Many of our most pressing challenges, like managing ecosystems and economies, or preventing mass epidemics and market crashes – require a better understanding of complex systems. In recent years, the science of “complexity” came into existence and has grown rapidly. “Complexity” has a precise meaning in science. We call a system “complex” if the whole transcends the parts and if multiple agents participate in it. Most complex systems consist of diverse entities that interact in space and in time; they can be real or virtual. Examples of complex systems are ecosystems, cities, universities, or the stock market. Systems that are merely based on a feedback loop, like automatic temperature regulators, are not complex. Complicated systems are also not necessarily complex. Complicated systems may have diverse parts or many variables, but they are not adaptive.
They consist of interdependent, diverse entities, which adapt to or respond to the local and global environments.
They are often unpredictable: they can produce large-scale events, and they can withstand substantial pressure. They produce phenomena that emerge from the bottom. What occurs on the macro level differs from what happens on the level of the elements. Emergence takes many forms, including self-organization. Due to emergence, complex systems are capable of producing amazing novelty, from coral reefs to modern traffic systems.
We live in a world with increasing complexity. Modern science searches for the smallest components of reality, or the the most general unifying theories of everything. The scale dimension from the smallest to the largest leaves out complexity, or the systems that emerge when multiple agents interact. Traditional science was based on the Cartesian model, which separates the subject from the object of inquiry; eliminating the fact that in many sciences the subject cannot be separated from the field of research. Science that focuses on our living environments forces us to take an interest in complexity, and it is important to map out the elements of this new paradigm. The first step consists in formulating a reasonably precise definition of complexity so that we can accurately compare the complexity of situations. We still need to find ways to reduce the massive amounts of data or the seemingly diverse number of phenomena to basic structures; this work can now be achieved better and better with new computational tools, which allow us to simulate situations, thereby enhancing scientific methodology. Computers allow us to move beyond metaphors and investigate old questions (for instance: what is life, and how did it come into existence?) with new tools.
A system is complex if its agents meet four criteria: diversity, connection, interdependence, and adaptation. There should be diversity among the agents, but the agents need to be connected. This means that they react to each other and learn from each other, which makes their actions interdependent. They adapt to the environment as well as to each other. We can develop measurements for each one of these dimensions and then compare the results across different systems.
This gives us a way to analyze complexity, because it makes the definition of complexity less vague. Rather than just saying “economies are complex” or “rainforests are complex,” we can now base those statements on precise definitions. These four qualifications can also be used to demonstrate that the world we live in is becoming more complex in most regards: the social, economic, and political spheres grow in complexity, and subsequently our whole world system (physical, ecological, or biological spheres) is becoming more complex as well. We begin to see structure in complexity due to a conceptual framework that evolves based on contributions from diverse disciplines: Systems theory, cybernetics, computer science, biology, sociology, economics, or earth sciences.
Complex systems can be nested: the components of one complex system can be another complex system. The global economy, for instance, can be the result of a system that contains national or regional economies as participants. These systems can also have memory: when the adaption to changed environments occurs as a consequence of the history of the system.
In addition to adaptability and robustness, complex systems can produce large events. In spite of their stability, they don’t always behave as expected – they can exhibit sudden dynamic shifts into new states of equilibrium. That’s why so many experts fail to predict stock market crashes, for instance. They expect changes withing the normal distribution curve, but complex systems can reach tipping points. This seemingly unpredictable or even paradox behavior can be decoded retroactively with a deeper knowledge of the parameters mentioned above, but some of these systems are complex enough that they simply remain unpredictable. This also means that the boundary between the system and its environment can never be sharply drawn.
These sudden changes, like political revolutions, or phase transitions in chemical reactions, are the results of tipping points. Phase transitions occur when forces within a system reach critical thresholds. Then, the state of the system changes; often drastically. A phase transition is a form of non-linearity. Non-linearity can occur in many ways; which leads to the unpredictability of the system.
Tipping points can also be the moments when something new emerges – a new trait, or quality of the system, like intelligence in biological organisms. We can call this main feature of complex systems also the mystery of emergence. The macro-level differs qualitatively from the micro-level, not just in terms of scale. The phenomenon of emergence can be observed in the self-organization of systems, for instance when spatial pattern or structures emerge, such as in flocks of birds or schools of fish. The mystery lies in the fact that emergent phenomena arise from the bottom up, without superimposed formalism. Before the occurrence of the new trait, we could not have predicted it, but after it came into existence, we can retro-actively try to explain it.
A complex system is dynamic – it does not settle into a simple pattern; it is capable of generating novelty as long as it exists, and since it evolves and adapts, it can last for a long time. It is neither equilibrium, nor chaos. Complex systems somehow overlap with live; they can be studied in biological evolution, or in aspects of human civilization. Multiple system-levels are possible; the whole earth can be seen as a system of systems.