Today's column is the third in a three part series on Teilhard de Chardin's conception of the texture of the evolutionary cosmos by Kathleen Duffy, SSJ. Kathleen Duffy, SSJ, received her PhD in Physics from Drexel University. As Duffy observes:

"Teilhard names complexity as a third infinite along with the infinitesimal and the immense and laments the fact that physics has ignored it. For him, 'the gap between the extreme simplicity and the extreme complexity is as astronomically great as that between stellar and atomic magnitudes' (T, 166). He tries to quantify complexity and defines it in a way similar to the connective approach (Albright, 2) used by complexity theorists. He says that complexity can be expressed 'numerically . . . simply by the number of elements in combination.' He wants to include complexity as a state variable, envisioning a complexities-axis 'to connect the phenomena of life-consciousness, freedom, inventive power-to the phenomena of matter: in other words, to find a natural place for biology as part of physics' (T, 167)."

Furthermore, Duffy adds that "Teilhard extrapolates his knowledge of the cosmos into the social and spiritual realms. He notes that 'there is not . . . a single phenomenon extracted by biology . . . for which we cannot find an equivalent in the human social complex' (S, 89)."

Please read on to explore the role of complexity in Teilhard's view of the texture and tapestry of the universe, engaging both the warp and the woof, the physical and the spiritual.

Currently, she is professor of physics at Chestnut Hill College where she chairs the physics department. Formerly, she has also taught physics at Drexel University, Brun Mawr College, Ateneo de Manila University, and University of the Philippines. She has published research in atomic and molecular physics and in chaos theory in journals such as Physics Review Letters, Journal of Chemical Physics and Chemical Physics Letters, as well as Philippines journals and bulletins. She is a member of the Board of Directors of the Metanexus Institute for Religion and Science and a regular participant in Cosmos and Creation.

This article can be found in Teilhard Studies Number 43, Fall 2001. Teilhard Studies is a monograph series concerned with the future of the human in light of the writings of Teilhard de Chardin. It is published by the American Teilhard Association for the Future of Man, Inc.

-- Stacey E. Ake

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Subject: The Texture of the Evolutionary Cosmos: Matter and Spirit in Teilhard de Chardin, Part 3/3 From: Kathleen Duffy, SSJ Email: <kduffy@chc.edu>

E. TEILHARD AND COMPLEXITY THEORY - THE RESONANCE

Clearly, Teilhard senses and is attracted by the same deep laws of organization that complexity theorists are searching for. Just as Teilhard finds the evolutionary paradigm an overarching theme, so he would probably consider the emergence paradigm central to his synthesis. In fact, even though he knew nothing of complexity theory as it is practiced today, his words resonate with the amazement of scientists like Beloussov and Zhabotinsky who first noticed that a far-from-equilibrium structure such as a chemical clock exhibits complex order (Goodwin, 45) or Swinney and Golub as they watched the patterned flow of fluid between two cylinders rotating with respect to each other that formerly would have been thought to produce turbulence (Gleick, 128-31).

It is interesting to compare Teilhard's references to order, chaos and complexity with concepts from complexity science. Santa Fe Institute's Stuart Kauffman, for instance, is struck by "the extraordinary surge toward order" (Kauffman,10) and expects his research to uncover "a deep theory of order in biology" (Lewin, 43). Teilhard, too, has an innate sense of complex order. And like the complexity scientists, he realizes that order often masquerades in apparent chaos. In the essay entitled "My Universe," he alludes to this.

"My only concern will be to show how it is possible, by approaching the vast disorder of things from a certain angle, suddenly to see their obscurity and discord become transformed in a vibration that passes all description, inexhaustible in the richness of its tones and its notes, interminable in the perfection of its unity." (S, 39)

Just as the chaotic-looking data that describe Lorenz's butterfly attractor turn out to be quite orderly when plotted in a certain way, so too, for Teilhard, the data that support evolution make sense of the world-but only if viewed from a certain angle. Otherwise, he tells us, what is "fundamentally directed by a power that is eminently in control of the elements that make up the universe" will seem like "an unimaginable tangle of chances and mishaps" (S, 41).

Teilhard names complexity as a third infinite along with the infinitesimal and the immense and laments the fact that physics has ignored it. For him, "the gap between the extreme simplicity and the extreme complexity is as astronomically great as that between stellar and atomic magnitudes" (T, 166). He tries to quantify complexity and defines it in a way similar to the connective approach (Albright, 2) used by complexity theorists. He says that complexity can be expressed "numerically . . . simply by the number of elements in combination." He wants to include complexity as a state variable, envisioning a complexities-axis "to connect the phenomena of life-consciousness, freedom, inventive power-to the phenomena of matter: in other words, to find a natural place for biology as part of physics" (T, 167).

