Gilles Deleuze's aesthetics suggest that the viewer's mental perception of objects is tied to a single, bending visual surface that is contingent on motion in time. In The Fold, the cultural critic sketches out an aesthetics of variable curvilinear shapes and forms in non-Euclidean geometric spaces. "Non-Euclidean" may be equated in layman's terms with dynamic, vectorial, transitional, or durational spaces that do not fit into the Cartesian triple-axis coordinate space. The visual surface in curving space is transpositional, meaning that it transcends point-positions in space. It reflects the unending movement of flat, asymptotic spheres and unreal, distorted hyperbolic planes.

The mind experiences event-perceptions that combine senses and affects, tenses and durations, and spaces and dimensions in a single surface, or field of vision. This phenomenon may be explained best by one of the skewed, hyperbolic geometries, such as Beltrami's theories. [1] The notion that geometries of curvilinear space may explain the idiosyncrasies and distortions of visual perception is everywhere present in early twentieth-century Cubist practices and Dutch graphic design explorations. [2] In many ways, the new geometries became the lingua franca of early twentieth-century modernism in its search for "neoplastic" and "constructivist" architectures. This is evidenced in anti-decorative (flat, abstract), asymmetrical, kinetic, and colorful explanations of spatial displacement. Non-Euclidean geometries had a strong influence on artists from Picasso and Malevich to Moholy-Nagy and Vantongerloo. [3]

New, hyperbolic geometries may also shed light on the abstractness of digital spaces that contradict the conventional spatial reality of material objects. [4] Today, as advances in technology introduce more complex challenges to "media literacy" and "visual grammars," it is necessary to reconsider Deleuze's alternative theories of the relational configurations of image, word, sound, and form. The argument presented in The Fold works against the grain of Cartesian algebra as the dominant contemporary metalanguage.

By adopting some aspects of Leibniz's pluralist ontology, Deleuze resists Cartesian clarity, the manifestations of optic science, and rationalist assumptions of transparency and realism in art. Instead, he constructs an alternative architecture of vision that affirms a radical diversity in point of view derived from infinite perceptions and a curvature in the molding of color, shape, surface and form.

Like the ideas of Leibniz and Whitehead, this aesthetics is premised on a perspectivism that accepts the possible existence of numerous profiles, styles, interpretations, and scenographies. Perspectivism encourages the diversity of ontological realities—constructed, plastic, and self-referential universes of the mind's inner space. As an important precept of the postmodern moment, perspectivism provides a viable explanation for a diversity of subjectivity and point of view in contemporary art. The writing of an "aesthetics of curvature" involves the construction of new pathways, connections and concepts concerning the expression of abstract, fluid curvature in sculpture, architecture, and design.

Curvature and the plastic forces of transformation

The Fold revives Leibniz's fascination with infinite and curvilinear forms in the creative transformation of matter. For Deleuze, as for Leibniz, the curving line or surface traverses all matter: In its abstraction, the infinity of the curve locates the ongoing process of the compression of the world under elastic or mechanical forces. Deleuze's notion of the body/object is contrary to the Cartesian notion of absolute fluidity of line (which involves transparency), and more fluid than the atomistic hypothesis of absolute hardness and finite bodies. The body/object is the partially liquid composite of organic form that is not comprised of separable minima, but of cohering, curving parts.

For example, Brian Massumi in Parables for the Virtual mentions the biogram, a lived, involuntary, topological superfigure that cannot be separated from its temporal dimensions. Biograms are mnemonically useful event-perceptions that combine senses and durations, but cannot be equated with determinate configurations, or intuited in triple-axis Cartesian space. Massumi compares them to radar dopplerings and the strange geometry of digital surfaces. Biograms occur in place, at a workstation, for example, but cannot be measured in Euclidean space. Massumi describes them as "qualitatively intensive movements" in a "synaesthetic space of variation" (187). He surmises that they may be distinguished modally from one another, by their variations, overcodings, or potential speeds on the curving surface of time. Biograms may reference Leibniz's idea of monads of relation, or patches of motion that reference our individual self-variations (see the passages below on Leibniz and perception).

