Duchamp, moreover, uses Poincaré's exact, technical term "unstable equilibrium" to describe his machine (Matisse, 1980, note 15; Poincaré, 1908, pp. 67-68). The vapor cloud emitted from Pendu's "swinging to and fro" (Duchamp, 1960, p. 16), he calls the "Milky Way" which, like the pendulum, is an example of a probabilistic system (p. 26). The "draft pistons," the three window-like cuts in the Milky Way cloud, Duchamp calls the "nets" or "triple cipher" (p. 27). Duchamp claims that he made the draft pistons by using netted fabric with dots and placing the fabric in front of three literal (and open) windows, with air currents blowing through. The three resulting "snapshots" (his words) captured subtle differences in the movements. Chaos scientists similarly refer to "Poincaré cuts" as "snapshots" of probabilistic systems of chance (Peterson, 1993, pp. 160-165). For both Duchamp and Poincaré, it is the initial conditions, and the forces of air resistance and gravity, which create irregular and irrational movement in the pendulum (Peterson, pp. 160-165). For his draft pistons (Poincaré cuts) within the Milky Way (a large-scale probabilistic system), Duchamp mockingly borrows from his Pendu (pendulum) the effects of "air currents" (Duchamp, 1960, p. 18). These currents create irregularities of motion and literally represent all scales of probabilistic systems in nature (vapor as microcosmic, pendulum as intermediary human scale, and the Milky Way as macrocosmic-all scales are impacted by the small effects of their initial conditions).

Look at Duchamp's three Poincaré cuts in his Milky Way system (see again the cloud shape in Illustration 4). They closely resemble the Poincaré cut shown in Illustration 7A (see also Illustration 8 showing one of Duchamp's draft piston photographs). Poincaré frequently used the very same examples to illustrate nature's three major scales: the Milky Way, dust in fluid, and gaseous molecules-all of which are probabilistic systems whose Poincaré cuts would look alike (see Illustration 7A).

However random the movement in a probabilistic system, the Poincaré cut proves that something remains constant across vast scales. Poincaré states that this intangible "something" allows us to recognize that, despite any overt changes that we perceive in nature, it is only our concept of nature's laws that really changes. Nature itself always remains essentially the same. For both Poincaré and Duchamp, the creativity game is played by changing our perspectives in two ways. We may manufacture and choose our perspectives in our unconscious but, at the same time, we must explicitly recognize and challenge our beliefs in order to be able to change perspectives and win the game by making discoveries and innovations. Since "logic proves" whereas "intuition discovers," we need both conscious logic and unconscious intuition to be creative (Poincaré, 1908. p. 129).

Duchamp's Large Glass includes all four of Poincaré's examples of probabilistic systems-the top half of the Bride has the pendulum, gaseous molecules (vapor) and the Milky Way; and the bottom half has dust in fluid and gaseous molecules. Duchamp made the sieves in the Large Glass (see Illustration 9) function just as Poincaré described in his theory of the unconscious creative process. In the Large Glass, the "sieves" are the only visibly active part of the machine. Duchamp used actual dust in lacquer fluid to represent gaseous molecules ("illuminating gas") in his sieves, employing the same analogy for "invariance" within nature (despite nature's overt changes of scale) that Poincaré characteristically uses. We note that the dust increases in density from the first to the last sieve. The last sieve occupies that critical point of final unconscious choice of a new perspective which will be launched, as if "readymade," into the conscious mind of the discoverer.