5.1.Perspectives of Perception of the Natural World

Developments in the cognitive sciences in the later part of this century make possible for visual semiotics the tasks defined by both Wölfflin and Panofsky, and as yet unfulfilled. In particular, they permit us to understand the so-called artistic systems of perspectives as representational constructs based partially upon the perspectives of the perception of the natural world.

A basic postulate in the study of systems of perspectives is the observation that each human being occupies a particular point in space-time and that, by virtue of this unique and different physical and psychological position, one necessarily perceives, stricto sensu, a different aspect of reality from that which is perceived by one’s neighbor. In effect, the activity of perceiving reality is realized only through a perceiver’s occupying a particular position, permitting him to establish an immediate and unique relation with reality. It is only through a denial of the perceptual process on the abstract plane of concepts that several individuals can claim to see the same thing, when they look at the same object. An existential position can yield only a particular point of view in space-time, revealing only certain aspects of things and leaving others concealed.

A second postulate is that perception of reality is successive, made up of the accumulation of various sensorial centrations on different aspects of phenomena. The egocentric and partial character of all perceptual centrations obliges the human being to adopt the largest possible number of points of view of objects, (that is to multiply centrations from different positions in a more or less gradual temporal unfolding) if access to the most adequate informational data on specific objects or environments is desired. The necessity of such an active and plural interrelating with reality does not, however, exclude some similarities between the mechanisms of perception, adopted by individuals relative to various sensorial fields.

As far as apprehension of natural objects in space is concerned, important factors influencing the perceptual constructs can be related to the observer’s position and visual apparatus as well as to specific characteristics of the object apprehended. The psychologist James J. Gibson (1950) has called the constant regrouping of typical information according to different categories of factors “perspectives” of natural perception. These thirteen varieties of perspectives have been summarized by E. T. Hall (1966; 191) and classified into four different principal classes, as follows: 1) The perspectives of position (by texture, dimension, linearity); 2) Parallax perspectives (by binocularity and movement); 3) Positions independent of position and movement of the observer (aerial or atmospheric), shuffled, relative location in height, linear space by textural change, modification of double images or acceleration of an object, transition between light and shadow; and 4) Perspectives produced by completion or not of contour. Although Gibson has devoted extensive research to the perception of the world through vision, each of the senses could be described as establishing different points of views/perspectives on reality. These would lead to the construction of various sensorial organic space representations.

The term ‘perspective’, which we would like to use more in relation to concrete modes of representation, refers in Gibson’s context to particular aspects of perceptual determinisms. It is nonetheless particularly efficacious for expressing the way that ambient reality appears extremely different according to how particular modes of relating to the world are used and valued.

These perspectivist modes of perception produce particular channels which assemble the elements of reality in a more or less constant way. At more local levels, the continuity or prevalence of certain perceptual attitudes, within these perspectives, also produce regular percepts and modes of interrelation with limited features abstracted from reality. No one of these “images” produced by only one of these perspectives can be considered as equivalent to reality. From different points of view or perspectives, other aspects of reality can also be regrouped in regular and significant ways, sometimes conflicting with the previous, or with perspectives that have been deemed more important in different cultures.

The multiplicity of organized points of view or perspectives developed by the perceiver to provide different information about reality obliges him/her not only to proceed to accommodations with a plural visual field in constant transformation but also to attempt to conceive a possible unification of these heterogeneous groups. According to Piaget, the coordination of perspectives “raises three sorts of conflicts, that can be surmounted only by dialectical syntheses” (1980; 189).

The first conflict results from the duality between the identity of the object, presumably existent and permanent, and “the multiplicity of its observable forms in function of changing points of view.”

The second conflict corresponds to the need to conciliate our points of view with those of others. It invokes: “. . . the necessary passage from the absolute to the relative, no perspective being privileged and each remaining relative to the position of the observer” (Piaget, 1980).

The third conflict arises from the need to complement actual perceptions by anticipations, that is, by perspectives that will be required to represent changing phenomena. This would mean the production of a synthesis between the differentiations and their integration “into a grouping assuring the existence of an all new invariance; this will be of a transformational nature and not any more static as was the initial identity of the object conceived as having to keep an apparently constant form” (Piaget, 1980; 190).

This synthesis or integration of distinct sensorial/perceptual points of view into a new “transformational” invariance is achieved in the elaboration of more complex spaces which permit the unification of the diverse organic spaces. By virtue of its immediately spatializing nature, visual language is the privileged linguistic tool through which the organism is able to experiment and produce “spatial dialectical syntheses” that establish relations not only between the fragments of actual emotional and conceptual experience, but also between these and fragments that are retained, consciously or unconsciously, from past conceptual, sensorial, or imaginary experience.

However, whatever the spatial model used for representing groups of elements experimented with by perception, the most fundamental point to emphasize is that the spatializing model of semiotic representation, that is a representation constructed with material components, cannot be the same as that of perception or conceptualization. These are formed by totally different constituting elements, reunited in a context heterogeneous to that of actual experience. Just as words are not the things they represent, so visual representations, spatial models, diverse perspectives are not of the same order, and do not possess the same existential status as elements which constitute reality. If certain acquired codes of perception allow us to recognize certain images as resembling real external objects, it does not render the space of representation that constructs the visual representation the same as that of reality and any more “real.” This fruitless opposition, in this respect, between pictorial movements, from one generation to another, results from shifts in the definition of what is the essence of reality: static substance, movement, hidden structures, light, and so on. It should have terminated from the moment, as Lessing tells it, when the ancient author Lucien discovered that he did not know how to decode a painting of Zeuxis, which was of so “natural” a complexion that it could deceive the birds. Not only did the animals seem better tuned to the concept of the real, but they were better semioticians than the writer who admitted his incapacity to distinguish whether a given figure was placed behind or over another (Panofsky, 1975; 86).

Even if certain natural perspectives used in perception maintain an influence in the construction of spaces of representation, these two sorts of spaces cannot be assimilated one to the other. The first offers a dynamic and substantial discontinuity, whereas the second attempts a symbolic function in terms of a continuity requiring a basic homogeneity in its constituents. Panofsky well understood this:

In the space of perception, the concept of homogeneity cannot be applied as it is in representation, where at each point of space, it is believed possible to effect similar constructions in all places and in all directions. In the space of immediate perception, this postulate can never be satisfied. We do not find in this space any homogeneity of places and directions; each place has its own modality and value. The visual space and tactile space, agree on one point: at the inverse of metric space of Euclidean geometry, they are ‘anisotropic’ and ‘unhomogenous’. In these two physiological spaces, the three principal directions: before and behind, top and bottom, right and left, are not equivalent. (42-43)

And following Cassirer, he underlined the fundamental difference of value between “solid bodies” and the intermediate expansions of the void between them in a tactile field, which is not in fact observable in a pictorial work, since it is everywhere occupied by visual variables.

It is necessary, furthermore, to remember the great difference that exists between the act of perceiving an object in external reality and the perception of an artwork. The pictorial work, or the sculptural work which we will discuss further on, is not made up of objects possessing the structure of external objects, but rather by paradoxical objects that are determined by their linguistic function as specified in the representational visual field.

Visual works are indeed real objects, whether or not suspended on a wall or installed on a pedestal, and subjected in this regard to the normal perspectival constraints in the so-called natural space. But at the same time, instead of being constituted simply by relatively planar marks affixed to planar supports, these works present the effects of depth and distance, as used in a fictional space different from that of natural space. This has been demonstrated by experiments conducted by R. L. Gregory. “Among other things, (these experiments) tell us that seeing pictures is very different from seeing normal objects. This means that pictures are not typical objects for the eye, and must be treated as a very special case” (Gregory, 1980; 50).

5.2.Perspectives of Semiotic Representations

If the perceiver must transform the usual mechanisms of visual perception, which are regulated by survival and functionalism, in order to be able to enter into a relationship with the visual linguistic field that constitutes a work, he finds there another order of major difficulties. Not only is this work not a simple object of reality, but it is also a symbolic place where another human being organizes a representation of his own experience of reality, of his own perspectives and points of view. The perceiver is called upon to confront or compare, volens nolens, his own perceptual mechanisms and perspectives with those that are used by the producer of the work in his apprehension of the world. The perceiver can only infer these as they are represented in the work by the instrumentation of certain visual variables.

Models of various sensorial perceptions of reality, or models of internal perceptual representations, always interrelated with sensori-motor, emotional, and conceptual elements, must not be confused with the modeling potentialities of the material, visual language. At the same time, it would be hazardous to identify the perceptual and referential constructs of experience and language produced by one individual with the positions, points of view, and perspectives of another individual. All visual works propose, therefore, a simultaneity of sensorial perspectives, more or less integrated or for that matter, integrable: the natural perspectives of the producer, which are inscribed more or less adequately in the work, and those of the perceiver, issuing from his own possibilities and habits of sensorial spatialization, acting on the actual stimuli of the work in a temporal succession of points of view taken on that work.

