras croisés, 1901-02, oil
  on canvas,32 x 23 in. (81.3 x 58.4 cm).
  Private Collection.

here are several explanations that could account for this failure. First, the works by Duchamp had been recently on the market: the L.H.O.O.Q. had come from a Duchamp exhibition at a commercial gallery in New York (a show that I had organized), where the asking price for this work had been set at $1,300,000 (considerably more than the auction estimate), and the valise had been offered privately by several dealers in Europe and in the United States at prices that ranged from $650,000 to $750,000 (still lower than the auction estimate).⁽⁸⁾But even more importantly, the works by Duchamp were placed in the wrong context. The sale included paintings by some of the most renowned Impressionist and Post-Impressionist artists— Monet, Renoir, Gauguin, Cézanne — as well as some of Duchamp’s most notable contemporaries: Picasso, Kandinsky, Léger, Miro, Magritte, Ernst, and Giacometti, the majority of which fared well in an evening of heavy bidding (the Giacometti sculpture, for example, sold for over 14 million dollars).

For Duchamp, context is everything. A shovel in a hardware store is, after all, only a shovel; place it into a museum, and it is magically transformed into art. This is a concept that most collectors of classic European modernism would either fail to understand or flatly reject. Most collectors of contemporary art, on the other hand, accept the philosophical and aesthetic implications of the readymade as an important if not critical precedent to the underlying conceptual strategies of modernism (which, in part, explains Sotheby’s success in sellingFountain for a record-breaking price).

The lesson of placing Duchamp’s work within the context of vanguard art is one that was well understood by the organizers of a sale on May 13, 2002, of Contemporary Art at Phillips de Pury & Luxembourg in New York. The auction featured all fourteen of the readymades that had been issued by the Galleria Schwarz in 1964, these examples from the collection of Arturo Schwarz himself. The sale also included sculpture by Dan Flavin, Donald Judd, Carl Andre, Joseph Beuys, Jeff Koons, Rachel Whiteread, and Maurizio Catelan; photographs by Cindy Sherman, Andreas Gursky, Thomas Struth and Thomas Ruff; paintings by Francis Bacon, Joan Mitchell, Agnes Martin, Gerhard Richter, Andy Warhol, Jean-Michel Basquiat, Damien Hirst, Neo Rauch, and Ed Ruscha, whose untitled 1963 painting of the word “NOISE” in yellow against a dark blue ground graced the cover of the lavish, oversized catalogue (Duchamp’s Bicycle Wheel appeared on the back cover: Figs. 10.1 and 10.2).

click images to enlarge

• Figure 10-1
• Figure 10-2

• Contemporary Art &
  14 Duchamp Readymades,
  Phillips de Pury &
  Luxembourg,New York, May 13,
  2002, catalogue (cover).
• Contemporary Art & 14
  Duchamp Readymades,
  Phillips de Pury &
  Luxembourg, New York, May 13,
  2002, catalogue (back cover:
  reproduced: Marcel Duchamp,
  Bicycle Wheel,
  assisted readymade: bicycle
  wheel and fork mounted upside
  down on a kitchen stool painted
  white, 49 13/16 x 24 13/16
  x 10 ¾ in.(126.5 x 63 x 27.3 cm).

The sale was accompanied by as much advance publicity as the auction house could muster, including a regular run of advertisements in the New York Times reproducing the various readymades. The only newspaper to run a feature article about the sale, however, was the London Daily Telegraph. The Bicycle Wheel was reproduced, and the article was given the amusing title “Wheel of Fortune,” for as its author Colin Gleadell remarked, it was “estimated to sell for up to $3 million.” Gleadell also informed his readers that in contrast to the issuing of readymades in 1964, which were designed to be sold intact (as complete sets), these fourteen examples were being offered individually, so that collectors were at liberty to chose whichever one they wanted and could afford. He reminded readers that Fountain had sold a few years earlier for $1.7 million, and that, although this information could not be confirmed, an example of the Bicycle Wheel had “sold for more than $2 million on the private market.” Moreover, when the evaluation assigned to all fourteen readymades is tallied, “the overall pre-sale estimate for the set is $8.5 million to $12.6 million,” which, we are told, falls short of the $15 million guarantee Schwarz was given. “Clearly Phillips has taken a gamble,” Gleadell concluded, “one that Duchamp, who had a weakness for risk-taking when playing chess, might have enjoyed.”⁽⁹⁾

In fact, Duchamp took few risks when playing chess, and, as I demonstrate in the first part of this article (Art in America, April 2003), even fewer when it came to his art dealings, whether pertaining to the sale of his own work, or to the investments he had made in the work of others. In the case of the Phillips auction, however, the owners and administrators did undertake a fairly serious financial risk, for it was later revealed that they issued Schwarz a guarantee of $10 million, an amount that fell in the middle of the low and high estimates. If the readymades sold for the low estimate of $8.5 million, the auction house stood to lose $1.5 million; if they sold for their high estimate, they would have made $2.5 million. Apparently, this was a risk the auction house was willing to take, drawing a certain degree of confidence, perhaps, in their recollection of the successful sale of Fountain two years earlier in a sale of Contemporary Art at Sotheby’s.

On the evening of the sale at Phillips, it was raining steadily in New York, which, we can only imagine, must have filled the auctioneers with trepidation, for they knew that if they were to meet their guarantee, they would need as many potential bidders to compete against one another as possible. The eighty-one year old Schwarz, however, who came from his home in Milan to attend the sale, appeared confident and relaxed. Just before the bidding began, a collector asked him if he was nervous. “Why should I be nervous?” Schwarz responded. “As far as I am concerned, they have already been sold.⁽¹⁰⁾

The sale began with Duchamp’s Paris Air, one of the smallest and least known of the readymades, which was given an estimate of $200,000 – $300,000. Bidding was slow and halting. It eventually stopped at a hammer price of $150,000, short of the low estimate but still higher than the reserve, for, to everyone’s surprise (probably even the successful bidders), the auctioneer announced that the work had been sold. A similar pattern continued for the remaining thirteen readymades, where, in most cases, prices only reached approximately half the low estimates, yet were repeatedly announced as having been sold. Only the Bottle Rack (estimated at $800,000-$1.2 million) and snow shovel (estimated at $700,000-$900,000) failed to meet their reserves. Fountain, which was given a conservative estimate of $1.5 – $2 million (a range that reflected the price it had attained two years earlier at Sotheby’s), sold for a hammer price of just over $1 million, still nearly one-half million dollars short of its low estimate. When the bidding stopped, a quick tally showed that the entire set of readymades sold for $5,370,000, exactly $4,630,000 short of the amount Schwarz was guaranteed, a substantial loss for the auction house, but a huge gain for Schwarz, who, in all likelihood, with a fat check in his pocket, scurried back to Milan the next morning.

By contrast, the rest of the auction went rather well: eight artists had achieved record prices for their work, including the Ruscha cover-lot painting, which sold for over $2.5 million, and a Judd sculpture, which sold for over $1.3 million. The entire auction fetched $29,686,350, with 91% of the offerings sold by value. In a report issued by the auction house after the sale, these facts were of course emphasized, and in an effort to put a positive spin on the sale of readymades, it was even announced that Duchamp’s “iconic Bicycle Wheel tied the record for any Readymade,” which it did, since it sold for the same price as Fountain two years earlier at Sotheby’s. Of course, there was no mention of the fact that Phillips lost over $4.5 million on its guarantee to Schwarz, which was perceived by many to have been a total disaster for the Duchamp market⁽¹¹⁾

Perception is, of course, only a reflection of the person doing the perceiving. In describing the sale of the readymades in her regular column for the New York Times, Carol Vogel reported that “collectors sniffed at what some consider icons of modern art,” and Christopher Michaud, writing for the Reuters News Agency, reported that the prices of the readymades “fell far short of expectations, eclipsed by works of more current artists.” Josh Baer summarized the evening best when he wrote in his newsletter that “people will look back on [the sale] and wish they had bought.⁽¹²⁾

So far as the sale of Duchamp’s work is concerned, the failure of the readymades to attain their estimates may inhibit sales in the short term, but in the future, there will be little — if any — harm done to the general Duchamp market. To my way of seeing things, there are two reasons why Duchamp’s work continues to be assigned comparatively low evaluations: rarity, and, perhaps even more importantly, an unrelenting cerebral content.

Rarity is a factor that in most commercial markets causes an item gradually to escalate in value over time. Precisely the opposite occurs in Duchamp’s work, for its rarity creates a situation in which reliable evaluations of comparable prior sales cannot be established. The best way to demonstrate this point is by citing a hypothetical example: Say that you own a work of art by a notable artist that you are interested in selling. When an attempt is made to evaluate the work, comparables are cited, earlier examples by the same artist from the same period that have sold — either at auction or privately — within the recent past (in the art market, up to five years is usually considered a fair indicator). If you should manage to find a comparable work that sold for X-number of dollars, naturally you want the work of art that you own to be evaluated at a somewhat higher figure, an amount that reflects the time passed since the comparable work was sold. When it comes to unique works by Duchamp, however, there are preciously few comparables. During his lifetime, he saw to it that his most important work was placed into important private collections (such as with Arensberg or Dreier), which he knew would one day be donated to museums.⁽¹³⁾In the Duchamp market, then, the “snowball effect” that causes works of art to escalate in value over time is virtually nonexistent. As a result, one can ask whatever one wants for a unique work by Duchamp, but even here, the price must remain within reason, that is to say, controlled by some knowledge of prices that were paid for other works by artist in the comparatively recent past.

click to enlarge

Figure 11
Marcel Duchamp, Belle Haleine:
Eau de Voilette (Beautiful
Breath: Veil Water),
1921, assisted Readymade,
perfume bottle (6 in.) in cadrdboard
box, 6 7/16 x 4 7/16 in..

