The Ulterior Dimension of the Line
by Ryul Song


On the afternoon of July 4th 1960, between 4:00 and 6:55 p.m., Piero Manzoni executed a line with a length of 7200 meters at a printer’s in Herning, Denmark, and enclosed it in a lead cylinder made up of square plates. This line was the first of the series "Linea di lunghezza infinita" (Line of Infinite Length). After completion, each further line will be tightly rolled together, enclosed in a vacuum-tight stainless-steel container, and will be placed in each of the principal cities around the world, until the sum of the "Line of Infinite Length" had reached the length of the earth’s circumference.


I. Associations of Lines

In Klee’s works, the line appears as a constitutive formal element characterizing the picture. The focus of his teachings at the Bauhaus was on his theory of pictorial means and laws and their development and interaction in the creative process. His statements on his artistic means, especially on the function and significance of the line, elucidate the amount of analytical clarity the line possessed in his oeuvre in regard to its potential for statement. In the first section of his essay "Graphic" in his "Theory of Art", he mentions its special artistic possibilities under the aspect of the tendency towards abstraction inherent in graphic arts.

Pure art is created when the statement of the formal element and the statement of the formal organism visibly coincide with the spirit of the content.

In the second section, he discusses the possibilities of statement, which the line has in giving shape to formal as well as contentual ideas. The poetic image of a journey along a line begins with the movement away from an 'endlessly small surface element, proto-element - point', thus creating the line. While at first the line merely bears the characteristic of direction, it then attains various functions and meanings in relation to its changing surroundings and therefore, in turn, changes its surroundings.
(...)
The sequences of the line produce all possible types of movement, while the line retains its essence or alters it as a result of integrating the context it has changed. The quality of the line defines itself anew through its interaction with the context. The line in Klee’s oeuvre is thus to be understood as representation of this new meaning of line.

Using examples, he distinguishes between different types of lines. He subsumes two types of lines under the concept 'linear active'. The first one 'indulges (...) freely and unbound, goes for a walk for its own sake. Without a destination'. The second is the 'limited' one, overcoming as quickly as possible the distance between two points in the form of a straight line, as an 'errand'. Under the title 'linear medial' he deals with lines that circumscribe shapes and thus define a plane, a form, or an object, while simultaneously losing their characteristic once these have come into being. This leads to the concept of 'linear passive' which deals with 'linear results from surface actions'. From this he concludes that the effects of the surface created by the lines stand, in the way they appear, in reverse relationship to the lines. The essence of the line is lost, and only its result, the surface-effect, remains; the line works only as an element for the surface. The more active the line is, the weaker the surface-effect; the more active the surface, the weaker the effect of the line appears.

Klee’s further descriptions of the line as stream into the distance. Thought. Path. Attack. Épée, stab, arrow, ray. Sharpness of a knife. Scaffolding. Form of all carpenters: plumb are aspects of the contentual and functional dimension of the line as opposed to plane and body. The drawn line directly takes on a meaning in relationship to its context. Klee thus negates the existence of the line for its own sake, 'linearity' as abstract principle.
For Klee, the line is the 'most primitive means' of pictorial art. Shortly after putting the pencil, or whatever else sharp there is, to paper, a line is created. Beyond that, the line can be grasped foremost as infinity, without a tendency towards direction, without indicating any position, without dimensionality. The invisible, infinite 'linearity' is the ontological concept of the line. As soon as a line is drawn or perceived, interaction between the line and what is beyond the line commences. The perceived or perceivable line can be understood beyond its ontological concept, in terms of its relationship to its surroundings.
Klee says that the lines subsumed under 'linear medial' and 'linear passive' lose their characteristic as line, and that it is an idealistic thought that the nature of the line is retained in the result. If this analytic process follows inductive logic, i.e. the line does not lose its characteristic on account of the surface effect, but only alters its meaning and trait, then it is newly defined in the interaction with the surface.

The most essential feature of Klee’s line is the possibility of movement. This possibility of movement evokes associations in relation to each other via a process of metaphoric further development. This relationship does not describe a physical, but a mental phenomenon. (...) Klee demonstrated in his teachings at the Bauhaus his view of the associative potentials of the line. (...)

