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NEOPLASTICISM 1921 - 1944 o oooPart 3 o1941 - 1944 o ooosee Part 2 1933 - 1940o ooosee Part 1o1921 - 1933

 

 

 

 

1

2

3

4

Victory Boogie Woogie, 1942-44

5

6

7

8

The compositional layouts Mondrian has used between 1932 and 1938 ca,. which have been discussed in Neoplasticism Part 2 under Charts 1 - 2 - 3 - 4 and represented here by 1, 2 and 3, merge finally into new works (4, 5, 6) between 1939 and 1942. These works represent the final phase of Neoplas ticism, preambel of the last two canvases Broadway Boogie Woogie (7) and Victory Boogie Woogie (8) which represent a marvelous sythesis of Mondrian entire work.

We shall now examine some of these works of this last phase.

 

 

This painting, restored in 1977, is again crowded with lines, as in 2 (see above).
Details supplied by Joop M. Joosten suggest that the painting could be a reworking of a canvas begun in 1938.

In addition to brushes and oil paints, New York 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. Mondrian used tape during his work on this composition but never got round to the definitive application of paint. From what can be seen of this canvas today, he used yellow, red, and blue lines at the same time accompanied by two black lines and, unusually enough, also five white lines. The latter appear such in virtue of the fact that the canvas, if I remember rightly, was never primed and is therefore ivory in color.

The combination of lines of different colors produces forms that change constantly in appearance. The different visual weights of the colors used for the lines emphasize certain forms with respect to others.The areas marked out with white lines are less conspicuous than those with red. A yellow plane can be seen in the upper left section and a blue one of uncertain nature on the right edge of the canvas.

 

4 - New York City 3, (unfinished), 1941, Pencil, Charcoal, Oil on Canvas, cm 110,5 x 116,8

The only area that appears to express something more permanent is the yellow plane. This extends horizontally but is led by a red vertical line on the right toward a square formed by another red line on the left and a blue line below (Diagram 4a). In the plane in a state of dynamic equilibrium between the horizontal expansion of the yellow and the concentrating force of the red, the opposing directions and the three primary colors attain equivalence for an instant in a square of yellow, red, and blue.

 

Diagram 4a

Diagram 4b

Diagram 4c

Another square form (Diagram 4b) can be seen on the right formed by a yellow line at the top, a blue line below (the horizontals forming the square in diagram 4a), and two new red vertical lines. We therefore have another equivalence of yellow, red, and blue. With respect to "a", however, the inner field of the square is no longer yellow, being crossed by a white vertical line. The latter works with a second white line on the left to generate a third square form (Diagram 4c).
As noted above, square "b" stands out more than square "c" due to the visual weights of the colors. The silent white line that subtly disturbs the equilibrium of square "b" is strengthened (becomes red) inside "c". Observe the two squares "b" and "c"" "in sequential order. The red line dividing square "c" seems designed to tell us that the equivalence of the opposites - the unitary synthesis of vertical and horizontal, yellow, red, and blue - is dissolving which is what happens in diagram 4d.

An area of horizontal predominance (the yellow plane) is transformed into an equivalence (a) that then dissolves gradually (b, c, d). We note once again that different parts of a Neoplastic composition prove to be a single entity represented in its process of becoming.
The content of a Neoplastic painting stretches far beyond the limiting and partial descriptions that verbal language can supply. The reading of a composition must be reiterated in order to capture all of its substance. Through bright and exuberant colors, above all on beholding the original paintings, the eye addresses a dynamic set of relations. The eye reads and rereads the same pathways, which evoke new relations every time and thus express a rich and varied "landscape".

 

Diagram 4d

Diagram 4e

Diagram 4f

The lower section of the composition presents a square form made up of three red lines and one black (Diagram 4e - 1).
The inner field of the large square area is crossed by lines of different color that generate a variety of more or less obvious rectangles.
Traveling along the lines, we then find a new form balanced between a slight vertical predominance (Diagram 4e - 2) which then becomes a horizontal rectangle (Diagam 4f - 3). Uncertain square forms scarcely have time to manifest themselves before being pulled away by the rapid continuity of the lines (see alco diagram 4f - 1 and 2)

The dynamic movement of the lines causes pressure and crisis for the equilibriums manifested for an instant through the equivalence of the opposite directions and the dif- ferent colors. While the eye pauses on a single form, the space begins to move anew with an alternation of expansion and concentration. The planes are barely visible when formed by white lines. The greater or lesser permanence of the square forms now depends also on the color of the lines forming them.

The blue plane on the right is so markedly vertical as to look almost like a segment of line. This plane appears designed to compensate for the absence of blue lines in that area of the composition and, at the same time, to endow the whole with a certain weight and counterbalance the horizontal yellow plane.
With respect to the square seen in diagram 4e - 1, the blue plane is in the same position as the small accents of color in the canvases based on the N. III layout. The position of the yellow plane also confirms a trace of N. III layout.

 

 

Like 2 and 4 again 5 presents a multiplication of space with fourteen horizontal and ten vertical lines generating a complex set of varying relations.

Two black lines can be seen at the upper and lower edges of the painting. Four black vertical lines and three horizontals were covered by Mondrian with colored tape.

As Joosten says, this suggests that the canvas is a reworking of a composition of the previous years.

We are faced once again with space that changes constantly in appearance, a whole variety of situations produced by different combinations of the same elements.

 

5 - New York City 1, (unfinished), 1941, Oil and Painted Paper Strips on Canvas, cm. 115 x 119

   

Diagram 5a

Diagram 5b

Diagram 5c

We contemplate the variety of measurements and proportions on the one hand while seeking on the other conditions of more constant space (diagrams 5a, 5b, 5c),
which is then always challenged by sudden horizontal or vertical expansion, the presence of one color or another.