This confrontation of the points of view and of the organizational systems of the perceiver and the producer in the visual field can only multiply and intensify the conflicts and heterogeneities that the perceiver had already discovered within himself, as referred to earlier. These have now to be confronted with those of another human being. Without recourse to Freud or Lacan, a simple psychological hypothesis about the emotional development of the human being and the intensity of his ‘mechanisms of defense’ would explain certain difficulties of the perceiving public in placing themselves in a fruitful relation with works which upset their own acquired schemas of reality. This hypothesis would also explain how the occident was able for a great length of time, to persevere in the belief that there was only one single true visual perspective on the world, namely its own, and that all others were inferior, underdeveloped or simply incapable of producing works of art.

Indeed, the observation of forms of visual representation produced by diverse groups or human societies obliges us to recognize more than two dozen of systems of perspectives, favored at one time or another. These representations are accessible through museums, collections, and general information, to any producer of the visual artwork today. They offer an extremely large number of modalities of spatial structures that may respond to new needs of thought and communication. This richness in grammatical resources in visual language is to be contrasted with the rigidity of natural verbal living languages, reluctant to borrow from or to revive grammatical categories used by dead or foreign languages or to create new ones.

One cannot insist enough upon the multiple meanings of the term ‘perspective’, in view of a certain usage which would still pretend that it may only refer to the system of artificial perspective that the Renaissance, following Brunelleschi and Alberti, opposed to medieval “natural” perspective. Hubert Damisch has pointed out how the new perspective of the Quattrocento appeared revolutionary, indeed “as a rupture with the very idea of tradition” (1979; 113). It took a long time before this system of representation was accepted by the popular sensibility, which was more familiar with the structures of representation of natural perspective inherited from the Middle Ages and with those of northern societies.

The artificial and calculated character of this linear perspective was embarrassingly obvious. It required from the perceiver a single and motionless position, in a prescribed area in relation to the visual field; it demanded a viewing with one eye closed and held immobile, and so on. In fact, it tried to identify spatially the perceiver with the producer of the image. One may recall from Damisch analysis the curious process of production of the perspectivist apparatus by Brunelleschi, with his arbitrary recourse to a mirror in order to produce figures on the upper part of the work. This subterfuge, he wrote, “made perspective appear as a structure of exclusion, in which coherence was based on a series of refusals” (Damisch, 1979; 171).

One has stressed less often the exclusion that it placed on all visual representations involved in a medium or near distance, because of its incapacity to resolve the lateral distortions that its mode of representation imposed. As much as his contemporaries, Leonardo da Vinci recognized that the works representing objects at a short distance had a particularly strong power of illusion. But the painter had to renounce this point of view because it could not be rendered by linear perspective:

If you want to represent a thing nearby which produces the same effect as natural objects, then it is impossible that your perspective not have a false air . . . Otherwise, do not undertake to represent a thing without the distance that you adopt being at least twenty times greater than the largest height or width of the object that you must represent; then your work will content every spectator in whatever place he finds himself. (Panofsky, 1975; 46-47)

Wherever he finds himself, except close to the object! Elsewhere, da Vinci (who will be followed by Lomazzo), established that the distance where objects are placed in a field of representation must correspond to the largest dimension of the artwork multiplied by a factor of three (Panofsky, 1975; 169).

This is still recognized as an important constraint in visual representations today: “One assumes, by convention, at least since Leonardo da Vinci, that occidental artists create a painting with a perspective appropriate to a visual distance ten times greater than the size of major depicted objects” (Hagen, 1984; 33).

This artificial perspective developed by artists—and, as Damisch noted, more so by architects than by painters—is applicable more to the constructed or built object, or even better “to the space of the town such as it is defined by the buildings which enclose and delimit it” (1979; 22, 124), than to the pictorial space.

This system describes “the effects engendered by distance, not only by relation to the object, but in relation to the plane of projection” (Damisch, 1979; 130). This notion of plane, as mentioned earlier, was a substitute interpretation of the Basic Plane and reveals itself here as fundamental, in the geometrical construction of volumes on a flat surface. But the adjunction required of points of distance, of several vanishing points along the horizon line, of calculations of foreshortening scales, as well as the introduction of rules pertaining to the atmospheric perspective, the exploration of different points of view, and the juxtaposition of double horizon lines explain the pluralistic character of perspectives in use between the 14th and 16th centuries, as demonstrated by the studies of P. Francastel (1965). Other systems of perspectives were elaborated from the baroque 17th century up to our time. These have not been duly studied and described, since they were seen as superficial and accidental deviations from the one “true” system of perspective that appeared at the Renaissance.

For our part, we will define perspectives as those organized groups of sensory marks placed on the Basic Plane, offering parameters for the suggestion of distance and depth in visual representations. These parameters depend as much on the characteristics of visual variables as on their modes of junction.

In other words, the perspectives are constructed, on the foundation of perceptual data, as different systems of spatialization, so as to interrelate a multiplicity of coextensive elements in a simultaneous context, according to certain needs of feeling and understanding. However, even in those works offering a dominant perspective, one will often find another or several other perspectivist systems, translating diverse sensorial experiences, seeking unification through a more abstract spatial model. This complexity will be perceived as harmonious and well integrated in certain instances, and as chaotic and discordant in others.

Other types of contradiction appear as well in some mimetic perspectives that claim to account for certain codes of perception of natural objects. The perceiver is engaged in choosing a hypothesis of recognition of objects able to correspond to certain visual stimuli, so that the work can be interpreted in terms of a similarity of objects as seen in external reality. He must therefore necessarily appeal to visual memory in order to identify, starting from several parameters, certain agglomerates as corresponding to real objects hypothetically posed in a particular situation. Visual memory, however, as Richard L. Gregory has pointed out (1980; 86-87), furnishes only fragments of rough objects or larger aggregates of these, with no information about their context, namely the particular distances between these objects and others, or their orientation, their movement, or even their objective dimension. These spatial characteristics can only be constructed through pictorial representation itself. Even visual mental images must accommodate or adapt to the points of view adopted by the producers. If it is true that the first human made visual representations had as their function the reproduction of mental visual images rather than the production of images resembling perceived reality, one will recognize with R. L. Gregory that it “is not so very surprising that representation of distance and orientations occurred late in art history” (1980; 120).

What is important to remember is that the perception of distance in three dimensions has to be made from the sensorial data offered by a particular pictorial work, and not from the recollection of mental visual images as such. As for isolated visual variables, certain references can be established between the color, texture, and dimensions offered by certain pictorial stimuli and the recollection that is associated with them in the perceptual souvenirs of objects in reality, where they were inserted into the widest possible variety of contexts.

The relativistic character of the notion of perspective has been known in the theory of art for several centuries. It reached a culminating point, for example, in the proposition of Charles Blanc who opposed a utopian ‘geometrical’ image to that of natural perspective: “The geometrical is the image of an object seen by an eye as large as itself, in its real dimension: all that is larger than our eye is seen in perspective, that is, in its apparent dimension” (1880; 513).

In this regard, the perceived coloreme in a foveal angle, equivalent to the dimension of the source of vision, would be the most truthful object of perception, other objects being subject to distortions of perspective. We believe it is more heuristic to recognize in the “geometrical” of Blanc that which depends on parameters of topological geometry constituting a type of perspective or specific point of view structuring the object, whereas other sorts of perspective will refer to different geometries: Euclidean, projective, and so on.

Reapplying its primary meaning to the term ‘perspective’, as handed down from the ancient Greeks, namely, “the science of the transmission of light rays” from a reflecting surface up to the organ of sight, we would define perspective as any unified system, implicitly coded, that determines the choice and use of visual variables in precise interrelations, with a view to producing different types of “distance effects” (Klein, 1970; 237).

While retaining the terms ‘points of view’, ‘positions’, ‘sightings’ and ‘aimings’ to describe the physical and mental characteristics of the producer of the visual representations, we apply the term ‘perspectives’ to those representations of points of view that are realized materially by visual variables in visual texts.

In the context of this interpretation, perspectives are organized forms, codifying not the position required of a given spectator, but the position chosen by the producer in relation to the object of his representation. It is by no means necessary that the spectator physically occupy the position of the producer which he has to infer from the syntax of the text. Indeed this exigency would seem a virtual impossibility—either on the theoretical or physical plane. This postulate of the Renaissance perspective attempts to reduce or negate the plurality of points of view in human experience and to construct a hypothetical universal subject.

