To summarize, Duchamp described his Large Glass as four-dimensional; the fourth dimension cannot be physically seen, yet we see the Glass in three-dimensions. The Poincaré cut itself can translate a fourth-dimensional system that we can't see into a lower third-dimensional slice that becomes visible. Look at Illustration 2B. Objects in irregular orbits from Duchamp's initial conditions, although separating from each other in trajectories generated from initial conditions in time and space, eventually return to a 3-D slice in an unstable 4-D equilibrium. This reduction of 4-D mentality (in Duchamp's chosen metaphor) to 3-D visibility represents a new application of Poincaré's technique -- a device that was conventionally used to translate 3-D systems to 2-D cuts or 2-D systems to 1-D cuts. Duchamp stretched Poincaré's dimensional technique to suit his belief that processes beyond the senses -- i.e., those that can only be mentally comprehended -- are 4-D, whereas visible objects and schematics are 3-D and 2-D. In a note, Duchamp defends his right to extend Poincaré's technique to include the fourth-dimension in a dimensional continuum [Duchamp always said that he wanted to "stretch" the laws of physics just "a little" (Tomkins, p. 34)]. Duchamp writes:

Poincaré's explanation about n-dim'l continuums by means of the Poincaré cut of the n-1 continuum is not an error. It is on the contrary confirmed and it is by even basing oneself on this explanation that one can justify the name of the fourth-dimension given to this continuum of virtual images in which the Poincaré cut could only be obtained by means of the 3-dim'l prototype object considered in its geometric infinity (Sanouillet & Peterson, p. 98).

Just as the draft piston dots represent return movement on a 2-D plane from the larger 3-D probabilistic system of the Milky Way cloud in the Large Glass Bride, the Large Glass (appearing as a 3-D whole) is a Poincaré cut of the 4-D universal creativity machine, where Duchamp's specific probabilistic system represents one part in the same continuum. See Illustration 3. The whole of nature stands outside Duchamp's 3-D cut, but the cut is also embodied within, capturing a slice of nature's whole. Leonardo's windows are two-dimensional cuts or "snapshots" of a static, 3-dimensional nature. Duchamp's window begins where Leonardo's ended. Duchamp's window goes beyond 3-D nature and the retinal, allowing us to see into the vastness of nature's creativity through his non-retinal representation of this vastness as a cut (an abstract schematic "snapshot").

Duchamp said that he hated "repetition" and rejected simple cause and effect explanations of causality and Newtonian determinism. Duchamp correctly said that "formulas and theories are based upon repetition" (see DeDuve, 1991, p. 238; Gold, 1958, Appendix 41). This statement had been true until Poincaré's probabilistic system of chance. In an unstable equilibrium, one can discover definite patterns with a Poincaré cut. These "return trajectories" are not exact, but only similar, and by definition, can never be the same. In Poincaré's mechanism, Duchamp found a creative machine that couldn't repeat movements. His ideas and objects would emerge and disappear through time and space, and always stay similar across all scales of nature.¹² Duchamp's ideas were generated from his initial conditions (notes), and then emerged as a variety of words, schematics and objects (never art).