Spatial knowledge and geometric representation in a child blind from birth

Distinct neural mechanisms for heading retrieval and context recognition in the hippocampus during spatial reorientation

Reorientation, the process of regaining one's bearings after becoming lost, requires identification of a spatial context (context recognition) and recovery of facing direction within that context (heading retrieval). We previously showed that these processes rely on the use of features and geometry, respectively. Here, we examine reorientation behavior in a task that creates contextual ambiguity over a long timescale to demonstrate that male mice learn to combine both featural and geometric cues to recover heading. At the neural level, most CA1 neurons persistently align to geometry, and this alignment predicts heading behavior. However, a small subset of cells remaps coherently in a context-sensitive manner, which serves to predict context. Efficient heading retrieval and context recognition correlate with rate changes reflecting integration of featural and geometric information in the active ensemble. These data illustrate how context recognition and heading retrieval are coded in CA1 and how these processes change with experience.

Précis of What Babies Know

Where does human knowledge begin? Research on human infants, children, adults, and nonhuman animals, using diverse methods from the cognitive, brain, and computational sciences, provides evidence for six early emerging, domain-specific systems of core knowledge. These automatic, unconscious systems are situated between perceptual systems and systems of explicit concepts and beliefs. They emerge early in infancy, guide children's learning, and function throughout life.

A language of thought for the mental representation of geometric shapes

In various cultures and at all spatial scales, humans produce a rich complexity of geometric shapes such as lines, circles or spirals. Here, we propose that humans possess a language of thought for geometric shapes that can produce line drawings as recursive combinations of a minimal set of geometric primitives. We present a programming language, similar to Logo, that combines discrete numbers and continuous integration to form higher-level structures based on repetition, concatenation and embedding, and we show that the simplest programs in this language generate the fundamental geometric shapes observed in human cultures. On the perceptual side, we propose that shape perception in humans involves searching for the shortest program that correctly draws the image (program induction). A consequence of this framework is that the mental difficulty of remembering a shape should depend on its minimum description length (MDL) in the proposed language. In two experiments, we show that encoding and processing of geometric shapes is well predicted by MDL. Furthermore, our hypotheses predict additive laws for the psychological complexity of repeated, concatenated or embedded shapes, which we confirm experimentally.

Navigable Space and Traversable Edges Differentially Influence Reorientation in Sighted and Blind Mice

Reorientation enables navigators to regain their bearings after becoming lost. Disoriented individuals primarily reorient themselves using the geometry of a layout, even when other informative cues, such as landmarks, are present. Yet the specific strategies that animals use to determine geometry are unclear. Moreover, because vision allows subjects to rapidly form precise representations of objects and background, it is unknown whether it has a deterministic role in the use of geometry. In this study, we tested sighted and congenitally blind mice (Ns = 8-11) in various settings in which global shape parameters were manipulated. Results indicated that the navigational affordances of the context-the traversable space-promote sampling of boundaries, which determines the effective use of geometric strategies in both sighted and blind mice. However, blind animals can also effectively reorient themselves using 3D edges by extensively patrolling the borders, even when the traversable space is not limited by these boundaries.

Euclid's Random Walk: Developmental Changes in the Use of Simulation for Geometric Reasoning

Euclidean geometry has formed the foundation of architecture, science, and technology for millennia, yet the development of human's intuitive reasoning about Euclidean geometry is not well understood. The present study explores the cognitive processes and representations that support the development of humans' intuitive reasoning about Euclidean geometry. One-hundred-twenty-five 7- to 12-year-old children and 30 adults completed a localization task in which they visually extrapolated missing parts of fragmented planar triangles and a reasoning task in which they answered verbal questions about the general properties of planar triangles. While basic Euclidean principles guided even young children's visual extrapolations, only older children and adults reasoned about triangles in ways that were consistent with Euclidean geometry. Moreover, a relation beteen visual extrapolation and reasoning appeared only in older children and adults. Reasoning consistent with Euclidean geometry may thus emerge when children abandon incorrect, axiomatic-based reasoning strategies and come to reason using mental simulations of visual extrapolations.

How ageing and blindness affect egocentric and allocentric spatial memory

Egocentric (subject-to-object) and allocentric (object-to-object) spatial reference frames are fundamental for representing the position of objects or places around us. The literature on spatial cognition in blind people has shown that lack of vision may limit the ability to represent spatial information in an allocentric rather than egocentric way. Furthermore, much research with sighted individuals has reported that ageing has a negative impact on spatial memory. However, as far as we know, no study has assessed how ageing may affect the processing of spatial reference frames in individuals with different degrees of visual experience. To fill this gap, here we report data from a cross-sectional study in which a large sample of young and elderly participants (160 participants in total) who were congenitally blind (long-term visual deprivation), adventitiously blind (late onset of blindness), blindfolded sighted (short-term visual deprivation) and sighted (full visual availability) performed a spatial memory task that required egocentric/allocentric distance judgements with regard to memorised stimuli. The results showed that egocentric judgements were better than allocentric ones and above all that the ability to process allocentric information was influenced by both age and visual status. Specifically, the allocentric judgements of congenitally blind elderly participants were worse than those of all other groups. These findings suggest that ageing and congenital blindness can contribute to the worsening of the ability to represent spatial relationships between external, non-body-centred anchor points.

