Duchamp scholar William Camfield (1991) discusses Duchamp's determination to maintain a constant relation between his Large Glass and three of his readymades: 50 cc's Paris Air (at the top of the stack), the urinal (at the bottom), and the traveler's folding item (typewriter cover) in between, and located on the line separating the Bride and the Bachelors (called the Bride's clothes -- see Illustrations 1A and 1B).⁷ Duchamp kept this consistent relation in his Bôite (the three readymade miniatures are similarly stacked, and placed to the left of the Large Glass), and in his exhibitions in Pasadena and Stockholm at full scale. When Duchamp asked why he wanted this relation between these readymades and the Glass, he said: "because they were 'readymade talk' about what was going on in the Large Glass" (Camfield, p. 165). Certainly we know now that the readymades spoke loudly about their deceptive perspectives which, if seen in the correctly chosen perspective of Poincaré's mechanism, leads us to understand what the Large Glass really is -- a 3-D slice of a 4-D creativity machine.

When specifically asked why the typewriter cover occupied the level of the line or "Bride's clothes" (in between the Bachelors and Bride), Duchamp stated, "Oh, it was removed from its machine" (1991, p. 166). The double meaning of machine (typewriter and Large Glass) is typical of Duchamp's humor. However, with Poincaré's theory in mind, we can reach several conclusions: First, he three readymades are probably analogous to Poincaré's three scales of universal probabilistic systems that Duchamp also uses in his Large Glass; gaseous molecules (50 cc's Paris Air, at microcosmic scale), dust in fluid (the typewriter cover at human scale) and the Milky Way (the Fountain urinal as part of the universal water system at macrocosmic scale).⁸ Duchamp's use of the Bride and Bachelor metaphor for universal creativity relates directly to the metaphor used by Poincaré to explain how and why laws change while nature stays the same. He states that laws act as "frames" and are the only means to perceive nature. Poincaré literally said that we periodically change the "garb" or "vestments" in which we "clothe nature" with broader perspectives or generalizations. But "she" (nature) always remains the same (Poincaré, 1902, p 161-162, p 145, 1904, p 95, 139). Poincaré gives the various scales of probabilistic systems including "the pendulum" as his example of this "parallelism" (p 161-162).⁹

Poincaré's metaphor, in relation to Duchamp's, reveals that: the Bride is nature, a probabilistic system at all scales; the bachelors, with their sieves, are discoverers. Most Bachelors, as molds, are vessels in which only old ideas can be cast and cut up to be recycled. They live as a "cemetery" of liveries and uniforms (nature's old clothes), dead fixed beliefs acting as old uniforms of convention that we unthinkingly wear (and act as old molds where old ideas are cast). The sieves in contrast, can periodically "strip the Bride" of old laws in which we dress her by the chance choice of a better perspective within this creative continuum ("every fifty years").¹⁰

The typewriter cover is literally made of rubber. Laws that are stretched until they change, but never completely break, every fifty years act like rubber. If nature is essentially made of raw facts that we can never directly access except through laws, and if the "Underwood" typewriter cover represents the rubber-like flexibility and persistence of law, then perhaps the Underwood cover is, by analogy, under nature's facts (Under Wood) and over the invisible creativity machine. [According to Schwarz (1969, p. 146), Duchamp said that the Large Glass "is like the hood of an automobile that covers an invisible motor."] Taking Duchamp's dimensional analogy, the raw facts of nature, in totality, would be 4-D (as they are vast and unaccessible to the senses). Laws are 3-D and visible at human scale (as they represent the means to see nature), and the creativity mechanism (the "sieves" for both Poincaré and Duchamp) that chooses the law is also 4-D and unseen. Note too that typewriters are also a common device for creating ciphers. In fact, a famous and supposedly "unbreakable" typewriter "code" was popular at the beginning of the 20th century. (The code was broken, of course.¹¹

From Poincaré's descriptions, Duchamp would have known that a probabilistic system operates like a cipher. Simple initial conditions (a message) in a probabilistic machine are generated, and through time become very complex and seem jumbled. But a relation (in a cipher, or probabilistic initial conditions, or Duchamp's notes) is maintained and can be deciphered with the right technique. See Illustration 2B. Duchamp's notes orbit from his initial conditions. A Poincaré cut allows us to decipher the relations between the readymade orbits and the initial conditions of Duchamp's mock probabilistic system. With this relation of readymades and initial conditions (notes) in mind, we can now see the role of the Large Glass as a Poincaré cut. In telling us that the readymades came out of his Large Glass machine, Duchamp relates the readymades to his Large Glass, just as Poincaré relates readymades to the overall creative process (the readymades begin in the unconscious mind as "gaseous molecules" chosen by "sieves." After dropping into the conscious as "sudden illuminations" they must be "verified by measure and experience"). The readymade, in this sense, like the projections of 2-D shadows from a sphere, lead us to mentally see that the Large Glass is the universal 4-D creativity machine we are meant to discover. No wonder Duchamp said his readymades "look trivial, but they're not ... they represent a much higher degree of intellectuality" (as cited in Roberts, 1968, p. 62).