Infants’ Enumeration of Actions 1 Running Head: Enumeration of Actions by Infants Infants’ Enumeration of Actions: Numerical Discrimination and its Signature Limits

Are abstract representations of number – representations that are independent of the particular type of entities that are enumerated – a product of human language or culture, or do they trace back to human infancy? To investigate these questions, four experiments investigated whether human infants discriminate between sequences of actions (jumps of a puppet) on the basis of numerosity. At 6 months, infants successfully discriminated 4vs. 8-jump sequences, when the continuous variables of sequence duration, jump duration, jump rate, jump interval and duration and extent of motion were controlled and rhythm was eliminated. In contrast, infants failed to discriminate 2vs. 4-jump sequences, suggesting that infants fail to form cardinal number representations of small numbers of actions. Infants also failed to discriminate between sequences of 4 vs. 6 jumps at 6 months, and succeeded at 9 months, suggesting that infants’ number representations are imprecise and increase in precision with age. All of these findings agree with those of studies using visual-spatial arrays and auditory sequences, providing evidence that a single, abstract system of number representation is present and functional in infancy. Infants’ Enumeration of Actions 3 Infants’ Enumeration of Actions: Numerical Discrimination and its Signature Limits Recent research provides evidence that human infants discriminate between large sets of elements on the basis of numerosity, when a variety of continuous quantitative variables are controlled. For example, 6-month-old infants discriminate visual arrays of 8 vs. 16 dots when array size and density, dot size, summed area and brightness, and summed contour length are equated either during habituation or during test (e.g., Brannon, 2002;Brannon, Abbott, & Lutz, in press; Xu & Spelke, 2000; Xu, 2003; Xu, Spelke, & Goddard, in press). Infants also discriminate auditory sequences of 8 vs. 16 sounds when sequence duration, rate, item duration, and duration and amount of sound are controlled and rhythm is eliminated (Lipton & Spelke, 2003; in press). In these studies, infants’ numerical discrimination shows four signature limits. First, it is imprecise: for example, 6-month-old infants discriminate 8-dot arrays from 16-dot arrays but not from 12-dot arrays (Xu & Spelke, 2000). Second, discrimination depends on the ratio of the two numerosities: infants who discriminate 8 dots or sounds from 16 but not from 12 also discriminate 4 dots or sounds from 8 but not from 6 (Xu, 2003; Lipton & Spelke, in press). Third, discrimination increases in precision with development: from 6 to 9 months, the critical ratio decreases from 2.0 (e.g., 4 vs. 8) to 1.5 (e.g., 4 vs. 6) (Xu & Arriaga, under review; Lipton & Spelke, 2003). Fourth, discrimination fails for the smallest numerosities when infants are tested with the same methods and controls: for example, 6-month-old infants show no evidence of discriminating 1 vs. 2 or 2 vs. 4 dots or sounds, and 9-month-old infants show no evidence of discriminating 2 vs. 3 dots or sounds (Xu, 2003; Xu et al.,in press; Lipton & Spelke, in press; see also Clearfield & Mix, 1999; Feigenson, Carey & Spelke, 2002). These four signature limits characterize a system of numerical representation that human infants appear to share both with Infants’ Enumeration of Actions 4 human adults and with adult non-human primates tested with similar displays (Barth, Kanwisher & Spelke, 2003; Hauser, Tsao, Garcia & Spelke, 2003; see also van Oeffelen & Vos, 1982), suggesting continuity in numerical representations over primate phylogeny and human ontogeny. Although the convergence among the above studies is striking, the extent of infants’ numerical capacities, and the abstractness of their numerical representations, are still debated. Human adults enumerate diverse entities, including visual forms, sounds, parades, flocks of birds, home runs, and arguments. Does the ability to enumerate varied types of entities depend on a later-developing mechanism that emerges as children gain skill at verbal counting or symbolic arithmetic, as some have suggested (Mix, 1999), or does this ability trace back to infancy? In landmark research, Wynn (1996; Sharon & Wynn, 