Piet Mondrian - Broadway Boogie Woogie


	Broadway Boogie Woogie, 1942-43,Oil on Canvas, cm. 127 x 127 (50" x 50"), MoMA, NYC, USA

A certain form of art criticism has accustomed us to start with romantic digressions on themes of a general character rather than addressing the most concrete and essential elements of a painting, namely its forms and colors. I hope that the necessary degree of detail in certain passages does not unduly inhibit the overall view that remains one of the aims of my work. Readers will therefore have to be patient and go through the details of the analysis first before being able to take a broader look at aspects of a more general character which is, indeed, the major goal of these studies. I consider Broadway Boogie Woogie a sort of "bible" of our times.

In order to understand the genesis of this painting it is necessary to start from the preceding canvas New York City and, of course, from the studies Mondrian made for his new canvas. The existing bibliography indicates two certain studies for Broadway Boogie Woogie: Study I and Study II.


New York City, 1942	Study I for Broadway Boogie Woogie, 1942	Study II for Broadway Boogie Woogie, 1942	Broadway Boogie Woogie, 1942-43

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.
Study I for Broadway Boogie Woogie 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 segments provided Mondrian with the way to express a finite and more constant dimension inside a space based exclusively on lines (New York City). 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.

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.


New York City, 1942	New York City - Diagram A	Broadway Boogie Woogie - Diagram A

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 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 - Diagram A 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. This is the genesis of Broadway Boogie Woogie. (Diagram A)

My explanation of the painting will be based on diagrams, in which I have broken down and analyzed its geometry. Please note that 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.


A	B	C

D	E	F

Viewed as a sequence, the diagrams help us to visualize a dynamic process: A frenzied succession of small squares (Diagram A) give birth to planes (Diagrams B and C) which are nearly all different from one another in terms of size, shape, and color. In diagram C and D we see some planes express a vertical predominance and others greater horizontal development. Some consist of a single color (Diagram C) and others of two (Diagram D). One plane (Diagram E - 17), the largest in this painting, expresses a balanced interpenetration of the three primary colors.

A yellow, red, and blue space of virtually infinite expansion (New York City) concentrates in a finite dimension of those three colors in Broadway Boogie Woogie. A virtually infinite space finds a moment of more solid permanence and duration.

As mentioned, after completing New York City 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. Broadway Boogie Woogie will satisfie this need.

Diagram F shows how the synthesis of yellow, red and blue fades away and returns to the multifarious space of small squares randomly moving along endless lines from which the process had begun (Diagram A). We shall return on this in a moment.

New York City, 1942

Broadway Boogie Woogie, 1942-43

The interpenetration of colored lines generates a multitude of small gray, yellow, red, and blue squares in Broadway Boogie Woogie .
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. 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 Broadway Boogie Woogie are therefore mostly yellow.


Broadway Boogie Woogie		Diagram A

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 actual 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.

The relationship between the lines and the small squares is one of interaction between a space of infinite extension (absolute space of an exclusively horizontal or exclusively vertical nature) and a finite space (the small square) that seeks instead to concentrate and maintain equilibrium between the two opposing directions. Mankind also lives in a condition of inner duality between the natural instincts and the intellectual or spiritual quests. The human being experiences a finite dimension in relation to the infinite space of the universe in much the same way as the small square (finite) on a line (infinite) in a two-dimensional space.

The locating of a small square on a horizontal or a vertical line generates opposition respectively with its own vertical or horizontal component. The small squares move back and forth between the horizontal and vertical lines so as to rectify every instance of momentary imbalance.
It often occurs in our lives that internal imbalance generates external movement (action) and the attainment of a new internal equilibrium is then challenged by a new external situation in a constant dialectic between interior and exterior.


Broadway Boogie Woogie		Diagram B

As seen, the small square is born when two perpendicular lines meet for an instant before moving on. It is the point in which an infinite and absolute space (the line) becomes finite and relative space (the small square) for a moment. 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.

