Overview of Complexity (Holland)Complexity science is a multidisciplinary scientific field that studies systems “with many interconnected parts”.

(Holland, 2014) Examples of systems range from a rainforest to an economic market to a multicelled organism. What these systems have in common is the property of emergence: the system as a whole is greater than the sum of its parts.Beyond emergence as a defining characteristic, most complex systems exhibit other common properties. With nonlinearity, for example, inputs in the system can lead to changes that do not progress in a predictable, linear fashion. Many complex systems exhibit self-organization into patterns, like when a flock of birds knows to change directions in a synchronized manner, despite not having a single leader telling it to do so. Another common property is adaptive interaction, in which agents in the system change their behaviours based on the behaviours of other agents.

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Finally, complex systems display hierarchical organization with different phenomena occurring at different levels of the hierarchy — the “building blocks” of emergence.Under the broad umbrella of complex systems, Holland (2014) delineates two main categories — Complex Adaptive Systems and Complex Physical Systems. Complex Adaptive Systems (Holland)Complex Adaptive Systems (CAS) are comprised of agents that interact and learn from one another to form emergent properties. (Holland, 2014) CAS often have feedback loops, causal loops in which one action feeds into another in a pattern of self-reinforcement. In a CAS, constant adaptation and evolution mean that no two situations are exactly the same, though there are some common patterns that can be used as guidelines. But because these systems change constantly and very rarely settle on an ‘equilibrium’, it can be challenging to predict or measure them.

An ant colony is a well-known example of a Complex Adaptive System. A colony, made up of numerous individual ants, is an emergent force capable of creating remarkably intricate nests, carrying heavy objects, and building bridges with the ants’ own bodies. (Mitchell, 2009)Complex Physical Systems (Holland)Holland (2014) describes Complex Physical Systems (CPS) as “geometric (often lattice-like) arrays of elements, in which interactions typically depend only on effects propagated from nearest neighbours.” (P. 31) An example of a CPS is a cellular automaton, a discrete grid of cells that is self-reproducing based on a set of governing laws.

(Scheffler, 2017) At the time it was created in the 1950s, the cellular automaton demonstrated that self-reproducing behaviour was not only limited to living systems — computer algorithms could reproduce themselves, too.Holland (2014) outlines the following characteristics that are present in some (but not all) CPS:Self-similarity — In fractal curves, the same geometric patterns repeat at progressively smaller scales. Scientists have observed his sort of self-similarity in various natural systems, including tree branching, seashells, snowflakes, and romanesco broccoli.Scaling — Some CPS exhibit scaling patterns, in which a system’s growth adheres to a uniform set of rules. The metabolic rate in animals of many different sizes, for example, scales according to a 3/4 power law, meaning each doubling of organism size requires a 75% increase in food intake, rather than an (intuitively-assumed) increase of 100%. (West 2014) Similar scaling patterns are pervasive in biological systems, and can also extend to social systems such as cities and corporations.

Networks — Some CPS and CAS can be represented through network theory, in which a system is mapped as a set of nodes connected by linkages. (Mitchell, 2009) Network theory aims to understand the relationships between elements or agents of a system based on the number and frequency of interactions.Complexity Applications: Biology (Ma’Ayan and Mazzocchi)The emerging field of systems biology aims to convey biological phenomena in a holistic, global way. (Ma’ayan, 2017). Mazzocchi (2008) contrasts a complex systems approach to biology with the reductionist approach that has been at the centre of biological research for the past few centuries.

Reductionism attempts to explain biological mechanisms through simplified laws and models of a system’s component parts. However, Mazzocchi notes, reductionism fails to capture a number of the complex characteristics that give rise to many biological systems: emergent properties, self-organization, and the contexts that shape phenomena through interaction. From the systems biology perspective, Ma’ayan (2017) cites the aggregation of human cells as a prototypical example of a complex system.

While all human cells contain copies of the same genetic code, they are able to specialize and create structures informed by the signals they receive through intercellular communication. Cells display self-reproducing behaviour through the cell cycle apparatus, and self-repairing behaviour in their reaction to viral pathogens. Mitochondria are able to initiate programmed cell death (apoptosis) where they see it could be beneficial to the organism as a whole. Due to these complex interactions, it may be challenging to adequately understand the behaviour of human cells when approached from a reductionist perspective.

Thus, Ma’ayan (2017) describes the potential of new computational techniques, including artificial intelligence and machine learning — particularly a subfield called deep learning — to provide insight on phenomena through knowledge imputation. This contrasts the previous reductionist methodological trend of scientists spending their entire careers to study a small number of isolated genes.Complexity Applications: Cognitive Science (Goertzel and Mitchell)In the field of psychology, researchers have struggled to find an overarching theory that unites various lines of inquiry, from memory to neurology to behavioural science. The field of cognitive science, which encompasses “cognitive psychology, artificial intelligence, and cognitive neuroscience,” (Goertzel, 1997) shows promise as a potential unifying concept. Goertzel argues, however, that cognitive science researchers have placed too much emphasis on the mind/brain debate, in which they argue that either the mind’s processes or its underlying physiological structures in the brain are most important to understanding human psychology. Goertzel (1997) contends that a complex systems view of cognitive science can help overcome the challenges of reconciling disparate understandings of cognition. Mitchell (2009) notes that the brain and its emergent cognitive properties can be viewed as a complex system.

While the brain is made up of simple subcomponents called neurons, upon signaling to one another neurons give rise to complex thoughts, emotions, and behaviours which researchers do not yet fully understand.The modeling of neural structures is one of four applications of complexity science to cognition that Goertzel (1997) identifies. In addition, he posits, concepts from complexity such as adaptation and self-reproduction can be used to create models of psychological phenomena, analyze empirical data about cognition, and examine the underpinnings of the philosophy of mind.