EX NIHILO OR THE AESTHETIC PROBLEM OF NEGATIVE SPACE

      “...The art in it is the forever mute part you can talk about forever”.
Willem De Kooning

      Like a glowing worm, art has always subverted the palladium of culture from within, slowly digging a net of ‘negative spaces’, the holes that permeate the structure of the social edifice until it shrinks to another architectonic form. Hence, the history of art can be viewed as the history of human perceptual devolution – the gradual dismantling of cultural perception – in the search of the unknown, undefinable, the nothingness that resides within the multitude of form occupying the socio-cultural space.
      The first arrtis whose work survived until today drew a bull so realistically and out of pictorial context that it stood like a solitary sign of the animal. It hardly symbolized its signified subject for the minute detail suggested a rather indexical relationship of drawing to bull. Thus the srtistic creation was not an end in itself, it referred to something encapsulated in and extended beyond the shape. Something, the power of which would perhaps magically connect hunter to prey. The semantic ambivalence of such an ‘indexical’ art was determined by its relation to a mystic realm residing beyond the common sensorium.
      An ancient Egyptian statue of Akhenaten, for instance, did not merely represent Akhenaten. According to ancient Egyptian conception, it was Akhenaten just as much as Akhenaten was himself. Spatially multiplied in this manner, his personality was further elaborated in yet another, inner, multiplication. As in the case of the exemplary illustration (fig. 2), two inscriptions, one on the bracelet and one on the chest, bear the title of god Aten while the head is embellished with the traditional insignia of god Osiris. Respectively, the statue was not only the pharaoh but also the two gods. The sculpted form was the indexical host of the three identities equalized by the essential, for the ancient Egyptians, powers of kha and ba. Sustained by the existence of form, those powers were the actual subject of most of ancient Egyptian art in general, and of the presently discussed sculpture in particular. Through the artwork, they would ensure the life of Akhenaten-Aten-Osiris even after the physical death of the pharaoh.
      Although connected to form, kha and ba were transcendental powers. Undetectable, polyvalent and omnipresent they resided within and betond the work of art as its true ‘negatively’ visible subject. Belonging to the spatio-temporal dimensions of death and disappearance, their realm was necessarily hidden, inescapably identified with the sealed wombs of the tombs. Whether labeled funerary or religious, most of ancient Egyptian art was placed in the perceptually ‘negative’ space of the tombs’ interiors, its visual and tactile isolation suggesting that those works were not intended to communicate to the living. Their message was addressed to a mystical ‘beyond’ approachable only through the gates of death.
      Although a central concept in mytho-religious art, death was typically represented by a space that was metaphoric rather than indexical. The dark interior of the tombs, the winter season referring to Dionisus’ ever recurring death, the seclusion of the initiation trials – all these translated the concept of death into a conventionalized ‘negative’ imagery. Although rooted in the idea of provoking perceptual shock (and thus violating the personal conception of order), it had crystallized into an intellectual device that would increasingly spare the senses a direct perceptual experience.
      The idea of death as the hidden, esoteric vehicle of life was structurally inherent to the mytho-ritual fable of narrative transition from cosmos to chaos to cosmos. To pass to a higher order of existence, the mythological hero or the person to be initiated had to undergo a process of complete disintegration of his previous order of existence to the point of encountering primordial elements. The passage through one’s own death was represented by a symbolic action that would introduce the person to a symbolic space of darkness and isolation, such as a wood, a keg, a cave, etc. Thus the temporary blockage of the senses would only imitate a perceptual isolation and negation in a space that was like negative, hence essentially metaphoric and eventually, through its establishment as a conventional device for representation, symbolic.
      The formation of epistemological categories in ancient Greece led to the demarcation of art from religion in terms of social function. Although art preserved its genealogical link with myth, it lost its indexical aspect but reinforced the metaphoric one. An image would no longer be itself, it would represent something outside itself. A sculpture of Athens would not be the goddess but her visual representation in social space. Athens would be the subject matter of the work, the work – an abstraction of Athens, a more or less conventionalized image of her. It would be taken out of the sacred space and exposed for public viewing.
      The problem of ‘nothingness’ shifted from the space beyond form to the borderline distinguishing artistic form in terms of what was included in and what was excluded from it. This marked the emergence of the notion of beauty as the prime criterion for art. Beauty was defined by the optimal balance between the spaces of formal inclusion and exclusion, a balance that would solidify spatial elements and bring emptiness into rhythmic terms with object-iveness. This resulted in the ‘formation’ of the undefinable, hence its objectification as the enframed negative space, no longer perceptually ungraspable. It became an abstraction of itself, formally transplanted to the domain of ‘cosmos’.
      It was not until after the Renaissance that art started slowly moving away from the definite. Especially apparent in painting, this tendency was mainly visible in composition where empty and excluded (suggested) space was allowed to semantically and visually dominate the representation (fig.3). However, this was a slow pace movement. It would occur symptomatically rather than systematically and would be integrated as an aspect of academic principles.
      The second half of 19th century marked the threshold that would change European culture to the point where space, time and art would never be the same again. Nietzche wrote in The Birth of the Tragedy:
      “Is there pessimism of strenght? Some intellectual inclination towards the cruel, the frightful, the evil, the problematic in being, rising from prosperity, from overflowing health, from the abundance of being?… What does it mean for the Greeks who have lived in the best, strongest, most heroic time, the tragic myth?… And also: what led tragedy to its death, the socratism of moral, the dialectics, the lack of exigency and the jolly speculative mood of the theoretician – how?… And the whole scientificness isn’t it perhaps only a fear, an effort to escape the pessimism? An artful protection from truth?”