Quite opposed to his Bauhaus colleague László Moholy-Nagy, who in his theoretical writings prolonged the movement of point to line and line to plane by the further development from plane to space, Klee saw no such analogous possibility.
For the "construction in three dimensions", Klee continues to utilize the visual impression of railway tracks approaching the viewer frontally. The parallel lines of the tracks appear to the eye of the viewer as linear movement (longitudinal gradient) converging at a distant point, supplemented by cross-ties (latitudinal gradient) with a horizontal rhythmic structure. Klee places onto these lines the frontal view of a locomotive and projects the grid of longitudinal and latitudinal gradients of the ground plane over the side and top edges of the locomotive front.
(...)

Using this spatial net, Klee discusses the possibilities of 'perspectival progression'. If the longitudinal gradient is multiplied, a ground surface with a fan-like line structure unfolds before the viewer. The middle line becomes a vertical running towards a distant point. Due to its visual emphasis, it can be equated with the position of the viewer. Once horizontal lines are introduced, the viewer then associates a perspectival representation.
When the vertical axis (position) is altered, the viewer’s visual field changes, creating a new visual depth between the viewer’s retina and the objects. This, in turn, leads to the lines effecting new associations due to the altered visual depth; reality is perceived differently. The movement of the 'eye point' extends the 'depth of a breadth seen in profile' of an object and the change of visual depth between the subject and the viewed object. This phenomenon impresses on the synthetically thinking subject the respective new sensation.

(...) A subjectively perceived reality is represented by the simultaneous composition of different perspectival points of view. View from above and view from below are combined simultaneously by making use of different positions. The varying visual depths between viewer and object constantly evoke new associations. The work depicts subjective reality in the interaction of multi-dimensional simultaneity.

Art does not reproduce what is visible, but makes visible.

In his reflections on the possibility of statement the line has, Klee defines the interrelationship between the line’s movement and the further dimensions originating from the line. In his sketchbook, he uses linguistic definitions and exemplary drawings to illustrate the diverse results the line leads to, the 'bodily and spatial' surface effects. The concepts Klee uses solely in regard to the process of artistic creation, 'bodily two-dimensional / spatial two-dimensional', remain valid in regard to physical, three-dimensional space, although they do require, in face of the changing interrelationship between viewer and viewed when including the spatial aspect, a more complex examination.


II. Three-dimensional Two-dimensionality

Klee’s concepts of 'bodily two-dimensional' and 'spatial three-dimensional' can be transferred from two-dimensionally depicted three-dimensional space to actual three-dimensional space via James Turrell’s architectural works.

Bodily Two-dimensional

James Turell’s works experimenting with 'borderline', such as the series "Space Division Construction" and especially the later series "Wedgework", deal with the experiences of perception in an intense way. They deny the only through individual experience. He develops spaces the dimensionalities of which change depending on how long they are viewed and on the duration of the viewer’s movement, thus playing with the viewer’s perception.

A frame defines a surface which becomes visible as borderline, as something in between, physically indefinable, but mentally perceivable as a borderline between two spaces. The 'borderline' is a surface of air, which only comes into being in the perception of the viewer within a frame described by the interaction between surface edges. This surface is filled with intense, homogenous light, i.e. it becomes visible through the materialization of light within the frame. Thus, in reversal of one’s perception, the frame created by the spatial edges and edges of the dividing walls, itself turns into edges of a surface.

The infinite density of the field of light dissolves the lines of the visible space continuing beyond; height, breadth, and depth of the space are lost. The viewer approaches the field of light, the virtual place, as if it were a two-dimensional picture, until the homogenous field of light fills the entire field of vision. Inevitably, one has the desire to touch the faceless surface, but there is no object to touch. What can be seen is the flat frontality of the solid picture and the undulating depth of the homogenous color surface. Only after traversing the field of light and physically touching (or rather: not touching) this two-dimensional object (or rather: non-object) does the perceived dimensionality of the place change.
Turrell increases this enigmatic nature of the space and its dimensionality by the materialization of the 'borderline'. The space limited by the 'borderline' never changes, yet it still oscillates between the dimensions, between the viewer’s perception and the awareness when entering the space. The field of light is a transition from visible space to the space of vision; it changes the perceived dimensionality of the place. Perception constantly takes place on the borders of what is perceivable and causes a feeling of uncertainty.

