Two Ways that Things Happen--Linear and Nonlinear Dynamics: Underlying the emergent properties of self-organization and the self-directing operations of complex system networks is a basic distinction in dynamic activities, or 'how things happen.' Linear dynamics involve predictably consistent events, represented by mechanical processes. In contrast, what are termed nonlinear dynamics involve unpredictably inconsistent events.  These are central to both the unpredictable yet often self-organizing activities of chaotic systems such as hurricanes, and to the self-directing actions of complex adaptive systems, such as societies. This range of dynamics can be simplistically represented by a spectrum from mechanical process, representing orderly stability, to chaotic ones, representing extreme instability in which self-organization can emerge but cannot sustain itself. In between, in a mix of these extremes, arises the dynamics of complex adaptive systems, with their self-sustaining, self-directing agency. Thus, this zone of "dynamical complexity" can be thought of as the 'creative zone' because it is here the ultimately unpredictable, biosphere-shaping agency of networks can emerge from complex adaptive systems. This dynamical 'mash up' between predictable stability and chaotic instabililty is 'where' the animating impulses of lie mysteriously emerge.

 

A mix of linear and nonlinear dynamics enables emergence of self-organizing networks

but also obscures our ability to fully analyze and explain events 

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To appreciate the mysterious order creation of complex dynamics we must learn to distinguish

between the predictably mechanistic character of linear dynamics and the 

interdependently interactive, unpredictably emergent ordering of nonlinear ones:

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For it is the interplay of these different 'ways that things happen' which gives rise

to self-organization and network agency. And that mysteriously creative interplay

is what mythic symbolism seeks to represent--

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With its nonlinear dynamical metaphors:

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Mysterious Creativity Without Control--Interdependency in "Distributed Connectivity": Network agency is known to emerge from interdependent interactions in feedback flows within a system network. Though this dynamic matrix of feedback flows is not fully accessible to scientific scrutiny, it has been shown to arise in networks where connectivity among parts is described as "distributed." This means that the parts are not connected in a sequential, centralized, or hierarchical manner. Thus, with distributted connectivity feedback between parts tends to flow in many directions at once and not be regulated by any unified control mechanism. Yet that seemingly chaotic interactivity produces the interdependent relationships from which emerge a self-directing thus self-animating 'whole,' with its own characteristic behaviors. This connective architecture of network relationships--their distributed connectivity--is crucial to the emergence of network agency. It turns out to be typical of complex adaptive systems, whether those of the biosphere or of human societies.

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The wholes of characteristic agency in systems arises from distributed connectivity in feedback networks

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This dynamical knowledge reveals how assumptions that the world is ordered primarily by mechanistic causation and hierarchical order are dangerously misguided. What we design or perceive as hierarchically controlled systems, from persons to corporations, are in fact manifestations of mysteriously self-organizing dynamics.

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Appearances are deceiving--

despite our attempts at hierarchical design, our own social and economic systems

involve distributed connectivity that gives them agency we cannot control:

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The Great Unseen--Distributed Connectivity's "Hidden Layer" of Agency:  What we are aware of about our behaviors, or those of other complex adaptive systems, from ecologies to economies, is in effect 'the tip of the iceberg.' But it is from that "hidden layer" that a characteristic 'me' continually emerges. Though we can never fully analyze how it emerges we can 'get a sense' of how it 'tends to behave.'

Hidden network interactivity continually  generates a system's traits and behaviors--its character:

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Though scientific analysis cannot fully examine and explain the actions of distributed connectivity, it has provided models of how inputs result in a "hidden layer" of transformative feedback interactions that result in identifiable "out puts"--such as changes in form, function or behavior. These are termed "neural networks" and a used in creating computer-based "artificial intelligence."

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The "hidden layer" of feedback interactions of network dynamics that generates self-organization and self-direction

is an on-going, every improvising emergent property of a system over time:

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This continual flow of interdependent feedback results in complex systems having a kind of 'memory.' The past forms, functions, and behavior they have produce continue to influence present ones, thus also future behaviors.  Thus the emergent 'character' of a system's behavior, be it a person or a forest, has distinctive traits arising in part from its history. BUT, because network agency is ever-emergent from significantly unstable feedback interactions, complex system behavior is also unpredictably creative and adatpive.

