Tom Hibbard


Linear/Nonliner: Simplifying the Complex

"...the act of measurement…cannot merely correspond to discovering
the numerical values of...various quantities.
" - Paul Davies

Two terms might be important down the road (or perhaps already are important) that in my opinion need to be considered. The terms are 'linear' and 'nonlinear'. The word 'nonlinear' is used in several contexts, most reliably at the moment in science. It has begun to be brought into aesthetics, which I think is natural and should be fruitful. The concept of nonlinear encompasses a lot. It's not a simple or instinctual concept and already has several specific associations.

McLuhan's Influence

One of the problems I want to bring out is that the term 'linear' as it still comes to us from the nineteen-sixties and seventies is so vague and overused that it misleadingly affects the general impression of the meaning of the term 'nonlinear'.

The term linear is deeply affected by the writings of Marshall McLuhan. I've expressed reservations about this many times, and every time I feel I learn more and see more in the discussion. Certain ideas in McLuhan indicate a variety of directions that could be taken from his writings. The idea that 'the medium is the message' seems excellent and quite true. As McLuhan expresses it,

What we are considering here, however, are the psychic and social consequences of the designs or patterns as they amplify or accelerate existing processes. For the "message" of any medium or technology is the change of scale or pace or pattern that it introduces....

This idea that the mode of expression affects the direction of the thoughts is analogous to the notion of Marx and Engels that social institutions as they developed in history shaped human behavior and consciousness.

McLuhan doesn't merely argue that the medium is the message. He goes on in his works to express the idea that the (then) new electronic media constitute a breakthrough for the senses, one that brings people together in a more vital, visceral, 'uninhibited' and 'tribal' (more natural) way. In contrast, he finds the old medium of the printed word, its forms and patterns, to be--without prejudicing my argument--overly intellectual, elitist, mechanical and limiting. It is the appearance of words on the page that leads to his pronouncement of writing as 'linear'.

To be sure, McLuhan's argument, influenced by books such as Freud's Civilization and Its Discontents and Spengler's Decline of the West, goes beyond the arrangement of words on the printed page. McLuhan discusses the phenomena of nationalism and privacy which he relates to the medium of books. He talks about uniform appearance, about literacy, about the unconscious, about privilege and class. He contrasts writing to music and discusses speed, participation and tactile freedom as virtues associated with the newer media. McLuhan gives little credence to the virtues of artificiality and consciousness.

But McLuhan sometimes startlingly furnishes evidence that goes against his own arguments. One of the primary examples of this is his books themselves. McLuhan criticizes civilization, knowledge, literacy, but his books, despite the sometimes self-conscious poetic speculativeness in their style, are extensively literate, scholarly, professorial. In the first chapter of Understanding Media, McLuhan invokes no musician or painter but Shakespeare, Walt Rostow, John Kenneth Galbraith, Arnold Toynbee, David Hume, Alexis de Tocqueville, Cardinal Newman, E.H. Gombrich (an essay titled Art and Illusion), E.M. Forester, C.P. Snow and C.G. Jung--to mention only a few!

McLuhan credits those under the spell of what he himself describes as (in a special context) 'semantically meaningless letters' with inventing individualism and says of them, 'To act without reacting, without involvement, is the peculiar advantage of Western literate man'. This is not only a 'peculiar advantage' it can easily be construed as an admirable and long-standing quality of character, a virtue, the definition of responsibility, judiciousness and intelligence itself. It also leaves McLuhan's 'tribal man' open to the charge of being 'reactionary', that his heightened senses and unconscious actions are subject to emotionalism and the herd mentality. Many have said the new media have turned out to be merely a mass media, not better than the old media but worse.

McLuhan's writings, admirable and interesting, seem to approach the 'old' medium of writing and language from the point of view of the new media which he favors. He doesn't apply his dictum in any creative or constructive way to the printed word. McLuhan's writings appear directed at academia and do not consider newer, contemporary interests and writers, such as Sartre, Robbe-Grillet (the new novelists) Roland Barthes (Degree Zero of Writing, 1953), Chomsky, Derrida (the growing field of linguistics) and many others. McLuhan does not even mention Wittgenstein. To return to the notion of 'linearity', this notion simplistically presented by McLuhan, which Derrida doesn't bother to address in a book such as Writing and Difference (1967) for example, pervades McLuhan's writings, the idea that the straight horizontal lines of written language are the primary and damning message of the 'aggressive' 'high-brow' language medium. McLuhan's idea seems in another world from writings about 'articulation' 'structure of consciousness' 'the logos' the 'trace' 'tissue of meaning' 'the text of my body' 'the scene of writing' 'the differentiated duration and depth of a stage, and its spacing'. Writing, in any case, could only be metaphorically 'linear' since scientists say there is no such thing as a line and call the idea a 'fiction' (a medium in itself). Lines of type are irregular and have an intricate sequencing, a sequencing of which McLuhan himself says (in citing David Hume), 'There is no principle of causality in a mere sequence. That one thing follows another accounts for nothing'. If it accounts for nothing it hinders nothing. In other words, sequence then does not have the limiting effect that McLuhan tries to imply with the term linear, especially in relation to the key concept of causality.

