Doing Socrates experiment right: controlled rearing studies of geometrical knowledge in animals

Hierarchical processing of feature, egocentric and relational information for spatial orientation in domestic chicks

Animals can use different types of information for navigation. Domestic chicks (Gallus gallus) prefer to use local features as a beacon over spatial relational information. However, the role of egocentric navigation strategies is less understood. Here, we tested domestic chicks' egocentric and allocentric orientation abilities in a large circular arena. In experiment 1, we investigated whether domestic chicks possess a side bias during viewpoint-dependent egocentric orientation, revealing facilitation for targets on the chicks' left side. Experiment 2 showed that local features are preferred over viewpoint-dependent egocentric information when the two conflict. Lastly, in experiment 3, we found that in a situation where there is a choice between egocentric and allocentric spatial relational information provided by free-standing objects, chicks preferentially rely on egocentric information. We conclude that chicks orient according to a hierarchy of cues, in which the use of the visual appearance of an object is the dominant strategy, followed by viewpoint-dependent egocentric information and finally by spatial relational information.

Dlk1 dosage regulates hippocampal neurogenesis and cognition

Neurogenesis in the adult brain gives rise to functional neurons, which integrate into neuronal circuits and modulate neural plasticity. Sustained neurogenesis throughout life occurs in the subgranular zone (SGZ) of the dentate gyrus in the hippocampus and is hypothesized to be involved in behavioral/cognitive processes such as memory and in diseases. Genomic imprinting is of critical importance to brain development and normal behavior, and exemplifies how epigenetic states regulate genome function and gene dosage. While most genes are expressed from both alleles, imprinted genes are usually expressed from either the maternally or the paternally inherited chromosome. Here, we show that in contrast to its canonical imprinting in nonneurogenic regions, Delta-like homolog 1 (Dlk1) is expressed biallelically in the SGZ, and both parental alleles are required for stem cell behavior and normal adult neurogenesis in the hippocampus. To evaluate the effects of maternally, paternally, and biallelically inherited mutations within the Dlk1 gene in specific behavioral domains, we subjected Dlk1-mutant mice to a battery of tests that dissociate and evaluate the effects of Dlk1 dosage on spatial learning ability and on anxiety traits. Importantly, reduction in Dlk1 levels triggers specific cognitive abnormalities that affect aspects of discriminating differences in environmental stimuli, emphasizing the importance of selective absence of imprinting in this neurogenic niche.

Extra-Visual Systems in the Spatial Reorientation of Cavefish

Disoriented humans and animals are able to reorient themselves using environmental geometry ("metric properties" and "sense") and local features, also relating geometric to non-geometric information. Here we investigated the presence of these reorientation spatial skills in two species of blind cavefish (Astyanax mexicanus and Phreatichthys andruzzii), in order to understand the possible role of extra-visual senses in similar spatial tasks. In a rectangular apparatus, with all homogeneous walls (geometric condition) or in presence of a tactilely different wall (feature condition), cavefish were required to reorient themselves after passive disorientation. We provided the first evidence that blind cavefish, using extra-visual systems, were able i) to use geometric cues, provided by the shape of the tank, in order to recognize two geometric equivalent corners on the diagonal, and ii) to integrate the geometric information with the salient cue (wall with a different surface structure), in order to recover a specific corner. These findings suggest the ecological salience of the environmental geometry for spatial orientation in animals and, despite the different niches of adaptation, a potential shared background for spatial navigation. The geometric spatial encoding seems to constitute a common cognitive tool needed when the environment poses similar requirements to living organisms.