1998) addressed this question by investigating whether infants individuate and enumerate actions. Individuating actions is a complex task, because each action consists of a structured series of motions (see Wynn, 1996). In these studies, 6-month-old infants were habituated to a puppet jumping either 2 or 3 times and then were tested with both numerosities. Infants dishabituated to the sequences containing the novel number of puppet jumps. The convergence of these findings with those of earlier studies of infants’ discrimination of arrays of 2 vs. 3 visual forms (e.g., Starkey & Cooper, 1980; Strauss & Curtis, 1981; van Loosbroek & Smitsman, 1990) or sounds (e.g., Bijeljac-Babic, et al. 1991) suggested that infants formed a fairly abstract concept of “individual,” encompassing diverse entities. Nevertheless, recent findings suggest three alternative interpretations of Wynn’s findings. First, infants may discriminate between sequences of 2 vs. 3 jumps by attending to perceptual information such as the rate of movement in habituation vs. test. In particular, Clearfield (2003) Infants’ Enumeration of Actions 5 found that 6-month-old infants dishabituate equally to new and old numbers of actions when the rate of motion is not a reliable cue to numerosity. Second, infants may discriminate 2from 3jump sequences by forming a summary representation of one or more continuous variables. Because each jump in Wynn’s study was identical in extent and duration, the number of jumps was positively correlated with the total duration and extent of motion in the sequence. Infants have been found to form summary representations of continuous extent or contour length when presented with small numbers of objects (Clearfield & Mix, 1999; Feigenson, et al., 2002). These findings call earlier evidence for representations of small numerosities into question, and they raise the possibility that a summary representation of continuous amount of motion underlies discrimination of small numbers of actions (Mix, Huttenlocher & Levine, 1996). According to a third proposal, the infants in Wynn’s (1996) experiments represent each individual action with a unique symbol without representing or storing an explicit cardinal value (Carey, 2001). This account gains plausibility from evidence that infants’ representations of small numbers of visible objects depend on mechanisms of parallel individuation, or “object files” (see Simon, 1997; Scholl, 2001; Feigenson, et al., 2002b; Feigenson & Carey, in press). A fourth proposal is Wynn’s (1996, 1998, 2000): infants’ discrimination of 2vs. 3-jump sequences depends on a dedicated numerical mechanism. In the latter case, however, note that Wynn’s results fail to accord with two of the signature features of numerical discrimination: the ratio limit of 2.0 at 6 months and the failure of discrimination for small numerosities. The present studies were undertaken both to disentangle these four proposals and to test Wynn’s original hypotheses that infants individuate actions and form numerical representations of diverse types of entities. First, we investigated whether 6-month-old infants discriminate action sequences presenting large numerosities (4 vs. 8 jumps of a puppet) on the basis of Infants’ Enumeration of Actions 6 number when the continuous variables of sequence rate and duration, jump duration and extent, and motion duration and extent are controlled and rhythm is eliminated (Experiment 1). Such a finding would suggest, following Wynn (1996), that infants can individuate and enumerate actions. Next, we investigated whether infants’ discrimination of action sequences shows the four signatures of infants’ discrimination of visual-spatial arrays and auditory sequences: lack of precision, success at a 2.0 ratio at 6 months, success at a 1.5 ratio at 9 months, and failure for small numerosities. We investigated 6-month-old infants’ discrimination between sequences of 2 vs. 4 jumps (Experiment 2) and both 6and 9-month-old infants’ discrimination between sequences of 4 vs. 6 jumps (Experiments 3 and 4). To preview our findings, infants’ discrimination of jump sequences showed all the signatures found in past studies of discrimination of visual-spatial arrays and auditory-temporal sequences, contrary to the specifics of Wynn’s (1996) findings but in support of her general claims for an abstract mechanism of enumeration.