PRINT March 1971

Unveiling the Consort: Part I

The question of shop windows..
To undergo the interrogation of shop windows..
The exigency of the shop window..
The shop window proof of the existence of the outside world..

When one undergoes the examination of the shop window, one also pronounces one’s own sentence. In fact, one’s choice is “round trip.” From the demands of the shop windows, from the inevitable response to shop windows my choice is determined. No obstinacy, ad absurdum, of hiding the coition through a glass pane with one or many objects of the shop window. The penalty consists in cutting the pane and in feeling regret as soon as possession is consummated. Q.E.D.1
—Neuilly, 1913

MARCEL DUCHAMP WROTE THE ABOVE when he was planning his first Ready-mades. Ending his observations with the abbreviation for quod erat demonstrandum, a term applied in mathematical and logical assertions meaning which was to be shown or demonstrated, he indicates that the Ready-mades are to be a demonstration of various esthetic principles. A brief introductory interpretation of this obscure series of statements should prove helpful before we return to the sources of Duchamp’s metaphors.

Shop windows are the veils between mythic cognition and reality. Or more literally, as in the case of painting, shop windows embody the notion of the picture plane and, as Michel Foucault has pointed out in his analysis of Velasquez’s Las Meninas2, what transpires both behind and in front of it. Here the artist’s understanding of the external situation, vis-à-vis history and culture, critically affects the construction of pictorial space. Moreover the “goods” within the shop window validate “the existence of the outside world.” The artist examines the shop window, or more accurately what lies behind the window, by tentatively making art and searching for a mature and viable style. By doing so, he “pronounces [his] own sentence.” The word sentence has a double meaning here: Duchamp is implying that all works of art adhere to specific semantic and syntactical relations which resemble any one of all possible sentence forms. Hence the artist defines his artistic destiny (that is, sentences himself) by the linguistic choices he makes. An artist’s only possible reprieve is to review the shop window and in so doing shift to another sentence structure. One’s choice is “round trip” for two reasons: first because any choice, if carried out rigorously and to its farthest limits, will result in the same destination (all sign combinations ultimately become symbols that lose their semiotic capacity); and second because all sentence types form a circular chain of relationships, leading back to the same structure when pursued latitudinally. Ostensibly every artist’s entry into art is controlled by the exigences of past historical change in painting and sculpture. To a large extent, available choices are predetermined. But Duchamp insists that he is not going to allow any personal propensity or psychological quirk to define his choice of objects in the window; he speaks of not “hiding the coition through a glass pane with one or many objects in the shop window.” In this case, as we shall later see, coition is a synonym for the act of sentence construction. That Eros is the basis of all art and human culture is a fact Duchamp has never tried to hide. So Duchamp’s erotic relation to art is that of a man who understands that all forms of coition are permissible under recognized circumstances, and he insists that he is going to experiment with all forms. Only then does he admit that there are certain psychological drawbacks to practicing art logically and not intuitively like every other artist: “The penalty consists in cutting the pane and in feeling regret as soon as possession is consummated.” Apparently art is a virgin construct which is about to be deflowered. Being burdened with the secret of knowing the logic mechanisms of art, Duchamp chooses to express his conquest in a series of esoteric works that proclaim the knowledge only to those who share the same degree of information.

Initially we must acknowledge the ancient taboos attached to magic, those restrictions of which the artist was acutely aware. Duchamp gained his mastery over art through inspired readings into literature, philology, cultural anthropology, linguistics, and especially through deciphering some of the sources of Western magic including ancient Egyptian religion and science, the diagrams of the Cabala and their implications in the Tarot cards, the real purposes of Astrology and Alchemy, and the rituals and goals of Freemasonry. All of these occult disciplines more or less represent the same body of esoteric wisdom. Each source maintains very heavy strictures against imparting its knowledge to outsiders or to those who might use it for malevolent purposes. So, as the great teacher Eliphas Levi insisted, “Those who know do not say, those who say do not know.”

