Why the Hatrack is and/or is not Readymade:
with Interactive Software, Animations,
and Videos for Readers to Explore

by Rhonda Roland Shearer with Gregory Alvarez, Robert Slawinski, Vittorio Marchi and text box by Stephen Jay Gould

<PART III>

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.

click each image to enlarge
Illustration 46A.	Illustration 46B.	Illustration 46C.
Stieglitz version of Duchamp's Fountain urinal	Etching,Marcel Duchamp, An Original Revolutionary Faucet: Mirrorical Return, 1964 © 2000 Succession Marcel Duchamp, ARS, N.Y./ADAGP, Paris	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.

click to enlarge

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.

click each image to enlarge
Illustration 49A.	Illustration 49B.	Illustration 49C.	Illustration 49D.
Perspective view, The Bride Stripped Bare by Her Bachelors, Even, 1915-23 © 2000 Succession Marcel Duchamp, ARS, N.Y./ADAGP, Paris	Plan section of Bachelor Apparatus: Facsimiles of Plan and Elevation, 1913/1934 © 2000 Succession Marcel Duchamp, ARS, N.Y./ADAGP, Paris	Elevation section of Bachelor Apparatus: Facsimiles of Plan and Elevation,1913/1934 © 2000 Succession Marcel Duchamp, ARS, N.Y./ADAGP, Paris	Perspective drawing, The Bride Stripped Bare by Her Bachelors, Even, 1913 © 2000 Succession Marcel Duchamp, ARS, N.Y./ADAGP, Paris

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.)

click each image to enlarge
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)

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.

click to enlarge
Illustration 51D. 3D model	Illustration 51E. 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 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.

click to enlarge
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.