Edge of Chaos
The term edge of chaos is used to denote a transition space between order and disorder that is hypothesized to exist within a wide variety of systems. This transition zone between the two regimes is known as the edge of chaos, a region of bounded instability that engenders a constant dynamic interplay between order and disorder. This point or interface between the two is hypothesized to be a locus for maximum complexity and the dynamics driving evolution. Mitchell Waldrop in his book Complexity: The Emerging Science at the Edge of Order and Chaos1 describes the term as such: “Right between the two extremes [order and chaos] … at a kind of abstract phase transition called the edge of chaos, you also find complexity: a class of behaviours in which the components of the system never quite lock into place, yet never dissolve into turbulence, either. These are the systems that are both stable enough to store information, and yet evanescent enough to transmit it. These are systems that can be organized to perform complex computations, to react to the world, to be spontaneous, adaptive, and alive.”
Much of the ideas surrounding the edge of chaos hypothesis derive from chaos theory. The idea of order and chaos has fascinated people from many different domains for millennia, but these very big ideas in their abstract form have remained largely outside the scope of modern science. With the rise of chaos theory and complexity, a new language formed for approaching these fundamental concepts. Chaos theory has worked to explore the transition between order and disorder, which often occurs in surprising ways.2 Chaos theory has provided some understanding of how systems turn chaotic, while the study of synchronization has dealt with the question of how things come into and go out of coordination. Another central element of this enterprise has been the growing understanding of the process of self-organization. With the theory of self-organized criticality and catastrophe theory, we are starting to get real quantitative models as to how these macro-level processes of change between order and chaos might develop along the edge of chaos. Since the beginnings of the modern era, science has largely dealt with change as moving from one stable equilibrium to another. The Newtonian paradigm did not cope well with the random, near-chaotic messiness of the actual transition itself. Much of physics, chemistry, and other fields, have been focused on the study of equilibria.3 Engineers and economists similarly favored equilibrium conditions because neither analysis nor modeling techniques available to them could handle these in-between transition states.4 However, inexpensive computational power has changed this. Nonequilibrium and nonlinear simulations are now possible. These developments, along with the study of complex systems, have enabled us to better understand the dynamics of this “in-betweenness” or messy state at the edge of chaos that is a lot more representative of how our world actually looks in reality.5
One of the original stimuli that lead to the idea of the edge of chaos come for computer experiments with cellular automata done by Christopher Langton.6 Christopher Langton defined a quantity called lambda for any cellular automata. Lower values of lambda corresponded to rulesets with less change. Higher lambdas led to more change. He showed that cellular automata with low lambdas were more prone to rapidly moving towards a balanced or static point. Those with a high lambda value tended toward complete randomness. A lambda value toward the mid-range, a “critical” lambda, resulted in programs that could generate long periods of complex aperiodic non-random behavior before settling into either a fixed point or randomness. This was the edge of chaos. Kauffman saw in these programs new and useful developments as emerging “on the edge of chaos,” the boundary between ordered and chaotic regimes. In the paper Langton published on the topic he wrote: “Above a certain level of ‘complexity’, the process of synthesis is also degenerative. In other words, we find that there exist an upper limit as well as a lower limit on the “complexity” of a system if the process of synthesis is to be non-degenerative, constructive, or open ended. We also find that these upper and lower bounds seem to be fairly close together and are located in the vicinity of a phase transition. As the systems near the phase transition exhibit a range of behaviors which reflects the phenomenology of computations surprisingly well, we suggest that we can locate computation within the spectrum of dynamical behaviors at a phase transition here at the “edge of chaos”. 7 This edge of chaos condition within cellular automata was previously noted by Von Neumann8 and it can be seen within Conway’s game of life where he had to figure out how to get rules that would create complex patterns. If the rules to the game of life are slightly changed they will not produce interesting phenomena.
