Bulletin 29/1977, The National Gallery of Canada

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

When in 1970 the National Gallery of Canada acquired the Composition 12 with Small Blue Square by Piet Mondrian, 1872-1944 (see gatefold), the painting already was widely recognized for its high quality and special position within the artist's late œuvre . Among the eleven paintings begun in Europe and finished in New York which were included in his one-man exhibition of January-February 1942 at the Valentine Dudensing Gallery (whence its title "Composition 12" and inscribed date lower right "36/42"),1 this all but exclusively black-and-white canvas most clearly prefigured the diversified grid structure found in New York City I of 1942 (Sydney Janis Gallery), the most recently completed painting then exhibited.

Mondrian himself implied this relationship while posing for a photograph in his studio (see cover), wherein he is seen focusing his attention upon Composition 12, which he holds upright, while New York City I is comparably featured by placement upon an easel. The use, in the latter New York period painting, of a larger number of lines, now coloured in primary hues, seemingly interlaced on the canvas and heavily concentrated towards the picture edges, would allow for the presumption that Mondrian, through the photograph, had wished to stress the difference between his European and American stylistic phases, even implying improvement due to the New World environment. Tempting as this might be for American audiences to believe, one might as easily deduce an intention to stress continuity within the previous six years of activity on the two continents.

The issue is intriguing, but by no means the only one in the solution of which Composition 12 figures prominently. For example, the degree to which conceptual as opposed to perceptual concerns dominated Mondrian's thinking equally affects our understanding of his contribution. Reflecting the traditional distinction within Western art between intellectually inclined “painter-poets,” and presumably less thoughtful “pure painters,” this polarity in modern times has also implied a respectively greater and lesser dependence upon scientific analysis of the norms of form and colour.

Thus the Neo-Impressionist movement led by Georges Seurat is classified as hyper-intellectual, or conceptual, for its derivation of Divisionist laws of colour usage from a number of nineteenth-century grammars of art or optics, while Realism and Impressionism are believed to have been created by more instinctively or perceptually motivated colourists. The Cubist-Abstract Art movement, as might be expected, generally is described as heavily inclined towards conceptualization, doubtless in large part due to the considerable number of therein participating artists who have produced theoretical writings in defence of radical stylistic innovation. Certainly Piet Mondrian is widely considered an archetypal exponent of conceptualized abstraction in art, both for his seemingly pitiless dissection of the painting surface into rigid, geometrically conceived components of line, plane and colour, and for the published explanations of these practices which accompanied his later periods of development. Here, too, Composition 12 offers an unusual opportunity to examine the validity of characterizing Mondrian essentially as a conceptual artist. This issue is especially pertinent to his advanced stylistic phases, but also applies insofar as these embody, in distilled form, the totality of his extended involvement with earlier movements and precepts. For all these reasons this singular painting may be considered a major signpost in the general history of twentieth-century abstract painting.

Whatever the proper resolution of the conceptual versus perceptual dilemma might be for his mature periods, the early naturalistic œuvre clearly manifests a greater emphasis upon the latter criteria. Throughout an approximate twenty-year period, ending circa 1908, Mondrian worked primarily as a landscape painter, principally in a Dutch mode of the plein air Barbizon tradition, wherein he produced the greater part of his surviving output. As an epigone representative of the Hague School of painting, he followed with relative fidelity the tonal impressionism of such Dutch masters as Anton Mauve and the Maris brothers, whose realist depiction of picturesque landscape settings embodied the then current motto alleen maar schilderen (that is, "merely paint"), a Dutch variant of the pure painting credo. Within this historical context the depiction of nature as perceived in  all its fig. 1 House on the Gein, 1900detail and atmospheric nuance was the primary goal. The conceptualization of subject themes inherent in historical and other forms of elevated narrative painting was banned as involving false, or at least  unnecessary, literary content. While it is impossible to summarize the diversity of Mondrian's naturalistic experimentation in a single example, the watercolour, House on the Gein (fig. 1) of 1900, represents  with marked comprehensiveness that blend of detailed realism and atmospheric tonalism which typified the Hague School and the bulk of his own early landscape production.

At the same time, this example betrays a minor element of personal innovation, since the near lozenge, or diamond shape, formed by the triangles of the central house facade and its reflection, though in fact true to natural appearance, foreshadows later com positional features present alternatively within, or as the framing format, of a number of major canvases. If not very likely a conscious prediction of things to come, this otherwise historically retarded and minor example of pictorial naturalism nonetheless shows its author to have been set upon a path leading about as far away from Barbizon habits of design as anyone then, or perhaps now, could imagine.

The Mondrian of the years circa 1908-1911 might be described as a stylistic chameleon of many colours. His interspersed involvements with the Fauve, Art Nouveau and Divisionist movements, all encountered second-hand via native Dutch practitioners, were manifested in such a diversity of unorthodox modes that few critics, then or since, have viewed this body of work as anything more than an anomalous parade of misunderstood and eclectic, if sometimes interesting, borrowings. Yet it was precisely during this period that the artist's attachment to modernist, largely French-derived tendencies commenced.

In particular, he adopted the use of bright, intensely radiant colour combinations, afig.3 Church at Domburg, c 1965 development he was to characterize in later fig. 2 Church at Domburg, 1910-1911years as his first major departure from tonalised naturalism.2 However, one should not suppose a precipitous abandonment of realist canons of design merely because of the radical simplification of form and colour application which occurred. Throughout this experimental phase, Mondrian's landscapes continued to be produced, largely en plein air, and a remarkable allegiance to the actual proportions of the objects depicted survived. This can be illustrated in a comparison of the 1910-1911 painting, Church at Domburg (fig. 2), with a photograph of the site (see fig. 3), in both of which the scale proportions and starkly flat appearance of the building facade appear almost identical. Even the sienna red of the facade and the blue and green of the surrounding areas found in the painting correspond with the general contrast in natural colouration between, respectively, the brick architecture and the mixture of sky and foliage observable in the photograph. Admittedly, these last two entities would be transformed in form and colour for the painting.

