Intentions: Logical and Subversive
The Art of Marcel Duchamp,
Concept Visualization,
and Immersive Experience

by Richard K. Merritt

Symbolic Logic and Visualizing Concept in the Work of Marcel Duchamp

The seemingly innate propensity of the human mind to binary, "this not that thinking" may be fruitfully illustrated by using symbolic logic in an interpretation of the intentions of Marcel Duchamp. With symbolic logic as a form of information or concept visualization one can demonstrate the difficulty and visual complexity of examining Duchamp's work using a deterministic system of equivalencies.

First let us use the most oft sited interpretations of Duchamp's oeuvre and their corresponding significances and assign to each a variable. The following is by no means an exhaustive codification of the many interpretations of Marcel Duchamp's works it is essentially a categorization of a few of the major theories.

A. The use of the "ready-made" or "found object" asserts that by altering the context of a commonplace object it can become art.

D. The statement A allows that Duchamp in challenging the definition of the art object by exalting the primacy of the idea over the creative act he subverted the modernist convention of the artist/object and viewer relationships

B. The work was an exploration of the mathematics of uncertainty pioneered by Henri Poincaré and the study of the fourth dimensional space theorized by Élie Jouffret (Traité Élémentaire de Géometrie à Quatre Dimensions 1903).

H. The statement B. allows that Duchamp called into question the discipline boundaries between art and science and destroys the notion of the artist as creator of 'retinal art" or the aesthetic object.

C. The work was engineered to be reassembled by the patron or viewer, who followed complex, often informed by chance, instructions. This process is evident in Duchamp's assemblage book works such as La Bôite Verte.

The statement C allows that Duchamp transformed the boundaries between producer and consumer in the art market and engaged the artist/manufacturer and viewer in the process of creation.

We will next make a formula that contextualizes more precisely the relationship between the upper level referent variables A, B and C (in this case those variables that refer to the condition of Duchamp's work rather than his intentions). Supplanting a corresponding lower case Greek letters, A becoming a(alpha), B becoming b(beta), and C becomes g(gamma) the following is the rule, universal quantifier or binding of variables governing their relationships. (Fig. 8)

Figure 8

The above statement allows that there can only be a single interpretation of the work of Duchamp. In accordance with the current highly polarized arguments about his work the equation illustrates that, of the contemporary hypothesis, only one can be correct. The next equations maintain that there can only be a single derived intention from the overall statement of the condition of Duchamp's work. In other words the statement: "The work is an exploration of the mathematics of uncertainty pioneered by Henri Poincaré and the study of the fourth dimensional space theorized by Élie Jouffret" may only be linked to the intention, "Duchamp calls into question the discipline boundaries between art and science and destroys the notion of the artist as creator of 'retinal art' or the aesthetic object". We may express this with symbolic logic in the following: (Fig. 9)

Figure 9

The next section of this exploration of the work of Marcel Duchamp through symbolic logic will determine the consistency of each of the condition/intention hypotheses. First we will examine the consistency of the argument A, if and only if, D: (Fig. 10)

Figure 10

The statement A if and only if D proves logically consistent. Next we have the hypothesis B, if and only if, H: (Fig. 11)

Figure 11

Having proved the statement B if and only if H consistent we address the theory C if and only if P: (Fig. 12)

Figure 12

Having proved the consistency of all three hypotheses given the a priori context that only one of them is correct where are we left in this complex visual analysis of Duchamp's intentions? His intimate knowledge of Henri Poincaré's theories and his use of chance in the construction of many of his key works would seem to indicate that Duchamp had been quietly challenging the notion of deterministic reasoning in both the interpretation of art and physical and experiential phenomena. As Poincaré suggests in 1895;

Experiment has revealed a multitude of facts which can be summed up in the following statement: it is impossible to detect the absolute motion of matter, or rather the relative motion of ponderable matter with respect to the ether; all that one can exhibit is the motion of ponderable matter with respect to ponderable matter.

