Chapter Four


Holistic Symmetry in Modern Art


   Symmetry has been a concept of beauty, harmony, balance, and awe in a great variety of cultures and in many historical periods.  In fact, symmetry has represented perfection for many people.  A modern poet, Anna Wickham, addresses deity as “Thou great symmetry”:


   God, Thou great symmetry

   Who put a biting lust in me

   From whence my sorrows spring,

For all the frittered days

   That I have spent in shapeless ways

   Give me one perfect thing.



                      from the Contemplative Quarry


   Symmetry is a feature of nearly all artistic traditions, although its prevalence and significance have fluctuated from time to time and from place to place.  In the Western artistic tradition, a symmetrical format provided the main pattern for organizing visual information until the late Renaissance.  Since then, other compositional formats have developed and have been preferred.  In the last three decades, however, symmetry has again emerged as an important pictorial means in such traditions as chromatic abstraction, color field  and one image  art.


   A number of prominent artists of the last four decades, such as Frank Stella, Barnett Newman, Jasper Johns and Jackson Pollock, employed symmetry as a primary structural means.   Stella in his pin stripe  painting, Die Fahne Hock (1959), offers a virtual diagram of horizontal-vertical symmetry, while Newman, in his search for the sublime, employed simple symmetry and investigated the symmetry of color, a topic about which we will have much more to say later in this chapter.  Johns sought images that in their natural state were symmetrical, using them to make them seem to concern themselves simultaneously with flatness and dimensionality, although his works are essentially flat.  The feature of symmetry probably led most of these artists to see a connection between their own art and that of the American Indian.


   Stella and Johns acquired significant collections of American Indian art, and Newman made a study of it.  Jackson Pollock, the revolutionary American painter, often referred to the influence that Navajo sandpainting had on him when he was exposed to it in his youth. 


   The abstract painters Hans Hofmann and Piet Mondrian also wrote about the importance of bipolarity in achieving holism.  Hofmann states:  “The pictorial life as a pictorial reality results from the aggregate of two-and-three dimensional tensions: a combination of the effect of simultaneous expansion and contraction with that of push and pull” (Hofmann 1955:150).


   Although Hofmann does not state the exact proportions necessary for unifying opposing forces, he does present the contrast of two-dimensionality and three-dimensionality that subdivides into the two bipolarities of “expansion and contraction” and “push and pull.”  When combined, these bipolarities supply the “aggregate” image.  However, by observing Hofmann's paintings (e.g., The Gold Wall), one sees that these polarities form a harmonious whole.  For example, one can perceive separately the action of either two-dimensionality (which reads across the picture plane) or three-dimensionality (which retreats behind and advances beyond the picture plane), depending on the focus of concentration.  In other words, one force does not dominate the other in the visual perception of his works--both operate simultaneously and with equal intensity.  A further examination of Hofmann's painting in Plate 39 provides an example of how these bipolarities are affected by field forces.


   In his classic essay, “The Plastic Art & Pure Plastic Art,” Mondrian (1964) expounds on the bipolar nature of art and proposes a corresponding theory for constructing dynamic space.  Basic to his idea is the bipolarity between the cultural and the individual, the objective and the subjective:


Although art is fundamentally everywhere and always the same, nevertheless two main human inclinations, diametrically opposed to each other, appear in its many and varied expressions.  One aims at the direct creation of universal beauty, the other at the esthetic expression of oneself, in other words, of that which one thinks and experiences.  The first aims at representing reality objectively, the second subjectively.  (in Herbert 1964: 115).


   Because organization of pictorial elements deals directly with the underlying field forces, this aspect of Mondrian's theory provides insight for us here:


The only problem in art is to achieve a balance between the subjective and the objective.  But it is of the utmost importance that this problem should be solved, in the realm of plastic art--technically, as it were--and not in the realm of thought.  The work of art must be “produced,” “constructed.”  (in Herbert 1964:115-116).


   Jack Burnham (1971:57) also maintains that a balance of bipolar factors is essential to a work of art.  The terms that he identifies and establishes for his own search of a common structural mode are naturalism and culturalism.  According to Burnham (1971:57), a balance of these two forces in art must always be preserved since art, like myth, is engaged by society to mediate between the natural and the cultural.  As such, art serves to naturalize the cultural and culturalize the natural.  But what constitutes the natural and the cultural?  “Within the Natural-Cultural dialectic the process of art-making is always natural, while the concepts and choices of the artist are invariably cultural.  This is a mediation which the author finds to be consistently observed” (1971:56-57).


