The concept of Complexity is classically defined with the help of two terms, namely element and relation. This definition responds to the problem that with the number of elements the possible relations between them increase disproportionately, namely in geometric progression; the more elements one has, the more each individual element is overwhelmed by linkage requirements. If one imagines that linking requirements or contextuations of an element determine the quality of an element, then one sees that the increase in linking capability has limitations, depending on what kind of system is under discussion. This is true for cells as well as for communications; if one starts from individuals, from people, it is true for the number of possible contacts a person can have with others in a given time. So it applies formally and relatively independent of the question, what actually is the element and what the relation consists of.
The consequence is that from a certain order of magnitude onwards it is no longer possible to link every element with every other and therefore one can only establish relations selectively: For example, in the form of a circle, where everyone is dealing with two neighbors, perhaps providing a direction of information or flow, so that you always get something from one and pass it on to the next, but cannot communicate across the circle; or in the form of a hierarchy, where there is a top and many basal elements, but each can communicate only with the next higher element, or perhaps still horizontally at the same level. A secretary of state cannot call directly into another ministry's registry from the top down. This is very unusual and not welcomed. There is in each case a network of exclusions and inclusions of possible communications, and accordingly there are attempts in the literature to test whether star, hierarchical, or circular models are practically superior with respect to information processing capacity, innovation capacity, and the like. Network analysis in this formal sense is research that took place in the 1950s. The problem was to test selection patterns, selectivity in comparison with the no longer feasible condition that everything is linked to everything else.
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Luhmann, Niklas. Einführung in die Systemtheorie. Herausgegeben von Dirk Baecker. 2. Aufl. Sozialwissenschaften. Heidelberg: Carl-Auer-Verl, 2004, p. 173–174
See for example Alex Bavelas, Communication Patterns in Task-oriented Groups. In: Dorwin Cartwright, Alvin Zander (Hrsg.), Group Dynamics, Research, and Theory. Evanston: Row, Peterson & Co. 1953, S. 493-506; ders., Communication Patterns in Problem-Solving Groups. In: Heinz von Foerster (Hrsg.), Cybernetics. New York: Josiah Macy Jr. Foundation 1952.
Coenenberg, Adolf Gerhard. „Betriebliche Kommunikation als System“. In Die Kommunikation in der Unternehmung, herausgegeben von Adolf Gerhard Coenenberg, 78–141. Betriebswirtschaftliche Beiträge. Wiesbaden: Gabler Verlag, 1966. https://doi.org/10.1007/978-3-322-99165-2_4.
> A direct influence of different communication systems on the groups' speed of solving problems cannot be demonstrated, once the groups have established a suitable organizational scheme. In contrast, depending on the nature of the constraints, certain communication systems can have both positive and negative effects on the groups' ability to organize themselves optimally.
Determining an organizational scheme appropriate for the problem is already part of the problem-solving process - and part of the problem.