      There is nothing that can illustrate better the notion of negative space as used in the present essay but that paradox of ancient Greek culture and its subsequent extension into the cultural history of Europe. The understanding of that notion depends on its demarcation from the space that is negative, namely the space assigned with meaning by the formality that occupies or frames it. It is the space of three-dimensional reality whose aesthetic shrinkage in the development of modern art constitutes the interest of this part of the essay. The negative space exists in between or, by its exclusion, underneath the perceptible space. Residing in the tiny border that splits consecutive moments apart or in the ‘quantum’ silence between consecutive sounds, it is the space that is squeezed by the abundance of form to the size of an undetectable void. For, the threat it presents to the system of three-dimensional perceptual order has always required its social negation. As it was hitherto hinted and shall be explained further on, the negative of space is the space of time. Like in the myth of Chronos, it has been culturally ‘squeezed’, diminished, imprisoned (by its own children, not accidentally ruling the ancient Greek pantheon) so that the three-dimensional order can be established. The negative space is, above all, the spatial aspect of time as a category of another dimensional order. Minimized to unperceptibility, it is actually the pause that causes the irrevirsibility, the death of every consecutive moment in space, the chaos of the spatial segment’s temporal disintegration.
      The integration of the negative space within the parameters of formal representation was the ultimate hypocrisy of ancient Greeks. Institutionalizing the ‘a-form’ as a part of their formal system, they turned the tragedy of Being into the dialectics Neitzche talks about, thus pacifying the dynamics of counter-action into the dynamics of counter-reaction (or rather, the statics of it).
      After the emancipation of art, the principle of the ever-dying Dionis was preserved in the emergence of the tragedy as a genre, i.e. with the creation of the principle’s socio-cultural metaphor. And the metaphor, like the symbol, structurally belonged to the spatial domain of conventional three-dimensional reality, serving as translator to formally inconceivable notions and phenomena. Such devices were actually to strip the negative of its structurally subversive nature and to epidermally incorporate it in the three-dimensional domain. Henceforth, art would be under the spell of ancient Greek cosmos for centuries. And what was once a revolution in human worldview, a liberating attempt to set opposites in harmony, would naturally become a system of conceptual limitations.
      It was not before the shock of the technological revolution that certain Western thoreticians and artists alike started to persistently revise the dominating system of perceptual order. Around the time Nietzche was writing in Germany, in France a group of artists were abolishing Classical tradition in their search for new ways of formal representation. Their revolt attacked the established ‘logic’ of cultural perception by approaching the work of art as the projection of an inner vision of reality rather than a representation of a reality of objects.
      The effort of the Impressionists and the Post-Impressionists to liberate their perception and their art from cultural determination crystallized theoretically in Husserl’s phenomenological method. It opposed the visible space as optical result of the culturally constructed sensorium to the visionary space taking place within the individual, bearing the essence of the perceived object as a phenomenon. The object-ive world became a subjective category, its claim to reality was shttered.
      Henceforth the subject matter of art would rapidly shift from the object to the vision of its essential appearance (phenomenon) until art’s complete or partial emancipation from subject matter in some abstract and minimalist works. With the parallel tendency of increasing interest in the undetectable form that lies beyond the '‘ormal'’field of vision, art would gradually start to return , with a qualitatively new awareness, to its indexical format. Signifying its own imagery more than ever, gradually squeezing visible form and its space to exclusion, it would more and more consciously refer to a realm beyond the immediate perceptions, allowing for the negative of space to expand.
      Yet, this tendency had its retrograde version and art would still often trick itself into the trap of defining and framing the newly revitalized negative space, as Willem De Kooning shrewdly observed:
      “The ‘nothing’ part in painting until then – the part that was not painted – had a lot of descriptive labels attached to it… Anyhow that ‘nothing’ that was always recognized as a particular something – and as something particular – they generalized, with their bookkeeping minds, into circles and squares… That ‘something’ which was not measurable, they lost by trying to make it measurable.” (2)
      From the early abstractionists until today this translation of the ‘negative’ into certain forms has done little more than redefining the classical principles in modern terms. However, by the mid-20th century works like those of Pollock’s and De Kooning’s exhibited a considerable movement away from perceptual pre-conception and the related object-ive focus of vision.
      The nature of film as a three-dimensional medium – two-dimensional plane plus time as an aspect of space – allowed for a broader manipulation of negative space.
      A preoccupation of early experimental cinema with myth sprang from the necessity of the medium to identify its artistic roots as well as from the revolt of early 20th century art against the abundance of rational space-time. The reincarnation of the mythic narrative in experimental film brought back the metaphoric negative space.
      Although never particularly interested in the problem of negative space as such, Maya Deren consistently and systematically approached it as a part of the mythic spatio-temporal treatment:
      “The camera can create dance, movement and action which transcend geography and take place anywhere and everywhere; it can also… be the meditative mind turned inwards upon the idea of movement, and this idea, being an abstraction, takes place nowhere or, as it were, in the very center of space.”3
      Highly conscious of the film’s capacity to manipulate both space and time, Maya Deren presents her visionary space as an archetypal extension of the mythic. In Choreography for Camera a single action – a dance – starts at one place and continues through different spaces, in varying speeds of motion, to end at the starting point. Thus the action transcends space as a physical establishment, squeezing its relationship with time to the size of a movement. The distance between spatial moments (or moments in space) is emancipated from the moments of movement – time and space are no longer intermeasurable. The action takes place nowhere in particular, yet it is a particular nowhere (i.e. a set of somewheres) which only intellectually suggests the nowhere of the anywhere.