As in 4, the squares appear to be formed by more than four lines. They thus expand and contract, alluding to the loss and subsequent re-establishment of the equivalence of opposites. The squares are now less sharply defined and even more precarious than those formed by single lines.
There are no longer any colored planes appearing in this composition.
A greater density of elements seems to be concentrated in the lower section, where the horizontal lines are so close to one another as almost to suggest a single area made up simultaneously of the different colors. The greater weight observed near the bottom of the painting seems designed to anchor the composition as a whole so as to counterbalance the movement of the lines that accentuate the dynamism of the composition, especially in the upper and central section.

The uniformly black lines were thus transformed around 1940-41 into lines of color. The blossoming of colored lines constitutes a further development in the process of opening up unity to multiplicity that began around 1932 with Composition B with Double Line, Yellow and Grey.
Some critics have suggested a connection between the use of color for the lines and the above-mentioned availability of colored tape. I do not believe that this tape suddenly triggered a change that the foregoing analysis clearly shows to have been implicit in the development of Mondrian's work since 1915, i.e. since the unitary synthesis in square form that opened up to color.

 

 

The opening up to color took definite shape in 6, where the lines are yellow, red, and blue and there is no black at all. The composition apparently presented nothing but yellow lines and a red plane in its initial state but was later reworked by removing the plane and adding red and blue lines.

We see no fewer than 23 lines in this work, 15 of which are yellow, 4 red, and 4 blue.
The visual weight of the three colors seems to influence their distribution. Blue and red have greater visual weight and are therefore present in smaller quantities than yellow, which is visually the lightest color (the closest to white). A larger quantity of yellow is needed to compensate for the greater visibility of red and blue. The painter seeks to redress the qualitative balance of the colors through quantitative distribution, providing an example of the dynamic and asymmetric conception of equilibrium.

Yellow, red, and blue 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 in the different areas. Horizontal and vertical sometimes attain equivalence and assume proportions of comparatively greater stability.

 

 

6 - New York City, 1942, Oil on Canvas, cm. 114,2 x 119,3

 

Diagram 6a presents a series of square forms numbered from 1 to 7, some of which interpenetrate. Each square differs from the others also in relation to the position assumed within it by lines of the same color. 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.

Squares 1, 2, and 7 are formed by six or eight lines of different colors and appear to be less sharply defined. Mondrian seems to have been intent above all in square 2 on combining the three colors so as to express a synthesis of yellow, red, and blue. The equivalence dissolves toward the right and the square becomes a rectangle. The unitary synthesis marked out with the three primary colors is lost if only one color is taken into consideration.

Other squares are formed of only two colors (3 and 4). In 6 a completely yellow horizontal rectangle attains equivalence with a red line; the same thing happens in 5 with blue.

In 1 a field formed by four yellow lines has the proportions of a horizontal rectangle. The rectangle attains an equivalence of vertical and horizontal if seen in relation to the blue line above or without this but in relation to the red line below. If the yellow rectangle is instead observed in relation to both the blue line and the red, the slightly horizontal initial proportions become slightly vertical.
We thus see a dynamic square that oscillates between a slight horizontal predominance (all yellow) and a slight vertical predominance (yellow, red, and blue).

Diagram 6a

 

 

6 - New York City

Diagram 6b

Diagram 6b shows part of a vertical red line and part of an horizontal blue line which tend to concentrate a yellow rectangle into a square form made of the three primary colors (8). Each color needs the other one to reach balance and unity seen in the square proportion.

With 9 we glimpse at a yellow horizontal rectangle which becomes for a monent a square form made of the three primary colors before being pulled away toward the left by an imposing red vertical line. The different visual weight of the colors has an influence on the immediacy with which the relationships are perceived.
The eye travels along the lines, stops, singles out a certain configuration, and lingers on it, but all around the space is set in motion again with the alternating predominance of the different colors and directions.

Square forms generate and dissolve in a variety of combinations between yellow, red and blue lines. The permanent black and white square unit of the 1920's has now become dynamic and multiple; not only in terms of form as we have seen in Composition N. 12 with Blue but also in terms of color.
True balance and unitary synthesis of opposites is now attained only when the different colors are simultaneously present and no longer solely when there is an equivalence of horizontal and vertical.

Diagram 6b: It strikes me as important that in the lower right section (10) it is yellow and yellow alone that expresses rectangles with a predominance of one direction or the other. These three forms are made up of lines of the same color. In this case, the variable relations between the opposite directions are wholly homogeneous in chromatic terms and it is form alone that expresses mutation. The rectangles that remain entirely yellow are smaller than those that are formed by lines of different colors. They can be seen as small basic units that can only grow if they open up to diversity by mixing with the other colors. Which is what happens with the fourth shape to the right which attains balance (square proportion) by combining with red.

 

Diagram 6c

6 - New York City

Diagram 6c shows how a square form is developed inside a vertical field that runs through the center of the canvas from the bottom to the top (see the following diagrams 6d, 6e, 6f, 6g and 6h in sequence).

 

Diagram 6d

Diagram 6e

Diagram 6f

Diagram 6g

Diagram 6h

Reading up from the bottom, we see a red line and a blue line marking out a rectangular field (d) crossed by two horizontal yellow lines that seem to suggest a possible square (e), which takes shape in "f". The slight vertical predominance generated in this square by the simultaneous presence of the blue and the red produces a counter-reaction higher up and the square now expands horizontally once again (g). The greater visibility of two horizontal blue lines draws attention for an instant to a vertical shape that undergoes expansion in the opposite direction (h) and flows back into the dynamic space of the endless horizontal lines. The finite dimension of the square form (balance of opposite drives) flows back into the infinite dimension of the lines, that is to say, either one or the opposite direction only.

This recalls, mutatis mutandis, the compositional development of Pier and Ocean 5. See diagram below.

 

Pier and Ocean 5, 1915 - Diagram

New York City, 1942 - Diagram

 

 

1 - 1920

2 - 1921

3 - 1932

4 - 1933

5 - 1942

Observe 1, 2, 3, 4, 5 as a single sequence. In 1920 the colored planes had the function of decentralizing and dynamizing a space dominated by a single large white square formed by black lines. The square absorbed color over a span of 20 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.