The relationship to natural reality is further retained through suggestions of evening atmosphere, signified by the shadow found in the lower areas of the church brickwork. From all these attributes one may conclude that a highly intense perception of natural appearance was as integral a part of Mondrian's artistic approach in this 1910-1911 painting as was the equally evident de-emphasis of particularized realistic detail. By such means could this, in actuality, modestly- sized village chapel, emerge as a monumentally pro portioned and seemingly timeless icon of mankind's striving for spiritual enlightenment.

It also would be deceptively easy to write off this idiosyncratic, immediately pre-Cubist, style of Mondrian as some kind of art historical aberration. According to this sometimes voiced opinion, the stark simplicity of Art Nouveau design, a reductio ad absurdum of primary colour contrasts, and a tentative knowledge of Cubist formalism, arc here blended  syncretically into what was, at most, a personally innovative cul-de-sac, from which only his 1912 move to Paris and direct contact with French Cubism could provide an escape. Of course there is some truth to this analysis, which Mondrian himself later encouraged by describing the use of "exaggerated" natural colouration as being too linked with the particularism, or lack of universality, of traditional art.3

Nevertheless, as a stepping-stone along the path to pure abstraction this work indicated a new direction of major importance. In terms of hindsight, it displays Mondrian's initial declaration of freedom from those specific source influences cited above, which justify the charge of previous eclecticism. Whereas a general tendency towards geometrizing design within Dutch art and architecture, including an influx of Egyptianizing elements, helps to account for the frontality, the expressive severity, and the triangulated figuration within the composition of Church at Domburg, no single source model in the work of another artist provides a sufficient explanation for these factors. Similarly, if owing much to his previous experiments with colour in terms of Divisionist and other temporary borrowings, the reduction to three or four basic hues, applied in flat, relatively uniform compartments, not only transcends his sources but also firmly predicts his later colour conceptions as well. In short, Mondrian here forcefully emerges for the first time as his own master, and some inquiry into the theoretical justifications for this abrupt personal development is in order.

The theoretical support for Mondrian's initial departure here from traditional modes of style towards a manifestly proto-abstract pictorial structure appears to have been based upon two major intellectual traditions: one generalized, the other quite specific. Unfortunately, his involvement with treatises on art theory, even those by Dutch writers, is poorly documented, chiefly for lack of first-hand knowledge of how far-ranging were the artist's reading habits during youth and early maturity. However, one guideline is suggested by his oft-repeated distinction between the vertical line, as emblematic of the spiritual or male principle in nature as in art, and the horizontal line as the material or female principle. This convention was already so deeply rooted in Western art tradition, and so widely propounded in nineteenth- and early twentieth-century writings on art, that by Mondrian's time it had become virtually a cliché.

Hence, whether learned first during his schooling at the Amsterdam Academy, or from texts by writers such as David Humbert de Superville, Charles Blanc or Wilhelm Worringer, as might equally be assumed, this fundamental precept could be applied to a variety of subjects: standing or reclining figures; natural growths such as trees, and the contrasting horizon line; and also the ascending quality of Gothic, as opposed to the trabeated, ergo earthbound, aspect of the classical (or Greek) style in architecture.4 Doubtless, one may therefore read the vertical format and internal  design  elements  in  Church  at  Domburg, among other examples, in terms of an iconographic analogy between Gothic ascending lines and masculine spirituality.

One may also assume that Mondrian was to some degree acquainted with this convention as embodied in contemporary Dutch architectural theory. Reflecting such earlier nineteenth-century French-language writers as De Superville and Viollet-le-Duc, the major Dutch Art Nouveau architects, H. P. Berlage, K. P. C. dc Bazel, and J. L. M. Lauweriks, all considered geometric figuration of some sort as necessary to the successful practice of architecture – for themselves as for previous ages.5 This association, moreover, was applied to both the overall design of buildings, whether of religious or secular function, and to ornamental details, the analysis of which received extended treatment by these and other Dutch writers at the turn of the century. Given the pervasiveness of this type of analysis of geometric design principles in art and architecture, it must be given credit for having played at least a minimal supportive role in the evolution of Mondrian's art theory. Probably it also helps explain the progressive reduction of virtually all natural subject motifs to the more-or-less straight-edged geometric figures which subsequently occurred in his paintings.

The personal commitment which most profoundly influenced Mondrian's art and theory before his encounter with Cubism was his involvement with the spiritualist Theosophic Movement. A registered member of the Dutch Theosophic Society by 1909, Mondrian not only mentioned this occult philosophic doctrine approvingly in writings belonging to his pre-Cubist, and early De Stijl phases, but he also reregistered with the Parisian Theosophic Chapter as late as 1938, or on the eve of his departure from France to London. The contact with Theosophy was thus maintained until after he had begun - and, as we shall see, completed in preliminary form, - Composition 12.

For the period circa 1909-1911 this influence is most thoroughly documented in the veritable Theosophic testimonial piece, the Evolution triptych.6 The Church at Domburg, by analogy of style, may be thought equally imbued with implications of mystical content, intended to lead the viewer in a tandem of religious and aesthetic experience from the mundane level of observed reality to the so-called "higher spheres" of clairvoyant initiation. Thus, while it remains uncertain to what extent Mondrian felt himself to be the recipient of clairvoyant visions when painting such works as these, his figural subjects of the period appear as if transported to some higher level of occult experience.

Church monuments, especially if, as was the local Domburg example, in less than a perfect state of preservation, like flowers, number prominently among those "centres of spiritual force" which Theosophic initiates arc advised to contemplate as a means of producing visionary thought-images of the so-called astral world. As the then still Theosophist Rudolph Steiner explained it, devotional concentration upon such objects pertaining to the "soul-world," would produce, in properly attuned sensibilities, transformations of natural appearance which are chiefly characterized by purification of the observed colours into radiantly luminous hues, and of the form into progressively simplified shapes. Indeed, throughout Theosophic literature, elementary geometric forms, such as squares, triangles, circles, ovals, and crosses are treated as emblematic of the most fundamental and universal spiritual truths.

It is within this rarified religious context that the essential aspects of colour and form found in the Church at Domburg are to be explained, even if, as stated above, an accurate perception of the natural world does not vanish completely before the power of super-sensory vision. In similar fashion, the remarkable reduction of the total imagery to a virtually two-dimensional principle of composition seems no less reflective of the innate design sense which had informed the House on the Gern than a distillation of artistic, art theoretical, and spiritualist doctrines derived from outside sources. To a larger degree than generally realized, the fundamental principles of Mondrian's later abstract œuvre were already stated in his ultimate production of the pre-Paris years in Amsterdam.