What the work presents to the spectator’s view is an ensemble of relations established by the producer between the different elements that he himself has chosen as means of representation and by relation to which elements he situates himself. Consequently, a duality always exists between the position of the spectator of a work and the position occupied by the producer, reflecting their existential statuses. This maintains a psychological distance between the two and requires a specific strategy, more or less successfully accomplished on the part of the spectator, in order to imagine himself experiencing the perceptual position of another subjectivity. This psychological distance is masked only when, in a frontal or oblique trompe-l’oeil, as in the case of a vertical panel the height of a person or of a distant perspective taken on a ceiling, the producer stipulates that the perceiver imitate his own fixed position, by way of which he intends to prolong the natural perspective of perception. But as Ernst Gombrich has explained, this illusion requires the mental suppression of a very large number of characteristics of natural perception; soon enough, the illusion is rejected as inadequate by the perceiver who regains his free mobile point of view on the representation (1960).

The various systems of perspectives can be regrouped according to their aptitude to model a spatial experience close to the body of the speaker/producer, or at a great distance from him. This distance constitutes one of the fundamental factors defining the potentialities of one’s body in obtaining informational data about the world within specific organic spaces.

Distance has been given different names in the domain of visual representation. The distance established in one dimension is called length; in the second dimension, it is called height and width, whereas the distance observed on a perpendicular axis in front of or behind the body is called depth.

As a constitutive element of the “construction” of space, this quantitative notion of distance is not necessarily measurable mathematically. That notion of distance defined by constant metric length is an operational concept developed in an epistemological and conceptual human context which is relatively foreign to amorphous and continuous matter in movement, and the more so to mental subjective phenomena. Non-Euclidean geometries will consider points infinitely close to each other, within a continuity ruled by field-laws and distant actions.

Mental spaces of representation, concerned with experience or knowledge, are not amenable to metric quantification, except for the indirect accompaniment of minute electric discharges. As such, they have to be modeled with qualitative quantifications, establishing continuity between particularly dynamic events.

Once integrated in pictorial space, the concept of continuity will require an analogous transformation of the notion of distance-in-depth, which remains an indispensable parameter of any spatial experience. Thus, the parameters of distances which will be utilized in the description of depths in visual representation must remain as hazy and shifting as the field of reality that they designate, that is, the tactile, olfactory, thermic spaces, and so on, that have become the subjects of the representation. In fact, visual stimuli, strictly understood, are the only sensorial data that lend themselves to both measurable and unmeasurable interrelations in distances of depth. The other sensory stimuli are more related to a very close internal or external range of experiences that constitute the range of the “proxemics.”

These notions of distance will play a major and multiple role in the development of perspectives, since they derive from the position taken by the producer in relation to distinct and indistinct objects which form his representational field. This distance will be evaluated from four principal parameters:

(1) The distance instituted in the three dimensions by the type of ocular vision (foveal, macular, or peripheral) demanded by the characteristics of coloremes in the visual field;

(2) The angle of ocular vision adopted by the producer in relation to the represented field;

(3) The distance where the producer is situated in relation to the representational field that he constructs;

(4) The effect of distance inserted between the represented elements/ regions constructed in the field.

These effects of points of view and of distances find a syntagmatic expression in varied historical systems of perspectives. These latter present themselves as coded and normative superstructures, defining the use and position of diverse visual variables for the principal purpose of producing different levels of depth. They range from topological proximities to the extreme distances dealt by Euclidian or projective spaces.

5.3.Topological Depths and Illusory Depths

Any definition of space as a three-dimensional construct postulates that the perception of any visual field can be articulated in three planes, whatever the mechanisms of perception or the perspectives utilized: 1) the forefront plane, 2) the background plane, and 3) the intermediary planes. These notions will serve to describe the effects of distance in visual representation.

The forefront plane is the region of the visual field that seems the nearest, the closest to the perceiver. Inversely, the background plane is that region which seems to correspond to the furthest point from the perceiver in the visual field. An indeterminate number of intermediary planes are staggered between the forefront and the background plane, connected to these and to one another by various types of liaisons: superimposition, parallelism, linear oblique, vectorialities, contrasts, and so on. The forefront and background planes are thus conceived as the equivalents of a nearness and a remoteness, but always in a relative context. Thus, the distant one can be located in a relative proximity, as in certain close-up portraits, still-lifes, or certain interiors, when it refers to different hypotheses of objects, such as skins, clothes, walls, mirrors, and so on, or it may seem to recede into an indefinite or very remote distance, sometimes called infinity.

The different systems of perspectives will radically differentiate themselves as to the distance in depth which will be selected and treated and the specific interrelations established between the various groups of planes mentioned above. This articulation in depth is obtained through a great many devices using a mnemonic reference to natural perceptual processes, even if they introduce some symbolic conventions. For instance, the staggered perspective system divides the global visual field into various superimposed stripes, from bottom to top, assigning to those on top the function of signifying the furthest point in space, and often in time. The fundamental perceptual triad of the forefront, background and intermediary planes always reconstructs itself at the interior of each of these stripes, creating the rhythm of the visual field.

The distances between regions both in the two and in the three dimensions have also been called ‘intervals’. If 20th century artists, such as Hofmann and Albers, have emphasized this notion as an important dialectic element in the elaboration of continuity between the categories of planes, the tradition by contrast has habitually connected this very notion to that of Euclidean discontinuity or illusions of voids between objects and planes. Thus, according to Wölfflin (1950; 150), Leonardo da Vinci insisted on the introduction of distances between the objects he was representing: “Although things in front of me are all replaced in a continuous relation, I will not maintain any less my rules of ‘distances,’ of 20 and 20 aunes like the musician has established between tones, of which each holds nevertheless to all the others, a scale of several degrees going from one tone to the next (the intervals).”

5.3.1.Topological depths

As we have just mentioned, various distances in depth can be regrouped into two distinct categories: proxemic or topological depths and distant or illusory depths.

The proxemic depths, as they are called by E. T. Hall (1966), can be described as pertaining to the narrow distances surrounding one’s own body, in an intimate or personal distance. In the realm of perception, they refer to the virtual totality of organic spaces which seem to invade even the endodermic regions of the body (thermic, tactile, kinesthetics, and so on). The characteristics of the more polyvalent auditory and visual spaces undergo a complete metamorphosis at near or far distances. As a rule, the stronger the intensity or energetic aspect of sensorial percepts, the closer to oneself its source will appear. In the same way, perception of intensities of energies, endowed by internal dynamics and continuous volume, will be basic for the construction of depths in the representational field.

On the grammatical plane, one must emphasize that topological depth, or the intuition of the internal volume of a mass, is contained in the parameters of the Basic Plane in which the periphery, strongly energized by the formative elements, opens at the center—through a concave/convex movement—a potential state of oscillation around the hub of the internal axes and the reflux of the periphery. The Basic Plane can thus be represented as an undulatory space of depth, both narrow and shifting in character, determined at all its points by a potential/virtual energy. This depth in the visual field is fabricated by the perceptual mechanisms of centration and attention which multiply the field energies, producing chromatic adaptations, effects of figure-ground and so forth, according to the interactions between the energies of the Basic Plane and those added by the pictorial plane.

To a hypothetical lateral vision (sighting by the side), the Basic Plane thus presents itself as a space of extendable depth which cannot be precisely, mathematically measured, but immediately offers to perception a distance of proxemic depths (figures XIVb, XIVc and XIVd).

This undulation or this “push-pull” effect, produced by the interactions between percepts of diagonals and cruciform energies emanating from the mass, remains as a characteristic of the visual field in any other type of sighting: frontal, horizontal, oblique, etc. This is a fact of perception and not a metaphoric or codified symbolic connotation. Kandinsky already described this perceptual experience, insisting in particular on the role played there by what we will call in the following paragraphs the optical perspective: “The elements which go backwards or forewards expand the Basic Plane towards the spectator and away from the spectator, as an accordion does. It is primarily the color-elements which possess this force” (Kandinsky, 1975; 226).

Figure XlVa: Energetic Structure of Space in the Basic Plane

Figure XIVb: Proxemic Space of the Basic Plane Viewed from Side, Frontal, and Oblique Sightings

Indeed, interrelations established by perception between whatever visual variables (dimension, texture, vectoriality, etc.) will involve this movement of aggregates of coloremes foreward or backward, modified further by the influence of one or several hypotheses of integration or of continuity. Often, as Arnheim noted (1954; 226), to avoid the possibility of a perforation or an interruption in the spatial continuity, the perceiver will establish a maneuver in depth, which maintains the integrity of the whole.

Arnheim’s analysis of a woodcut by Arp, in Art and Visual Perception, is particularly enlightening in this regard. The work is constituted, according to a gestaltian regrouping of its whites and blacks, as three regions which envelop one another. At the periphery, an irregular form—curved, black, speckled with white marks, and oriented to the right—envelops another irregular form—a white curve oriented according to the disharmonic diagonal. This second form envelops in turn a third irregular form of the same black speckled texture as the peripheral form, but oriented on a more horizontal axis.