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). The small square strives to concentrate space upon itself so as to maintain balance between the two opposing directions. Think of the situations in our daily life when we try to reach a certain balance between opposite drives within us.

Observation of the frenzied succession of small squares reveals some that join up with others of same color to generate some symmetrical configurations along the lines (Diagram B). 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. Human beings also endeavor during their lives to transform the variable flow of existence as far as possible into a more orderly and constant rhythm of foreseeable events.
Careful observation of the symmetries formed on the lines shows however 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 highlighted in diagram B 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 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.


Broadway Boogie Woogie			Diagram BC

A certain vertical correspondence between two horizontal symmetries can be seen in the section of diagram BC 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 (2), 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	Diagram C

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. 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.

The dialectic between symmetrical aggregation of small squares (Diagram B), which try to maintain their finite simultaneous presence of horizontal and vertical, and disintegration (the infinite, either horizontal or vertical line) gives birth to larger planes where the relationship between opposites (the nature of the small square) finds a relatively more stable situation. Every instance of opposition can subsequently work in a broader context to generate a new and more stable balance.
What appears negative today can become positive tomorrow. Our plans are sometimes obstructed by random and apparently extraneous factors that can, however, perform a useful function in prompting us to reformulate a project during its execution and ultimately improve it. The opposition of events should always be welcomed as an opportunity to adjust and develop the initial idea. Only in this way can equilibrium and dynamic unity be attained between individual and universal interests, subject and object, thought and nature. In everyday life, this presupposes a certain amount of patience, mental openness, and wisdom, qualities that are not always forthcoming among human beings.

Some planes are still partially combined with the space of the lines (3), some are partially isolated (4, 5, 7) and some appear to be totally self-contained (6).
The two planes 5 and 7 appear to be equal on first sight but closer observation shows that 5 has slightly greater vertical development.

If we see the geometry of Broadway Boogie Woogie as a two-dimensional representation of our inner space, we can interpret the various entities (opposite lines, small squares and planes) of different colors as symbolizing the contradictory reality existing within us. Consider the inherent complexity of each and every one of us. We must all contemplate within ourselves the most disparate and sometimes apparently irreconcilable aspects, just as apparently irreconcilable as horizontal and vertical or yellow, red, and blue are in Neoplastic space.

As a whole, the planes indicated in diagram C 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.


Broadway Boogie Woogie	Diagram D

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 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 Neoplastic painting demands, this band is nothing other than the transformation of the plane 8 into 9.

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.

We can regard the transition from the frenetic and precarious space of the small squares to the more constant space of the planes (from an external to an internal space) as a plastic symbol of the gradual consolidation of an inner world through resistance to the conflicting pressures of the external world (symbolized in Broadway Boogie Woogie by the lines) and reinforcement of the equilibrium within (synthesis and the equivalence of opposites). Every small square has one part of itself (horizontal) that is opposed to the other (vertical). Every line strives to open up the concentration that every plane endeavors in its own way to consolidate and preserve. This generates a dialectical process of evolution between external (the lines) and internal (the planes) space.

Internalizing the exterior means opening up, going beyond the narrow boundaries of the conscious self, and allowing this to be enriched as far as possible by the unpredictable diversity of the world, not only the external world but also the internal, the almost infinite reality that we bear within us and often find it difficult to decipher. It means taking cognizance of the duality existing within us; understanding that our every act (thought or action) is the result of opposing drives, just as every small square or plane of Broadway Boogie Woogie is born out of impulses that unavoidably undergo a vertical shift while intent on developing horizontally and vice versa.

Indian wisdom says that the self is the friend of the self for those who overcome the self through the self. Those who resist initial impulses and overcome situations of duality transform conflict with the self into synthesis and unity of being. At the same time, however, the process of growth and enrichment would not be possible without conflict and opposition.


Broadway Boogie Woogie	Diagram D

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 Broadway Boogie Woogie is made up of constant contrast and reciprocal opposition.

