But what was Duchamp testing? He says that he made the 3 Standard Stoppages to obtain a new measuring system and to "can chance." If we use one of the mathematical meanings of chance, and not the vernacular definition of randomness, Duchamp's repeated experiments in dropping threads imitates scientific method and an approach to statistical sampling. As Poincaré noted, in an empirical world replete with both irregularity and pattern, all facts or events are unique and never exactly repeated. But as a savings grace for science, and despite all these irregularities, hidden patterns can lead to a "right" choice of facts that will reveal some sort of unity or law. Discerning the similarity across numerous facts, allows us to generalize about the series itself and nature as a whole.

In this way, creativity is a mysterious process where the right fact can nudge us to a new perspective, and lead us to see an entire system in a new way. Poincaré claims that this right "choice" of a fact -- a process that can transform a group of facts from a pile of stones to a house -- is the essence of creativity and discovery. Human beings, with their limited minds and senses, can never hold all perspectives at once. Yet all possibilities still exist. Since we can only hold one perspective at a time, chosen from the mixture in our unconscious, one must, in order to be optimally creative, always try to move perspectives and continually to choose the best combinations.

Poincaré tells us that we do this unconsciously by our intuitive "sieves," thereby making conscious verification by measure and experiment so important! If we "read out" perspectives from our unconscious and then merely accept them, we will likely be placed in the position of false perception that Apolinère Enameled imposed. Without critical thinking, and without verification by our conscious minds, what we see may be wrong. Even with verification by measure and experiment, any one perspective will still be incomplete, and will change (as indicated by the history of discovery). But having the best possible perspective at any one time is different from being wrong for lack of logical verification. If better choices could have been made with critical thinking, -- then we clearly have not attained our best choice of perspective.

By dropping a meter thread three times, Duchamp creates a sample from a larger infinite series of events. Duchamp doesn't have to drop threads one hundred times. From logic and experience, we can induce, from three events, what will approximately happen for the next 100 or 1,000 tries. Even though no two facts or events are exactly alike, with the right choice of facts, nature will reveal "her" unity. Duchamp regarded three as a minimal number of events from a larger continuum needed for making a generalization. Duchamp stated that he believed "three or three million it's ... the same thing as three" (Cabanne, p 47). He was also well aware of "generalizations" and spoke of how the mind uses them in constructing reality (Gold, appendix 24).

Duchamp's use of the Milky Way, dust in fluid, and gaseous molecules as three related probabilistic systems borrowed by Poincaré's own example to illustrate the ultimate power of generalization in revealing nature. If one makes the right choice of a fact (as a specific example, he cited the probabilistic behavior of microcosmic gaseous molecules and the Kinetic Theory of Gases), then when we apply this fact to other scales (the macrocosmic Milky Way or the human scale of dust in fluid) we will find a similar, or what Poincaré called a "qualitative," measure or a match in appearance (Diacu, Holmes, p 27-48). We will then have an example of the most powerful kind of generalization -- revealing a pattern in nature existing at all scales. Poincaré tells us that, throughout the history of changing laws, the "frames" through which we view nature are stretched into broader generalizations that give us a better perspective (through new laws) of nature's entirety. Yet nature remains the same.