page1

Duchamp's Perspective:
The Intersection of Art and Geometry

by Craig Adcock

click to enlarge

Figure 1

Marcel Duchamp, Three Standard Stoppages, 1913

Marcel Duchamp's readymade, but "not quite," as he called the Three Standard Stoppages (Fig. 1), is a highly ramified work of art.⁽¹⁾  The pieces of string used in its construction are related to sight lines and to vanishing points.  In addition to their ostensive references to perspective and projective geometry, the Stoppages allude to happenstance.  They are perhaps the artist's best known work that incorporates uncertain outcomes into its operation.  (In one of his Green Box notes, Duchamp says that the Stoppages are "canned chance.")⁽²⁾ To make the work, he glued three pieces of string to three narrow canvases painted solid Prussian blue.  (Each string had a different randomly generated curvature.)  He then cut three wooden templates to match the shapes of these "diminished meters."⁽³⁾

click still images to enlarge
Figure 2	Figure 3
Marcel Duchamp, Network of Stoppages, 1914	Marcel Duchamp, Bride Stripped Bare by Her Bachelors, Even, 1915-23

As this description indicates, the piece was quite unusual physically, and it was conceptually unprecedented.  In terms of his personal development, Duchamp said the work had been crucial: "... it opened the way--the way to escape from those traditional methods of expression long associated with art. ...For me the Three Standard Stoppages was a first gesture liberating me from the past."⁽⁴⁾ Duchamp used the Stoppages to design the pattern of lines in his painting Network of Stoppages (Fig. 2) and then, after rendering this plan view in perspective, transferred it to The Bride Stripped Bare by Her Bachelors, Even (Fig. 3).  In the Large Glass, as the Bride Stripped Bare . . . is also known, the "network" comprises the "capillary tubes," iconographical elements that connect the "nine malic molds."⁽⁵⁾ The Three Standard Stoppages, the Network of Stoppages, and the Large Glass are associated with one another through geometrical projection and section.  Duchamp's approach, with respect to establishing their mutual relationships, is complex.  He not only redrew the Network of Stoppages in perspective so that he could incorporate the scheme into the imagery of the Glass, he also recast physical counterparts of the Stoppages into the actual structure of the Glass:  the three plates used in the Three Standard Stoppages are conceptually related to the three narrow sections of glass used to construct the "garments" of the Bride (Fig. 4).  In each work, two plates are in green glass, and one is in white glass.⁽⁶⁾  The strips of glass at the horizon line of the Large Glass are seen edge-on, an arrangement comparable to looking down into the box of the Three Standard Stoppages with the sheets of glass inserted into their slots.  To my knowledge, this relationship was first pointed out by Ulf Linde:

click to enlarge

Figure 4

Marcel Duchamp, Bride Stripped Bare by Her Bachelors, Even (Detail:The "garments" of the Bride), 1915-23

Figure 5

Marcel Duchamp, Chocolate Grinder, No. 2, 1914

Although some of what Linde says here is unclear, at least to me, it is nonetheless suggestive, especially his proposition that the Stoppages are hidden in the Bride's clothing.  Duchamp's use of different colored glass in just the same way in both applications (and the colors are more apparent when the glass plates are seen edge-on) indicates that he somehow meant for the Stoppages and the Bride's "garments" to be linked together.  I believe that their most important affiliation is perspectival:  the vanishing point at the horizon line of the Glass is tied to the "garments" through geometry.

In a note from the Box of 1914 that was subsequently republished in the Green Box, Duchamp explains that pieces of string one meter long were to be dropped from a height of one meter, twisting "as they pleased" during their fall.  The chance-generated curvatures would create "new configurations of the unit of length."⁽⁸⁾  Although we do not know exactly how he constructed the work, we do know that he almost certainly did not use this method.  The ends of the pieces of string in the Stoppages are sewn through the surfaces of the canvases and are attached to them from behind.⁽⁹⁾  Presumably, Duchamp sewed down the strings, leaving them somewhat loose, jiggled and jostled them back and forth until he obtained three interesting curves, and then glued the segments to the canvases using varnish.  Sewing would not have been out of keeping with his general working methods, especially since he was also at this time (1914) sewing thread to his painting Chocolate Grinder, No. 2 (Fig. 5).

Duchamp wanted to relate his various works to each other.  The moving segments of thread in the Three Standard Stoppages are conceptually similar to the moving lines and shapes in his cubo-futurist paintings.  They are also conceptually similar to the parallel lines on the drums of the "chocolate grinder," which can, in their turn, also be related to the chronophotographic sources of the earlier paintings.  Chronophotography was among Duchamp's primary interests during this period.⁽¹⁰⁾  What I have in mind here can be seen by comparing Duchamp's works with Étienne-Jules Marey's images of moving lines (Figs. 6 and 7).  These kinds of time-exposure photographs not only recall such paintings as Sad Young Man on a Train (Fig. 8) and Nude Descending a Staircase, No. 2 (Fig. 9), but also the Three Standard Stoppages and Chocolate Grinder, No. 2.⁽¹¹⁾ >>Next

click still images to enlarge
Figure 6	Figure 7	Figure 8	Figure 9
Étienne-Jules Marey, Image of moving lines	Étienne-Jules Marey, Image of moving lines	Marcel Duchamp, Sad Young Man on a Train, 1911	Marcel Duchamp, Nude Descending a Staircase, No. 2, 1912

page 1 2 3

Figs. 1-5, 8-9
©2003 Succession Marcel Duchamp, ARS, N.Y./ADAGP, Paris. All rights reserved.