Preface: Part Three
None of us would wish to pass onto our children the kind of problems we now face. A global society where the disparity between those who have and those who have nothing fuels war, international terrorism, the race for weapons of mass destruction. An environment plagued by global warming, oceanic collapse, a looming energy crisis, human over-population. We are pressing the limits of our planet’s ability to sustain us.
We set out in Part One to understand what brought us to this edge. We acknowledged that our decisions and actions, even our perceptions, follow from what we believe — the stories we tell ourselves. We explored language, narratives and the narrative field. We concluded that a mistaken set of beliefs about our identity, a master narrative that conflates individuality with separation, lies at the root of our problems.
In Part Two, we investigated alternatives to the master narrative. We observed that narratives based on relationship, cooperation and Love have long been proposed by our religious and spiritual traditions. We explored alternative understandings of the Universe implicit in various discourses of contemporary science. We followed threads of alternative practice and counter-narrative woven through the history of the arts. Finally, we outlined an alternative center around which we could organize personal experience: the identity emergent in the connection between Self and the Stars.
In Part Three, we turn to using these understandings to save our World. Earlier, we briefly touched upon Complexity Theory. Here we will delve more deeply into this science developed for studying situations that defy simple description, explanation and prediction. Complexity Theory / Chaos Theory has much to offer our effort, since we face a complex and chaotic set of problems. Complexity Theory not only suggests models with which to understand that complicated multiplicity, but also brings our thinking closer to the Referent. With better comprehension of our situation, we stand a better chance of finding and enacting successful solutions. Perhaps most importantly, Complexity Theory can help us believe it possible to do what we must do. Chapter Eight explores this Theory. Chapter Nine sketches an outline for a plan of action.
Chapter Eight: The Edge of Chaos
A Fractal Universe
Science has now reached the threshold of affirming what artists and religious traditions have long maintained. Our Universe turns out to be much more complex and nuanced than our sign system conventions and logical reasoning have permitted us to grasp. Even the borders between dimensions have proven less distinct than Euclidean geometry would have had us believe. We live not only in the multi-dimensional Universe discussed in earlier chapters, but also — and more accurately — in a fractal multi-dimensional Universe.
What do we mean by “fractal” universe? Commonplace understandings can help to explain. At first glance, the kitchen floor, a tabletop, the computer screen all appear smooth planes — two dimensional objects of length and width. We know, however, that greatly magnifying either one of them will reveal hills, valleys, craters, mountainous regions scattered across the surface. To take this “roughness” into account — to match the complicated irregularity that we are describing — we need to add a fraction of depth or height to our description. This is the fractional or “fractal” quality that permeates our world.
Fractals surround us. “Lightning doesn’t travel in a straight line,” said Benoît Mandelbrot, the mathematician who gave fractals their name. In fact, you cannot describe a lightning bolt mathematically without dealing with its jagged movement. Or measure the length of a shoreline without taking into account its irregularities, how it changes over time or your means of measuring it. Rivers, rocks, plants, clouds, our faces, galaxies... All are examples of naturally occurring fractals. We live in a fractal Universe.
We have long known that such natural forms result from repetitive processes. Cells divide again and again. Waters cut the Grand Canyon. Gravitational forces and crashing meteorites shaped the moon. When we developed computers capable of iterating mathematical operations with a speed and to an extent previously impossible, we found that the chaotic anomalies that could sometimes appear themselves generate patterns. The stunning graphics most commonly associated with the term ‘fractal.’ The inexplicably beautiful fractal music.
Computer generated fractals describe and visualize the irregular and fragmented. Studying them gave us vocabulary and tools with which to look at complex form and change. We learned not only that apparent chaos has “emergent patterns,” but also that these patterns become embedded throughout the fractal entity. Magnification of a part reveals recurring details, a likeness to the whole, a “self-similarity” that reaches through every scale of fractal structure to infinity. The individual leaves of a fern, for example, differ in size; while the basic shape of each leaf and the veins within it repeat the overall pattern of the frond.
This self-similarity does not manifest in rigid and exact symmetry, but rather in a statistical resemblance. The branching in trees repeats from root to bud; yet with a variability that illustrates Nature’s irreducible spontaneity. Trees grow in relationship with their environment and all its unpredictability. And as part of that whole, they express the unpredictable beauty at the heart of our World.
