International Encyclopedia of Systems and Cybernetics

Any exchange between elements, subsystems or systems.

A. BAHM explains the concept of interaction within a system (an existing system in his terms, i.e concrete or real, opposed to constructed systems, which are mental and cultural models):

"Interaction: The whole and parts of each existing system interact. That is, they act upon and influence each other (casually or conditionally) in ways that constitute it and maintain it:

"(1) Interaction involves action and action involves change. Each existing system changes. Existence itself involves existing or remaining through changing times, so every existing system involves changes, at least "changing times". A system may be involved in many kinds of changes, e.g. (a) changes within its parts (when a part changes internally it causes the whole to be a whole with a part changed internally); (b) changes between parts (becoming more like or unlike, more or less interactive); (c) loss of a part or parts, addition of a new part or parts, exchange of a part or parts; (d) changes in the whole (as more or less unitive, more or less strongly uniting its parts, or as a whole or more or fewer parts); and (e) changes in the interrelations of whole and parts (etc., more below).

"(2) Interaction involves permanence. Each existing system endures or remains the same from its beginning to its end. To be permanent is to remain through change. Interaction of whole and parts involves the whole remaining the same while it is acting on its parts (each part and all of its parts) and while it is acted upon by its parts (by each part and all of its parts). Interaction involves the parts remaining the same while acting on the whole and being acted upon by the whole. Interaction involves interrelations and interdependence of whole and parts remaining the same.

"(3) Interaction thus involves both change and permanence. Permanence and change involve each other because to be permanent is to endure or to remain through change and change can continue to be a change only by enduring or remaining a change. Both permanence and change may be variable, some systems existing for a shortest instant and some for a longest duration, and some characterized more by permanence and some more by change" (1986, p.178-9).

This kind of verbal fireworks, apparently somewhat paradoxical, becomes very meaningful when considered from the viewpoint of autopoiesis and organizational closure, which sustains that the set of internal interactions within the system is what defines which interactions it can operate with its environment and which not. These internal interactions lead to cyclical or hypercyclical self-reproduction of the system. Thus it maintains its permanence thanks to change.

On the other hand, interactions among individuals, i.e. elemental systems, as for example in ants colonies, are the driving force of communal self-organization, i.e. sociality. Interactions create at an emergent level, more complex units, endowed with new properties, simultaneously limiting and expanding the scope of individual activities.

The complete set of possible interactions within a system, when not too intricate, can generally be represented by a Markovian matrix. This idea has been adapted to sociology by W. BUCKLEY as the "interactions matrix" between individuals and small groups.