Deleuze's sensuous view of the world derives from the curving shapes that Leibniz creates from differential geometry. Following Leibniz's vision, the entire universe continually undergoes curvilinear transfiguration, as it appears compressed by an active force that endows matter with a curvilinear or spinning movement (The Fold 7). With the tonal flow of semi-liquid matter, all matter forms and changes like the ripples, waves, and the surface crests of turbulent water. Deleuze describes how the coherent parts of fluid and elastic bodies form folds: They are continually divided to infinity in smaller and smaller pleats and compressions of time and space. In its extreme form, the growing turbulence of folding curvature ends in a "watery froth" and the erasure of recognizable contour (17). As Tom Conley, English translator of The Fold, points out, all forms of curvature tend to disappear in the eye's view, and therefore the interpretation of aesthetic turns of style may be as beguiling as the pursuit of folds of ethereal matter that waft and waver (xiii).

The "plastic forces" of artifice transform raw materials into "organic" matter, thus determining the curving shapes and twisting surfaces of art. These plastic forces are material, conceptual, and mechanical in their inception and practice: They construct the liquid architectures that are the basis of the plastic arts.

In its capacity for the reconfiguration of images within new spatial and temporal relationships, digital motion graphics construct liquid architectures in flexible, plastic digital surfaces. Images, forms, and type condense and morph in the stretched and shrunken strata of time. Visual-textual strategies in digital video (DV) and emerging, innovative e-poetries embody the capacity to sculpt time in the spatialized layers and fragments of visual collage. These strategies also introduce new transformations of framed images.

For example, Typorganism's experiments in communication design and interactive, kinetic typography are based on the notion of "type as lifeform," which lives in cyberspace and has algorithmic intelligence. The hyperbolic motion play between type and visual surface exemplifies the discordance and displacement available in digital spaces. Matted and layered video images in thickly-composited space may create new, hybrid space-time structures that are unique to the digital domain: They appear anti-Cartesian in nature. These orderings are constructed through the unconventional reconfiguration and dynamic rendering of new media objects.

In addition to this semi-liquid visual distortion, the use of agrammaticality can bring out the tensile dimension of language by stretching its limits beyond familiar forms and conventional functions. Visual imaging, compositing, and animation tools allow language concordances, discordances, word plays, permutations, and morphemic substitutions to be actualized in kinetic, digital space: Loss Glazier's (go)fish (1998), Komninos Zervos's Life, A Navigation (2002) in strange geometric space, and Brian Kim Stefans' "The Dreamlife of Letters" (2001) are good examples of some experimental visual-typographic work that are pushing these boundaries. In digital environments, within a state of temporal flux and intensity, recursion and deformation are processes that enact the folding and unfolding of language. [5]

The aesthetics of folding, hyperbolic surface are manifest in styles and iconographies of art and design that hide shapely figurations in pleated and billowed fabric, or in chiaroscuro effects that lead the eye to confuse different qualities of space and surface. [6] They draw on curvilinearity and its application in art from Caravaggio to Klee and beyond. Deleuze acknowledges attempts to create a new art through the elaboration of geometric form, abstraction, and the experimentation with curvature and skewed perceptions—the strange pearls of hyperbolic geometry. [7] He asks observers to speculate about objects without recourse to the three dimensions in conventional Cartesian terms and measurements.

Hyperbolic vision, perspectivism, and multiple points of view in art

Deleuze reconfigures classical reasoning by dividing divergences into as many worlds as possible, into continuous and interrelated brackets or enclosures. His ontology distinguishes in quality and degree between microperceptions as partial representations of the world and distinct, conscious apperceptions that comprise a larger "worldview." The Fold opens up the possibility of multiple perspectives on art that exist both in actual material worlds and in virtual, fluid and intangible domains.