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Characterizing Character Graphically--Conceiving Network Behaviors as "Attractor" Driven:  The 'force' that drives a system's typical behavior has been abstractly conceived as an "attractor." This idea can be thought of in terms of a magnetic field in that it represents something that orders materials and actions by 'pulling' these into some pattern . An attractor is a graph represents a time sequence of the "trajectory" of a system's behavior.  Simple examples are the swinging of a pendulum or a whorl pool in water. The patterns of movement or change in a system over time create an "attractor pattern" and delineate its "basin." A toilet bowl is the literal physical basin of a whorl pool in it. Relatively simple attractors are termed "fixed-point" or regularly "periodic."  But the behaviors of complex systems produce vastly more intricate and changeable attractors. Thus these are termed "strange attractors." Such attractor patterns are not what actually shapes system behaviors but rather a characteristic 'finger print,' as it were. Different types of attractors suggest fundamental types, or archetypes, of systems behavior--such as fixed-point, periodic, or strange.

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The concept of attractors gives us a way to 'image' how both physical forces and network agency

shape system behaviors by imaging their trajectory over time:

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This concept of "attractors" correlates with mythic symbols of 'spiritual agents' that provide metaphors for characteristic network behaviors in complex systems. The traits of a god, goddess, or monster can 'stand for' behavioral traits of specific systems or types of systems.

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The Greek god Apollo characterizes more orderly and deliberate network behavior while

the god Dionysys represents impulsive, transformatively creative character:

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A complex system's behavior can manifest through multiple attractors, which it cycles through in unpredictable ways. In addition, system behavior is conceived as being influenced by an opposing force termed a "repeller," meaning an influence the 'pushes' system behavior 'away' from certain patterns of behavior.  In complex adaptive systems, self-directing network agency is one of the primary impulses generating an attractor pattern or multiple ones. Thus we can think of the ways the selective behavior of network agency in a given system influences that system's forms and purposeful functions as expressing its characteristic attractor pattern.

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A complex system can express its behaviors through multiple attractors

or in the 'push pull' of attractors and "repellors":. 

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By associating the differing traits of personified 'spiritual animators' or gods and goddesses, mythic symbols  give a sense of 'atractors' combine or interact to influence system behaviors.  The brutal and terrifying god or warfare, Ares, is represented as the primary lover of the goddess of love and beauty, Aphrodite.

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Butterfly Effects--The Sensitive Dependence of Unknowable Details and Behavioral Unpredictability:  The unpredictability of complex systems involves what is termed "sensitive dependency on initial conditions."  Minute, ultimately obscure differences can set a complex system on a variety of very different behavioral trajectories.  This concept is referred to as the "butterfly effect" because, conceivably, even the motions of a butterfly's wings could potentially set a weather system on a trajectory towards becoming a powerful storm--or not. Thus infinitesimal influences can contribute to the emergence of radically different systems and attractor patterns. When considering complex adaptive systems, whose behavior is at least to some degree self-directed in response to diverse flows of feedback, even more unknowable variables are involved, making even probablistic predictions unreliable. 

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Sensitive dependency makes complex systems unpredictable and this uncertainty

seems to underlie the emergence self-organizing agency in complex adaptive ones:

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Complexity from Simplicity--The Emergence of Self-Directing Wholes from basic rules in "Agent Based Systems":  The concept of agent based systems is used to describe meta-systems such as ant colonies, bird flocks, and stock markets. Such systems arise from the interactions of individual agents or sub-systems like single ants, birds, or investors. Even agents acting according to quite simple rules for responding to feedback from other agents can result in collective behavior that is purposefully adaptive. Birds in flocks or fish in shoals are observed to track only their closest neighbors in flight. Yet from this simple rule, and the absence of any centrallized control function, the entire group becomes a single network capable of acting as a whole system to evade predators.  This is termed "swarm intelligence."

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The individual agents of birds or ants interact with their closest neighbors according to simple rules.

Yet when this occurs in a large interconnected group, purposeful meta-system behavior or "swarm intelligence" emerges:

 

 

 

 

 

 

 

 

 

 

 

 

Similarly,  the interactions of individual ants with rudimentary modes of responding to feedback from each other enable the emergence of a highly sophisticated social network agency. The entire system is purposefully animated by the interactions of its agents that individually have no capacity to direct the whole of the system--the ant "queen" does not direct this collective intelligence. This emergent effect exemplifies the fundamental mystery of an intrinsic self-directing, thus self-animating, thus spiritual impulse in Nature.

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To appreciate the concurrently interacting feedback relationships of parts/factors that generate self-organizing, adaptive system networks requires a radical shift in how we experience the way things happen. Our ordinary sense of events as mechanistic sequences of predictably proportional actions cannot grasp these dynamics.   Scientific diagrams and schematics give us some impression of these simultaneous, disproportional dynamics. But these abstractions are difficult to appreciate without extensive technical knowledge.

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Science represents the dynamic actions of complex systems in abstract schematic diagrams:

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The unpredictable emergence of spontaneous agency represented here cannot be fully explained--

thus our normal logical worldview cannot grasp the scientific facts being illustrated:

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In our search for complete description and explanation we are destined to be confounded by our own science

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