 

* * * * *

 

Study I for Broadway Boogie Woogie, 1942

Study II for Broadway Boogie Woogie, 1942

Broadway Boogie Woogie, 1942-43

 

The existing bibliography indicates two certain studies for Broadway Boogie Woogie: Study I and Study II . There are also two drawings (catalogued as "Studies for Broadway Boogie Woogie?") that are seen as possibly related to the canvas. Some regard them instead as studies made by the artist after completing the painting with a view to alterations. I would interpret them as studies in their own right for a new work, but this is just an impression. I believe that the authentic studies for Broadway Boogie Woogie are the two sketches shown above.

In the two studies Mondrian drew a series of perpendicular lines that run uninterruptedly all the way through the visual field, as in New York City. He then inserted between them some short segments that, by virtue of their proportions, almost look like small planes.

 

1 - New York, 1941-42

2 - New York City 3, 1941

3 - New York City 1, 1941

4 - New York City, 1942

Mondrian's lines were illuminated between 1941 and 1942 with red and then simultaneously with yellow, red, and blue. As a result, the colored planes disappeared. In the Neoplastic compositions, planes express finite space and lines virtually infinite continuity. Previously reserved exclusively for planes, color was applied to line in 1941, at which point Mondrian found himself grappling with compositions in never- ending development (3 and 4).
In 4 the dynamic aspect seems to overwhelm the more measured and constant aspect previously expressed with planes; infinite space prevails over finite and multiplicity over unity. The eye scarcely has time to identify a more stable relationship before finding itself immersed in the dynamic and continuous flux of lines. Even the segments that had always been present in the previous Neoplastic compositions disappear in 4, which lacks a finite and more durable component to counterbalance the dynamic movement of the lines and thus suggest a certain degree of spatial permanence.

While the need felt as from 1934 had been to open up the unitary synthesis to multiplicity, it was now necessary to re-establish a greater degree of synthesis and constancy in a space that had undergone considerable multiplication in the meantime and continued uninterruptedly with the lines alone (4)

As pointed out above, all the compositions developed throughout the European phase of Neoplasticismwere not only made of black lines and colored planes but included also segments that helped to delimit the planes in some points. The segments are finite measures and hence an intermediary between the infinite space of the lines and the finite space of the planes.

In the two studies for Broadway Boogie Woogie Mondrian focuses precisely on this transition from lines to planes, from infinite space to finite space, and expresses it by means of small segments that are, however, no longer black segments delimiting fields of color (as throughout the European Neoplastic phase). They are colored segments (like the lines) as from 1941 and thus become small planes of color when they increase in thickness (as can be seen especially in the second drawing).

 
   

It should be recalled in this connection that lines of increased thickness seemed on some occasions to suggest planes back in 1925, 1926, 1930, and 1933.

The first sketch seems to have been made in one go and the second, which is more sharply defined, to clarify the ideas of the first. The second drawing clearly shows the artist's intention to channel the dynamic and continuous space of the lines toward finite and more constant relations. Some segments are clearly vertical, some markedly horizontal, and some display an equivalence in which horizontal and vertical are reciprocally neutralized.
Originating in the line and tending toward the plane, the segment provided Mondrian with the way to express a finite and more constant dimension inside a space based exclusively on lines. This was to mark the point of transition from New York City to Broadway Boogie Woogie, where areas of color are generated in the form of slices of finite space tending toward greater constancy that counterbalance the dynamic movement of the lines.

 

New York City

NewYork City Diagram

Broadway Boogie Woogie

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. With the exception of one point, the blue line always passes "behind" the yellow and the red, which passes "in front of" the yellow four times and always "in front of" the blue. 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 an equally unexpected and unwelcome 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 the reality of the world 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.

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 (see diagram above). 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. This is the ideal genesis of Broadway Boogie Woogie.

The painting is referred to as BBW from now on. My explanation of it will be based on eight diagrams, in which I have broken down and analyzed its geometry.
Viewed as a sequence, the diagrams help us to visualize a dynamic process. The following examination will use larger size of the eight diagrams.

 

As mentioned, after completing New York City in 1942 Mondrian felt it was necessary to re-establish a greater degree of synthesis and constancy in a space that had undergone considerable multiplication in the meantime and continued uninterruptedly with the lines alone.

 

Comparison of the two canvases shows a yellow, red, and blue space of virtually infinite expansion in the first and its concentration in a finite dimension of those three colors in the second.

The space that continues uninterruptedly in New York City finds a moment of more solid permanence and duration in Broadway Boogie Woogie.

New York City

BBW

 

 

Let us now see in detail how BBW develops the synthesis which was missing in New York CIty.

 

New York City

Diagram

Broadway Boogie Woogie

The interpenetration of colored lines generates a multitude of small gray, yellow, red, and blue squares in BBW.

 

BBW

BBW Diagram A

To be more precise, there are no yellow squares but only larger intervals of space between the gray, red, and blue squares. Yellow appears very rarely in the form of a small square and more frequently as a linear segment. The lines of BBW are therefore mostly yellow. The uniform lines of New York City come into direct communication here, with fragments of the horizontal entering the vertical and vice versa. For the first time in a painting by Mondrian, each line expresses opposing thrusts clearly and explicitly within itself. I recall some lozenges of the mid-1920s and especially Lozenge with Four Yellow Lines, where increase in the thickness of the lines suggests an opposing thrust but in a way that is still only virtual.

Every horizontal line contrasts with the vertical part of the small squares just as their horizontal component expresses opposition when situated on a vertical line. They are therefore entities in a state of unstable equilibrium between horizontal and vertical. Closer examination shows indeed that the small squares present variable proportions, with some developing a slight horizontal predominance, some a vertical predominance, and some apparently attaining square proportions. The small squares continuously undergo slight expansion and contraction inside the lines.

