Our perception of the world begins with an act of separation. With our first breath, we see the interaction with our surroundings as an individual experience. The world and all of its inhabitants are the other in a mindset dominated by a sense of self. Most of our early developmental efforts involve coming to terms with that separation. Once we learn to cope with all of the external stimuli, it is a natural consequence that we might continue to perceive the world as a place where individuals mix with the environment.
Many of the cultural mantras that Americans, in particular, are brought up to believe—the general praise of hard work with the lure of big rewards—imply an absolute control an individual has over his environment. More and more, research is showing us such is not the case. The world may be filled with individuals, but individuals who are inseparable from each other. We are all connected in ways that affect our social, emotional, physical and mental well-being. If there is a societal lesson to be learned from investigating complex systems in areas such as biology, economics and network science, it is that emergent properties of a system are not dictated by any single component. Individuals matter most in aggregate form.
Complexity, as it is defined at Indiana University’s School of Informatics, is differentiated from complication. The example given to illustrate complication is a 747 airliner. Remove any one of it’s thousands of components, and you run the risk of breaking the plane. It is a complicated machine because it has many parts working together, but it is not a complex system because there is no emergence occurring. The plane flies by design, with specific components playing critical roles in that function. If one could imagine a complex plane, its flight would arise out of the interaction of many similar parts. Such a machine might be much more difficult to control with precision but much less susceptible to failure of a specific component.
Complexity is also defined by change over time. We can examine a network, for example, as a snapshot. The nodes and connections between them might reflect an instant in time or an aggregation of a longer period of time. Our measurements and understanding of that network are static, and the value of static networks is through comparison (this system is more than that system, or this network has a property another one does not) and in anticipating its potential (information dispersed along this network is likely to spread at a certain rate).
A static network is never a practical model for real systems. All real networks change over time. Connections between nodes are not always persistent, and the absence of that relationship at any given point in time changes the network properties. In a social network, for example, a scale-free property may depend on an individual engaging all of their friends at once. In reality, we are only connected with a handful of people at a time, with parts of our daily lives spent disconnected from that network. As a result, this dynamic cycle of connection and disconnection over time is a vital part of the emergent properties that define systems.
Dynamics are the key to application of complexity research. It is not enough to understand static relationships—they are merely representative of interactions, and interactions occur over time. Relationships have beginnings, endings and intensities. The changes in relationships lead to emergent forces that drive the system back and forth around critical points of interest. In a sense, dynamics is the movement in and out of complexity, from the potential to the real and back.
The topics of study in our seminar included a review of network modeling and search, genetic evolution, food webs and game theory. These areas help illustrate four important concepts serving as a foundation for complex system dynamics: scaffolding, hierarchy, computation and modeling.
Scaffolding is the arrangement of components and potential relationships. This is most easily visualized in networks as nodes and links. Newman’s great summary of scale-free networks focuses on that key emergent property, tying it to the math culled from actual measurements of real-world networks. These measures do not reflect dynamics, but the structure they imply does frame the system. Over a long enough period of time, these relationships—and hence, the scale-free properties evident in power law distributions—are actively engaged. A static system described through its scaffolding, therefore, represents its potential properties of complexity.
When the component parts are not equivalent, the system contains a hierarchy. In food webs, this is evident in the abundance of creatures at the lower levels of the web. A delicate balance is struck between the rates of reproduction and consumption, with those up higher in the food chain tending to live longer and eat more than those at the bottom. Hierarchies also reflect a distribution of power that differentiates one class of components from another. Some nodes in a network benefit from both placement within the scaffold and the propensity to improve that advantage by connecting with other nodes. Dynamics, therefore, reflect either changes to this hierarchy or the balance of driving forces that results from the differences between top and bottom.
There is also a hierarchy of systems, which increases in complexity as more and more systems are embedded in the components. A social network, for example, is composed of human beings composed of organs composed of tissues composed of cells composed of proteins. Because a human network contains within it the emergent properties of all of its component systems, the complexity of the dynamics increases and becomes much more difficult to model.
Computation in a complex system comes from both change and emergence. Systems can become computational tools by examining the emergent properties evident in the system. This is sort of like the relationship between bits and ASCII letters in computer logic. Turning bits one and off dictates a specific value that is interpreted at the system level as a character. Likewise, complex systems can create emergent properties that are read in a similar fashion. Computation is also about evolution of parameters. Using duplication and mutation of components, better strategies can arise. The dynamic of a system will adjust as components change. If scaffolding is the structure and hierarchies are a distribution, then computation is the function of a system.
Models come in two main varieties: explanation and understanding. Explanation models try to mimic the real world, creating simulated labs in which to conduct experiments by manipulating components or making use of the system properties. Models of understanding try to explore the world, changing the parameters of a system to figure out how the dynamics may change to find a new balance. Models tie together scaffolding, hierarchy and computation with a purpose of explaining or understanding the world.
It is through constructing dynamic models that the driving forces of a complex system can be understood. Precision is not the goal of such investigation. Approximation is a technique of blurring complicated component behavior into a series of few, simple rules. The more accurate the depiction of the interaction between component types, the better the model is at describing the real world.
Two kinds of models focus attention on these system forces. In a driven-dissipative system, the model is constructed to reveal two forces working to keep the system oscillating around a critical point. One force works slowly and steadily, increasing the energy invested into the system. The second is a fast force working quickly to dissipate that energy and keep it from accumulating unevenly. Both forces are a product of component interaction. The other model is the HOT model, which attempts to accommodate more than two system forces through optimization of multiple goals.
The benefit to studying complex systems is derived from our understanding of system dynamics. We study such systems by simplifying and differentiating component rules of interaction. The outcomes of those interactions are system-level properties, which can be used for computational purposes or to model the real world. We do not control the world by ourselves, but through more informed quality of interaction with each other will change those outcomes for the better.
