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Piet Mondrian’s ideal of an equivalence of opposites
Opposite concepts are an expedient devised by human thought to reduce and concentrate the vast range of variation present in nature. Given the impossibility of conceiving and representing the real extension and immense variety of the world, the human mind has recourse to the two most different values. It is a device serving to make finite – i.e. thinkable and comprehensible (in the sense of containing, encompassing) – an extension that is actually infinite and hence unthinkable as a whole.
To give a concrete example, there is a virtually infinite range of grays between black and white that we really cannot conceive in all its real breadth and variety. The reference to opposite values is a mental stratagem serving to encapsulate the multiplicity of reality. It should always be remembered that this reduction is not the reality of nature but rather of thought.
The Neoplastic compositions of the early 1920s provide a necessarily limited exemplification of the variety of the world, since the canvas can only contain a certain number of forms and colors. The Neoplastic lines thus began to continue uninterruptedly as from 1923 in order to allude to the wealth of forms and colors of real space, which no canvas will ever be able to present exhaustively.
The interaction between opposites such as multiplicity and unity goes on with new works.
As we have seen in the previous page, along with the compositions that feature a large square enclosed by four sides:
1922
1922
1922
Some works of the same period present a large or medium-sized square left open on one or two sides:
This trend took shape around 1925, when some canvases of rectangular format began to present the common characteristic of an opening on one side of the large square previously bounded on all four sides. The square field appears to expand beyond the finite plane of the canvas:
Tableau X with Yellow, Black, Red and Blue, 1925, Oil on Canvas,
cm. 42,5 x 49
Composition with Red, Black and Gray, 1927,
Oil on Canvas,
cm. 56 x 56
Composition with Red, Yellow and Blue, 1927,
Oil on Canvas,
cm. 35 x 38
Open up the square to the dynamic continuity of the lines; compenetrate finite space (the closed square) with infinite space (virtually expressed by the lines).
This tendency to open up and expand the square beyond the boundary of the canvas is developed in new lozenge compositions Fig. 4 and Fig. 5:
Tableau N. 1 – Lozenge with Three Lines and Blue, Gray and Yellow
Tableau N. 1, Lozenge with Three Lines
and Blue, Gray and Yellow, 1925,
Oil on Canvas, cm. 80 x 80
One horizontal and two vertical lines run across the canvas and divide it into sections. The horizontal and the right vertical appear to be of equal thickness while the vertical on the left is thicker, which seems to make up for its lesser extension. The thickness of a line can also serve in a space moving toward ever-greater synthesis to calibrate the weights and influence the overall economy of the composition.
The closed square to be seen in the central area of Lozenge Composition with Red, Black, Blue and Yellow now becomes a field that is open at the top and appears simultaneously to expand also toward the right by virtue of the fact that the area corresponding to the right corner of the lozenge is the same shade of white as the square field, whereas the area below is gray. A small yellow plane appears in the lower right section and the overall balance is restored toward the left by the thicker line and the blue plane.
Diagram A
Diagram B
Examination of the horizontal line in relation to the right vertical reveals a rectangular area extending upward (Diagram A), while the relationship between the same horizontal, the left vertical and the blue plane tends to generate a horizontal field that the right corner of the lozenge draws toward itself (Diagram B). The eye is drawn respectively downward and upward by the horizontal (Diagram B) and the vertical (Diagram A) areas, the relationship between which generates an indefinite square field that expands and contracts under the influence of the contending directions.
The space as a whole is in a state of unstable equilibrium and attains unified expression for an instant through the progressive and almost simultaneous recombination of parts, none of which – it should be noted – constitutes in itself a definite unitary synthesis like the square bounded on four sides:
Tableau N. 1, Lozenge with Three Lines
and Blue, Gray and Yellow, 1925
The virtual square expands upward beyond the perimeter of the canvas, projected ideally toward the infinite, while the notes of color (above all the blue on the left) draw the eye back toward the lower central area. White symbolizes the spiritual and the primary colors the natural in the Neoplastic vocabulary.
We can therefore imagine this composition as a metaphor of the relationship between the absolute drives of the spiritual drawn back toward the concrete by the part of man that is closest to the natural world: a dynamic relationship between opposite drives that attain equilibrium for an instant through reconciliation.
