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## Refining Neoplastic means

We examine here some compositions Piet Mondrian created between 1930 and 1933. With these works the artist continues to refine the most suitable plastic means aimed at making visually concrete his ideal of an intrinsic multiplicity of unity and a unity of an endless multiplicity.

We start analyzing works pertaining to what we have called the compositional Layout C. This appears to have developed out of the vertical line that comes to occupy the center of the canvas in the layout B, where the line runs through the square area, which remains open on the sides:

In the Layout C the square area is reduced in size and moved to the lower right section but remains closed and its inner field remains whole, unlike what happens in Layout 2. The peremptory presence of the large square, which occupied the center of the composition around 1921 (Layout A), gives way first to a vertical line (Layout B) and then to two perpendicular lines (Layout C). Where there was once a finite space (the square of Layout A), we now see a space that continues uninterruptedly (lines). This makes the center of the canvas more dynamic.

The central area of the canvas has always played a crucial role in Mondrian’s compositions. Recall the rectangle, the square or the white rectangle and the large square form. All this always involves the central area of the composition. With the new works based on Layouts B and C, Mondrian appears to have felt the need to inject greater dynamism into the center and with it the equivalence of opposites (the square) and the composition as a whole.

### Composition with Yellow

The two perpendicular lines seem intent on pulling the square unit toward the upper section and the left, while the accent of color again exerts a pull to the right. The composition is therefore in dynamic equilibrium between a space expanding to infinity (the opposite lines) and the same space momentarily concentrated in a finite relationship (the square proportion).

Unity (the square) is challenged by opposite directions. How often this happens within ourselves during our lives:

## Composition II with Blue and Yellow

The rectangular and square fields, large or small, are in unstable equilibrium between the infinite extension of the lines and the finite space of the canvas.

These fields are defined and undefined at the same time. This interaction between definite space and indefinite makes the closed and stable square appear uncertain:

Our quest for balance and unity (evoked by the square form) is challenged by the unforeseeable course of life (the endless lines and the variable proportions nearing unity without ever really attain it).

### Undefined squares

Fig. 3 presents four areas verging to the proportions of squares (1, 2, 4) which are fully accomplished in area 2 only which however remains open and therefore subject to the expanding action of the opposite lines:

The closed area 1 appears as the only well defined square (slightly horizontal to compensates the vertical prevalences of areas 3, 5, 6) while area 5 again suggests indeterminate proportions.

It is worth remembering that the square form is for Piet Mondrian a plastic symbol of an ideal balance between the infinite and multifarious outer space of nature and the inner quest for synthesis and unity. At the same time the square symbolizes the balance between opposite drives we always look for within ourselves. The uncertain square module symbolizes all this in the two-dimensional space of painting.

## Uncertain unity

Fig. 4 consists of seven different areas. Some verge to proportions of squares (Fig. 4 Diagram – Shapes 1, 2, 3) while others show a prevalence of one direction over the opposite. Shape 2 appears as a square which remains open at the bottom and to the left while shape 3 opens toward the top and to the right.

As mentioned before, areas 2 and 3 extend beyond the canvas and it is therefore the finite perimeter of the painting which make us perceive these two areas as square; in point of fact they are quite undefined squares:

Area 1 is the only fully accomplished square closed on four sides. This connection between a completed square and a series of open, uncertain squares reminds of Pier and Ocean 5 of 1915. The red and the blue areas unpredictably extend beyond the canvas as well.

The red and blue planes show unbalances between horizontal and vertical. They are plastic symbols of the ever-changing appearance of things (the natural) whereas white open squares (2 and 3) suggest the on-going search for synthesis and balance (the spiritual) which is finally fully achieved with 1 where opposites reach a relatively stable and well defined unity. Unforeseeable and ever-changing events (the colored planes) gradually become (2 and 3) certain and relatively constant (1).

The lines, which continue beyond the canvas, seem to connect with the far more complexed real world the painting is a part of; a part which aim at ideally concentrating the whole in its essence.

## Composition with Blue and Yellow

The same thing can also be seen in Fig. 5 where the closed square shows a slight vertical predominance.

As observed it is the sides of the canvas that determine the proportions generating the composition:

The rectangular and square fields, large or small, are in unstable equilibrium between the infinite extension of the lines and the finite space of the canvas. These fields are finite and infinite at the same time.

This interaction between infinite space and finite space generates the relations and proportions that work together with the weight of the colors toward a dynamic balancing of the whole. On observing these works, we are faced with a space that lasts and is already different a moment later.