      This metaphoric approach to negative space as the axis of semantic gravitation for the existential problems early experimental film deals with, is directly related to the specifics of the mythic fable. The hero who undergoes his own disintegration, encountering the primordial chaos, reappears in Jean Cocteau’s Le Sang d’un Poete where he throws himself into the ‘nothing’ represented by a mirror of water. Likewise, Maya Deren’s heroine from Ritual in Transfigured Time drowns in the negative space of the sea represented by a negative film of the shot. (fig.4). The influence of psychoanalysis in this mythologemic search for the unconscious is exhibited in Sidney Peterson’s conception of the visual art work:
      “The necessary ambiguity of the specific image is the starting point… And the statement itself is at least as important as what is being stated. The quality, for example, of rectangularity in the maternal tomb is a primary consideration. Psychologically it constitutes a negation of the uterine principle. Aesthetically it derives its force from what has been called the geometric as opposed to the biological spirit. The definition and unification of the opposing spirits is one of the functions of a visual work.”4
      This approach to from as a dialectical entity enframes negative space back into the binary opposition of Classical balance, granting it an equal status as the ‘positive’, yet dislocating it, abstracting it from itself. The ‘necessary ambiguity’ is to be ‘defined’, hence to be deprived of its ambiguity, by the symbolic manipulation of form. On fig.5 the camera is focused on the empty space between itself and the background of a busy street as well as on the central figure that conducts the semantic message of the shot. The invisible plane of focus, is counter-balanced by the occupied plane of focus, thus bringing negative space into a complementary relationship with the object of the shot.
      During the same period surrealists like Rene Magritte and Salvador Dali were working on their oneiric vision with a keen consideration of realistic representation. Bringing the ambiguous to a formal steadiness they attempted to reclaim its place and reality. In his painting, Dali systematically ignored three-dimensional spatial laws (melting flesh, figures floating in the air, etc.) but the realism of his imagery still confirmed and appealed to three-dimensional perceptual order. In his co-production with Louis Bunuel Un Chien Andalous the absurd became an aspect of the three-dimensional world challenging the viewer’s intellectual conceptions rather than his perceptions.
      However, this stage in the development of experimental film prepared the grounds for more radical explorations. Of course, many of them simply redefined conventions in modernistic language but others went far in the direction towards formal subversion.
      The ultimate academism-in-modernism crystallized in the works of Norman McLaren. In his film Mosaic spatial compositions do not make the slightest deviation from the academic principles of organizing ‘negative’ and ‘positive’ imagery within the visible frame. The balance of abstract forms, the rhythmic treatment and synchronization with sound exhibit the approach called by De Kooning an attempt to make the immeasurable measurable. It can be compared to the abstract academism of Mondrian whose break with narrative representation was only in terms of representational imagery.
      While Harry Smith to a large extent confirms to the same principles, his personal style brings a twist of freedom from academism in his works. Not only does Smith’s No7 aesthetically approach Kandinsky, as Adam Sitney rightly compares (5), but the entire body of Early Abstractions shares the subtly unbalanced restless spirit of the Russian abstractionist. Both artists treat the image as an entity in transition within the chosen ‘piece’ of space. The irregular flow of eccentrically composed images and the off-screen orientation of the movement in Smith’s work correspond to the slightly off-frame compositions of Kandinsky. Subverting in this manner the status quo of the established formal relationships, those compositions allude to the excluded space which is actually the field of their gravitation. The striking similarity in their aesthetic visions is largely informed by the mystic aspirations of both artists. Thus, their imagery acquires a quality of gravitation split between the metaphor and the abstraction.
      The ‘necessary ambiguity of the specific image” is only an ambiguity of the symbolic message in Peterson’s cinematic vocabulary – the specific image being the linguistic symbol and the ambiguity being its semantic discontinuity (fig.5). The image acquires its inherent ambiguity when emancipated from its linguistic significance. Willem De Kooning’s women, for instance, exhibit a treatment of the ‘specific image’ through the ‘ambiguity’ of its transition. The ‘woman’ is simultaneously built up and destroyed, disintegrated by the strokes of color. Abiding in a space of formal entropy, the strokes catch the visual apparition of that fraction of a second where the spatial moment dies to recreate itself in the next one. Like in film, the eye doesn’t catch the negative space of the black strip that separates the frames. The realm of the black strip is somewhere beyond the picture, yet its absence creates the focus of the visible space.
      A long sequence of such apparitions constitutes the fabric of Circus Notes by Jonas Mekas. In its movement, the camera grasps the transition of the images as they pass in front of the eye like momentary apparitions, like spatio-temporal slices that emerge and sink back into the discontinuity of memorial perception even before the viewer has been able to pull his mental focus on the vision. The ambiguity of the images is the ambiguity of the phenomenon as it appears, not as it is seen. Abiding in the magnified spatial particles of its transition, the image never rests into the viewer’s field of depth long enough. It drags the eye to the ‘nowhere’ of its disappearance.
      The sensation of the momentary experience, free from cultural associations, is like the taste of ‘a fool’s happiness’ which yields ‘the deepest intuitions of the tragic sense of life. “ (Jonas Mekas (6)) Perhaps this is what meant ‘for the Greeks who lived in that best, strongest, most heroic time, the tragic myth.” And in that tragism, in the turbulent relation to the ‘nothing’ of the non-three-dimensional order of ‘things’, lies the essencial drive of art.
      “The new artist, by directing his ear inward, is beginning to catch bits of man’s true vision… In this sense, an old art is immoral – it keeps man’s spirit in bondage to Culture. The very destructiveness of the modern artist, his anarchy… is, therefore, a confirmation of life and freedom.” (Jonas Mekas (7))
      Stan Brakhage approaches the visible with a rigorous ‘destructiveness’ provoked by the necessity to ‘construct’ the visionary. As Pollock himself observes “the method… is the natural growth out of need” where “there is no accident, just as there is no beginning and end.” The works of Brakhage become cinematically endless in their meditative lack of external dramatism. The long, stained with superimpositions, shots of Faust turn the ambiguity of the images into the ambiguity of space itself. The smooth metamorphosis of the latter happens in rhythms of sound and continuous eruption of silence referring to a realm beyond the formal abundance on the screen. As in a painting by Pollock, the focus is both everywhere and nowhere. Negative space envelopes the picture yet is not in it, what the eye perceives as negative imagery is just another form of imagery not belonging to the ‘immeasurable’. Referring to no-thing outside itself, the work of art becomes the ultimate index.
