PRINT April 1971

Unveiling the Consort: Part II

IN 1912 MARCEL DUCHAMP DISCOVERED that all works of art conform to five types of sentence structure: A) Simple sentences B) Compound, complex and ambiguous sentences C) “Ready-made utterances” D) Elliptical sentences and E) Sentences with some disagreement between subject and predicate. He realized that as art these sentence structures have a particular diachronic relationship to each other, thereby defining the historical trajectory that modern art was to follow for the next six decades.

If, as Claude Lévi-Strauss maintains, myths function phonetically at the lowest level of articulation, syntactically and semantically at the next level, and through unconscious cultural discourse at a third level of articulation, then quite probably the same is true of art. There are, however, fundamental differences between the communication modes. Any writing or string of spoken words subjected to linguistic analysis is considered to be an ordered and finite text. The stories recounted to anthropologists in ethnological research, sometimes second or third hand, are only partially ordered and provisionally fixed texts, since verbal myths undergo constant variation. Linguistically, works of art are considered unordered and finite texts. From a semiotic standpoint these resist segregation by the usual means.

If this is true, then the phenomenon of art must function on a level beyond the normal analogical resources of poetry. Octavio Paz, the Mexican poet and essayist, alludes to this in his study of Lévi-Strauss’s techniques:

The poetic function (I am citing Jakobson again) transfers the principle of equivalence from the axis of selection to the axis of combination. The formulation of every verbal message comprises two operations: selection and combination . . . Selection is carried out “on the basis of similarity or dissimilarity, synonymy or antonymy, while combination, the construction of the sequence, rests on contiguity.” Poetry turns this order around and “promotes equivalence to the rank of a constituent process of the sequence.” Equivalence works on all levels of the poem: sound (rhyme, meter, accents, alliterations, etc.), and the semantic (metaphors and metonymies).1

According to Paz, poetry and mythic tales operate according to parallel categories of equivalency. But he misses the point which Lévi-Strauss seems to have mastered; namely that the mechanisms of poetry do not constitute all the levels of analogy to be found in a work. Analogies on one plane usually provide the basis for those on another. Many of Lévi-Strauss’s four-part equations are nothing more than myth reduced to sentence structure—although there seems to be no real indication that he is aware of this, or the fact that a number of sentence structures are possible. Moreover formal and verbal equivalencies are sometimes apparent in art works, but normally these function within a broader context of semiotic analogy.

One of the linguists responsible for this discovery was Louis Hjelmslev. His Prolegomena to a Theory of Language attempts to extend the theories of Ferdinand de Saussure so that an “algebra of signs” is feasible. While his Glossamatic techniques have limitations for contemporary linguists, their real value lies in a symmetry, elegance, and simplicity that reveals the separation of sentence components on all levels. This approach recognizes that languages consist of content (semantics and syntax) and expression (phonological analysis) which are connected to each other through commutation (i.e. reciprocal relationships and limitations).

It would seem that the double articulation inherent to both language and art is quite similar: hence formalism is to art what phonology is to language. Both analyze or account for the organization of phenomena at the sensory or physiological level. What must be considered the equivalents of semantics and syntax in art (content) can only be ordered through the agency of principles of formal organization—but these are not necessarily visual. Moreover, it is apparent that no coherent theory of art semiotics can be based on formalism alone. Note that in some art forms (Dada, Surrealism, Pop art, and some Conceptualism) formal organization exists as a substratum of content, yet this plays a negligible part in defining the art’s Plane of Expression. In most such instances the Plane of Expression is defined by the particular nature of the making process and the lexical attributes of the items depicted by the work of art.

There is no one-to-one relation between content and expression even when both planes are broken into smaller components. What is important to linguistic structure is the algebraic relation between the signifieds and signifiers of the planes of content and expression. In Hjelmslev’s words, “It turns out that the two sides (the planes) of a language have completely analogous categorical structure, a discovery that seems to us of far-reaching significance for an understanding of the structural principle of a language or in general of the ‘essence’ of a semiotic.”2 He goes on to say that it appears that such an analysis does not yield up “a syntax or science of the parts of speech,“ meaning, as we shall see, that such divisions do not make complete distinctions between syntactical, semantic, and phonological components, but that these extend to both planes.

It is this “analogous categorical structure” of language relationships which subsumes all types of purely poetic analogy. For a sentence or a work of art these relationships assume the following form:

Syllogistically this takes the form: Content Signifier is to Content Signified as Expression Signifier is to Expression Signified, or, reproducing Duchamp’s equation:

In The Structure of Art3 I describe procedures for defining the parts of this equation. These directions, however, leave something to be desired in terms of diagramming all the linguistic possibilities of art. At the time I was writing I did not fully appreciate the importance of Noam Chomsky’s theory of transformational grammar, nor the implications of “deep structure” for understanding sentence construction. Mention is made of Chomsky, however, and the significance of his theories for understanding art with ambiguous structures (e.g., when a sentence possesses more than one kernel sentence in its deep structure). Also I have made a very incomplete explanation of how neutralization and concord define the paradigmatic and syntagmatic features providing the illusion of change in modern art.

Until the advent of Zellig S. Harris’s research and Noam Chomsky’s Syntactic Structures in 1957, linguists analyzed sentences according to the conventional categories of grammar or what is known as constituent structure. Chomsky’s main point was that many sentences cannot be understood through existing methods of parsing. Supported by mathematical proofs, he hypothesized that all sentence forms can be reduced to one or more kernel sentences. The kernel sentence is a basic linguistic structure consisting of no more than a subject (determiner and noun) and a predicate (the present tense of any verb, including an object if the verb is transitive). Many distinctions of conventional grammar are discarded by Chomsky’s theory. In their place are word markers and transformational rules providing directions for the reconstruction of normal Lentences (surface structure) from the underlying deep structure. The theory behind these transformations is intricate and still undergoing considerable revision.

