Cary Neeper

Writer, Blogger, and Painter -- esteeming life wherever it might be.

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A thousand years from now a young woman with an identity crisis defends the personhood of her alien and animal friends, as humans tackle their most difficult challenge.
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ESSAYS
COMPLEXITY
Exploration of complexity, its indicators, embedded chaos, and value in human organizations.

Built-in Meaning

Complex systems are everywhere in existence, including our own. Our personalities are emergent phenomena. Most natural systems, including humans, self-organize in ways that reveal their true nature. Simple rules guide this process, but chaos and chance can intervene. As a result, very little is truly predictable, but anything that happens can be amplified in the future, often unpredictably. When I realized that, I wrote the following essay, published by Collegium and The Process Theology Network of the Unitarian Universalist church.

For an extensive bibliography on complexity
click here.
For recommended readings in science and religion
click here.

Built-in Meaning Inspired by Complexity Principles
by
Carolyn Almond Neeper, Ph.D.

Abstract
A reason, or an inspiration, for faith in built-in meaning can be found in the scientific observations of complexity studies (here broadly including chaos, systems thinking and network theory). A source of hope for people of all religious persuasions--or none--is in complexity sciences' conclusion that “…individual activity is not doomed to insignificance.” (Ilya Prigogine and Isabelle Stengers Order Out of Chaos New York: Bantam Books, 1984). The price we pay for this faith, besides its scary implications, is the unpredictable nature of long-term outcomes of the complex processes that enmesh us. Meaning is suggested by the extreme sensitivity to initial condition in chaotic processes embedded in complex systems, by sensitivity at critical points, by the “irreducible random elements” (Prigogine, p. 162) at bifurcation points in complex pathways, and by the occasional unexplained amplification of small events into large effects.
In order to provide a framework for looking at complexity and the faith it generates, I have here first summarized generalizations and suggested indicators coming out of chaos theory and complexity studies (including network theory and systems thinking). Following this summary is the suggestion that scientific observations be distinguished from the statements of belief inspired by those observations. An attempt at defining science inclusively is followed by my favorite question: How should one test for, characterize or verify—prove, if you will—the phenomenon of emergence? Suggested emergent phenomena include thought, life, even mind— subjects traditionally dealt with in philosophy.
In my search of the literature and current dialog in science and religion, I found little emphasis on the importance of knowing that nothing we do as caring human beings is inconsequential. A brief overview of theological ideas related to complexity science in the work of John Polkinghorne, Ian Barbour, Arthur Peacocke, and Niels Gregersen reveals an emphasis on divine action and suggests other areas for consideration, such as theodicy. In considering their work I have focused on three sets of observations in complexity studies: 1) Self-organization and emergence throughout nature, 2) power law distribution, fractals, and the regularity of catastrophes, and 3) ubiquitous chaotic phenomena embedded in complex systems, exhibiting sensitivity to initial conditions and unpredictability, along with randomness at bifurcation points, sensitivity at critical points, and unpredictable amplification of small events into large effects. Built-in meaning for life found in this science provides a source of hope for people of all religious persuasions— if we can forgive the creative process its unpredictable nature.
Distinguishing Science From Faith
The findings of the still emerging sciences of deterministic chaos and complex systems can be regarded as imperatives for ontological and epistemological consideration. These sciences are having major impacts on all fields of study—from physics to economics, from cosmology to the origin and evolution of life. In particular, mysteries in biology now make awe-inspiring sense. We are beginning to see universal principles working in vast interacting networks throughout nature, including those that produce the early cosmos and the origin of life. Those principles—extreme sensitivity to initial conditions and long-term unpredictability in embedded chaos, extreme sensitivity at criticality and an "irreducible random event" (Prigogine 1984, 162 at bifurcation points, occasional amplification of small changes to large effects, self-organization (simple entities obeying their own internal rules to develop into higher orders of complexity), emergence, and ubiquitous power laws (which include the regularity of catastrophes)—suggest revisiting concepts of omnipotence and agency in theology while clarifying problems in theodicy and providing a source of inspiration and verity for built-in meaning in our lives.
Partly because of difficult concepts like emergence in the new science, I suggest we take care to distinguish well verified, falsifiable information from beliefs, statements of faith, that are suggested or inspired by science. Ideas invoking non-falsifiable concepts should not be construed to be extensions of science— they are inferences, projections inspired by the science. A working definition of science might help to distinguish where rigorous scientific conclusions, which are always tentative by definition, depart from religious statements of faith, as in the use of the word meaning. A source of confusion lies in using words like meaning as if they had tested, falsifiable origins.