      The recognition of time as an aspect of space allowed for the interpretation of the film medium in the context of Einsteinian physics and prepared the ground for the exploration of negative space in a qualitatively new light. Peter Kubelka’s insights on cinematic movement marked a significant step in that direction:
      “Cinema is not movement. This is the first thing,,, Cinema is a projection of stills – which means images that do not move – in a very quick rhythm… Where is then the articulation of cinema? Eisenstein, for example, said it’s the collision of two shots. But its very strange that nobody has ever said it’s not between shots but between frames. It’s between frames that cinema speaks.” (8)
      This statement touches the conception assumed in the present essay, that movement is not the transportation of the same object in space-time but the object’s continuous disappearance and reappearance in spatial moments (or spatio-temporal infinitesimal) divided by unperceptibly small cuts of negative space. Hence, the moment is a spatial category, a freeze frame in life. Zeno’s paradox is no longer a paradox – an object doesn’t really have to travel half the way and so on until infinity, because the object actually never moves. It is the ‘spatial moments’, never entirely repeating each other, that create the illusion of movement. The reason why this illusion is perceived as reality is the persistence of vision preventing the human eye from seeing the gaps between the smallest quantities of space-time. If those infinitesimal elements are still determined by their form, the gaps are unbound, invisible and limited by no-form. They can be traversed even harder than the infinity of Zeno’s division. What we arrive at is a geometrodynamic worldview, derived through the ‘paradoxical’ combination of logic and supralogical intuition. It gives no proofs of itself except the mystifying creative will to nothing, reciprocal to the ‘gaps’ to recreate the next moment of change.
      The magnification of the static unit of time is the conceptual focus of Kubelka in Adebar where the freeze frame confronts movement on the screen, altering the proportional relation between temporal elements and challenging time in terms of perceptual relativity. Implicitly emphasized, the relationship between the freeze and the movement is the invisible slit of negative space. The negative space within the shot’s composition can be entirely spatial and is characteristically approached in terms of its semantic inclusion or exclusion in the frame:
      “…I wanted the whole tree on it. I managed one side of it, but only where it comes out of the earth. I know that half of the tree is inside. So the trees are like when you screw together two things. The trees screw together the sky and the earth.” (9)
      Thus Kubelka grants space to the invisible in its semantic emancipation.
      In Schwechter negative space is approached by Kubelka as a proportional variable in relation to the frames it separates. The perception of the film is focused equally on image and black frame thus altering the weight, semantic and perceptual, ascribed to them by virtue of the human physiology of vision (the inability to perceive minimally, yielding the illusionary sense of time). Although it might appear that the ancient Greek principle of incorporating negative space within the formal composition is back, in Kubelka’s film negative space is distinguished from the space of imagery (which may still retain its metaphoric ‘negative’ or whatever). However, it is still within the composition of the work as a single entity but it is not given any particular form besides the unavoidable, necessarily limiting, form of the film leader itself. The varying length of the black leader suggests a quantitative affixation of the negative, its capacity to extend in the infinity of the large and the small. Unlike the negative space composed within works of other visual arts such as painting, sculpture and architecture, where it becomes primarily spatial and thus persisting in time, when composed within a film like Kubelka’s it retains its temporal essence thus minimizing the possibility of translocation.
      That achievement of Kubelka was incorporated and further explored in experimental film, gaining an increasing recognition for the black frame. Paul Sharits’ film T,O,U,C,H,I,N,G is built entirely on frame by frame cutting with repeated intercutting of black frames. In spite of its metaphoric message about sex, the film has a significant indexical value associated with its interpretation of violence as a tactile experience. The aggressive confrontation of colour, light and dark in the editing resulting in a heavy flickering effect attacks the viewer’s perception almost to the point of pain. The work becomes a literal act of violence. On the other hand, the negative frame loses its semantic independence becoming a part of the cinematic phonology that builds up the film’s message. Negative space is no longer instrumental only for the destruction of cultural perception, it becomes instrumental for the construction of a symbolic unit. This ideological deviation is somewhat equilibrated by the title of the work where a word (as a symbolic unit) is treated in terms of the relationship between the phonemes and the space (of silence) separating them from one another.
      The introduction of the frame as an independent spatial element in film marked the beginning of the quantitative shrinkage of space. While the process of diminishing three-dimensional space dated back to the Impressionists, the efforts since then had been primarily concentrated on the qualitative negation of the visible in terms of the laws characterizing it. From Cezanne’s visionary treatment of the visible to the shamanistic abstractions of Pollock, three-dimensional space was gradually shrunk to a qualitative absence. Kubelka initiated the enlargement of the negative ‘quantity’ to the detriment of the visible space altering their proportional relationship and thus challenging the quantitative dominant in visual perception. The growing unimportance of visible space became a process of its gradual exclusion from the artistic vision.
      In its turn, the theoretical concern with negative space can never grasp the essence but can only keep talking ‘forever’ about ‘the forever mute.” Because it belongs to the realm of magic and art, of ecstasy, chaos and irrationality moving according to their own driving laws, or the absence of such. It belongs to no category and is a category of nothing. Yet it is the occult force that drives art as a legitimate destructor within the cultural parameters:
      “There can be no question today of art for pleasure, whatever transcendent meaning, including aesthetics, one gives the word, however elaborate, however farfetched it may be. Art is made elsewhere, outside it, on another plane of that Reality which we perceive in a different fashion: art is other…” (Michel Tapie (10))

CONCEPTUAL BACKGROUND

      The main tendency of modern art to revise perception and the perceived was not a solitary development. Although the entire history of art was slowly advancing in that direction, its crystallization and dynamization began in 19th century when the conditions and the respective development of human conceptual thought allowed for such a process to accelerate. The search for dimensions beyond the immediate perceptions became a prime concern in a number of fields. Mathematics remains until today the sphere where the problem is most systematically worked upon.