Core knowledge of geometry can develop independently of visual experience

Geometrical intuitions spontaneously drive visuo-spatial reasoning in human adults, children and animals. Is their emergence intrinsically linked to visual experience, or does it reflect a core property of cognition shared across sensory modalities? To address this question, we tested the sensitivity of blind-from-birth adults to geometrical-invariants using a haptic deviant-figure detection task. Blind participants spontaneously used many geometric concepts such as parallelism, right angles and geometrical shapes to detect intruders in haptic displays, but experienced difficulties with symmetry and complex spatial transformations. Across items, their performance was highly correlated with that of sighted adults performing the same task in touch (blindfolded) and in vision, as well as with the performances of uneducated preschoolers and Amazonian adults. Our results support the existence of an amodal core-system of geometry that arises independently of visual experience. However, performance at selecting geometric intruders was generally higher in the visual compared to the haptic modality, suggesting that sensory-specific spatial experience may play a role in refining the properties of this core-system of geometry.

A Critical Review of Spatial Abilities in Down and Williams Syndromes: Not All Space Is Created Equal

Down syndrome (DS, Trisomy 21) and Williams syndrome (WS) are two neurodevelopmental disorders of genetic origin that are accompanied by mild to moderate intellectual disability but exhibit distinct cognitive profiles. In this review we discuss our recent work characterizing the real-world spatial learning and memory abilities of adult individuals with DS and WS. We used several different paradigms in which participants locomote freely and have access to coherent input from all sensory modalities to investigate their fundamental egocentric (body-centered or viewpoint-dependent) and allocentric (world-centered or viewpoint-independent) spatial abilities. We found unequivocal evidence that most individuals with DS exhibit low-resolution egocentric and allocentric spatial learning and memory abilities similar to typically developing (TD) children in the same mental age range. In contrast, most individuals with DS exhibit impaired high-resolution allocentric spatial learning and facilitated response learning as compared to TD children. In comparison, whereas most individuals with WS also exhibit facilitated response learning, their low-resolution allocentric spatial learning and memory abilities are severely impaired as compared to both TD children and individuals with DS. Together with work from other laboratories using real-world or virtual reality paradigms, these findings indicate that in order to navigate in their environment most individuals with DS may use either egocentric route learning that does not integrate individual landmarks, or a low-resolution allocentric spatial representation that encodes the relationships between different locations (i.e., cognitive mapping). In contrast, since most individuals with WS are unable to build or use a low-resolution allocentric or configural representation of the environment they may use visually and verbally encoded landmarks as beacons to learn routes. Finally, we discuss the main neural structures implicated in these different spatial processes and explain how the relative preservation or impairment of specific brain functions may engender the unique cognitive profiles observed in individuals with these neurodevelopmental disorders.

Spatial Representation by Persons who are Blind: A Study of the Effects of Learning and Development

Children and adolescents who are congenitally and adventitiously blind were divided into four age groups and introduced to two different unfamiliar environments (small and large) in a maximum of four trials. Spatial representation was assessed through the subjects’ construction of models and estimates of distance. It was found that age is the most important factor, while learning seems to play a subordinate role in the development of spatial representation of blind people.

Wayfinding Information for Congenitally Blind Individuals

The paper reports on a wayfinding study aimed at identifying the information needs of the congenitally totally blind population. A route-finding experiment in a complex architectural setting was undertaken with a group of 15 congenitally totally blind and a matched control group of 15 sighted subjects. The experiment showed that, compared to the sighted control group, the blind persons planned the journey in more detail, requiring for this purpose additional environmental information. During the journey, they formulated significantly more decisions and used significantly more units of information than the sighted control. Furthermore, the nature of the information used and its source were also different for the two groups. A cognitive mapping exercise, on the other hand, showed the blind to perform virtually as well as the sighted person.

Can Visually Impaired Children Use Tactile Maps to Estimate Directions?

This article reports on three experiments in which totally blind children and children with residual vision were asked to estimate directions between landmarks in a large-scale layout of objects. The children experienced the layout either directly, by walking around it, or indirectly by examining a tactile map. The authors found that the use of tactile maps considerably facilitated the performance of the totally blind children. The theoretical and practical implications of these findings are discussed.