I adopt here V. V. Raman's definition of meaning: "…the relevance, significance, and importance, contextual or absolute, of something" (Raman 2001, 544). To his comprehensive discussion of the definitions of science and religion and their demarcation, I would add a rigorous definition of scientific method to help distinguish (especially for writers of religious issues impacted by science) the source of our thinking. Perhaps science is best regarded as a method leading to generalizations that remain open to public scrutiny and revision. John Polkinghorne agrees that the essential difference between science and religion is in their contrasting methods. Science and religion are complements; scientists are "mapmakers of the physical world" (Polkinghorne 2000, 79).
Science, then, is the gathering of experiential, falsifiable evidence that remains open to re-verification and public scrutiny in any context. Evidence is organized into coherent logical structures as more evidence is collected or observed. Such evidence includes the coherent logic of mathematics and the continual accumulation from the natural, physical world of results from repeated experiments and/​or collections of observations that fit coherent historical models. In addition, scientific results must be repeatable in any context.
I am not suggesting that science and religion should be kept rigidly separate to do battle or go their separate ways, as Stephen Gould has suggested. Rather, I would add inspiration to Ian Barbour’s categories of the relationship between science and religion (Ian G. Barbour 2000). There are many ways of knowing and formulating beliefs. Science and religion are two of them, and they share a passion for understanding the universe, material existence, and conscious being. We serve ourselves and others best when we recognize—and identify for our readers and listeners—which process, science or religion, we are using when we make a statement of belief. Recognizing the unavoidable leap from the falsifiable statements of science to a religious belief inspired by those statements is a prerequisite for clarity.
Too many scientists have inserted in their scientific writing statements of belief that follow as if derived from scientific information or theory, as if their belief statements are conclusions as falsifiable as the science considered. Conversely, religious concepts are sometimes stated as if they were testable when they are not falsifiable in physical terms. If ideas, beliefs, or theories are not falsifiable—if they point to predictions that are not testable by repeated observations or confirmed by experiments performed by enthusiasts eager to prove them wrong— they are simply not science. Falling outside of science, however, may not necessarily diminish their truth or value.
In the case of the word ‘complexity’, many definitions have been suggested, and no rigorous theory is yet commonly accepted. Generalizations about complex systems come out of an ongoing inductive process from observations of nature and from computer simulations mimicking those observations. Computer models are demonstrations and tests of simple rules used by virtual agents acting independently in networks. The parameters or rules selected for computer simulation are very simple relative to those that actually operate in nature and must be selected with great care if the simulation is ever to mimic nature and increase understanding. Examples include the study of termite mounds and Stuart Kauffman’s modeling of genetic problems with cellular automata (Stuart A. Kauffman 1995).
Of interest is the suggestion by Harold J Morowitz that we add "knowledge by modeling the world" to knowledge by reason, empirical verification and falsification, tradition, and faith. (Morowitz, 2002.) It is time we honor all these other ways of knowing for the deeper truths they can explore and look to science to inspire and guide and inspire us toward areas where it cannot venture.
Science cannot encompass all valid ways of knowing, but, in addition, within the sciences there are places where science cannot go. If we consider knowledge limited to probability being a limit, we can identify at least three limits to science. The first is the Heisenberg Uncertainty Principle, nonlocality, entanglement— quantum effects with their unknown relationship to the macroscopic world. With "…our inability to solve the measurement problem in quantum theory…we are ignorant of precisely how the microscopic and macroscopic levels relate to each other" (Polkinghorne 2000, 148). The second limit to science is seen in Gödel’s theorem, which proved that any system including arithmetic is essentially incomplete. There are truths that cannot be demonstrated formally. The third limit to science is obvious in the findings of deterministic chaos theory and complexity studies, in which long-term effects, even results of simple deterministic equations, can be unpredictable, subject to sensitivity to initial conditions and sensitivity at critical points, subject to the unpredictable amplification of small event into large effects, and to Prigogine's "irreducible random event" at a bifurcation. At "…the threshold of the stability of the 'thermodynamic branch.'…the macroscopic equation cannot predict the path the system will take. Turning to microscopic description will not help....We are faced with chance events..." (Prigogine 1984, 160-62).
In conclusion, note that as new information accumulates, the generalizations of science provide a moveable and expanding foundation. Therefore, the relationship of science and religion must remain fluid and indeterminate, an ongoing source of re-evaluation and inspiration for our time, perhaps for all time—perhaps not.

