The Philosophy of Lines:
From Art Nouveau to Cyberspace
Palgrave 2021, 259 pages
In 2012, American President Obama designated a “red line” about the use of chemical weapons in Syria, a line that Bashar Al-Assad’s regime was not supposed to cross. Assad did not adhere to the “red line,” but no action was taken. Lines change their meanings according to the contexts they are embedded in. What appeared to be new to many political observers, has been common knowledge for generations of aestheticians and artists.
This book offers a philosophical exploration of lines in art and culture and traces their history from Antiquity onwards. Lines can be physical phenomena, or cognitive responses to observed processes, or both at the same time. Based on this assumption, the book describes the “philosophy of lines” in art, architecture, and science. The book compares Western and Eastern traditions. It examines lines in the works of Paul Klee, Wassily Kandinsky, and Henri Michaux, as well as in Chinese and Japanese art and calligraphy. Lines are not merely a matter of aesthetics but also reflect the psychological states of entire cultures. In the nineteenth century, non-Euclidean geometry sparked the phenomenon of the “self-negating line,” which influenced modern art; it also prepared the ground for virtual reality. Straight lines, distorted lines, blurred lines, hot and cold lines, dynamic lines, lines of force, virtual lines… Lines narrate the development of human civilization.
Lines can represent realities not only through affirmation but also through negation. This idea has been developed by many Western philosophers and artists as well as by representatives of Buddhist and Taoist thought. Virtual reality is the last stage of this “adventure of lines.” Virtual Reality is not a random phenomenon enabled by advanced technology, but that it has been prepared over hundreds of years. But I also criticize the abstract space of Virtual Reality, which no longer offers a concrete place in which lines are embedded. There is no hand, no body, no gesture, no surface, and no environment. The instantaneously configured geometrical output of Computer Assisted Drawing leaves no traces. I show that some Western and Eastern philosophies offer alternatives and help us to think lines differently.
Wassily Kandinsky, Composition 8
Paul Klee, Highways and Byways
Much has been written about lines from an anthropological, philosophical, and scientific point of view. In this book I concentrate on the most peculiar characteristic of the line, which is its ambiguous ontological status. The twofold status of the line as both a physical fact and a concept grants the line a unique place in human civilization. The line is not simply empirically given but also an experience constantly developing future events out of its own past.
Despite the big advancements in geometrical presentations of lines, nobody (not even Euclid) attempted to give a serious definition of the line. While in mathematical terms, a line is a consecution of points, in non-mathematical contexts, lines can appear in many different ways. A line can be material, for example when it is represented by a string, or it can be non-material as in geometry. Lines can be mere thought products or closely linked to bodily action as it happens in calligraphy or in dance. A line can be visually (or acoustically) assumed though at the same intellectually challenged. Furthermore, lines produce spatial experiences not only in the one who draws them but also in the observer. However, as long as lines are produced or seen by humans, all lines have one thing in common: they require some form of spatial reasoning.
The adventure of lines that I describe consists in a process of self-negation through which the line – paradoxically – attains its full potential. How do we experience a phenomenon shifting back and forth between the material and the non-material? As the word “line” is often used in a metaphorical fashion, these questions concern not only art but also politics, science, and many other human activities. The procedure culminates in the phenomenon of the virtual line that is decisive for today’s virtual reality in which we go “online.”
“When I see the tiles at the bottom of the swimming pool through the depth of the water I see them not in spite of the water and the reflections, but rather through them, by them.” (Maurice Merleau-Ponty)
PART I: WHAT IS A LINE?
2. Strings, Traces, and Structures
What is a Line?
