By Amy Clanton
“…the fundamental issues confronted by any civilization in its history,
or by any person in his or her life are issues of meaning.”
–Morris Berman
Science and art. Science and religion. To the modem mind these are pairs of opposites; their duality seems obvious. Different disciplines, different functions, different methods, different purposes. The key here is that these distinctions are recognized by the modern mind. But are these differences inherent?
Before the birth of modem science the world was seen as a living, magical place. Art and religion provided meaning in the presence of overwhelming Nature. Nature engulfed us. We experienced ourselves as a part of it. Art and myth explained the “Whys” of the world. This world view is what Morris Bennan calls “participating consciousness” in his book, The Reenchantment of the World. This consciousness was formed by images rather than concepts. (Berman, 73)
With the emergence of modern science, the concern with why shifted to an overriding need to know how. We began to stand apart from the Nature that once contained us. We began to observe dispassionately. Experimental science removed things from their context to be looked at objectively, unhindered by extraneous variables. Each thing was dissected, reduced, atomized to its barest essentials.
The affective qualities of the world that had been evident in our animistic, pre-modern culture were ignored by science. The quantifiable attributes of things became all that mattered. Nothing could be more than the sum of its parts. Eventually, quantifying and reducing became such a successful method for explaining Nature that it became the only right way of seeing anything. This resulted in the attitude that if a question could not be answered in this way, it was not even worth asking. The question to be answered became, “What is it?” rather than “What does it mean?”
According to this world view art was frivolous, unreliable, suspect. “The arts are based, at least in part, upon myths, superstition, on that religion which is the opium of the people… relics of.. ‘the magical view of life.’ Science, by contrast, is the living example of reason in all things.” (Henn, 4) This opinion, written in 1967, is only a recent example of the modern attitude toward art. Its origin actually traces back to long before the scientific revolution. Plato believed art corrupt and degenerate. Human-made images were copies of copies, too far removed from their ideal forms. “At the bottom, Platonism is an appeal to substitute a conceptual discourse for an imagistic one.” (Eric Havelock, in Berman, 72)
What place does art have in a world that sees images as illusory and irrelevant? What can be the role of a discipline whose methods are subjective: a practice that seeks to describe the qualities of things rather than to quantify them? Is art truly as separated from science as the Cartesian duality would have us believe?
Art is a discipline with its own terms and methods, but it is not disconnected from science. In fact, art is intertwined with more different fields of study than perhaps any other. This is because art is the creation of meaning. Art can take what the sciences discover, hypothesize, quantify and prove and interpret it for humanity; art can give knowledge purpose.
Art is a visual image, object, process, or experience that expresses and creates meaning for the artist or viewer. (1) This can include the meaning intended by the artist as well as any meaning later interpreted by others. Meaning is created by both the artist and the viewer. It is not static– it changes through time. “Now the possibility of there being a right reading or interpretation has given way to the prospect that there may be multiple interpretations of the meaning of a work of art.” (Neperud, 36)
Art is created and viewed within the context of time and culture. This context can directly or indirectly influence the artist. Sometimes the relationship between the art work and the greater world of events and ideas is not purposely undertaken by the artist, but is later interpreted by the viewer. This makes the relationship between art and its context no less valid. An example of this was the critic Paul Laporte’s reading of Picasso’s work as being influenced by the Theory of Relativity. There are arguments for and against Picasso’s having intentionally chosen Relativity as the content of his early Cubist works. However, in the end, Picasso’s original intentions are not as important to the viewer as the meaning the viewer finds in the work. Whatever Picasso’s intentions, the art was created and viewed (by Laporte) in the context of the early 20th century when Relativity was an important new theory.
An artwork is more than the sum of its formal elements and the intentions of the artist. The context of a work of art gives it a life of its own. It will acquire successive layers of meaning from every viewer and every artist who creates work after it. An artwork cannot be reduced to its elements and principles and be completely understood.
Any work of art is probably most meaningful for the artist. Through being engaged in the process of creating art, the artist creates and experiences its meaning. The artwork can never have the same meaning to the viewer as it does the artist when the viewer is not part of the creative process. Creating is a mystical, participatory (to use Berman’s term) way of knowing. The artist does not stand outside and objectively observe what he or she creates. Creation is like a conversation between the creator and the created: it is a give and take through which both are transformed.
The definition of art I have proposed can be called Postmodernism in the reconstructive sense. This is unlike Deconstructive Postmodernism which is an outgrowth of the traditional scientific method: a seemingly valueless system of taking things apart to see how they work.