Everything seems to change incessantly in Diagram A, where 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.

 

BBW

BBW Diagram B

Observation of the frenzied succession of small squares reveals some (red or blue) that join up with pairs of small gray squares and yellow sections of lines. The red or blue square thus appears as the central point of a small symmetrical configuration (Diagram B).

 

BBW

BBW Diagram C

Some larger symmetrical configurations made up of an increasing number of small squares are highlighted in diagram C. The first, sporadic symmetries highlighted in diagram B a gain space inside the lines. Symmetry can be described as an extension of space that presents an orderly rhythm generated by repetition of the same elements. The changing space of the lines - i.e. the ephemeral progression of different small squares - is endowed with greater constancy through symmetries.
The symmetries highlighted in diagram C can be seen as portions of measured and hence finite space generated inside an infinite space like that of the lines, as though the incommensurable space of the lines contracted for a moment into a finite segment (the symmetrical sequence) before reverting to infinite expansion.

The small square is born when two perpendicular lines meet for an instant before moving on. It is the point in which an infinite reality becomes finite reality for a moment. The absolute space of every single line becomes a relative space in the small squares. The finite and relative character of the small square thus contrasts with the infinite and absolute nature of every line.
What we shall observe from now on is a dialectic between the tendency of the small squares to concentrate the infinite space of the lines toward a finite dimension (i.e. toward their own nature) and a contrary tendency of the lines to expand boundlessly toward an absolute space (only one direction or the other). This expansion severs the relationship between horizontal and vertical represented by the small square and therefore tends to negate it as a unitary synthesis of the opposite values.
The concomitance of horizontal and vertical, which constitutes the very nature of every small square, is "inevitably" called into question by every single line in which the small square is located. The static vocation of the small square is placed under constant pressure by the dynamic nature of the line. It should be noted that these are two opposing tendencies of one and the same space.

Careful observation of the symmetries formed on the lines shows in fact that they are not wholly regular and precise geometric structures. While the alternation of colors is symmetrical, both the size of every small square and the space between them vary. We are thus faced with flexible symmetries under constant pressure from the dynamism of the lines. The symmetries must be seen in an elastic way as they seek to restrain and articulate the infinite space of the lines, which instead subject the concentration triggered by the symmetries to an expansive momentum. I am reminded of the relationship the artist saw in the period around 1910 between the space of buildings (windmills, lighthouses, churches) and dunes, the former concentrating the physical extension of the world into a mental space and the latter expressing its virtually infinite expansion.

 

BBW

BBW Diagram C

A certain vertical correspondence between two horizontal symmetries can be seen in diagram C 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 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 surface, which covers the space between the two vertical lines. At that very point, we see the birth of a small blue plane and then of other planes (Diagram D).

 

BBW

BBW Diagram D

Like the small squares, each of these new entities expresses a certain relationship between the opposing directions. The relationship between horizontal and vertical lasts for a longer period of time, however, in the more extended space of a plane than in the small squares inside the lines.
By comparison with the small squares from which they originate, the planes appear more stable with respect to the dynamic and unstable flow of the lines; more stable but still in a state of dynamic equilibrium between the two opposing directions. Some undergo greater horizontal influence, some vertical predominance, and some appear to attain a relative condition of equilibrium between the two opposite directions. Some are still partially combined with the space of the lines, some are partially isolated and some appear to be totally self-contained. The two planes 5 and 7 appear to be equal on first sight but closer observation shows that 5 has slightly greater vertical development.
As a whole, the planes indicated in diagram d represent a variety of different situations in a state of unstable equilibrium between horizontal and vertical, between yellow, red, and blue; a space of change but tending toward greater synthesis than its counterpart in diagram A.

 

BBW

BBW Diagram E

Plane 8 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 9.
Planes 8 and 9 should be seen as two successive moments in a dynamic sequence transforming a yellow surface into one made up of two colors (yellow and gray).

If the painting is observed in a static way, the two planes 8 and 9 are seen as a single vertical band. When viewed in dynamic terms, which is what Neoplastic painting demands, this band is nothing other than the transformation of the smaller plane 8 into 9.

New planes are thus born (Diagram E) that differ from those observed in diagram D by presenting an inner space marked with a different color.

Due to the vertical predominance in plane 9, the internal gray band displays slightly greater horizontal development. Analogously, but in the opposite sense, plane 10 is counterbalanced by a red vertical segment just as the red vertical predominance of 11 is offset by a gray horizontal segment. The space of BBW is made up of constant contrast and reciprocal opposition.

 

BBW

BBW Diagram E

Observation of the sequence 9, 10 , 11, 12, 13, 14 shows that the process of spatial internalization (beginning with 9) continues in other planes where the gray field, which is still open on the sides in 9, is concentrated and stabilized in the form of a small square (12, 13, 14). A sign of linearity opposing the layout of he plane (9, 10, 11) gives way to a more balanced configuration showing approximate square proprotions that reduces the opposition to the interior of the same plane (12, 13, 14).

Consider plane 12 for a moment in relation to plane 13. The former undergoes greater horizontal influence while the latter develops a marked vertical predominance. The two internal quadrangles seem to reduce the imbalance manifested so obviously with the respective yellow parts of the planes. The internal quadrangles are the first timid sign (gray is the most tenuous chromatic value) of a shared inner nature that is more constant and detached from the frenzied and contradictory movement produced on the external lines.

Let us now summarize the various phases of spatial transformation observed so far as visualized in a single sequence.

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 the outside to the inside. The lines become planes; an infinite space is transformed into a finite space. While we observe the finite fields of the planes, the lines continue uninterruptedly and the eye therefore finds itself in a state of unstable equilibrium between an extended space (symbolizing the incommensurable reality of the physical world) and the same space undergoing inward concentration (the relational space of thought evoked with the planes).