Figure 12
Marcel Duchamp, L.H.O.O.Q.
, 1919,7 ¾ x 4 7/8 in.

Today, the most common way to the check prices paid for an individual artist’s work is on the Internet. A variety of sites offer postings of recent auction records, but it is virtually impossible to find any verifiable information pertaining to private sales. Of course, when a collector of means is matched with a work of art that he or she absolutely cannot live without, the question of comparable evaluations is of no relevance. In the André Breton sale that took place recently in Paris, for example, the Monte Carlo Bondsold to the Principality of Monaco for 240,000 euros (well above its pre-auction estimate of 50,000 to 60,000 euros). A similar situation occurred in the mid-1990s, when a collector and former art dealer living in Paris sold Duchamp’s Belle Haleine (Fig. 11) perfume bottle to Yves Saint-Laurent and Pierre Bergé for five million dollars. The collector originally purchased the work some twenty-five years earlier from the Forcade-Droll Gallery in New York, and, at the same time, he also purchased the original L.H.O.O.Q. (Fig. 12), which is still in his collection. Some years ago I was approached by a curator at the Museum of Modern Art in New York, asking whether I knew if this work could be acquired. I called the collector in Paris and asked if he would consider selling it. He responded to my inquiry by asking if I knew the highest price ever paid for a work of art. Recalling Renoir’s Moulin de la Galette, I said that I thought it was around 65 million dollars (having forgotten that a van Gogh sold a few years later for some 20 million more). He said: “Bring me a collector willing to pay 66 million dollars, and we’ll talk.⁽¹⁴⁾

Even if the information pertaining to private sales were made public, I doubt that it would affect the comparatively depressed financial evaluation given to works by Duchamp. This, I believe, can be traced to a single overriding factor: the importance of vision over thought. Unlike more traditional works of art, which rely primarily upon visual comprehension for understanding their importance — and, thus, financial value — a work by Duchamp (particularly the readymades) relies upon more complicated processes of thought. We can look at a painting by Matisse, for example, and appreciate it on a purely visual level. Indeed, Matisse himself encouraged precisely this method of viewing when he stated that “an art of balance, of purity and serenity” is “something like a good armchair that provides relaxation from fatigue.”⁽¹⁵⁾By contrast, any viewer who looked at Duchamp’s readymades in this same fashion would derive little or no aesthetic pleasure; no matter how long you look at a shovel — whether hanging in a museum or in a hardware store — it remains a shovel. In this case, viewers are forced to echo a strategy employed by the artist himself when selecting these objects, for he wanted the readymades to exhibit no exceptional visual interest, or, as he said, they are objects possessed of “visual indifference… a total absence of good or bad taste… a complete anesthesia.”⁽¹⁶⁾

If we apply this reasoning to the marketplace, then an art dealer or seller is placed in a somewhat unusual position. He or she can no longer present a work of art to his or her client and allow a purely visual response to convey its content. I have come to refer to this predicament as the triangle theory, where, under normal circumstances, three specific points must be identified and understood before a sale can take place: (1) the client’s eyes; (2) the work of art; (3) the client’s pocketbook. In trying to sell a work by Duchamp, one point in this triangle must be adjusted slightly, for in considering a readymade, one cannot rely solely upon a client’s vision. Instead, the seller is obligated to move that point one or two inches back, to a position well with the client’s gray matter. Only then can he hope to come anywhere near the client’s pocketbook. If the person’s intellect is not stimulated, then, as in the case of looking at a readymade like Duchamp’s In Advance of a Broken Arm, a shovel remains a shovel, which in most hardware stores sells for about fifty dollars (not $600,000, which is the amount for which this item reportedly sold in a private sale to a European client a few days after the Phillips sale).

It is my belief that, in the future, works of art will be increasingly appreciated for their cerebral content, although for the present moment, at least, vision is still required to comprehend the existence of the object. At this point in time, we can only imagine a work of art that would stimulate our minds before reaching our eyes (of course, the same could be said for all kinds of social situations, from race relations to geographic borders, as in John Lennon’s use of the word “Imagine”). Meanwhile, as was his habit, Duchamp seems to have timed things perfectly: if there is any correlation between the aesthetic value of a work of art and the amount of money that someone is willing to pay for it, at the very moment in our history when intellect and vision strive to achieve union, there are virtually no important works by Duchamp available to test the market. He was not only successful in thwarting attempts to commercialize his work in his lifetime. In having kept his production of unique works of art to a minimum, only replicas and works in edition remain within the marketplace today, and even these items come up only rarely. Some thirty-five years after his death — in both aesthetic and monetary terms — Duchamp remains securely one step ahead of the game.

Notes

1. Quoted in a letter to the author from Diana Nemiroff, Curator of Modern Art, National Gallery of Canada, 25 September 2002.

2. Information provided in an email message to the author dated October 14, 2002, from Nan Esseck Brewer, Curator of Works on Paper at the Art Museum of the University of Indiana at Bloomington. Additional details concerning the purchase was relayed to the author in a telephone conversation with Thomas T. Solley from his home in England on October 15, 2002.

3.It should be acknowledged that I was among those who negotiated to acquire these works, eventually acquiring the Network of Stoppages (now collection of the Yale University Art Gallery, New Haven),Bottle Rack, In Advance of a Broken Arm, Fountain,
and Fresh Widow (the latter four now in the collection of the Maillol Foundation, Paris).

4.Quoted in Carol Vogel, “More Records for Contemporary Art,” The New York Times, November 18, 1999.

5. See Jeffrey Deitch, ed., The Dakis Joannou Collection (Ostfildern: Cantz, 1996), p. 93.

6.At the time when this essay was written, I had mistakenly concluded that no. 4/8 of the edition was in the collection of the Toyama Museum of Art in Japan.That information proved incorrect, for no. 4 of the edition appeared on the market in 2002 at the Gagosian Gallery in New York (with a provenance that can be traced to Sarenco & Sarenco of Milan, Italy).

7.The friend, Nura Petrov, is an artist who lives in Riegelsville, Pennsylvania.

8.The Duchamp show was entitled “Marcel Duchamp: The Art of Making Art in the Age of Mechanical Reproduction,” and was held at Achim Moeller Fine Art, New York, 2 October 1999 — 15 January 2000.

9.Colin Gleadell, “Wheel of Fortune,” The Daily Telegraph [London], April 22, 2002. I am grateful to the author, who kindly provided me with a photocopy of his article.

10.The collector wishes to remain anonymous.

11.“Phillips, de Pury & Luxembourg Set 8 Artist Records in $29 Million Sale of Contemporary Art on May 13, 2002,” Click here to view the link.

12.Josh Baer, The Baer Faxt # 318, May 13, 2002; Christopher Michaud, “Rare Duchamps Collection Sold at N.Y. Auction,” Reuters Press, May 21, 2002; Carol Vogel, “An Uneven Night at Auction for Phillips,” New York Times, May 14, 2002. See also Brooks
Barnes, “Phillips Contemporary Art Auction Brings in a Healthy $30 Million,” The Wall Street Journal, May 14, 2002.

13.When he served as executor of Dreier’s estate, he arranged for several of his most important works to be placed into the permanent collection of the Museum of Modern Art, which demonstrates that, in some measure, he wanted his work to be seen and understood
within the context of a larger, more international audience.

14.The collector wishes to remain anonymous, and even though he has refused to confirm the sale price of the Belle Haleine,its current owners requested an insurance evaluation of five million dollars when they lent the work to a show I organized for the Whitney Museum in 1996 (see the catalogue, Making Mischief: Dada Invades New York, Whitney Museum of American Art, distributed by Harry N. Abrams, New York, 1996, pp. 146 and 292).

15.Henri Matisse, “Notes of a Painter,” 1908; quoted in Alfred H. Barr, Jr., Matisse: His Art and His Public (New York: Museum of Modern Art, 1951), p. 122.

16.“Apropos of ‘Readymades’,” a talk delivered by Duchamp at the Museum of Modern Art, New York, 19 October 1961; published in Art and Artists,vol. I, no. 4 (July 1966), p. 47.

Figs. 6-8, 11-12 ©2003 Succession Marcel Duchamp, ARS, N.Y./ADAGP, Paris. All rights reserved.

Marcel Duchamp está frente al tablero de ajedrez, muy concentrado en una partida contra (o con) una joven completamente desvestida, sentada en el lado opuesto. La escena captada en esta fotografía se desarrolla en una sala del Pasadena Art Museum (California) el 18 octubre de 1963, con ocasión de la primera exposición retrospectiva que se le dedicó al artista, apenas cinco años antes de su muerte. Todos los testimonios de la época coinciden al describir a aquel Duchamp como un hombre saludable y jovial, aunque su edad, 76 años, no pareciera ya la más adecuada para jugar con chicas desnudas. La foto, en efecto, tiene obvias implicaciones eróticas, situados como están los jugadores delante de una réplica deLa mariée mise à nu par ses célibataires, même, que había elaborado Ulf Linde ante la imposibilidad de que el vidrio original pudiera trasladarse desde el Museo de Filadelfia hasta Pasadena.