Once aware, by accident and design, of this knowledge, Duchamp had to decide whether or not to publicly divulge it. If versed in drawing up horoscopes, one soon realizes that Duchamp used his information according to the strict dictates of astrological conditions for his birth sign, July 28, 1887, and its conjunctions. Without laboriously presenting an in-depth demonstration of this, several observations may be easily made. According to astrology Duchamp’s weaknesses lay in self-centeredness and a tendency to boast of personal achievements. The antidote is modesty, equanimity, and the pursuit of strategies allowing the artist to hide his knowledge while revealing it. Duchamp’s strength lay in his ability as a true alchemist, a man who knew the secret of transforming base materials into gold and its cultural equivalents. Therefore it is not surprising that lead is the metal proscribed as the vehicle for Duchamp’s successes; the iconography of The Large Glass is tediously affixed to sheet lead mounted on glass panes. Worldly success is assured for the person following these and other dictates—providing his horoscope coincides with Duchamp’s.

Presently, though, there is reason enough for breaking the secrecy surrounding Duchamp’s work. Not with minimal perversity Duchamp chose the occult sciences as the basis for his iconography, even though after 1912 his art was constructed purely by the application of logic and intellect. Ironically the key to this knowledge is expressed in symbols overwhelmingly rejected by science after the 17th century. Still it is perfectly clear from Pierre Cabanne’s Entretiens avec Marcel Duchamp3 that he maintained a steadfastly rationalist approach towards all questions of human culture.

The reader is free to draw his or her conclusions. Yet deductive evidence overwhelmingly points to a single possibility: the so-called occult sciences are based on a conception of social relationships just beginning to be studied by contemporary science. Duchamp was well aware that occult wisdom has little to do with mystical illumination. Rather it is rooted in the language-based cognitive patterns that define human social systems. His supplementary writings are occasionally interlaced with sophisticated allusions to the mythic isomorphisms found in primitive societies. Consequently we are no longer dealing with occult secrets, but with insights that have their origins in linguistical analysis.

Most importantly, the purpose of Duchamp’s later art, and particularly The Large Glass, is the creation of a mythology that looks into the future, outlining a certain trajectory for the fate of modern art. In his first collection of notes, the Box of 1914, he wrote:

The Bridge of Volumes
On top and under the volumes
In order to see pass the small passenger steamer4

In esoteric symbolism yellow is the color of illumination and intellectual penetration. Duchamp creates a panoply of forms that define the social and psychological mechanisms responsible for modern art. Installed within The Large Glass these volumes become an intellectual overpass whereby the progression of modernist styles in art is made visible. The word mouche in the term la bateau mouche also refers to “beauty-patch” or any artifice that would tend to enhance the environment, such as a painting. I contend that the trajectory of The Large Glass is historically complete and has been since about 1968. So that in terms of thwarting any possible avant-garde art of the future, there is no danger.

We should proceed by outlining some of the most basic tenets of transcendental magic, or at least those immediately applicable to Duchamp’s iconography. In part, the origins of modern chemistry were an attempt to rectify mistaken ideas held by alchemists concerning the properties of physical substances and processes. Some of these false notions are simply overly literal interpretations of the correspondences between metaphysical symbols and their material equivalents. Most essentially alchemy is a philosophy for the perfection of the human soul, a series of prescriptive teachings insuring fundamental understanding of human and natural law. The central theory of alchemy revolves around the configuration of the four primal elements: AIR, FIRE, EARTH, and WATER. All entities are thought to be combinations of these elements in varying proportions. These transmutations are based on an “eternal principle” and not on any physical admixture of the four elements. A set of four contingent properties is positioned between the elements: Wet, Hot, Dry, and Cold. Their function is to influence elements adjacent to one another. For instance Heat may change WATER into vapor, thus making it a form of AIR. Or the Wetness of WATER has the power of dissolving EARTH. Also Heat may drive the moisture out of AIR, making it ignite as FIRE.