 

BBW

BBW Diagram F

We can see at points 15 and 16 of Diagram F 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 15, red and gray in 16. 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. A single plane expressing a synthesis of the three primary colors is finally reached at point 17.

The opposite directions colored yellow, red, and blue, which disrupted our visual field at the beginning of the process by keeping the eye in constant motion, attain unitary synthesis here. Note how a quadrangle expresses equilibrium and synthesis of the opposing directions in the two planes 15 and 16 while a segment still opposes the field containing it.

We have seen in diagram E how an internal quadrangle (14) develops (9) from a segment (8).
The segment inside the two planes 15 and 16 is therefore an indication of a potential second internal quadrangle, which is shortly to develop in plane 17.

The segments inside the two planes 15 and 16 tell us that they are still influenced by the dynamism of the external in comparison with plane 17, where the entire space (yellow, red, blue) instead attains a more balanced relationship between horizontal and vertical. 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 this plane expresses a comparative state of calm, albeit in an asyimmetric and dynamic way, by comparison with the surrounding space.

 

BBW

BBW Diagram A

BBW Diagram C

BBW Diagram D

BBW Diagram E

BBW Diagram F

Again recapitulating the geometry analyzed so far in its individual parts, we see that the lines in BBW generate a multitude of small squares, which 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. The space of BBW undergoes uninterrupted transformation from a condition of multiplicity to one of unity, from the many to the one.

 

While BBW thus again displays a visible unity within the composition, this now takes place in a wholly new and original way.

 

 

 

 
   

New York City

BBW

 

1 - 1915

2 - 1919

3 - 1927

4 - 1933

In BBW, for the first time, the unitary synthesis is no longer a white rectangle (2) or a white square marked out with black lines (3) or yellow lines (4), but a concentration of yellow, red, and blue, a free and unpredictable interplay of form that depends on the respective qualities and quantities of the colors.

The equilibrium attained in the unitary plane of BBW is dynamic in nature and not tending toward the static, unlike the square taken by Mondrian as the equivalence of opposites from 1915 on. While it is true that he had always made flexible and dynamic use of the square form, it is equally true that the square dominated the evolution of Neoplastic space in certain phases, at least up to 4. The square form served Mondrian from 1915 to the mid-1930s as a sort of cornerstone or starting point to open his compositions up to change. At the end of this process, his space was asymmetric and colored all the way through, simultaneously multiple and unitary (BBW).

 

       

1

2

3

4

For the first time, the unitary synthesis is a plane made up simultaneously of the three primary colors. I am reminded of the scattered rectangles lacking unity of 1917 (1), which now find synthesis in a single plane. I am also reminded of 2 where Mondrian tried to unify the planes as well as 3 with the three larger rectangles (one yellow, one red, and one blue) surrounding a white rectangle in the center. Of course I think of all the Neoplastic compositions Mondrian accomplished during the 1920's where a white square field plays the role of an ideal synthesis of the three primary colors (4).


The unsuccessful attempt to attain unitary interpenetration of the white rectangle and the colored rectangles in one large square form (5) is now finally achieved in BBW, where a synthesis of horizontal and vertical and yellow, red, and blue is attained with great visibility.

 
   

5

BBW

   

 

* * * * *

 

BBW

BBW Diagram G

Plane 18 in diagram G is the same size as plane 17 but consists solely of red and gray rather than the three primary colors.
The inner space of the plane presents a gray quadrangle and two gray segments, one of which is part of a horizontal line running through the plane.
The quadrangle is a sign of permanence and greater equilibrium between the two opposing directions while the two segments, especially the one belonging to the line, are signs of movement that accentuate the horizontal direction in sharp contrast to the vertical layout of the plane itself.

After the equivalence and the synthesis of three primary colors attained in plane 17, the colors are again reduced in plane 18 and the external dynamism of the lines reappears to generate new opposition. The horizontal line running suddenly through the vertical plane tends visually to disrupt the previously attained equivalence of opposites. After the degree of comparative calm, constancy, and unity achieved in plane 17, spatial movement thus seems to reappear in plane 18. The unitary synthesis opens up to external space and the colors are separated and flow back toward the more dynamic and variable space of the lines.

The indication provided by plane 18 finds further confirmation in plane 19, where blue, yellow, and red are juxtaposed but no longer interpenetrate as they did in plane 17. The juxtaposition produces the impression that the whole is less compact and solid, whereas the interpenetration combines the three colors in a single structure of greater stability. Note how the yellow on the right of 19 already seeks to cross the perimeter of the plane and flow into the yellow of the surrounding lines. Plane 19 can therefore be seen as plane 17 in the process of dissolution.

 

BBW

BBW Diagram H

Configuration 20 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 19. The yellow section that tends to emerge to the right in 19 becomes the external space of the lines in 20. Still contiguous in 19, the three areas of blue, yellow, and red open up and separate in 20 under the dynamic influence of the lines to turn again into a variety of small yellow, red, and blue squares (Diagram H). The space proceeds from a comparatively static and wholly internal condition (Diagram G - 17) toward one of growing instability (Diagram G - 18) that is gradually transformed into the more dynamic and variable external space of the lines (Diagram H - 19 - 20).

The lines are first concentrated into small squares and then into planes that became a single plane. This unity now opens up again and reverts to the more dynamic and variable condition of the lines. Observe this process as a single sequence.

 

 

BBW Diagram D

BBW Diagram G

It will not have escaped notice that the configuration labeled 20 is made up of two planes (one red and one blue) labeled respectively 2 and 3 in diagram D.
2 was identified as the first plane generated in the transition from symmetries to planes and 3 as one of those belonging to the first stage of development of monochromatic planes. The same planes now play a completely different role. On the interpretation offered here, the first plane (2), which triggers the process leading to the unitary synthesis (17), would also be its last fragment (20). The same parts perform different roles in BBW depending on the context and the moment.

