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Illustration 1

Marcel Duchamp, Note from the Green Box, 1934 (typographic version by Richard Hamilton, translated by George Heard Hamilton, 1960)

Duchamp states in notes written between 1911-15 (see illustration 1, showing Duchamp's Green Box Note published in 1934) that the time and date of his readymades is important "information" in addition to the "serial characteristic of the readymade."⁽¹⁾

The "snapshot effect"⁽²⁾ of this timing of the readymade, to which Duchamp refers in this note, makes sense when we examine Duchamp's readymades with his mathematical notes (written 1911-15 but held back for publication by Duchamp until 1967, a year before his death.)⁽³⁾

First, let us begin by "looking" at Duchamp's readymades through time. Since Duchamp claims that he "lost" most of his original readymade objects, Duchamp's 1915 hatrack, as well as his urinal, snow shovel, coatrack, bottlerack and bicycle wheel and stool, exist only in a series of varied representations given to us by Duchamp over an extended period of time.

As an example, the following time-line illustrates the sequence of appearances of Duchamp's "lost" hatrack. We see "the serial characteristic of the Readymade" just as Duchamp described in a presentation of his "Readymade" (the title he used for his hatrack in the 1941 representation, see illustrations 2A, B, C, D, E, and F below).

Time Line of Readymade Series of Hatracks - As Seen by Spectators
2A	2B	2C	2D	2E	2F
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1918	1941	1960s (made 1916-17 found 1960s)	1960s (made 1918 found 1960s)	1964	1991 (made 1964 seen 1991)
2D Shadow in Oil Paint Tu m' (detail)	2D Print made with Photo Boite-en-Valise	2D Photo Studio Photo	2D Shadow in Photo Cast Shadows (detail)	3D Wood Model Hatrack (limited edition of 8)	2D Blueprint Hatrack

Thus the tally of Duchamp's hatrack representations is as follows:

2 2D shadows
(one painted [1918, Tu m']; one photographed [1918, Cast Shadows])

2 2D photographic images
(one made into a print [1941, Boite-en-valise]; and one altered studio photograph [1916-17, found in 1960s]. Note both photographs are altered -- to be discussed later in this essay.

1 2D blueprint (1964)
that, one assumes, generated
1 3D wood model (1964)
(in an edition of 8)

In effect, Duchamp gives us only 6 "snapshots" in time of his Hatrack Readymade (with "all kinds of delays")⁽⁴⁾.The limited total of information that we have, obviously, does not equal the quantity of data that we would have if we had access to the lost 3D original or if we suddenly possessed many more 2D photographs that carefully depicted the original 3D hatrack "in the round."

Indeed, with the paltry set of data that Duchamp provides, the only physical or mental construction we can make, based upon the hatrack's original form, is by fusing or averaging and filling in among the 6 representations previously listed -- 5 images in 2D and 1 model in 3D. This procedure can be done mentally via visualization, or physically via model-making, with conscious effort on the part of spectators. However, interpreting 2D depictions, mentally translating them into 3D, and then rotating and joining them (with visual filling in), is not a skill equally possessed by everyone and has, in fact, been frequently used as one measure of intelligence.⁽⁵⁾

Alternatively, if we do not help ourselves by consciously combining the 6 hatrack depictions, the result is an ad hoc, automatic conclusion or assumption-generated "readymade" from the unconscious mind. A single depiction -- such as the first Duchamp hatrack that we see in a photograph or a print, or the 3D Schwarz model, or any one of a combination of Duchamp's 6 particular depictions -- has served to evoke in our minds a "general idea of a Duchamp hatrack" that is surely derived from an uncertain mixture taken from among Duchamp's 6 hatrack representations and our prior experience with hatracks.

But does our present "generalization" or "knowledge" of Duchamp's hatrack hold up to testing? In other words, will the generality that we have made about Duchamp's readymades, and have long held in our minds and in our written art history -- that such readymades as the hatrack are simply store bought, unaltered, mass produced objects -- be maintained after more snapshots are added to the 6 that we have already tallied. Yet, you may challenge: how can we add more snapshots to our generality when Duchamp gives us only 6 representations and the original is lost?

Herein lies the key to Duchamp's insight, conveyed within his In the Infinitive [a.k.a. the White Box](1967) mathematical notes (1911-15). After identifying the 6 representations that Duchamp has given us as 6 distinct and separate snapshot views of his original hatrack, we have, essentially, a set of 6 "cuts" or 2D parts taken from a larger set of information, or the hatrack as a 3D whole. These 6 "cuts" are, in essence, 6 perspective views or observations. Each cut is also, itself, an "aggregate" (made of parts) of additional "cuts" or observations -- ad infinitum. In other words, to add more cuts to our set of 6 hatrack representations, we must simply repeat our previous operation. Just as we took 6 cuts (parts), beginning from our generality of Duchamp's hatrack, we must now take these 6 cuts (now themselves a set or whole) and cut each of these cuts into more cuts.

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Illustration 3A, 3B

Marcel Duchamp, Note from In the Infinitive [a.k.a. the White Box], 1967 Note: labels 3A and 3B are for clarity added by author

Duchamp clearly indicates his grasp of this recursive nature of our mental operations in the White Box Notes. Several drawings illustrate two perspectives that behave as one process split into two alternating mental states. Our perspectives mechanically move back and forth between the general (a single perspective of the AGFC figure, see illustration 3A) to the particular (multiple snapshots [cuts] or perspectives of A,G,F,C in a series over time, see illustration 3B). Immediately after perspectives A,G,F and C are cut as in figure 3B, we have created a new set that functions as a generality, as in figure 3A. We then begin the cycle all over again, with more cuts of this generality, then another generality, then cuts in a series, again at finer and finer scales. Essentially, we are mentally and observationally moving back and forth between states 3A and 3B -- wholes and parts at different levels of details.

Illustrations 4A and 4B show how the schematic diagram of Duchamp's two mental operations contained in illustration 3A and 3B apply to his hatrack. Illustration 4A matches the relation of the single perspective in 3A (Here Duchamp's hatrack in particular, and prior experience of hatracks in general, are fused together), whereas illustration 4B matches the relation of a series of perspectives taken over time as in 3B (Where Duchamp's hatracks are reduced to multiple but discrete snapshots in a time-series). Illustration 4C depicts a possible series of mental steps that could occur immediately after 4B. This series illustrates how we now cut each of the 6 cuts from step 4B into more cuts, at an even finer scale of observation, ad infinitum.

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Illustration 4A.

Illustration 4B.

Step 4 of illustration 4C above answers the challenge previously mentioned: how do we add more cuts to our limited set of 6 representations of Duchamp's hatrack?

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Illustration 5

Cube seen in 2D parts as eye moves around it

Illustration 6

Perspective distortions of cube in relation to fixed eye

When we actually take Duchamp's hatracks representations and add the cuts (beyond merely identifying the 6 snapshots as in step 2 in illustration 4C), we discover that every one of the 6 representations (5 in 2D and 1 in 3D) is not, as we might have expected, a single cut from the same 3D hatrack object. By way of example, see illustration #5, if we reassemble all observations (cuts) resulting from the set of all eye positions looking at this particular cube, we would be able to predict, and easily to build, a symmetrical cube object from the resulting limited set of cuts. Each cut, upon examination, fulfills our expectation of a cube's form with its 6 faces, 12 edges 8 vertices -- all we have to do is just count them to confirm. Illustration #6 depicts how the perspective distortions change according to the angle of eye's observation of the cube.

Our expectations are not fulfilled upon examining the 6 hatrack snapshots. Not only are the curvatures of the hooks different in all 6 representations, but we must conclude that even the number of hooks varies after we count them. For example, the Schwarz 3D model, (the "corrected" second version) has 6 equal length hooks, symmetrically placed as 3 on one side and 3 on the other side of the base's circular form. In contrast, the blueprint (approved and signed "okay, Marcel Duchamp") has a weird tangle of 2 long and 3 short hooks.

Click here for Interactive Presentation (Shown below at only 60% of actual size)
To download the plug-in, click here

Please test out the interactive hatrack software that we have installed⁽⁶⁾. To select a hatrack click on one of the 5 icons shown on the upper left. Hold the left side of the mouse down. Making sure the cursor's hand icon switches on (while the arrow is moving) roll the mouse on the hatrack's round base and "pull" the 3D model off its fixed position in the 2D representation. Interactive challenges include; the 1941 print of a studio photo (and an early stage of our hatrack 3D computer model), the 1917-18 studio photo (and an early stage of our hatrack 3D computer model), the 1964 Schwarz blueprint (with a computer model of the Schwarz 3D version), the 1964 Schwarz blueprint (with an early stage of our hatrack 3D computer model) and, a 1904 Thonet hatrack catalogue diagram (and equivalent 3D computer model)⁽⁷⁾. To explore these 5 models, keep the left side of the mouse down, (always beginning with the hatrack's base) and roll the mouse in various directions, and compare the 3D shape of the hatrack to the 2D representation. Rotate each of the 5 hatrack 3D models in all x, y and z directions that are possible in 3D space (north, south, east, west, up and down). Try to visualize the 2D representation that you choose as a 2D slice (cut), or only one fixed perspective view of the 3D hatrack form. Also, practice placing the 3D models back into the best possible position matching the 2D depiction you have chosen.

The 5 computer models shown in the hatrack interactive design result from early stages of our geometric analysis of the 6 hatrack representations in combination with our research of available mass-produced hatrack models in the historical record (found in period catalogues, patents, museum collections and design books).

The 5 interactive hatracks are meant to offer spectators a shortcut and assistance in their efforts, not only to review my arguments but to allow them to experience, and to explore and build upon their own analysis to process, and later to generalize from the facts before us.

The order of occurrences and the quantity and choice of 5 interactive models above differs from the earlier illustrations #2A, B, C, D, E, and F that I originally sited as Duchamp's 6 hatracks cuts. For clarity, I will discuss each of the 5 interactive models separately starting with the 1904 Thonet catalogue image and 3D model.

What To Look For:

1. 1904 Thonet Hatrack - Interactive Model

After examining Duchamp's 6 hatrack representations, and after canvasing the historical record, I concluded that; A. Six different 3D hatracks were described by Duchamp's 6 representations (five 2D, one 3D); B. No duplicate, mass produced, readymade store-bought hatrack matched any of the five 2D representations or the one 3D Schwarz model. C. The closest possible mass-produced hatrack circa 1915 or before that I could find (after considering the varied deviations within the five 2D depictions and the one 3D model), was the common Thonet bentwood hatrack (a design still commonly found today in both metal and wood).