Like the complexity scientists who are looking for deep fundamental laws of arrangement, Teilhard notices that "deep down, there is in the substance of the cosmos a primordial disposition . . . for self-arrangement and self-involution" (HM, 33). Arrangement, for him, consists not simply in the homogeneous interlocking of similar units as in crystal formation (HP, 15), but the coherence brought about by the complex interaction that occurs in the formation of living things. He finds that "the multiple is bound together into the coherence of one solid whole or one single impulse" (W, 49); thus the cosmos cannot be reduced to its constituent parts. If it is, if the inherent interconnection among all the seeming fragments is ignored, then, the borders of the cosmic network fray and come undone (HP, 15).

Unlike most complexity scientists, Teilhard extrapolates into the realm of spirit. He would remind us, for instance, that complex wholes are not purely spatial; they can also be psychic. The longer he considered the evidence, the more he found himself "inevitably, and paradoxically, obliged to identify the extreme Solidity of things with an extreme organic complexity" (HM, 28). He was convinced that "the progressive spiritualization of conscious being is . . . the only parameter that enables us to follow . . . the essential curve of Becoming through the labyrinth of individual evolution" (W, 154).

In some of his later works and his Journals, Teilhard draws a simple curve, "the arrangement-curve," plotting a variable he calls arrangement as a function of time. He uses this plot to illustrate how matter and spirit complexify. He explains: "Thus, in the process of becoming, organic complexity and psychic simplicity are not in opposition: the one, in fact, is the condition for the appearance of the other" (W, 157). Thus, both matter and spirit increase proportionately in complexity up to a certain peak value at which point they bifurcate. At death, matter follows the law of entropy and decays back to its most probable form while spirit continues to rise (King, 18). The tapestry threads of matter unravel in order to be recycled, but those of spirit survive and continue to complexify.

Though unaware of the existence of the term, "the edge of chaos," Teilhard realized that the creativity of the cosmos depends on two opposing processes. The

"process of 'arrangement' . . . produces the infinite variety (ever more complex and ever more 'psychized') of atoms, molecules, living cells, etc. . . . and the process of 'dis-arrangement' (Entropy), which is constantly bringing arranged Energy back to its most probable . . . forms." (HM, 84)

Sometimes he calls them two tides of consciousness. They are, for him, the two spiritual ingredients that, when brought together, react "endlessly upon one another in a flash of extraordinary brilliance, releasing by their implosion a light so intense that it transfigured . . . for [him] the very depths of the World" (HM, 83).

Teilhard describes a personal encounter with the "edge-of-chaos" in one of his early essays, "Nostalgia for the Front." As he reflects on his experience in the trenches while serving as a stretcher-bearer during World War I, he notices the feelings of freedom, unanimity and exhilaration (HM, 168-80) that only those experience who know the danger of the battle front. Writing to his cousin, Marguerite, he describes the front as "the final boundary between what has already been achieved and what is striving to emerge . . . the extreme boundary between what one is already aware of, and what is still in process of formation" (quoted in HM 167-68). The front becomes a metaphor for the far-from-equilibrium region, "essentially relative and shifting" (D, 108), like "the edge of chaos" that separates the chaotic zone from the stable zone. It is a place of creativity where there is enough stability to maintain a structure but also enough dynamism to keep the system alive and seeking for new ways to stabilize.

The focus throughout the history of science on linear systems that produce only orderly limit cycles has distorted our perception of the dynamics of the cosmos. By avoiding the difficult case of turbulence as if it were an exception we expect too narrow a spectrum of physical outcomes. This approach has affected our perception of social and spiritual phenomena as well. Teilhard alludes to this in the following passage.

"The visible world formed a completely unvarying framework, within which, until the end of time, man was to repeat himself, ever identical; and with no function other than to restore to God, by intellectual obedience and temperance in their use, the manifold objects which were harmoniously ordered once and for all by the Creation (T, 15)."

Referring to powerful thinkers such as Aristotle, Plato, Thomas Aquinas, Bossuet and Ignatius of Loyola, Teilhard notes how for these sages all change was cyclical. Much like the limit cycles of classical physics, cyclical change "never amounted to more than accidental diversification or repetition of uniform cycles" (T, 14-15). As his own synthesis becomes more fully formed, Teilhard becomes disappointed with his Church's fear of evolution and its lack of interest in integrating evolutionary insights into its doctrine. Likewise, he grows weary of the science of the past. Instead, he becomes more and more interested in how the creative, dynamic processes that have influenced the past and have led the cosmos to the present are moving humanity into the future. In his later years, he expands his interest more and more beyond science toward the social implications of cosmic tapestry-weaving.

Teilhard alludes to the fractal texture of the cosmic tapestry noting that at each scale of the cosmic hierarchy, self-similar structures reappear. He points, for example, to patterns on diatoms that resolve "almost indefinitely under stronger magnifications into new patterns" (HP, 12). He also notes that humanity, if it could be viewed by a distant observer, appears "if not the same as, at any rate akin to, all the other magnitudes of which the cosmos is the assembly" (S, 88). He argues that we can see similarities between levels only if we treat the cosmos as a whole. The cosmos, he says, "taken as a whole, discloses with increasing clarity strange analogies which oblige us to treat it as a single organic object" (S, 89).