Non-Euclidean Geometry and the Fourth Dimension in 19th Century

      Although the fifth postulate of Euclid, stating that only one parallel to a given line can be drawn through a given point, has always been problematic in terms of its successful proof, it was not until the works of Lobachevsky and Bolyai that a formulated system of non-Euclidean geometry appeared. Both the Russian and the Hungarian geometers, working simultaneously but independently of each other, approached the problem by proposing the same alternative of disproving the parallel postulate. They both suggested that through a given point not on a given line more than one line can be drawn not intersecting the given line, the sum of the angles of a triangle being less than the 180 degrees of Euclidean geometry.
      The other major type of non-Euclidean geometry was suggested by Reimann in 1867. He approached geometry as the study of manifolds of any number of dimensions and of any curvature. Drawing the distinction between unbounded and infinite space, he used the sphere as a model of the former and as an exemplary space of non-Euclidean geometry where no parallel line is possible and the sum angle of a triangle is higher than 180 degrees. Reimann’s geometry suggested a space of varied curvature meaning that the movement of a shape through it would experience a variation of properties.
      Reimann’s view of non-Euclidean geometry of n-dimensions contributed to the already existing outgrowth of analytic geometry, the geometry of n-dimensions. A method of analogy with the formation of three-dimensional solids by means of two-dimensional planes was used to approach the formation of hyper-solids by means of three-dimensional solids. Stringham produced one of the Earliest sets of illustrations of hypersolids using the formula of polyhedra to establish the number of the properties in four dimensions. This had a considerable impact on Schlegel in his extensive work on the problem. In the 1880s Schlegel published a number of articles on n-dimensional geometry and went to the extent of producing actual models of the projections of the polyhedroids in three-dimensional space.
      In 1884 this method was popularized by Abbott’s fiction novel Flatland. His entertaining tale about a two-dimensional being experiencing the problems of conceiving three-dimensional space, wrapped up the major points of the comparative methodology in n-dimensional geometry and became an important reference used until today.
      In the beginning of the 20th century the idea of time as the fourth dimension was established by Malinowski’s space-time continuum which became an essential part of Einstein’s Theory of Relativity. In fact, this idea was first expressed as early as 1754 by d”Alembert in his article “Dimension” but it was not before the turn of the century that it could be developed as a scientific hypothesis.
      By the end of the 19th century and the beginning of the 20th the development of n-dimensional geometry, itself conditioned to a great extent by the development of non-Euclidean geometry, did not only revolutionize its field but attracted considerable popular attention.

The Problem of Higher Dimensions in Other Spheres of Human Thought

      The fourth dimension became widely popular mainly through the ideas of authors like Hinton, Ouspensky and Blavatska. The increased interest in the occult arts was a reflection of a symptomatic search of the period for a middle ground between the increasingly authoritative science and a respective mystico-religious crisis. The occult authors attributed supernatural phenomena to the fourth dimension in an attempt to explain the irrational scientifically. Among them the works of Ouspensky are the most noteworthy in respect to the problem of the fourth dimension.
      A significant event in the development of late 19th century thought was the foundation of phenomenology as a methodological school. Its basic concepts were set by Husserl who claimed that perception was culturally conditioned hence observed reality was a projection of the cultural ideas about it. In order to perceive the essential objects, the phenomenon as it was, one had to strip one’s senses of any aqcuired knowledge and approach the object without pre-conceived ideas. The phenomena of object, according to Husserl, transcended space and time occupying everyone’s inner visionary space. Thus the illusion of visible objects was opposed to the pure phenomenon of vision. One of the properties of visible, culturally constructed space was, for instance, the one-vanishing-point perspective (an essential part of the perception of three-dimensional Euclidean space). Although Husserl did not refer directly to higher dimensions, his methodology of dismantling the perceived three-dimensional space was pointing unequivocally in that direction.
      A consideration of perception in direct relation to higher dimensions was central to Poincare’s theoretical works on the spatial problem. He attributed three-dimensional space not so much to cultural conditioning as to hereditary and experiential factors. According to him the space of three dimensions was “only a property of our table of distribution, an internal property of human intelligence, so to speak. It would suffice to destroy certain of these connections, that is to say of the association of ideas to give a different table of distribution, and that might be enough for space to aqcuire a fourth dimension.” (11) Contemporary mathematicians are also increasingly inclined to regard the problem of higher dimensions as primarily related to human sensory-conceptual system for information processing, as it was expressed by Bill Thurston in an article published in the July 1993 issue of Discover magazine:
      “When we talk about higher-dimensional spaces, we’re learning to think in and plug into this other spatial processing system. The going back and forth is difficult because it involves two really foreign parts of the brain. We don’t have a good way of communicating this spatial information. The problem isn’t with the substance of the mathematics; it’s with how to think about it.” (12)
      The circle of relationships can be closed in a further cross disciplinary look at the notion of higher dimensions. In mathematics this notion represents the building block of one of the main models for infinity consisting of an infinite succession of unbound spaces, each of a higher dimension. A similar concept is presented by Carlos Castaneda who describes the cosmology of a Yaqui Indian sorcerer Don Juan, according to which the universe is regarded as the coats of an onion with every coat representing another ‘parallel’ yet qualitatively different reality. The goal of Don Juan’s mystic practices is precisely to liberate the human sensorium from its cultural deposits in order for the senses to be capable of grasping those parallel realities.