In contrast, Reconstructive Postmodernism (first proposed by Suzi Gablik in her book. The Reenchantment of Art) “seeks to overcome the modern world view not by eliminating the possibility of world views as such, but by constructing a postmodern world view through a revision of modern premises and traditional concepts. This constructive or revisionary postmodernism involves a new unity of scientific, ethical, aesthetic and religious intuitions.” (Griffin, x)
If this new Postmodernism seeks to unite science, art and religion, a valid question is: how truly different are these things? Although they have different methods, are their purposes in the broadest view truly dissimilar? All of them attempt to describe and explain the world. It is true that art and religion attempt to explain why things are and science to describe how they work. However, in an anthropological sense (that is, the way they function in our culture) these differences may be less significant than their similarities.
The anthropologist Clifford Geertz defined religion as “a system of symbols which acts to establish powerful, pervasive and long-lasting moods and motivations in men by formulating conceptions of a general order of existence and clothing these conceptions with such an aura of factuality the moods and motivations seem uniquely realistic.” (Geertz, 79) Undoubtedly, science can fit this definition as easily as religion. Science is symbolic. It does not show what nature truly is any more than mythology. Science explains phenomena through the use of models just as mythology explains through the use of metaphor. (2) Thus, light is both a particle and a wave. It is also neither! The concepts of particle and wave are metaphors for what cannot otherwise be described. These metaphors exist not because the universe cannot be known, but because it cannot be directly described. In accordance with Geertz’s definition, religion and science can be seen as systems of symbols that perform similar functions in society. Although art is less organized or systematic than science or religion, it also uses symbols to formulate and express conceptions of reality.
Seeing science as another set of symbols or metaphors for describing the world helps to close the gap between science, religion, and art. Viewed in this perspective, science does not hold a monopoly on truth. In creating and expressing reality, it performs the same function as religion and art. However, aren’t the realities they express still diametrically opposed? Aren’t their purposes and methods still far removed? Can we reconcile the how with the why? Doesn’t traditional science still takes things apart to quantify them while art seeks to discover the purpose and qualities of things by putting them together? Isn’t science still objective and art subjective?
The answers to these questions are changing. Science is finding limits to what can be discovered through objectivity. The new sciences of quantum physics and chaos theory question the very possibility of man as an objective observer. The once great chasm between art and science is narrowing every day.
My recent art has been a process of linking science and mystical religious tradition. The symbol I am primarily exploring in my art is the Tree of Life of the ancient Hebrew Qabalistic tradition. This symbol is comprised of a geometric structure of ten circles (called Sephiroth from the Hebrew word for spheres) connected by twenty-two lines (called paths). Each Sephira and path has numerous meanings and correspondences. The Sephiroth correspond with the numbers one through ten and the paths with the twenty-two letters of the Hebrew alphabet. Together, the Sephiroth and the paths are known as the Thirty-two Paths of Wisdom. The Tree of Life is essentially a model of the universe as well as of man.
The prototype of this Tree is found in Babylonian culture. In approximately 1500 B.C.E. the Babylonians had a Tree of Life with thirteen fruits interconnected by paths. In 450 B.C.E. the concept of the Tree was recorded in the Torah. Sometime between 200 and 900 C.E. the Sepher Yetzirah or “Book of Formation,” was written. This further developed the Qabalistic school of thought. In 1200 C.E. Moses de Leon based his work, the Zohar, on the doctrines of Simeon Ben Yohai who lived in approximately 150 C.E. The symbolism of the Tree has since been expanded by many outside the Jewish tradition. It has been corresponded with Asian systems such as the I Ching and East Indian and Tibetan thought as well as the Western Masonic and Hermetic traditions. (Hulse, 35-37)
As Above, So Below
This tenet of Hermetic philosophy indicates the holism of the universe. What is found in the greatest view is also seen in the smallest. The Tree of Life’s apparent similarity to a molecular model is significant. The Tree is a model for the Microcosm and the Macrocosm. It describes the structure of Man as well as the universe.
Although each Sephira represents a different circle or sphere of the universe, the Sephiroth are intertwined and connected by the web of paths. Each Sephira is a connected part of the whole. Each Sephira contains all of the others. Malkuth (the bottom-most Sephira) is in Kether (the upper-most) and Kether is in Malkuth.
The structure of the Tree is said to contain a duality between the Pillar of Mercy on the right side of the Tree and the Pillar of Severity on the Left side of the Tree. However, rather than being opposing forces, the sides of the Tree represent complementary energies that give and receive from each other. This is similar to the Eastern concept of Yin and Yang. The journey through the paths on the Tree cycles between expansion and restriction, and masculine and feminine energies. The seed of each of these is found within the others. The alchemical paradigm “has as a central tenet the notion that reality is paradoxical, that things and their opposites are closely related.” (Berman, 82) This wholeness and unification of opposites is symbolized by the Ourobouros, the snake eating his own tail.
