Patterns of Conceptual Integration

Representation of sets: introductory comment

Anthony Judge

Herbert Simon notes: "An early step toward understanding any set of phenomena is to learn what kinds of things there are in the set--to develop a taxonomy. The step has not yet been taken with respect to representations. We have only a sketchy and incomplete knowledge of the different ways in which problems can be represented and much less knowledge of the significance of their differences." (5 p. 78)

Fig. 2: Illustration of the project approach of the "Assessment of Future National and International Problems" (Reproduced from a document of that title, published by the National Science Foundation, 1977.)
The problem of representation is generally considered to be of little interest compared with the subject matter of the representation and is seldom a matter of scholarly concern [10]. One reason derives from the prevalence of evidence that the physical and social environment is hierarchically ordered (10) [11]. Now hierarchical structures are those in which the interactions amongst the subsets are weak in comparison with interactions between the elements within the set. They are therefore referred to as "nearly decomposable" and as such the high-frequency dynamics within subsets are distinguished from the low-frequency dynamics between subsets. Herbert Simon relates this property to the comprehensibility of such systems: "The fact, then, that many complex systems have a nearly decomposable, hierarchic structure is a major facilitating factor enabling us to understand, to describe, and even to "see" such systems and their parts" (5, p. 108). And clearly once it is assumed that the subsets can be represented individually, or separately in relation to the set and to each other, representation is merely a question of a hierarchy of "maps". Each can be made as detailed as necessary and can be comprehended separately.

It may be argued, however, despite the apparent ease of this approach, that widespread understanding of the many systems within which man functions (or with which he interacts) remains elusive. Indeed complaints about "increasing complexity" are now common. And studies of psycho-social systems have not produced insights to make them more manageable, in fact such systems appear to have become less manageable whilst such studies are produced.

There are three weaknesses in the conventional stress on the prevalence of hierarchical ordering. Herbert Simon follows the previously cited remark with: "Or perhaps the proposition should be put the other way round. If there are important systems in the world that are complex without being hierarchic, they may to a considerable extent escape our observation and our understanding." (5, p.l08). Such systems, possibly exerting a "field effect" or based on non-hierarchically ordered networks may indeed be at the root of our difficulties. It is interesting that the 1970s has witnessed a rapidly burgeoning interest in networks of all kinds and a suspicion of hierarchically coordinated social structures (13). The relationship between sub-sets of different hierarchies is recognized as being increasingly critical (e.g. in environmental systems). The problem of representing such complex patterns of relationship to facilitate comprehension has not been resolved [12].

A second weakness derives from lack of clarity on the nature of the set of which the hierarchical set under consideration is a sub-set--namely the super-ordinate set. Each discipline is responsible for its own hierarchical sets, none is responsible for the super-ordinate set (and the interactions between its sub-sets). This relates back to the first weakness. There is little understanding of what happens at the "top" of hierarchies and especially "above" them [13].

A third weakness derives from lack of clarity on the relation of the person creating or observing the set--to that set. Some aspects of this question are discussed separately below. It is particularly important where one or more such sets are expected to order the comprehension of the individual who therefore has the problem of "juggling" them into a suitable configuration in relation to his own psychic ordering [14]. This raises the question of the iconicity of any representation which is discussed below.

In discussing the description of complexity, Herbert Simon makes a basic distinction between state descriptions and process descriptions [15]. "These two modes of apprehending structures are the warp and weft of our experience. Pictures, blueprints, most diagrams and chemical structural formulas are state descriptions. Recipes, differential equations, and equations for chemical reactions are process descriptions. The former characterize the world as sensed; they provide the criteria for identifying objects, often by modeling the objects themselves. The latter characterise the world as acted upon; they provide the means for producing or generating objects having the desired characteristics.... Given a desired state of affairs and an existing state of affairs, the task of an adaptive organism is to find the difference between these two states and then to find the correlating process that will erase the difference. Thus, problem solving requires continual translation between the state and process descriptions of the same complex reality."(5, pp. 111-112).

Some of the ways of representing sets are discussed below.