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Articles

Examining Evidence:
Did Duchamp simply use a photograph of
"tossed cubes" to create his 1925 Chess Poster?

by Rhonda Roland Shearer and Robert Slawinski

 

Introduction

Click to enlarge
Figure 1
Marcel Duchamp, Poster for the Third French Chess Championship, 1925
Rhonda Roland Shearer Collection

Duchamp claimed that he created his 1925 Poster for the Third French Chess Championship from a photograph (Fig. 1).  Schwarz writes in his Catalogue Raisonné of Duchamp's works (708):
To make this image, Duchamp tossed an "accumulation" of building blocks into a net bag, then photographed it, printing an enlargement of the picture that eliminated all details except the chance configuration of the blocks in the net.  This enlargement was the basis for the final drawing in which he colored the cubes light pink and black.(1) 
Duchamp's explanation, which sounds direct, simple and plausible, was the basis for the final drawing in which he colored the cubes beige, pinkish brown and black.  This explanation has also remained unchallenged by scholars.  Francis Naumann writes: "The position of the cubes--their three visible sides colored black, white and beige--was determined, as Duchamp later explained, by tossing them into the air and taking a picture" (101, 103).(2) 

If Duchamp's positioning of the cubes in his 1925 Chess Poster came "readymade" from a photograph that he took of tumbling blocks in a net, then we should be able to take various camera lenses used in 1925, place cubes in the positions depicted, and be able to generate a "photograph" matching Duchamp's poster. 

We tried this experiment using computer modeling and animation software, and made a surprising discovery.  In order to co-exist simultaneously in the spatial position that Duchamp depicts in his poster, the individual cubes that Duchamp photographed would have to have interpenetrating surfaces, edges and vertices--a completely different scenario and physical reality from Duchamp's story of photographing free falling cubes.

 

Step 1    Look at the Poster itself

Click to enlarge
Figure 2
Numbered diagram of the Poster for the Third French Chess Championship (1925)
Figure 3
Oscar Reutersvärd, The Impossible Tri-Bar, 1934

Examine Figure 2 and more specifically cube 2 or cube 11.  The shapes of these cubes, as well as others, appear to be anomalous.  In other words, these objects are not symmetrical cubes with six square sides, at right angles to each other and depicted with edges that follow all the rules of perspective, as would be captured by a photographic lens.  Cube 2's black top square appears smaller than the vertical length of its cream colored square, instead of the same size and symmetry as in our expectation and prior experience of cubes drawn in perspective.  We note the same situation for cube 16.  The pinkish brown cube's vertical square (on the right side) seems taller than wide, when carefully compared to the shape of the top black square.  The more you study these individual cubes by observation alone, even without test or measure, the more maddening the subtle feeling of contradiction becomes--from "yeah they're cubes" to the eye, to "what the hell, something is wrong with these cube shapes when I compare the squares to each other more carefully" in the mind.

We noted the similarity between the shifting sense from distortion to regularity (or non-cubes to cubes) in Duchamp's Chess Poster, and a class of optical illusions called "impossible figures" and named by Penrose and Penrose in the 1950s (R. R. Shearer, "Marcel Duchamp's Impossible Bed and Other "Not" Readymade Objects," Part I and Part II)(3) Impossible Figures, such as "The Impossible Tri-Bar" discovered by Oscar Reutersvärd in 1934, (See figure 3), characteristically capture us in a cycle of acceptance based on familiar visual cues, followed by a looping back to rejection resulting from nagging contradictory information.  Then, after further mental examination, we again visually accept, but then again reject, what we see, ad infinitum.  Nigel Rogers, in his book Incredible Optical Illusions, writes about the tri-bar figure: "All those sides appear to be perpendicular to each other and to form a neat, closed triangle.  But when you add up the sums of their three right-angled corners, you reach a total of 270 degrees--that is 90 degrees more than is mathematically possible" (62).(4)