Chomsky’s assertion of the primacy of the kernel sentence is an important issue for all structural studies. It appears that simple declarative sentences have much the same consistency as logical or mathematical propositions—a unity of subject and predicate through the copula—but by means of double articulation. Herbert Simon, one of the pioneers in artificial intelligence research, supports the essentiality of the kernel sentence. In a conclusion to a paper on decision making he states, “. . . ordinary mathematical reasoning, hence the ordinary logic of declarative statements, is all that is required for a theory of design processes.”4 The child psychologist Jean Piaget also seems to side with Chomsky on the matter of the “formative kernel,” but with different conclusions as to its meaning. He sees deep structure not as the result of innate syntactical mechanisms, but as a biological dialectic (“equilibration”) which fuses the brain’s practical functions into a mechanism for transforming temporal formation (experience) into non-temporal interconnection (sentence formation).5

One of the better semiotic explications of the subject-predicate relationship is in the work of Michel Foucault. He points out that all verbs and verb forms begin with the copula, the verb to be: “So that the essential function of the verb to be is to relate all language to the representation that it designates.”6 Foucault also assures us that it is the generality of naming words, particularly nouns, that allows us to designate attributes for it in the form of propositions. In other words, the multiple possibilities afforded by limited taxonomies make general (and ambiguous) propositions in natural language possible.

One of the problems encountered in Duchamp’s titling and iconography is that of treating the subject and predicate as if they were the same as the planes of content and expression. In Foucault’s terminology all language manifestations, including speech, texts, and art objects are subsumed under the heading of representation. He insists that it is the conjoining of subject and predicate (i.e. the proposition itself) that results in the representation, and not the parts (of speech) themselves: “The relations between the elements of the proposition are identical with those of representation; but this identity is not carefully arranged point by point, so that every substance is designated by a substantive and every accident by an adjective. The identity here is total and a matter of nature . . .”7 Thus the analysis of a sentence or a work of art by glossamaticians is carried out holistically, and not according to constituent structure. Each signified and signifier results from segregating specific relations found in an entire proposition.

At this stage, it might be well. to outline the semiotic relations of the various sentence types as they correspond to works of art. Needless to say, Duchamp gives us more or less specific notions of these in his writings. And considering the state of linguistics at the time he was writing, he can hardly be blamed for their incompleteness. Duchamp’s real verification of art’s linguistic nature are the ready-mades themselves.

Simple sentences possess signifieds and signifiers for the planes of Content and Expression. Complex and ambiguous sentences need two equations or more with multiple sets of signifieds or multiple sets of signifiers and signifieds, depending on whether the ambiguities in question are visual or conceptual.

Ready-mades function with a Plane of Content but no Plane of Expression in what Roland Barthes terms the “Real System” or the basic equation describing the art itself. A Plane of Expression is constructed for ready-mades by shifting analysis to the Connotative System at a higher level. All nonobjective art reverses this procedure by recovering the Plane of Content on the higher Metalanguage level.8 So-called contradictory or illogical sentences possess the same structure as declarative sentences, but where signifieds in the Plane of Content point to the nonsensical nature of art, this lack of meaning is always “rectified” by explanation of hidden relationships (usually in terms of set theory) in the signified of the Plane of Expression. Examples of such art include Louis Carroll’s nonsense poetry and Joseph Cornell’s constructions. Here is what Paz means when he writes that equivalence is shifted from selection (according to meaning) to combination (according to sound or lexical association) in the creation of poetry.

In nonobjective art color, line, form, and format comprise the basic phonological structure. For any work in this category, semantic content is totally absent. Rather meaning becomes about phonological or formal relationships, and so passes into Metalanguage. This tendency expresses the strongest diachronic force in modern art. All nonobjective avant-garde art is predicated on the unconscious assumption that innovation means reducing prevailing phonological (formal) relationships. The last five years have seen a conclusion to this. As we shall see with the ready-mades, combinations of sentence types are also possible, and these have undoubtedly increased the life span of the avant-garde. It was stated in Part I of this essay that the idea of the copula in sentence construction is equivalent to sexual copulation. When Duchamp declared that “I want to grasp things with the mind the way the penis is grasped by the vagina,”9 he was graphically making the point that both propositions and works of art demand a symmetrical union of two components. Such a unity of being, in either sexuality or language, automatically joins the two levels of articulation into a propositional form, thus signifying the nexus of culture.

In the Box of 1914 Duchamp placed two notes that clearly indicate his use of semiotic concepts. The first is the “Algebraic Comparison” covered in The Structure of Art. The second is a description of the semiotic diagram (presented earlier in this essay) for a specific historical occurrence. He begins by stating:

The right and the left are obtained
by letting trail behind you a
tinge of persistence in the situation.
This symmetrical fashioning of the situation
distributed on each side of the vertical axis
is of practical value
(as right different
from left) only as a residue of experiences
on fixed exterior points.10

In this case the right and the left refer to the sign for the Plane of Content and the sign for the Plane of Expression. The word “tinge” in the translation is teinture in the original; teinture also refers to “tincture” or “dye” which is the alchemical symbol for art. What follows indirectly states that the left and right sides of the semiotic are essentially equal or equivalent. And as a work of art is analyzed and segregated (“situation distributed”), its different references point to an entity outside the signs themselves, namely the art object.

Duchamp proceeds to explain a certain fundamental conclusion of the semiotic which occurs in nonobjective art.