4 Hatracks from the Art Science Research Laboratory (ASRL) Collection click each image to see video
Illustration 7A Thonet Hatrack, circa 1904	Illustration 7B Metal Hatrack, circa late 19th, early 20th
Illustration 7C Bentwood Hatrack, circa late 19th, early 20th century	Illustration 7D Thonet Bentwood Hatrack, circa late 19th century

See illustrations and videos 7A, B, C, and D showing lab members hanging hats on four hatracks from the Art Science Research Lab collection. The first wood model below is the closest one that we have found that has characteristics common to all six of Duchamp's hatrack representations, and appears similar to Thonet bentwood style #11022. Thonet Brothers mass-manufactured and shipped their original Bentwood designs throughout the world. See illustration #8A, B showing the title page for the 1904 catalogue and the page for hatrack #11022. Try the Thonet 1904 interactive 3D model. Note how symmetrical the hatrack appears and how it matches the catalogue drawing.

The patented technology that allowed Thonet to permanently shape wood for furniture without carving (hence bentwood), became immediately recognizable by the "S" curve module units. Note too, that the illustration 7A Thonet hatrack has three "S" curves on a round base. The 7B and 7C Thonet-style hatracks, one in metal and the other in wood, also have 3 "S" hooks. Click to see videos of each hatrack in the ASRL collection. The illustration 7D video shows the official Thonet paper label on the back. As you can see from all 4 videos, each of the hatracks are wall units, and each can easily hang hats. Both Thonet catalogue pages illustrations #9 and 8B show examples of the common bentwood hatrack/coatrack free-standing models still in use today.

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Illustration 8A	Illustration 8B	Illustration 9
Frontispiece of "Thonet Bentwood & Other Furniture," illustrated catalogue, 1904 New York: Dover Publication, 1980	"Thonet Bentwood & Other Furniture," illustrated catalogue, 1904, p. 80 New York: Dover Publication, 1980	"Thonet Bentwood & Other Furniture," illustrated catalogue," 1904, p. 81 New York: Dover Publication, 1980

2. 1917 Hatrack (2nd Interactive hatrack model from bottom)

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Illustration 10

Wireframe of a computer generated Hatrack based upon 1917 studio photo

This studio photograph was reproduced as a retouched print in the 1941 Boîte en Valise. Count the hooks. There are 2 long hooks and 3 short hooks. We took the 3D model of the Thonet hatrack with the 3 "S" hooks, compared it to this studio photograph print and noted the differences. If the first long hook and short hook are, together, one "S" hook of the Thonet model (with a total of three "S"s), then the second long curve and short curve could together be the second "S". But the second long hook (having a much more open and soft curved shape when compared with the first long hook's curve) cannot be the same shape as the first long hook.

Rotate the 1917 (above the Thonet 1904) interactive hatrack 3D model away from the 2D photo underneath and compare the differences. Note that the 3D model's second "S"'s long curve is not open and soft like the second "S"'s long curve in the photograph⁽⁸⁾. Yet, the second "S"'s long curve in the 3D model approximately matches the first "S"s long curve in the photograph.

Moreover, the 2nd "S"'s bottom, small hook is a wider shape and less curved when compared with the first "S"'s bottom small hook. Finally, the third small hook is missing the top, long hook part of the "S". In order to represent Duchamp 1917 2D depiction in 3D, we had to cut off the long curve from the "S" hook and leave the bottom small hook curve in yet a different angle from the first and second "S"'s two bottom small hooks. See illustration #10 that shows a front view of this hatrack with its cut off long hook. Rotate the interactive 1917 3D model into the face forward position (like the Thonet 1904's position) and then go back to compare the Thonet 1904 3D model. Importantly, try to place this Thonet 1904 into similar positions as the first or second "S" hooks in the 1917 Duchamp 2D depiction. (The 3D Thonet model here is slightly squatter than Duchamp's 1917 hatrack.)

3. 1917 Hatrack (3rd Interactive hatrack model from the bottom)

This studio photograph immediately appeared to be a more promising match for both the Thonet 1904 model and the 1918 shadow in the Tu m' painting (see illustration 2A). However, all attempts to match a 3D model with three identical and symmetrical "S" curves to the depiction that Duchamp provides failed, as one can see by examining this 1917 Interactive 3D model. Again, return to the 1904 Thonet 3D model and try to place each of the model's three "S" hooks into similar positions as the 1917 hatrack "S" hooks found here. As observed in the previous 1917 photo (2nd hatrack from bottom), the Thonet 3D computer model has tighter curves and shorter hooks then in our actual wooden Thonet 3D model from the ASRL collection shown in #7A.

4. 1964 Blueprint with Interactive 3D model of lost version, Schwarz 3D Hatrack model

This blueprint turns out to be a poor interpretation made by an anonymous draftsman while tracing the 1917 Boîte en Valise (see illustration 11A, showing overlay of 1941 Boîte hatrack [placed on its side] with the blueprint. See the circled section on #11B and compare this to the circled part of #11C, instead of interpreting the first small hook (from the right) making a continuous "S" shape moving from the first long hook on the right, the blueprint indicates that the 1st short hook is a separate piece awkwardly sticking out from within the side of the first long hook. It is interesting to note that there is no indication of the draftsman having had a conception that the hatrack was made of "S" shapes anywhere in this muddle of 3 small and 2 long hooks, (with each hook having its own size and unrelated curved shape).

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Illustration 11A Overlay of the 1964 Hatrack blueprint with the 1941 Box in a Valise photograph (detail); individual images shown on the right Note: circles are for clarity added by author	Illustration 11C Illustration 11B

My examination of other 1964 blueprints for other Schwarz readymades might be helpful to mention here. Also signed "Marcel Duchamp, okay," the bicycle stool blueprint is similarly ambiguously and inaccurately drawn (most likely because Schwartz's draftsman did not know how to interpret the broken legs and rails as depicted in the 1941 Boite-en-valise print of the bicycle wheel (also showing the coatrack). See illustration #12A, B and C, notice that the two most right horizontal rails in the blueprint go in two different directions and are cut off oddly, as depicted in the original studio photograph (12C). In addition, the 3 legs are not evenly spaced as one would expect in a blueprint (and the fourth leg is missing completely) and yet in the final Schwarz edition (12D), all legs are completely symmetrical. Note that illustration 12B also contains the within 3D model we made using the information contained in the 1964 stool Blueprint (also 12B).

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Illustration 12A	Illustration 12B
Print made from of the original studio photo (1916-17) for the Box in a Valise, 1941	Comparison of 1964 Blueprint of the Bicycle Wheel (Stool) with the ASRL 3D model made from its information
Illustration 12C	Illustration 12D
Original Studio Photograph, 1916-17	Bicycle Wheel, 1913/64, Schwarz edition of 8

The shovel blueprint indicates that the handle was literally traced from a well known Man Ray photograph that captured the shovel hanging high above eye level, (see illustration 13A and B). At this height, as the eye looks up the shovel's wooden shaft's outside edges appear to converge (and get narrower with more distance.) To create a blueprint, perspective distortion must be accounted for (and discarded) if you use a photograph as a source to recreate an accurate 3D model. See the shovel blueprint illustration 13B, the front and side elevation views both depict the converging lines that were later, amusingly translated in the construction of Schwarz's 3D model. The shovel's wood shaft, literally gets progressively more narrow from metal blade to the handle. See illustration 13C showing the final Schwarz 3D model built from the blueprint as a much smaller 3D model on the left than the shovel on the right that was built from measurements of actual example of the Schwarz edition of 8 snow shovels)⁽⁹⁾.

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Illustration 13A	Illustration 13B	Illustration 13C
Photograph of Duchamp's Studio by Man Ray, 1920	Marcel Duchamp, Blueprint for In Advance of the Broken Arm, 1964	Front and side views of the ASRL 3D models of actual Schwarz shovel (left and longer) and a shovel made from the blueprint (the smaller one on the right)

Let us return to the hatrack blueprint 1964 and the 3D model. If Schwarz's 1st version of the hatrack 3D model, indeed, looked like the geometry in this blueprint, it's no wonder why Duchamp insisted upon throwing it out and felt he had to redesign it.. . and yet his 2nd and final version of the Schwarz hatrack looks even less like the photographs of the "original" 1916-17 hatrack in his studio! (I will later discuss the likely reason why Duchamp approached his hatrack in this technique of "information" that decays in a series of snapshots over time).

5. 1964 Blueprint with Interactive version of 3D Schwarz model

Click to see video

Illustration 14A

Marcel Duchamp, Hatrack, 1917/64

Before considering the interactive 3D model, one can see that the blueprint has nothing to do with what ends up as the 2nd and final version of the Schwarz 3D hatrack model. See video and illustration 14A of the Schwarz 3D model, in addition to the interactive model, how do we install this hatrack? Does it go on a wall? If so, how? If you place the 3 hooks up, the other 3 hooks go down, and half are therefore useless. Placing 3 on the left side and 3 on the right side is not much better. Sitting on a table does not make sense; neither does somehow hanging it upside down from the ceiling. The radial, symmetrically distributed series of curves definitely reminds one of the top the free standing-type Thonet coatrack/hatrack shown in illustration 14B and video 14E. However, as much as we are vaguely reminded of such a hatrack, a critical comparison quickly reveals that the tops of these Thonet free standing structures are a circular series of "S" curves. Moreover, Schwarz's hatracks (edition of 8) are not even bentwood but have been carved as shown earlier in illustration 14C and D (our study model of the Schwarz editions). Moreover, note that the 6 equal length hooks curve out whereas the real free standing Thonet "S" hooks at the top curve in⁽¹⁰⁾, see illustrations 14 C and D. 14C reminds us of the top part of the "S's" in the standing Thonet (14B); whereas, 14D reminds us of the S's lower set of curves that turn up.

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Illustration 14B	Illustration 14C, 14D	Illustration 14E
Thonet standing hatrack, "Thonet Bentwood & Other Furniture," illustrated catalogue, 1904, p. 80	ASRL wood model of Schwarz 1964 Hatrack wood 3D model in two positions	1999 version of 'Alice in Wonderland' uses Thonet hatrack as prop ©1999 Babelsberg International Filmproduktion GmbH & Co. Betriebs KG and Hallmark Entertainment Distribution Company

Compare 5 Interactive Models with Tu m' and Cast Shadows Depictions

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Illustration 15A

Marcel Duchamp, Tu m' (detail; rotated by 180º), 1918

Illustration 15B

Historical Thonet hatrack, 1904

The final 2 representations from Duchamp's 6 depictions that we will discuss are Tu m's 1918 hatrack and Cast Shadows' hatrack, 1918. These are both shadow projections that can also be compared to five interactive 3D models (1904, 1917, 1917, 1964, 1964)

The Tu m' shadow's 2 long hooks and 3 short hooks, in particular, (see illustration 15A, B) if viewed upside down and then compared to the 1904 Thonet model when rotated into similar position, can readily be seen as fragments of 3 "S" shape hooks (albeit, that the 3 "S"'s in Tu m' are incorrectly and asymmetrically angled in relation to each other and the top of one is cut off when compared to the Thonet 1904 3D model below).

