Rhonda Roland Shearer / Marcel Duchamp's Impossible Bed...

NOTES Part I
1. Martin Garner (personal communication, Fall, 1997) pointed out to me that Bruno Ernst (1969) wrote about an eighteenth century artist, Giovanni Piranesi, who predated Duchamp and the Penroses with his intuitive application of conflicting depth clues. Ernst, however, states that the first "conscious construction" of an "impossible object" was in 1934 by Oscar Reutersvärd who did not realize the scientific importance of what he had done with his systematic working out of various impossible cubes, configurations and "forks" until he read the Penroses' 1958 paper. Ernst quotes Roger Penrose's statement that his "own interest in impossible objects stems from the year 1954" (p. 71), when he discoverd Escher. But, as Ernst (1992) correctly points out, Escher had not done anything we "would call an impossible object" until after 1958 (pp. 71, 72)! Penrose goes on to say that he did not learn of Oscar Reutersvärd until 1984 (p. 72).
Evidence indicates that Duchamp's "Impossible Bed" was not an intuitive appreciation of an "impossible object" but a specific exploration of one case within his general category of perceptual illusions (for example, the convex/concave illusion in both Duchamp's "fig leaf" sculpture and magazine cover; and his cheese cover for the "first Papers of Surrealism") (Schwarz, 1997). Ernst (1992, pp.28-29) discusses the convex/concave illusion. Moreover, I recently discovered that Duchamp drew both an "impossible object" and a convex/concave illusion in his 1925 chess poster with its cascading and impossible and ambiguous cubes (Schwarz, 1997). With both his impossible cubes and bed, Duchamp beats out Oscar Reutersvärd as the first artist to make a series of consciously constructed optical illusion/impossible figures in a conscious series (see Ernst, 1992, pp. 69, 70).

2. Ernst (1992, p. 82) incorrectly claims that the bed of Apolinère Enameled was only "semi-consciously or unconsciously" known by Duchamp as an impossible object. Also wrong is Ernst's claim that "Duchamp never pursued this line any further." As I shall show in a forthcoming article with Stephen Jay Gould, Duchamp consciously used or drew several other impossible figures in other works; moreover, an analysis of Duchamp's text in Apolinère Enameled shows that the bed's status as impossible is specifically and consciously indicated (see Shearer, 1998).

3. See Maharaj (1996, p. 68) who mentions that Richard Hamilton visited Roland Penrose's library in 1948 and saw Duchamp's Green Box for "the first time." Therefore, we know that Roland Penrose owned Duchamp's work at least since 1948.

4. In a conversation with Richard Hamilton, he told me that he recalls Duchamp visiting Lionel Penrose's house one time. Since Duchamp was an old friend of Roland's, who had known Roland before he had met Richard Hamilton, Hamilton could not say how many times Duchamp had visited Roland Penrose's house. (R. Hamilton, personal communication, Fall, 1997).

5. I had a personal conversation with Roger Penrose in the Fall of 1997 and he was the one who suggested that I call Tony Penrose.

6. I recently discovered that Duchamp had made other impossible figures; like his 1925 chess poster, composed of impossible cubes, which predated Reutervärd cubes done 9 years later in 1934.

7. In 1935, Duchamp was the third person to develop such optical discs and had vastly improved upon the the previous two scientists' designs (Benussi in 1921 and C.L. Musatti in 1925) (see fineman, 1981).

8. Roland Penrose (1973) wrote about Duchamp's optical discs and machines.

9. I am grateful to Francis Naumann for providing this image.

10. Hulton's book has no page numbers. It is organized by dates.

11. Duchamp's use of the fourth dimension as an unconscious mental process is metaphorical. Massive amounts of information and patterns, beyond what the physical eyes or conscious mind can see or know, are clearly utilized in professional chess: 64 squares and 32 chess pieces have vast potential combinations-169, 518, 829, 100, 544, quintillion in the first 10 moves alone-a number of choices beyond conscious 3-D thought and constituting what Duchamp defined as 4-D.