Complex dynamic systems
Long before the development of chaos/complexity theory, Henri Poincaré forewarned us of the problems associated with predicting anything. In 1889, Poincaré demonstrated that Newton’s Laws of Gravity could not foretell the future of the solar system. He showed that even if we knew the initial positions of the three-body system of Sun, Moon and Earth, the slightest perturbation afterward would result in dramatically different orbits. Since we do not know and have no way of knowing what the initial conditions might have been, Poincaré concluded that, “Prediction becomes impossible.” To science, unpredictability equals chaos. And scientists preferred to focus on more promising fields of inquiry, such as electromagnetism, radiation, relativity, quantum mechanics.
In the 1960’s, the topic of unpredictability re-emerged. Edward Lorenz, a meteorologist at MIT, was using a computer to study atmospheric change. His hopes of improving weather forecasting were suddenly dashed, however, when he tried to reproduce a pattern by re-entering data from his printout. He did not think it would matter that his printer worked with three decimal points while his computer worked with six. But his model weather system produced a dramatically different pattern in response to this slight variation of input. Lorenz dubbed the phenomenon, “the butterfly wing effect.” That is, a butterfly wiggling its wing in Brazil could literally affect the weather over Texas. Lorenz could only conclude to the unpredictability of weather. Chaos again. Some years later, as biologists, mathematicians and medical science confirmed instances of similar “sensitivity to initial conditions,” the importance of understanding chaos and complex dynamic systems became apparent.
Complexity Theory took so long to emerge partly because computer technology provides the main tool of exploration. Researchers rely on computers to graph complex dynamic systems. They then use these models to follow the phases and states of such systems as they change through various frames of spacio-temporal reference.
In a relatively short period of time, we’ve learned an enormous amount about chaos, complexity and how complex systems behave and evolve. For some, the results have been disappointing. Critics of Complexity Theory see little value in models and descriptions of systems that, in the end, defy prediction. For others, the recognition that such systems share characteristics — some of them universally — holds tremendous potential for understanding our world and ourselves.
No one would disagree that Complexity Theory has a cross-disciplinary following. Discoveries made in one field translate readily into another. Details of turbulence in thermodynamic contexts contribute to understanding the behavior of financial markets and devising advertising strategy. Investigations of evolving microbiological worlds provide insights for computer software design and earthquake prediction. Research into the noise of electric circuitry proves valuable to space exploration and business administration. Complexity Theory can appeal to economists, biologists, physicists, psychologists, astronomers, mathematicians, meteorologists, historians, politicians, sociologists and military strategists. Because complex dynamic systems share certain attributes whether such systems are ecological units, living cells, immune systems, clouds, sociological networks, stock markets, neurophysiological phenomena, periods of historical transformation, language, sand piles or traffic jams.
One might reasonably wonder how a single theoretical approach could yield useful insights about phenomena as diverse as sand piles and human societies. Certainly, Complexity Theory recognizes different varieties of complex systems. Some are fixed, static over time rather than dynamic. Others change with time, but within limits set by the fixed or “frozen” character of their agents. In a third category, “adaptive” complex dynamic systems have relatively free agents and are able to change themselves.
Things such as the molecules in a cup of coffee, the mouse or motherboard of a computer do not exercise Subjectivity in the way of living organisms, especially human beings. At the atomic and sub-atomic levels, deep within and from long ago, choices and decisions created bondings that make “fixed” things what they are. Their apparent stillness — in our frame of reference — disguises activities continuing at these deeper levels. A system composed exclusively of such agents behaves in a more limited fashion than a system including living organisms. When you pour cream containing too many bacteria into your coffee, you’ll get unpredictable curdling as well as the black-to-brown turbulence.
Living systems such as ecological networks exercise greater freedom, choosing direction and movement without outside intervention. Some can adapt their very forms to harmonize with information gathered from the environment. A human society exemplifies such an “adaptive” system. This is especially the case in societies with increasingly voluminous cultural output, sophisticated communications technology, cultural pluralism and a widening array of possible activities open to individual agents. Anything that adds randomness increases complexity.
All complex systems are made up of many parts in differing relationships with each other, interacting in ways that change over time and with randomness a defining factor. However, a clarified sense of “not simple” only begins to unfold what we now know about complexity. Complex systems share several intriguing features. They are self-organizing and non-linear, characterized by iteration, emergent patterns and a universal order/chaos dynamic.