Arnheim does not, unfortunately, specify the dimension of the Basic Plane that he will use in the determination of the planes of varying depths that the elements described above can occupy. A two-dimensional organization cannot be proposed, as it would suppose an absence of the white colored material in the intermediate layer, since visually this white can only be situated in front of the surrounding white. Arnheim describes four different types of superimposition of elements in depth which require different perceptual modes of cutting-out energetic planes. The selection of the criteria will vary from tonality or an accrued privilege attributed to the closing of forms, and so on. Arnheim will point out that this type of fluctuating space—which we will qualify as being of a reversible order—has been explored by certain modern artists as they question the material solidity of the visible world.

He also adds that it would be wise to analyze in the same way the spatial structures of paintings, relief sculptures, free-standing sculptures, or buildings belonging to different stylistic periods.

One could discover characteristic differences in the number of levels of depth used as well as in their arrangement. The number of objects assigned to each level of depth would be examined as well as their type of distribution in the frontal plane. One would find there varied types of reliefs in depth: the global relief could be concave with objects at the center located at the greatest distance or, to the contrary, a convex relief offering a protrusion from the center. The effect of the factor of interruption versus that of coherence and continuity could be studied equally well in dimensions of depth as in the two dimensions (Arnheim, 1954; 227-228).

It is solely through this systematic analysis of depths, in effect, that spatial fields can be described in their proper structures as to the relative positions of their elements. Only in such a way can the very structure of the pictorial statement be determined, which is to say the particular spatial curve which interrelates the elements, following their interactions/ interventions in the global visual field.

The disclosure and naming of these various levels of topological depth will be accomplished by semiotical analysis in relation to coloremes and their insertion into the infrastructure of the Basic Plane through a more or less minute or extensive scale, according to particular needs. These means of measurement constitute the development of a system already carried out by Edward T. Hall, for the notation of all behaviors of a proxemic species (1972).

The proxemic depths, inherent in movements produced by percepts in the visual field, play a fundamental structural role in the syntactic development of any visual text, whether or not it offers a further iconic or mimetic function. It is not unusual, however, that the spatial energetic infrastructure that they construct should modify or contradict dialectically those visual causalities brought about by other regroupings of visual variables in the same work, which would be oriented towards illusory depths, thus complicating the syntactic structure of the whole. But if a visual work may present only proxemic depths or topological depths, the illusory depths themselves can only be developed on the basis of topological movements in depth and surface, without reducing their efficacy, which is irremediably wed to the very process of perception.

5.3.2.Illusory depths

Illusory depths result from movements suggested over larger distances in the visual field, not by mechanisms specific to visual perception itself or the structure of visual variables, but rather by specific organizations of these, associated with interpretations resulting from a code of specific cultural learning.

The representation of a large distance in the depth of a visual field does not stem from the energetic structure of the Basic Plane, nor from that of coloremes as vibratory energies. It is the product, rather, of an interpretation of a certain group of marks or signs dependent upon conventional codes (Eco, 1970; 12). These metaphorically constructed depths refer to the social, public, and remote distance where the producer situates himself in relation to an imaginary perceptual field. The greater the distance that a producer chooses to be from the object or the environment he calls forth, the less sensorial stimuli will be accessible to perception. In addition to this elimination of organic proxemic spaces, great distances nullify the experience of volumetry in the object. The potentiality of volumetric perception disappears indeed after five meters, and objects appear as cut-out silhouettes on a background. Visual space itself, the only one establishing a relation to remote objects, becomes more and more confused since it induces mainly peripheral vision. Paradoxically, the very remote space—indefinite or to infinity—which offers far less precision of stimuli to perception, will frequently borrow, in a semi-visual or informal organization, the organizational structures of proxemic space, experimented with here in a putting-in-distance. This is what is revealed by an analysis of skies and clouds, in which respect Damisch pointed out that it instituted a perspectivist duality in Renaissance painting (1972; 29).

The dualities or pluralities of perspectives in a given visual work are more often the rule than the exception, given the multiplicities of points of view from which the producer endeavors to form a synthesis in his visual discourse. They result also from the fact that the constituting elements which are interrelated to form an organic space (auditory, kinesthetic, buccal, and so on) present a different structure which must be modeled by different types of spatialization.

In this context, the determination of the distance taken by the producer in relation to the object of his representation is a syntactic modality that is as revealing as the uses of tenses in verbal language allowing for the identification of categories of signifiers. As in a novel or other work of fiction, the analysis will identify in the visual text, at different stages of the treatment granted to aggregates of coloremes, structural traits which the positioning of other elements in the distance often contradicts.

Thus, some characteristics of foveal vision, which are only realized at distances less than five meters, are sometimes attributed to regions theoretically situated according to other marks at further distances, such as the effects of proxemic textures to remote elements. Or, contiguous objects are defined by heterogeneous and contradictory perspectivist parameters. The production of a spatial synthetic unity in these complex visual fields seems to have been the aim of a certain number of ancient artists, still esteemed today, whereas producers of less scope or merit are often content with having recourse to a verbal metaphor or label, which unifies logically but not spatially the works in question.

Figure XIVc: Topological Depth (Continued Line) and Illusory Depths (Dotted Curves)

For the requirements of the analysis, a system of notation of medium and remote distance, evoked by an illusory depth, can be developed, on the basis of those categories of distance determined by Edward T. Hall (1966). It will serve to establish the spatial curve of a representation in its relation with topological and illusory depths. Figures XIVc and XlVd indicate models for an estimation of positions of objects in various distances in depth.

5.4.Distances in Height and in Width

The distance taken by the producer in relation to the visual field that he constructs determines not only variations in depth for the third dimension, but also for the two other dimensions of height and width. These angles of surface vision give rise to various sorts of expanses or of angles of opening of vision and of field, which can be of a topological or illusory type.

In height and laterality, the object of representation can be described as:

• transversal (of height from top to bottom of the Basic Plane);

• in close up (or microscopic);

• macroscopic (close vision from about one meter),

• at the interior of a room (three or four meters), or of several rooms (five or six meters);

• at the inside of a building (10 meters or more);

• at the exterior: urban (streets, buildings);

• at the exterior: landscape without sky;

• at the exterior: landscape with sky.

Figure XIVd: Topological Depth and Illusory Depths, Estimated in Meters, under a Representational Lateral Viewing

Any representation suggesting an object or an environment which would be measurable approximately mathematically and which would evoke a dimension in height/width larger than the dimension of the Basic Plane, would present an illusory bidimensionality. A nonmeasurable or indefinable expanse, which does not seem arbitrarily cut up inside another measurable visual field, is immediately structured by the topological and energetic limits of the Basic Plane.

Even in illusory height, as in the evocation of the interior of a house, the depth-distance can be treated as proxemic or distant. Panofsky commented on this short type of distance in the interior scenes of northern European art, in contrast to the remote distances in Italian art (1975; 169).

The distance in width instituted by the field of representation can, in the same manner, be said to be topological or illusory in the following modalities:

• Close up (an object occupying all of a field);

• Lateral transversal (from left to right);

• Macular: an angle of 15 degrees and about 10 meters;

• Peripheral: an angle of 60 to 100 degrees (70 meters);

• Very distant: an angle of 200 degrees (130 meters).

The narrower the angle of vision is in width, the more it suggests closeness and foveal vision. A similar effect is produced by a strict juxtaposition of objects in the field. Some systems of perspectives, namely the Byzantine frontal one, calls for an equally precise treatment for objects which are localized in the center and those on the far sides, thus contradicting the natural perception.

5.5.Positions of the Producer in Relation to the Field

Regions of the visual field, suggesting a plural series of perceivers, or a perceiver who occupies a multiplicity of positions at the same time, or better, a perceiver moving in front of it, are in fact making explicit the spatial positions taken by the producer of the representation. The subject/ producer of the visual discourse identifies his position in relation to a given visual field according to a set of syntactic elements that one could term ‘explicit performatives’ or indices of subjectivity (Recanati, 1981; 102). Thus, given that foveal vision is the only way one can see a precise detail on an angle of one or two degrees on this side of five meters, any determination of coloremes which affords such a precision indicates the distance of the producer from this object and eventually from the totality of the field he constructs. Similarly, variations of visual variables, in particular certain large textured planes or a formal confusion that implies a closer distance, can correspond to such a close proximity that it calls to mind more tactile and kinesthetic sensations than a representation of the organic visual space.

Thus, macular vision, which allows one to perceive colors but with a lesser degree of precision, still produces clear vision inside a vertical angle of three degrees and on a horizontal angle of 12 to 15 degrees and a medium distance ranging from five to ten meters. In between macular vision and peripheral vision, more sensitive to movements and tonalities than to colors, visual ‘scanning’ allows one to cover an angle of 60 degrees at the horizontal and at the vertical at a far distance.

The reader is advised to consult the list established by Edward T. Hall of the possible types of sensorial perception and experiences accessible, according to the different positions of objects in the distance.