Composition with Two Lines and Blue
On a new canvas (Fig. 5) the space is pared down even more to the bare essentials with two perpendicular lines running across the canvas and alluding to a square field now open on two sides. The top and right corners of the lozenge seem to expand the inner area of the “square”:
Composition with Two Lines and Blue, 1926,
Oil on Canvas, Diagonal: cm. 84,9 x 85
It is, however, legitimate to wonder whether this is still a square or instead an evocation of a possible square that has already moved outside our visual field before being able to make its appearance.
The lines expand the white field to infinity; the blue draws the space back toward a more concrete dimension. In the meantime, we see that all the lines now continue resolutely beyond the edges of the canvases in order to evoke the continuity of space manifested in less explicit form since 1919.
The square opens to reappear in enclosed form
While the large square opens up and expands in various works of this period, Mondrian was working on other compositions (Fig. 6 and Fig. 7) where a large square again appears in a closed form clearly defined by four sides:
Tableau I – Lozenge with Four Lines and Gray
In Fig. 6 the square field is again defined by four lines. The square expands slightly beyond the perimeter of the canvas toward the right and the bottom. The upper and left sides are of equal and the lower and right of increased thickness. The field outside the square in the lower section is gray:
Tableau I, Lozenge with Four Lines and Gray, 1926, Oil on Canvas,
Diagonals: cm. 113,7 x 111,8
Note how the point of intersection between the horizontal and vertical lines becomes less visible inside the canvas. Two lines still meet in the upper left section but practically on the edge. The other lines express no points of visible opposition.
Composition 1 – Lozenge with Four Lines
Fig. 7 presents a square defined by four sides. We use the term “square” in order to facilitate communication even though this is not really the shape if considered in strictly geometric terms. We shall, however, continue to describe it as such for the sake of convenience.
Composition 1, Lozenge with Four Lines, 1930, Oil on Canvas, cm. 75,2 x 75,2
The meeting points of the opposite directions are practically no longer visible in this work. The contrast and opposition between vertical and horizontal lines is resolved here in a continuous space that finds unity by following the square form uninterruptedly from one side to the other. For the first time, all the four lines forming the square field differ in thickness, which increases as we proceed clockwise from the vertical on the right. We thus see a square that progressively tends to expand beyond our field of vision (the canvas).
The tendency toward expansion generated by the position of the lines (above all the upper horizontal) is counterbalanced by an opposite tendency toward concentration. The line moving furthest away (upward) is in fact also the thickest and therefore the one that exerts the greatest downward pressure. Proceeding clockwise from the right vertical side, we see a square that grows heavier as it exits the canvas, i.e. tends to become more solid and permanent while it disappears: a simultaneously changing and comparatively constant space.
In this phase Mondrian is like a composer who gradually reduces the orchestra to a solo instrument, an almost imperceptible sound that can still be varied in an effort to express the whole. It is relations that count in Neoplastic space rather than things in themselves. In a white field crossed by three black lines, a slight variation in thickness becomes more obvious than a red or yellow in a field full of colors.
“Weniger ist mehr” (less is more) was the credo of Mies van der Rohe. It is obviously necessary to know what this “less” that succeeds in expressing “more” actually consists in. The approach is in any case somewhat rare nowadays, when many aspirant artists resort so frequently to redundancy in order to disguise a lack of substance.
Square fields newly closed on all four sides also appear around 1927 in rectangular format canvases:
Komposition II with Red, 1926, Oil on Canvas,
cm. 50,8 x 50,8
Composition N. III with Red, Blue, Yellow, 1927,
Oil on Canvas, cm. 35,5 x 38
Composition with Red, Yellow and Blue, 1927,
Oil on Canvas, cm. 51,1 x 51,1
Whether open or closed, the large squares appearing in all the works produced during the first half of the 1920s are always counterbalanced by planes with a marked horizontal or vertical predominance as seen in Fig. 8 (plane red), in Fig. 9 (blue plane) or in Fig. 10 (yellow plane) but also by planes in which the imbalance between the opposing directions is reduced, i.e. attains proportions verging on the square as seen in Fig. 9 (yellow and red planes) as well as in Fig. 10 (lower section of the red plane).