And on the other hand:
the vertical axis considered separately turning on
itself, a generating line at a right

in the direction A, 2nd direction B.—

Thus, if it were still
possible; in the case of the vertical axis at rest, to consider 2 contrary directions for the generating line G., the figured engendered (whatever it may be.) can no longer be called left or right of the axis—As there is gradually less differentiation from axis to axis, i.e. as all the axes gradually disappear in a fading verticality the front and back,the reverse and the obverse acquire a circular significance; the right and the left which are the 4 arms of the front and back melt along the verticals.

This obscure statement is the crux of Duchamp’s historical semiotic. He begins by describing the disappearance of the signifier and signified which occurs as there is a merger of the ready-made and nonobjective art. The first six lines are clarified by another note in the Box of 1914:

The game of barrel (roll, horizontal spin) is a very beautiful “sculpture” of cleverness (skill) . . .11

The “sculpture” in question consists of transforming a ready-made into non-objective art or vice versa. (How this is accomplished will be explained later in the essay.) But then Duchamp amends the conditions by stipulating that such a figure, if allowed to roll in either direction, will lose all orientation vis-à-vis right and left. This means that the Plane of Content of a work (left side) and its Plane of Expression (right side) collapse into a single sign. At this point the double articulation of the semiotic ceases to function: “—As there is gradually less differentiation from axis to axis, i.e., as all the axes gradually disappear in a fading verticality . . .” The “fading verticality” represents a predilection in all nonobjective art to gravitate towards the appearance of a ready-made, i.e., ascend the apex of the Great Pyramid. As the formal relationships of the art drop away one by one, the final two define the Plane of Expression itself: these consist of the making process and the concept of set. At this point the work seems to be a ready-made without really being one.

Considering the fundamental dichotomy between Nature and Culture in Lévi-Strauss’s mythologies, his values for the Cooking Triangle,12 the evolution from myth to reality as specified in Edmund Leach’s analyses, and the linguistic characteristics for the Great Pyramid outlined so far, we discover a somewhat clearer diagram for language-based systems. Once its implications are understood, the singular importance of this diagram for comprehending art cannot be underestimated. For Duchamp the “beauty of indifference” exists in knowing that esthetics is a matter of logical selection rather than blind choice.

What remains for art historians, and a task of prime importance, is a comprehensive semiotic study of Medieval and Renaissance art. This represents an area of study where the shift from symbol to sign is crucial in Western art. By nature symbols are anomalous and sacred; they mean one thing to the public, but at least two different things for the initiated. As Peter Fingesten notes, originally the symbol was a secret sign of recognition, one with collective rather than personal origins.13 Since symbols are fixed signs they possess no validity as esthetic forms; esthetics stems from the gradual admixture of visual syntax and symbolic meaning. Renaissance space—as Duchamp has implied—provides a set of unfixed relationships where the semiotic of secular events is integrated with symbolic representations. The Hunt of the Unicorn, a late 15th-century tapestry in the Cloisters Collection, eminently illustrates my point. In this scene a zoomorphic symbol of Christ is about to be run down by a contemporary party of hunters.

The only instance where Duchamp imparts a lesson in art history is found in his drawing for the Boxing Match (1913). Along with the Toboggan, Juggler of Gravity, and Picture of Cast Shadows, this diagram completes the omitted “Stripping Mechanism” of The Large Glass. (The reader may follow my interpretation by referring to the diagram in the Hamilton and Hamilton version of the Green Box notes.14) The notes begin with a historical highlights:

Boxing Match = Trajectory of the combat marble:
A. Departure—Contact of the marble at the
1st Summit—Unfastening of the clockwork and
fall to B.
B. 2nd very sharp attack—contact at the 2nd
Summit and release of the 1st Ram—Fall to C.
C. Direct to the 3rd Summit—Release of the 2nd Ram.

Point A represents the prehistoric beginnings of sign and symbol systems. The 1st Summit most probably represents Renaissance art, which is both the culmination of mimetic conventions and the beginning of the end of art based upon symbols. The “2nd very sharp attack” brings the “combat marble” or semiotic to the 2nd Summit. This summit appears to be the introduction of nonobjective art between 1908 and 1912. The first ram with part of the Garment of the Bride falls at this point. The Bride’s Garment is, in fact, the art myth itself; in this case the 1st Ram refers to all semantic and syntactical signs, so that C represents the beginning of art which functions phonetically (formally) or purely on a Metalanguage basis. The 3rd Summit is reached (about 1968), precipitating the exhaustion of the 2nd Ram or all possible formal signifiers. At this stage the Combat Marble returns to A—meaning in effect that the historical myth of avant-garde art is completed.

1st and 2nd Rams descending after the contact of the combat marble to the 2nd and 3rd Summits. This descent carries with it the garment of the Bride which the Rams Support. The juggler of centers of gravity, having his 3 points of support on this garment, dances to the will of the descending rams controlling the stripping.

The juggler of centers of gravity (Tarot) refers to the semiotic triangle: referent, signified, and signifier. Each subtraction of a signifying (formal) convention precipitates a kind of juggling act or recovery of balance between the parts of the semiotic.

A spring in red steel actuating the whole clockwork—the cog wheels by means of a rack, push the fallen rams up again.

As in alchemy, the color red is used to signify baser instincts: sexual lust, male power, and physical instincts unreformed by wisdom. This blind mechanism allows us to sense the presence of art without comprehending it. The red spring is responsible for holding the Garments aloft.

T and T’ release hinges of the rams which losing their support by the contact of the combat marble at X and X’, fall down.

