Mondrian: Order and randomness in abstract painting

Meyer Schapiro
Modern Art
(Nov. 1978)


Mondrian’s abstract paintings appeared to certain of his contemporaries extremely rigid, more a product of theory than of feeling. One thought of the painter as narrow, doctrinaire, in his inflexible commitment to the right angle and the unmixed primary colors. We learn that he broke with a fellow-artist and friend who had ventured to insert a diagonal in that fixed system of vertical and horizontal lines. “After your arbitrary correction of Neo-Plasticism,” he wrote to van Doesburg, “any collaboration, of no matter what kind, has become impossible for me,” and withdrew from the board of the magazine De Stijl, the organ of their advanced ideas.1

Yet in the large comprehensive shows of his art one discovers an astonishing range of qualities, a continuous growth from his twenties to his last years in fertile response to the new art of others and to a new milieu. Even while holding strictly to the horizontal and vertical in the painted lines, Mondrian brought back the abhorred diagonal in the frequent diamond shape of a square canvas. Diagonal axes are implicit too in his placing of paired colors. And in his late work he deviated from his long-held principle of the single plane by interlacing the lines to suggest a layered grid in depth. If his abstract paintings of the 1920s and 1930s seem dogmatically limited in their straight forms, these constant elements, through carefully pondered variation of length, thickness, and interval, compose a scale of forces that he deploys in always individual combinations. When studied closely, the barest works, with only a few units, reveal his canny finesse in shaping a balanced order; that variety in the sparse and straight is a ground of their continuing fascination. One need not analyze that structure, however, to sense its precision and strength. These qualities come to the eye directly like the harmony of a Greek temple. His gravely serious art unites in its forms the large regularities of architecture as a canonical constructed order with a complexity of relations inherited from the painting of nature and the city scene. The persisting white field, in heightened contrast to the black lines, is a luminous ground — it has what may be called after Keats: “the power of white Simplicity” — and, in its division by those lines, provides a measure of the rhythm of the enclosing rectangles.

Like Picasso’s art, Mondrian’s would have to be characterized very differently according to one’s choice of a particular phase as typical. Before the constructive abstract art by which he is best known, his works had been in turn impressionistic, romantic, lyrical, visionary, and symbolic; and in his last years, at seventy, after that severely intellectual style, his paintings became surprisingly sensuous and elated. In assimilating before 1914 the most advanced art of his time, he stood out unmistakably as a painter with his own qualities and powers. Moving from Holland to Paris and later to London and New York, this ascetic artist reacted to each new environment with a quiet enthusiasm, inventing new features that transformed the face of his art. When he worked in the style of Picasso and Braque in 1911 to 1913, he was not far behind them, having absorbed the most recent stage of their rapidly evolving art, and was soon able to move on to more strictly abstract forms of his own invention. Mondrian’s warm embrace of Cubism was the more surprising since he was forty then, with a long-matured practice that would have seemed to discourage the change to a style so different in principle from his own. Even more remarkable is that in adopting this challenging art from painters younger than himself, he derived from it conclusions still more radical, which were to stimulate and guide painters in Europe and America in the following decades. His later work was an outcome of reflection and a firm will to rigor, in keeping with a philosophizing habit and long meditated ideals. Few artists in our century have displayed so ardent a growth.


Mondrian wrote in more than one article that his goal was to achieve an art of “pure relations.” These, he believed, had been “veiled” in older painting by the particulars of nature which could only distract the viewer from the universal and absolute in art, the true ground of aesthetic harmony.

I wish in this essay to explore closely several of his abstract works in order to bring into clearer sight the character of those “pure relations” and to show their continuity with structures of representation in the preceding art. For this a minute analysis is necessary. It may be tedious or seem superfluous to one who grasps with feeling the order of a work of Mondrian on immediate view. I shall risk it in the belief that it will also bring us nearer to his sensibility and thought.