In the center of this diagram there exists a fifth element referred to variously as ETHER or the UNIVERSAL LIGHT. So that in looking at this configuration from the side it would appear to be a four-sided pyramid. The back of the Great Seal of the United States contains just such a pyramid with an illuminated eye at its apex. This eye represents the discovery that Duchamp made concerning the universal limitations of art. Notice that one only sees the front of the pyramid and a portion of the right side. In all occult science, right is the favored side (this is true also of the iconography of painting and sculpture) while the left is problematic and illusionary, extending into the future and the unknown. Life is represented by heat and dampness—prerequisites of mortal existence—while death is defined by dryness and cold. Here we must return to the preface of The Large Glass where Duchamp inscribes:

1. the waterfall
2. the illuminating gas5

Two things are Given: that AIR ignites through FIRE providing the illuminating gas and that WATER gradually erodes EARTH by virtue of the waterfall. The illuminating gas and waterfall represent a kind of dichotomy, a balance that must be maintained in human functioning. Please note Duchamp’s last major work in the Philadelphia Museum, entitled Etant Donnés: 1. la chute d’eau 2. le gaz d’éclairage (1946–1966). Peering through the door, one’s eyes are fixed upon a reclining female nude holding a gas lamp in her right hand, in fact her only visible limb. To the left in a wooded background is a waterfall. So in a sense the illuminating gas represents what is man-made and CULTURAL while the waterfall represents the NATURAL. Moreover we might quote Eliphas Levi on the obscurity of these symbols: “One does not invent a dogma, one veils a truth, and a shade for weak eyes is produced . . . Analogy is the key to all secrets of Nature and the sole fundamental reason of all revelations.”6

For the alchemist the triad above represents the unification of indestructible matter. We may look upon it as joining the front and rear faces of the Great Pyramid. Hence Sulphur, the fixed principle, unites EARTH and FIRE; Mercury, the volatile principle, unites WATER and AIR; while Salt is the quintessential state, comparable to ETHER. Salt is the medium for conjoining sulphur and mercury, a union of body and soul through the spirit. Being the male principle, sulphur bestows while mercury receives. In esoteric alchemy Sol (sun) and Luna (moon) represent King and Queen, gold and silver respectively. Lead may signify the medium through which base metals are transformed into gold and silver. And here note that Marcel Duchamp assumed the androgynous pose of Rrose Sélavy in the early 1920s and later adopted the title Marchand du sel for his writings.7 This last inversion of syllables in the artist’s name lends credence to the possibility that he possessed the Philosopher’s Salt and traded it freely to those artists with the wisdom to accept it. In the operation of the Great Work, the function of Salt is to provide the proper circumstances for conjunction between male and female principles. John Read in his Prelude to Chemistry quotes from an 18th-century alchemy text on the significance of these numbers in the Philosopher’s Stone: “Out of five—that is, the quintessence of its own substance . . . The four elements, fire, air, water, and earth, are shown as proceeding directly from God; the three principles, sulphur, salt, and mercury, from Nature; the two ‘seeds,’ the male and female—Sol and Luna, or sulphur and mercury—from the metals; and the one Tincture, from art.”8 The intention of this essay is to show that these five arithmetical symbols represent the semiotic principles of language fused to myth.

In Duchamp’s introduction to the notes of The Green Box he states that “The machine with 5 hearts, the pure child of nickel and platinum must dominate the Jura-Paris road.”9 The “machine with 5 hearts” is of course the Great Pyramid, the “pure child of nickel and platinum” is an old and cryptic allusion to the Philosopher’s Stone, namely that set of elemental relationships holding the key to art. The “Jura-Paris road” defines the destination of art from its 19th-century avant-garde origins in Paris to its destiny on the Moon, expressed by the expansion and contraction (“oscillating density”) of mercury and the eternal return to the female principle. This return is also emphasized in the cabalistic JOD (male)—HE (female)—VAU (joining)—HE (FEMALE). Such a shift is always the result of over culturalization and signifies the abandonment of harmful cultural illusions. Analogously the art myth ends when non-objective paintings appear to be simply paint-covered canvases tacked to wooden stretchers.