Deleuze, following Leibniz, resists Cartesian clarity and mimesis in art. Rosalind Krauss, art historian, suggests that the Cartesian grid is emblematic of the empirical grounded unity of abstraction: It is imbued with a pure disinterestedness, a promise of autonomy, an absolute purposefulness, a lack of movement and stasis, and a capacity to bring forth the material ground of the pictorial object. The grid structure may hold an anti-referential quality exemplified in its lack of content. In The Originality of the Avant-Garde and Other Modernist Myths, Rosalind Krauss goes further to suggest that the stillness, symmetry and lack of center (and therefore of inflection) in the Cartesian grid are openly hostile to narrative forms: The Cartesian grid, both impervious to time and to event, will not permit the projection of language into the supreme domain of the visual (158).

In Techniques of the Observer, Jonathan Crary suggests that the post- impressionist break with Cartesian realism involved the adoption of a new model of vision, a massive reorganization of knowledge, and big changes in the productive, cognitive and desiring capacities of the subject. In a post-Copernican framework, the absolutely privileged point of view had vanished. Visibility became a contingent fact. Unable to anticipate the Copernican revolution in philosophy, Descartes attempts to schematize a structure of the mind that is congruent with the material world in a specular way. Rather than in Descartes, Crary's sense of modernism is also embodied in Leibniz, whose goal is to reconcile universal truths with the inescapable fact of a world with multiple perspectives, with the fragmented and decentered world of monadic viewpoints (50).

Subsequently, in the twentieth century, the dominant Western speculative, or scopic, tradition unfolded in the invention of the photographic camera, the camera obscura and its descendants. The camera was a metaphor for the most rational possibilities within the dynamic disorder of the world: The photographic effect became a pivotal component of the economy of value and exchange in modern times.

Paradoxically, the genesis of specular modernism does not occur through rupture or visual revolution; rather, a continuity of mimetic practices is a necessary condition for the affirmation of an avant-garde breakthrough. The object of vision is made more exact, more precise in the photographic image, fulfilling all Cartesian expectations. At the same time, the original referential context for the image is lost, whether we are willing to admit it or not.

By expanding the horizon of perception with the use of technical devices, rational empiricism replaces the human, experiential character of vision. We witness the creation of things whose identity is defined by the particular manner in which they become objects of rational cognition, in a world where reflections cease to exist, where objective reality undermines, by its mechanical veracity, the capacity of the imagination to define thought. [8] Rather than employ an optic science that aspires toward absolute clarity of perception, Deleuze shows us that neo-Baroque aesthetics accept the effects of light angled or folded through small openings or by intermediary mirrors. Such angled and reflected light results in some illumination and some obscurity, a mixture.

In chiaroscuro effects, the color "white" is progressively shaded giving way to obscurity, to heavy shadows and fairly strong and well-handled colors. Such lighting effects are created by inverting or skewing perspective, or by replacing the luminous for the eye, the opaque for the object, or shadow for the projection. In strong contrast to Descartes, Deleuze iterates a neo-Baroque aesthetics that derives from the progressive transmission of light in degrees, the relativity of clarity, movement and point of view, the effacement of contour, and the inseparability/almost "schizophrenic tension" between transparency and obscurity (The Fold 32).

The Cartesian map of darkness-clarity-confusion-distinction is reworked with new meaning and a new set of relations: Hyperbolic geometries provide the automatism that at once plunges into obscurity and determines the degree of transparency of a number of minute perceptions.

The Influence of Leibniz and skewed perceptions

Leibniz's ontology resists Descartes mind-body dualism, and the premise that mental, perceptual, and representational states are dependent on the support of bodily substance. Cartesian perception is impossible without the body, but Leibniz rejects any suggestion that perception depends on the body in the sense that the subject of perceptual experience must be a physical object. For Leibniz, perceptual experiences may occur as instances of thought.

Consequently, monadic selves may select perceptual states as mental representations as part of their "natural," everyday practices. Objects, obscured or otherwise, exist within internal perceptual states and "inner spaces." As Deleuze describes Leibniz's ontology, the reciprocal determination of differentials refers to tiny perceptions as representatives of the world in the finite self. Every self (monad) expresses the entire world within itself. The monadic self is considered a metaphysical point without windows outwards, existing in a condition of closure or envelopment: What is folded is only virtual and currently exists only in a mental envelope, and on an abstract visual surface.

