Core systems of geometry in animal minds

Crows recognize geometric regularity

The perception of geometric regularity in shapes, a form of elementary Euclidean geometry, is a fundamental mathematical intuition in humans. We demonstrate this geometric understanding in an animal, the carrion crow. Crows were trained to detect a visually distinct intruder shape among six concurrent arbitrary shapes. The crows were able to immediately apply this intruder concept to quadrilaterals, identifying the one that exhibited differing geometric properties compared to the others in the set. The crows exhibited a geometric regularity effect, showing better performance with shapes featuring right angles, parallel lines, or symmetry over more irregular shapes. This performance advantage did not require learning. Our findings suggest that geometric intuitions are not specific to humans but are deeply rooted in biological evolution.

Seeing the Forest but Naming the Trees: An Object-Over-Place Bias in Learning Noun Labels

Objects and places are foundational spatial domains represented in human symbolic expressions, like drawings, which show a prioritization of depicting small-scale object-shape information over the large-scale navigable place information in which objects are situated. Is there a similar object-over-place bias in language? Across six experiments, adults and 3- to 4-year-old children were asked either to extend a novel noun in a labeling phrase, to extend a novel noun in a prepositional phrase, or to simply match pictures. To dissociate specific object and place information from more general figure and ground information, participants either saw scenes with both place information (a room) and object information (a block in the room), or scenes with two kinds of object information that matched the figure-ground relations of the room and block by presenting an open container with a smaller block inside. While adults showed a specific object-over-place bias in both extending novel noun labels and matching, they did not show this bias in extending novel nouns following prepositions. Young children showed this bias in extending novel noun labels only. Spatial domains may thus confer specific and foundational biases for word learning that may change through development in a way that is similar to that of other word-learning biases about objects, like the shape bias. These results expand the symbolic scope of prior studies on object biases in drawing to object biases in language, and they expand the spatial domains of prior studies characterizing the language of objects and places.

Dramatic changes to well-known places go unnoticed

How well do we know our city? It turns out, much more poorly than we might imagine. We used declarative memory and eye-tracking techniques to examine people's ability to detect modifications to real-world landmarks and scenes in Toronto locales with which they have had extensive experience. Participants were poor at identifying which scenes contained altered landmarks, whether the modification was to the landmarks' relative size, internal features, or relation to surrounding context. To determine whether an indirect measure would prove more sensitive, we tracked eye movements during viewing. Changes in overall visual exploration, but not to specific regions of change, were related to participants' explicit endorsement of scenes as modified. These results support the contention that very familiar landmarks are represented at a global or gist level, but not local or fine-grained, level. These findings offer a unified view of memory for gist across verbal and spatial domains, and across recent and remote memory, with implications for hippocampal-neocortical interactions.

From cognitive maps to spatial schemas

A schema refers to a structured body of prior knowledge that captures common patterns across related experiences. Schemas have been studied separately in the realms of episodic memory and spatial navigation across different species and have been grounded in theories of memory consolidation, but there has been little attempt to integrate our understanding across domains, particularly in humans. We propose that experiences during navigation with many similarly structured environments give rise to the formation of spatial schemas (for example, the expected layout of modern cities) that share properties with but are distinct from cognitive maps (for example, the memory of a modern city) and event schemas (such as expected events in a modern city) at both cognitive and neural levels. We describe earlier theoretical frameworks and empirical findings relevant to spatial schemas, along with more targeted investigations of spatial schemas in human and non-human animals. Consideration of architecture and urban analytics, including the influence of scale and regionalization, on different properties of spatial schemas may provide a powerful approach to advance our understanding of spatial schemas.

Navigational roots of spatial and temporal memory structure

Our minds are constantly in transit, from the present to the past to the future, across places we have and have not directly experienced. Nevertheless, memories of our mental time travel are not organized continuously and are adaptively chunked into contexts and episodes. In this paper, I will review evidence that suggests that spatial boundary representations play a critical role in providing structure to both our spatial and temporal memories. I will illustrate the intimate connection between hippocampal spatial mapping and temporal sequencing of episodic memory to propose that high-level cognitive processes like mental time travel and conceptual mapping are rooted in basic navigational mechanisms that we humans and nonhuman animals share. Our neuroscientific understanding of hippocampal function across species may provide new insight into the origins of even the most uniquely human cognitive abilities.