Children five-to-nine years old can use path integration to build a cognitive map without vision

Although spatial navigation competence improves greatly from birth to adulthood, different spatial memory capacities emerge at different ages. Here, we characterized the capacity of 5-9-year-old children to use path integration to build egocentric and allocentric spatial representations to navigate in their environment, and compared their performance with that of young adults. First, blindfolded participants were tested on their ability to return to a starting point after being led on straight and two-legged paths. This egocentric homing task comprising angular and linear displacements allowed us to evaluate path integration capacities in absence of external landmarks. Second, we evaluated whether participants could use path integration, in absence of visual information, to create an allocentric spatial representation to navigate along novel paths between objects, and thus demonstrate the ability to build a cognitive map of their environment. Ninety percent of the 5-9-year-old children could use path integration to create an egocentric representation of their journey to return to a starting point, but they were overall less precise than adults. Sixty-four percent of 5-9-year-old children were capable of using path integration to build a cognitive map enabling them to take shortcuts, and task performance was not dependent on age. Imprecisions in novel paths made by the children who built a cognitive map could be explained by poorer integration of the experienced turns during the learning phase, as well as greater individual variability. In sum, these findings demonstrate that 5-9-year-old children can use path integration to build a cognitive map in absence of visual information.

Path integration in large-scale space and with novel geometries: Comparing vector addition and encoding-error models

Path integration is thought to rely on vestibular and proprioceptive cues yet most studies in humans involve primarily visual input, providing limited insight into their respective contributions. We developed a paradigm involving walking in an omnidirectional treadmill in which participants were guided on two sides of a triangle and then found their back way to origin. In Experiment 1, we tested a range of different triangle types while keeping the distance of the unguided side constant to determine the influence of spatial geometry. Participants overshot the angle they needed to turn and undershot the distance they needed to walk, with no consistent effect of triangle type. In Experiment 2, we manipulated distance while keeping angle constant to determine how path integration operated over both shorter and longer distances. Participants underestimated the distance they needed to walk to the origin, with error increasing as a function of the walked distance. To attempt to account for our findings, we developed configural-based computational models involving vector addition, the second of which included terms for the influence of past trials on the current one. We compared against a previously developed configural model of human path integration, the Encoding-Error model. We found that the vector addition models captured the tendency of participants to under-encode guided sides of the triangles and an influence of past trials on current trials. Together, our findings expand our understanding of body-based contributions to human path integration, further suggesting the value of vector addition models in understanding these important components of human navigation.

How do we remember where we have been? One important mechanism for doing so is called path integration, which refers to the computation of one’s position in space with only self-motion cues. By tracking the direction and distance we have walked, we can create a mental arrow from the current location to the origin, termed the homing vector. Previous studies have shown that the homing vector is subject to systematic distortions depending on previously experienced paths, yet what influences these patterns of errors, particularly in humans, remains uncertain. In this study, we compare two models of path integration based on participants walking two sides of a triangle without vision and then completing the third side based on their estimate of the homing vector. We found no effect of triangle shape on systematic errors, while the systematic errors scaled with path length logarithmically, similar to Weber-Fechner law. While we show that both models captured participants’ behavior, a model based on vector addition best captured the patterns of error in the homing vector. Our study therefore has important implications for how humans track their location, suggesting that vector-based models provide a reasonable and simple explanation for how we do so.

Constructing Cognitive Maps from Partial Information: A Demonstration Study with Congenitally Blind Subjects

Congenitally blind subjects (mean age = 17:2) explored haptically a subset of spatial relations among four objects on a table top. They were then asked to walk all the paths connecting the objects in a large-scale environment. Subjects were able to deduce the overall arrangement of locations from any point in the large-scale environment with a fair degree of accuracy. It is argued that tactual maps could be used to introduce visually impaired individuals to the general rather than specific relationships among objects in a large-scale environment.

Spatial Mapping of Familiar Locations in Blind Children

This article reports on a 15-month study of the spatial mapping skills of totally blind, visually impaired, and normally sighted children. The children were asked to point to familiar locations in four areas (conditions) in and around their homes. The blind children never mastered all the conditions; the visually impaired children mastered them, but one of them did so over a year after the sighted children did so; and the sighted children easily mastered all the conditions. The results suggest that blindness interferes with the development of spatial knowledge in which Euclidean directions between locations are known.

Cognitive Mapping in Blind People: Acquisition of Spatial Relationships in a Large-Scale Environment

Examines the spatial ability of sighted, blindfolded sighted, and congenitally blind subjects. They walked through an unfamiliar, large-scale space in which target locations could not be seen simultaneously and were then taken to each target location and asked the position of the other locations. Results indicate that past visual experience helps individuals to acquire spatial information from large-scale environments.