What does such a complicated array of numbers and symbols mean to the structural anthropologist? Much of it comes under what has been called the resolution of the binary and unary principles. Simply stated, we strive to ignore the limitations of categories, assuming that the sum of all categories makes up the whole environment. Yet even the most comprehensive categories in natural languages omit and distort many entities. A category implies that things are both p and not-p; items are either in a category or outside of it. Things which are not named become taboo. Not referring to them is just one means of dealing with their ambiguous status as nonobjects. In Edmund Leach’s words, “If . . . we are only able to perceive the environment as composed of separate things by suppressing our recognition of the nonthings which fill the interstices, then of course what is suppressed becomes especially interesting.”10 It seems evident that taboos always involve entities falling into more than one category, and these categories are invariably irreconcilable. For instance, works of art are simply physical constructions; but we respond to them as if they embodied feelings and ideas transcending the limits of materiality.

Leach provides us with examples of two taboo areas. The first are substances which on occasion become detached from the human body—in particular, spittle, pus, hair clippings, semen, menstrual blood, urine, feces, and mother’s milk. These substances defy the boundaries of self; they are both personal and nonpersonal. Their anomalous character makes them excellent ingredients for magical rites. Secondly, men demand the existence of superhuman and immortal gods; but knowing that these creations have no material form, they fabricate an intermediate category of half humans/half gods. These include gods on earth, virgin mothers, prophets receiving the word of god, animal-like men and other doubtful creatures. Such beings have a foot in both worlds. Life is full of contrasting dualities; truth and falsehood, life and death, day and night. So it is the function of religion to mediate these opposites by constructing a world where the two are separable and one is seen to triumph over the other. Similarly, art employs social conventions that make spirit triumph over materiality.

While this is getting ahead of the explanation, I should point out that Duchamp was perfectly aware of art’s mediating function as a kind of ritual for materials incorporated into linguistic relationships. One of his notes in The Box of 1914 reads:

In this case Duchamp is making a number of assertions, but for our purposes I will just point out several. He is stating, in terms of sign functions, the formal relationships found in all works of art. Using the Saussurian convention he divides words into a fractional term: signifier or sound-image over signified or the concept of the word, thus arrhe/art. He also does the same thing for the word merde, dividing its common French pronunciation from its meaning. Yet he is saying much more than “art equals shit.” Duchamp is stating that the relationships between the parts of an idea (art) are equal to the relationships between the parts of a material substance (shit). He is also stating that both art and shit are anomalous and taboo categories, categories where we construct certain linguistical conventions to mediate overlapping associations. But most importantly he is demonstrating that art is the result of structuring analogical relationships between ideas and phenomena. And as Claude Lévi-Strauss has specified in his studies of myths, Duchamp also observes that signifiers are of feminine origin. Thus what we see or hear of an undifferentiated nature—unattached to meaning—relates to the source of creation: the female principle and nature.

All mythic structures, including art, are for appearance’s sake presented as a unity, yet these operate according to binary principles of opposition and contrast. For the time being I will represent this by setting down some of the values that Edmund Leach uses in his essay, Genesis As Myth.12 The reader, though, should keep in mind that we perceive the story of Genesis (written and spoken) as a whole; but conceptually and in terms of structural principles we analyze it through binary associations.

By segregating the Biblical text of Genesis, Edmund Leach attempts to prove—as Lévi-Strauss has done with a much broader range of ethnographic materials—that the narrative or story line of such myths mediates irresolvable problems. Whether it is in kinship, ruling rights, foods, or ontologies of culture, these problems seem to be asking the same basic question: namely _how do

we make one out of two?_ Thus myths become metamessages or information which does not at all seem to be related to the story conveyed. In the case of Leach’s Genesis categories, things that are confused, anomalous and sacred make up what we would call the content of “art”—that is they hide their relations to binary and unary categories.