By traversing the 'borderline', the viewing subject becomes the viewed object. When the 'seeing I' steps back, it indulges in the act of seeing and making visible. Another "seeing I" enters the space and sees the 'I which has become visible' in the background.

What allows us to see one part of the field as movable, the other as background, is the way in which we give reasons to our relationship to them in the act of perception.
Now the objects observe me.
(...)

In the series "Wedgework", Turrell uses lines, details, and colored surfaces generated by light, in order to draw the viewer into the unfathomable depth of an immaterial surface. The spatial depth of the walkable space to be viewed, of the virtual space, causes, in constant interaction with the surface, new relationships between that which immediately suggests itself (Here) and that which lies at a distance (There), between the viewer and the viewed. Merleau-Ponty describes this visual depth with the term 'voluminosity'.
As we have noted from the beginning, we have to rediscover beneath depth as a relation between things or even between planes, which is objectified depth detached from experience and transformed into breadth, a primordial depth, which confers upon the other its significance, and which is the thickness of a medium devoid of any thing. (...) This voluminosity varies with the color in question, and is, at it were, the statement of its qualitative essence. There is, then, a depth which does not yet operate between objects, which, a fortiori, does not yet assess the distance between them, and which is simply the opening of perception upon some ghost thing as yet scarcely qualified.

Spatially Two-dimensional

To draw a border or a frame with a line implies not only enclosing a visible object or directing the focus to it. In James Turrell’s "Skyspace", the systems of edges are a frame for the place between the heterogeneous conditions of visibility. In "Skyspace", the sky as neutral background is limited by a frame; the sky thus materializes itself within the frame as a surface. This active sky-surface transposes a passive location to a space of unforeseeable visual experience. The sky is re-defined as a viewable surface. In the process, the appearance of this sky disturbs the perception of the viewer, directing his/her way of perception from ordinariness to what is special. By bringing down the sky to the surface of the opening in the ceiling, a space is created which, although open towards the sky, conveys a feeling of confinedness. This feeling is intensified by the projection of the horizon line at eye-level into the interior of the space. What can be viewed is at a non-controllable distance and will therefore never disclose its innermost texture. The series "Skyspace" is the attempt to overcome the incomprehensible gap between the sky and the viewer using a frame system encompassing a sky surface so that its pure depth can be perceived two-dimensionally and tangibly close. The sky is no longer vaguely 'all around' or 'above' the viewer, but 'exactly there', framed by edges. The sky, having become a defined place, gives the space a further dimension through its constant changes, an unmediated presence of perception.

In view of the perceptual process, there is no objective edge of the visual field. Merleau-Ponty elaborates: It has been wrongly asserted that the edges of the visual field always furnish an objectively stable point. (...) the edge of the visual field is not a real line. He continues saying that it is rather a moment, a restless experience of time we require to see.
In "Skyspaces", however, it is exactly the real line that is meant to limit the viewer’s visual field. This is achieved through reversing the viewer’s process of perception in regard to what is viewed. The perceived reality (the object) is not altered by the change of the visual field, but the viewer’s visual field passively changes through the altered appearance of the sky. Even the 'hidden side' of the sky is perceived 'in front of us', as opposed to fathoming the hidden side by changing the visual field through motion.
The outline effects the absolute exterritoriality of the sky and denies the existence of the body, with the alteration in appearance of the sky determining the perceived space and the perception of the viewer. The real line of the edge between sky and viewer leads, within the viewer, to an internal ambivalence between infinite sky and sky materialized as surface, between the sky's openness and confinedness.

In the works of James Turrell, the movement and construction of lines is utilized in a new way. The concept of 'borderline', not 'border-line', implies that his lines are not used to create a linear effect, but for the impression of surface as a materialized place, for the further dimensionalities, as it were, originating from the line.


