PRINT January 1978

Mel Bochner: Getting from A to B

The long chains of simple and easy reasonings by means of which geometers are accustomed to reach the conclusions of their most difficult demonstrations, had led me to imagine that all things to the knowledge of which man is competent, are mutually connected.
René Descartes
Discourse on Method (1637)

THREE PLANAR ARCS WAS A painting done directly on the wall in casein and charcoal at the Whitney Biennial in 1977. It contained three “planar arc” configurations: one in the approximate center of the wall, the two others approximately equidistant from the center to the left- and right-hand sides near the corners. The three “planar arcs” were approximately the same height, along the bottom third of the wall, and they extended laterally across the whole area. Two-thirds of the wall’s height was thus “blank.” Each of the three configurations combined three basic elements: triangle, square and pentagon. In each of the three configurations one pentagon’s base length was horizontal, and a viewer’s line of sight connected these lengths to divide the wall visually (those pentagons were the ultramarine one in the left-hand configuration, the yellow one in the center, and the naples yellow one at the far right). These three sides or bases were possible echoes of the architectural givens, locking the shapes into place, except that the natural division of the wall according to eye level obviated any framing by parallelisms and allowed the shapes—individually and collectively—to expand across the wall without obstruction from site definition. The wall was defined and transformed in terms of the painting, rather than the other way around.

Although it is impossible to separate the three configurations without losing part of their collective effectiveness, I would like to discuss only the center configuration in detail. What is true of this one part can easily be extrapolated to the other two in any case. Yet in some sense this portion seems to be the most complete, the most fulfilling of the three. Several independent aspects of Bochner’s art which have previously existed in discrete quantities among individual works here coincide. Even the two other configurations have a square “missing” from one of the color forms, and lack the completeness of the central part, which has three differently colored forms that consist of all the three basic elements.

As a whole, this section looks spiky, irrational at first, and it seems to be falling off to the right by force of gravity. As with the unbalanced pictorial weight which plays a large part in Bochner’s “Fulcrum” drawings, this sense of gravity replaces a balanced composition of parts, or the immediate perception of a gestalt. There are three sets of the three shapes according to color, but also other sets of triangle/square/pentagon which cross color boundaries. These “hidden” series overlap and mirror each other. The combination of a yellow triangle and violet pentagon and square overlaps with its mirror inversion of the same combination reading from the violet triangle and pentagon to the green square. Another series runs from the violet pentagon across to the green square and triangle. And the whole outer green-and-yellow combinations mirror each other, although not on a 180-degree vertical. The yellow and violet triangles, and the violet and green squares, by touching at one point, also mirror each other but, again, not across a grid-controlled axis. It is not that they are slightly “off” from “normal” orientation: they simply find their position in reference to the other, local, shapes. There is a repetition of the entire green series in the combination of yellow square and triangle to violet pentagon. The green shape slopes down to the right, so the repetition is not coordinated. Just as the most ambiguous shape, the pentagon, cannot be aligned on a grid, neither can the relationships in this configuration be seen as conforming to a mapped space of uniform coordinates. All repetitions and mirrorings are achieved by internal accumulation rather than by external definition. Equivalences are not such that any portion of the configuration can be replaced by any other simply because they are created from the same elements. The building blocks—the geometric forms—are givens rearranged in increasing orders of complexity; positions cannot be reduced to another, simpler set of relationships, just as no one of the shapes can be reduced to another.

Without alignment on a grid system, the shapes and “lines” created by them are all skew in relation to other shapes and lines. (Perhaps “limits” best describes how the viewer perceives the edges of the shapes.) The expansiveness of each form can be traced to the freedom from a covert structure that could be imposed upon the painting. The expansiveness activates a complex network of “imaginary” lines which extend their physical definition as boundaries or limits, reaching out over the entire wall. Although it is easy to see the interior angles of the individual shapes because they are “colored,” the hidden exterior angles are just as visually important. And again, it is easy to see the acute angles, but just as important are the obtuse and “negative” angles—for instance, the angles around any of the four exterior sides that make up three 252-degree angles of the yellow pentagon. It is important to say that these things, when seen, are not as complicated as they must seem when described—no better indication of the precision of the visual in contrast to the difficulty of words.

