April 10, 2010
Nonlinear dynamics are concerned with messy systems. Examples for these systems are the human brain, the evolution of life itself and the weather. There is not a single science of non-linearity, but there are different streams of research such as chaos theory or the theory of complex adaptive systems. The latter strand takes up an agent- and rules of interaction-based approach to modeling complexity. The first explains the behavior of systems that can be modeled by complex equations where the output of one calculation is taken as the input for the next. These equations are repetitive and iterative.
Chaos theory explains how the parameters in the equations cause patterns in time. These patterns are called attractors. A parameter might be the flow of information or the amount of energy in the system. At low rates the system moves forward displaying a repetitive, stuck behavior. This pattern is called a point attractor. At higher rates the pattern changes. At very high rates of, for example information flow, the system displays a totally random behavior. The pattern is highly unstable. However, there is a level between repetition/stability and randomness/instability. This level is called the edge of chaos. The pattern in time is called a strange attractor.
Never the same but always recognizable
The strange thing with a strange attractor is that the ongoing movement is never the same but always recognizable. The pattern is paradoxically stable and unstable, predictable and unpredictable at the same time. These patterns are spatially called fractals. Chaos describes a dynamic that is not a synthesis of order and disorder. It is about orderly disorder or disorderly order. The very meaning of these words is new.
The weather is normally used as an example of a system that displays this pattern. The overall weather patterns can be (almost) predicted over short periods of time. Over long periods, the behavior cannot be predicted. The long-term behavior of a system like this is determined as much by the smallest changes in the smallest of parts of the system, as it is determined by the laws governing it. The conclusion is very clear. Predictability is always short-term. Long-term predictions would only be possible if absolutely all the variables in the system could be measured with absolutely infinite accuracy. But it is impossible to know all the variables and it is totally impossible to measure all the variables with the accuracy needed.
The smallest overlooked variable or the most minute change can escalate up by non-linear iterations into a major transformative change in the later life of the system. Another conclusion is that from a chaos theory perspective, movement towards equilibrium is always movement towards death. If a system is healthy, successful and alive, it is “at the edge of chaos” where the long-term cannot be seen.
Classical physics took individual entities and their movement (trajectories) as the unit of analysis. Chaos theorists such as Ilya Prigogine, claimed that these trajectories cannot be calculated because of the impossibility of measuring with the precision needed. But there was something even far more exciting going on. Henri Poincaré was the first scientist to identify two distinct kinds of energy. The first was the (kinetic) energy in the movement of the particle itself. The second was the energy arising from the interaction between particles. When this second energy is not there, the system is in a state of non-dynamism. When there is interactive energy, the system is dynamic and capable of novelty and renewal. Interaction creates resonance between the particles. Resonance is the result of coupling the frequencies of particles leading to an increase in the amplitude of motion. Resonance makes it impossible to identify individual movement in interactive environments because the individual’s trajectory depends more on the resonance with others than on the kinetic energy contained by the individual itself.
Every interaction of any particles is thus potentially meaningful and can lead to amplification of the slightest variation. Interactive systems with even the smallest variations take on a life of their own that is under continuous construction. The future form and direction of the system is not visible in the system at any given time. The future is not in the system and it cannot be chosen or planned by anyone.
The scientists at the Santa Fe Institute developed the other strand of research: the complex adaptive systems approach. A CAS consists of a large number of agents. Each agent behaves according to its own intentions and rules for local interaction. Local here means that no agent can interact with the whole population of agents at the same time. No individual agent can determine the pattern of behavior that the system as a whole displays. These adaptive systems display the same dynamics as the chaos theorists found: stable equilibrium at one end of the spectrum, random chaos at the other, and in-between the newly found complex dynamic of stability and instability, predictability and unpredictability, paradoxically at the same time: the edge of chaos.
From complex adaptive systems to complex responsive processes
The conclusions are important for us. Firstly, novelty always emerges in a radically unpredictable way. Secondly, the patterns of healthy behavior are not caused by competitive selection or independent choices made by independent agents. Instead, what is happening, happens in interaction, not by chance or by choice, but as a result of the interaction itself.
The Internet changes the patterns of connectivity, transforms our understanding what “local” is, and makes possible new enriching variety in interaction. The changed dynamics we experience every day through social media have the very characteristics of the edge of chaos.
The sciences of complexity change our perspective and thinking. Perhaps, as a result we should, especially in management, focus more attention on what we are doing than what we should be doing. Following the thinking presented by Ralph Stacey, the important question to answer is not what should happen in the future, but what is happening now?
Our focus should be on the communicative interaction creating the continuously developing pattern that is our life.