Within the past ten years “cognitive anthropology” has been formulated for the purpose of defining culture in terms of linguistically connected conventions. Taxonomies, or conceptual categories, relate groups of things both hierarchically and by contrast. In effect all languages are based on taxonomies or contrast sets which in turn help to define other taxonomies.13 What is important in a particular environment not only defines a taxonomy for a given language, it also influences all connected taxonomies and thus the general consistency of semantic relationships. In essence this means that words in a language have value-functions and not truth-functions. As Jerrold Katz states in The Philosophy of Language14, the reason logical empiricists failed in their analysis of natural language is that they mistook the rules of formal logic derived from metamathematics for the syntax of grammatical forms in ordinary language. However the difference is fundamental and critical. Without embarking upon a lengthy explanation, all forms of algebra and mathematical logic ark semiotics with a single level of articulation. This means that a symbol in algebra can be assigned a single fixed meaning for all contexts. On the other hand, the “signs” of natural language, which are composed of words and/ or morphemes, are connected by a double system of oppositions (syntagmatic and paradigmatic on the planes of content and expression) so that they possess a double articulation. Stated another way, the taxinomic principle of language allows for shifts in the meaning in words according to contextual changes which are accommodated phonetically and through the subtle logic of ordinary grammar. Double articulated semiotic systems, while potentially more flexible and efficient than singly articulated systems, are also more imprecise. Consequently we can make art from language-based systems but not from communication or logic systems singly articulated.

Doubtlessly no other principle has caused more confusion and misapplication by art critics, estheticians, and historians. The reason is fairly evident. All forms of art analysis (iconology, historical determinism, psychology, and formalism) deal with symbol interpretation or simple mappings of logic principles applied to works of art and their circumstances. Any real analysis of art, however, demands the use of linguistic techniques that take into consideration the peculiar idiosyncrasies of doubly articulated systems. The implications this raises for Western epistemology have been brilliantly developed by Michel Foucault in his book Les mots et les choses.15 The substance of his thesis is that we have traditionally structured our social systems (economics, art, speech, natural history, etc.) according to linguistic principles, while we have sought Cartesian precision in the singly articulated methods of analysis found in the hard sciences.

It is patent that these three notions—mathesis, taxonomia, genesis—designate not so much separate domains as a solid grid of kinships that defines the general configuration of knowledge in the Classical age. Taxmomia is not in opposition to mathesis: it resides within it and is distinguished from it; for it too is a science of order—a qualitative mathesis. But understood in the strict sense mathesis is a science of equalities, and therefore of attributions and judgements; it is the science of truth. Taxonomia, on the other hand, treats of identities and differences; it is the science of articulations and classifications; it is the knowledge of beings. In the same way, genesis is contained within taxonomia, or at least finds in it its primary possibility. But taxonomia establishes the table of visible differences; genesis presupposes a progressive series; the first treats of signs in their spatial simultaneity, as a syntax; the second divides them up into an analogon of time, as a chronology.16

Part of the deception is due to the fact that art analyses are based on taxonomic associations which are largely homogenous to the works they describe.

It is hoped that the reader will forgive this long digression into linguistic principles. But it is absolutely necessary for an understanding of Marcel Duchamp’s contribution to art. Duchamp’s discovery was simple yet fundamental: he gradually perceived in the spring and summer of 1912 that Saussurian semiotics (those methods of analyzing language through sign functions) are consistent with the secrets of transcendental magic and alchemy. In my recent book, The Structure of Art (1970)17, I have dealt with the meaning of the semiotic triangle in terms of Lévi-Strauss’s diagram of food preparation; variant triangles also appear in his analysis of kinship structures and other mediation functions.18 In alchemical terms the basic triangle maybe conceived as the union of Sulphur (male-body), Mercury (female-soul), and Salt (androgyny-spirit). Semiotically, this reads as Referent (or entity signified), Signifier, and Signified—the three values needed to define the existence of a sign.

The semiotic triangle that Lévi-Strauss alludes to in food preparation, and sometimes in sexual relations, is of a different order. This is connected to ways of doing things, for instance: 1) Smoked food 2) Boiled food and 3) Roasted food—or 1) Monogamy 2) Promiscuity and 3) Celibacy. In my book the triangle unites 1) Mimetic art 2) Non-objective art and 3) the Ready-made. Surveying my own semiological analyses of various art works and Lévi-Strauss’s variety of human habits, it seemed that this construction did not adequately represent the complete semiotic. But by adapting the Great Pyramid of Alchemy, and employing the qualities signified by the Four Elements, one arrives at a more complete semiotic configuration.

