COMPLEXITY AND THE CONTROL OF VARIETY

The hierarchical structure which made Hora successful, because he built his watches In successive subassemblies he did not lose all he had done whenever he was disturbed, is as fundamental to the evolution of the universe as for the success of Hora's business. That is, It is the most efficient way to organize any system above the simplest. But what Is not as evident Is that this same hierarchical structure is a natural mechanism for Increasing variety. There are many more possible compounds, for example, than there are elements from which the compounds are derived. In the case of the beach the complex systems Involved range from the materials on the beach to the ecological system that ultimately determines their distribution.

In addition to increasing variety, complex hierarchical structure allows Individual levels of the system to interact as though they were simple systems. The ant, for example, is a highly complex organism. But, as Simon explains, seen as a behaving organism wending its way across the beach, it is quite simple. When we analyze the problem of the ant finding his way home, we can treat it as though it was a machine with one predominant property, an instinct for knowing the direction to its nest. Each obstacle then becomes a single isolated event, a simple choice between often arbitrary outcomes. The property which allows us to consider the ant in this manner is what Simon called "near decomposability", which simply meant that each level of a complex system has a limited amount of autonomy and within those limits can be considered a simple system with only the variety faced by this level to contend with.

Luhmann frequently used the term "reduction of complexity" In his works. If we see that the mechanism he was referring to was this property of complexity of reducing the amount of variety a system is forced to contend with through hierarchical structure, we can overcome one contradiction In Luhmann's descriptions and at the same time open the door to more and deeper insights Into social structure. Luhmann does make a distinction between what he called "structured complexity", which follows the criteria I have set up here, and "unstructured complexity" which Is what I refer to as simple variety., but he does not make use of the concept In his descriptions

An example of completely unstructured complexity would be the limiting case of primeval plasma, when all possibilities are arbitrary and equal. Structured complexity comes Into being to the extent that possibilities are mutually exclusive or limiting. Problems of compatibility or coexistence arise with structured complexity. The actualizing of a particular possibility prevents that of others, but, on the other hand, permits the construction of new possibilities which the former requires as precondition.

The problem of choice, however, is as Important to Luhmann's theories as Is autonomy, but it cannot be described strictly In terms of Simon's complex hierarchical structure. This view of complex structure is seen from the Inside looking out. Robert Rosen has developed a picture of complex systems as they might be seen from the outside looking in." As he explained it, a system Is Complex If we can Interact with It at several different levels. When we analyze any complex system we use a set of measuring Instruments. Different sets of Instruments will give different partial descriptions of the system. The difference between the system as described by one set of Instruments end as it exists In reality Is called error. The descriptions given by different sets of measuring instruments he called relative descriptions. Because levels developed through such relative descriptions do not correspond to Simon's structural levels, It is not possible to obtain a complete description of a system by concatenating relative descriptions. However, because the Instruments we use are sensitive to those characteristics of the system that are relevant to our purpose, the error developed by a set of measuring instruments may not be significant when it is applied to that purpose. This means that the average person facing a sea of environmental variety can apply a number of sets of social, political, and Ideological Instruments to his understanding of his environment and thus develop a number of differing relative descriptions.

Luhmann's statement, "Complexity in this sense increases with the functional differentiation of society and the separating out of different possibilities" is intuitively contradictory. What he meant was that the development of social systems, for example legal systems, economic systems and so forth, increases the number of ways that the Individual can interact with the world. This mechanism would then meet the first requirement for evolutionary change, a source of variety. At the same time, each of these systems also provides the second requirement, a mechanism for choice. Each system chooses from among the possible interactions those which will best accomplish Its specific purpose. It can do this because through the use of each such system people analyze their environment with different sets of measuring Instruments and thus develop different sets of relative descriptions. These relative descriptions are not treated as partial descriptions. They are considered as though they were complete descriptions of a single, or at most a small number of, heuristically determined levels of a complex system which have fuzzy boundaries. To put It another way, the demarcation that separates each level from Its environment Is a set of threshold conditions. That Is, conditions which occur when specific measuring Instruments with a specific level of magnification sense a sudden change of relevance In the properties of a continuum change at one point along that continuum. Differentiation at that point, however, increases the breadth of that threshold. Those behavior patterns that enhance the differentiation are selected from the variety of possible activities because the members of the society relate them to the success of the system. We can take this description as one of the differentiation of social structures. We can take It as well as a general description of the emergence of new permanent structures through the evolutionary process.

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