The equilibrium attained between exterior and interior is never static. Neoplastic space is therefore grounded on a dynamic relationship between opposing entities. These are moments of equilibrium attained, lost, and then regained in a new form. The greater the effort to establish an equilibrium in a stable and absolute form, the more it opens up to a new movement making it unstable and relative. So it is in our lives.

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 the plane (9, 10, 11) gives way to a more balanced configuration that reduces the opposition to the interior of the same plane (12, 13, 14).

Let us 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.


Broadway Boogie Woogie	Diagram E

We can see at points 15 and 16 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 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.


New York City	New York City - Diagram	Broadway Boogie Woogie - Diagram

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 (New York City - Diagram), attain unitary synthesis here ( Broadway Boogie Woogie - Diagram).


Broadway Boogie Woogie	Diagram F

Diagram F: 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 plane 14 how an internal quadrangle 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 a dynamic way, by comparison with the surrounding space.

Again recapitulating the geometry analyzed so far in its individual parts, we see that the lines in Broadway Boogie Woogie 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 Broadway Boogie Woogie undergoes uninterrupted transformation from a condition of multiplicity to one of unity, from the many to the one.


Broadway Boogie Woogie	Diagram G

Diagram G: Plane 18 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 (19, 20). 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.

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.


Diagram B	Diagram C	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 C.
Plane 2 was identified as the first plane generated in the transition from symmetries to planes (Diagram B) and 3 as one of those belonging to the first stage of development of monochromatic planes. The same planes now (Diagram G) 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 planes we have identified as the starting moments of the process now play a role in the ending phase of that process. in Broadway Boogie Woogie the end coincides with a new beginning.

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. The space proceeds from a comparatively static and wholly internal condition (17) toward one of growing instability (18) that is gradually transformed (19, 20) into the more dynamic and variable external space of the lines.

Observe the six diagrams as a single sequence:


A	B	C

D	E	F

The lines (A) are first concentrated into small squares (B) and then into planes (C) that became a single plane (D) which expresses in a unitary form the multiplicity of A and B. The unity then opens up again (E) and reverts to the more dynamic and variable condition of the endless lines (F and A).

The geometry of Broadway Boogie Woogie 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. An external and manifold space gives way to an internal and unitary space and then again moves outward from the inside. From expansion toward increasing concentration and then from concentration back to expansion: this is the way Broadway Boogie Woogie 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.

It is necessary to view Broadway Boogie Woogie in a state of dynamic equilibrium between one stage and another of the process rather than stopping on the isolated states of the individual parts; to see the geometry in its 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.

The space of Broadway Boogie Woogie blossoms in a multitude of different entities that gradually turn into a single "thing", which then splits and reverts to a manifold condition. This happens endlessly in accordance with an interminable flux that is necessarily depicted by the painter in a certain form but not exhaustively captured within it. Expansion and concentration: something changes every time there is expansion and every instance of concentration will appear in new and different form while consisting of the same energy or matter. Like nature: immensely varied but nevertheless one. Like every single thing: simultaneously one and many. Recall the example of a tree seen from far and close distance.

In addition to the external landscape, however, I am thinking also and above all of its internal counterpart made up of varied and contradictory signs that sometimes display a certain continuity and become like pieces of a jigsaw puzzle, ultimately revealing a single overall design.
We often feel the presence within us of conflicting selves that generate discordant animation. We must all know ourselves. Ours is the sometimes difficult task of understanding the sense of the conflict and opposition and finding a "guiding self" which can resolve oppositions into a synthesis capable of endowing our actions with a sense corresponding to our true nature. The unity we see in Broadway Boogie Woogie is a vertical plane colored blue that succeeds in reaching a horizontal "soul" colored yellow through an equivalent plane colored red. All this is a synthesis of the greatest diversity, which is expressed in painting by means of the most contrasting values. BBW urges us to attain full and conscious self-fulfillment through a dynamic process.

Without realizing it, we address relations between unity and multiplicity every day.

