International Encyclopedia of Systems and Cybernetics

"A limitation or restriction imposed upon a system or a sub-system that curtails resources or operations" (Adopted from B. BANATHY, 1973, p.85).

More specifically, constraints limit the possibilities of interactions between elements or subsystems. They also limit the interactions of the system with its environment.

In a more formal way, W. ROSS ASHBY, who introduced the concept, defines it as follows:

"A relation between two sets, (occuring) when the variety that exists under one condition is less than the variety that exists under another" (1958, p.127).

ASHBY gives the example of the traffic lights: with three different colours and two different states (lit, unlit) for each one, eight combinations are possible. However, only four are used: Red and green are not compatible simultaneously; two of the three lights may always be lit or unlit simultaneously; all the three lights cannot be used simultaneously (the message would be self-contradictory); and when all three are unlit, there is no message. Thus, constraints imply restrictive rules. For simple cases, this is very clearly described in a matrix.

As a result, when all the possible combinations or interrelations are not used or admitted, an observer should look for constraints.

J. BRUNET writes:"… the set of the constraints has the effect of reducing the number of freedom degrees associated to a system, therefore to diminish its variety level and, thus its entropy".

"Within the frame of the 2nd. postulate (of thermodynamics), the set of the constraints appears by means of the invariants to which the global system is submitted; these invariants are associated to the great law of conservation in nature (mass, energy conservation)" (1987, p.21).

Considering the gigantic variety that would result from the irrestricted set of all the possible interrelations between the components of any complex system, its internal flows of information, energy and matter would become clogged and blocked if no constraints should exist.

Thus, as stated by L.J. KOHOUT and B.R. GAINES, constraints "… limit the unwanted or the dangerous interactions which would otherwise destroy the most essential functions and characteristic features of a system" (1976, p.18).

Constraints are mostly reciprocal, be it between the system and its environment or among sub-systems, but they may also be hierarchical, as for example in the case of the constraints imposed by regulators on the regulated variables.

As observed by F. HEYLIGHEN, constraints have an evolutive or historical origin: "… the system may simply be the result of a natural selection, where unstable configurations have been eliminated so that only a restricted or constrained set of configurations remains. The concept of an "attractor" as a region in state space that a system can enter but not leave, exemplifies such a spontaneously arising constraint" (pers. comm. p.10).

Of course, constraints are also learned, be it through evolutive selection, or individual activity, or as a computational technique ("multiple constraint-satisfaction"), within the limits of organizational closure.

In fact, learning consists of, and implies the acquisition of constraints. In M. BODEN's words: "A connectionist network trying to understand an analogy can consider many different constraints in parallel, and settle on the best available match even though this match may be somewhat flawed (and, by hypothesis, is never perfect).

A system in which every element should be connected with every other one, would be at the same time totally constrained and completely undefined, i.e. would have no heterogenety, no structures and no differentiated specific functions. It would indeed be no system at all. Constraints are thus an absolute necessity for systems.

Paradoxically, however, the same situation would result if no interconnections at all should exist.

In synthesis, constraints in systems, when not excessive and stiffling, are freedom-limiting, but order- creative. They constitute algorithms for some productive ways to act. Striking examples are classical, or dodecaphonic harmony, or the hindu raga-style.

M. BODEN even states: "… far from being the antithesis of creativity, constraints on thinking are what make it possible" (1990, p.82).

The constraints characterizing a system are potentially present at the time of its autogenesis, for reasons and in ways that are not yet very well understood. They become actualized through the process of morphogenesis and lead to autopoiesis through organizational closure, but this results also from the system interactions with its environment… But, the more the system closes on itself, the less it remains able to adapt to a more global, and changing environment.

ASHBY, who much developed the constraint concept, states: "… the organism commonly faces a world that repeat itself, that is consistent to some degree in obeying laws, that is not wholly chaotic. The greater the degree of constraint, the more can the adapting organism specialise against the particular form of environment that do occur" (1960, p.139).

ASHBY also observed: "The constraint is thus a relation between observer and thing: the properties of any particular constraint will depend on both the real thing and on the observer. It follows that a substantial part of the theory of organization will be concerned with properties that are not intrinsic in the thing but are relational between observer and thing" (1968, p.109).