How Evolution Constrains Human Numerical Concepts

The types of cognitive and neural mechanisms available to children for making concepts depend on the problems their brains evolved to solve over the past millions of years. Comparative research on numerical cognition with humans and nonhuman primates has revealed a system for quantity representation that lays the foundation for quantitative development. Nonhuman primates in particular share many human abilities to compute quantities, and are likely to exhibit evolutionary continuity with humans. While humans conceive of quantity in ways that are similar to other primates, they are unique in their capacity for symbolic counting and logic. These uniquely human constructs interact with primitive systems of numerical reasoning. In this article, I discuss how evolution shapes human numerical concepts through evolutionary constraints on human object-based perception and cognition, neural homologies among primates, and interactions between uniquely human concepts and primitive logic. KEYWORDS—brain; counting; evolution Human infants, children, and adults can estimate numerical values without counting and with crude precision. Human infants dishabituate to changes in the numerosity of a visual set during studies of looking time (1). Young children can choose the numerically larger of two sets of objects (2). Adults can rapidly tap out the approximate number of flashes they see in a sequence while also doing a verbal distractor task (3). Across these groups and studies, participants’ ability to discriminate is constrained by the numerical differences between the sets they compare. While estimating number, the fidelity of an individual’s representation decreases with the magnitude of the set, which results in lower accuracy for proportionally small differences compared to large differences (4). This constraint is known as Weber’s law: The ability to discriminate depends on the ratio between the quantities being compared. Even people in parts of the world where counting is not part of the language or culture can nonverbally estimate and compare numerical values from sets of objects, and obey Weber’s law in their accuracy (5). The ability to estimate numerical values nonverbally is apparently universal in humans and independent of verbal counting. In this article, I propose that number representation in humans is a result of the joint satisfaction of many evolutionary constraints on primates’ perceptual and cognitive systems. I discuss four types of constraints: First, I propose that numerical reasoning provides a rational solution to a vexing problem, which is how the disparate vocabularies of distinct sensory modalities and spatiotemporal dimensions are integrated into a holistic representation of quantity in the environment. Second, I propose that the disposition of humans’ quantity system to represent number, beyond other continuously varying quantitative dimensions, is driven in part by a bias in primates’ perceptual systems to parse inputs into discrete objects. Third, I argue that the neural substrates of human quantitative cognition are constrained evolutionarily, which imposes functional constraints on the organization and flow of numerical information. Fourth and finally, I argue that the human symbolic counting system interfaces with these evolutionarily primitive numerical and logical operations, evidence of continued constraints on numerical cognition in modern-day humans. These four constraints operate at different levels and are not mutually exclusive; rather, they jointly constrain the basic organization of numerical processing in the human mind. NUMBER REPRESENTATION IS A RATIONAL QUANTITATIVE STRATEGY Despite evidence that numerical representation is widespread in humans and animals, some recent work has questioned Jessica F. Cantlon, University of Rochester. The work reported in this article was supported by the National Science Foundation (DRL1459625) and the National Institutes of Health (R01 HD085996 and R01 HD091104). Correspondence concerning this article should be addressed to Jessica F. Cantlon, Department of Brain & Cognitive Sciences, University of Rochester, Rochester, NY 14607; e-mail: jcantlon@ rcbi.rochester.edu.