The German painter Ludwig Kirchner, as he developed in the artistic style known as expressionism wrote,

...observing movement excites my pulse of life, the source of creation. A moving body shows its different partial aspects, which then fuse in a complete form; the Internal Image. [I] discovered that the feeling that pervades a city presented itself in the qualities of lines of forces. A purely linear scaffolding with almost schematic figures nevertheless represents the life of the streets in the most vital way. (italics added)

To me, Kirchner is using the term 'linear' in a much purer and more sophisticated way. Line is associated with movement, life and basic structure. The painting of his that I attach to this quote is a remarkable and prophetic painting of a post-World War I German street scene that in its dim colors, especially an unreal and out-of-place light green (a painted presence of physical light), gets at the darkening mood of the scene and makes it as seen by the artist from a vantage outside the action.

We are reminded by Kirchner that linear doesn't simply mean 'in a line', nor does it mean one line but can refer to several lines or many lines--an infinite number of lines, lines parallel or intersecting or perpendicular to each other, lines in three dimensions. Nor is there any reason to confine linear to referring only to straight lines. Linear can mean 'curvilinear' referring to curved, to spiral or to any assortment of otherwise non-rectilinear, non-straight lines. Linear is not relegated--as I think is generally the intent in current usage--to confining thought patterns. The complicated discoveries of early 20th century physics belong to the realm of linearity. Einstein himself believed that the end of physics would be geometric and symmetrical.

In my opinion, the general meaning of the term linear, in its fullness and without attempting to use the word in a demeaning way, is visible. The visible world can be characterized as linear.

Basic to McLuhan's ideas is his contrast of the written word to the experience of viewing films:

The message of the movie medium is that of transition from lineal connections to configurations.

In comparing, McLuhan seems to consider the medium of writing a visual medium ('...writing is only the principle manifestation of our visual senses'.) But this is not really the case. If you compare the printed page to a wonderful painting, a light show of bright moving colors or a photograph or any sort of picture, the light show and picture are, obviously, more interesting visually. But this is not a fair comparison. Writes Wittgenstein (in the 1930s), 'What a picture tells me is itself'. What language tells is something other than itself. Language characters, letters, words have evolved in such a way that they have negligible visual in the sense of pictorial meaning on a page. In doing this, they serve better as words. We do not stop to consider their forms. The meaning they carry uniquely functions within the verbal medium. The word 'car' does not look like a car. Its purpose relates more to the system of writing. So that the cursive, neutral, black-and-white, non-pictorial (still acausal) printed word springs to life as a thought, a connection, a conceptual image or series of images moving in the fantastical, varied, psychic, virtual, administrative place known as the mind.

In other words, the qualities of language that McLuhan decries as linear are only part of the medium of writing. Only if you consider writing a purely visual medium can you call it linear, which, in my view, is somewhat obviously not the case. What is more, the mundane uniform visual qualities of writing which McLuhan describes so well are the very mechanism that produces the virtual referential cognitive meanings that language has. The limited appearance of the written medium is the means through which it becomes an infinitely complex system.

The printed word is ordered, unobtrusive, not pictorially familiar; it is generally horizontal, sometimes read from left to right, sometimes from right to left (the difference is mere convention and unimportant, like the difference between French and English words). (Language is not always horizontally arranged; certain forms of Chinese, Japanese and Korean languages are read vertically.) The printed word is an unknowably extensive system of rules, symbols and autonomous changing definitions. The words are generally confined within margins on a page, often of standard size. Visually, the written word is not linear in Kirchner's sense but something much, much less--organized, systematic, confined and standardized. (Scattered on a page words do lose their meaning as words and sentences and become merely visual.) Admittedly the visual arrangement writing on a page could be called 'linear' or 'lineal' (perhaps 'symmetrical' would be more accurate), but relegating the medium of writing to a monarchical seventeenth-century mode of thought based on this observation is seriously misleading. The appearance of the words is linear, but the medium itself is not. (Early twentieth-century literature, writing of Faulkner, Joyce, Svevo, Pound and others, did much to advance the quantum conception of the universe.)

