International Encyclopedia of Systems and Cybernetics

"The name we are giving to the condition of human beings, objects, phenomena, process, concepts and feelings because:

a) they are difficult to understand or explain

b) their causes, effects or structure are unknown

c) they require either a great deal of information, time or energy to be described or managed or a huge coordinated effort on the part of the persons, equipment and machinery

d) they are subject to a variety of perceptions, interpretations, reactions and applications that are often contradictory or disconcerting

e) they produce effects that are simultaneously desirable and undesirable (or difficult to control)

f) their behaviour, depending on the case, may be unpredictable, relatively unpredictable, extremely variable or "counterintuitive" (F. SAEZ VACAS, 1990, p.83).

Complexity is rather different from complication.

The latter can be simplified more or less easily by classification, reduction to some few types, as for example in MENDELEEV's periodic table of chemical elements.

Complication may merely be an aspect of complexity.

The periodic classification is a mere consequence of the complexity of interactions at the atomic and nuclear level.

The contrary of complexity is not simplicity: J.L. LEMOIGNE even proposes the neologism "implex" to caracterize a unit that cannot anymore be decomposed, at least at the level of the intended research. For example, individuals would be "implexes" in social systems, irrespective of their biological complexity.

As stated by G. MIDGLEY, we may distinguish natural world complexity, social world complexity and internal world complexity. The first two ones are necessarily and selectively filtered by the third one. For this reason, according to MIDGLEY: "… it is the explicit emergence of ontological complexity that is the real challenge facing us" (1992, p.154). In the same vein, W KARGL observes that a good systemic understanding should not aim "… at reducing complexity between system and environment, but seek to (discover) order, regularity and invariance" (1991, p.582).

Such a view is further developed by W.R. REEVES: "Complexity… is a concept… used to measure… the relative ratios of the following semantic pairs: order and disorder; confirmation and novelty; predictability and unpredictability; redundancy and variety; signal and noise; constraint and chance; differentiation and undifferentiation; symmetry and symmetry breaking; and negentropy and entropy" (1992, p.1101).

On the other hand, the condition described by F. SAEZ VACAS is also proper to living systems in general, to ecosystems (and even many physical systems, as for example, the solar system or the geosphere), societies, animal as well as human, small organizations as well as great corporations or nations, men-machine systems, and brains (of men and animals).

Besides, we already understand some general characteristics of complex systems, as for example:

- they are multi-functional: different parts attend simultaneously different needs. However there are coordination devices, which help to maintain coherence, strongly in individual systems (like a living being, as a whole) or loosely as in social groups of any kind.

- they maintain a relatively permanent identity during a more or less extended period of time (entitation, organizational closure in individuals – some basic templates or patterns in social groups).

- they have an adaptation capacity in the case of individuals, or of evolution in the case of groups

It is possible to study complexity from bottom up or from top down, but the main subject must always be global coherence and the interconnecting devices which maintain it.

Of course, as stated by R. VALLÉE: "… it is difficult to speak of complexity in an absolute form and it seems more sensible to contemplate a perceived complexity, depending of the observer viewpoint, considering complexity as a relation between the observing system and the observed one" (1990, p.50).

In a quite similar way L. LÖFGREN introduces a d-complexity (description) and an i-complexity (interpretation), both obviously superposed by our own level of knowledge on the supposedly complex situation or system considered. (1977).

Here, information becomes a measure of complexity, as stated by H.T. ODUM (1983, p.169).

Thereupon we should still add a modelization complexity, due to the interferences of our mental and computational tools within the representation (for our specific ends) of the system or situation.

Viewed from another angle, we may say that complexity begins with nonlinearity and with a multiplicity of initial situations in various parts of the entity under study.

According to E. LASZLO: "On higher levels the amount of complexity that can be developed in a system is greater than on lower ones due to the greater diversity and richness of the components and subsystems" (1992, p.244).

This is related to the progressive build-up of hypercycles, which results of the appearance of potentially complementary elements in a given level and within a given environment.

This in turn is consonant with H. SIMON statement that: "Complexity frequently takes the form of hierarchy" (1965, p.64). In his terms, there is an "architecture of complexity".

