Thinking, expertise and diagrams that encode laws

Among diagrammatic representations, law encoding diagrams (LEDs) are a special class. A LED captures the important laws or relations of a domain in the structure of a diagram using geometrical, spatial and topological constraints, such that a single instantiation of a diagram represents one instance of a phenomenon. Research on LEDs uses a combination of approaches, including the analysis of properties, computational modelling and empirical studies. The overarching theoretical context of this work is the paradigm of complex information processing, which sees problem solving as symbol processing by the means of heuristic searching. This paper considers how different LEDs can be used to solve diverse problems, and contrasts them to common Cartesian graphs, to argue that LEDs may be useful representations for expert problem solving. LEDs seem to be able to support some of the abilities that experts appear to possess, such as: being able to perceive large meaningful patterns; solving problems fast and with little error; seeing problems at a deep level; and doing large amounts of qualitative analysis of problems. Various forms of problem solving are examined in a particular domain, using different LEDs and conventional graphs. One LED and some sample problems are described. The domain is that of collisions among bodies moving in a straight line, with no frictional resistance.