Equivalence and difference is the tension maintained in Three Planar Arcs. The logical equivalences of each shape’s sides and angles somehow create a confusion of divisions, intersections, and disorientations: these characteristics of the painting reflect the parallel discrepancies between eye and mind. Such concerns served as the basis for earlier drawings like Mental Exercise: Estimating a Circle, where two circles were drawn, one freehand and one with a compass; one perfect as the mind conceives a circle, and one imperfect, as every materialization of a circle must be. In the present painting four large, gaping exterior angles are measurably equivalent, but they are visually quite different: the angles bounded by the yellow pentagon and square at the left, the upper angle bounded by the outer edges of the violet triangle and square, the lower angle bounded by the green square and pentagon, and the angle bounded by the yellow square and violet pentagon. Here the differences are a direct consequence of color: the “yellow” angle looks “large”; the “yellow/violet” one, smaller; the “violet” one, smaller still; the “green” one, the smallest—all because the darker, denser colors make the white they surround appear larger in relative contrast. The action of the mind in simplifying the relationships between the angles while the eye is drawn to the differences in color—the idealizations of the mind versus the discriminations of the senses—this is part of the experience of Three Planar Arcs.

The title itself indicates how discrimination made by the eye recedes as the viewer draws back from the wall—the shapes take on a sweeping, arclike movement which extends, defines, and activates all the white space above it. The wall is defined by the painting; the painting in turn is defined by the actual location and biological characteristics of the eye—of vision. At a distance, the eye tends to see the general sweep of the configurations; up close, the individual shapes can be read as touching base lengths or points of intersection. As a combination of points, there is a strong directional motion to the shapes. But as there is no absolute separation in Bochner’s work between point, line, plane and color, there is no real separation between the action of the eye and the process of the mind (“The eye is a part of the mind”). Point, line and shape are the logical outcome of the measuring and estimating pieces; so every element implies the existence of every other element, and the comprehension of space implies the intimate coordination of eye and mind and the impossibility of either pure visibility or pure conception.

Numbers for Bochner have yielded points; points, lines; lines, shapes; shapes, planes (as in One, Two, Three, Four and Rules of Inference). But these elements have led to color, too, although using color wouldn’t seem to be the necessary outcome of anything else. Color is responsible for some of the most subtle qualities in the center configuration of Three Planar Arcs. Certainly the whole is rendered more comprehensible by its division into three “equal” color areas. But at a certain point, color, too, reinforces the extension of lines beyond the physical boundaries set by the forms. As different series of the three basic elements can be read across color line, so the extension of base lengths takes place across these limits, where they divide and intersect the neighboring, differently colored shapes. For instance, the eye does not stop seeing the line which is the violet pentagon’s lower base length, when that length stops at an interstice; but the eye continues that line, extending it into and then beyond the green square. The square is intersected by this line, and the line divides it into two new, unnameable shapes. The eye oscillates between the whole square and its division into irregular parts. Repeating this kind of extension of any and all base lengths helps to establish ever more complex intersections of skew lines not contained in the actual painting. These lines of sight become more challenging as they divide the white space: an extended lower base length of the yellow triangle intersects exterior angles on either side, or the upper yellow pentagon base horizontal to the floor cuts through the very tip of the violet triangle and square.

Color is yet another way in which Bochner achieves open unboundedness within the specific definition of his materials. Even the particular application of paint to the wall—the touch—works with color to emphasize this. Far from functioning only visually or esthetically—although the visual texture was marvelously feathery and subtly mottled—the very thin, brushy casein covered the wall with minimal visual interference with the wall itself. The paint was neither opaque nor transparent; it had just enough body to hold the color. Even from a considerable distance, the wall was visible through the paint, allowing the eye to “see through” and pass from painted to unpainted surface without obstruction, facilitating the divisions, intersections and extensions outlined here. The characteristics of point, line, shape, and plane are further implied in color, not sequentially but as an elucidating bond between logical consistency and esthetic complexity—with Bochner the artist acting, so to speak, as chemical bonding agent. So the use of color—and of more than one color—doesn’t interfere with the other basic qualities at all.

But what about the colors’ relationships to one another? It is senseless to analyze what is happening on the microstructural level if the color relationships are left unconsidered. The three colors are a light yellow, a violet, and a deep green (the indefinite article signaling the inexactness of color names). From the systematic or conventional point of view, this series of colors seems arbitrary, irrational (and visually, it is not expressionistic). With violet and green, Bochner could have used orange instead of yellow for the three secondary colors; he could have used red instead of yellow for the suppression of tonal value; he could have used blue instead of yellow for the three “cool” colors. So yellow seems “wrong” if color must function sensibly. Yellow is the color out of all six basics which would disrupt the relationship suggested by violet and green. In effect, Bochner systematizes inconsistency by selective exclusion (at least in this painting).