Sabemos en realidad que la foto forma parte de una inocente performance preparada por el fotógrafo Julian Wasser con la complicidad de Walter Hopps, comisario de la exposición de Pasadena, y de una amiga de éste, Eve Babitz, que accedió a posar para ésa y para algunas otras tomas (como la que muestra a Duchamp fumando un puro junto a su Fuente con la muchacha al fondo). No consta quién ganó aquella partida o si llegó a terminarse siquiera, pero sí nos han contado que casi todos parecían estar algo nerviosos. Eve se mostró aliviada cuando supo que en la fotografía seleccionada por Wasser para la publicación, el pelo caía sobre el lado derecho de su rostro, tapándolo por completo⁽¹⁾ . Las contraposiciones de la obra eran, así, completas: un hombre mayor, vestido de negro, con la cara descubierta, juega al ajedrez con una mujer joven y desnuda, de piel muy blanca, y en cuya cabeza sólo se percibe una lisa melena negra. Distanciamiento y “belleza de indiferencia”, por utilizar la propia formulación duchampiana. El artista mira las piezas del ajedrez cuyos ecos formales evidentes se hallan en los moldes málicos y en el molino de chocolate de la maquinaria soltera, muy visibles al fondo; el cuerpo de Eve Babitz, por su parte, remite a la “vía láctea carne”, colgada en la parte más elevada del Gran vidrio, en el vértice superior de un triángulo perfecto cuyas esquinas inferiores están constituidas por los asientos de ambos jugadores. El azaroso mecanismo amoroso de la creación duchampiana se proyectaba así sobre la vida real, testimoniada por el documento fotográfico. En ese primer plano, con la esqueletizada y metafísica obra de arte al fondo, la novia ha sido desnudada ya por su(s) soltero(s), y bien podría adivinarse que el juego va muy adelantado. No está lejos el final feliz.

Pero Elena del Rivero se ha apropiado de esta fotografía y la ha digitalizado, para imprimirla en múltiples fragmentos rectangulares que ha dispuesto luego como un mural en cinco hileras horizontales. Hay unos pequeños marcos blancos de separación entre los cuadraditos, como si éstos fueran las viñetas de una gran fotonovela. Y es esta sutil contaminación de un género narrativo lo que convierte al documento de Pasadena en una historia: cada fragmento del espacio se transmuta en una unidad de tiempo, como si la nueva lectura secuencializada de la imagen obedeciera a cada uno de los movimientos sucesivos de las piezas en el juego del ajedrez. Ahora bien: delante de Eve Babitz, tapándola por completo, hay otra mujer, sentada en la misma posición, y con el rostro oculto, igualmente, por una melena negra. No es la Eva (del) original, ofrecida desnuda al juego más o menos interminable, sino una mujer mundana, notoriamente vestida, entregada a la contemplación ensimismada de unos collares de perlas, símbolos tradicionales de la vanidad. Se diría que el relato continúa así fuera, en el ámbito donde se ha situado ahora la fotógrafa. Esa modelo (la propia artista, al parecer), con camisa de malla negra y amplia falda dorada, sería una seguidora hipotética de la narración que está detrás de ella, y su “identificación” con la chica que juega al ajedrez se opera en términos ficticios, como cuando vivimos vicariamente las peripecias de un personaje novelesco. ¿O tal vez no? Su atuendo y su postura recuerdan un poco al tema tradicional de la Magadalena arrepentida (pensamos, por ejemplo, en la interpretación de Caravaggio); la ropa, desde luego, no es la de un vestido de novia, y bien podría ser la de una (falsa) princesa o la de una prostituta de lujo ataviada para una fiesta de “solteros”, même. En cualquier caso, una mujer anónima (no tiene un rostro visible), tan completa y ostentosamente vestida, sentada delante de esa foto de Duchamp, ¿nos está invitando al desnudamiento?

Y dado que la narración debe seguir, ¿quién lo ha de realizar? O más claramente, ¿quién ha de suplantar, por obvias razones de simetría, a la figura de Marcel Duchamp que continúa visible en los recuadros escaneados clavados en la pared de atrás? Parece evidente, en fin, que esta presencia femenina exige la de un ente masculino, même, situado en frente, presumiblemente desnudo, que daría una vuelta de tuerca en el interminable proceso del desnudamiento. No creo que sea disparatado hacer una lectura algo feminista de una obra como ésta, que parece hacer recíproca la proposición duchampiana: “el (recién) casado desnudado por su(s) soltera(s), mismamente”. Pero es el vacío de ese hipotético ente masculino, su hueco espacial, lo que parece obligarnos a situar a Les amoureuses (Elena & Rrrose) de Elena del Rivero (2001) en la estela de los Étant donnés. En efecto, en la instalación póstuma de Duchamp que conserva el Museo de Filadelfia, es el mirón el que completa la obra, participando en una actividad amorosa que se ofrece, como promesa, a través de los agujeros del portalón. Elena del Rivero parece invitarnos, igualmente, a plantar nuestra silla frente a su muchacha vestida: soy yo, el espectador, un ser humano concreto (o más específicamente un hombre), el protagonista que falta. La artista sugiere de esta manera que mirar es sólo una actividad preliminar, y que nada percibiremos, tal vez, si no nos desnudamos y si no estamos dispuestos a jugar.

J.A.R., enero de 2002

NOTES

1. Todos los detalles de aquella sesión, incluyendo reproducciones de las tomas fotográficas descartadas, pueden encontrarse en Dickran Tashjian, “Nothing Left to Chance: Duchamp’s First Retrospective”. En Bonnie Crearwater (editor), West Coast Duchamp. Grassfield Press, Miami Beach, Florida, 1991, pp. 61-83.

Dear John,

Thank you for the thorough reading of my pieces (yup, and Hirschhorn is certainly an intelligent enough artist not to have fallen into my little trap!). There is, of course, a very detailed article on the 8/9 bachelors in the pages of Tout-Fait: The Bachelors: Pawns in Duchamp’s Great Game

In terms of the 1964 edition, your thoughts are intriguing, yet the numbers do not quite add up. It becomes pretty tricky. The number of the entire set of Ready-mades (and semi-ready-mades, etc.) in this edition is 14. Each of them is numbered 1/8-8/8. Yet in addition to those there are three replicas reserved for artist (MD), publisher (A. Schwarz) and the Philadelphia Museum. On top of that, there are two more replicas for museum exhibitions, bringing the number up to 13 (!). Research throughout the years has led us to conclude that a much higher number was produced (some stolen from Schwarz’s warehouse, missing the small copperplate or the case and/or the signatures. All in all, it’s a pretty fuzzy affair.

Best, Thomas Girst

Tom Girst, Editor in Chief:

Have been greatly enjoying latest issue of Tout Fait, after noting not once, but twice you brought attention to Duchamp’s 1964 Readymades edition. In the Barns interview it was surrounded by the usual dismay this edition brings, fair enough. Then, in the corespondence with Hirschhorn you appeared to have taken a decidedly heavy hand in reference to this edition, using it as a form of entrapment to elicit a responce from Hirschhorn in regards to his own recent works potential “commercial” value. It was to Hirschhorn’s credit that he did not “trip” on this edition or reference it to his own works, but he clearly rebuked any notion that Duchamp ever compromised his own works, Bravo, Hirschhorn. I believe I can shed some light around the “dismay” of this Duchamp/Schwarz venture. First, in the Barnes interview he preferences his concern by stating that at least in regards to Etant donnés the work appears “to flesh out the Bride” placing it full cycle in relation to the Large Glass. The very same statement can be said of the Ready-mades edition, as usual with Duchamp the “shock” is hidden in plain sight. The answer, Dear Tom, is in the exact number of the editions “8”.

Does this number ring any bells? As Etant Donnés belongs to the realm of the Bride, so the Ready-mades belong to the realm of the Bachelors. Return to the notes in the Green Box, where Marcel lets us know that the Bachelors were conceived as a game of 8!, only changed to 9 with the addition of himself, a reluctant station master (in an non-autobiographic way as possible). As reluctant as the “lost” original Ready-made brings the number 8 to 9! In fact seen from this angle the Ready-mades appear as a collective form of “portraiture”, a sort of Bachelors composite (although non-auto, you understand). Keep up the great work.

Sincerely,

John Mcnamara
mac2u22@hotmail.com

click to enlarge

Figure 1
Marcel Duchamp,
Bicycle Wheel
(Fork), 1964

As a small point, the ‘straight fork’ (Fig. 1) might not be a functional on the road fork at all, but rather a wheel truing stand. These are still available to those of us who ride regularly, and resemble forks. When wheels go over bad bumps, over time, the spokes can loosen and the rim needs to be pulled back into shape. It is adjusted in such a bracket with added measuring tools to detect wobble and roundness. I don’t know how this enters into the thinking about the bike wheel, but I thought it might be useful to share. I am delighted to contribute to anything Stephen Jay Gould had a hand in. His work has given me so much pleasure and clarity of thought. Thank you.