   The plastic art theory of Mondrian, which includes the objective-subjective bipolarity, and the structural art theory of Burnham, which he describes as the natural-cultural dialectic, both stress the requirement of balancing or synthesizing bipolar contrasts.   Mondrian proposes the concept of equivalence that offers insight into precisely how these opposites are holistically integrated.  Concerning the meaning of balance in his own theory, Mondrian (1964:122) claims that, “The important task . . . of all art is to destroy the static equilibrium by establishing a dynamic one.”  The “fundamental law of equivalence” to which Mondrian refers is “unified expression through the balance of two opposites.”  (1964:115).   For him, a unified aesthetic expression was created by “equalizing” the energies produced through the action of the field forces, the final result of which was dynamic.  Mondrian's idea of unifying opposites is exemplified in his painting Tableau I (1921).


   The foregoing discussion of bipolar symmetry in modern art stresses the unification of opposing visual forces through the idea of equivalence.  This approach to holism produces a new summative entity, instead of merely furnishing an even distribution of parts across a picture plane.  This holistic entity exists in dynamic equilibrium, which is commonly perceived as spatial tension.


   The synthesis of contrast, as a means of creating unity, has become increasingly important during the historical development of modern art, from Monet to Olitski.  Early twentieth century artists such as Picasso, Braque, and Mondrian all produced spatial tension in their paintings by equalizing strong dark-light relationships (see Navajo textile in Plate 24).  Mattise and others applied complementary colors with equal energies to create forceful expressions of the emotional qualities of life (see Navajo compositions in Plates 23, 25, 28, and 30).  All these artists reduced complex orchestrations of values and colors to high contrasts of opposing fundamental pictorial elements.  Later, the emphasis on bipolar dualism evolved as the primary method of pictorial organization, especially with the advent of color field painting.


    In color field painting, contrasting red, yellow, and blue energies are equalized to envisage overall holistic configurations (see Navajo composition in Plate 24).  We propose that the equalization of dualistic color properties supplies the primary organizational means -- in conjunction with the field forces -- for constructing the pictorial configuration of holistic symmetry.  This leads to a color theory based on bipolar symmetry.


   Mondrian's idea of balancing bipolarities through the principle of equalization provides the foundation and springboard for developing an understanding of color symmetry based on the unification of binary pairs.  Central to Arnheim's color theory, as it relates specifically to pictorial organization, is color completion.  Color completion, a form of holism, is the unifying effect of space that occurs when combinations of complementary hues are applied with contrasting, neutralizing energies.  Bipolar symmetry results from opposing properties of complementary colors; holistic symmetry develops where the neutralization of energies occurs when the intensities of contrasting energies are brought to a state of dynamic equilibrium.


   The effect of color symmetry can be produced by a single unification of two bipolar hues.  It can also be accomplished to a larger degree by unification or integration of several bipolar colors.  Hue basically divides into three bipolar pairs: red and blue, blue and yellow, yellow and red.


They are the only set of complementarities in which all constituents are pure hues and therefore totally exclude the other two.  There is nothing yellow in the pure blue, nothing blue in the pure red, and so forth.  At the same time the three colors require one another. This particular structural combination of mutual exclusion and attraction is the basis of all color organization . . . (Arnheim 1974:357).


   The basic bipolarity of the fundamental triad is the principle by which all three hues exclude each other in terms of their individual properties but also require each other to ensure the creation of a full or holistic color union.  Color symmetry, the unification of a bipolar color pair, constitutes a new singular, summative entity.  Thus, the total concept of color completion, which encompasses the ultimate effect of color symmetry, is holistic and interactional (see Figure 20 below)



Figure 20








   Exclusion   -vs-    Attraction    =      Completion










   When the basic bipolarity of hue, exclusion, and attraction is applied to secondary hue mixtures, we find that any combination of two primary hues opposes and complements the third:


This produces a symmetrical system of three intertwining pairs of complementarities.  Each pair consists of a pure hue and the balanced mixture of the other two:  blue and orange, yellow and purple (or violet--whichever word one prefers for describing a balanced red-blue), blue and orange.  This amounts to a two-level hierarchy, consisting of the three primary pure hues and three secondary balanced mixtures (Arnheim 1974:358).


This “symmetrical system of three intertwining pairs of complementarities” at first appears to be merely what is commonly referred to as complementary colors or hues that lie opposite each other on the color wheel.  However, Arnheim postulates that all three hues of the fundamental triad are included in each pair of complementarities -- one pure color and a “balanced mixture of the other two.”  The principle of bipolar symmetry is still operative, but on a less obvious level (see Figure 21 below).




















   If we focus our eyes on an intense red for a period long enough to saturate the cone receptors for red in the retina (usually only a few seconds), then suddenly take our eyes off the red and focus on a neutral color or white, we will for a short moment see green.  This is because the red receptors tire from the saturation and the other receptors for blue and yellow take over and try to balance our perception of color.  This phenomenon in the physiology of the eye is an optical effect or illusion called simultaneous contrast.  This is evidence that the central nervous system in human beings is constantly oriented toward achieving some kind of balance, harmony, or equilibrium.  The law of pragnanz, another functional aspect of the central nervous system, seeks the simplest solution or clearest resolution to any imbalance or disequilibrium.  In this case, green is the best hue to balance red because green is exactly opposite red on the color wheel.