It must not be thought that the intertwining of occult religious precepts and his work as a painter ceased when Mondrian arrived in Paris. His sketchbook annotations of approximately the period 1912- 1914 are replete with Theosophic jargon, and the male-female duality associated respectively with vertical and horizontal lines was principally derived from this same source.7 Even Picasso, whom Mondrian repeatedly credited with having exerted a profound influence upon himself, and whom the Dutch artist would have known not to be Theosophically inclined, was nonetheless credited with having furthered, albeit unconsciously, the same historical process of spiritual evolution which is the declared task of Theosophy.

Rather than appearing as a secular challenge in art to spiritualist preoccupations, Cubism clearly appeared to Mondrian as a justification of such beliefs, and as offering a fruitful means of realizing such ideas in a contemporary artistic style. After all, had not Cubism accomplished more than any previous art movement since the Renaissance in de-emphasizing both literary subject matter and the normal appearance of material reality? If such an association between Cubism and pan-spiritualism would seem, by objective standards, to be a forced marriage at best, its tenacious grip on the mind of Mondrian contributed in no lesser measure to the evolution of his own art towards ever greater degrees of anti-naturalism and abstract canons of style.

Concurrently, incorporation of spiritualist ideas in his art assumed a quite individual form which had more significant consequences for the history of art than for the Theosophic movement. In Paris, the artist reduced his subject preferences to an all but exclusive reliance, first upon trees, and then upon building facades, neither motif being more than barely recognizable as such.8 By these means, he simultaneously preserved subject predispositions reaching back to his early naturalistic period, and yet gainsaid any possibility that standard Theosophic doctrines might be comprehensibly illustrated.  As a consequence of this tendency towards iconographic camouflage, a large proportion of Mondrian's Cubist paintings were for many years thought to be relatively pure abstract configurations of line and colour. Only by reference to the more easily decipherable preliminary drawings which survive has it been possible in recent years to discover the actual sites of a number of architectural and other motifs which served as a basis for his "compositions" - as, beginning circa 1912, he preferred to label his paintings.

fig. 4 The Flowering Appletree, 1912With the tree themes the issue is particularly complex. Along with verbal reports and sketchbook evidence of his having executed drawings of trees in situ while in Paris, certain major paintings, such as The Flowering Appletree (fig. 4), clearly derive ultimately from earlier subject treatments, in this case the isolated motif employed in the "blue tree" series of circa 1909.9 Given the fluid character of the web of linear patterns and brushstroke in-filling, the extreme painterliness of Mondrian's approach would, at first glance, seem at odds with the tendency towards geometrizing design found in the Church at Domburg from a year or two earlier. On closer examination, however, a deft combination of spiralling branch configurations, and opposing abstract linear and colour contrasts, grant this composition definite structural stability despite the coruscating movement of its surface patterns. The radiating sweep of lines, which, especially at the top and sides, imply projection beyond the actual picture plane, constitute a centrifugal force held in check only by those fewer convolutions of line which constitute a centripetal force, and by the knotted massing of darker colouration at the centre. Finally, within this vortex, one senses an underlying grid of vertical and horizontal line segments, a central cross-motif formed by the bisecting picture axes. Perhaps one even senses the implication of a lozenge, if the points of the cross are felt to be connected, albeit, in our example, with sides bent inward, in keeping with the overall curvilinear character of the design.

This latter aspect of the painting doubtless suffices to classify it as dominantly female in theme, as does also the greater emphasis upon the horizontal interlace of branches. At this time, the iconographic combination of largely curved lines and dominance of the horizontal axis signified for Mondrian the female, or material, principle, although it should be remembered that the presence of this force was thought to be as necessary as the vertical-spiritual entity for the preservation of universal harmony, that is to say, according to the artist's Theosophically inspired convictions.  With this in mind, it is possible to interpret The Flowering Appletree as both an iconographic antipode to, and yet a striking compositional precedent for, Composition 12.

Despite the manifold differences which one easily observes - in particular, curves versus straight lines and tonal nuances versus stark geometric contrasts of line colour and plane - these two paintings betray a deep relationship in basic conception. Thus the rhythmic dispersion of irregular compositional patterns, the implication of linear extension beyond the picture plane, and the counterbalancing factor of greater density in the central areas, represent elements of design which intimately link the two canvases as products of a single artistic imagination. Because such similarities of conception were maintained over the last forty-odd years of his career, we can doubly appreciate why Mondrian himself, in 1914, was anxious to credit the Cubist movement with having incited a major breakthrough in his art, even while, as he also said, the basis of his art was different from that of Picasso, his then-avowed model. 10

To be sure, only circa late 1913-1914, in reaction against the late analytic Cubism of Picasso, did Mondrian begin to employ systematically his classic elements of line, plane and colour, all embodied in a visible grid structure, in a manner which boldly forecasts his mature art of the De Stijl period, and after. And this was accomplished principally in reference to a repertory of Paris building façade subject motifs, which were as foreign to the preferences of Picasso as they were devoid, with the exception of a single church façade motif, of inherent sacerdotal, not to say Theosophic, associations.

fig. 5 Paris Courtyard Facades, c. 1913-1914Here, too, appearances may be deceiving, since the complexes of apartment dwellings, located near Mondrian's own residence adjacent to the Gare Montparnasse, which area largely provided the subject motifs of his final pre-First-World-War year of work in Paris, apparently assumed in his thinking the status of archetypal, cosmic images. For example, the mixture of compositional and yet iconographically elevated functions that such secular structures served are combined in a previously unpublished compositional sketch which, although allowing for no ready supposition of use with any specific painting, relates in subject matter to several major “Paris Façade”  canvases from early 1914.11 The drawing. Paris Courtyard Façades (fig. 5), thus retains from observed appearance the disproportionate areas of wall surface which, in a final painting,  almost certainly would have been   transformed into rectangular units of a more uniform scale. In terms of naturalistic representation, the artist obviously has been concerned here with compressing "hollowed-out" spatial illusionism into an essentially "flattened-out" design. Gone, too, in any final painted version, would have been the details of architecture, which in the drawing might allow for certain identification of a specific site.