When they approach and/or attain the proportions of a square they seem intent on competing for the space with the large white square (Fig. 10), which therefore appears less absolute because the moment in which the opposites attain equivalence is no longer expressed solely through a single large square but also in the form of smaller squares.
A great date in his life will be 1926. That year he received a visit from Miss Katherine S. Dreier, who bought a large diamond-shaped canvas from him, which was exhibited again that year in Brooklyn at the International Exhibition of the Société Anonyme.
In the book which appeared on this occasion, and in which almost all the representatives of abstract art from all over the world had their place, the courageous organizer wrote: “Holland has produced three great painters who, while being a logical expression of their country, rose above it by the first was Rembrandt. the second was van Gogh, the third is Mondrian.
One realizes Rembrandt’s strong personality when one compares him with the men of his time, with men as great as Frans Hals. Van Gogh also contrasts strongly with Mauve, Israëls and the very good painters of his time.
And now here is Mondrian again, who, starting from this strongly individualistic expression, has reached a clarity that before him was never achieved. To have written this in 1926 is a great proof of clairvoyance and, in my eyes, an immense title of glory.
Michel Seuphor, Piet Mondrian, Sa Vie, son Oeuvre, 1956
No mathematics
Neoplastic squares are never really such because it is the eye rather than mathematics that decides on their proportions. Their extension can be slightly more vertical in some cases and horizontal in others depending on the spatial context in which they are developed. Every canvas presents a different square that serves, however, to meet the need for equilibrium in that particular composition and not in others.
There are no elements in Neoplastic space endowed with absolute validity. It is therefore not the square in itself but the whole, i.e. a space that starts from a condition of change, attains momentary equilibrium, and then flows back into the unstable alternation of situations. If constancy predominates, the space is atrophied in a static square and bears little resemblance to life.
Conversely, if change prevails, the space is in danger of becoming chaotic and appeals less to the human mind. The subtle balances produced in Neoplastic space are a transposition of the far more complex and never achieved equilibriums of existence. How many times in our lives have we had the impression of being able to attain a stable and lasting balance that is then always challenged by existence?
Composition with Red, Yellow and Blue
Fig. 10 presents a vertical yellow plane with the proportions of a linear segment developing around a large area tending toward the square. We then see a horizontal blue area where the imbalance between horizontal and vertical is less marked than in the yellow, and finally a red field where the horizontal component increases again and the imbalance between the opposites is further reduced:
Composition with Red, Yellow and Blue, 1927, Oil on Canvas, cm. 51,1 x 51,1
A horizontal line divides the red field into two areas, the lower of which presents square proportions while the other is a rectangle of greater horizontal development.
On rereading this as a single sequence, we see a vertical yellow plane that passes through a horizontal blue field, gradually attains an equilibrium of vertical and horizontal (the red square), and then opens up again to predominance, this time horizontal, with the red rectangle positioned above. The marked predominance of one value gives way to a momentary equilibrium of opposite values that then opens up again to new forms of predominance and imbalance.
All this happens around a large white square that appears to constitute a sort of ideal vision or model of absolute equilibrium attained by the various areas of different colors in a temporal and hence relative succession that could be described as reflecting everyday reality. The ideal vision of absolute equilibrium is expressed in white, a color Mondrian identified with the spiritual, while the relative vision developed in a space-time sequence is expressed with the three primary colors, which the artist identified with the natural.
In 1921 financial problems induced Mondrian to consider abandoning painting altogether. However, various friends in Holland helped him to obtain commissions either for copies, watercolors and drawings of flowers which finally enabled him to keep his head above water.
In the same year a painting by Mondrian was included in the exhibition “Les Maitres du Cubisme” organized by Léonce Rosenberg at his Galerie de l’Effort Moderne in Paris. Rosenberg, unable to sell Mondrian’s work, promised Mondrian the purchase of six paintings. This promise was not kept because of the failure of the exhibition.