The orientation of homing pigeons (Columba livia f.d.) with and without navigational experience in a two-dimensional environment

Homing pigeons are known for their excellent homing ability, and their brains seem to be functionally adapted to homing. It is known that pigeons with navigational experience show a larger hippocampus and also a more lateralised brain than pigeons without navigational experience. So we hypothesized that experience may have an influence also on orientation ability. We examined two groups of pigeons (11 with navigational experience and 17 without) in a standard operant chamber with a touch screen monitor showing a 2-D schematic of a rectangular environment (as “geometric” information) and one uniquely shaped and colored feature in each corner (as “landmark” information). Pigeons were trained first for pecking on one of these features and then we examined their ability to encode geometric and landmark information in four tests by modifying the rectangular environment. All tests were done under binocular and monocular viewing to test hemispheric dominance. The number of pecks was counted for analysis. Results show that generally both groups orientate on the basis of landmarks and the geometry of environment, but landmark information was preferred. Pigeons with navigational experience did not perform better on the tests but showed a better conjunction of the different kinds of information. Significant differences between monocular and binocular viewing were detected particularly in pigeons without navigational experience on two tests with reduced information. Our data suggest that the conjunction of geometric and landmark information might be integrated after processing separately in each hemisphere and that this process is influenced by experience.

Producing or reproducing reasoning? Socratic dialog is very effective, but only for a few

Successful communication between a teacher and a student is at the core of pedagogy. A well known example of a pedagogical dialog is 'Meno', a socratic lesson of geometry in which a student learns (or 'discovers') how to double the area of a given square 'in essence, a demonstration of Pythagoras' theorem. In previous studies we found that after engaging in the dialog participants can be divided in two kinds: those who can only apply a rule to solve the problem presented in the dialog and those who can go beyond and generalize that knowledge to solve any square problems. Here we study the effectiveness of this socratic dialog in an experimental and a control high-school classrooms, and we explore the boundaries of what is learnt by testing subjects with a set of 9 problems of varying degrees of difficulty. We found that half of the adolescents did not learn anything from the dialog. The other half not only learned to solve the problem, but could abstract something more: the geometric notion that the diagonal can be used to solve diverse area problems. Conceptual knowledge is critical for achievement in geometry, and it is not clear whether geometric concepts emerge spontaneously on the basis of universal experience with space, or reflect intrinsic properties of the human mind. We show that, for half of the learners, an exampled-based Socratic dialog in lecture form can give rise to formal geometric knowledge that can be applied to new, different problems.

Comparative cognition of number and space: the case of geometry and of the mental number line

Evidence is discussed about the use of geometric information for spatial orientation and the association between space and numbers in non-human animals. A variety of vertebrate species can reorient using simple Euclidian geometry of the environmental surface layout, i.e. in accord with metric and sense (right/left) relationships among extended surfaces. There seems to be a primacy of geometric over non-geometric information in spatial reorientation and, possibly, innate encoding of the sense of direction. The hippocampal formation plays a key role in geometry-based reorientation in mammals, birds, amphibians and fish. Although some invertebrate species show similar behaviours, it is unclear whether the underlying mechanisms are the same as in vertebrates. As to the links between space and number representations, a disposition to associate numerical magnitudes onto a left-to-right-oriented mental number line appears to exist independently of socio-cultural factors, and can be observed in animals with very little numerical experience, such as newborn chicks and human infants. Such evidence supports a nativistic foundation of number-space association. Some speculation about the possible underlying mechanisms is provided together with consideration on the difficulties inherent to any comparison among species of different taxonomic groups.This article is part of a discussion meeting issue 'The origins of numerical abilities'.

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.

Origins of Knowledge: Insights from Precocial Species

Behavioral responses are influenced by knowledge acquired during the lifetime of an individual and by predispositions transmitted across generations. Establishing the origin of knowledge and the role of the unlearned component is a challenging task, given that both learned and unlearned knowledge can orient perception, learning, and the encoding of environmental features since the first stages of life. Ethical and practical issues constrain the investigation of unlearned knowledge in altricial species, including human beings. On the contrary, precocial animals can be tested on a wide range of tasks and capabilities immediately after birth and in controlled rearing conditions. Insects and precocial avian species are very convenient models to dissect the knowledge systems that enable young individuals to cope with their environment in the absence of specific previous experience. We present the state of the art of research on the origins of knowledge that comes from different models and disciplines. Insects have been mainly used to investigate unlearned sensory preferences and prepared learning mechanisms. The relative simplicity of the neural system and fast life cycle of insects make them ideal models to investigate the neural circuitry and evolutionary dynamics of unlearned traits. Among avian species, chicks of the domestic fowl have been the focus of many studies, and showed to possess unlearned knowledge in the sensory, physical, spatial, numerical and social domains. Solid evidence shows the existence of unlearned knowledge in different domains in several species, from sensory and social preferences to the left-right representation of the mental number line. We show how non-mammalian models of cognition, and in particular precocial species, can shed light into the adaptive value and evolutionary history of unlearned knowledge.