Fig. 1
©2003 Succession Marcel Duchamp, ARS, N.Y./ADAGP, Paris. All rights reserved.

click images to enlarge

• Figure 1
  Bicycle Wheel
  (1913) on a Stool.
  Photograph taken
  at Duchamp’s studio,
  circa 1917
• Figure 2
  Bicycle Wheel
  (1913) on a Stool.
  Photograph taken
  at Duchamp’s studio,
  circa 1917
• Figure 3
  Bicycle Wheel
  (1913) on a Stool.
  Photograph taken at
  Duchamp’s studio,
  circa 1917

In response to a discussion of the Duchamp bicycle sculpture on the massbike listserv, I have a couple of quibbles about statements on bicycle history on your pagehttp://asrlab.org/articles/why_bicycle_wheel.htm

The following statement is not entirely accurate:
”The straight fork bicycle might have looked fine, but the irregular twists, turns, throws and pitches of a Bicycle Wheel, when attached to a straight fork, were dangerous and unstable–hence, the name given to the bicycle with a straight fork design: the “Bone Shaker.”

The term “boneshaker” applies to bicycles built from approximately 1863 to 1878, with a relatively small front wheel constructed like a wooden wagon wheel–the bicycle shown inIllustration 6 on the page is of this type. Most bicycles made from approximately 1878 to 1890 had tensioned steel spokes, a larger front wheel and a smaller rear wheel. These bicycles had straight forks and were called “ordinaries”, highwheelers” or, with derogatory intent “penny farthings”–not “boneshakers.”

The rough ride of the boneshakers was due largely to the solid steel or rubber tires. Highwheelers also had solid rubber tires, but the ride was smoother–the large front wheel, nearly directly under the rider, bridged road surface irregularities better. The rear wheel was small, but it was far behind the rider, and the frame member between the rear wheel and the saddle was rather long and flexible.

The real breakthrough in ride quality came with the introduction of Dunlop’s pneumatic tires in the 1890s–along with chain drive, this invention made for a comfortable ride with the bicycle frame design still in use today.

Straight forks were used on highwheelers as well as boneshakers. A curved fork does somewhat smooth the ride, because it is springier than a straight fork–however, its effect in smoothing the ride is much less than the effect of the pneumatic tires or the highwheeler’s large front wheel.

The boneshaker in your illustration has a vertical steering axis, a straight fork and therefore zero trail. It was discovered at some time in the early development of the bicycle that a bicycle was self-steering (like a supermarket shopping cart caster) if it has trail–that is, if the tire contact patch is behind the projection of the steering axis to the road surface. Only a bicycle with trail can be ridden no-hands. This was the case with typical highwheelers; the slight tilt of the fork’s attachment to the frame created the trail.

With the rear-wheel chain-driven safety bicycle, the steering axis had to be tilted even further so the front wheel would clear the rider’s feet. Although the fork of such a bicycle is curved (“raked”) *forward* at the bottom, the tire contact patch is still *behind* the steering axis. A straight fork would bring the wheel closer to the rider’s feet and place the tire contact patch too far behind the steering axis, resulting a heavy feel to the steering, and excessive response to shifts in rider position.

What is the provenance of the fork in the Duchamp construction? It might be from a unicycle — unicycles still use straight forks to this day. Or it might be from an old highwheeler, and cut down to fit the smaller wheel used in Duchamp’s construction. Or, more likely in my opinion, the fork could be from an early safety bicycle, for example, the “bantam” bicycle shown on page 20 of the book *Bicycle Science*, 1983 edition (MIT Press), by Whitt and Wilson and also on page 158 of the wonderful 1896 book *Bicycles and Tricycles*, by Archibald Sharp (reprint edition from MIT Press, 1979). Many early safeties had a straight fork. There are other examples of such bicycles on pages 154, 280 and 288 of Sharp’s book.

And in connection with this, the following statement is not accurate:

”Manufacturers had not produced bicycles with straight forks for over 30 years Many safeties made in the 1880s and early 1890s had straight forks. So 20 years is accurate; 30 years is not. That is why I consider it most likely that the Duchamp for was salvaged from an old, disused safety bicycle.”

I am not a real expert on old bicycles. A member of the Wheelmen, who collect and restore old bicycles, might have a more definite opinion of the provenance of the fork. I am sending this message to the massbike list and Prof. Wilson, who, I’m sure, will be interested in having a look at your page.

John S. Allen
jsallen*at*bikexprt.com
http://www.bikexprt.com

 
In the conclusion of my article for the fourth issue of Tout-Fait Journal ⁽¹⁾, I identified a possible theme in the artistic events of the 1900’s. I’m referring to the gradual emergence, in art, of important ideas and conceptual themes which also belong to the grounding kernel of the complexity sciences.
As a first step, my concern was (and still is) to illuminate some unexpected links, all of them directly related to some fundamental ideas of complexity, between some leading figures in twentieth century art, namely Klee, Duchamp and Escher. This unexpected relationship is even more surprising considering the radical differences between their personalities and their artistic results, or at least the retinal (to use a duchampian term) ones. Furthermore, as far as I know, there is nothing in their writings that links these artists. Relations between Duchamp, Klee and Escher cover a huge range of ideas, and the complexity sciencesprovides us with a realm in which we can unify them.
At the yearly conference “Matematica e Cultura” in Venice ⁽²⁾, organized by Prof. Michele Emmer, I gave a talk titled “Strands of complexity in art: Klee, Duchamp and Escher”, ⁽³⁾where I presented some preliminary findings of my research. This article supplements those preliminary findings with new analogies. I’ll start by summarizing those first ideas; and then I’ll introduce other subjects, such as evolution, topology, impossible 3D objects and enlarged conceptions of perspective. Finally I’ll try to relate these themes with those of complexity.

1. A summary of preliminary findings

I divided the common traits between Klee, Duchamp and Escher into three groups, all of them mathematically relevant and strictly related to each other and to corresponding complexity themes. They are:
a. Recursion and fractals
b. Feedback loops and self organization
c. Instability and chaos
(Particularly for the a. and b. points, I took the most part of my argument about Duchamp from my article on Tout-Fait Journal cited above, where the reader can find some detailed explanations about the subjects summarized below).

a.

In Escher’s work the role of recursion, and the presence of fractal structures have been well known and accepted since the appearance of Hofstadter’s classic book ⁽⁴⁾.
As far as Duchamp is concerned, recursive structures underlie not only several individual works, but also creative processes on a larger scale, involving several works at once. I also suggested the presence (at least in embryonic form) of the idea of fractal structures, mainly linked to the typical duchampian procedure of repetition on a lower (reduced) scale.
Much of Klees work is based on recursive (iterative) procedures. Klee called themprogressions. They are mainly related to natural processes. In relation to natural processes Klee’s intuition of abstract mathematical concepts, like fractal dimensions (ie non-integer dimension), is notable, especially in relation to the botanical world.

b.

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Figure 1
Marcel Duchamp, The Bride
Stripped Bare by Her
Bachelors, Even, 1915-23

Here Escher’s use of tessellation comes to mind. A game of symmetries could be seen as a complex system, where very simple rules (namely the given symmetries) exert their reciprocal feedback locally; as well as interacting to have dramatic, global and complex consequences on the whole tiling system. This can be (meaningfully) related to concepts regarding morphogenesis: simple rules can create global complexity, provided that the components of the system are sufficiently connected to each other.
In most of Klee’s works we can see feedback loops in action, both negative and positive. True dynamic systems are the results of these loops. Klee relates them to morphogenetic processes. Once again, the key point is: local simplicity coupled with a huge network of connections) can determine the emergence of global organizational patterns.
Several of Duchamp’s wordplays show self-organizing properties. In a broader sense there are similar random self-organizing processes acting in the Glass. (Fig. 1)

c.

Looking at Escher’s prints, exposure to conflicting stimuli (such as black-white, concave-convex, figure-background) destabilizes the observer. This theme has been already widely discussed by scholars ⁽⁵⁾. Also, Escher is particularly interested in whirling structures that draw together self-reference, fractal structures and whirling, chaotic motions.

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Figure 2
Marcel Duchamp, The Bride
Stripped Bare by Her
Bachelors Even [The
Green Box], 1934

It is well known that instability plays a key role in Klee’s compositions. Moreover Klee was attracted by what nowadays is called deterministic chaos, ie. unpredictable, irregular behavior, rising from the iterations of simple deterministic procedures. A number of different figurative frameworks are borne out of iterative procedures that have been triggered to behave irregularly. The most interesting thing, however, is that from such quite chaotic tangles of lines, often perfect vital and shiny forms emerge. An interesting analogy can be drawn here with the edge-of-chaos idea of complexity.
Instability and chaos are quite typical duchampian themes. His wordplays depend on predetermined lexical conditions; the slightest differences in either a single syllable or letter or even simply intonation could cause radical shifting in the meaning of a sentence (here we have a true sensitive dependence on initial conditions). Furthermore, Duchamp saw the creative power of instability. In the loosest sense it could be seen everywhere in the Glass and in theNotes of the Green Box, (Fig. 2)but more specifically we see that in the works based on rotatory motion, where highly unsplanar sets of rotating circles can create the illusion of the sthird dimension. Here again the creative power of instability has been exploited which is also powerful edge-of-chaos idea.

