An explanation of Piet Mondrian's work by Michael Sciam

Toward one final painting

Composition B with Double Line, Yellow and Gray, 1932, Piet Mondrian
Composition B with Double Line, Yellow and Gray, 1932, Oil on Canvas,
cm. 50 x 50

This composition presents an area of square form closed on four sides in the lower right section. The square field expresses a moment of equilibrium between the opposing directions, which elsewhere give birth to variable proportions and then expand in a univocal and absolute way (in exclusively horizontal or vertical terms) beyond the canvas toward infinite space. The large yellow field in the upper left section and the gray one lower down to the right help to keep the square in a state of unstable equilibrium.

Composition in Black and White with Double Lines, 1934, Piet Mondrian
Composition in Black and White with Double Lines, 1934, Oil on Canvas, cm. 59,4 x 60,6
Composition in Black and White with Double Lines, Diagram

A relationship is established between a small square of sharply defined and definite size appearing in the center and a larger indefinite square placed in the lower section, which could almost be seen as the smaller one an instant after the lines have passed. By adopting a dynamic vision different parts of the composition become successive moments of one and the same element undergoing transformation. The dynamic movement of the lines drags along the small central square, which opens up while remaining in unstable equilibrium between vertical and horizontal predominance. Another way to open unity to multiplicity, certainty of the square form to the uncertain.

Only by adopting a dynamic vision of reality we shall be able to interpret the temporary imbalances and asymmetries of our daily life as necessary fragments of a much wider picture where a universal balance is to be found. A picture, however, daily life does not show us at once. Every situation in life which appears as an obstacle today may become part of a unitary, more balanced process tomorrow. Every opposition may turn to our advantage in the course of time. This is one of the fundamental messages of the Neoplastic geometry.

The two horizontal lines running through the previous canvases become four in Composition with Yellow (1936):

Composition B with Double Line, Yellow and Gray, 1932, Piet Mondrian
Composition B with Double Line, Yellow and Gray, 1932
Composition in Black and White with Double Lines, 1934, Piet Mondrian
Composition in Black and White with Double Lines, 1934
Composition with Yellow, 1936, Piet Mondrian
Composition with Yellow,
1936
Composition with Yellow, 1936, Piet Mondrian
Composition with Yellow, 1936, Oil on Canvas, cm. 66 x 74

The field inside the square form is no longer white here but yellow and presents a vertical segment echoed by an external horizontal segment in the lower section. The square form appears in a state of unstable equilibrium between an internal vertical and an external horizontal. In this respect, one should recall that Mondrian saw the vertical as a symbol of the spiritual (inner world) and the horizontal as a sign of the natural (outer world). The linear segments seems designed to indicate the beginning of a process of interpenetration between square and lines.

According to Joosten-Welsh Catalogue Raisonné Composition with Blue was first begun in 1937, left unfinished and re-worked between 1937 and 1942 with the addition of N. 12 to the title.

Composition N. 12 with Blue, 1937-42, Piet Mondrian
Composition N. 12 with Blue, 1937-42, Oil on Canvas, cm. 60,5 x 62
Composition 12 with Blue, 1937-42, Piet Mondrian, Diagram B
Composition 12 with Blue, 1937-42, Diagram A

Thirteen black lines intersect in the central field of the canvas and form a large number of white planes. Areas of greater or lesser horizontal and vertical extension can be seen (Diagram A). Vertical and horizontal attain equivalence in some points to form smaller or larger squares.

Space expands and contracts under the pressure of the two contending directions, which attain equivalence and a more stable equilibrium for an instant before opening up again to the more or less marked predominance of one or the other. Equivalences of opposite values are born and dissolve, are lost and found again in forms that are always new, without ever being fully attained. The idea of the square, i.e. an equivalence of opposites, seems to be expressed here too more as a process than a state. The solid and definite square of the 1920s now appears to undergo dilution on contact with the lines. The latter interact to expand and contract the space, above all in the central area, outside which they become entities in their own right; all horizontals or all verticals, one thing excluding the other. The space becomes absolute and eliminates any possible relationship between the parts.