Most striking of all is the marked suppression of Cubist peculiarities of style, particularly of those elements which typically render ambiguous the distinction between volumes and surrounding space. Along with his simplification of facade areas Mondrian has sought to preserve each rectangulated component as a separate entity, and thus to harmonize the total design pattern which emerges. This feeling of unity within the overall design is all the more remarkable considering the probability that the actual setting, for full visual appreciation, required a sweeping, constantly refocused viewing of what must have appeared as a complex juxtaposition of interlocking planar surfaces. In any case, this drawing represents a sophisticated attempt to deal with the problem of reducing conventions of spatial illusionism to an essentially two-dimensional system of design.

That Mondrian nonetheless interpreted the setting as of more than mundane significance is indicated by the inscription of the Dutch word leven (that is, "life"), lower left of centre. In contrast the “R” above centre almost certainly indicates red, whichever of the Dutch rood or French rouge was intended. Apart from the axiomatic reference to the depiction of a place where people live, the word leven, as found in contemporary writings by Mondrian and the Dutch Theosophist, Dr. M. H. J. Schoenmaeker, refers to the substantive concept of a fuller or higher life, in which polarities of male and female vertical and horizontal, movement and rest and also space and time are reconciled in a balanced manner.12 One may therefore hypothesize that in this otherwise non-religious, abstractly depicted sanctuary, Mondrian discovered further corroborative possibilities for embodying content of a presumed universal significance. As for his artistic means, the drawing embodies the reductionist credo stated as an aphorism in a contemporary sketchbook annotation: “For the spiritual artist colour and brush-work sufficiently represent matter” 13

During the subsequent period of isolation in the neutral Netherlands of the First World War Mondrian evolved his own "abstractionist" style, this in concert with other like-minded Dutch artists, and in partial reaction against Cubism, which "did not accept the logical consequences of its own discoveries.14 It was now that his cumulative aversion to naturalistic representation was finally manifested through reduction of "natural forms to the constant elements of form and natural colour to primary colour." 15 Although often thought to have constituted a radical step taken abruptly, and to have produced a dogmatically unchanging art theory and accompanying personal style, this historical breakthrough actually allowed for a wide range of expressive choices, which Mondrian exploited throughout all subsequent periods.

fig.6 Pier and Ocean, 1915Initially while back in The Netherlands, for example, he displayed a preference for linear compositional structures, based primarily upon concatenations of short vertical and horizontal line segments, whifig. 7 Beach with pier at Domburg, c. 1965ch often cross. This phase is designated popularly as the "plus-and-minus" style, and is illustrated synoptically in the ultimate version of Pier and Ocean (fig. 6). We can see, by comparing this painting with a photograph of the actual subject site (see fig. 7), a beach segment with a wooden pier breakwater at Domburg, what Mondrian meant when he stated:  “Impressed by the vastness of nature, I was trying to express its expansion, rest and unity." 16

On one level, the peculiarities of this composition may be thought to have resulted from a hold-over study of the appearance of nature, since the artist added to the statement cited immediately above: "Observing sea, sky and stars, I sought to indicate their plastic function through a multiplicity of crossing verticals and horizontals." And it was doubtless in large part, the rhythms inherent to the reflected surface configurations of beach, pier, sea, sky, and stars that inspired the subtle nuances of spatial recession and surface pattern found in Pier and Ocean. No less than the sensed convolutions of trunk and branches for The Flowering Appletree, and the rectilineated wall compartments for the Paris facade paintings, the more staccato and broken rhythms of Pier and Ocean seem to reflect a surviving Romantic attachment to the representations of particularized form within a cosmic landscape setting. 17

On a second level, that of the intended iconography, this painting may be considered a quintessential expression of Theosophic doctrine, in which primary geometric shapes embody allusions to fundamental spiritualist ideas. Thus, the oval border of the interior composition implies the cosmic egg born of the sea which Theosophy derived from Hindu tradition.18 Similarly, both the central cruciform image, formed by the major vertical and horizontal axes, and the many smaller line-crossings, imply one or another of the several cross-forms (for example, the Latin, Greek and Tau types), which are cited in many basic Theosophic writings as signifying profound cosmological truths. Like the simple opposition of vertical and horizontal elements, the white-versus-black contrast had, for Mondrian, come to imply an ultimate polarity, that common to most religious systems: namely light versus darkness. Henceforth, both the basic black-and-white colouration, and the "plus-and-minus" connotations of vertical and horizontal lines in grid paintings by Mondrian, should be interpreted to involve a cosmic principle of attraction of opposites, rather than simple arithmetic symbols for addition and subtraction.

On a third level, however, we can view the "plus-and-minus" style as evidencing the emergence in Mondrian's thinking of a less spiritualist outlook than that resulting from contact with Theosophy. This would be a basic concern with the dissolution of the distinction between form and space as substantive absolutes, traditional to Western art. In reference to his Dutch wartime experimentation, Mondrian thus later wrote:

At this point, I became conscious that reality is form and space. Nature reveals forms in space. Actually all is space, form as well as what we see as empty space. To create unity, art has to follow not nature’s aspect but what nature really is. Appearing in oppositions, nature is unity; form is limited space concrete only through its determination. Art has to determine space as well as form and to create the equivalence of these two factors. 19

 On the one hand, the development of this theory should not be thought to signify a precipitate termination of his Theosophic involvement, since an interpretation of the Pier and Ocean, as representing a species of universalized visionary landscape, is easily reconcilable with, perhaps enhanced by, the innovative significance it had for Mondrian's conceptual abandonment of the Renaissance form-space dichotomy. On the other hand, as he gradually abandoned reliance upon the various expressive and symbolic associations of specific subject motifs (including those predicated by Theosophy), his style and content increasingly took on a more independent and individual cast. To the extent that his conception of pictorial space appears more and more analogous to the general anti-Newtonian bent of twentieth-century astronomy and physics, there is, of course, a heightening of the secular or scientific aspect of his art. Nonetheless, until the end of his career, Mondrian's primary theoretical preoccupation continued to be "liberation from oppression in art and life," as he entitled one of his late essays. 20 In this search, both religion and science were found necessary to his theory of art, chiefly insofar as they illuminated or coincided with his primary pursuit of artistic goals.