The 1918 Tu m' painting brings us back to the issue, previously mentioned, of the difference in making objects in 3D, versus interpreting what these same objects look like, due to distortions, in a photograph, or in perspective drawings. Just as a bicycle wheel can objectively be perfectly round in shape and yet appear in a photograph as an ellipse, the same is true of any object's representation. Representations must be interpreted. We, in fact, because of a prior experience, can safely guess that the bicycle wheel is round but only appears to be an ellipse due to perspective distortions. However, an alternative hypothesis could be true, though not as likely -- that the bicycle wheel is not round but shaped like an oval. How can we know? The answer is two-fold. If we have access to the original wheel, we can test it (roll it and see if it smoothly and evenly rolls) and measure it (and see if the axis is in the middle of the circumference of a circle).

In the case of Duchamp's hatracks and other readymade objects, we are in the same position of discovering that a bicycle wheel that we assumed was round in a photograph was, in fact, oval. Since we only had a set of photographs of the second version of the Bicycle Wheel, and not the actual object, the only thing we could do was to take measurements from the 2D representations, fuse and build 3D models (both physically and in computers) based upon the group of photographs, and then test and measure again.

Click for video

Illustration 16B

Assembled 3D model of Bicycle Wheel by Rhonda Roland Shearer

Ironically, my bicycle wheel example turns out not to be hypothetical. See illustration 16A, B. From the set of bicycle wheel photographs, after we made measurements and models, and tested them, Robert Slawinksi, in our ASRL group, concluded that the axis of the Duchamp bicycle wheel was, in fact, not in the center of the wheel! Duchamp had lengthened some spokes and shortened others to create a large and surprising effect that is based upon only a very small difference in the decentered positioning of the axis. Click on #16B to see the video of what happens when our 3D model of one of Duchamp's bicycle wheels turns⁽¹¹⁾.

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Illustration 16A

Set of photographs showing the 2nd version of the Bicycle Wheel, 1916-17 (Both the original and this 2nd version are lost. There are no representations known of the 1913 original Bicycle Wheel and Stool.)

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Illustration 17

Marcel Duchamp, Ombres Portées (Cast Shadows), 1918 Note: arrow is for clarity added by author

The Cast Shadows 1918 photograph should also be examined by spectators in comparison with the 5 interactive hatrack models, see illustration 17. This representation of the hatrack indicates 3 long hooks and two short hooks. The first long hook on the left, hanging by a string, ambiguously appears as if it could be attached in a whole "S" shape with the first small hook on the left. A more likely interpretation is that the middle long hook is one "S" curve with the first (left) small hook and that the long hook at the most right is connected to the right most small hook. Yet this is unclear for the right most long hook could share an "S" shape with the left most small hook. In addition to the hatrack shadow ambiguities, other ambiguities reign in this photograph. For example, Duchamp's work Hidden Noise (see illustration 18A, a closeup of the Cast Shadows, 1918) oddly appears twice (he supposedly only had one original in 1918 -- the multiple edition of 8 was made much later in 1964, see #18B that shows the original Hidden Noise.) One has to conclude that Duchamp either somehow used mirrors to multiply the Hidden Noise shadow, or he created a photographic composite where he layered different photographs together into one image⁽¹²⁾. Duchamp used both techniques in his photographs, a topic we will explore in the next section.

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Illustration 18A	Illustration 18B
Ombres portées (Cast Shadows), detail showing two shadows projecting from With Hidden Noise (1916), 1918 Note: circles are for clarity added by author	Marcel Duchamp, With Hidden Noise with mirror, 1916

Duchamp's readymade hatrack only
exists in the mind not in factual nature.

After duly noting the geometric distortions in Duchamp's six hatrack representations, we must conclude that the simple history and definition of the hatrack that everyone believed -- that a readymade is an unaltered, mass-produced object -- must be completely reassessed and rewritten.

We can return to the six representations of the hatrack and explore some of the issues now raised such as to how Duchamp generated the six depictions? Did he alter hatrack objects or doctor photographs or both? We are presently working with forensic scientists to help us determine more about the exact nature and type of photographic or physical manipulations that Duchamp may have used. Duchamp, obviously, put us all on notice that he was doing the photographic tricks well known in the late 19th and early 20th century by both amateur and professional photographers, see illustrations #19A, B. In both photographs 19A and B, Duchamp himself appears to be a ghostly apparition, a typical photo trick of the time.⁽¹³⁾

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Illustration 19A	Illustration 19B
Studio photograph (1916-17) with Duchamp's ghost image found in 1960's	Photograph of Duchamp's studio by Man Ray with Duchamp as ghost image, 1920

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Illustration 20A

Original Studio Photograph, 1916-17

Forensic experts that I have consulted also noted that the scale, shadows and light directions in many of Duchamp's photographs are inconsistent throughout the whole image.⁽¹⁴⁾ As an example, strong shadows will, inconsistently, be cast from one object but not from the other object directly next to it. (Closely examine illustration 20A, Note that the stick leaning against the wall cast a shadow and yet the Bicycle Wheel does not! Moreover, the pillows in the foreground cast strong shadows and yet the Coatrack does not!)

For another example, look at illustration 20A, B and C. A full size snow shovel could not possibly be hanging physically from a height indicated in these studio photographs. We discover that the wood shaft would have to be too short when we compare the shovel's size to the ceiling.

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Illustration 20B	Illustration 20C
Photograph of Duchamp's studio used for making print for the Box in a Valise, 1941 Note: circle is for clarity added by author	Note that shovel could not be hanging at its full length from the ceiling. Photograph of Duchamp's studio with Duchamp's ghost image, 1916-1917 Note: circle is for clarity added by author

Click to see video

Illustration 21A.

Marcel Duchamp, In the Manner of Delvaux, 1942 Note: arrows are for clarity added by author

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Illustration 21B

Mathew Brady used composite techniques in the earlist days of photography. From Dino A. Brugioni, Photo Fakery: The History and Techniques of Photographic Deception and Manipulation, Virginia: Brassey's, 1999, p. 34 Note: circles are for clarity added by author

Our resulting hypothesis must be that the shovel's wood shaft and handle have been somehow cut off. Duchamp (or someone in his behalf) shortened the wood shaft either physically or photographically. In the later case of trick photography, instead of hanging a short snow shovel in his studio, Duchamp, or someone at his behest, could have; 1); taken a photograph of a snow shovel and carefully trimmed away the background; 2), Next, this snow shovel shaped photograph part (with short wood shaft) would then be inset into a precisely sized and shaped cut out receptacle in the studio photo's emulsion (similar to putting a cut out cookie back into its negative space within the rolled out dough); 3), the studio background and shovel fragment now appear as one photograph that is rephotographed and printed for the final resulting composite that we see. Examine here the video of the work, In the Manner of Delvaux (1942) which documents only one example among many of the expert skill Duchamp (or someone at his request) demonstrated in creating photographic composites. (See Illustration 21A) Adding or subtracking subjects from photos was done with numerous techniques from the earliest days of photography. Mathew Brady seamlessly added an eighth Civil War general in illustration 21B.

The aforementioned studio photographs (19A, B and 20A, B) present many other instances of photographic manipulations that I will leave for future discussions. However, please see Stephen Jay Gould's text box here to read his observations and discovery regarding Duchamp's studio photograph, illustration 19B. For now, I will limit myself to analysis of two studio photographs of readymades to continue my argument (see illustrations 22A and 22B that show Duchamp's "original" 1916 coatrack and "original" 1917 urinal.)

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Illustration 22A	Illustration 22B
Marcel Duchamp, Trébuchet, 1917	Marcel Duchamp, Fountain, photograph by Alfred stieglitz from Blindman No. 2, 1917

Did Duchamp Give Us a Ghostly and Partial Seventh Cut of His Hatrack? Stephen Jay Gould Click to enlarge Photograph of Duchamp's studio by Man Ray, 1920 Man Ray's 1920 photograph of Duchamp's Rotative plaque de verre (with one plate broken and scattered on the floor) raises many questions that have never been addressed by art historians. In particular, although the photo, at first glance, might seem to be a casual snapshot of a messy studio, even a cursory examination reveals complex changes, careful placements, and interpolations - particularly to imbue the entire composition with a "circle" theme (understandable since the centerpiece Rotatitive plaque is a device made of glass rectangles that, when spun, produces the appearance of a set of rotating circles.) But note all the other circles, not so casually placed or imported into the composition: the "target" beneath the chess pieces on the wainscotting, the circle cut out of glass in front of the frame on the floor next to the crate, the bicycle wheel to the left (but not resting on the stool that should be visible if the famous readymade roue de bicyclette just happened to be present in its reality and entirety, and, especially, the blurred circular forms that look like cooking pots with handles at the upper and lower right, and that create such an interesting triangular composition with the bicycle wheel at center left. (Thomas Girst suggests that these large circles may be parts of the lighting equipment that Man Ray set up to take the photo). One can go on ad infinitum: why, in an otherwise complete chess set of white pieces on the wainscotting, is a single pawn missing? Why is the Russian eye chart hanging upside down? Click to see video Animation of the Rotary Glass Discs in stationary position (left), and in motion (right), 1920 Click to enlarge Carpet Beater like the one in Duchamp's studio photo from the ASRL Collection. On left, second example from the bottom matches carpet beater Duchamp displayed. Logan-Gregg Hardware Company, Pittsburg, 1912, p. 631 But moving to the main point of this note, look just to the left of the large wheel at the left end of the rotative plaque. Here we see a ghost figure of the top half of a man's body, perhaps Duchamp's. We can hardly make out the head, but we see the right arm fairly clearly, even including the creases of the shirt. The figure then cuts off abruptly at the waist, but we can easily be fooled into missing the cutoff because the photo includes what seems to be an old-style carpet beater, business end pointing down and handle pointing up, extending just where the man's right leg would be. (Why?) Now, look above the right forearm just behind the shirt cuff. The image is blurry, but I'm fairly sure that I see a single full hook of a Thonet hatrack (the presumed original for Duchamp's series of manipulations and redoings). I originally thought that the ghost man was cradling the hook in the crook of his arm. But I now think that the hook just lies in front of the arm. The hook seems to be tied to a string extending rigidly upwards and affixing nowhere. The hook then curves around to the right, passing over the figure's arm, and then completing its curve just under the arm and towards the waist. A second string seems to emerge from the top, under the first, and to run downwards and slightly to the left, finally passing over the figure's arm just to the left of the hook itself. Click to enlarge See Coatrack hook in photograph of Duchamp's studio by Man Ray (detail), 1920 Note: circle added by author Outline surrounds ghostly hook. Wooden base added to illustrate the position of this hook in an unaltered Thonet hatrack model with three "S" shaped curves. Note that string is tied to the top hook as in the two studio photos below. Click to enlarge Photograph of Duchamp's studio by Man Ray (detail), 1920 Now, both Duchamp's 1941 Boite print of a 1916-17 studio photo and a second studio photograph of the hatrack show the entire device hanging from the ceiling, affixed by a similar string tied near the upper end of a hook in positions comparable to the tie of the single hook in the ghost photo. (Duchamp, by the way, produced several photos with ghost images of himself emplaced into an interior scene). However, one of the two studio photos of the "full" hatrack in the 1941 Boite print seems to be missing one of the three large hooks. Did Duchamp remove the hook from this photo and then give it back to us as a single ghostly item in this later photo? Hooking and roping us in yet again; pulling our leg with his legless ghost; kicking us in the pants with a rug beater acting as a surrogate for a leg? Click to enlarge 1941 Photo to make print for Boite-en-valise (detail) Note: String tied on the top hook 1916-1917 (found in 1960s) Studio Photo (detail) Note: String tied to the top hook

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One, might think at this point, "So what. I can already see that Duchamp probably altered, physically or photographically, his readymade objects -- what difference does this make?" Let's set aside the fact that all books of art history or cultural criticism (and even cookbooks! See illustration 22C) state, as their premise, that Duchamp's readymades are unaltered, store bought mass-produced objects - and that this claim can now be dismissed as factually incorrect.⁽¹⁵⁾ I will use illustrations 22A and 22B to show that Duchamp's original coatrack and urinal help explain why I believe Duchamp altered readymade objects in his photographs in the first place. Since the quality and approach that Duchamp used for his numerous distorted "readymade" representations are similar, such a frequency of occurrence suggests that Duchamp was applying a single geometric system. Perhaps this system that I have been observing throughout Duchamp's readymade works is the new and mathematically rigerous "rehabilitated perspective" geometry Duchamp spoke about in interviews. Moreover, I also found evidence that Duchamp used this new geometry in the Large Glass, just as he had claimed.