Visual object detection biases escape trajectories following acoustic startle in larval zebrafish

In this study, we investigated whether the larval zebrafish is sensitive to the presence of obstacles in its environment. Zebrafish execute fast escape swims when in danger of predation. We posited that collisions with solid objects during escape would be maladaptive to the fish, and therefore, the direction of escape swims should be informed by the locations of barriers. To test this idea, we developed a closed-loop imaging rig outfitted with barriers of various qualities. We show that when larval zebrafish escape in response to a non-directional vibrational stimulus, they use visual scene information to avoid collisions with obstacles. Our study demonstrates that barrier avoidance rate corresponds to the absolute distance of obstacles, as distant barriers outside of collision range elicit less bias than nearby collidable barriers that occupy the same amount of visual field. The computation of barrier avoidance is covert: the fact that fish will avoid barriers during escape cannot be predicted by its routine swimming behavior in the barrier arena. Finally, two-photon laser ablation experiments suggest that excitatory bias is provided to the Mauthner cell ipsilateral to approached barriers, either via direct excitation or a multi-step modulation process. We ultimately propose that zebrafish detect collidable objects via an integrative visual computation that is more complex than retinal occupancy alone, laying a groundwork for understanding how cognitive physical models observed in humans are implemented in an archetypal vertebrate brain. VIDEO ABSTRACT.

Evaluating landscape knowledge and lithic resource selection at the French Middle Paleolithic site of the Bau de l'Aubesier

We report on the application of a novel approach to exploring the degree of landscape knowledge, wayfinding abilities, and the nature of decision-making processes reflected in the utilization of stone resources in the French Middle Paleolithic. Specifically, we use data from the site of the Bau de l'Aubesier to explore the reasons why a majority of the 350 raw material sources cataloged in the surrounding region appear not to have been utilized, including several located near the site and yielding high-quality lithic materials. To this end, we focus on the spatial relationships between sources as an explanatory variable, operationalized in terms of minimum travel times. Using geographic information system software and a generalized linear model of resource selection derived from the Bau assemblages, we compute source utilization probabilities from the perspective of hominins located off-site. We do so under three optimization scenarios, factoring in the intrinsic characteristics (e.g., quality) and time required to reach each source on the way to the Bau. More generally, we find that in slightly more than 50% of cases, seemingly viable sources may have been ignored simply because the minimum cost path leading back to the Bau passes through or requires only minimal deviations to reach, higher quality options. More generally, we found that throughout the entire region, a cost/benefit analysis of competing sources favors those from source areas known to have been utilized. Virtually all the available information on lithic procurement at the Bau is consistent with a model of landscape utilization premised on detailed knowledge of a very large area, an ability to accurately estimate travel times between locations, and a pragmatic strategy of stone resource exploitation based on minimizing costs (travel and search times) and maximizing utility.

Parts and Wholes in Scene Processing

During natural vision, our brains are constantly exposed to complex, but regularly structured environments. Real-world scenes are defined by typical part-whole relationships, where the meaning of the whole scene emerges from configurations of localized information present in individual parts of the scene. Such typical part-whole relationships suggest that information from individual scene parts is not processed independently, but that there are mutual influences between the parts and the whole during scene analysis. Here, we review recent research that used a straightforward, but effective approach to study such mutual influences: By dissecting scenes into multiple arbitrary pieces, these studies provide new insights into how the processing of whole scenes is shaped by their constituent parts and, conversely, how the processing of individual parts is determined by their role within the whole scene. We highlight three facets of this research: First, we discuss studies demonstrating that the spatial configuration of multiple scene parts has a profound impact on the neural processing of the whole scene. Second, we review work showing that cortical responses to individual scene parts are shaped by the context in which these parts typically appear within the environment. Third, we discuss studies demonstrating that missing scene parts are interpolated from the surrounding scene context. Bridging these findings, we argue that efficient scene processing relies on an active use of the scene's part-whole structure, where the visual brain matches scene inputs with internal models of what the world should look like.