Bochner began using color seriously after direct exposure to pre-Renaissance Italian art. Color in Trecento art is unsystematic, free from the scientific theories of the Renaissance, and intimately connected with environment as the expression of feeling for space. In the drawing Three Shapes, Bochner uses the same formal configuration as the center of Three Planar Arcs, but he changes the colors to a chalky light green, a dark violet and a dense black. Here color cannot be understood except as emotionally expressive and specific to the world of the drawing, an indication of the feeling of the precise space rendered. When it comes to color, the installation painting is a more fragile experience than the drawing—all the more so since color as a physical sensation cannot be accurately described. And there is always, in Bochner’s paintings in situ, a feeling of exasperation with the painting’s transience and the protracted length of time it takes to understand its nature fully. The exasperation is a feeling that brings one to the limits of memory. Here it is to Bochner’s credit that Three Planar Arcs is so eminently memorable.

This long description only begins to outline some of the salient features of but one part of a painting. It has been a simple matter in this century to dispense with description as a tool when the level of visual decisions is reduced to zero, as in Minimal art and late modernist painting. The curiosity of Bochner’s art is that the description isn’t even of an object, but of an instance of esthetic relationships extended into nothing but the space of the mind.

The driving force behind modernist art history is reduction, that progressive refinement of stable, universal solutions to pictorial problems which eliminates everything except that essence clarifying the parameters of an art medium. “The most successful picture will so synthesize the means of design that line will be no longer separable from shape, nor shape from color, nor color from light,” as Leo Steinberg capsulizes in his Other Criteria (New York, 1972).

What is left after art reduces itself to self-definition, tautology?

In viewing Bochner’s art as a whole, the question is crucial, because his early language pieces could be seen as the very end-point of reductive art (doing away with all the “baggage,” even the elements of design). Art seemed stripped of everything it had to offer and was left with the idea or statement (“Language is not transparent” as a work of art). Bochner had achieved a preeminent position in the art world with such severe essentializing. However the artist himself may now view his earlier work (as being nonreductive), anyone with an eye can see that there has been, on a basic level, a change in attitude. How else to explain the fact that Bochner now paints, draws, uses pastel, casein, charcoal, even uses handmade, deckled paper—and to the dismay of his earliest admirers?

Bochner’s investigations into the relationship between words and actual experience led him to a problematic discovery: things, ideas, intentions, meanings, perceptions, could not be reduced to language. Perhaps he knew that all along; in any event, it is not an earth-shattering discovery. But in context, it destroyed the succession of reductive moves away from the main source of American art after 1960—Johns’ paintings. In a nutshell, this move substituted names for things. Johns, of course, always understood the differences (and similarities) between the word and the object, and took pains to expose them whenever possible. Only the most deadly serious artists thought that a Johns flag could mean that a painting could only be what it literally is and nothing else (Stella), or that all importance lay in the idea or words that the painting “stood” for (Conceptual art). Eventually, I think, Bochner found visual coincidences and separations were more to the point than the sometime correspondences between word and object.

When Bochner laid down masking-tape squares, and placed pennies so that they were either “in” or “out” of the squares, it was left uncertain what to say about pennies that were “on” or touching the tape. It became a question of semantics, not a question of vision, because the eye knows all the various degrees of “in” and “out” and “at” without having to name them; in fact, naming them becomes unnecessary in the context. There was, in this piece, no need to resort to the mind for “comprehension,” and there was no continuity between the mind’s conception and the eye’s perception. On the other hand, there was a problem with two similar divisions of space in these works, between touching masking-tape squares. At the boundaries or limits of the squares, what was created, and what was the relationship of their contact? What did it mean simply to add another piece of tape next to another; how could they be convincingly presented—two forms with individual insides, sharing outsides? And when Bochner estimated a circle, a diagonal, a center point, what was created between the places where the drawn and the measured differed? What did it mean that they touched at some point? The discovery of Bochner’s drawings and paintings is how these areas of contact—inessential from the point of view of language—are the foundations on which to build an art of extension, accumulation, attraction and addition. Indefinables like “point,” “line” and “plane” still function as the basis of human perception of space; Bochner’s art creates and defines real space in a form continually subject to the presence of human vision.