Almost all complex dynamic systems share the trait of “non-linearity.” That is, the dynamic of such systems, rather than following step-by-step sequences, functions by way of feedback loops. In a feedback loop, the information generated by the system goes back into the system, and contributes to directing the system as it moves to the next moment. Turning on the air-conditioning and setting the thermostat, for example, activates a feedback loop. When the air-conditioner cools the room to the desired temperature, the thermostat informs the air-conditioner to shut down. The information moving from air-conditioner to room to thermostat and back to the air-conditioner represents a relatively simple feedback loop.
The master narrative and our institutions exemplify feedback loop activity in a highly complex adaptive system. The master narrative and its many sub-narratives teach us to think of ourselves and our interests as separate from one another and our planet. Overlapping micro-theatres of power enact this narrative. Micro-theatrical power relations shape and are shaped by our macro-level political, social and economic institutions. Which generate environments, structures and ways of doing things that reflect, reinforce and reproduce that same narrative of ego identity.
Like fractals, complex dynamic systems function by iteration. The parts or agents of the system repeat moves, formulae, schemas. Through this repetition, system-wide patterns emerge. These patterns map the system’s trajectory: where the system is going, what it’s doing. The “emergent patterns,” sometimes unexpected and changing, could never be studied were the system taken apart and analyzed piece by piece. The property of “emergence” draws our attention to an underlying principle of complex dynamic systems: the whole is greater than the sum of the parts.
This in no way diminishes the importance of individual agents in such systems. Indeed, it is exactly the individual agents of the system that create the emergent patterns. All complex dynamic systems are “self-organizing.” That is, they are moved and directed from within, rather than from outside.
The agents or constituent parts are likely to have differing relationships with one another, different roles or functions in the system. Some may have more information than others, more power to influence the system’s trajectory, more opportunity to effect change. Parts within the nucleus of a living cell, for example, direct metabolism and reproduction; while other parts produce energy from food, remove waste material, maintain the cell walls, etc. In successful complex dynamic systems, such differentiation is based on competency to perform the particular function in service to the whole.
Other criteria, however, underlie the hierarchy of the complex dynamic system we are trying to understand and change. Societies informed by the master narrative privilege certain agents — not on the grounds of competency — but rather according to arbitrary criteria such as birth to a particular social group, “connections” and so forth. In addition, ego-identified societies distort behavior by teaching that individual responsibility entails taking care of oneself and perhaps a narrowly defined family, but does not require concern for the welfare of anyone outside that circle. These particularities further complicate a system where agents vary in power.
In all complex dynamic systems, however, the impulse to change can and often does come from below. Equally important, those above do not simply control the system. Indeed, efforts to do so increase the likelihood that the system will veer out of control.
Whatever their configuration, the agents of a system create the emergent pattern. The preferred pathways of the actors converge along similar lines. Gathering together these trajectories results in boundaries that define favored activities or behavior attractive to the system. These boundary areas appear as a basin of attraction or sometimes several basins. In a computer generated mapping, the basins look like lakes or snaking rivers. Informing these favored regions, at the heart of the basins, reside attractors.
Several types of attractors have been identified. Fixed-point attractors appear in systems with limited degrees of freedom. Trajectories of a fixed-point attractor might radiate from or toward a single location, such as the eye of a hurricane. Periodic attractors occur in systems with an added focus of interest. Such systems oscillate between two possible positions, as in the repetitive behavior of a metronome. Donut-shaped torus attractors emerge in systems with greater dimensionality, capable of diverse movement and activity; but which ultimately return to the original state. A metropolitan traffic pattern, for example. The strange attractor arises in systems capable of spontaneous self-organization and change. Strange attractors are all about exploration. They never bring a system back to the same condition.
These concepts can throw light on the functioning of narratives and the narrative field. We ourselves, of course, are the agents who generate and iterate the narratives in the field. From conversations to formal conferences; water coolers to dinner tables; billboards, newspapers, magazines and the evening news; music lyrics, websites, television and film scripts — we fill our world with reiterated narratives. Our decisions and actions embody narrative. If we were to assign a dot to every narrative we encounter each day, and align the dots according to their underlying narrative, we would eventually find the lines swirling about an attractor — the master narrative. One might argue about which category the master narrative fits. Perhaps some kind of fractal torus?
Researchers use the term “nested” to describe another shared characteristic: how complex dynamic systems reside within one another. Systems communicate and interact with surrounding and neighboring systems, yet behave independently. The agents that comprise a system are themselves complex dynamic systems, especially in the case of highly adaptive systems such as human societies. The agents carry on their own interior iteration, creating emergent patterns by making choices or “bifurcations.” Decisions or solutions to problems move toward a constantly transforming goal state. In a healthy or successful system, information flows freely among agents across all levels, guaranteeing the well-being of individuals and the system at large.