2. Evolving systems
Before the twentieth century it was physics, not biology, that was the leading area of scientific endeavour. It was from physics that models and protocols for science were drawn. The 1900s saw a shift towards biology. This shift was consistent with the progressive affirmation of the new paradigm of complexity.
This interest in biology is reflected in the work of Klee, Duchamp and Escher. Firstly Klee, whose interest in Natural History (especially in botany) is well known; like a naturalist he focused (as both artist and teacher) on the central problem of organic growth. He investigated both morphology (the study of forms) and morphogenesis (the study of processes leading to form); his intuitive, biological investigations are notable.
Escher, for his part, was more attracted by abstract ideas; more mathematical than biological, but was nonetheless intrigued by the natural world. He dealt especially with the inanimate world of minerals and crystals. However biologists drew analogies of his abstract ideas with corresponding biological concepts; sometimes Escher dealt with biological processes themselves.

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Figure 3
Marcel Duchamp,Bride’s
Domain from the Large
Glass, 1915-23

Figure 4
Marcel Duchamp,Bachelor
Apparatus from the Large
Glass, 1915-23

Perhaps Duchamp is the artist who best expressed (both in advance and inadvertently) the inversion of the relationship between biology and physics: by distendingthe laws of physics and chemistry he bypassed the rigid determinism and the reductionism of those disciplines. By grafting the organic forms of the Bride (in the higher part of the Glass) (Fig. 3) onto the mechanical machinery of the Bachelors (in the lower part) (Fig. 4)Duchamp not only expressed the idea of a marriage between physics and chemistry (at the bottom, in a three dimensional world), and biology, (above, in a four dimensional world) but perhaps even the superiority of the latter: after all the bride is queen.
This new kind of interest in biology is related to the development in every scientific field of systemic theories. This began in the 1940’s with cybernetics and ended up with the establishment of complexity sciences: what better paradigm of a system is there than an organism? Biology teaches us that complex systems adapt and evolve, we call them complex adaptive systems (CAS) Adaptation and evolution are key in all areas of the complexity sciences. Can artists, that were aware of world-system complexity, have been unaware of these notions of adaptation and evolution, at least at some intuitive level? In my opinion no. Being sensitive to complexity implies having some awareness of evolutionary processes (not necessarily biological), driven by random probabilistic events coupled with adaptation, which make the world-system ever changing.
In Klees’ writings we find a number of references to evolutionary biology ⁽⁶⁾. He clearly had some understanding of the subject matter. However, it is what he did as a painter, more than what he thought as a naturalist, that is interesting here.
He would lovingly cultivate mistakes he made, and embed them in his paintings. He would encourage pupils to draw with their left hand, and to nurture the irregularities that ensued. He also would introduce subtle and repeated variations into his work that would form mobile, ever changing patterns. Klee clearly loved chance.

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Figure 5 Paul Klee, Red fugue,1921
Figure 6 Paul Klee, Sheet from the
town book, 1928

Here, two of Klees’ groups of work are of note: those of Red fugue (1921) (Fig. 5) andSheet from the town book (1928) (Fig. 6). Both groups are based on repetitive horizontal sequences, which are gradually transformed by introducing constant, apparently random variation in the repetitions of the starting shape. The representation of an evolutionary process could be seen in these paintings, where random mutations seem to be somehow selected to obtain certain properties of the resulting patterns. I discussed the subject in some detail in the article already cited ⁽⁷⁾, and I showed by means of computer simulations that evolutionary algorithms can produce quite similar patterns.
Let us consider now Escher’s use of tessellation or tiling (i.e. covering of the surface by means of repeated tiles, without empty gaps and overlapping), such as the one signed E15(1938) (Fig. 7). Each single piece of tiling contains the complete information necessary to build the whole surface; of course this holds.

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Figure 7
M.C. Escher, E15, 1938

Figure 8
M.C. Escher, Metamorphosis, late 1930s

Figure 9
M.C. Escher, Verbum, 1942

Meaningful analogies with the idea of complete genetic information contained within each cell of an organism. Parallels between Escher’s tessellation and mechanisms in biochemistry have been developed by Edward Whitehead ⁽⁸⁾.
Interestingly, Escher’s tiling often depicts a process which gradually transforms the structure of the tiles. This transformation is rendered infinite by the introduction of a circular narrative pattern, which leads it back to its starting point. The strips namedMetamorphosis (the process which turns the larva into insect) are examples of this (Fig. 8) which Escher created in the late 30’s. Such transformation can be seen to some extent as a metaphor for evolutionary process. This, at least, was the opinion of Nobel chemist Melvin Calvin on Escher’sVerbum (1942) (Fig. 9) ⁽⁹⁾.
Let us thirdly consider Duchamp.
The theme of the dichotomy mother – egg, and the paradoxes that lie therein are worthy of investigation. I discussed the subject in the already cited article ⁽¹⁰⁾.
Duchamp used objects and moulds to signify the idea of mother and egg. The mould represents the egg, the object the mother. He used these in a number of different contexts, including the Malic Moulds of the Glass. (Fig. 10)The object and the mould are self-perpetuating and codependent : the object is used to cast the mould and the mould to shape the object. Similar ideas are identifiable in Three Standard Stoppages (1913-14) (Fig. 11)and Tu m’ (1918) (Fig. 12). For the latter he made three wooden templates, for transferring the outline of the threads contained in the Stoppages onto the oil painting. In Tu m’ these templates appear again, depicted in the bottom-left corner; their respective threads in the right hand corner. We have the old threads; their templates, and the new threads… The two elements (thread-Mother and template-Egg) are present in both the Stoppages and Tu m’. (En passant: notice that in Tu m’ the representations of templates and threads stand at the opposite sides of the picture, as we said above; in the middle, the psychological epopee of Bride and Bachelor is abridged, maybe as the necessary step to link egg and offspring).

Figure 12
Marcel Duchamp,Tu m’, 1918

Now the key question is: is this chain deterministic? Could this cyclic process repeat itself unchanged, giving rise to ever equal objects? It couldn’t. Indeed, remember that Duchamp explicitly connects the idea of mould with the idea of infra-thin difference:

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Figure 13
Marcel Duchamp,
Cemetery of Uniforms and Liveries, No. 2, 1914

Infra-thin separation. 2 forms cast in the same mould (?) differ from each other by an infra thin separative amount. All “identical” as identical as they can be, (and the more identical they are) move toward this infra thin separative difference. (Note posthume).
Thus the process contains an important random event (possibly corresponding to biological mutation). A parallel could be drawn between evolutionary process and the cyclical alternation of the object and the mould(Mother-Egg). At the very least, this observation would be consistent with Shearer’s idea that the cemetery of liveries (Fig. 13)(the Malic Moulds) could be seen as the place where scientific knowledge is recorded ⁽¹¹⁾. An empty livery is a repository for a scientific idea as well as being a mould that produces new ideas on which are encoded new theories, thence new liveries and so on.

3. Topology

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Figure 14
M. C. Escher, Moebius band I, 1961
Figure 15
M. C. Escher, Moebius band II, 1963
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Animation 1
Animation of Moebius Strips

Klee, Duchamp and Escher were all three attracted by topologically interesting figures.
Several of Escher’s works deal with topological figures, such as knots (Knots, 1965) and Moebiusstrips (as in Moebius band I, 1961 (Fig. 14) andMoebius band II, 1963 (Fig. 15)).
Moebius strips (see Animation 1 which explains a possible genesis of the strip starting from a cylinder) exhibit a number of interesting properties; I’ll recall and briefly explain some of them.
First, unlike the cylinder, which has both an internal and external surface, the Moebius strip has only one surface; This can be easily verified by mentally painting its whole surface, without lifting the brush from the strip.
Second, whilst a cylinder has two edges (lower and higher) the Moebius strip has one only edge; once again you can follow this edge completely with the finger without having to lift it from the edge.
Furthermore, if one cuts the cylinder longitudinally, two distinct cylinders will be obtained, whereas by cutting the Moebius strip the same way, one only new strip is yielded.
Escher carefully showed these properties in his prints. In Moebius band I he cut the strip longitudinally and obtained three snakes eating each other’s tail, while in Moebius band IInine ants in line walk on the strip, so as to highlight the single edge and single face concepts.
Escher was interested in the circularity of his knots and strips. He drew them together in a monograph ⁽¹²⁾ under the chapter heading spatial circles and spirals. His knots, Moebius strips, as well as planar and spherical spirals, were all drawn together in this section. The knots follow circular pathways which end up at the starting point after torsions and self-intersections. The same holds for the Moebius strips.
Klee too, was interested in knots, and had been since childhood. Several of his early drawings show knotted worms hanging from a fisherman’s hook. We see the same worms, now abstract knots, in later drawings such as Ways Toward the Knot (1930) (Fig. 16). 2D knots are also drawn according to even more essential forms, like the infinity-shaped motif (and its polygonal variants) shown in his pedagogical sketch (see Sketch 1). We see a huge collection of similar patterns in pictures like Dynamically polyphonic group (1931) (Fig. 17), which is based on a feature of those 2D knots Klee was interested in (see Animation 2): a hatch follows the course of the knot with continuity, but always remaining on the same side of the line; in so doing, the hatch highlights the inside of one half of the motif, and the outside of the other half. How is it possible to pass from inside to outside, while remaining on the same side of the line? It is due to the self-intersection of the 2D knot (corresponding with the torsion in the Moebius strip), which allows passage from an inner to an outer region, without passing from one side of the line to the other. As we saw before, Moebius strip has a similar property. Let us return to Klee’s 2D knots. He amplified them, to form complex, perpetual pathways, once again formed by uninterrupted, closed, self-intersecting lines (often polygonal instead of curved) and always returning to the starting point. This is typical of Klee’s drawings of the late 20’s and the early 30’s. An example is the drawingMechanics of an Urban Area (1928) (Fig. 18).