R and R’ —R engaged position of the red transmission with the rack System—R’ unfastened position in consequence of the contact at the 1st Summit of the combat marble; DG moves to D’G and like a door gently returns to DG (Automatic closure F) leaving time for the marble to produce the 2 following releases._

The latching mechanism at G, D, and D’ is important. Culturally, the engagement of the lever at R represents the Classical impulse in action. When this is engaged, the gears—by means of a rack and pinion system—keep the Bride’s Garment aloft, thus holding the veils of the art myth before our eyes. Duchamp specifies, though, that disengagement of this mechanism is not final since the mechanism works on the principle of an automatic door close. A return to DG implies a return to the classic principles of equilibrium and self-knowledge. Comprehension of this obscure but important historical mechanism demands a very elementary understanding of mechanical principles: “Mécanisme de la pudeur/Pudeur mécanique” or “Modesty’s mechanism is to be mechanically modest.”

Marcel Duchamp in an interview with Jjames Johnson Sweeney: “. . . . art is produced by a succession of individuals expressing themselves; it is not a question of progress. Progress is merely an enormous pretension on our part. There was no progress for example in Carot over Phidias. And “abstract” or “naturalistic” is merely a fashionable form of talking—today. It is no problem: an abstract painting may not look at all abstract in 50 years.”15

Duchamp specifies in his introduction to the notes in the Green Box that “This headlight child could, graphically, be a comet, which would have its tail in front . . .”16 The “comet” (Duchamp) was to create all possible variations and combinations of art necessary to outline the semiotic between 1913 and 1926, thus anticipating every type of art to be produced for the next fifty-five years. For the most part this was achieved with standardized objects, since these are sufficient to articulate semiotic relationships. In many instances Duchamp’s constructions are not true ready-mades, but rather are the principles of ambiguity, ellipsis, declaration, and contradiction integrated into assortments of found objects. As we shall see, the titling of works of art plays an essential role in defining a work’s position semiologically; frequently, in fact, a work’s esthetic validity depends upon a title; in other cases titles serve as linguistic explications. Yet some of Duchamp’s canniness is due to the fact that he constantly shifted the purposes of his titles; on the surface they display no perceivable pattern.

The 3 Standard Stoppages is obviously a commentary on non-objective art, and as such its descriptive title acts as a Metalanguage signified, specifying the artist’s intention since the piece has no perceivable content. Originally Duchamp dropped three one-meter threads, held one meter high, on to three stretched canvases painted Prussian blue (notice the use of Prussian blue corresponding to WATER and putrefaction). These were glued down, the canvases trimmed and glued to glass plates, and the results then boxed with a corresponding set of templates. The objective here is a comparison of doubly and singly articulated semiotic systems. The piece is merely a box with certain objects in it; nevertheless Duchamp is saying that all non-objective works of art are simply objects devoid of any meaningful content. Consequently in a Metalanguage system the signifier replacing a signifier in the normal Plane of Content is a physical description of the art object. He clarifies this in one of his notes for the Green Box.

To lose the possibility of recognizing (identifying) 2 similar objects—

2 colors, 2 laces

2 hats, 2 forms whatsoever
to reach the Impossibility of
sufficient visual memory

to transfer
from one

like object to another
the memory imprint
—Same Possibility
with sounds; with brain facts17

The idea of a “memory imprint” corresponds to what happens when we consider nonobjective art as a generic form derived from mimetic conventions. Duchamp is posing a question: namely, how far does nonobjective art proceed in the process of dropping formal signifiers before we are unable to recognize an object as art? II would seem that the validity of the nonobjective impulse depends absolutely upon its historical derivation from art with content.

The one-meter threads become something other than the meter unit codified by a National Bureau of Standards, just as—as in the case of all articulated systems—the letter a will always mean the same quantity or entity as long as it remains in an algebraic equation; but as soon as it is talked about with language, it becomes distorted (and transformed) by various descriptive elaborations. Michel Foucault suggests the same difference in his discussion of logical and linguistic comparison:

After being analyzed according to a given unit and the relations of equality or inequality, the like is analyzed according to its evident identity and differences: differences that can be thought in the order of inferences. However, this order or generalized form of comparison can be established only according to its position in the body of our acquired knowledge; the absolute character we recognize in what is simple concerns not the being of things but rather the manner in which they can be known.18

So in effect, the “standard stoppages” are no longer standard but deviate from a norm, displaying somewhat the same consistency as Process Art. The thread and templates are merely materials—as Pollock stressed paint was in his paintings—materials explicitly defined by a making process given over to gravity and chance. Duchamp has nearly succeeded in erasing the “memory imprint” which is also necessary to Pollock’s art. So here in the Stoppages “l’idée de la Fabrication” is all that remains.

Bicycle Wheel is the deceptive title of the first ready-made. A 1951 version was eventually signed and dated in green ink, intimating that it deals with subject-predicate contradiction and therefore qualifies as an “assisted ready-made.” In conversations with Arturo Schwarz, Duchamp emphasized its chance aspect—and this is purposefully misleading. Although the work is seemingly meaningless and could be given any number of interpretations, such is not the case. In philosophy, one encounters “analytic” and “synthetic” propositions. Roughly described, synthetic sentences are statements whose truth is contingent on facts or conditions external to the sentence itself. Analytic sentences are true by virtue of their own internal consistency, both semantic and syntactic. In the statement All bachelors are married men, for example, the two terms bachelors and married men are mutually exclusive; therefore the sentence is inherently false. In the same sense Bicycle Wheel is functionally contradictory. By definition a kitchen stool is something to sit on, while a bicycle wheel moves along the ground supporting the weight of a rider. In this instance both functions are nullified through deliberate juxtaposition which transforms their status into a false analytical proposition.