Composition N. 12 with Blue, 1937-42, Piet Mondrian
Composition N. 12 with Blue, 1937-42, Oil on Canvas, cm. 60,5 x 62
Composition 12 with Blue, 1937-42, Piet Mondrian, Diagram B
Composition 12 with Blue, 1937-42, Diagram B

This canvas appears to offer a summary of all the compositions that Mondrian produced between 1927 and 1932 involving variations on the theme of the square. See here below four works exemplifying compositions made of a variety of proportions tending to approximate squares: 

Composition 1 with Yellow and Light Gray, 1930, Piet Mondrian
1930
Composition with Yellow, 1930, Piet Mondrian
1930
Composition with Blue and Yellow, 1932, Piet Mondrian
1932
Composition with Blue and Yellow, 1932, Piet Mondrian
1932
Composition N. 12 with Blue, 1937-42, Piet Mondrian
Composition N. 12 with Blue, 1937-42, Oil on Canvas, cm. 60,5 x 62
Composition 12 with Blue, 1937-42, Piet Mondrian, Diagram A
Composition 12 with Blue, 1937-42, Diagram A

To escape the war, Mondrian had moved from Paris to London in 1938 and by the end of 1940 he arrived in the USA. In addition to brushes and oil paints, New York City offered Mondrian a new tool to use in producing his works, namely colored tape, which allowed him to change the positions of the lines and thus work on the composition with greater flexibility. Once a satisfactory configuration had been obtained, it could be made permanent in oils. 

Composition B with Double Line, Yellow and Gray, 1932, Piet Mondrian
1932
Composition in Black and White with Double Lines, 1934, Piet Mondrian
1934
Composition with Yellow, 1936, Piet Mondrian
1936
Composition N. 12 with Blue, 1937-42, Piet Mondrian
1937-42

In New York City we see no fewer than twenty-three lines, fifteen of which are yellow, four red, and four blue. The lines expand and contract the white surface of the canvas, which is maintained in a state of unstable equilibrium between the two opposing directions. There is an alternating predominance of horizontal and vertical together with different combinations of colors. Horizontal and vertical sometimes attain equivalence and assume proportions of comparatively greater stability:

New York City, 1942, Piet Mondrian
New York City, 1942, Oil on Canvas, cm. 114,2 x 119,3
New York City, 1942, Piet Mondrian, Diagram A
New York City, Diagram A

Squares of variable size and proportions generate and dissolve in a variety of combinations between yellow, red and blue lines. Diagram A: Squares 1 and 2 are similar in terms of form but differ as regards their respective distribution of colors. The same holds for 3 and 4. Mondrian seems to have been intent above all in square 2 on combining the three colors so as to express not only a synthesis of horizontal and vertical but of yellow, red, and blue at the same time.

Observe the four canvases below in sequential order:

1920
Composition with Blue and Yellow, 1932, Piet Mondrian
1932
Lozenge with Yellow Lines, 1933, Piet Mondrian
1933
New York City, 1942, Piet Mondrian
1942

A white square field (1920) absorbed color over a span of twenty years and multiplied all over the surface of the canvas in 1942, changing in terms of position, proportions, and relations between the different colors. The single black and white unity of 1920 has undergone interpenetration with manifold space and is now wholly imbued with color and dynamism (1942). The one is now manifold. Even perhaps too much. The eye scarcely has time  to identify a more stable relationship between opposites (a square) before finding itself immersed in the dynamic and continuous flux of the lines. This happens because when color was applied to lines and the former colored planes disappeared the painter found himself grappling with compositions in never-ending development:

Composition C, N. III, with Red, Yellow and Blue, 1935, Piet Mondrian
Composition with Yellow, Blue and Red, 1937-42, Piet Mondrian
New York City, 1942, Piet Mondrian
New York City, 1942, Piet Mondrian
New York City, 1942

Another aspect that appears unsatisfactory in New York City is the fact that the points where lines of different color intersect are no longer marked by a single homogeneous plane, as happened with the black lines, but instead by the predominance of one color over the other. The colors seem to be on three different planes, with yellow, red, and blue appearing respectively on the first, second, and third. This superimposition creates a three-dimensional effect with which Mondrian could hardly be satisfied, since one of his aims had always been precisely the elimination of any perspective-based illusion of supposed and nonexistent third dimensions in order to express reality in the two real dimensions of painting. The problem arising as from this moment was to bring the three different planes of the yellow, red, and blue back onto a single plane. 

New York City, 1942, Piet Mondrian, Diagram C
New York City, 1942, Diagram C

New York City, Diagram B shows how the predominance of yellow over red or red over blue is resolved by ensuring that each line allows the perpendicular section covered over to reappear shortly after. A single plane is re-established and the three colors are brought together while preserving their specific qualities: sections of yellow, red, and blue begin to interpenetrate within every line in the shape of small squares and this will give birth to Broadway Boogie Woogie.

Broadway Boogie Woogie, 1942-43, Piet Mondrian
Broadway Boogie Woogie, 1942-43,
Oil on Canvas, cm. 127 x 127

The painting will be referred to as BBW from now on. My explanation of it will be based on diagrams in which I have broken down and analyzed the composition. Viewed as a sequence, the diagrams help us to visualize a dynamic process. The diagrams should not be intended as an indication of how Mondrian did progressively paint the canvas, rather as a visual aid to understand its meanings.

The interpenetration of colored lines generates a multitude of small gray, yellow, red, and blue fragments which appear as small squares. To be more precise, there are no yellow squares but only larger intervals of space between the gray, red, and blue squares. Yellow appears rarely in the form of a small square and more frequently as a linear segment. The lines of BBW are therefore mostly yellow. 

Broadway Boogie Woogie, 1942-43, Piet Mondrian
Broadway Boogie Woogie

Everything seems to change incessantly; every point and every moment appear unique and unrepeatable, changing slightly in form when repeated in color and vice versa. Every point lasts for just an instant before changing into the next point-instant. A space of this sort is well capable of representing both the changing variety of shapes that follow one another in the space of physical reality and a succession of drives lasting only a few seconds in the inner space.

Observation of the frenzied succession of fragments reveals some that join up with others to generate some symmetrical configurations along the lines (Diagram A):

Broadway Boogie Woogie, 1942-43, Piet Mondrian
Broadway Boogie Woogie, Diagram A

The changing space of the lines – i.e. the ephemeral progression of different small squares – is endowed with greater constancy through symmetries which present an orderly rhythm generated by a constant alternation of same colors. The symmetries highlighted in diagram A can be seen as portions of ordered and hence measurable space generated inside a virtually infinite space like that of the lines, as though the space of the lines contracted for a moment into a finite segment (the symmetrical sequence) before reverting to infinite expansion.

Broadway Boogie Woogie, 1942-43, Piet Mondrian, Diagram B
Broadway Boogie Woogie, Diagram B

A certain vertical correspondence between two horizontal symmetries can be seen in the section of diagram B labeled 1. The correspondence appears to be slightly staggered by the movement of the lines. An analogous situation can be seen between two vertical symmetries at point 2, where the correspondence is now fully attained. Two vertical symmetries with a red center establish a horizontal symmetry between them:

Through the act of contemplating a horizontal relationship between two vertical symmetries, we actually generate a field of greater extension, i.e. a plane, which covers the space between the two vertical lines. In that very point, we see the birth of a small blue plane and then of other planes which are being shown in diagram C:

Broadway Boogie Woogie, 1942-43, Piet Mondrian
Broadway Boogie Woogie, Diagram C
Broadway Boogie Woogie, 1942-43, Piet Mondrian
Broadway Boogie Woogie

In the planes the relationship between horizontal and vertical appears more stable and durable even if it is always subject to temporary prevalence of one or the other direction. Some undergo greater horizontal influence, some vertical predominance, and some appear to attain a relative condition of equilibrium between the two opposite directions. The relationship between horizontal and vertical lasts for a longer period of time in the more extended space of a plane than in the small squares inside the lines. 