In 1961, the meteorologist Edward Lorenz discovered what was to be the beginning of the study of chaos: that the most minuscule differences in initial weather conditions would cause extreme differences in the outcome of weather predictions. Because the slightest change in temperature, air pressure, wind direction, or any other of a million variables will throw a prediction off course in a matter of days, long term weather prediction is impossible. This is because of the complexity and interconnectedness of dynamical systems like the weather. Each element affects all the others in a pattern of causation that is more like a web than a string. There are so many causes, so intricately and intrinsically woven, that even if every action, every minuscule event were recorded in the most powerful computer, a result could not be predicted, for even the act of predicting would alter the result. “Dynamical systems imply a holism in which everything influences (or potentially influences) everything else. ” (Briggs, 21) Thus, such a system (like the weather or an ecosystem or even the economy) is whole and not simply a collection of separate events: “…because everything is in some way constantly interacting with everything else…, the study of chaos is also the study of wholeness.” (Briggs, 21)
The alchemical phrase Solve et coagula “meant reduction to chaos — watery solution, a primal state — followed by fixation into a new pattern.” (Berman, 89) To the alchemist, this was not just a process applied to metals in order to transform them into gold, but a process applied to one’s own self to transform the soul into spiritual gold. The process of destruction and rebirth in a new form is a universal religious symbol. This metaphysical cycle of chaos to order (and back again) mirrors the natural one.
Dynamical systems often cycle between chaos (unpredictability) and order. For example, the population of a species of insect will fluctuate in a predictable pattern for a period of time and then suddenly shift into a period wherein the population of each successive generation will be completely unpredictable. Just as suddenly, the cycle will seem to “reset” itself and continue in a predictable pattern until it again reverts to chaos. This cycle, called a bifurcation pattern, is found in many systems. M. Mitchell Waldrop gives an excellent example in his book, Complexity. “The drip-drip-drip of water from a leaky faucet, for example, could be as maddeningly regular as a metronome– so long as the leak is slow enough. But if you ignored the leak for a while and let the flow rate increase ever so slightly, then the drops would soon start to alternate between large and small: DRIP-drip-DRIP-drip. If you ignored it a while longer and let the flow increase still more, the drops would start to come in sequences of four– and then eight, sixteen, and so forth. Eventually, the sequence would become so complex that the drops would seem to come at random– again, chaos.” (Waldrop, 66)
The upper Sephiroth on the Tree each has a traditional geometric significance. Kether, the top-most Sephira which is the Crown and the Source of All, corresponds with the point. The second Sephira, Chokmah, corresponds with the line. Binah is the plane, and Chesed is the three-dimensional form. Geburah is movement. The point, line, plane, and form correspondences of the Tree arise from Euclidean geometry and the traditional Platonic aesthetic. These are “pure,” ideal forms. They are appropriately assigned to the uppermost Sephiroth on the Tree which lie beyond manifestation.
In artistic terms, this is similar to the Modernist aesthetic which saw art media as similar ideal forms: paintings were always to be flat, sculpture to have form and texture but not color, etc.
Although the Tree presents itself at first as a group of regular geometric forms, in conception the Tree is actually fractal. This is because each of the Sephira is said to contain another entire Tree. Inside each of these is another, and so on to infinity. Thus, the Tree is self similar. Additionally, the shape of the Tree when viewed in perspective (as I have shown in my artwork above) is reminiscent of the shape of the Mandelbrot Set (below). Philosophically, the Tree is as infinite in meaning as the Manbelbrot Set is infinite in detail.
Paradoxically, as complex as dynamical systems are, they can be modeled by relatively simple mathematical equations. This was discovered by the mathematician Benoit Mandelbrot in the 1960’s and 70’s. He explained this relationship between simplicity and complexity with a new kind of geometry which he called fractal geometry.
Now science has long used math (and geometry in particular) as a way to model nature. However, Euclidean geometry with its regular Platonic forms could never quite compare with Nature’s complex shapes. Not surprisingly, this was seen as a deficiency of nature rather than a limitation of mathematics. Mandelbrot’s fractal geometry, however, is not based on the linear equations that Euclid used. Computer generated fractal images are created using non-linear equations and the resulting shapes are vastly different from the Platonic solids. Fractals spiral, curve, twist, and radiate in ways that qualitatively imitate the irregularity of nature. These forms are not symmetrical in the traditional geometric sense, but exhibit a kind of symmetry called self-similarity.