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Figure 19
Paul Klee, Excited, 1934

Sketch 2
Folding recursive process

We have other evidence of the special topological meaning of Klee’s images, such as labyrinths. Labyrinthine lines and signs are indeed among the most important patterns in Klee’s late style. Several hypotheses could be made to explain the genesis of such patterns, and in my opinion they are often linked to morphogenetic processes ⁽¹³⁾. There are, however, some drawings, such as Excited (1934) (Fig. 19) and all the others, based on the same framework, which particularly show the underlying presence of the folding recursive process (seeSketch 2). Similar (but reversed) processes are sometime used for classifying labyrinths in topology ⁽¹⁴⁾ unrolling them, to obtain the simpler equivalent form. But, interestingly, similar folding processes can also give rise to fractal and/or chaotic structures ⁽¹⁵⁾ which in turn can be connected with the corresponding themes highlighted above.
With reference to the use of Duchamp’s topological figures, I have already underlined the importance of the Kleinian bottle, along with some related Moebius-strip-like structures in his writings and works ⁽¹⁶⁾, and I have already stressed a possible meaning of this circular self-penetrating and self-encompassing figure, this is recommended further reading.
Now I’ll focus on further interesting links between Klee, Escher and Duchamp with respect to the use they made of the well-known topological properties of those surfaces. The analogy between the infinity-shaped motif of Klees’ and Eschers’ Moebius strips is further reinforced by observing some other prints of Escher’s, which came 10 or 15 years before his Moebius strips; Horsemen (1946) (Fig. 20) and Predestination (1951) (Fig. 21)show the planar infinity-shaped motif.
Let us take Duchamp’s Steeplechase (Fig. 22): it is a self-made racing course, for a childish horserace game in which there is a clear connection with both Klee’s infinity-shaped motif and Escher’s prints Horseman and Predestination. This could be seen as an antecedent ofSculpture for Travelling (1918). (Fig. 23)

Jean Clair ⁽¹⁷⁾ suggested an interesting analogy between the kleinian bottle and some alchemic symbols, such as the one of the pelican devouring itself, and then he connected it with Duchamp’s Air de Paris (Fig. 24). Look now at Escher’s preparatory sketch (Sketch 3)of a Pelican; although in the definitive print he substituted the pelican with a dragon (Dragon, 1952) (Fig. 25), he maintained however the same idea of a self-penetrating and self-eating animal (after all, the snakes eating each other’s tail in Moebius band I refer to the same theme). As far as Klee is concerned, we saw similar self-eating structures, though abstract, in the meandering lines of the drawings around 1934, use the same techniques as the previously mentioned Excited: the basic motif (see Sketch 4) is formed by two curves penetrating one another, the end of the one into the belly of the other.

In his latest style Klee used a typical pattern whose genesis and meaning we can better understand by looking at a detail of the drawing The fugitive is Looking Back (1939) (Fig. 26); the body of the fugitive is based on branching curved lines, the one starting from the back of another. The head too is formed by a similar, curved line, but it is branching from its own back, in a circular, self-referential scheme. This motif is further amplified in innumerable drawings and paintings around 1939-40, where we find a lot of self-embedded, self-encompassed figures, such as in Fastening (1939) (Fig. 27).

What is the significance of this trend for using topological figures? What relationship can we establish between that and complexity?
First, with Klee, Duchamp and Escher there is a tendency to represent very complex things, where the parts are widely connected to each other, interacting with non-linear pathways, often looping and returning to some crucial points. Thus the tangled intricacy of some knots or labyrinths visually and effectively expresses the corresponding intricacy of the components of their complex systems.
Second, such intricacy of connections within a system often produces unexpected outcomes, which in turn imply new unexpected outcomes, and so on. Thus in the complex system represented in their works by our artists, it is difficult to discern clearly causes and effects, because of the network of their reciprocal feedback. The unexpected, often strange and sometimes paradoxical outcomes rising from systems subjected to circular feedback and self-referential loops have corresponded with the strange and paradoxical properties of figures such as knots, the Moebius strip or the Kleinian bottle, due to their circularity, their self-intersections or self-penetrations. The same could be said for those figures discussed above, often used by the late Klee, which are self-encompassing.
Particularly in the case of Duchamp, as I have already shown ⁽¹⁸⁾, the topological properties of the kleinian bottle were used to express the paradoxical identity Egg–Mother (or Bride–Glass). This was discussed in the previous section, and in general to express the autopoetic properties of the duo Glass–Box.
 
4. Enlarged perspective and Impossible 3D objects

Figure 28
Marcel Duchamp,
Apolinère Enameled, 1916-17

Figure 29
Paul Klee, Chess, 1931

Sketch 5
Trihedral junction
versus DihedralT-junction

Sketch 6
Trihedral
junction versus Dihedral
T-junction in Apolinère Enameled

Rhonda Shearer ⁽¹⁹⁾ thoroughly discussed the relationship between some of Eschers’ and Duchamps’ works, based on 3D impossible objects. She documented how Duchamp’s Apolinère Enameled(1916-17) (Fig. 28) predates by forty years the seminal paper of Lionel and Roger Penrose on impossible 3D figures ⁽²⁰⁾. She also stresses the bond of friendship between Duchamp and Roland Penrose, a close relative of Lionel and Roger. The cited Penrose article is the professed source of inspiration of Escher’s famous impossible figures, so that the reading of Shearer’s article cements a direct link between Escher and Duchamp via the Penroses.
But, what about Klee’s impossible 3D objects? We shall discuss some works, which are representative of corresponding frameworks, all of them developed in about 1930 and deeply linked with one another.
The first we shall consider is Chess (1931) (Fig. 29). I have elsewhere already examined this painting, its genesis and its possible meaning ⁽²¹⁾. Here I want only to recall that the bare, empty room in the background is an impossible 3D object (as a matter of fact, many other elements in the painting are spatially inconsistent, but here we shall confine ourselves to the background only).
The walls of the room are joined to each other by means of vertical edges, three of which are explicitly traced, whilst the fourth (the dotted one in Sketch 5) is only suggested by the left side of the paler rectangle in the upper right hand corner of the painting. Three of those vertical edges have mutually inconsistent junctions at the opposite extremities: one end shows a trihedraljunction, where three distinct edges converge, while at the opposite end, two of the three edges line up one another, giving rise to a dihedral T-junction. Thus, the background is an impossible, puzzling 3D object, and the checkerboard covering over the scene may suggest something like a chess problem, just to emphasize the spatial enigma posed by the background.
Look now at Apolinère Enameled: one among the ingredients for making this 3D object impossible, is just the same as for Klee’s Chess: mutually inconsistent ends of a edge, highlighted in Sketch 6.
Klee used to express the concepts and the ideas he was interested in, by means of graphic simplifications, focusing his attention on only the essential parts. He would discard irrelevant and non-essential details, that might mislead the observer and would especially avoid repetition and redundancy. If necessary they wold just suggested.
That’s the reason why we find traces of other impossible 3D objects in a very simplified form; as is the case for The Conqueror (1930) (Fig. 30). Look at his banner. Though a banner is essentially a flat object, at first sight we actually perceive something like a cube, a solid figure; but counting the peripheral sides of the overall silhouette, we find that there are five, not six, as we would generally expect (Sketch 7). Something here is wrong: as soon as we accept the hypothesis of a possible 3D vision, we immediately recognize that it is inconsistent with some details of the motif. There is something missing. To better understand what really is missing, let us examine a further simplified versions of the same motif in another of Klees’ pictures: Six species (1930) (Fig. 31). Look at the flower displayed in Sketch 8. To make it spatially plausible, we have to mentally add a missing edge to form a trihedron; the same holds of course for each other flower in the painting. Without the addition of the missing edge we perceive something oscillating between a dihedron and a trihedron, which leads us back to the analogous ambiguity we saw in Chess.

Notice now that Duchamp was interested in exactly the same ambiguity. Look indeed at the recto side of the Hershey Postcard note (circa 1915) (Fig. 32), or even at the miniature reproduction of Why Not Sneeze Rose Sélavy? in the Boite-en-Valise (1941) (Fig. 33).