A problem of ’60s art, as inherited from Newman and institutionalized by Stella, was how to get parts to touch—what to do with all the spaces in between the stripes and boxes (Johns, with typical ingenuity, didn’t have this problem). Bochner’s first drawings that proclaim the importance of shape (like Five and Four and Five and Three, both 1973) had different shapes touching, but their base lengths were different, so congruence across boundaries was impossible. When the shapes were given identical bases, a continuity between parts was achieved, creating extension across boundaries of similarity (such as two shapes of identical color) or difference (two shapes in different color series). With the basic elements and the process of recombination—addition which yields extension and not dumb repetition—Bochner could generate art with an inner consistency unencumbered by the logic of the materials themselves. With the pentagon, shape was at its most complex without being reducible to another shape. (Cage once said that he used no less than five things in a composition because “things start happening around five.”) Two pentagons, with equal base lengths and sharing sides (Five and Five, 1973), is already a combination where the separation of the elements seems impossible because of a magnetic, centrifugal force that operates between the shapes. This combination of elements creates a universe of diversity from simplicity. Bochner’s shapes have a strong “attraction” to one another—on a huge wall, they are somehow attached in groups—and their identities change as they shift and recombine.

There is such allusiveness in the work that I would like to be more specific about how it works, this chemistry of shape. It is possible to say that the basic elements take on “characteristics” of their own when used in different relationships with other shapes. In that same center configuration in Three Planar Arcs, not only do the elementary shapes differ in color, but they also take on separate identities by location and exposed boundaries. The yellow pentagon, with four exposed bases, is very different from the violet one, with four bases touching or hidden. The green pentagon may also have four exposed bases, but it points outward, identifying itself as an intersection of three points rather than a combination of four bases (like the yellow pentagon). As the configuration is based on threes, the triangle is seen in each of its identities, with one, two and three sides exposed (or touching)—it is spiky (violet), arching or stretching (green) or connective (yellow). In short, it is possible to see each shape as having its own center, identifying it as a unit, and also to see it as belonging to a larger chain of shapes, like atoms in molecules or cells in organisms.

The differences, and changing characters, of similar shapes appear in the most seemingly straightforward drawings. These drawings have instigated the criticism that they are no more than puzzles. It is the inability to reduce the overlapping and mirrored pentagons in Duple to a static finality that causes this puzzlement. The point is not to reduce the confusion to a solution, but to go deeper into the unresolve. In Duple, the forms are “simple”; it is the interior “cuts” which incompletely describe base lengths that complicate matters, alternately clarifying and obscuring the areas of intersection. The possibility of seeing what the mind wants to see as two discrete forms is thwarted by the eye’s inability to come to grips with the implied rotation of the figure. When Bochner painted these two figures on the wall in the “Drawing Now” show (Museum of Modern Art, 1976), they were placed on opposite ends of a long, low wall. To understand the similarity and difference between them was even more exasperating than in Duple, because to go back and forth from one to the other required mental stamina of a fairly high order. Even from a distance, when the figures could be taken in at once, they strained peripheral vision to the point where Bochner’s idea of “splitting vision,” first appearing in the “Non-verbal Structures: RYB,” was totally realized. In the world, we focus sight, unify our binocular vision, and edit out information on the periphery.

Bochner holds out not just memory as a stumbling block, but also vision itself, vision which attempts to unify a field and reduce experience, while the painting holds out for the possibility that we cannot see things as continuous or discrete, but in constant mediation between the two. By taking vision to the edge of its abilities, Bochner makes us aware of its limits, but also of what is most central to it, the space of the mediation. This is reflected in the cuts in the shapes themselves—between the two forms, there is nothing, like the space between our eyes (the mind?); the in-between steps of rotation are left out, and the mind cannot reconstruct the process of rotation from one shape to the other. This disorientation is compounded by the sensation in Duple of frozen movement around a center point.1 The mind not only has to jump back and forth between the shapes to get the “difference,” but, visually, the eye must “jump” over the cuts—the breaks in the surface. Each pentagon has its own center as well, and this only intensifies the shapes’ mystery, especially as they pull away from the taut, blank area in the center of the page. All these centers compete for our attention, and our frustration is possible only by their isolation on a large sheet of paper and uniformity of color.