Self-similarity is the basic symmetry of nature. It is the repetition of shape at different scales. For example, the smallest twig of a tree repeats the basic form of the entire tree. The shapes seen in a mountain repeat themselves in different scales down to the smallest pebble. The rough shape of a coastline is repeated again and again in smaller sizes no matter how closely you look– even at the microscopic level. Computer generated fractals are also self-similar. Mandelbrot’s most famous fractal, the Mandelbrot Set, repeats its own image over and over at different scales the deeper into it you go.
It is appropriate that the Tree as a whole corresponds with non-Euclidean geometry through its fractal nature. But can non-Euclidean, non-linear geometry be said to originate in any one Sephira on the Tree?
Fractals are modeled by non-linear equations. These equations do not give a single answer, but a multitude of answers which in turn become part of the question. Iteration is an equation in motion. The numbers of it do not sit still. Seldom do they end in a single answer, but instead they dance, skip, and jump. The answer might move carefully and slowly or it might race with abandon, but the equation never sits still. It is this quality of motion which leads me to place the essence of fractal geometry in the Sephira Geburah.
The nonlinear mathematical process by which these fractals are created is called iteration. An equation is iterated when its answer is plugged back into the equation and this process is repeated numerous times. Therefore, the answer to an iterated equation is actually a set of answers. This set can behave in several different ways. It can escape to infinity at varying rates, It can bounce back and forth between two or three or more answers, or it can behave chaotically: never repeating or escaping to infinity.
Fractal images are generated in the computer by using the pixels on the screen to represent points on the complex plane. The numbers represented by each point are then used as the basis of an iterated equation. Each pixel is assigned a color based on the behavior of the equation’s set of answers. The resulting images are unspeakably beautiful.
The result of this new science is nothing less than a new scientific paradigm. Human knowledge, like the snake eating its tail, is coming full circle. Science is beginning to realize what art and mystical religion have expressed since pre-history. With the scientific realization of wholeness, scientists no longer limit themselves to trying to reduce things to the simplest parts. The parts of a whole, through their complex dance of interaction, create something more than the sum of themselves. Like art and religion, science is beginning to create the understanding that knowledge can be gained by joining with that which one wants to know. Science might be beginning to balance the cognitive with affective ways of knowing.
The new (and old) model of the universe is an organism rather than a non-living machine. The re-realization that we are part of Nature and the discovery that Nature is ultimately unpredictable and will never be entirely ours to control will hopefully lead to a science (and culture) which molds itself to Nature’s needs (which are ultimately our own) rather than forcing Nature to conform to its.
Up to this point, this has been a discussion of ways of knowing. But what are the ramifications of the preceding discussion on ways of teaching and learning? Art has always been a way of learning through experiencing. As a method of visual and intuitive learning, it supercedes all other fields. However, understanding is attained when knowledge is placed and applied within context. Students need to see that art is a part of the world in which it is created; they need to understand the context of their own ideas. Therefore, learning about art involves more than simply making things. Wholeness implies a dynamic balance and interaction between the affective and the cognitive. An art student needs to discover not only how to create, but why. Why do artists create? How is their art influenced by the world around them? What does art mean?
It is important for art educators to teach students the skills they need to create art. It is also important for students to develop the vocabulary needed in order to discuss art. But one truly learns when one creates knowledge rather than simply receiving it. Teachers must provide a structured environment in which to guide students in their personal process of discovery. Questions of meaning do not have a single answer. There are as many answers as there are artists.
Notes:
1. I primarily refer to visual art in this discussion. However, this definition can be extended to the literary, poetic, musical, and theatrical arts as well.
2. I am indebted to Joseph Campbell for my understanding of myth as metaphor.
Resources
Books:
Berman, Morris. The Reenchantment of the World. Ithaca, NY: Cornell, 1981.
Briggs, John. Fractals: The Patterns of Chaos. New York: Simon and Schuster, 1992.
Briggs, John, and F. David Peat. Turbulent Mirror: An Illustrated Guide to Chaos Theory and the Science of Wholeness. New York: Simon and Schuster, 1992.
Gablik, Suzi. The Reenchantment of Art. New York: Thames and Hudson, 1991.
Garcia, Linda. The Fractal Explorer. Santa Cruz, CA: Dynamic Press, 1991.
Geertz, Clifford. Religion as a Cultural System, Anthropological Approaches to the
Study of Religion, Association of Social Anthropologists Monographs, no 3, London: Tavistock Publications, 1965.
Gleik, James. Chaos: Making a New Science. New York: Viking, 1987.