Those that call the medium of writing linear, from my vantage, proceed to define nonlinear as visual complexity--along the lines of McLuhan--similar to film for example. But, as far as I understand it and envision it, nonlinear doesn't mean visual complexity. It means non-visual. It means conceptual or cognitive. It refers to the realm of consciousness that is detached from visible reality. It refers to calculation, measurement, to solutions of problems that are beyond visualizing. It describes, in the instance of writing, the experience of reading in its totality which only begins with the words on the page. Strictly speaking, the printed word is not linear but a nonlinear system.

* * *


It's fascinating the way ideas from one discipline can sometimes fit with another. In an early part of his book Hyperspace, Michio Kaku recounts that the idea of the fourth dimension became popularized in the late nineteenth and early twentieth century. Psychics communicated with ghosts in the fourth dimension. Magicians defied the properties of nature. Edwin Abbot wrote a novel titled Flatland: A Romance of Many Dimensions by a Square in which he used the fourth dimension as a way of criticizing rigid thinking. Monsters attacked earth from the fourth dimension. H.G. Wells used the fourth dimension (which he called 'duration') in The Time Machine to put forward his ideas regarding class struggle. Even Lenin was obliged to defend communism from the possibility of multi-dimensions. When Einstein gave the fourth dimension an actual meaning, the measurement of time, which he linked with space, philosophers and writers were obliged to move out of reach of science to the 'nth' dimension.

What is relevant about Kaku's book is that, in his attempt to outline the idea of hyperspace, he writes,

'Higher-dimensional spaces are impossible to visualize'.

In the book The Matter Myth, Paul Davies and John Gribbin consider directly the meaning of the term nonlinear. They write, 'In physics, a linear system is, simply speaking, one in which the whole is equal to the sum of its parts...The sum of a collection of causes produces a corresponding sum of effects'. Nonlinear systems are affected by phenomena that are uncooperative with natural laws. These phenomena can be as simple as friction or as complex as the fundamental uncertainty of matter as described by Heisenberg's magnificent uncertainty principle. 'When nonlinearity becomes important, it is no longer possible to proceed by analysis, because the whole is now greater than the sum of its parts'. The writers state that nonlinear systems are difficult to understand using mathematics. And, 'Generally speaking a nonlinear system must be understood in its totality'. Nonlinear generally deals with wholes.

This burgeoning study of nonlinear systems is causing a remarkable shift of emphasis away from inert "things"--lumpen matter responding to impressed forces--and toward 'systems' that contain elements of spontaneity and surprise.

Davies, author of the excellent book Other Worlds, presents the nonlinear system as a nonvisual and sometimes non-schematic dimension of conceptualizing, average, probability (and improbability), estimate, measurement, creative understanding. The basis of Newtonian physics is cause-and-effect. But in the late 1800s in France scientists confirmed what probably most people had already begun to suspect: not everything happens for a reason. The discovery of radioactive decay and radioactive particles showed that there are phenomena that are entirely unpredictable. Quantum scientists showed, in many ways, that this inability to predict was not due to a lack of sensitive enough equipment. It was due to a fundamental inexplicability. Equations describe phenomena, but they only furnish a reliable probability; they are never exact. In its totality, nature is ordered but inexplicable.

Nonlinear systems can display a rich and complex repertoire of behavior, and do unexpected things--they can, for example, go chaotic. Without nonlinearity, there would be no chaos, because there would be no diversity of possible patterns of behavior on which the intrinsic uncertainty of nature could act.

Does this mean that language, especially written language is nonlinear? I think writing is nonlinear. I think that the conventional arbitrary man-made cursive marks that form words and sentences amazingly produce an infinite completely non-visualizable universe of meanings, concepts, thoughts, activity the sources of which cannot be known and the diversity of which is unending--this despite the fact that words can also be extremely practical, precise, clear and imperative. I think that computers enhance this nonlinearity, because writing on a computer screen means that not only are the thoughts produced in a virtual, non-visualizable realm, but the print itself is also in a virtual realm that has no physical existence (except perhaps as an instantaneous spark flowing at the speed of light inside wire circuitry). The information highway exists in an entirely different realm from the interstate highway. (It could be said that the martyrdom of the Twin Towers turned its existence from linear to nonlinear.) From The Matter Myth: 'In many cases the same basic nonlinear phenomena are manifesting themselves in systems that are not really material at all, including computer networks and economic models'. Or language.

