1.1. The Bride stripped bare by her Bachelors, even

The Bride stripped bare by her Bachelors, even commonly known as The Large Glass (or simply The Glass) is the masterwork of Marcel Duchamp, and it is also one of the most representative and influential works of art of the 20th century. Duchamp spent several years completing his project, but the work was left unfinished in 1923. The actual execution of the work starts in 1915, but the first ideas date back to the Summer of 1912.

Duchamp planned each detail of this complex work, and left a huge corpus of notes, sketches, and blueprints, documenting not only his intentions and the desired final outcome, but also the different executive techniques for each single part of the Glass. These notes were published by Duchamp himself in three main collections.

The first one, edited in 1914, commonly known as The 1914 Box (Fig. 1) (because of the Kodak box containing the reproductions of the originals) contains sixteen notes and drawings; the second collection, dated 1934, is known as The Green Box (Fig. 2) (because of the green color of its binding) and contains a larger group of notes and sketches; finally, the third collection, named A l’infinitif but commonly known as The White Box, (Fig. 3) edited in 1966, contains for the most part a quantity of notes regarding mathematical
speculations on the fourth dimension, directly related to the Glass and other works. Duchamp asserted that this huge apparatus of notes must be considered an integral part of the Glass.
click to enlarge

Figure 4
Marcel Duchamp, Bride’s Domain, in the
Large Glass(detail), 1915-23

Figure 5
Marcel Duchamp,Bachelors Apparatus, in the
Large Glass (detail), 1915-23
    

Two main parts constitute the Glass: the higher and the lower ones. The higher part is the realm of the Bride, (Fig. 4) and according to Duchamp’s intention, it depicts the 2D
projection of a 3D shadow of a 4D Bride. Thus, the realm of the Bride is intended to be a true 4D realm, which however cannot really be seen, since it is as depicted on a 2D support (the sheet of glass). The lower part is the realm of the Bachelors (Fig. 5) or the Bachelor apparatus (or utensil). In contrast with the Bride’s realm, the Bachelor’s realm is a 3D world. Thus it is imperfect in comparison with the 4D higher realm. In a note belonging to the White Box (but already issued with some minor variants in the Green Box), Duchamp wrote:

Principal forms, imperfect and freed
The principal forms of the bachelor apparatus or
utensil are imperfect:
Rectangle, circle, square, parallelepiped, symmetrical handle; demisphere.-i.e. these forms are mensurated (interrelation of their actual dimensions and relation of these dimensions to the destination of the forms in the bachelor utensil.)
In the Bride – the principal forms will be more or less large or small, no longer have mensurability in relation to their destination: a sphere in the Bride will have any radius (the radius given to represent it is “fictitious and dotted.”)

Likewise, or better still, in the Pendu Femelle parabolas, hyperbolas (or volumes deriving from them) will lose all connotation of men-surated position. ⁽¹⁾

Thus, the two parts of the Glass represent two distinct realities. The lower realm is imperfect and only tries to emulate the higher dimensionality of the Bride’s realm by means of expedients and tricks (very effective, as we shall see).

These tricks are largely based on perspective representations and on elementary geometric transformations. These transformations will gradually become more and more general, and, as we pass through the threshold of the horizon (the area which divides the two parts of the Glass) from the lower half into the 4D realm of the Bride (following the pathway described by Duchamp), we finally reach a world where, abandoning any metrical trait of the objects, only more general geometrical transformations take place: the topological ones. The subject is already thoroughly discussed by scholars ⁽²⁾.

Perspective is not only the drawing system used by Duchamp to compose the lower part of the work, but also (and better) perspective in itself is one of the most important themes of the Glass. Indeed, we have quite explicit statements by Duchamp, such as the following,
given during a famous interview with Pierre Cabanne, that supports this contention:

Duchamp: […] In addition, perspective was very important. The “Large Glass” constitutes a rehabilitation of perspective, which had then been completely ignored and disparaged. For me, perspective became absolutely scientific.

Cabanne: It was no longer realistic perspective.

Duchamp: No. It’s a mathematical, scientific perspective.

Cabanne: Was it based on calculations?

Duchamp: Yes, and on dimensions. These were the important elements. […] ⁽³⁾

Scholars largely speculated (and still speculate) on the meaning of such a rehabilitated perspective, no longer having a realistic purpose, being instead a mathematical and
scientific procedure.

Duchamp’s authoritative biographer Calvin Tomkins wrote for instance:

Vanishing-point perspective, which gave the illusion of three dimensions on a two dimensional surface, had been abandoned by modern artists who wanted their art to be a real thing rather than an imitation of reality. Why, then, did Duchamp, who certainly shared that ambition, choose to master such a discredited device? Was he looking for a mathematical formula through which he could actually evoke the presence of a fourth dimension? Whatever serious ambition he may have had along these lines he abandoned soon enough.⁽⁴⁾

Rhonda Roland Shearer suggests that Duchamp could have used a complex technique based on the overlapping of several different perspectives at once. According to her, such
a technique could explain both some strange features in the historical photos of the readymade and the difficulties one encounters as he or she tries to recreate the perspective of the lower half of the Glass, starting from its original blueprint (plan and elevation)⁽⁵⁾. She says for instance:

Most Duchamp scholars have either accepted or praised Duchamp’s perspective skills. The problem remains, however, that I and a few other scholars have actually made 3-D models from Duchamp’s plans
— and none of us can find any one perspective projection view that matches Duchamp’s perspective drawings! Moreover, the process of trying to recreate the Large Glass perspective drawing from what a viewer would see of the 3-D model via perspective (equivalent to what one eye or camera lens sees) quickly becomes maddening. When you fit one part of the Large Glass model to its projection in Duchamp’s perspective drawing (say; part A, the ellipse in one wheel of the Chocolate Grinder, for example — see illustration 49A), the rest (parts B through Z) immediately fall out of place. We lose the fit of part A, and all the other parts C through Z, once part B is matched — etc.⁽⁶⁾

A few lines above, we also read:

My discovery that the strangely distorted Chocolate Grinder uses the same systematic characteristic approach also found in the hatrack, coatrack and urinal (and a large set of other examples not discussed in this essay) returns us to Duchamp’s words that I used at the beginning of this essay — a quotation that now bears repeating. ⁽⁷⁾

Shearer shows a complete map of “at least” 43 different viewpoints which could have been used by Duchamp for the perspective of the Glass. Unfortunately, Shearer’s article is mainly focused on Duchamp’s readymades. The procedure used to inspect the Glass’s perspective is only briefly described, and only supported by means of 3D animations.

In the present paper, I will describe with some details the procedures I used to check the perspective of the Bachelor apparatus and will present and briefly discuss the outcomes reached.

In addition, considering some serendipitous discoveries I made by moving the elements of the Bachelor, as a further thesis, I would like to point out that the internal motions of the Bachelor apparatus (carefully planned and described in the Notes by Duchamp himself)
could be considered ways that permit the Bachelors to emulate the higher dimensionality of the Bride.
 

 

1.2. General procedures and remarks

Cabrì Géomètre II⁽⁸⁾ is the software I
used to reconstruct the perspective of the Glass. It is a world wide known pedagogical software, commonly used to teach geometry in high schools, thus it is not specifically oriented to graphic applications or to professional 3D rendering, but instead it is aimed at building geometric objects (even very complex) which can be dynamically transformed according to well defined geometric constructions and rules.

The basic objects that Cabri furnishes are the basic geometric elements of Euclidean geometry, as usually taught at school, such as points, straight lines, segments, angles, polygons, conics, and so on.

Cabri works essentially on the plane, but following the rules of projective geometry, it makes it possible to represent 3D objects in perspective (or even higher dimensional objects, such as a hypercube, for instance).

Just such a feature interested me, as I intended to verify Duchamp’s statement about his mathematical, scientific use of perspective. Indeed my concern was to reconstruct the correct perspective of the Glass, starting from the detailed and precise metric information we read in the autograph sketches of the elevation and plan of the Bachelor apparatus (Duchamp carefully gave us even the exact position of the vanishing point).

As a second step, I intended to compare the aseptic geometric drawings obtained with Cabri, with the reproductions of the actual Glass and of its parts. To do that, I used a second tool developed for using Cabri in Internet-like environments: CabriJava⁽⁹⁾.

This program allowed me to superimpose Cabri figures on the corresponding reproductions by Duchamp and to adjust them in a continuous way until the figures and the reproductions matched (or did not).

Here is the key question: Which kind of adjustment is allowed in order to state that Duchamp’s perspective matches the mathematical construction?

To answer that question, let us consider the perspective construction of a simple parallelepiped. Once we have the metric values for both the plan and the elevation of the parallelepiped (refer to Applet 1)and once we choose the vanishing point VP and the ground line (i.e. the elements given by Duchamp with the sketches of the plan and the elevation of the Bachelor apparatus), a degree of freedom still remains: following the standard perspective rules, we have to choose a couple of corresponding straight lines r and r’, for example the diagonal AC and the corresponding diagonal A’C’ ⁽¹⁰⁾.

Applet
1 depicts the situation. You can drag the straight line r’ to modify the figure, but always obtaining a perspective consistent with the given data, i.e., the metric of the parallelepiped, its position in the space, and the position of the vanishing point and the ground-line.

Perspective constructions and adaptations of Duchamp’s originals have been made for the overall view of the Bachelor apparatus and for each of its main elements. We shall discuss them later with some details.Fig. 6 shows how Duchamp’s elevation and plan sketches were inserted in Cabri.⁽¹¹⁾.

Fig. 7 and Fig. 8 illustrate the two basic steps followed to construct the perspective rendering of an A point in the plan sketch, passing through the A’ image of A on the ground-plane, and then elevating it at the A’’ position, according to the position of A in
the elevation sketch.

click to enlarge

• 
  
  Figure 6
  Duchamp’s elevation and plan sketches
  inserted in Cabri
• 
  
  Figure 7
  Two basic steps illustrating the construction of the perspective rendering
  of a single point, given its position in plan and elevation sketches
• 
  
  Figure 8
  

 

2.1. The overall view

Let us start with the perspective of the overall view.

To make pictures more suitable for the internet (therefore with not too heavy files) the elements of the Bachelor apparatus are inserted schematically, just to check the correctness of their mutual positions according to the rules of perspective. The corresponding details for each inserted element are checked in separate figures.

click to enlarge

Figure 9
Marcel Duchamp, The Bride stripped
bare by her Bachelors, Even, 1913

Figure 10
The straight line r’

The overall perspective is compared with both the Glass and the preparatory sketch of 1913 named The Bride Stripped Bare by Her Bachelors, Even, like the Glass itself. We shall refer to it simply as the 1913 Sketch (Fig. 9).For the lower part of the actual Glass, see below Applet 2 and Applet 3). This double superimposition is necessary because the important element called the Toboggan, one of the most difficult pieces to render in perspective, is actually absent in the Glass (remember that it was left unfinished by Duchamp) while it is present in the 1913 Sketch.

In both Applet 2 and Applet 3, CabriJava has some problems in displaying the ellipses of the Water Mill, which indeed are incomplete, and in addition an unexpected straight line is drawn starting from them. The same problems still remain for some curves of the Toboggan. However, despite these problems, I think that Applet 2 and Applet
3 will help understand the overall perspective.

Why? Look at the straight line r’ in Fig. 10

r’ is the perspective correspondent of the straight line r in the plan, which passes through the bottom-left point of the so called Chariot (the parallelepiped containing the Water Mill) and through the centre of the circle representing the Chassis of the Chocolate Grinder. The choice of line r’ is free, but according to that choice we obtain different perspectives. Thus, by dragging the blue line in Applet 2 and Applet 3, you will see how the perspective could change accordingly, always remaining consistent with Duchamp’s data ⁽¹²⁾.

Anyway, the problems of the applets are definitely overcome with Fig. 11 and Fig. 12 (which are static), where the geometrical perspective of Cabri is correctly displayed on the background of Duchamp’s originals.
click to enlarge

 

• 
  Figure 11
  The geometrical perspective of
  Cabri correctly displayed on
  top of Duchamp’s original
  1913 sketch and the lower half of the Large Glass
• 
  Figure 12
  The geometrical perspective
  of Cabri correctly displayed
  on top of Duchamp’s original
  1913 sketch and the lower half of the Large Glass

Look at Fig. 11. The major discrepancies between 1913 Sketch and the Cabri figure are on
the right side of the picture:

one of the blades of the Scissor (the lower on the right) doesn’t match perfectly with its counterpart⁽¹³⁾;

The right Sieve (the Sieves are the conical shapes just under the Scissor) is slightly in a lower position relative to the Cabri figure;

the Toboggan (the spiralling line on the right) is slightly shifted down.

In contrast, the left part of the 1913 Sketch matches quite well the remaining elements of the Cabri figure particularly the ellipses of the Chocolate Grinder. The left Sieve also matches perfectly the one in the Cabri figure.

In my opinion, some trivial explanations can be considered for the mismatches: maybe the reproduction of the 1913 Sketch used here is slightly rotated in the clockwise sense, around a centre located somewhere near the centre of the Chariot; this could explain why the
most evident discrepancies are on the right half of the picture, whereas the better matching is on the left. A second explanation could be that the sheet used by Duchamp for the 1913 Sketch could be somehow deformed. Indeed the squaring of the drawing (as I saw in all the photos I could examine, including the one used here) is not perfect.

Consider now the singular shape of the Toboggan. It is a strange mix of semicircles and semiellipses disposed on oblique planes: its correspondence with the Cabri figure, even though imperfect, is quite shocking; remember, indeed, that Duchamp drew it by hand;
it means that the drawing was made point per point. The exact placement of even just one of those points (starting from its position in plan and elevation) can be considered a very difficult task for anyone having only an intuitive knowledge of projective geometry.

click to enlarge

Figure 13
Possible construction lines of the Toboggan

To have the right idea of such difficulties look at Fig. 13 which displays the construction lines necessary for just one point for each of the four arcs forming the Toboggan (thus multiply these construction lines al least 4-5 times).

Consider now Applet 3 and the corresponding static Fig. 12, which superimposes the Cabri
figure on the lower part of the actual Glass.

Look at Fig. 12. The reproduction of the Bachelor apparatus matches quite well the Cabri
figure: look especially at the Scissor and the Sieve on the right, which fit a lot better with Cabri figure than the ones of 1913 Sketch. Also, the ellipses circumscribing the Water Mill seem to match it perfectly.

Consider finally the supports of the Chariot named the Runners with their four semicircular shapes. They scarcely match the Cabri figure. Note however that the Runners were not
yet present in the sketches of plan and elevation, thus we have no measures for them. I simply used four semi-circumferences without making any attempt to recreate the correct image.

In conclusion, the inspection of the overall perspective seems to suggest that the reciprocal positions of the main elements of the Glass are consistent with the hypothesis that Duchamp correctly used the rules of perspective. It is worth noting in particular his skill in managing very complex constructions such as the one for the Toboggan, especially considering that he was self-trained in perspective.

 

2.2. The Chariot with the Water Mill, the Capillary Tubes and the Cemetery of Uniforms and Liveries

The simplest solid to render with perspective is the parallelepiped with edges parallel and perpendicular to the horizon: it is the case of the Chariot. Not equally trivial is to draw the wheels of the Water Mill contained in the Chariot. Nonetheless the perspective rendering of this elements is almost perfect.

Applet 4 shows how the geometric construction fits the corresponding detail of the Glass. Because of some possible problems with CabriJava in displaying objects, we shall refer to Fig. 14, which is static, but displays the picture correctly.Here is a problem: the overall framework of the Chariot is made by rods which actually have thickness and width, whilst in Duchamp’s preparatory sketches of plan and elevation they are considered as pure linear elements without thickness and width. This implies a quite arbitrary superimposition of Cabri figure on the Glass picture (unless one considers a number of different possible assumptions regarding the passage from the sketches to the actual Glass, which I didn’t).

Apart from this problem, the perspective created with Cabri matches quite well the parallelepiped of the Chariot.

Observe now the wheels of the Water Mill.

click to enlarge

Figure 14
Static image
showing how the
geometric
construction fits
the
corresponding detail of the Glass

First, let us consider the ellipses circumscribing the Water Mill (in red in Fig. 14): they touch exactly the peripheral points of each paddle (as we already noticed in the overall perspective of the Bachelor apparatus), except for the paddle in the foreground. But there is no error here: indeed, Duchamp preferred to clip the parts of the paddles which fall beyond the limits of theChariot.

Look now at the ellipses (in blue) touching the internal points of each paddle. Duchamp didn’t insert them in the sketches of plan and elevation. Therefore, we don’t know the actual radius of such circles. Just for this reason, I inserted in Applet 4 the red large point. As the user drags it vertically, the radius of the internal Water Mill wheels varies accordingly. The match with the Glass is satisfactory.

Consider now the eight spokes of the Water Mill wheels. I drew them under the assumption that they formed a regular octagon, and placing two of them along a vertical line. They also perfectly match the originals.

Some minor mismatching are there with the paddles of the Water Mill, but they are not severe, in any case.
Let us finally consider the perspective of the nodes of the so called Capillary Tubes, from which the 9 Malic Moulds hang, forming the so called Cemetery of Uniforms and Liveries.

In the sketches of the elevation and plan, the positions of the 9 numbered nodes are present, but, unfortunately, some measures are missing, namely those necessary in the plan sketch. Therefore I deduced them by measuring and scaling the distances directly on the sketch. The outcome displayed in Applet 5 is quite unsatisfactory. In particular, the nodes (and accordingly the Uniforms) nos. 2, 3, and 7 are clearly misplaced, whereas the remaining ones are only approximately right. Even by dragging the red diagonal (which modifies the perspective viewpoint), the drawing remains wrong (at least with respect to the preparatory sketches).

In conclusion: the perspective of the Water Mill shows some minor mismatches with the Cabrifigure; namely: some paddles seem to be not properly drawn. For the rest, the geometric construction easily fits the corresponding parts of the Glass.

In contrast, the nodes of the Capillary Tubes are misplaced. We must consider however, that the sketches are quite reticent regarding this detail, and we cannot rule out the possibility that the Capillary Tubes were more carefully planned before the execution of the actual perspective of the Glass.

 

2.3. The Chocolate Grinder

The Chocolate Grinder is often said to have the most problematic perspective. Indeed, it seems “strangely distorted” according to Shearer⁽¹⁴⁾.In a second, stimulating essay, written in collaboration with Stephen Jay Gould, it is argued that:

Scholars have simply and uncritically accepted Duchamp’s claim that he rigorously used these principles in his major works. Ironically, however, no one who actually attempted the experiment has ever been able to render the bachelor machinery of the Large Glass under classical perspective, unless they alter Duchamp’s own drawings and therefore conclude that he was not, after all, a very accurate geometer. The Chocolate Grinder, especially, does not seem properly drawn, and no one has been able to show how the device might turn without the wheels interpenetrating and thus, to make the metaphor literal, grinding to a halt.⁽¹⁵⁾

click to enlarge

Figure 15
Marcel Duchamp, Chocolate Grinder, No. 2 ,
1914

Figure 16
Marcel Duchamp, Chocolate Grinder, No. 1 ,
1913

Figure 17
Geometric features of the Chassis and the
Rollers

The second and definitive painting of the Grinder (namedChocolate Grinder, No. 2 (Fig. 15), dated 1914) is quite different relative to the first one (dated 1913) (Fig. 16), not only because it openly shows its second important identity (connected with electromagnetism and wireless telegraphy), discussed by Linda Henderson⁽¹⁶⁾, but also because (as we shall see further on in this section) it acquires well-defined perspective construction, unlike the first version, whose perspective is quite problematic.

The first problem to solve in order to check the perspective of the Grinder, is to understand its geometry. Indeed, the sketches of plan and elevation are quite incomplete.

Essentially the Grinder is formed by three rollers (which seem to be frusta of a cone) placed on a Chassis (a cone with altitude much smaller than the radius of its base).

Duchamp’s sketches give us the complete measures necessary to reconstruct the Chassis, but for the roller, only two measures are given: the diameter of the circle of the major base and the length of the generatrix. No measures of angles are given. Reconstructing the rollers without additional assumptions is thus impossible.

At first I thought that the roller had to roll without sliding on the Chassis, and (of course) always rotating on theChassis itself, without leaving it. Geometrically speaking, this implies that the vertexes of the cones of each roller must coincide with the vertex of the cone of the Chassis; but looking at the actual Grinder we immediately understand that it is not the case: their vertexes clearly lay far beyond the vertex of the Chassis(Fig. 17). Thus the rollers grind the chocolate by sliding on the Chassis. Thus the assumption about the kind of friction of the rollers on the Chassis was wrong ⁽¹⁷⁾.

If we start from the measures of the roller given by Duchamp (radius of the major base and length of the generatrix), accepting their conical shape, and giving the angle the major base forms with a horizontal line, then the frustum of the cone is completely assigned (see Fig. 17).

In order to find the exact value for the measure of the unknown angle, I inserted in the Cabrifigure a corresponding further degree of freedom, allowing the user to drag the line corresponding to the major base of the roller in the elevation.

click to enlarge

Figure 18
Contact lines of the rollers with
the Chassis

Duchamp’s sketch of the plan doesn’t contain information about the mutual positions of the rollers and the exact positions of the contact points of the rollers with the Chassis. Thus, further assumptions must be made. Fig. 18 shows the simplest assumption (plan view of theChassis): the axes of the rollers form 120° angles, and one of them is parallel to the ground-line of the perspective. This hypothesis will prove exact (except for minor mismatches indicated below).

Finally let us examine Applet 6, which superimposes Cabri figure of the Grinder onto the 1914 picture Chocolate Grinder (No.2). I used the 1914 picture instead of the actual Grinder of the Glass, because we know that the latter was obtained by simply transferring on glass the former; thus using the 1914 picture I avoided considering those mismatches possibly derived from the transfer on glass, maintaining instead the focus on possible true perspective mismatches.

The outcome is once again unexpected, because the matching is almost perfect.

Applet 6 allows the user to see that:

The two ellipses corresponding to the Chassis and to the Necktie match well the Cabri figure (the ellipses of the Chassis are slightly smaller than the corresponding ones in the Cabri figure). The blue point on the top of the Grinder axis (or Bayonet) over the Necktie also matches well the point where the handle of the Necktie intersects the axis of the Grinder.