Click images to enlarge
Illustration 22A	Illustration 22B	Illustration 22C
Marcel Duchamp, Trébuchet, 1917	Marcel Duchamp, Fountain, photograph by Alfred stieglitz from Blindman No. 2, 1917	Even a cookbook refers to Duchamp's readymades as only humble, store-bought objects. David Rosengarten with Joel Dean and Giorgio DeLuca, THE DEAN & DELUCA COOKBOOK, New York: Random House, 1996, P. 206

Time Line of Readymade Series of "Trébuchet" Coatracks -- as Seen by Spectators click each image to enlarge
23A	23B	23C	23D	23E
Click	Click	Click	Click	Click
1941	1960s (made 1916-17 found in 1960s)	1964	1983 (made in 1940 found in 1983)	1991 (made 1964 seen 1991)
Retouched 2D print in Boite-en-valise	2D photo original Coatrack	3D iron and wood model	2D print found by Ecke Bonk (made in 1940 by Duchamp for Boite)	2D Blueprint

Let's look at the Coatrack (see illustration 23A, B, C, D, and E) as a series of snapshots in time, just as we did to examine Duchamp's hatracks, as he instructed us to do in his notes (refer again to illustration #1).

Note that the geometries of the coatrack series (as we also found in the hatrack series), is different in every 2D and 3D representation. (For example, the iron hooks are straight in the 1964 Schwarz 3D model and 2D blueprint, whereas they lean backwards in the original 1916-17 studio photograph and in the 1941 Boîte print. And as in our treatment of the hatrack series, we must mentally visualize or, alternatively, make literal 3D models of the coatrack 2D representations, in order to observe the differences among all of the 5 coatrack representations (four 2D and one 3D).

The particular distortions contained within the original studio photograph provide the greatest interest for our immeditate discussion. Again, as we found in the hatrack, the coatrack hooks bend and turn in unanticipated ways. (We expect mass-produced objects to have characteristics of the factory-made, traits that include standardization and regularity of form -- the very opposite of custom-made variations). Look at the last hook of the 4 (moving from left most hook to right), the top small sub-hook (the middle of the three sub-hooks) bends so far up and in that it reaches the top largest sub-hook. Duchamp told us that he nailed the coatrack to the floor after having "kicked it around" his studio. However, this trauma to the coatrack (that he aptly titled "trap" or Trébuchet -- a term from a move in chess where a player sacrifices one of his own pieces to trap an opponent's piece) the physical properties of cast iron determine that such a hook would crack and break before bending. This rigidity of material proves useful for withstanding the stress of hanging heavy coats. Duchamp, on the 1964 blueprint, even specifies that his 3D 1964 Schwarz hooks must be made of iron -- not soft copper.

Testing and Comparison of Perspective Geometry: A Technique Applied from CIA Expert Dino A. Brugioni in Photo Fakery Click each image to enlarge
23F Duchamp's distorted Coatrack in original studio photo, 1916-17
23G Actual historical coatrack in ASRL Collection with correct perspective
Illustration 23 F and G
Analysis done by Yong Duk Jhun and Rhonda Roland Shearer

Click each image to enlarge
Illustration 23H	Illustration 23I
Method of identifying perspective distortion in a photograph -- thus demonstrating evidence of photo manipulation -- from Brugioni's Photo Fakery	Cover of Photo Fakery: The History and Techniques of Photographic Deception and Manipulation, by Dino A. Brugioni, Virginia: Brassey's, 1999, p. 90

Note the shapes and count the holes in hook 24A and 24B and contrast these to the general form and number of holes found in Duchamp's original Coatrack hooks in the studio photo and in the Schwarz model in 24C

In fact, when Robert Slawinski and I began working on creating a coatrack 3D computer model (equivalent to the information contained in the 1915-16 2D studio photograph) we quickly recognized that the hooks used by Duchamp were; a) a common type readily found in the historical record (see illustrations 24 A and B); b.) that his 3D Schwarz model of the coatrack looked nothing like the "original coatrack" found in the studio photograph of 1915-16 (for example, note that the hooks are straighter in the 3D model and that the wood board bottom extends too far past the hooks on each end in comparison to what we find in the original 1915-16 2D studio photograph, see illustration 24; c) not only is the last hook (moving from right to left) distorted in the original studio photo above (in 24C) (its top small sub-hook with an impossible upward curve), but the other 3 main hooks of the four, and the wood board itself, are also distorted. In other words, we cannot take the matching historical hooks (as in illustration 24B), place them evenly on a symmetrically rectangular wood board and then find one single perspective viewpoint to make a projection that matches all the shapes of the coatrack, as Duchamp has depicted them in the original studio photograph (see illustration 23A).

Click images to enlarge
Illustration 24A	Illustration 24B	Illustration 24C
Historical coathook in the ASRL Collection that matches the one Duchamp used in original 1916-17 studio photo	Historical coatrack in the ASRL Collection	Comparison of Schwarz 3D model's wood base (bottom) and wood base as depicted in 1916-1917 original studio photograph (top) Note: circles are for clarity added by author

Click to enlarge

Illustration 23E

2D working print found by Ecke Bonk that Duchamp made in 1940 in the process of creating a pochoir print for his 1941 Boite-en-valise

See illustration 25 showing how the cube's shape changes according to the position of the viewer's eye position. When we know the original shape -- such as a cube or a series of identical coat hooks in a row -- we can then accurately predict what the shape of the cube or coat hooks will be from various observer's eye positions. In other words, if the resulting cube or coatrack shapes follow our predictions (based upon both our prior experience and perspective rules), then we say that the representation is "correct" (in perspective geometry); if the cube and coathook shapes are not in accordance with our predictions, then we say that the representation is distorted. As in our previous hatrack series, our two hypotheses are possible: first, that Duchamp altered the coatrack physically; or second, that he altered it photographically. The last image in the coatrack series of snapshots reveals, I believe, the photo composite technique that Duchamp used to make his coatrack and other "readymades" as well as disclosing the underpinnings and general methodology of his new form of perspective geometry. (see illustration 23E)

Illustration 25A depicts the perspective found in photography -- one fixed eye sees a continuous and related set of distortions from the perspective of this one eye. (The four different cube descriptions in 25A are what the eye sees from 4 different fixed positions). Illustration 25B, however, more accurately depicts how we actually see objects, as our two eyes, head and bodies must continually move around 3D objects to fully see their forms, as shown with this cube. And yet, despite what must be the truly fragmented nature of the visual input, the mind and eyes work seamlessly together to create the appearance of discrete and fixed objects.

The two cube examples (25A and B) directly relate to the earlier discussion of Duchamp's White Box note, which, as I argued, describes 2 mental operations (see illustration 26A and B). The single fixed eye perspective of 26A is like the fixed eye looking at the cube in 25A; whereas the moving eye of 26B operates like the multiple perspectives described in 25B.

The notable difference between illustrations 25A,B and 26 A,B is the dimension. Using Duchamp's terminology, 25A,B describes an eye in 3D space ("eye³") looking at a 3D cube; whereas, 26A,B represents an eye in 3D space making observations of a 2D plane. Both 25B and 26B require time and movement in 3D space of the 3D eye ; whereas, 25A and 26A illustrate what Duchamp describes as the "vision" of the "same eye from a fixed point of view (linear perspective)."1

Click to enlarge
Illustration 25A	Illustration 25B
A set of continuous and related 3D cube distortions as seen from four fixed eye positions	3D cube is only seen as a 3D eye moves around it
Illustration 26A	Illustration 26B
Duchamp's diagram 26A illustrates what is seen from a single fixed eye as in 25A above	Duchamp's diagram 26B illustrates more accurately how an eye moves in time and space to collect information as also shown in 25B above

Click to see video

Illustration 27

Video of Coatrack animation analysis

In order to actually see all of the coatrack information seen in Duchamp's original studio photograph in real 3D space, our eye would need to be moving in time -- see Illustration 27 showing a video of Robert Slawinski and my animation. Our analysis of the original coatrack depiction reveals that Duchamp used a common composite photo trick to "cut and paste" together his "whole" coatrack. Using 6 different photographs from 6 different fixed eye viewpoints, we believe that Duchamp cut out one section of the coatrack from each photo and then carefully fused these parts together for the final appearance of only one readymade coatrack. The spectator would only "see" this actuality of multiple points of sight "non-retinally," with conscious effort via mental visualization or actual model-making.

We made both physical and computer models here in the lab. Our computer animation diagrams the 6 cuts we believe that Duchamp made from 6 separate photographs taken in 6 different perspective positions. Robert Slawinski and my analysis concludes that Duchamp used 3 whole hooks, 1 hook split into 2 parts and 1 whole wood board as the 6 parts (from 6 different photos) as he assembled into what appears to be the single, whole and readymade coatrack in his studio photograph. See Illustrations 28A, B, C, D, E, F, the 6 coatrack parts that Duchamp cut out and later assembled together are color coded (in these still images taken from the computer animation) to emphasize the separation of the part selected by Duchamp from the rest of the coatrack (that he then discards, and that follows the same perspective geometry of the targeted part.)

click each image to enlarge
28A	28B	28C
28D	28E	28F
This series of stills shows each of the 6 coatrack positions from which Duchamp selected parts to composite (Note: The selected parts are color-coded)

Illustration 29A and B show a comparison of the parts that Duchamp selected (in color coding) with an image that assembles the 6 whole coatracks, in their 6 different perspectives, together into one event simultaneously seen (using the same color coding).

