6.1.Preliminaries

In 1956, the art historian Herbert Read wrote that sculpture did not truly exist before the turn of the century, as it is only since 1900 that it has become conscious of its own “autonomous fundamental laws” (1954; 28). While clearly defining the syntactic structure, these laws would shed light on the process by which an object is constituted as a sculpture; that is, as a linguistic object differing in its functions from any other objects of the natural or human environment. The lack of semiotical foundations for the decoding and interpretation of sculpture is certainly still felt to the present in a most distressing way. And the task of providing such foundations has by no means been entirely achieved to this very day, as Rosalind Krauss, another historian of sculpture, pointed out more recently: “The issue of what might be properly considered a work of sculpture has become increasingly problematic” (1977; 2).

It should be recalled that it is only through a conscious understanding of the role played by the Basic Plane that painting can be constituted as an autonomous system of representation and not merely as the attenuated mirror image of a mimetic reference. Introduced by Kandinsky, the semiotics of the Basic Plane allows for the definition of a system describing the necessary fictional (since it is linguistic) space of pictorial representation, as well as those syntactic structures which regulate the energies of plastic variables in spatial depth.

However, in developing the syntactic hypothesis of the Basic Plane, Kandinsky did not believe in extending its application to sculpture. Furthermore, he denied the possibility of the autonomy of this artistic medium. He said: “The identity of the basic elements in sculpture and architecture explains in part the victorious subjugation of sculpture by architecture today” (1976; 83, n. 1). And if some decades later, the developments of sculpture in minimal art have been accompanied—and then principally on the part of the producers themselves—by interesting theoretical work, it was mainly constructed on the basis of the fundamental findings of Gestalt theory, as we see in the case of Donald Judd, Carl Andre, Robert Morris, and others (Battcock, 1968). The absence of a hypothesis such as that of the Basic Plane seemed to render questionable the whole discourse on sculpture, if one listens, for instance, to the nostalgia expressed in this regard by Carl Andre:

There is no sculptural space before the elements are projected.

There is no canvas and no field of retinal vision, only empty

space. The block of brute marble is not the space of the empty

canvas . . . The sculpture has no interior (1980; 13-14)

The need for a rationale for the description of sculpture led to the postulate that there can be no syntax without the definition of a smaller particle, discrete and nonsignifying in itself, that acquires meaning through specific modes or organization. The sculptor Carl Andre proposed, under the name of constructivism, a theory of sculptural forms as structured from an accumulation/repetition of discrete elements such as cement blocks that generate their own field, akin to the modular elements of Seurat, the atomist touch of Cezanne, or the mode of production of concrete poetry (1980; 18, 3).

On the one hand, as the constructivist Strzeminski had previously remarked, the principle of repetition cannot constitute a system of construction, but at the most a mode of production of arbitrary aggregates: “When the requirement is limited to the necessity of repeating the same segment on demand, there is no construction, there is an almost total freedom” (1977; 119). This freedom can be asserted, but more under the name of an informal art than that of a constructivist one.

On the other hand, the temptation to come to terms with the sculptural system in determining the basic particle or element, and then of performing a leap to the syntactic level remains aleatory. We have noted Chomsky’s observation to the effect that nothing at the level of the phoneme, or verbal sound unit, can reveal the organizational modes of verbal syntax. Verbal linguistics has also shown that the determination of a basic element is always questionable, since it results from a certain number of analytical hypotheses which are only justified by virtue of their heuristic character. Thus, as demonstrated by research measuring the aptitudes of infants in recognizing linguistic sounds, it is now suggested that the syllable be substituted for the phoneme as the first element of perception/ comprehension of audible language, despite the convenience of the notion of the phoneme in the learning of alphabetic writing (Mehler, 1981; 36).

If one can speak of an epistemological failure in the attempt to construct a syntax of sculptural language, it certainly follows from the complexity of perception of what visual semiotics would constitute as the ‘semiotic’ material of this medium; that is, volumetry defined as real three dimensionality. As described by Edward T. Hall, depth is a “hidden dimension” which cannot be the object of direct perception, but can only be a product of a cortical synthesis of many visual percepts. Similarly, the eye cannot perceive a ‘volume’ in any one centration, but has to multiply its positions and angles and establish relations between them in order to “reconstruct” the notion of the “invisible” internal volume. In any horizontally-sighted perspective, the eye cannot perceive volume as such, but rather a semi-volume or a semi-relief on the background plane. The restricted depth of this relief can itself be determined only through a complex mental elaboration.

The notion itself of a three-dimensional volume or object—which one would often consider as the most concrete characteristic—is the result of a perceptual synthesis effecting a leap in relation to the perceptual data given. In Strzeminski’s words, “from whatever vantage point that we observe the work of art, depth is hidden from us” (1977; 115) Or, as expressed by Herbert Read:

The volume, the notion of tri-dimensional mass, is not given by direct visual perception. We see objects from several points of view and we retain a particular and significant aspect as mnemonic image . . . Also an imaginative effort or, at least, a mental effort is necessary in order to move beyond the mnemonic image to construct a tri-dimensional image. (1964; 27)

This construction of volumetry requires further the contribution of specific signifiers, in mnemonic images, to evoke a volume, particularly those of modelling or tonal differences (light/dark) in certain regions of the object. As previously noted, from a distance of more than five or six meters, the eye is not able to perceive the marks of the fullness of the human silhouette, which appears similar to a cardboard-cutout figure. This means that the perception of sculpture involves certain strategic approaches that are not required for the apprehension of pictorial representations.

Information about volumetric perspectives, acquired in the 19th and 20th centuries, can help us in clarifying the various orders of development of the many-sided meanings of the word “sculpture.” Without a doubt, confusion about this subject reached its apogee in the Dadaesque and conceptual era which applied this term to all existing objects, visible or invisible, concrete or not, through a metaphoric liaison between things. Not only does the hypothesis of Tristan Tzara and Marcel Duchamp, which says that “all that man does is art,” complete symmetrically the hypothesis that nature can create art, but one has also added that “any portion of the universe,” delimited by an artist who affixes his signature to it, would belong to art and to sculpture, since it presents itself in a tridimensionality foreign to painting. This hypothesis, a legacy of theories of Einfühlung, perpetuates a confusion between the expressivity of things and the expressivity or the power of representation of a language. The simple projection of subjective phantasms, imaginary or emotional, on various objects constructed by perception in reality, is not sufficient to constitute these things as elements of a given linguistic system. Colors, forms, and constructed images such as those which Leonardo da Vinci advised us to recognize or project on a wall serving as a “paranoic screen” (that is, a neutral surface made the recipient of purely subjective projections) do not belong to a linguistic system until they are recovered and inserted in a structure of representation which endows them with specific syntactic functions.

This identification of perceptual products with elements of a system of representation is at the very foundation of the semiotics of the natural world as developed by A. J. Greimas. This theory does not establish any distinction among: (1) the natural world, which, unless one is a solipsist, exists before being the object of a perception; (2) the visual percepts that one can construct from this reality; and (3) the representative or symbolic function of a language whose function is to model the relation of the organism to reality. Proceeding from the basis of a naive realism, which maintains an identity between nature and our perceptual constructs, as well as a similarity and uniformity of the visual percepts produced by everyone, Greimas wrote: “The natural world is a figurative language in which figures . . . are made up of perceptible qualities of the world and act directly—without linguistic mediation—on man” (1979; 234).

How a language can function without being “a linguistic mediation” is not apparent, but one can also ask who in this context is supposed to be speaking, of whom and about what, when for instance the temperature rises or falls, when a fly bites us, or when the law of gravity hinders us from lifting too heavy a weight?

Perceptible qualities of the world cannot as such form a language, except in a metaphoric sense. They can acquire a semiotic function only when they are used as elements in the construct of a linguistic structure, where the level of expression can be distinguished from that of meaning. For instance, a red element, or a circle, or a wooden component in a work, which are visual variables carrying specific dynamisms, cannot be said, as some doubtful theory of auto-referentiality would demand, to have redness, roundness or woodenness as meaning or reference.

These visual variables are parts of a linguistic system trying to represent a wider scope of human experience rather than drawing attention only to the immanent material quality of its sensorial, perceivable semiotic constituents. A word expressed in a high pitched voice is not intended to refer to a point in the sound scale, but to a semantic network different from the auditory reality. The case is the same in visual language, whose meaning cannot be identified with one or another of its visual variable components. This was the lesson offered by the artist Magritte, when he wrote under a drawing whose contours and colors resembled a pipe: “Ceci n’est pas une pipe” (This is not a pipe). Many similar occurrences in the work of the Belgian surrealist do not raise, as M. Foucault said (1968), the problem of nomination in both verbal and visual systems, but that of the structures of both semiotic systems in relation to the production of meaning.

In addition, how from Greimas point of view can this semiotics of the natural world propose a language when it offers nonindividualizable and nonlexicalizable percepts? What is a cloud among thousands of clouds specifically saying to us, or a portion of a lake in which one swims, the gait of a horse, the trajectory of a balloon? To project in such instances an association or an anthropomorphic interpretation does not make these natural phenomena elements of a language. To experience an emotion at the sight of a natural phenomenon or to speak of an object in this way (to refer to a sea as “angry” or to steel as “cold” or, again, to a landscape as “sad”) does not make of this object a language. As is the case with sound phenomena, visual phenomena must present particular properties if they are to become flexible functions in a coherent syntactic structure, aiming at representation and communication. A. J. Greimas had realized the dead end character of a semiotics ultimately based on percepts already lexicalized and semanticized by verbal language, when he protested against a visual semiotics based on iconicity, that is, on a global analogy with the world. He offered many arguments against this approach which have remained unheard:

At the same time, it is also to deny visual semiotics, as such, since the analysis of an articulated flat surface will consist of, in this perspective, identifying the iconic signs or symbols and lexicalizing them in a natural language; it is not surprising, then, that research on principles of organization of signs thus recognized, is led to be confused with that of their lexicalization; and that the analysis of a work, for example, is transformed as a matter of fact into an analysis of the discourse on the work. The specificity of visual semiotics is diluted, then, in these two macro-semiotics, which are the natural world and natural languages. (1979; 177)

It seems to us that not only has this danger not been avoided by certain visual analyses inspired by Greimasian semiotics but also that it is inevitable in any context which understands verbal language as the only complete and universal language.