So good is the matching of the fixed parts of the Grinder with the Cabri figure that we see even the same very small portion of the Chassis visible in its higher part between the rollers!

Let us consider now the rollers. The grey line in the elevation, running along the major base of the roller allows the user, by dragging it, to choose the better unknown angle we talked about above (my best estimate is 81,9°).

The vertexes of the equilateral triangle (in the little circle under the Grinder) indicate the positions of the rollers (namely their contacts with the Chassis). The green point can be dragged in order to rotate the roller, and to test its matching with the original picture for each of the three positions.

In two cases (the two rollers in the background), the matching is almost perfect, whereas the roller in the foreground shows a minor mismatch, because the ellipse corresponding to its major base is slightly larger than in the Cabri figure.

In particular, note the blue points that indicate the center of the bases of the frustum of the cone. In the case of the roller to the right, the blue point coincides exactly with the insertion point of the roller on its axis. In the case of the roller in the foreground, one of the blue points matches perfectly the center of the major base of the roller.

click to enlarge

Figure 19
Tentative position
of the Louis XV legs
as vertex of an
equilateral triangle

Figure 20
One only visible leg
under the
assumption of
Fig. 19

Let us now consider the Louis XV legs of the Chassis. At first I thought that, because of the equilibrium of the whole device, the three legs had to be placed at the vertices of an equilateral triangle. Accordingly, the vertex corresponding to the leg in foreground is such that the exact position of the equilateral triangle must be as in Fig. 19.
Look now again at Applet 6. The three grey vertical segments and the corresponding cyan extremities indicate the position of the legs of the Chassisin case the legs were planned to be positioned as in Fig. 19. The background legs are clearly misplaced, whatever was their planned shape. The only visible leg in the perspective drawing would be that in foreground, whereas the others would be covered by the Chassis, as in Fig. 20.

Fig. 20 shows the Grinder with one only leg: even though appropriate for both the equilibrium and the perspective, it makes the whole Grinder seem to be supported by one only leg, which, of course, would be impossible.

The addition of the background legs makes the drawing acceptable for the eyes, but wrong for perspective. Indeed, in order to make the perspective we see in Chocolate Grinder (No.2), the background legs wouldn’t be placed according to Fig. 19 (the only disposition ensuring the equilibrium of the device): they have to be slightly shifted forward, which however makes the equilibrium impossible.

So far we have faced something paradoxical: if you pay the tribute required by the retina, you will obtain a thing which cannot stand up (a quite Duchampian statement, we have to acknowledge). Here I emphasize the Duchampian key concept of instability. Interestingly, a similar kind of paradox between retinal and mental data, with similar conflict between equilibrium and instability concepts, has been already discussed in terms of the Bicycle Wheelby Shearer⁽¹⁸⁾.

click to enlarge

Figure 21
A further investigation of the perspective project
in the 1913 Sketch

A further investigation of the sketches makes things clear. In both the 1913 Sketch and the elevation, we can see the legs actually drawn (see Fig. 21). In fact nothing tells us that they are disposed as an equilateral triangle; this misleading assumption was made because the visible legs are three, but very probably they actually are four, disposed as a square, like in Fig. 21. Indeed three of them are clearly visible in both of Duchamp’s sketches, whereas the fourth would-be leg (the posterior one) couldn’t be seen in neither of them: in the elevation because it is exactly behind that one in the foreground, and in 1913 Sketch because it is hidden by the Chassis. But this fourth leg is necessary for the equilibrium. According to this new assumption Duchamp’s perspective would turn out to be correct, and the equilibrium of the device would be safe. On the other hand, no actual datum contradicts this hypothesis of four legs, which in my opinion is thus confirmed. In conclusion: the perspective rendering of the legs is correct.

Consider now the threads sewn through canvas in the Chocolate Grinder, (No. 2) then carefully reproduced in the Glass.

Applet 7 shows the roller completed with similar threads, and helps check the correctness of their orientation. It proved to be consistent with the adopted perspective in two cases (the right and the foreground rollers) but also revealed some minor mismatching in the third case (the roller in background). In my opinion just the wrong perspective of the threads of the background roller makes the overall perspective of the Grinder difficult to be accepted for the eye.

To convince that what we said about the perspective of the Grinder No. 2 holds its validity in the passage to the Glass, look at Applet 8, which displays the Cabri figure superimposed on the actual Grinder of the Glass. Once again the matching is almost perfect.

Before concluding this section, I want to say a few words comparing the perspective rendering of both the first and the second version of the Grinder.

Applet 9 clearly shows that the perspective of the first Grinder is definitely wrong (at least accepting the measures of Duchamp’s sketches and the assumptions I declared above). The user can try to adapt the Cabri figure to the picture of the first Grinder, by dragging either the red diagonal or the green point (which have the same meaning as in Applet 6), but the outcome will be in any case unsatisfactory. Particularly the Necktie and the rollers seem to be totally wrong.Thus we can say that the passage from the first to the second version of the Grinder shows an extraordinary leap in Duchamp’s perspective skill.

In conclusion we can say that despite its strangely distorted view, and in spite of its intrinsic difficulty, the Grinder is one of the best executed elements in the perspective of the Glass. In any case the mismatches revealed above are consistent with the hypothesis that Duchamp drew the Glass according to the ordinary rules of perspective.

Recall Gould’s and Shearer’s statement that : «…no one has been able to show how the device might turn without the wheels interpenetrating…». Look now at Animation 1⁽¹⁹⁾. It shows theGrinder in action. Definitely, the rollers do not interpenetrate as the device is grinding.

Please refresh the page, if the animation stops

Animation 1
2.4. The Sieves or Parasols

click to enlarge

Figure 22
The Yport sketch, 1914

The Sieves (or Parasols) are the conical shapes that are disposed in semicircle behind the Scissor.

Unlike other elements of the Glass, we have detailed sketches which describe not only the measurements and the position of the cones, but also the detailed perspective procedures followed by Duchamp. We can see such perspective sketches and projects in the Green Box. ⁽²⁰⁾ But the most important sketch, drawn at Yport during the summer of 1914, is not published in any of the cited collection of notes. We shall refer to it as the Yport sketch. (Fig. 22)

Particularly, we note the following shortcut Duchamp used to speed his work.

Once the drawing of the base-circle of the first cone was executed by interpolating 8 reference points (clearly visible in the sketch), Duchamp exploited the semi-circumferences where the corresponding points of the other cones lay, and divided them with the vertices of the inscribed dodecagons (which is a quite simple and speedy procedure). As I worked with Cabri, I used the same procedure.

click to enlarge

Figure 23
The actual geometry of the Sieves

The Yport sketch also clearly shows a further detail: the declared altitude of each single cone (we read twelve cm in the elevation sketch) was probably modified by Duchamp on the basis of the geometry displayed in Fig. 23, in turn based on Yport sketch.

The shared altitude CH of the cones is such that the perpendicular to the base AB of the first cone intersects the base of the second one exactly at point C (and similarly for the others as well). Thus, the involved angle being of amplitude 30°, and being OH=23 cm, the measure actually used for the Sieves is CH=13.28 cm.For construction of the Sieves, I followed the geometry of Fig. 23, instead of using the measurements given in the elevation sketch.

Look finally at Applet 10. It shows that, once the best inclination of the diagonal (the red one) is chosen, the matching is perfect.

2.5. Some conclusion about the perspective of the Glass: the static viewpoint

Duchamp composed the Glass by hand and, above all, used absolutely unconventional media, which required him to invent ex novo appropriate techniques of execution. In general, we must suppose that drawing on glass is not as easy as drawing on paper or on canvas, especially if one of the main goals was precision, as in the case of the Glass.Just to have a correct idea of what this could mean, read the following description, regarding the execution of a preparatory study for the Chariot:

His first idea was to etch the design on the glass with fluoridic acid, a powerful corrosive used by commercial glass workers. “I bought paraffin to keep the acid from attacking the glass except where I wanted,” he said, “and for two or three months I struggled with that, but I made such a mess, plus the danger of breathing those fumes, that I gave it up. It was really dangerous. But I kept the glass. Then came the idea of making the drawing with the lead wire – very fine lead wire that you can stretch to make a perfect straight line, and you put a drop of varnish on it and it holds. It was very malleable material, lovely to work with.” (Duchamp used fuse wire, a coil of which was a staple in Paris apartments then.) ⁽²¹⁾.
We also already reminded that Duchamp was substantially self trained in perspective. In a note of the White Box we read:

Perspective.
See Catalogue of Bibliotèque St. Geneviève
The whole section on Perspective :
Niceron, (Father Fr., S.J.)
Thaumaturgus opticus ⁽²²⁾

The note suggests that while Duchamp was working at the library of Sainte Geneviève (1913-14) he read the whole section on perspective, and particularly (at least so we may assume from the note) the treatise on perspective and optics by mathematician Jean-François Niceron (1613-1646), titled Thaumaturgus opticus ⁽²³⁾.

Thus, in the years Duchamp was composing the first elements of the Glass, he also was concluding his education in perspective.

We can obtain the exact measure of his progress in perspective skill in those years by comparing the two versions of the Grinder (dated 1913 and 1914), as we did in section 2.3.

On the other hand, regarding now my reconstruction of the perspective, remember that procedures and tools I used are quite non-professional:

– the used software is perfect to study and teach geometry, but in general not for 3D rendering;

– the reproduction used are photos whose reliability is not certified (think for instance about possible parallax errors or perspective deformations);

– the photos were in addition reduced or enlarged to match the scaled measures I used withCabri, and such adaptations could be imperfect…

These considerations surely reduce each pretension of precision, but at the same time they also reduce the relevance of the minor mismatches revealed above.

Let us finally reconsider the perspective elements of the Glass that we have examined, in order to answer to the question: is the perspective of the Glass canonical (and/or correct)? Are there elements which permit us to hypothesize a non-canonical (and/or incorrect) use of perspective?In my opinion, the only mismatch one can consider a true error, or possibly as a non-canonical use of perspective, is the one regarding the nodes of the Capillary Tubes. For the rest the execution of perspective is quite stunning, especially for some elements such as the Grinderand the Toboggan.I believe that the matching between the geometrically reconstructed perspective and the actual perspective of the Glass is in general good or even perfect in some cases.Let us then reconsider Shearer’s argument. She describes the minor mismatches between computer aided designs and Duchamp’s originals

When you fit one part of the Large Glass model to its projection in Duchamp’s perspective drawing (say; part A, the ellipse in one wheel of the Chocolate Grinder, for example — see illustration 49A), the rest (parts B through Z) immediately fall out of place. We lose the fit of part A, and all the other parts C through Z, once part B is matched — etc.

Her statements can be discussed at two different levels.

At the level of single parts of the Glass, such as the Grinder, the Chariot, and so on (the micro level), I think that her statement is substantially wrong. With the exceptions of the nodes of theCapillary Tubes, the mismatches revealed by the inspection above are completely acceptable and consistent with the hypothesis that the Glass was drawn according to the usual rules of perspective, and must be considered as absolutely minor imprecisions due to Duchamp’s free-hand execution. I believe this conclusion holds unless a unitary theory can be formulated that explains all the mismatches at once.

Shearer proposes a unitary theory of this kind about the perspective of the historical photos of the readymade, but there are no explanations about the way that theory could be extended to theGlass.

Let us pass now to the higher level (the macro level), that of the overall view. Some further preliminary considerations are needed.

I executed Cabri figures in different sessions by separating the principal elements of the Glass.

This procedure risks creating a trivial error: choosing different and mutually inconsistent diagonals (possible diagonals are, for instance, the straight lines r and r’ in Fig. 10) for different figures can generate mistakes (remember that Duchamp’s measures allows such a degree of freedom). This implies the possibility of an overall perspective inconsistency, even if each individual element was rendered in correct perspective. In other words, choosing inconsistent diagonals would be equivalent to choosing different viewpoints. (This possibility agrees to some extent with Shearer’s proposal concerning the presence of several, different viewpoints in the perspective of the Glass).

The same considerations I did for the computer aided reconstruction of the perspective, could be applied to the execution of the actual Glass by Duchamp: remember indeed that the elements of the Glass were added by him one by one (even because each piece had to be executed with an appropriate technique) through successive and separate steps, which could expose Duchamp himself to the same risk of error I was exposed to.

Thus, it was very important to verify the mutual consistence of the details. In the contrary case, it would have been an important evidence for applying Shearer’s theory of multiple viewpoints to the perspective of the Glass (but, in such a case, there would be no evidences for an intentional choice by Duchamp, and consequently we couldn’t rule out the possibility of a simple mistake).

Now, in order to verify the perspective consistence of the single details with the overall view there were two possible ways:

either choosing every time the same couple of diagonal lines (which sometimes was very inconvenient), or choosing different couples of corresponding line, but verifying that they were consistent to each other.

I chose the second way. The check for consistency was done by comparing in each figure the position of the same straight line, namely r’ (refer to Fig. 10).

The check returned a positive response: each diagonal r passing trough the left lower point of the Chariot and the centre of the Chassis in the plan, corresponds to a straight line r’ in the ground plane of perspective, forming the same angle (16.3°) with the ground line. Hence, the details are perspectively consistent with each other and with the overall view.

Definitively, Duchamp used the canonical perspective rules, and mastered them at the highest level.

What is then the meaning of his mathematical, scientific perspective?

Often people think of mathematics as something which deals essentially with numbers. If there are no numbers there is no mathematics.

Remember for instance that after Duchamp’s claim about the mathematical use of perspective, Cabanne asked: «Was it based on calculations?» (we shall consider Duchamp’s interesting reply below), or even recall what Tomkins told about a possible formula.

Now, geometry is mathematics, and I think that Duchamp meant (among other things) that he used thoroughly projective geometry. Try to execute the perspective of the Toboggan to understand how much projective geometry he used.

Let us return to Cabanne and Duchamp dialogue.

Cabanne: Was it based on calculations?
Duchamp: Yes, and on dimensions. These were the important elements.

A few lines below we also read:

I almost never put any calculations into the “Large Glass” ⁽²⁴⁾

but again, a few lines below:

At the same time I was doing my calculations for the “Large Glass” ⁽²⁵⁾

I think that Duchamp used here the word calculations in the more general meaning of mathematical (namely geometrical) operation, construction, deduction: the only true calculations actually necessary for the drawing were the proportions possibly necessary for scaling the measures and a few minor operations ⁽²⁶⁾; for the rest there are only geometrical constructions.

Here, I want to emphasize the second element of Duchamp’s answer: that of dimensions, which of course refers to the fourth dimension.
Remember the already-cited Tomkins’ statement:

Was he looking for a mathematical formula through which he could actually evoke the presence of a fourth dimension? Whatever serious ambition he may have had along these lines he abandoned soon enough.

In other words Tomkins says that, even admitting the attempt to find the mathematical key which could open the door of the fourth dimension, Duchamp soon abandoned it, possibly (I’m hypothesizing) in favor of speculation on non-Euclidean geometry. I don’t agree with Tomkins. Not to diminish the importance of non-Euclidean geometry, but to emphasize the importance of the concept of higher dimensions in relation to perspective.

So far, we regarded Duchamp’s perspective from an eminently static viewpoint, and (consequently, I say) no reference to higher dimensions were highlighted.
The main goal of the remaining part of this article is just to establish a connection between the perspective of the Bachelor apparatus and the emancipated spatiality of the Bride realm, by introducing a new important element: that of motion.

3.1. The Chariot in the fourth dimension

In the introduction I argued that the Bachelor apparatus emulates the higher dimensionality and the topological properties of the Bride realm by coupling perspective with motion.

click to enlarge

Figure 24
Marcel Duchamp, Glider
Containing a Water Mill (in
Neighboring Metals), 1913-15

Let us start our course along this strand with the demonstration of a subject already widely discussed by scholars, regarding the Chariot ⁽²⁷⁾. In the years 1913-15 Duchamp worked at a preparatory study of the Chariot, named Glider Containing a Water Mill (in Neighboring Metals). (Fig. 24)It is the same element of the Glass, executed on a semicircular hinged panel of glass, which can rotate.

Applet 11 shows the situation. The red point on the bottom can be dragged to rotate about its hinge the plane where the Chariot is drawn. To simplify the drawing, the Water Mill is missing, to better focus the attention on the essential details.

The actual Chariot is drawn on a 2D support (the sheet of glass), and emulates its own status of 3D object by means of perspective. Accordingly, the 2D sheet of the glass emulates the ordinary 3D space. Hence the rotation of the Glider around its hinges suggests the rotation of a 3D object in a 4D hyperspace. Notice that just the sheet of glass used as support of the drawing allows to complete correctly the metaphoric turn in the fourth dimension: indeed just the transparency of the glass allows us to see the Chariot specularly reversed, as it reaches its final position. In fact we face an inverse congruence between two figures; just the exit from the 3D space and the rotation into the hyperspace allows two 3D figures inversely congruent to overlap on one another.

This idea is clearly presented by Duchamp in a note of the White Box and is widely discussed by Adcock ⁽²⁸⁾.Returning now to the applet, we can see a strong optical effect (also known as the Necker cube inversion), which can be described as if the Chariot would turn inside out as if it were a glove. Just this effect can be considered as a mental turn into the fourth dimension⁽²⁹⁾.

We can understand the variety and the subtlety of the game that Duchamp plays here, by comparing the rotation of the Glider with many other rotations of planes, everywhere present in the Bachelor apparatus. Consider for instance the rotation of the plane which ideally sustains the first Sieve (which we can actually see in the Yport sketch). Applet 12 allows the user to see this rotation by dragging the red point. Here we face a plane which rotates in a 3D space, giving rise to cones (which are 3D shapes) directly congruent with the starting one; on the contrary the glass plane of the Glider, which is 2D but perspectively simulates a 3D space, rotates in a true 3D space which accordingly simulates a 4D hyperspace, and gives rise to a second Chariot, inversely congruent to the starting one.

Now we can understand why Duchamp chose just the reproduction of the Glider as the cover of the White Box: remember indeed that the notes of this collection are mainly focused on the fourth dimension and its properties.

In short, with the Glider Duchamp suggests a rotary motion which allows the observer to look at two different Chariots, the one being the specular reversed image of the other, with the involvement of the fourth dimension concept we presented above.

Now, consider that the same thing can actually be done with the whole Glass, by simply walking around it. Once again the transparency of the glass permits the observer to look at two different Bachelor apparatuses, specular one to another, with analogous involvement of the fourth dimension concept. The motion of the observer around the Glass corresponds to the rotary motion of the Glider about its hinge as the observer stands still.

We shall exploit similar relative exchanges in motion (observed object rotating about its hinge and fixed observer vs. fixed object and observer moving around it) especially with the Sieves(in section 3.3.) and we shall consider the notes which carefully describe this inversion.

3.2. A new possible identity of the Grinder

One of the most important innovations of the 1914 painting Chocolate Grinder (No.2) are the threads directly sewn on the canvas; they obviously recall the coil-winding of an electromagnet.

Consider now a new possibility. The threads could also be related to the geometric concept ofruled surface.

A ruled surface is one which can be obtained by a straight line moving in the ordinary 3D space and leaving wherever it passes its trail: the ruled surface.

A note of the Green box, usually considered as the only one of this collection directly related to the theme of the fourth dimension ⁽³⁰⁾, also describes rotational motions of lines considered as generatrix; in addition the note contains ubiquitous suggestions of moving lines which leave a sort of trail forming surfaces; also, the note connects such a practice with the idea of circularity:

The right and the left are obtained by letting trail behind you a tinge of persistence in the situation. […]
And on the other hand: the vertical axis considered separately turning on itself, a generating line at a right angle e.g., will always determine a circle in the 2 cases 1^stturning in the direction A, 2^nd direction B. –
[…]
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 the back, the reverse and the obverse acquire a circular significance […] ⁽³¹⁾

Further examples possibly related to the idea of ruled surface can also be found in the White Box, such as the following:

On an infinite line let us take two points, A and B. Let us rotate AB about A as hinge. AB will generate some sort of surface, i.e. either curved, broken or plane ⁽³²⁾

or even this one:

Elemental parallelism: repetition of a line equivalent to an elemental line (in the sense of similar at any point) in order to generate the surface. ⁽³³⁾

click to enlarge

Figure 25
Marcel Duchamp, Sad Young Man on a
Train , 1911

Figure 26
Marcel Duchamp, Nude descending a Staircase no. 2, 1912

The formula of Elemental parallelism was not a sterile speculation, but one of the most important conceptual foundations of a whole creative period: we know that Duchamp used it for capital painting, such as Sad Young Man on a Train(1911) (Fig. 25) or Nude descending a Staircase (no. 2) (1912).(Fig. 26) He carefully explained it in the dialogue with Pierre Cabanne ⁽³⁴⁾.
As an example of how a ruled surface can be generated, imagine a luminescent straight thread moving about in the darkness; also imagine a camera with the shutter opened, to capture the luminous trail left on the film by the moving thread. This trail could be an example of ruled surface. The example is not chosen by chance: this explicative metaphor is used by E.J. Marey in one of his photography books ⁽³⁵⁾. Duchamp was interested in similar photographic experiments (chronophotography), and scholars already related the painting of 1912 Nude Descending a Staircase (No. 2) to chronophotography⁽³⁶⁾.
Thus, for a moment let us think of the threads of the Grinder as a suggestion of straight lines moving about, while the rollers are grinding, generating trails corresponding to several kind of ruled surfaces.

The connection between the glued threads of the Grinder and the duchampian concept of elemental parallelism has been already stressed by Craig Adcock, who also recalled that Duchamp spoke of the threads as generatrices⁽³⁷⁾

Let us start with the simpler example: what is the geometric locus of the diametric threads of the circular bases of the rollers, as they rotate around the axis of the Grinder, without rotating around their own axis? Animation 2⁽³⁸⁾ shows a rotating roller. The surfaces described by the diametric blue lines are one-sheeted hyperboloids.

Animation 3 : shows that as the diametric lines vary their inclination, the hyperboloids gradually change their shape, giving rise to the degenerate case.