Interactions among agents in a system do not always result in agreement, however. Whether in a living cell or a human community, sometimes information being passed has become out-dated, even corrupted. Interests of the agents may fail to align or fall out of alignment. Disagreement can appear in the bi-directional flow of information; resonance give way to conflict. In stable systems, such disturbances last for only a short period of time and have little effect on the overall pattern. When fluctuations or alternatives convey new information preferred over the old by large enough numbers of individual agents, the system may shift to a new solution. Differences also produce untried possibilities that may prove useful later.
A system is “healthy” when the microscopic to macroscopic behavior leads to successful adaptation with the outside world. As the whole system responds to the micro-intentions of agents on local levels, the system moves from one attractor to another, climbing to peaks of fitness, complexification, adaptation, progress. These moves and shifts are made possible by maintaining a balance between reliance on existing solutions: order; and openness to implementing innovations including their unpredictable outcomes: chaos. This middle ground is often referred to as the “edge of chaos.”
Complexity Theory observes a surprising universality to the order/chaos dynamic of systems. Because they are nested within other evolving systems, successful solutions will inevitably encounter changed circumstance over time. And not all solutions are equal to the new requirements. If a system fails to change and evolve in relation with neighboring systems or proposes an inadequate solution to altered circumstance, destructive forces set in. When changing ambient conditions threaten survival, the only hope is that a new solution might emerge before the system falls into extinction.
Systems can lose their order/chaos equilibrium along several pathways. In hierarchicalized adaptive systems such as human societies, agents at higher levels may not agree with communications coming from micro-levels that call for change — when change is required. Depending on the magnitude of the problem, this could lead to several possible scenarios.
If upper level agents do not perceive the issue clearly or their intelligence is overwhelmed, they may reply that nothing needs to be done; that there is nothing that can be done; that the best possible is being done; or that minor adjustments will suffice. Since upper level actors have greater access to communication networks, they can to some extent suppress lower level urgings. They might “canalize,” that is, limit and distort the information available system-wide. Thus agents in the system at large end up making decisions on the basis of limited or inaccurate information. Or upper level agents can introduce “noise” that drowns out the fluctuations, thereby destroying strange attractors or alternative basins trying to form. This failure to respond to the need for change can drive the system over the edge.
In a similar scenario, empowered agents might recognize the need for change, but attempt to force the system back into failed solutions of the past. This strategy causes the entire system to lose stability. A series of such of backward-looking non-solutions, each failing in turn, can cascade through the system and lead to total collapse.
Another possible scenario finds an alternative attractor forming, but without stability. Or properly forming, but meeting with indifference. A system recognizing the need for change might generate such an alternative attractor or even a series of them. Without focus or sustained energy, however, they disappear and reappear, repeatedly — without being able to save the system.
Successful complex dynamic systems respond to small problems long before total disorder and destruction set in. They perform well, even when sudden and unpredictable catastrophic circumstances arise. If threatened with complete dissolution, complex adaptive systems can respond by wholly recreating themselves. Complexity Theory calls such total transformations “phase transitions.”
Phase Transitions
Phase transitions represent dramatic transformations. So striking the changes after a phase transition, the outcome seems improbable, almost inconceivable, from the original state. We see a grand scale example in the transition undertaken when the bacteria that were Earth’s first Life-form had used up the carbon dioxide they needed and filled the atmosphere with oxygen that was poisonous to most of them. Faced with mass extinction, one group of carbon dioxide using bacterial paired with a group of oxygen breathers to form a wholly new kind of creature with different parts performing different functions. Yet phase transitions also take place on a small scale, everywhere, every day. Water, a liquid, turns into ice, a solid. You add milk to your coffee. You fall in love.
Phase transitions do not unfold previously existing patterns. Even the metamorphosis of caterpillar through chrysalis to butterfly does not represent a phase transition, since the transformation is pre-programmed. Most adaptations also do not qualify. Complex systems such as cells, organisms, ecosystems, societies or individual human beings undertake phase transitions when faced with issues of survival. In a phase transition, agents risk everything to create an entirely new solution. The outcome is unprecedented and unpredictable.
Most phase transitions take place rather rapidly and appear to be spontaneous. Yet from another perspective, systems appear to approach phase transition boundaries slowly, then suddenly leap them. Historians have applied the term to the 1929 stock market crash and the Great Depression; as well as the late-nineteenth-century transformation of Japanese culture and society. One could dispute whether such historical events qualify as phase transitions. Just as one can argue whether phase transitions are effected by sudden events; or prepared by longer term developments in previous periods. In any case, examples involving human societies permit us to imagine how the kind of phase transition we need could take place.