Without recapitulating discussions on the nature of aesthetic experience and the fact that it can be more general than the relation with so-called artistic objects or discussions concerning the definition of art itself, it appears to us that one can only affirm that an object is part of a linguistic system (which permits it to convey messages other than its own immanence or simply be the target of verbal projections of a perceiver) on the basis of a specific linguistic hypothesis. Furthermore, we think that, historically, the particular problem of sculpture has always been the resolution of this dilemma concerning the conditions under which an object ceases to be a thing among other things in order to become a representative linguistic object called sculpture.

Another of the many difficulties encountered in the development of a theory of a sculptural object derives from the credibility that is still ascribed to the unfortunate distinction made by Lessing, in his Laocoon of 1766, between the ‘spatial arts’ (painting, sculpture, architecture) in which objects are perceived in a global and instantaneous way, and the ‘temporal arts’ (music, poetry, dance) which are perceived in a successive fashion. This concept takes into account certain characteristics belonging to the manifestations of these two types of objects but effects an abstraction of the human subject that constitutes these objects in a perceptual event which, in either case, occurs always in time. As Rene Thorn wrote: “Now every symbolic activity is displayed necessarily in time . . . We will localize, therefore, temporally, the signifier at the moment where the interpreter perceives and interprets it; in contrast there is often ambiguity as to the temporal localization of the signified” (1980; 195).

The accumulation and diversity of gathered data at the time of perception raises the problem of the constitution, of the manipulation, and of the integration of mnemonic images, that is, memorized mental, visual images through which the signifiers/signified of these perceptive ensembles are retained and connected in the cortex, to be elaborated upon in successive tempi of the experience of the object. This perceptual memory is twofold: a short-term memory, retaining several instances of actual perceptual experiences, and a long-term memory retaining and connecting them as accumulated mnemonic percepts in the cortex. This essential mechanism of the relationship with any visual work, this putting of the multiple actual percepts resulting from different perspectives and sightings in relation with mnemonic percepts, is not necessarily a feat easily accomplished by the majority of human beings. It corresponds in fact to the difficult task of constructing a mental space of representation, the term ‘space’ being defined, as mentioned earlier, as the simultaneous coexistence of multiple stimuli, which may be quite heterogeneous to one another.

If the almost uniquely frontal position of the perceiver before a pictorial work and the potentialities of peripheral vision give him the illusion of an instantaneous perception, the reality of the perceptual process is quite different. Contrary to Lessing’s proposition, the pictorial work can require a longer perceptual time than a sculpture or an architectural facade, and the perception of these visual works can demand a longer time than listening to a musical or theatrical work, whether that time is successive or continuous. In a general way, however, as we will see here, the perception of a sculpture requires particularly protracted and complex perceptive trajectories, which explains without any doubt the epistemological difficulty relative to its study.

But, before explaining the nature of the perceptual trajectories required by any sculptural object, let us repeat that the use of the organ of sight in the apprehension of a sculpture does not put into play only visual percepts, or only tactile percepts, such as a fruitless opposition between painting and sculpture would like to establish.

This opposition is often reasserted by common sense which does not possess, however, any instrument to determine what distinguishes the tactile from the visual in the perception of reality and, in turn, their differences within the visual representation itself. This discrimination requires a specific knowledge of the processes of perception and of the modes of representation of visual language. In this matter, one can fully agree with the phenomenological observation made by Merleau-Ponty: “And, inversely, any experience of the world that has always given to me, in the context of movements of the gaze, the visible spectacle, belongs to touch no more or less than the ‘tactile qualities’ themselves. We must become used to thinking that anything visible is shaped in the tangible . . .” (1968; 165).

In his Historical Grammar of the Plastic Arts, which is more of a semiology of styles than of visual language, Riegl nevertheless needed to define some basic elements of the work of art in order to establish semiotic variables by which these styles are perceived and recognized. If volume, which he called simply the ‘form’, constitutes the basic paradigm, Riegl knew enough to distinguish, and in an exemplary way, its tactile and visual constituents:

All things in nature have a form, that is, they are extended in accordance with the three dimensions—height, width and depth. Only touching them permits us, however, to directly assure ourselves of this state of fact. In contrast, that of the five senses which serves for man to receive impressions which exterior things give to him—sight—is rather prone to induce in us error about the three dimensions of what we see. Because our eye is not in a position to see through bodies and sees therefore, only one side presented to it as two-dimensional surface. It is only when we have recourse to experiences of touch, that we complete in mind the two-dimensional surface perceived by the eyes in order to make it a three-dimensional form. This process is effected much more rapidly and easily when the object contemplated presents aspects which evoke memories of experiences of touch. (1978; 121)

We will return to the consequences of this structure of the perception of volume through bidimensioniality.

However, one must add that senses other than the tactile and visual are involved in the apprehension of a sculpture: kinesthesic, postural, buccal, and so on. This will widen the problem defined by Reigl in the perception of the natural object as well as in that of the sculptural object.

In effect, one must insist on the facts that: a) one must not identify the mechanisms of perception with those of visual representation; b) this semiotic representation does not have as an unique reference visual perception and, even less, its products in external reality. We have already explained how visual language, by its spatial characteristics, serves to represent experiences issuing from all organic spaces. Visual variables are thus used in order to represent experiences as different and heterogeneous as those which are linked in buccal, postural, auditive or thermal space.

Vice versa, different perceptual systems may concur in gathering similar types of information, but within different intensity, context, and treatment: “Of further importance is the idea that a particular kind of information is not necessarily the special domain of a particular perceptual system, but rather that different systems can detect the same information, either singly or in combination” (Turvey, 1974; 168).

If one easily admits that words, in which the semiotic material is audible, can refer to nonauditory objects (such as, say, an apple or cancer), one identifies, again mistakenly, visual language with the unique representation of the visual. Indeed, if human beings resort to visual language, it is because its spatializing character is directly suitable for the modeling of a reality which is deployed simultaneously in three dimensions but across different sensory spatial levels.

Therefore, one must recognize that the eye is as important in the perception of a sculpture as it is in that of a painting. Furthermore, its role is more important than that of the sense of touch, contrary to widespread belief. Sculpture is mainly revealed by the visual variables which constitute it, texture being only one element among many others. Indeed, the most important differences between painting and sculpture reside in the different and much stronger way in which the other sensory organs besides vision and touch are called upon. Thus, the postural dimension, which operates in relation to the proportion and vectorialities of the body itself with those of a painting or sculpture, stakes more of a claim in the modes of perception of sculpture. Kinesthesic experience, whether it deals with the projection of possible movements in reality or the felt awareness of the results of a prehension and manipulation of certain parts of a sculpture, is more important perhaps than that of the tactile experience which prefers the exploration of the object’s surfaces by the body or the hand. If tactility is important on the plane of reference, when vision recognizes certain types of textures, the tactile sensation most often plays a minor role in the perception of the work. At times, distance, most often the fragility of materials, even of marble or bronze, prohibit this type of sensory relation between the perceivers and the sculptural work.

This leads to the consideration that, with respect to the pictorial and the sculptural fields, the basic mechanisms of perception are the same. Perception can only be realized by an ocular fixation or centration in the visual field, which, when foveal, gathers a given ensemble of visual variables which we have called a coloreme. Any centration can only establish a dynamic correspondence with one section of a visual region, which is itself animated by energies conveyed by the visual variables which have been used and whose nature we have previously explained. Parallel to the number of centrations, the coloremes multiply and form more or less strongly interconnected regions, of subgroups diversely integrated or separated. Every time the perceiver modifies the angle or the direction of his view or positions himself differently before or around the work, he is confronted with an ever-changing disposition of stimuli with respect to their structure, their density, their energy, and so on, which modify their spatial interrelations. Perception does not provide information only about characteristics of individual objects, but as stressed by J. J. Gibson (1966), informs about the spatio-temporal relations between dynamic perceptual events in the three dimensions of space.

The greater complexity in the perception of sculpture as opposed to that of a pictorial representation stems from the fact that the physical movements of the perceiver before the pictorial field place him/her in relation to given data which, from the containing properties of the Basic Plane, appear in immediate relation to other data of a similar field, whereas the different positionings of the perceiver before the sculptural object can allow him/her access to regions of the visual field which appear completely different from the previously perceived ones, these having become inaccessible to centrations because they are situated at an opposing angle or because certain elements in relief hide what was previously apprehended.

Not only must the perceiver proceed to a precise imbrication of coloremes which are provided by each region, as in pictorial experience, but he/she must also put into relation what appear as completely heterogeneous regions. The perceiver has to organize, in a constant process of transformation, a type of infrastructure which can reveal the nature of their dynamism and function in the construction of the global object. Each of the regions so interconnected in the perception must be relayed to perceptual memory in proportion as the displacement of the perceiver opens him/her to new percepts which will transform the equilibria or groupings already realized, by the insertion of actual new sensorially active percepts. These will transform in the perceived field and in memory the groupings or subgroupings already established. Not only are these interconnections between the coloremes and regroupings of coloremes necessarily produced by the perceptual mechanisms, and liable to be continually modified by later movements of the gaze, but the coloremes that are not linked to others can with great difficulty be entrusted to memory so they can serve in the construction of the object to be perceived, as research on memory has revealed (Pribram, 1971).

Perception can result only from a lengthy accumulation of centrations producing percepts which are always different, constituting subregions, each interlinked to the other in regions or superregions, suited to integrate them and the subsequent percepts into a unified totality. This temporal sequence, where the accumulation and organization of anterior percepts soon takes precedence, despite the constant afflux of new percepts, must be reconverted into a spatial ensemble, or in other words, into a simultaneous coexistence of percepts, through the development of a dynamic three-dimensionality or volumetry, as the unifying spatial structure of sculptural representation.