• 
  Animation 2
• 
  Animation 3

The genesis of a single-sheeted hyperboloid by means of a rotating straight line is also displayed by Marey in his already cited photography book which Duchamp surely knew (Fig. 27).

click to enlarge

Figure 27
The genesis of a
single-sheeted
hyperboloid displayed
in Marey’s book

Figure 28
Two single-sheeted
hyperboloids forming a
special type of gearing

Figure 29
Marcel Duchamp,
Coffee Mill ,
1911

Look now at Fig. 28: being the single-sheeted hyperboloids (doubly) ruled surfaces, it is possible to use them to create a special type of gearing. The interest of Duchamp in similar devices is documented by a painting which can be considered as the most direct antecedent of the Grinder: the Coffee Mill (1911),(Fig. 29) which clearly displays the gearing machinery allowing the device to work.

We already recalled that Linda Henderson thoroughly documented that theChocolate Grinder is strongly related to electromagnetism and wireless telegraphy: it is its second identity, after the first one as both a true and metaphoric grinder (connected with the autoerotic activity of the Bachelor, resumed with the slogan: The bachelor grinds his chocolate himself⁽³⁹⁾). Now, I like the possibility of a third identity of the Grinder, as a geometric device to generate ruled surfaces.

Maybe it can be seen as a flight of fancy, but not so much, after all; read indeed once again the Green box note about the geometric properties of theBachelor apparatus:

Principal forms, imperfect and freed
The principal forms of the bachelor apparatus or utensil are imperfect:
Rectangle, circle, square, parallelepiped, symmetrical handle; demisphere.-i.e. these forms are mensurated (interrelation of their actual dimensions and relation of these dimensions to the destination of the forms in the bachelor utensil.)
In the Bride – the principal forms will be more or less large or small, no longer have mensurability in relation to their destination: a sphere in the Bride will have any radius (the radius given to represent it is “fictious and dotted.”)
Likewise, or better still, in the Pendu Femelle parabolas, hyperbolas (or volumes deriving from them) [emphasis mine] will lose all connotation of men-surated position.

The question is: where are those hyperbolas and volumes deriving from them (and the corresponding surfaces, we could add) which, once passed into theBride realm will lose their connotation? Are they maybe the ones generated by the Grinder? It is possible.

Accepting this hypothesis, let us take some further step.

What happens if, while rotating around the Grinder axis, the roller also rotates around its own axis? Applet 13 will help visualize the possible resulting surfaces for such a composition of motions.

The different possible outcomes depends on the different sliding component in the motion of the rollers (remember indeed that in their motion rollers also slide on the Chassis). It means that, once a complete turn around the Grinder axis is completed, the rollers also turn around their own axis by a certain variable angle ω, whose amplitude depends on the sliding component.

Look finally at Applet 13⁽⁴⁰⁾: at its opening, the parameters are fixed in order to have the roller making a half turn around its own axis, while making a complete turn around the axis of theGrinder.

The surface described by the diametric line of the major base of the roller is a Moebius band.
At the bottom of the figure you find two green points which can be dragged.

By dragging the upper one the roller will rotate and make a complete turn around the Grinderaxis: you can see that the diametric line actually rules the band. As you drag the lower green point you simply modify the ω parameter and accordingly the locus surface will gradually change its shape, giving rise to more complex bands.

A further step could be taken by observing the surfaces obtained by the longitudinal lines of the rollers as generatrices. Applet 14 visualizes them. Once again the two green points can be dragged, with the same meaning as before.

Now the question is: accepting the present hypothesis about the Grinder, what could be the meaning of the surfaces generated by it, in the general project of the Glass? In my opinion surfaces such as the Moebius band, with their topological properties, could be a means for theBachelor to emulate the higher and more complex space of the Bride; it could be a sort of bridge, between the Bachelor and the Bride realms: remember indeed that the Bride is characterized by topological properties where the metrical traits governing the lower half of theGlass lose their meaning. The same holds (all the more reason) for the more complex bands obtainable with the Grinder.
To be precise, I don’t mean that Duchamp thought exactly of the Moebius band (or of similar and possibly more complex surfaces), but it is possible that he could imagine similar figures, maybe knowing neither their name nor their status of well-defined and studied geometrical objects. Possibly he guessed some of their strange properties; after all we have a number of evidences of its astonishing geometric imagination. Jean Clair already discussed some works of Duchamp referring them to well defined topological objects (such as the Kleinian bottle). Also Clair informs us that in the 60’s Duchamp discussed the properties of such topological objects with the French mathematician Le Lionnais. Following this suggestion I discussed other possible examples, referable to the properties of both the Kleinian bottle and the Moebius band⁽⁴¹⁾.

In conclusion we could think of the Grinder as a ruled surfaces generator, or better, as a true surfaces grinder. The complex surfaces generated by Grinder’s motion could emulate the topological essence of the hyperspace of the Bride realm in the higher part of the Glass. The thesis is supported by some facts:

1. Notes from both the Green Box and the White Box (cited above) prove that Duchamp knew and used the concepts of ruled surface and quadric surfaces (at least on a qualitative level);
2. The idea of ruled surface is strictly connected with the practice of chronophotography which Duchamp praised and in a way used;
3. The surface of the rollers is carefully ruled by the threads sewn on the canvas, and as theGrinder is supposed to work, they rotate moving about in several complex ways; and, above all, the Grinder actually works as a surfaces generator;
4. It is proved that (at least) in the 60’s Duchamp knew at some qualitative level both the Moebius band and the Kleinian Bottle;

3.3. The Sieves’ perspective: a possible antecedent of Duchamp’s optical devices
Let us now consider the Sieves (or Parasols) and their function in the Bachelor apparatus. TheGreen Box notes describe the process which produces the so called Illuminating gas; as it leaves the Capillary tubes, it is then cut into bits, called spangles, which must run through the circular pathway of the Sieves:

As in a Derby, the spangles pass through the parasols A,C D.EF…B. and as they gradually arrive at D, E, F, … etc. they are straightened out, i.e. they lose their sense of up and down ([more precise term]). – The group of these parasols forms a sort of labyrinth of the three directions. –
The spangles dazed by this progressive turning. Imperceptibly lose [provisionallythey will find it again later] their designation of left, right, up, down, etc, lose their awareness of position.⁽⁴²⁾

By this way, the spangles, straighten out

[…] like a sheet of paper rolled up too much which one unrolls several times in the opposite direction ⁽⁴³⁾

lose their sense of space. The way it happens is described as a loss of distinction between left, right, up, down, etc. as they pass through a labyrinth of three directions.
The following note from the Green Box makes clear that in Duchamp’s thought the identifications left-right, front-back, hi-low and so on are connected with the suggestion of a higher dimension::

[…] the front and the back, the reverse and the obverse acquire a circular significance: the right and the left which are the four arms of the front and back. melt. along the verticals.
the interior and exterior (in a fourth dimension) can receive a similar identification.⁽⁴⁴⁾

Hence we can think that the circular pathway through the Sieves and the consequent loss of distinction between opposite orientations could be somehow connected with the suggestion of a higher dimension.
The pathway followed by the Spangles is strictly circular, because the seven Sieves (originally they were six and semi spherical) have nine holes (originally eight) which repeat exactly the shape of the polygon connecting the nine (originally eight) Malic moulds, where they come from.

The sieves (6 probably) are semispherical parasols, with holes. [The holes of the sieves parasols should give in the shape of a globe the figure of the 8 malic moulds, given schematic. by the summits (polygon concave plane). by subsidized symmetry]⁽⁴⁵⁾

Thus the Sieves convey the Spangles according to well defined circular trajectories.
Applet 15 shows the pathway of 5 possible Spangles, assuming for simplicity five arbitrary convenient positions of the holes. The blue point can be dragged to move the Spangles through the Sieves. The actual course of the Spangles is semicircular, but Applet 15 displays a complete turn, in order to emphasize some aspects we will discuss as we shall go along.
Applet 15 helps understand why the dazed spangles lose the sense of up-down and left-right (follow for instance the course of the blue one); in addition it displays a strong depth effect due to perspective rendering of the Spangles in motion.

click to enlarge

Figure 30
Five semcircumferences used by
Duchamp to perform the
perspective drawing of the cones

Figure 31
Because of the perspective,
the arcs are not concentric:
their centers are the points A, B, C.

Let us now return to the perspective of the Sieves. Particularly let us consider the Yport sketch of 1914. The following Fig. 30 summarizes those, among its features, relevant in this context.

We clearly see five semcircumferences used to perform the perspective drawing of the cones. Four of them were used to rotate four diametric points of the first ellipse, in order to easily obtain the corresponding transformed points of the remaining ellipses; the fifth arc was used to obtain the centers of each ellipse, starting from the first. Maybe other circumferences were used, also considering how perfectly the ellipses are drawn; however the sketch doesn’t show any trace of possible further arcs. Note that, because of the perspective, the arcs are not concentric: their centers are the points A, B, C, visible in Fig. 31, which also displays the complete circumferences.
I used for convenience just these circumferences as circular pathways of the spangles in Applet 15; according to the original project by Duchamp, nine similar circumferences must be used (one for each of the nine holes).
The White Box contains notes which specifically connect linear perspective with circular shapes, by means of the concept of gravity:

Gravity and center of gravity make for horizontal and vertical in space³
In a plane² – the vanishing point correspond to the center of gravity, all these parallel lines meeting at the vanishing point just as the verticals all run toward the center of gravity.⁽⁴⁶⁾

This association between perspective and gravity (which interestingly and meaningfully was made in the same way by Klee⁽⁴⁷⁾) leads Duchamp to the following conclusion:

Resemblance –
Between a perspective view and a circle –
The vanishing point and the center –
To what in a perspective view would the
Circle itself correspond?

Horizon⁽⁴⁸⁾
Elsewhere in the White Box we also read:

Difference between “tactile exploration” or the wandering in a plane by a 2-dim’l eye around a circle, and of this very circle by the same 2-dim’l eye fixing itself at a point. Also: difference between “tactile exploration,” 3-dim’l wandering by an ordinary eye around a sphere and the vision of that sphere by the same eye fixing itself at a point (linear perspective).⁽⁴⁹⁾

Here Duchamp adds the motion as a further key ingredient in the perception of higher dimensions of space. Perspective representation and vision must be integrated by the motion of the eye in order to reach a better representation and understanding of higher dimensional objects:

A 3-dim’l tactile exploration, a wandering around, will perhaps permit an imaginative reconstruction of the numerous 4-dim’l bodies, allowing this perspective to be understood in a 3-dim’l medium.⁽⁵⁰⁾

Perhaps, the rotational motion of the Spangles through the Sieves may be intended as a suggestion of a wandering or tactile exploration of the space surrounding the Sieves, or, in general of the medium which the Glass is immersed in.
Following this course, the next step seems to be quite obvious: maybe the same effect could be reached if, instead of the wandering around an object, this very object could turn in front of the observer which remains in a fixed position.
In our case, what happens if the circumferences conveying the Spangles rotate around a fixed center (not necessarily one among points A, B, C in Fig. 31 in front of us?
Applet 16 illustrates the outcome: a set of seven eccentric circles (which I used before for the perspective construction) rotate around a center near to their own centers, which however doesn’t coincide with any of them. Use the blue point to fix the center of rotation into the desired position; drag the red point to shift the set of circumferences backward or forward; finally drag the green point to rotate the set of circles.
The depth effect is quite remarkable, and is further reinforced if the circles are colored, like in the following Animation 4.

Please refresh the page, if the animation stops    

• 
  Animation 4

 

 

Thus we passed from a true 2D plane to the illusion of a 3D space. Hence, once again we have the emulation of the higher dimensionality of the Bride realm.
Only speculations? Possible, but it is exactly what Duchamp did a few years later with the filmAnemic Cinema (1925) (Fig. 32) and especially with the optical devices such as the Rotary demisphere (1925) (Fig. 33) and the Rotorelief (1935). (Fig. 34)

click to enlarge

 

• 
  Figure 32
  Marcel Duchamp, Anemic Cinema, 1925
• 
  Figure 33
  Marcel Duchamp, Rotary demisphere, 1925
• 
  Figure 34
  Marcel Duchamp, Rotorelief, 1935

 

 

There Duchamp used once again sets of eccentric circumferences, which while rotating produce remarkable effects of depth (see for instance Animation 5, where a facsimile of the optical disc named Verre de Boheme, 1935 produces the effect of a three dimensional stemmed glass). The effect of depth produced by the Rotorelief has no relation with the stereoscopic vision; on the contrary it is even more surprising if seen with a single eye.

Please refresh the page, if the animation stops

 

 

• Animation 5

Interestingly scholars generally don’t consider the connection of the Rotorelief with the previous efforts of Duchamp in perspective, but I think it is an important element to consider, as Adcock already carefully stressed⁽⁵¹⁾. Let us look once again at Animation 5. We see a 3D stemmed glass rotating in front of us, and it happens also because our mind perceives the set of circles as a Gestalt, and this can be possible all the more reason if the circles have some perspective consistence. Duchamp himself makes clear this point talking about his Rotorelief :

Thanks to an offhand perspective, that is, as seen from below or from the ceiling, you got a thing which, in concentric circles, forms the image of a real object⁽⁵²⁾

Thus, once again we have a strict correspondence between rotary motion, perspective, and suggestion of higher dimensions, with the optical illusion of depth, known as stereokineticeffect.
Indeed the rotating circles were drawn on the same sheet of paper (the Yport Sketch) and implicitly are present on the same sheet of glass; thus they actually belong to a plane; however in the perspective fiction they belong to different planes (parallel to each other) which determine a 3D space. Now, if the stereokinetic effect allows us to pass from the 2D plane to a 3D space, then according to the perspective fiction in the meantime we also pass from the ordinary space to a hyperspace.
Concluding this section, we shall consider an additional interesting feature of the Sieves which is to be stressed.
With their semicircular course, the circular bases of the conical Sieves ideally generate an half torus.

click to enlarge

Figure 35
If we identify the
diametrical points of a torus,
the surface we obtain
is a Kleinian
bottle.

With reference to Fig. 35, consider for a moment the whole torus, and its centre of symmetry C; also consider the couples of symmetric points of the torus, such as P and P’, or Q and Q’ and so on; call the points of such couples diametrical points. The loss of distinction (described above) between left-right, up down and so on, can be expressed in terms of identification of diametric points of our torus. Now, it is known that if one identifies the diametrical points of a torus for each possible couple, the outcome is a surface topologically equivalent to the Kleinian bottle. For those interested in the subject, it is clearly and simply presented in a classic text of David Hilbert ⁽⁵³⁾.
Thus let us reconsider the notes dealing with the Spangles and their run through the Sieves, which I reported at the beginning of this section. The loss of distinction (or identification) between left and right, up and down, interior and exterior already interpreted in terms of reference to higher dimensions, can also be interpreted in terms of possible reference to the topological properties of a Kleinian bottle.
The different possible interpretations are not in conflict; on the contrary, they are somehow related, if we think that only in the fourth dimension the Kleinian bottle could be properly built.
Hence we can think of the Sieves machinery of the Bachelor apparatus as a further emulation of the topological properties of the Bride realm.
In conclusion I suggest three things:
first, we have some further evidences that coupling perspective and rotary motion allows theBachelor apparatus to emulate the higher dimensionality of the Bride realm;
second, the perspective construction of the Sieves could be seen as the most direct and relevant antecedent of the successive optical devices;
third, the Sieves could be thought of as a sort of topological apparatus which returns objects with non ordinary properties (such as the Kleinian bottle); thus the Sieves could also be considered as an apparatus emulating the topological properties of the Bride realm.

3.4. Rotating the Water Mill: an unexpected further bridge toward the fourth dimension
The Water Mill perspective offers a further unexpected surprise.
Let me start with the description of the course which led me to the serendipitous discovery about the Water Mill that I will describe in this section; indeed I think this very course contains in itself some insight about the way one could possibly approach the Glass in particular and Duchamp in general.
Once the perspective of the Water Mill was obtained with Cabri, it was only a question of few additional contrivances, to allow the wheels to rotate, thus I did it.
In order to better appreciate the rotary motion of the Water Mill wheels, I filled the polygons corresponding to the eight paddles (which originally were transparent) with a solid grey color.
The unexpected outcome is displayed in Applet 17. What kind of motion was there? What happened to the Water Mill? Was it turning forward or backward?
Along with the widely explored category of the 3D impossible objects, do we deal here with a new category, that of the impossible motions?
After a few moments I realized what the problem was:
The grey filling color is opaque, and if there is overlapping of paddles, each new filling operation causes the covering of the previously filled paddle. As the animation is running, for each frame Cabri repaints the screen, and the paddles are repainted accordingly, following the same order used to fill them the first time. So, it happens that from time to time, the order followed by Cabri for filling the paddles can be the right or the wrong one. If it is right, the paddles are drawn consistently with their position and with the forward motion (the foreground upon the background ones). In the contrary case the filling order is wrong, so that paddles which actually must be in background, are filled as they were in foreground and vice versa, and the global outcome is the perception of a backward motion. In addition, consider that originally the paddles were filled by chance, without a precise order, so that the animation actually shows a continuing and unpredictable change of direction.

click to enlarge


Figure 36
Impossible Water
Mill wheel

Now look at the static picture of the Water Mill in Fig. 36 (it is a single frame captured from Applet 17). In spite of its correct perspective, we face an impossible 3D object, similar to that of Escher’s print Belvedere, based on the Necker cube. Indeed Fig. 36 shows a similar situation, namely the simultaneous presence of two different and inconsistent versions of the same object.
The first version is based on the perspective shortening of the background paddles compared with the major ones in foreground.
The second version of the Water Mill wheels is based on the reciprocal coverage of the elements: in our mind the element which covers another isover, and the covered element is under.
Thus our perception continuously oscillates between two different possible choices, each one corresponding to a different orientation of the Water Mill.
These two possible simultaneous orientations of the same object are specular: it means that no rigid motion inside the ordinary 3D space allows us to overlap these figures, which are inversely congruent. To physically obtain this result, we would have to rotate the figure in the forth dimension. Thus, once again the mental effort we make to invert the figure corresponds to a rotation in the fourth dimension.⁽⁵⁴⁾
The interesting thing is that the key element to achieve such a result is just the rotary motion, coupled with the perspective rendering of the wheels with their paddles, and not the coverage order of the paddles (which however propitiated the discovery) as we shall see.
Indeed, if you look at the static Fig. 20 and try to do the mental inversion of the object, is a lot harder than do that by observing the animated Applet 17.
The following applets are intended to enable the reader, step by step, to progressively lay aside the coverage order of the paddles, but always maintaining the optical effect of inversion.
Using Applet 18, you will learn to follow a single paddle (the red one, in this case) and to perform a stable mental inversion each time the paddle reaches its higher and lower positions.
Applet 19 will help you fix a single paddle (the one with the red border) but laying aside the coverage order, because the paddles are drawn transparent.
Finally Applet 20 shows a transparent Water Mill which you can invert without any help.
Use it to convince yourself that just the rotary motion of the paddles allows you to easily invert the object: stop it by passing with the mouse over its area and then leave it. Try now to invert the static frame. Once again it is a lot harder than with the moving picture.
With patience you will obtain a surprising result (even though only for a few instants at once):at the same time the wheels will rotate forward and backward, the paddles will be over and under, in front and back, the view point being both from the left and the right of the wheels.
This meaningfully agrees with some details of Duchamp’s speculations about the fourth dimension. Remember the already-cited note from the Green Box:

[…] the front and the back, the reverse and the obverse acquire a circular significance: the right and the left which are the four arms of the front and back. melt. along the verticals.
the interior and exterior (in a fourth dimension) can receive a similar identification.⁽⁵⁵⁾

As a further detail consider the Green Box describing how the Water Mill works⁽⁵⁶⁾: one of its interesting features is that the rotation of the water wheels determines the onanistic left-right motion of the whole Chariot (which sustains the water wheels): this motion in fact could propitiate the left-right shifting of the viewpoint from where the wheels are viewed.
As a matter of fact, if you look at Applet 20 by shifting to the left and the right your head according to the rotation, it is a lot easier to make the required mental inversions than holding the same fixed position.
Now the question is: did Duchamp think of the Water Mill as a machinery allowing the observer to make possible these inversions, thus to make possible a turn into the fourth dimension? To be honest I don’t believe it, at least specifically for the Water Mill: we have no evidences that he thought of or planned what I said above.
However some objective data remain:
– the Water Mill wheels were planned to rotate;
– among other results, the infinite rotary motion of the water wheels was intended to enable the onanistic left-right motion of the Chariot (which sustains the wheels); the left-right motion of the Chariot with the Water Mill could be somehow connected with the specular inversions of the wheels, which accordingly seem to be viewed from the left or from the right;
– by means of the Glider (discussed in section 3.1.) Duchamp suggested us to specularly reverse just the Chariot and the Water Mill as a trick to make somehow visible the fourth dimension;
– and, especially, just a rotary motion (of either the observed object or the observer) makes possible such an inversion.
As a final objective datum to be added, consider now that using the water wheels and that mix of further ingredients, one obtains the outcome described by the applets above, which perfectly agrees with Duchamp’s speculation on fourth dimension.
By this way I don’t mean that Duchamp exactly thought about what the applets showed above, but simply that Duchamp’s recipe (that of mixing perspective and rotation in order to emancipate the spatiality of the Bachelor realm) does work effectively!

3.5. Further conclusion about the perspective of the Glass: the dynamic viewpoint
Let us return to Tomkins’ statement already cited:

Was he looking for a mathematical formula through which he could actually evoke the presence of a fourth dimension? Whatever serious ambition he may have had along these lines he abandoned soon enough.

We already said that Duchamp’s execution of the perspective drawing is absolutely canonical. As Tomkins suggests, no special mathematical formulas were used to carry out neither calculations nor geometrical constructions, but simply Duchamp carefully and thoroughly applied the rules of projective geometry.
However I think Duchamp didn’t abandon his ambition about evoking the presence of higher dimensions. Higher dimensionality being one of the declared (and most important) subjects of the Glass, he couldn’t abandon, because it meant to abandon the very project of the Glass, which he actually didn’t; the Glass was left unfinished, but after a period which covers more than ten years, not to consider Duchamp’s activity around the Glass in the years after his decision to leave it unfinished (thus he didn’t abandon soon enough).
I think that he behaved according to his claims: perspective effectively was one of the main ingredients in order to reach the illusion of the fourth dimension.
But, on the other hand we demonstrated that no special perspective tricks were used to modify what the canonical rules prescribe. And, of course, no special or magic effects are there inlooking at the Glass. The key is in thinking of the Glass, as Duchamp recommended, by stating the primacy of the grey matter over the retina.

