C. THE TEXTURE OF MATTER IN TEILHARD’S WORK
Early in his major work, The Human Phenomenon, Teilhard notes “each element of the cosmos is woven . . . from all the others” (HP, 14). We might wonder how elements which are generally thought to be particle-like can be woven together. To illustrate the meaning of his claim, Teilhard introduces a space-time view of the cosmos that allows him to look at the evolutionary process as a whole.
Ever since Einstein proposed the Theory of Relativity, it has become increasingly clear that time is inextricably connected to space. Because our senses have been fashioned to perceive only what is happening at the present, and because our experience of the cosmos is so short compared to its approximately-fifteen-billion-year history, we experience only a relatively minuscule cross-section of its complex texture at each moment and perceive matter as ultimately made of particles, hence, our predilection for reductionism. Taking both time and space into account, however, enhances our ability to see the cosmos as a whole.
To set up such a cosmic view, Teilhard suggests plotting the activity of evolution in space-time, coupling the idea of a dynamic topological surface with an image of an emerging tapestry. Consistent with the Aristotelian view of matter still prevalent in his day, Teilhard envisions an early universe filled with proto-matter waiting to be called into being. Then, as this proto-matter begins to react, proto-particles begin to form new unities, giving birth to elementary particles, atoms, and molecules, and then, with the coming of life, more and more complex structures. When the positions of the original particles of the evolving cosmos are plotted as a function of time, a surprising texture is generated. The curve for the position of a single particle forms a thread that intertwines and unravels with other curves as forces attract and repel, form new entities and fall apart. Duration thus provides texture to a world that only appears particulate.
In the early universe, the weaving fibers which are the extensions of the proto-matter of the early universe, are not at all correlated (HP, 17). At first the particles (and thus the threads) repel one another. Then the weaving begins. The space-time fibers become much more interrelated, more interconnected as they learn, despite their natural tendencies, to form complex wholes. Each new complexity prepares the way for still richer forms. The cosmic fibers experience what Teilhard calls Creative Union. As they interweave, they preserve their identities while yet becoming something more (W, 155).
As the cosmic drama unfolds and the threads intertwine and unravel and intertwine again, organic connections within the dynamic four-dimensional fabric are enhanced. Even though the number of species and individuals within each species multiplies with time, more of the once disparate elementary matter is now interrelated and weaving more complex patterns. Individual patterns come undone, but as time progresses, the texture of the fabric as a whole becomes more complex, more beautiful. Rather than as a sea of particles, then, matter can be viewed as a network of threads weaving in and out, responding to forces that encourage complexity, originality and beauty. In fact, if the evolutionary project could be viewed from outside rather than from the center, it would look like a giant tapestry in process, “woven in a single piece” (HP, 15), presenting a holistic and integrated approach to the cosmogenic process. However, this is ordinarily so difficult to envision because we are so firmly immersed within it (HP, 16).
To provide further insight into the structure and texture of space-time, Teilhard singles out one of the many threads to guide his encounter with the cosmos. Centrally placed in The Human Phenomenon, “Ariadne’s Thread,” as he calls it, acts as a pivot on which he re-enacts for us his own experience of reversal. This thread is not only a guide but also becomes for him an arrow pointing in the direction of increasing complexity-consciousness in the cosmos (HP, 92). It is this thread that convinces him that evolution has a direction.
Ariadne was the daughter of King Minos of Crete, who attacked Athens after his son was murdered there. The Athenians submitted and, as a consequence, each year had to sacrifice fourteen youths to the Minotaur, a monster - half bull, half-human, who stayed in the king’s labyrinth. The princess, Ariadne, fell in love with Theseus, a young man who had volunteered to be sacrificed to the Minotaur. To rescue him from disaster, Ariadne gave Theseus a ball of thread directing him to fasten one end close to the entrance of the maze and to unwind it as he went. Theseus confronted the Minotaur asleep in the depth of the labyrinth and, after destroying the monster, led the youths to safety by rewinding the thread (Ward, 15-16).
Teilhard grasps Ariadne’s thread and begins his descent into his own cosmic labyrinth. There he confronts his minotaurs: pantheism, luring him to merge with Matter (HM, 24), and materialism (CE, 105), suggesting that he objectify it. As he gapes down into the maze of fibers, “the innumerable strands which form the web of chance, the very stuff of which the universe and [his] own small individuality are woven” give him pause. He feels “the distress characteristic to a particle adrift in the universe” (D, 78). At each step of the descent, once-familiar patterns seem to come and go at random and finally unravel. As he reaches the disparate multiple and watches the dissolution of all that is familiar, he concludes that although we are all made from the same stuff, its principle of unity is not to be found within matter itself (W, 157).