Diversity must not prevail and invade the self, the many must not prevail over the one, but still less can the self avoid confrontation with multiplicity. The goal is to find equilibrium within oneself through continuous interaction with the external world. Discover to our deep sorrow that external conflict is often born out of unresolved tension within us. It is essentially a question of measure and proportion. Neoplastic space tells us that the excessive predominance of any part of us will sooner or later generate an opposite reaction. In Broadway Boogie Woogie , as in life, excess generates its opposite. A traveler who keeps heading east will eventually arrive in the west. This is how things seem to work on this planet. This is how the space of Broadway Boogie Woogie works. We are reminded of Dante Alighieri and his law of divine retribution.

In Broadway Boogie Woogie an infinite space (lines) becomes finite space (planes), the external internal, and multiplicity unity. Opposing concepts assume the same value.They appear as antithetical realities in the human dimension; in actual fact, they are the same thing. Opposites become one only through a dynamic process that ideally reunites the two contrasting aspects without either being able to obtain permanent value on its own. In a dynamic vision, which therefore entails a certain temporal sequence, the duality present within us reveals an intrinsic unity, which is instead experienced as lacerating duality when a static vision, restricted to the particular facts of the moment, prevails. The purpose of these reflections is, however, not to explain life but to show the relations between an abstract painting and life.

* * * * *

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 planes has been merely "drawing" in oil color. In drawing, the lines are the principal means of expression; in painting, the color planes". (The New Art - The New Life, The Collected Writings of Piet Mondrian, Edited and Translated by Harry Holtzman and Martin S. James, Thames and Hudson, London, 1987, p. 356)

Form and color were kept separate throughout the European phase of Neoplasticism with the only exception of the Lozenge with Four Yellow Lines. Black lines delimited the colored planes from the outside with no direct involvement in their space. Drawing (the black lines) became color for a moment in 1933 and then permanently from 1941 onward and when the lines became planes with BBW, there was no longer any distinction between lines and planes, form and color, drawing and painting.

Piet Mondrian, Broadway Boogie Woogie, 1942-43

Blue is the darkest value in the range of colors in Broadway Boogie Woogie and therefore appears to perform the function previously assigned to black. In actual fact, there are two different shades of blue, 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 Broadway Boogie Woogie 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 Broadway Boogie Woogie 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 Broadway Boogie Woogie . We are reminded of the double black lines of 1932-38 enclosing a white line.

I do not agree with the readings that see yellow in the foreground in Broadway Boogie Woogie 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.


	Diagram M	Diagram N

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 (Diagram M).

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 horizontal line running through that plane and pushing it to the right. 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 N).
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 (Diagram N).
The space around plane 17 appears constant because the proportions of the same plane 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.
Broadway Boogie Woogie seems to present a unity that is expressed with the three primary colors and at the same time white.

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 Broadway Boogie Woogie 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 observed in Broadway Boogie Woogie - from lines to symmetries, then one or two-color planes, and finally the unitary plane - tells us that life is change (the dynamic lines) but if people are to live, they need to reduce and stabilize the ever-changing flux of existence, which does not, however, allow itself to be governed all that much (the unitary plane flowing back into lines).

As Mondrian put it, "It is important to distinguish two types of equilibrium in art: 1) static equilibrium and 2) dynamic equilibrium. It is always natural for human beings to seek static equilibrium. This equilibrium is obviously necessary for existence in time. But vitality always destroys this equilibrium in constant temporal succession. Abstract art is a concrete expression of this vitality."

The lines, which express the maximum degree of energy and continue to infinity, represent vitality. The symmetries and planes, which express a measured space and are endowed with greater permanence, albeit not total immobility, represent the equilibrium required for existence in time.

In this dialectic between what persists and what changes, crucial importance will attach to establishing rules, laws, and institutions capable of remaining open to the changes that existence brings with it and hence of performing their regulatory function without stifling vital demands any more than necessary. When laws and institutions oppose the movement and transformations that life brings with it, all they do is generate greater unrest over time, which in turn generates greater resistance on the part of the institutions and so on in an exhausting vicious circle where it is ultimately life that prevails and not our "symmetrical" stubbornness. This is what human history teaches. This is what is shown by the geometry of Broadway Boogie Woogie, where space arrives at a certain degree of control and then opens up again to becoming.