Reading Leibniz, the world is included in each finite self obscurely or dimly in the form of infinitely minute elements, curving inflections, perceptions, or representations. These obscure, confused microperceptions eventually comprise the conscious, clear and distinct apperceptions held within the finite self.

To master the various ontological realities and infinitely artificial, plastic universes, the monadic self must know how to move from minute perceptions to conscious apperceptions, or from the level of the molecular to that of the molar. Deleuze writes that the task of perception entails "pulverizing the world," but then "spiritualizing its dust" (The Fold 87). As Massumi explains, each "micro" or molecular perception falls in a self-organizing stratum, or mini-subjectivity. Each molecular stratum has an autonomously relational nature with other strata in the mind; each is a "part-subject." Microperceptions occupy the rungs of interlocking strata before they move to the molar level, where they can be experienced as memories, thoughts, or sensations in the realm of apperception (Shock xxx).

Contra the Hegelian tradition, Deleuze, following Leibniz, turns back to the Stoics for a definition of the world itself as an event and as an incorporeal, virtual predicate of a subject. Hardt mentions, regarding Deleuze and the poststructuralists, that only anti-Hegelianism provides the negative point of support necessary for a post- Hegelian, or non-Hegelian project (x-xii). Consequently, the Stoic world must be included in every subject, in every monadic self, from which each one extracts her aspects, or point of view (The Fold 53).

As Massumi points out, we may perceive the virtual world as a form of "superlinear abstraction" that does not obey the laws of the "mediated middle," and denies the necessity of a Hegelian zone for the synthesis of events and terms. In his early work, Deleuze explicates the virtual as a provocation to thought, or as a chaos of chance that impinges on us the violence of an idea (Difference 94). In a creative moment of difference, or divergence, a virtual object is actualized from the realm of thought (itself a zone of indetermination and groundless chaos). It follows, then, that Deleuze understands virtuality as the liminal realm of emergence, and the superlinear, abstract realm of imminent potential.

Deleuze stresses Leibniz's strong denial of the Hegelian doctrine of the universal spirit. Absolutes and universal attributes do not exist, but organic, composite, and alternating living things are ubiquitous, like swarms of beings. There are numerous worldviews corresponding to numerous, irreducible monadic selves. Leibniz moves from inflections of the world to its inclusion in its subjects: Inflection is an ideal condition or a virtuality that currently exists only in the monad that envelops it, as it is related to the inflection of the plastic point-fold (The Fold 23). The subject is the expression of the world (actuality), because the world is what the subject expresses (virtuality).

Deleuze's geometry of point of view provides a viable explanation for an infinite diversity of perspectives and subjectivities in art based on the infinite inflection of curves. New geometries of the visual surface cast aside tactile notions, contact and figures in favor of the status of the object in the declension of its profiles, as parabolas and hyperbolas. Perspectivism is a variety of relativity. The world is an infinite series of curves or inflections, and the entire world, itself defined as a curve with a unique variable, is enclosed in each subject's point of view.

The geometry of point of view provides a viable explanation for an infinite diversity of subjectivities in contemporary art based on the inflection of curves, or scenographies. Deleuze reinvigorates Leibniz's pluralist ontology and methodology of series of variations and points of view that multiply articulate and determine each artistic form and example.

Perspectivism, then, from Deleuze's reading of Leibniz, as for Nietzsche and Whitehead, is clearly a pluralism and a particular type of relativity that implies distance and not discontinuity between subjectivities. It is a multiplicity that makes for inclusion. Deleuze identifies distance and continuity as qualities of perspective: Continuity is made up no less of distances between points of view than the length of an infinity of corresponding curves. Points of view are synonymous with points of inflection that are continuous, noncontiguous singularities in space, which constitute minute envelopes in accord with indivisible relations of distance. [9] Inner perceptions are separated from each other as distant enclosures within a single, continuous, curving, visual surface.