Duchamp: I was mixing story, anecdote (in the good sense of the word), with visual representation, while giving less importance to visuality, to the visual element, that one generally gives in painting. Already I didn’t want to be preoccupied with visual language…
Cabanne: Retinal.
Duchamp: Consequently, retinal. Everything was becoming conceptual, that is, it depended on things other than the retina⁽⁵⁷⁾

In fact we have to consider the Glass as a continue and stimulating invitation to use the grey matter; this is one of the reasons for conceiving the notes as integral part of the Glass: they often are the starting point for successive mental activity, or even they are further integrations or suggestions to complete ideas born somewhere else.

I wanted that album [the Boxes] to go with the “Glass,” because, as I see it, it must not be “looked at” in the aesthetic sense of the word. One must consult the book, and see the two together. The conjunction of the two things entirely removes the retinal aspect that I don’t like. It was very logical.⁽⁵⁸⁾

We know that the range of speculations underlying Duchamp’s notes (and works) is wide enough to cover a plenty of different disciplinary fields. As an evidence of that, look at the monumental volume of Henderson⁽⁵⁹⁾ which however deals only with the scientific and technological humus from where the Glass took origin.
Why this digression on the disregard of Duchamp for the retinal, and consequently the accentuation of the importance of the notes? It is to stress that we have not to limit ourselves to the visual data we are facing. The Glass is not only the sheet of glass we can see at Philadelphia Museum but also that multilayered stratification of meanings that Duchamp himself suggested by means of the notes.
Thus, no surprise if I talk about a perspective which has to be moved to be fully understood, whereas the actual Glass is definitely static.
Indeed we already saw that the Glass was conceived in perpetual ubiquitous motion, with a particular inclination for circuital courses. We also have a number of claims about Duchamp’s attraction for circular motions:

Always there has been a necessity for circles in my life, for rotations. It is a kind of narcissism, this self-sufficiency, a kind of onanism. The machine goes around and by some miraculous process that I have always found fascinating, produces chocolate.⁽⁶⁰⁾

As a further reinforcement of the importance of rotary motions in Duchamp, I like also to remember here the extraordinary analysis which Stephen Jay Gould did of an historical photo representing (probably) Duchamp as a sort of ghost, surrounded by a myriad of suggestions of circular motions and shapes ⁽⁶¹⁾.

click to enlarge

Figure 37
Marcel Duchamp, Rotary Glass Plates (Precision
Optics) , 1925

If the Glass contains only suggested virtual motions, Duchamp also inserted actual rotary motions in the optical devices, starting from theRotary Glass Plates (Precision Optics) (1920, thus the execution of theGlass was still ongoing). (Fig. 37)
Thus I think that it is absolutely acceptable to consider the importance of mobile perspective in the Glass even though its exterior appearance is static.
After these necessary preliminary remarks, the thesis I presented in the third part of the present article can be resumed as it follows:
It is well known that the Bride belongs to an actual 4D realm (which we can see only by means of a 2D rendering of her 3D projected shadow). Also, her realm is characterized by the absence (or by the loss of meaning, which is the same) of the metric traits: the spatiality of the Bride realm is governed by more general topological (or even non-Euclidean) laws, where things no longer have mensurability (to use Duchamp’s word).
Also, it is known that the Bachelor realm is a true 3D domain, and its forms are imperfectobjects belonging to the standard Euclidean geometry (such as rectangles, parallelepipeds, circles…): the Bachelor can only try to emulate the higher dimensionality and the topological and non-Euclidean properties of the Bride realm⁽⁶²⁾, to make possible his (impossible) conjunction with the Bride.
Here the examples I presented in the third part of the article come into play. To emulate the emancipated spatiality of the Bride, the Bachelor can only use tricks and contrivances.
The key elements allowing such an emulation of higher dimensionality are:
perspective,
transparency,
and (rotary) motion.
Indeed just moving (rotating) the perspective elements of the apparatus, drawn on a transparent medium, we can reach the illusion (pay attention: just only the illusion) of a higher and emancipate spatiality.
Basically, the examples regarding the Chariot (see 3.1. and 3.4.) rise from a simple reasoning led by analogy: if two figures laying on the same plane (2D) are inversely congruent to one another (the one is specular to the other), no rigid plane motion allows to overlap them: to reach the result, a rotation into space (3D) is necessary to invert the congruence and allow the overlapping. By analogy, two spatial figures (3D) inversely congruent have to rotate in a 4D medium in order to overlap.
In the first example, the rotation of the Glider about its hinges allows the Chariot to turn inside out as if it were a glove (allowing, in fact, the identification left = right).
In the second example the rotation of the Water Mill wheels help us conceive (at least for a moment) the identification of both the specular version of the same 3D object and the contrary motions back and forth of the wheels.
Similarly, in the most part of the notes about the fourth dimension Duchamp led the reasoning by analogy: he observed what happens in the passage from 1D to 2D, or from 2D to 3D, and then extended the reasoning to the next passage from 3D to 4D.
But he clearly understood the limitations of such contrivances:

Will the passage from volume to 4-dim’l figure be produced through parallelism? Yes. But this elemental parallelism being a geometric process requires an intuitive knowledge of the 4-dim’l continuum [emphasis mine]. One can give the following definition for a 4-dim’l continuum. (By analogical reasoning, it is an enumeration of a few characteristic common to all the n-dimensional continuums rather than a definition): A representation of the 4-dim’l continuum will be realized by a multiplication of closed volumes evolving by elemental parallelism along the 4th dimension. Of course one has still to define by intuitive knowledge the “direction” of this 4th dimension [emphasis mine].⁽⁶³⁾

This note stresses Duchamp’s discontent, because, apart from giving a first possible key in guessing about higher dimensionality, it is sterile unless one has an intuitive knowledge of the“direction” of the fourth dimension.
Possibly Duchamp looked for other solutions.
The example regarding the Grinder (3.2.) could be seen as a possible alternative to analogical reasoning. The Grinder is based on a double rotary motion (around its own axis and around the axes of the rollers). On the one hand, the resulting ruled surfaces are connected with previous experiments concerning so-called elemental parallelism (thus, the Grinder looks backward). On the other hand those surfaces show interesting and unexpected topological properties, allowing the space of the Bachelor apparatus to expand (thus, at the same time, the Grinder looks forward).
The example regarding the stereokinetic effect applied to the Sieves (3.3) could be seen as a further different solution, involving perspective and rotary motion.
Also, the motion of the Spangles through the Sieves establishes a direct connection with the topological properties of a Kleinian bottle, which, in turn, is another way for the Bachelors to emulate the higher spatiality of the Bride.
In conclusion, we can say that the emancipation of the freed forms of the Bachelor apparatuspass through a dynamic perspective.
Duchamp did not abandon his ambition to make visible the presence of higher dimensions.

 

Acknowledgements

I want to express my thanks to Prof. Silvia Pianta, for some clarifications about the hyperboloids, and to my friend Paolo Mazzoldi, who checked the article for the linguistic correctness.

Notes

1. Michel Sanouillet and Elmer Peterson (eds), The Writings of Marcel Duchamp (New York: Da Capo Press, 1989), 83.
For the corresponding note issued in the Green Box see also pp. 44-45.    

2. See for instance:
Craig Adcock, Marcel Duchamp’s Notes from the « Large Glass » : An N-Dimensional Analysis, (Ann Arbour: UMI Research Press, 1983).
Jean Clair, Marcel Duchamp et la fin de l’art (Paris: Gallimard, 2000).
For some further details see also:
Roberto Giunti (a), “R. oS. E. Sel. A. Vy” in Tout-Fait, Vol. 2, Issue 4 (January 2002): Articles.
Roberto Giunti (b), “Complexity Art” in Tout-Fait, Vol. 2, Issue 5 (April 2003): Articles.

3. Pierre Cabanne, Dialogues with Marcel Duchamp, trans. Ron Padget, (New York: Viking Press, 1971), 38.

4. Calvin Tomkins, Duchamp, A Biography, (New York, Henry Holt and Company, 1996), 128.

5. Sanouillet and Peterson [1], 40, 41.

6. Rhonda Roland Shearer, et al., “Why the Hatrack is and/or is not Readymade: with Interactive Software, Animations, and Videos for Readers to Explore” in Tout-Fait, Vol. 1, Issue 3 (December 2000): 9.

7. Roland Shearer, [6], 9.

8. Cabrì Géomètre II, The Interactive Geometry Notebook, by Jean Marie Laborde and Franck Bellemain. Cabrì Géomètre II is a trademark of Université Joseph Fourier.

9. Information on CabriJava and free download of the software at this site:
http://www-cabri.imag.fr/cabrijava/

10. Of course the choice of such couple of corresponding lines determines the position of the viewpoint, or, equivalently, the distance of the observer from the picture. The matter was already known in the Renaissance. See for instance Tony Phillips, who carefully and simply explains it at

http://www.math.sunysb.edu/~tony/whatsnew/column/alberti-0102/alberti1.html

11. Note that the plan sketch is symmetrically reversed upside-down with respect to Duchamp’s original orientation. This was done to allow simpler prospective procedures with Cabri
12. Be patient with dragging, because the applet must recalculate the entire perspective; it requires up to tens of seconds, according to the speed of the used processor. Also, drag only by a little step at a time.

13. In addition, the blades of the Scissor in Cabri figure are shorter than the original; but in this case we cannot speak of mismatch, simply because Duchamp’s sketches don’t include the exact measure of the length of the blades.

14. Roland Shearer [6], 9.

15. Gould, Stephen Jay and Rhonda Roland Shearer “Drawing the Maxim from the Minim: The Unrecognized Source of Niceron’s Influence Upon Duchamp” in Tout-Fait, Vol. 1, Issue 3 (December 2000): News.

16. Linda Henderson, Duchamp in Context: Science and Technology in the Large Glass and Related Works(Princeton, Princeton University Press, 1998).
17. Anyway this wrong assumption could perhaps be useful, at least to clarify a minor detail about the Grinder. We know that Duchamp saw such a machine in the window of a confectionary shop in Rouen. See for instance the entry for March 8, 1915 in:
Jennifer Gough-Cooper and Jacques Caumont, and Pontus Hulten, ed. ‘Ephemerides on or about Marcel Duchamp and Rrose Sélavy, 1887-1968’, in P. Hulten, ed., Marcel Duchamp: Work and Life (Cambridge, Mass.: MIT Press, 1993).
We still have a hatching of that window, showing the very machine seen by Duchamp; we can clearly see the three rollers which are very elongated, and this shape could indicate that their vertexes coincided with that of the basement; thus maybe they rolled without sliding. However Henderson (in [16], 59) points out that similar grinders standardly have only two rollers, and shows a hatching of such a grinder (fig. 67 of her book): here the rollers slide on their basement, because their vertexes lay far beyond the centre of it. I’m not an expert in grinding chocolate, but maybe we could have an explanation for everything: if there is no sliding (as we could suppose for the Rouen grinder) a minor power is required to rotate; on the contrary, if there is sliding (which gives a better grinding) higher power is required to rotate, and in addition there is the risk to break the machine for the higher friction; the solution could be to remove one roller, to diminish both required power and risks of breaking.

18. Roland Shearer, Rhonda: “Why is Marcel Duchamp’s Bicycle wheel shaking on its stool” <http://asrlab.org/articles/why_bicycle_wheel.htm>

19. In general I inserted Animations instead of the usual Applets if (as in the present case) the visualization is too complex to be rendered correctly with CabiJava.

20. Sanouillet and Peterson [1], 55.

21. Tomkins [4], 137.

22. Sanouillet and Peterson [1], 86.

23. In the stimulating article cited in [15] Stephen Jay Gould and Rhonda Roland Shearer doubt that theTaumaturgus could have influenced Duchamp, and as a further support of their hypothesis they stated:
At least three scholars well versed in the science of Duchamp’s interests in optics and perspective (Jean Clair, Linda Henderson and Craig Adcock) have followed Duchamp’s literal instruction, and searched Thaumaturgus opticus to locate the influence of classical works upon Duchamp’s understanding of perspective. But they found nothing beyond the undoubted status of Thaumaturgus as a good and standard text for its time.
In short, Gould and Roland Shearer argue that the Thaumaturgus is a quite conventional book, which academically resumes the standard knowledge then available on geometric optics and perspective; it was written in highly formal Latin and with academic purpose. His spirit is quite far from Duchamp’s personal style. Thus the Authors suggest a possible different influence of Niceron upon Duchamp: La perspective curieuse, ou magie artificielle des effects merveilleux, published in 1638; it is a shorter and amusing handbook, written in French, in a very different style (“chatty and irreverent”, say Gould and Roland Shearer) than the opus maior. A number of tricks (based on optics and perspective) are presented, which undoubtedly could better match Duchamp’s interests. Particularly, some of them were in fact used (or projected to be used) by Duchamp, for instance the now called Wilson-Lincoln effect, present in the project of the Glass (see Sanouillet and Peterson [1], 65).

24. Cabanne [3], 40.

25. Cabanne [3], 41.

26. To have an example of similar necessary and very trivial calculations, consider the project of the Tobogganin the elevation sketch. Starting from the overall altitude of the Toboggan (26 cm), Duchamp divided it into four parts, three of them measuring 7,73 cm, and one of 2.78 cm. Notice however that 7,73X3+2.78 gives 25,97 instead of 26. Other similar minor mistakes in calculations can be found elsewhere in the project.
27. See for instance Henderson [16], 82-83; and Adcock [2], 176-77.

28. See Sanouillet and Peterson [1], 97 and Adcock [2], 164-65, 177.

29. On the Necker cube inversion, and its meaning with reference to the fourth dimension, see particularly:
Rudy Rucker, The Fourth Dimension. A Guided Tour of the Higher Universes, (Houghton Mifflin Company, Boston Massachusetts, 1984).
30. Henderson [16], 82.

31. Sanouillet and Peterson [1], 29.

32. Sanouillet and Peterson [1], 96.

33. Sanouillet and Peterson [1], 92.

34. Cabanne [3], 29, 34-35.

35. E. J. Marey, Le Mouvement (Paris: G.Masson, Editeur, 1894)

36. See Henderson [16], 9; See also Cabanne [3], 34:
Cabanne: Didn’t films influence the “Nude Descending a Staircase?”
Duchamp: Yes, of course. That thing of Marey…
Cabanne: Chronophotography.
Duchamp: Yes. In one of Marey’s books, I saw an illustration of how he indicated people who fence, or horses galloping, with a system of dots delineating the different mouvements. That’s how he explained the idea of elementary parallelism. As a formula it seems very pretentious but it’s amusing.
37. Adcock [2], 188-189.

38. The same remark of note [19] holds.

39. Sanouillet and Peterson [1], 68.

40. In general the red surfaces are displayed only for the first turn of the roller around the Grinder axis. The geometric loci displayed in Applet 11 are quite complex, and the same applet could work not perfectly and too slowly.

41. Clair [2]; Giunti [2a]

42. Sanouillet and Peterson [1], p. 49

43. Ibid., 50.

44. Ibid., 29.

45. Ibid., 49.

46. Ibid., 87.

47. Roberto Giunti, “Analysing Chess. Some deepening on the chaos concept by Klee”, VisMath, Vol. 4, No. 3 (2002), http://www.mi.sanu.ac.rs/vismath/pap.htm

48. Sanouillet and Peterson [1], 87.

49. Ibid., 88.

50. Ibid., 88.

51. Adcock [2], 183.

52. Cabanne [3], 72.

53. David Hilbert and S. Cohn-Vossen, Geometry and the Imagination (New York: Chelsea, 1999).

54. See once again Rucker [29]

55. Sanouillet and Peterson [1], 29.

56. Ibid., 57-59.

57. Cabanne [3], 38-39.

58. Cabanne [3], 42-43.

59. Henderson [16].

60. Tomkins [4], 125.

61. Gould’s analysis is contained as a separate box inside the already cited article of Roland Shearer [6]

62. It is well known that the Capillary Tubes (alias the Standard Stoppages, the starting point of the whole machinery of the Bachelor apparatus), sound like a non-Euclidean axiom, but they seem to be unable to generate something emancipated, maybe because of the mechanic gearing of the parts of the apparatus, which in turn recalls a too rigid (non-emancipated) logic.

63. Sanouillet and Peterson [1], 92.
Fig. 1-5, 9, 11-12, 14-16, 20-22, 24-29, 32-34, 37 © 2007 Succession Marcel Duchamp, ARS, N.Y./ADAGP, Paris.

1

click to enlarge

Figure 1
Marcel Duchamp, L.H.O.O.Q.

Tentant tardivement de préciser quand, en 1919, a été “fait” L.H.O.O.Q., Marcel Duchamp fournira deux dates: au début 1953, dans ses entretiens avec Sidney, Harriet et Carroll Janis, il dira décembre⁽¹⁾ ; en juin 1966, dans ses entretiens avec Pierre Cabanne, octobre⁽²⁾ .

Ceci, autant en regard des faits rapportés que de la lecture qu’on peut en faire, n’est pas sans conséquence.

Du début août au 27 décembre 1919, en effet, Duchamp habite, avenue Charles-Floquet (Paris 7e), chez Francis Picabia et Gabrielle Buffet (cette dernière enceinte d’un quatrième enfant de lui, qui naît le 15 septembre). Picabia, lui, a emménagé depuis quelques jours ou semaines déjà rue Émile-Augier (Paris 16e), chez Germaine Everling, sa maîtresse (également enceinte de lui, et dont l’enfant naîtra le 5 janvier 1920⁽³⁾). Il faut déduire de cette situation particulière que, durant ce séjour de presque cinq mois, les contacts Duchamp-Picabia n’ont été que très épisodiques, sinon inexistants (sauf, selon toute vraisemblance, vers la fin du séjour), cela permettant d’ “expliquer” pourquoi L.H.O.O.Q. n’est pas publié dans les n 9 (novembre 1919), 10 (décembre 1919) ou 11 (février 1920) de 391, la revue de Picabia, mais bien, dans une version Picabia intitulée Tableau dada par Marcel Duchamp⁽⁴⁾ , dans le n 12 (mars 1920). Michel Sanouillet ajoute sur ce point une précision: “Picabia lui demanda par lettre l’autorisation de “refaire” une Joconde pour 391, autorisation qui fut naturellement accordée. Mais Picabia, qui n’avait conservé de l’oeuvre de Duchamp qu’un souvenir imprécis, se borna à dessiner la moustache⁽⁵⁾.” Picabia, en effet, ne reprend sur le coup que “L.H.O.O.Q.”, l’inscription qui deviendra le titre du readymade⁽⁶⁾, l’inscrivant à son tour, verticalement et sans les points, sur l’une de ses toiles, Le double monde⁽⁷⁾, datée de [décembre] 1919 et exhibée sur scène par André Breton lors du Premier vendredi de (la revue) Littérature, le 23 janvier 1920, première manifestation de Dada à Paris.

À cause de son titre (Tableau dada par Marcel Duchamp), la version Picabia passera pour l’original pendant plusieurs années, cet original n’étant montré pour la première fois qu’en mars 1930 à Paris, en même temps qu’une réplique agrandie (faite fin janvier ou début février 1930⁽⁸⁾), lors de l’exposition intitulée La peinture au défi et préfacée par Aragon.

Pour un poète, romancier et critique comme Aragon, un readymade n’est pas, dès cette époque, qu’un objet industriel, déplacé de son contexte et détourné de sa fonction utilitaire.

3

Il faut préciser que la reproduction en couleur qui en est la base n’est pas une carte postale, malgré que tant de gens l’aient dit ou écrit⁽⁹⁾. Il n’y a qu’à regarder le verso, publié par Arturo Schwarz dès 1969 dans la 1re édition de son catalogue, pour constater qu’il n’y a pas le dispositif habituel de la carte postale avec la place pour l’adresse et le timbre (à droite), pour le “message” et la légende de l’illustration (à gauche), mais plutôt, par Duchamp, telle indication technique (au crayon) sur comment photographier le recto, et, plus tard, par dessus la précédente, telle déclaration officielle devant notaire (à l’encre) comme quoi il s’agit bien de l’original⁽¹⁰⁾. Ce petit palimpseste, au verso, n’ayant d’égal, au recto, que cette mine (de crayon ajoutant les moustaches et la barbiche⁽¹¹⁾) sur la mine (de la Joconde).

Mais où Duchamp s’est-il procuré cette reproduction en couleur? Le plus vraisemblable, comme il le raconte aux Janis en 1953, est qu’il l’a achetée dans quelque boutique installée près du Louvre, rue de Rivoli, afin de vendre à bon marché telle ou telles reproductions des grandes oeuvres de ce musée, façon de faire bien connue dans toutes les grandes villes où il y a d’importants musées. Faut-il rappeler qu’en avril 1911 le déjà très célèbre tableau de Léonard, peint au début du XVIe siècle, a été volé au Louvre et que, parce qu’on pouvait le croire disparu ou détruit (il ne sera retrouvé qu’en décembre 1913), on en a massivement diffusé, durant ces années ou immédiatement après, diverses reproductions couleur, photos retouchées ou non, dont certaines au format d’une carte postale⁽¹²⁾. Sans doute sait-on également qu’en 1919 c’est le 400e anniversaire de la mort du peintre. Il est fait allusion à ces deux événements (telle perte peut-être irrémédiable et tel anniversaire) dans le choix de Duchamp.

Quand Duchamp demande par lettre (New York, 9 mai 1949) à son ami Henri-Pierre Roché d’aller acheter une ampoule de sérum – devenue ampoule d’Air de Paris – pour remplacer celle, actuellement cassée, qu’il a rapportée de Paris, fin décembre 1919, à ses amis Louise et Walter Arensberg, il écrit:

Pourrais[-]tu aller dans la pharmacie qui est au coin de la rue Blomet et la rue de Vaugirard (si elle existe encore, c’est là que j’avais acheté la première ampoule) et acheter une ampoule comme celle-ci: 125c.c. et de la même dimension que le dessin […]
— Si pas rue Blomet ailleurs, mais autant que possible la même forme, merci.⁽¹³⁾

La simple consultation d’un plan de Paris nous indique tout de suite qu’il n’y a pas de coin Blomet-Vaugirard, ces deux rues (15e) étant parallèles! Je rappelle cet exemple pour indiquer qu’une indication précise, même venant de l’auteur, peut être tout simplement inexacte, voire erronée. Ainsi en est-il de L.H.O.O.Q., carte postale.

