Complexity and Chaos

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Complexity and chaos are intuitive notions not easily rendered into formal definitions, and yet they have become increasingly important to both science and technology—and thereby to ethics. One useful way to approach complexity is through the analysis of dynamic systems.

Dynamic or changing systems are of two types: those in which knowledge of current states enables the prediction of future states, and those in which knowledge of current states does not enable the prediction of future states. In general ethics has attributed the first type of system to the world (because this appears to reflect a large part of reality, and in the absence of such a system it would be hard to hold human beings responsible for the consequences of their actions), and the second type to human beings (again because this appears confirmed by some aspects of human behavior, and without it humans could not be held accountable for voluntarily choosing to perform one action rather than another). Only since the last third of the twentieth century has scientific understanding of dynamic systems been advanced enough to explain the intellectual framework behind these two attributions.

Linear Dynamics and Its Limits

In the wake of the scientific revolution of the sixteenth and seventeenth centuries, science projected that all natural phenomena, including human actions, could be fully explained with the same logic used to predict planetary motion. According to this view, events are fully explained only when their occurrence is inferred from a covering law together with initial condition statements. The following assumptions framed this approach to explanation: (a) All phenomena are essentially atemporal or, in the case of near-equilibrium thermodynamics, independent of their history; that is, only the future, not the past, is packed into the present; (b) All phenomena are linear, that is, similar causes, under similar conditions, always produce similar results; and
(c) Wholes are epiphenomenal by-products no different from aggregates and can therefore be functionally decomposed into their component parts. Insofar as these assumptions hold, all phenomena were taken to be reducible and decomposable in a way that made them tractable to deductive explanation, and thus predictable. For many centuries, in short, a deterministic, clockwork universe served as the ontological underpinning for Western epistemology and ethics.

Because free will is commonly viewed as a precondition of normative behavior (if everything is fully determined and predictable, responsibility and agency go by the board), a mechanistic worldview makes it necessary either to conclude that human beings are as determined as the rest of the universe (which yielded Calvinist ethics as its axiological counterpart), or to imagine free will as a nonnatural faculty itself uncaused but with the ability to exercise causal power (a view espoused by Immanuel Kant). For ascriptions of moral responsibility to be possible, behavior must be voluntary and caused or controlled by a meaningful intention, reason, or purpose (and not just triggered by a forceful Newtonian cause). Postulating free will as a nonnatural trait in human beings allowed theorists to account for the philosophical concepts of moral value and responsibility. Grounding moral responsibility on an uncaused act of will is, however, as problematic a tactic for ethical theory as the determinism it was supposed to correct: If intentions are caused by external events, then they are not freely formed; if intentions just pop into existence for no reason whatsoever, ascriptions of moral responsibility are as arbitrary as their causal origins. In any case, according to the received worldview (and paralleling the received logic of explanation), moral education consists in learning a set of universal moral principles and then exercising free will to implement the specific normative prescriptions that follow from those principles in particular circumstances.

In the nineteenth century, the mechanistic framework was challenged by the appearance of two new scientific theories: thermodynamics and evolution. Unlike the time-reversible equations of Newtonian mechanics, the second law of thermodynamics postulates an arrow of time. For near-equilibrium thermodynamics, usable energy decreases inexorably over time, a death march that will ultimately end in a state characterized by a complete lack of energy potential. Since usable energy is associated with order, and unusable energy is associated with disorder, Victorians worried about the ethical implications of thermodynamics.

Charles Darwin's theory of evolution, by contrast, appeared to identify the mechanism responsible for the increasing complexity and order characteristic of ontogeny and phylogeny. Nineteenth-century moralists did not quite know what to make of Darwin's ideas. On one hand, they were welcomed because the sequence of creation described by Genesis—from simple organisms to the most complex human beings—seemed to find support in the trajectory of evolution. On the other, his ideas were uncomfortable insofar as evolution suggested that nature was red in tooth and claw, removed altruism and agape from the natural realm, and called into question the origin and ontological status of the human mind and soul. Finally, because of the role of random mutations in evolution, its trajectory was shown not to be predictable and determinable, even in principle, an obstacle that made Darwin (who subscribed to the deductive logic of explanation) doubt that evolution was even explicable.

Attempts to force evolution (and biology in general) to fit the mechanistic view met with failure time and again; it became clear that organisms are not clock-work-like. Because complex systems (including biological organisms) are described by second order, nonlinear differential equations that are not formally solvable, they were for centuries considered intractable.