In short, Poincaré asserts that all quantifiable and qualifiable information pertaining to any phenomena can only be measured relative to other qualified and quantified data. As the first to elucidate this "principle of relativity" Poincaré discerned that all explicit information about any physical phenomena in motions is best expressed in the form of a probability. Poincaré's critique of determinism extends to other disciplines as well as he states, "The science of history is built out of bricks; but an accumulation of historical facts is no more a science than a pile of bricks is a house." This kind of reasoning is the bedrock of semiotics (meaning in language is ascertain through the relationship between the symbol and its meaning relative to the culture that produced it). It has also been used to critique symbolic logic. The discipline itself relies on abstract patterns, its meaning determined not from the symbols themselves but from the relationship between the marks and other patterns and more significantly cultural meanings.

Duchamp's connection to logic is most clearly noted in two of his most significant areas of concern: chance and chess. As a chess master Duchamp was, on several occasions, a member of the French championship chess team. For Duchamp chess was an organized, integrated and ordered whole, composed of rule based interactions wherein outcomes were as influenced by unquantifiable elements such as guile or desire as by systematic reasoning. This led Duchamp to assert that complexity in any system was inherently non-deterministic. We see this questioning of aggregation, perhaps more clearly, in his use of chance in aesthetic production.

click to enlarge
Figure 13
Marcel Duchamp, Three Standard Stoppages, 1913-14
Duchamp's subversion of deterministic systems through chance finds vent in his Trois Stoppages-Étalon [Three Standard Stoppages], 1913 (Fig. 13), He first measures three sections of thread each precisely one meter in length and drops them from a height of exactly one meter. He then uses the curves of the threads to produce three templates cut from a straight edge to produce the work. The templates are then enshrined in a box and become the piece Trois Stoppages-Étalon. This work and activity albeit unusual, is a subversion of the concept of immutable standards of measurement, thus questioning the validity of a system based on a platinum-iridium bar stored in a Parisian vault. His attention to chance not only posited an alternative to early twentieth century "laws" of science but also undermined early twentieth century conventions about aesthetic production.

Le Penseur Multi-Dimensionnelle

Duchamp's work Nude Descending a Staircase (1912) was first displayed at the Cubist Exhibition at the Damau Gallery in Barcelona and later at the Armory Show (New York, 1913). This painting took the observational cubist penchant of displaying an object from multiple spatial vantagepoints and added a temporal element by rendering a nude figure in motion. This work explored the conceptual possibility of 2d painting, which displayed and illustrates a 3 dimensional figure traversing time. The piece arrives at a visceral form of multi dimensional cognition. Partial inspired by his interest in chronophotography and the mathematics of Henri Poincaré Nude Descending a Staircase is perhaps his last clear attempt to use a traditional modality of retinal art to express a conceptual or gray matter art. It is also his first widely exhibited work to express his interest in the merger of science and art.

His continued interest in multiple dimensions, though I cannot prove this, is probably where we may find the solution or at least a map to a clear understanding of his work. Though we may never have a concise definition of "what his work was about" Duchamp may have left us clues as to how we may begin to "make sense" of his intentions.

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Figure 14
Front view of the postacrd in the White Box, 1967
Rhonda Shearer and Stephen J. Gould In their article Boats and Deckchairs  present the most profound example of Duchamp's trickery and play with the multi-dimensional mathematics of Henri Poincaré and Élie Jouffret. Inside Duchamp's 1967 piece White Box Francis Nauman discovered a "commercial" postcard (1914) (Fig. 14). The postcard displays on its front three boats floating on a placid lake or river and on the reverse some writing. Nauman categorize d this discovery as a "random notation" written on a "found object" citing that "on the verso of a postcard, Duchamp notes 'a possible means by which the fourth dimension could be visually established through the optical illusion of two deck chairs'." This note was accompanied by an illustration of parallel lines bisected by a perpendicular. The true nature of this object has never been addressed by art historians as the work could be safely categorized as one of Duchamp's "ready-mades."

The piece is in fact, an original painting not a commercial postcard. The curious parallel and perpendicular lines on the back are in fact obscure instructions. Duchamp's fascination with rotation and relative vantagepoints indicates that a new dimension may be experienced through altering ones position relative to an object. When the postcard is turned 90º to the right the boats become an orthogonal rendering of deckchairs viewed from a bird's eye vantagepoint. The mysterious "random note" on the verso is a plea to adjust your perspective when viewing the postcard but also, when correlated with the image from the front the piece becomes a profound statement about the relationship between the second third and fourth dimensions.