Et quand Duchamp, dans “Apropos of Myself” (1962-1964), décrit cette reproduction en couleur comme étant “a cheap chromo”, il faut préciser qu’en français comme en anglais chromo est l’abréviation de chromolithographie “image lithographique en couleur” (Petit Robert I), chromolithograph “a color print produced by chromolithography”(The American Heritage of the English Language). En français, cependant, chromo, maintenant au masculin (et non plus au féminin), a un sens péjoratif: “toute image en couleur de mauvais goût”. Ce sens supplémentaire, qui met en scène le goût, fait intervenir la question esthétique, voire artistique, ce qui n’est pas le cas en anglais, cheap signifiant dans cet exemple “of poor quality” (dont la reproduction est de mauvaise qualité), mais surtout “inexpensive” (qui est bon marché⁽¹⁴⁾).

4

Quand Duchamp, dans ses entretiens de 1966 avec Cabanne, parle de Picabia et de L.H.O.O.Q., il en profite, si je puis dire, pour ajouter:

Une autre fois Picabia a fait une couverture de 391 avec le portrait de [Georges] Carpentier; il me ressemblait comme deux gouttes d’eau, c’est pour cela que c’était amusant. C’était un portrait composite de Carpentier et de moi.⁽¹⁵⁾

Cette autre fois, c’est l’été 1923, quand Georges Carpentier, le boxeur, est venu chez Picabia, au Tremblay-sur-Mauldre, le petit village où il habite depuis 1922, et que ce dernier a fait son portrait de profil; le boxeur, alors, a même signé le portrait. Quand Picabia, plus d’un an plus tard, a décidé de mettre ce portrait en première page du dernier numéro de 391 (n 19, octobre 1924), il a barré incomplètement cette signature (qu’on peut lire sous la rature) et a ajouté “Rrose Sélavy / par Picabia”, frappé après coup par la ressemblance entre Carpentier et Duchamp (dont Sélavy est le pseudonyme depuis 1920)⁽¹⁶⁾. Duchamp ne faisant qu’entériner, en 1966, cette “interprétation” de Picabia.

De la même façon, si, par contiguïté, ce “portrait composite” désigne aussi L.H.O.O.Q., il faut en déduire que Duchamp rappelle, en 1966, sa déclaration de 1961 à propos de ce readymade:

La chose curieuse à propos de cette moustache et de ce bouc est que, lorsque vous regardez le sourire, Mona Lisa devient un homme. Ce n’est pas une femme déguisée en homme, c’est un vrai homme; voilà ma découverte, sans qu’à l’époque je le réalise.⁽¹⁷⁾

En 1919, une femme (La Joconde dans L.H.O.O.Q.) est aussi un homme comme, en 1920-1921, un homme (Marcel Duchamp en Rose, puis Rrose, Sélavy) est aussi une femme.

5

Sans vraiment entrer dans l’interprétation du célèbre readymade, il peut néanmoins être remarqué que ce 400e anniversaire a pu être non seulement un déclencheur (en tant qu’anniversaire), mais aussi une contrainte (en tant que chiffraison), le 4 disant qu’il ne faut utiliser que quatre lettres, les 00 suggérant que l’une d’elles, qui doit être un O, soit redoublée⁽¹⁸⁾. Ces quatre lettres, comme Duchamp le dit dans “Apropos of Myself”, étant, comme on peut ici aussi le constater après-coup, dans l’ordre alphabétique – H, L, O, Q – dans le nom de la rue (cHarLes-flOQuet) où il habite alors. Mais aussi dans le nom du procédé à la base de cette reproduction: elle est cHromoLithOgraphiQue.

Et il me plaît de constater qu’à New York la notaire choisie par Duchamp et qui, signant, certifie, le 22 décembre 1944, qu’il s’agit de l’original (“This is to certify that this is the original “ready made” L H O O Q Paris 1919”⁽¹⁹⁾ ), se nomme Elsie Jenriche⁽²⁰⁾: comment ne pas voir qu’elle est là aussi parce qu’elle a ce nom (qui, de ce fait, revient métatextuellement sur l’un des enjeux de l’oeuvre), mixte de “je” (I en anglais ou Ich en allemand) et d’”autre” (else), et qu’il y est question de “genre” (jenre), else rimant avec le féminin (elle: La Joconde, La Gioconda) qui rime avec le masculin (L: Léonard, Louvre), elle étant devenu il!

Enfin, si l’on trace une ligne verticale à angle droit avec le haut de l’oeuvre et qu’on passe par le centre des moustaches, on voit bien que, à cause de l’angle du visage, on longe le nez, à gauche, du personnage femelle et désormais aussi mâle et qu’on arrive, “down below” (comme dira Duchamp en 1961), exactement entre “L.H.” et “O.O.Q.”. Ce redoublement du O est alors, une fois de plus, désigné.

Notes

1. Toujours inédits, les entretiens avec la famille Janis (Sidney, le père, Harriet, la mère, et Carroll, le fils) ont été faits à l’occasion de la préparation, par Duchamp, du catalogue et de l’accrochage de l’exposition Dada 1916-1923 à la Sidney Janis Gallery, New York, 15 avril-9 mai 1953. Dans la chronologie intégrée du catalogue Joseph Cornell / Marcel Duchamp… in resonance Joseph Cornell / Marcel Duchamp… in resonance, Philadelphia Museum of Art, 8 octobre 1998-3 janvier 1999, et The Menil Collection, Houston, 22 janvier-16 mai 1999, Ostfildern-Ruit, Cantz Verlag, 1998, p. 277, Susan Davidson, sans dire d’où elle tire cette précision, retient également le mois de décembre.

2. Pierre Cabanne, Entretiens avec Marcel Duchamp, Paris, Belfond, 1967, p. 114.

3. C’est un jour après la rencontre d’André Breton, invité là, et douze jours avant que, le 17 janvier, Tristan Tzara n’arrive là pour y habiter, ce séjour coïncidant avec le début de ce que Michel Sanouillet a appelé “Dada à Paris”: voir sa somme, Dada à Paris, Paris, Pauvert, 1965. Le siège du “MoUvEmEnT DADA, Berlin, Genève, Madrid, New York, Zurich”, dit le papier à lettre qui arbore cet en-tête, est maintenant à Paris. Par ailleurs, je note la coïncidence (qui n’en était peut-être pas une en 1919, étant donné l’état des connaissances sur l’oeuvre de Léonard): lorsque Duchamp est à Paris cette année-là, les deux femmes (l’épouse et la maîtresse) de Picabia sont enceintes de garçons; lorsque Francesco del Giocondo, au printemps 1503, passe une commande à Léonard pour qu’il fasse un portrait de son épouse, celle-ci lui a déjà donné deux garçons (en mai 1496 et en décembre 1502). Voir, autre somme, Daniel Arasse, Léonard de Vinci. Le rythme du monde [1997], Paris, Hazan, 2003, p. 388-389. La rime, ici, dans les deux cas: Joconde / féconde.

4. À Cabanne, Duchamp dit Tableau dada de [sic] Marcel Duchamp.

5. Michel Sanouillet, Francis Picabia et “391”, tome II, Paris, Losfeld, 1966, p. 113. (Le tome I est, en fac-similé, la réédition de 391 [1917-1924] augmentée de divers documents inédits, Paris, Losfeld, 1960.) Duchamp étant à New York depuis le 6 janvier et le no 12 de 391 ne paraissant (précise Sanouillet) qu’à la fin mars, on peut penser que Duchamp, interviewé par Schwarz (The Complete Works of Marcel Duchamp, New York, Abrams, 2e édition, 1970, p. 476), se souvient erronément de ce qui s’est passé à l’époque (je retraduis): “Mon original n’est pas arrivé à temps et, afin de ne pas retarder indûment l’impression de 391, Picabia a dessiné lui-même la moustache sur la Mona Lisa mais a oublié la barbiche.”

6. Je dis “l’inscription qui deviendra le titre du readymade” car, dans le catalogue-affiche de l’exposition chez Sidney Janis, Duchamp écrit: “La Joconde, postcard with pencil”. Ce n’est qu’à partir du premier catalogue de l’oeuvre duchampienne, celui de Robert Lebel (Sur Marcel Duchamp, Paris, Trianon Press, 1959), que ce readymade a L.H.O.O.Q. comme titre. Et ce n’est qu’à partir du catalogue Schwarz (Arturo Schwarz, The Complete Works of Marcel Duchamp, New York, Abrams, 1re édition, 1969) qu’on a les dimensions exactes dudit readymade: 19.7 x 12.4 cm ou 7¾ x 4⅞ pouces.

7. Les deux O de “L H O O Q”, eux-mêmes au centre de deux autres O qui ont la forme de ficelles formant des 8 ou encore la forme des pales d’une hélice, mais d’une hélice sans axe et molle, courbée par le vent, sont également – et doublement – les O de “double” et de “monde”. Le petit manque, en haut à gauche, dans l’un de ces autres O n’a d’égal, en bas à droite, que le petit manque dans le À de “À DOMICILE”, une autre inscription, et que le petit supplément – la queue – du Q de “L H O O Q”. Façon de faire coïncider ironiquement spéculations mathématiques (topologie) et spéculations marchandes (livraison “à domicile”, c’est-à-dire au logis).

8. “J’ai fait juste avant de quitter Paris une Joconde pour Aragon […] / Man Ray a la 1ère Joconde” (lettre de Duchamp à Jean Crotti, Villefranche-sur-mer, 6 février 1930, dans Affectionately, Marcel. The Selected Correspondance of Marcel Duchamp, édition de Francis Naumann et Hector Obalk, traduction de Jill Taylor, Gand et Amsterdam, Ludion Press, 2000, p. 171).

9. Trois exemples: Duchamp lui-même en 1953 (voir note 6); Ecke Bonk, Marcel Duchamp, The Box in a Valise. Inventory of an Edition, New York, Rizzoli, 1989, p. 241; Calvin Tomkins, Duchamp. A Biography, New York, Henry Holt and Company, 1996, p. 221.

10. Faut-il ajouter que Duchamp, dans les répliques ultérieures, n’a jamais utilisé une carte postale.

11. J’utilise ici le pluriel, comme Duchamp en avril 1942 lorsqu’il indique à l’encre, au bas de la maquette de l’une des deux versions Picabia (celle qui est reproduite dans 391), “Moustaches par Picabia / barbiche par Marcel Duchamp”. En français, on dit indifféremment, par exemple, ciseau et ciseaux (car il y a deux lames), pantalon et pantalons (deux jambes), moustache et moustaches (deux joues ou, simplement, deux côtés au visage). Je note par ailleurs que l’indication technique, inscrite par Picabia sur deux lignes au crayon verticalement à droite de la reproduction, commence par deux liaisons – celle qui amorce le 1 de “1 cliché” sur la première ligne et celle qui amorce le s de “sans” sur la deuxième ligne – qui n’ont d’égal que l’extrémité des moustaches! Pour une reproduction et des commentaires, voir Francis Naumann, The Art of Making Art in the Age of Mechanical Reproduction, catalogue de l’exposition chez Achim Moeller Fine Art, New York, 2 octobre 1999-15 janvier 2000. Si le voyage à Paris fait par Arp en avril 1942 est bien celui durant lequel il entre en possession de ces deux versions, la rencontre Arp-Duchamp (qui se connaissent depuis 1926) ne peut avoir lieu qu’en zone inoccupée (à Grasse où habite Arp, à Sanary où habite Duchamp, avant le départ de ce dernier pour les États-Unis le 14 mai).

12. Voir les deux cartes postales, datées 1914, reproduites dans Roy McMullen, Les grands mystères de la Joconde [1975], traduction d’Antoine Berman, Paris, Éd. de Trévise, 1981, p. 223.

13. Affectionately, Marcel, ouvr. cité, p. 272.

14. C’est d’ailleurs la traduction, par Michel Sanouillet, de ce passage: “un chromo […] bon marché” (“À propos de moi-même”, dans Duchamp du signe, Paris, Flammarion, 1975, p. 227). Naumann emprunte exactement la même voie: “an inexpensive chromo-lithographic color reproduction” (The Art of Making Art in the Age of Mechanical Reproduction, ouvr. cité, p. 10).

15. Pierre Cabanne, Entretiens avec Marcel Duchamp, ouvr. cité, p. 115.

16. Voir Michel Sanouillet, Francis Picabia et “391”, ouvr. cité, p. 166. On peut voir (391, ouvr. cité, p. 127) la signature de Carpentier et l’ajout de Picabia sous quelques-unes des lignes imprimées en caractères typographiques au bas de la page.

17. Herbert Crehan, “Dada”, Evidence, Toronto, n 3, automne 1961. Je traduis.

18. Ces deux “O.” ne sont pas sans évoquer aussi, par la rime “O.” / eau, le lac de montagne et le lac de plaine dans le célèbre tableau, respectivement en haut à droite et un peu plus bas à gauche dans le paysage dominé par la loggia où est le modèle, Lisa. Et que dire du chemin sinueux venant du lac de plaine, répercuté dans la queue du “Q.” (calligraphié par Duchamp)?

19. Une phrase présentative dans une autre, le référent de “This” (Ceci, comme dans “Ceci est mon corps” ou dans “Ceci est une oeuvre d’art”) étant cataphorique (c’est-à-dire qu’il suit le pronom): dans le premier cas, c’est “the original “ready made””; dans le second cas, c’est l’ensemble de la proposition formant le premier cas.

20. Dans son bref article, ““Desperately Seeking Elsie”. Authenticating the Authenticity of L.H.O.O.Q.’s Back” (Tout-Fait, New York, vol. I, n 1, décembre 1999), Thomas Girst nous apprend que cette dame, installée à l’Hotel St. Regis, New York, de 1943 à 1945, est une sténographe publique.

click to enlarge

Figure 1
Antonio
Sant’Elia, La Città Nuova, Italy, 1914
Figure 2
Shiro Kuramata,
Glass Chair, 1976

Marcel Duchamp (1887-1968) was a French painter turned conceptual artist, film maker, erotic guru, and chess player. He was, however, never an architect, nor specifically interested in architecture, and yet, he has exerted a tremendous influence over a generation of architects practicing after 1975, as well as over current architectural historians and theorists. Contemporary literature in architectural theory has gone so far as to argue that architectural works created before many of the works of Duchamp, such as La Città Nuova (Fig.1), be understood within the context of Duchamp’s works.Architects have, in roughly the past twenty-five years, picked up on concepts in which Duchamp was interested and integrated them into their works. This has been possible largely because of dramatic shifts in the way that art is defined in this new postmodern era.Sundry Duchampian concepts or fascinations, such as projection, chance, and metaphor, seen throughout the wide range of his post 1912 works, have been interpreted and used by numerous architects and designers. This phenomenon has occurred both in a sort of direct homage to one or more of Duchamp’s works as well as in a more subtle, intellectual sort of homage, incorporating a Duchampian concept, such as chance, not only into a single architectural work, but into the way that an architect creates any architectural work.Some work, such as that of furniture designer Shiro Kuramata (Fig. 2), has been preoccupied with the former. Some architects claiming to be Duchamp’s standard-bearers, such as California team Morphosis, acknowledge Duchamp’s influence in both ways.Even famous and influential contemporary architects Frank Gehry and Robert Venturi also occasionally directly base a work on a work by Duchamp. However, the works of Gehry and Venturi are particularly useful in illustrating the latter, intellectual type of acknowledgment of Duchamp, as permeating all of their works are evidence of Duchampian thinking about concepts such as chance and metaphor.A final architectural firm, Diller + Scofidio, has incorporated so many Duchampian concepts, not only projection, chance, and eroticism as metaphor, but also ideas such as the infra-thin, ambivalence, ambiguity, and ephemerality, that their work can be seen as truly Duchampian architecture. This discussion seeks to establish why and how Marcel Duchamp has been so influential in contemporary architecture by thoroughly exploring the Duchampian concepts of projection, chance, and metaphor both within Duchamp’s work and that of contemporary architects whom he has influenced, and then further exploring these and other Duchampian ideas through the work of two postmodern architects upon whom Duchamp has been extraordinarily influential, Elizabeth Diller and Ric Scofidio.

click to enlarge


Figure 3
Marcel Duchamp, Given:
1. The Waterfall / 2.The
Illuminating Gas,
1946-1966, Philadelphia Museum of Art

Figure 4
Image of Antonio
Sant’Elia, 1914

At first it may seem somewhat strange, that Marcel Duchamp should be so influential on the theory and practice of architecture and design of the period after 1975, considering that Duchamp was not an architect. The only works that could be termed ‘architectural’ for which he was responsible, the door and room of Étant Donnés (Fig. 3) and the door that is neither open nor closed, would hardly elevate Duchamp to the status of a guru in contemporary architecture on their own. Duchamp did receive training in technical drawing, which including drawing mechanical and architectural objects, such as doors⁽¹⁾ but this, too, fails to qualify Duchamp as an architect. This problem is complicated even more by the fact that there were practicing architects in his milieu with interests similar to those of Duchamp. One such architect was Antonio Sant’Elia (Fig. 4), the Italian Futurist architect best remembered for his drawings for La Città Nuova. Sant’Elia, like Duchamp and many others living in the 1910s, was interested in non-Euclidean geometry, and the Futurists, like Duchamp, were affected by the new technological innovations of their day, such as the discovery of x-rays and the appearance of the incandescent lamp, the hydraulic generator, the skyscraper, cinema, and the automobile.⁽²⁾Duchamp was very familiar with the ideas of the futurists⁽³⁾, and both men were similarly a product of their cultural milieu. Furthermore, unlike Duchamp, Sant’Elia actually created detailed urban plans and architectural drawings for a city of the future, La Città Nuova, integrating into an urban spatial form the new ideas about a space-time continuum.⁽⁴⁾

click to enlarge

Figure 5
Marcel
Duchamp, The Bride Stripped
Bare by Her Bachelors, Even
[a.k.a. The Large Glass], 1915-23

Figure 6
Marcel Duchmp,Cover of
The Bride Stripped Bare
by Her Bachelors Even [a.k.a.
The Green Box], 1934 (regular edition)

If Sant’Elia was infinitely more involved in architecture than Duchamp, and sharing many of the ideas Duchamp held in the 1910s, it is perhaps astonishing, then, that a current scholar of La Città Nuova, Sanford Kwinter, believes that La Città Nuova should be viewed within a Duchampian context.Kwinter argued in 1986 that, “La Città Nuova may be understood in this light less as a literal, realizable program than as a set of instructions [as Duchamp’s procedural Green Box], governing not only the assembly of isolated modules of (bachelor) machinery…”⁽⁵⁾ Antonio Sant’Elia was killed in 1916 and the bulk of his work on La Città Nuova is from 1914,⁽⁶⁾while Duchamp’s The Bride Stripped Bare by Her Bachelors, Even (Fig. 5), hereafter referred to as the Large Glass, referenced by the phrase ‘bachelor machinery,’ dates from 1915-1923. The Green Box (Fig. 6), an explanation of the Large Glass, dates to 1934.⁽⁷⁾ In claiming that La Città Nuova be viewed within the context of works by another artist, not even an architect, which were created after La Città Nuova, Kwinter, besides pulling Sant’Elia’s work totally out of context, demonstrates the passionate love affair of contemporary architectural historians and theorists with Marcel Duchamp. The question remains, though, why is Duchamp so influential within contemporary architectural theory, while other seemingly valid figures, such as Sant’Elia, while still important, are much less cited than Duchamp?The simple answer is that the nature of Duchamp’s influence has nothing to do with architecture directly, and everything to do with his ideas. Duchamp did not specifically write, or at least did not intend to write, architectural theory, yet, it is in the realm of theory that he has been most influential, chiefly because he was the first truly idea-oriented artist, the antecedent of the conceptual artist.

Throughout his life, Duchamp was fascinated by chance. The Three Standard Stoppages (Fig. 7) are chance forms of measurement. The appearance of the Three Standard Stoppages, their lengths and shapes, were determined entirely by chance. His Monte Carlo Bond (Fig. 8) was created so that others might invest in a gambling trip that he wished to take. Would others take a chance and invest so that Duchamp could play a game of chance?There was also a strong element of chance in the creation of the readymades. The objects chosen as readymades were chosen at random, mass-produced, and were aesthetically indifferent, that is one would not usually go up to the object and feel anything about its aesthetic qualities one way or the other because it had none in its normal context. Fountain (Fig. 9), a urinal not markedly different from any other urinal, bought by Duchamp in an everyday New York plumbing shop, has been elevated to cult artistic status and was branded by some as an abomination and hailed by others as a beautiful form. Any other urinal would have served the artistic function just as well as the one that became Fountain, just as any other mass-produced urinal would serve a man who needed to relieve himself just as well. Each readymade involved an element of chance in this way.

click to enlarge


Figure 10
Frank O. Gehry, Guggenheim
Museum in Bilbao (in two views),
Spain,1997

Figure 11
Le Corbusier, Villa Savoye,
1928-30

Figure 12
Morphosis, Diamond Ranch
High School, Pomona,
California, 2000

Figure 13
Marcel Duchamp,
bôite-en-valise, 1935-41

In an explanation of how the design for his Guggenheim Museum in Bilbao (Fig. 10), Spain, came about, Frank Gehry noted that it just happened, was a lot like a chance fluke.⁽⁸⁾ This is in stark contrast to the Modernists of the early-middle twentieth century, who were obsessed by perfect proportions and the golden mean. Le Corbusier, for example, used a precise geometric formula in his early high International Style work of the 1920s (Fig. 11). He had rules controlling how line and form could be used and tried to adhere to a difficult system of proportion called the golden section. This required room proportion ratios to be 1:1.618.⁽⁹⁾

Gehry observed this in a statement concerning the freedom that chance gives an architect,

“I used to be a symmetrical freak and a grid freak. I used to follow grids and then Istarted to think and I realized that those were chains that Frank Lloyd Wright was chained to the 30-60 grid, and there was no freedom in it for him, and that grids are an obsession, a crutch. You don’t need that if you can create spaces and forms and shapes. That’s what artists do, and they don’t have grids or crutches, they just do it.”⁽¹⁰⁾

While International Style and earlier architects rigorously adhered to meticulous formulas, an architect today chooses the forms of a building, of a space, in the same way that Marcel Duchamp walked into a store and chose a readymade. They just do it. Much contemporary architecture, then, from the works of Frank Gehry to Robert Venturi to Peter Eisenman can be read as Architectural readymades.

