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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In any case, although there is no reason to believe Mondrian was acquainted with the Schumann analysis, which appeared, after all, in a learned German-language journal, his 1918-1919 grid paintings may be considered to be elaborate variations on the same theme. In the Lozenge with Gray Lines, and several related canvases, some form of visible or implied underlying grid (readable either as rows of squares, set parallel to the canvas edges, or as lozenges, if appreciated according to the vertical-horizontal axis), appears to have superimposed upon it a heavier, irregular grid of vertical and horizontal lines, enclosing groups of one to six square units. These irregular sub-divisions are so dispersed throughout the total composition that the viewer is led to put together, so to speak, in his mind's eye, various possible combinations of rectangulated areas, perceived as multiples of Mondrian's delineated groupings.

None of these rearrangements, however, appears as a definitive solution, even with the artist's own total arrangement, because the picture edges unavoidably truncate all the subdivisions which they bisect, implying a fragment of a larger whole extending beyond the canvas edges. The same contrast between a regular underlying grid, and superimposed irregular groupings (in this instance, the separate colour subgroups contain merely from one to four units), informs the Checkerboard. Here the total kinetic effect is further enhanced by irradiations of the bright colour contrasts, the pseudo-popping or pulsating sensations of the colour blocks, mentioned above, and even the tiny, indeed, scarcely noticeable gray flickers at the line intersections. Moreover, if Composition 12 is less variegated in its internal subdivisions than the earlier, regular grid paintings, it nonetheless also lends itself to visual analysis by a similar process of imagining various groupings of the rectangular units. For this possibility, too, Composition 12 may be considered a recapitulation of past preoccupations.

Other phenomena of visual perception, which have been exploited more systematically in recent op or kinetic art, already had received considerable attention in scientific circles by the turn of the century, as might easily have been known to Mondrian through popularized forms of publication. (28) In an influential book, published in 1886, Ernst Mach described how a square placed on its side would never be perceived as the same geometric figure as when viewed as a lozenge, except after a mental process of comparison, presumably accompanied by a conscious adjustment of vision. In addition, Schumann noticed that this difference in appearance is enhanced by the viewer's greater awareness of the distances from opposite corners of a square when it is viewed as a lozenge. (29) In the occasional choice of lozenge formats for his paintings, Mondrian doubtless appreciated the further escape from particularized rectangular form and the implication of open, dynamic composition, which this usage allowed. At the same time, his lozenge compositions are by no means merely camouflaged perfect squares.

Lozenge with Gray Lines, as we have seen, asymmetrically placed squares and rectangles formed by the heavy vertical and horizontal line segments dominate over the underlying regular grid of squares viewed as lozenges. Strangely, while one remains generally aware of the opposition between the square and lozenge grids within this counterpoint of kinetic activity, except by squinting, which can produce in the viewer a near-vertiginous experience, it is not possible to appreciate the two systems as an integrated whole. Instead, one's attention fluctuates between the two opposing patterns, thus substantiating further the Mach-Schumann observations, despite the apparent potential here for simultaneous perception.

This principle remains intact, amazingly, even with the Composition with Yellow Lines (fig. 13), one of the seemingly least complicated designs among Mondrian's lozenge-format paintings. Presumably this unique substitution of coloured for the normally black lines during the classic, pre-New York period was motivated by a knowledge that yellow lines might more effectively appear to sit within the picture plane than those in black, red or blue, all of which tend to stand out in greater relief. Moreover, once the yellow bands are imagined to imply extensions which intersect, and thus complete a square figure, according to the Gestalt principle of "closure," a maximal opportunity exists for visually identifying the square and lozenge images, since the yellow lines also define an almost perfect square, approximately the same size as the lozenge picture plane. (30)

Yet, when actually viewed, not even the substantially proportioned multiple set-back strip frame, with its inevitable shadow lines, submits to simultaneous perception as part of a single, total design in which square and lozenge overlap. Instead, here too the heavier yellow lines predominate as a motif, unless the viewer consciously shifts his attention to the picture format, in which instance the yellow lines appear diminished as a focus of attention. Consequently, whether or not he was aware of its discovery within the realms of science, one may assume that Mondrian could not have remained unaware of this law of visual perception, if only from the countless hours he is known to have spent in front of his own paintings.

A somewhat related question is the degree to which Mondrian knew and cared about various optical inversions and illusions, which though again known and examined in some detail by nineteenth-century scientists and art theorists, in more recent times have been examined exhaustively within the circles of Gestalt psychology, and op or kinetic art. One thinks, for example, of the so-called negative after-image, which relates to his gray flicker effects, but which applies particularly to spectral colours, especially if the hues chosen are as saturated and pure as those of Mondrian. As can be best substantiated in front of the paintings themselves, but often even with colour illustrations, this effect is achieved through fixation (that is a concentrated focusing of at least fifteen seconds) on any isolated colour area, such as the blue square of the National Gallery painting, or even the yellow lines of the 1933 lozenge. One then transfers one's concentration to an area of white, and the complementary colour, respectively yellowish-orange and bluish-purple in the examples cited, will briefly appear as a shape corresponding to the original colour area.

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