As with other phenomena in complex dynamic systems, phase transitions result from the micro-level activities of the agents. In a phase transition, agents respond to circumstances threatening the entire system. The magnitude of the concern displaces issues that previously dissociated upper- and lower-level interests. The survival of the system and the welfare of interdependent neighboring systems is at stake.
In the earliest stages of such a phase transition, individual agents perceive that something is wrong — and needs to be fixed. These first responders begin to understand the severity of the situation when they recognize that the problem is system-wide and associated with the system’s attractor itself. Initially, agents and system may cling to the formulae that they had so carefully and laboriously evolved. These very individuals now grappling with the unforeseen challenge may earlier have rigorously defended the attractor informing the existent system. When it becomes clear that adjustment, reform or mere tweaking cannot address the underlying logic of the crisis, more agents throughout the system awaken. Because complex dynamic systems are sensitive to initial conditions, a micro-fluctuation can bring macro-results — “the butterfly wing effect.” An alternative narrative begun on a lower level could cascade upward.
If the individual actors processing this new information belong to networks with robust and wide-reaching lattice structures, horizons rapidly expand. The alarm percolates through the system by media and word of mouth. Local fluctuations increase and engage ever larger sets. With the stakes involved increasingly well-articulated, the desire for change grows. As urgency offsets hesitancy, agents begin accepting the risks and taking up the costs. Efforts multiply. This paradigm shift prefigures what will follow.
The second stage opens with system-wide desire for survival driving the search for solutions. Availing itself of all possible input, the system draws on its full potential. The value of alternatives, which may not have been acknowledged up to this point, now becomes apparent. Elements at the margins have been pushed there exactly because they differ from the system attractor. The system now reconsiders these bits and pieces of information.
In a phase transition, the sought-after passage does not come from simple repetition of peripheralized previous formulae, however. What was marginalized may form the basis of the new solution, but not its entirety. Agents sort through and build with such side-lined information, creating an unforeseen, unexpected new way. A strange attractor.
The third stage sees implementation. As individuals and clusters of individuals make the choice to abandon the original basin of attraction and migrate to the new pattern, bifurcation cascades. Agents generate, sustain and elaborate the alternative by constructing institutions that conform to the new schema. If the strange attractor truly does represent a viable alternative, it now informs the entire system — no matter how radically improbable or unbelievable the solution may have seemed earlier.
In order to succeed, each stage of a phase transition requires communication and input of energy. However large or complex the system, the individual agents — with their varying degrees of knowledge and influence — carry the drama forward. The smallest act can have immeasurably far-reaching effects. As agent evolve within the larger evolving system, they bring about the phase transition.
Conclusion
In Chapter Five, we mentioned three key phase transitions in the story of the Universe. The phase transition created by the quarks at the Beginning; the one initiated by the long-chain molecules at the onset of Life; and the one brought about by the early bacteria when they found the pathway to oxygen breathing and the eukaryotic cell. In the first, quarks create Relationship — and matter — by sharing their excess energy. An act of trust opens the world. Love begins the Universe. In the second, long-chain molecules start passing smaller molecular structures back and forth with one another. Giving to others, molecules invent metabolism, the basis of Life. In the third instance, bacterial agents act with intelligence when they recognize that their own metabolic activity is threatening Earth’s fragile biosphere. Before the phase transition, the Sugar-making Thermo Spirochettes probably had little to do with the Purple Oxygen breathers. In the end, both sacrifice their separate identities to become organs of a larger body — and open vistas previously unimaginable.
We now stand at a similar crossroads. We have a world broken and breaking; we want a world of Love. Complex as our conditions may be, we’ve already begun to understand how we can reach this goal. Complexity Theory provides a model for profound change and affirms the fundamental insight that we ourselves are the agents responsible for our personal psychology as well as our social, economic and political systems.
Our future, that of our children and our planet, hinges on the exercise of human freedom. Must we let the sign system, the master narrative and our micro-theatres of power lock us into relationships and institutions that spell our doom? Do we not have the freedom to use our words, language and cultural tools to create a new organizing narrative of Love? A narrative leading to a world of real equality, greater freedom; cooperation and care; Peace on Earth. Complexity Theory cannot predict the outcome. That future is ours to create.