An Overview of Deterministic Chaos and Complexity
Since Newton gave us so many useful laws of physics, we have more or less assumed that nature obeys rules (often defined by linear equations), that nature is predictable and can be controlled. Noise and “aberrant” unpredictable math were ignored or estimated step by step, and a kind of technological eschatology was assumed: “They” would find a fix for it, whatever it was. Nay-saying is still considered naïve, for faith in the technological fix has been reinforced too often in our lifetimes. Negative estimates of human material “progress” have been regularly overturned.
However, in the last thirty years we have come to realize that Newton’s laws apply to special cases in nature—to things that are contained and move toward equilibrium, to relationships that are linear. Now we can look at noise and determine that, sometimes, the data is not random. It may be bounded and chaotic, included in the patterns of a strange attractor. If so, it is unpredictable in the long run, predictable only in the near future. Infinite accuracy in infinite time is required to re-plot a chaotic reaction exactly, even with simple deterministic equations. An early definition of chaos by a 1986 conference of the Royal Society of London states: “[Chaos is]…stochastic [random or lawless] behavior occurring in a deterministic [simple, ordered] system” (Ian Stewart 2002, 12).
In How Nature Works, Per Bak, Professor of Physics at Brookhaven National Laboratory, clearly distinguishes the terms chaos and complexity by pointing out that chaos theory cannot explain complexity. "Chaos signals have a white noise spectrum, not 1/​f [a power law signal]. One could say that chaotic systems are nothing but sophisticated random noise generators. Chaotic systems have no memory of the past and do not evolve. However, precisely at the 'critical' point where the transition to chaos occurs, there is complex behavior, with a 1/​f-like signal…the complex state is at the border between predictable periodic behavior and unpredictable chaos" (Bak 1996, 30-31) By evolve he meant change in the form of physical, biological or social systems to higher ordered states via self-organized criticality.
The strange attractors that describe chaotic motion have fractal properties, but they are mathematical objects using abstract phase space; they do not represent the “…geometric fractals in real space like those we see in nature as a result of complex processes. Chaotic behavior cannot produce a spatial fractal structure like a coastline. Chaos theory shows that dynamical systems described by simple equations can exhibit unpredictable behavior—no matter how much is known about their initial state” (Bak 1996, 31).
As we shall see later, John Polkinghorne has suggested that the equations of deterministic chaos can be regarded metaphysically as approximations to the more subtle complex system in which they are embedded.
Complex systems, on the other hand, are networks of independent individual units open to sources of energy and material, where chance and chaos work with order to ratchet the system to higher orders of complexity. "Self-organization processes in far-from-equilibrium conditions correspond to a delicate interplay between chance and necessity, between fluctuations and deterministic laws. We expect that near a bifurcation, fluctuations or random elements would play an important role, while between bifurcations the deterministic aspects would become dominant" (Prigogine 1984, 176). "When we examine a biological cell or a city…not only are these systems open, but also they exist only because they are open. They feed on the flux of matter and energy coming to them from the outside world" (Progogine 1984, 127). Complex systems are networks of independent agents interacting with nonlinear reactions and lots of feedback, their reactions running far from equilibrium in most natural systems. See Solé and Goodwin for an expansion of these ideas.
The observations common to complexity in natural systems can often be approximated by computer modeling, computer programs (with carefully selected parameters given rules relatively simple compared to those in the natural system) that approximate and hopefully imitate what is seen in nature. Such tools are extremely valuable in studying extremely complex systems, such as human organizations and ecological systems.
Complex systems evolve (change their overall form or character) via self-organization—pattern formation occurring through interactions internal to the system, with no external application of template or pattern imposition and no reference to a global pattern. Self-organization works with natural selection at all levels to ratchet a complex system into higher states of complexity, until the whole becomes more than the parts can explain. This is called emergence.
Solé and Goodwin warn against confusing the “…intrinsic unpredictability of complex systems made of many parts with chaos.” The fascination with “well-identified chaotic systems” comes from its “…deterministic and low-dimensional character.” Though both chaotic and complex systems are inherently unpredictable, complexity involves both “…stochastic and deterministic ingredients….” (Ricard Solé and Brian Goodwin 2000, 250). Truly random events in complex systems are seen at the bifurcation points, where the choice between two paths cannot be determined, due to unknown historical influences as well as to the system’s extreme sensitivity to random, changing environmental influences.
Thus, only complex systems exhibit self-organization and emergent behavior, which come about through order, laws of chemistry and physics, working with chance and chaos. In addition, according to Per Bak (Bak 1996, 12), any theory of complexity will have to explain fractals (self-similarity at all scales, a phenomenon ubiquitous in nature) and 1/​f noise (which includes the regularity of catastrophes and produces the self-similarity of fractals). One over f (1/​f) noise is a power law: on a logarithmic plot, the frequency of events decreases in a straight line as the size or rank of the event increases; there are many small earthquakes, fewer medium-sized quakes, and rare catastrophic earthquakes. In other words, objects that come in different sizes or at different time intervals have a self-similar power law distribution of their relative frequency of occurrence over large size ranges
Indicators of complexity in nature also include 1) the unpredictable amplification of small input into large effects over time, and 2) criticality, in which a particular value, like an increase in density, suddenly produces a change to another new complex order and/​or on to a chaotic state, as in the Logistic Map. If values leading to criticality are supercritical, chaotic rules will wash out complex phenomena. (Butterflies probably can't have much effect on a tornado.) If subcritical, the rules produce simple or more boring outcomes.
Stuart Kauffman’s thesis is that biological systems exhibit complex features by evolving on the edge of chaos, to self-organized criticality (Kauffman 1995), just inside the ordered state, where stability is in delicate balance with flexibility, and collective properties are understood to be a complex emergent whole. The beauty of Kauffman’s ideas is that they are testable. Life is the inevitable consequence of “…selection [acting] on systems that exhibit spontaneous order [self-organization]…”
Paul Davies elaborates:

"The degree of complexity in living organisms far exceeds that of any other familiar physical system. The complexity is hierarchical, ranging from the elaborate structure and activity of macromolecules such as proteins and nucleic acid to the exquisitely orchestrated complexity of animal behavior. At every level, and bridging between levels, is a bewildering network of feedback mechanisms and controls…each new level in the hierarchical organization of matter brings into existence new qualities that are simply irrelevant at the atomistic level." (Paul Davies 1986, 94).