Still clutching his prized thread, Teilhard reverses his direction still in search of cosmic consistence. Following the arrow of time, he notes that the cross-sectional patterns, made by slicing the four-dimensional tapestry at particular points in time, display more complex structures. He wonders at the “slender . . . threads from which [his] existence is woven, extending from the initial starting-point of the cosmic processes…to the meeting of [his] parents…Had but a single one of those threads snapped [his] spirit would never have emerged into existence” (W, 228). Like Theseus, he sees clearly the importance of Ariadne’s thread which begins “to disclose a complex and delicate fabric in what had been thought our most spiritual substance.” Although he had considered himself extremely simple and very much his own master, in the ascent, he finds himself, “made up of all sorts of fibres…fibres that come from every quarter and from very far afield, each with its own history and life” (AE, 188). Now he sees himself as part of humanity, as part of the cosmos, as part of a synthetic process.
As Teilhard approaches the present, it becomes clear that today, “evolution is now busy elsewhere, in a richer, more complex domain, constructing spirit, with all our minds and hearts put together” (HP, 198). This reassures him that not only is the cosmos complexifying but it also has a “psychically convergent structure” (HP, 28). Teilhard concludes that “Matter is the matrix of Spirit” (HM, 35).
He continues to follow Ariadne’s thread to the end to see where it is leading (HP, 99), to extrapolate into the billion of years that lie ahead. He discovers that the texture of the ever-complexifying tapestry does in fact “disclose to us the fundamental texture of Spirit” (W, 162). As the weaving proceeds, the cosmic fibers will continue to become more tightly knit and more complex patterns will continue to emerge.
This holistic view of the cosmic tapestry changes Teilhard’s perplexity to ecstasy. He says that “as the scales fall from our eyes, we discover that we are not an element lost in the cosmic solitudes, but that within us a universal will to live converges and is hominized” (HP, 7). Teilhard returns from his labyrinthian journey full of insight. The universe has become for him a dynamic, organic whole with humanity at the front riding the crest of a wave as evolution moves into the future.
For Teilhard, Spirit and Matter are not separate entities since they are so intricately woven together. Rather, like the threads of the cosmic tapestry and the spaces between them, Matter and Spirit form complementary textures, textures carved and shaped by complementary processes (HM, 28). They form “two states or two aspects of one and the same cosmic Stuff” (HM, 26). The quanta of Matter and Spirit that once permeated the early universe become fibers of Matter influenced by gravity and threads of Spirit drawn by love. Together, they form what Teilhard calls a mystical milieu, a “support common to all substances” (W, 125), “a universal substratum, extremely refined and tenuous, through which the totality of beings subsists” (W, 123), a matrix on which “spirit is made through the medium of matter” (W, 157). It is the interplay of Spirit with Matter on the cosmic loom that encourages the creativity needed for quanta of Spirit to weave a common soul.
Extrapolating from his own experience of confronting the tensions within his spirit, Teilhard realizes that there must be something or someone at the center of the evolution drawing all creation together. He speculates on the nature of the force that allures the threads. He finds that “a transcendent form of action begins to emerge, which embraces and fuses together…the whole medley of things which…appear to us to conflict with and neutralize one another (AE, 55). He suggests that as we explore the texture of the space-time tapestry, “we are gradually introduced…to the concept of a first, supreme centre, an omega, in which all the fibres, the threads, the generating lines, of the universe are knit together” (S, 48). For Teilhard, the irresistible and universal center of convergence to which we are attracted (LTF, 107) is a Person whom he calls Omega and eventually identifies with the cosmic Christ.
To Teilhard’s surprise, the elusive “Durable” for which he was searching is found not in rocks and metal but in a tapestry of organic complexity. On the cosmic loom, the dissonance he experienced between the God of evolution and the Christian God (HM, 54-55) resolves into a single, unified Force. What began for him as grief over perishable strands of hair, culminates in ecstasy over durable threads of Spirit. He summarizes the weaving process.