 

The geometry of BBW can therefore be summarized as a dynamic sequence that moves from a multiplicity of lines to the unitary synthesis of a plane and then expands from the unity of a plane toward a multiplicity of lines. From expansion toward increasing concentration and then from concentration back to expansion: this is the way BBW breathes. It is an idea expressed by the painter as early as 1915 in Pier and Ocean 5 with a sign of equivalence enclosed in a square that then opens up again to manifold space above. It is the horizontal which opens up the unity both in Pier and Ocean 5 and BBW. If the horizontal is a plastic symbol of the natural and the vertical of the spiritual, both images tell us that every synthesis generated by thought (the spiritual) is necessarily partial and temporary, and must therefore open up again to the multiform and ever-changing aspect of physical reality and life (the natural). This is what all sensible people do when they call their certainties into question in the light of experience. This is what philosophy has been doing for centuries, as have the arts and above all the experimental sciences.

 

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. 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.

Mondrian wrote as follows in a note sent to J.J. Sweeney on May 24, 1943: "Only now I become conscious that my work in black, white and little color pla- nes has been merely "drawing" in oil color. In drawing, the lines are the principal means of expression; in painting, the color planes".

Form and color were kept separate throughout the European phase of Neoplasticism. Black lines delimited the colored planes from the outside with no direct involvement in their space. Drawing (the black lines) became color in 1941, and when the lines became planes with BBW, there was no longer any distinction between form and color, drawing and painting.

Blue is the darkest value in the range of colors in BBW and therefore appears to perform the function previously assigned to black. In actual fact, there are two different shades of blue in BBW, the darker hue of the small squares inside the lines and the lighter hue of the planes. This dual tonality is found in none of the other colors and seems designed to underscore the function of the blue of the lines as a darker value also with respect to the blue of the planes. White, gray, yellow, red, and blue constitute a gradual progression from the lightest value to the darkest, from ethereal and indistinct (white) to solidity and sharpness of definition (blue). The yellow lines draw upon white through the small gray squares and then arrive through red at the opposite value in blue.

The monotonous continuity of the black lines turns in BBW into a variable sequence of tonalities that range within the same line from light to dark, from weightless to heavy, from indefinite to definite. Yellow is the value intermediate between the extreme of white and gray (light, weightless, indefinite) and the opposite extreme of red and blue (dark, heavy, definite). In the stretches where it becomes gray and is almost confused with white, the line of BBW seems to tend toward the indistinct, the invisible, the interconnection of all phenomena, and in fact toward the negation of drawing itself. In the more clearly marked stretches with red and blue, it tends instead toward sharp definition, i.e. the separation of one thing from another. The duality of light and dark acquires tension and turns within the same line into a flexible structure in a state of unstable equilibrium between the two opposite hues (white and dark blue).

Mondrian succeeds with this painting in establishing direct and visible communication between the opposite values: horizontal in vertical at the level of form; lighter in darker and vice versa at the level of color. In point of fact, form is already color in BBW.
We are reminded of the double black lines of 1932-38 enclosing a white line. In BBW a more gradual transition toward black ultimately blossoms from white (gray, yellow, red, blue). The yellow lines of 1933, an intermediate value between light and dark, also come to mind.

I do not agree with the readings that see yellow in the foreground in BBW and blue in the background. It makes no sense to see Neoplastic space in terms of the three dimensions. Even in the case of planes consisting of two or three colors, it is a matter of juxtaposition or interpenetration but not of overlapping interpretable as space developed in depth. I am not convinced by certain academic rules, according to which a blue surface would suggest depth while a yellow one, for example, would remain in the foreground. If anything, we can talk of the colors as possessing different visual weights. Blue proves heavier because it is visually darker than yellow. But this is not necessarily always so. There are canvases in which a yellow of a certain proportion can weigh more than a red or a blue. In the art of painting as a whole, but especially in the Neoplastic vision, the visual weight of the colors, their value, always depends on their measure and position with respect to one another.

 

* * * * *

 

BBW

BBW Diagram G

Plane 18 is described above as plane 17 undergoing disintegration. In addition to the reasons already given, I should like to make some further observations in this connection. The small vertical segment on the left of plane 18 underscores the position occupied above by plane 17, from which it appears to derive. With respect to the position occupied by plane 17 in the upper section, this can be seen as a movement in the lower section, plane 18, caused by the horiontal line running through that plane and pushing it to the right.

 

BBW

BBW Diagram O

It is, however, the geometry not only of the "solid" space (gray, yellow, red, and blue) but also of the "void" space (white) that generates the impression of an entity of greater solidity and visual constancy in the case of plane 17 and a disintegrating entity in the case of plane 18. We note in fact that the proportions of plane 17 are repeated identically to its right with a white field (Diagram O). In the left part of plane 17 the white field would have the same proportions as the plane but for the interference of the shorter line.

The space around plane 17 appears constant because the proportions of the same surface reappear unchanged nearly three times. The "void" is equivalent to the solid in that area, and this helps to give the solid greater equilibrium and stability. The invisible (white) becomes visible (the plane of three colors) for an instant.

 

 

 

 

 

 

1

2

3

4

BBW seems to present a unity that is expressed with the three primary colors and at the same time white (as throughout the European Neoplastic phase). This would appear to confirm the value Mondrian attributed to the white square area (1), of the rectangle (2) and then again of a white square field (3 and 4) as an ideal synthesis of the three primary colors.

 

BBW

BBW Diagram O1

The proportions of the white space around plane 18 are instead completely different and in no case underscore those of the plane itself. There is a lack of proportion between solid and void, with the former predominating to such an extent that the "void" is under pressure to redress the balance. The space around the plane appears to be agitated by the movement of that vertical segment and that horizontal line, which will soon gain the upper hand and open the plane up again.