For me, this is the point I am getting at: Linear refers to the visible world. Nonlinear, of which writing is a part, puts together parts of the visible everyday world, parts of the psychological, mathematical and philosophical worlds into an important dimension of conceptual understanding that is primarily interested in wholes. Nonlinear is an escape from visibility. Nonlinear is not myopic; it envisions. It can be sketchily schematic. It solves problems at hand by getting outside local contexts and bringing in missing information. It digests the logistics of tasks that cannot be solved by merely looking at them. It measures interstellar distances. It fathoms subatomic activities and quantities. It accommodates geologic time periods. It appreciates and remains calm in the face of pandemic and global transformations. It 'sees' imaginatively by piecing seemingly unrelated entities together.

* * *

Visual Writing

The written word (on the page) is non-visual in the sense that objective pictures from the world do not appear in it. The evolution of writing has been away from markings that resemble animals, geometric shapes, symbolic diagrams and so forth. (Ezra Pound in The ABC of Reading made the case for returning to pictorial references in languages in hopes of getting away from abstraction. Pound believed illustration and examples had more impact. Of course Pound's Cantos are strongly intertwined with the development of abstract art.)

The written word (on the page) in another sense is entirely visual, keyed entirely on well-recognized cursive marks in various styles presented in organized patterns on various sorts of surfaces. It is these visual qualities, uniquely associated with language, as they have become recognized, that form the basis of 'visual writing' since its beginning in the early 20th century. Writing tools and writing machines such as typewriters, early printing presses, hand-set type, legalistic forms, ancient archeological texts and scripts, casual handwriting, varieties of calligraphy offer ways to present meanings in artworks associated with language to convey certain messages about the importance of communication, society, books, art, laws, meaning and meaninglessness, morality, system, creativity, consciousness, vision and many other things. Language is explored as a symbol of humankind and its activities, especially its history (and future).

Visual writing of this sort, artworks using language symbols as their primary content, has blossomed into a wonderful body of work. Venerable oversized hand-painted letters are viewed from impressive lopsided fonts. Letters and mathematical symbols sail on stormy elemental seas of paint or ink marked with diagrammatic or commercial mythic monsters of the deep. Subatomic models are formed from letters instead of electrons, as in work of Jukka-Pekka Kevernian (whose early blog name was NonLinear Poetry) and John Bennett. Cursive marks of half-formed alphabets of future millennia float like clouds of undulating miscellaneous spatial meaning. One work from a recent exhibit has a double-set of writing lines superimposed on each other, of two distinct colors, to symbolize a duality and contradiction in language analogous to the uncertainty of matter. Words like 'dog' and 'spot' are scratched on ultra-simplistic children's wide-lined paper. Writing appears as an ancient map or as geological layers. Writing is mixed with human hands and faces. Word fragments appear as prehistoric fossils or in collective unconscious dreamscapes. Colorful realistic logos are propagated.

Visual writing has roots in abstract art. Following World War Two, as it began to contemplate the phenomenon of fascism and related phenomena of the fifties, the art community began to reject familiar pictorial visual imagery. In the tradition of earlier abstract art, it reduced traditional content into less recognizable, more essential elements. In extreme instances no visual content was offered at all. In the more successful of these, such as Ellsworth Kelly's smooth surfaces of one bright color, the absence of content posed not merely a puzzle for the viewer's imagination to follow but became highly referential, suggesting and alluding to the mind of the viewer itself along with the problem of understanding it. The more minimal the artwork the more referential it became.

Recently, from the influx of minimalism and 'absence', a type of visual writing has grown that hearkens more to the idea of language as a nonlinear system. This work forgoes surface success and beauty. It can look ominous or despairing or simplistic or it can contain an endless visual complexity of computer or mechanical typographical images. Often it is done in black-and-white rather than in pleasingly composed color schemes. It appears incomplete, somewhat senseless or random, ragged and unhealthy, with missing elements. The missing compositional elements in this type of work make it strongly referential to an unpictured conceptual (perhaps future) world of well-being and peace. As is the case with abstract art, the visual success of an artwork can hinder its ability to gain a meaningful response. This is illustrated in some works by Carol Stetser (inky menacing phantoms) or Al Ackerman (whose recent works are divided into half writing and half blank space). The visual world is only a part of existence, its visibility only part of the sometimes more important meaning that is not and cannot be viewed. I would say that these types of referential works are more nonlinear than an artwork that presents a self-complete visual image. They exist more in the hyperspace of nonvisualization.

