Elizabeth S. Spelke

Core systems of number.

What representations underlie the ability to think and reason about number? Whereas certain numerical concepts, such as the real numbers, are only ever represented by a subset of human adults, other numerical abilities are widespread and can be observed in adults, infants and other animal species. We review recent behavioral and neuropsychological evidence that these ontogenetically and phylogenetically shared abilities rest on two core systems for representing number. Performance signatures common across development and across species implicate one system for representing large, approximate numerical magnitudes, and a second system for the precise representation of small numbers of individual objects. These systems account for our basic numerical intuitions, and serve as the foundation for the more sophisticated numerical concepts that are uniquely human.

Large number discrimination in 6-month-old infants.

Six-month-old infants discriminate between large sets of objects on the basis of numerosity when other extraneous variables are controlled, provided that the sets to be discriminated differ by a large ratio (8 vs. 16 but not 8 vs. 12). The capacities to represent approximate numerosity found in adult animals and humans evidently develop in human infants prior to language and symbolic counting.

Origins of Knowledge.

Experiments with young infants provide evidence for early-developing capacities to represent physical objects and to reason about object motion. Early physical reasoning accords with 2 constraints at the center of mature physical conceptions: continuity and solidity. It fails to accord with 2 constraints that may be peripheral to mature conceptions: gravity and inertia. These experiments suggest that cognition develops concurrently with perception and action and that development leads to the enrichment of conceptions around an unchanging core. The experiments challenge claims that cognition develops on a foundation of perceptual or motor experience, that initial conceptions are inappropriate to the world, and that initial conceptions are abandoned or radically changed with the growth of knowledge.

Principles of Object Perception

Research on human infants has begun to shed light on early-developing processes for segmenting perceptual arrays Into objects. Infants appear to perceive objects by analyzing three-dimensional surface arrangements and motions. Their perception does not accord with a general tendency to maximize flgural goodness or to attend to nonaccidental geometric relations in visual arrays. Object perception does accord with principles governing the motions of material bodies: Infants divide perceptual arrays into units that move as connected wholes, that move separately from one another, that tend to maintain their size and shape over motion, and that tend to act upon each other only on contact. These findings suggest that a general representation of object unity and boundaries is interposed between representations of surfaces and representations of objects of familiar kinds. The processes that construct this representation may be related to processes of physical reasoning.

Perception of partly occluded objects in infancy

Abstract Four-month-old infants sometimes can perceive the unity of a partly hidden object. In each of a series of experiments, infants were habituated to one object whose top and bottom were visible but whose center was occluded by a nearer object. They were then tested with a fully visible continuous object and with two fully visible object pieces with a gap where the occluder had been. Patterns of dishabituation suggested that infants perceive the boundaries of a partly hidden object by analyzing the movements of its surfaces: infants perceived a connected object when its ends moved in a common translation behind the occluder. Infants do not appear to perceive a connected object by analyzing the colors and forms of surfaces: they did not perceive a connected object when its visible parts were stationary, its color was homogeneous, its edges were aligned, and its shape was simple and regular. These findings do not support the thesis, from gestalt psychology, that object perception first arises as a consequence of a tendency to perceive the simplest, most regular configuration, or the Piagetian thesis that object perception depends on the prior coordination of action. Perception of objects may depend on an inherent conception of what an object is.

Object permanence in five-month-old infants*

Abstract A new method was devised to test object permanence in young infants. Five- month-old infants were habituated to a screen that moved back and forth through a 180-degree arc, in the manner of a drawbridge. After infants reached habituation, a box was centered behind the screen. Infants were shown two test events: a possible event and an impossible event. In the possible event, the screen stopped when it reached the occluded box; in the impossible event, the screen moved through the space occupied by the box. The results indicated that infants looked reliably longer at the impossible than at the possible event. This finding suggested that infants (1) understood that the box continued to exist, in its same location, after it was occluded by the screen, and (2) expected the screen to stop against the occluded box and were surprised, or puzzled, when it failed to do so. A control experiment in which the box was placed next to the screen provided support for this interpretation of the results. Together, the results of these experiments indicate that, contrary to Piagets (1954) claims, infants as young as 5 months of age understand that objects continue to exist when occluded. The results also indicate that 5-month-old infants realize that solid objects do not move through the space occupied by other solid objects.

Domain-specific knowledge and conceptual change

Overview We argue that human reasoning is guided by a collection of innate domain-specific systems of knowledge. Each system is characterized by a set of core principles that define the entities covered by the domain and support reasoning about those entities. Learning, on this view, consists of an enrichment of the core principles, plus their entrenchment, along with the entrenchment of the ontology they determine. In these domains, then, we would expect cross-cultural universality: cognitive universals akin to language universals. However, there is one crucial disanalogy to language. The history of science and mathematics demonstrates that conceptual change in cognitive domains is both possible and actual. Conceptual change involves overriding core principles, creating new principles, and creating new ontological types. We sketch one potential mechanism underlying conceptual change and motivate a central empirical problem for cognitive anthropology: To what extent is there cross-cultural universality in the domains covered by innate systems of knowledge? Domain-specific cognition The notion of domain-specific cognition to be pursued here is articulated most clearly by Chomsky (1980a). Humans are endowed with domainspecific systems of knowledge such as knowledge of language, knowledge of physical objects, and knowledge of number. Each system of knowledge applies to a distinct set of entities and phenomena. For example, knowledge of language applies to sentences and their constituents; knowledge of physical objects applies to macroscopic material bodies and their behavior; knowledge of number applies to sets and to mathematical operations such as addition. More deeply, each system of knowledge is organized around a distinct body of core principles.

Sex differences in intrinsic aptitude for mathematics and science: A critical review

This article considers 3 claims that cognitive sex differences account for the differential representation of men and women in high-level careers in mathematics and science: (a) males are more focused on objects from the beginning of life and therefore are predisposed to better learning about mechanical systems; (b) males have a profile of spatial and numerical abilities producing greater aptitude for mathematics; and (c) males are more variable in their cognitive abilities and therefore predominate at the upper reaches of mathematical talent. Research on cognitive development in human infants, preschool children, and students at all levels fails to support these claims. Instead, it provides evidence that mathematical and scientific reasoning develop from a set of biologically based cognitive capacities that males and females share. These capacities lead men and women to develop equal talent for mathematics and science.

The native language of social cognition.

What leads humans to divide the social world into groups, preferring their own group and disfavoring others? Experiments with infants and young children suggest these tendencies are based on predispositions that emerge early in life and depend, in part, on natural language. Young infants prefer to look at a person who previously spoke their native language. Older infants preferentially accept toys from native-language speakers, and preschool children preferentially select native-language speakers as friends. Variations in accent are sufficient to evoke these social preferences, which are observed in infants before they produce or comprehend speech and are exhibited by children even when they comprehend the foreign-accented speech. Early-developing preferences for native-language speakers may serve as a foundation for later-developing preferences and conflicts among social groups.

Numerical abstraction by human infants

Across several experiments, 6- to 8-month-old human infants were found to detect numerical correspondences between sets of entities presented in different sensory modalities and bearing no natural relation to one another. At the basis of this ability, we argue, is a sensitivity to numerosity, an abstract property of collections of objects and events. Our findings provide evidence that the emergence of the earliest numerical abilities does not depend upon the development of language or complex actions, or upon cultural experience with number.