Davies goes on to describe how Ilya Prigogine characterizes self-organization in nature. “It is hard to overemphasize the importance of the distinction between matter and energy in, or close to, equilibrium...and far-from equilibrium dissipative systems. Prigogine has referred to the latter as active matter, because of its potential to spontaneously and unpredictably develop new structures. ‘…Disequilibrium,’ claims Prigogine, ‘is the source of order’ in the universe; it brings ‘order out of chaos.’” (Davies 1986, 87). The Second Law of Thermodynamics is not violated; entropy increases in the universe as payment in the production of waste by living organisms. Entropy as such is not a good measure of complexity (Sole and Goodwin 2000, 34).
To come full circle, Kaufman (Kauffman 1995) notes that reductionist approaches will continue to be necessary and “spectacularly successful,” but we are now able to grasp collective properties, emergent features, a holistic view to add to our understanding.

Questions Out of Complexity Science
How does this relatively new information impact our thinking about philosophical or theological questions? Does it inspire faith? In what?
Is there an emergent property to all of existence? Does emergence explain concepts like thought and mind? Beauty? Love?
What does long-term unpredictability, amplification of small events, Prigogine's "irreducible randomness" at bifurcation points, self-organization, and the regularity of catastrophes tell us about deity acting in history? About theodicy? What do they suggest about the idea of free will in living creatures? If we exercise free will, and though the effects of what we do are unpredictable in the long run, are they bounded, falling within the orbit of a Supreme Attractor? Or is nature’s self-organized architecture something apart from its Architect? Does emergence explain concepts like thought and mind? Beauty? Love? Transcendence?
Is the meaning that contains and gives shape to all existence to be found in the ubiquitous self-organization and naturally selective chemical processes of cosmology and biology? Or does the meaning of our lives lie in the pervasive sensitivity to initial conditions we influence? Though what we do may be unpredictable in the long-run, can we extract meaning for our lives from the fact that we might make big differences by changing the initial conditions or impacting the critical point in the myriad hierarchical systems in which we live? Does it matter that those differences may result in unpredictable disasters? Is there a mechanism to keep good deeds on track? Is the responsibility we own in such a sensitive, unpredictable world too frightening?

Leaps of Faith— Theological Answers
Three major topics from complexity studies of theological interest are discussed below: 1) self-organization and emergence throughout nature, 2) power law distribution and the regularity of catastrophes, and 3) mathematical, isolated deterministic chaos, or the ubiquity in nature of embedded chaos in complex systems with extreme sensitivity to initial conditions and its resulting unpredictability of long-term effects; irreducible randomness at bifurcation points; sensitivity at critical points; and amplification of small events into large effects in complex systems.
1) Self-organization and Emergence Throughout Nature.
What do emergence and self-organization mean for our philosophy or our theology? Is God the Emergent property of the Universe, as thought or mind, soul or personality are emergent properties of our lives? Does self-organization suggest the working of divine immanence as in process theology?
Charles Hartshorne (Hartshorne 1991) anticipated the idea of God being self-organization and/​or the emergent property of the universe with his idea of God as cosmic evolution. His theistic naturalism regards God as the whole of which we are contributing parts with an “…appropriate degree of autonomy.”
Paul Davies attributes a similar view to Harold Morowitz: “According to Harold Morowitz, an emergentist worldview suggests that the divine immanence unfolds into the domain of an evolving world that makes transcendence possible. The transcendence of God is itself an emergent reality" (Davies 2003, 15).
Arthur Peacocke views emergence and information as a means of divine patterns shaping, and backs off from his earlier thought on divine action through top-down causality (Peacocke 2001).
Contrary to Peacocke's view on divine action, John Polkinghorne stresses "…the holistic character of top-down active information. It is a complete misrepresentation of my ideas to suggest that they imply that agency arises from the local manipulation of either boundary conditions or microscopic processes, either by human or by God." (John Polkinghorne 2000, p. 101).
Polkinghorne strengthens his characterization of top-down causality as holistic by pointing out that since chaotic systems are so sensitive they can never be isolated from environmental influences, hence must be "discussed holistically" (2000, 122). He refers to this "pattern-causing causality" as "active information," familiar to readers of Per Bak as "self-organized criticality," Per Bak's proposed mechanism for complex phenomena.
Niels Gregersen sees God as designing the whole, not the details, which are left to self-organization, resulting in “fecundity, beauty and grace in effectiveness"(Gregersen 2003b). Divine action in his view seems to follow precisely the path described by complexity, in that energy fuels both self-organization and natural selection; law and chance work together in evolution. God’s action is seen as non-interventionist since complex paths are not reducible to laws. God’s breaking laws in order to intervene is not possible since there are no laws.
From these thoughts one could identify God with the self-organizational processes of nature and the emergent “comprehensibility, beauty, progress, love, and religious experiences” Gregersen points to as evidence of God’s existence, along with anthropic coincidences (the unexplained universal physical constants required for material existence), which “presuppose emergentist monism.”
Arthur Peacocke seems to accept God acting through self-organization when he says that God creates with a complex interplay of law and chance. The Creator made things make themselves with chance and law, and this is divine creativity.
Polkinghorne addresses the problem of meaning in the following quote:

“How does a sense of meaning emerge from a universe of inanimate matter subject to blind and purposeless forces? Perhaps the lesson to be learned from complexity studies (a feature that links it so well with evolutionary theory) is that nature is not only a self-repetitive structure but a structure that seems as if it is geared for letting specified autonomous agents appear and propagate further. If this is so, we need both scientific explanations of the general principles underlying natural processes and accounts that are sensitive to the specifics and capable of explaining to us why we have evolved to be the particular creatures we are today” (Polkinghorne 2000, 16).

Note that Polkinghorne may have used the word why either in a teleological sense or to mean physical causation. It is important to point out that scientific accounts, by definition, are not capable of answering teleological “why” questions, which are not falsifiable. In any case, his statement emphasizes "blind and purposeless forces," which cannot always avoid riding along with our personal choices.
Niels Gregersen states outright that self-organization is God’s continuous creativity, a process driven by the local behavior of individual agents. It is the apex of divine purpose. He denies intelligent design concepts as being too close to a God of the gaps, but he uses the word immanent to describe God as a Metadesigner. “The theory of self-organized complexity needs no divine designer to solve the problem of fine-tuning. This problem is already solved by the flexible, internal dynamics of self-organizing systems" (Gregersen 2003b, 224).
Gregersen goes on to discuss possibilities of “new options for theology” in self-organization. While carefully distinguishing the science of complexity from the theology it suggests or challenges, he points out the awe-inspiring use of simple laws in self-organization to drive very diverse and complicated complex systems.

“[By] focusing on relations and interactions rather than on particular objects, complexity theory supports a shift in world-view from a mechanical clockwork view of the world into an emergentist view of the world as an interconnected network, where flows of information take precedence over localized entities. Complexity theory also offers a road for understanding the evolution of co-evolution. By balancing the principle of individual selection by principles of self-organization, the focus on individual genes is supplemented by the importance of interconnected living organisms, a view closer to ethical and religious sentiments than the inherited view of the omnipotence of selection” (Gregersen 2003a).

Note the importance of interactive networks in this quote. Within complexity principles are found guidelines for human organizations— namely, looking to the importance of relationships, enhancing information exchange and feedback, keeping in mind both the emerging whole and individual members of a networked system, then selecting guiding principles that all members can develop, accept, and act freely to implement.
Gregersen then continues, suggesting a relationship of self-organization to the idea of God’s self-limited omnipotence.

“(10) The seminal idea of self-organization may help overcome the idea that God and nature are contraries, so that God is powerless, if nature is powerful, and vice versa. A more adequate view may be to understand God as the creator who continuously hands over creativity to nature so that natural processes are the signs of a divine self-divestment into the very heart of nature’s creativity. On this view, God is at work ‘in, with and under’ natural and social processes, and self-organization takes place within a world already created and continuously gifted by God” (Gregersen 2003a).

I find myself very close to Gregersen’s position, feeling awe at the way order acting with chance and chaos produces increasing complexity. With him, I believe self-organization is a natural process with significance for the limitation or self-limitation of divine action in nature, that is, limitation to and immanence in the processes required for material creation.
How close are these ideas to process theology? A study of the following books is suggested: Jungerman and Cobb's World in Process: Creativity and Interconnection in the New Physics (2000, State University of New York) and Nicholas Rescher's Process Metaphysics: An Introduction to Process Philosophy (1996, State University of New York) and Mesle and Cobb's Process Theology: A Basic Introduction (1993, Chalice Press)
Referring to process theology, which seems to require a fairly easy leap from self-organization in complexity science, Polkinghorne notes, "The punctuated discrete events ('actual occasions'), which form the basis of the picture of the nature of physical process presented in the thought of A. N. Whitehead and his followers, are difficult to reconcile with our scientific knowledge….In between macroscopic interventions [of measurement], a quantum system evolves in a perfectly smooth and continuous way…[also] process theologians' view of God's action is based solely on the power of divine persuasion" (Polkinghorne 2000, 151-52).