The reader already may have noticed certain general structural similarities between the Pier and Ocean, and the Composition 12. There is no reason to think that Mondrian was consciously returning to the earlier painting in determining the composition of the National Gallery example. Yet the occurrence in both of a central cruciform image, and a common reliance upon stark black-white and vertical-horizontal contrasts, allows us to see the two works as generically related, in contrast, for example, to the much greater number of mature period paintings, in which asymmetrical design elements predominate. Most important, the rhythmical dispersion of vertical and horizontal lines against a luminous white ground provides the principal source of aesthetic interest in both paintings. To this extent, since Composition 12 seemingly represents the only major painting to have been begun in Europe and finished in New York while leaving intact a dominant centralized cruciform image, it may be considered the final elaboration of a theme in Mondrian's œuvre of which the Pier and Ocean constituted his most definitive statement during the immediate post-Cubist years.

fig. 8 Composition in Colour - A, 1917Another major precedent was set for Composition 12 when Mondrian, before returning from The Netherlands to France in 1919, which is to say, during his early De Stijl period, adopted an exclusive reliance in his art upon three basic plastic elements: namely, straight lines, rectangles and primary colours (that is variants of blue, red and yellow, employed with the rectangles). Initially, this usage retained a form-space dualism, as is embodied in Composition in Colour-A (fig. 8) finished in early 1917. Here, space is still represented by the white ground as in Pier and Ocean whereas the square or rectangular colour planes, and the conceptualized black lines, are treatedfig. 9 Detail Study of the Domburg Church Facade as particularized forms which appear to overlap and to float against the lighter background. Just how difficult it must have been for Mondrian to abandon this residual attachment to observed subject matter is illustrated in another previously unpublished drawing, which one can designate a Detail Study of the Domburg Church Facade (fig. 9), from the remnants of Gothic window contours which survive from earlier versions of the subject (for example, fig. 2 and S: cc 250, 252-257; see also photograph, fig. 3). However, as the only known version to use a square, rather than vertical format, this modest exercise in achieving a disequilibriated balance of lines and implied planes must be considered a uniquely related preliminary study for Composition in Colour-A, and the companion piece Composition in Colour-B (S: cc 291), both only slightly higher-than-wide canvases.

Moreover, in contrast to the few other known precedents, for example. Pier and Ocean, the Detail Study more consistently employs a network of straight lines in order to form a pseudo-grid composition, the individual linear components of which ambiguously act both to divide and to enclose areas of white ground. In this respect, the drawing functions as a link between the loose grid compositions of the Paris Facades, and the regular mathematical grid works which occurred exclusively during the years 1918-1919. In terms of the National Gallery Composition 12, it serves as yet another reminder of the variety and depth of experimentation that preceded the achievement of the late classic phase which began in the early 1920s. Thus, Composition 12 employs a near-perfect square picture format, and a basically cruciform interior composition, which, upon closer examination cannot be viewed as a homogeneously unified configuration of lines and planes. This complexity of internal structure is due chiefly to an irregularity of internal intervals between the lines, all of which, like those of the Detail Study, function as much to divide as to contain the various white rectangles.

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 in any other painting essentially of the late 1930s, and is exceeded thereafter only in the New York City and Boogie-Woogie coloured line-and-plane paintings of his final years. Hence, 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. 11). 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 l 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 docs 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 herewith 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 œuvre. 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 intersections, 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.

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 cither 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 subdivisions 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.

In 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.

Similarly, with intense and prolonged viewing, effects of glowing irradiation (for example, an exaggerated tonal contrast in the purity of the white and black, where line edges and ground meet) and distortion of size (the seeming slight expansion and contraction of particular areas of line, colour and background) gradually become visible in Composition 12, as indeed they do in paintings having a less rhythmically syncopated linear structure. One may deduce from an ultra-violet photograph of Composition 12 (fig. 14) that the final overpainting of the white surface area in New York involved renewed emphasis upon a visibly striated brush technique during this final period of activity. In consequence, the muted sensation of overall surface glow, or vibration, which is hereby produced, must be considered a consciously sought expressive effect.

Regarding these observable kinetic effects, the painter was doubtless aware of at least most of them. However, given his overriding concern for an essentially balanced mode of composition, it seems probable that he considered them no more than secondary expressive phenomena, of merit only insofar as they add an additional minor element of dynamic movement or rhythm to his paintings. Instructively, the climactic stylistic development from the New York City I of 1941-1942 to the Victory Boogie-Woogie, which he still was revising at time of death in 1944, displays a progressive integration of the popping phenomenon, found at the line-crossings of the former painting, into the actual structural fabric of the even more rhythmically complex, latter example. If by no means as kinetically and expressively variegated an exercise in visual dynamics as these major canvases of the New York period. Composition 12 does, nevertheless, number among the most rhythmically, which is to say optically, active creations of his total career. As such, it lends support to the possibility that Paris, rather than New York City, initially bore witness to the jazz-like syncopations of his ultimate stylistic phase.

This possibility is further strengthened through a precise knowledge of the date at which Composition 12 was initially conceived. This question involves its classification as one of the so-called "double-line" paintings of the 1930s, a term the meaning of which never has been fully explained. Although not mentioned as having constituted a fundamental change or breakthrough in his own published writings, a number of close artistic friends seem to have considered it just this, and the usage certainly entered his œuvre , approximately 1932, rather abruptly, and as a pervasive habit of style. Possibly Mondrian was in part inspired by the example of the female painter, Marlow Moss, whose Composition in White, Black, Red and Gray (fig. 15) of 1932 is bisected horizontally by a closely-spaced pair of lines. Admittedly, this practice by Moss was by no means followed exactly by Mondrian, whose own pairs of lines almost invariably are bisected by lines in an opposing direction.31

In Composition in Gray and Red (fig. 16) of 1935, for example, the picture plane is traversed vertically and horizontally by sets of double lines, which, incidentally, preserve the Greek cross image of which the internal line structure of Composition 12 may still be thought a direct, if diversely expanded, descendant.32 It is generally  believed  that  Mondrian introduced those closely-spaced, thin-line pairs, in the belief that by replacing one or more of the wider black bands, which typically characterize works of circa 1930-1931, he was divesting his paintings of what he had come to consider a "tragic" dominance of one direction over the other.33 Moreover, the double-line paintings in general allow for a greater sense of movement and intricacy of design than the immediately preceding wide-line paintings. This must have been part of the artist's intention in contrasting the Composition with Yellow Lines with a now lost, double-line painting, when he placed one above the other for a photograph taken in his studio, circa 1933 (that is, fig. 17).34