Besides living legends such as Venturi and Gehry, younger, up and coming architects, are also interested in Duchampian ideas, specifically in the Architectural readymade. Thom Mayne, a younger California architect with an interest in the work of Frank Gehry and who practices under the name Morphosis, claims Duchamp as his idol. Morphosis tries to make every building an Architectural readymade. He claims that he, “treats materials, sanitary fittings, and bits of plan with innocent astonishment, that is, as objets trouvés.”⁽¹¹⁾ It can be said, then, that Morphosis selects its urinals along with the rest of the building components as Duchamp did. A recent Morphosis project, though, the Diamond Ranch High School in Diamond Bar, California, (Fig. 12), shows that Morphosis has made use of chance, of the Architectural readymade, in much the same way as Gehry.⁽¹²⁾ For the school, Mayne created jutting, or projecting, forms, brought together at random, or at least to give that effect.

Eroticism as a metaphor was a constant motif throughout Duchamp’s career. Sometimes this was simply playful, such as issuing his bôite-en-valise (Fig. 13), portable museums, in an edition of the sexually significant number 69. Most often, these works were not specifically about eroticism, they just used eroticism as a metaphor for something else, namely art. Duchamp’s masterpieces, the Large Glass and Étant Donnés, first and foremost raise issues about the nature of artistic practice in light of technological, societal, and artistic change. The Large Glass was about the act of painting in an age in which abstraction challenged the mimetic nature of the craft, the fallacy of one-point perspective in relation to actual sight was well known, and photography and cinema could produce mimetic works more quickly, accurately, and cheaply than painting. This is shrouded in an elaborate game in which nine bachelors try to satisfy their desire and impregnate the ‘bride.’ Étant Donnés, on the previous page, was created in a time in which there was a crisis, a near-death incident, in the life of representational art. His hyper-realistic painted landscape in the background of the work and the complete illusionary nature of the work as a whole challenged the assumption of the middle of the twentieth century that painting, or art in general, should be abstract. This was in the guise of a nude woman with her sex exposed in the foreground. Duchamp not only used eroticism as metaphor, but used his own works as metaphors of each other. The Large Glass and Étant Donnés are both metaphors of each other not only because they are reverse projections of each other, but also because they allude to each other through having the same theme, the bride, the waterfall, and the illuminating gas.Architects have been, since the 1970s and ‘80s, using metaphor in a downright Duchampian manner, to explore what it means to be an architect in the face of the information technology revolution, computers replacing the t-square and drafting table, the ‘cult of the box’ of architecture of the middle twentieth century, the impact of the automobile and the highway on architecture and urbanism, and the increasing prevalence of mass architecture, such as strip malls. The issues raised by much current architecture because of and in response to these technological and societal shifts, is the same raised by Duchamp in works such as the Large Glass and Étant Donnés.

click to enlarge

Figure 14
Golden Goose. Downtown
Las Vegas (Fremont Street) by night

Figure 15
Mies van der Rohe,
Chapel, Illinois
Institute of Technology,
Chicago, 1953

Robert Venturi’s Learning from Las Vegas (1977) , a seminal work in postmodern architectural theory, uses metaphor, though definitely not of an erotic nature, to explain the state of architecture in America in the 1970s. Las Vegas is used as a metaphor for the need for increased decoration and less of the International style high seriousness of Le Corbusier and Mies van der Rohe (Figs. 14 and 15). Like Duchamp, who also rejected the high seriousness prevalent in artistic circles in his own time, Venturi used humor throughout the work. After the metaphor of Las Vegas itself, the book’s most overriding metaphor is that of the duck and the decorated shed. The duck, a building shaped like a duck, is a metaphor for buildings which are symbols. This is based on a real duck-shaped building, a restaurant specializing in roast duck, from God’s Own Junkyard.⁽¹³⁾ A decorated shed, on the other hand, refers to any of the various average looking buildings by the highway which are heavily decorated with signs and logos, and more globally to any building covered with ornament. Within this framework, Chartres Cathedral is a duck (though it is a decorated shed as well), while Renaissance buildings are all decorated sheds.⁽¹⁴⁾ (Figs. 16 and 17) Sentences from Learning from Las Vegas, such as “Minimegastructures are mostly ducks,”⁽¹⁵⁾ show just how heavily Venturi relied upon metaphor. Really, Venturi’s duck and decorated shed are Duchamp’s bride in this respect.

click to enlarge

Figure 18
Marcel Duchamp, L.H.O.O.Q., 1919

In Learning from Las Vegas, Venturi also suggested placing a replica of the shape and text of a marquee from Caesar’s Palace in Las Vegas advertising popular comedian Flip Wilson to perform in the ‘Circus Maximus’ over a print by Piranesi of the Pantheon.⁽¹⁶⁾ This gesture is the equivalent of Duchamp’s iconoclastic gesture in his painting L.H.O.O.Q.(Elle a chaud au cul.), or ‘she has a hot ass’, on a print of the Mona Lisa (Fig. 18). This work by Venturi, advertising Flip Wilson on the front of the Pantheon, is both a direct homage to a single work of Duchamp, L.H.O.O.Q., as well as a more intellectual homage to Duchamp through the use of metaphor.With Duchamp, the metaphor is again eroticism, with Venturi, it is Las Vegas. This work is also important in that it is so clearly directly indebted to Duchamp, one may surmise that Learning from Las Vegas, arguably one of the most important works in architectural theory of the late twentieth century, perhaps an important work in the whole history of architectural theory, would not have been written, or at least not have been written in nearly the same way, were it not for Marcel Duchamp.Marcel Duchamp’s ideas have been so important in contemporary architectural theory and practice that many architects and designers have created works which are inspired by literal or stylistic elements of Duchamp’s works. This is directly in contrast with Duchamp’s views on avoiding repetition and on the irrelevance of style or the visual, and is certainly not that most reverential way to pay tribute to the father of conceptual art. Works such as the readymades went against the ‘mimetic’ or ‘retinal’ nature of art, yet as Tilman Kuchler argued in a discussion of the ‘end of modernity and the beginning of play’, theysolicit processes or artistic representation and reproduction in the postmodern era.⁽¹⁷⁾This goes beyond reproducing Duchamp’s work, such as the inaccurate assertion hand-crafted reproductions of Fountain made to sell in Arturo Schwarz’s gallery. This type of homage involves miming the visual aspects of one of Duchamp’s works.Shiro Kuramata, a prominent Japanese furniture designer of the 1980s, frequently used this sort playful retinal homage to Duchamp in his work. Kuramata, like many postmodern artists, architects, and designers, called Duchamp his idol.⁽¹⁸⁾ Works such as his Miss Blanche armchair of 1988 ( Fig. 19), left, playfully allude to Duchamp’s works, while ignoring much of the intellectual content of Duchamp. The chair’s title is actually a reference to Blanche Dubois of Tennessee William’s A Streetcar Named Desire, but Kuramata admitted that the embedding of paper roses within the acrylic body of the chair is a homage to Duchamp’s female alter ego, Rrose Sélavy.⁽¹⁹⁾ A detail of Miss Blanche also elicits a visual, or retinal, comparison with a detail of the Large Glass. The visual effects achieved by the roses and by the nine malic molds are quite similar, though the thinking behind them could not be more different. Kuramata also created a set of acrylic perfume bottles, inspired by Rrose Sélavy’s perfume bottle, Belle Haleine, eau de voilette (Figs. 20 and 21). These works by Kuramata take their inspiration from Duchamp in a very literal way, and are therefore not Duchampian at all. This honorific literalization of Duchamp’s works has not, however, been the sole way in which Duchamp has appeared as an influence in current visual production. Rather, some have tried to copy or acknowledge Duchamp’s ‘style’ or ‘look,’ if such a quality even exists, because the larger and more important theoretical implications of Duchamp have made him such a popular figure, a veritable guru, in the contemporary era.

click to enlarge

Figure 22
Morphosis,Kate Mantilini
Restaurant, Beverly Hill,
California, 1986

Figure 23
Marcel Duchamp, Chocolate
Grinder No. 1, 1913

In the past, Morphosis, too, sometimes dabbled in a more literal and, therefore, less successful use of Duchamp. For Kate’s, a Hollywood restaurant completed by Morphosis in 1987 (Fig. 22), the architects made the centerpiece of the interior space a large mural of boxers and a chocolate grinder.⁽¹⁾(At this time, Michael Rotondi, another young California architect, was also a principal of Morphosis. Rotondi and Mayne were partners until 1991.) This is meant to recall Duchamp’s amusing painting of a Chocolate Grinder (1911) (Fig. 23), amusing because it takes its inspiration from the French saying “Bachelor grinds his own chocolate [masturbates].” In the same article about Morphosis, “Duchamp Goes West”, Rowan Moore goes on to note that instances such as this are part of the reason that subtlety and originality are all too often lacking in current architectural practice.⁽²¹⁾ Duchamp, Moore argues, mentioned too frequently or lightly, will become as meaningful as a Campbell’s Soup can, a Leon Krier pediment, or a Gehry fish.”⁽²²⁾

Even Frank Gehry has, on occasion, been mildly guilty of this mimetic crime. The look of Gehry’s Telluride Residence in Telluride, Colorado, which has been in the planning stages since 1995, is based, in Gehry’s words, on Duchamp’s Nude Descending a Staircase. (Figs. 24 and 25)⁽²³⁾ The house will step down the hill for which it is intended, just as Duchamp’s Nude steps down the stairs. Unlike Kuramata, however, who used roses to recall Rrose Sélavy, Gehry’s house does not go so far as to have an abstracted, monochromatic nude figure painted on it. Instead, the Telluride Residence is the mechanomorphic nude. The house serves as a metaphor for Nude Descending a Staircase, as well as a simple visual recollection of the painting, and thus escapes the mimesis of Kuramata.

Many contemporary architects, not only Gehry, have been visually inspired by Nude Descending a Staircase. For example, the fire station designed by Zaha Hadid for the Vitra complex in Germany (1990-1993) (Fig. 26), was also inspired in part by Duchamp’s Nude,⁽²⁴⁾ and the aerial computer plan of Morphosis’ Diamond Ranch High School can also visually be likened to Nude Descending a Staircase. There is even debate over whether Gehry’s Guggenheim Museum, Bilbao looks more like Nude Descending a Staircase or like Futurist artist Umberto Boccioni’s sculpture, Unique Forms of Continuity in Space. (Fig. 27)⁽²⁵⁾ Again, these comparisons and debates lead away from the true nature of Duchamp and the reasons for which he is so much discussed and quoted. It is perhaps partly coincidental that contemporary deconstructivist architecture looks so much like Nude Descending a Staircase, partly that the deconstructivists are visually stimulated by works of Boccioni and of early Duchamp, and partly due to the fact that, as mentioned previously, Duchamp’s cult status encourages many writers as well as architects to invoke Duchamp and identify with him. When one realizes that works such as Antonio Sant’Elia’s preliminary drawings for La Città Nuova also have much visually in common with structures such as Diamond Ranch High School, the explanation of Duchamp’s stylistic influence through cult association becomes the most convincing.

click to enlarge


Figure 28
Liz Diller and Ric Scofidio,
Blur Building by day
and night, Yverdorn-les-Bains,
Expo 2002, Switzerland

Figure 29
Marcel Duchamp,Manual
of Instructions
for the Assembly of “Etant
donnés”: “Approximation démontable,
exécutée entre 1946 et
1966 à New York”, 1966,
Collection of Philadelphia
Museum of Art

For the architectural firm of Diller + Scofidio, sex and eroticism, as well as other Duchampian fascinations, are important themes in their work. Architects Liz Diller and Ric Scofidio achieved much fame in 2001 for their pavilion for the Swiss Exposition of 2002), the Blur building, a ‘building’ made almost entirely of water vapor, with a little steel used (Fig. 28).⁽²⁶⁾ In 2002, Diller + Scofidio published their notes (four years worth) for the project in a book called Blur: The Making of Nothing. The book contains reproductions of the notes in all their forms, on cocktail napkins, on lined yellow notebook paper, and with photographs of the rings of binders and colors of folders, much in the same way that Duchamp’s manual for the Étant Donnés were published by the Philadelphia Museum of Art (Fig. 29). Numerous other parallels with Duchamp can be seen in the work of Diller + Scofidio. This architectural work shares the ephemeral quality of the readymades. Just as many of the original readymades were thrown away when their exhibition was over, this building literally faded away, evaporated when the exposition was over.This pavilion can be read as the ultimate expression of another Duchampian concept, the infra-thin. Dawn Ades described the infra-thin as follows,

“An example of ‘visible infra-thin’ is iridescent cloth, or shot silk, which has a different character or colour according to the -light…Infra-thin then points to a condition of liminality, that is, something on the threshold (between inside and outside, for example); the interface between two types of thing (smoke and mouth); a gap or shift that is virtually imperceptible but absolute…Infra-thin encompasses time and space as well…”⁽²⁷⁾

Like iridescent cloth, a pavilion made of water vapor can be seen through, its appearance changing with light and weather conditions.Indeed, in the making of the pavilion, many photographs were taken with time, relative humidity, and temperature noted.⁽²⁸⁾ Such a building would hover within the threshold between inside and outside, its bounds being imperceptible and ever-changing, its duration ephemeral. The walls of such a building would be walls and not walls (again, the door is neither open nor closed), ever shifting, and either barely visible or oppressively opaque depending on the amount and type of light filtering through the vapor. Ben Rubin, a project manager for Diller + Scofidio, called the cloud building “pure visual noise.”⁽²⁹⁾ This is undoubtedly what Duchamp meant by the infra-thin, noise which could be seen but not heard, a building made of water vapor, a building that was there and not there. Just as an advertisement for Flip Wilson could never have been placed on a print of the Pantheon had it not been for Marcel Duchamp’s L.H.O.O.Q., neither could a structure made of water vapor have been ‘erected’ without the antecedent of Duchamp’s infra-thin.

This infra-thin building straddled the line between the material and the immaterial, between reality and fantasy, and between conceptual art and architecture. Marcel Duchamp explored new media in his own work, such as the use of mass-produced, purchased objects as his readymades. Similarly, Diller + Scofidio explored a new architectural medium, water vapor, in this highly innovative structure. As with Duchamp, the work was meant to be experienced. Just as one can not fully appreciate Étant Donnés without going to the Philadelphia Museum of Art where it is installed and looking through the peepholes, the experience of the water vapor pavilion lay in the experience. By only reading about it or looking at photographs of it, one loses the experience of getting wet and of losing one’s way in a cloud. Another part of the experience of the water vapor pavilion was the ambiguity and anonymity into which visitors were submerged as they moved through the space. Each visitor was given an identical raincoat, a costume which reinforced the participatory nature of the spectacle (as well as being very useful for remaining somewhat dry). Looking forward to the work, Liz Diller commented on the blur effect,

“We use vision to assess identity; a quick glimpse of another person allows us to identify his/her gender, age, race, and social class. Normally, this visual framework precedes any social interaction. Within the cloud, however, such rapid visual identification is not possible. The foggy atmosphere, combined with visitors in identical raincoats, produces a condition of anonymity. It will be difficult to distinguish a 25-year old Japanese fashion model from a 13-year old Indian boy from a 70-year old Russian grandmother.”⁽³⁰⁾
Diller + Scofidio seek to put architecture at the service of the mind just as Duchamp sought to put art at the service of the mind. The pavilion was not designed to be aesthetically pleasing through its lines or forms. It had no lines and its forms were ever shifting. Rather, the work was designed to make people think about the meaning of architecture and the interface of technology, humans, and the natural environment. Whether a person was even willing to consider the pavilion ‘architecture’ or not was not at issue. Diller + Scofidio gave the viewer, the participant the same experience that Duchamp gave viewers of Fountain when it was exhibited in 1917. The experience, the fun in viewing these works was the chance to think about them afterward and decide whether or not they really were art or architecture.

click to enlarge

Figure 30
Marcel
Duchamp, Comb, 1916/1964

Figure 31
Marcel Duchamp,
Rendez-vous du Dimanche
6 Février 1916, 1916

In the works of both Duchamp and Diller + Scofidio, performance art plays an important element.⁽³¹⁾Duchamp created one of the readymades, the dog comb (Fig. 30), in front of his patron’s Walter and Louise Arensberg. He had created a textual message on four postcards sent two weeks prior to the event, inviting the Arensbergs to this rendez-vous (Fig. 31). This event can be seen as the precursor of the happening of the 1960s, just as attendance at the Diller + Scofidio pavilion can be seen as the latest generation of the happening. In their book, Diller + Scofidio included numerous pictures of themselves working with their crew to create the ‘Estructur.’ They drew crowds and media attention, and this was an integral part of the conception of the work.⁽³²⁾Finally, eroticism was a very important part of both the pavilion, the Blur building, and the entire Swiss Expo.02. There were four sites for Expo.02, Neuchatel, Murten, Biel, and Yverdon.⁽³³⁾ Yverdon, the site of the pavilion, was themed “Sexuality and Sensuality,”⁽³⁴⁾ and Diller + Scofidio and their team, “to avoid contentions of individual authorship, the group members would merge identities to become ‘Extasia’, or ecstasy, in anticipation of winning the preferred site of Yverdon [Diller + Scofidio favored the theme of sexuality and sensuality above the other themes].”⁽³⁵⁾ (Though Diller + Scofidio did produce Blur at the Yverdon site, Extasia was eventually disbanded.)⁽³⁶⁾As the building was to be created on the Yverdon site, themed sexuality and sensuality, the building was expected to take on the Yverdon characteristics.

The organizers of the exposition created detailed explanations of what each of the four themes was all about by comparing each of the four’s responses and attitudes, much like a personality quiz in a popular magazine.
For Yverdon, some of these were:

“Code words: sensuality, sexualityAntonym of code words: asceticismKey questions: Can sensuality and transcendence, eroticism and
sexual drive coexist?Architecture: round, amoeba-like, soft, bubbly, knobby, smallForms: round, organic, soft, amorphous, flowing, carnal, curved,
bumpyDuration: moments, phasesSymbols and cult figures: Romeo & Juliet, Cupid, Aphrodite,
CasanovaActivity: kissing, letting goSeason: summerA phrase: you kiss wellPhilosophical model: hedonism, passion, self-surrenderWhat’s going on, baby?: gender debate, imposedIndividuality: intimacyDrug: aphrodisiacs, alcoholForms of communication: whispering, pillow talk, shoutingTones/noises: lip-smacking, Bossanova, heartbeat, panting, jukeboxObjects: electric plug, dam, a lonely lost ski, vibratorDeath: heart failure, death at orgasmDrink: Bloody Mary, water”⁽³⁷⁾

So, the initial task faced by Diller + Scofidio was to create an innovative temporary exposition pavilion recalling the many qualities listed above. Diller + Scofidio chose the site because of their interest in eroticism, and are showing a Duchampian influence in this way as well. These architectural constraints owe, however, to the phenomenon of postmodernism. In 1910 or 1950, for example, no government organization would have asked an architect for a building which recalled lip-smacking and a lonely lost ski. Though the actual pavilion itself was probably not the least bit erotic, it achieved a certain eroticism by using verbal means, the list on the previous page, to make people think about sex when they think about the Blur building. This is much the same tactic which Duchamp used in the Large Glass. His notes for the Large Glass explain the complicated process of desire and visualize undressing of the bride which is inherent in the work, though not visually detectable without the notes to instruct the viewer. A large mass of water vapor in Switzerland may be very erotic, just as Duchamp’s completely non-representational rendering of a bride may be; it is all dependent upon the framework of ideas within which the viewer approaches the work, and has nothing to do with the visual. The eroticism of Diller + Scofidio can be traced both to an interest in Marcel Duchamp and to the rule breaking of the culture of today. In a final analysis, though, the mere idea of a building, which is not a building, made of water vapor, and devoted to thinking about sex (as opposed to sex itself) detached from any visual or retinal mode of artistic expression, is decidedly Duchampian.

Marcel Duchamp has been quoted and acknowledged time and time again by contemporary architects and theorists because of particularly Duchampian ideas, such as eroticism as metaphor, his uses of new media, and his desire to move away from the retinal qualities of art towards an art which was at the service of the mind. Some writers and architects, including Sanford Kwinter, Shiro Kuramata, and Morphosis have at times misused Duchamp because his name is so en vogue. This has occurred by either invoking Duchamp’s name when no connection really exists or by paying a literal, retinal homage to one or more of Duchamp’s works. Many others, though, have incorporated Duchampian ideas into their own works in a more intellectually based homage. The Deconstructivists are indebted to his ideas about projection and chance, and Robert Venturi (Fig. 32) could not have made his playful jabs at the high seriousness of International Style architecture without Duchamp. Finally, the firm of Diller + Scofidio created a building which can be read as a truly Duchampian building, an embodiment of the infra-thin, playful performance and experiential art, and of a highly intellectualized eroticism. Though Duchamp was never an architect, his thinking has made possible deformed forms, has allowed Flip Wilson’s act to enter into the once sanctified realm of high art, and has allowed architects to literally erect buildings of clouds.

Figure 32
Robert Venturi, Fire Station No. 4,
Columbus, Indiana, 1967 (left);
Vanna Venturi House, Chestnut Hill, Philadelphia, Pennsylvania,
1962 (middle); Trubek and Wislocki Houses, Nantucket Island,
Massachusetts, 1972 (right)

Notes

1. Pierre Cabanne, Duchamp & Co (Paris: Terrail, 1997) 32.

2. K. Michael Hays, ed., Architecture Theory since 1968 (Cambridge, Mass: The MIT Press, 1998) 586.

3. Ibid

4. Sanford Kwinter, “La Città Nuova: Modernity and Continuity,” Architecture Theory since 1968, ed. K. Michael.Hays (Cambridge, Mass: The
MIT Press, 1998) 608.