In a painting of 1926 in the Museum of Modern Art labeled Composition in White and Black, what seems at first glance a square set within a diamond square — a banal motif of decorators and doodlers — becomes to the probing eye a complex design with a subtly balanced asymmetry of unequal lines. We see the square as partly covered and extending into an imaginary field beyond the diamond canvas. If modeling and perspective have been given up, another cue for depth comes into play in this flat painting on the impenetrable plane of the canvas: the overlapping of forms. The intercepting edge advances and the intercepted square recedes as if passing underneath the edge. The whole appears then as a cropped representation of an object in a three-dimensional space. The missing parts are cut off from view at the limits of the diamond field. Only at the upper left corner of the square is the angle closed; but its vertical and horizontal lines cross at that point and are prolonged just enough for us to suppose that what we first perceived as a partly masked square belongs to a larger whole, a lattice or grid formed by bars of varied thickness.2 We are induced by that single crossing to imagine a similar completion of the other bars and their continuity beyond the square. The black grid seems to exist in a space between the plane of the diamond and the white voids enclosed by the painted bars.

Even if we fix our attention on the canvas as a limited plane surface with a painted set of flat marks complete in themselves as a balanced asymmetric design, another mode of spatial intuition is soon aroused: our habitual response to recognizably incomplete forms. The black bars are envisioned unreflectively as parts of a whole continuing beyond the limits of the overlapping diamond field, although no familiar object has been depicted (unless we regard the thick lines of the “abstract” square as a concrete object like the surface of the canvas itself). Each black line is seen then as an intercepted side of a complete square, just as in a perspective view we identify a partly covered object with its whole. The diamond form of Mondrian’s canvas reinforces this effect by the strong contrast of its diagonal edges with the painted lines of the square and by providing between the angles, and especially those above and below, a much greater span than between the parallel lines of the inscribed form. The latter stands out even more decidedly from a larger field in which two lines of the square cross and four triangles are marked as opposing shapes.

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El Lissitzky pangeometrie

El Lissitzky on “pangeometry” and art (1925)

In the essay A. and Pangeometry  El Lissitzky analyses the changing role of perspective in art and introduces axonometric projection (or parallel perspective) as a new means to represent and perceive space. It was first published in German in Europa-Almanach, (Carl Einstein and Paul Westheim, Kiepenheuer Verlag, Potsdam, 1925, p.103-113) and was reprinted in 1984.

This English translation was published in the book El Lissitzky. Life – Letters – Texts, Lissitzky-Küppers, Thames & Hudson, London, 1992 (out of print). The blog The Detached Gaze posted it a few months back.

NOTE: Abbreviations: A. = art, F. = form.

europa-almanachKunst und pangeometrie lissitzky

Art and pangeometry

El Lissitzky
Europa Almanach
Potsdam (1925)

Seeing, of course, is also an A.

In the period between 1918 and 1921, a lot of old rubbish was destroyed. In Russia we also dragged A. off its sacred throne “and spat on its altar” (Malevich 1915). At the first Dada-event in Zurich, A. was defined as “magical excrement” and man as the “measure of all tailors” (Arp).

Now after five years (five centuries in the old chronology) in Germany for example, Grosz brings only one reproach upon himself: “our only fault was that we ever took the so-called A. at all seriously.” But a few lines further on he writes: “Whether my work is therefore called A. depends on the question of whether one believes that the future belongs to the working classes.” I am convinced that it does, but neither this conviction nor the excrement and the tailors are universal criteria for A.

A. is a graduated glass. Every era pours in a certain quantity: for example, one puts 5 cm of Coty perfume, to titillate the nostrils of fashionable society: another throws 10 cm of sulphuric acid into the face of the ruling class; yet another pours in 15 cm of some kind of metallic solution which afterwards flares up as a new source of light. So A. is an invention of our spirit, a complex whole, combining the rational with the imaginary, the physical with the mathematical, √1 with √-1. The series of analogies which I am going to bring to your attention is put forward not to prove — for the works themselves are there for that — but to clarify my views. The parallels between A. and mathematics must be drawn very carefully, for every time they overlap it is fatal for A.