Deleuze further describes the perspectivism associated with Leibniz as the unfurling of divergent series in the same world, the creation and subjective production of novelty in the objective world, the "emancipation of dissonance," and the liberation of the "true quanta" of private subjectivity (The Fold 79-82). The multiplicity of interconnected forces admits no stable entities, but only dynamic quanta, and must therefore be understood in terms of multitudinous identities.

In Leibniz's metaphysics of monads, monadic selves are possibilities that are actualized in composite substances, perceived qualities, colors, material things, or other figures and extended phenomena. Reasoning monads are correlative to reflexive objects, similar to Whitehead's thought, where thinking prehensions relate to eternal objects. Ontological configurations, figures, things and qualities are permanent forms that are reflected and actualized in monadic selves, but even their composite substances are realized in flux and in a state of identity shift.

Paralleling Whitehead's ontology, monadic entities are fluvia, endlessly being altered, forever entering and leaving variable components in movement. Reflexive objects are weightless, because they are pure possibilities that are realized in permanent flux, and pure virtualities that are actualized in individual, thinking prehensions. Discord, irruption and irreconcilable dissonance are resolved in a sense of polytonality, unresolved accord, and continuous, but noncontiguous series of perceptions across a visual surface. The perpetual motion and transformation of the abstract, visual surface forever conditions both perceptions and thought.

The Influence of Whitehead and conceptual possibilities

Whitehead's ontology, as schematized in Process and Reality and related, supplemental writings, extends the center of perceptual experience beyond the self-organizing Kantian subject to the relational, pluralistic field of things in themselves. Avoiding the "transcendental idealism" of post-Kantian thinkers, Whitehead puts forth a framework that locates the object of experience within the objective conditions of the world, in a realist system of "objective constructivism."

Perceptual experience involves the presentation of autonomous, external objects or events as efficacious elements in subjective experience. Whitehead writes that the actual elements perceived by our senses are in themselves the elements of a "common world." The world of complex things is "transcended" by our thought, but the things experienced and the thinking subject enter into worldly relationships on equal terms (Process 88). In preserving the form of subjectivity in the general nature of things, Whitehead is able to preserve the structural features of self-construction as an ingredient in the nature of things, while avoiding the pitfalls of idealist and pan-psychist thought.

In the act of synthesis and self-construction, every event stands at the center of orientation for its objectively inherited environment. It functions as a self-organizing perspective and a valuative reflection of the objective relations it inherits (Whitehead 210). For Whitehead, events are synthetic, relational entities and conjunctive moments of antecedent, contemporary, and consequent relations between things in a structure of subjective, or "tensed" time. Events also stand as primary "elements" or "realities" to which other modes of being must be related: Whitehead suggests that both events and objects may move beyond the conditions of past and present in a process of contingent creation, toward a novel, indeterminate, open-ended future. Events become the material forms of reality that capture the distinction, the liminal qualities, between the possible (virtual) and the relationally situated (actual). Objects represent the conceptual possibilities drawn from the pool of potential realities.

The present, prehending event is therefore a novel expression of some qualities and properties inherited from past occurrances. Whitehead's perspectivism becomes a vehicle for Deleuze to avoid a static, monistic universe devoid of unrealized possibilities. It support Deleuze's notion that thought is wider, more encompassing, and more divergent than finite actuality in its capacity to create Leibnizian contingent futures and points of view. Thought takes place within the realm of perverse reflections.

Concluding thoughts

In a concise and direct manner, Deleuze remarks that the neo-Baroque in both form and thought represents the most forthright attempt to reconfigure classical reasoning by dividing divergences into as many worlds as possible, and then creating infinite, numerous borders, variable configurations, interactions, and captures between worlds. Multiple perspectives are not contained in isolated self-enclosures, but are held in innumerable sets of brackets and captures, and inflected in manifold twists of curvature and point of view across a mobile, visual surface.