“Crimson gleams of Matter, gliding imperceptibly into the gold of Spirit, ultimately to become transformed into the incandescence of a Universe that is Person – and through all this there blows, animating it and spreading over it a fragrant balm, a zephyr of Union” (HM, 16). Viewed in space-time, gleams of Matter become crimson threads that swirl into the golden fibers of Spirit. Supported by an alluring and ensuring presence, the threads of the cosmic tapestry experiment with novel patterns as they grope their way toward the incandescence of the Cosmic Christ (HM, 50), who is, for Teilhard, truly and “organically clothed in the very majesty of his creation” (HP, 213).
It is its holistic character that makes Teilhard’s synthesis so compelling. Over and over, he insists “order and design appear only in the whole”(HP, 15), in the tapestry that is “endless and untearable, so closely woven in one piece that there is not one single knot in it that does not depend upon the whole fabric” (S, 79).
D. CHAOS and COMPLEXITY – WHAT ARE THEY?
Given Teilhard’s propensity for texture and for the holistic, and given the holistic nature of the complexity theories, it would be interesting to try to imagine how Teilhard might incorporate them into his synthesis. Although his work preceded the onset of chaos and complexity theory by several decades, they hint that he would have applauded many of their features.
Defining precisely what is meant by complexity is still difficult. There are presently at least three ways to approach it. The first two define ways to measure the complexity of a system. The mathematical approach counts the number of steps in the shortest program that will accomplish a particular task while the connective approach counts the number of significant connections among the subunits of a complex system. Instead of an operational definition, the inductive approach, enumerates the main properties of a system that can be considered complex: it is nonlinear, open, dynamic, emergent, poised between order and disorder (Albright, 2-3).
Because of their nonlinearity and openness to the environment, complex systems tend to be spontaneous, disorderly, and alive. They are made up of a great number of elements that interact with one another in complex ways. The richness of their interaction allows them to undergo spontaneous self-organization. Every living organism is a complex system. So too are a flock of birds and a group of individuals in economic interaction with each other. The elements that make up a complex system somehow manage to transcend themselves, constantly adapt to each other, organize themselves into exquisitely-tuned patterns and together acquire collective properties such as life, thought, and purpose that they would never have possessed individually (Waldrop, 11-12).
On the forefront of research into the nature of complex systems, the Santa Fe Institute in New Mexico is an interdisciplinary group of scientists headed by Nobel laureate in physics, Murray Gell-Mann. These scientists want to determine the fundamental mechanisms that systems use to construct complex wholes. They are trying to provide a mathematical language to describe the stable yet flexible creativity found in the cosmos, phenomena as diverse as spiral galaxies, the colorful and intricate patterns on butterfly wings and the complex social organizations of cultures.
To plumb the nature of such phenomena, complexity scientists are asking new questions, devising new theories, discovering new relationships. Their questions address topics such as morphogenesis, emergence and self-organization. They are interested in how organisms evolve and why certain structures exist. Theirs are questions that treat the dynamic, emergent processes at work in the cosmos. They are finding that when a few simple rules are applied to a variety of simple systems, intricate patterns begin to emerge. Because the fate of a complex system is so profoundly intertwined with its environment, its study requires a more holistic treatment than has generally been practiced in the sciences.
Classical biologists, for instance, have been interested in how organisms work. They ask questions about their makeup and the mechanisms that affect their behavior. Once they understand how organisms function, they try to predict their behavior and sometimes find ways to interact with them to their own advantage. Many advances have been made in biology in recent years by focusing on the gene as primary in determining the properties of organisms. According to neo-Darwinian evolutionary theory, new types of organisms arise from the interplay of random mutations of genes and natural selection. Complexity theorists, on the other hand, point to the inadequacies of natural selection as the sole explanation for emergent phenomena [iii] and try to go a step further. They want to understand how the cell organizes itself into stable patterns of activity. Obviously, the pattern depends on genetic activity, but the new question is, in what particular ways.
One of the properties characterizing the complex response of a dissipative system made up of huge numbers of particles is its coherent behavior. An example of this kind of behavior occurs in a Benard convection cell in which fluid is trapped between two plates, one heated at the bottom to sustain a constant temperature difference. To set up a convection pattern, the fluid is driven far from equilibrium by increasing the difference in temperature to a critical value. At this value, millions of molecules begin to move coherently, forming hexagonal convection cells of a characteristic size (Prigogine and Stengers, 142). These patterns are obviously absent when there is no temperature gradient and the fluid becomes turbulent for larger temperature gradients. In the convective fluid, molecules seem to be independent and usually interact only through short-ranged intermolecular forces. However, when they are in the chaotic regime, correlations between particles become long-ranged (Nicolis and Prigogine, 13, 15). That means, for instance, that even though a molecule is situated at a relatively large distance from its partner, it acts as if it knows what its partner is doing and responds accordingly. Through the interplay of two opposing forces, convection and gravitation, molecules almost seem to be communicating with one another.