This integration of the innumerable regions, subsystems of regions and of superregions, of which the interrelations and dependencies are engaged in continuous transformations, is already a lengthy and very complex operation in the perception of the pictorial plane, requiring operational projections which stem from the dialectical structure pertaining to the subject who perceives. But this equilibrium is much more difficult to realize for the sculptural object, because the changes in points of view are not only those which are chosen by the eye with respect to a given field and which can be integrated by assimilation/accommodation. The changes in position of the perceiver who strolls around a sculptural object imply transformations which the object itself offers, in a volumetry to which one relates through completely different perspectives. The perceiver must proceed to accommodations to a visual field different from one position to another, in order to arrive at the conception of a possible perceptual unity of these dissimilar ensembles in one and the same work.

Thus the perception of a sculpture hardly differs from that of a pictorial work in the need for the development of a lengthy series of percepts of regions and of interactions between regions which, according to their respective positions, dimensions, colors, vectorialities, and so forth, define the different quantities of energy and the intensities which bring them together or dynamically separate them, thus creating effects of depth. But to the effects of depth produced by perceptual mechanisms involved in one single positioning of the perceiver, the sculpture requires the integration of the percepts and the effects of depth, multiplied by numerous points of view, in order to construct its rotundity. The perceiver must occupy multiple positions around the object in order to obtain the data with which he can construct the global object—unless the object itself is in mechanical rotation around its axis—and from these, look at it from a multiplicity of angles. This physical movement has as an immediate consequence the production of kinesthetic percepts in the endogenous or internal space of the perceiver, of a different order from those which result from visual percepts and which can come into conflict with the dynamic relations that the latter tend to produce. In addition, one must recall Merleau-Ponty’s observation: “Touching . . . is to touch oneself” (1968; 308). If the tactile senses give data, mnemonic or actual, about the endo-epidermic reality as much as about the external object, one can hence suspect the magnitude of the sensory-motor and kinesthetic experiences aroused, which can present an obstacle to the apprehension of other kinesthetic movements inscribed in the semiotic materials themselves.

The reflections of Strzeminski on sculpture have underlined some of these complexities of perception: “The optical impression of a plastic three-dimensional work of art presents itself as a sequence of projection planes which are quite numerous, different and separated from one another. Each plane is separated from the others by a certain lapse of time corresponding to the movement of the spectator and the positions from which he chooses to observe the work.”

He concludes from this description that one can thus:

compare to a chain the impression of the ensemble which results from the observation of a three-dimensional work of art:

The verticals represent the visual impressions (projection planes) and the horizontal lines the lapse of time which separates these visual impressions from each other. (Strzeminski, 1977; 113)

If the temporal sequence is well illustrated in this diagram, we cannot accept the linear and regular character of the model as representative of the process of production of percepts. This process must instead be conceived as a dynamic activity which transforms some elements inside the perceiver as well as the global unity of the work being perceived. On the other hand, the linear chain thus evoked cannot properly account for the diversity of the interrelations and the heterogeneity of perceptual networks, constructed in different and successive changing networks which are always at work in the perception of a sculpture.

6.2.Networks of Perspectives

At a first level, the sculpture presents itself to perception as a physical object belonging to the natural macroscopic world and which, whether or not labeled as an object of art, is understood in its relation to the physical objects which surround it according to the perspectives of natural perception. Situated in a given space, the sculpture is necessarily apprehended according to the network of parameters which ordinarily defines any natural object, from a view at a near, medium or far distance. In certain cases, explicit indications must be given so that this object is isolated from others and recognized as a work of art. It is the case with any of the so-called “ready-made” objects, as Duchamp called those more or less modified prefabricated objects borrowed from external reality, that would not have any symbolic function without the subjective affirmation of the artist. But whatever the perceptual treatment accorded to a three-dimensional object and the particulars of its symbolic structure, it will always already have been first understood according to the perspectives linked to the perception of any physical object. These will have to be compounded with the different perspectives which will be established or recognized in the course of a perceptual trajectory, constructing the volume as a linguistic object.

In the majority of natural perspectives, from a horizontal viewing, objects in reality appear as demi-reliefs against their background as long as changes in position inform us, not of a perceivable rotundity, but rather of different facets of the object, always in demi-relief on a plane, with which we construct the notion of volume. Even when the contrasts of chiaroscuro are used to construct the depth in demi-relief presented by the front of any object, the conclusion that the object is round, rather than in demi-relief, results from a conceptual leap and not from any direct perceptual data.

Indeed, the recognition by the perceiver of the fact that an ensemble of percepts can be identified as the “good gestalt” of a tree or a house, that is, a known volumetric object, constitutes most often a permission he/she gives himself to perceive no longer the visual variables which constitute the object. The economy of pragmatic functions devalues the perceptual trajectory which is no longer essential to the “substantialist” identification of the object, to the benefit of a quick interpretation where what one knows of the object is more important than what one actually sees. The decoding of the visual language, serving symbolic representation, requires for its part an active perceptual relation with all visual components, of which the modes of interaction constitute the specific syntactic network. As observed by K. Bühler:

“The structure of any particular language is largely field-independent, being determined by its own convention rules, but the field determines how the rules are applied” (Blumenthal, 1970; 56).

In this context, empty or redundant visual variables do not exist, since each contributes to the specific structuring of the visual fabric, according to its organizational rules.

One must, therefore, not confuse the natural perspectives of perception with the pragmatic behaviors and functions which have been added to it, and which forsake as much as possible the steps of the perceptual trajectory under the pretext of an economy of efforts, time or energies. The natural perspectives of physical reality cannot be constructed through nonvisible data, under threat of becoming abstract perspectives. One cannot maintain, as it has been done to certain minimal sculptures, that a work can be seen instantly and globally in a single moment of perception (Judd, 1964; 36, 37). The fact of “recognizing” a cube in the Black Box of Tony Smith, from percepts obtained in a given position, does not reveal to us in any way the particular aspects that a strolling around it, requiring time and made at different distances, would reveal, such as successive angles and proportions, lightings, surfaces, always-changing vectorialities, which all lead to volumetric syntheses in continual transformations. The perceptual data have the farthest removed relations from the form that a certain geometric representation or a mental visual image would give to a cube.

Furthermore, when the perceiver moves nearer to the sculpture to obtain an appropriate distance from which he feels he can best perceive it, he will adopt various sorts of positionings and of visual orientations and will multiply these angles of vision in an active movement, producing a certain number of fragmentary percepts from the zones on which his centrations will be made. Locally, these percepts of regions are regrouped into subensembles and consigned to memory, continuously being added to other subensembles resulting from different points of view, leading to a more or less fragmented apprehension of the ensemble of stimuli presented by the totality of the work. Whereas it is difficult to evaluate the mnemonic impact of percepts produced at the first level of natural perspectives, which position the object in its environment, the more proxemic and extraordinarily varied perceptive paths of the second level have to be actively interconnected with them, so as to represent the structure and the characteristics of the work at the cortical levels.

In addition, on a third level, the perceiver must also take into account the points of view, sightings, and perspectives that the producer has himself inscribed in the work. These are apparent in his choice, treatment, and organization of the visual variables constituting the objective observable marks defining the object of the representation. Certainly, in order to become a language and stop being a simple thing, the sculptural object must not only be endowed with a syntactic structure allowing material signifiers to acquire permutable functions in the ensembles, but it must also be able to incorporate in the object organizational schemas of perspective stemming from the intentions and needs of the producer. This means that besides the natural networks of perspectives in which it is necessarily inserted as a physical object, the sculptural object must find the possibility of integrating a network of foreign perspectives, sometimes contradictory to the first perspectives, likely to signify and represent sensory and spatial organizations of a different order.

In both a natural and semiotic attitude, the sculptor Cellini defined in the sixteenth century eight points of observation for a sculpture, corresponding to points issuing from the main vertical, horizontal, and diagonal axes. While prescribing or programming a minimal path of perception—which is not spontaneously taken before a natural, physical object—the artist was still describing only an abstract theoretical schema, applicable to any physical object. This requirement was, in fact, minimal, as this schema should ideally extend to the 360 degrees of rotation and of possible transference of the object, if one wished to have an adequate knowledge of it. This is particularly the case of the small discrete sculptures that can be held in the palm of one’s hand, which by their autonomy and perceptual openness seemed for some time to correspond to the very paradigm of sculptural art.

The aesthetics of the ancient Greeks emphasized the sculptor’s need to harmonize the points of arrival of the mobile path of the eye around an object, in relation to the fundamental axes. Contemporary thought has particularly questioned the absolute and static character of these perceptual sightings, oriented in an arbitrary manner on a few points only of the object’s periphery. They do not seem to correspond to the nature of usual human mechanisms of perception nor to other types of intentionality governing the production of the sculpture whether they are mimetic or nonmimetic. Besides being a three-dimensional physical object, the sculpture would appear the vehicle of particular messages which must be read in a linguistic or symbolic context and not only through simple physical or static structures of the object. The origins of sculpture in human societies—curiously still somewhat inscrutable today—certainly indicate the intention not of producing without reason other physical objects to be juxtaposed to natural objects but rather of transmuting physical materials into semiotic materials, as carriers of a particular language.

This path of “syntaxicalization” was developed over time in an extremely varied way by artistic production. It corresponded to the fundamental parameters of space as near distance and as remote distance: “The distance from which sight perceives things is therefore of primordial importance for the reception of things in nature by the inner senses of man and, consequently for the competition with these things in which man is engaged when he forms plastic works” (Riegl, 1978; 122).

Given this finding, we will proceed to distinguish the syntactic correlatives of this basic dimension of distance in all the heterogeneous objects subsumed under the same label of “sculpture.”

6.3.Proxemic Sculptures

The hegemony of the free-standing sculpture that emerged in the Renaissance, as well as that of styles of painting reflecting it, singularly obscured the possibilities of an analysis of a sculptural phenomenon, all the more since it was linked to an illusory mimetic function whose magical aspect seems to still fascinate our contemporaries even one century after the invention of photography (Gombrich, 1960).

Historically, sculpture seemed to have sprung up from two totally different syntactic sources: (1) the ‘kleinplastik’, the small sculpture, the figurine or amulet, that is, an autonomous and small round object which one could hold and turn in one’s hand, and (2) the low-relief obtained from the hollowing-out of a slab or plate in order to obtain a series of concavities and convexities. Even if these two types of sculpture posit most frequently a field of proxemic representation, they are ultimately capable of creating illusory distances.