Broadway Boogie Woogie, 1942-43, Piet Mondrian, Diagram C
Broadway Boogie Woogie, 1942-43, Diagram C

Diagram C: Plane 1 extends downward and drags with it a fragment of horizontal gray line, which is transposed into the vertical and becomes a rectangular field inside plane 2. Planes 1 and 2 should be seen as two successive moments in a dynamic sequence transforming a yellow plane into one made up of two colors (yellow and gray). If the painting is observed in a static way, the two planes are seen as a single vertical band. When viewed in dynamic terms, which is what Neoplasticism demands, this band is nothing other than the transformation of plane 1 into plane 2.

New planes are thus born, as shown by diagram D, that differ from those observed in diagram C by presenting an inner space marked with a different color:

Broadway Boogie Woogie, 1942-43, Piet Mondrian, Diagram D
Broadway Boogie Woogie, Diagram D
Broadway Boogie Woogie, 1942-43, Piet Mondrian
Broadway Boogie Woogie

The intersecting of individual lines that continue uninterruptedly generates a multitude of small squares that cluster to produce symmetrical configurations. The symmetries extend beyond the thickness of the individual lines to become planes. The space undergoes gradual transformation from the condition of lines (an infinite and absolute space) to the condition of planes (a finite and relative space). The lines can be regarded from now on as an external situation and the planes as the genesis and development of an internal condition of the same space that proceeds uninterruptedly from an outer to an inner space. 

Going on with our examination of BBW, we see at points 8 and 9 of diagram E how the self-internalization of space continues and there are now four colors concentrated in the area of just two planes: blue and yellow in 8, red and gray in 9. The two planes are equivalent in their degree of formal development but prove opposite and complementary in terms of color, each being in fact characterized by the colors lacking in the other: 

Broadway Boogie Woogie, 1942-43, Piet Mondrian, Diagram E
Broadway Boogie Woogie, Diagram E
Broadway Boogie Woogie, 1942-43, Piet Mondrian
Broadway Boogie Woogie

A single plane expressing a compact synthesis of the three primary colors is finally reached at point 10.

The manifold space made of yellow, red and blue fragments expanding on lines toward opposite directions which disrupted our visual field at the beginning of the process by keeping the eye in constant motion, attain now unitary synthesis (Diagram F):

Broadway Boogie Woogie, 1942-43, Piet Mondrian
Broadway Boogie Woogie, Diagram F

In BBW a manifold and fragmentary external space is united in inner space. Color yellow, which define the lines is in fact the one which most interiorize within the unitary plane. Though partaking of the interaction between the opposite directions, this “vertical-horizontal” unity seems to resolve the opposition and contrast in felicitous equilibrium. The space of the unitary plane expresses a comparative state of calm, albeit in a dynamic way, by comparison with the surrounding space. 

Recapitulating what we have seen so far:

The small squares give rise to symmetries that then generate monochromatic planes. These are transformed into a certain number of two-colored planes that then become a single plane constituting a synthesis of the three primary colors. Space undergoes uninterrupted transformation from a condition of multiplicity to one of unity, from the many to the one.

It is necessary to observe BBW in a state of dynamic equilibrium between one stage and another of the process highlighted in these diagrams; we need to see the geometry in a state of becoming; to see the planes an instant before, as they develop out of symmetries, and to see the symmetries while they are generated by the small squares, which are generated in turn out of the interaction of opposing lines, each of which, taken in itself, expresses an absolute and infinite space that eliminates any possible relationship.