5. Amy Dempsey, Art in the Modern Era ( New York:Harry N. Abrams, Inc., 2002) 91.

6. Cabanne, op. cit.132.

7. Gehry Partners, Gehry Talks: Architecture + Process (New
York: St. Martin’s Press, 2002) 140.

8. John Pile, A History of Interior Design ( New York: John
Wiley & Sons, Inc:, 2000) 278.

9. Gehry Partners, op. cit. 140.

10. Rowan Moore, “Duchamp Goes West,” Blueprint 36 (May 1987):20.

11. Alice Kimm, “Morphosis Diamond in the Rough,” Architecture Week4 (June 2000): 11.

12. Robert Venturi and Denise Scott Brown, Learning from Las Vegas
(Cambridge, Mass.:The MIT Press, 1977) 88.

13. Ibid.89.

14. Ibid.105-6.

15. Ibid.160.

16. Ibid.61.

17. Tilman Kuchler,Postmodern Gaming: Heidegger, Duchamp, Derrida(New York: Peter Lang, 1994)121.

18. David Hanks and Anne Hoy, Design for Living: Furniture and Lighting,1950-2000 (Paris: Flammarion, 2000)186.

19. Ibid

20. Moore, op. cit. 20.

21. Ibid

22. Ibid

23. Gehry Partners, op. cit. 183.

24. Puglisi, op. cit. 28.

25. Puglisi, op. cit. 27-8.

26. Diller + Scofidio Firm, Blur: The Making of Nothing (New
York: HenryN. Abrams, Inc., 2002) 1.

27. Cox Ades, and Hopkins, op .cit. 183.

28. Diller + Scofidio Firm, op. cit. 70-1.

29. Ibid. 192.

30. Ibid. 209.

31. Cox Ades, and Hopkins, op. cit. 208.

32. Diller + Scofidio Firm, op. cit .285.

33. Ibid. 10.

34. Ibid. 16.

35. Ibid.

36. Ibid. 109.

37. Ibid. 10.

Bibliography

Adcock, Craig. “Duchamp’s Eroticism:
A Mathematical Analysis.” Marcel Duchamp: Artist of the Century.
Ed. Rudolph E. Kuenzli and Francis M. Naumann. Cambridge, Mass: The MIT Press, 1996.___.“Marcel Duchamp’s Approach to New York: ‘Find an Inscription for the Woolworth Building as a Ready-made’.”

Dada/Surrealism. Vol. 14 (1985): 52-65.
Ades, Dawn, Neil Cox, and David Hopkins.

Marcel Duchamp. London: Thames & Hudson, 1999.
Baird, George. “La Dimension Amoureuse

in Architecture.” Architecture Theory since 1968. Ed. K.
Michael Hays. Cambridge, Mass: The MIT Press, 1998.

Banham, Reyner. Theory and Design
in the First Machine Age. New York: Praeger, 1960.

Cabanne, Pierre. Duchamp & Co.
Paris: Terrail, 1997.

Colomina, Beatriz. “L’Esprit Nouveau
between Avant-Garde and Modernity: The Status of Artwork and the
Everyday Object.” Architecture Theorysince 1968. Ed. K. Michael
Hays. Cambridge, Mass: The MIT Press, 1998.

Dempsey, Amy. Art in the Modern
Era. New York:Harry N. Abrams, Inc., 2002.

de Solà-Morales, Ignasi. Differences:
Topographies of Contemporary Architecture. Cambridge, Mass:
The MIT Press, 1997.

de Vries, Hilary. “What’s Doing in
Los Angeles.” New York Times 28 Sep. 2003, section 5: 14.

Diller + Scofidio Firm. Blur: The
Making of Nothing.New York: Henry N.Abrams, Inc., 2002.

Duchamp, Marcel, Iconoclast.“A Complete
Reversal of Art Opinions.” (reprinted from Arts & Decoration,
Sept. 1915)In Studio International (Jan./Feb. 1975): 29.
Gehry Partners. Gehry Talks: Architecture
+ Process. New York: St. Martin’s Press, 2002.

Giedion, Sigfried. Space, Time and
Architecture. Cambridge Mass.: Harvard University Press, 1949.

Girst, Thomas. “(Ab)Using
Marcel Duchamp: The Concept of the readymade in Post-War and Contemporary
American Art.” Tout-Fait: The Marcel Duchamp Studies Online
Journal 2. 5 (April 2003): Articles.

Hanks, David and Anne Hoy. Design
for Living: Furniture and Lighting, 1950-2000. Paris: Flammarion,
2000.

Hays, K. Michael., ed. Architecture
Theory since 1968. Cambridge, Mass: The MIT Press, 1998.

Henderson, Linda Dalrymple. The
Fourth Dimension and Non-Euclidean Geometry in Modern Art. Princeton,
N.J.: Princeton University Press, 1983.

_ _ _.”X-Ray and the Quest for
Invisible Reality in the Art ofKupka, Duchamp and the Cubists.”
Art Journal (Winter 1988): 323-40.

Kuchler, Tilman. Postmodern Gaming:
Heidegger, Duchamp, Derrida. New York: Peter Lang, 1994.
Kuenzli, Rudolph E. and Francis M.

Naumann, eds. Marcel Duchamp: Artist of the Century. Cambridge,
Mass: The MIT Press, 1996.

Kwinter, Sanford. Architectures
of Time: Toward a Theory of the Event in Modernist Culture. Cambridge,
Mass.: MIT Press, 2001.

Kwinter, Sanford. “La Città Nuova:
Modernity and Continuity.” Architecture Theory since 1968.
Ed. Hays, K. Michael. Cambridge, Mass: The MIT Press, 1998.

Maxwell, Robert. Sweet Disorder
and the Carefully Careless. New York: Princeton Architectural
Press, 1993.

Moore, Rowan. “Duchamp Goes West.”
Blueprint 36 (May 1987): 18-20.
Pasadena Art Museum. Marcel Duchamp.
Exhibition catalog, 1963.

Pile, John. A History of Interior
Design. New York: John Wiley & Sons, Inc:, 2000.

Powers, Edward D. “Fasten
your Seatbelts as we Prepare for our Nude Descending.” Tout-Fait:
The Marcel Duchamp Studies Online Journal2.5 (April 2003): Articles.

Puglisi, Luigi Prestinenza. Hyper
Architecture: Spaces in the Electronic Age. Basel, Switzerland:
Birkhauser, 1999.

Reichenbach, Hans. The Philosophy
of Space and Time. New York: Dover, 1958.

Venturi, Robert and Scott Brown, Denise.Learning from Las Vegas. Cambridge, Mass.: The MIT Press,1977.

Wood, Beatrice. “Marcel.” Marcel
Duchamp: Artist of the Century. Eds. Kuenzli, Rudolph E. and
Francis M. Naumann. Cambridge, Mass: The MIT Press, 1996.

Figs. 3, 5-9, 13, 18, 21, 23, 25, 29-31© 2005 Succession Marcel Duchamp, ARS, N.Y./ADAGP, Paris. All rights
reserved.

See I have placed
before you an open door that no one can shut.
-Revelation 3:8
The successful criminal brain is always superior…
-Dr. No

I.
In The Trial of Gilles de Rais, Georges Bataille writes, “Crime is a fact of the human species, a fact of that species alone, but it is above all the secret aspect, impenetrable and hidden. Crime hides, and by far the most terrifying things are those that elude us.”⁽¹⁾
Marcel Duchamp, in both his work and practice, is the elusive artist par excellence. He is the ultimate fugitive of art historical investigation, leaving a trail of tricks, twists, contradictory meanings, and duplicitous identities that lead to epistemological dead-ends. Upon close inspection, Duchamp’s tactics to elude definitive conclusions and vex the viewer reveal themselves as criminal, not unlike those of the con man, fugitive, and even the killer.

click to enlarge

Figure 1
Marcel Duchamp, Given: 1. The Waterfall
2.The Illuminating Gas
(interior),
1946-1966, Gift of the
Cassandra Foundation,
Philadelphia Museum of Art

This paper suggests that Marcel Duchamp consciously toyed with criminal methodologies to elude interpretation and heighten the inconclusive nature of his work. I propose that criminal tactics were one means for Duchamp to enact his rebellion against traditional morality and aesthetics that followed his introduction to the philosopher Max Stirner in 1912. This program emphasizes a continual play on presence/absence, both in the artist’s modes of production and identities. After a brief overview of the apparent criminality of his work, I focus on his final project, Étant donnés (Fig. 1), and suggest that the installation partly derived from a notorious unsolved murder in 1947 known as the “Black Dahlia.”⁽²⁾ This macabre event reveals remarkable consistencies with Étant donnés, particularly in the identity and character of the victim, Elizabeth Short. Short’s lifestyle embodies uncanny similarities to Duchamp’s decade-long obsessive erotic narrative of the “Bride and her Bachelors,” thus revealing his appropriation of certain details as an enactment of a “copycat” crime in art. Finally, I relate Étant donnés to Duchamp’s earlier works to suggest a reversal of his criminal modus operandi from elusion to hypervisibility. This shift is evident in Étant donnés, which trades conceptual for physical modes of production and complicates the presence/absence of the artist. By furthering the inconclusive nature of Duchamp’s work (through the use of what Jean-Francois Lyotard terms the “hinge”) and being itself most enigmatic, Étant donnés is stamped with the same status as the Black Dahlia murder: open and unsolved.

click to enlarge

Figure 2
Marcel Duchamp,
Nude Descending the Staircase No. 2, 1912

Figure 3
Marcel Duchamp,
Three Standard Stoppages, 1913-14

Figure 4
Marcel Duchamp,In
Advance of the Broken Arm, 1915/1964, 132 cm, Musée national
d’art moderne, Paris

In 1912, Duchamp first read Max Stirner’s The Ego and His Own, an anarchic text that promoted individualism based on a self-exploration of the ego outside predetermined moral and societal values.(3) The abrupt shift in Duchamp’s aesthetic philosophy that followed his introduction to Stirner, from chronophotographic works such as his famous Nude Descending the Staircase, (Fig. 2) toward works of a more conceptual nature that challenged or defied metaphysics and the values of art and society, such as Three Standard Stoppages (Fig. 3) from 1913-14, is considered a consequence of his introduction to Stirner.⁽⁴⁾Moreover, Amelia Jones has argued the locus of this system was the incorporation of eroticism in both subject and object, which served as the agent to aggressively challenge bourgeois cultural values.⁽⁵⁾ The following discussion demonstrates that the nexus between Stirnerite philosophy and eroticism forms an artistic program that produces works that break the “laws” of art, imply criminal play and behavior, and exploit and celebrate the erotic in ways that imply violence to the body.
Duchamp “broke” many artistic rules after his shift toward self-determination. The readymades, such as In Advance of the Broken Arm from 1915 (Fig. 4), are now classic examples of his defiance of the imposed aesthetics of bourgeois society.⁽⁶⁾ They not only break the “laws” of art, but also illustrate a form of elusion through their absence of traditional notions of artistic production. As Walter Hopps points out, Duchamp’s career is marked by efforts to suppress the artist’s hand, to remove or disassociate himself from the object through an absence of visual signs that suggest the physical mark of the artist.⁽⁷⁾ Duchamp, defying the tradition of physical craft, creates a work that bears only conceptual evidence of its production, having been designated a work of art.⁽⁸⁾ The hand and its mark is dangerous to Duchamp. “It’s fun to do things by hand,” he stated, but “I’m suspicious because there’s the danger of the ‘hand’ which comes back…”⁽⁹⁾ Direct appropriation of these objects hides the handprint of the artist, as in the lack of fingerprints at a crime scene (is not appropriation, unlike imitation, a kind of stealing?).⁽¹⁰⁾ It is here that Duchamp’s elusion seems to elicit a specifically criminal tone. Moreover, any investigative attempt to trace the sources of these works through the available evidence leads us to hardware stores or factories, not the studio, where any number of these objects were purchased or produced.⁽¹¹⁾ Ironically, in a recent attempt to do just this, Rhonda Shearer found that the origins of the readymades are often untraceable to any context due to slight alterations by Duchamp, no doubt meant to further complicate attempts to “solve” these works and hinder their investigation.

Nowhere did Duchamp defy conventional aesthetic authority more than in the submission of his famous Fountain (Fig. 5) to the first annual exhibition of the American Society of Artists in 1917.⁽¹²⁾ An object so defiant of the “laws” of art, made by simply re-naming and shifting the base of a common urinal, Fountain led a supposedly unjuried exhibition to censorship through its blasphemous suggestions. In addition, Duchamp mocked the committee by signing the work with the alias “R. Mutt” rather than his own name. In this clever tactic, the artist hid his association with the scandalous submission and thus insured his innocence. As a member of the exhibition committee, Duchamp debated the fate of “Mr. Mutt’s” entry much like a criminal who watches their crime scene from a physical distance or under disguise. This, no doubt, amused Duchamp, who continued to emphasize this play on criminal behavior in works such as L.H.O.O.Q., (Fig. 6) defacing the Mona Lisa with a graffiti-style moustache and goatee. Graffiti, itself an illegal form of art, involves the elusive presence/absence of an artistic “criminal” for its production and reception. In other capers, such as his fraudulent checks such as Tzanck Check (Fig. 7) from 1919, Duchamp focused on the act of counterfeiting. And in Wanted (Fig. 8), from 1923, the artist fashioned a literal image of himself as a fugitive with multiple aliases (again emphasizing absence), complete with profile photographs like those of an ex-convict with a prior record.⁽¹³⁾

click to enlarge

Figure 9
Marcel Duchamp,
Note in the Green Box (1934)

Figure 10
Marcel Duchamp, Bride Stripped Bare by Her Bachelors, Even [a.k.a.
The Large Glass], 1915-23

All of these acts might be described as “petty crimes” when compared to his last work, the installation in the Philadelphia Museum of Art entitled, Étant donnés: 1 la chute d’eau, 2 le gaz d’éclairage – translated as Given: 1. The Waterfall 2. The Illuminating Gas. The title of this piece, taken from the opening lines of an introductory note to Duchamp’s Green Box (Fig. 9), signals its association with his earlier work The Large Glass, (Fig. 10) and suggests its representation as a three-dimensional version of the narrative of the Bride and her Bachelors.
Étant donnés has baffled scholars since its discovery after the artist’s death in 1968, when following Duchamp’s instructions, it was reinstalled in the Philadelphia Museum of Art by Anne d’Harnoncourt and Paul Matisse in 1969. With the exception of a select group of individuals that included the artist’s wife Alexina Matisse and her son Paul, the work was created by Duchamp in secrecy in New York City, first in his studio at 210 West 14th Street and later moved to another small room on 80 East Eleventh Street around 1965.⁽¹⁴⁾ The majority of scholarship that discusses the body in Étant donnés focuses on readings that emphasize violation, murder, rape, or other acts that associate criminal violence, eroticism, and the body.⁽¹⁵⁾ It has been described as a “mutilated woman” and a “seemingly dead female body,” suggesting that some form of criminal activity either already transpired or is about to occur.⁽¹⁶⁾ The erotic nature of these violent interpretations is based largely on the positioning of the body and Duchamp’s choice to explicitly display the female groin region, which is overtly shown to the viewer who peers through the small eyeholes in the door that houses the installation. The body, in its placement before us with legs spread apart, shocks the viewer because of what numerous scholars refer to as its “hypervisibility.”⁽¹⁷⁾

II.

click to enlarge

Figure 11
Photograph of Elizabeth Short
for civilian employee ID

Figure 12
LAPD Detectives Harry Hansen
and Finis Brown with Elizabeth Short’s
body, January 15^th, 1947,
Museum of Death

On the morning of January 15th, 1947, the mutilated body of Elizabeth Short, an aspiring starlet known as the “Black Dahlia” for her stunning beauty and jet black hair, was found purposefully placed on the edge of an open lot on Norton Avenue in Los Angeles, California (Fig. 11).⁽¹⁸⁾ For the next few months at first, then years as the case went on, her name littered the headlines of West and East coast newspapers that described in detail both her flamboyant lifestyle and macabre death. To this day, the Black Dahlia murder case remains California’s most notorious unsolved crime. The following discussion suggests that the media presentation and crime photographs of the Black Dahlia murder, contemporaneous to Duchamp’s conception of Étant donnés, may have affected its design and progress.
The parallels between the Black Dahlia and Étant donnés are numerous. By far the most striking similarity involves the two bodies. In a photograph of Elizabeth Short’s body at the crime scene, she lies in thick, tall grass not unlike the twigs that surround the body in Étant donnés; her legs spread wide displaying her sex (Fig. 12). And, in the most grisly detail of this heinous crime, her body is no longer whole; it has been severed at the waist. In a surrealist fantasy become reality, the Black Dahlia represents a real-life example of what was envisioned in the contemporaneous paintings, photographs, and installations of artists such as Hans Bellmer, Rene Magritte, Man Ray, and even Marcel Duchamp. Often times, for example, these surrealist artists would manipulate mannequins in their works for both their uncanny mixture of life-like and lifeless qualities, as well as their constructive and deconstructive potential through detachable anatomical parts. As the photograph illustrates, Short’s mid-section was not only severed in a manner similar to these detachable dummies, but, coincidentally, her body was actually mistaken for a mannequin by a passer-by who, observing the severed torso and skin that was “white as a lily,” believed it came from a department store.⁽¹⁹⁾

click to enlarge

Figure 13
Marcel Duchamp, Lazy
Hardware, window display for André
Bretons Arcane 17, 19.-26.
April 1945, Gotham Bookmart, E. 57^th
St. New York,
Photography Maya Deren,
Philadelphia Museum of Art,
Marcel Duchamp
Archive.

Duchamp found both inspiration and direct use for mannequins throughout his career. He explained to Man Ray in the early 1920’s that the origin of the Bride theme came from the “brides in booths” at French Country Fairs, where dummies dressed as a bride and groom were used as targets for people to throw balls in an attempt to decapitate them.⁽²⁰⁾ Closer in time to the Black Dahlia and Étant Donnés is his display window at the Gotham Book Mart in New York City from 1945 to promote Andre Breton’s surrealist publication Arcane 17 (Fig. 13); where Duchamp installed a headless female mannequin that immediately caused a scandal with the League of Women.⁽²¹⁾
The two most forceful formal similarities between the Black Dahlia and the body in Étant donnés are located in the groin region of each figure. First, both Elizabeth Short’s body and the body in Étant donnés have no pubic hair. The lack of hair in Étant donnés has been discussed in relation to Duchamp’s interest in gender indeterminacy, as well as a tale of the Baroness Else von Freytag-Loringhoven, who had her pubic area shaved by a barber in a film that both Duchamp and Man Ray collaborated on.⁽²²⁾ Furthermore, in the memoirs of Lydie Sarazin-Levassor, Duchamp’s wife for eight months in 1927-28, she claims that Duchamp requested she remove her body hair, owing to his “almost morbid horror of hair.”⁽²³⁾ In light of these past incidents, the absence of pubic hair from Short’s body, in itself, could have proved alluring to Duchamp.
But Short’s body also offers an explanation for the strange, incorrect anatomy that suggests a female vagina in Étant donnés. Amelia Jones has negated the conclusions of earlier scholars who discussed the genitalia of Duchamp’s figure in terms of the anatomy of the female sex, proving that there is in fact no labia majora or labia minora. What exists instead is what she calls an “aggressively visible and grotesque gash that goes nowhere.”⁽²⁴⁾ In the photograph of the Black Dahlia murder one can see a literal gash that was incised above the vagina into the lower abdomen of the body of Elizabeth Short (Fig. 14). It is now known through the disclosure of the autopsy reports that Elizabeth Short’s pubic area was underdeveloped. Detectives and crime experts suspect that the gash was a means for the sexually ravenous killer to insert himself into Short, whose genitals were underdeveloped and therefore unable to engage in vaginal intercourse.⁽²⁵⁾
Thus, the Dahlia could not offer her bachelors a natural way to fulfil their lustful desires, much like the failure of the love operation in Duchamp’s narrative of the Large Glass where the “bachelors grind their chocolate.”⁽²⁶⁾ The “gash” in Étant donnés first appeared in a vellum study for the figure in 1948-49 (Fig. 15), and the transition from a drawing dated controversially either 1945 or 1947 (Fig. 16), which features a female body without head and arms (severed?) with natural pubic hair, to the hairless body with a single “gash” in the vellum study has never been explained.⁽²⁷⁾ If Duchamp was exposed to the Dahlia murder, either in 1947 or 1949 (this will be discussed in more detail shortly), then perhaps this event was the impetus for these design alterations. Chronologically, the murder (and his exposure to it) fits neatly between the otherwise inexplicable transition from the drawing to the vellum study.

click to enlarge

Figure 17
New York
Daily News Headline, January 18^th, 1947

Figure 18
Marcel Duchamp, Fresh Widow, 1920

The story of Elizabeth Short presented in the newspapers during the investigation also parallels aspects of Duchamp’s own erotic narrative. Short’s failure to fulfil the “love operation,” while not directly stated through a medical explanation, was implied through accounts in the papers that spoke of her teasing nature and relationships that ended “before the love was consummated,” echoing Duchamp’s non-consummation and frustration in the theme of the Large Glass.⁽²⁸⁾ Moreover, the newspapers on both coasts played-up a controversial aspect of her past, in which she claimed to have married an air force pilot who in fact died before the ceremony could take place.⁽²⁹⁾ Thus, Elizabeth Short appeared to be paradoxically married and unmarried. The newspapers furthered the confusion when they obtained information from her address book, which contained “an album of pictures ranging in rank from sergeant to lieutenant general.”⁽³⁰⁾

Several newspapers ran stories that published a long list of “Bachelors,” as in the New York Daily News headline from January 18^th 1947 that reads, “Many Loves in Slain Girl’s Life”(Fig. 17).⁽³¹⁾ As Jean-Francois Lyotard and others point out, Duchamp complicates attempts to locate fixed meanings in his works through what has been called a “hinge” effect.⁽³²⁾ The hinge, represented in language by the juxtaposition of “and/or,” as in the double alias of Marcel Duchamp and/or Rrose Sélavy, is both single and multiple, definitive and simultaneously inconclusive. To extend the “hinge” interpretation, the Dahlia was a Duchampian fantasy come to life―single and/or married, Elizabeth Short and/or the Black Dahlia, whole and/or severed, life and/or art. Like the Bride in Duchamp’s tale, who has “no singular, definitive groom,” the Dahlia represents eroticism and violence staged in these photographs as a literal “Bride Stripped Bare By Her Bachelors, Even(ly) cut” as a symbol of the artist’s concept of infra-mince, a physical cut that in this context plays itself out in a long list of Duchampian metaphors.⁽³³⁾She is a “Fresh Widow,” like the French women Duchamp referred to after the First World War in his 1920 work of the same name (Fig. 18); a work whose title also, coincidentally (?), references the guillotine―“the Widow, in popular French jargon.”⁽³⁴⁾ Lastly, in several of the crime scene photographs and those of the newspapers, the detectives, policemen, and reporters seem to echo Duchamp’s description of his Occulist Witnesses and bachelors, who “stand, sadly, in ‘uniforms and liveries’” and observe the spectacle before them.⁽³⁵⁾ (Figs. 19 & 20)

click to enlarge

• 
  Figure 19
  Marcel Duchamp,
  Occulist Witnesses,
  from Green Box
  (1934), 1920
• 
  Figure 20
  Marcel Duchamp,
  Cemetery of Uniforms
  and Liveries, No. 2,
  1914

III.