Returning now to Klee’s Conqueror, it is easy to see similar treatments in its banner. Especially in this case, as we said above, the perception oscillates continually between the 2D and 3D: no sooner have we arrived at a 2D hypothesis, then we are pushed to reject it and embrace 3D one, and vice versa. The relevance of some of Duchamp’s and Escher’s ideas is here clear, for it is well-known that the conflict between surface and space is one of the most important among their themes.
Let’s now turn our attention to Klee’s Soaring, Before the Ascension (1930) (Fig. 34) which is representative of several paintings based on the same framework, worked out in the years we are considering. The framework is based on rectangles freely soaring over the whole surface of the work, connected to each other with colored bars.
At the first glance we realize that the whole is spatially inconsistent, though the local details are not. Particularly, it happens that focusing our attention on a couple of connected rectangles at once, there is no problem; but considering three or more connected rectangles at once, in the most cases it yields spatial inconsistencies, that prevent the observer from seeing which are the closest or the farthest planes (unless one admits the bars could make a hole in the rectangles and pass through them).
In Soaring Klee used several skewed perspective boxes at once, like the ones in his pedagogical sketch (Sketch 9). Here we are confronted with the desired effect of spatial ambiguity, for a face (the red one in see Sketch 10) might simultaneously belong to several boxes, each of them suggesting a different perspective; thus, that face has an ambiguous spatial collocation. We can easily see the practical effects of such a strategy in Sketch 11, which displays several of the possible simultaneous perspectives contained in a single detail ofSoaring. Interestingly, because of their shared surfaces, the perspective boxes used by Klee form a wide network of connected elements. Notice: not just a linear chain of elements, but a true net, which allows a multiplicity of possible circular courses ⁽²²⁾.
This kind of construction makes me think to something like the hypercube displayed in Sketch 12and this of course recalls the Duchamp’s pet; the fourth dimension. Thus, look at Poster for the Third Chess Championship (1925) (Fig. 35), where Rhonda Shearer ⁽²³⁾ showed several analogous spatial inconsistencies.
One of the most famous 3D impossible objects of Escher’s is Ascending and Descending (1960) (Fig. 36): on the roof of a building we see an endless staircase. Once again we have a circular course ever returning to its starting point. It is well-known, and Bruno Ernst ⁽²⁴⁾ explained it carefully, that the building, which has the impossible staircase on its roof, has a strange perspective structure, shown in Sketch 13. More than any verbal explanation, animations 3 and 4 help us understand the key reason for this. Animation 3 is a perspective sketch with one only vanishing point. It starts by showing three distinct parallel planes. They are perspectively represented with three closed polygonal lines (namely three rectangles) whose edges are of course not connected with each other. But by slightly rotating one of the edges of the optical pyramid around the vanishing point, we get a spiraling polygon, which joins in a single connected line the edges of several planes. The same holds if perspective has three vanishing points: look at Animation 4, which explains the perspective structure of Escher’s impossible building. Here is the surprise. Look at Sketch 14: the impossible room in Klee’sChess is based just on the construction presented in animation 3, thus it is deeply linked to the impossible building of Escher’s Ascending and descending. (Further explanation for this can be found in the article cited above ⁽²⁵⁾).

Thus, in these cases both Klee and Escher conceived perspective in terms of an iterative process, whose outcome is the spiraling, growing motion we saw in their buildings, as well as in a nautilus shell; thus they thought of the vanishing point as a sort of attractor of a dynamic system.
Can we see anything of this in Duchamp’s work? Not exactly the same, but in a way the answer is: yes, there are.
One of the major achievements of Duchamp on perspective is of course the lower half of the Glass (we shall consider the Completed Large Glass, 1965 (Fig. 37)). Thus, look at the Slide, a perfect perspective box which contains the rotatory element named the Water mill. Many other rotatory elements can also be found in the lower part of the Glass, such as the Chocolate grinder or the Oculist chards, but particularly the pathway described by the Sieves or the Toboggan have the feature of a spiral shell we are interested in.
The analogy between these elements and the perspective spirals we saw above is admittedly weak. But look now at Rotary demisphere (1925)(Fig. 38). Animation 5 can help visualize the surprising perspective depth effect one yields once a similar device is rotating. This is quite close to Klee’s and Escher’s idea of considering the perspective vanishing point as a sort of attractor of an iterative process which implies spiral motions.

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Figure 34
Paul Klee, Soaring,
Before the Ascension, 1930

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Sketch 12
Hypercube
Figure 35
Marcel Duchamp, Poster for the
Third French Chess Championship, 1925

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Figure 37
Marcel Duchamp,
Completed Large Glass, 1965

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Figure 39
M.C. Escher, Another
world II, 1947
Figure 40
Paul klee, Perspective
with inhabitant, 1921

What I said so far shows clearly that the theme of the impossible 3D objects and the one of an enlarged conception of the perspective are tightly linked to each other. Thus I want just to recall some of Escher’s experiments on perspective which Klee and Duchamp also did with similar outcomes.
In Escher’s Another world II (1947) (Fig. 39)the only vanishing point (roughly in the center of the print) must be considered at once on the horizon, or at the zenith or at the nadir, depending on which bird (and which wall) we are considering. The same holds for Klee’s Perspective with inhabitants (1921)(Fig. 40).
In Relativity (1953) (Fig. 41) Escher needed three distinct vanishing points to represent a world with three different gravitational fields, where people can walk on the walls as well as on the floor or the ceiling. In Klee’s Arab town (1922) (Fig. 42) we see a similar effect: the ground plane containing the floor of the higher part of the painting is the same plane containing the back walls in the lower part.
The fluid perspective in Escher’s House of stairs (1951) (Fig. 43) could be also explained by Klee’s idea of a stray viewpoint, and the final outcome could be compared with the one ofSoaring.

Finally, as far as Duchamp’s perspective experiments are concerned, Shearer showed a quantity of different perspective tricks devised by Duchamp, ranging from stray viewpoints, multiple vanishing points, fluid perspective, photographic overlapping, and so on ⁽²⁶⁾. Of course, they maintain an high degree of similarity with the ones of Escher and Klee.
Let’s now return to the impossible objects, and see them from another viewpoint.

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Figure 44
M.C. Escher, Waterfall, 1961

Sketch 15
The simple tribar
underling the building
of Waterfall

What do they represent? Especially in Escher’s case it is evident that they are variation on a leitmotiv: the one of perpetuum mobile. Look at Waterfall (1961) (Fig. 44) or even at Ascending and Descending, which explicitly show endless motions. But look even at the simple tribar (Sketch 15) which underlies the building of Waterfall. As we go with the eye along its bars, we perceive a sense of depth, we feel we are leaving the plane where the bars are actually drawn, to enter in the third dimension; and the pathway is really endless because, once the turn is completed, we can repeat it again and again; every time we find ourselves at the starting point.
Thus the impossible objects belong to a world which isn’t subjected to the law of thermodynamics: here entropy doesn’t increase, but reduces itself, to allow perpetual motions, such as inWaterfall.
A similar overturning is exactly what happens in complex systems with self-organization, which is one of the key concept in complexity sciences. Self-organization means that a system, provided certain conditions (one of them being the complexity of the system itself) spontaneously reduces its entropy, by introducing new levels of order among its elements. The slogan coined by Stuart Kauffman ⁽²⁷⁾, Order for free, effectively captures the essence of the stunning and seemingly paradoxical discover of a self-established order.
Now, if Klee, Duchamp and Escher guessed something about self organization as I believe and as I tried to highlight, then the impossible objects in a way could express with their paradoxical properties the surprising order-for-free nature of complex systems.
After all, something similar has been already said by Jean Clair about the Glass:
Michel Carruoges ⁽²⁸⁾ noticed that the intricate machinery of the Glass shows several analogies with other imaginary machines and engines, devised in same period by Jarry, Roussel, Kafka… Several years after, Jean Clair ⁽²⁹⁾ recalled Carrouges’ statement, and further deepened the parallelism, including in the list a quantity of pseudoscientific inventions which were popular in those years. One of the leitmotivs of those peculiar machines (Glass included) was that they produce more energy than they use, said Clair, thus they are variations on the theme of the perpetuum mobile. In fact they overturn the reality principle (the second law of thermodynamics) into the pleasure principle (the dream of an energy completely free and available).
In short, in my way of seeing things, we can group impossible objects and these machines together.

click to enlarge

Sketch 16
Necker Cube

But a further connection can also be found, particularly referred to the Necker Cube (Sketch 16), which underlies several impossible objects, such as the Impossible Bed of Apolinaire enameled. Indeed, as Rosen ⁽³⁰⁾ observed, the Necker Cube encompasses within itself, thus we can connect it to the same themes we discussed for the self-encompassing topological figures: hence feedback looping and self-reference.