By way of some final thoughts, Deleuze's reading of aesthetics attempts to make some connections between sensuous, multiple views of the world and abstract, fluid algorithms of thought that are grasped visually and aesthetically. The effects of the ideas deriving from hyperbolic and non-Euclidean geometries continues to have an impact on the contemporary arts and poetries, digital design, and aesthetic theories of perspective. In his depiction of multiple realities bracketed within monadic selves, of reflexive, weightless bodies in perpetual displacement and shift, Deleuze discloses a futurism containing an infinity of swarming parts and perceptions in quasi-liquid form and curvilinear motion. His futuristic ideas lend credence to the realization of alternate, perspectives on the contemporary arts, and between the blurred boundaries of the virtual and actual.

Notes:

1. Beltrami provided the formula for a true hyperbolic plane, infinite in all directions. Hyperbolic geometries create asymptotic geodesics that tend to tangency at infinity: Beltrami's projective model of the hyperbolic plane distorts angles as well as lengths; surfaces can be mapped onto planes in such a way that their geodesics, planetlike surfaces of constant negative curvature in ordinary space, were flattened out to infinity. See David Hilbert and Stephan Cohn-Vossen, Geometry and the Imagination (Providence: AMS Chelsea Publishing, 1991), 1-11. (back)

2. The signatures of the 1917 manifesto published in the Dutch journal De Stijl set forth a plan of collaboration to create new conceptions of art based on emerging theories of time and space. The De Stijl artists advocated the "neoplastic" aspect of art that follows the mathematical-artistic trend of a geometric space in other than three dimensions. See Georges Vantongerloo, Paintings, Sculptures, Reflections (New York: Wittenborn, Schultz, 1948), 38-39. (back)

3. Linda Henderson, The Fourth Dimension and non-Euclidean Geometry in Modern Art (Princeton: Princeton University Press, 1983), 339-340. (back)

4. See Marcos Novak, "Liquid Architectures in Cyberspace," in Michael Benedikt, ed., Cyberspace: First Steps (Cambridge, MA: MIT Press, 1991), 225-54, and N. Katherine Hayles, "The Condition of Virtuality," in Peter Lunenfeld, ed., The Digital Dialectic: Essays on New Media (Cambridge, MA, MIT Press, 1999), 58-95. (back)

5. See Brian Massumi, "Introduction: Like a Thought" in Brian Massumi, ed., A Shock to thought: Expression after Deleuze and Guattari (New York: Routledge, 2002), xxii-xxiii. (back)

6. In The Fold, the art of paper folding, a semi-fluid origami, becomes the model for both the plastic arts and the sciences of matter. Following Leibniz, Deleuze affirms that curvature affects all materials (metal, paper, fabrics, water, living tissue, the brain), because it determines and materializes form. Curving materials become "expressive matter" with different scales, speeds, and vectors of force. Since folding and the chiaroscuro effect are Baroque traits, pleating surfaces of color can be said to resemble the overlaying folds and depths (crevices) of fabric or paper. The neo-Baroque is an "operative function" or "trait" which endlessly produces curvy folds, then twisting, turning, and pushing them into infinity, fold over fold, one on the other (3, 34). (back)

7. The study of algebraic curves, equally useful for formalism and the plastic arts, was extended by abstract algebra and remains inseparable from geometric ideas. Deleuze discusses how Leibniz posits the idea of families of curves depending on differential parameters (The Fold 18-19). (back)

8. See David Levin, Modernity and the Hegemony of Vision (Berkeley: University of California Press, 1993), 73. (back)

9. Leibniz defines extension (extensio) as continuous repetition of the situs, position, or point of view: Extension is not an attribute of point of view, but an attribute of space (spatium) and the order of distances between points of view that permits repetition and continuity between related perspectives. (back)

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Citation Format:
Kafala, Ted. "Deleuze's Aesthetics: Curvature and Perspectivism." Enculturation 4.2 (Fall 2002): http://enculturation.net/4_2/kafala.html

Contact Information:
Ted Kafala, University of Cincinnati
Email: kafalat@email.uc.edu
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