The small sculpture which can be manipulated seems to obtain an autonomy in relation to the surrounding milieu because, in a perspective of height, from a more or less oblique sighting, the distance which is established between two opposing points on its circumference, multiplied in continuous rotations, offers most rapidly the experience constituting a volume or rotundity.

It seems to define itself by the system of its external volume, closed and constant, by the particulars of the visual variables of its surface, where inclinations and variations in texture multiply its accidental relations with surrounding illumination. Its autonomy is rendered possible, however, only by the consideration of its external volume seen as isolated and constant, while its relations with visual energies which dynamize the surrounding milieu are placed between parentheses and disregarded.

The diverse vectorialities and the inclinations in the peripheral contour of the small sculpture allow us to “imagine” an internal structure of the volume which could explain the variations in the external regions. This internal structure remains, however, always imagined and not perceived; what is given to be seen/touched only constitutes the external volume. Without repeating our earlier reflections on this notion, let us recall the definition of Jean Piaget of the system produced by a dominance of this concept. The ‘external volume’, he wrote, makes of the object that it envelops “an indefinable solid in the sense of being incompressible and nondilatable” in radical opposition with the properties of “interior volume” (1980; 189).

The internal regions of an object conceived from the notion of external volume remain in a state of “coalescence” for perception, according to the term used by Piaget in order to stress the absence of the previous separability of a field, where one could determine similar/dissimilar factors capable of being coordinated into subensembles. Indeed, these undifferentiated regions correspond to the notion of a topological point, being a region inaccessible to experience as well as to knowledge.

A sculpture which centers its structural constituents on the properties of external volume puts into play signifiers which cannot be transformed or interrelated and interact in perception in a way that will produce the tools of a syntactic structure sufficiently developed to construct representations other than their immanent images. The external volume tends to freeze the object as a “thing”, and no longer as a medium where syntactic functions result in a mobility of positions and interrelations between the constituting elements.

The small sculpture that one can hold in his hand, as well as the more recent kinetic sculpture which turns on itself under the action of the hand or a motor, necessitates most often only a frontal position on the part of the spectator in a more or less oblique viewing. But it does induce an integration of visual, tactile, kinesthetic, sensory percepts in an actual or virtual spatialization founded on one of the fundamental topological relations—that of envelopment. Tactile/visual percepts of linear and planar regions confirm that the hand/eye has returned or could return to its very point of departure. In this sense, the experience of external volume is always that of a closed-in object limited by a closed form.

However, archeological residues of primitive or historically ancient societies lead us to believe that the small sculpture was, since the very beginning, accompanied by another type of sculptural production—that of low-relief realized in sand or clay or on the walls of caves. The most ancient productions of India or Egypt have reached us in the form of reliefs, at first slightly marked, then more obtrusive, obtained by hollowing out a surface, which constituted the very support-plane of the work.

This artistic production was overshadowed in the theory of art by free-standing sculpture, a state of affairs against which Wörringer has vigorously protested, but it seems, in vain:

“But it is still the history of Greek relief, of which we have underestimated for too long a time the meaning and the decisive role to devote exclusive consideration to free-standing sculpture, which does show how the flat presentation was chosen for itself and not following external requirements, because it was that which responded the best to the artistic wish” (1953; 107)

We would say rather that representation in low relief offered more possibilities for the development of sculpture as a language than did free-standing sculpture. In effect, low-relief seems to borrow its syntactic possibilities from pictorial art, since its support constitutes, like the pictorial Basic Plane, a dynamic gestaltian data, already strongly structured, in which the interior volume and mass play with the semi-rotundities produced by the artist. It produces a fictional space suitable for structuring an indefinite series of spatial representations. Low relief also resembles the pictorial Basic Plane in that the perceiver’s approach is mainly frontal at a relatively close distance, even if it does evoke, as well, the illusory, distant spaces of painting within the same repertoire of perspectives. Thus, sculpture in low-relief, even when situated in a vast architectural ensemble, determines its own fictional space which differentiates it from other objects of the natural world.

In an intuition close to that of the pictorial, even if tonality plays a more important role there than chromaticity, this type of representation showed a remarkable understanding of the necessity of opening itself to spatial potentialities in order to organize a language capable of saying more than the mere connotations of its materiality. It is only through the structuring of an internal volume in sculpture, which engenders in turn countless virtual volumes, that the conjunction, juxtaposition, and integration of different experiences and different points of view about reality can become representable.

What is described today as a willingness to “flatten-out” or collapse volumes on the plane in a low relief was, in reality, a coherent and powerful way of exploring the expressive possibilities of virtual or topological volumes through a structuring of internal structures.

Even when, by the accentuation of protuberances into the third dimension, these low reliefs became high reliefs, the relation of this volumetric object with the wall was maintained for a long time. In spite of the interruption caused by the emergence of Hellenic sculpture after the third century before Christ, the sculpture of the Middle Ages registered a very slow progression from low relief toward high relief in sculptures which still lean against the wall, inside a niche, or under a canopy. Panofsky queried the meaning of this curious phenomenon:

“The incapacity of the classic Gothic statue to live without its dais is heavy with a symbolic value that is highly significant. The role of this dais is not only to connect it to the mass of the edifice but, moreover, to delimit and assign a certain portion of free space to it” (1975; 112)

Panofsky underlines the acuity with which the architect and theoretician Bertani had understood “the problematic of perspective relief, that he sees as an amalgam of fiction and reality, reprising in many instances the analyses of Leonardo da Vinci, in No. 37 of his Treatise” (168).

In the 15th century, the most extreme reliefs produced by Ghiberti, as well as the first free sculptures, did not exclude leaning on a side of a wall. In a less extended way, these sculptures conserve the dynamic parameters which permit them to make potential their internal tensions, to constitute virtual energies, in a word, to make their elements dialectic in a specific linguistic function.

The evolution from low relief toward high relief and semi-free standing works, and of volumes of sometimes quite larger diameters, while these were still embedded in a plane or an original slab, was without doubt accelerated by the desire of sculpture to become autonomous in relation to painting. This has been a secular conflict which still prompts Carl Andre to say that he feels “an instinctual hatred for Leonardo and low relief” (1980; 27). But once sculpture was progressively liberated from the wall and transposed to public places in a wide, complex and changing environment, it underwent a profound change. It lost the syntactic and semantic system of former bas-relief, which allowed it to give an operational structure and a linguistic function to the organization/production of potential internal volumes, and began its search for an equivalent element acting as a Basic Plane.

6.4.Sculptures Situated at a Distance

The free-standing sculpture of the Renaissance, most often of a monolithic nature, seemed to return to the dilemma of the “external volume,” autonomous and unchangeable, isolated within its frontiers and in which only the axes and peripheral protruberances could offer information about its structural elements. Except for its mimetic function which defined it as a specular subproduct of which one did not know how to make a system, sculpture threatened to vanish as a linguistic system in order to become only an object among others. As such, it could be said to be perhaps more beautiful, suiting the variability of aesthetic taste, or it became endowed with a magical function, actually reduplicating or competing with the productivity of nature itself, as explained by Riegl and Gombrich.

However, on the plane of its apprehension, free-standing sculpture, larger than the previous small sculptures, was confronted with a major problem concerning its true autonomy in the milieu where it was placed. This environment offered energies vibrating from light itself, reflecting on natural objects or constructions in which the visual characteristics of dimensions, colors, vectorialities, and other factors possessed an obvious dynamic force. The first question can be readily asked: what part should the scope of peripheral vision, active in natural perspectives, play in the apprehension of a free-standing sculpture, situated in a public place or in a vast architecture? With which environmental elements could it or should it establish relations of proportionality, of contrast, of vectoriality? In other words, did sculpture possess a specific space in which one could apprehend it, or was it an integral part of a much larger environment, where most of its means of expression greatly lost their visual efficacy? Riegl argued that the refusal of color or its parsimonious use in the polychromy of antique statuary derived from a willingness to make autonomous the work of art of large dimensions in relation to natural objects or other objects produced by man. The small figures could better capitalize on the possibilities of chromaticism, because their “format excluded all possibility of taking them as something other than the work of man” (Riegl, 1978; 159). This would explain the refusal of sculpture to exploit the resources of color until the beginning of the 20th century, accompanied by the curious theory that the color of materials did not act as chroma, but as simple revelations of the nature of constituent materials. For a long time, the best solution for sculpture remained to define the distance within which it existed and could be seen from parameters which a wall or a series of edifices offered in the distance, these playing on a larger scale the role of the fictional wall of the low relief.

It is necessary to wait until the end of the 19th century in order for artistic practice and theoretical reflection to grasp the fact that freestanding sculpture had in fact substituted the supporting ground for the syntactic function of the original wall of the low relief. The ground is the ultimate physical support to which sculpture is linked by a base or pedestal, isolating it from an environment where it could otherwise be nothing more than an object among others. This base, already a low or a high relief, allowed sculpture to be displayed in a specific fictional space, involving a limit linked to the support, where the spatial potentialities necessary to the production of a symbolic representation could be engendered.

This global structure, however, remained dualist and fixed, the connections between the two regions being predefined. A functional role was superficially assigned to the base and a dynamic or expressive role to the upward figure that it supported. In a certain sense, this figure on a base reconstituted the status proper to the relation of the pictorial figure on a ground, where only the first element is the object of a valorization and of a dynamic development. By this fundamental nonvalorization, even if the base were the site for many ornamentations of which one denied a linguistic role (as would be the case in any ornamental art), the base of the sculpture conserved an intermediary status between that of a linguistic instrument and that of a purely functional object.

Furthermore, free-standing sculpture, with its closed external volume, does not allow any more than small sculpture any observation of how the visual variables used by the producer interconnect in the central layers where the energetic sources of the occurrences perceived on the surface are localized. The system of external volume does not permit the constitution of the material energies forming the central layers as semiotic signifiers nor the description of them by an articulation which would specify their syntactic function. Perception only exercises itself on the particulars of external volume, according to a certain number of perceptual parameters of position, distance, angularities, and vectorialities, defining the object only from the exterior. This epistemological gap will be filled in part by the development of the notion of internal volume at the end of the 19th century.