Click each image to enlarge
Illustration 29A A color-coded diagram showing the 6 parts Duchamp composited together taken from 6 photos.	Illustration 29B This still from our coatracks from which Duchamp selected parts to composite (as in 29A).

Click to enlarge

Illustration 30

A photo trick book points to the problem of "fluffy contours" created by the unintentionally cut and paste method, revealing that photo compositing has been made.

Illustration 31A Illustration 31B Here are two pages from a photo trick book discussion about the "cut and paste" method used for creating photo composites.

In addition to the evidence resulting from our analysis of the perspective geometries, 2 other examples of internal evidence indicate that Duchamp used both "masking" and "cut and paste" techniques from the photo alterations used in hobby and trade.

Examine illustration 30, a close up view of Duchamp's original coatrack photo, revealing what a photo trick book calls the "fluffy edges" that can easily appear as a soft whitish outline around a photo cut-out after being pasted, if special measures are not taken. Forensic experts look for tell-tale signs -- such as fuzzy contours -- as indicators that photo prints have been combined. See illustration 31A and B,two pages from "The Secrets of Trick Photography" by O.R. Croy discussing this particular problem within the cut and paste method.

Our second example of internal evidence for our hypothesis that Duchamp altered his original coatrack photograph by combining parts returns us to illustration 23E. Only after making our animation analysis of the geometries in the coatrack did I notice the potential importance of Duchamp's "working" prints of the coatrack first published in 1983 by Ecke Bonk. These prints were described by Bonk as preliminary stages of Duchamp's 1940 process in preparing pochoir prints for his publication of 300 copies of the Boîte-en-valise, (see illustration 32A and B). Bonk does not explain what the method was, or why Duchamp was cutting and pasting a separate paper cutout of the coatrack onto the background studio photo (where 3 hooks are masked out of the scene with white). Illustration 32B indicates an attempt to position only the first hook of the cutout onto the coatrack underneath. This "working print" also suggests (as judged by their two positions) that the paper cut-out coatrack is in one perspective view and the coatrack underneath, imbedded into the studio photo background, is in another perspective.

Compare this working print (32B) to our still from the video animation, where we concluded that Duchamp used 6 different viewpoints (cutouts of hooks and a wood board from 6 photographs), see illustration 32C. The similarity between 32B and C is striking. Was Duchamp using the same method of compositing multiple viewpoints into one coatrack for his pochoir print that he had used earlier to create his original coatrack in the studio photograph?

Click each image to enlarge
Illustration 32A	Illustration 32B	Illustration 32C
Marcel Duchamp, Boite-Series F, 1966	Working print used by Duchamp to create his 1941 pochoir print for the Boite-en-valise	A still from our coatrack analysis that appears strikingly similar to Duchamp's working print above

I believe that this working print serves as a "smoking gun" in our case. Not only is the cut and paste method and the geometries of the forms similar between the alterations in the studio photograph and in Duchamp's Boîte pochoir print, but his separate white-out and maskings of the wood board and the hooks now makes sense. For what purpose would the separate masking and treatment of the 4 hooks and the wood base serve (as is clearly indicated in his "working print") other than as a matrix for creating a composite image?

Click each image to enlarge

Illustration 33A

Known stieglitz version of Duchamp's Fountain urinal published in Blindman N. 2,1917

Illustration 33B

Second version of stieglitz's Fountain photo (1917) -- not publicly known until 1989

Related to evidence of photo compositing, as found within Duchamp's "working print" of the coatrack, is a curious 2nd version of a photograph of Duchamp's Fountain urinal taken by stieglitz in 1917, and shown in illustration 33A and B. William Camfield's 1989 book, a chronicle of the odd history of Duchamp's Fountain urinal, presented this second stieglitz photo for the first time after it quietly appeared within the archive of Duchamp's main patrons, the Arensberg's, in the 1950's.

Before discussing the potential importance of this particular photograph, and its delayed appearance for spectators, let us again examine, as we did with the hatrack and coatrack, the consistent approach that Duchamp uses to present his readymades -- as a series of snapshots over time -- now applied to Duchamp's urinal.
As we discovered with his snow shovel, hatrack, coatrack, bicycle wheel and stool, Duchamp's original 1917 urinal does not exist today. Historians such as William Camfield and Michael Betancourt have documented the contradictions and conflicting stories that leave us with effectively no definitive evidence about the urinal's existence -- including any potential witnesses of the object (the few testimonies that exist conflict); who photographed it (stieglitz himself, who supposedly photographed the urinal for the 1917 Blindman publication, only briefly mentions the urinal in writing, and no negative or print was ever found in his archive); or how it quickly the urinal vanished into thin air in 1917. I will not go into the details here, for they are so well pursued and documented by Camfield and Betancourt. All that we do have, as for Duchamp's hatrack, coatrack, and other readymades, is a series of urinal representations in 2D and 3D that we can put together in a set (as in step A of Duchamp's mental operation). We can then examine each depiction as its own snapshot or cut (as in Duchamp's step B, where we take separate observations over time). Since the original 3D urinal is "lost" as a source for collecting more information, we must depend upon our ability to average among, and compare differences between, each urinal representation, see illustrations 34A, B , C, D, E, F, G and H. The tally of our representations, encompassing what we know of Duchamp's urinal, follows:

Time Line of Readymade Series of Urinals -- As Seen by Spectators (click each image to enlarge)
34A	34B	34C	34D	34E	34F	34G	34H
1917	1941	1941	1960s (made 1916-17 found in 1960s)	1964	1964	1964	1989 (found 1950s published 1989)
2D photo by stieglitz from Blindman #2 journal, 1917	3D miniature model in Boite-en -valise	2D print made from studio photo in Boite-en valise	2D photo, studio photo	2D etching, edition of 100	3D pottery model Schwarz edition of 8, second corrected version by Duchamp	2D set of blueprints (first 3D model, based upon blueprints, lost)	2D photo fragment published by William Camfield (original dating not known)
Note: This time line excludes urinal versions that Duchamp did not originate.

As we discovered when examining Duchamp’s hatrack and coatrack, the above set of urinal depictions in 2D and 3D do not describe one consistent 3D urinal. For example, our analysis of the studio photo 1916-17 (illustration 34D found in the 1960's), the 1941 print (illustration 34C created from a 1916-17 photograph) and the 1^st version of the stieglitz photograph (illustration 34A published in the Blindman #2) reveals an inescapable conclusion -- namely, that two different urinals were represented in 1917. Again, our key question involves casualty -- did Duchamp change urinals literally or photographically? Evidence for both hypotheses exists. Duchamp did make his original 3D miniature urinal model in 1940, and he did commission others to manufacture the full edition of 300. Surprisingly, after Duchamp authorized Schwarz to make editions of 14 of his "readymades," Schwarz failed, despite intensive search, to find even one of the 14 mass produced objects close enough to Duchamp’s originals in 2D or 3D to serve as prototypes for the editions. Therefore, Schwarz had to organize the manufacture of all 14 editions himself. Stranger still, no duplicate urinal has even been found in any catalogue, including the literature from the very company that Duchamp specifically named his source for his urinal -- the Mott company.

Click to enlarge

Illustration 35A

Urinals were purchased by Mott, Crane and other plumbing companies from Trenton Potteries in Trenton, NJ. The Bedfordshire urinals in the ASRL collection are all stamped Trenton potteries.

Art historians William Camfield and Kirk Varnedoe report that they strenuously searched the historical record for urinal models that matched the geometry of Duchamp’s urinal. My own research agrees with their conclusion -- that the closest urinal to Duchamp’s is a model called the "Panama" or "Bedfordshire with Lip." In the early 20^th century, Mott, Crane and other distributers purchased urinals from Trenton Potteries, Trenton, NJ (a.k.a. "the sanitary pottery capital of the U.S."). Models of urinals and other pottery products, such as toilets, were so basic and so infrequently changed that only freelance workers were needed to serve as modelers for the entire sanitary pottery industry. ASRL owns three of the Bedfordshire urinals, and all are stamped, "Trenton Potteries," NJ; see illustration 35A. The duplication of shape among these urinals speaks both to the minimal variation that occurs among urinals, and to the easy standardization of form resulting from their mold making process.

Just as one hatrack studio photo, found in the 1960's, provided a closer match (but no cigar) to the Thonet historical model than any of Duchamp's other 2D or 3D hatrack depictions, his urinal in two studio representations (34C and 34D) provide a close, but not exact, match to the Mott historical model (see illustration 35B,C and D,E). Duchamp’s two studio photo urinals are here compared to the Bedfordshire urinal with lip from the ASRL collection, placed in a similar position. The general appearance is similar among 35B,C and D,E. However, the "side ear-like" brackets are larger and different, both from each other and from the Mott model, as are the pipe connections at the urinals’ top and bottom. Moreover, we have concluded from our analysis that one should be able to see Duchamp’s "R. Mutt 1917" signature and date (and one cannot) on a urinal when placed in both positions 35B and 35C, if the inscription were indeed there.

click each image to enlarge
35B	35C
2 studio photos (35B, C) look similar to the Mott/Crane Bedfordshire with lip in 35D,E below; Compare with detail images below

35B detail	35C detail		35D
The 35B position would show the signature "R. Mutt 1917" if it were there in the above studio photo -- as indicated by our 3D computer model when placed in a similar angle.	The 35C position would show the "R. Mutt 1917" inscription if it were there in the above studio photograph -- as indicated by our 3D computer model placed in a similar angle.		35E
			ASRL Bedfordshire urinals placed in similar positions to urinals in Duchamp's studio photos look easily similar, see 35B, 35C

However, when we examine 35B,C,D,E various attempts to place the Bedfordshire model in a position to match the stieglitz photo 36A completely fail. Only when we composite together the top part of the urinal from one photograph, the bottom part from another and the drain holes and pipe hole from yet others in different perspectives, does the urinal begin to look vaguely like the stieglitz urinal 36A. Note that the bottom and top of the urinals in 35B,C and 35D,E easily appear similar in size, scale and perspective view, whereas, in 36A, the stieglitz original photograph appears to be in one perspective view in the top half and in yet another camera viewpoint in the bottom half where the pipe connection rests. Moreover, when you look at our actual Urinal, 36D for example, the upper half with the drain holes looks further away from us in the photo; whereas, the bottom pipe hole part appears closer to us, in the foreground. Curiously, no similar "near and far" positions are transmitted by the forms in 36A, Duchamp's 1917 stieglitz photograph. In fact,in our Bedfordshire urinal photos, 36B,C,D,E, the drain holes appear smaller, and therefore further away, and the pipe hole reads larger and therefore closer to us than in the 36A stieglitz photograph -- giving credence to my observation that the stieglitz photograph, strangely, does not depict the significant distance between the back of the urinal and the front (as clearly indicated in 36B).