In social life too, greater importance now attaches than ever before to the ability to handle the relationship between the one and the many, moving constantly back and forth between the parts and the whole so as to avoid the predominance of either the multitude of particular interests or the will of the few. The former brings chaos and makes it impossible to work for the common interest; the latter brings the paralysis of democracy if not indeed oligarchy and dictatorship.

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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 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 landscapes or a single tree, with still-lifes and with the Pier and Ocean 5. 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 Broadway Boogie Woogie 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 much 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.” (Paul Cézanne, La Vita e le Opere Attraverso i Suoi Scritti, Istituto Geografico De Agostini, Novara, 1989, p. 304)

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 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.

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.

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 Woogie is 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.

The immediacy of the painted image is certainly very different from the much longer and more intricate processes of real life. Neoplastic space expresses the instantaneous life of the moment while simultaneously evoking processes that can last a long time in reality and ultimately suggesting the unity of all things, i.e. a dimension that we associate with the eternal. Broadway Boogie Woogie is to be seen as a concentrate of space and time: what lasts the length of time required for perception of the visual fact in the representational dimension of art can instead dilate and last for days, months, and years in the space-time of real life.
The thousands of different situations that orchestrate the rhythms of our existence are condensed in the work of art that represents life in essential and hence abstract terms. If it were not abstract, if it were concerned with the fleeting aspects of each individual situation and thing, it would lose sight of the whole and be unable to express life at a universal level.

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1	1915	2	1920	3	1933	4	1942-43

For the first time in Broadway Boogie Woogie, the unitary synthesis is a plane made up simultaneously of the three primary colors.
In BBW the unitary synthesis is no longer a square outlined with charcoal (1), or a painted white square marked out with black lines (2) or yellow lines (3), 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 (4).

The equilibrium attained in the unitary plane of Broadway Boogie Woogie 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 Lozenge with Four Yellow Lines (3)

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.




1	1917	2	1919	3	1919	4	1920

I am reminded of the scattered rectangles lacking unity (1), which now find synthesis in a single plane.
I am also reminded of three squares (one yellow, one red, and one blue) joining up to suggest unity in terms of color (2) and those three larger rectangles of primary colors surrounding a white rectangle in the center of 3.
1 and 3 show a solution where a central white unit (a square area in 1 and a rectangle in 3) works as an ideal synthesis of the colors around it. At that time white, gray and black were for Mondrian a symbol of the spiritual whereas yellow. red and blue of the natural.
2 and 4 show the attempt to merge yellow, red and blue in a colored unit. A unity, however, that does not emerge with the evidence the artist had wished.
The unsuccessful attempt to attain unitary interpenetration of the white rectangle and the colored rectangles of 3 in one large square form (4) is now finally achieved in Broadway Boogie Woogie , where a synthesis of horizontal and vertical and yellow, red, and blue is attained with great visibility.

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1	1933	2	1941	3	1938-41	4	1942

Mondrian's lines were illuminated in 1933 with yellow, in 1941 with red (2) and then simultaneously with yellow, red, and blue (3 and 4).

Previously reserved exclusively for planes, color was definitively applied to line in 1942. As a result, the colored planes disappeared in 4.
In the Neoplastic compositions, planes express finite space and lines virtually infinite continuity. With 4 Mondrian found himself grappling with compositions in never- ending development. 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.

As pointed out above, the composition was developed throughout the European phase of Neoplasticism not only with black lines and colored planes but also with segments that helped to delimit the latter 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 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.

* * * * *

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 nothing 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 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." (Piet Mondrian, Tutti gli Scritti (a cura di Harry Holtzman), Feltrinelli, Milano, 1975, p. 400)
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 Broadway Boogie Woogie , 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, that is to say forms and colors.

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." (Piet Mondrian, Tutti gli Scritti (a cura di Harry Holtzman), Feltrinelli, Milano, 1975, p. 46)

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