It is by returning to the mechanisms of perception that the reflection of a sculptor such as Adolf von Hildebrand (1907), whose thinking would be broadly disseminated by Riegl and Wörringer, allowed the questioning of the notion of external volume in its association with that of internal volume. Hildebrand reestablished, in effect, the fundamental distinction between what near vision sees and what far vision sees, which will revivify the notion of both the plane and that of relief in the cube.

This proposition is widely discussed by Riegl:

If one brings totally together the object and the eye—what we will define as near vision—we have an impression that procures simply a two-dimensional surface. If the eye distances itself a little, it has the possibility of perceiving in the object aspects which awake in him the memory of experiences of touch . . . If the distancing between the eye and the object exceeds the possibilities of normal vision, it is again the opposite process which is produced: the shading disappears more and more behind the growing density of the layer of air between the eye and the object and, to finish, the retina perceives nothing more than a uniform surface of light or color; we will qualify this process as far vision. (1978; 122)

Because far vision gives the illusion of a planar surface where there actually exists a volume in three dimensions, Riegl considered this a sensory illusion and called this percept a “subjective” surface, whereas the first, obtained by near vision, which is not an illusion, is called the “objective surface.”

Thus, bodies in three dimensions are all perceptually delimited by surfaces in two dimensions, which fragment in a continuous fashion the contour of the external volume, the latter always only a theoretic reconstitution from several points of centration of perception. Riegl used this hypothesis to define volumetry altogether differently, since “the surface that the eye sees from near and transmits to the interior sense is a part of an effectively existing body, of which the eye, in this precise case, cannot perceive anything other than this surface which is a part of it” (1978; 123). Indeed, the internal sense which is thus awakened by a perceptual contact with partial surfaces of the volume becomes aware of the reality of an internal volume of which the surface is only the visible limit. This interior volume is, according to Riegl, perceptibly different under an objective surface and a subjective surface: “The contents of the objective surface is larger than that of the subjective surface. Because the objective surfaces of an object do not rest absolutely in the same plane, they are bent towards the interior or towards the exterior; and partial surfaces belonging to these curves escape distant vision” (1978; 147).

This is what caused Hildebrand to conclude that only near vision could be the basis of the work of the sculptor, and not the distant vision which serves rather a purely empirical activity.

The inclinations of the planes in partial surfaces, perceived by near vision, being necessarily linked to differently oriented internal masses, reveal these as individual units, characterized by axial energies specific to each and offering, according to Wörringer, “the image of the closed material individuality,” that no theory of contour or silhouette can procure, because “relations of depth had to be, as much as possible, transformed into surface relations” (1953; 70).

Wörringer used the notion of the internal limit of interior volume in his analysis of Michelangelo’s sculpture: “Here, in turn, for Michelangelo, the enclosure of material is not rendered perceptible from the exterior but from the interior; according to this artist, the rigidly enclosing limits of the material are less factual than imaginary, which does not prevent them from appearing with utmost clarity to our consciousness” (1953; 109).

But this hypothesis about the organization of partial surfaces as signifiers of depth required, at the same time, recourse to a basic parameter by which these “closed material individualities” could be measured and compared, not metrically but topologically. It required the postulate of a primordial plane in relation to which these reliefs or distensions of matter were displayed. Thence a resurgence of a vocabulary linked to low relief, but with a completely different meaning, since the Basic Plane postulated for all these agglomerates of matter is now dialectic and fictional and not linked to a material support like that which the Basic Plane provides in the pictorial.

This made it possible for sculpture to resume a function of representation as a finality in the artistic act. Hildebrand, who was strongly aware of this, wrote: “The activity of the plastic arts takes possession of the object as an object uniquely explainable by the mode of representation and not as an efficient or meaningful object in itself, poetically or aesthetically” (in Wörringer, 1953; 40).

Hildebrand also remarked that the apprehension of a free-standing sculpture as a simple cubic volume does not take into account its true artistic function:

Inasmuch as a plastic figure is made the most of, at the first, as cubic, it is only the first step of the configuration and it is only when it will act as a plane while remaining cubic that it will have acquired an artistic form. It is only by the consequent accomplishment of this apprehension of relief of our cubic impressions that the representation finds its consecration, and the mysterious benefit that we experience owing to the work of art rests only on this same accomplishment, (in Wörringer, 1953; 56)

The perceptual necessity that any region of a sculpture must present itself as a surface in two dimensions, as Riegl had said, but on a surface which possesses, nevertheless, a content, an inclination, or an internal thickness, constitutes this region indeed as a topological mass inserted in the virtual Basic Plane determining the dynamisms of its constituent visual variables. The depths behind the partial surfaces will be interpreted through the elaboration of a series of partial Basic Planes, making explicit their internal cubic volume. This interrelation will first be described as that of an undulatory plane. “All the separate judgements concerning depth must be unified in a unitary and encompassing judgement. So that, finally, all the richness of the form of a figure is placed before us as a continuity towards the rear of a single simple plane” (Wörringer, 1953; 93).

The necessity that any representation of volumetric depth be constructed through the planar dimension was reaffirmed by a number of artists. Certain of them, following Greenberg’s theory of “planeity,” claim even to interpret it as a true bidimensionality and no longer as the external limit of an interior depth. Hans Hofmann, for example, while affirming that we always see bidimensionally, added that a sculpture which, by the interplay of its lights and shadows, does not offer an absolute bidimensionality, expresses only an irritating tridimensional disequilibrium, because static and incomplete, through the absence of the dynamic of negative spaces, that is to say, spaces constructed from the background itself (1948; 53).

This undulatory continuity of the sculptural structure derives, according to Hildebrand, from a system of interactions of lights and shadows in the periphery of the volume, emphasizing the reliefs through the inclinations of external planes which multiply the revelatory energetic events in the near vision of internal volumes. Even if this opens to a first level of “syntaxicalization” of interior volume, the theoretical considerations of Hildebrand and Riegl remain strictly linked to the structural problem of the low relief and also to its subordination vis-à-vis the pictorial Basic Plane. It stresses also the sculpturally restricted possibility of the treatment of peripheral regions, to the scorn of the expressive potentiality of a more affirmed internal volume. It is through a more radical explosion of the external volume notion that the revolution of sculpture at the beginning of this century was realized.

6.5.Cubist and Constructivist Rupture

In a development from Degas to Brancusi, the concept of the base of the sculpture was first questioned, with the view of eliminating it or integrating it more into the global structure. With Rosso and Rodin, the notion of external contour was eschewed in favor of a more flexible and incisive treatment of peripheral layers, a multiplication of textures and angles of luminous reflection, a multiplication of axes and vectorial tensions in unstable equilibria which intensify the connection between central and peripheral layers.

The decisive rupture of cubism operated on two levels. As a first stage, the syntax of low-relief and of medium relief was introduced once more by the return of sculpture to the basic mural support. But it substituted for simple hollows the superimposition/juxtaposition of elements generating virtual volumes of projected shadow, creating a first effect of positive and negative space. This alternation creates a dialectic in the internal layers of sculpture, between zones of radiant and reflected light and gradations of shadow accessible to perception. These volumes created by chiaroscuro resulted in complete hollowings of regions at the interior of the global volume, incorporating light and air in sculptures. This revived both the hypothesis of centered construction, supported by a base, and the virtualization of the base in the disposition of various resting points on the ground.

The second stage produced a more complete rupture of the external volume in redoubling the elements, so that the intervals of real space could play a greater part. As already defined in Les Bourgeois de Calais by Rodin, the positive vectorialities and projected shadows multiply on the background-plane of a base lying on the ground, integrating with axes and tensions of the elements, all while maintaining by means of its base a structural boundary to the invasion of surrounding light.

In the contrast made possible by the relation between zones in relief and those hollowed out: a) in the background-plane of the wall; b) on the vertical base of the low relief; c) on the ground in the high-relief or d) in the relation of positive and negatives zones in the hollowed volumes, cubist sculpture opened the road to futurist and constructivist thought, which demanded the rejection of monolithic sculpture with closed external volume, and the necessary integration of internal space of sculpture to the ambient spaces, or vice versa (Boccioni, 1975). Once the base on ground was eliminated, several solutions for the replacement of the physical support were proposed, without always, however, being recognized as such: angularity of corners, suspension from the ceiling, and so on.

This evolution made possible the presemiotical elaborations on sculpture conducted by W. Strzeminski in collaboration with K. Kobro. They spoke out against the persistence in cubo-futurist sculpture of the centered construction, that is, of a sculpture which maintained, in spite of excrescences or vectorialities oriented toward various peripheral points, a compact and dense central volume, serving as a substantial basis for these movements toward the external (1977; 103). The Polish constructivists questioned the fundamental nature of the site or the space which could properly be called sculptural. Through a general notion of space as isomorphic, homogeneous and stretching out toward infinity, derived from projective geometry, they first denied any dualism between the surrounding space and the space of the sculpture, as exemplified by the notion of boundaries or of limits assigned to the latter.

Sculpture did not possess any natural boundaries and it could be constituted without establishing boundaries of any other type. Sculpture would share with architecture, both arts of space, this prerogative of being able to structure themselves independently of any assignation of limits for its constituents: “Architecture and sculpture do not have bounds. To impose a limit on a spatial work of art is not compatible with its definition. What becomes spatial, plastic art is the space without natural boundaries, not limited by anything” (Strzeminski, 1973; 106).

But the tradition of sculpture had not realized that ideal. Baroque sculpture, for instance, which had succeeded in substituting the notion of a sculptural zone for that of external volume, had led “to the definition not only of exterior limits to sculpture, but to that of the interior of volume itself which is then open to us” (1977; 104). Strzeminski and Kobro recognized the importance of that stage constituted by this determination in baroque sculpture of a limit to the form. This was defined as “the limit of the zone of influence of its dynamic forms. We can define it in linking all the points which emerge from sculpture” (1977; 97). They called “limiting-imit” this sculptural zone which is opposed to the direct limit constituted by the old contour of the external volume: “The utilization of limiting-limit affords the advantage of making apparent, for the first time, the notion of sculpture as an ordering not of material but of a definite part of space”. In other words, for sculpture “the formation of the space in which it appears is the most important thing and the quality of material with which one fills up the different parts of these spaces is only a secondary problem” (Strzeminski, 1977; 44). The sculptural zone reunites at the same time, therefore, a region of the sculpture localized in the central volume and “the zone of transition which is included between the central volume and the limiting-limit, partially by free space” (1977; 98).