Translation of the Pyramid for food preparation and sexual relations produces these values: 1) Smoked food 2) Boiled food 3) Roasted food 4) Foods mixed and baked and 5) Naturally poisonous foods prepared for edibility; 1) Monogamy 2) Promiscuity 3) Celibacy 4) Polygamy and 5) Incest. For art the following types may be defined: 1) Mimetic art 2) Non-objective art 3) the Ready-made 4) Ambiguous art and 5) Contradictory or illogical art. Superficially these categories appear to have little to do with one another. It must be reiterated that each alchemical function is duplicated by several symbols, all having overlapping association. Quite normally, meanings are obscured in esoteric writings by mixing symbols in different sets.

The four essential materials possess characteristics that seem obvious enough on the surface, but these are more exclusive when viewed in relation to each other: for instance EARTH joins falsehood, evil, materiality and impenetrability; WATER relates to creativity, emotionalism, intuition, death and eventual rest; AIR signifies what is good, spiritual, essential and intellectually vital; while FIRE defines the formative principle, impulsiveness, life, motion and instability.

In The Structure of Art, I attempt to use the Glossamatics techniques of the Danish linguist Louis Hjelmslev. Not only do these serve as a test in establishing compatible planes of content and planes of expression for works of art, they suggest that works of art conform to the same deep-structure conceptualizations responsible for the construction of sentence forms in ordinary language. Also there is enough evidence in Duchamp’s writings to support the same conclusion. As a result I find the following sentence structures for the Great Pyramid: 1) Simple sentences 2) “Elliptical sentences” or sentences with an implied subject that must be understood contextually 3) “Phatic” expressions or phrases so idiomatic that they lose all meaning if a single word is altered 4) Sentences which are complex or compound or both, sentences which are compound in deep structure, and sentences possessing surface structure ambiguities 5) Ungrammatical sentences, “nonsense” sentences, and false analytical statements. These sentence categories cover all conceptual possibilities and correspond to the properties of 1) AIR 2) WATER 3) ETHER 4) FIRE and 5) EARTH. Semiotically these sentences may also be segregated according to their sign properties. Simple sentences have a single signifier and signified; elliptical sentences possess a signifier but no signified; phatic expressions use a signified but no signifier; complex, compound, and ambiguous sentences have more than one signifier and/or more than one signified; sentences in semantic conflict are made to “agree” by phonological manipulation (as in the case of poetry) but in any case show surface disagreement between signifier and signified.

Fundamentally this defines the discovery made by Marcel Duchamp during the winter of 1911–1912 and through the summer of 1912. His painting during this period mirrors the artist’s emotional response to an enormous intellectual awakening (i.e. “. . . of feeling regret as soon as possession is consummated. Q.E.D.”). For instance there is the painting Young Man and Girl in Spring completed in Neuilly during the spring of 1911. Arturo Schwarz’s analysis of the iconography is quite revealing. The pair represent a brother-sister relationship with both figures stretching their arms towards an overhead tree. If we look back to Leach’s diagram of the Genesis myth we find that in their original state Adam and Eve are siblings who, because Eve partakes of the Tree of Knowledge, suffer expulsion and go on to live in the real world as man and wife, i.e., they undergo the transition from myth to reality. Duchamp’s peculiar inscription on the back of the painting to his sister, moreover, supports this interpretation. Just as important is the centrally positioned figure of Mercury or Hermes imprisoned in a glass, alchemical vessel, signifying Mercury’s potential power to unite opposites and spread knowledge. In this case the Sun (King) and the Moon (Queen) are about to be joined as a function of the Great Work. (See also the author’s notes for Paradise (1910) in Arturo Schwarz’s The Complete Work of Marcel Duchamp).

A caption on the back of a painting finished toward the end of the same year—“Marcel Duchamp nu (equisse) leune homme triste dans un train”—explains clearly enough that the artist himself is the “sad young man.” In alchemical terms sadness or melancholia represent the transition (premonition) from worldly attitudes to enlightenment. The train signifies the mechanical means towards such understanding.

