Definition of a complex system

As the systems theory gave place to complexity science, the term

‘system’ transformed into ‘complex system’. Researchers of complex systems acknowledge that there is not one science of complexity, but different ‘sciences’ that all have their own notion of a complex system and complexity (Mitchell, 2009). Therefore, there is no unequivocal definition of a complex system and there is no established method for measuring the level of the system’s complexity. In spite of these different approaches and definitions, Mitchell discerns some common properties of complex systems:

- Complex collective behaviour (a high number of components triggers complex patterns of behaviour);

- Signalling and information processing (systems produce and use signals from internal and external environments) ;

- Adaptation (systems change their behaviour to improve their chances of survival through, e.g., evolutionary process).

Furthermore, Mitchell defines a complex system as “(…) a system in which large networks of components with no central control and simple rules of operation give rise to complex collective behaviour, sophisticated

information processing, and adaptation via learning or evolution” (Mitchell, 2009: 13).

A crucial feature of a complex system is the difficulty to predict its behaviour. A chaotic behaviour of complex systems consists in the fact that even minuscule uncertainties in the initial state of a system (measurement of initial positions and momentum of its elements) can result in large errors in predicting its subsequent states. This phenomenon is known as “sensitive dependence on initial conditions” (Mitchell, 2009: 20). Understanding of the mechanism of chaos, ‘buried’ the hope of perfect prediction of complex systems’ behaviour.

Sensitive dependence on initial conditions is not necessarily an effect of a large number of elements and connections. Complexity can also emerge from simple rules. Sensitive dependence on initial conditions takes place even when investigating three simple bodies: “to determine, using Newton’s laws, the long-term motions of three masses exerting gravitational forces on one another” (Mitchell, 2009: 21). Newton solved the two-body problem, but the three-body problem turned out to be much harder.

Some scientists regard the complexity of a system as a key factor in its description. Seth Lloyd (2001) considers three different questions in defining a complex system:

- How hard is it to describe?

- How hard is it to create?

- What is its degree of organisation?

The first question is challenging, because random or chaotic systems are the most difficult to create or describe. Indeed, the lack of regularity or recognizable pattern makes the description of such systems difficult. To overcome this difficulty, physicist Murray Gell-Mann proposed an alternative definition of complexity. He developed a measure called ‘effective

complexity’, which fits well our intuitive understanding of complexity. A basic assumption of effective complexity is that complexity is always a combination of regularity and randomness. Gell-Mann (1995) gives as an example the DNA of a living organism, in which regularities coexist with randomness (called ‘junk DNA’). According to Gell-Mann, the effective complexity can be measured in two steps. First, by figuring out the best description of the regularities of a given system; second, by defining the amount of information contained in this description. The complexity of a system would then be the amount of information contained in the description of the system’s regularities.

Yet another definition of complexity was proposed by Herbert Simon. In Simon’s definition, complexity is related to the hierarchic degree of a system.

Hierarchy is a universal, common feature of all complex systems. He defines hierarchy as a composition of interrelated sub-groups within a larger entity (Simon, 1962: 468). Simon speaks also of a ‘span of control’. In formal human organisations, for example, a span of control is specified by a number of subordinates who report directly to the manager. The term span of a system denotes the subsystems that compose the system as a whole.

The hierarchical construction of a system is significant, because it gives a system an advantage in the evolution process. An organism (or an artificial system) undergoes permanent reconfigurations in the process. Stable subsystems facilitate a faster reconfiguration of the organism, because the organism does not need to be reconstructed from its basic elements: “The time required for the evolution of a complex form from simple elements depends critically on the numbers and distribution of potential intermediate stable forms” (Simon, 1962: 471). In natural evolution, the genetic

modification involves the subsystems of an organism (cells, tissues, organs) rather than its basic elements (organic compounds). Applying this principle to car design one can say that a blueprint of a car is developed hierarchically, at the level of its components, and that the designer goes down to its basic elements and redefines them only if needed. Even if a single component is redesigned, the operation is carried on roughly within the boundaries of this component (subsystem). For example, designing a seat of a car, there is no

need to go much beyond the boundaries of this particular seat (as long as the size of the seat is correct). One can say that because the plan of a car is conceptually divided into subsystems, it is easier to manipulate the whole system during a design process. An adjustment in a subsystem does not require a total decomposition of all the elements, but rather decomposition of the subsystem in question. In sum, even though a system is a whole, the density of relations between its elements is not distributed homogeneously.

Daniel McShea (2001) elaborated Simon’s idea further. McShea observed that the complexity of organisms increases over time in an evolutionary process. He proposed a scale of hierarchy as a measure of the level of an organisms’ complexity. In this context, he coined the term nestedness: “a higher-level entity contains as parts entities from the next lower level.” Each level is more complex that the previous one.

Both Simon’s and McShea’s ideas are relevant to the approach presented in this thesis. Hierarchy as an essential feature of a complex system will be further discussed in section V.

In his paper Life and Complexity in Architecture from a Thermodynamic Analogy, Nikos Salingaros (1997) presents an interesting approach to complexity. This approach is worth mentioning because it addresses the context of a building form. Salingaros proposes two building qualities, with which he defines complexity: a temperature T, and a harmony H. In broad terms, “The architectural temperature T is defined as a degree of detail, curvature and colour in architectural form, whereas the architectural harmony H measures the degree of visual coherence and internal symmetry in the visual structure” (Salingaros, 1997: 87). Temperature and harmony are related, so that usually more harmony results in ‘lower’ temperature. For example, reducing colour differences in certain areas increases the building’s harmony while at the same time it reduces the contrasts and thus the

temperature. Salingaros applies the two terms to define complexity in the following formula:

C = T x (10-H), where T and H are between 0 and 10

This formal definition of ‘C’ reflects an intuitive understanding of a building’s complexity, or a quality that “arouses a viewer’s interest (…) the inverse measure of how boring a building is” (Salingaros, 1997: 99).

Salingaros speaks of two types of complexity: disorganised complexity and organised complexity, where C is a measure of the ‘disorganised

complexity’. The notion differs from a common understanding of complexity

as a disorganised variety. Biological organisms, for example, are highly complex but they are not disorganised.

Salingaros’ notion of complexity is derived from yet another key term in his model: ‘life’. The quality of ‘life’ of a building is formulated as a product of a building’s temperature and its harmony. The two notions of complexity and life seem to be very relevant to the algorithmic description of an architectural form and are discussed further in the context of building characteristics in section VI.