„I think the next [21st] century will be the century of complexity“ — Stephen Hawking

Complexity science is an emerging approach to research focusing on a study of systems. It’s an ensemble of theories and tools applicable to various disciplines, technical, natural or social sciences. The concern with the system is with its complexity, multi-dimensionality, dynamism and unpredictability as a result of interconnectedness of its parts. The traditional linear thinking in „cause and effect“ is elevated to a non-linear viewing of the multi-layered nature of systems and networks we exist within and that exist within us. They require more than a simplistic approach towards problem solving. Considering the nature of issues that are occurring, complexity science is applicable to any aspect of today’s world. While other disciplines may attempt to reduce problems in smaller scales and focus on the partial disciplinary analysis, complexity science views relationships among smaller parts and scales.

Professionals in the field of urbanism deal with complex scenarios while strategizing for bettering of urban systems. Being dynamic, non-linear and comprising basically everything that is happening in the built environment, cities are becoming increasingly more complex. Involvement of complexity science is becoming essential, especially when regular strategic approaches are not applicable on a large scale. Complexity theory says that if we really want to understand failure in complex systems, we need to explore how things are related to each other and how they are connected to, configured in, and constrained by larger systems of pressures, constraints, and expectations [1]. Embracing the challenges stemming from complexity and introducing complex systems thinking addresses solutions in regard to their systemic localization and interrelatedness to other issues, not just the issue itself independently from the systemic continuum.

Local interaction of components on smaller scales can spontaneously self-organize to exhibit non-trivial global behaviors and structures on a larger scale. We are talking about organizations without intervention of any leaders or centralized authorities. Individual components in the organization, or a collection, are not to be fully understood or have their state predicted based on information about their constituents alone. That is why such a collection is called a complex system and requires new mathematical frameworks that include the influence of the other components. Investigating complex systems therefore differs from a focused disciplinary inquiry. Complexity science as a study of a system applies to everything regardless of area, considering the following aspects of investigation on a large-scale:

Interactiveness

Complex systems consist of many components embedded into an interactive network. The components interact with each other and with the environment in multiple ways. The network is characterized by multiple types of interactions, sometimes involving more or less components at a time, generating novel information that makes it difficult to study isolated components or predict their future behavior. Additionally, the components of the system can form or are subsystems. The key factor is the multi-scalar interconnectedness and computational dependence that give us an overview of how systems arise as a whole.

Related concepts: interdependence, inter-relatedness, inter-connectedness, network interaction, heterogeneity, system of subsystems, open/closed systems

Dynamism

Systems are being analyzed based on change of their dynamics over time. They undergo a constant adaptation, which sets a basis for long-term unpredictability of their behavior. A state of a system is described by variables. When any of the variables change, the system changes its state and communicates it as a message to its environment. These changes that are directly proportional to time are called linear, whereas changes become nonlinear if they are not proportional to it. Complex systems are typically non-linear and it is rare for such systems to function linearly. The change happens at different rates and are dependent on the variables coming from the environment. They may have phases of stability at which they remain so even in the case of perturbation, or they may be turned into an unstable state caused by a small perturbation. In some cases even small environmental input into the system can completely diverge the system's behavior, which is known as phase transitions, bifurcations or tipping points. If a system is extremely sensitive to small perturbations, chaotic and consistently showing long-term unpredictability, it is called the butterfly effect. System can also be influenced by accumulated imprints of its past functioning, in that case it is path-dependent.

Related concepts: chaos, non-linearity, non-equilibrium, non-predictability, uncertainty, path dependence, context dependence, dynamic behavior, butterfly effect, volatility, non-ergodicity [A]

Emergence

Properties of simple systems can be understood and their behavior predicted based on its components.  In other words, in a simple system the macroscopic properties can be deduced from the microscopic properties. On the contrary, the character of a complex system in its entirety may vastly differ from the properties of its individual sub-parts. The properties of the whole cannot be deduced because of the emergence phenomenon. Emergence refers to a process of surfacing of novel information as a reaction among components and generation of non-trivial collective structure that emits certain behavior. This can be summarized by a popular phrase „the whole is more than just the sum of its parts“.

Related concepts: scale, non-reducibility, non-linearity, breakdown of statistical thinking, surprise, unexpected effects, indirect effects

Self-organization

Interactions between the components of a complex system produces a global behavioral pattern. There is no external initiator or facilitator. Instead of an external course of influence, the system’s self-organizing capability is distributed across sub-systems and their parts integrated through interactions. Self-organization may produce physical structures manifested in physicality as inherent morphologies of organisms or crystalline structure of materials. They are results of informational behaviors translated into system dynamics. As system becomes more organized by its own processes, new information as a form of behavior emerges over time, producing greater complexity. Complex system may also self-organize into a critical state. Patterns that arise in such states exist in subtle balance between regularity and randomness, showing obscure properties like self-similarity [B] or power-law distributions in pattern properties [C].

Related concepts: self-organization, spacetime, self.similarity, burst, self-organized criticality, distributed control, decentralized control, morphogenesis, collective behavior, hive mind, order from disorder, swarms

Adaptability

Instead of following a linear movement towards a steady state, a complex system is active and responsive to the environment. The adaptive processes run on multiple levels — sharing information in the social sphere, psychological development and comparative exchange of cognitive information, operative decision variation, genetic variation, natural selection etc. In case of a component damage or removal, systems are able to adapt to a new state and recover their functionality. Sometimes the ability to withstand perturbations makes the system more resilient and better functioning. Such systems are known as complex adaptive systems.

Related concepts: adaptation, evolution, resilience, artificial intelligence, artificial environments, swarm intelligence, hive mind, open-endedness, robustness, learning, environmental assimilation, landscape assimilation

Universality

Complexity science is applicable to a wide range of disciplines in lancing urban science, blockchain technology, communication technology, physics, social science, finance and business, medicine, technical sciences or information technology. We live in a complex world operating as a global complex system. Universality is the key component of complexity science, as all functioning is system-based. System is everywhere and in everything, and creates a mathematical/computational framework of all happenings. This branch of science therefore provides interdisciplinary and comprehensive analytical inquiry into essential aspects of each domain.

Related concepts: global system, ecosystem, universality, multi-/cross-/trans-/interdisciplinarity, social system, cultural system, economic system, political system, multi-applications

Notes:

[A] Non-ergodicity is a fundamental, but little known scientific concept. It stands as a contrast to ergodicity. Ergodic means that the system in question visits all its possible states and has no deep sense of history. Non-ergodic systems do not visit all of their possible states.

[B] In mathematics, self-similarity is a property of a structure that is exactly or approximately similar to a part of itself, i.e. the whole has the same shape as one or more parts. Many objects in the world are statistically self-similar, because parts show the same statistical properties at many scales. Self-similarity is a property of fractals. There is an exact form of self-similarity called scale invariance, where at any magnification there is a smaller piece of a structure that is similar to the whole.

[C] In statistics, a power law is a functional relationship between two quantities, where a relative change none quantity results in a proportional relative change  in one quantity results in a proportional relative change in the other quantity, independent of the initial size of those quantities: one quantity varies as a power of another [2].

References:

[1] Dekker, S. (2010) We have Newton on a retainer: Reductionism when we need systems thinking. The Joint Commission Journal on Quality and Patient Safety, 36(4), p. 147-149.

[3] Bar-Yam, Y. (2015) Concepts of Power Law; New England Complex Systems Institute.