In Trivalent, Bochner sets three pairs of overlapping pentagons next to each other, in rotated positions, and the result is striking. There is rotary movement and an expansive drift as the pairs rise up the right-hand side of the paper. The internal divisions of Duple are gone, and there is a loss of definition. The continuity of forms more than makes up for this lack of definition, however, as it underlines the outer, irregular form itself, and how the extension of lines across to contiguous forms divides space without actually cutting into it.

In Untitled, a painting done on the wall at the Sonnabend Gallery in the summer of 1977, the simultaneous breaking apart and extension of forms and shape combinations was brought to fulfillment. A configuration from Three Planar Arcs and its mirror image were painted on opposite ends of a large wall. (The ratio of painted form to wall in Three Planar Arcs was one-to-two; Untitled has two configurations and the ratio is one-to-one.) Separately, the two combinations display all the characteristics described above as integral to the center form in Three Planar Arcs. Together, they exhibit the additional issues of experiencing Duple: the separation of right and left, circular movement implied by described arcs, a tension between knowing the configurations are simple mirror reversals (another kind of rotation) and the difficulty of reducing their differences to such a formal procedure.2

The properties of the paintings and drawings do not function as ends in themselves. The details of formal construction lead to something which will penetrate directly and expose the nature of space in the act of experiencing it—which is not at all to deemphasize the construction itself. They act as points of entry for the viewer to apprehend fundamental space. What is there is not all of what is there.

It has been suggested in this essay that Bochner’s art exhibits qualities which are antithetical to modernist art. This explains the importance placed on the works’ irreducibility and liberation from grid structure. The question is, what is Bochner showing us that is different?

Bochner has spoken of the grid as a product of the architect Brunelleschi’s studies, and how this system was transmitted to painting by Masaccio. Far from being an isolated technical device to facilitate the illusion of perspective on a flat surface, the grid was indicative of a general view of the world as comprising a quantifiable series of relationships coordinated on a field of horizontals and verticals. This “entrenched Cartesianism”—to jump two centuries—reflected a long series of dualisms in Western thought: mind/body, individual/society, whole/part, conception/perception, culture(man)/nature, political left/right, painterly/draughtsmanly, etc. The problem of Western culture was to synthesize these dialectical opposites.

Leo Steinberg, in discussing Monet’s late water-lily paintings, maintains that Monet broke through the depiction and perception of space that was Masaccio’s gift to art—“that extended underprop of space on which in former times all bodies had found rest, on whose gravitational pull you could count as on a reassuring constant. It meant a great deal to a man to have ground under his feet, to know even in the rapture of a jump that such a ground exists, and preferably not too far away” (Other Criteria, p. 237). Monet inadvertently destroyed the “local space” of the Newtonian world of earlier painting and replaced it by concentrating on the space itself rather than on objects located in the space. His was an insight into the reality of space, as it was being redefined in the early 20th century. Monet found this space in the natural world, in his own backyard, so to speak—the endless, expanding universe of the ponds, with an infinitely deep sky mirrored on a flat water surface which was both flush with the picture plane and an unframeable horizontal plane (and beneath which was an unfathomable depth). This is Monet’s “impossible” space, no longer reassuring to the solidity of the human presence. It was space approaching the purely optical. As Steinberg says, we enter at our own risk, unable to ascertain our position in relation to other things. In a word, we are disoriented. That is the consequence of a world floating free, expanding, unframeable, loosened from the grid system of certainty, with its constant of man (vertical) against the world (horizontal).

Later artists, sensing this radical alteration in the perception of space, understood what was most obvious: vision which extended into a continuous, unitary field, undifferentiated by tone, color, contrast, scale or incident. So we can see the visual correspondences between Monet, Pollock, and Olitski in terms of an increasing abstractness, as a progressive attempt to reduce and synthesize the formal structure of painting. The problem was that they also reduced Monet’s original formulation of that space. It is not a unitary space; it does not exist singularly. It is a succession of superimposed, reflected, mirrored and folded spaces, irreducible. As Steinberg again explains, the “real” world and the “illusory” world of reflections are divided and connected; they only seem to be “one” in Monet’s paintings.