The Bottle Dryer of 1914 is Duchamp’s first true ready-made. Actually since it has also been entitled a Bottle Drainer, Bottle Rack, and Hedgehog, the title is not particularly important—although “hedgehog” does imply something beyond the superficial resemblance that the restaurant appliance has for the animal. In an essay by Isaiah Berlin, the philosopher comments on a line written by the Greek poet Archilochus, “. . . ‘mark one of the deepest differences which divides writers and thinkers, and, it may be, human beings in general.’ The one type, ‘the fox,’ consists of men who live by ideas scattered and often unrelated to one another. But the man of the other type, the ‘hedgehog’, relates ‘everything to a central vision, one system more or less coherent or articulate a single, universal, organizing principle . . .’”19 And so an artist who knows how to choose a ready-made also has the same synoptic vision in terms of all art. All the effective ready-mades are standard manufactured objects, neither precious nor worthless, but possessing some intermediate value. Their most important quality is their inherent contact with both Nature and Culture; therefore ready-mades are in some way affected by or function with the help of the natural elements. The Bottle Dryer assists in the evaporation of water. A subsequently lost ready-made of 1915 is entitled Tiré à quatre épingles, an idiomatic expression which means “well groomed” or literally, in English, Pulled at 4 Pins. The object was an unpainted, galvanized, sheet steel chimney ventilator, the kind placed on chimney copings. These turn in the wind, protecting flues from violent down-drafts. More than likely this object mediates the four prime Elements: it protects the FIRE against wind (AIR), dust (EARTH), and rain (WATER) and turns to the four points of the compass.

A more enigmatic piece of the same year is the suspended snow shovel, In Advance of a Broken Arm. When Duchamp was questioned about the hanging of various ready-mades from the ceiling, his usual answer was an excuse that he was tired of seeing sculptures always situated on pedestals. But this had nothing to do with his reasoning; his purposes are semantic and syntactical. A snow shovel suspended out of reach is merely an object deprived of its use and functional meaning (nonobjective art, hence WATER). But Duchamp reassigns this object’s meaning in a very curious way. The phrase “in advance of a broken arm” is nonsensical and an incomplete sentence, thus related to both EARTH and WATER. So the shovel is an omen of the corner of the Great Pyramid represented by frozen water (Cold), and signifying the final stages of nonobjective art. The “broken arm” comes when art is no longer served by the process of fabrication.

The ready-made Comb, chosen and inscribed in 1916, is an ordinary steel comb with the words lettered on its back edge: “3 OU 4 GOUTTES DE HAUTEUR N’ONT RIEN A FAIRE AVEC LA SAUVAGERIE” (3 or 4 drops of loftiness have nothing to do with savagery). Any interpretation of the Comb is open to dispute, so my analysis is by no means definitive. The Comb appears to be, and probably is, an assisted ready-made because its contact with a natural element is questionable. Duchamp’s inscription implies that WATER has nothing to do with (it) savagery. Looking back at the semiotic diagram, we observe again that WATER refers to nonobjective art in which the final stages reduce art to pure materials, hence Nature or savagery. We also know that there is a considerable amount of lofty intellectualism attached to nonobjective art. Is he saying that the WATER that comes in contact with the Comb, namely the intellectual justifications which validate nonobjective art, have nothing to do with the naturalizing tendencies behind the art itself? Possibly. There is also Duchamp’s note in the Green Box of September 1915 which refers to a comb as a kind of space divider; this is done under the heading of Rattle. The comb, he states, exerts “proportional control” over the hair by means of the number of teeth it has, its broken teeth, and its curvature. Is it possible that Duchamp is looking at the comb as a kind of taxonomic structure, one that would define a natural continuum (head of hair) into a given set of terms (or in this case, spaces)? A famous linguistic example of this may be found in the relativity of terms used in naming the color spectrum. A comparison of terms used in different languages shows that each language makes its own unique divisions of the spectrum; there is never a one-to-one correspondence between terms in various languages.

The comb relates to an assisted ready-made, Duchamp’s piece for Walter Arensberg entitled With Hiddert Noise. It is a ball of twine sealed at both ends by brass plates screwed together. Arensberg placed a secret object inside the ball so that only the noise of this rattle was known. This corresponds to the “content” of nonobjective paintings which seems to be “there” but really is not; only its “bouquet” or “memory” is present.

Duchamp insisted on a different interpretation for Comb. A remote possibility is the fact that the upper point of the alchemist’s Pentagram represents the same values as the Apex of the Great Pyramid, uniting the spirit, intellect, and the head of the body. Thus the comb’s relation to the head associates it with the seat of the intellect and consequently the ready-made. Still, there is a more plausible interpretation. The teeth of the comb form a set within finite boundaries—just as Carl Andre’s floor units define sets. This and the comb’s enigmatic prescription turn it towards the quadrant of EARTH on the Great Pyramid.

The famous Urinal is an “Assisted ready-made” according to Arturo Schwarz; Duchamp has turned it on its back and given it the title Fountain. The physical displacement makes it slightly less recognizable and the title intimates that the piece is a legitimate variety of sculpture—needless to say, abstract sculpture. Both transformations overlap, shifting the urinal towards the category of nonobjective art (i.e., “R. Mutt”).

While in Buenos Aires in 1919, Duchamp sent instructions to his sister Suzanne for the preparation of an assisted ready-made entitled Unhappy Ready-made. The project consisted of hanging a geometry book out a window for a number of days and nights, exposing it to all kinds of weather. In this instance Duchamp chose the quadrant AIR of the Great Pyramid. This means that the work represents a simple declarative proposition, e.g. an art object with its content “naturalized” due to some direction or activity of the artist. This act provides the “emotion” (unhappy) for the Plane of Expression. The work is simply the choice of some subject matter and its exposition through appropriate directions for fabrication.

