Bulletin 29, 1977

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The Place of "Composition 12 with Small 
Blue Square" in the Art of Piet Mondrian

by Robert Welsh

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Almost immediately upon the achievement of freeing his various 1916-1917 compositions with colour planes from all overt references to specific subject motifs, Mondrian became concerned with the tendency of rectangles to be seen as particularized forms. His answer was to neutralize this effect by forming them, as he put it, as a "logical consequence of their determining lines, which are continuous in space," rather than as self-contained entities. (21) The initial manifestation of this principle, which concomitantly destroyed the age-old form-space dichotomy in Western art, was the above-mentioned use of a regular mathematical grid during the years 1918-1919. Although the origins of this usage are complicated, and as yet poorly documented, the supreme relevance of this group of paintings to an understanding of the Composition 12 cannot be doubted. In terms of general composition, the density of the line structure in the National Gallery painting is greater than that found apart from its role in predicting the line-structure of several major New York period examples, Composition 12 quite possibly signified a conscious return to the compositional complexity of such earlier grid works as Lozenge with Gray Lines (fig. 10), and Checkerboard with Light Colours (fig. II).

Ironically, with its square picture plane divided into an underlying grid, containing eight rows of eight smaller squares (hence, viewed as diagonal rows of lozenges, in the manner Mondrian intended the painting to be seen), Lozenge with Gray Lines might more correctly be called a "checkerboard composition" than the two canvases at present so termed, which, in fact, deviate from such a model, both for being rectangular, and for containing rows of sixteen units in each lateral direction. (22) As finished, Composition 12, but for the omission of a single dissecting horizontal line, could also be read as divided essentially, if of course disproportionately, into rows of eight-by-eight square, or rectangular, units.

In all these examples, and in the New York City I and Victory Boogie-Woogie (fig. 12) as well, the checkerboard analogy clearly is fallacious in relation to the artist's derivation of composition. But it does call attention to an essential necessity in viewing them; namely, that one's attention to the compositional structure is forced to shift constantly from a single or small group of units to the next, and that a visual comprehension of the total configuration is virtually impossible, except as a broadly perceived pattern. This requisite process of analysis does thus approximate the constantly changing contrast of regular and irregular grid patterns which one experiences while figuring out the possible moves in a checker match.

A rather more profound analogy is that with the requirements of listening seriously to a piece of music, in which individual notes or sound combinations are also necessarily appreciated fundamentally as a sequence, and only by later reflection as a compositional whole. (23) At the least, such necessities tend to confuse the perceptual-conceptual issue in these Mondrian examples and also dramatically raise the possibility that he here with intended an art of the fourth dimension in painting. To be sure, a wish to indicate an analogy with music as an art of the fourth dimension, which is to say of time, is implied not only in his several painting titles, designated "Fox Trot" or "Boogie-Woogie," but also in the term "dynamic equilibrium," with which he characterized the aim of his late oeuvre. That this concern was already present in the De Stijl period works is documented in a letter of December 12, 1918, to his colleague, Theo van Doesburg. (24) In lieu of further detailed discussion of this issue by Mondrian, we are forced to depend for our understanding on an analysis of the paintings themselves, supported by a select few intriguing possibilities of source influence which are available in the extant record of De Stijl activities.

The most easily recognized aspect of optical kinetics which links the Composition 12 to the Lozenge with Gray Lines is the so-called flicker, or popping-effect, of intermediate gray spots which appear at the line inter-sections, involuntarily of the viewer's wishes, as his glance traverses the grid network. This effect is particularly strong if one focuses upon a single line crossing, in which instance the spots of the surrounding intersections appear and disappear in a lively tempo of kinetic activity. A similar but more subdued effect occurs with the Checkerboard, where the squares surrounding the area of focus seem to glow in a pulsating fashion. Yet, while it is tempting to interpret these phenomena as a prediction of the "op art" of the 1960s, Mondrian's own explanation was to link such flicker effects with twinkling stars, an association he made in another contemporary letter to Van Doesburg, quite likely in reference to a companion piece of Lozenge with Gray Lines. (25) To this extent, the subject references and cosmic iconographic associations of the Pier and Ocean seem to have been preserved in the grid paintings which followed, and it is just possible that they survive even in Composition 12.

A second manner of reading the early grid paintings, which devolves unavoidably from their structural components, is in terms of grouping, a principle which recently has been found of basic importance to the art theory of Paul Klee. (26) As explained already in 1900 by the scientist Franz Schumann, when confronted by a regular grid pattern containing large numbers of units, the human eye involuntarily becomes selective, and focuses upon relatively small unit groupings, most readily those made up of four, mutually adjacent, blocks. (27) If one seeks to focus upon a larger number of squares, for example, nine arranged in rows of three, the normal tendency is to see a pattern of subdivision appear. Either one notices the horizontal and vertical rows of three, or groups of - five units, emerge in the configuration of either a Greek (the "plus" sign), or St Andrew's (the "x"- shape), cross. A larger grouping, such as sixteen squares, arranged in rows of four, is normally comprehended as a four-fold multiplication of the above-mentioned basic unit of four adjacent blocks. All these examples hence confirm a general preference of the human visual response for selective simplicity. As an anticipation of Gestalt psychology, this theory tends to further confuse the perception-conception issue, depending upon whether the physical mechanism, or also a process of mental ratiocination, is credited for the response.

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