Monet experienced this space where two equals could both share and separate across a limit or horizon, because they were always analyzable as phenomena in the natural world. Modernist art history disregarded Monet’s insight into real space and placed value only on what he was using as a means to communicate his insight. As the “Poplar” paintings make clear, we sense infinite extension only through the successive mirrorings of singular spaces, and these spaces are not the same at all (the tree and its reflection are objectively different things). Only the reflections are disembodied effects of light. The repetition in the “Poplars” implies a constant oscillation, a dialectic, between similarity and difference without resolve—that there is no reduction of real space to a single, privileged constant, or a unique, timeless space; that all the phenomena of experience are equally real.

This suggests a dualism not in terms of Cartesianism, but one that allows (as does modern mathematics) the reality of the infinite—and the infinite in different sizes. Space and its double, both in ever-expanding states, establish a one-to-one correspondence across a line or plane of the water’s surface: a direct visualization of the discreteness of infinity. Monet visualized irreducible difference within repetition.

Malevich’s White on White, a tipped white square on a white ground, represents another, equally challenging instance of this vast, infinite space in painting. The tipped square is a repetition of the plane it “rests” on, but it is disoriented in relation to it. The white planes are both “flat” and infinitely deep; this is a simultaneous expression of the expansiveness of dual spaces. In Monet, it arrives from a vision of nature; in Malevich, from transcendental experience, supernatural vision. Like Monet, Malevich identifies the two spaces by color; he connects them visually. The detection of boundaries between spaces in Monet becomes, in Malevich, the faint pencil line describing superimposition of planes. The forms in Malevich sometimes “fade” into one another, or are repeated side by side or rotated and superimposed into chiastic forms.

Bochner has said of White on White that we have no way of understanding how the tipped square got into that particular position. The square echoes the frame without deriving from it (just like the configurations in Bochner, and unlike the geometries of modernist painting). It is not deduced from the frame, and it is not transferred from another space onto the other white plane: it cannot be reduced to another, more general set of relations. It lacks “coordinates.” The square is a given, expanding from a center point. Each form in a Suprematist composition, in fact, has its own center, as do the lily pads that freely float on the plane of Monet’s picture. Malevich’s “subjectivity” is the ground for the presentation of manifold space. It is just as “impossible” a task to communicate this experience as it was for Monet, who thought his late work should be burned. As viewers, it is not so difficult to “get” Monet’s intention—it is grounded in a naturalism of which it can be seen as the very endpoint. But Malevich’s “nothingness,” his nonobjectivity, asks for a different viewer. The paintings are small; they do not scale themselves to the size of the human body or to the extension of eyesight, as Monet’s paintings do. The viewer strains to find orientation to this space, absolutely without resolve; it is space defined without reference even to eyesight, but which is only visible.

The surprise of Johns’ patterned paintings was that they indicated a shift for him in terms of the use of space, of the nature of space. They obviously offered a radically different space from the flat, deadpan space of his paintings in the ’50s or the disintegration of space in the ’60s. Again Steinberg instructs us in the meaning of space in Johns’ art: it is, for example, the space which affects the viewer in the “Targets,” space defined by subject matter unconcerned with human presence.

Repetition has always played a great part in Johns’ art. That repetition was always quite discrete; it was left to later painters and sculptors to take up the implication of infinite repetition. With characteristic subtlety, Johns used the circle (as the abstract descendant of the target) for simultaneous unity and discreteness. The “Device Circles” present a form which is never at rest (variable), always equidistant from the center (constant) without beginning or end yet created with a palpably real, finite length of wood. No matter how far you moved on this described line, you always came back to the same place; the movement was always frustrated. The kind of movement and space these paintings had was held in limbo until it “surfaced” again in the patterned paintings. Their abstractness allowed Johns to consider the actual nature of space for the first time, while expanding the repertoire of emotional response available from such space.