In Duchamp’s present to Walter Arensberg of Paris Air, a 50 cc. glass ampoule of air fabricated in Paris, he again chose to work with the qualities of AIR. In this case his desire is to make air “content” for an art work. Encapsulating air completes the making process. A printed label on the glass reading “Serum Physiologique” is a restatement of the essentiality of the alchemist’s AIR. This corresponds to another note in the Green Box which reads:

Establish a society
in which the individual
has to pay for the air he breathes
(air meters); imprisonment
and rarefied air, in
case of non-payment
simple asphyxiation if
necessary (cut off air)20

AIR, of course, remains the archsymbol of linguistic communication and ritual. He seems to be saying that we take these things too much for granted because they have the same commonness as does air. Duchamp may also be suggesting that nonobjective art represents a kind of rarefied air, if not a vacuum.

Fresh Widow, a semi-ready-made of 1920, consists of a miniature French window, painted light green, with sheets of black leather covering window panes. Except for the wordplay between “Fresh Widow” and “French window,” the piece precipitates almost no comprehension; however its green paint indicates that the window is concerned with the element EARTH. Moreover some of Arturo Schwarz’s observations on the ready-made appear apt. For instance he notes the female sexual symbology implied in a window opening and the French colloquial term for guillotine: “widow.” In this respect, the space behind the window appears to be pitch dark, but upon opening the window we see otherwise. There are, moreover, strong sexual taboos against relations with widows in many societies, just as there are taboos against incestuous dealings, remembering that EARTH and incest are conjoined. So in essence what Duchamp may be saying is that the delights of having intercourse with youngish widows have to be weighed against sexual guilt (consequently castration) accompanying such pleasures.

The Door: 11, rue Larrey is in accord with the principle of FIRE or syntactical ambiguity. Such ambiguity depends upon a perceiver experiencing split second shifts between various interpretations of a phenomenon. Duchamp had a door made which is hinged to open and shut on two door frames. Consequently the door is open when it is closed and closed when open. So the ambiguity in question is not expressly perceptual nor physical but conceptual.

By far one of the most sophisticated semi-ready-mades is Why Not Sneeze Rose Sélavy? Its title announces that the work joins two quadrants of the Great Pyramid, EARTH and WATER. The title takes the form of a question with an implied subject. If we transform this into a kernel sentence the result is the command “[Rose Sélavy] sneeze.” But at the same time, since sneezing is usually involuntary, the title combines partial ellipsis with nonsense. The ready-made consists of elements that simulate nonobjective art but are combined with other components to form a hidden set based on analogical properties, hence suggesting nonsense art.

Much has been made of the fact that the bird cage contains sugar cubes which are not sugar. The artist had fabricated 152 marble cubes which exactly resemble sugar cubes. This again is the essence of nonobjective art: “To lose the possibility of recognizing/identifying 2 similar objects.”21 Duchamp has also stressed the differences between the weights and heat coefficients of sugar and marble. These are important clues, but they should not be taken in Duchamp’s sense. The false sugar cubes in the bird cage are absurd by themselves. But the cage contains two other items: a French rectal thermometer and a cuttlebone. All of the objects together form a set and they function by virtue of the cage’s excluded occupant.

It becomes necessary to know that a cuttlebone is a kind of mineral supplement which is placed in a cage to balance a bird’s diet. On preliminary examination the four objects—cage, sugar or marble cubes, thermometer, and cuttlebone—seem to compose an empty class or a set of items which have no attributes in common. Yet if we complete the natural opposition expressed by the bird cage, the result is a different set: (bird), cubes, thermometer, and cuttlebone. Now various intersections between classes become apparent. The cuttlebone is composed of minerals—just as the marble cubes are mainly limestone. Yet the cuttlebone is food for a displaced bird just as the sugar cubes are not really food but displace the bird. Such a set relationship is “interconnected” since it is not only transitive, but reflexive and symmetric. On the other hand, the rectal thermometer—in spite of Duchamp’s suggestion—does not measure the heat of sugar and marble, since these are both approximately room temperature, but rather measures the body heat of the missing bird in relation to the “cold” marble. This coldness, which Duchamp refers to in his conversation with Arturo Schwarz, is really the corner between EARTH and WATER of the Great Pyramid. Thus the thermometer’s relation to the set of objects is “connected” or simply transitive. But it was included by Duchamp to emphasize the linguistic area dominating this semi-ready-made.

In conclusion, I will touch upon Duchamp’s mural of 1918, Tu m’, a complex and rather atypical effort. The subject is the illusions that historically define the course of nonobjective art. This is a theme that Duchamp returns to again and again, representing virtually an obsession. A hint to his feelings may be gained from Arturo Schwarz’s thoughts on the title: “Although the pronoun m’ in the title could be followed by any verb at all so long as its first letter is a vowel, the phrase is really a polite contraction for the French colloquialism tu m’emmerdes (you bore me), a feeling which could perhaps be referred both to the tedium involved in making the work and the person who commissioned it.”22 Duchamp’s boredom stemmed from both of these, but more than likely also from the subject of the painting. In effect he is saying that artists and the art world are going to make an enormous fuss in the years to come over the vitality and importance of nonobjective art; but he understands the linguistic mechanisms that will control their attention; he has anticipated all of them, so that the entire business is boring.