In 1923 Mondrian met the Belgian writer, poet, painter and art theorist Michel Seuphor who became Mondrian’s colleague and friend. In the first Mondrian biography (1956) Seuphor writes: “Once he had laid the foundations for the new language called Neoplasticism, Mondrian worked to explore all its possibilities without ever exhausting its potential. How many times, during this long Parisian period, did I have to listen to comments referred to Neoplastic compositions such as “laziness of spirit”, “stupid stubbornness”, “incapacity for renewal” etc.? I used to caricature these kind of remarks by ironically stating that Mondrian did in fact repeatedly paint only one work.”
Michel Seuphor, Piet Mondrian, Sa Vie, son Oeuvre, 1956
Interpenetrating straight lines and square, infinite and finite
We spoke earlier of works in which the large square form opens up and its inner field expands beyond the finite area of the canvas. Let us now consider the following sequence of works. In Fig. 1 the large white field of square proportions is nearly all contained inside the perimeter of the painting. The large square expands toward the left (Fig. 11) and is mostly outside the canvas in Fig. 12, where the areas to be seen are in actual fact vertical rectangles:
Tableau X with Yellow, Black,
Red and Blue, 1925,
Oil on Canvas, cm. 42,5 x 49
Komposition IV with Red, 1926, Oil on Canvas,
cm. 30 x 40
Composition with Yellow and Red, 1927, Oil on Canvas,
cm. 35 x 52
If we, however, consider in Fig. 12 all the area of space between the two horizontal lines, we realize that it combines with the two vertical sides of the canvas to form a new shape tending toward the square, a square with a vertical line running through it. The same thing is to be seen in some later works (Fig. 13 and 14):
Large Composition with Red, Blue and Yellow, 1928, Oil on Canvas,
cm. 80 x 123
Composition 1 with Red, 1931, Oil on Canvas,
cm. 54,7 x 82,5
There is a vertical line running through the square in these new compositions.
Indications of infinite space (lines) appear inside the finite space (the square); the dynamic element (the line) penetrates the constant element (the square):
We have examined some works pertaining to compositional layout A. Let us now have a close look at three works based on compositional layout B:
Composition with Yellow and Red
Composition with Yellow and Red, 1927,
Oil on Canvas, cm. 35 x 52
Two horizontal lines and the two vertical edges of the canvas form a large square. The square area is left open on either side to continue with the two horizontals beyond the finite space of the canvas.
The vertical line combines outside the square with the lower horizontal to generate a red rectangle and with the upper to form a small yellow square. The two colored planes perform the function of accentuating the asymmetrical nature of the whole but also of emphasizing the square block of the central area in a complementary fashion, the red at the bottom occupying the part not filled by the yellow at the top and vice versa. Added together, the two colored planes would express the absolute continuity of the horizontal lines, which are instead disrupted and distanced by the intervention of the vertical.
It is necessary to imagine the two horizontals an instant before the appearance of the vertical, when they presumably formed a single line which splits in two by the sudden interaction with the vertical to form a white central block that works with the edges of the canvas to generate the large square.
The vertical line shatters the uninterrupted continuity of the horizontal, which thus shifts from an absolute to a relative condition in which one part appears as red and another as yellow; one is situated below and the other above; one partakes more of the horizontal (the red plane) and the other to the same degree of both contrasting directions i.e an equivalence of opposites.
It could be said that the interaction between the vertical (symbolizing the spiritual, i.e. the subject) and the horizontal (symbolizing the natural universe) gives birth in the twinkling of an eye to all the variety of shapes and colors, just as the interaction between an observer and the continuity of the natural landscape generates a whole variety of parts that we develop into mental content and then call reality.
As it remains open on either side, the space between the two horizontal lines is in a state of unstable balance between a square shape (if seen in relation to the edges of the canvas) and a rectangle expanding beyond the perimeter of the canvas (if the eye is left free to follow the two horizontal lines in their continuation toward virtually infinite space).
A relationship arises spontaneously between the red rectangle, the yellow square, and the larger, unstable square shape in the middle, which would close up in the absence of the vertical line and revert to its prior state, with the horizontal lines reconnecting to form a single and once again absolute line of horizontal tension, red and yellow dissolving into white, and the relative again becoming absolute also in terms of color.