Like E. A. Abbot's famous book Flatland (1885) whose main character, a square, is shockingly introduced to the third dimension, Duchamp has demonstrated for us that one can examine from a three dimensional vantage point all sides of a two dimensional object. In turning the postcard we are taking a clearly two-dimensional image and viewing it from the third dimension wherein the objects in question become something entirely different. In postcard he begs the analogy: that when viewed from the fourth dimension a three-dimensional object may be seen from all sides. From years of singular interpretations of Duchamp's oeuvre art historians have safely ignored Duchamp's multiple interpretations: one obvious and the others subversive. When the work is proclaimed (by the artist himself) and interpreted as a "ready-made" the hidden intention with all of its possible significance is obscured.

Duchamp disavowed models of reasoning, which relied on singular definitions. This kind of one or two-dimensional interpretation is inherently flawed when attempting to ascertain his intentions. With this in mind, Duchamp's work requires that any conceptual model of his intentions necessitates three-dimensional thinking and thusly is well suited to three-dimensional visualization.

Immersive Experience and Concept Visualization

As demonstrated, the use of symbolic logic as a means to visualizing concept in the work of Marcel Duchamp is extremely difficult. Though I have not examined the use of more advanced forms of symbolic logic (I am not a logician) it is apparent that the data, as envisaged, is not of the highest utility.

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Figure. 15
Screen still from the author's Immersive Duchamp Concept World an interactive virtual reality computer art piece.
Figure. 16
Screen still from the author's Immersive Duchamp Concept World an interactive virtual reality computer art piece.
Clearly, Duchamp had multiple intentions and the existence of seemingly inconsistent hypotheses about his work point more to the human propensity for dualistic thinking rather than to grasping a more pluralistic possibility. Engaging data that is not quantifiable and highly subjective is difficult to manage logically and exceedingly difficult to graph. However if we create a 3d cartographic form of the logic equations introduced earlier in this paper, we make the data more intuitive and thus cognitively manageable. (Figs. 15 & 16) Using interactive virtual reality software[the software we use in this example is the Glass Virtual Reality Engine, created by the author] one can have an immersive experience of the main theories about Duchamp's work.

The virtual reality computer art piece Immersive Duchamp Concept World, presents the theories concerning the artist's work. At the center of the virtual space is the entrance point to the world. The immersant or viewer may follow the map which branches off to various nodal points. Each of these nodal points represents a single theory. From the vantagepoint of the theory the immersant sees the other possible theories through a fog and translucent sheets, they are barely visible, as the immersant/viewer has chosen an alternate path (Fig. 15). In Immersive Duchamp Concept World the immersant is also introduced to various interactive media; readings of Duchamp's Notes as well as to still images and animations of his work and to the writings of Henri Poincaré. If the immersant chooses to fly above the object it is from this vantagepoint the viewer sees all of the theories as a totality (Fig. 16). This totality, is essentially a relativistic rather than a fixed deterministic system as the viewer governs the experience. This model for information visualization does not stand in opposition to symbolic logic, however it does allow a form of concept visualization that merges reason quantification, qualification and the visceral.


The body of work produced by Marcel Duchamp was a programmatic, if playful, undermining of deterministic thinking. He demolished arbitrary discipline boundaries between artist scientist and mathematician. His clues to altering our perspective were equally pertinent to viewing and understanding his oeuvre as they were to viewing individual works of art. His implicit and explicit call for altering our vantagepoint relative to his intentions inherently calls into question modernist singular interpretations. Yet, through the use of concept visualization, we can create more exploratory modes of information visualization; modes which allow for simultaneous multiple dimensional thinking. In an immersive environment the viewer can experience a panorama of Duchamp's intentions, one that does not enforce strict rules of consistency, but nonetheless leads us to comprehension of a poly-dynamic yet visceral logic.



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Figs. 13, 14
©2003 Succession Marcel Duchamp, ARS, N.Y./ADAGP, Paris. All rights reserved.