The ideal world of happiness as typified by Adam and Eve in Paradise was transformed in 1912 to the theme of the King and Queen. In May of 1912 Duchamp painted The King and Queen Surrounded by Swift Nudes. The “Swift Nudes” are perhaps the “Sons of Hermes,” those forces let loose to inform us of the secrets of the hermetic arts. Here it becomes increasingly apparent that the paintings of this period are a didactic attempt to biographically illustrate the artist’s intellectual progress in unraveling the alchemical secrets of art. Eventually Mercury symbolizes for Duchamp the combined forces of AIR and WATER in the transition from mimetic to progressively denuded non-objective art.

One might well make a case that the pivot-point in Duchamp’s career occurred in the summer of 1912 during his visit to Munich. According to Marcel Jean, “he traveled to Germany third-class by local trains, so that the journey should last longer.”18 This visit, or the artist’s reluctance, has never been adequately explained, particularly since the stay in Munich produced his technically most accomplished paintings plus the first notes and drawings for The Bride Stripped Bare by Her Bachelors, Even. My hypothesis for this visit is unsubstantiated, but a theory nevertheless that dovetails with the artist’s earlier and later iconography. Duchamp in his reading had come close to the alchemical origins of art, close enough perhaps to know that very few books on the subject reveal the real secrets of esoteric science. Possibly Duchamp found that a certain necessary text or manuscript on alchemy existed in Munich. This would account for any possible remorse or trepidation. Going there he would believe in art, returning he would know art. This also explains the studies for the Virgin in July 1912; the painting The Passage from the Virgin to the Bride in July and August; and finally, The Bride in August. Since art is mythic, and therefore female, Duchamp’s discovery would lead to a sudden change in her sexual status, one where his conquest of the Virgin would not be comprehended for nearly sixty years.

Duchamp’s use of the iconography of “the machine with 5 hearts” is rare. In 1918 as a study for The Large Glass he produced To Be Looked at (from the Other Side of the Glass) with One Eye, Close to, for Almost an Hour. Here a central lens is balanced on the point of an obelisk and aligned under the apex of a distorted pyramid. In reality one of the “Oculist Witnesses” located underneath is a Masonic symbol for omniscience. The distorted obelisk is a “reading” for a projected life, while the pyramid is, of course, the symbol for all the possibilities in mediating life’s activities. The corner of the pyramid between AIR and FIRE touches the right side of the Glass, thus informing us that this historically represents the beginnings of art. The pyramid extends off the left side of the Glass, signifying that in 1918 art still had a future before the stripping of the Bride was complete. Significantly, the corner missing unites EARTH and WATER, or that art defining the last formal transitions of non-objective art. In the notes for the Boxing Match in The Large Glass, Duchamp indirectly specified that the last stages of non-objective art will appear “realistic” to those viewing it. One sure clue that the subject of this glass is the de-evolution of non-objective art is in the work’s title. Grammatically the title is an indirect command using the infinitive construction. In esoteric literature the infinitive represents the infinite, while a very rough interpretation of the deep-structure of this title would yield: [You] look at [it]. All in all this title has at least four kernel sentences in its deep-structure. The Glass itself contains four types of optical ambiguity, thus mixing FIRE and AIR, or ambiguous art with non-objective art. Duchamp intimates that historically such art ends when it is phonetically (formally) exhausted, thus completing the corner edge of the Great Pyramid.

A work such as To be looked at . . . illuminates the underlying meaning of Barnett Newman’s Broken Obelisk of 1967. The obelisk, and its inversion over the pyramid, recognizes the fulfillment of Duchamp’s earlier prophecy. In Masonic symbology the two forms represent the conjoining of human intellect with the secrets of the Great Pyramid, in this case the completion of modern art through its comprehension.