EXPANDING TIME

       Unlike Yaqui Indian culture, the late-19th early-20th century Europe of the technological revolution, with its rise of materialist ideologies (including the ideology of science!), had its shamans mainly in the face of the artists who emancipated themselves as creators of non-material culture, refusing allegiance to any institution. All this in the name of art liberated – Art for its own sake.
      Although none of the Neo-Impressionists or their predecessors the Impressionists ever mentioned Husserl, many of them consciously or not applied his methodology. Whether this was the result of their, even only on a popular level, competence in the current ideas about space or phenomenology (or both), or it was just a parallel development conditioned by the same cultural trends (or, as Jung might have argued – a manifestation of the collective unconscious) is neither a question of interest in the present essay nor a question that could ever be clarified. The fact remains that works of the Neo-Impressionists, and especially those of Cezanne, Van Gogh and partially Gauguin, exhibited a systematic approach of dismantling the visible object to capture its essential form, the vision. Cezanne’s rejection (Van Gogh or Gauguin would ignore it rather than reject it) of the one-vanishing point perspective would be inherited and developed by the Expressionists, the Fauvists and most systematically by the Cubists. Thus, once established in painting, non-Euclidean space would alter the course of art altogether.
      The works of the Cubists in the beginning of the century were rather unequivocally informed by phenomenology, Poincare and the geometry of n-dimensions. Braque and Picasso created a style that attempted to brak down the visible form to its essential geometrical components. The image would be depicted from several viewpoints to stress the entirety of its phenomenon rather than a visible aspect of it. This multiple perspective referred to a non-Euclidean space – the capacity of perceiving three-dimensional objects in their entirety simultaneously – a quality functionally carried out by time in the third dimension. The limitation of viewing an object in time was eliminated thus suggesting an elimination of the main limitation of three-dimensional space itself. The evoked simultaneity of perception introduced time as a spatial aspect in the Cubist paintings. A new direction regarding spatio-temporal relationship, this would be explored widely by the Futurists and would lead to a qualitative reexamination of space-time in modern art. The works of the Cubists provided the first major reference to the new geometries approaching, at the same time, the Einsteinian conception conception of time as the fourth dimension.
      One of the first masterpieces of experimental film, Balet Mechanique, was a collaborative work of Dudley Murphy and one of the major modern painters, the Cubist and predecessor of Futurism, Fernand Leger. This was emblematic for experimental film’s genetic link with modern painting. Accelerating the development of the new medium, the relationship between the two eventually led to the establishment of film as a distinct art form with an autonomous place in the intellectual space-time continuum.
      However, the conceptual emancipation from painting would be a gradual process and many of the most avantguard films would remain no more than reflections of aesthetic trends in painting. Thus, in spite of its aesthetic significance for film, Balet Mechanique cannot be detached from the paintings of Leger and his fascination with machines. The importance of Leger’s works as the bridge between Cubism and Futurisn with the latter’s focus on movement is inherent to the film where the artist makes the most of the temporal quality of the medium (absent in painting) to conduct his aesthetic message. At the same time this disconnects his film art from the fourth-dimensional connotation of Futurism where movement is fixed as a sequence of movements imprinted in space, liberating time from its linearity, granting it a permanent spatial realization as the fourth dimension.
      Likewise, the films of Maya Deren rejoice in the idea of time without actually contributing much to its conceptual development. Although the filmmaker devoted a significant part of her work to the exploration of time, her semantic preoccupation with the subjective experience and her film language charged with symbolism imply a psycho-mythological approach in a Jungian spirit. It is true that the mythological space-time is the first form expressing aesthetically the notion of higher realities (and one of the most powerful in this respect). On the other hand, as it was already discussed, its persistence throughout the centuries has turned it into a poetic convention the metaphoric reading of which has become confrontational to the cultural system of sensorial conditioning.
      The abstraction of time in Maya Deren’s Choreography for Camera is exemplary for the mytho-aesthetic approach. The action takes place ‘everywhere and nowhere’ turning the experience inwards, toward a meditative reflection of the concept of time. It is detached from space, the convention of space-time is broken. The spatio-temporal paradox creates a mythic reality, intellectually implying the supernatural laws of a hyper-reality that could be interpreted existentially, aesthetically, psychologically but hardly literally. It does not challenge physical perception but only the intellectual interpretation of the perceived. This is confirmed by the writings of the author herself who always gravitates toward the one-vanishing point of intellectual reading. What starts as a promising insight on space-time ends as a structuralist analysis:
      “The (…) manipulation of time and space (…) becomes itself part of the organic structure of film. There is, for example, the extension of space by time and of time by space. (…) Time may be extended by the reprinting of a single frame,… the frozen frame becomes a moment of suspended animation which, according to its contextual position, may convey either the sense of critical hesitation… or may constitute a comment on stillness and movement as the opposition of life and death.” (13)
      However, this was precisely the role of early experimental film. Although, compared to other conceptual fields of the time, it contributed little to the notion of higher dimensions, through the shock of introducing unconventional (for the film language of time) approach to imagery and narrative, it contributed to the questioning of the ‘space processing system’ thus paving the way for the battle against constructed sensorium.
      Among the most significant achievements of the film medium that profoundly influenced the development of the art, and more specifically of its experimental branch discussed here, was the introduction of discontinuity in montage by Eisenstein. Above all his extension of time through overlapping editing would shift the perception of temporal linearity and would break the notion of flowing time. A single motion would be presented from sharply differing angles edited in a sequence where every shot would repeat a portion of the movement shown in the previous one. Thus every fraction of time-space acquires an autonomy in liberating itself from its functional relationship with its predecessive and consecutive ones. Time as such is extended through its own repetition in a varying space. The shot, the part of space represented, becomes its building yet formally and directionally independent element.