Since the distance taken in relation to an object may express physical relations as well as psychological ones, it will not be unusual to find confirmation that the position of the producer can vary in relation to various objects that he places simultaneously in a given scene. We will call these ‘mixed viewpoints or sightings of the ocular apparatus’. Some examples are the foveal vision on the macular field as in the Primavera of Botticelli, the foveal vision on a peripheral field as in the same artist’s La Calomnie; macular vision inserted in a peripheral as in the Erato by Lippi, or foveal vision simulated at a peripheral distance, across macular fields, as in the L’Ecole d’Athenes of Raphael. If the three types of ocular vision function simultaneously within their respective potentialities, in any point of the natural field of perception, it may happen that the visual field of representation is divided into autonomous regions where the trajectories of the eye are realized differently and sometimes in a heterogeneous and contradictory manner in relation to one another.

In addition to these marks which are attached to isolated objects (mimetic or nonmimetic) by the visual process, which situate and define them, the producer can also indicate a particular position of his whole body in relation to some objects or the totality of the field of representation as such. We give the name “sighting” to this relation in the field, from above or below, sideways, and so on. This constitutes one of the most important characteristics for the differentiation of systems of perspective which have as their function to position the producer’s body in his space of representation and not only the direction aimed at by the eye.

Thus, in a frontal sighting, the producer will situate elements of representation parallel to the vertical plane of his own body, or, again, as Wölfflin commented, apropos the classical art of the Renaissance, parallel to the plane/surface of a work, that is, to the base which constitutes the Basic Plane.

In a sighting perpendicular to the vertical plane of the producer, one can dispose the elements along an illusory horizontal plane in the deployment of width, height, and depth, often offering linear points of convergence on one or several horizon-lines. In this horizontal sighting, certain portions of the field may be situated, nevertheless, beneath the producer’s gaze or his own body, and certain others above, producing local angular sightings.

Angular sightings can be of different types: 1) an angular sighting from the top to the bottom, as if the producer were positioned above the field of representation; 2) an angular sighting from the bottom to the top; 3) an angular sighting proceeding from the right side in gazing towards the left or from the left side towards the right, either in a horizontal or oblique path.

These angular sightings have always been present in visual representations of every epoch, used in a global or partial way, but they have taken on a new significance in the development of the baroque and mannerist periods and in various experiments with linear perspectives, such as anamorphosis. Robert Klein (1970; 171) underlined their dominant role: “But already in his epoch (Tintoretto), a new use of perspective, that which Rubens preferred, was ushered in with Veronese: the angle of taking sights plays the role there, for an expressive purpose, which today movie producers assign to it.”

It is on these fundamental data that Jan Peters (1981) founded the semiotics of the cinema, invoking the basic role played by perspective in pictorial art itself.

Unfortunately, pictorial semiotics has been slow to recognize the fact that cultural norms do not assure an absolute status to the artificial perspective of the Renaissance, whose restrictive and ideologically repressive character had for a long time been pointed out by artists as well as a number of art theorists.

But, following Panofsky’s research, it can be said that any system of perspective is restrictive, because it is based on a specific point of view, in relation not only to the visible but to the ensemble of sensorial experience. It institutes a specific context in the midst of which very particular statements are developed. The partial and limited character of each is a point that it possesses in common with any modal category in other types of human language. Nevertheless, it is necessary that certain types of sighting be opened to several sorts of perspectivist organizations which thereby conserve common points, in spite of the specific modes of interrelation that each commands. The semiotical analysis of systems of perspective will allow us to define, at the same time as their specificity, their particular positioning in the group of points of views of reality that human beings have succeeded in spatializing.

5.6.Systems of Perspectives

At the level of a syntax of visual language, one must envisage systems of perspective developed by the spontaneous or learned practice of this language, as essentially programmatic schemas of organization of constitutive elements of visual texts. These vary with respect to times and societies, as well as within the genetic development of the human being. We have already devoted a book to the study of how systematically and regularly the structures of children’s art evolve, relatively free from sociocultural conditionings during the child’s first emerging years (Saint-Martin, 1980). Various schemas of organization of visual elements have been recognized there for a long time, but except perhaps for the “folding back” perspective, they have not been interpreted as bona fide perspectivist systems, endowed by specific elements and modes of liaisons, with a view to fulfilling different linguistic functions.

Extensive research is still necessary in order to develop the area that Panofsky opened up in The Perspective as Symbolic Form, but did not pursue while engaging in his remarkable works on the iconology of the art of the past. The enterprise was perhaps not realizable without the development of a theory of the grammar of visual language, given the fact that any system of perspective requires a type of variations in visual variables or interrelations between groups of coloremes, that cannot be analyzed before being identified.

But even before any further development of visual semiotics, it is necessary to present a taxonomy of this vast body of research and to describe, in however minimal a way, these essential signposts in the visual syntactic field that are the various modalities of perspectivist systems. We will endeavor to clarify a terminology and concepts that have remained until now far too confused, and to construct the first levels of description of these programmatic regroupings so particular to elements of visual language. While offering these few parameters, we are deeply aware of the volume of research still required in this fledgling area of investigation.

Let us recall that modalities of perspectives are syntactical tools and do not constitute the object per se of representation in visual language. Being always implied in the enunciation, they signal the illocutionary aim of the producer as well as his orientation within certain semantic contexts (Searle, 1970; 65). Its recognition in the syntactic structure of the enunciated corresponds also to that which Austin has called “the uptake,” or “the comprehension on the part of the listener of the illocutionary force in which the speaker has invested his enunciation” (Recanati, 1981; 42). This force, furthermore, is one which cannot exceed its actual meaning since “it is the image of the force which is a part of the meaning of the enunciated, not the force itself, which must be inferred by the listener (spectator) on the basis of the speaker’s intentions” (Recanati, 1981; 37).

Perspectives therefore constitute unified systems of treatment and of regroupings of coloremes, working at the level of topological, gestaltian and chromatic laws and presenting themselves as more or less rigid grids orienting the dynamisms of the visual variables. Given that their principal function is the regulation of effects of distance in the three dimensions from a certain position taken by the producer, the systems of perspective will be regrouped according to how they tend to model spatial experiences which occur close to the producer, at an intermediate distance, or at a great distance from him. A special case is encountered in distances presented as indefinite/infinite, which escape any concrete experience because they are indefinable in relation to the developed visual context, as for instance with certain Medieval blue backgrounds, or Byzantine and Chinese golds, or even Mondrianesque whites. They will be paradoxically assimilated to proxemic spaces because of a particular function of their mass, which, as Panofsky pointed out (following Wölfflin’s pictorial analyses), resembles unification rather than remoteness. These organizations differ so much from the usual treatment of the effects of distance, that these depths have sometimes been qualified as ‘spiritual’ or ‘internal’ depths.

Categories of proxemic and remote systems are specific, but not exclusive. A visual text is certainly able to simultaneously present regions organized according to both of these hypotheses. They remain, however, distinctly perceptible and localizable, in one region or in another, through their own syntactic structure.

The syntactic operators which ground proxemic perspectives are juxtaposition, or a contiguous/distant neighboring produced most often by a system of parallels. The operators of perspectives at a distance are superposition and oblique vectoriality.

Moreover, secondary operations in the establishment of distances derive from variations in the treatment of visual variables, such as an enlarging or an abridging of the dimension, an accentuation of the textural effect, the treatment of tonalities, and so on. But these internal fluctuations of the spatial curve of the text must be integrated and interpreted in the general context of perspectivist systems which regulate the ensemble of regions.

The fundamental matrix level of the two systems of operators in the perspectivist syntax of visual language will allow us, moreover, to establish correspondences and similarities between styles of visual representation which have been seen in the past as foreign to each other.

5.6.1.The proxemic perspectives

We use the term ‘proxemic perspectives’ for those perspectives which organize the visual field in a close distance to the organism. These have been defined as “intimate” and “personal” regions by Edward T. Hall. These perspectives can aim at the spatialization of endo-epidermic (under the skin) experiences as well as to an illusory evocation of objects resembling those of the external world or belonging to an imaginary universe. But all are seen as being near the viewer’s own perceptual apparatus, that is, with the precision of linear variables, saturation of color, minimalization of the environment, and so on. These illusory allusions to things that are nearby in reality frequently involve, as noted earlier, conflicts with rules of perspective that regulate the seeing of things in the far distance.

The narrowest depths constructed by proxemic perspectives stem from an overt dialectic and use of energies belonging to the infrastructure of the Basic Plane in the organization of various regions. Thus there is a reiteration of the energetic reverberation of the formative parallel sides or corners; of the horizontal, vertical, and diagonal axes; of the checkerboard grid; of harmonic and disharmonic triangles; or of the cruciform juncture. Dynamically energized and virtually contained in the depth of the Basic Plane, these depths are essentially topological and not metrical.

The most fundamental among them are here described first: the optical perspective, which underlies all the other possible proxemic or illusory perspectives, and the parallel perspective, which offers an organizational matrix for a large number of modes of visual representation, in primitive, oriental and occidental art. In addition, they have played a major role in the classical art of the Renaissance and have known considerable development in the art of our own century.