Pyramids again appear in Handmade Stereopticon Slides (1918–19). But now they are reflected with double opposing forms both below and above. This octahedron with its elongated superstructure has a different meaning. It represents the values of the Great Pyramid, culminating in domination by the Ready-made, but inverted to show their completion. The upper point of the polygon represents the same commanding intelligence as its lower counterpart. Moreover it signifies a higher degree of wisdom and understanding: recognition that involvement in art is no longer necessary. The vanishing points of the octahedron extend to the horizon. Marcel Jean quotes Duchamp as labeling this superimposed exercise in perspective a “collage in space.”19 As a rule collages function by juxtaposing materials with different sign values although they have the same surface meaning. In this case it is the surface meaning which is obscure and the underlying meaning which is the same. In both mythic and esoteric terms the sea represents the caldron of life, good and evil, change in all of its manifestations: the dense ether. The air is cold ether. Yet the air in the higher firmament is touched by the sun’s rays. At a very high altitude the sky transforms into the ideal and absolute realm of heaven, a state where concern with mundane matters is irrelevant.20

Jack Burnham



1. Marcel Duchamp, A l’infinitive (1912–1920) New York: Cordier & Ekstrom, Inc., 1966, p. 5.

2. Michel Foucault, The Order of Things (Les mots et les choses) (1966) New York: Pantheon Books, 1970, pp. 3–16.

3. Pierre Cabanne, Entretiens avec Marcel Duchamp, Paris: Editions Pierre Belfond, 1967.

4. Marcel Duchamp, Marchand du sel, (Michel Sanouillet ed.), Paris: Le Terrain Vague, 1958, p. 31.

5. Marcel Duchamp, The Bride Stripped Bare by Her Bachelors, Even (typography by Richard Hamilton and translation by George Heard Hamilton), New York: George Wittenborn, Inc., (no page number).

6. Eliphas Levi, Transcendental Magic (1896) (translation by Arthur Edward Waite), New York: Samuel Weiser, Inc., 1970, p. 180.

7. Duchamp, Marchand du sel.

8. John Read, Prelude to Chemistry (1936) Cambridge, Mass.: The M.I.T. Press, 1966, pp. 208–209.

9. Duchamp, The Bride Stripped Bare . . . (no page number).

10. Edmund Leach, “Animal Categories and Verbal Abuse” in New Directions in the Study of Language (edited by Eric H. Lenneberg), Cambridge, Mass.: The M.I.T. Press, (1964), p. 37.

11. Duchamp, Marchand du set, p. 33.

12. Edmund Leach, Genesis as Myth, London: Jonathan Cape Ltd., 1969, p. 20.

13. Stephen A. Tyler, Cognitive Anthropology, (Stephen A. Tyler, ed.) New York: Holt, Rinehart, and Winston, Inc., 1969, pp. 1–23.

14. Jerrold Katz, The Philosophy of Language, New York: Harper & Row, 1966, pp. 15–68.

15. Foucault, op. cit.

16. Ibid., p. 74.

17. Jack Burnham, The Structure of Art, New York: George Braziller Inc., 1970, pp. 58–61.

18. Marcel Jean, The History of Surrealist Painting, (1959, translated by Simon Watson Taylor), New York: Grove Press, 1960, p. 99.

19. Jean, The History of Surrealist Painting, p. 101.

20. For many readers the correspondence between the symbols of the sides of the Great Pyramid and sentence structure will seem nothing less than incredible. The fact that these represent an eminently logical system is shown in an essay on the mathematics of structuralism, entitled “Some Problems in the Theory of Structural Balance: Towards a Theory of Structural Strain” by Peter Abell in Introduction to Structuralism, edited by Michael Lane, New York: Basic Books, 1970, pp. 389–409. Using some theorems developed in sociology for defining patterns of strain and tension-maintenance, Abell generalizes their use into a series of balance theory axioms. These are demonstrated particularly for structures with three independent entities, manifesting stable and unstable relationships. The reader is encouraged to substitute the values of referent, signified, and signifier in these 3-cycle relationships and then work out the stability of these according to the semiotics of the five types of sentence structure. Mathematically they reveal that all sentences are stable except for compound-ambiguous types and so-called elliptical sentences—this corresponds to the nature of the art generated by these sentence types.