However attractive a device the use of quite closely spaced and compositionally isolated pairs of thin bisecting lines proved to be in the early 1930s, by circa 1936, when Composition 12 was begun, a development was in motion towards even more complex compositions, containing greater numbers of lines than had characterized his paintings since the beginning of the 1920s. In particular, it is no longer possible to interpret whatever double lines do occur as simply a single, broad line, split up the middle, like railway tracks. Virtually all lines, whether or not part of a pair, now must be read as functioning simultaneously as space dividers, and as boundary edges of various rectangular planar units, both white and coloured. This multiplicity of linear configurations, of course, anticipates the systematic breakdown in the separate identities of the elements - line, plane and colour - which characterize the major paintings of the New York years. Since Composition 12 was finished in time for exhibition in early 1942, it is of no little importance to know just which alterations to its condition in Europe may be thought to have been made in New York.

Fortunately a photograph has recently come to light (see fig. 18), which records the appearance of several paintings arranged along a wall of Mondrian's second Paris studio in 1937, the year being ascertainable from the apparently just completed state of the easel-mounted Composition with Small Blue Rectangle (S:cc 395, now in the Gemeentemuseum, The Hague), which bears that date. More instructive still is the inclusion, at the upper right of the photograph, of two paintings in unfinished state which may be identified as Composition in Red, Yellow and Blue (fig 19) of the Tate Gallery, London, and Composition 12. Apart from indicating Mondrian's continuing habit (circa 1937) of mounting his paintings upon a flat board, thereby inducing the effect of projecting reliefs, this photograph allows for certain deductions about the kinds of changes he made in New York to certain paintings begun in Europe. Most significantly, the Tate and Ottawa paintings indicate the addition of respectively only three and two additional vertical lines, all at the outer peripheries, while no horizontal lines appear to have been added.

Thus, the working method was to expand the compositional nexus outward, hereby further reducing the cruciform aspect derived from earlier precedents, although this is still identifiable to a degree in Composition 12. Whereas the Tate painting also gained colour squares, which were added to the single enclosed colour rectangle visible in the 1937 photograph, this does not hold true for Composition 12, supposing that the single blue square was already present, but excluded from camera view. Assuredly, the blue, unbounded bar of colour at lower left in the Tate painting constitutes the most radical known species of New York addition, since it intentionally fuses the elements of line, plane, and colour. By way of contrast, the use of only one or two smallish colour planes consequently may be thought more typical of at least one compositional type favoured by Mondrian circa 1937.35 Such a lean and stark application of colour as we find in these examples, may or may not have something to do with the sobriety of Mondrian's own life, and the general political climate at the time. However, it docs offer a decided contrast with the more exuberant and colourful art style, which, despite the continuing war, he evolved while in New York.36

In total, we have seen how trenchantly the Canadian National Gallery Composition 12 summarizes the many rich years of Mondrian's European experience, while also forcefully anticipating the sense of dynamic, rhythmic equilibrium which was the dominant feature of his New York period. An essential dualism  between kinetic factors, and their resolution into an overall structural harmony, is the most striking quality of this rigidly composed, yet radiantly luminous and structurally imposing painting. Somewhere beneath its geometrically abstract surface doubtless survive those involvements with the world of natural appearance, spiritualise meditations, and artistic-scientific investigations with which he had been so strenuously engaged during earlier phases of his career. It would be going too far to suppose a conscious reference to either some natural subject-motif, an occult emblem, or any mathematical-spatial formula, in this relatively late painting. Yet there is adequate reason to believe that Mondrian's contemporary concepts of dynamic equilibrium and pure abstraction in art, were meant to subsume all three areas of experience in one fundamental system of imagery. It was doubtless due to this same, all-embracing, universalist philosophy that he was able to sustain, to the end, his belief in the unity of art and life, and in the prospect of enhanced happiness for mankind, despite the many adversities which surrounded him. Almost needless to say, it also explains why, for him, no strict separation of conceptual and perceptual modes of art was possible. A forceful interaction  of the two is what chiefly accounts for the sublime beauty embodied in Composition 12.


1.   A former designation as "Composition No. 2" apparently resulted from a misreading of the artist's stretcher inscription, the actual "12" of which is confirmed by the "1936-1942" listed for that catalogue number by Dudensing at his New York Fifty-Seventh Street gallery. While Nos 1 and 2 were works begun and finished in New York, 3 to 13 were all begun in Europe.

2.   See Piet Mondrian, "Towards the True Vision of Reality." Plastic Art and Pure Plastic Art (New York: George Wittenborn, 1945), p. 10; hereafter: "True Vision."

3.  E.g., on January 29, 1914, Mondrian wrote to the influential Dutch art critic, H.P. Bremmer: "In that period [i.e., previous to adopting Cubism] I sought for monumentality just as now, and I sought to realize [a process of] abstracting by transforming the colours of nature into several exaggerated colours. But later I became convinced that such works were still too externalized [in conception] and, although perhaps good after their kind, nonetheless too little 'constructed'" (trans. from "Documentatie over Mondrian I," ed. J.M. Joosten, Museumjoumaal xiii: 4, 1968, p. 211).

4.   De Superville's stresses on "abstract" geometric shapes, the matter-spirit duality, and vertical, horizontal and oblique linear directions, as contained in his Essai sur les Signes Inconditionnel dans l'Art (Leyden: 1827-1832), not only were incorporated into Blanc's Graimmaire des Arts du Dessin (Paris: 1867), but were cited by Mondrian in his essay series, "De Nieuwe Bedding in de Schilderkunst," De Stijl I: 8 (June, 1918), p. 136, note 14 (or Complete Reprint Edition I; Amsterdam: Athenaeum, 1968, p. 160). Worringer in Abstraction and Empathy (London: Routledge and Kegan Paul 1953; first German edition, 1908) stressed an association among Gothic art, abstraction and spirituality, which, if not likely to have been known to Mondrian directly, was doubtless based upon the same nineteenth-century source tradition from which the Dutch artist's own theoretical formulations emerged.

