Complex system

Emergence

What distinguishes a complex system from a merely complicated one is that some behaviors and patterns emerge in complex systems as a result of the patterns of relationship between the elements. Emergence is perhaps the key property of complex systems and a lot of work is being done to try to understand more about its nature and the conditions which will help it to occur.

Relationships are short-range

Typically, the relationships between elements in a complex system are short-range, that is information is normally received from near neighbours. The richness of the connections means that communications will pass across the system but will probably be modified on the way.

Relationships are non-linear

There are rarely simple cause and effect relationships between elements. A small stimulus may cause a large effect, or no effect at all.

Relationships contain feedback loops

Both negative (damping) and positive (amplifying) feedback are key ingredients of complex systems. The effects of an agent's actions are fed back to the agent and this, in turn, affects the way the agent behaves in the future. This set of constantly adapting nonlinear relationships lies at the heart of what makes a complex system special.

Complex systems are open

Complex systems are open systems[?] - that is, energy and information are constantly being imported and exported across system boundaries[?]. Because of this, complex systems are usually far from equilibrium: even though there is constant change there is also the appearance of stability.

The parts cannot contain the whole

There is a sense in which elements in a complex system cannot "know" what is happening in the system as a whole. If they could, all the complexity would have to be present in that element. Yet since the complexity is created by the relationships between elements that is simply impossible. A corollary of this is that no element in the system could hope to control the system.

Complex systems have a history

The history of a complex system is important and cannot be ignored. Even a small change in circumstances can lead to large deviations in the future.

Complex systems are nested

Another key aspect of complex adaptive systems[?] is that the components of the system - usually referred to as agents - as themselves complex adaptive systems. So an economy is made up of organisations which are made up of people which are made up of brains, which are made up of cells - all of which are complex adaptive systems.

Boundaries are difficult to determine

It is usually difficult to determine the boundaries of a complex system. The decision is usually based on the observer's needs and prejudices rather than any intrinsic property of the system itself.

For instance, the boundary of an individual human being may appear easy to determine but a little more thought will show some of the ambiguities. For instance, are clothes inside or outside the boundary? If someone stares at you across a room or crowded train, especially in a lustful or aggressive way, have they invaded your boundary? When do waste products, such as hair or nail clippings, cease to be part of the body (certainly, those who practise magic feel that they remain within the boundaries)?

We often hear of groups having "strong" or "weak" boundaries but without any clear sense of the meaning. I believe that it is possible to gain some clarity by considering connectivity. I hypothesise that an individual agent can only have a certain number of connections to other agents (with human agents this number will change according to the state of the individual and also the state of the environment). We can then think of the strength of a group's boundaries as the proportion of connections which are made within the group - the greater the proportion, the stronger the group boundaries. If all connections are made within the group it forms a closed system[?].