Mental Processes Mediating Independent Travel: Implications for Orientation and Mobility

Despite advances in the professional areas of orientation and mobility, processes of spatial learning and orientation are not well understood, and the benefits of existing teaching techniques vary widely from client to client. Wayfinding is mediated by mental processes through which travelers learn the spatial layout of a locale, update their own positions relative to their surroundings, and apply general spatial concepts to particular travel situations. In this article we describe these three components, describe what is well known about each and what we need to know to improve professional practice, and provide a detailed description of three experiments which are focussed on the use of one component (spatial updating) by early-blinded, late-blinded, and sighted adults.

Enhanced gaze-following behavior in Deaf infants of Deaf parents

Gaze following plays a role in parent-infant communication and is a key mechanism by which infants acquire information about the world from social input. Gaze following in Deaf infants has been understudied. Twelve Deaf infants of Deaf parents (DoD) who had native exposure to American Sign Language (ASL) were gender-matched and age-matched (±7 days) to 60 spoken-language hearing control infants. Results showed that the DoD infants had significantly higher gaze-following scores than the hearing infants. We hypothesize that in the absence of auditory input, and with support from ASL-fluent Deaf parents, infants become attuned to visual-communicative signals from other people, which engenders increased gaze following. These findings underscore the need to revise the 'deficit model' of deafness. Deaf infants immersed in natural sign language from birth are better at understanding the signals and identifying the referential meaning of adults' gaze behavior compared to hearing infants not exposed to sign language. Broader implications for theories of social-cognitive development are discussed. A video abstract of this article can be viewed at https://youtu.be/QXCDK_CUmAI.

Bayesian validation of grammar productions for the language of thought

Probabilistic proposals of Language of Thoughts (LoTs) can explain learning across different domains as statistical inference over a compositionally structured hypothesis space. While frameworks may differ on how a LoT may be implemented computationally, they all share the property that they are built from a set of atomic symbols and rules by which these symbols can be combined. In this work we propose an extra validation step for the set of atomic productions defined by the experimenter. It starts by expanding the defined LoT grammar for the cognitive domain with a broader set of arbitrary productions and then uses Bayesian inference to prune the productions from the experimental data. The result allows the researcher to validate that the resulting grammar still matches the intuitive grammar chosen for the domain. We then test this method in the language of geometry, a specific LoT model for geometrical sequence learning. Finally, despite the fact of the geometrical LoT not being a universal (i.e. Turing-complete) language, we show an empirical relation between a sequence’s probability and its complexity consistent with the theoretical relationship for universal languages described by Levin’s Coding Theorem.

On the role of visual experience in mathematical development: Evidence from blind mathematicians

Advanced mathematical reasoning, regardless of domain or difficulty, activates a reproducible set of bilateral brain areas including intraparietal, inferior temporal and dorsal prefrontal cortex. The respective roles of genetics, experience and education in the development of this math-responsive network, however, remain unresolved. Here, we investigate the role of visual experience by studying the exceptional case of three professional mathematicians who were blind from birth (n = 1) or became blind during childhood (n = 2). Subjects were scanned with fMRI while they judged the truth value of spoken mathematical and nonmathematical statements. Blind mathematicians activated the classical network of math-related areas during mathematical reflection, similar to that found in a group of sighted professional mathematicians. Thus, brain networks for advanced mathematical reasoning can develop in the absence of visual experience. Additional activations were found in occipital cortex, even in individuals who became blind during childhood, suggesting that either mental imagery or a more radical repurposing of visual cortex may occur in blind mathematicians.

The language of geometry: Fast comprehension of geometrical primitives and rules in human adults and preschoolers

During language processing, humans form complex embedded representations from sequential inputs. Here, we ask whether a "geometrical language" with recursive embedding also underlies the human ability to encode sequences of spatial locations. We introduce a novel paradigm in which subjects are exposed to a sequence of spatial locations on an octagon, and are asked to predict future locations. The sequences vary in complexity according to a well-defined language comprising elementary primitives and recursive rules. A detailed analysis of error patterns indicates that primitives of symmetry and rotation are spontaneously detected and used by adults, preschoolers, and adult members of an indigene group in the Amazon, the Munduruku, who have a restricted numerical and geometrical lexicon and limited access to schooling. Furthermore, subjects readily combine these geometrical primitives into hierarchically organized expressions. By evaluating a large set of such combinations, we obtained a first view of the language needed to account for the representation of visuospatial sequences in humans, and conclude that they encode visuospatial sequences by minimizing the complexity of the structured expressions that capture them.