Planimetric space

Plastic F. begins, like elementary arithmetic, with counting. Its space is the physical two-dimensional flat plane. Its rhythm — the elementary harmony of the natural numerical progression 1, 2, 3, 4, …

Man compares the newly-created object [1] — for example, the relief, the fresco — with natural objects. If, for example, in a relief, the animal in front covers a part of the animal behind, this does not mean that that part has ceased to exist, but that there is a distance, space, existing between these two bodies.

image1_a_and_pangeometry_el_lissitzky_1925 image2_a_and_pangeometry_el_lissitzky_1925

One comes to know from experience that there is a distance existing between individual objects, that the objects exist in space. This two-dimensional plane ceases to be just a flat surface. The plane begins to presume upon space and there arises the numerical progression, 1, 1½, 2, 2½ …

Perspectival Space

The space of the plane developing into view lengthens and widens, increases to a new system, which finds its expression in perspective. It is generally accepted that perspective representation is the clear, objective, obvious way to represent space. It is said that, after all, the camera also works perspectivally and at the same time one is forgetting that the Chinese once built the object-lens with concave instead of convex lenses as we have, and so would also have produced an objective and mechanical image of the world, yet quite a different one. Perspective has comprehended space according to the concept of Euclidean geometry as a constant three-dimensional state. It has fitted the world into a cube, which it has transformed in such a way that in the plane it appears as a pyramid. [2] The tip of this visual pyramid either lies in our eyes — therefore in front of the object — or we project it on to the horizon — behind the object. The former concept was chosen by the East, the latter by the West.

Perspective defined space and made it finite, then enclosed it; but the “universal set” [3] of art became richer. Planimetric space provided us with the arithmetical progression. There the objects stood in the relation: 1, 2, 3, 4, 5…In perspective space we acquired a new geometric progression; here the objects stand in a relation: 1, 2, 4, 8, 16, 32… Up to the present time the “universal set” of A. has acquired no new enrichment. In the meantime science undertook fundamental reconstructions. The geocentric Ptolemaic conception of the universe was replaced by the heliocentric system of Copernicus. The Euclidean conception of fixed space was destroyed by Lobatschewski, Gauss, and Riemann. The impressionists were the first to begin exploding the hereditary notion of perspectival space. The cubist method was more decisive. They transposed the space-confining horizon to the foreground and identified it with the area being painted. They made improvements to this fixed area through psychic features (walls covered with wallpaper and so on) and by destroying some elementary forms. They built from the perspective plane forward into space. The latest sequels are: the reliefs by Picasso and counter-reliefs by Tatlin. Continue reading

ladovsky's class1

Space architecture: Training the Soviet avant-garde (1921-1930)

The “space” course for
architects at Vkhutemas

Spatial modeling

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El Lissitzky proun 1c 1919a banner


The “way station” between
painting and architecture

Image: El Lissitzky,
PROUN 1-C (1919)


From “Theses on the PROUN: From painting to architecture” (1920)

Not world-illusion
but world-reality

We have named PROUN a station on the path to the construction of the new form. […] From being a simple depicter the artist becomes a creator (builder) of forms for a new world — the world of objectivity. This does not mean the creation of a rivalry with the engineer. Art has not yet crossed paths with science.

2. PROUN is understood as the creative construction of form (based on the mastery of space) assisted by economic construction of the applied material. The goal of PROUN is progressive movement on the way to concrete creation, and not the substantiation, explanation, or promotion of life.

The path of the PROUN does not lie within the narrowly limited, fragmented, and isolated scientific disciplines — the builder consolidates them all together in his own experimental investigation.

The path of the PROUN is not the incoherent approach of separate scientific disciplines, theories, and systems, but is rather the straightforward path of learned influence over reality. […]

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