5. A unifying reading perspective
In conclusion, I would like to delimit the context in which this paper should be read.
Often it happens that many people at once, unconsciously, independently and following different courses, elaborate the same new ideas and concepts, and help cement them into the Zeitgeist. In fact they contribute to the emergence of new sensibilities and new ways of observing, interpreting and understanding the world. This was the case for Klee, Duchamp and Escher: I believe they expressed (being in advance on their time) and contributed towards ideas that would grow and be affirmed. Nowadays, this new paradigm, this new way of seeing things is expressed by the so called complexity sciences.
Reiner Hedrich ⁽³¹⁾ stressed some salient traits in the development of complexity sciences. Here I’m interested in two of them. First, the gestation period of the new theories has been very long, about one hundred years. This long latency period, necessary to find a solid mathematical theory useful to describe dynamic systems behavior generously covers the lifetimes of Klee, Duchamp and Escher. Thus, in a way, they were immersed in a stream of ideas and concepts which were still under construction and organizing in theories. I’m talking about a nascient stream in the cultural subconscious, not one that was flowing on the surface of the well established scientific culture of those years; thus I don’t think that our artists could have been directly influenced by those scientific ideas; generally speaking, even admitting the possibility of such an exchange of views, in my opinion it is easier to think it happened in the opposite direction. With a few exceptions: for some aspects (I think of concepts such as instabilities and chaos) scholars acknowledge Duchamp has been influenced by the reading of Poincaré; but they are just only some aspects of his complex thought; the same holds for Klee’s possible understanding of (evolutionary) biology and natural sciences, or for the mathematical readings of Escher, which moreover in some cases he admitted to be unable to understand. The second feature in the development of complexity sciences stressed by Hedrich is that the grounding ideas of the new paradigm, the kernel of complexity, didn’t deal with a specific disciplinary field: instead, they are a sort of conceptual foundation, a shared background for any empirical discipline dealing with complex systems. This fact makes it conceivable that there was, to some extent, a widespread and unconscious emergence of such ideas, even though in purely qualitative and intuitive terms. In other words, I’m talking about quite general concepts, and not about specific subjects or details of a well-defined disciplinary field: it makes possible that the same ideas could have been grasped by someone in more intuitive forms, which is what I’m suggesting for Klee, Duchamp and Escher.
The concepts I’m talking about are closely related to each other, they form a tangle of interconnected ideas, that bringing one of them to the light, mostly implies that many (or even all of) the others could also somehow come out. Really, it is impossible to examine thoroughly one of them without revealing a cascade connection with each other. Indeed, the idea of cyclic dynamism of a system entails feedback, recursion and self-reference; in turn self-organization, fractals and chaos are entailed, and again emergence, dynamic and unsequilibria, (co)evolution; further, the visual expression of such a complexity needs new and different ways to conceive the space, where new and more complex relations may occur between its elements; thus, the represented space has strange topological properties.
It is well-known that complexity introduces several relevant changes in the way we used to know the world. This is not the place to discuss them: I’ll limit myself to summarizing some of them.
First: mainly due to both deterministic chaos and sensitive dependence on the initial conditions which characterize the dynamical systems, we have to accept two weaker versions of both the causality principle and determinism.

click to enlarge

Sketch 17
Diagram explaining
concept of complexity

Second: because of the concept of emergence, the reductionist approach is not more suito study complex systems. This is sometime expressed by opposing reductionism and holism. I like the way Chris Langton expresses the concept by means of Sketch 17 which I took from Roger Lewin ⁽³²⁾.
To effectively explain the radical change in the way of seeing the world implied by complexity, a set of dichotomies is often used, which confronts old paradigms with new:
simplicity-complexity, reductionism-holism, determinism-uncertainty, quantity-quality, necessity-contingence, predictability-unpredictability, reversibility-irreversibility, repeatability-unrepeatability, causality-randomness, law-chaos… Interestingly, if we attempt to describe Klee, Duchamp and Escher by choosing either of the poles in such dichotomies, we always have to choose the second one.
As far as Duchamp is concerned, the discussion about the crisis of determinism and reductionism has been already widely discussed, particularly in relation to the ideas of Poincaré’s.
Coming to Klee, I want just recall his essay titled Exact experiences in the field of art ⁽³³⁾, where he expressed a concept which is one of the leitmotiv of his activity as both artist and teacher: the freedom and the intuition of the artist act in the space between law and unpredictability, but always remembering the necessity of both:
Oh, don’t let the eternal spark become completely smothered by law’s measure! Take steps in time! But don’t go away from this world completely. ⁽³⁴⁾
Escher expressed a similar ambivalence with his prints, in the paradoxical coexistence of extreme formal rigor and uncertainty, mathematical exactness and instability, rigorous application of exact principles and unpredictability in the outcomes.
On the other hand, only a few words are needed to recall that Klee, Duchamp and Escher built their work as organisms, composed by a number of interacting elements, where the whole is always greater than the sum of its parts. In their works complex processes are mostly represented, whose outcomes can be emergent, unexpected properties. We can dissect them, but in so doing we always lose something. This is the true essence of their holistic art.

Notes

1. Roberto Giunti, “R. rO. S. E. Sel. A. Vy”, Tout-Fait : The Marcel Duchamp Studies Online Journal 2.4 (January 2002) Articles <https://www.toutfait.com/duchamp.jsp?postid=1240&keyword=>.

2. < http://www.mat.uniroma1.it/venezia2005/>.

3. Roberto Giunti, “Percorsi della complessità in arte: Klee, Duchamp ed Escher”, in: M. Emmer (ed.)Matematica e Cultura 2003 (Milano, Springer Verlag – Italia, in print)

4. Douglas R. Hofstadter, Godel, Escher, Bach: an Eternal Golden Braid (New York, Basic Book, 1979)

5. Teuber M. R. “Perceptual theory and Ambiguity in the Work of M. C. Escher against the background of 20^th Century Art”, , in H. S. M. Coxeter, M. Emmer, M. L. Teuber, R. Penrose (ed.) M. C. Escher: Art and Science, (North-Holland, Amsterdam, 1986)

6. Giunti, R. “Una linea ondulata lievemente vibrante. I ritmi della natura nell’opera di Paul Klee”, Materiali di Estetica No. 2, (2000)

7. Giunti R. [6]

8. Whitehead E. P.
“Symmetry in Protein Structure and Functions”, in H. S. M. Coxeter, M. Emmer, M. L. Teuber, R. Penrose (ed.) M. C. Escher: Art and Science (North-Holland, Amsterdam, 1986).

9. Calvin M. “Chemical Evolution”, Oregon State System of Higher Education, Eugene, Oregon, 1961

10. R. Giunti [1], p. 13, <http://www.toutfait.com/duchamp.jsp?postid=1240&keyword=>.

11. Shearer, R.R.
“Marcel Duchamp’s Impossible bed and Other Not Readymade Objects: A possible route of Influence from Art to Science (Part I and II). “ Art & Academe, 10:1 & 2. (Fall 1997 and Fall 1998) <http://www.marcelduchamp.org/ImpossibleBed/PartI/> and <http://www.marcelduchamp.org/ImpossibleBed/PartII/>

12. Escher M. C. The Graphic work (Bendikt Taschen Verlag, Koeln, 1992)

13. Giunti R. “Paul Klee on Computer. Biomathematical models help us understand his work” in M. Emmer (Ed.) The Visual Mind 2, (The MIT Press, Cambridge MASS, in print)

14. Tony Phillips “The topology of Roman Mozaic Mazes” in M. Emmer (Ed.) The Visual Mind (The MIT Press, Cambridge MASS, 1993).

15. D. J. Wright, Dynamical Systems and Fractals Lecture Notes, <http://www.math.okstate.edu/mathdept/dynamics/lecnotes/lecnotes.html>.

16. R. Giunti [1], p. 11, <http://www.toutfait.com/duchamp.jsp?postid=1240&keyword=>.

17. J. Clair, Duchamp at the turn of the Centuries, ToutFait Journal, Issue 3. <http://www.toutfait.com/duchamp.jsp?postid=877&keyword=>.

18. Giunti R. [1], p. 13,<>

19. Shearer R. R. [11]

20. Penrose L.S., Penrose R. “Impossible Objects: a Special Type of Visual Illusion”, Brit. Journal of Psycology, vol. 49, 1958

21. Giunti R. “Analysing Chess. Some deepening on the concept of Chaos by Klee”

<http://www.mi.sanu.ac.yu/vismath/giunti/00Chess.htm> or <http://members.tripod.com/vismath/pap.htm>

22. Indeed, Klee gradually passed from a first conception, where things are mechanically enchained to each other in a rigid, linear successions, with a well defined cause-effect relation (look at the drawing Parade on the track, 1923) Fig. 45 to a final conception where each thing is connected with each other in a complex network, and causes and effects are not clearly distinguished: look at the pedagogical sketch (sketch 18). Its caption is says: «Building of an higher organism: the assembling of parts viewing at the overall function».

The framework of Soaring is just the first important achievement of such a creative course, which will lead in the late works to the theme of morphogenesis.

23. Shearer R.R. “Examining Evidence: Did Duchamp simply use a photograph of “tossed cubes” to create his 1925 Chess Poster?” Tout-Fait Journal, issue 4, <http://www.toutfait.com/duchamp.jsp?postid=1375&keyword=>.

24. B. Ernst, Der Zauberspiegel des M. C. Escher (Taco, Berlin, 1986)

25. Giunti R. [21]

26. Shearer R. R. “Why the hatrack is and/or is not Readymade: with interactive software, animations and videos, for readers to explore”, Tout-Fait Journal, Issue 3, <http://www.toutfait.com/duchamp.jsp?postid=1100&keyword=>

27. Kauffman S. At Home in the Universe. The Search for the Law of Self- Organization and Complexity(Oxford University Press, 1995)

28. Carrouges M. Les Machines célibataires (Arcanes, Paris, 1954)

29. Clair J. Marcel Duchamp ou le grand fictif (Galilée, Paris, 1975)

30. Rosen, S. M. “Wholeness as the Body of Paradox”. 1997 <http://focusing.org/Rosen.html>.

31. Hedrich R. “The Sciences of Complexity: A Kuhnian Revolution in Sciences?” Epistemologia XII.1 (1999) <http://www.tilgher.it/epiarthedrich.html>

32. Lewin R. Complexity. Life at the edge of chaos (The University of Chicago Press, Chicago, 1999)

33. The essay is contained in: Klee P. Das Bildnerische Denken (Basel: Benno Schwabe & Co., 1956)

34. P. Klee, Tagebücher von Paul Klee 1898-1918 (Köln:Verlag M. Dumont Scauberg, 1957), note 636, 1905

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