Nonlinear dynamics are concerned with messy systems. Examples for these systems are the human brain, the weather and the evolution of life itself. 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 what is going on. The first explains the behavior of systems that can be modeled by complex mathematical equations where the output of one calculation is taken as the input for the next.
Chaos theory explains how the parameters in the equations cause patterns in time. These patterns can also be described as phase diagrams. Then they 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, “spatially”, 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 and stability or randomness and instability. This level is called the edge of chaos. The pattern in time is called a strange attractor when it is described as a phase diagram.
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. Chaos theory describes a paradoxical 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 often 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 longer 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, if it is possible, is always short-term. Longer-term predictions would only be possible if absolutely all the variables in the system could be measured with absolutely infinite accuracy.
As it is impossible to know all the variables and as it is totally impossible to measure the variables with the infinite 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.
The scientists at the Santa Fe Institute developed another strand of research: the complex adaptive systems (CAS) 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 or cause 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 simultaneous stability and instability or predictability and unpredictability, paradoxically at the same time.
The conclusions are hugely important for us. Firstly, novelty always emerges in a radically unpredictable way. Secondly, the patterns of healthy behavior are not just 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 competitive/collaborative 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 may 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. The important question to answer is not what should happen in the future, what the goals are, but what is happening now that creates the continuously developing pattern that is our life.