5.   See A.W. Reinink, K.P.C. de Bazel Architect (Leyden: Universitaire Pers, 1965) and Pieter Singelenberg, H.P. Berlage, Idea and Style (Utrecht: Haentjens, Dekker and Gumbert, 1972). Both authors provide rich documentation on the importance of geometric, especially triangulated, elements of design within these circles, in which, moreover, Theosophy (see below) made a significant contribution. In germ form, a geometric and symbolic basis for Gothic architecture already was posited in J.A. Alberdingk Thijm's De Heilige Linie of 1857 (significantly, reprinted 1909 in

Amsterdam); see esp. p. 133 ff., where rectangles and triangles, as embodied for example in pointed-arch windows, are said to embody, respectively, the material and spiritual, or temporal and eternal, aspects of the Gothic church. This theory, if actually known to Mondrian, would help explain the geometrizing imagery of his various church and other architectural facade subjects, beginning circa 1909-1910.

6. See R.P. Welsh, "Mondrian and Theosophy," ex. cat. Piet Mondrian Centennial Exhibition (New York: S.R. Guggenheim Museum, 1971), for an expanded version of the present analysis.

7. See ibid., Joosten, "Documentatie over Mondrian I," and R.P. Welsh and J.M. Joosten eds. Two Mondrian Sketchbooks 1912-14 (Amsterdam: Meulenhoff International, 1969), for evidence that Cubism and Theosophy were closely linked in Mondrian's contemporary thinking.

8. See J.M. Joosten, "Mondrian and Cubism," Piet Mondrian Centennial Exhibition for this development.

9. Illustrated in M. Seuphor, Piet Mondrian, Life and Work (New York: Harry N. Abrams, 1956), classified catalogue nos 169-174 (hereafter: S: cc).

10I.e., in letter cited note 3, above.

11.  E.g., S:cc 271-274; for documented instances of compositional drawings being used circa 1912-1914 for "Paris Facade" paintings, see R.P. Welsh, ex. cat. Piet Mondrian 1872-1944 (Toronto: Art Gallery of Toronto, 1966), pp.144-155.

12. Cf., Two Mondrian Sketchbooks, esp. pp. 65-66, and Schoenmaeker's Mensch en Natuur (Bussum: 1913), in both of which texts the concept of a successful "life" is predicated on a balance of vertical-horizontal, male-female and spiritual-material forces.

13. Ibid., p. 71; the original Dutch, moreover, includes the spirit-matter duality (i.e., "geest-stof"), as represented by the artist and his materials.

14. "True Vision," p. 10.

15. Ibid., p. 17.

16. Ibid., p. 13.

17. See R. Rosenblum, Modem Painting and the Northern Romantic Tradition: Friedrich to Rothko (New York: Harper and Row, 1975), pp. 173-194.

18. E.g., as illustrated in a diagram of the Hindu Cosmology which accompanied Madame H.P. Blavatsky's two-volume first testament of Theosophy, Isis Unveiled (first edition. New York: 1877; reprint edition, Wheaton, Ill.: Theosophical Publishing House, 1972).

19. "True Vision," p. i3.

20. Included in Plastic Art and Pure Plastic Art (see note 2, above), pp. 38-48.

21. "True Vision," p. 13.

22. The second checkerboard painting, With Dark Colours, is S:cc 293. Viewed as a square, the underlying grid of Lozenge with Gray Lines of course conforms to the octopartite divisions of a chessboard rather than the ten-by-ten rows of squares on a checkerboard.

23. For a fuller discussion of this point, see R.P. Welsh, "Landscape into Music, Mondrian's New York Period," Arts Magazine XL: 4 (February, 1966), pp. 33-39.

24. In this letter (at the De Stijl archive, estate of the late Nelly van Doesburg), Mondrian wrote, "I much sympathize with your idea that 'the negative' should comprise the fourth dimension, but I cannot write about this." Possibly Van Doesburg's "negative" was the usage in certain works of a black ground which he adopted from Bart van der Leek in 1917; see R.P. Welsh, "Theo van Doesburg and Geometric Abstraction," Nijhoff, Van Ostaijen, "De Stijl," ed. F. Bulhof (The Hague: Martinus Nijhoff, 1976).

25. In a letter of August 1,1919, apparently his first to Van Doesburg after returning to Paris, Mondrian suggested shortly placing in De Stijl a reproduction of the last painting (i.e.,  "laatste ding") that he had shown Van Doesburg, "among other reasons just because a starry sky provided the first inspiration for making it." Indeed, that very month (De Stijl n: 10, 1919, as "Illustration xix") a coloured variant of Lozenge with Gray Lines (namely, S:cc 299) was reproduced.

26. By M.L. Teuber, "Introduction," ex. cat. Paul Klee: The Bauhaus Years (Des Moines: Art Centre, 1973), pp. 6-17.

27.  See F. Schumann, "Beiträge zur Analyse der Gesichtswahrnehmungn," Zeitschrift fur Psychologie xxiii (1900), pp. 1-32.

28.  Yet the question remains moot. Of the several volumes dedicated to such topics as the fourth dimension which were listed by Van Doesburg in the April 1919, issue of De Stijl (II: 6, pp. 70-72), as available on request via mail  to the periodical's subscribers, none of those consulted (alas, J.B Ubink De Vierde Dimensie, which promised to be the most rewarding of the listed titles, because it apparently was of a popularized character, proved unavailable in major Dutch libraries), contained diagrams or discussions relevant to this issue  It even remains uncertain whether Mondrian read such a favourite author of Van Doesburg as the distinguished mathematician, Henri Poincaré, since the name does not appear in Mondrian's known writings.

29.  See The Analysis of Sensations (New York: Dover Paperback, 1959), p. 106 (original German edition, 1886); also Schumann, op.cit., pp. 17-19.

