An agenda of basic questions about the impact of social science and research on real life problems. How social scientists are often crippled by a misunderstanding of their own trade.

When a group has applied the Interpretive stuctural modeling process to develop a map of a theme or Issue, they typically Inspect visually the map they have produced to see whether it is intuitively satisfactory. While this practice is useful and may play a role in map amendment, a more thorough approah is recommended. The working space of the map consists of the ordered element pairs belonging to the Cartesian product S × S, where S is the set of elements modeled through a contextual reation represented by the binary relation R. In a systematic modeling effort it is desirable to establish the completeness of the relation R without requiring mathematical sophistication on the part of the modeling group. (If R Is not complete, only part of the knowledge germane to the working space is embedded in the model.) Moreover, some of the useful knowledge content of the working space may only be implicit in R. if the modeling group is to take full advantage of the knowedge embedded in a map, it is esential that the group understand a systematic procedure for reading maps. Such a procedure is presented, and it is postulated that the group knows how to use it.

The substantive complexity of a complex system or issue can be diminished by the introduction of structural complexity to describe that system or issue. To minimize the negative impact of the introduction of structural complexity, graphics should be translatable into prose. To assure that this can be done it is necessary to define a metalanguage that is not only appropriate for use in modeling, but also is adequate to bridge the structural gap to applications. The availability of well-defined structural types helps minimize the impact of structural complexity. Several structural types are defined, and a principle of definition is set forth as a reasonable basis for choosing and distinguishing these types. The set inclusion relation is the most critical one in the metalanguage of structuring in problem definition, because of its key role in the definition of terms, hence of systems or issues. To assure that this relation can be constructively applied, especially with graphics representations, mappings are developed that provide a basis to convert poorly structured information into well-structured information, suitable for a translatable graphic presentation.

The development of citizen capacity to function from a systems perspective on major public issues is needed to combat the "politics of selfishness' as practiced through single-issue political action groups. Environmental education offers an opportunity to develop citizenship functions through the challenge set forth in the Environmental Education Act of 1970. Systems methodologies have been developed that offer the possibility of citizen learning and doing through participative effort. Examples of the use of various systems methodologies relate to defining environmental education, exploring core themes for use in environmental education, classroom learning, and acceptance in field testing of methodology. Design of a regional environmental learning system (RELS) offers another opportunity to apply systems methodology. A general methodology for conceptual design of systems can be readily applied to public design of environmental learning systems.

Techniques are introduced which are applicable to machine construction of digraph maps. These techniques are oriented toward reduction of the number of crossings in a map as a means of improving the readability of hierarchical structures. Permuting, psi-factoring, rotating, twirling, and absorbing are among the techniques considered. Examples are given to illustrate these techniques. When these and related procedures are fully developed for use with machine-interactive processes, they will facilitate group modeling efforts.

The problem of interconnecting two multilevel subsystem models defined by binary matrices A and B and a common, transitive, contextual relation to form a system model defined by matrix M is solved. The entries of the unknown interconnection matrices X and Y are shown to form a multilevel implication structure. A method for finding this structure is given. The implication matrix that defines the structure furnishes a simple means of determining the inference opportunity of any unknown in X or Y at any point in the development of these matrices. Transitive bordering of A corresponds to the special case B = 1. When the system has many elements, it may be advisable to form a matrix A for a subset and then use transitive bordering iteratively to complete the structuring process.

A major requirement for structural modeling is that the necessary data be acquired and organized into a form from which a structural model can be developed. A reachability matrix is one such form. It is very useful when the contextual relation being modeled is transitive and multilevel. A significant step in the development of a reachability matrix consists of the ordering of elements of the system in such a way that much of the data required can be computed from supplied data, using the transitivity condition. The process described for orderimg the element set suffices to define a set of subsystems and reduces the problem of developing a reachability matrix to one of developing a set of its component interconnection matrices that join these subsystems. The process described assigns much of the burden of structural modeling to the computer, leaving to the developer the tasks requiring substantive knowledge of the system being modeled.

A procedure is described for developing an interconnection matrix that specifies a cascade connection of two known digraphs to form a digraph. The solution of this form of the interconnection problem can be applied to complete the process of description of a binary relation initiated by the process of partitioning on elements described in a companion paper [3]. It is assumed that the contextual relation being modeled is transitive. Based on this assumption, it is shown that the possibilities of interconnection can be completely prescribed in a characteristic logic equation. This equation can be used as the complete basis for development of an interconnection matrix. An example of its use is given. Much of the burden of structural modeling is assigned to the computer, leaving to the developer the tasks requiring substantive knowledge of the system being modeled.

The interpretation of complex structural models is facilitated by a variety of operations that can be carried out by a computer. Several of these involve partitions on a reachability matrix, which describes a contextual relation among the elements of the system under study. When partitioning of the reachability matrix in various ways does not permit adequate interpretation, cycles are usually the source of difficulty. A weighting matrix applied to the elements of a maximal cycle set permits a set of digraphs to be developed, which allows for more detailed interpretation of a cycle. When still further development is needed, the maximal cycle sets can be identified and placed in a hierarchy based on an inclusion relation. This hierarchy suggests a natural order of study of the system proceeding from the least complex maximal cycle sets to the most complex sets.

Hierarchies are fundamental in the study of many kinds of complex systems. Methods are presented that assist in the development of a hierarchy or a set of hierarchies. Once the element set and the relations among the elements are established, the rationalizing procedure presented allows computer determination of how many separate hierarchies are represented by the relations among the elements. An example of the rationalization process is given. Two methods-the element method and the level method-are given for developing a hierarchy for a connected subordination matrix. Each method is illustrated with an example.

The process of goal formation is presently inefficient- suffering from neglect, confusion of nomenclature, problems of group dynamics, and other difficulties. Intent structures furnish a practical mechanism for use in individual or group formation of goals. Such structures can become a kind of portrait of an organization, characterizing it much more effectively than an organization chart. Intent structures can also serve as a basis for managing complex system programs. Examples of intent structures are given which relate to education and new city design.

This primarily tutorial paper on the use of binary matrices in system modeling also includes new material related to the initial development of such matrices. The decomposition of binary matrices into levels such that all feedback is contained within the levels is illustrated. A method for developing a binary matrix en route to a structural model of a system is outlined. The development procedure partitions the matrix on the basis of supplied data entries. Then the interconnections between subsystems are added. This procedure permits transitivity to be used in developing the matrix.

Program planning begins with problem definition and ends with planning for action. The key products that result from the problem definition, value system design, and system synthesis steps are discussed and interrelated through the use of interaction matrices. Particular emphasis is given to defining objectives and to defining a set of measures on the objectives by which to determine their attainment. Interaction matrices relate objectives measures to objectives and link activities and measures of their accomplishment to the attainment of objectives. A major consequence of program planning is the choice of a program to pursue, and identification of the projects that will be carried out as a part of a selected program. Selecting the set of projects is discussed in terms of consistency with corporate or agency policy, and the economics, risk, and potential benefits associated with each project. A criterion function that incorporates the latter three factors is described and proposed as a practical way of evaluating the relative merits of projects.