In this perspective, “to construct sculpture is to give form to a part of space contained in its limiting-limit” (1977; 105). If Polish constructivism did not fully accept this intuition of a sculptural zone as a valid one, it did not altogether deny its worth as a replacement for the ancient notion of the limiting external volume: “As much as the union of forms found in the zone included between the limit of the volume and the limiting-limit with space can be considered, as much the union of volume itself with space is impossible” (1977; 100).

But through its opposition to any dualisms and to the values of movements, of dynamisms, or of structural asymmetries, it could not accept the persistence of the contrast between the materialized form and that form which can be called negative, circumscribed by the limiting-limit and the global space: “A work of sculptural or architectural art, placed in an illimited space, should be united with it as an inseparable part” (1973; 107). However, this inseparability does not proceed from characteristics offered by the visual variables themselves, but rather by a system of proportions calculated mathematically, which encompasses simultaneously the positive elements and the external space integrated into the global structure. What is more, Strzeminski and Kobro will transform this notion of the limit of sculpture into that of a place where action is reversible, structuring at the same time an internal space and the external space itself:

The limit of sculpture is the demarcation which distinctly separates the space situated outside of the sculpture from the space contained in the sculpture. We can thus consider that this limit determines either the interior or the exterior space. The essential characteristic of sculpture rests in the fact that it is not uniquely the mise-en-forme of the interior space. One can entirely, for that matter, consider that its surface, its limit, confers a form on exterior space, a form in accord with that of the volume. (1977; 85)

This total opening of sculpture outward into exterior space appears to us, nevertheless, to render impossible the proportional relationship which must assure the inseparability of positive and negative elements of the very sculpture itself.

This inseparability between positive space and negative space is first presented by Strzeminski and Kobro as result of a calculation in the process of the production. It will be subsequently affirmed by later sculptural theory as a given perceptual datum, if one refers to the propositions of Hofmann, for example, to the effect that positive and negative spaces “exist simultaneously—both conditions the other—neither is conceivable without the other” (1948; 51). But this proposition valid for painting evades the problem of the limits of the sculptural object. Many sculptors have been unwilling to accept the constructivist hypothesis that the unified reality of sculpture should be achieved by the intermediary of mathematical equations and not by some proportions born from material characteristics of visual variables constituting the sculpture. This involves forgetting, perhaps, that any syntactic structure is necessarily anterior to the semiotic materials which it puts into play and belongs to specific theoretical levels. For our part, we find this mathematico-formal solution promulgated by Strzeminski unacceptable because it is not general enough to explain the structure of sculptures constructed according to different a priori assumptions.

Not that sculpture as a system should not be based on a priori concepts or postulates. This necessity has already been recognized and discussed by Wörringer under the name of ‘legalism’, but it was only used in reference to Gothic sculpture:

These figures lose the arbitrary and obscure character which is attached to free-standing sculptural presentation, since having become aware so to say of their own relativity, they come to be integrated with a system of legal formation exterior to them. Maximal closure of the material and violent submission of the object to a geometric or cubic legality, these two plastic stylistic laws are valid from the very beginning of all sculptural art and remain more or less determinant during all its evolution as long as sculpture . . . can the least renounce, in virtue of the three-dimensionality, to ‘stylization’ and carry at the most, in opposition to the other arts, the characteristics of a need for abstraction. (1953; 49)

Whether this need for abstraction is epistemological or psychological, Wörringer recognized rightly that “no natural object can serve as a model for this abstraction” (54). The semiotical hypothesis will propose rather that this internal structure is defined by the syntax which permits the understanding of the various functionings of the linguistic system that is known as sculpture.

According to other theoreticians, the emergence of the hypothesis of a positive/negative space has given rise to a new questioning of this space which immediately surrounds free-standing sculpture. Arnheim expressed his reluctance to consider the relation between the volume of sculpture and the transparent volume of the air which envelops it as opposing plenum and emptiness or the relation of figure to ground: “It may seem more proper to say that a piece of sculpture is surrounded by empty space than by a substantial ground” (1966; 249). But how to explain then the transmutation of this empty space which, when it is perceived through holes introduced in the full volume, as in Moore’s sculptures, appears an intermediary transparent substance which is added to the substance of positive materials? Faithful to the notion of the Euclidean void, Arnheim is reluctant to accept the contemporary intuition of the ambient air as plenum: “This is a daring extension of the sculptural universe, made possible perhaps by an era in which flying has taught us through vivid kinaesthetic experience that air is not empty space but a material substance like earth or wood or stone, a medium that carries heavy bodies and pushes them and can be bumped into like a rock” (1966; 253).

Even if one accepts this point of view, he emphasized, it is necessary to see if air is a substance which is added to the more material elements of the sculpture or if it makes the sculpture indistinguishable in the magma of the real, since the inclusion of the space eliminates any clearly defined delimitation between the work and its environment. The sculptural phenomenon becomes again, therefore, indefinable and unthinkable, as long as it vacillates between these notions which Focillon had distinguished as the space-limit, which limits the expansion of the form, and the spacemilieu, by which the same work opens itself to a dynamic expansion in the multifaceted space of natural reality.

6.6.Syntax of Sculptural Language

Even if it depends entirely upon perceptual processes in order to constitute itself, as does any language, visual or otherwise, sculpture can only be defined as a linguistic object through specific internal structures, different from definitions of natural nonlinguistic objects. It cannot refer to its simple materiality, but this must be the instrument through which its elements and their interactions become suitable for the construction of open and complex spatializing models responding to the various needs of the visual representation.

At the level of its elements, sculpture is constituted, like any other medium of visual language, by the ensemble of the visual variables which are specific energetic sources submitted to movements engendered by perceptual processes. Even if they can in a very sporadic way be perceived by touch, in which the recording of data remains reduced, the sculptural visual variables are most often grasped by the sense of sight, as a product of the luminous rays reflected on a more or less opaque material support.

As such, sculpture is submitted to the discontinuous structure of visual perception which is effected through a succession of centrations of the gaze, itself constituted by the different perceptual levels of foveal, macular and peripheral vision. The ensemble of variables perceived by foveal/macular vision, at any given moment, constitutes a coloreme. Each coloreme structures, in height, width and depth, an aggregate of energies in a mass or a region more or less flat or undulated. The ensemble of coloremes perceived successively will be regrouped similarly in larger regions, into subensembles or more complex ensembles, through the basic syntactic rules which regulate the interactions of the visual variables constitutive of the visual language. These syntactical laws are as follows:

(1) The topological relations.

(2) The gestaltian mechanisms of visual interactions.

(3) The laws of interactions of color.

At this point, we refer the reader back to the preceding chapters for the explanation of the functional modes of these three first groups of syntactic regulations.

The syntax of sculpture will differ, however, from that of the pictorial through significant variations in the two last levels of structural organization, which are as follows:

(4) The infrastructure of the Virtual Cube and its series of Basic Planes.

(5) The interactions between fictional and natural groups of perspectives.

Sculpture shares with pictorial representation the impact of the structural modalities produced by systems of perspectives. But here, the proxemic and illusory systems of distance effects will have to come to terms with other effects of the natural perspectives as they have developed in perception of the external world. Perceptual constructs of sculpture will have to take into account the different relative weight opposing: a) the topological or illusory perspectives constructed by the producer through a certain manipulation of visual variables; b) the perspectives arising from the movements, points of view, angles of vision, and so on, produced by the perceptor; and c) the important dialectical function of the ‘natural’ perspectives resulting from the interrelations of sculpture—as a physical object—with its global environment.

The perception of regions or regroupings of coloremes in the sculptural object is realized, at a first level, in a way similar to the perception of pictorial regions. Perception can always only select an ensemble of masses in the sculpture, at first topological, variously undulating and inclined, that it must regroup in visual fields through the establishment of an actual or virtual Basic Plane. Furthermore, some limiting parameters must be bestowed on sculptures.

Otherwise, not only would they be unknowable, but nonexistent as linguistic systems since no means could assess the intensities of the energies and dynamic interrelations in this specific section of the global visual field. Moreover, as the theory of sculpture has already proposed, the eye perceives, in looking at a sculpture, only partial surfaces in which dynamisms and vectorialities can only be felt through a temporary limitation of the field and an estimation of the particular inclination on the recessed plane or recessed ground of the internal volume of which this surface is the facet that is accessible to perception.

The essential difference between painting and sculpture would appear, first of all, in the fact that all inclinations in depth (or the spatial curve) in painting are constructed in relation to a unique Basic Plane in which peripheral energies are very strong, whereas the perception of sculpture implies the perceptual construction of a series of Basic Planes in which energy is less condensed, given the virtual and more diffused character of the vectors which define it. This series of Basic Planes, in relation to which perception of partial surfaces of sculpture can be effected, could seem to be infinite, since their dimensions can vary from the reunion of several coloremes to the regroupings of intermediary or superregions. But this series is seen here as constructed to return to its point of departure, that is, to form a closed and limited configuration. If the perceptual process is made up of a succession of centrations leading to increasingly subjective reappraisals of the visual field, the temporary halts allowed after an adequate gathering of information will have to deal with more different and more numerous data in the case of sculpture than of painting. Moreover, this succession in perception of “partial surfaces” of sculpture requires a real movement, an actual kinesthetic experience of the body and not a subtle blink of the eye on the part of the perceiver in order to perceive regions which are to him/her at first virtually imperceptible or inaccessible.

Inversely, in this ambulatory movement, regions already perceived are completely expelled from the field of vision, thus prohibiting the realization of perceptual interactions between the former and the latter, except at the cortical levels of perceptual memory. At the basic level of the internal volume, the perception of sculpture already seems like a much more abstract operation than that of painting. It calls for a greater number of interactions between actually perceived regions and a series of multifarious memorized regions, made difficult by the fact that a simple change in the angle of the gaze is not sufficient to recall the anterior percepts.