Chaotic maps form by stretching and folding in on themselves. With the emergence of the human, Teilhard sees a similar development in the Universe as it folds in upon itself through the process of reflection (HM, 87; W, 22). According to Teilhard, thought, that specifically human phenomenon, has been developing in the cosmos since the beginning within even the simplest of elements. He sees it emerging in proportion to the complexity of the material matrix, the interconnectedness of the threads. Little by little, this latent power within the cosmos becomes consciousness, and as it does it, more responsibility for the future of the cosmos rests with the human species.

Using self-similar arguments, Teilhard extrapolates his knowledge of the cosmos into the social and spiritual realms. He notes that "there is not . . . a single phenomenon extracted by biology . . . for which we cannot find an equivalent in the human social complex" (S, 89). He also alludes to the power of self-similarity in directing his spiritual life and encouraging his continued participation in what he calls the great work, the continual knitting together of the cosmic tapestry. Embedded within this tapestry, we never see what is happening to the tapestry as a whole. We can only imagine the patterns that emerge as the threads intertwine. Drawing on the wisdom he acquired in his labyrinthian journey, Teilhard recognizes that "all the roads that life tries in order to effect the synthesis of the Multiple are not equally profitable" (W, 158). However, since threads of Matter and threads of Spirit interweave in self-similar ways, he suggests that the self-similarity of nature can act as a guide as we try to construct a more coherent tapestry design. Because what is learned from nature can help in discernment, Teilhard places a high value on the study of science, on learning more about cosmic processes. He concludes that "to explain the shape of the world means to explain the genesis of Spirit" (W, 154). Perhaps, today, he would say that the fractal texture of matter reveals the fractal texture of spirit (W, 162).

The strange attractors of chaos theory, with their fractal basin boundaries, would enhance Teilhard's image of the cosmic tapestry. Teilhard realizes, for instance, that evolution is not a matter of a "gentle drift toward equilibrium" but an "irresistible 'Vortex' . . . spinning it into ever more . . . complicated nuclei" (HM, 33). Teilhard's cosmic tapestry threads swirl like currents of water moving in whirlpools, behaving like streams of water draining from a basin under the influence of gravity (V, 272). From the chaos perspective, the cosmic tapestry threads form orbits or local patterns within the attractor. The mystical milieu corresponds to the basin of attraction in which the orbits unfold. Limit cycles, fixed points and strange attractors intertwine to form tangles at each level of the cosmic hierarchy. Each thread weaves a fractal attractor in phase space. If the states of all of these threads as they whirl in space-time are projected onto phase-space diagrams, the result would be a tangle of intertwined orbits, weaving the rich texture of a supporting matrix for spirit (AE, 28).

Yet, these orbits are not forming simply local patterns. Each local pattern, responding to the Center of Centers, is being attracted to an absolute, common center (W, 175) and participating in a single cosmic orbit. In the language of chaos theory, Omega would be the Super-Attractor who guides the cosmic becoming, the unification of matter and spirit. Yet, just as a chaotic orbit is extremely sensitive to its environment, so each local orbit responds to influences that make its dynamics unpredictable. This allows naturally for both the freedom and the novelty that characterize the universal becoming. Responding to Omega, the Center of Centers, each local pattern would participate in patterns of varying magnitudes. These would eventually "meet together at a deeper level" (W, 175) in a single cosmic orbit. They would not necessarily be packed tightly in space but would behave like coherent macroscopic systems communicating with and responding to one another at great physical distances. As it becomes more inter-correlated, Matter provides a better milieu for Spirit formation since, according to Teilhard, Spirit can complexify only in proportion to the complexity of the Matter with which it interacts.

Teilhard would extrapolate this centering process to the end. Eventually, in a final act of union, all will become one with Omega, the attractor who draws all to the Center. Thus, the multiple is made one under the influence of the Super-Attractor. Teilhard says, "If things hold, and are held together, it is only by reason of complexity, from above." In fact, "the world would have no internal coherence were Christ not at hand to give it a centre and to consummate it. Christ, on the other hand, would not be divine if his spirit could not be recognized as underlying the processes which are even now re-creating the soul of the earth" (T, 38).

As a boy at play, as a paleontologist at work and as a traveler on the way, Teilhard noticed, delighted in and was extremely sensitive to texture in whatever form it appeared. This interest encouraged him to create a holistic, synthetic image of cosmogenesis that not only models the science and theology of his day but is also flexible and farsighted enough to include some present developments. In science, there is a resonance with pioneering work in complexity theory, fractal forms and chaotic dynamics and, in theology, with the notion of the Cosmic Christ. Because Teilhard's cosmic tapestry can be viewed alternatively as a topological space-time surface with convergent properties by the scientist and as a tapestry of finely woven threads by the artist, it finds itself somewhere between a mathematical model and a poetic image. Scientific layers of meaning add depth to an already powerful image capable not only of conveying scientific information but also of stimulating an aesthetic response. Thus, the tapestry image acts as a bridge between two disciplines that are rarely able to communicate so well.

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.

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Published   2002.06.26