2) Power Law Distribution and the Regularity of Catastrophes.
Niels Gregersen points out that instability is the price we pay for complexity; that there are built-in necessities such as self-sacrifice and self-productivity. I would use different wording— that material existence includes unavoidable requirements for energy and a vulnerable susceptibility to outside forces.

“…both equilibrium and catastrophes are governed by the same underlying principles of complexity. The instability of complex systems seems to be the inevitable price to be paid for the immense creativity in evolution. …Re-described theologically, evolution is not a risk-free thing but includes the labor of nature. The groaning and suffering of creation is thus not to be seen as specifically designed by a malicious, all-determining God. Setbacks and suffering are part of the package deal of participating in a yet-unfinished creation. However, there is also a principle of grace built into the whole process” (Gregersen 2003b, 227).

I see such grace in the universal penchant for beauty in nature, especially in the ingenious and beautiful patterns of fractals, in the continuum of love and empathy seen in conscious beings, and in the built-in physiological and chemical mechanisms for protecting material creatures from unbearable pain. Faith in this inherent goodness suggests to theology an empathic Source of creation sensitive to creature needs and limitations.

“(4) Even though natural evils (from earthquakes to selection) remain a challenge to religions that presuppose a loving almighty God, the costs of evolutionary creativity are now being placed in a wider framework of evolution. If the same underlying dynamics of SOC (self-organized criticality, defined by Per Bak as a mechanism for complexity) produces both stability, criticality and catastrophes, and the constructive aspects of nature cannot exist without the destructive aspects, a theodicy of natural evils may be facilitated." (Gregersen 2003a).

Is the phrase natural evil an oxymoran? Is there evil inherent in natural consequences of material existence? Personal experience and faith inspired by self-organization drives me to the conclusion that creation is good, that pain is minimized where possible, that love and beauty are emergents built into material existence. Evil rests squarely on the shoulders of sentient beings with conscious intent and should not be attributed to “acts of God,” hence left to continue. Unpredictability works with regularity of catastrophes to suggest a Creator helpless to intervene if we are in the wrong place at the wrong time. Thus, absolute omnipotence is out of the question for a Creator locked into the requirements of the essential anthropic constants and the properties of matter needed to realize conscious creatures.
Polkinghorne talks of the self-limited omnipotence of God (Polkinghorne 2000), that He interacts with creatures in history but does not overrule them.
Limited omnipotence in theology goes far to explain why bad things happen to good people in a well-intentioned creation. God can only weep for creatures caught in the inevitable consequences of material existence, even as divinity rejoices in their consciousness. The paradox: Evil is done by creatures whose complexity is essential to consciousness. As the most complex object in the universe, the brain seems to be susceptible to going off in unpredictable, catastrophic directions.
The ubiquity of power laws with the regularity of catastrophes in nature affirms that material existence is costly and suggests that the notion of omnipotence in the Source of creation is a mistake. Much grief could be avoided by the recognition that our Source is helpless to intervene when accidents of nature harm us or cause us pain.
Perhaps not contrary to these conclusions, Peacocke affirms God’s omnipotence and omniscience but qualifies them with the requirement that God knows only that which is logical to do or know and that He is limited by love (Peacocke 2001). Peacocke agrees with Hartshorne that God “…suffers with the inherent constraints of creation,” including pain and death.

3) The Ubiquity in Nature of Mathematical, Isolated Deterministic Chaos, or Embedded Chaos in Complex Systems with Extreme Sensitivity to Initial Conditions and the Resulting Unpredictability of Long-term Effects; Irreducible Randomnes at Bifurcation Points; Sensitivity at Critical Points, and Amplification of Small Events into Large Effects in Complex Systems.
Four sources of unpredictability are noted here as distinguishing features of deterministic chaos and complexity. These features are also where the system might be influenced by human activity. In the sources surveyed here, authors usually don't mention all four possible sources of agency, particularly randomness at bifurcation points and critical sensitivity.
In contrast to the other sources of unpredictability in complexity, little is known about the sources of uniqueness in emergent phenomena, hence its unpredictable aspect is not discussed here in considerations of agency. Also, the occurrence of emergence in complex systems is often expected. John Holland (1998, 4) does not call a phenomenon emergent unless it is recognizable and recurring. The details of its emergent manifestation, its unique character, however, cannot be predicted, though complexity scientists have devised methods for selecting details to model successfully the patterns seen in emergent properties.
My purpose here is to highlight references related to complexity science suggesting that human agency has lasting, though unpredictable impact. The concept of built-in meaning I find so inspiring was suggested by Ilya Prigogine: "We know that such [dissipative or complex] systems are highly sensitive to fluctuations….even small fluctuations may grow and change the overall structure. As a result, individual activity is not doomed to insignificance." Emphasis is mine. (Prigogine, 1984, 313)
In a summary statement to the symposium Chaos and Complexity: Scientific Perspectives on Divine Action, Robert John Russell states that

“…some authors…stress the ‘supple’ and ‘subtle’ nature of chaotic and complex systems,…focusing on their vulnerability to minute changes in their environment and their ability to amplify these effects. Since this view is entirely restricted to the classical level…we can call this view ‘lateral causality.’ Perhaps, then, chaos and complexity would offer a new, non-interventionist understanding of God’s objectively special action in nature, or at least suggest that new, holistic laws of nature might be indicated, which in turn could lead to new insights into divine action.” (Robert John Russell 1997, 13).