5.6.1.1. THE OPTICAL PERSPECTIVE

This perspective designates the variations in the position in depth of simply juxtaposed plastic elements, resulting from their chromatic/tonal, textural, vectorial, or size interrelations, the most potent factor being chromatic disjunction as described in our remarks on the interactions of colors. The well-known effect of a figure which detaches itself from a ground because of a greater density of its visual variables is a product of the optical perspective, since it is a movement of distancing between parts of the field inseparable from the visual process.

Usually the latter is not reversible, as it has a tendency to immobilize perceptually the levels of ground and form, to provide the figure with a metaphorical “thingness,” which prevents further perceptual movements. Proper optical depth, which is more fluctuating and less ‘substantialized’, endows the visual field with more supple energetic phenomena which are open to transformations. Distances between two regions constituted by optical perspective are proxemic and topological, although an intense contrast between a black and white plane has been called “infinite,” as in the case of the artist Borduas’s working vocabulary (1978). As long as the “infinite” cannot be an object or a referent for a perception, it might better be called “indefinite,” or better yet, “indefinitely close or distant.”

5.6.1.2. THE PARALLEL PERSPECTIVE

Based on a topological order of succession in depth parallel to the Basic or pictorial plane, the parallel perspective strongly relates regions which may differ as far as some variables are concerned. It establishes them as neighbors in spite of the intervals which seem to keep them at a distance. These elements are seen as aligned in a series, at a more or less equal distance from one another, and while strictly parallel, they can be projected in frontal or oblique points of view, in a vertical or horizontal superposition. This continuity can be reinstated at another level of depth by other series of parallel planes, but always in a depth which suggests closeness.

The parallel perspective partially reconstructs a potentiality of the layered spatial structure from the Basic Plane. The effect of proximity produced by this perspective results from the repetitive frontal and foveal visual orientation of the producer toward his various objects, whatever their particular location in space happens to be.

In this perspective, the intervals between the more gestaltian regions no longer help to distinguish, differentiate, and reject these regions farther from others. On the contrary, they seem to be inherently endowed by vectorial energies which connect the elements and place them in a strong neighboring. By the dynamic effect of the topological relation of neighboring and by the parallel disposition, the intervals acquire a new role which does not stress the individuality of the elements, but allows them to be massed together in a strong homogeneity. A continuum is established between regions, not through metaphorical or logical considerations but as a result of a cohesion which is produced by the distribution of regions along the main axes of the Basic Plane.

The spatializing effect of this perspective is partly similar to Panofsky’s description of the kind of renewal which Gothic works of art presented in relation to those of antiquity: “Their tri-dimensionality and their substantiality is, on the contrary, that of an homogenous substance constituted from an aesthetic point of view through relations between un-dissociated elements, complying in their extension (infinitely weak), their form and their function (‘particles’) to a principle of uniformity” (1975; 111). But it is not necessary for elements to be isolated in order to be put in form by the parallel perspective.

The parallel perspective can be achieved by the partial or total superpositions of elements vertically, horizontally, and diagonally. It serves as the foundation for the development of symmetries and asymmetries around the central axis, as long as the components retain a parallelism with the formative energies of the Basic Plane.

The effect of proximity produced by the parallel perspective derives in large part from the fact that the producer as a perceiver adopts a similar position and a sighting in relation to variously located elements, as if he/she displaced himself/herself in order to grasp each of them in a frontal way. This abandonment of marks attributed usually to lateral objects can only serve to reinforce the proxemic effect of frontal perception.

Parallel perspectives have served as a matrix for a large number of proxemic or intermediate representations of distances: in children’s art, in primitive societies, Egyptian, Greek, Byzantine, Chinese, medieval and Renaissance artworks, as well as in the myriad proxemic spaces of 20th century abstract art.

5.6.1.3. THE ARABESQUE PERSPECTIVE

This perspective derives from an application of the optical perspective to linear, parallel, or crossing pictorial marks, juxtaposed or superimposed, which alternately uplift or push back the topological mass of the Basic Plane from the front toward the back. It is an immediate, more or less reversible product of the figure on ground construct. Capable of infinite developments, diversifications, and ramifications, this perspective has been used in all kinds of formats and contexts, as documented by E. H. Gombrich in The Sense of Order (1979). The choice of symmetric and vectorialist elements may be considered as ordered topological representations, which may lend themselves to psycho-sociological interpretations, as attested to by Claude Lévi-Strauss’s analysis of the corporal art of Brazilian Caduveo tribes (1973; 203-258).

While excluded from a representational status by the hegemony of narrative structures since the Renaissance, this topological perspective was widely used in primitive, Oriental, Persian, Egyptian, medieval pictorial, sculptural and architectural productions, as well as in most of the so-called minor decorative arts. Most of feminine artistic productions in the past belonged to this form of representation that Riegl has described as ‘ornamental’. This perspective has since made a comeback, but without being duly recognized as such, in the works of Jackson Pollock in the 1940s and the subsequent developments of Op Art, “patterning” art, and so on.

5.6.1.4. THE FOCAL PERSPECTIVE

One can define as proxemic the focal perspectives which establish in the representation an object across the breadth of the pictorial plane, occupying almost its entirety, save for a narrow band at the periphery, and constituting the object as a central and mostly closed form. A very large number of portraits have been so structured, advancing the model forward in a personal distance from the perceiver/producer. In many cases, garments, when seen very close up, with an abundance of detail in the fabrics and textures, point to tactile and kinesthetic sensorial percepts. A dualism may be produced by a slight recession or diminution of the size of the head, thus inducing more visual percepts. This perspective of a closed, more massive central region contrasted with a more opened, linear environment, served as a crux for Joseph Albers’s late production. The representation of the nude, favoring the whole of the body, is subjected to another sort of perspective; since it has to be positioned at a greater distance to be seen in its entirety, the central figure has to enter into stronger interrelations with a more distant environment.

5.6.1.5. THE REVERSIBLE PERSPECTIVE

The reversible perspective is an optical perspective which regularizes an alternation backward and forward of the elements that it links. Thus, by a simple continuation of the gaze, a region which had been seen in front, as a figure, slides toward the rear, and the region which was situated at the rear advances as a new figure toward the front. At times this reversible space lends itself to the gestaltian fabrication of different mimetic images in what was at one moment given as a form and what seemed to be the ground. This perspective is, however, used more in the 20th century in a more global trajectory which aims to destroy the fixity produced by positionings in depth by traditional linear perspective.

5.6.1.6. THE UNISTIC PERSPECTIVE

The “Unistic Perspective,” elaborated upon by W. Strzeminski (1977), has the objective of producing a “homogeneous mass of forms,” through the rigorous juxtaposition of internal elements within a strict definition of the format of the Basic Plane: “Thus the dimensions of the work become the most important element, and not a secondary element, existing in some way outside of our consciousness, as was the case in the Baroque; they are fundamental and are dictated by the construction and its character” (1977; 78).

Most contrasts of color and tonality, as well as contrasts of forms, dimensions, texture, are banished, along with the central form of construction. This regular uncentered construction is based upon “a line linking all colors of equal saturation,” principally through their luminosity. In avoiding separations caused by contrasts, the unistic perspective aims to produce an equally energized mass at all its points, by way of “a concordance of all elements of the work with its primary data” (Strzeminski, 1977; 78), a concordance which will be elaborated upon by calculations and numeric proportions.

Although it is produced through different semiotic means, the unistic perspective is related to the “all-over” perspective seeking to extend and equalize the pictorial energy across the totality of the canvas, so as to create an energetic plenum or rigorous continuum. The same organization prevails in some periods of children’s art where large sections of the visual field are filled up by regular or similar types of visual variables or coloremes often interpreted as, say, snow, birds, clouds, or flowers.

5.6.1.7. THE TACHIST PERSPECTIVE

Whereas the syntactic mechanisms of optical perspective based on juxtaposition apply to all visual texts, figurative or nonfigurative, geometric or informal, the term ‘tachist’ is reserved for the application of the optical perspective to ensembles of informal regions with closed or diffused frontiers, stressing particularly textures, tonalities, and vectorialities. This perspective appears mixed when it permits the operation of superimposition in addition to juxtaposition, more capable of evoking illusory depths. Even if it uses the disjunction of figure/ground or of multi-oriented levels of depth, this perspective produces masses sharing elastic topological internal volumes occupying indefinite distances in depth. It then offers marks of textures, better apprehended in proxemic distances.

5.6.1.8. THE CHECKERBOARD PERSPECTIVE

The checkerboard perspective is constructed upon the internal or, as it has been called, the deductive reiteration of the formative straight lines and corners of the Basic Plane, forming a focal or nonfocal grid. These regular and orthogonal bidimensional coordinates can be actualized over all of the pictorial plane, but some may remain virtual. They regulate the localization of elements in staggered levels, while maintaining their proximate or ‘indefinite’ distance. The position in depth of the segments is regularized by the optical perspective, as well as the vectorial effects of contiguous series.