Click each image to enlarge 36A 36B The original stieglitz 1917 photo of Duchamp's urinal, unlike Duchamp's two other studio photos, could not be easily approximated when we photographed our Bedfordshire urinals. The Bedfordshire is the only urinal model, circa 1917, that appears close to, but not identical to, the original urinal depicted in the stieglitz photo. 36 B,C,D,E are a series of photographs of our ASRL Bedfordshire models that show our attempts to reproduce a shape similar to the urinal in the original 1917 stieglitz photo. 36C 36D 36E

Click to enlarge

Illustration 37A,B,C,D

We combined four different photographs to create 37A,B,C,D -- as our Bedfordshire urinal's drain holes, pipe hole, urinal top and bottom parts could not be captured in one photograph with positions that match the drain holes, pipe hole, and top and bottom parts in the stieglitz photo (36A).

We provide the 2D Interactive Presentation below to allow the spectator to experiment with the cutting up and pasting together of different urinal photo parts. There are 9 possible combinations. One combination matches the stieglitz photo. Also, try placing the pipe in the middle as we suggest. One can begin to see how pieces that do not originally go together can be moved and will there appear to be better, or at least, equally correct in their form, when in a new position -- especially if you had the ability to fill in gaps with even more cut-out parts then we provide in this presentation.

		click here for 2D Interactive Presentation
		To download Flash Player plug-in, click here
Partial stieglitz photo found in 1980s is combined with part cut from stieglitz 1917 photo (see part below)
This bottom part is cut from the original stieglitz photo, 1917

Click each image to enlarge
Illustration 38A	Illustration 38B
In 1917, Duchamp places, what I believe to be, a composited photograph, in a journal titled The Blind Man	The Blind Man No. 2: P.B.T., May 1917

More specifically, this Interactive Presentation places together the bottom part, cut from the entire Stieglitz original photograph (36A), with the mysterious partial version (also printed from an original negative) as the top. Perhaps, as in our coatrack example, where the working print probably revealed Duchamp’s methodology for compositing his coatrack together from a series of photos in different perspectives, perhaps this partial photo of the urinal, printed and left as a complete image, represents the smoking gun, also found to reveal similar evidence of being a photo composite. For if we can, (1), easily create a likeness of the two 1917 photos of Duchamp urinals using the Bedfordshire 3D models and yet, (2), run into difficulty when doing the same experiment by trying to recreate the 1917 Stieglitz original urinal photo with the same Bedfordshire 3D model (the main difference being that the top part of the urinal, as in the partial Stieglitz photo, lies in one perspective and the bottom part in another), then perhaps the partial photo discloses itself as a step that Duchamp used in a process of creating his final photo composite, then aptly published in The Blind Man as he realized that we would not readily see his alterations. (see illustrations 38A and B.)

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Illustration 39A

Is the Partial Stieglitz photo itself a photo composite?

Is this partial Stieglitz photo itself, that we see in illustration 39A, also made of parts? And is the complete version of the Stieglitz photo (38A) essentially a fusion of yet more parts added to parts already composited in the top photo of the partial version (39A)? Moreover, is the fusing of different perspectives passing as one perspective in Duchamp's urinal, hatrack and coatrack, the same "rehabilitated perspective" geometry that he claims to have been using in his Large Glass?

Beyond "cut and paste" -- what other photo tricks did Duchamp use?

As previously described, I had suspected that the Stieglitz partial urinal photo represented a step in Duchamp’s photo compositing process, and that this photographic part, was itself, perhaps, made of photo parts. Illustration 40B suggests that, indeed, the drain holes were added within the Stieglitz partial photo, which, as a subtle but visible vestige, remains in the original Stieglitz photo, see illustration 40A.

Note that in illustration 40B, when the contrast of light and shadow are amplified, the drain holes reveal a distinct boundary that is, unexpectedly, and without apparent reason, lighter in value, thus giving the literal appearance of having been added as a patch.

	click to enlarge
Illustration 40A Known Stieglitz version of Duchamp's Fountain urinal published in Blindman No. 2,1917	Illustration 40B When the contrast of light and shadow are amplified, the drain holes reveal a distinct boundary that is, unexpectedly, and without apparent reason, lighter in value and gives the literal appearance of having been added as a patch.	Illustration 40C Examine the circled area in illustration 40C. The indefinite shadows and discontinuous lines and edges indicate this lower left corner as a likely site of photographic compositing and retouching.

The urinal in the Stieglitz photo, shown close up and large, created a greater technical challenge for hiding alterations than in our previous examples of the hatrack or coatrack, that are depicted as farther away and small, and therefore creating less expectation of perceiving visible detail. Since hatracks and coatracks are, literally, made of parts (the hooks and wood base are all physical parts put together), photographic cutting and pasting of parts can naturally exploit these predetermined and expected joinings, whereas, the urinal’s smooth and continuous, singular form does not offer such easy opportunities.

Illustration 40C depicts yet another important piece among numerous pieces of evidence (pun intended). Porcelain urinals are molded forms that produce clean, clearly unambiguous lines and edges as shown in illustration 40D, E, F, (depictions of Bedfordshire type urinals taken from Mott, Crane and Trenton Potteries catalogues of the period [circa 1917]). Examine the circled area in illustration 40C. The indefinite shadows and discontinuous lines and edges suggest this lower left corner as a likely site of photographic compositing and retouching.

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Illustration 40D Trenton Potteries	Illustration 40E Mott	Illustration 40F Crane
Three different company catalogue entries (circa 1917) featuring the same urinal type that looks most like Duchamp’s urinal

We are presently working, along with forensic experts, on a substantial list of other oddities found within the Stieglitz photo (40A) including: (1), more precise determination of the nature of the distortions, first noted by William Camfield, between the urinal in the foreground as depicted in relation to the painting in the background. We will also analyze and try to relate the seemingly strange scale differences among objects in the Stieglitz photo; such as the size of the urinal itself in comparison to the gauge of the string tied to the left "ear-bracket"; or the relatively too large appearance of the rough hewn texture of the wood pedestal; (2), testing the feasibility of placing the urinal (whose actual form, not shown, is hollowed out underneath) so off center on the pedestal, as depicted on the photo; and (3), studying the strange shadows, lighting, as well as the peculiar reflections (reminiscent of pooling urine), in the top upper lip of the urinal -- a pooling that appears to be defying gravity. (If these reflections were actually urine, we would have to be standing above, strattling a normally installed urinal in a novel orientation -- with our backs against the wall looking down into the pool of urine and facing out to whoever would be peeing.)

A second compositing method, beyond cut and paste, is suggested within the two studio photo depictions of Duchamp’s urinal, see illustrations 41A, B, C, D. A common but more difficult method of combining photo parts uses a dark or black background (cardboard or cloth) placed into a scene with a corresponding space left blank on the photographic plate in the camera. In this blank space, a second image (not in the immediate scene) can then be seamlessly added into both the plate, and also into the (formerly) plain black background.

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Illustration 41A	Illustration 41B
Two Photographs of Duchamp's studio taken in 1916-17 A common but more difficult method of combining photo parts depends upon the use of a dark or black background (cardboard or cloth) placed into a scene and a corresponding space left blank on the photographic plate in the camera.

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Illustration 41C	Illustration 41D
Close-up views of the Duchamp’s studio photographs (41A and 41B) Carefully note the general blackened area behind the urinal in illustration 41B and 41D and the dark cloth hanging directly behind the urinal in illustration 41A and 41C.

Illustrations 42A, B, C, D show a few early examples from a 1898 book written for the general public, and titled, Magic; Stage Illusions, Special Effects and Trick Photography. Compare these four illustrations to illustrations 41 A, B, C, D, Duchamp’s two studio photos that depict his urinal. Carefully note the general blackened area behind the urinal in illustration 41B and 41D and the dark cloth hanging directly behind the urinal in illustration 41A and 41C. Not only do the other photo alterations, as previously discussed, exist in these two studio depictions (remember, the ghost figure in 41A and the likely cutting and pasting of the hatracks and shovels in 41A and B) but the urinal appears to be "applied" to the scene using the classic black background composite technique as the device. Look at our animation analysis in illustration 43A and 43B.

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Illustration 42A	Illustration 42B	Illustration 42C	Illustration 42D
Four 19th century examples of the "black ground method" of compositing multiple photographic images taken at differnet distances

The irregular shadowing, unsure line and edges of the urinal’s silhouette (especially prominent in 43A) indicate a careful but, imperfect, masking and transfer of the urinal onto the blackground placed in the scene. Note, in the animation, that the studio depictions of the urinal’s interior lip shape, when outlined, comes very close to matching the form of our standard Crane/Mott/Trenton Potteries Bedfordshire model; whereas form of the interior lip on the ideal Stieglitz urinal (that is, when the drain and pipe holes are corrected to be centered) is very different, see animation 43C. Of course, these data conform with my prediction (derived from my hypothesis) that the two studio photos are slightly altered representations of an actual Bedfordshire urinal (and, therefore, that a Bedfordshire model would predictably almost match.) However, a 3D model -- even a corrected one -- based upon the geometry in Stieglitz photo would not match either the two studio photo urinals or the Bedfordshire model. As I have argued, the Stieglitz image is not representing, factual urinal different from either the 2 studio urinals or Bedfordshire model. I believe that the Stieglitz urinal is a photo composite made of varied parts taken from photographs of an actual Bedfordshire 3D urinal from different perspectives and at different scales).

click each image to see animations Animations by Gregory Alvarez and Rhonda Roland Shearer
Illustration 43A	Illustration 43B	Illustration 43C
Video of Urinal animation analysis that compares the 3D Crane model to the Stieglitz model and this studio photo	Video of Urinal animation analysis that compares the 3D Crane model to the Stieglitz model and this studio photo	Video of Urinal animation analysis that compares the Stieglitz photograph, the corrected ideal shape and a 3D model (made with depicted distortions) are compared.

Looking back at the historical examples of the black background method of photo compositing, in 42C and D (now circled and labeled as illustrations 44A and 44B), we see how the compositing of separate images can play havoc with scale (when we see multiple images of the same figure taken at two different distances, we interpret these figures in the final photograph as small and large sizes.) Other cues reinforce our interpretation of small and large figures standing side by side (as opposed to the small figure suggesting greater distance, and the larger figure as the same size standing in the foreground). In illustration 44B, for example, the table’s position in space (directly opposite to the larger standing figure), along with the feet of the small figure physically happening to meet the table’s horizontal plane, immediately evokes our most absurd and impossible interpretation -- a real Tom Thumb!

According to forensic experts, the only way to get a better grasp on why and how the scales of urinal parts, and other objects in the Stieglitz photo look out of whack, is to determine as much as possible about actual sizes. For example, how large are the tags used at the 1917 Exhibition? (see illustration 45A, of the Stieglitz photo with its tag circled.) The urinal looks disturbingly small in comparison to the string, hang tag, and wood pedestal texture. We have already determined, by our prior analysis, that the "ear-brackets" as depicted in the Stieglitz photo appear too large when compared to the actual Bedfordshire models of the period. Perhaps the ear-bracket [with the string and tag] are from a single photo taken at a different distance, a photo that was then fused with the rest of the urinal parts?)