Models of Sensory Deprivation: The Nature/Nurture Dichotomy and Spatial Representation in the Blind

It is argued that models of sensory deprivation often depend on a nativist versus empiricist dichotomy which has little basis in empirical fact. Fallacies about the nature of abilities and learning and about the interaction between sense modalities which follow from the dichotomy are examined in relation to explanations of spatial development in the blind. It is suggested that interactions between cognitive and perceptual factors need to be taken into account in order to explain the effects of sensory deprivation more adequately.

Blind and Sighted Children's Spatial Knowledge of Their Home Environments

The development of spatial knowledge of the home environment was longitudinally studied in three groups of school-age children who varied in their visual ability: totally blind, visually impaired, and normally sighted. The children were asked to judge which of three locations in their homes was the closest to a designated position: (1) judging by the routes necessary to get to the locations; and (2) judging by straight-line distances to the locations. Locations were either on the same floor as the designed position, on a different floor, or in the yard. Totally blind children were delayed in mastery of the tasks compared to the other children, particularly in judging straight-line distances between familiar locations. Their mistakes suggest that their spatial understanding of their home environments is based on their knowledge of routes between places rather than on their knowledge of the overall layout of the familiar space.

Spatial navigation by congenitally blind individuals

Spatial navigation in the absence of vision has been investigated from a variety of perspectives and disciplines. These different approaches have progressed our understanding of spatial knowledge acquisition by blind individuals, including their abilities, strategies, and corresponding mental representations. In this review, we propose a framework for investigating differences in spatial knowledge acquisition by blind and sighted people consisting of three longitudinal models (i.e., convergent, cumulative, and persistent). Recent advances in neuroscience and technological devices have provided novel insights into the different neural mechanisms underlying spatial navigation by blind and sighted people and the potential for functional reorganization. Despite these advances, there is still a lack of consensus regarding the extent to which locomotion and wayfinding depend on amodal spatial representations. This challenge largely stems from methodological limitations such as heterogeneity in the blind population and terminological ambiguity related to the concept of cognitive maps. Coupled with an over‐reliance on potential technological solutions, the field has diffused into theoretical and applied branches that do not always communicate. Here, we review research on navigation by congenitally blind individuals with an emphasis on behavioral and neuroscientific evidence, as well as the potential of technological assistance. Throughout the article, we emphasize the need to disentangle strategy choice and performance when discussing the navigation abilities of the blind population. WIREs Cogn Sci 2016, 7:37–58. doi: 10.1002/wcs.1375

For further resources related to this article, please visit the WIREs website.

Virtual environments for the transfer of navigation skills in the blind: a comparison of directed instruction vs. video game based learning approaches

For profoundly blind individuals, navigating in an unfamiliar building can represent a significant challenge. We investigated the use of an audio-based, virtual environment called Audio-based Environment Simulator (AbES) that can be explored for the purposes of learning the layout of an unfamiliar, complex indoor environment. Furthermore, we compared two modes of interaction with AbES. In one group, blind participants implicitly learned the layout of a target environment while playing an exploratory, goal-directed video game. By comparison, a second group was explicitly taught the same layout following a standard route and instructions provided by a sighted facilitator. As a control, a third group interacted with AbES while playing an exploratory, goal-directed video game however, the explored environment did not correspond to the target layout. Following interaction with AbES, a series of route navigation tasks were carried out in the virtual and physical building represented in the training environment to assess the transfer of acquired spatial information. We found that participants from both modes of interaction were able to transfer the spatial knowledge gained as indexed by their successful route navigation performance. This transfer was not apparent in the control participants. Most notably, the game-based learning strategy was also associated with enhanced performance when participants were required to find alternate routes and short cuts within the target building suggesting that a ludic-based training approach may provide for a more flexible mental representation of the environment. Furthermore, outcome comparisons between early and late blind individuals suggested that greater prior visual experience did not have a significant effect on overall navigation performance following training. Finally, performance did not appear to be associated with other factors of interest such as age, gender, and verbal memory recall. We conclude that the highly interactive and immersive exploration of the virtual environment greatly engages a blind user to develop skills akin to positive near transfer of learning. Learning through a game play strategy appears to confer certain behavioral advantages with respect to how spatial information is acquired and ultimately manipulated for navigation.

Reading angles in maps

Preschool children can navigate by simple geometric maps of the environment, but the nature of the geometric relations they use in map reading remains unclear. Here, children were tested specifically on their sensitivity to angle. Forty-eight children (age 47:15-53:30 months) were presented with fragments of geometric maps, in which angle sections appeared without any relevant length or distance information. Children were able to read these map fragments and compare two-dimensional to three-dimensional angles. However, this ability appeared both variable and fragile among the youngest children of the sample. These findings suggest that 4-year-old children begin to form an abstract concept of angle that applies both to two-dimensional and three-dimensional displays and that serves to interpret novel spatial symbols.

