Human Problem Solving and Problem-Solving Systems
At an abstract level, problems can be represented synthetically or analytically. Synthetic representations are structures, organizations, patterns, configurations, gestalts, schemata. Analytic representations are elements, infinitesimals, reduction, components, subgoals. The process of problem solving can involve either or both of the following: (a) The discovery of an effective synthetic representation of the problem, (b) the discovery of an effective analytic representation of the problem. The discovery of an effective synthetic representation of the problem may result from any or all of the following: (a) restructuring the configuration of the problem, (b) differentially emphasizing different aspects of the problem, (c) interpreting the problem at a higher level of abstraction, (d) applying a structural analog of the problem, (e) applying relevant knowledge. The discovery of an effective analytic representation of the problem may result from any or all of the following: (a) decomposing the problem into familiar components, (b) partitioning the problem into minimally small and equivalent units, (c) reducing the problem to a known formalism, (d) applying knowledge to a subgoal of the problem.
These methods for discovering effective synthetic and analytic representations of problems are discussed in the following section in the context of examples drawn from a variety of disciplines, but primarily from gestalt psychology, cognitive psychology, and clinical psychology.