Geometry intuitions without vision? A study in blind children and adults

Geometry intuitions seem to be rooted in a non-verbal system that humans possess since early age. However, the mechanisms underlying the comprehension of basic geometric concepts remain elusive. Some authors have suggested that the starting point of geometry development could be found in the visual perception of specific features in our environment, thus conferring to vision a foundational role in the acquisition of geometric skills. To examine this assumption, a test probing intuitive understanding of basic geometric concepts was presented to congenitally blind children and adults. Participants had to detect the intruder among four different shapes, from which three instantiated a specific geometrical concept and one (the intruder) violated it. Although they performed above the chance level, the blind presented poorer performance than the sighted participants who did the task in the visual modality (i.e., with the eyes open), but performed equally well than the sighted who did the task in the tactile modality (i.e., with a blindfold). We therefore provide evidence that geometric abilities are impacted by the lack of vision.

Coherent natural scene structure facilitates the extraction of task-relevant object information in visual cortex

Looking for objects within complex natural environments is a task everybody performs multiple times each day. In this study, we explore how the brain uses the typical composition of real-world environments to efficiently solve this task. We recorded fMRI activity while participants performed two different categorization tasks on natural scenes. In the object task, they indicated whether the scene contained a person or a car, while in the scene task, they indicated whether the scene depicted an urban or a rural environment. Critically, each scene was presented in an "intact" way, preserving its coherent structure, or in a "jumbled" way, with information swapped across quadrants. In both tasks, participants' categorization was more accurate and faster for intact scenes. These behavioral benefits were accompanied by stronger responses to intact than to jumbled scenes across high-level visual cortex. To track the amount of object information in visual cortex, we correlated multi-voxel response patterns during the two categorization tasks with response patterns evoked by people and cars in isolation. We found that object information in object- and body-selective cortex was enhanced when the object was embedded in an intact, rather than a jumbled scene. However, this enhancement was only found in the object task: When participants instead categorized the scenes, object information did not differ between intact and jumbled scenes. Together, these results indicate that coherent scene structure facilitates the extraction of object information in a task-dependent way, suggesting that interactions between the object and scene processing pathways adaptively support behavioral goals.

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.

The Environmental Geometry in Spatial Learning by Zebrafish (Danio rerio)

During navigation, disoriented animals learn to use the spatial geometry of rectangular environments to gain rewards. The length of macroscopic surfaces (metric: short/long) and their spatial arrangement (sense: left/right) are powerful cues that animals prove to encode for reorientation. The aim of this study was to investigate if zebrafish (Danio rerio) could take advantage of such geometric properties in a rewarded exit task, by applying a reference memory procedure. The experiment was performed in a rectangular arena having four white walls, where fish were required to choose the two geometrically equivalent exit corners lying on the reinforced diagonal. Results showed that zebrafish encoded the geometry of the arena during reorientation, solving the spatial task within the first 5 days of training. With the aim to avoid the possible influence of extravisual cues on the zebrafish success, we performed a geometric test in extinction of response after the learning day. At test, fish persisted in choosing the two correct corners, thus confirming that the navigation strategy used at training was based on geometric cues. This study adds evidence about the role of geometric frameworks in fish species, and it further validates an effective spatial learning paradigm for zebrafish.

Places in the Brain: Bridging Layout and Object Geometry in Scene-Selective Cortex

Diverse animal species primarily rely on sense (left-right) and egocentric distance (proximal-distal) when navigating the environment. Recent neuroimaging studies with human adults show that this information is represented in 2 scene-selective cortical regions-the occipital place area (OPA) and retrosplenial complex (RSC)-but not in a third scene-selective region-the parahippocampal place area (PPA). What geometric properties, then, does the PPA represent, and what is its role in scene processing? Here we hypothesize that the PPA represents relative length and angle, the geometric properties classically associated with object recognition, but only in the context of large extended surfaces that compose the layout of a scene. Using functional magnetic resonance imaging adaptation, we found that the PPA is indeed sensitive to relative length and angle changes in pictures of scenes, but not pictures of objects that reliably elicited responses to the same geometric changes in object-selective cortical regions. Moreover, we found that the OPA is also sensitive to such changes, while the RSC is tolerant to such changes. Thus, the geometric information typically associated with object recognition is also used during some aspects of scene processing. These findings provide evidence that scene-selective cortex differentially represents the geometric properties guiding navigation versus scene categorization.

