Geometry as a Universal Mental Construction

Izard, Véronique; Pica, Pierre; Dehaene, Stanislas; Hinchey, Danielle; Spelke, Elizabeth S.

doi:10.1016/b978-0-12-385948-8.00019-0

Cited by 32 publications

(34 citation statements)

References 33 publications

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“…Four paper plates (diameter, 10cm) placed on the floor at the four corners, served to hide the targets (colorful stickers). Visual form analysis was tested with materials adapted from Dehaene et al (2006) and Izard et al (2011). On each trial, six images were presented on 28 × 21cm laminated paper.…”

Section: Methodsmentioning

confidence: 99%

“…The visual form analysis task procedure was based on that of Izard et al (2011). Children were asked to find the intruding image in each array of six images.…”

Section: Methodsmentioning

confidence: 99%

“…Evidence for geometry-based object recognition and form analysis also comes from multiple sources (see Izard, et al, 2011; Landau & Lakusta, 2009, for reviews). Sensitivity to 2D shape begins in human infancy (Schwartz & Day, 1979) and underlies object recognition and visual form analysis in children (Izard & Spelke, 2009) as well as adults in diverse cultures (Dehaene, et al, 2006).…”

mentioning

confidence: 99%

“…Consistent with these findings, disoriented children relocate hidden objects to the left or right of equal-length surfaces that differ in distance, but not equidistant surfaces or corners differing in length or angle (Hupbach & Nadel, 2005; Lee, Sovrano, & Spelke, 2012). Studies of visual form analysis and object recognition reveal nearly the reverse pattern: young children use relative length and angle to distinguish one form from another, but their perception of forms is invariant over changes in scale (i.e., distance) and sense (i.e., the asymmetric directional relation that distinguishes a shape from its mirror image; see Izard, et al, 2011, for review). Many animal species show the same performance pattern (see Spelke & Lee, 2012).…”

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confidence: 99%

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Core Knowledge and the Emergence of Symbols: The Case of Maps

Huang

Spelke

2014

Journal of Cognition and Development

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Map reading is unique to humans but present in people of diverse cultures, at ages as young as 4 years. Here we explore the nature and sources of this ability, asking both what geometric information young children use in maps and what non-symbolic systems are associated with their map-reading performance. Four-year-old children were given two tests of map-based navigation (placing an object within a small 3D surface layout at a position indicated on a 2D map), one focused on distance relations and the other on angle relations. Children also were given two non-symbolic tasks, testing their use of geometry for navigation (a reorientation task) and for visual form analysis (a deviant-detection task). Although children successfully performed both map tasks, their performance on the two map tasks was uncorrelated, providing evidence for distinct abilities to represent distance and angle on 2D maps of 3D surface layouts. In contrast, performance on each map task was associated with performance on one of the two non-symbolic tasks: map-based navigation by distance correlated with sensitivity to the shape of the environment in the reorientation task, whereas map-based navigation by angle correlated with sensitivity to the shapes of 2D forms and patterns in the deviant detection task. These findings suggest links between one uniquely human, emerging symbolic ability, geometric map use, and two core systems of geometry.

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Section: Methodsmentioning

confidence: 99%

“…The visual form analysis task procedure was based on that of Izard et al (2011). Children were asked to find the intruding image in each array of six images.…”

Section: Methodsmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Core Knowledge and the Emergence of Symbols: The Case of Maps

Huang

Spelke

2014

Journal of Cognition and Development

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“…Converging findings from all these strands of research provide evidence that animals from insects to humans recognize objects primarily on the basis of their shapes, regardless of task demands [58]. Object recognition depends on a system of visual form analysis that builds shape representations with three properties (see [59] for review and discussion). First, representations of visual forms are scale-invariant over a considerable range: they fail to capture information about the absolute lengths of parts or distances of one part from another.…”

Section: Recognizing the Shapes Of Visual Formsmentioning

confidence: 99%

Core systems of geometry in animal minds

Spelke

Lee

2012

Phil. Trans. R. Soc. B

110

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Research on humans from birth to maturity converges with research on diverse animals to reveal foundational cognitive systems in human and animal minds. The present article focuses on two such systems of geometry. One system represents places in the navigable environment by recording the distance and direction of the navigator from surrounding, extended surfaces. The other system represents objects by detecting the shapes of small-scale forms. These two systems show common signatures across animals, suggesting that they evolved in distant ancestral species. As children master symbolic systems such as maps and language, they come productively to combine representations from the two core systems of geometry in uniquely human ways; these combinations may give rise to abstract geometric intuitions. Studies of the ontogenetic and phylogenetic sources of abstract geometry therefore are illuminating of both human and animal cognition. Research on animals brings simpler model systems and richer empirical methods to bear on the analysis of abstract concepts in human minds. In return, research on humans, relating core cognitive capacities to symbolic abilities, sheds light on the content of representations in animal minds.Keywords: cognitive development; animal cognition; navigation; geometry CORE COGNITIVE SYSTEMS IN ANIMAL MINDSFor well over 2000 years, studies of higher cognition have focused primarily on capacities that are unique to humans, such as language and geometrical intuitions. Debates about the nature and sources of these capacities continue to the present day, however, and progress in resolving them pales by contrast with the progress achieved in understanding the perceptual capacities that humans share with other animals. This contrast highlights problems faced by attempts to study higher cognition in any species, and it hints at a solution to those problems.The modern study of perception began with research on humans, who experimented on themselves to probe the physical events that evoke conscious experiences of colour, tone or motion. The power of these 'psychophysical experiments' was greatly enhanced, however, by parallel research on animals. Studies of perception in humans and in other animals were mutually illuminating: while human psychophysical findings guided research on animal perceptual systems, animal research shed light on the development and architecture of those systems, using methods of controlled rearing, neurophysiology and (more recently) genetics. Research from evolutionary biology and computer science enriched both sets of insights, by shedding light on the computational problems that visual systems evolved to solve.The study of higher cognition has not experienced the same synergies. Indeed, attempts to use human conscious experience as a guide to animal research often lead to blind alleys, because human intuition is a poor source of insights into animal minds. This failure stems, we suggest, from three prominent differences between perceptual systems, on one hand, and higher cognitive...

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Basic mathematical cognition

Gaber

Schlimm

2015

WIRES Cognitive Science

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Mathematics is a powerful tool for describing and developing our knowledge of the physical world. It informs our understanding of subjects as diverse as music, games, science, economics, communications protocols, and visual arts. Mathematical thinking has its roots in the adaptive behavior of living creatures: animals must employ judgments about quantities and magnitudes in the assessment of both threats (how many foes) and opportunities (how much food) in order to make effective decisions, and use geometric information in the environment for recognizing landmarks and navigating environments. Correspondingly, cognitive systems that are dedicated to the processing of distinctly mathematical information have developed. In particular, there is evidence that certain core systems for understanding different aspects of arithmetic as well as geometry are employed by humans and many other animals. They become active early in life and, particularly in the case of humans, develop through maturation. Although these core systems individually appear to be quite limited in application, in combination they allow for the recognition of mathematical properties and the formation of appropriate inferences based upon those properties. In this overview, the core systems, their roles, their limitations, and their interaction with external representations are discussed, as well as possibilities for how they can be employed together to allow us to reason about more complex mathematical domains.

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Geometry as a Universal Mental Construction

Cited by 32 publications

References 33 publications

Core Knowledge and the Emergence of Symbols: The Case of Maps

Core Knowledge and the Emergence of Symbols: The Case of Maps

Core systems of geometry in animal minds

Basic mathematical cognition

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