As in Illustration 1, the impossible cube example, one ordinarily does not have to see all the corners and edges to note the logical congruence of a typical cube. We can guess. Just as with the sphere projection of shadows, once we learn the shadow pattern from experience, we don not have to actually see the sphere. Interpolation-or filling in the blanks-is the modus operandi of perception. The key, however, according to Poincaré (1908), lies in not accepting everything "readymade" from the unconscious. For no matter how inspired an unconscious intuition might be, Poincaré insists that we still need conscious logic, or to use Poincaré's exact words, "verification by measure and experiment" (pp. 62-63).

Let us temporarily suspend our attachment to the traditional view that "readymades" mean easily purchased, manufactured objects and consider Poincaré definition of "readymade" as our new hypothesis for what Duchamp meant by the term. We soon see that Poincaré's definition of a "readymade series" leads us to knowledge of the true mechanism of the Large Glass, just as the series of shadows of the circles leads us to the sphere. Poincaré defines "readymade" as one stage of a larger process of creativity. Moreover, he claims that discovery in any field (art or science) operates identically to the larger-scale, machine-like creativity of universal nature itself.

According to Poincaré (1908), all systems-from the largest (Milky Way) to the smallest (gaseous molecules)-operate like "probabilistic systems of chance) (pp. 254-255). In fact, modern chaos theory is based on Poincaré's idea of probabilistic systems. Beyond Newton's simple world view of cause equals effect, in Poincaré's probabilistic world of "unstable equilibriums," small differences in "initial conditions" create indeterminate or chance results (Ruelle, 1991, p. 45). Poincaré offers roulette and the weather as examples of these systems: small muscular differences that occur while spinning the roulette wheel can greatly effect, in a way that we cannot measure, the red or black outcome; similarly, the smallest item falling in one geographical location can effect the weather on the other side of the world six months later. Although we may be able to predict that a cyclone will occur, we cannot determine exactly when or where it will occur (Poincaré, 1908, pp. 68-70).

Individual creativity, Poincaré (1908) tells us, operates similarly. There are three distinct steps, and one intermediate step (p. 56). Conscious Step 1 includes the discoverer's desire, the facts of nature and conventional law as the initial conditions. Unconscious Step 2 entails the disaggregation of these facts of nature, law and desire into gaseous-like molecules which bounce and randomly collide, forming new combinations.¹⁷ The next step falls in between Unconscious Step 2 and Conscious Step 3, where, if you are a genius, unconscious sieves choose the "right combination" while the conscious mind does nothing, and these combinations (gaseous molecules in a new aggregate) drop like "sudden illumination" (converting from gas to ideas) into the conscious mind, as if "readymade" (pp. 62-63).¹⁸

Poincaré explains that ideas seem readymade, in part at least, because they suddenly drop from the unconscious mind into consciousness and appear disconnected from conscious effort. But, Poincaré declares, the idea is not "readymade," nor is it to be trusted and declared a discovery, until Conscious Step 3 is performed-that is, conscious verification by measure and experiment (pp. 62-63). When we adopt Poincaré's definition of "readymades" as part of a larger creative process that requires both unconscious "intuitive choice" and critical thinking, we are led to conclude that Duchamp's three-dimensional "readymades" are intended to represent shadows of his fourth-dimensional creativity machine! The Large Glass is an (observable) three-dimensioanl slice of the (invisible) fourth-dimensional universal system of creativity in nature.