Complex Systems

When engineers design a system, they often want to ensure the system achieves the desired outcomes as closely as possible. Disorders and uncertainties need to be limited at all costs.  However, in many naturally occurring systems and human organizations, i.e., complex systems, the disorder is part of the system that cannot be completely removed. The relevant notion is called stochasticity. 

Stochasticity in complex systems means that the outcomes of complex systems cannot be precisely predicted due to uncertainties or disorders in individuals' behaviors or interactions [8-9]. Compared to systems that always generate the exact same result based on the same input, stochastic systems may produce different results for the same inputs. 

Stochasticity can arise from random processes within the systems. For example, mutation is an inherent random process in biological systems that never stops. Stochasticity can also be caused by multiple interactions among individuals. Because these interactions occur parallelly across the system, varied local sub-outcomes may yield in different parts of the system. When these sub-outcomes feed to one another over time,  the overall system outcomes can be unpredictable. Besides, system outcomes can be hard to predict if the environment introduces external noise.  

Finally, we come to emergence, a core aspect of complex systems. 

Emergence refers to the generation of nontrivial, robust patterns or behaviors at the system level through self-organization within a complex system [9-10]. The key to this characteristic lies in the fact that the robust patterns or behaviors are collectively, rather than additively, caused by the continuous interactions among all individuals in the system [5-7]. Decentralization and stochasticity also influence the emergence process. Thus, the emergent patterns or behaviors may be very different from the individuals’ behaviors and cannot be reduced to individuals’ behaviors, highlighting the notion of levels of organization. For example, in ant colonies, intricate social structures and roles emerge from the simple behaviors of individual ants. Despite each ant following relatively simple rules, their collective actions lead to organized colony behavior such as foraging, nest building, and defending. The most fantastic emergent phenomenon is the human consciousness. While the individual elements, such as neurons and molecules in our brains, are not conscious on their own, the interactions among billions of them can give rise to a higher-level phenomenon—consciousness. 

Time plays an important role in emergence because interactions often require time to accumulate changes that become visible to human beings. For example, in the states of matter model, it takes time for particles to attract each other when cooled down, forming the liquid phase, as seen in real life. Noticeable changes in ecosystems or human organizations, whether beneficial or detrimental, may take decades to emerge. Understanding this will help us anticipate long-term consequences.