The Graphic and the Geometrical
The Idealized Line
Lines, Strings, and Structures
Western Lines and Eastern Dots
The Unbearable Straightness of Lines
3. Lines in Modern Society
McLuhan on Hot and Cool Lines
History is a Line
Linear and Non-Linear Science
Liquid Lines (Lines as Networks)
Part II: Lines: An Aesthetics of Disappearance
4. Differential Lines
5. Dynamic Lines
Henry van de Velde
6. Drawing as Thinking
The Lines we Draw
Drawing as Thinking
Lines versus Images
The Calligraphic Sign as Thought
7. Non-Euclidean Geometry
Euclid vs. Non-Euclid
The Line as Cognition: Fichte
The Non-Euclidean Revolution
Non-Euclidean Geometry and Art
God and the Map of the Universe
The Crisis of Geometry and the Crisis of Science
From Lines to String Theory
8. “The Movement that the Eye Cannot See:” Flexuous Lines
Bergson and Merleau-Ponty
Futurist Lines of Force
Further Developments: Rhizomes, Twistings, and Virtualizations
Traces and Deterritorializations
Twisting the Lines: Heidegger’s Verwindung
Virtual Lines in Virtual Reality
Part III: Living Lines of the East
9. Calligraphic Lines
Calligraphy and Chinese Painting
Lines, Traits, and Strokes
Vision and Bodily Presence
10. Organic Lines of the East
Lines and Surfaces
Alan Watts on Lines
Calligraphy as Thinking
11. Dream Lines
Ma and Kire
The Lines of Virtual Architecture
12. Two Kinds of Virtual Realities
Technical and Existential Virtual Reality
Most thinkers interested in this intriguing aspect of the line are working in the realm of aesthetics. Some approaches towards lines have become famous. Heinrich Wölfflin perceives the “depreciation of the line as a boundary,” and Maurice Merleau-Ponty sees lines as dynamic phenomena. Henri Bergson, whilst creating his philosophy of time, speaks of the line as of a succession of events. Ludwig Wittgenstein suggests that lines challenge the human intellect not through their blurred character but through a more sophisticated procedure of self-negation. More radically, Piet Mondrian believes that in his paintings lines “destroy” each other through an effect of mutual opposition. Finally, the French painter Henri Michaux relies on the “divestment” (désaisissement) of the line, that is, on the line’s “negative values.” For all these thinkers and artists the line is not simply present (abstractly or concretely), but its existence is linked to a complex ontology employing both affirmation and negation. This process culminates in the phenomenon of the virtual line. Virtual lines, which have no physical existence, are neither actual nor potential but still they are real because they can be intellectually assumed. They are not just appearances created by our imagination but acquire a new status generally called “virtual.”
A part of my analysis focuses on the use of lines in Far Eastern art and culture where a similar idea of the “self-negating line” is central. The line drawn in calligraphy has an ontological status similar to that of the “divested” or “negative” line that has been on the agenda of the above-mentioned Western artists. In East Asian aesthetics, the “self-negating line” is determined by Taoism but also by Buddhism, especially by the Zen-Buddhist branch.
Geography is the science of lines measuring the three-dimensional space of objects. “Cyberspace,” which is the space in which different pieces of Virtual Reality are imbedded, has no map because it knows no physical limits. In virtual reality, Euclidean geometry, which remains essential for any kind of geography, becomes non-Euclidean. Four-dimensional theories match perfectly well with the idea of Virtual Reality: time and space are configured through mutable lines that are constantly negated as “real” lines. I show that throughout human history, lines have always been – at least to some extent – virtual in precisely this sense. The latest stage of this development, which is virtual reality, must be seen as the accomplishment of a long process.
Paul Klee, Chambre habitée
Japanese architect Tadao Ando designs houses with labyrinthine structures in which “walls become abstract and negated.” Darell Wayne Fields invites us “to discover the lines that are the essence of Ando’s work – [which are] the lines that are not seen.” Though Fields finds that Ando’s manner of sketching is “more attuned to carving than to drawing,” he also states that Ando’s lines constantly fluctuate between “ideas of materiality and voidedness.”
Tadao Ando, Church of Light
Air Architecture (1961). Yves Klein was looking for a “cartography” able to make visible the invisible, and, paradoxically, he found it in the architecture of those elements that have neither lines nor clear limits: air, fire and water.
SANAA Glass Pavilion Toledo Museum of Art. Continuation of Yves Klein?
Rembrandt, Seated female nude, 1658
Albrecht Dürer, Female Nude, 1493
“The difference between Dürer and Rembrandt [is that] in the one case the masses appear with stressed, in the other with unstressed edges.” (H. Wölfflin)
Klee, Fleeing line
The rhizome has best been visually realized by a famous painter of errant lines: Jean Dubuffet. In his paintings called Recits (1974) and Non-Lieux (1984), Dubuffet explores the interweaving of auto-generating lines. These lines are also erratic traces because they are not submitted to the constraints of a preexistent shape but simply materialize the rhizome.
Dubuffet, Recits (1974)
Dubuffet, Fluence (1984)
Peter Schwenger: Asemic Writing.
Mondrian, "Composition with Large Red Plane, Yellow, Black, Gray and Blue" 1921,
A musical improvisation on Piet Mondrian. Click here.