Chapter 8 - Cognitive Inferences, Mental Representations

Summary

This chapter elaborates what you learned in Chapter 7. It points out that despite the fact that many problems have an obvious visual representation, we need to be able to incorporate more abstract cognitive representations in our theory of problem solving. Traditionally, multidimensional scaling (MDS) has been used to infer Euclidean representations of concepts based on judged similarities. Here, after providing an example of how MDS has been used in vision, some cautionary comments are made about what MDS can and cannot provide. Because MDS is usually used to represent clusters of concepts, a formal discussion of clustering is included in this chapter. The chapter continues with two examples: one that is related to clustering in long-term memory and the other related to clustering in short-term memory. In both cases, clustering is used to interpret the mental navigation of memory representations as being analogous to navigation in our physical environment, just as it was when we discussed the TSP. The last section of this chapter illustrates how MDS can be used to explain how TSP tours are produced in the presence of obstacles where obstacles change the pairwise distances and make the distances not Euclidean. MDS can use the pairwise distances around obstacles to produce a Euclidean approximation. Preliminary experimental evidence suggests that this is what the human mind does.