Nonlinear Dynamics and Its Achievements

The advent of computer simulation changed all this. Computer simulation research during the last quarter of the twentieth century demonstrated that turbulent flow and other seemingly chaotic processes in fact exhibit a very sophisticated form of order that is nevertheless unpredictable in detail. In the early 1960s, Edward Lorenz of the Massachusetts Institute of Technology (MIT) discovered the underlying mechanism responsible for deterministic chaos. Working with meteorological models, Lorenz showed that systems with only a few variables, even though deterministic, display highly complex behavior that is unpredictable in fact because slight differences in one variable produce dramatic effects on the overall system. This feature of complex and chaotic systems has come to be called sensitivity to initial conditions.

In 1977 the Russian-born Belgian scientist Ilya Prigogine received the Nobel Prize in chemistry for his formulation of the theory of dissipative structures, whose fundamental insight is that nonequilibrium is a source of order and complexity. Prigogine demonstrated that open systems (which include organisms) that exchange matter and energy with their environments can show a reduction of local or internal entropy; that is, they are able to self-organize and complexify. Complex systems are dynamical systems whose cooperating and interacting parts display spontaneous, self-organized pattern formation with emergent properties that are not reducible to the sum of their constituent parts. Early-twenty-first-century proponents of a complex dynamical systems approach to the mind (Scott Kelso, Francisco Varela) maintain that mental and axiological properties are high-level dynamical neurological patterns.

For a dynamical system to show structure formation, the process must take place far from equilibrium; it must be nonlinear; and the system must be open to exchanges with its environment. Nonlinearity appears whenever there is interaction among components, whenever the organizational relationships among parts determine the overall systemic behavior. Such nonlinear dynamical systems are typically characterized by feedback loops that embed the systems in their environment and history in such a way that their trajectory history is inscribed in their very structure. Thus the dynamical systems become deeply contextual and extremely sensitive to initial conditions. After a few iterations, the trajectory of two initially close nonlinear dynamical systems will diverge exponentially, and long-term predictions become impossible.

Phenomenologically, however, it was evident that some systems eventually settle down to an oscillatory pattern. Others, such as the Belousov-Zhabotinsky reaction (B-Z reaction), trace complexly patterned trajectories. Yet others, such as turbulent flow, become chaotic, displaying (not no order at all, as had initially been thought) a highly complex form of order. These complex and chaotic systems are described by second order nonlinear differential equations and, as noted, had previously been considered intractable.

The B-Z reaction sequence is an illustration of the abrupt self-organization of hidden order that occurs in open systems far from equilibrium. It shows what can happen when potassium bromate, malonic acid, and manganese sulfate are heated in a bath of sulfuric acid. The first three reactions of the sequence are not remarkable, but the fourth has the unusual feature of being autocatalytic: The product of the process is necessary for the activation of the process itself. Instead of damping oscillations, positive feedback loops around autocatalytic cycles increase system fluctuations around a reference value.

With the system driven far from equilibrium by this runaway process, at a certain critical distance an instability occurs: a threshold point at which small, randomly occurring fluctuations can no longer be damped. Instead the internal dynamics of the autocatalytic cycle amplify a fluctuation, driving the reaction to a new mode of organization. The new system is characterized by the coherent behavior of an amazingly large number of molecules that synchronize to form a chemical wave that oscillates from blue to red. A colorful macroscopic structure (the visible evidence of a phase change) appears. True self-organization has taken place because the internally driven dynamics of autocatalysis precipitate the sudden change.

Biological complex systems are adaptive: As a result of feedback, they change their internal structure to respond to a changing environment. Virus mutations are a good illustration. Fundamentally rooted in their environment and history through context-dependent constraints, complex adaptive systems are thus deeply enmeshed in their surroundings. Nor do they start from scratch; they are fundamentally historical entities that embody in their structure the very conditions under which they were created and the trajectory they followed. Snowflakes are examples of such systems. Not only is each unique; its very structure carries its history on its back by embodying the pressure and temperature conditions in which it formed. At the same time, self-organizing systems such as slime molds display an autonomy that effectively decouples them from their environment.

Such complex adaptive systems, a category that includes people and their actions, are not isolated atoms. They are always already networked and entangled in both time and space. Their relationships create an interdependent whole that is ontologically new. Thus the environment coevolves with human beings; niches change in response to the organisms that occupy them, every bit as much as the organisms are selected by the niches. And both ontogenetically and phylogenetically, they become increasingly individuated over time.