A slice of definite space (the closed square) coexists with slices of indefinite space which may change a moment later. The painter appears to have wished to express a variety of possible unitary syntheses, i.e. to multiply unity.

### Multiplying unity

A tendency to multiply and color the synthesis was displayed in some works as early as 1921, e.g. both works shown below, where the equivalence of opposites (the square unit) is expressed through four different areas verging to proportions of squares:

With Layout D the multiplication of the square unit is effected above all through color:

A large red square and a smaller blue square appear to contend for the space in Fig. 6 whereas a small yellow plane or a black horizontal segment serve to redistribute the weight and keep the composition in a state of dynamic equilibrium. A variety of squares is to be seen in Fig. 8 including two in color and two in white, one large (blue) and three smaller (yellow and white).

The interaction between virtually infinite lines and the planes contained within the perimeter of the canvas generates the proportions that work together with the weight of the colors toward a dynamic balancing of the whole.

The space of these compositions is markedly asymmetric but everything is kept in perfect equilibrium. It does the mind good to think that asymmetry and diversity can be resolved in a harmonious space. If only this could be achieved more often in social life.

## Composition 1 with Yellow and Light Gray

Fig. 7 is based on the interaction of two perpendicular lines and two segments, which generate planes tending toward square proportions. Six of these can be seen, one of which is larger (with a slightly greater degree of vertical development) and one yellow. Though colored white or grayish-white, the others are in turn differentiated through barely perceptible variations in their proportions:

The horizontal line is slightly thicker than the vertical. The two segments are visibly thicker than the two lines and have greater weight, especially the vertical one, which also serves as a counterweight in the lower right section to the visual weight of the yellow square in the upper left section. The segments act as intermediaries between the dynamic and infinite space of the lines and the more stable and finite space of the squares.

The three squares in the lower section appear more balanced than the others, which instead develop a slight vertical predominance.

While the lines “run away”, something remains to generate a variety of more or less square fields on the point of change. We are thus faced with the idea of a probable but not definite square.

The message of the compositions based on both Layouts C and D seems to be that there is nothing more different than entities that appear to be almost the same.

## Evolution of Neoplastic space

Neoplastic space evolves between 1920 and 1932. On the one hand, the closed square of Layout A opens up and its inner field is made more dynamic with Layout B by running a vertical line through it:

Click on images to see the respective paintings:

On the other, the field inside the square remains whole with Layout C but is reduced in size and exposed to the dynamic influence of two lines running through the center of the composition. With Layout D the large square opens up on two sides, splits in two, and multiplies in red, blue, and yellow. As has already been widely discussed, the common denominator of the three new layouts is the effect of making the equivalence of opposites more dynamic and relatively multiple while opening it up to color.

It should be pointed out that the schemata I use here for explanatory purposes (the four layouts) are to be understood as interpretive models that can clearly be applied to Mondrian’s work but in no way exhaust it. They must be seen in an open and flexible way. In actual fact, the work proceeds as a single corpus and we can therefore find combinations and overlappings of the various layouts that constitute different solutions to a single need, namely to make the equivalence of opposites dynamic.

Mondrian made sketches and used them as a basis for the compositions he wished to produce. These sketches were, however, like variations on a single inner design that took different forms on emerging at his fingertips. The painter proceeded intuitively and that the schemata used in this explanation should not distort what was actually a fluid and uninterrupted process by making it rigid and discontinuous.

### Intuition more than cool elaboration

With respect to the works of 1920-22, the primary colors display saturated tonalities in the canvases of 1928-32. The greenish yellows of the early 1920s have become fully yellow. The composition seems to undergo distillation and deft calibration in some of these canvases.

The parts express an intimate sense of permanence and duration while everything is nonetheless on the verge of flux and motion. The impending inconstancy of life transforms our equilibriums, our definite squares, into variable entities. The play of equilibrium regards not only form but also very subtle vibrations of color. The planes appear to have been painted there and then, thus suggesting intuition more than cool elaboration. The fields of red are splendidly rendered, as indeed are those of white, which have none of the flatness unfortunately seen in reproductions.

There are extremely subtle variations of every primary color, as there are of every shade of gray. As H.L.C. Jaffé wrote: *“The painter let himself be guided by his feeling for color and rhythm, and he made alterations and corrections as he worked; over paintings to change the color of some of the areas can still be detected. The skilled treatment and masterly balance of the canvases are the result not of a theory but of a long experience as a painter.”*

It is not easy to give an adequate description of the painterly quality of these canvases, the masterly combination of hues, the fine textural layering, or touches such as a sparkling note of yellow. It is also and perhaps above all essential to see the original canvases, which are endowed with energy that no reproduction will ever be able to convey, energy imparted by the man who brought them lovingly to life.