Unlike complex systems, chaotic systems are usually simple. However, because they are nonlinear and influenced by positive feedback and information from their environments, they respond to stimuli in very complex ways. The order found in chaotic systems is radically different from previous notions of order. Although chaotic systems are deterministic, that is, governed by universal physical laws and not by chance, they are extremely sensitive to the environment. A small change in energy input, in the initial values of their variables, produces an entirely new response. Before the dawn of the computer, it was literally impossible to determine and describe chaotic behavior. Now, the availability of high-speed computers has made it possible to explore their response. A flurry of research into all sorts of nonlinear phenomena in a variety of disciplines has resulted.
Graphs help scientists to see and understand a system’s dynamics. A particularly helpful kind of graph often used to explore chaotic behavior is the phase plot. On a phase plot, the state of a system is plotted in a space with as many dimensions as there are variables needed to describe the state of the system. For instance, a mass oscillating on a spring in one dimension can be described by two variables, its position and its velocity. When the velocity of the mass is plotted against its position, a picture of its orbit results. The orbit provides insight into the behavior of the mass. For regular oscillatory or circular motion, the phase plot is called a limit cycle. Its elliptical shape represents the orderly behavior of a dependable, periodic process that continually repeats preserving a fixed pattern. If the motion of the spring-mass is over-damped as it would be if the oscillating mass were immersed in molasses, the orbit will spiral in to a stable point. This kind of attractor is called a fixed point since all initial conditions within the attractor will eventually lead to the same final state of rest.
When the spring-mass system is operating in the chaotic region, on the other hand, a collection of profoundly intricate and beautiful orbits arise. Patterns, such as the well-known Lorenz attractor, often called the “butterfly attractor” because of its shape, have captured the public imagination. Called “strange attractors,” these orbits embody an unpredictable and intricate order. A strange attractor is often compared to a lake that exerts an attractive, gravitational force on the water from the rivers and streams that flow into it (Kauffman, 78). Water from these streams always moves toward the lake to which it is attracted and never escapes in the reverse direction. However, since the lake has no drain, any stream of water that flows into the lake remains there and, as if driven by an invisible force, continues to flow in complex spirals throughout the lake. The orbit of a truly chaotic system executes fairly complex dynamics within the limits of its center of attraction. Although the motion of a particular orbit never repeats itself and is hard to predict, order is maintained because, despite its tendency to wander, it is always being pulled back in toward its center of attraction.
Chaotic dynamics produce fractal structures whose irregular yet beautiful shapes are so unlike Euclidean geometrical forms. Fractals are intricate images that can be produced by the iteration of a few simple coupled nonlinear equations. The turbulent flow of air in the atmosphere forms fractal cloud patterns from condensing water vapor; over millennia, buffeting winds and rain produce jagged mountains; turbulent oceans form jagged coastlines; the violent pumping of blood by the heart fashions a fractal blood stream. The surf-pounded coastline, the blood vessels of the heart (a very violent pump), and the wind- and rain-buffeted mountain exhibit fractal shapes. The resultant fractal shapes are due to the interplay of powerful and turbulent driving forces and the strong damping forces that act to subdue them. Because of the aggressive nature of both types of force, the resulting fractal forms often turn out to be more robust than other forms (Pickover, 120-21). Fractal boundaries also tend to be more fluid and their patterns are more graceful and artistically appealing.
The study of these intricate structures reveals several interesting features. First of all, fractals are self-similar; that is, as the fractal image is enlarged, the pattern of the whole is found embedded in each smaller scale. Because a characteristic pattern appears on many scales, no scale predominates. Secondly, fractals have no characteristic length; each level is as important as any other. Fractal boundaries are also curious. As the fractal boundary is magnified, more and more detail can be seen and the length of the boundary becomes infinite. Finally, every fractal structure has a characteristic dimension that is non-integer. Unlike our familiar one-, two- and three-dimensional spaces, a fractal fits into a non-integer dimensional space that seems strange to our Euclidean way of thinking.
