5.       Conclusion

In the course of the artistic events of the first half of the twentieth century it is possible to recognize a pathway, not yet sufficiently explored: that of the gradual emergence of a new sensibility, a new perspective in the observation of the world, a new paradigm, which scientifically has an accomplished expression in the so-called complexity science, definitively established in the 1970s.

Following Hedrich's The Sciences of Complexity: A Kuhnian Revolution in Sciences?, by the term complexity science I refer:

1)       To Dynamic Systems Theory (DST) which describes and characterizes the behavior of coupled non-linear differential equations, and

2)       To the applicative contexts that admit such mathematical models as a proper description.

Hedrich also classifies these applicative contexts according to their distance from the central conceptual kernel of the DST:

a)       In the first shell, immediately contiguous to the central kernel of the DST, we find those sectors of empirical sciences which directly deal, in different contexts, with the phenomena of dynamic instability, deterministic chaos, and sensitive dependence on the initial conditions;

b)       In the next shell we find the scientific theories which deal with abstract models of complex systems, such as cellular automata, neural networks and fractal geometry;

c)       In the last shell we finally find the theories which from different points of view deal with self-organization, such as the non-linear thermodynamic by Prigogine, the synergetic by Haken, the molecular self-organization by Eigen, and the autopoiesis by Maturana and Varela.

In previous papers (Giunti, 2001a, 2001b) I pointed out the sense of this research, focusing my attention on some phenomenal manifestations, peculiar to the behavior of complex systems. Several artists (with more or less awareness) shared a particular attention for these manifestations and tend to express them in their works; these manifestations deal with concepts such as circular feedback as basic causal mechanisms, recursion, self-reference, self-organization, fractals, intricate topologies, dynamic instability, sensitive dependence on initial conditions, deterministic chaos.

These aspects are so deeply related to each other that when they appear (even only in embryonic form), the presence of one almost automatically implies the presence of many or all of the others. The shared sensibility for these phenomenal manifestations of complex systems makes it possible to establish deep and unexpected ties between artists, which otherwise would seem to reside in totally different planets, like Duchamp, Klee or Escher.

As for Duchamp, my previous considerations are confined to the b) and c) shells of the above mentioned classification. This doesn't mean the impossibility to refer Duchamp's thought and work to the scientific ideas contained in the a) shell. The exact contrary is true: chiefly the ideas of dynamical instability and sensitive dependence on initial conditions constitute the most evident aspect and, in fact, the most widely explored by the scholars (consider for instance the Harvard Symposium: The Case of Duchamp and Poincaré, 1999). In any case, in my opinion a more detailed study on the concept of chaos in Duchamp would be necessary, because it is sometimes confused by the commentators with the idea of randomness, obviously present in Duchamp, which is a different concept, even if related to the chaos one.

In the previous section I related the Large Glass (and more generally the whole work of Duchamp) to the concept of autopoiesis. One has to consider such a relation for its correct meaning, i.e. it is just a simple association and absolutely not an identity. I don't state that Duchamp's work is an autopoietic machine. However, it exhibits some features which can be well-described by means of some aspects of the theory of Maturana and Varela. Particularly, I want to underline that this comparison isn't a new hermeneutic, substitutive of some or all of the previous ones. Contrarily, I would like to argue that this reading perspective furnishes some explicative element to understand the inexhaustible richness of the possible hermeneutics, and their reciprocal compatibility, both for the past and present ones and for the ones (I am sure) that will be added in the future.

Finally, as for my opinion, the synthesis of my viewpoint on the discussed subject is in the title of this paper:

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