Objects, Sets, and Ensembles

Abstract

This chapter discusses how different types of entities such as individual objects, sets of objects, and ensembles can function as items to be maintained in working memory (WM). All of these types of representations can be relevant to thinking about quantities, and each supports different kinds of quantity-relevant computations. One way to overcome the three- to four-item limit of WM is to bind together representations of individual objects into representations of sets of objects. Binding multiple individuals into a single higher-order group can increase the number of individual items that can be remembered, as in the well-known demonstrations of chunking by adults. Set representations play a critical role in many numerical processes, including representing the nested relationships between as well as representing the cardinality of an array. Many real-world scenes contain stimuli that do not lend themselves to representation qua individual objects or sets of objects. One can imagine enumerating a flock containing dozens of individual birds.