Core foundations of abstract geometry

Human adults from diverse cultures share intuitions about the points, lines, and figures of Euclidean geometry. Do children develop these intuitions by drawing on phylogenetically ancient and developmentally precocious geometric representations that guide their navigation and their analysis of object shape? In what way might these early-arising representations support later-developing Euclidean intuitions? To approach these questions, we investigated the relations among young children's use of geometry in tasks assessing: navigation; visual form analysis; and the interpretation of symbolic, purely geometric maps. Children's navigation depended on the distance and directional relations of the surface layout and predicted their use of a symbolic map with targets designated by surface distances. In contrast, children's analysis of visual forms depended on the size-invariant shape relations of objects and predicted their use of the same map but with targets designated by corner angles. Even though the two map tasks used identical instructions and map displays, children's performance on these tasks showed no evidence of integrated representations of distance and angle. Instead, young children flexibly recruited geometric representations of either navigable layouts or objects to interpret the same spatial symbols. These findings reveal a link between the early-arising geometric representations that humans share with diverse animals and the flexible geometric intuitions that give rise to human knowledge at its highest reaches. Although young children do not appear to integrate core geometric representations, children's use of the abstract geometry in spatial symbols such as maps may provide the earliest clues to the later construction of Euclidean geometry.

Elevation easier than plan for sighted and early-blind adults in a perspective-taking task

Plans show shapes of objects from above, and represent both their left-right order and their order in the z-dimension (the distance of the objects). Elevations show only the vertical shapes of objects arranged from left to right. Plans, having more spatial information, may be more difficult for participants to construct. Results from a study with sighted, sighted-blindfolded, and early-blind participants on Piaget's perspective-taking three-mountain task support this hypothesis. The plan task was judged more difficult than the elevation task even when participants performed with the same level of accuracy on both tasks. In visual and tactile tasks, amount of spatial-order information may determine difficulty, rather than plan versus elevation per se.

Two-year-old children interpret abstract, purely geometric maps

In two experiments, 2.5-year-old children spontaneously used geometric information from 2D maps to locate objects in a 3D surface layout, without instruction or feedback. Children related maps to their corresponding layouts even though the maps differed from the layouts in size, mobility, orientation, dimensionality, and perspective, and even when they did not depict the target objects directly. Early in development, therefore, children are capable of noting the referential function of strikingly abstract visual representations.

Insights into the origins of knowledge from the cognitive neuroscience of blindness

Children learn about the world through senses such as touch, smell, vision, and audition, but they conceive of the world in terms of objects, events, agents, and their mental states. A fundamental question in cognitive science is how nature and nurture contribute to the development of such conceptual categories. What innate mechanisms do children bring to the learning problem? How does experience contribute to development? In this article we discuss insights into these longstanding questions from cognitive neuroscience studies of blindness. Despite drastically different sensory experiences, behavioural and neuroscientific work suggests that blind children acquire typical concepts of objects, actions, and mental states. Blind people think and talk about these categories in ways that are similar to sighted people. Neuroimaging reveals that blind people make such judgements relying on the same neural mechanisms as sighted people. One way to interpret these findings is that neurocognitive development is largely hardwired, and so differences in experience have little consequence. Contrary to this interpretation, neuroimaging studies also show that blindness profoundly reorganizes the visual system. Most strikingly, developmental blindness enables "visual" circuits to participate in high-level cognitive functions, including language processing. Thus, blindness qualitatively changes sensory representations, but leaves conceptual representations largely unchanged. The effect of sensory experience on concepts is modest, despite the brain's potential for neuroplasticity.

Visual experience determines the use of external reference frames in joint action control

Vision plays a crucial role in human interaction by facilitating the coordination of one's own actions with those of others in space and time. While previous findings have demonstrated that vision determines the default use of reference frames, little is known about the role of visual experience in coding action-space during joint action. Here, we tested if and how visual experience influences the use of reference frames in joint action control. Dyads of congenitally-blind, blindfolded-sighted, and seeing individuals took part in an auditory version of the social Simon task, which required each participant to respond to one of two sounds presented to the left or right of both participants. To disentangle the contribution of external—agent-based and response-based—reference frames during joint action, participants performed the task with their respective response (right) hands uncrossed or crossed over one another. Although the location of the auditory stimulus was completely task-irrelevant, participants responded overall faster when the stimulus location spatially corresponded to the required response side than when they were spatially non-corresponding: a phenomenon known as the social Simon effect (SSE). In sighted participants, the SSE occurred irrespective of whether hands were crossed or uncrossed, suggesting the use of external, response-based reference frames. Congenitally-blind participants also showed an SSE, but only with uncrossed hands. We argue that congenitally-blind people use both agent-based and response-based reference frames resulting in conflicting spatial information when hands are crossed and, thus, canceling out the SSE. These results imply that joint action control functions on the basis of external reference frames independent of the presence or (transient/permanent) absence of vision. However, the type of external reference frames used for organizing motor control in joint action seems to be determined by visual experience.

