In the 3 Standard Stoppages, Duchamp takes the three threads and uses Poincaré's scheme to verify probabilistic systems of chance. Duchamp writes,
    The Idea of the Fabrication

    -- if a straight horizontal thread one meter long falls from a height of one meter onto a horizontal plane distorting itself as it pleases and creates a new shape of the measure of length

    -- 3 patterns obtained in more or less the similar conditions: considered in their relation to one another they are an approximate reconstitution of the measure of length.

    -- the 3 standard stoppages are the meter diminished (Bonk, 1989, p 218). (Emphasis original).

Duchamp emphasizes that it is the relation among the three thread events, in approximate reconstitution of his measure system, that "diminishes" the authority of the meter. Duchamp tells us that his new measurement scheme is, like Poincaré's, a qualitative system taking the approximate relation among events as the measure, instead of the quantitative method of the meter. Duchamp states:

    I'd say the Three Stoppages of 1913 is my most important work. That was really when I tapped the mainstream of my future. In itself it was not an important work of art, but for me it opened the way -- the way to escape from those traditional methods of expression long associated with art ... For me the Three Stoppages was a first gesture liberating me from the past (Moure, 1984, p 232).
Elsewhere, Duchamp elaborates on this:
    This experiment was made in 1913 to imprison and preserve forms obtained through chance, through my chance, at the same time, the unit of length: one meter was changed from a straight line to a curved line without actually losing its identity (as) the meter, and yet casting a pataphysical doubt on the concept of a straight line as being the shortest route from one point to another (d'Harnoncourt, McShine, 1973A, pp 273-274).
Duchamp's idea seems similar to that of Poincaré (1902/1952) demonstrating that the curved space of non-Euclidean geometry, and the different convention of straight lines in Euclidean geometry, yield two worlds that are connected and interchangeable in the mind, given familiarity with the rules of both systems and the right geometric method for moving from one system to the other (Poincaré, 1902, p 43).6 Duchamp states that he captured and froze the three thread forms -- and that, despite the general laws of chance, and the chance in his individual efforts, similarity and continuity remained evident across the forms. The line of the meter (Euclidean) smoothly meets, in continuity, the curves of another new geometry (non-Euclidean). The new geometry teaches us, as Duchamp stated, that we should doubt any single system, for even though the smooth curves of the threads meet the lines in continuity, the differences are important. Duchamp gives the key case that distinguishes the new geometries (with non-Euclidean and Poincaré's new qualitative methods as examples) from the old, Euclidean, metric quantitative system. Duchamp states that even though the meter doesn't completely "lose its identity" (meaning that, from the perspective of the new, we can still see the old), our "doubt" must lead us to give up our belief in the absoluteness of the old perspective of the meter. The new perspective of non-Euclidean geometry in Duchamp's experiment, demonstrates (as the discovery of non-Euclidean geometry actually did) that "the shortest route from one point to another" in curved space is not a line.

Poincaré had argued that, to do empirical science, we must do experiments, and from these experiments create new measuring systems. Duchamp, in the 3 Standard Stoppages, performs his experiments and derives a result that makes a qualitative measurement system sensitive to relations among events of chance despite coexisting differences. Duchamp's measuring sticks, based upon the lines and curves created by the chance dropping of threads, becomes his new qualitative system (measuring sticks that he used later in his Large Glass and
Tu m' painting.) His wooden qualitative meter sticks "measure" by indicating similarities or unities across scales, despite chance and complex variations or irregularities.

This process of mending similarities among events (individual facts and perspectives) is analogous to the invisible mending (as in the French word stoppage) of perspectives in the unconscious. One might say that an invisible mending among events, despite their differences, represents what we must do to make any generalization. The important thing is to choose an emerging similarity that floats above apparent differences. The 3 Standard Stoppages is a tool box for making generalizations. We have both a readymade (from Duchamp's unconscious mind) that he used to test his Poincaré discovery, and his actual measuring system within the creative process for detecting new generalizations emerging from facts. Since laws and generalizations come and go, Duchamp has poetically given us the tools that he or anyone needs for making discoveries -- experiments (three trials resulting in three facts that allow us to generalize), and new meter sticks (to measure qualitative similarity needed for making generalizations).

Part II of Rhonda Roland Shearer's was originally published in
Art & Academe (ISSN: 1040-7812), Vol. 10, No. 2 (Fall 1998): 76-95.
Copyright © 1997 Visual Arts Press Ltd.
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