   Whereas color symmetry in Navajo weaving is often very subtle in terms of hue, color symmetry found in contemporary art is more overt and dramatic.  Examples of three-way color symmetry (in terms of hue) are found in Hofmann’s Memoria in Aeterne and in Mondrian’s Tableau I.  Three-way hue symmetry is also illustrated in my own paintings that I call Images in Motion (see Plate 32).  In my work, I have combined all three of the primary hues in an attempt to acheive a dynamic equalization of the visual energies found in each.


   Although Cezanne's painting is considered the precursor to the trend of reductivism, the early twentieth-century artists Kasimir Malevich and Marcel Duchamp produced works and expressed theories germinal to its conceptual evolvement:  “Both the yearnings of Malevich's Slavic soul and the deductions of Duchamp's rationalist mind led both men ultimately to reject and exclude from their work many of the most cherished premises of Western art in favor of an art stripped to its bare, irreducible minimum” (Rose 1968:277).  This passage denotes the two primary components of the reductivist trend, the emotional yearning for primary elements of expression and the intellectual drive to alter the course of Western art, which were integral in the development of “primitivism” in modern art.


   The intellectual component of this trend, called “Modernist reduction” by Clement Greenberg, eventually evolved into a major movement during the 1960s in which symmetry surfaced as a dominant feature.  This movement, composed of field painters, sculptors, and environmentalists, came to be called minimal art (Rose 1968:274-279).  Minimal art stressed holistic symmetry, where the concept, the image, and the space all reduce to a singular entity.


   The accelerating momentum of the reductivist trend, combined with the intense rejection of abstract expressionist principles, provided the motivating force that led to the emergence of systemic symmetry and the logical unfolding of color field painting.  A number of New York painters, such as Stella, Johns, and Noland, were dissatisfied with the overemphasis on gesturalism and all that its application implied.  Lawrence Alloway (1968:39-40) described some of these artists' innovations, which were in opposition to abstract expressionist principles as  “the mounting interest in symmetrical as opposed to amorphous formats, clear color as opposed to dirty, hard edges as opposed to dragged ones.”  In a sense, systemic symmetry was born out of amorphic asymmetry.  This occurred in conjunction with the increased concern for the reduction of imagery to fundamental forms.


   The major type of systemic symmetry identified by Alloway (1968:56-58) is one-image, which generally refers to paintings which consist of a single field of color.   This general definition includes paintings based on modules, grids that are contained in a rectangle or expand beyond their edges.  In addition, it encompasses paintings that are freer, but which end up with a reduced number of colors.  All of these pictorial conditions stress holistic symmetry:


The field and the module (with its serial potential as an extendable grid) have in common a level of organization that precludes breaking the system.  This organization does not function as the invisible servicing of the work of art, but is the visible skin.  It is not, that is to say, an underlying composition, but a factual display.  In all these works, the end-state of the painting is known prior to completion (unlike the theory of Abstract Expressionism).  This does not exclude empirical modifications of a work in progress, but it does focus them within a system.  A system is an organized whole, the parts of which demonstrate some regularities.  (Alloway 1968:56-58).


   This passage describes the link between holistic symmetry and systemic art. The characteristics of holistic symmetry are systemic, synthetic and summative.  Holistic symmetry reduces compositional parts and integrates them into summative wholes.  This is often achieved by the addition of repetitious parts, which together form allover patterns.  Summative wholes and allover patterns possess the qualities of simplicity, clarity, directness, and immediacy.


   Newman, an artist whose works are exemplary of early one-image painting, offers two distinct variations of this concept.  One is the overt or obvious emphasis on the center of the picture plane and the other consists of a subtle system of proportions.  The first variation is illustrated by his painting, Onement I (1948).  In this work, a single band is centrally positioned:


The thick paint is irregular enough to diffuse the symmetry of the line and make it impossible to speak of division.  The band is more like a zipper in its function of joining them . . .  The unity of the piece is stressed, too, by the fact that the band goes from edge to edge of the canvas, with no internal veering or stops.  The image is the result of all the painting, not of its parts.  (Alloway 1970-71:30).


   Specific examples of other one-image paintings are by artists who turned away from gestural art, as well as those who never entered it.  The former are represented by Pollock's drips of 1951, Leon Smith's stitching patterns of 1954, Liberman's hard edges of 1950, and Noland's chevrons of 1960.  The latter group includes Stella's symmetrical black paintings of 1958-59, John's targets of 1955, Kelly's panels of 1952-53, Newman's Onement series of 1948, Rothko's dominant colors of 1950s, and Reinhardt's crosses from 1953.