Complex arrangement requires that two opposing forces such as convection and gravitation simultaneously act on the system. This is what the complexity scientists call conflicting design criteria. While one force dissipates energy, the other force supplies energy to the system to keep it far from equilibrium. One force seeks to bring it into homeostasis; the other, to destabilize it. The overall result is that, because the system is not in equilibrium, it is able to avoid thermal disorder and create new forms. The process of evolution also relies simultaneously on two opposing forces: self-organization and natural selection. Self-organization is the energy-enhancing process and natural selection the limiting process (Kauffman, 8, 112). Together they maintain a complex order.
The transition region that exists between ordered stability and chaotic instability is called “the edge of chaos.” Although it is a place of homeostasis, “the edge of chaos” is a particularly creative region, a regime of complex order. In this regime, the complex system is slightly unstable, and thus able to interact with its environment. In the process, stable structures are formed. Complex systems are not rigid. In fact, they cannot evolve unless they become somewhat unstable, unless they begin to fall apart. In nature, a process of radical change necessitates the movement of a stable structure from its stable environment into a far-from-equilibrium situation, into a more turbulent environment, into “the edge of chaos.”
NOTES:
[iii] Emergent phenomena are regularities of behavior that somehow seem to transcend their own ingredients. For instance, the color of a chemical does not reside in the individual atoms or molecules that make it up but emerges only because of the complex interaction of one element with the other (Cohen, 232). Life is also an emergent property since it is present only in the whole.
Work by Other Authors Cited in this Essay
Albright, John R. “Order, Disorder, and the Image of a Complex God.” Presented at ESSSAT, April 2000.
Casti, John L. COMPLEXification: Explaining a Paradoxical World Through the Science of Surprise. New York: HarperCollins Publishers, 1995.
Cohen, Jack and Ian Stewart. The Collapse of Chaos: Discovering Simplicity in a Complex World. New York: The Penguin Group, 1994.
Cuenot, C. Teilhard de Chardin: A Biographical Study. (V. Colimore, Trans.) London: Burns & Oates, 1965.
Gleick, James. Chaos: Making a New Science. New York: Viking Penguin Inc., 1987.
Goodwin, Brian. How the Leopard Changed its Spots: The Evolution of Complexity. New York: Simon & Schuster, 1994.
Kauffman, Stuart. At Home in the Universe: The Search for the Laws of Self-Organization and Complexity. New York: Oxford University Press, 1995.
King, Thomas M. Teilhard’s Mysticism of Knowing. New York: The Seabury Press, 1981.
Lewin, Roger. Complexity: Life at the Edge of Chaos. New York: Macmillan Publishing Company, 1992.
Lyons, J. A. The Cosmic Christ in Origen and Teilhard de Chardin. New York: Oxford University Press, 1982.
Nicolis, Gregoire and Ilya Prigogine. Exploring Complexity: An Introduction. New York: W. H. Freeman and Company, 1989.
Pickover, Clifford A. The Loom of God: Mathematical Tapestries at the Edge of Time. New York: Plenum Publishing Corporation, 1997.
Prigogine, Ilya and Isabelle Stengers. Order out of Chaos: Man’s New Dialogue with Nature. New York: Bantam Books, Inc., 1984.
Waldrop, M. Mitchell. Complexity: The Emerging Science at the Edge of Order and Chaos. New York: Simon & Schuster, 1992.
Ward, A. G. The Quest for Theseus. New York: Praeger Publishers, 1970.
List of Abbreviations for the Works of Teilhard Cited in This Essay
AE Activation of Energy. (Rene Hague, Trans.) New York: Harcourt Brace Jovanovich, Inc., 1970.
CE Christianity and Evolution. New York: Harcourt Brace Jovanovich, Inc., 1969.
D The Divine Milieu. (Bernard Wall, Trans.) New York: Harper & Row, Publishers, 1960.
HM The Heart of Matter. (Rene Hague, Trans.) New York: Harcourt Brace Jovanovich, Inc., 1978.
HP The Human Phenomenon. (Sarah Appleton-Weber, Trans.) Portland, OR: Sussex Academic Press, 1999.
LTF Letters to Two Friends 1926-1952. (Helen Weaver, Trans.; Ruth Nanda Anshen, Ed.) New York: The New American Library, 1967.
S Science and Christ. (Rene Hague, Trans.) New York: Harper & Row, Publishers, 1968.
T Toward the Future. (Rene Hague, Trans.) New York: Harcourt Brace Jovanovich, Inc., 1975.
V The Vision of the Past. (J. M. Cohen, Trans.) New York: Harper & Row, Publishers, 1966.
W Writings in Time of War. (Rene Hague, Trans.) New York: Harper & Row, Publishers, 1967.