Navigation as a source of geometric knowledge: young children's use of length, angle, distance, and direction in a reorientation task

Geometry is one of the highest achievements of our species, but its foundations are obscure. Consistent with longstanding suggestions that geometrical knowledge is rooted in processes guiding navigation, the present study examines potential sources of geometrical knowledge in the navigation processes by which young children establish their sense of orientation. Past research reveals that children reorient both by the shape of the surface layout and the shapes of distinctive landmarks, but it fails to clarify what shape properties children use. The present study explores 2-year-old children's sensitivity to angle, length, distance and direction by testing disoriented children's search in a variety of fragmented rhombic and rectangular environments. Children reoriented themselves in accord with surface distances and directions, but they failed to use surface lengths or corner angles either for directional reorientation or as local landmarks. Thus, navigating children navigate by some but not all of the abstract properties captured by formal Euclidean geometry. While navigation systems may contribute to children's developing geometric understanding, they likely are not the sole source of abstract geometric intuitions.

The role of visual experience for the neural basis of spatial cognition

Blindness often results in the adaptive neural reorganization of the remaining modalities, producing sharper auditory and haptic behavioral performance. Yet, non-visual modalities might not be able to fully compensate for the lack of visual experience as in the case of congenital blindness. For example, developmental visual experience seems to be necessary for the maturation of multisensory neurons for spatial tasks. Additionally, the ability of vision to convey information in parallel might be taken into account as the main attribute that cannot be fully compensated by the spared modalities. Therefore, the lack of visual experience might impair all spatial tasks that require the integration of inputs from different modalities, such as having to represent a set of objects on the basis of the spatial relationships among the objects, rather than the spatial relationship that each object has with oneself. Here we integrate behavioral and neural evidence to conclude that visual experience is necessary for the neural development of normal spatial cognition.

Flexible intuitions of Euclidean geometry in an Amazonian indigene group

Kant argued that Euclidean geometry is synthesized on the basis of an a priori intuition of space. This proposal inspired much behavioral research probing whether spatial navigation in humans and animals conforms to the predictions of Euclidean geometry. However, Euclidean geometry also includes concepts that transcend the perceptible, such as objects that are infinitely small or infinitely large, or statements of necessity and impossibility. We tested the hypothesis that certain aspects of nonperceptible Euclidian geometry map onto intuitions of space that are present in all humans, even in the absence of formal mathematical education. Our tests probed intuitions of points, lines, and surfaces in participants from an indigene group in the Amazon, the Mundurucu, as well as adults and age-matched children controls from the United States and France and younger US children without education in geometry. The responses of Mundurucu adults and children converged with that of mathematically educated adults and children and revealed an intuitive understanding of essential properties of Euclidean geometry. For instance, on a surface described to them as perfectly planar, the Mundurucu's estimations of the internal angles of triangles added up to ~180 degrees, and when asked explicitly, they stated that there exists one single parallel line to any given line through a given point. These intuitions were also partially in place in the group of younger US participants. We conclude that, during childhood, humans develop geometrical intuitions that spontaneously accord with the principles of Euclidean geometry, even in the absence of training in mathematics.

Beyond core knowledge: Natural geometry

For many centuries, philosophers and scientists have pondered the origins and nature of human intuitions about the properties of points, lines, and figures on the Euclidean plane, with most hypothesizing that a system of Euclidean concepts either is innate or is assembled by general learning processes. Recent research from cognitive and developmental psychology, cognitive anthropology, animal cognition, and cognitive neuroscience suggests a different view. Knowledge of geometry may be founded on at least two distinct, evolutionarily ancient, core cognitive systems for representing the shapes of large-scale, navigable surface layouts and of small-scale, movable forms and objects. Each of these systems applies to some but not all perceptible arrays and captures some but not all of the three fundamental Euclidean relationships of distance (or length), angle, and direction (or sense). Like natural number (Carey, 2009), Euclidean geometry may be constructed through the productive combination of representations from these core systems, through the use of uniquely human symbolic systems.

All sex differences in cognitive ability may be explained by an X-Y homologous gene determining degrees of cerebral asymmetry

Male superiority in mathematical ability (along with female superiority in verbal fluency) may reflect the operation of an X-Y homologous gene (the right-shift-factor) influencing the relative rates of development of the cerebral hemispheres. Alleles at the locus on the Y chromosome will be selected at a later mean age than alleles on the X, and only by females.