Order and Chaos
These ideas originating in computer programs have since been generalized to all forms of systems that exhibit complex evolutionary behavior. Today, in the sciences in general, the phrase “edge of chaos” has come to refer to a metaphor that some physical, biological, economic and social systems operate in a region between order and either complete randomness or chaos, where the complexity is maximal.9 This edge of chaos phenomenon is thought to be a characteristic of many different types of complex systems, as complexity can not be understood in terms of simple symmetries but neither is random: it is some combination of both. This in-between state that complexity is thought to lie in, makes it un-amenable to our traditional scientific methods. In the book Complexity and Organization, the authors write: “Nothing novel can emerge from systems with high degrees of order and stability – for example, crystals, incestuous communities, or regulated industries. On the other hand, complete chaotic systems, such as stampedes, riots, rage, or the early year of the French Revolution, are too formless to coalesce. Generative complexity takes place in the boundary between regularity and randomness.”10 A system with no order can not exhibit useful behavior. But also a system with too much order can become overconstrained and likewise not exhibit functional results. It is possible that processes organize themselves into conditions so complex that no usable functionality can result from it i.e. there can be too much accumulated information and constraints. The systems in between, i.e. at the edge of order and chaos, can exhibit a more flexible and organized behavior. Therefore, it appears likely that self-organisation needs to find a balance between lack of order and too much order.11
The edge of chaos phase transition area is then thought to be the locus for evolutionary processes, that involve the perpetual collapse of local structures that then give rise to new patterns of organization, creating a dynamic life-cycle.12 Too much order and change will not cross rigid boundaries. Too much chaos and the system loses its organization. Complex adaptive systems – such as ecosystems, societies, and economies – maintain themselves between this randomness and order where they can somehow use both in order to configure and reconfigure themselves, going through both integration and differentiation in evolving to become more complex. Mitchell Waldrop gives an account of this when he writes: “The edge of chaos is where life has enough stability to sustain itself and enough creativity to deserve the name of life. The edge of chaos is where new ideas and innovative genotypes are forever nibbling away at the edges of the status quo, and where even the most entrenched old guard will eventually be overthrown. The edge of chaos is where centuries of slavery and segregation suddenly give way to the civil rights movement of the 1950s and 1960s; where seventy years of Soviet communism suddenly give way to political turmoil and ferment; where eons of evolutionary stability suddenly give way to wholesale species transformation. The edge is the constantly shifting battle zone between stagnation and anarchy, the one place where a complex system can be spontaneous, adaptive and alive.”13
The idea of the edge of chaos represents a highly abstract but intuitive concept that has come to be applied to many different areas, from business management,14 to ecology,15 to psychology,16 political science,17 and various other domains of the social sciences.18
The idea of the edge of chaos is expressed within the work of the economist Joseph Schumpeter who formulated the idea of creative destruction as the driving force within a market economy. The idea of creative destruction describes how new innovations are constantly being generated by entrepreneurs in order to displace older ones in a continuous cyclical dynamic. Schumpeter starts in The Theory of Economic Development with a treatise of circular flow which, excluding any innovations and innovative activities, leads to a stationary state. This stationary state is, according to Schumpeter, described as the classical economic equilibrium of order and predictability. The entrepreneur is the one that disturbs this equilibrium and is thus the prime cause of economic development, which proceeds in cyclical fashion along several time scales.19 Schumpeter contributed to the ideas of evolutionary economics. According to Christopher Freeman, a scholar who devoted much time researching Schumpeter’s work: “the central point of his whole life work [is]: that capitalism can only be understood as an evolutionary process of continuous innovation and ‘creative destruction.'”20
The idea of the edge of chaos has come to be associated with human cognition.21 When looking at the many possible cognitive states, it is possible to identify the highly predictable and orderly states from those that are more unpredictable and chaotic. In more chaotic regimes, network states are more disconnected from those in the ordered regime. However “at the edge of chaos,” the states can be seen to be maximally novel while still connected to states in the ordered regime, and thus are most likely to exhibit the combination of novelty and utility that is the hallmark of innovative thinking. A similar conceptual approach was used to distinguish between chaos, rigidity, and integration to characterize semantic network states in people with Asperger’s syndrome, schizophrenia, and healthy semantic processing, respectively.22
The edge of chaos hypothesis has been used as a model for studying creativity within individuals. In any system, there are forces pushing towards organization and order and others introducing unpredictability and randomness, a truly creative idea, or creative process, is seen to bridge both of those states. Robert Bilder a psychology professor at UCLA who has studied creativity, says “The truly creative changes and the big shifts occur right at the edge of chaos.”23 Professor Bilder has tested this by asking children what dimension of a particular learning environment makes them feel most creative. “One of the things they found most valuable in their art classes was the freedom not to have to seek right and wrong answers,” Bilder said. “It was that freedom to explore that led them to be increasingly engaged and allowed them to forge connections that allowed them to be more creative.” But equally, the creative process also requires some structure in “The ability to inhibit the first thing that comes to mind in order to get to the higher hanging fruit in the cognitive tree is one of the cornerstones of creative achievement.”24
The edge of chaos hypothesis can be applied to understanding society in terms of the dynamic interaction between micro and macro-levels within social systems. Whereas macro-level social structures, such as laws, religions, governments and other social institutions offer the potential for order and stability within the system, they can also impose too much order on the individuals, limiting their individual development in the name of conformity and group cohesion, ultimately leading to stasis and lack of novelty with which to innovate and evolve the social structure. Likewise, the micro-level diversity of agent’s agents can be seen as a constant source of disorder, pulling in different directions and without macro stable institutions can create the potential for conflict between the many individual agendas of the agents and special interest groups. As Thomas Hobbes famously stated a society in a state of nature without strong political institutions would be “solitary, poor, nasty, brutish and short.” A functioning society can be seen to be one that is able to maintain itself on the edge of chaos with both stable macro institutions that are capable of maintaining sufficient order but can also maintain individual autonomy as much as necessary for the individual to develop. Functioning constitutional democracies that both maintain social order and individual rights through laws, while also providing mechanisms for the individual members to change those institutions when needed, many be an example of this. As such they enable both an upward and downward interaction in a cyclical fashion that is characteristic of evolutionary processes, where new diversity comes from below while constraints and selection come from above to continuously generate new and relevant variants in response to changes in the environment.