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  • Abstraction, Action Painting, Ready-Mades and All That
  • Jacques Mandelbrojt, Leonardo Honorary Editor

Those who write about art tend nowadays to favor the intelligent and ironic attitude of Marcel Duchamp over abstraction as it was practiced in the 1950s and in particular to the supposedly purely physical action painting.

I wish here to defend an opposite point of view, by analyzing the "epistemological" meaning of abstraction in general, and by showing that action painting, in particular, relates to characteristics of the most subtle human thought, as exemplified in mathematical and scientific research.

If one compares, as I have often done [1], the relationship between abstract and figurative art to that between mathematics and physics, it becomes evident that abstract art is not an art movement among so many others, but that it can truly be considered the true basis of art: Just as mathematics, which is the study of structures that the human mind can invent or discover, underlies physics, which is the application of these structures to reality, abstraction is the exploration of the shapes and structures that an artist can create, and figurative art is the application of these structures to reality. Abstract art then clarifies figurative art, just as mathematics clarifies physics by explicating its underlying structures. Conversely physics can enrich mathematics by showing the necessity of new structures: thus Newton invented calculus, which was necessary for his gravitational theory. In the same manner, wishing to represent a new theme, a new object, can force an artist to enrich his or her abstract vocabulary, as Paul Klee did by looking for the abstract structure best adapted to each object that he wished to represent. All artists know that it is by going back to nature, or to new themes, that they enrich their pictorial vocabulary.

This comparison of abstraction with mathematics does not imply that abstraction should be geometrical: mathematics, prior to its formal, finished expression, such as in the axioms of geometry, is based on the intuition of mathematicians, and this intuition as often as not has a dynamic, kinesthetic and, so to speak, muscular aspect. This stood out clearly in the inquiries led by the mathematician Jacques Hadamard [2], who was among the leading mathematicians of his time. Einstein, in a letter to Hadamard [3], emphasized the pictorial and kinesthetic aspect of his thought and the extreme difficulty he had to then translate it into words and formulas. Recent research in neurology [4,5] confirms that for many mathematicians mathematical thought is of a kinesthetic nature, while for others it occurs in language. In other sciences too, thought often has a kinesthetic aspect: "Each scientist knows that his thought at the deepest level is not verbal, but is done in terms of shapes, forces, interactions" writes biology Nobel laureate Jacques Monod [6]. This description of scientific thought could very well be that of an action painting. Action painting thus appears to be just as "mathematical" or just as "scientific" as more formal or more geometrical art but at a deeper level, the intuitive level. The difference between art and mathematics or science is, of course, that mathematics or science cannot remain at this intuitive level, it must be continued by formal reasoning . . . but why should art not express this fundamental aspect of thought?

Now to return to Marcel Duchamp: his "ready-mades," which initially had a liberating aspect by showing that anything can be considered as art independent of its aesthetic aspect, has often led his followers to reject the physical process of making a painting-in particular [End Page 461] the gestural aspect of action painting-the idea being seemingly that gesture necessarily obliterates thought. However, as I have shown above, there is often, even in such "pure" thought as mathematical thought, a dynamic and, so to speak, a muscular or kinesthetic thought at the intuitive level on which mathematical, ultimately more formal, thought is based. This rejection of the making of a painting seems to me to favor talk about art to art itself. Maybe we could counter these followers of Duchamp with the motto of Saint Teresa of Avila: "Obras que no palabras" (actions, not words).

Jacques Mandelbrojt, Leonardo Honorary Editor


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