Large Composition with Red, Blue and Yellow
Large Composition with Red, Blue and Yellow, 1928, Oil on Canvas, cm. 80 x 123
Fig. 12 leads to Fig. 13, where the layout is analogous but the resolution different.
The vertical line is shifted further toward the center and two horizontal lines generate areas of different proportions including a large square, as in Fig. 4. The vertical line divides the square into two vertical rectangles, one white and the other blue. We see a yellow plane in the lower section and in the upper section a red plane that works together with the blue one to give the composition a strongly asymmetric character.
Reading from the bottom up, we see a yellow horizontal rectangle that becomes a blue vertical one and then a red area which is slightly horizontal. With respect to the other two rectangles, the opposing directions approach equivalence in the red plane.
Moving upward from the bottom, the vertical line guides a development of the composition that shows the three colors and the opposing directions generating different and complementary situations that are then encompassed in the large square to be glimpsed between the two horizontal lines.
Equivalence is attained here for an instant between the opposite directions, while in terms of color the square already appears to be on the borderline between white and blue.
The square form appears to be torn between the blue rectangle, which pushes it from inside toward the right, and the yellow and red rectangles, that pull it from outside toward the left.
Composition 1 with Red
Composition 1 with Red, 1931, Oil on Canvas, cm. 54,7 x 82,5
Fig. 14 reiterates the compositional development of Fig. 13 while purging it of color. The only one of the three primary colors to be seen here is red, which acts as an accent, while most of the composition develops through a rhythmic arrangement of white planes.
In comparison with Fig. 13, the vertical line typical of compositional layout B is shifted still further toward the center of the canvas. Starting from the red plane and following the lower horizontal line, the space opens up toward the right while: being simultaneously pushed upward by the vertical, thus giving rise to a square form divided into a number of areas (Fig. 14 Diagram).
Fig. 14 – Diagram: In the large central square field we see a vertical rectangle (Diagram B), a horizontal rectangle (C), and one in which the opposite directions approach equivalence (A), which is finally attained in the large square field constituting a synthesis of three different situations.
The proportions of the small red plane are similar to those of the canvas as a whole. When we contemplate the variety present in the large square field, the red accent calls out to concentrate the manifold aspect within itself once again. It appears to be color more than equivalence (the square) that works in this composition to maintain the unity of a space which diversifies and multiply.
The lines and segments present at least five different thicknesses. In some cases almost imperceptible, the difference in thicknesses helps to increase the level of multiplicity in a composition where colors have been reduced to a minimum.
Reducing compositional parts
In point of fact, during the second half of the 1920’s Mondrian progressively reduces the elements, often working with white, black, and small accents of color:
While the elements are reduced, the painter increases their reciprocal diversity with subtle variations, as exemplified in several cases by the differing thicknesses of the lines. The whole is thus rich in nuances that help to evoke multiplicity while conveying unity; a dialectic to which the artist attached such importance, even in a space moving toward ever-greater synthesis.
As seen in the previous page, with a large square visibly structured and colored within, Mondrian seeks in Composition B to present a unitary synthesis open to multiplicity:
but in so doing the square looses cohesion and unity and this is why the painter closes it again to an homogeneous white field momentarily:
and then opens it up again to differences in size, proportion, and color:
As mentioned, the goal is to compenetrate unity and multiplicity while keeping both aspects visible. This is because Mondrian believes that the two seemingly opposite aspects are actually the same thing observed now as one and now as multiple. Once again I recall the example of a tree observed from far (a synthetic green spot) and very close distance (an endless complexity). A single leaf unveils a multiplicity of parts:
Mondrian’s hopes of being “recognized” in Paris were dashed.
In a letter written a little earlier, van Doesburg, who had just passed through Paris, wrote to a friend in Holland: “In Paris, everything is totally dead, Mondrian suffers a lot, and I know that he would recover if he only wanted to understand that in the Latin reactionary soil nothing new can grow. It is for me a certain fact that the new area of culture is the North.”
This idea was also dear to Fernand Léger at the time: “The new spirit comes from the North”, he wrote in head of an article. We would easily find some matter for discussion, fed by all that has happened since then in the field of art … and politics.
