Duchamp acknowledged in his
notes that he was aware of "Poincaré cuts"
(Sanouillet & Peterson, 1973, p. 94).19
A Poincaré cut is a method invented by Poincaré, similar to his use of
two-dimensional shadows, to convey an invisible three-dimensional sphere. A 3-D
Poincaré cut allows us to visually represent a moment or "snapshot" of a
fourth-dimensional non-linear system that could not be physically seen from our limited, human
perspective (Diacu & Holmes, 1996, pp. 34-41)
(see Illustrations 7A and
7B). A Poincaré cut is a window
into a system of chance and complexity, which captures emergent patterns of randomly-generated
order. A simple set of conditions may initiate the original process (as in roulette,
we begin with a spin of a wheel, gravity, a ball bouncing against metal pins, etc.), but
soon the resulting dynamic of actions and effects transcends any obvious connection to the
original simplicity of the initial conditions. Similarly, Duchamp, from
1911-1915, wrote an initial set of notes (his initial conditions) from which
he generated both a system and all his major work for the rest of his life. For example,
"a clock in profile," first written about before 1915, does not return as an object
until the 1960s. The cryptic note, "Given 1. the waterfall, 2. the illuminating
gas," is written before 1915, yet we do not learn of the existence of this work until
his death in 1968 (Duchamp, 1960, pp. 3, 4, 94).
By putting out a "net" and mapping return movements within large and small probabilistic systems across time and space (whether these be Duchamp's creative movements, the movements of the Milky Way or the fluctuations of gaseous molecules) we, in effect, have "tamed chance," because such maps reveal order within seemingly overwhelming randomness from our 3-D human perspective. Using a probabilistic mechanism for his creativity, initial conditions in Duchamp's mock system operate just as in roulette, or the weather. Given his original notes (his initial conditions), we can make fairly good predictions. However, neither we nor Duchamp himself could have said exactly what or when. Perhaps this was the joke when Duchamp (1960, p. 97) said he would plan "a kind of rendezvous" with his readymades.20
People familiar with Duchamp's writing and works know that he was extremely interested in chance (he even wrote a note about "canned chance") (Duchamp, 1960, p. 87) Chance, in science, need not be synonymous with the vernacular definition of randomness. During Poincaré's period-that is, when Duchamp recorded his initial notes in 1911-1915-one common meaning of chance referred to our inability to exactly predict an outcome due to our limited perspective and our incomplete knowledge of nature. Probabilistic systems are called "indeterminate determinism" because if we knew everything we could determine everything; but such knowledge is impossible since the smallest initial variations (which can never be completely known or measured) can create large-scale effects.
Although constraints of length debar me from going into great detail in this essay, I will present evidence indicating that Duchamp's Large Glass is a "Poincaré cut" of Poincaré's "unstable equilibrium" of universal creativity. Moreover, I will demonstrate that Duchamp's "readymades" are three-dimensional shadows from his creativity machine, intended to lead us toward a fourth-dimensional realization of the significance and meaning of his Large Glass.
Before one can discover anything new, one has to suspend present beliefs in order to surpass them. In Poincaré's mechanism of discovery (and in his striking and admittedly curious metaphor), this leap takes the form of a disaggregation and remixing of gaseous molecules. Duchamp proclaimed that he "doubted everything" (Tompkins, 1965, p. 17) and did not "believe in fixed positions" (Cabanne, 1967, p. 89). How can we believe in a single dominant perspective if, as we have learned from Apolinère Enameled, any one perspective is actually a combination of perspectives chosen by the unconscious, susceptible to error and capable of improvement, as is amply demonstrated by the changing history of ideas. If doubt, as Duchamp believed, is fundamental to the beginning of the discovery process, then perhaps the readymades were the seeds of doubt he sowed. If we find that the rest of the readymades are in the "wrong perspective" and have fooled us, the seeds of doubt should bear fruit in a full-scale inquiry into The Large Glass machine (identified by Duchamp as the source of his readymades.)
Art & Academe (ISSN: 1020-7812), Vol. 10, No. 1 (Fall 1997): 26-62.
Copyright © 1997 Visual Arts Press Ltd.