In other words, Reutersvärd squeezed into his representation (and into triangles themselves which, in Euclidean space, are defined as limited to 180 degrees) more  degrees of freedom than would be allowed by real 3D space.  The paradoxical positionings in Reutersvärd's impossible cube drawings (1934, Fig. 4; 1934 Fig. 5; 1940 Fig. 6) remind one of Duchamp's 1925 chess poster cubes. In fig. 5, as you look at the three cubes--you must ask how the two lower cubes can be equal in height at the bottom and of such different heights at the top, yet still be the same size all at the same time?  Since Reutersvärd has been credited as the first discoverer and developer of Impossible Objects (before Escher in the 1950s), the chess poster indicates that Duchamp himself was actually first, having predated Reutersvärd by at least nine years. (Shearer previously argued that Duchamp's impossible bed in the Apolinére Enameled work of 1916-17, indicates that Duchamp already understood the concept of impossible objects, and the optical illusions based upon them, eighteen years before Reutersvärd's discovery in 1934 (see Shearer, Part I and Part II.)

Click to enlarge
Figure 4
Figure 5
Figure 6
Oscar Reutersvärd, Hommage à Bruno Ernst, perspective japonaise nº 293 a,
Colored Drawing, 1934
Oscar Reutersvärd,
Opus 1 nº 293 aa
, 1934
Oscar Reutersvärd, opus 2B, 1940

 

Step 2       Place blocks in position

Using SoftImage 3D modeling and animation software as a tool, we placed 21 red/blue/green blocks, following the pattern of the falling cubes in Duchamp's poster (see Fig. 7A, a video computer animation of our 3D model of red/blue/green shaded cubes, and Fig. 7B an illustration of our 3D model cubes in the places determined by Duchamp chess poster blocks).

click to see video animation (QT 187KB)
download QuickTime Player
click to enlarge
 
 
Figure 7A
Figure 7B
 
The computer animation of 21 red/blue/green shaded cubes following the pattern of the falling cubes in Duchamp's poster
An illustration of our 3D model cubes in the places determined by Duchamp chess poster blocks

 

Step 3       Note and then characterize the differences in ten locations

The striking difference in relationships among cubes that we immediately saw when we tried to arrange our red/blue/green blocks into Duchamp's beige/pinkish brown/black cubes, pattern shows the necessity for imbedding the cubes into each other.  With this new arrangement, the odd distortions in the original poster disappeared (see Fig. 8A & Fig.8B, a video animation that circles ten embedded locations and then magnifies the circled area, both in the original poster, and in our 3D model arrangement for making comparisons, and a still image that can be enlarged for study.) »Next

click to see video animation (QT 1.2MB)
Click to enlarge
Figure 8A
Figure 8B
A video animation that circles ten embedded locations and then magnifies the circled area, both in the original poster, and in our 3D model arrangement for comparisons
A still image from the video animation that can be enlarged for study

 

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Notes

 

1. Arturo Schwarz, Complete Works of Marcel Duchamp, revised and expanded paperback edition
(New York: Delano Greenidge Editions, 2000) 708.

2. Francis M. Naumann, Marcel Duchamp: the Art of Making Art in the Age of Mechanical
Reproduction
(Ghent, Amsterdam: Ludion Press, 1999) 101, 103.

3. Rhonda R. Shearer, "Marcel Duchamp's Impossible Bed and Other "Not" Readymade Objects:
A Possible Route of Influence From Art To Science," Part I & II, Art and Academe 10,1 & 2 (Fall 1997; Fall 1998)
<http://www.artscienceresearchlab.org/nav/articlesf.htm>.

4. Nigel Rodger, Incredible Optical Illusions: A Spectacular Journey through the World of the Impossible
(London: Quarto, Inc., 1998) 62.

 

Figs. 1, 2, 4, 7A
©2002 Succession Marcel Duchamp, ARS, N.Y./ADAGP, Paris.
All rights reserved.