Ethics in and of Nonlinear Dynamics

The dynamical systems approach suggests an interesting new ethical discussion (Dupre 1993, Juarrero 1999). From the perspective of this new science, the prerequisite for moral action known as free will is not the absence of external determining (Newtonian) causes, but the human capacity to impose order on a progressively disordered world. Because all self-organizing systems select the stimuli to which they respond, their behavior is constrained top-down and becomes increasingly autonomous from environmental impact. More complex systems are more autonomous. Self-organized processes, in other words, act from their own point of view. Furthermore the more complexly structured the entity, the more varied its organization and its behavior, and the more decoupled from and independent of its environment—the more autonomous and authentic, in short.

In another sense, the more complex a nonlinear dynamical system is, the freer it is because increasing complexity corresponds to an increase in state space: The system has new, different, and more varied states to access. Intentional human action is free to the degree and extent that the behavior is controlled by higher-level neurological contextual constraints, those with the emergent properties of meaning, value, and even awareness to a certain degree. Insofar as a wink is an action for which an agent can be held morally responsible precisely because the behavior is caused and controlled by a meaningful intention, and the agent is aware of so acting, a wink is freer than a blink because the latter originates in less complex neurological structures that do not embody meaning and value, and may occur as a reflex reaction.

The atoms of a Newtonian universe are independent of one another. So too are moral agents in a Kantian world. Because they are essentially relational entities, however, complex adaptive systems show how interdependence can create an ontologically distinct phenomenon, an organic whole greater than its parts. This is a fundamental axiological lesson of nonlinear dynamics.

Beginning with Plato's utopia, The Republic, Western philosophers have attempted to design fail-safe social systems (whether legal, educational, penal, or other) that are perfect and so never go wrong, morally or otherwise. Complex systems theory shows this is a hopeless task. First, since people carry their history on their backs, they can never begin from scratch, either personally or as societies. Second, perfection allows no room for improvement. Plato was one of the few thinkers who understood that if a utopia were ever successfully established, the only way it could change would be for the worse. Stasis and isolation are therefore essential to maintaining the alleged perfection, not only of Plato's Republic, but of most other utopias as well. The nou-menal self that Kant postulates as the seat of moral choice and free will is likewise not part of this world. The possibility of perfection requires isolation.

The only choice, from an evolutionary perspective, is to cobble together safe-fail family and social organizations, structures flexible and resilient enough to minimize damage when things go wrong as they inevitably will. But to do so, human beings must recognize the potential of interdependence to create an ontologically distinct, metastable entity. Society needs to reintegrate those pieces torn apart by the old Newtonian framework, whether personally or socially, in both its means of communication and its advocacy of public policy. "Personal ethics must now be augmented by policy making" (Mitcham 2003, p. 159).

The downside of historical and environmental embeddedness is that, as members of a community, human beings do lose some of their freedom. Living in society can and often does cramp one's style. By contrast, components in a system acquire characteristics and identities they previously lacked (and could never acquire on their own): They become nodes in a network of relationships that permits new forms of life and acttypes unavailable either to the hermit or to Kant's nou-menal self: Only as members of complex social systems can humans be citizens and senators, teachers and wives, scientists and philosophers. The more complex the entity, the more meaningful the choices as well: As citizens and teachers, senators and wives, whatever roles they choose, people can be responsible or irresponsible, conscientious or careless, virtuous or not.

Because of their sensitivity to initial conditions, complex dynamical systems are not only unpredictable, they also become increasingly individuated over time making each developmental or ontogenetic trajectory unique. In contrast to the science of both Aristotle and Newton, non-linear dynamical systems theory incorporates individuation and concreteness into its conceptual framework. Knowing that each complex system's trajectory is unique raises questions about the universality at the heart of Kant's famous moral command, the categorical imperative. Human individuality, historicity, and contextuality are forced into a one-size-fits-all mold. Unacknowledged recognition of the inevitable interdependence and entanglement highlighted by both complexity and quantum theories might well be behind the more recent emphasis on Kant's second formulation of the categorical imperative: Always treat people as ends, never merely as means.

In a world with room enough for both societies and unique individuals, and the creativity and novelty they promote, precise prediction is impossible. Accordingly, dynamical systems theory calls into question the morality of consequentialism, whether in the utilitarianism of John Stuart Mill or elsewhere. In a world where precise consequences cannot be predicted, and where phenomena are intertwined and entangled in their own histories, basing morality on the actual outcome of individual behavior is a poor foundation for moral decisions and judgments.