Seuphor describes the canvases of the period 1928-30 as classic Neoplasticism, perhaps because nearly all the planes in these works approach square proportions, unlike the compositions of 1921-22. Some of these works are indeed authentic little masterpieces.

## The lozenge compositions

A further variation on the theme of the painter’s drive for a dynamic transformation of the equivalence of opposites is to be found in the lozenge compositions Mondrian produced between 1921 and 1933.

The choice of the lozenge format gives greater breadth to the composition. It makes it possible to use lines of various lengths. New relations of tension are established between the orthogonal planes and the diagonal sides of the painting. The four corners of the lozenge generate a centrifugal energy and seem to expand the plane of the canvas along its two median axes. The lozenge therefore already seems in itself a way to make the equivalence of opposites, i.e. the square, more dynamic.

We have already examined four of the ten lozenges painted during those years:

We shall now examine other two lozenges, which Mondrian produced at the same time as the rectangular canvases we have just discussed:

The artist seeks in these compositions to open and expand the square while maintaining its visibility at the same time. The concept of space here is still essentially the one that inspired his work from the very beginning: opening up to variety and mutability on the one hand while tending to concentrate on the other and thereby generating a more constant synthesis to which the human soul aspires, which then should always re-open to the endless variety and mutability of life and this is what we have seen since 1915 with *Pier and Ocean 5* where a square, symbol of unity, opens up to multiplicity.

In *Pier and Ocean 5* the unity expressed by means of an oval is replaced with a unity taking the shape of a relationship between horizontal and vertical (the square field).

From then on, the oval is projected beyond the finite field of the paintings to coincide with the reality of the world, of which the canvas constitutes a part that seeks to represent the whole:

With the gradual withdrawal of the oval, the square remains inside the painting as the subjective symbol of an assumed but no longer visible objective unity (the oval).

If the subjective unity (the square) is to symbolize the objective unity (the totality expressed by an oval), the square will need to contemplate all of its multiplicity.

This is why the entire body of work Mondrian creates in the course of the 1920’s shows the interpenetration of the square (equivalence of opposites) with all sort of imbalanced relationships between horizontal and vertical, yellow, red and blue. The square unit opens up to multiplicity.

The square opens up to multiplicity but at the same time it should remain identifiable as unity. In point of fact, after seeking to open the square unit up to color, the painter closes it again to an homogeneous white field momentarily, and then opens it up again to differences in size, proportion, and color.

With these lozenge compositions Mondrian endeavors to open up unity to multiplicity by operating exclusively on the one, i.e. on the square, which is opened to the point of practically coinciding with the infinite space of the lines, in other words, with the oval. The lozenge compositions constitute the moment of greatest correspondence between the one and the many.

The peak is reached with Fig. 9:

## Lozenge with Two Lines

In Fig. 9 we see just two black lines which allude to a “square field” that can barely be intuited, a square that is no sooner generated than it becomes an infinite space:

Here too, the top and right corners of the lozenge accentuate the dynamic expansion of the central field. The space of a presumed square is no longer delimited by the lines but extends with them far beyond the canvas. The finite space almost seems to coincide with infinite space. The subjective unity (the square) extends so as to encompass ideally all the multiplicity of objective space that the canvas can never contain (the oval).

It is like the squaring of the circle.

These lozenge compositions constitute the moment of greatest correspondence between the one and the many. One could say that the square and the oval we of *Pier and ocean 5* (1915 tended now to become one and the same thing.

## Lozenge with Four Yellow Lines

After the extreme synthesis observed in Fig. 9, we see in Fig. 10 a square that again appears to be defined by four sides but extending partially beyond the edges of the painting.

The square in this lozenge has the same proportions as the canvas:

Once again, the four lines show a progressive increase in thickness as we move clockwise from the vertical on the right. The increase in the thickness of the lines can be seen as the vertical incorporating a slight horizontal expansion or conversely as the horizontal growing thicker in response to barely perceptible vertical pressure. For a fraction of a second, the space of the lines is simultaneously vertical and horizontal, i.e. a synthesis of the opposite directions. From this point of view the lines seem to transform into embryonic planes. Ten years later the lines of *Broadway Boogie Woogie* will become planes and the planes will then revert to lines.

## Invisible unity

We actually talk about a square that we do not really see in full since the lines never meet inside the canvas. In point of fact each line could well continue on its own towards infinite space without being really concerned to relate with the opposite lines as to give birth to a square proportion.

Our mind translates infinite space (the uninterrupted lines) into a presumed finite space (a square form); four different elements (their variable thickness) hint at probable square unit which is, however, beyond our field of vision.

