On Complexity 

Complexity is an inherent property of many systems that constitute the environment in which we grow, develop, live and work. The most important ones are: ecological, cultural, educational, social, scientific, technological, economic and political.


Until recently levels of complexity of our environment were low and consequently complexity was largely ignored. However, with the rapid development of digital technology the situation has changed, particularly when the Internet transformed the world into a genuine global village and linked regional and national markets into a single global market.


The trend is for the complexity of our environment to continue increasing. 


As complexity increasingly affects our capability to carry out our work and cope with our life, it becomes more and more necessary to intensify effort on developing a coherent body of knowledge about complexity; in other words, to develop Complexity Science.


But how do you start assembling a coherent body of knowledge on complexity?


The most productive way is by building complex systems and then conducting experiments aimed at gaining insight into their behavior.


This text outlines research results of George's team obtained by experimenting with very large-scale complex systems built for industrial clients for many diverse applications, including:

  • Real-time supply chain management in Denmark and Germany
  • Real-time scheduling of road transport in the UK and Russia
  • Real-time scheduling of 2,000 taxis in London
  • Real-time scheduling of car rentals for Avis
  • Real-time scheduling of railways
  • Real-time logistics for delivery of crew and cargo to the International Space Station
  • Real-time management of aircraft lifecycle
  • Adaptive data mining for an insurance company
  • Adaptive semantic processing for an USA research client

Definition of Complexity - Complexity is a property of open systems consisting of a very large number of diverse components, called agents, engaged in rich interaction, without central control, and characterised by the following features:

  1. Conectivity – Agents are interconnected. Complexity of the system increases with the number of links that connect agents to each other. The strengths of agent links also affects system complexity; the weaker the links, the easier is to break them and form new ones, which increases system complexity. Adjusting agent connectivity is an effective method for tuning complexity.

    Complex systems often consist of regions of high connectivity (and high complexity) interconnected by low-connectivity (and low complexity) links, as exemplified by clustering of activities in the human brain. For example, human brain has a very high degree of connectivity of 1,000. Left- and right-hand sides are differeently wired. The right-hand side of the brain, the creative side, has weaker connections and therefore higher complexity. 

  2. Autonomy – Agents have certain autonomy limited by laws, rules, regulations and/or norms, depending on their nature. The increase in autonomy of agents increases complexity and if all constraints on agent behaviour are removed, the system switches from complex to random behavior. It autonomy of agents is reduced by tightening of laws and regulations, the system complexity will decrease and, in the extreme, the system may become deterministic. For example, human agents have a considerable autonomy limited by legal constraints, rules, regulations and norms of behaviours, whilst the autonomy of physical agents is limited by laws of nature.

  3. Emergent Properties – Properties that emerge from agent interactions. For example, global behaviour of complex social systems emerges from the interaction of constituent agents and so do properties such as intelligence and creativity,
  4. Nonequilibrium Complex systems are subjected to perpetual change experienced either as a succession of discrete disruptive events or as a slow, imperceptible drift into failure. Frequency of disruptive events varies with complexity. In systems of high complexity disruptive events occur so frequently that the system has no time to return to stable equilibrium before the next disruption occurs. When complexity levels are very high the system is said to be at the edge of chaos because the uncertainty of behavior is close to 1. For example, in the Internet-based global market, the frequency at which transactions are made, modified, or cancelled by billions of participants is so high that the equilibrium of demand and supply can never be reached. Hence the market is volatile and it is always "far from the equilibrium".
  5. Nonlinearity – Relations between agents are nonlinear. Nonlinearity may amplify a small, insignificant disruptive event and cause a catastrophic outcome (an extreme event), the property called butterfly effect. The butterfly effect increases with complexity. In complex systems outcomes are, as a rule, consequences of numerous interacting causes, and therefore the cause-effect analysis is inappropriate.
  6. Self-Organization – Complex systems have a propensity to react to disruptive events by autonomously self-organizing with the aim of eliminating or, at least, reducing consequences of the disruption. This property is called Adaptation. Self-organization may be also caused by a propensity to improve own performance, the property called Creativity or Innovation. To initiate and perform adaptive and creative activities the system must be Intelligent. Intelligence, adaptation and creativity are emergent properties exclusive to complex systems. 
  7. Co-Evolution Complex systems irreversibly co-involve with their environment.


If you are interested to learn more, please look up the page on George's publications, most of them can be downloaded.

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