Impaired behavioral and neural representation of scenes in Williams syndrome

Boundaries are crucial to our representation of the geometric shape of scenes, which can be used to reorient in space. Behavioral research has shown that children and adults share exquisite sensitivity to a defining feature of a boundary: its vertical extent. Imaging studies have shown that this boundary property is represented in the parahippocampal place area (PPA) among typically developed (TD) adults. Here, we show that sensitivity to the vertical extent of scene boundaries is impaired at both the behavioral and neural level in people with Williams syndrome (WS), a genetic deficit that results in severely impaired spatial functions. Behavioral reorientation was tested in three boundary conditions: a flat Mat, a 5 cm high Curb, and full Walls. Adults with WS could reorient in a rectangular space defined by Wall boundaries, but not Curb or Mat boundaries. In contrast, TD age-matched controls could reorient by all three boundary types and TD 4-year-olds could reorient by either Wall or Curb boundaries. Using fMRI, we find that the WS behavioral deficit is echoed in their neural representation of boundaries. While TD age-matched controls showed distinct neural responses to scenes depicting Mat, Curb, and Wall boundaries in the PPA, people with WS showed only a distinction between the Wall and Mat or Curb, but no distinction between the Mat and Curb. Taken together, these results reveal a close coupling between the representation of boundaries as they are used in behavioral reorientation and neural encoding, suggesting that damage to this key element of spatial representation may have a genetic foundation.

Discrimination of Small Forms in a Deviant-Detection Paradigm by 10-month-old Infants

Using eye tracking, we investigated if 10-month-old infants could discriminate between members of a set of small forms based on geometric properties in a deviant-detection paradigm, as suggested by the idea of a core cognitive system for Euclidian geometry. We also investigated the precision of infants' ability to discriminate as well as how the discrimination process unfolds over time. Our results show that infants can discriminate between small forms based on geometrical properties, but only when the difference is sufficiently large. Furthermore, our results also show that it takes infants, on average, <3.5 s to detect a deviant form. Our findings extend previous research in three ways: by showing that infants can make similar discriminative judgments as children and adults with respect to geometric properties; by providing a first crude estimate on the limit of the discriminative abilities in infants, and finally; by providing a first demonstration of how the discrimination process unfolds over time.

Rapid Invariant Encoding of Scene Layout in Human OPA

Successful visual navigation requires a sense of the geometry of the local environment. How do our brains extract this information from retinal images? Here we visually presented scenes with all possible combinations of five scene-bounding elements (left, right, and back walls; ceiling; floor) to human subjects during functional magnetic resonance imaging (fMRI) and magnetoencephalography (MEG). The fMRI response patterns in the scene-responsive occipital place area (OPA) reflected scene layout with invariance to changes in surface texture. This result contrasted sharply with the primary visual cortex (V1), which reflected low-level image features of the stimuli, and the parahippocampal place area (PPA), which showed better texture than layout decoding. MEG indicated that the texture-invariant scene layout representation is computed from visual input within ∼100 ms, suggesting a rapid computational mechanism. Taken together, these results suggest that the cortical representation underlying our instant sense of the environmental geometry is located in the OPA.

Navigating cognition: Spatial codes for human thinking

The hippocampal formation has long been suggested to underlie both memory formation and spatial navigation. We discuss how neural mechanisms identified in spatial navigation research operate across information domains to support a wide spectrum of cognitive functions. In our framework, place and grid cell population codes provide a representational format to map variable dimensions of cognitive spaces. This highly dynamic mapping system enables rapid reorganization of codes through remapping between orthogonal representations across behavioral contexts, yielding a multitude of stable cognitive spaces at different resolutions and hierarchical levels. Action sequences result in trajectories through cognitive space, which can be simulated via sequential coding in the hippocampus. In this way, the spatial representational format of the hippocampal formation has the capacity to support flexible cognition and behavior.

Violations of Core Knowledge Shape Early Learning

Research on cognitive development has revealed that even the youngest minds detect and respond to events that adults find surprising. These surprise responses suggest that infants have a basic set of "core" expectations about the world that are shared with adults and other species. However, little work has asked what purpose these surprise responses serve. Here we discuss recent evidence that violations of core knowledge offer special opportunities for learning. Infants and young children make predictions about the world on the basis of their core knowledge of objects, quantities, and social entities. We argue that when these predictions fail to match the observed data, infants and children experience an enhanced drive to seek and retain new information. This impact of surprise on learning is not equipotent. Instead, it is directed to entities that are relevant to the surprise itself; this drive propels children-even infants-to form and test new hypotheses about surprising aspects of the world. We briefly consider similarities and differences between these recent findings with infants and children, on the one hand, and findings on prediction errors in humans and non-human animals, on the other. These comparisons raise open questions that require continued inquiry, but suggest that considering phenomena across species, ages, kinds of surprise, and types of learning will ultimately help to clarify how surprise shapes thought.