      As it was already discussed, the new medium had one great advantage - it occupied two dimensions of the screen space (with the capacity of creating the illusion of the third spatial dimension) and the dimension of time. Unlike theater or dance, it could manipulate time not only by imitation (backward movement and repetition are possible manipulations of time in the scenic arts) but directly and in any conceivable fashion. Unlike literature, film could provoke not only a mental but also a physical (sensory) experiencing of its time treatment.
      The autonomous significance of experimental film in the context of modern art was achieved more or less through the works of Brakhage, Kubelka and Jonas Mekas. For the first time film provided adequate and aesthetically autonomous grounds for the exploration of the questions concerning higher dimensions. The works of those three authors offered three different but essential interpretations of time.
      The endlessly monotonous imagery of the late Brakhage renders a vision of time as an extension of space in an eternal moment. The viewer experiences every bit of the meditative sequence yet, when over, the sequence collapses to the memory of the moment. The image, blurred with scratches and superimpositions, has no objective focus. Its even obscurity flows through the screen in a movement that essentially remains the same – time passes and time stays. It becomes a legitimate spatial category permanently imprinted on the screen while retaining its characteristic quality of movement. The information that can be encapsulated in a minute is blown up to an hour – an hour of a spatial minute – an hour that proves to the perceptions the discontinuity of time. The transcendence of time into space is only an abstract vision of the missing temporal part. Challenging the habitual senses, Brakhage forces the viewer to grasp the missing part, to try to capture it beyond the visible object-iveness of the mundane world, in the blurred boundaries of a continuous phenomenon of form relieved from any reference other than itself.
      But what is film time? It is just the illusion of running static frames divided by tine strips of black at 24fps, the speed of normal motion, the speed that disallows the eye to detect those tiny strips. Film time is just an illusion. But since, in certain conditions, the eye is unable to detect something as visible as the space separating the frames how can one be sure that the persistence of vision does not block the perception of reality itself. Could not time in life be essentially the same as that in film? Could time be a sequence of static forms separated by tiny strips of death, of void, of no-form. Just as one is constantly accompanied by death in the passing of time, the continuous loss of every single moment (I am not anymore the person who wrote the previous word and I have forever lost that moment), so possibly death exists on a miniature or quantum level where it persists in its essential spatial form and not as a category (or a mere final proof) of a detached concept of time. But the senses are blocked or constructed so as to perceive time as passing and death as its mere finality for a given form.
      The contemporary methodologies of literary psychoanalysis and post-structuralism continue the tradition set by phenomenology in its attempt to deconstruct the cultural structures spelled out by the unimaginative predecessors of the post-structuralists, the structuralists. Noteworthy in this respect is the approach of Julia Kristeva analyzing language in terms of its perceptual focus on words, i.e. on language’s object-iveness. Kristeva shifts the focus to the disregarded yet essential linguistic elements such as pause, rhythm, etc. Those elements, called by her the ‘semiotic’, represent the culturally neglected, perceptually negative aspect of language, characterized by spatial absence.
      Kubelka used a similar approach to analyze the temporal structure of film. Giving the frame a temporal status almost equal to its spatial existence (two-three freeze frames a shot) or often equal (one freeze frame), he allowed time to expand over space by challenging the human eye to attempt perceiving the miniature spatial fraction, that builds up the temporal continuity, in its autonomous existence. Thus fractions of form start to coexist in the discontinuity of their motionlessness. Only time passes on the screen to allow the viewer a glimpse at those elliptical slices of space: “There is never ever movement on the screen.” Time becomes visible in the attempt of the film-maker to ‘establish for [the] eyes a harmonic time as music establishes a harmonic… time for the ears.” (14) In a way alternative to that of Brakhage, time becomes the permanent category and space – the relative. Furthermore, the black strip is extended to a black frame that occupies an amount of space temporally equilibrated with that of the image. The imperceptible particle of time, of death, of no-thing, is rendered visible in its semantic emancipation.
      A noteworthy extension of this principle was achieved by a film-maker from British Columbia whose film The Discreetness of Time or What Happens Between the Frames was almost informally shown at filmmakers’ gathering in late 1993 in Montreal. Although the name alone implies the relevance of the film to the present discussion, it was the film itself that proved it. Sequence of airplanes moving slowly and unimpressively on a runway were intercut with sequence of black leader, while a female voice-over was telling fragmentary impressions of her separation with her lover, an event claimed to have happened ‘between the frames’. This simple solution lacks the structural sophistication and the perceptual impact of Kubelka’s treatments but it presents an adequate alternative to the ‘fractioning’ approach. It aims at unimportant imagery and even the perceptually less important lack of it (black leader) provoking the viewer to concentrate on elements that are usually disregarded as conveying no meaningful message. Those elements become precisely the semantic focus where the emptiness of the visual pause, the magnified particle of time, becomes the vehicle of the film’s movement.
      Time and space as such do not convey any meaningful message, all messages are implied. The ephemeral contraction of time and the unbound expansion of space are the only messages one receives through one’s repressed sensorium. The interchangeability of those processes would mean the detection of another reality, of a qualitively different space. The films of Brakhage and Kubelka attempt to provide at least a glimpse of that other reality, and so do the films of Jonas Mekas.
      The aesthetic approach approach of Jonas Mekas is profoundly and explicitly related to the phenomenological methodology. Starting his work without a preliminary preparation, he uses the camera as a natural eye, undirected, pure, without pre-conceived ideas or expectations. The result is a visual dance of the camera running through only partially differentiated space where the boundaries of objects melt in the projection of their movement of the camera, or both. Nothing is focused, stopped at or observed. What is essential are the tines projected in space by the movement, like in Futurism where the segments of a movement abide simultaneously in space, where movement becomes a constant spatial category.