In mid-January 1947 Duchamp returned from a stay in Europe, arriving in New York at the moment the Dahlia case began to unfold. The particulars of the murder and its surrounding controversies were appearing daily in newspapers. The New York Daily News ran headlines and follow-up stories about the Dahlia murder for several weeks.⁽³⁶⁾ More importantly, at the time of the killing Los Angeles was the home of the artist’s close friend Man Ray. The relationship between these two artists is well documented, and Man Ray’s influence on Duchamp’s conception of Étant donnés has already been suggested.⁽³⁷⁾ In addition to being engulfed in a sea of newspaper headlines and Hollywood gossip about the killing, Man Ray, like Elizabeth Short, frequented the popular bars and clubs in Hollywood and knew many people in the jet set of the movie community.⁽³⁸⁾ With his lifelong fascination with sado-masochism, Man Ray would certainly have taken an interest in the particulars of this crime.⁽³⁹⁾ As a photographer of such repute, Man Ray might have been able to obtain one of the many hundreds of crime scene photographs taken by reporters that circulated through the Hollywood community.⁽⁴⁰⁾ These photographs were reproduced and passed from hand-to-hand, and were not censored like the newspaper photographs that displayed the body in situcovered with a sheet, nor were they the “cleaned-up” autopsy photographs that appeared in detective and crime magazines.

click to enlarge

Figure 21
Marcel Duchamp and
Man Ray in Los Angeles,
California, 1949

On his way back from Paris in 1947, the year of the murder, Man Ray spent a week in New York City.⁽⁴¹⁾ This could have served as an occasion for him to share this information with Duchamp, either simply for its grisly, surrealist nature or for its many similarities with his own and Duchamp’s beliefs and work. If this was not the case, Duchamp may have heard or seen something about the Black Dahlia during his visit to the Arensberg’s home in Los Angeles two years later in April 1949 after his participation in a Round Table discussion in San Francisco.⁽⁴²⁾ The Black Dahlia case was again making news with new suspects, and moreover Duchamp spent each afternoon secretly meeting with Man Ray by taking “afternoon walks.”⁽⁴³⁾ In this photograph (Fig. 21), the two artists, in a witty false “alibi,” sit on a stage set in Hollywood designed as a Parisian street corner. Why wouldn’t someone with a penchant for criminal tactics, who characterized his interest in eroticism as “Enormous. Visible or not underlying in every case…” be fascinated by this crime?⁽⁴⁴⁾ In an interview with Walter Hopps during his stay in Los Angeles, Duchamp declared he was going through his “sex maniac” phase, a phrase which coincidentally appeared in newspaper articles such as the first Los Angeles Times piece on the Dahlia Murder, which opened with the lines, “Butchered by a sex maniac…”⁽⁴⁵⁾ It is not surprising then, that upon his return to New York, Duchamp sent the clay model for the body in Étant donnés out for casting in plaster and, as Calvin Tomkins describes in his biography on Duchamp, “by summer he was working on it with great intensity―up to eight hours a day…”⁽⁴⁶⁾

click to enlarge

Figure 22
Marcel Duchamp,
Female Fig Leaf,
1950

Figure 23
Marcel Duchamp,
Wedge of Chastity,
1954

These events and shared interests between Duchamp and Man Ray in the context of the Black Dahlia suggest new meanings for two of Duchamp’s later erotic objects, Female Fig Leaf and Wedge of Chastity (Figs. 22 & 23). If Man Ray was partly responsible for introducing Duchamp to the Black Dahlia in 1947 or 1949, this may explain the nature of Duchamp’s gift, Female Fig Leaf, to the photographer. On his return to Paris with his new wife Juliet in 1951, Man Ray was surprised by Duchamp, who was waiting onboard in the couple’s cabin in port in New York City.⁽⁴⁷⁾ Duchamp presented Man Ray with an object described as a “wax impression of what looked like a woman’s vulva.”⁽⁴⁸⁾ Could this be a hint, or subliminal reference to the body in Étant donnés (or the Dahlia)?⁽⁴⁹⁾

Did this object imply something more than a simple shared interest in eroticism in the form of a farewell gift? With Duchamp’s love of puns and double meanings, one wonders if a linkage to Étant donnés and/or the Black Dahlia continued with the verbal/visual play in another erotic object,Wedge of Chastity. A wedding gift to his wife Alexina (Teeny) Sattler, Duchamp inscribed the object with the phrase, “Pour Teeny 16. Jan. 1954.” The spoken phrase, “Pour Teeny,” in English carries an additional meaning; “poor teeny,” as in the poor starlet who could not fulfil the “love operation” because of her “Wedge of Chastity.” Is it surprising that this “wedge” seems to fit snugly into a kind of “gash?” Or that January 16^thwas also the day after the murder of Elizabeth Short, the first day the headlines appeared in New York City papers?

IV.

click to enlarge

Figure 24
Marcel Duchamp,
The Bride Stripped Bare
by Her Bachelors Even [a.k.a.
The Green Box], 1934

Similar to Étant donnés, the Black Dahlia case perplexed investigators, and “facts” were constantly being undermined by the introduction of contradictory evidence. These inconclusive theories were played out, among other places, in newspaper headlines that emphasized the “gender indeterminacy” of the suspect. Authorities, first suspecting a man, reversed their hypothesis. The press ran headlines such as “Woman Now Sought In Black Dahlia Killing.”⁽⁵⁰⁾ Ironically, the case’s most plausible suspect is now a female impersonator―how Duchampian.⁽⁵¹⁾Quotes from detectives appeared in the papers as well, such as a statement from Detective Harry Hansen who regrettably admitted, “No lead had any conclusion, once we’d find something, it seemed to disappear in front of our eyes. Following any of those leads was like going down one-way streets with dead-ends.”⁽⁵²⁾ When a suitcase of the victim’s belongings turned up, it was filled with all kinds of objects―beauty supplies, photographs of men she had known, letters, etc. In a stunningly similar manner to Duchamp’s Box in a Valise, or better yet Green box, the suitcase’s contents guided detectives in their investigation much as the Green Box serves as a “guide” to the Large Glass. (Fig. 24)
In this sense, the Black Dahlia/ Étant donnés comparison can be viewed as the complicated performance of what criminologists term a “copycat” crime, played out within the sphere of art. Elizabeth Short’s life represents Duchamp’s pre-existing tale within the context of a specific time and place. Yet Étant donnés, continuing Duchamp’s penchant for criminal play, becomes a kind of “copycat” crime by re-using a specifically criminal mode of appropriation, and possibly specific details from this crime, as a “readymade” for certain features of his installation. The cyclical indeterminacy of “who copied who” once more suggests the “hinge,” represented this time by the Dahlia murder, which negotiates between the narrative of the Large Glass and Étant donnés (it is amusing as well that the linguistic symbol for Lyotard’s hinge has at its center a slash that “severs” the “and/or” indeterminate). Thus, Duchamp’s narrative and/or the life of Elizabeth Short―the Dahlia murder and/or Étant donnés.
Unlike the Large Glass, however, which presented cryptic visual versions of erotic narratives, Duchamp in Étant donnés, shocked his art audience by performing a spectral flip of his criminal modus operandi. What was, up to this point in his career hidden, was suddenly blatantly revealed.⁽⁵³⁾ As detective Jess Haskins said of the Dahlia murder, “It was not unusual―the ‘display idea’ as part of a sex crime…Hiding it had been the least of the perpetrator’s concerns.”⁽⁵⁴⁾ Duchamp, it is well known, claimed that eroticism was “a way to bring out in the daylight the things that are constantly hidden….because of social rules.”⁽⁵⁵⁾Thus, the earlier use of criminal and erotic subjects and actions emphasized the elusive absence of the living artist and cryptic narratives. Conversely, Étant donnés presents a hypervisible, blatant operation through another kind of artistic absence, first by, as he said, “going underground” during the secret and elusive production of Étant donnés, then through his literal absence in death.⁽⁵⁶⁾ In this role reversal, Duchamp exposes the crime and hides himself, like a serial killer, whose “psychosexual nexus is terra incognita.”⁽⁵⁷⁾
As in many famous unsolved murders, Elizabeth Short’s body was not simply dumped in a lot; it was deliberately arranged.⁽⁵⁸⁾ Her two halves were placed to repeat the natural position of the body several hours after the actual crime occurred. This gave the crime scene what detectives characterized as a “sacred setting,” implying that messages or meanings could be yielded by its purposeful display.⁽⁵⁹⁾ Duchamp also stresses his intentional positioning and display of the body in Étant donnés, controlling among other things our line of vision. As his title implies, we are presented with certain “evidence” from which to attempt to solve this artwork and/or crime.⁽⁶⁰⁾ The title, presented in the format of a mathematical equation, ironically suggests that this piece can be “solved” through a logistical program. “Given” it implies, “the waterfall, the illuminated gas, and whatever else you can see.” Here the spectral flip appears to hide the conceptual and offer an overtly constructed physical art environment.⁽⁶¹⁾ Moreover, Duchamp’s strategic placement of Étant donnés at the far rear of the Arensberg room in the Philadelphia Museum of Art creates two further paradoxes. One, it is literally “hidden” in a dark retreat at the back of the “display,” yet shockingly reveals itself within the darkness when the viewer looks through the peepholes. Second, the entire Arensberg room creates an exhibition narrative based on a body of work, that ends with a literal body. The post-Stirnerite works in the brightly lit outside gallery hide the physical mark and presence of their creator and engage us through the conceptual and extra-dimensional. The dark hidden room of Étant donnés offers us the physical, both as literal body and as an attempt in understanding based on the empirical act of seeing.

click to enlarge

Figure 25
Marcel Duchamp, epitaph
inscribed on Duchamp’s
grave stone, 1968

In death, Duchamp left a corpus and a corpse. His permanent absence was certainly his ultimate act of elusion. As in the Black Dahlia murder, the death of the “suspect” stamps Étant donnés permanently “open and unsolved.” We can never “break the case” of Marcel Duchamp (although we can break his works of art). In denying us solutions, Duchamp also denies us from closing the book on his work; its inconclusive nature leaves it inevitably open and alive. Thus, by defying solution, perhaps he and his work even defy death. “Besides,” his self-written epitaph reads, “it’s only the others that die.”⁽⁶²⁾ (Fig. 25) This, it seems, is Duchamp’s only truth.

Notes

1. G. Bataille,The Trial of Gilles de Rais, trans. Richard Robinson (Los Angeles,1991) 13. I was inspired to begin this essay with these words by Stuart Swezey, who included Bataille’s statement in his preface to John Gilmore’s book, Severed:The True Story of the Black Dahlia Murder, Los Angeles, 1994.

2. For a full account of this tragedy, see J. Gilmore, Severed: The True Story of the Black Dahlia Murder (Los Angeles, 1994).

3. F. M. Naumann,“Marcel Duchamp: A Reconciliation of Opposites”, Marcel Duchamp: Artist of the Century, ed. R. Kuenzli and F. M. Naumann (Cambridge,Massachusetts, 1989) 29.

4. M. Stirner, The Ego and Its Own (New York, 1907) 361. Duchamp himself stated that his reading of Stirner “marked his complete liberation.” A. Antliff, “Anarchy, Politics, and Dada”, In Making Mischief: Dada Invades New York (Whitney Museum, 1996) 212.

5. A. Jones, “Eros, That’s Life or the Baroness’ Penis”, In Making Mischief: Dada Invades New York (Whitney Museum, 1996) 239.

6. Antliff makes the connection between Duchamp’s adoption of Stirner’s philosophy and a revolt against what he calls “the rules ‘art’ imposed on the individual.” Antliff, op. cit., p. 213.

7. W. Hopps and A. d’Harnoncourt, Etant Donnés: 1 la chute d’eau 2 le gaz d’éclairage: Reflections on a New Work by Marcel Duchamp, Philadelphia Museum of Art Bulletin (second reprint) Volume LXIV, Numbers 299 and 300, (April-September 1969, Philadelphia, 1987) 37.

8. In this sense, I disagree with Antliff’s characterization of the American readymades.He states, “Here Duchamp undermined the metaphysical aesthetics and socially imposed conventions that defined ‘art,’ replacing painting and sculpture with mass-produced objects devoid of aesthetic deliberation and any trace of the creative process.” In my opinion, the readymades are neither devoid of aesthetic deliberation nor lacking any trace of the creative process. What the readymades lack are physical traces (visually recognizable) of creation. Instead, the evidence of a creative process is solely conceptual. Antliff, op. cit., p. 213.

9. P. Cabanne,Entretiens avec Marcel Duchamp (Paris, 1967) 165, trans. D. Judovitz, “Rendezvous with Marcel Duchamp: Given”, Marcel Duchamp: Artist of the Century, ed. R.E. Kuenzli and F. M. Naumann (Cambridge, Mass, 1989) 197.

10. As Steven Levine pointed out during the discussion of this paper at the Symposium for the History of Art at the Philadelphia Museum of Art, imitation could certainly be considered “criminal” as well. As early as Antiquity, the deceitful nature of artistic imitation led Plato to exclude it from his ideal Republic.

11. As Rhonda Shearer points out, it is possible that these objects were not appropriated exactly as they were “found” by Duchamp. Manufacturer catalogs contemporary to the readymades do not contain illustrations that directly match some of Duchamp’s objects. Thus, she suggests the artist may have altered them slightly to further confuse their “origin.” In L. Cambi, “Did Duchamp Deceive Us?”, Art News, v 98 (February 1999) 98-102. Moreover, we know from photographs and remarks by Man Ray that Duchamp’s studio was, for the most part, bare. This also suggests that the artist wished to confuse any attempts to “trace” the source material or influences of his work.

12. It could be argued that Duchamp’s “outlaw” status began even earlier, when he submitted his Nude Descending the Staircase to the 1913 Armory exhibition.

13. Judovitz first suggested that Duchamp possessed criminal qualities in her discussions of Tzank Check and Wanted in Chapter 4 of Unpacking Duchamp: Art in Transit. Her interpretation and discussion of criminality, however, rests solely on the idea of counterfeiting and fake transactions. D. Judovitz, Unpacking Duchamp: Art in Transit (Berkeley, 1995) 167-78. This paper suggests that these are but two of many examples within Duchamp’s artistic career in which he looked to criminality as a means of reconciling his philosophical and aesthetic/non-aesthetic programs. Moreover, Duchamp’s Wanted is included here to emphasize, through his multiple aliases and criminal image, the connection between criminality and elusion (absence).

14. J. A. Ramirez, Duchamp: Love and Death, Even (London, 1998) 199.

15. The most complete investigation of the nude body in Etant donnés, its influences, and location within a history of nudes in the landscape is Antonio Juan Ramirez’s discussion in his book Duchamp: Love and Death, Even. In an attempt to separate fact from hearsay, Ramirez asks an important question: “What kind of things might Duchamp have seen or read; with which intellectual wave and artistic movement was he associated at any given moment?” ibid., p. 12. Ramirez’s discussion focuses, for the most part, on art historical sources beginning as early as the end of the 15^th century and ending with the surrealist work of Hans Bellmer and others. While he does briefly mention that popular photographs of pornographic subjects were more important than art historical images of the nude, his discussion of this material is brief, and indirect. Rather than answering his own question in relation to this material, Ramirez offers visually similar images but fails to contextualize them and discuss the direct avenues through which Duchamp may have seen or obtained them. Therefore, re-asking Ramirez’s question, I offer the Black Dahlia as a more convincing non-art historical influence.

16. A “seemingly dead female body” in A. Jones. Postmodernism and the Engendering of Marcel Duchamp (Cambridge, 1994) 192 and a “mutilated woman” in Ramirez, op.cit., p. 234.

17. This is discussed, among others, by J. A. Ramirez, D. Judovitz, and A. Jones.

18. As Gilmore explains, soldiers began to call Elizabeth Short by this name as a re-worked version of a recent film entitled “The Blue Dahlia.” The “Black Dahlia” quickly became a nickname that soldiers would use in their queries as to whether she had been spotted somewhere on the streets each day. Gilmore, op. cit., p.56.

19. Elizabeth Short’s body had been drained of blood prior to being dumped in the lot, explainingwhy it appeared “white as a lily.” ibid., p. 5.

20. A. Schwartz,Man Ray: The Rigour of the Imagination (New York, 1977) 188.

21. Hoppsand d’Harnoncourt, op. cit., p. 32.

22. D. Hopkins,“Men Before the Mirror: Duchamp, Man Ray and Masculinity”, Art History,v 21 (September 1998)s 317.

23. Le Recit de Lydie, Rrosopopees 19-20 March 1989: 489.

24. Jones, Postmodernism and.., op. cit., p. 201.

25. Gilmore,op. cit., p. 124.

26. L.D. Steefel, Jr., The Position of Duchamp’s Glass in the Development of His Art (New York, 1977) 167.

27. This suggests a more convincing date for the first drawing as 1947 rather than 1945. If Duchamp had seen the photographs of the Black Dahlia, then perhaps they might explain an origin for the pose of the figure, usually referred to as Marie Martins. In addition, the last number of the date inscribed on this drawing, in my opinion, looks much more like a “7” than a “5.” Calvin Tomkins also identifies the date of this drawing as 1947. C. Tomkins, Duchamp: A Biography (New York, 1996) 357.

28. Detective Brown, speaking about the letters found in her suitcase. Gilmore, op. cit., p.

29. “Mother of Hero Doubts Marriage to Short Girl”, Los Angeles Times 19 Jan. 1947: 3.

30.Daily News, New York, 18 Jan. 1947: 1,3.

31. ibid.

32. See J.F. Lyotard, Duchamp’s TRANS/formers, Venice, CA, 1990, pp. 58-61, and D. Judovitz. Unpacking Duchamp, op. cit., p. 215.

33. For a detailed discussion of infra-mince, see M. Nesbit “Last Words: (Rilke, Wittgenstein) (Duchamp)”, Art History 21 (December 1998): 547. There are other striking similarities between the images of the Black Dahlia crime scene and Duchamp’s studies for Etant donnés, especially a drawing from 1959 in which the Large Glass is juxtaposed with a landscape that includes telephone poles. These appear in the same area as some of the telephone poles in several crime scene photographs. Moreover, the Occulist Witnesses in Duchamp’s drawing occupy the same position as the policemen and detectives in the crime scene photographs.

34. O. Paz, Marcel Duchamp, New York, 1978, p. 122.

35. A. Jones, “Eros..”, op. cit., p. 240.

36. From January 18^th, 1947 through early February the New York Daily News ran three front-page stories, and fourteen other articles that appeared somewhere on the first five pages of the newspaper (most on them on page three).

37. See for example Ramirez, who claims that these “aspects (photographs), along with the adventures shared by the two friends suggests (as we shall see) Man Ray’s considerable influence on Duchamp.” Ramirez, op. cit., p. 221.

38. Elizabeth Short is known to have frequented the following locales: Four Star Grill, Florentine Gardens, The Rhapsody, the Dugout, the Loyal Café, and the Streets of Paris. Moreover, in an email correspondence, John Gilmore informed me that there was a strong possibility that Man Ray may have known the Black Dahlia, or at least met her.

39. For a summary see A. Schwartz, Man Ray, p.187-190. The articles in the

Los Angeles Times and the Examiner, for example, discuss the sado-masochistic aspects of the crime.

40. In John Gilmore’s book, Detective Brown is quoted in the autopsy room as saying, “There are already a thousand photographs… You can see most of what’s been done…..” Gilmore, op. cit., p. 126.

41. M. Ray, Self Portrait: Man Ray, Boston, 1988, p. 291.

42. For a summary of Duchamp’s participation in this event, as well as a chronology of his California experiences, see B. Clearwater, West Coast Duchamp (Miami, 1991).

43. Tomkins, op. cit., p.370.

44. Cabanne, op. cit., p.165.

45. “Girl Victim of Sex Fiend Found Slain”, Los Angeles Times, Thursday, 16 Jan. 1947: 2. The interview with Hopps is quoted from Tomkins, op. cit., p.423.

46. Tomkins, op. cit., p. 366.

47. M. Ray, op. cit., p. 295

48. Tomkins, op. cit., p. 370.

49. To my knowledge, no one has ever made a cast of the female groin region of the body in Etant donnés. It could be possible that Female Fig Leaf is directly linked to Etant donnés in this way. 50. “Woman Now Sought in Black Dahlia Killing”, New York Daily News 21 Jan. 1949:5.

51. See Gilmore, Chapter 17.

52. ibid., p. 173.

53. Some scholars were disappointed because this seemed to point to a return to representation that negated Duchamp’s “progress” toward conceptual art.

54. Gilmore, op. cit., p.8.

55. N. Baldwin, Man Ray: American Artist (New York, 1988) 276.

56. Duchamp told Cage that having as second studio “was a way of going underground”, J. Masheck, Marcel Duchamp in Perspective (Englewood Cliffs, N.J, 1975) 155.

57. S. Swezey, Preface, in Gilmore, op. cit., p. iii.

58. ibid., p.12.

59. ibid., p.9.

60. Interestingly, a 1945 work sometimes thought to be the earliest model for the nude body was sent to forensics and FBI specialists to test and confirm the material as human semen. Ramirez, op. cit., p. 233. How interesting to think that Duchamp, in an erotic act, used the chance design of his ejaculated semen on a piece of paper as a possible “origin” for a body in Etant donnés.

61. The physical construction of Etant donnés is emphasized by its context in the museum, and also by the fact that it was posthumously re-constructed by others, “put together” again, so to speak.

62. This is Duchamp’s self-written epitaph.

Figs. 1-10, 13, 15-16, 18-25 © 2005 Succession Marcel Duchamp, ARS, N.Y./ADAGP, Paris. All rights reserved.