Thinking outside of the box II: Disrupting the cognitive map

A number of influential spatial learning theories posit that organisms encode a viewpoint independent (i.e. allocentric) representation of the global boundary shape of their environment in order to support spatial reorientation and place learning. In contrast to the trial and error learning mechanisms that support domain-general processes, a representation of the global-shape of the environment is thought to be encoded automatically as part of a cognitive map, and without interference from other spatial cues. To date, however, this core theoretical assumption has not been appropriately examined. This is because previous attempts to address this question have failed to employ tasks that fully dissociate reorientation based on an allocentric representation of global-shape from egocentric reorientation strategies. Here, we address this issue in two experiments. Participants were trained to navigate to a hidden goal on one side of a virtual arena (e.g. the inside) before being required to find the same point on the alternative side (e.g. the outside). At test, performing the correct search behaviour requires an allocentric representation of the global boundary-shape. Using established associative learning procedures of overshadowing and blocking, we find that search behaviour at test is disrupted when participants were able to form landmark-goal associations during training. These results demonstrate that encoding of an allocentric representation of boundary information is susceptible to interference from landmark cues, and is not acquired through special means. Instead, the results suggest that allocentric representations of environmental boundaries are acquired through the same kind of error-correction mechanisms that support domain-general non-spatial learning.

Geometry of Pictorial Relief

Pictorial relief is a quality of visual awareness that happens when one looks into (as opposed to at) a picture. It has no physical counterpart of a geometrical nature. It takes account of cues, mentally identified in the tonal gradients of the physical picture-pigments distributed over a planar substrate. Among generally recognized qualities of relief are color, pattern, texture, shape, and depth. This review focuses on geometrical properties, the spatial variation of depth. To be aware of an extended quality like relief implies a "depth" dimension, a nonphysical spatial entity that may smoothly vary in a surface-like manner. The conceptual understanding is in terms of formal geometry. The review centers on pertinent facts and formal models. The facts are necessarily so-called brute facts (i.e., they cannot be explained scientifically). This review is a foray into the speculative and experimental phenomenology of the visual field.

Language, gesture, and judgment: Children's paths to abstract geometry

As infants, children are sensitive to geometry when recognizing objects or navigating through rooms; however, explicit knowledge of geometry develops slowly and may be unstable even in adults. How can geometric concepts be both so accessible and so elusive? To examine how implicit and explicit geometric concepts develop, the current study assessed, in 132 children (3-8 years old) while they played a simple geometric judgment task, three distinctive channels: children's choices during the game as well as the language and gestures they used to justify and accompany their choices. Results showed that, for certain geometric properties, children chose the correct card even if they could not express with words (or gestures) why they had made this choice. Furthermore, other geometric concepts were expressed and supported by gestures prior to their articulation in either choices or speech. These findings reveal that gestures and behavioral choices may reflect implicit knowledge and serve as a foundation for the development of geometric reasoning. Altogether, our results suggest that language alone might not be enough for expressing and organizing geometric concepts and that children pursue multiple paths to overcome its limitations, a finding with potential implications for primary education in mathematics.

Intelligent machines and human minds

The search for a deep, multileveled understanding of human intelligence is perhaps the grand challenge for 21st-century science, with broad implications for technology. The project of building machines that think like humans is central to meeting this challenge and critical to efforts to craft new technologies for human benefit.

Dual roles of the hippocampus and intraparietal sulcus in network integration and segregation support scene recognition

Effectively recognizing surroundings is a critical ability in human navigation. Previous neuroimaging studies have depicted distributed brain regions underpinning spatial navigation, but little is known about how these regions are formed into the navigation network (NN) supporting scene recognition. In this study, we addressed this issue by using a voxel-based global functional connectivity method to characterize the integration (i.e., within-network connectivity, WNC) of the NN and its segregation (i.e., between-network connectivity, BNC) from non-NN networks. We found that the majority of the voxels in the NN showed a stronger WNC than BNC, indicating the encapsulation of the NN. Importantly, individuals with stronger WNC and weaker BNC in the left hippocampus (Hipp) and intraparietal sulcus (IPS) performed better in scene recognition, suggesting that the left Hipp and IPS were involved in scene recognition by both integrating regions in the NN and separating the NN from non-NN networks. Further analyses showed that the integration of these two regions in the NN serves different functions, that is, while the WNC of the left Hipp was only related to scene recognition, the WNC of the left IPS was also related to the general executive control function of attention. In short, our study demonstrated the dual roles of the Hipp and IPS in integration and segregation of the NN to support scene recognition, suggesting that scene recognition involves not only regions specialized in spatial navigation, but also those with general functions.