This very strong matrix which corresponds to the bidimensional surface of the Euclidean grid forms the infrastructure of the principal modes of representations used in children’s art before the adoption of the oblique deep-setting of an horizon line and vanishing points.

It generates potent symmetries/asymmetries, various lateral parallelisms, or juxtaposition in height, regular orders of succession, dynamized by the virtualities of the diagonals. Given a privileged role in the work of Mondrian, this perspective has been subsumed under the rubric of “modernist grid” (Krauss, 1986) as one of the most important substructures evolved in contemporary art.

5.6.1.9. THE MICROSCOPIC PERSPECTIVE

This notion evokes a variety of visual representations obtained by the optic use of magnifying glasses or mixed lenses, producing an enlargement and bringing near of the components of matter which are regrouped in indefinite topological spaces.

Chromaticisms are illusory there, only added in with a view to a recognition of distinctive aggregates. Allowing for a spatial visualization of internal organizations of ultimate and minute constituents of matter, these perspectives do not constitute new repertories of visible matter, but are the products of specific points of view enabling the analysis of internal volumes. They present similarities with the perspective of arabesque.

5.6.2.The intermediate or middle distances perspectives

5.6.2.1. THE SPHERIC PERSPECTIVE

In connection with Greek art, Panofsky (1975; 55) described a correspondence between certain structures of representation and an intuition of “real” space as being finite, closed, and spheric. From empirical experience, still accessible to the average man, the Greeks identified space with the “image” of the natural curve of the world around the perceiver. This seemed to be corroborated by the fact that in perception, straight lines are seen as being, at a distance, curved, and curved lines as straight, the right angle at a distance as roundish, and so on. In this perspective, distance is not signified by any variation in foreshortenings, but by the result of a different aperture in the angle of vision.

Furthermore, the modes of regrouping elements in this perspective are aggregative in the sense that these elements remain autonomous from one another, independent in their relative proportions, freed from the spectator’s point of view or the particular evocation of a remoteness. Neither a vanishing point nor a horizon line was instituted although, at times, various earth lines were added. This perspective is structured, additionally, inside a parallel succession of focalized, isolated elements, devoid of any environment which accentuates an effect of nearness, in spite of the predilection for figures to be seen in full, that is, at an intermediary distance from the viewer.

5.6.2.2. THE AXIAL PERSPECTIVE

Panofsky has also identified and described an axial or “fishbone” perspective which was used in late Greek art, in Roman paintings, and throughout the course of the Middle Ages. This structure simplifies the previous parallel perspective in dividing the field in two through a virtual central axis upon which converge at regular or graduated intervals a series of oblique vectors, originating from the front or from the background. For a long time, this axial perspective applied only to circumscribed regions of the field and not to others. When the whole field is submitted to this perspective of organization, the way is open to convergent perspectives, not on the central axis but on one or several points on the line of horizon. This perspective, however, was never global, the elements maintaining therein an autonomy of aggregates and the effects of distance of peripheral elements being still submitted to the parallel perspective.

5.6.2.3. THE FRONTAL PERSPECTIVE

Derived from the parallel perspective, it proposes one main vertical and continuous plane as mostly parallel to the surface plane, or to the inferior side of the painting, as observed in Byzantine art. If the recession of parallel planes toward the background establishes a more remote depth than that which we classify as proxemic, the force of cohesion and regrouping of these elements in parallel establishes, above all, a strong interrelation which emphasizes their neighboring and indefinite positioning. Other uses of frontal perspectives are also more or less proxemic, such as presentations of objects reflected in water in a strict verticality which eliminates all the marks of distant spaces. On the other hand, Malevich’s suprematism and Mondrian’s neoplasticism developed frontal perspectives, often monumental, as can also be seen in the work of Barnett Newman, Clifford Still, or the more recent works of the Quebec Plasticiens and the Minimalists. This perspective is widely used in children’s art, Byzantine and Egyptian art, in Greek reliefs, and in the art of the Canadian northwest coast Indians.

5.6.2.4. THE FOLDING-BACK PERSPECTIVE

Panofsky called this organization “perspective by echelon.” Frequently used in Egyptian, Persian and medieval works, it is also one of the most extraordinary facets in the development of children’s art. ‘Invented’ by all children at around the age of five years, it will be used more extensively in following years. It involves a high and frontal point of view where some elements, oriented differently in the same spatial field, see some of their contours elevated in a perpendicular plane in relation to the projection plane, while others are folded back on the ground. It places the elements within a strong parallel continuity and symmetrical relationships, in refusing any allusion to a void in the intervals. While the emphasis is on the energies of the ‘corners’, as Panofsky observed (1975; 83-85), this enveloping structure, affirming the external limits of the field, generates a strong intensity in the central regions. This is the result of the vivid vectorial contrasts created by its relations of angularity and perpendicularity.

Whereas Dubuffet borrowed this perspective from children’s art within a definite proxemic representation, Mondrian developed, in an indeterminate distance, the structural dynamism of potential folding-backs of asymmetrical and orthogonal planes.

5.6.2.5. THE CAVALIER PERSPECTIVE

Often used in the pictorial organization of the still-life and particularly developed in the work of Cezanne and the cubists since the beginning of this century, this perspective presents a relatively close view of the object, seen from above in an angular vision. It often creates conflicts with the marks used for distant surrounding objects; it emphasizes the contiguity of elements, of precarious pilings, of slanted surfaces, and so on. It produces a fully dense space where regions of passages are as dynamic and signifying as the closed clusters forming the ‘iconic’ objects. Instead of a frontal view, it is here a plunging and oblique view which subjects volumes to a pressure which freezes them in a sort of equivalent distance, in spite of their “objective” different positionings.

5.6.2.6. THE PERSPECTIVES OF CUBISM: ANALYTICAL AND SYNTHETIC

The analytical cubist perspective may be the first one to be recognized in art history as aiming at the construction of a narrow distance in depth, or in Robert Rosenblum’s words: “an extreme shallowness of the space” (1976; 32). Although its depth distance is clearly limited by a vertical or dark background, analytical cubism has maintained the method of superimposition, oblique vectorialities, and the contrasts of tonalities, common to the production of distant perspectives. But proximity is accentuated by the piling of variously oriented vectorial elements which seemingly reveal the internal mechanism of gestaltian forces which constitute the volumes. In cubist analytical perspective, the representation is focalized, constructed as in a low-relief and enveloped by a peripheral oval layer, often dark and diffuse, which neutralizes the Basic Plane’s peripheral energies and reinforces the focal affirmation.

In some works constructed in a topological distance, contours dissolve themselves in vibrating textures and optical perspectives; reversible effects are at work, pushing into the foreground that which was perceived as the background. As R. Rosenblum observed: “In the new world of Cubism, no fact of vision remained absolute. A dense, opaque shape could suddenly become a weightless transparency; a sharp, firm outline could abruptly dissolve into a vibrant texture; a plane that defined the remoteness of the background could be perceived simultaneously in the immediate foreground.” (1976; 14)

The “synthetic cubist perspective” is radically different from the analytic cubist perspective. Except for linear allusions to volumes and mimetic objects, this synthetic perspective deals mainly with interactions within the topological parameters of the Basic Plane. It strongly juxtaposes closed and open chromatic planes, angles, straight lines and curved vectorialities, contrasting textures in a series of parallel planes, frontal and susceptible to the effects of symmetry and folding-back.

5.6.2.7. THE PROJECTIVE PERSPECTIVES

This expression is largely polysemic when used outside a strictly mathematical context. It may refer, as Panofsky said to the decisive step when the occident saw the limits of Renaissance perspective and began to transform it. It gave birth:

following the researches of Desargue . . . to a general projective geometry, and—owing to replacement, operating for the first time, of the unilateral ‘visual cone’ of Euclid by the multilateral ‘geometrical cluster of rays—achieving a totally abstraction of the direction of the gaze and opening thus uniformly all directions of space. (1975; 174)

Instead of focussing on already existing, stable properties, this geometry studies relations which permit the production of forms, mainly from a point of view postulated at an “infinite” distance. Developed by Poncelet, Felix Kline, and others, and having become one of the important non-Euclidean geometries, this new conception of space was disseminated in Europe at the beginning of the century by the theosophist and scientist, Rudolf Steiner, who was also the first to offer an English translation of Goethe’s Theory of Colors (Whicher, 1971). Adopted by Russian suprematists and constructivists, it influenced Mondrian’s and Kandinsky’s spatial intuitions. It received considerable elaboration in El Lissitsky’s works. In a space defined as a homogeneous continuum, and from various points located at a point in the infinite in all directions, an ensemble of elements coexist, produced by heterogeneous points of view or distances. These forms or volumes were seen from below, from the side, and from above, according to various orders of juxtapositions, successions and superimpositions regulated by multiple and ‘discontinuous’ positions adopted by the producer.