However, the syntactic relations established from the external surface of the sculpture are not sufficient to explain the structure of this material object which obviously possesses a central region—perceptible or not—which regroups the most fundamental structural elements on which the surface energies depend.

Our hypothesis proposes, in the first place, to define sculpture, in a global way, as a topological mass essentially structured by vectors linking its central layers to its peripheral layers, and these two zones in turn to their immediate environment.

This definition excludes, on the one hand, the conception of sculpture as a simple external volume in which the periphery is autonomous and immutable in relation as much to internal energies as to those of the environment itself. It postulates that sculpture is always endowed with an interior volume—at once shifting and differentiated—capable of increasing or diminishing, diffusing or concentrating its levels of energy, and of transforming its vectorialities in relation to the structure of the peripheral layers and of the surrounding environment.

This definition entails the determination of the boundaries of the sculptural object, at whose interior a structural proposition can be verified. Like all material objects unfolding in types of spaces variously defined by geometries, sculpture can be endowed with an internal structure which defines its limits, even if these remain in a dynamic interrelation with the objects and intervals of its milieu. Conceived as a linguistic object, sculpture must necessarily assimilate itself to open structures of negative entropy, accentuating its heterogeneous functions, which cannot be materially prolonged in the entropy of the infinite and the radically illimited. Syntactically, it must be endowed with a basic limiting structure within which the components of the sculpture may acquire definite spatial characteristics, qualities and energies.

6.6.1.Virtual cube

It does not appear fruitful to use literally the notion of the “limiting-limit” whereby “the sculpture is contained at the interior by the limits formed by its extreme parts” and requiring that this limit is obtained in connecting, such as they are, “all the points which emerge from the sculpture” (Strzeminski, 1977; 97). The reasons are that the action of these extreme parts influences and transforms not only the other material parts of the sculpture that are thus interlinked, but also the intervals which separate and surround them, constituted by luminous and atmospheric material.

We propose, by contrast, that the immediate limit of a sculpture, which does not exclude the possibility of secondary limits, will be contained in a larger unit, the Virtual Cube. This construct finds its dimension in the contour which reunites, in effect, the extremities of the sculpture, but conceived as a regular form which incorporates the surface-planes, volumes, and vectorialities of ‘positive’ regions of the sculpture as well as those of ‘negative’ regions. This cubic, regular and virtual form, possessing its own proper internal structure, would thus interconnect actualized as well as virtualized energies, a necessary precondition for the development of linguistic functions.

This Virtual Cube also offers a basic volumetric structure, corresponding to a topological three-dimensional mass and according to which the potential and synthetic volumetries of the structure can be constructed. In this sense, its dimension and form will vary with the parameters offered by the most extended “positive” elements of each sculpture, producing parallelepiped forms of cubic square, rectangle, trapezium, or a regular or flattened sphere, cone, or cylinder, all these forms being topologically similar. On the one hand, the fundamental continuity of a topological mass requires that this Virtual Cube be presented in a unified structure which can encompass the totality of a sculpture, even of an irregular or idiosyncratic form, without potentially severing it into two or more parts. On the other hand, this inclusive form must possess a maximum internal energy, the sum of its formative factors, that will intensify the forces generated by the components of the sculptural planes or volume.

The Virtual Cube thus corresponds to the contour of the most unified geometrical forms which as gestaltian “good forms” have a preeminent status in the perceptual process. Under each of these forms, the Virtual Cube possesses an internal structure endowed with specific energies whose pressures are equilibrated by the condensed energies in the external contour. Whether peripheral or central, the energies of the Virtual Cube are deemed to have effects on the perceptual plane analogous to the actual energies emanating from the visual variables constituting the sculptural material.

In the majority of cases, the Virtual Cube of sculptures is constituted as a parallelepiped, that is, as a square or rectangular cube. Thus, when the “small sculpture” presents one prominent axis, it is endowed with a rectangular cubic infrastructure. The low and high relief are endowed, from their highest protuberances, with planes which close their frontal and lateral expanses to form a cubic box, usually rectangular. The free standing sculpture sees its virtual cubic limits most often defined and its peripheral energies partially reiterated by the format of its base, its pedestal, or its supporting points on the ground. The cubic form issues from the points of maximum expansion in the “figure” or the base sections (figures XVa, XVb, XVc, XVd, and XVe).

Given the stability and the stronger dynamism of its internal/external equilibria, the square or rectangular Virtual Cube prevails even when the sculpture borrows relatively simple and primary forms on the geometric plane—such as the pyramid, the cone, or the sphere. But material sculptures presenting incomplete or truncated versions of these basic forms, such as the truncated cone or triangle, would, in an immediate way, obey the gestaltian pressure for the completion of its “good form,” before interconnecting with the stronger square or rectangular Virtual Cube.

Paradoxically, it must be recognized that “minimal” sculptures actualizing the form of a cube have an equal need to be endowed with a Virtual Cube, to define their “hidden” internal structure. In fact, the “external” cube is poorly revealed and always deformed by the partial surfaces, which are provided by the different points of view and movements of the perceiver around the sculpture.

Determined in the first moments of the perceptual process, most frequently through widened vision and at a distance of peripheral vision, the already constructed Virtual Cube may seem inadequate for other points of view subsequently taken on other parts of the work which were not accessible to the primary perception. This first Virtual Cube developed by perception will yield its place to a more encompassing Virtual Cube which can account for the totality of vectorial expansions of material volume. Though difficult to assess, the mnemonic traces of this first global effect will interfere with the energetic functions later recognized in the sculpture.

On the other hand, the shadows cast by the strict lighting of a sculpture by its producer serve as parameters for the construction of the Virtual Cube encompassing the total work, since the virtual volumes generated by these shadows must be put into relation with the positive/negative volumes produced by the other visual variables.

Figure XVa: Structural Axes of the Virtual Cube

Figure XVb: The Virtual Cube of the Small Sculpture

Figure XVc: Virtual Cube of a Low Relief on a Wall, Laterally, and on the Floor

Figure XVd: Virtual Cube of a Sculpture with a Base

Figure XVe: Virtual Cube and Positive/Negative Volumes

Figure XVf: Sculpture with Multiple Elements on the Floor

One can only regret, in this respect, the habitual discourse on sculpture which, while recognizing the volumetric specificity of the sculptural object, reduces it always to the description of a pseudo-frontal plane on a surrounding ground, as if all sculpture could be reduced to the structure of low relief, but this time on a nonexistent background, or worse, to that of a pictorial drawing.

In an immediate way, the hypothesis of the Virtual Cube and its a priori infrastructure appears essential to unify, in a volumetric system, both the diversity and heterogeneity of the various internal/external volumetric masses with their particular dynamic characteristics. The trajectories, movements, positions, and points of view that the perceiver establishes in the various perspectives allow a complex synthesis where each plays its proper role.

We should point out that the hypothesis of the Virtual Cube does not have as a function the substitution or withdrawal of a certain external volume as paradigm of the sculpture, but rather to define and render explicit the internal energetic structure of the object. It serves to determine the grammatical functions of the parts which cannot be perceived in the apparent visual statement. In the same way as deep structures had to be assigned by Chomsky, for the understanding/description of the surface structure of the verbal phrase, the syntactic structure of sculpture often cannot be observed at the surface level of its visual variables but must be developed by way of more encompassing structures possessing a specific energy.

Similarly, the function of limits filled by the Virtual Cube must not be conceived as a metric determination, but rather as an individuating determination analogous to the role played by the notions of cells or atoms in the biological and physical sciences which are not strictly measurable but necessary for the development of hypotheses about the function of certain elements in the whole. If, in one sense, we agree with Strzeminski’s observation to the effect that “the limits of a sculpture appear only after its execution” (1977; 87), it should not however be applied in such a manner to the variations in the dimensions or the format of a sculpture, because these differences do not radically modify the possible interrelations at the core of the Virtual Cube between the forces of the infrastructure and those of the positive elements themselves.

In addition to its individuating function, which allows for the cognition of a given sculpture without denying its environmental interrelationships, the Virtual Cube fulfills the major function of establishing and maintaining the fiction of volumetry at the heart of the sculpture. As mentioned repeatedly, volumetry is never a given in perception, but is solely deduced from partial surfaces by the cortical processes. The proposition of the volumetric structure of the Virtual Cube serves to keep present and active this volumetric notion which is too often neglected in the perception of a sculpture. It defines systematically the relations between those energies perceived on the plane or in demi-relief and the fundamental energies which structure the interior volume in a permanent way.

This syntactic matrix also proves indispensable for the apprehension of the energetic events produced in the peripheral layer of sculpture, through relations of its material boundaries with the surrounding, luminous energy at different levels. The strongest juxtaposition of a sculpture’s visual variables to the surrounding luminous radiation produces two different types of phenomena. The first are constituted by the refraction of luminous rays which reach the periphery of the sculpture, causing tensions and expansions of all variables (form, color/tonality, texture, dimension, position, vectoriality) and producing varied spatial curves and inclinations. The second type of phenomena is constituted by the perception of luminous energy itself, natural or ambient, gathered and rendered dense in the so-called negative regions as well as in those regions which are contained by the formative sides of the Virtual Cube itself. This allows the material extremities of the sculpture to be interrelated with the peripheral negative regions that their expansion has incorporated into the sculpture.

Thus the orientations, pressures, extensions, and radiating expansions in which the visual variables are deployed at the periphery of the sculpture are the meeting points between the internal vectorial energies, the characteristics of the frontiers, and the light energies in which the sculpture is immersed and which it reflects. It is uniquely in a relation with the energies of the Virtual Cube that the vectorial dynamisms can be felt and estimated as well as the expansions and contractions of volumes and partial surfaces, the tangential energies, the variations in texture, the proportional relations between sections of a sculpture of which the nature, meaning, and function would otherwise be dissipated in the indefinite context of the surrounding environment.

Through the virtualization of these peripheral sides, reiterated partially or not at all by a sculptural work, the internal structure of the Virtual Cube is at first defined by its central, vertical, and horizontal axes. Hofmann already proposed these as essential parameters: “All volumes can be considered as having imaginary, vertical and horizontal axes. All volumes move around such axes. And each of these axes can be brought in opposition to the other. The result is movement and countermovement in spatial opposition” (1948; 51). However, it must be added that the diagonal axial energies constitute to a similar degree a source of tensions and countertensions at the volumetric core.