Still far too sexy a topic

Geary is highly selective in his use of the literature on gender differences. His assumption of consistent female inferiority in mathematics is not necessarily supported by the facts.

Mating, math achievement, and other multiple relationships

Although Geary's partitioning of mathematical abilities into those that are biologically primary and secondary is an advance over most sociobiological theories of cognitive sex differences, it remains untestable and ignores the spatial nature of women's traditional work. An alternative model based on underlying cognitive processes offers other advantages.

How important is spatial ability to mathematics?

This commentary focuses on one of the many issues raised in Geary's target article: the importance of gender differences in spatial ability to gender differences in mathematics. I argue that the evidence for the central role of spatial ability in mathematical ability, or in gender differences in it, is tenuous at best.

Spatial visualization and sex-related differences in mathematical problem solving

Spatial visualization as a key variable in sex-related differences in mathematical problem solving and spatial aspects of geometry is traced to the 1960s. More recent relevant data are presented. The variability debate is traced to the latter part of the nineteenth century and an explanation for it is suggested. An idea is presented for further research to clarify sex-related brain laterality differences in solving spatial problems.

Sexual selection and sex differences in mathematical abilities

The principles of sexual selection were used as an organizing framework for interpreting cross-national patterns of sex differences in mathematical abilities. Cross-national studies suggest that there are no sex differences in biologically primary mathematical abilities, that is, for those mathematical abilities that are found in all cultures as well as in nonhuman primates, and show moderate heritability estimates. Sex differences in several biologically secondary mathematical domains (i.e., those that emerge primarily in school) are found throughout the industrialized world. In particular, males consistently outperform females in the solving of mathematical word problems and geometry. Sexual selection and any associated proximate mechanisms (e.g., sex hormones) influence these sex differences in mathematical performance indirectly. First, sexual selection resulted in greater elaboration in males than in females of the neurocognitive systems that support navigation in three-dimensional space. Knowledge implicit in these systems reflects an understanding of basic Euclidean geometry, and may thus be one source of the male advantage in geometry. Males also use more readily than females these spatial systems in problem-solving situations, which provides them with an advantage in solving word problems and geometry. In addition, sex differences in social styles and interests, which also appear to be related in part to sexual selection, result in sex differences in engagement iii mathematics-related activities, thus further increasing the male advantage in certain mathematical domains. A model that integrates these biological influences with sociocultural influences on the sex differences in mathematical performance is presented in this article.

Inferential functioning in visually impaired children

The current study explores the inferential abilities of visually impaired children in a task presented in two formats, manipulative and verbal. The results showed that in the group of visually impaired children, just as with children with normal sight, there was a wide range of inference types. It was found that the visually impaired children perform slightly better in the use of inductive and relational inferences in the verbal format, while in the manipulative format children with normal sight perform better. These results suggest that in inferential functioning of young children, and especially visually impaired children, the format of the task influences performance more than the child's visual ability.

Brain and cognitive evolution: forms of modularity and functions of mind

Genetic and neurobiological research is reviewed as related to controversy over the extent to which neocortical organization and associated cognitive functions are genetically constrained or emerge through patterns of developmental experience. An evolutionary framework that accommodates genetic constraint and experiential modification of brain organization and cognitive function is then proposed. The authors argue that 4 forms of modularity and 3 forms of neural and cognitive plasticity define the relation between genetic constraint and the influence of developmental experience. For humans, the result is the ontogenetic emergence of functional modules in the domains of folk psychology, folk biology, and folk physics. The authors present a taxonomy of these modules and review associated research relating to brain and cognitive plasticity in these domains.

Vestibular and vestibulo-proprioceptive perception of motion in the horizontal plane in blindfolded man--III. Route inference

The inference of direction and length of a subsequent route during performance of a triangle completion task was studied in blindfolded human subjects. Subjects were transported and walked with guidance along two sides of left- and right-oriented isosceles triangles. Subjects had to walk without assistance along the inferential bases of triangles back to a starting point. The influence of two variables in the triangular trajectory--the side length (2, 3 and 4 m) and the angle between sides (30-150 degrees--on route inference accuracy was investigated. Changes in the length of the movement trajectory with retained configuration lead to an alteration in the linear but not the angular estimation of the inferred route. Changes in the configuration of equidistant movement trajectories result in an alteration in both the linear and angular estimations of the inferred route. Estimations of direction and length of inferred routes following passive transportation and those following walking along triangular sides showed similar degrees of accuracy. When the inference of a route was regarded as a geometrical sum of subjective angular and linear estimations of displacements, trajectories of backward paths could be predicted. The results obtained show that the vestibular cue can only provide a gross orientation when moving along a complex trajectory in the horizontal plane; the proprioceptive cue does not improve accuracy adequately.