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.

Thinking outside of the box: Transfer of shape-based reorientation across the boundary of an arena

The way in which human and non-human animals represent the shape of their environments remains a contentious issue. According to local theories of shape learning, organisms encode the local geometric features of the environment that signal a goal location. In contrast, global theories of shape learning suggest that organisms encode the overall shape of the environment. There is, however, a surprising lack of evidence to support this latter claim, despite the fact that common behaviours seem to require encoding of the global-shape of an environment. We tested one such behaviour in 5 experiments, in which human participants were trained to navigate to a hidden goal on one side of a virtual arena (e.g. the inside) before being required to find the same point on the alternative side (e.g. the outside). Participants navigated to the appropriate goal location, both when inside and outside the virtual arena, but only when the shape of the arena remained the same between training and test (Experiments 1a and 1b). When the arena shape was transformed between these stages, participants were lost (Experiments 2a and 2b). When training and testing was conducted on the outside of two different-shaped arenas that shared local geometric cues participants once again explored the appropriate goal location (Experiment 3). These results provide core evidence that humans encode a global representation of the overall shape of the environments in, or around, which they navigate.

Rats Fed a Diet Rich in Fats and Sugars Are Impaired in the Use of Spatial Geometry

A diet rich in fats and sugars is associated with cognitive deficits in people, and rodent models have shown that such a diet produces deficits on tasks assessing spatial learning and memory. Spatial navigation is guided by two distinct types of information: geometrical, such as distance and direction, and featural, such as luminance and pattern. To clarify the nature of diet-induced spatial impairments, we provided rats with standard chow supplemented with sugar water and a range of energy-rich foods eaten by people, and then we assessed their place- and object-recognition memory. Rats exposed to this diet performed comparably with control rats fed only chow on object recognition but worse on place recognition. This impairment on the place-recognition task was present after only a few days on the diet and persisted across tests. Critically, this spatial impairment was specific to the processing of distance and direction.

Core geometry in perspective

Research on animals, infants, children, and adults provides evidence that distinct cognitive systems underlie navigation and object recognition. Here we examine whether and how these systems interact when children interpret 2D edge-based perspectival line drawings of scenes and objects. Such drawings serve as symbols early in development, and they preserve scene and object geometry from canonical points of view. Young children show limits when using geometry both in non-symbolic tasks and in symbolic map tasks that present 3D contexts from unusual, unfamiliar points of view. When presented with the familiar viewpoints in perspectival line drawings, however, do children engage more integrated geometric representations? In three experiments, children successfully interpreted line drawings with respect to their depicted scene or object. Nevertheless, children recruited distinct processes when navigating based on the information in these drawings, and these processes depended on the context in which the drawings were presented. These results suggest that children are flexible but limited in using geometric information to form integrated representations of scenes and objects, even when interpreting spatial symbols that are highly familiar and faithful renditions of the visual world.

Core knowledge and the emergence of symbols: The case of maps

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.

Learned predictiveness training modulates biases towards using boundary or landmark cues during navigation

A number of navigational theories state that learning about landmark information should not interfere with learning about shape information provided by the boundary walls of an environment. A common test of such theories has been to assess whether landmark information will overshadow, or restrict, learning about shape information. Whilst a number of studies have shown that landmarks are not able to overshadow learning about shape information, some have shown that landmarks can, in fact, overshadow learning about shape information. Given the continued importance of theories that grant the shape information that is provided by the boundary of an environment a special status during learning, the experiments presented here were designed to assess whether the relative salience of shape and landmark information could account for the discrepant results of overshadowing studies. In Experiment 1, participants were first trained that either the landmarks within an arena (landmark-relevant), or the shape information provided by the boundary walls of an arena (shape-relevant), were relevant to finding a hidden goal. In a subsequent stage, when novel landmark and shape information were made relevant to finding the hidden goal, landmarks dominated behaviour for those given landmark-relevant training, whereas shape information dominated behaviour for those given shape-relevant training. Experiment 2, which was conducted without prior relevance training, revealed that the landmark cues, unconditionally, dominated behaviour in our task. The results of the present experiments, and the conflicting results from previous overshadowing experiments, are explained in terms of associative models that incorporate an attention variant.