30.  As documented in ex. cat. Piet Mondrian 1872-1944. p 198; ill'd in colour in H.L.C. Jaffe, Piet Mondrian (New York: Harry N. Abrams, 1970), p. 147. The Gestalt principle of closure, which denotes, among other things, a human tendency to read interrupted geometric configurations as if completed, was codified by Max Wertheimer in 1923 ("Untersuchungen zur Lehre von der Gestalt,” Psychologische Forschung iv: pp. 301-350), having been anticipated by Schumann in 1900 (op.cit., pp. 12-15). However apart from the unlikelihood that Mondrian knew any such scientific source text, his Composition with Yellow Lines is far more complex in structure than a reading merely as an illustration of closure would purport.

For example, one may also explore the formal transmutations the painting undergoes if one focuses alternatively upon (1) the individual lines as dividers of space rather than edges of an imagined square; (2) the lines read in perspective  (since, if the 45° angles of termination at the picture edge are imagined as receding in space, the line surfaces will seem to tilt outward); (3) the tensions and visual adjustments which occur among any two or more of the, in fact disproportionate lines, opposite or adjacent, whether viewed simultaneously or successively; (4) the  containing  figure, read as an octagon (i.e., four yellow hues and connecting picture-edge segments); and even (5) the unstable double image which occurs if one slightly "crosses" one’s eyes. While all such readings of course do violence to the final sense of equilibrium sought by the artist, it is difficult to believe that he was himself totally unaware of these possibilities, or of the dynamic, kinetic visual experiences which they induce.

31. The only exceptions to this rule are three paintings conceived in the mid 1930s, and proportioned with the height twice as great as the width (i.e., S:cc 385-387). However, in all three, the gap between two dominating and unbisected vertical lines is too broad to allow for their categorization as illustrative of the double-line concept.

32. This evolution is treated more fully by the present writer in ex. cat. Piet Mondrian 1872-1944, pp. 196ff.

33. For Mondrian's art theory and view of the tragic in the 1920s and early 1930s, see Seuphor, Piet Mondrian pp. 166-168, and H.L.C. Jane, De Stijl 1917-31, The Dutch Contribution to Modem Art (London: Tiranti, 1956) pp. 209-258. Regarding the meaning of the double line A.H. Nijhoff ("Introduction," ex. cat. Marlow Moss; Amsterdam: Stedelijk Museum, 1962, n.p.), a close personal friend of Moss, relates how upon first publicly exhibiting a double-line painting, circa 1930-1931, the artist received a written request for an explanation from Mondrian. Her illustrated reply cited three basic reasons: (1) single lines produce an impression of planar surfaces; (2) single lines render the composition static; and (3). double, or multiple, lines have a dynamic effect by ensuring "a continuity of related and interrelated rhythm in space." Such reasoning certainly would have appealed to Mondrian, whether or not one considers Moss the principal stimulus for Mondrian’s adoption in 1932 of the double-line convention (i.e., with S:cc 368); although Composition with Yellow Lines is dated 1933, according to documentation kindly supplied by H. Henkels of the Hague Gemeentemuseum, it was commissioned and presumably begun the previous year, which allows it to be considered the final major "single-line" painting.

34. The Cas Oorthuys photograph of Mondrian’s 1937 studio shows the Tate painting (in New York misdated by the artist "39-42"), and Composition 12, plus another against which the latter leans, to have been then in an unfinished state, presumably that in which the paintings were brought to London then New York. In contrast, not only Composition with Small Blue Rectangle, but the canvas seen fragmentarily at the left of the photograph, appear as finished, even coated with varnish. The latter example, moreover, might represent the painting dated 1937-1942, recently given by Sidney Janis to the Museum of Modern Art New York (ill 26 in ex. cat. Mondrian; New York: S. Jams Gallery, 1957) if one predicates an even greater number of additions than ascertainable in the Tate example. The assumption that Mondrian did indeed transform several finished European paintings for the 1942 Dudensing Gallery exhibition is demonstrable from two forms of evidence. First, two of the three vertical format paintings of the mid-1930s (namely S:cc 386-387; see note 31 above exhibited publicly in 1936, respectively in New York and London, (e.g., see A.H. Barr Jr., ex cat. Cubism and Abstract Art [New York: Museum of Modern Art, 1936], p.152, ill 158) but now contain additional line segments and unenclosed colour blocks, doubtless added before at least one of them was included at the Dudensing exhibition as indicated by the double date, 1935-1942. Second, among other possible instances, a painting now owned by the Kunstsammlung Nordrhein-Westfalen, Dusseldorf (S:cc 396), bearing the date "35-42" (but probably begun only circa 1937, as indicated by Mondrian's stretcher inscription verso) would appear to be a transformed version of the middle painting, illustrated p. 34, in Plastic Art and Pure Plastic Art. Similarly, the 1936-1942 painting, now at the Moderna Museet, Stockholm (S:cc 412), quite likely is the same painting, illustrated in its preliminary state, circa 1937, i.e. as S:cc 292, and Plastic Art, p. 45, at left.

The explanation for these cases of double exposure would seem to reside in Mondrian's habit of having a number of paintings, which he executed in Paris photographed by the late Marc Vaux, at least some of which reproductions accompanied him to New York, and were unwittingly published posthumously, as still extant untransformed canvases (my thanks to Michel Seuphor, who in recent conversation supplied the information about Marc Vaux, and who now agrees with my belief in several such instances).

35. Apart from the Ottawa, Dusseldorf, Stockholm, Hague, and Tate Gallery examples already discussed, an unfinished composition (S:cc 433, where for lack of inscribed date, or other evidence to indicate Mondrian’s preference,  it was reproduced upside-down)  can also be ascribed in genesis to circa 1936-1937, since it appears in its present state in another, as yet unpublished Cas Oorthuys photograph, taken in the 1937 Mondrian Paris studio.

36. For an alternative interpretation of Mondrian s evolution of the grid principle, see F. Saint-Martin, Structures de l’Espace Pictural (Montreal: Editions HMH, 1968), pp. 83-116.

Photograph Sources

Colour: The National Gallery of Canada, Ottawa. Black-and-white: All photographs supplied by owners with the following exceptions - Oliver Baker Associates. Inc. New York, 5; A. Dingjan, The Hague, I; B. Frequin, Voorburg, The Netherlands, 16; The Solomon R. Guggenheim Museum, New York, 12; Cas Oorthuys Archive, Amsterdam, 18; Robert Welsh, Toronto, 3, 7.

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