Broadway Boogie Woogie, 1942-43, Piet Mondrian
Broadway Boogie Woogie

Any slight horizontal expansion of the yellow would produce an imbalance and set the mechanism of oppositions back in motion, as would even the slightest vertical increase in the blue. While each color remains such, its size and proportions – and hence its value – depend on the tonality, proportions, and size of the other color. It is necessary to see the respective measures and positions of yellow, red, and blue give birth to a free interplay of reciprocal tensions. Every proportion depends on another in an unpredictable development of form that now depends directly on color, unlike the works produced between 1915 and 1940, where the scale of colors was established a priori by form (the black lines).

In the unitary plane of BBW the dynamic and virtually infinite space of the lines is transformed into a finite and lasting space. It would, however, be a mistake to see this as calm in the sense of a total absence of inner tension. The unitary synthesis of BBW should rather be seen as a temporary equivalence of opposing thrusts that neutralize one another.

The dynamic nature of the unity is confirmed by the following:

Diagram G: Plane 11 is the same size as plane 10 but consists solely of red and gray rather than the three primary colors. Moreover the horizontal line running suddenly through the vertical plane tends visually to disrupt the previously attained equivalence of opposites:

Broadway Boogie Woogie, 1942-43, Piet Mondrian, Diagram G
Broadway Boogie Woogie, Diagram G
Broadway Boogie Woogie, 1942-43, Piet Mondrian
Broadway Boogie Woogie

After the equivalence of the opposite directions and the synthesis of three primary colors attained in plane 10, the colors are again reduced in plane 11 and the external dynamism of the lines reappears to generate new opposition. After the degree of comparative calm, constancy, and unity achieved in plane 10, spatial movement thus seems to reappear in plane 11. Unity opens up to external space and the colors are separated and flow back toward the more dynamic and variable space of the lines (12, 13). 

The indication provided by plane 11 finds further confirmation in plane 12, where blue, yellow, and red are juxtaposed but no longer interpenetrate as they did in plane 10. The juxtaposition produces the impression of three separate planes, whereas the interpenetration combines the three colors in a single structure of greater stability. Note how the yellow on the right of 12 already seeks to cross the perimeter of the plane and flow into the yellow of the surrounding lines. Plane 12 can therefore be seen as plane 10 in the process of dissolution. 

Broadway Boogie Woogie, 1942-43, Piet Mondrian, Diagram G
Broadway Boogie Woogie, Diagram G

Configuration 13 possibly represents the conclusion of the process of reopening the unitary synthesis in that it can be seen as a continuation of the disintegration of 12. Space proceeds from a comparatively static and wholly internal condition (10) toward one of growing instability (11) that is gradually transformed into the more dynamic and variable external space of the lines (12, 13).

Broadway Boogie Woogie shows a process where an expanded manifold space of yellow, red and blue fragments concentrate in one compact plane which then reopens to a multiplicity of small colored fragments. From expansion toward increasing concentration and then from concentration back to expansion: this is the way BBW breathes. Through a dynamic process the one and the many merge and transform into each other. In this light, we can regard the unitary plane and the entire painting respectively as synthetic and as complex versions of one and the same thing. I am thinking once again of the tree that looks like a condensed point when seen from a distance but reveals increasing complexity on closer observation. Each single thing and every aspect of life can unveil the one and the many while all things can be seen as one.

Nature and life still remain the primary source of inspiration for abstract art. The enchanting fragrance and the incredible wealth of forms that nature offers to our gaze. The ten thousand different things that we see around us prove on closer examination to be a single interminable line, because in nature everything is different, manifold, infinite, and at the same time one. Everything is one just as every individual thing is a complex set of parts. Modern technology reveals that the apparent simplicity of a leaf is a small universe and that the immensity of earthly nature is a bluish-white spot in the infinite space of the macrocosm. The immensity of earthly nature is as simple as a leaf, which is as complex as the entire planet. Multiplicity becomes unity and unity reveals multiplicity.