Doesn’t an invisible unity bring to our mind what some call God while others try to investigate and eventually explain through a rational never ending process named science?

The more important innovation is obviously the fact that, for the first time, the lines are no longer black but yellow. The field is uniformly white and the yellow shape almost appears to be born out of the white rather than in opposition to it, as in the case of the black. Yellow is an intermediate value between black and white, sufficiently dark to be differentiated from white but, at the same time, not so radically opposite as black.

The opposite values now seem communicate and achieve unitary expression in terms both of form and of color, with horizontal and vertical simultaneously present for an instant in every line and the synthesis of black and white in an intermediate color, which yellow appears to constitute in this case.

## A dynamic square

On observing this square and contemplating the differing thickness of the lines, we are faced with a unity undergoing transformation from one side to the other; a synthesis that already appears comparatively manifold in itself. We perceive a unity that tends to become rather than to be. It endures but changes at the same time; a square that is open, dynamic, asymmetric, and entirely expressed by color.

This composition goes to the heart of the problem: to show the manifold in unitary form; to open up unity, i.e. the postulate of consciousness, to the changing aspect of the natural universe and existence in time but without losing sight of it. This is a fundamental issue. The one and the many appear as antithetical realities in the human dimension; in actual fact, they are the same thing.

## One and the same thing

The dialectic between unity and multiplicity continued throughout the 1920s and early 1930s. The single white square field (1920) took on color, underwent duplication while opening up on one or two sides (1930) or remaining closed while developing out of the dynamic continuity of the lines around 1931:

The square unit is sometimes more horizontal, sometimes more vertical; sometimes larger, sometimes smaller; sometimes blue, sometimes yellow. The single square of 1920 gradually gave way to a variety of probable square forms. Unity opened to multiplicity.

In actual fact, the square opened up and interpenetrated with the variety of forms and colors in the rectangular canvases while seeking in the lozenge compositions to absorb that variety with no extensive change to itself. In the first case, the square opens up in the direction of multiplicity; in the second, the square absorbs multiplicity (the changing thickness of the lines) while remaining substantially one:

As mentioned, 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. In a white field crossed by four black lines, 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.

In the rectangular canvases on which the painter worked at the same time as the lozenges, a stable white square opens up, undergoes interpenetration with the lines, moves off-center decreasing in size, and becomes yellow or blue in some cases, but never attains expression with such a degree both of articulation and of synthesis as in this lozenge of 1933.

With the canvases of the late 1920’s and above all this lozenge of 1933 (Fig. 10), the artist appears to have given material expression to an idea that had guided him, canvas after canvas, for roughly twenty years of work, namely to express the multiple in unitary form and endow it with the stability required by consciousness without, however, causing it to atrophy in overly rigid and constant geometric forms. The artist felt for a moment that he had achieved his objective with a square undergoing transformation while remaining relatively stable.

Nonetheless, if we compare Fig. 10 with the previous works and in particular with those produced up to 1920:

it appears immediately obvious that by 1933 the multiple aspect had been considerably reduced almost to the point of elimination. Around 1930 Mondrian painted in black and white or with one or two colors inside predominantly white fields. In the span of a decade, the manifold space (1919**)** appears to have been completely absorbed by one single square in an attempt to reformulate in conceptual synthesis a space that is in reality far more structured and complex.

The square we see in Fig. 10 is a symbolic representation that does not suggest the variety of the real world. With colored lines changing also in thickness, this square alludes to multiplicity without, however, showing it in all of its far greater breadth. The variety found in the early Expressionist or Cubist works – an aspect to which the artist had always been very sensitive and which formed the starting point of his plastic explorations – was absent in 1933.

With Fig. 10 the space of external reality had undergone marked internalization in the far more condensed forms of thought; the physical seemed to be expressed in excessively mental terms. The painter was soon to realize that his canvases did not convey a sense of the variety perceived by the eye in nature or urban space, the rich and multiform aspect of color previously captured with his dunes and trees, his Cubist works, and his checkerboard compositions. While *Lozenge with Four Yellow Lines* Fig. 10 can therefore be regarded as a point of arrival, at the same time, as in other moments of Mondrian’s artistic development, the work also represents a new point of departure.

As Michel Seuphor puts it in his beautiful biography of Mondrian: *“Sometimes he thinks he has found it. So he stops, observes the work, and says: It’s done. But the clock of his life keeps on ticking and is already driving him forward. He soon realizes that nothing is done and everything has to start all over again.”*

Next page: Neoplasticism – Part 4

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