There is another way that a certain type of absence in visual writing can become strongly referential and nonlinear. With the given that the basic element of visual writing is language and language material, any purely pictorial element introduced takes on an interesting meaning. It becomes a missing text, something unexplained, a problem unsolved, a discourse as yet unopened. Some of the best examples I've seen of this are recent works by Derek White and Wendy Colin Sorin in which appear, among other things, a native tropical island girl's face, bright-colored exotic birds and kidney beans. These images contrasted with letter-like glyphs, mathematical symbols, swatches of color, anatomical parts and other collage elements introduce into the works interesting subjects such as exclusion, sadness, perhaps jealousy or anger, forbidden subject matter, self-suppression, parts of life that cannot be discussed but remain inherent and vital.

Some crude earlier Xerox copier collages in which appeared (along with bodies of text) black-and-white beetles were the first instance I saw of this type of symbol used. Some recent vispo by Jim Leftwich, whose work always searches for innovation and variations on elements of visual writing, is composed entirely of visible objects without any text, representing it would seem a subject on which much needs to be said (or little is capable of being said) (or all has been said).

* * *

There are some odds and ends that can be brought into this discussion. For one, I was recently reminded that probably the pinnacle of German Expressionism was reached through black-and-white works mainly done from pre-World War I woodcuts. This raises them in my estimation. The black-and-white artwork conveys the present-day world and references more dramatically the invisible values and beauty of the complete and colorful ideal spiritual world.

German Expressionism was greatly affected by the breakthroughs in physics made at that same time. Painting began to move beyond nature studies toward representing the nature of reality. The ideas of infinity and space-time, I want to say, complicated as they are belong with reality and visibility and, thus, linearity. Presumably black holes are real thing. Yet they revolutionized the mind. To repeat: the complexity of the visible world is not what is meant by nonlinear. Nonlinear is measuring and generally trying to understand that complexity conceptually as a whole.

* * *

Also, odd-and-end: Another type of current art that seems to me nonlinear is paintings with cartoon figures in them. A recent gallery exhibit had an artwork that included a cartoon rabbit imposed on a jumbled inky tangle which seemed an archetypal image. Superman, certainly conceptual, combines a mixture of both physical and mental faculties of heroic though everyday people into what is a nonlinear representation of the powers of virtue in toto. Also, it seems to me that the plain art of collage (such as is practiced by Belgian artist Luc Fierens) is nonlinear in the way it combines dissimilar elements like text with crowds of people with wallpaper designs with dishwashing liquid brand names to produce what might be called a super- or hyper-reality.

* * *

Another recent example of the nonlinearity of visual writing is from Miekal And's collection of Logokons. The work, titled 'astral goat', is simple, black-and-white. It's visual qualities do not refer primarily to the real world but seem rather to refer to letters, diagram, structure, strength, architecture --attractive attributes from many realms (which overall resembles a schematic armored architectural insect on wheels). What struck me in this particular work were the step-like diagonals ascending like antennae from the main structure. These steps are similar to certain well-known trompe l'oeil (fool-the-eye) artworks in which stairs in square castle ramparts always appear to be ascending. Trompe l'oeil has much in common with nonlinear. Recent exhibits of sculptings of Degas and Duane Hanson seem to argue that anything that is visible, especially the human body, is a trompe l'oeil because of the essential spiritual components that are beyond seeing.

* * *

The most pristine examples of the convergence of visual writing and the nonlinear nature of written language are in the artworks of Agnes Martin. Generally employing horizontal lines, etched in stone like side-by-side ancient writing characters or mechanically ruled on a cloudy white-painted canvas, Martin's minimalism exactly parallels the inter-relation of the visible aspect of writing with the universe of its cognitive meanings.

* * *

We speak of the world as having three dimensions. It seems that science is leading toward a redefinition in which the three dimensions become 1) the visual 2) the temporal and 3) the conceptual or cognitive.

* * *

An oriental saying quoted from Sartre is "My eyes lie to my soul'. At least writing, text upon standard letter-sized paper, that might discuss anything and everything visibly existing in the universe, that might discuss many things that do not visibly exist, such as mediational conceptualizing, explanation, a body of knowledge, emotions, dull and simple as it appears, has the capacity of speaking truthfully to our poor deceived and beleaguered souls.