No rationalization of this mainly visual type of arrangement can be offered through the traditional mechanisms of the production of illusory far distances. Dimensions, for instance, do not obey laws of foreshortening, and contradictory viewpoints are juxtaposed in the same spatial field.

On the other hand, Jean Piaget determined within the evolution of children’s modes of representations a transitory period, called ‘projective’, interposed between topological and Euclidean constructs. This stage is characterized by the child’s intuition of the notion of his own personal point of view in the construct of the ‘straight line’, a prerequisite for the setting up of the ‘spatial box’ of Euclidean space. While still pre-Euclidean, this projective perspective differs entirely from the one described above. It does not incorporate the mathematical notion of the infinite. And in the latter perspective, in spite of some contradiction among viewpoints, strong textural effects point to a still tactile proximity.

5.6.2.8. THE BAROQUE PERSPECTIVE

This angular or “baroque” perspective, described with beautiful lucidity by Wölfflin (1961), deploys in a proximate or intermediary distance an entanglement of planes with accentuated chiaroscuros, in a harmonic or discordant vectoriality. Even when it signals a distanced lighted region in one of the upper corners of the work, this perspective is more involved in an accumulation of elements in the foreground, strengthening their dimensions, color densities, tonal contrasts, and sudden foreshortenings. It produces a “kinesthetic” excess in the proxemic levels in relation to the treatment of elements in the medium or background levels.

5.6.2.9. THE ISOMETRIC PERSPECTIVE

One can situate within the intermediary distances the isometric perspective which may reveal the internal volumes of the polygons it represents, while maintaining the parallel vectorialities and thus excluding the impact of the environment and the effects of perceptual vision in a far distance. It is used particularly in architecture and industrial design, and is sometimes borrowed for particular effects in pictorial works.

5.6.3.The far distance perspectives

5.6.3.1. THE LINEAR OR CENTRAL PERSPECTIVE

Under various labels such as legitimate, artificial, convergent, central, or linear, this syntactical organization of the visual field has been the subject of many analyses. It has also been erroneously identified as the sole perspective true to reality and as the unique pictorial space. As summed up by J. White (1972), it is characterized by an infrastructure composed of a group of lines, regularly distributed on the inferior side of the painting, converging on a vanishing point located on a horizontal line whose height may vary, called the ‘horizon line’. This frame serves to calculate the proportional foreshortenings or gradual decrease of the dimension of the elements in distances approaching the vanishing point. It defines the represented objects as endowed with a noncompressible external volume requiring a contiguous ‘empty’ environment in order to achieve and maintain ‘roundness’ and constant contours. In the case of landscape, this grid is applied only to the earth’s plane; the portion treating the sky and clouds is submitted to heterogeneous forms of perspectives. It imposes a rigid selection and hierarchy of objects to be represented since, owing to the superimposition, only relatively small objects can be positioned on the first plane. All objects in reality of a large dimension (cities, mountains, etc.) are pushed toward the background, to be then rendered in quite reduced dimensions.

This perspective, based on a planar conception of the Basic Plane, tends to establish the illusion of very far distances, which would coincide with the perceptive experience of natural perspectives. Its longtime acceptance as the ‘true’ and unique form of representation of space is linked to the postulate that perception of far distances is the more common or valuable sensorial experience of man, and should be established as the paradigm for all intuition of space. Though it may present objects in a foreground, its organizational structures prevent the possibilities of representing not only proxemic visual experiences, but also other forms of sensorial experiences that unfold strictly in the proxemic distances. Its artificiality in representing perceptive vision as a whole has led artists, as early as the Italian artists of the 15th century, to correct, by various means, the specific distortions it produced with regard to binocular and peripheral vision. Like the photographic camera, which was constructed in order to produce an image in a similar perspective, it is not able to appropriately accommodate various focuses and peripheral vision. It is seldom used without the accompaniment of the atmospheric perspective with a view to realizing a better illusion of great distance.

5.6.3.2. THE INVERTED PERSPECTIVE

Developed before the central or linear perspective, this perspective offers a reverse organization where lines converging toward a unique point are not directed toward an illusory depth in the background of the representation, but to a point in front of the projection plane, often below the inferior limit of the Basic Plane.

This point of convergence may be located in the region where the producer/perceiver of the work would stand or upon any arbitrary point on the side or the front of the picture plane, in the same way distance points were distributed in later constructs of the linear perspective. This perspective has also been called the ‘oblique perspective’, notably by Julia Kristeva (1972) in her remarkable analysis of the organizational structure of Giotto’s works.

5.6.3.3. THE OBLIQUE PERSPECTIVE

We apply the term ‘oblique perspective’ to those implying a particularly distinct oblique sighting from the producer himself which, while unfolding horizontally in a field defined by linear perspective, opens to a very large extent its angle of vision toward upward illusory heights in order to create the illusion of highest buildings or mountainous reliefs, for example. These regions belonging to the most extreme heights are often described as seen frontally in a degree of precision and neatness of detail which are inappropriate for their remoteness or inapplicable to peripheral vision, the only instrumentation that can in fact apprehend them.

This oblique perspective is differentiated from the perspective in height, which amplifies the vertical angle of sighting in the same way by a continuity maintained between high and low regions.

5.6.3.4. THE ATMOSPHERIC PERSPECTIVE

Although the organ of sight is the only one of our senses that can give us data about the environment situated at a great distance from us, this information is extremely reduced compared to the data offered by vision at a close or average distance, since it stems only from peripheral vision.

The perspective known as atmospheric ‘mimics’ the transformations which objects perceived in external reality undergo, when situated at great distances. Visual foreshortening, as well as atmospheric layers which are interposed between object and spectator, reduce the distinctiveness of their visual variables, rendering them more and more intractable to perception. This perspective therefore introduces the dissolution of the contours and chromaticity of objects and the reduction of intervals between them, stressing their dark character and formal masses. It provides distant representations with marks not unsimilar to those used to represent objects in a close proximity, or objects referring to nonvisual organic spaces. This perspective is also frequently called the ‘aerial’ perspective, because it is linked with the air or atmosphere, but the expression may be misunderstood to refer to a bird’s eye or perspective taken from a high point in the sky. It provides distant representations with the marks of peripheral vision, reducing chromatic properties and precision of contours and accentuating both blurred effects and dark tonalities.

5.6.3.5. THE BIRD’S EYE PERSPECTIVE

As its name implies, this perspective proposes the point of view of the producer being positioned at a very great distance in height from the surface of the earth. Though it may have acquired a realistic connotation in the aeronautical era, it was first developed millenia ago. It frequently produces an effect of flattening of the earth’s curvature under a direct or oblique vision. At other times, it provides for simulations of reliefs or concave-convex undulations of the pictorial plane which assimilate its syntax with that of low reliefs.

5.6.3.6. THE STAGGERED PERSPECTIVE

This perspective, frequently witnessed in early forms of representations in western and oriental cultures, suggests very large distances in depth by the simple superimposition of more or less horizontal bands or layers from bottom to top of the Basic Plane. Metaphorically it produces an illusory path from the front toward the background, endowed with correlative spatial or temporal connotations. When confined to geographical connotations linked to various layerings, it may preserve a strong unification of the visual field.

5.6.3.7. THE PERSPECTIVE IN HEIGHT

In contrast to the bird’s eye perspective, this perspective positions the producer not completely above the earth, but at the height of highly elevated terrestrial elements as in the case of very high mountains. It was widely used in Chinese art, where, however, it was rarely used alone, but most often juxtaposed with an ‘eye-level’ perspective, as many commentators have demonstrated (Cahill, 1977). The perspective in height situates the producer at very elevated levels from which some linear perspective is either spaced out or not, possessing its own horizon line and various curved trajectories at fixed points.

However, if the linear and atmospheric perspectives are easily integrated in the occidental’s point of view, the two perspectives used in oriental art appear to stem from a duality in the position of the producer in relation to his field of representation. First, in a medium height looking down upon a vast region and then, secondly, in the upper part of the visual field, in a horizontal confrontation with the most elevated objects possible. These visual discordances, often attenuated by a uniform monochromy, may result from an aleatory definition of the limits of the Basic Planes of representations, horizontally or vertically unfolding in the scrolls of painting, in accordance with the aesthetics of asymmetry that is the basis of much oriental art.

5.6.3.8. THE ANAMORPHIC PERSPECTIVE

In medium or distant depths, this perspective modifies in a gradual way the dimensions of one of the coordinates (height or width) of the Euclidean grid, without applying the correlation defined by the law of foreshortenings in the linear perspective. Destroying the strict proportionality of the grid, it allows for a reconstruction of an iconic resemblance from a particular point of view on the side of the visual work.