III. Metaphysics of Two-dimensionality

Unlike Turrell, Lucio Fontana, in his space-related, gestural works, applies lines to surfaces in order to stress the two-dimensional nature of the surface and to allow the unlimited spatiality of the surface to be perceived through the fourth dimension of space. The fourth dimension of space, according to Fontana, is the exploration of the inner dimension beyond all time and unity of space and time, as it was created by cubism and futurism. (...)

Next to Seurat, who attempted to create a relationship between the pictorial sign and the spatial dimension of the picture, Fontana, like the symbolists, aimed at expressing mental and emotional conditions in his mostly linear handwriting, with reversal and anomalies allowing a glimpse of psychic dimensions. His drawings are less the statement of an effort than of taking pleasure in the motion of drawing, the linear tangles of which are not altered and corrected afterwards. These drawings make comprehensible purity in the sense of highly expressive clarity which, in the end, lets Fontana’s work arrive at a white surface with a single cut line.
(...)

In "Concetto spaziale", 1951, and "Concetto spaziale", 1953, from the series 'Concetti spaziale' starting 1949, Fontana arranges translucent openings with their opposite, the stones, as a sensory experience of positive–negative. The perforations constitute a substantial step in his effort to overcome the illusionary representation of space. The canvas becomes a permeable membrane between the space in front of and behind it. In general, Fontana utilizes the mathematical concept of lines as signs of infinity. In this sense, a point-formed opening of the canvas can be understood as a line which will loose its body in the infinite depths and, when viewed, refers to the infinite space behind the canvas. By damaging the canvas and the resulting calling into mind of unknown, boundless spaces, Fontana intends to free himself from the surface of the wall.
In the later continuation of 'Concetti spaziale', starting in 1958, in which Fontana damages the canvas with linear cuts, the cuts attain a similar, spatial significance. The mostly monochrome canvases are cut with straight, convex, or concave lines which structure and rhythmitize the surface. A line with a certain height and breadth creates a line surface that again allows an infinite spatial depth to be perceived.
As opposed to the cubists and futurists, who created new dimensions by referring to the unity of space and time and projected these to a surface, Fontana opens up the surface itself for spatial access. Fontana’s work can be understood as realizing the unity of space and time, as well as making experienceable the various aspects of perception that the viewer associates with space. The fourth dimension is intrinsic in Fontana’s work. (...)


IV. Pieces of Infinity

(…) a surface that simply is: (…) Even if this indefined surface (uniquely alive) cannot in fact be infinite because of the material contingent of the work, it certainly is unfinishable, repeatable to infinity, and has a continuity that remains unresolved. This is more obvious in the "Lines". (…) the line develops only in length: it runs to infinity: its only dimension is time. It goes without saying that a line is not a horizon or a symbol, and that its value lies not in the degree to which it is more or less beautiful, but in the extent to which it is more or less a line: its existence lies in this (…)

From 1959 to 1961, Piero Manzoni produced lines of various lengths, between 1.76 and 1140 meters. These lines were enclosed in black cardboard cartons and labeled with length and date. Parallel to the "Linea" series, in 1960, he began with the series "Linea di lunghezza infinita" ("Line of Infinite Length"). His intention with this work was to overcome the conflict between the insufficiency of the limited surface and the metric extension of the lines. By describing the individually defined limit, the limit of the entire world defines itself. His actions and statements are metaphors of the significance of what is undefinable and definable, of the timeline and the time of the line, of the absence of limitation of line and time, of the relativity of space and time due to the infinity of their extent and span. Now, the time of the line is enclosed in a container. The infinity of time is defined using a human dimension, the measurement of the line in meters and centimeters and the duration of creating it in minutes. The time of the line is enclosed within itself, within the limits of its transformation, and the limit of time is thus defined by linearity. In this manner, the invisible is linked to the visible, one becomes aware of time through the line, the line reflects time.

The nature of the Linea is eternal and infinite, (…) I put the Linea in a container so that people can buy the idea of the Linea. I sell an idea, an idea closed in a container.