Moreover, our forensic expert’s initial analysis echos my suspicion that the urinals in the two studio photos (45B, 45C) are, in addition to our sense that the scale of the urinals’ size is off, in comparison to the rest of the room, most likely composited in, and also do not seem to hang according to gravity, (We need to try to measure Duchamp’s old studio room. If any original woodwork exists, we can learn a lot more about Duchamp’s photos.)

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Illustration 45A.	Illustration 45B	Illustration 45C
Perhaps the ear-bracket [with the string and tag] are from a single photo taken at a different distance which was then fused along with the rest of the urinal parts.	The two urinals appear applied upon black backgrounds and seem to not hang according to gravity.

A closer examination of Duchamp’s 1964 urinal etching shows that, although Duchamp did base his tracings on the Stieglitz photograph to create this etched image, he, also and importantly, added a separate and specific extra part -- in a yet another perspective view, more radically different from the rest. Note, when comparing illustration 46A, B and C with 47A and 47B, the extreme leftward position that the whole urinal would have to occupy (47B) for us to see this one urinal part in the upper right side (47A). Why else would Duchamp move so far away from traditional perspective in one exaggerated and isolated part of this drawing, if not from a desire to push his point further, probably because we are likely not yet again to notice his new rehabilitated perspective system based upon fusions of multiple points of view in his drawings, models or photographs. Remember this etching was done at the end of his life, in 1964. Duchamp had already exposed his new perspective system to the world since his 1912 Chocolate Grinder painting and no one noticed. Moreover we continue to not notice because the mind creates and depends on such composites of information that Duchamp was presenting as perspective all the time.

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Illustration 46A	Illustration 46B	Illustration 46C
Stieglitz version of Duchamp's Fountain urinal	Etching,Marcel Duchamp, An Original Revolutionary Faucet: Mirrorical Return, 1964	An overlay of Duchamp’s etching (1964) when flopped , and placed onto the Stieglitz’s photograph of Duchamp’s Fountain (1917) indicates that used a tracing method.

	click left image to enlarge; click right image for animations
Click to see a video of our animation analysis, comparing the 3D model made from the idealized Stieglitz urinal (without the distortions in the original photo) that Duchamp draws with the varied positions that it would have to occupy to match the multiple perspective descriptions contained within the etching.
	Illustration 47A	Illustration 47B
	Video of Urinal animation analysis based on the 1964 etching. Note: Extra perspective part Duchamp added to Stieglitz urinal image for his Etching, as well as how far turned to the left, the urinal would have to be turned to see the perspective view of this added part. (Animation created by Gregory Alvarez and Rhonda Roland Shearer.)

Given Duchamp's claim that he studied the entire section on perspective at the Paris’s main library, and that, it is a "no-brainer" to trace the basic shape of the Stieglitz urinal without mistakes, it would be difficult to believe that this extra and distinct perspective part added by Duchamp to his urinal etching, would have occurred through accident or incompetence. We are especially encouraged to conceive of Duchamp's extra perspective piece as intentional, since the rest of the etching captures the spatial relations of the Stieglitz photo so well, including the pipe hole offset to the left, and so forth.

I must add one final point to buttress my case about the urinal. In the quotation on perspective that I cited at the beginning of this essay, Duchamp claimed that he added language, in addition to anecdote, in his rehabilitated form of perspective. Bonnie Garner suggested that when Duchamp signed his urinal Mutt, he, in effect, communicated linguistically the same structure that he used geometrically (with his fusing of multiple perspective parts into one whole). For what else is a "mutt" than an entire mongrel dog composited of many dog breeds (or parts) put together in time -- an entity that only appears to be, in a traditional perspective, a low quality whole.

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Illustration 48

Cover of The Blind Man, No. 2: P.B.T., 1917. Just as Duchamp did with the Urinal, Duchamp combined the Chocolate Grinder with the title of the journal, The Blind Man.

The other colloquial definition of mutt as "a stupid person" brings me back to thoughts about the first appearance of Duchamp’s urinal in The Blind Man (1917). Not only was the Mutt urinal essay and image placed under The Blind Man heading, but Duchamp and his close friends also(and, I believe, not coincidentally) used Duchamp’s Chocolate Grinder painting on the front cover, under The Blind Man banner, as well -- see illustration 48.

I argue that this placement of the Chocolate Grinder painting with the Blind Man heading relates directly, in meaning, to Duchamp’s similar positioning of his urinal. For as spectators in 1917, we would have been specifically blind to Duchamp’s new rehabilitated perspective used in both his Fountain urinal and Chocolate Grinder forms, as well as generally blind, as a consequence our foolish dependence (as Duchamp believed) on conventional perspective and "retinal vision" for determining factual reality.

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.

Duchamp’s claims in this interview (albeit cryptically) that he has done something rigorous and different to rehabilitate perspective, and that he has embodied this novelty in his new geometry in the Large Glass -- with the Chocolate Grinder as one part!

In 1956 Duchamp stated "I was already beginning to make a definite plan, a blueprint for the Large Glass. All of this was conceived, drawn, and on paper in 1913-14. It was based on a perspective view, meaning a complete knowledge of the arrangement of the parts. It couldn’t be haphazardly done or changed afterwards. It had to go through according to plan, so to speak." In the Cabanne interview Duchamp further claims that "I had worked eight years on this thing, (the Large Glass) which was willed, voluntarily established according to exact plan. . ."

Duchamp carefully provided us with his "Sears Roebuck-like" catalogue of notes and drawings describing his Large Glass project. Mostly written between 1911-15, these notes include a separate plan view and a side elevation of the lower "bachelor half" of the Large Glass, (but no 3-D model) and a perspective drawing illustrating measurements at 1/10 scale of the final Large Glass work, see illustration 49A, B, C,D.

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Illustration 49A	Illustration 49B	Illustration 49C	Illustration 49D
Perspective view, The Bride Stripped Bare by Her Bachelors, Even, 1915-23	Plan section of Bachelor Apparatus: Facsimiles of Plan and Elevation, 1913/1934	Elevation section of Bachelor Apparatus: Facsimiles of Plan and Elevation,1913/1934	Perspective drawing, The Bride Stripped Bare by Her Bachelors, Even, 1913

Architects or engineers depend upon similar plan views and side elevations as Duchamp’s Bachelor half to manufacture 3-D projects and small scale 3-D models. As discussed earlier, perspective drawings, in contrast, indicate the relative position of a particular observer in visual relation to the object or building. A "precise and exact aspect" in the science of perspective (an "aspect" that Duchamp said he was interested in following), dictates that the perspective in the lower half of the Large Glass drawing should relate to the geometry of the "blueprint" plan and elevation. In other words, if you make a 3-D model following Duchamp’s plan view and side elevation blueprints, you should readily be able to find and replicate the perspective view that Duchamp depicts in his perspective drawing by using this very same 3-D model.

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.

We may then be tempted to somehow change the plans so that the perspective projection, as laid out in Duchamp’s actual Large Glass, can be generated from the 3-D model (built from the plan and elevation view) -- which is, in fact, what some scholars have done. But that’s cheating, and such a providence also assumes that Duchamp was incompetent, or did not care about accuracy of perspective, although he claimed otherwise in earlier interviews, as well as to Cabanne.

If both the plan view and side elevation construct a consistent 3-D model of the Chocolate Grinder and the overall Large Glass itself, how and why have I and other scholars failed to generate a similar, if not exact, perspective drawing from this 3-D Large Glass model? I will argue that the reason why we cannot generate a single perspective view (in duplicating, what should has been the process that Duchamp followed to create his perspective drawing) must be Duchamp himself did not used perspective geometry, but, rather his new rehabilitated perspective -- the method that created his perspective drawing and the Large Glass (a.k.a. The Bride Stripped Bare by Her Bachelors, Even 1915-23.)

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Illustration 50A	Illustration 50B
Cube seen in 2D parts as eye moves around it	Perspective distortions of cube in relation to fixed eye

If we analyze the parts of the Large Glass (a 2D perspective view), using a 3D model constructed from Duchamp’s plans, we can only duplicate the depictions in what is rendered in Duchamp’s Large Glass 2D perspective drawing when we move our eye in time around the Large Glass 3D model to collect snapshots (cuts), and then fuse these separate perspective parts together into one depiction -- the very same method that Duchamp uses in his coatrack, hatrack and urinal 2D representations. Recall the illustrations (now #50A,B) showing the different perspective depictions resulting from 4 different fixed eye positions, in contrast to an eye that moves around a cube.

Illustration 51A, B, C present three animations from our analysis of Duchamp’s Chocolate Grinder and Large Glass in 2D and 3D. The first animation (51A) shows the camera’s perspective while moving around a 3D model of the Chocolate Grinder in 3D space. Colors highlight the part that corresponds to the equivalent section of the 2D Chocolate Grinder in the Large Glass perspective drawing. In other words, the animation shows a position that both the camera and 3D Chocolate Grinder would have to occupy to create the particular 2D Chocolate Grinder part shown in color code.

click each image and see animations
Illustration 51A	Illustration 51B	Illustration 51C
Three animations from our analysis of Duchamp’s Chocolate Grinder and Large Glass in 2D and 3D (created by Gregory Alvarez and Rhonda Roland Shearer)

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Illustration 51D 3D model	Illustration51E 2D composite
Due to perspective constraints, we would have to move one eye or lens in 3D space and time approximated 43 times around the 3D model to actually see the same information as Duchamp shows us in his Large Glass work in only one instant.(Created by Gregory Alvarez and Rhonda Roland Shearer

The next animation, 51B, shows our 3D computer model of the Chocolate Grinder as fundamentally based upon Duchamp’s 1913/1934 plan view and side elevation plans. The animation further depicts how the position of the camera determines the particular set of distortions seen by the lens in any one 2D snapshot of the 3D Chocolate Grinder. Moreover, this animation depicts that once one camera position allows a match in one part of the Chocolate Grinder, the other parts of the Chocolate Grinder and the Large Glass depart from this single perspective position. When other Chocolate Grinder parts are matched, each exists in its own perspective framework. Our efforts to tame all Chocolate Grinder parts into one perspective view, slips hopelessly away with each successful match of a single part, and the consequent complete rejection of the rest in lock step.

The next animation sequence, 51C, illustrates the cut and paste method that Duchamp probably used to create not only his Chocolate Grinder (and also his coatrack, urinal, hatrack, etc.), but the entire bottom half of the Large Glass itself. As any one photograph yields a single perspective view (with its own particular distortions), Duchamp’s selection of one part from each snapshot, after he pastes them together, creates a multiple fusion of varying perspectives. The last frame, showing the Large Glass in color coding, indicates each of the (approximately) 43 parts that live in their own perspective world, see Illustrations 51D and 51E. Due to perspective constraints, we would have to move one eye or lens 43 times in 3D space to actually see the same information that Duchamp shows us in his single Large Glass work! Illustrations 51F and 51G map the 43 camera positions in relation to the Large Glass 3D model that produced the 2D color coded projections in 51D and 51E.