We address relations between unity and multiplicity every time we summarize something that strikes us as unduly complex. We create a relationship between the parts and the whole both when we strive to see all the different facets of reality and when we are driven by emotion to trace everything back to a few elements and make generalizations. Though aware that the reality is far more complex, we often tend to make narrow, summary judgments. The reality before us is always more complex than our descriptions but we cannot always concentrate on it and investigate every single aspect in depth, not least because every single aspect is in fact an infinite reality in itself. This has always been true and is even more so today given the level of complexity attained by modern societies. I therefore believe that the question of the one and the many is one of the most relevant to the present day. Nor is this something purely intellectual. We often experience a drive for concentration when rational explanations give way to an urge that transforms all the complexity and fragmentation of a vision thought into the almost absolute synthesis of a vision felt. When we fall in love, for example, the whole of our fragmented daily life seems to come together in a concentrated form of energy that makes us feel in harmony with the world. Here too we can talk of fragmented multiplicity becoming unity. Of course the relationship between the many and the one pertains to spiritual, philosophical and scientific thinking.

The process which links together in a dynamic structure multiplicity and unity is at the same time one of progressive internalization of external space (the lines) into one plane which unifies yellow, red and blue within itself and then reopens to the expanded external space of the lines. The color of the lines (yellow) is the one that is most internalized within the unitary plane. “Through the internalization of what is known as matter and through externalization of what is known as spirit – until now too separate! – matter-spirit becomes a unity.” (Mondrian)

The process I have pointed out in Broadway Boogie Woogie might make one think of it as the result of a premeditated design. After reading the explanations provided above, some will indeed wonder whether Mondrian actually thought of the image in the way described here while painting it. We would have to ask the artist himself, but I think I can safely say that the answer would be no.
The process observed in BBW is not the result of a plan of the moment. This is a work constituting the compendium of an entire life, an image in which the artist finally succeeds in adequately expressing the synthesis he had always sought within himself in response to the immensity of the world. A world which was rapidly changing and therefore demanding new ways of visual representation. Reconnecting the outer world with the inner world was the purpose of The Dutch artist’s entire life.

I do not believe that Mondrian ever consciously visualized the process showed in Broadway Boogie Woogie even after finishing the work. In his interview with J.J. Sweeney in 1943, he declared his inability to express what he was doing with sufficient clarity. Mondrian did not conceive Broadway Boogie Woogie in the way it is explained here. He painted it, and for a painter, for a true artist, painting is equivalent to thinking. The reflections and explanations come only later, if at all, when it is all over and done with. A true artist is wholly involved in the intuitive interplay dictated by the eye and not in reflective reasoning.

Processes of this nature can certainly not be thought out but only carried through, step by step, following your intuition. If your intuition reaches such depths and succeeds in seeing so far, the results acquire all the astonishing and organic coherence that, it should be recalled, is displayed only upon completion. It is much easier for us today to see the entire work as a whole. It was certainly impossible for the painter to take full cognizance of everything he was creating when he let himself be guided by his eye in addressing the canvas with his brushes. 

Mondrian’s pictorial evolution shows that, contrary to common belief, the artist had no intention whatsoever of forcing existing reality into rigid geometric schemata but rather of making his geometry as open and flexible as possible. In Broadway Boogie Woogie every form is born, grows and develops as every natural form does. As in natural space, nothing lasts forever; no entity is pre-established but becomes such in that particular situation, in that particular positional relationship with respect to the other forms undergoing reciprocal determination. Every point of Broadway Boogie Woogieis unique and unforeseeable but, at the same time, part of a process that brings all of the elements together like a universal rhythm. A fluid space that gives concrete form to becoming more than being, to relations more than the individual things in themselves; a geometry that is anything but rigid, cold, or exclusively rational; a space that strikes me instead as very similar to life. Neoplastic geometry has very little to do with the rather antiseptic geometric approach of certain forms of abstract concrete art in the second half of the 20th century.