Manzoni creates specimens of infinity with clearly defined lines in order to define eternity. His idea can be understood as interaction between unlimited time and unlimited space.
However, if the time of the line has a relationship to a space corresponding to human measure, the line can change its achromatic meaning through human movement, i.e. the stretching of time. The sequence of the modeled lines at a place is enclosed in a cylinder as metaphor of architectural thought.
Via the atmosphere in the interior space of the cylinder, the viewer sensorily perceives the physical length of the line individually. This can be compared with the way lines with physically identical lengths are rolled together in differently tight ways. The interrelation between cylinder and the modeled lines or lines to be modeled can be seen as the beginning of an architectural process: the change in perception of the physically defined object due to the experienceable surroundings.

Time is something different from what the hands of a clock measure, and the line does not measure meters or kilometers, (…)

The condition of a line is movement, perceived differently in its physical length by its surroundings, with the individually perceived length of the line influencing the feeling of time in which the line is physically experienced. Experienceable space is created by the interaction of line of movement with its surroundings.

The essence of movement is the physical reaction to the individual perception of what is seen. The perception of the line intrinsically existent in nature follows the unconscious movement along this line. Thus, the conscious enclosure of a specimen of the 'infinite line of movement at a place' in a 'cylinder', i.e. the transformation of this line within the human dimension, becomes an architectural procedure in as far as the line of the expected movement is again converted, via its transformation, to an intrinsic state.
A perfectly completed space does not exist. It’s not about the sequence of the cylinder, but about how the states of the rolled-up lines in a cylinder are experienced and how this experience unfolds. Each space awaits its individual experience.

(...) in total space dimensions do not exist, but are constructed at all times.



bibliography
Piero Manzoni, "Alcune realizzazioni. Alcuni esperimenti. Alcuni progetti", Milan, 1962
Paul Klee, Die Kunstteorie von Paul Klee, in Festschrift Hans R. Hahnloser zum 60. Geburtstag 1959, Max Huggler (Ed.), 1961
Paul Klee, Form und Gestaltungslehre, Bd. 1: Das bildnerische Denken, Jürg Spiller (Ed.), Schwabe & Co Verlag, Basel, 1971, Bd. 2: Unendliche Naturgeschichte, Jürg Spiller (Ed.), Schwabe & Co Verlag, Basel, 1970
Paul Klee, Schöpferische Konfession, K. Edschmid (Ed.), Berlin, 1920
Maurice Merleau-Ponty Phänomenologie der Wahrnehmung, trans. by Rudolf Boehm, C.F. Graumen & J. Linschoten (Ed.), Walter de Gruyter & Co., Berlin, 1965
Lucio Fontana, Technical Manifesto of Spazialismo: on occasion of a convention on proportion during the 9th Milan, Triennale, 1951
Piero Manzoni, Free dimension, published in "Azimuth" no.2, Milan, 1960
Piero Manzoni, in Jens Jørsen Thorsen, "han scelger ideer på dåser", Aktuelt, Copenhagen, June 20., 1960
Piero Manzoni, in (peter Jepsen) Jep, "Søren Kierkegaard er grundlaget for Frihedan i liele verden", Herning Folkeblad, Herning, July 6., 1960



published in archiscape, pp. 140-143

(english) (german)





Piero Manzoni, ‘Linea’, 1959






Paul Klee, 'Construction in Three Dimensions’

























































































 1           2            3          4

1. bodily two-dimensional, limiting or medial (body limit)
2. bodily two-dimensional, external-material active-2D (outer surface of a body)
3. spatial two-dimensional, surrounding representation (activated passivity)
4. external- spatial, surrounding representation (non-bodily)





















James Turrell, ‘Wedgework III’, 1969 / ‘Wedgework IV’, 1974





























































James Turrell, ‘Skyspace I’, 1975 / ‘Air Mass’, 1993











































Lucio Fontana, ‘Concetto spaziale, Attesa’, 1960 / 1964-1965










































Piero Manzoni, the series ‘Linea’ / ‘Linea m. 7200’, 1960