Complexity cannot easily (if at all) be measured arithmetically, probably because it is structural and functional. It seems to be a geometrical and topological property of emerging systems becoming organized on higher levels. Thus, two or more systems of the same type could have somewhat different characteristics (for example, fossil ammonites), but be at the same level of complexity

Complexity is not merely statistical diversity. In this case, what we observe is merely absence of some coherent order, not complexity. Of course, in some cases a very complex explanation could possibly be reached, but merely relative to not coherent diversity.

Increasing complexity in systems seems to be related to four different but somehow connected evolutive processes.

The first one is dissipative structuration, which starts to occur when a system is pushed through increasing fluctuations far from its equilibrium level, toward an instability threshold. This is the result of increasing energy intakes, excessive for the system as it is organized at the moment. This process must be compensated by a corresponding increase of entropy production. It may lead to the destruction of the system or to the emergence of a new system at a higher level of structural and functional organization. Such a system would then stabilize at a corresponding higher minimal level of entropy production.

Increasing complexity also implies more numerous and intricated relations between more elements, i.e. the appearance of a new level of sociality, once the critical threshold has been crossed. This may correspond with an "increased computational ability" (N. PACKARD). There seem to exist a critical population density of elements of a same or of complementary classes leading to a kind of implosion provoked by a considerable multiplication in a limited or shrinking space. This changes the individual behavior of elements through more mumerous, frequent and strong interrelations. This in turn, leads to a more and more organized new collective behavior, i.e. to the appearance of a new social system on a higher level of complexity.

Such a system obtains a higher degree of control upon extended surroundings, leading to more stability, productivity and survival time. Ants societies and beehives, as well as presently expanding human societies are examples.

It should be noted that more control on the environment means more capacity to obtain energy inputs, which leads us back to PRIGOGINE's thermodynamics of irreversible systems far from equilibrium.

The third interesting process is criticality, which seems to be related to "would be" systems. In cases of avalanches and other critical threshold phenomena of this type, no higher level of organization sets in, possibly because all elements are of the same kind, or because energy is uselessly and prematurely dissipated in a non-structuring way. Colonial organisms that alternately aggregate and disaggregate, as for example the well known Dictyostelium discoideum, or sponges, or locust swarms, seem to be a limit case.

The fourth intervening process is semi-deterministic chaotic behavior, which results from multiple simultaneous local events within any intricate network of elements. At any precise moment the non-instantaneous and uneven propagation of effects allows for a limited and temporary leeway of indeterminism anywhere in the network, while its global behavior remains generally coherent. This makes the systems behavior always somewhat unpredictable.

J.L. LEMOIGNE considers that such a basic unpredictability is in fact the hallmark of complexity (1990, p.304).

At the most general level, complexity could be a cosmic innovative transformation toward a more efficient energy dissipation and entropy production process, compensated by higher global levels of organization. Such a view was introduced by A. LOTKA in 1924 as the ecological concept of the "world engine ", according to which energy is most efficiently used in "cascades" throughout the global ecosystem. (1956, p.331).

D.L. HARRIS, quoting A.B. CAMBEL (1993), states: "CAMBEL establishes and names three categories: the first is "static complexity", to include purpose and function as well as size and configuration. The second is "embedded complexity", consisting of structure and including composition and makeup. The third is "dynamic complexity" – a category to include various types of dynamics. Building upon the categories, CAMBEL then constructs fifteen heuristic statements, presented here in somewhat abridged form:

"1. Complexity may be found in natural and man-made systems, including social structures.

"2. Large and small components can live cooperatively in the same complex dynamical system.

"3. Physical shape may be regular or irregular.

"4. In general, the larger the number of systems parts the more likely the occurence of complexity.

"5. Both energy-conserving and energy-dissipating systems can be subject to complexity.

"6. The system is neither completely deterministic nor completely random, exhibiting both characteristics.

"7. Causes and effects of system events are not proportional.

"8. Parts of complex systems are linked and affect one another in a synergistic manner.

"9. There is positive or negative feedback.

"10.The complexity level depends on the character of the system, its environment, and the nature of the inter-action between them.

"11.Complex systems can exchange matter, energy and information with their surroundings.

"12.Complex systems tend to undergo irreversible processes.

"13.Complex systems are dynamic and not in equilibrium; they may pursue a moving target.

"14.Complex systems frequently undergo sudden changes, suggesting that the functional relations that represent them are not differentiable.

"15.Paradoxes exist, such as organic and inorganic bodies in cohabitation; fast and slow events, etc. " (1994, p.73).