I think it necessary to say a few words also about the title Mondrian gave this painting. It may have been as a tribute to the place that offered him a home, as he had already paid tribute to Paris with a work entitled Place de la Concorde and to London with Trafalgar Square. The title has, however, given rise to no small number of misunderstandings by suggesting superficial parallels with the outward appearance of New York City. The painting obviously has very little to do with the lights of Broadway, the skyscrapers, the traffic or the street plan of Manhattan. If we really want to stick to the city where the image took shape, we could if anything think in terms of its pulsating rhythm, of the contrasts, the constant movement, the infinite variety of humanity, situations, and disparate elements that make up New York City.
I would attach little importance to any direct links with boogie-woogie music, which the painter certainly loved. He pointed out in his interview with Sweeney that he saw true boogie-woogie “as harmonizing in intention to his own aim in painting: the destruction of melody, which is equivalent to the destruction of natural appearances, and construction through the constant opposition of pure means: dynamic rhythm.” Always keenly aware of the educational function of art, Mondrian used an analogy with boogie-woogie, as earlier with the fox trot and jazz, to suggest a parallel helping us to understand plastic expression at a different level from the image, with a language, i.e. that of music, which is perhaps the closest to Neoplastic painting, since music has been expressed in abstract terms from the very outset. I do not believe, however, that Mondrian ever intended with BBW, as with other works of his, to give pictorial form to a certain type of music, or indeed that music was the primary source of inspiration for his compositions. What the fox trot or boogie-woogie may have in common with Mondrian’s paintings is the fact that both music and images tend to create dynamic sequences. The analogy with music must, however, serve toward the full understanding and enjoyment of painting.

No, Broadway Boogie Woogie is not to be understood through reference to its title. The substance of things lies and remains wholly in the visual data. Those capable of seeing in the painting only what the title suggests to them will have to wait until their vision becomes more finely honed and reveals the deeper reality, which lies always and exclusively in images and not in words, at least in the case of the visual arts. As Mondrian observed, “A true critic can, simply by drawing upon the depths of his humanity and observing with purity, write about the new forms of art even without a knowledge of the working technique (…). But a true critic is somewhat rare.” 

North American critics often describe abstract art and especially the type involving precise, clear-cut shapes by means of the term “hard-edge”, as though we were talking about the outer aspect of some object. The value of Neoplastic visual thinking lies instead precisely in the abolition of every particular form in favor of the expression of pure relationships. The measurements, proportions, and chromatic or tonal variations in Neoplastic compositions are not pre-established but generated out of one another through reciprocal influence. The squares are never really such because it is the eye rather than mathematics that decides on their proportions. As mentioned, their extension can be slightly more vertical in some cases and horizontal in others depending on the spatial context in which they are developed. 

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? We often suffer imbalances between the opposing impulses of instincts and mind and we would always like to find balance, synthesis and unity, that is, our own inner paradise. Many times during an existence one can reach paradise and many times one can find oneself in hell; what Mondrian called the tragic; when duality (diabolus) (from the Greek dia = through and ballo = to put in the middle, to separate, to create fractures) lacerates the integrity of consciousness and unity is lost. Unity is manifested with an equivalence of horizontal and vertical (the square proportion) while elsewhere the horizontal prevails and dominates over the vertical and vice versa.

After forty years of patience work the one and the many, respective symbols of the spiritual and the natural, are now expressed in a sharp and bright form. Fundamental issues of Mondrian’s visual thinking have remained the same throughout his life while there has been a drastic change in the plastic means serving to give clear shape to a new vision of reality which has finally found a sharp and bright form with his last accomplished painting.

Life is a continued examination of the same thing in ever-greater depth” (Mondrian)