Griffin, David Ray, ed. Sacred Interconnections. New York: SUNY, 1990.
Henn, T. R. The Arts v. the Sciences. Arts v. Science, Alan S.C. Ross, ed. London: Methuen, 1967.
Hulse, David Allen. The Key of It All, Book One: The Eastern Mysteries. St. Paul, MN: Llewellyn, 1993.
McGuire, Michael, An Eye for Fractals: A Graphic and Photographic Essay Redwood City, CA: Addison-Wesley, 1991.
Neperud, Ronald W., ed. Context, Content and Community in Art Education. New York: Teachers College, 1995
Pappas, Theoni. Fractals, Googols and other Mathematical Tales. San Carlos, CA: Wideworld/Tetra, 1993.
Pickover, Clifford A. Computers, Pattern, Chaos, and Beauty: Graphics from an Unseen World. New York: Bantam, 1984
Pickover, Clifford A., ed. The Pattern Book: Fractals, Art and Nature. River Edge, New Jersey: World Scientific, 1995.
Prigogine, Ilya, and Isabelle Stengers. Order out of Chaos: Man‘s New Dialogue with Nature. New York: Bantam, 1984.
Waldrop, M. Mitchell. Complexity: The Emerging Science at the Edge of Order and Chaos. New York: Simon and Schuster, 1992.
West, Bruce J. and Bill Deering. The Lure of Modern Science: Fractal Thinking. River Edge, NJ: World Scientific, 1995.
Videos:
The Beauty and Complexity of the Mandelbrot Set. New York: The Science Television Company, 1989.
Chaos and Randomness. Nicasio, CA: Media Magic, nd.
Chaos, Science and the Unexpected. New York: Filmakers Library, 1992.
The Fractal Universe. Nicasio, CA: Media Magic, 1989.
Fractals, An Animated Discussion. New York: W.H. Freeman, 1990.
Fractals: Beauty in Chaos. Nicasio, CA: Media Magic, 1993.
Articles (Art):
Angermann, Peter. The Beauty of Fractals. Das Kunstwerk, v 41. (Aug ‘88) p 74.
Gray, Noel. “Critique and a Science for the Sake of Art: Fractals and the Visual Arts.”
Fonnat Sculpture. Leonardo, v 24 no 3 (‘91) p 317-20
Laramee, Eve. “Process and Natural Phenomena: Points of Departure in Extended Format Sculpture.” Leonardo, v 18 no. 1 (’85) p 28-31
Mandelbrot, Benoit B. “Fractals and an Art for the Sake of Science.” Leonardo, Supplement, 1989, p 2 1-4.
Neal, Margaret. “The Visual Think.” IEEE Computer Graphics and Applications. v 8 (Jan ‘88) p 3-5.
Ottoman, Klaus. “The Spectacle of Chaos.” Flash Art (International Edition), v 135, (Summer ‘87) p 60-1.
Pollock, George F., Sir. “Fractals: Are They Photographs?” The Photographic Journal, v 133 (July/Aug ‘93) p 267.
Shearer, Rhonda Roland. “Chaos Theory and Fractal Geometry: their potential impact on the future of art.” Leonardo, v 25 no 2 (‘92) p 143-52.
Tyc, Eric. “Fractals: pictorial pearls or electronic numbers game?” The Photographic Journal v 133 (July/Aug ‘93) p 266.
Wood, Keith. “Chaos, Fractals, and Computers (section: A great attractor, but is it
art?)” Electronics World and Wireless World, v 95 (Oct ‘89) p 957+
Articles (Science and Math:)
Bown, William. “Mandelbrot Set is as Complex as it Could Be.” New Scientist, v 131 (Sept 28, ‘91) p 22.
Dewdney, A. K. “Computer Recreations: a computer microscope zooms in for a look
at the most complex object in mathematics.” Scientific American, (Aug. ‘85) p 16-24.
Dewdney, A. K. “How to Transform Flights of Fancy into Fractal Flora and Fauna.” Scientific American. v 262 p 126.
Douglas, John. “Seeking Order in Chaos.” EPRI Journal. V 17 (June ’92) p 4-7+
Horgan, John. “Mandelbrot Set-to; Did the Father of Fractals “Discover” his Namesake Set?” Scientific American, v 262 (Apr ‘90) p 30+
Jurgens, Hartmut, et al. “The Language of Fractals.” Scientific American, v 263 (Aug ‘90) p 60-7.
Kenner, Hugh. “In Darkest Self-Similarity.” Byte, v 15, (June, ‘90) p 3 82-3.
Copyright © 1996 – 2021 by Amy Clanton