Complexity Science

Complexity science is a cross-disciplinary approach to scientific investigation that emerged late in the 20th century. It has demonstrated value in applications as diverse as information and communications technologies (ICT), social media marketing, machine learning, and state-of-the-art weather forecasting and epidemiology models.

This article describes some of the surprising attributes that “complex” phenomena have in common. 

The study of complexity is closely associated with the Santa Fe Institute who offers very informative tutorials about many aspects of complexity science

Complexity Implies Nonlinear Interactions

“Complexity” typically implies that there are interactions or relationships among objects or actors of some kind. These objects or actors, often called agents, can be physical objects like molecules, bacteria, or even human beings, but they can also be conceptual objects such as quantities represented as random variables related in a nonlinear expression. This means that to produce their combined effect, rather than simply being added or scaled linearly by constants, they are effectively multiplied together or appear in exponential expressions.

Nonlinear Interactions and Feedback

Nonlinear interactions that are characteristic of complexity are distinct from linear ones in that nonlinear expressions which predict collective output levels are not proportional to input levels. This nonlinearity is due to positive or negative feedback effects. Positive feedback suggests amplification or exponential growth of certain input effects, while negative feedback suggests exponential dampening or minimization of some input effects. One of the insights from complexity studies is that the feedback effect can have many surprising implications.

What makes an object or actor an “agent” is that it interacts with others according to a set of local rules of interaction. Outcomes from these micro-level fine-grained interactions typically involve some element of uncertainty because very often in complex systems, the precise state of inputs and processing within a given agent cannot be known precisely. As the complex system iterates from time step to time step, fine-grained uncertainty can be amplified by feedback effects with surprising implications.

Complexity science has spawned several disciplines and approaches that have found application in virtually all fields of modern science from cosmology and quantum electrodynamics to neuroscience, socio-technical systems, network dynamics and machine learning.