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Illustration 51F	Illustration 51G
Side view of set of 43 possible camera positions Duchamp used to create his Large Glass fusing approx 43 photo parts cut from photographs in 43 different perspectives.	Top down view of set of 43 possible camera positions Duchamp used to create his Large Glass fusing approx 43 photo parts cut from photographs in 43 different perspectives.

Duchamp’s Revolutionary Alternative
in the context of competing optical experiments

Within the larger Victorian framework of technological mania, the human desire to develop a better system of representation for expressing how we see the world evolved into a frenzy of public interest and private invention. The advent of stereoscopic drawings quickly led to a whirl of experiments among the expanding developments in stereo photography and moving picture images. Stereoscopic devices depend upon the mind’s ability to fuse together two 2D images that, when seen side by side at the same time, create an impressive 3D effect. (One 2D image is drawn and seen in the perspective of the left eye, and the second 2D image rendered and then seen when displayed in the position of the right eye). Seemingly endless variants and extensions of stereoscopic concepts and equipment were developed and patented into the early 20^th century. The use of various prisms, or mirror systems, in numerous combinations, led to even more unusual attempts to create stereo fusion with, for example, the use of three images, instead of two, for two eyes. (See illustrations 52A,B,C,D,E and F.)

Stereo viewers were all the rage in the late 19th, early 20th century Click each image to enlarge
Illustration 52A	Illustration 52B	Illustration 52A
Stereo viewers were used for entertainment and education around the world.	Saugrin Album Magique French made Stereo-Viewer and book with cards in one gadget.	Hundreds of different Stereoviewers were patented throughout the world; many types are here on this book cover. Paul Wing, Stereoscopes, The First One Hundred Years, 1996
Illustration 52D Stereo effect created with Prisms	Illustration 52E 90º Mirror system creates stereo effect	Illustration 52F
Various prism and mirror systems were tried to stretch and test the limits of what was possibile in creating stereovision.		This unusual optical devise uses three images instead of two!

The limitations of human perception and cognition lie at the center of our illusionary experiences evoked by 3D stereo vision or even by "moving pictures," where projections of film, when speeding by fast enough, appear continuous because our eyes and minds are, literally, too weak to detect separations between the 2D images. Moreover, it requires no great leap, for someone as intelligent as Duchamp, to understand that these 19^th century optical experiments expose not only this retinal weakness, but (and more importantly) also suggest, in general, how perception and cognition work. We learn that our eyes and minds take bits of information (from the past and present) and seamlessly fuse them together. However, what we actually think we see, unless we become directly analytical and override this automaticity, is much more dominated by a mental construction than we consciously realize.

For example, when we view a depiction of a cube, we are essentially guessing that this object is a cube, based upon both the direct information that we have in illustration 53 and upon prior experience. The idealized construction of "cubeness" in our minds completely erases the additional information of the cube that our two eyes literally see. In illustrations 54A,B, and C, two views of the same cube are separately represented as seen by the left and right eyes (54A,B), whereas 54C is the amount of information that both eyes actually see. Illustration 54D shows a schematic plan (in bird’s eye view) of two eyes’ field of vision and fusion when looking at a cube.

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Illustration 53	Illustration 54 A,B,C	Illustration 54D
We are guessing that this is a cube based upon direct perception and prior experience.	Both eyes see A and B as C when fusion occurs.	Bird's eye view of two eyes looking at cube, two eyes see more information in sterevision, than in one eye perspective.

We obviously see more information with stereovision’s two eyes than in photography and perspective’s "one-eyed vision." The mind’s action of fusing two 2D images into a single 3D experience has also raised the dimension of our perception and, therefore, also increases the information available to our senses, as shown in illustration 54C. Not everyone possesses the ability to see representations in stereo. Severe astigmatism, or blindness in one eye makes the 3D fusion of two 2D images impossible. In early books on stereo vision, 19^th century experiments that tested the possibility of an optical device that would allow a single 2D image to be seen as 3D with only one eye were cited and ridiculed as obviously fated to fail. The research of Stephen Jay Gould and me reveals that Duchamp himself was the first person, even before any scientist succeeded, to develop a system and a device (1923) that produced a 3D stereo fusion in the mind with a single 2D image seen by a single eye. Try the Interactive Presentation in illustration 55. Duchamp’s Rotorelief Discs (1935) surprisingly produce an even greater 3D effect when seen by one eye than by two. Click on any disc to select. Control speed by clicking on bar and dragging bar up and down (with depressed clicks) between fast and slow. Duchamp first made his Rotorelief Discs for phonographic record playing speeds, 78 or 33 3/1.

Click here for Interactive Presentation

Illustration 55.

Duchamp's Rotorelief Discs (1935) (machine modeled after 1964 version created by Vittorio Marchi and Robert Slawinski)

Duchamp created many other experiments using stereoscopic pairs. He included two examples in his Boîte-en-Valise miniature museum (Figs. 56A and 56B). These two stereoimages were made by Duchamp in 1918 and 1920 but not published until 1941. As I discussed at the Harvard symposium Methods of Understanding in Art and Science: The Case of Duchamp and Poincaré, Duchamp’s previously unrecognized stereo experiments, as detected by my studies, include one work, the Wanted Poster (1921), that was (since 1941) viewed as a "readymade" object that Duchamp only altered by personalizing the object with photos and text referring to himself. (See illustration 57A and 57B, the Wanted Poster print, first seen by spectators in the Boite-en-Valise (1941), as the original Wanted Poster (1921) work is "lost."

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Illustration 56A	Illustration 56B
Stereo pair (1920) included as print in 1941 Duchap's Boite-en-valise	Stereo pair made in 1918, also included as print in Duchamp's Boite-en-valise, 1941

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Illustration 57A

Duchamp Wanted Poster (1921) printed in 1941 Boite-en-valise

Illustration 57B

Wanted Poster detail, Duchamp's underground stereo experiment can be seen when this detail is placed into a stereo viewer.

Illustration 57C

The Hyper-Cube represented stereoscopically (Benham)

I noted that the red and blue colored boxes and the two portrait photos (of what may be, even in Duchamp’s original photo source used to recreate his work, a retouched composite of Duchamp and someone else -- a criminal perhaps?) are asymmetrically placed and shaped. In other words, the left Duchamp image is higher than the right image, and the lines of the boxes themselves are strangely designed to be uneven. I noticed one day that both the size and the separation between the 2 boxes seemed similar to a common stereo card. I scanned, printed and then cut off the top of the Wanted Poster at a duplicate size in the Boîte-en-Valise folder (56B) and then placed it in to a stereo viewer. When seen in stereo, the two asymmetrically shaped boxes in the Wanted Poster unexpectedly fuse into one symmetrical box. I now could see a single Wanted Poster image of Duchamp’s head that allowed me to see the front and side of his head all at once -- a single viewpoint that would not be possible for 3D eyes in 3D space. This visual result, I believe, expresses Duchamp’s verbally stated interest in extending a continuum to include transformations among 2, 3 and 4 dimensions. (See illustration 58, showing a traditional stereo card that reflects the popular and technical interest in 4D space and objects in the early 20^th century. This 2D stereopair, as seen here, depicts a 4D figure in two different perspective views. When seen in a stereo viewer, the dimension will then be increased into a single 3D view of this same 4D object, also shown in 2D.

Using what Duchamp called a 4D eye [eye⁴], only 4D space allows us to see 3D objects 360° in the round in one instant; whereas, in 3D space a 3D eye (eye³) must move in time around a 3D object to collect 2D observations (thus reducing an object from 3D to a series if 2D shapshots). Only after these cuts are fused together, can we recreate in our minds a sense or approximation of any actual 3D object in the round (thus increasing the dimension when transforming a series of 2D cuts into a 3D object). Duchamp’s note, illustration 59, uses the fist’s ability to hold and experience the form of a 3D object, all at once, as analogous to what would occur in 4D vision. Illustration 60, a portrait photograph of Duchamp, also mimics what could only be simultaneously seen in 4D space. This portrait is also similar to the experience evoked when seeing the two Wanted Poster heads and lined boxes in a stereo viewer. Significantly, Duchamp selected this very photo (60) as the cover for his own catalogue raisonné design in 1958.

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Illustration 59	Illustration 60
English translation of the Note: "The View3 of a plane P. corresponds in the hyperspace to a grasp4 of which one can get an idea by gripping a penknife in the hand, for example" Marcel Duchamp, mathematical note from In the Infinitive [a.k.a. the White Box], written in 1910s published in 1967	Cover design done by Duchamp for his Catalogue Raisonné (1953) includes this portrait photograph that illustrates the similar "4D" effect (seeing front and side view at once) found when placing the Wanted Poster (57B) into a stereo viewer.

With Duchamp’s underground experiment in the Wanted Poster, we may have increased our information with a 4D experience, but the data provided by Duchamp’s head are still incomplete. Panoramic painting and photography represented yet another 19^th and 20^th century experiment and approach to packing even more 3D information into 2D images. Illustration 61 shows a "panoramic" view of a woman’s head. The photo uncomfortably reads as if a 360° view of the woman’s head were rolled out, like cookie dough, onto a 2D plane. Such a panoramic photograph, by allowing us to see a 3D object (such as a head) on all sides at once, certainly yields more 3D information in

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Illustration 61

A panoramic photo of a woman's head captures a whole 3D object in 2D space, allowing it to be seen all at once.

2D than stereo experiments can provide, and also offers a perspective of something not possible in our normal 3D vision in 3D space. Yet, because the distortions produced by the panoramic technique, as seen in illustration 60, are so viscerally repulsive (probably because they evoke a sense of seeing flayed skin -- the only way to make such a flat geometric view literally possible), and so foreign to our actual experience, we are unable to disregard the panoramic distortions, whereas we routinely, and without effort, ignore or seamlessly filter out perspective distortions. Therefore, we can conclude that the panorama presents an interesting representational effect that would not challenge perspective photography as a dominant or popular convention.

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Illustration 62

Pablo Picasso, Violin and Grapes, spring and autumn, 1912

Cubism, in addition to its status as the beginning of one of the two biggest revolutionary departures in art (the other being the advent of perspective itself in the Renaissance), emerged, for Duchamp and others, as yet another experiment and alternative to static perspective representation in the larger cultural context of the early 20^th century (see illustration 61, a cubist painting by Picasso).

* Part IV through VI will be published in Tout-Fait, Perpetual 2005.

Illustrations 2A-2F, 12A-D, 13B, 14A, 15A, 16A, 17, 18A-B, 19A, 20A-C, 21A, 22A-B, 23A-E, 32A, 34A-H, 41A-D, 46B, 49A-D ©2005 Succession Marcel Duchamp, ARS, N.Y./ADAGP, Paris. All rights reserved.