Johns’ earlier paintings were based on the objectness of painting—that, at a certain point, the painting’s surface came to an end. The finite cultural symbols and systems were selected to enhance, to equal, the paintings’ own limits. The patterned paintings do not recognize these limits. Corpse and Mirror II, 1974–75, goes so far as to project the pattern onto the side of the canvas, onto the backing, and to the inside of the frame itself. There is no focal point on the surface, and the boundaries between contiguous planes aid rather than inhibit the extension of the stripe units. Scent, 1975–76, has a structure which repeats sideways only to end up at the right with the same plane of configurations that is on the very left: the closed line of the circle extended into a repeating series of spaces. Like Monet, Johns uses mirror reflection; it is, however, not the consequence of nature, but of a “device” to extend space. It is a mechanical extension; the mystery of structure is revealed. Johns works directly with space, but as a thing—and the relationship to his earlier painting is now clear. Space is not conceived in terms of the physics of light or the subjectivity of experience, which might almost be seen as “making themselves.” The markings on the surfaces seem unstructured except at the line where they are reflected or repeated. And although the units are uniform, they are rotated and abutted against one another so that individual parts of the plane contract or expand. The units do not fill a blank space, but show how it is articulated into a series of folding, shifting planes. This articulation appears impersonal, conforming only to some internal process. It is, in fact, an example of the kind of real space in Monet and Malevich.

In O Through 9, 1960, Johns created a space of simultaneous planes interpenetrating one another in “layers” which were identically flat and equal—just like the reflecting surface of Monet’s pond. In the patterned paintings, that space is unfolded like a piece of paper, exposing it to direct perception. It is never recessed in depth; it is always “there” rather than “here.” Its constantly changing coordinates conform only to the paintings’ individual rules of orientation. Again, the implication is that human beings are entirely absent from the picture.

But obviously not. A human being made the painting: human beings look at it. Monet makes the viewer feel uncomfortable about his presence in space; Malevich maintains that at least he himself has succeeded in breaking through to it; Johns refuses the viewer any entry at all. The human mind and hand are present all over the surface, however; this expansive field, with its mass of frantically shifting units, defies our penetrating it while seducing us with all those brushstrokes. Is the space beckoning us in, or turning us away? In Corpse and Mirror, 1974, one half is clear, with strokes laid down in manageable oil paint; the other half is dense, uncertain encaustic. Structurally a matter of mirror equivalents, it cannot be the patterning that makes the viewer feel so different about the two. It must be the space itself.

By now it should be more than clear exactly what Monet, Malevich and Johns have in common: the discovery of some visual form which would present the viewer with a direct experience of space, space of implied infinite extension. This space has characteristics of its own; what each artist brings to his painting is a differing idea of the viewer’s relationship to it. To a greater or lesser degree, this always involves some sort of disorientation. To be specific, each artist grounds his art in a disorientation by visualizing an idea the mind finds “impossible” at first: the discreteness of the infinite. The artists do not try to puzzle the viewer; in fact, the opposite: they try to take painting beyond its static frame and bring it into precise, direct experience. It is the space itself which is puzzling, not the artists’ use of it. To attempt security would be false to the actual character of the space.

And Bochner? He has found a way of extending space, of creating manifold, irreducible space and offering an entrance to it by placement according to “natural” fact: eye level, division of right and left eye, vision on the periphery, visual resolution and extension. Bochner places his configurations at his own eye level. When he splits the configurations apart, he focuses attention on the binocularity of vision. When he uses elements which expand from a center point, he appeals to centrifugal forces of vision at rest. If we have no way of knowing how the shapes “got that way” in Malevich, Bochner provides access to just such knowledge. He does more than state the facts of perception, or diagram real space. If embedded in each artist’s apprehension of the space discussed here is the relationship of the viewer to that space, in Bochner’s art that relationship is up front. And its obviousness reveals it as a means and not an end.

As different as Monet, Malevich, Johns and Bochner are as visual artists—that is, as different as their art looks—I think they form an unorganized opposition to dominant modern art history (and they are probably not the only ones). And because of this, they refute the categorical insistence on refined evolution of style. The reason that these artists’ art can look so different is because they don’t define the experience of space only in the formal terms of painting, but in terms of the space itself. What is true of the world is true of the painting. One artist has not “taken” this space from the other; one does not “improve” upon the other’s apprehension of it. The manifold nature of space, and of the viewer’s relation to it, is not something that can be reduced to a succession of styles or formal refinements. It is neither a “problem” nor an “idea,” but a preoccupation with the properties of space—something discovered, not solved.