The white space therefore also appears designed to suggest that the unity of plane 17 represents the utmost degree of synthesis, after which the space begins to disintegrate again. I cannot be sure, never having bothered to take precise measurements, but something tells me that in BBW the combined quantity of the four colors is equal to or slightly less than the amount of white. If the "solid" represents what appears in an obvious way to our senses while the "void" represents what we cannot see but nevertheless exists and provides us with constant sustenance, how can we fail to feel the deep wisdom and sorrow of this geometry? What we see depends also on what we do not see.

 

* * * * *

 

The process I have pointed out in BBW 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.

 

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4

The process observed in the painting 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: with still lifes (1), landscapes (2), a tree (3), and with the Pier and Ocean group of works (4). Reconnecting the outer world with the inner world was the purpose of his entire life.

Nor do I believe that Mondrian calculated the phases of the process observed in BBW in the way it is explained here. I am rather inclined to believe that the sequence took shape with no premeditation while the painting was being born. I say this on the basis of my experience as a painter, having worked on compositions the true meaning of which I only discovered later.

Cézanne: "If one feels in the right way, one will think in the right way. Painting is first of all a way of looking. The subject matter of our art is there, in what our eyes think.”

I believe that Mondrian gave shape to the composition in a spontaneous and intuitive way, adding, removing, and modifying the parts in no precise order. To tell the truth, I do not believe that Mondrian ever consciously visualized this process 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 BBW 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.

Consider a yellow line that continues uninterruptedly and a red small square inside it. When the painter adds one and then another small gray square that work with the red to form a symmetrical configuration, he is not thinking about its conceptual meanings. Not at all. He sees and takes pleasure in placing the second small gray square that lends slightly more stability to the red point immersed in the rectilinear yellow flow. His eye delights in seeing the brighter contrasting colors take on a measured form and an appropriate proportional relationship. Mondrian sees the line expand and the small square give birth to a movement of concentration. There is no need to think. The painter sees and what he sees goes straight to the heart. This is how I believe he worked, the way a true artist works.

 

* * * * *

 

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 the city of New York.

The painting obviously has very little to do with the theaters of Broadway, the lights of the skyscrapers, 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. 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, BBW 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."

 

* * * * *

 

Let us finally have a look at Victory Boogie Woogie, (from now on VBW) a canvas that Mondrian worked on at the same time as BBW and that was to remain unfinished after various episodes of reworking.


 

Victory Boogie Woogie, 1942-44 (Unfinished), Oil and Paper on Canvas, Sides: cm. 127 x 127 - Diagonal: cm. 178,4

 

It should again be stated (for lovers of dates) that Mondrian appears to have begun VBW before BBW. As in other periods of his development, however, the dates on which individual canvases were begun and completed do not coincide with the progress actually achieved, which it is our present concern to indicate and explain. I regard BBW as coming immediately after New York City and VBW as a continuation of BBW. My grounds for this will be stated below.

A photograph of 1942 shows the artist laying out VBW in continuous, uniform lines that he presumably then divided to form a variety of planes.
He believed that the painting was actually finished at a certain point but later felt dissatisfied with the result and reworked the canvas with modifications that death prevented him from making permanent. The canvas was thus left with the colored tape provisionally added during the phase of rethinking, and it is my impression that this was no coincidence. I believe that VBW was necessarily left incomplete. I shall explain the reasons for this conviction after analyzing the painting.

The canvas is the same size as the one used for BBW but this time in the lozenge position.

What characterizes the composition at first sight is a further increase in multiplicity. Another significant difference with respect to BBW consists in the almost complete absence of continuity in the lines, which are reduced to seven horizontal and two vertical rectilinear sequences. The lines appear continuous in BBW because the space between the small squares is predominantly yellow. The rectilinear sequences of VBW are instead made up of a tighter rhythm of small rectangles and squares, so closely arranged as to reduce the sense of linear continuity to the absolute minimum. In VBW the small planes are laid out in rectilinear sequences whose continuity disappears with changes in the color, size, and position of the planes.

In BBW the planes are generated by the lines and return to them; in VBW lines and planes seem to become one and the same thing.
While the space is nevertheless very dynamic (not least because of the lozenge format), its dynamism is the result of a virtually unlimited number of planes interacting with one another. While the finite dimension of the planes appears to predominate now, their enormous number and variety tend to evoke an infinite space. The infinite space of the lines is now expressed through the finite space of the planes.

Transition from smaller to larger planes involves an increase in spatial duration and vice versa. Everything varies in this painting, as it does in BBW, but we no longer see any process leading to a unitary synthesis. It is multiplicity that predominates here.

 

VBW

VBW  Diagram A

VBW appears to present an endless sequence of possible syntheses of yellow, red, and blue manifested in constantly varying forms (Diagram A). In actual fact, this is precisely what BBW tells us: unitary synthesis opens up again to multiplicity. We encounter a great many instances of partial unity (including white) in VBW, but not one that holds for the composition as a whole. All the planes are in a state of reciprocal motion. They are all relative and there is not one that establishes itself as a synthesis of all the others. I am reminded of the multiethnic society of New York, where all cultures and all religions necessarily assume relative value.
This difference between BBW and VBW recalls the transitional relationship of 28 years earlier.

 

VBW

VBW  Diagram B

We mentioned unitary syntheses in white. A white form verging on the square can be seen in the upper section (Diagram B labeled A). On the left we see a white plane (B) (with the same proportions as the unitary synthesis of BBW) inside which two small notes of color (yellow and red) are born. These then develop linear sequences inside a third white area (C), which is analogous in its proportions to the square (A). The synthesis we see in A is manifold at the same time (C). All the colors (C) blossom from the white (A): first the two small accents of yellow and red (B) and then more substantial sequences of yellow, red, and blue (C).

 

VBW

VBW  Diagram C

A quick view taking in the composition as a whole picks out a group of yellow planes that seem to evoke something more constant (Diagram C).
On closer observation, we note that the eight yellow planes present analogous amounts of color but vary in their proportions or present the same proportions but vary in terms of position and relations with the surrounding parts. We are thus observing either different entities that are related to the same thing or the "same" entity in a state of becoming, constantly changing in appearance: the one and the many.

