Not everything that exhibits evidence of the primitive components of complexity is itself complex. Emergent properties may be present in few-bodied systems, and many-bodied systems may lack a characteristic adaptability. In our definition of complexity (well, my definition, by way of the IU School of Informatics), three things are required: emergent behavior, many component parts, and evidence of dynamic evolution. It could be argued that there is a fourth requirement — dealing with the intentionality of the system and its impact on sustaining higher operations.
Emergent properties can take several forms but are all characterized by the distinction in behavior made between the system and its component parts. Emergence does not occur through the collaboration of agents with an intentional systemic goal. Instead, the agents focus on local awareness and self-interest, only to alter the context of their environment in an unanticipated manner — a new behavior emerges at the system level. There is no blueprint used by the components to dictate what that behavior will be.
The signature straight line of a log-log distribution graph is usually an indicator that complexity is afoot. Complex systems are typically (perhaps always) characterized by power law distributions. That is, big phenomena are not rare as they normally are, and the same properties are exhibited across all scales. Power laws are not the only emergent properties, however.
Complexity also requires a system with many component parts. Very small numbers of objects within a system lack the computational hurdles that make precision impossible. While the notion of objects in isolation is philosophically refuted, a system with few bodies comes closest to an isolated state — there are fewer objects with which to interact and therefore more predictability and less of a chance of unanticipated system behaviors. The laws of nature work when elements are few, but it is the mean value that becomes meaningful when N is large. Even if it were possible to know and calculate all, those calculations would apply to just one possible current state.
Finally, a complex system must be adaptive. Complicated systems — those with many parts existing for a systemic purpose — are not adaptive. If a part breaks down or is removed, functionality is lost and the properties of the system change radically. In complexity, the dynamics and size of the system components are able to respond to changes in the environment and seek a new equilibrium. A many-bodied, emergent system is not a complex one if it is dependent on the presence of a particular component.
A Requirement of Universal Intentionality
A naturalist might argue that a tree falling in the woods does make a sound, regardless of the presence of observers. Air is disturbed, energy is dissipated, and objects are displaced. One could visit the forest on two separate days and note the changes in these effects. However, the concept of sound is more than merely the evidence of its properties. It is also the experience of those who might give those properties meaning.
Although there has been no discussion of the philosophical nature of complexity, this may prove to be an integral part of the definition. Just as no component can act in isolation, so too will the resulting systems be in relation with other systems. It is not an inconceivable notion that complexity only exists if it is “heard†by other systems to contribute to a useful dynamic. A power law alone isn’t sufficient to have complexity; it must also become part of the intentions of the universe.
What Complexity is Not
Complex systems are not able to facilitate an exact prediction of events. The laws of nature are inherently probabilistic, which means emergence cannot be causal at the component level. One agent is interchangeable with another, and the system is reliant on size of environment, quantity of population, and quality of interaction. That does not mean complexity cannot be predictive or accurate, but it cannot be exact.