Russell says it is difficult to distinguish phenomenologically between chaos, complicated periodicity, and randomness, though they are defined mathematically. In nature, he says, one adds these features: 1) extreme sensitivity to environmental changes, 2) the fact that the development of a physical system can outpace the fastest calculations, 3) the causal connection of chaotic effect, and 4) whole-part relationship between the environment and the system—and one is still left with metaphysical determinism.
Note that this view differs from Polkinghorne's alternative view that chaos can be regarded metaphysically as an approximation of the more intricate, complex environment in which it resides. This reflects the view that mathematical equations are maps to reality and should not be confused with reality itself. "I have repeatedly emphasized that there is the alternative of interpreting the non-linear equations of [deterministic chaos] as approximations…to a more subtle, supple, and holistic account of physical reality" (Polkinghorne, 2001,100-101).
Russell seems to focus on deterministic chaos, neglecting the more stochastic features of complexity— the amplification of small events and the irreducible random events at bifurcation points described by Prigogine. However, in summarizing a paper by James P. Crutchfield et al, Russell says, “…Chaos theory places a fundamental and unexpected new limit on how well the hypothesis of metaphysical determinism can be supported…This opens a window of hope for speaking intelligibly about divine action in natural law, a window impossible to close.” (Russell 1997, 17).
Arthur Peacocke does not see unpredictability as the “causal joint” where God acts. Along with dissipative (self-organizing) systems of complexity, unpredictability (in chaos?) does not help with problems of divine action. He points out that infinite precision in infinite time would be needed to predict chaotic futures. “This newly won awareness of the unpredictability, open-endedness and flexibility inherent in many natural processes and systems does not, of itself, help directly to illuminate the causal joint of where God acts in the world—much as it alters our understanding of what is going on. This route for understanding special divine action based on our scientific perceptions has therefore proved to be a cul-de-sac” (Peacocke 2001, 104).
Here Peacocke concentrates on special divine agency and does not mention the role of created beings. However, as Polkinghorne points out, Peacocke distinguishes the acts of Creator from creatures by suggesting that God is a global Agent, while creatures' actions are local (Polkinghorne, 2000, 124).
Polkinghorne argues that God relates to creatures also. "My strategy has been to locate the Creator/​creature distinction in the contrast between God's acting through pure information input, and creaturely acts which involve a mixture of energetic and informational causalities, corresponding to the embodied status of creatures" (2000, 124). "Whatever their merits, the aim of these two strategies, Peacocke's and mine, is clear enough. It is to maintain a metaphysical distinction between God's providential agency and the intentional agency of creatures" (2000, 125). However, Polkinghorne adds a qualifier: There “must be intertwining” of agencies, immanence, therefore self-limitation of omnipotence with holistic top-down pattern formation (Polkinghorne 2000, 114). Note that he chooses to use the terms chaos and complexity interchangeably, probably to emphasize the observation that chaos is a feature embedded in complex systems, that its descriptive equations may be regarded metaphysically as approximations (Polkinghorne, 2000, 100-101).
Peacocke believes God is immanent and totally other (as in panentheism). In a careful review of complexity, he concludes that the random choices at bifurcation points and amplification in complex processes leave nature open and flexible (Peacocke 2001).
Here is where I see free will operating. Here is our chance for built-in meaning, along with whatever contributions sensitivity might make.
Of interest to an overall view of theology, our exploration of meaning, and concepts of Co-creation is Polkinghorne's summary statements about the "Twentieth-century exploration of the implications of the kenotic act of creation…The first point to be grasped was the divine self-limitation of omnipotence….an evolving world or true becoming is one in which even the Creator does not yet know the future, for the future is not yet there to be known….special providence is exercised as a cause among causes, active within the cloudy unpredictabilities of created process. The picture of the invulnerable, all-powerful God of classical theology has given way to the picture of the God who interacts within creaturely history but does not overrule the acts of creatures" (Polkinghorne 2000, 126-27).
Regarding process theology and chaos: "One might claim that the ontological interpretation of chaos theory offers an opportunity to express some of the more theologically congenial aspects of process thinking (such as openness of creation to the future) in a way that is scientifically more persuasive. A similar comment might also be made about some of the ideas of Teilhard de Chardin" (Polkinghorne 2000,152).
"…unpredictabilities will have to be interpreted, not just as epistemological defects, limiting our ability to know in detail what is going to happen, but as ontological opportunities, permitting the operation of additional causal principles, over and above the energetic transactions that physics describes" (Polkinghorne 2000, 112).
“Theologically, such ideas draw support from the related consideration that a physical world found to be sufficiently supple in its process to accommodate human agency, might also be expected to display an analogous ability to be open to divine providential action” (Polkinghorne 2000, 114).
Again, the idea of Co-creation, God acting with creation, comes to mind.
Regarding both divine and human agency, Gregersen makes his point about ontological opportunity with clarity.