   Other terms besides one-image have also been used to signify the singularity of the structure and the object.  They are “unitary fields,” “close-valued colors,” “non-relational,” “one-color,” “oneness,” “literalism,” and “all-over pattern.”  All of these terms indicate a holistic configuration and represent variations of systemic symmetry.


   Symmetrical, systemic painting served as a nucleus of avant-garde energy around which numerous artists with differing theories and techniques revolved.  The urgency to combine field and modular imagery with holistic configurations, in addition to the discovered compatibility of color and symmetry, inspired many artists to undertake a thorough investigation of the pictorial possibilities of the color field.  This specialized  investigation unfolded in a very logical fashion through its culmination in the late 1960s.  Since these works, which stressed color within a field context, were structurally sound and expressively clear, Walter Darby Bannard (1970:40) claimed they were the best and most significant paintings during that decade.  Others called this period of color research “The Great Decade of American Abstraction”  (Carmean 1974).


   The tradition of abstract art and the use of color as subject matter to convey interrelatedness and holistic essence were already in existence before Kandinsky, Malevich, Mondrian, and Pollock came on the scene in the first half of the 20th Century.  Abstract art and holistic concepts already existed among American Indians, and one of the highest and most extensive developments of abstract art was found in Navajo weaving.


   The use of color to convey abstract and holistic essences and themes is found in many aspects of Navajo language, art and culture, not just in Navajo weaving.  The concept of holistic essence -- hózhó -- is not new to the Navajo.  It permeates every aspect of the culture and its maintenance, celebration or restoration is the goal of all ritual action.  The concept of hózhó is too abstract and too contextual to express in simple and autonomous imagery; it must be conveyed in interactive, symmetrical, and holistic compositions that are presented in one-image formats:


In a sense, contemporary artists have led us to a new way of seeing these blankets, one which would not have been readily accessible thirty or more years ago.  That a great many of these artists have a serious interest in Navajo blankets is demonstrated by their personal collections.  The premises of "abstract art" are no longer controversial, but neither are they deeply rooted in our society.  Abstraction was not a special "artist's" vocabulary for the Navajo who wove these blankets; rather, it was a valid means of personal expression in their society.  The Navajo weaver dealt with many of the same concerns as contemporary artists, but in the more integral Navajo culture these concerns were central and shared by everyone.  (Kahlenberg and Berlant 1972:26-28).


   Navajo weavers, however, have never totally relied on abstraction and color as their visual means of expression.  They have also relied extensively on a variety of geometric patterns that are based on cultural motifs.  The color field painters also discovered that, in order to get the colors to interact freely across the picture plane, they had to use simple and archetypal geometric imagery -- much like that used by Navajo weavers, though not as extensive or elaborate.


   The concept of openness has proven to be a basic premise in color field painting.  By tracing the evolution of color field painting from Pollock to Louis to Olitski, Bannard (1972:66) demonstrates that the basis of continuity of these artists' work "has been openness, space between."  In Pollock's art, openness refers to the “open linear tangle” of drips of paint, which creates a “uniform, symmetrical density.”  Louis utilized this idea and applied it to his Veils and his Florals.  Here, the holistic configuration consisted of “forms within a single form,” centrally located.  In Louis's Unfurleds series, the center is vacant, banked with streamers of pure hue on opposite ends of a large horizontal canvas.  In this series, openness consisted of dispersing rather than converging pictorial elements.


   For colors to expand into a viable continuous surface, there must be a limited number of interruptions and contrasts.  An all-over structure, which supersedes the tendency of the surface to be divided and cut into individual pieces by line, is necessary to allow for dominant, outward flowing monochrome imagery.


   The effect of openness in color field painting allows hue to spread visually over huge, expansive areas, thereby creating a continuous surface.  This continuous surface is anchored to the picture plane by colored images positioned on or near the edges as exemplified by the paintings of Louis, Noland, and Olitski.


   Color field as an important type of holistic symmetry represents the most thorough investigation of the pictorial possibilities of color to date.  This concentrated effort to discover the structural properties of color and achieve its pictorial potential affirm the association of color field painting with holistic symmetry.


   As we have seen from the previous discussion of color symmetry, Navajo artists were working on these properties and possibilities with color long before the notion became popularized in color field painting.  Holistic symmetry has always been a basic premise of Navajo art, because the culture has such a powerful and pervasive emphasis on holism, not the least of which is conveyed by hózhó.


   Holistic symmetry is not just the sum of the parts but the compositional effect of the summative image.  Holistic symmetry is, then, aesthetic form in its most vital and its most significant manifestation, expressing an aesthetic and subjective comprehension of the universe and its basic features.  In the next chapter, we will see how this comprehension finds expression in the technical comprehension of the universe found in modern science.