The elongation of Tu m’ and the sequential organization of its parts intimate that the painting deals with time, particularly the chronology of an idea. The right is dominated by objects or ideas which signify eternal principles or truisms. The bicycle wheel without a kitchen stool may be taken as a karmic symbol, representing the cyclical nature of time. The templates from the 3 Standard Stoppages represent, most likely, the arbitrariness of linguistic relationships. Above ’these, and extending into infinity, is an unending series of paint samples, fastened by a real bolt. Just as it is phonetically possible to articulate an infinite number of noises (but not for doubly articulated systems), the painter can extend the range of painted surfaces almost indefinitely. As long as the artist is working with a singly articulated system, he can innovate superficially by always supplying unusual paint combinations or surfaces; significant innovation demands that the artist subtract some formal convention from the work itself.

Duchamp has chosen to pencil in three objects—a bicycle wheel, a corkscrew, and a hat rack—as shadows. In alchemy the shadow of an object stands for its spirit or intellectual essence. In a letter to Arturo Schwarz, Duchamp insisted that the corkscrew itself is not a ready-made (which it is not by any interpretation), but rather its shadow is a ready-made.23 Consequently it appears that the nature-culture mediation is achieved through the agency of light or as that source emanating from the apex of the Great Pyramid, spiritual illumination. The corkscrew refers to the “uncorking process” in The Large Glass. This allows us to capture the bouquet of a wine without sampling it. Analogously we read content into nonobjective art even though it is only there by implication. This latent content, a reminder of earlier art, is the “uncorking.” In Tu m’ the corkscrew extends far outside its normal length, becoming a kind of curling layer of gas reaching out of the past.

Juxtaposed to the corkscrew is a sign painter’s pointing hand, as if to say: the symbols to the right equal what is to the left. This sign painter’s convention also anticipates the time when it is no longer necessary for formalist artists to paint their own canvases. Still there is an even better reason for it. The pointing hand is signed, A. Klang, which means when translated from German, (a) sound. Duchamp is insisting that the content of all nonobjective art must be “borrowed” or defined in terms of verbal expression emanating from outside the art itself, and therefore on the Metalanguage Plane. In many instances this is supplied not by the artist, but by. a critic or art historian sympathetic to the artist’s work.

Concerning a painted diagonal tear running through the center of the painting, Arturo Schwarz writes: “Right in its center a trompe l’oeil tear in the canvas is mended by three real safety pins. From a hole in the tear a bottle brush, securely fastened to the stretcher, projects toward the spectator. The symbolism of this detail is clear—it is a transparent allusion to coitus, while the three safety pins that repair the tear may refer to a clumsy attempt to cancel out the consequences of the sexual intercourse.”24 Schwarz’s remark about coition is not unfounded since it depicts the “coming together” producing a work of art. But Duchamp is implying something more germane: the tear announces destruction of the picture plane as an illusionary device supporting the notion of content in painting. The safety pins reveal the painting for what it is: an object. In much the same way painters (such as Rauschenberg and Johns) will exploit the inherent syntactical-formal ambiguity between what is placed on and what is represented in the picture plane.

A dirty tannish color and drab yellow are the background colors for Tu m’. In alchemy these shades signify intellectual obtuseness and a lack of spiritual development. The top color swatch on the sample pile is a bright lemon yellow, representing the highest degree of intellectual illumination.

Below the bottle brush is a glass pane. More than likely this is the picture plane which Duchamp refers to on occasion as a “shop window(s).” Projected from the four corners of the glass pane are four sets of black and red lines generated from the templates of the Standard Stoppages. Red, as I have specified before, signifies sexual lust and unrefined character, a passion to conquer without understanding. Black, on the other hand, implies many things, yet in this case it may be a sign of termination or encompassment. Extended at right angles from these lines are a series of colored ribbons. These appear to be ordered in sequences, and quite possibly relate to the esoteric color groups found in the Tarot. Surrounding the multicolored strips is a concentric series of circles most likely representing infinity. Duchamp appears to be saying that many thousands of artists will continue to make abstract paintings by juxtaposing color relationships, and there is no reason why this activity cannot go on indefinitely—as semantically meaningless as it is.

This last interpretation is reinforced by the shadow of a hanging hat rack, a reference to an assisted ready-made prepared by Duchamp in 1917. The Hat Rack is rendered nonfunctional by being hung almost upside down. In such a position it becomes simply an object without reference to any context—just as a nonobjective painting is strictly an object assigned a context. On a Metalanguage level Duchamp restores meaning to the hat rack by simply titling it Hat Rack. In a note in the Green Box the artist describes the psychological mechanism by which colors are awarded significance in the mythic context of nonobjective art. For the Breeding of Colors:

Mixture of flowers of color i.e.
each color still in its optical state:
Perfumes (?) of reds, of
blues of greens or of grays heightened
towards yellow blue red
or of weaker maroons. (the
whole in scales). These perfumes with physiological
rebound can
be neglected and extracted in
an imprisonment for the fruit.
Only, the fruit still has to
avoid being eaten. It’s this
dryness of “nuts and raisins” that you
get in the ripe imputrescent
colors. (rarefied colors.).25

On one level this may refer to the significance of different color scales as they are used in transcendental magic. The heightening towards the primaries and maroon indicates some relation to the four Elements. More specific, though, are the artist’s allusions to the myriad color combinations that may be used to promote a sense of uniqueness—a most necessary feature in modernist art. Each, so to speak, generates its particular perfumed essence, the result of a cognitive mechanism at work. This mechanism may be the sophisticated memory of the art lover, a kind of totemic system that allows each viewer to make free associations with countless past recollections. Duchamp implies that this is perfectly acceptable as long as the art lover avoids eating the fruit, that is, rationally understanding the entire system of conceptual correspondences which is the mythic structure of art. Mythically the fruit represents forbidden knowledge, just as the “dryness of ‘nuts and raisins’” refers to those unisexual plants grown in the Garden of Eden that give the illusion of art’s oneness and relate to the quadrant of WATER. “Ripe imputrescent colors” become stronger reminders of art since they alone represent the phonological articulation of a single-leveled semiotic.