Almost all of the works Mondrian created between 1920 and 1936 can be grouped into four basic compositional layouts:
The guiding thread of all the compositions based on these four compositional layouts is a progressive interpenetration of the square form (representing unity i.e. a balanced equivalence of opposites) and the planes which present a variety of imbalanced relationships between the opposites as well as different colors.
New compositions
The interpenetration between unity and multiplicity continues with new compositions:
Katherine Dreier returned to Paris the following year and bought several Mondrian paintings again. Then came Germans, Swiss and other Americans such as Mr. Gallatin who had just founded the Museum of Living Art. But Mondrian sold his paintings at very low prices and, if the ordinary had improved a little, the end was never near without causing him some anxiety.
In spite of everything, the painter had happy days in Paris. He was surrounded by solicitous friends (the Stieltjes and Hoyack families, for example, the Vantongerloos, Dr. d’Eck, myself), he received many visits from Holland, sometimes from wealthy people who invited him to a good restaurant or to some fashionable dance hall.
At the beginning of 1930, in the Cercle et Carré group that he had founded with Torrès-Garcia and that had eighty members, he was admired and revered. In spite of his discretion and natural self-effacement, he was the spiritual center of the group.
Michel Seuphor, Piet Mondrian, Sa Vie, son Oeuvre, 1956
We have so far examined the first two compositional Layouts A and B. We will now examine a couple of compositions following the two layouts C and D:
In the new works based on Layouts C and D the lines acquire greater autonomy and the compositions become more dynamic.
In the canvases that followed layout A the lines can in fact almost be seen as framing the large square that occupies most of the central area and thus inhibits their dynamic continuity. In the works based on Layouts C and D the square instead seems to be generated by the space of the lines and to share their infinite quality. This is a feature that had already appeared in some lozenges.
The intuition of the whole
During the 1920’s The lines have grown in thickness and continue now beyond the perimeter of the canvases. As Maurizio Calvesi points out, the canvas is “an ideal center in which the spatial event is determined in its wholeness and totality no less than in its dynamic continuity. Mondrian wrote in 1920 that the straight lines intersect and touch one another tangentially but continue uninterruptedly. The result radiates out in fact from the painting to the infinite, but the canvas exhausts the intuition of the whole within itself.” The lines hint at the immeasurable extension of physical reality the canvas is part of; a part which aim at ideally concentrating the whole in its essence.
Between 1927 and 1929 the large white square field originating from Layout A (Fig. 10) decreases in size and moves toward the lower right corner leaving space for a second square colored red in the upper left corner (Fig. 15) or in the lower left corner (Fig. 16):
Composition with Red, Yellow and Blue, 1927
Composition with Red, Blue, Yellow and Black, 1929
Composition N. III with Red, Blue, Yellow and Black, 1929
This tendency gave rise to what I have called compositional Layout C.
Layout C is born out of the meeting of two perpendicular lines that run through the center of the canvas to generate four areas with proportions not too far removed from equivalence. The lower right area is further divided by three segments that work with the two lines to produce a white square field closed on all four sides and a smaller colored plane to its right:
Further compositions based on Layout C will be examined in detail on the next page.
In a different way, but with same purpose of diversifying the unity evoked by a predominant central square (Fig. 10) the compositions based on Layout D display the tendency to reposition the large central square toward the top right corner and make way for a smaller second square in the opposite bottom left corner (Fig. 17) or for additional small squares (Fig. 18 and Fig. 19):
Composition en Rouge, Bleu et Jaune, 1930
Composition 1 with Yellow and Light Gray, 1930
Composition with Blue and Yellow, 1932
All the squares are now open on one or two sides.
The first obvious difference between canvases based on Layout C and those following Layout D is that on the former we see a single square field that is white in color and closed on all four sides while on the latter the squares are open and often colored:
Once again this demonstrates how the artist wishes to open up and interpenetrate unity (the square parameter) with multiplicity (the changing set of different sizes, proportions and colors) evoked in Layout D without, however, losing sight of the one as seen in Layout C.
On the next page we shall examine in detail works of both Layouts C and D.
Next page: Neoplasticism – Part 3
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