Mondrian shows us this broader variation of yellow in order to suggest that the variety he intends to evoke is in actual fact far greater than the canvas can display. It prompts us to imagine all the other different shapes, sizes, and proportions that the white, gray, red, and blue could also assume in all the possible positions and reciprocal relations: a truly infinite "landscape".

 

BBW

BBW Diagram E

BBW already presents something similar. In diagram E the three yellow planes (12, 13, 14) containing a gray rectangle actually constitute a small variation of the same degree of spatial development, the variation of one and the "same" thing constantly changing in form. The degree of variability the painter wishes to express is far greater than what manifests itself on the canvas. The possible variants of every passage are in fact endless and in no way restricted to what the image can display.

As noted above, VBW is characterized by the almost complete disappearance of lines, a crucial component of Neoplastic space all the way up to BBW.
In VBW lines and planes become the same thing and the sense of multiplicity or totality previously expressed through the continuity of the lines now appears to be wholly concentrated inside the canvas. This has a precise meaning upon which it is necessary to reflect.

 

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Neoplastic lines were born when the oval of the Cubist period (1) expanded beyond the finite space of the canvas (2) and the planes joined to generate linear segments (3) that then became continuous lines (4). The totality of space expressed by the oval as a whole within the canvas (1) opened up and become a totality manifested through lines that continue uninterruptedly (4). The idea of totality conceived in a metaphysical form (the oval) gave way to the assumed totality of real space, to which the canvas belongs and the lines allude. 4 suggests, on the one hand, the boundless and colorful physical extension of reality (which is expressed also through the dynamic continuity of the lines) and tends, on the other, to concentrate inside the painting in an ideal synthesis expressed through a white central rectangle. The composition evokes the multiplicity of the external world and the syntheses human mind always tries to achieve while dealing with that endless variety.

 

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8

The manifold aspect of space underwent constant reduction as from 1919 (5, 6, 7, 8). Mondrian's Neoplastic compositions attained greater synthesis during the1920s because the artist saw the finite space of the canvas connecting with the objective space of the world through lines. The lines performed the vital function of maintaining a link between the limited space of the pictorial representation and the infinite space of reality. Mondrian thus concentrated all through the 1920s on unitary synthesis (the white rectangle of 4 that had meanwhile become a square form) (6), which admitted color (7), opened up, and multiplied (8). He saw the need for the finite space of the canvas to open up to the diversity of the world.

 

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12

The unitary synthesis manifesting through the square expanded beyond the canvas (9) almost as though in an attempt to coincide with the infinite space evoked by the lines, especially in the lozenge compositions (10 and 12). In 10 just two black lines allude to a square field that can barely be intuited, a square that is no sooner generated than it becomes an infinite space. The top and right corners of the lozenge accentuate the dynamic expansion of the central field. The space of the 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).

 

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16

As from 1934, when the compositions gradually opened up once again to complexity (13) and the lines blossomed into color (14), as a multitude of small squares (15), the sense of totality displayed in a virtual way only by the endless lines manifested itself in tangible and concrete form within 16. It was as though in this last composition the lines had contracted to draw all of the variety previously situated outside the painting back into the canvas.

In VBW the lines appear as sequences of small squares or planes that begin, develop, and end inside the canvas. The lines no longer continue beyond the edges of the canvas because "all" of the manifold aspect of the world is now manifested inside the canvas itself. Subjective representation seeks to coincide with the objective reality of the world.

Manifold space, previously expressed as assumed and non-visible infinite extension (the continuity of the black lines), gives way to manifold space understood as the largest amount of variation wholly visible inside the painting: variety that had not been seen since Checkerboard with Light Colors (5); multiplicity that the painter had endeavored between 1920 and 1933 to drive beyond the canvas with lines in order to concentrate on a unity designed to express both the one and the many at the same time (12).

From this viewpoint, the Neoplastic lines could be seen as a sort of "memorandum" serving for over twenty years as an ideal link between the representational space of art and the space of reality (the oval) and then dissolving on the return of the latter (the variety of planes).

The lines in VBW restore all the variety of the world to the composition, which means that the totality of space (formerly expressed by the oval) re-enters the canvas in the two last paintings.

 

The whole of the European Neoplastic phase is a slow and gradual opening up of unity to multiplicity. The one finally opens up to the point of coinciding with the many (VBW). While it is unity that alludes to virtual multiplicity in Lozenge with Four Yellow Lines (12), it is multiplicity that alludes to a series of possible unities in VBW.

This is probably what Mondrian felt in his heart but was not yet able to explain clearly when he said that there was too much that was old even in BBW. While the painting does express a high degree of multiplicity, he probably saw something old in the fact that it was still necessary to evoke a part of reality virtually through the continuity of the lines. In talking about this work, the artist is also said to have expressed dissatisfaction with the amount of yellow, which is tantamount to saying the same thing. He must have felt that lines were still excessively present in BBW. Lines are the primary means of expression in drawing, just as colored planes are in painting. The lines become planes in BBW, and everything is a plane in VBW.

Mondrian was again dissatisfied with VBW, and I can understand this. Some parts are not resolved very well and it is now impossible to understand what state the composition was in when the painter initially decided that it could be regarded as a finished work. The area of space in the left corner of the lozenge is weak because the two small black planes abruptly interrupt the rhythm flowing from the central section. There is also something wrong with the section on the right, where a marked concentration of small planes can be seen, and with the area by the upper corner of the lozenge, which appears to be unduly summary.
With compositions of this sort, one could obviously work for some years before obtaining an even barely satisfactory result. I myself recently finished a composition begun three years earlier and am still unsure whether it all works as it should.

I shall return to VBW and the artist's work as a whole in the next page and explain my reasons for believing that this painting was in any case bound to remain unfinished.


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