In summing up the ideas that have been put forth in this article, I must apologize for the brevity of the arguments. An adequate summation of alchemy and the linguistic principles necessary to understand the analyses put forth would take at least several chapters of a book. These findings do, however, suggest a radical new approach to semiotic studies. For instance, they tend to demonstrate the centrality of sentence structure as a linguistic unit, supporting the contention in linguistics that language universals do exist. The notion of universals is based on the theory that underlying cognitive rules determine kernel sentence structure for all languages. Consequently the foundations of syntax, phonetics, and semantics are the same for all human beings. To date most of the evidence for this stems from the phonological universals discovered by Roman Jakobson in the 1920s. During the last ten years there have been advances with the mathematical application of some of the rules of transformational grammar to widely divergent languages. To my knowledge, however, little progress has been shown in defining rules of syntax completely free from dependencies upon semantic features. In spite of Chomsky’s assertions, there is mounting evidence that the generation of unique sentences exists because of mutually dependent (“deep-deep structure”) rules of syntactical and semantic manipulation. If it can be proved that a number of extra-linguistic social semiotics also have their origins in the organizational properties of sentence structure, this would go some way towards establishing the presence of universals as multipurpose neural mechanisms.

Above all, the discoveries of Duchamp and Lévi-Strauss undeniably relate the origins of religion and magic to art. It gradually becomes apparent that within the wide latitudes of the Natural and Cultural, the Sacred and Profane, various strategies direct the rites of mediation. It is always the act of mediation (the semiotic unification of the conceptual and the physical) that gives psychological value to any object or subject matter. Sixty years ago Emile Durkheim realized the truth of this in his study of sacred objects:

The churinga are preserved in a sort of temple, upon whose threshold all noises from the profane life must cease; it is the domain of sacred things. On the contrary, the totemic animals and plants live in the profane world and are mixed up with the common everyday life. Since the number and importance of the interdictions which isolate a sacred thing, and keep it apart, correspond to the degree of sacredness with which it is invested, we arrive at the remarkable conclusion that the images of totemic beings are more sacred than the beings themselves.26

Durkheim was one of the first sociologists to sense that the sacred character of objects emanates from relations outside the objects themselves. Hence the world of art, like that of religion, encompasses a complete construct of cognitive relationships denying material importance. The associations connected to an object, and not the object itself, define its religious or esthetic value.

. . . when a sacred thing is subdivided, each of its parts remains equal to the thing itself. In other words, as far as religious thought is concerned, the part is equal to the whole; it has the same powers, the same efficacy.27

In closing we must remember that Duchamp would have gained scant attention and no credit if he had proposed his theories in 1912; at most he might have succeeded in diverting art from its predestined course. Instead Duchamp established his case by selecting a great many trivial objects—“the junk of life”—and transforming these into some of the most seductive and enigmatic art of the 20th century. In the end we comprehend the quintessence of language-based illusions through the agency of revelation and the limitations of logic.

Jack Burnham



1. Octavio Paz, Claude Lévi-Strauss: An introduction (1967) (translated from the Spanish by J. S. Bernstein and Marine Bernstein) Ithaca and London: Cornell University Press, 1970, pp. 74–75.

2. Louis Hjelmslev, Prolegomena to a Theory of Language (1943) (translated by Francis J. Whitfield) Madison, Milwaukee, and London: The University of Wisconsin Press, 1969, p. 101.

3. Jack Burnham, The Structure of Art, New York: George Braziller, 1970, pp. 43–57.

4. Herbert A. Simon, “The Logic of Heuristic Decision Making” in The Logic of Decision and Action, (edited by Nicholas Rescher) Pittsburgh: The University of Pittsburgh Press, 1967, p. 20.

5. Jean Piaget, Structuralism, (1968) (translated and edited by Chaninah Maschler) New York: Basic Books, 1970, pp. 106–119.

6. Michel Foucault, The Order of Things (Les mots et les choses) (1966) New York: Pantheon Books, 1970, p. 95.

7. Ibid., pp. 98–99.

8. Burnham, op. cit.

9. Arturo Schwarz, The Complete Works of Marcel Duchamp, New York: Harry N. Abrams, Inc., 1969, p. 114.

10. 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., 1960, (no page numbers).

11. Marcel Duchamp, Marchand du sel, (Michel Sanouillet ed.), Paris: Le Terrain Vague, 1958, p. 32.

12. Burnham, op. cit., pp. 58–61.

13. Peter Fingesten, The Eclipse of Symbolism, Columbia: University of South Carolina Press, 1970, pp. 129–130.

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

15. Duchamp, Marchand du sel, op. cit., p. 109.

16. Duchamp, The Bride Stripped Bare . . . op. cit., (no page number).

17. Ibid., (no page number).

18. Foucault, op. cit., p. 54.

19. Robert Redfield, “Thinker and Intellectual in Primitive Society” in Primitive Views of the World (1960) (edited by Stanley Diamond), New York and London: Columbia University Press, 1969, pp. 34–35.

20. Duchamp, The Bride Stripped Bare . . . op. cit., (no page number).

21. Ibid. (no page number).

22. Schwarz, op. cit., p. 471.

23. Ibid., p. 470.

24. Ibid., p. 471.

25. Duchamp, The Bride Stripped Bare . . ., op. cit., (no page number).

26. Emile Durkheim, The Elementary Forms of Religious Life (1915) (translated by Joseph Ward Swain), New York: The Free Press, sixth printing, February 1969, pp. 155–156.

27. Durkheim, op cit., p. 261.