      Jonas Mekas does not edit his films. Thus they acquire the significance of almost shamanistic revelations attempting to catch the essence of the vision by means of the camera. Unlike the phenomenon of the Cubists, that of Jonas Mekas does not belong to space but to time. His visions are essentially temporal, like music translated for the eye. But it is not Kubelka’s measured translation, Jonas Mekas translated the flowing spirit of music, the impossibility to stop and observe a fraction of it. He forces out the inner vision, the intent to find that ungraspable distance for focusing on a vague slipping memory of that vital something which has actually never happened. His ecstasy is not Kubelka’s abstraction but the madness of melting deeply into the form, or ‘aform’.
      Whatever the aesthetic approach, the interpretation of time by the discussed experimental film-makers goes beyond the intellectual flirt. It becomes instrumental to the liberation of the senses and the mind from the laws that bound them to the known reality. Provoking a state recognized by Kubelka as the “ecstasy, which comes from the Greek, and it means being situated out of it, and it’s a means to beat the laws of nature, not to be slaves of nature. It means to get out of the prison of nature – in English you have this great expression ‘to serve time’ in prison, and that really is what normal life is – you serve time.”

CONCLUSION

      Although the Relativity Theory can be conceived as a contradiction to the notion of geometrical higher dimensions, and more precisely of a geometrical fourth dimension, it is only superficial to automatically assume so. The problem is much broader, more complex and comprehensive than science alone could solve. It reveals aspects that challenge rationality and are beyond empirical proof, so the scientist is obliged to use any means, to become more or less a methodological anarchist, if he is to find plausible answers. The paradox becomes the ordinary element of the problem, so it is impossible to neglect it. Thus the rational confrontation between the concepts of a temporal (Relativity Theory) and spatial (geometry) fourth dimension might be completely irrelevant for the two could actually be viewed as one. What is conceived as time in the three-dimensional space, remains a concept. It is never directly sensed, or perceived. Like a mental apparition it is there and no-where, exhibiting the qualities of the higher dimensional objects passing through a lower dimensional space as illustrated by Abott’s famous example. Its aformality prevents the perceptions from grasping it directly and points at its qualitatively different nature. Time is an intellectual suggestion of a dimension, essentially related to space yet appearing in no particular spatial manifestation. Thus it becomes the invisible aspect of space, which can be the shadow of a fourth spatial dimension that reveals itself partially, as a principle rather than a physical quality. To perceive a three-dimensional object from all possible angles one has to walk around the object in time; a hyperspace would allow the simultaneous perception of all sides of a three-dimensional object thus eliminating the function of time in three dimensions, its intermeasurability with space. Time becomes incorporated in the fourth spatial dimension. It is hard to conceive how time can be translated geometrically but the geometry of higher dimensions is itself a qualitatively different type of geometry that can expand beyond the conceivable space, in the space of time.
      It is not a task of this essay to develop physical theories but since the regarded matter is interdisciplinary it requires a broader consideration. If one accepts the suggestion that the temporality of movement is spatial (the succession of spatial fractions perceived in one direction) then the question becomes even broader, it becomes closely connected with theories and phenomena of chaos, quantum physics, etc. The problem of perception is central to the quest for higher dimension and it has naturally become the focus of interest in art and epistemological theories. Although some of the modernist artists have expressed direct interest in the fourth dimension, it has never been the main axis of aesthetic consideration. However, it has become a central, though undernoticed, “vanishing point” in modern art’s development that often has been more fruitful in works whose authors had not consciously referred to the problem of spatial dimensions. The liberation of art from academic dogmatism was a historical rather than a conceptual tendency. It was hardly only the ‘belief in a fourth dimension’ that ‘encouraged artists to depart from visual reality and to reject completely the one-point perspective system that for centuries had portrayed the world as three-dimensional.” (16) The process of artistic subversion was rooted in the multifaceted economic, political and intellectual trends of 19th century Europe. The aesthetic movements were part od a socio-cultural phenomenon and inspired by the revolutionary spirit of the times. However, the will to freedom from the ‘abundance’ of three-dimensional space and its governing laws persisted as a guiding line throughout the decades of modern arts’ development bringing forth many revolutionizing concepts and forms of expression.
      The new found way to infinity called the artists to dismantle the three-dimensional reality, to liberate form from its spatial laws, to search for a diametrically opposite category of formal expression. Film allowed for such a category to crystallize in a reexamined notion of time that granted a true spatial status to the temporal thus enlarging its domain, liberating it from its ephemeral unilinearity incorporating it into a new hyperreal space-time continuum. This process offered a vision of an infinity of ever shrinking space and ever expanding time where the two become interchangeable categories of one and many that stretch endlessly in the small and the large simultaneously.
      But the will to freedom had been an original drive of art in all times. What modernism and experimental film introduced was a way to realize it through the violation of the senses, the enforcement of anti-rationalism, the destruction of habitual perception. It took rid of the allegory to go for the indexical instrumental use of form thus returning to the times when the initiation pain was a reality and not a poetic device.
      So, those attempts for historical contextualization, of taxonomic search for connections is nothing but a methodological hypocrisy. The connection is somewhere else – in an unconscious past or a forgotten future agonizing in the space enchained in its own eternal momentarity. Trapped between rationality and metaphysics (from a positivist perspective), this essay can only trace the aesthetic ‘apparitions’ of another realm, it can attempt to take a glimpse of the always growing and changing human conceptions, but it can hardly claim to give definite answers for, in this matter, answers can be given only by those who don’t know the answer.

NOTES:
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BIBLIOGRAPHY:
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Published in BALKANMEDIA Magazine, Volume III/3/1994