The vectorial axes can act in a linear way in the volume but can also exercise tensions of planes (or of two-dimensional units) which are not necessarily flat since they can be rippled by unequal energies. Naum Gabo has already described these planar axes as those occupying a surface in width and length in the continuity of central orthogonal axes (1964; 108). One must also include as syntactic elements the planar axes which deploy in two dimensions the diagonal energies, exerting their flat or curved pressures in all the regions of the sculpture.

The internal planar horizontal and vertical axes draw their energetic force not only from their own directional vectorialities, but also from the fact that they reiterate the condensed energies in the periphery of the Virtual Cube, that is, the planar facets which circumscribe and contain the internal energies of the cube. The planar energies of the six sides of the cube, because they are virtual and thus not as strong as the peripheral energy which forms the pictorial Basic Plane, are vividly felt at the same time as pressure on the internal, that is, on the vectorial regroupings of the volumetric regions and as limits of the system that they encompass.

In the internal global volume, the linear and planar axes, which are spread out to the sides in the three dimensions of the Virtual Cube, are in a state of constant dialectical relation to the actual energies of the visual variables realized in a sculpture, producing punctuations, reiterations, intersections, curves, junctures, and envelopments in the internal partial volumes which are juxtaposed, separated, or interpenetrated, according to topological or gestaltian rules. The Virtual Cube is the only theoretical structure which allows for the implantation of given regions in volumetric depth. Its most significant syntactic role is undoubtedly the activation of dynamic processes in the visual variables, by a continual relation between the elements actually produced by the sculptor and the energy of the infrastructure of the work.

The aim of the syntactic analysis of sculpture is to observe the nature of the energetic phenomena which are constructed at the periphery, that is, at the boundaries of the multiple, interior volumes and the interrelations of these with the infrastructure of the Virtual Cube. It will attempt to determine the spatial organization of a particular work, the type of rhythm that it conveys from the center toward the peripheries and vice versa. These internal dynamisms will be represented by syntactic analysis through a great number of vibratory schemas. Both centripetal and centrifugal, they expand in certain directions, rotate around certain axes, “breathe” along differentiated segments, react to virtual or negative adjacent volumes, and so on. Each of these dynamic structures will be the basis of reference to the perceptual field which it attempts to represent, so as to introduce it into human awareness and make it available to human communication.

The syntactic levels established by the topological and gestaltian relations and the infrastructure of the Virtual Cube account for the dynamic potentiality of the elements and structures of a given work, revealing topological and illusory perspectives that the producer effected by means of varying regroupings of the visual variables. However, like the linguistic structures of painting, these groupings of perceptual regions are interpreted first as linked inside various systems of organization of perspective, determined both by the widening of perceptual points of view and by specific relations of the work with its global physical environment.

6.6.2.Perspectives of perception

By no means can the perceiver of a sculptural work declare nonexistent or redundant the regions of the works he/she does not take the time to perceive. On one hand, we have already proposed as a postulate that the principle of redundancy cannot exist in the field of a visual work, since the effect of the smallest regions, and even of individual coloremes, can modify and disrupt all previously established relations between regroupings of the visual elements. On the other hand, if this postulate were rejected, how could one designate as redundant an element that one had not yet even perceived and whose influence on neighboring regions and consequently on the global structure could not be established? This principle of completion in perception requires taking into account not only elements and regions always organized in a perspective modality by the producer, but also the perspectives that result from the points of view taken on a given work by the perceiver.

It is the role of semiotical analysis of sculpture to determine the type of perceptual program that can insure a minimal and sufficient knowledge of the sculptural, visual text, since the subsequent semantic interpretation is normally dependent upon it. It is obvious, however, that the trajectory of perception of a sculpture is much more lengthy and complex than that which is operative in the perception of a painting, both by the multiplicity of factors contributing to the development of an intuition of volumetry and by the action of the natural modalities of perspective established by the perceiver, which must be integrated into modes of perspective inscribed by the producer in his particular treatment of the visual variables.

In contrast with the perceiver of a painting, who usually positions himself/herself in a frontal point of view (or in several frontal or oblique sightings when the work has large dimensions) which, in relation to a given format, will relate the totality of the visual field to the same Basic Plane, the perceiver of a sculpture has to multiply different frontal positions, giving him access to different visual fields, with wide angles of vision vertically and laterally offering constantly changing partial surface dynamisms. If one hypothetically reduced these surface fields to the four lateral faces of a cubic volume, those of the bottom or top being most often imperceptible as surfaces, the internal volume of the sculpture would be defined by the integration of these data in depth, in the central regions of the masses. However, not only will the dynamic pressures emitted from top and bottom transform the structure of this hypothetical lateral cut, but the faces of the sculpture organized along their various Basic Planes could not be reduced to the number of sides of the Virtual Cube. A sculpture does not possess four faces or “frontal planes,” but as many as the distances and positions chosen by the perceiver will produce. The syntactic structure of the Virtual Cube serves only as a theoretical parameter, with a view to the integration of these multiple faces and their respective depths in a synthesis where their differences can still be recognized.

Without entering into a detailed discussion of the possible inscriptions of the different types of perspectives enumerated earlier, one can point out that the same regroupings of objective visual variables will be perceived differently when the perceiver sees them from a different angle which modifies their context with their specific field. By a change in position, from frontal toward oblique, different percepts are produced in the same objective place by successive centrations which will require an integration at levels no longer sensorial, but operative and abstract.

Even in an approach which always remains frontal, which is rarely the case, the perceiver of a sculpture is also called on to multiply sightings toward the top and bottom which put into play the kinesthesia of his/her body itself, and not only his or her eyes. This generates different perceptual fields and perspectives which must be put into relation with the volumetric infrastructure of the Virtual Cube through a process of continual transformation and integration.

In addition to the perspectives resulting from different positions and movements on the part of the perceiver, in part conditioned by the producer since they are linked to his very manipulation of the visual variables, one must add, as a perceptual component, the natural perspectives which the sculptural object commands as one physical object among others. These perspectives cannot be entirely controlled by the producer.

The first natural perspectives are developed as the perceiver gets nearer to the sculpture which he has first perceived in a far or medium distance as part of a wider environment. The first percepts developed during the process of localizing the work are necessarily submitted to the structures specific to the perspectives of far or intermediate distance. Stored in memory, these first percepts will influence subsequent percepts developed at a more personal or proximate distance, establishing a level of ambiguity in the experience of sensory data, interpreted in a variable way as part of a spatial context. The effects of far distance are, moreover, often reiterated by the trajectories of the perceiver who, instead of maintaining a more or less close distance to a sculpture, moves himself/herself further away at times in order to reevaluate the work at a much greater distance, where foveal vision and sometimes even macular vision are no longer effective. Thus, in addition to the multiple topological and illusory perspectives resulting from the proxemic trajectory around a given work, which are already difficult to integrate into a dialectical unity, completely dissimilar perspectives must be added to the first, sometimes in an antagonistic context.

If the reflection of luminous rays constitutes the vibratory and energetic material that determines the nature of the visual variables, in any given visual language, it follows naturally that any change in the natural or artificial lighting of a work will transform it in all of its characteristics. This is certainly at odds with the status of the verbal text; the grammatical structure of the latter does not vary with a change in lighting, but only the potentiality that the text possesses to be or not to be the object of a perception. Lighting itself does not establish the syntactic structure of a visual work, but influences its apprehension. The effects of lighting on a pictorial work may generate different artworks according to its own variations. This fact has been put aside, so to speak, inasmuch as the lighting used in the locale of presentation of a painting is believed to correspond to the intentions of the producer.

This is rarely the case in the public presentation of a sculpture. Not only is it very difficult to reconstruct in another site the sort of ambient light and the system of lighting which exist in the producer’s studio, but the places of presentation (museums, galleries, and so on) use types of lighting whose chromaticity, intensity, angle of projection, and so forth, differ most often from the lighting which served in the production of the work.

One should then ascribe to the category of natural perspectives the modification of the visual variables and the total transformation of their modes of interrelation, resulting from the effects of various sorts of illumination the sculpture is subjected to when it is put in the open air or in diversely lighted interiors, as long as the producer cannot reproduce the light in which the work was created. The transformations of the work caused by these different light contexts are often radical, imposing on it specific syntactic interrelations in accidental perspectives. These vary with each place of presentation. Lighting, considered as a neutral and objective element in the case of a painting, is crucial in sculpture. The direction of the light sources, their intensity and chromaticity must be incorporated as elements in the description of the sculpture, since they establish types of perspectives which do not necessarily depend on the action of the producer nor on the perceptual process of the spectator, but which are derived from data in external reality.

Semiotics classifies in a different category the environmental propositions that, in refusing the postulate of the limits of sculpture, propose that a sculpture should be perceived in the globality of its physical or natural environment. In order for this kind of environment to enter into the perceptual field, it is necessary for the perceiver to position himself/herself at a remote distance which affords perception the unique advantage of peripheral vision. Having become an object of lesser dimensions with reduced visual characteristics, sculpture is distinguished in a more or less efficacious way from the objects which surround it. A selection of its more undifferentiated and macroscopic dynamisms, the largest, are compared to those of natural phenomena (sky, lake, mountain, trees) or to architectural instances which, even when reduced by distance, are generally more spacious and affirmative. Just as it occurs in the architectural environment itself, sculpture becomes only one region among others, subject to the logic of architecture or design which renders the dynamic of its visual variables to a large extent inoperative. These sculptural elements, thus integrated in a wider physical environment, receive considerably more light from the semiotics of architecture, or of environmental or garden design, than from the semiotics of sculpture.

These foregoing remarks do-not deny the sculptural character of monumental sculptural constructions, the limits and dynamisms of which are incorporated in elements sufficiently affirmed so as to be accessible to vision at a medium distance. Paradoxically, in effect, these gigantic works often seem to present themselves to perception at a medium or relatively close distance, if one considers the proportional dimension of the surface of the ground which is deliberately circumscribed to serve as their base or environmental support.