Both consequentialism and Kantian formalism reduce morality and ethics to a set of formal rules. The highly contextual nature of complex systems suggests, in contrast, a different approach to moral education, one that references the virtue ethics of Aristotle and the ancients. Instead of memorizing a set of moral principles, which the agent is then suppose to implement moral education would consist of a gradual shaping of character through feedback and habituation. Moral education under this approach is the process of molding certain desires and character traits that are activated in appropriate contexts.

Nonlinear dynamical systems theory also calls for an ethics appropriate to a universe of interdependence and uncertainty. The recent renewal of interest in virtue ethics seems to implicitly recognize this. By contrast, as Carl Rubino notes, because of the ruling mechanistic paradigm's continuing influence on axiology, uncertainty still carries negative connotations. It should not. Complex dynamical systems teach that "change, novelty, creativity and spontaneity are the real laws of nature, which makes up the rules as it goes along. This is good news, cause for rejoicing; we should lift up our voices, as the prophet says, and not be afraid" (Rubino 1990, p. 210).


SEE ALSO Free Will; Incrementalism; Systems.


Dupre, John. (1993). The Disorder of Things. Cambridge, MA: Harvard University Press. In a fundamentally disordered world in which different perspectives reveal distinct domains of partial order, our choices about which scientific project to pursue determines not only what kinds of order we observe in nature but also what kinds of order we impose on the world we observe.

Gleick, James. (1987). Chaos. New York: Viking. An excellent popular introdution to chaos theory by an award-winning science writer.

Juarrero, Alicia. (1999). Dynamics in Action: Intentional Behavior as a Complex System. Cambridge, MA: MIT Press. A rethinking of the concept of causality in terms of context-sensitive constraints, and applied to intentional action.

Juarrero-Roque, Alicia. (1991). Fail-safe versus safe-fail: Suggestions toward an evolutionary model of justice. Texas Law Review 69(7):1745–1777. A diagnosis of the failures of utopian literature, and pointers toward a new model of justice, both formulated from the perspective of complex adaptive systems theory.

Kant, Immanuel. (1952). "The Critique of Teleological Judgement." In The Critique of Judgement, trans. J. C. Meredith. Oxford: Clarendon Press.

Kauffman, Stuart. (1993). The Origins of Order. Oxford: Oxford University Press. Centered on the debate on the origins of life and the maintenance of order in complex biological systems, the book focuses on how self-organization can be incorporated into evolutionary theory.

Kelso, J. A. S. (1995). Dynamic Patterns: The Self Organization of Brain and Behavior.Cambridge, MA: MIT Press. A new general framework within which to connect brain, mind and behavior, from the perspective of self-organization dynamic pattern formation.

McIntyre, Alasdair. (1981). After Virtue. Notre Dame, IN: Notre Dame University Press. With a thorough analysis of the failure of the ethical theories of the enlightenment, this work singlehandedly revived the ancient classical approach to values known at virtue ethics.

Mitcham, Carl. (2003). "Interacciones de complejidades: Ciencia, tecnología, sociedad y ética" ("Interactions of Complexities: Science, Technology, Society, and Ethics"), Paradoxa 10 (137–163).

Prigogine, I., and I. Stengers. (1984). Order out of Chaos: Man's New Dialogue with Nature. Princeton, NJ: Princeton University Press. One of the classics of the breakthrough period of chaos theory, complex systems, and self-organization theories, the work explores the history of the relations of the human and natural sciences, to the present from the perspective of the theory of dissipative structures.

Prigogine, Ilya. (1996). The End of Certainty: Time, Chaos, and the New Laws of Nature. New York: Free Press. An account of how the end of certainty and determinism implied by theory of evolving self-organizing structures is the birth of a new formulation of the natural laws of both science and culture.

Rubino, Carl. (1990). "The Evolution of Our Choices: Notes toward an Ethic of Uncertainty." In Toward a Just Society for Future Generations: Proceedings of the 34th Annual Meeting of the International Society for Systems Sciences, 1: 205–212. A thoughtful analysis of the axiological implications of nonlinear dynamical systems theory.

Waldrop, Mitchell. (1992). Complexity: The Emerging Science at the Edge of Order and Chaos. New York: Simon and Schuster. An excellent if popular introduction to complexity theory as seen through the eyes of five of the major scientists responsible for the new science.

Yates, F. E. ed. (1987). Self-Organizing Systems: The Emergence of Order. New York: Plenum. The best anthology on self-organization, it includes articles from leading researchers in the field, on a wide range of topics including neural organization, morphogenesis, and the genesis and evolution of life.


Peterson, Gabriel. "The Belousov-Zhabotinsky Reaction." College of the Redwoods. Available from A cinematic demonstration of the reaction.