12. For all references to Duchamp's Notes in this article, see Sanouillet and Peterson (1973).

13. Davis explains that shadows from the spheres will be larger circle projections on the plane if nearer the top of the sphere, smaller if near the bottom.

14. When asked if he made shadows of his readymades on a wall [and photographed and included them in his Tu'm (1918) painting] "for any particular reason?" Duchamp answered that he wanted to show his readymades in a different perspective of "light projection." This Poincaré technique is precisely the way to see a new, higher dimensional perspective with shadows from light projections (see Hulton, 1993-June 21, 1967)!

15. For example, one can physically see an individual 3-D chess move, but a complex plan and a combination of moves is held 4th dimensionally in the head, according to Duchamp.

16. This computer analysis rendering was done for me by James Nazz.

17. As a "universalistic," Poincaré would want his theory of creativity to be related to all of nature. But Poincaré's specific metaphor of "gaseous like molecules" (his words) "colliding" (his words) in the unconscious, and then "sifted by seives" (his words) also in the unconscious mind sounds whacky and irrational when coming from a scientist! That this "irrational" description and theory was popularized by the foremost scientist in France (where even "shopgirls" were said to be seen reading Poincaré's popular works in parks) would have been an irony very appealing to Duchamp.

18. Poincaré frequently used the word "tout fait" which was translated in almost every instance as "readymade" in English.

19. In a personal interview (Fall, 1997) Cleve Gray (the translator of Duchamp's A l'Infinitif and these "Poincaré cut notes" who also worked with Duchamp) stated that "Duchamp frequently said that Poincaré was at the bottom of what he was doing." Duchamp mentions Poincaré cuts several times in his White Box notes (also called A l'Infinitif) (Duchamp, 1966). Also note that the English translation "Dedekind cut (Poincaré)" is incorrect. Duchamp's original notes in French read "Poincaré cut."

20. Duchamp also explains in this note that "the serial characteristic of the readymade" is like an event ("speech") "delivered" or returned on various "occasions" at various "hours." Duchamp, by analogy, illustrates Poincaré's notion of the co-existence of stability and randomness or "indeterminate determination" in his probabilistic system. Initial conditions effect events, so that we know they will occur but we cannot say exactly where ("occasions") or when.

21. Duchamp used the words "tout fait, en serie" before 1915, and then later refers to "Readymades" that have "serial characteristics" after 1915. Duchamp, in 1916, translated "tout fait" as "Readymade" (see Shearer, 1997a, 1997b).

22. Duchamp signed the urinal "R. Mutt, 1917."

23. Hence this explains Duchamp's contradictory statement that "Art isn't made in factories" (Miller, 1936) -an amusing statement since the "readymades," we were led to believe, were mass-produced objects from factories! As we shall soon see, readymades were indeed altered and decidedly not unchanged, store-bought objects.

24. I am presently doing a computer analysis to calculate this perspective. Yale provided the measurements for the Rotary Glass Plates wheel that I mention.

25. If Duchamp had put the coat rack on the wall in a "correct" orientation, we would have been much more likely to see that the hooks were wrong. Thus, by putting it on the floor, Duchamp increases the odds that it will take longer to discover his perceptual deception. Duchamp likely changed the perspectives of the Hat Rack and coat rack (to hang from the ceiling or nailed on the floor) to fool our eyes into not noticing (and thus "hiding them in plain sight") the incorrect or changed perspectives. "Hidden in plain sight" is a term from cryptology. Duchamp's main collector and friend Walter Arensberg was a cryptology fanatic. Duchamp shared mental and word games of all sorts with Arensberg.

26. Stephen Jay Gould and I are writing a more detailed essay reporting our research on the language and geometry of Apolinére Enameled. We have requested a non-invasive analysis to see if the paint is washable from the Philadelphia Museum of Art. We are waiting for our request and promised appointment for a UVA analysis and x-rays to be honored by the museum.

27. Duchamp supposedly lost the "original" Bicycle Wheel done in Paris and, in 1915, he made the first reproduction in New York, which also was lost!

28. In the Schwarz interview (1959-1968) and Cabanne interview (1967), Duchamp says red and green. In his readymade statement in 1961, Duchamp says red and yellow.