*Author:* F. Heylighen

*Date:* 20 March 1989

*Parent Node(s):* Network for Complexity Research

In order to efficiently organize a research program for studying complexity, it is best to agree about some fundamental concepts defining the problem domain. In view of the diversity of existing approaches, it is not obvious how this should be done. Yet in order to show that this is possible, a provisional outline of a unifying framework will be proposed below.

A first basic question is how complexity could be defined - as exactly as possible, but without unnecessarily restricting the field of application. Intuitively, a system will be called complex if it consists of many, differentiated parts, which have nevertheless strong connections and interactions. This entails that the behaviour of a complex system is very difficult to predict, to control and even to describe. Hence models of complex systems are in practice incomplete, ambiguous, and uncertain.

A complex system is characterized neither by global order (regularity, symmetry, invariance) nor by global disorder (chaos, entropy, randomness). Although pure disorder is sometimes called "disorganized complexity", its behaviour is basically simple if analysed by statistical methods. The reason is that in a disordered system (e.g. a gas) there are no strong relations between the parts, and so the law of large numbers is applicable. Real complexity will always be characterized by some form of organization, i.e. internal relations. However, this internal order is not absolute or invariant, and hence a complex system will be characterized by both the emergence (self-organization, order out of chaos) and the disappearance (entropy increase) of internal organization.

We must remark that the selection of a particular stable configuration can in general not be predicted by looking at the mechanism which generates variation. Although this mechanism may be either deterministic or stochastic, it is essentially "blind", it cannot foresee the reaching of a stable state. The invariant configuration is really emergent, it belongs to a different level, introducing new constraints and a new order with respect to the level of the variation mechanism. This process of emergence may be called "self-organization". Yet we must remember that no invariance is absolute: sooner or later the stability of the configuration will be destroyed by external perturbations or fluctuations, leading to a new variation process, which will result in the same or different selectively retained stable configurations.

The model sketched above is still simple because it assumes a single evolving system. In practice no system evolves on its own: it is always interacting with other systems, which evolve in parallel. In other words, complex evolution is distributed over different systems. The variation-and-selective retention paradigm can still be used by referring the other systems to the environment or background. The distinction between system (internal) and environment (external) entails a distinction between internal and external variation mechanisms, and between internal and external selection criteria.

External selection can be considered as adaptation to the requirements of the environment. Internal selection corresponds to the discovery of an intrinsically stable configuration, i.e. a configuration which is closed or invariant under the inner dynamics of the system: e.g. an "autopoietic" system has a closed organization. Internal variation can be viewed as a change which only affects the inner structure or state of the system. External variation finally is a change in which the relations between different systems are changed. Variety is injected from the outside.

External variation may result in the creation of a higher-order system which encompasses two or more lower-order systems. It suffices that the relations between the lower-order systems are changed in such a way that they become mutually adapted, i.e. that the one becomes invariant with respect to the other one, so that they constitute a globally invariant configuration, leading to a new "emergent" system. (Of course the opposite process is also possible: a system falling apart in separate components.) Thus formed higher-order systems may again function as building blocks, to be combined by external variation, generating a system of a still higher order. This process can go on indefinitely, leading recursively to ever more complex systems.

The interact (message-response) will in general lead to a new interact, i.e. A will send a new message or response to B, possibly a transformation of B's response. Eventually this variation-and-selection of messages may lead to the emergence of a stable message pattern, i.e. one which is accepted without further transformation by both systems. In this case the two systems may be said to be coupled - or to have reached an "agreement" - with respect to this invariant pattern. In this respect the two systems will now behave as one higher-order system.

A cognitive system can be characterized by its capability of solving problems. A problem can be defined as a situation confronted by an autonomous system (an "actor"), which is not stable (i.e. the actor is not happy with the status quo, but wants to change something). The larger the instability, the more serious the problem, the more variation the actor will experience. "Solving the problem" means finding a new situation which is more stable. Traditional paradigms for problem-solving are trial-and-error and generate-and-test. Both can be reduced to the paradigm of variation (i.e. generating variants or trials) and selective retention (i.e. evaluating the variants, retaining the good ones or (partial) solutions, and throwing away the bad ones or errors).

A further distinction can be made between well-structured (or simple) problems and ill-structured or complex problems. A well-structured problem is characterized by a well-defined goal, search space and initial state. This means that an internal variation mechanism, generating states in the search space starting from the initial state, is given, together with an invariant external or internal selection criterion, for recognizing the eventual solution. The search space, determining the problem representation is "closed".

In a complex problem (also called "wicked" or "externally structured" problem), on the other hand, there is also external variation, so that the search space and the goal will change during the search process. New systems, external to the original one, influence the problem, so that the problem formulation has to be continuously adapted. The problem representation is "open": elements, structures and distinctions are taken out of it, added, and replaced.

Modern, non-classical science has discovered that such complete, deterministic models are in principle impossible. This may be inferred from principles such as the theorem of Gšdel, the indeterminacy principle of quantum mechanics and the second law of thermodynamics. Yet until now these results are interpreted mainly in a negative manner: as a theoretical limitation which does not help us in any way to solve practical problems.

When studying complex systems, however, the difficulty is no longer theoretical: it is obvious in practice that there is no single model which can completely represent the behaviour of a complex system. We are suddenly confronted with a new freedom of choice: which model or models should we use for tackling a given problem? This question brings in a higher level of decision-making, a second-order or meta-decision: instead of choosing between different alternatives specified within a given model, we now must choose between different ways of representing or modelling a given system. Representing a domain is fundamentally a question of structuring, classifying, partitioning, i.e. of making distinctions. Hence the problem amounts to determining the adequate distinctions between alternatives, instead of determining the adequate alternatives defined by a given set of distinctions.

The positive interpretation of non-classical modelling is to search for a meta-theory, specifying how adequate models and distinctions can be constructed, and how they depend on the system to be modeled, the actor or observer, and the culture or society of consensual actors. The epistemological implication is that in complex situations the observer can no longer be completely separated from the observed. The practical implication is that model-building and the discovery of concepts and rules are no longer uncontrollable phenomena of inspiration or illumination, but can be supported by carefully designed theoretical and technological systems.