Scientists from many disciplines have been intrigued by the topic of how the mind represents number because of the question's relevance to controversial topics such as thought without language, the evolution of cognition, modularity of mind, and nature vs. nurture. Number is an abstract and emergent property of sets of discrete entities; two people and two airplanes look nothing alike, and yet the numerosity of the set is the same. Some researchers believe that the abstract nature of numerical representation makes it an unlikely candidate for a cognitive capacity held by nonhuman animals and human infants. However, a growing body of data suggests that both nonverbal animals and preverbal human infants represent number and even perform operations on these representations. In fact, a new synthesis of the data on numerical abilities in animals and infants suggests that there is an evolutionarily and developmentally primitive system for representing number as mental magnitudes with scalar variability (Gallistel and Gelman, 1992, 2000; see also Dehaene, 1997; Wynn, 1995). Furthermore, there is abundant evidence that adult humans also represent number nonverbally as analog magnitudes (Cordes et al., 2001; Dehaene, 1997; Dehaene et al., 1998; Moyer and Landauer, 1967; Whalen et al., 1999). For these reasons, numerical cognition has become an exciting area of research and an exemplary model of a cross-disciplinary field where comparative and developmental studies have influenced current conceptions of adult human numerical processing (e.g., Dehaene, 1997).

The goal of this chapter is to evaluate the evidence bearing on the nonverbal representation of number by animals and human infants. Specifically, we will (a) review the data demonstrating that nonhuman animals and human infants represent number and perform operations on these representations, (b) evaluate the proposed models of the nonverbal representation of number and the evidence for and against each model, and (c) describe what is known about the neurobiological basis of number representations. Finally, we will outline some of the outstanding questions that should guide future research aimed at understanding the evolution and development of numerical thinking.

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