Perhaps Unidimensional Is Not Unidimensional

Miller (1956) identified his famous limit of 7 ± 2 items based in part on absolute identification—the ability to identify stimuli that differ on a single physical dimension, such as lines of different length. An important aspect of this limit is its independence from perceptual effects and its application across all stimulus types. Recent research, however, has identified several exceptions. We investigate an explanation for these results that reconciles them with Miller’s work. We find support for the hypothesis that the exceptional stimulus types have more complex psychological representations, which can therefore support better identification. Our investigation uses data sets with thousands of observations for each participant, which allows the application of a new technique for identifying psychological representations: the structural forms algorithm of Kemp and Tenenbaum (2008) . This algorithm supports inferences not possible with previous techniques, such as multidimensional scaling.     

One or two dimensions in spontaneous classification: a simplicity approach

When participants are asked to spontaneously categorize a set of items, they typically produce unidimensional classifications, i.e., categorize the items on the basis of only one of their dimensions of variation. We examine whether it is possible to predict unidimensional vs. two-dimensional classification on the basis of the abstract stimulus structure, by employing Pothos and Chater's simplicity model of spontaneous categorization [Pothos, E. M., & Chater, N. (2002). A simplicity principle in unsupervised human categorization. Cognitive Science, 26, 303-343]. The simplicity model provides a quantitative measure of how intuitive a particular classification is. With objects represented in two dimensions, we propose that a unidimensional classification will be preferred if it is more intuitive than all possible two-dimensional ones, and vice versa. Empirical results supporting this proposal are reported. Implications for Goodman's paradox are discussed.