“God is the blessing God who creates by bestowing on nature a capacity for fruitful, albeit risky, self-development. The transcendence of God—revealed in the richness of possible pattern formations—is at work within the world. As such, God is not identical with the specific evolutionary patterns, but God is viewed as the wellspring of the always unprecedented and always changing configurations of order. God creates the world by giving free freedom—gratuitously. God creates by creating creativity” (Gregersen 2003b, ms 228).

A Conclusion of Faith
Gregersen makes the point of my thesis— that a new sense of meaning for our lives is "revealed" in the science of complexity and chaos theory. I regard this as an important, even a critical, observation at a time when the traditional sense of meaning for human life is challenged, when western culture seems to be groping for a contemporary source of spiritual meaning.
The problem that confronts us stems from our recent history heavily influenced by Newtonian assumptions— expecting existence to be predictable, hence subject to our control. Does meaning in human life depend on the outcome of our actions being predictable? One hopes not, in light of the unpredictability complexity studies suggest. Though we cannot predict the long-range outcomes of our actions, we can have confidence that what we do is consequential. We can only trust in our judgment of what is right and good, that our actions will trigger or inspire other good. Not choosing to act also has consequences that are likely to be more negative than acting with good intent.
We living beings can’t help but change small initial conditions in everything we do. Those changes and choices embedded in the complex systems of our lives may lead to enormous, long-reaching consequences, whether we know it or not. Unpredictable long-term effects may be all we can expect in our lives, but sensitivity to changes in initial conditions and at critical points and the additional penchant for amplification of small effects and randomness at opportunities for choice in complex systems can provide us with a sense of meaning built in to our very nature as complex beings living in complex societies. What is required is awareness of this new knowledge and faith in complex processes beyond the physical measure of science, regardless of personal ideas about the ultimate Source of existence, Whatever it may be.
The Reason for Being can be found in the ongoing interactions and universal laws governing self-organization—the natural impetus for creativity in the networks of independent agents we call complex systems. Panentheism nearly describes it, and Hartshorne’s metaphor that “God includes the world as an organism includes its cells” appeals to me as a biologist. Should we redefine God as the emergent property of all existence? Perhaps, but I see definition of lesser importance than the faith inspired by the undeniable fact of our influence on being, by the creative arrow of time as we experience and observe it, by compassionate biological triggers that shield us from unbearable pain, and by the emergence of beauty and love as natural expressions of creation.
We are independent agents in these vast networks of matter that shape our lives, free to take full advantage of the opportunities that sensitivity gives us, free to drive creation where we will, blessed with the consciousness of where we are in all the vastness of the cosmos.
We also know who we are—beings subject to the laws that, of necessity, govern physics and chemistry, Peacocke’s “inherent constraints of creation.” We know our brains pay the price of high complexity. Our wiring can go awry. We can do evil, as can other sentient beings, who differ from us in their degree of language or technological or manual capability. We independent beings must bear the entire responsibility for evil, especially that done consciously. I do not believe in "natural evil." Complexity informs us that what is created seems to be a result of "ahistorical universals" (Kauffman 1993, 487), subject to the requirements of material existence as seen in the sciences. Though order works with chance and chaos in complex systems, the regularity of catastrophes is also part of the universal properties we see in complexity studies. When we are in the wrong place at the wrong time, we pay the price for being made of flesh and bone.
Though awesome, there is nothing miraculous about self-organization. Whether divinity is part of the process or not, its universal principles operate on all of us, human, beast, and virtual computer agents alike. We must eat, and chemistry dictates that we must eat other life forms. We must die, and the earth recycles the atoms once again, the same atoms born in stars long ago.
If the Source of creation is in self-organization, we might call it divine immanence or process and take comfort that it knows how we suffer, that it suffers with us. The crucial point for our lives is that we know, from the science of complexity, that what we do and how we live is not inconsequential. Any other projection or theological fine-tuning— even the use of the word meaning— requires a leap of faith inspired by that knowledge. Of necessity, the leap is a highly personal endeavor, beyond the realms of science or empirical proof.
The theistic position that comes from and resonates with my understanding of complexity is a Co-creator continually active in the processes defined by complexity and constrained by the chemical and physical requirements for life. However, for many, theological conclusions may be of lesser concern than the scientific observation that what we do is unavoidably consequential, that what we do may be amplified at some indeterminate time in the distant future.


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