It is no coincidence that late Monet, Malevich and Johns could often have been seen as peripheral to the flow of modernist art history. It is no surprise that the admirers of Bochner’s early work are dismayed at his use of drawing and painting materials. Monet’s works were seen as “decorative,” as are Johns’ patterned paintings; Malevich “led” nowhere; Bochner is regressing. But their understanding of space is—at the risk of being boring—parallel to the scientific redefinition of space in the 20th century. Physics in this century has expanded to include the special case. The vision of these four artists is special—not central to the conception of the world as we live in it day to day. This vision is special—the special case—and these artists, by reminding us of its reality, extend us beyond a set of given conventions, and thus convince us of its importance—that “all those things are real which fully form the content of experience.”3

I have used a quotation from Descartes as an epigraph for an article devoted to art described as anti-Cartesian. The “mutual connection” between all things transcends differences of philosophical stance; it is the only way we know to make any sense of the world.

When an artist uses materials handed down from history, he inherits the uses and meanings attributed to them. By incorporating more traditional means to express his intention, Bochner loses nothing that his previous work had, and gains everything that it lacked. One of those things he gains is the ability to redefine those materials to suit his needs while drawing upon their histories for added texture, weight, and allusiveness. This is part of what I mean by “getting from A to B.”

In 7 Properties of Between, 1971, Bochner laid down one stone on a piece of paper. It was accompanied by the fallacious statement, “If nothing is between A and B, they are identical.” Many artists have been grouped with Bochner—sometimes under the rubric “post-Minimalist”—and he has become identified as sharing their concerns. This “sensibility” was outlined, only to be summarily dropped, as if the artists had vanished. In any event, the group stood as first defined, each artist, I think, exposed in the adolescence of his or her work.

Another “property of between” had stones for A, B, X, and Y: “If X is between A and B, anything between A and X is also between A and B.” Between any two As and Bs, there are, in fact, an infinite number of Xs and Ys—the infinite contained in the visually finite. After seven or more years of “post-Minimalism,” artists have gone their separate ways, having been allowed breathing space in a less hyped-up art-world atmosphere. Bochner has been able to break with the reduction of A to B, to split them apart, and to expand outward from the limits set upon him by an art historical moment in the late ’60s. So a variety of materials are showing up between the endpoints that define his concerns. This is getting from A to B: being contained only by the limits of intelligence.

Jeff Perrone

I would like to thank C. A. Monson of Yale University for assistance in the preliminary study done for this essay. He helped me identify the source of many of the complexities in Bochner’s art, some of which I have tried to outline here. Many of the ideas for this essay are taken from three sources: Jonh Coplans, “Mel Bochner on Malevich. An Interview,” Artforum, June. 1974, pp. 59–63; Brenda Richardson, “Number and Shape,” in a catalogue for an exhibition at the Baltimore Museum of Art in 1976; Ellen Johnson, “Art = Idea ± the Object: Talking with Mel Bochner, 18 April 1972,” in her Modern Art and the Object, pp. 204–15.



1. The painting which comes closest to a similar visual disorientation is Johns’ Device (1962), where there is a strip of wood down the center to emphasize the separateness of the two circular scrapings. These half-circles can be seen as mirrored or pulled apart from the back. The areas of scraped paint are both “fast” and “slow.” They have been subjected to a process which distinguishes them from the arbitrary bursts of paint which cover the rest of the surface. The half-circles are made different by simple process, the way the cuts in Duple make the overlapping pentagons different by implied internal rotation.

2. In light of Bochner’s interest in pre- and early Renaissance painting, it would be instructive, I think, to take a cue from Gombrich’s notion of “minimal sacrifice” as an alternative to reduction. Gombrich writes. “The problem was not the achievement of some order [in their painting] but that of increasing mastery of representation to which writers devoted all their attention. That this mastery had to function with the minimal sacrifice of order was apparently obvious. The problem was how far one could go in dissolving symmetry without sacrificing balance ” (E.H. Gombrich, Norm and Form, p. 95.) For the present discussion, two things seem relevant. One, the possibility of change to encompass ever more complex visual material with minimal sacrifice to the position Bochner had established. What were “necessary evils” in the past—pennies, stones—are replaced with traditional art materials. The problem was the concomitant increase in the qualities of those materials themselves possibly interfering with direct comprehension of Bochner’s intention. The second point is more tenuous. Gombrich again: “Piero della Francesca could still dare, in his hieratic Madonna del Prato, to paint the two flanking angels with one cartoon, which he reversed.” Besides the most obvious parallel with the mirror reversals in Bochner’s art, it is important to ask exactly how these reversals are residual from the late ’60s and how much they are redefined by Bochner.

3. Leo Steinberg, Other Criteria, New York, 1972, p. 237.