Asymmetrical interference effects between two-dimensional geometric shapes and their corresponding shape words

Nativists have postulated fundamental geometric knowledge that predates linguistic and symbolic thought. Central to these claims is the proposal for an isolated cognitive system dedicated to processing geometric information. Testing such hypotheses presents challenges due to difficulties in eliminating the combination of geometric and non-geometric information through language. We present evidence using a modified matching interference paradigm that an incongruent shape word interferes with identifying a two-dimensional geometric shape, but an incongruent two-dimensional geometric shape does not interfere with identifying a shape word. This asymmetry in interference effects between two-dimensional geometric shapes and their corresponding shape words suggests that shape words activate spatial representations of shapes but shapes do not activate linguistic representations of shape words. These results appear consistent with hypotheses concerning a cognitive system dedicated to processing geometric information isolated from linguistic processing and provide evidence consistent with hypotheses concerning knowledge of geometric properties of space that predates linguistic and symbolic thought.

Shape shifting: Local landmarks interfere with navigation by, and recognition of, global shape

An influential theory of spatial navigation states that the boundary shape of an environment is preferentially encoded over and above other spatial cues, such that it is impervious to interference from alternative sources of information. We explored this claim with 3 intradimensional-extradimensional shift experiments, designed to examine the interaction of landmark and geometric features of the environment in a virtual navigation task. In Experiments 1 and 2, participants were first required to find a hidden goal using information provided by the shape of the arena or landmarks integrated into the arena boundary (Experiment 1) or within the arena itself (Experiment 2). Participants were then transferred to a different-shaped arena that contained novel landmarks and were again required to find a hidden goal. In both experiments, participants who were navigating on the basis of cues that were from the same dimension that was previously relevant (intradimensional shift) learned to find the goal significantly faster than participants who were navigating on the basis of cues that were from a dimension that was previously irrelevant (extradimensional shift). This suggests that shape information does not hold special status when learning about an environment. Experiment 3 replicated Experiment 2 and also assessed participants' recognition of the global shape of the navigated arenas. Recognition was attenuated when landmarks were relevant to navigation throughout the experiment. The results of these experiments are discussed in terms of associative and non-associative theories of spatial learning.

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.

Navigation by environmental geometry: the use of zebrafish as a model

Sensitivity to environmental shape in spatial navigation has been found, at both behavioural and neural levels, in virtually every species tested, starting early in development. Moreover, evidence that genetic deletions can cause selective deficits in such navigation behaviours suggests a genetic basis to navigation by environmental geometry. Nevertheless, the geometric computations underlying navigation have not been specified in any species. The present study teases apart the geometric components within the traditionally used rectangular enclosure and finds that zebrafish selectively represent distance and directional relationships between extended boundary surfaces. Similar behavioural results in geometric navigation tasks with human children provide prima facie evidence for similar underlying cognitive computations and open new doors for probing the genetic foundations that give rise to these computations.

Modularity, comparative cognition and human uniqueness

Darwin's claim 'that the difference in mind between man and the higher animals … is certainly one of degree and not of kind' is at the core of the comparative study of cognition. Recent research provides unprecedented support for Darwin's claim as well as new reasons to question it, stimulating new theories of human cognitive uniqueness. This article compares and evaluates approaches to such theories. Some prominent theories propose sweeping domain-general characterizations of the difference in cognitive capabilities and/or mechanisms between adult humans and other animals. Dual-process theories for some cognitive domains propose that adult human cognition shares simple basic processes with that of other animals while additionally including slower-developing and more explicit uniquely human processes. These theories are consistent with a modular account of cognition and the 'core knowledge' account of children's cognitive development. A complementary proposal is that human infants have unique social and/or cognitive adaptations for uniquely human learning. A view of human cognitive architecture as a mosaic of unique and species-general modular and domain-general processes together with a focus on uniquely human developmental mechanisms is consistent with modern evolutionary-developmental biology and suggests new questions for comparative research.