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.

Newborn chickens generate invariant object representations at the onset of visual object experience

To recognize objects quickly and accurately, mature visual systems build invariant object representations that generalize across a range of novel viewing conditions (e.g., changes in viewpoint). To date, however, the origins of this core cognitive ability have not yet been established. To examine how invariant object recognition develops in a newborn visual system, I raised chickens from birth for 2 weeks within controlled-rearing chambers. These chambers provided complete control over all visual object experiences. In the first week of life, subjects' visual object experience was limited to a single virtual object rotating through a 60° viewpoint range. In the second week of life, I examined whether subjects could recognize that virtual object from novel viewpoints. Newborn chickens were able to generate viewpoint-invariant representations that supported object recognition across large, novel, and complex changes in the object's appearance. Thus, newborn visual systems can begin building invariant object representations at the onset of visual object experience. These abstract representations can be generated from sparse data, in this case from a visual world containing a single virtual object seen from a limited range of viewpoints. This study shows that powerful, robust, and invariant object recognition machinery is an inherent feature of the newborn brain.

Spatial reorientation by geometry in bumblebees

Human and non-human animals are capable of using basic geometric information to reorient in an environment. Geometric information includes metric properties associated with spatial surfaces (e.g., short vs. long wall) and left-right directionality or 'sense' (e.g. a long wall to the left of a short wall). However, it remains unclear whether geometric information is encoded by explicitly computing the layout of surface geometry or by matching images of the environment. View-based spatial encoding is generally thought to hold for insect navigation and, very recently, evidence for navigation by geometry has been reported in ants but only in a condition which does not allow the animals to use features located far from the goal. In this study we tested the spatial reorientation abilities of bumblebees (Bombus terrestris). After spatial disorientation, by passive rotation both clockwise and anticlockwise, bumblebees had to find one of the four exit holes located in the corners of a rectangular enclosure. Bumblebees systematically confused geometrically equivalent exit corners (i.e. corners with the same geometric arrangement of metric properties and sense, for example a short wall to the left of a long wall). However, when one wall of the enclosure was a different colour, bumblebees appeared to combine this featural information (either near or far from the goal) with geometric information to find the correct exit corner. Our results show that bumblebees are able to use both geometric and featural information to reorient themselves, even when features are located far from the goal.

Chicks, like children, spontaneously reorient by three-dimensional environmental geometry, not by image matching

Spatial reorientation by layout geometry occurs in numerous species, but its underlying mechanisms are debated. While some argue that navigating animals' sense of place is based on geometric computations over three-dimensional representations, others claim it depends on panoramic image-matching processes. Because children reorient by subtle three-dimensional perturbations of the terrain and not by salient two-dimensional brightness contours on surfaces or freestanding columns, children's sense of place cannot be explained by image matching. To test image-matching theories in a different species, the present experiment investigates the reorientation performance of domestic chicks (Gallus gallus) in environments similar to those used with children. Chicks, like children, spontaneously reoriented by geometric relationships of subtle three-dimensional terrains, and not by salient two-dimensional brightness contours on surfaces or columns. These findings add to the evidence for homologous navigation systems in humans and other vertebrates, and they cast doubt on image-matching theories of reorientation in these species.

Core knowledge of object, number, and geometry: a comparative and neural approach

Studies on the ontogenetic origins of human knowledge provide evidence for a small set of separable systems of core knowledge dealing with the representation of inanimate and animate objects, number, and geometry. Because core knowledge systems are evolutionarily ancient, they can be investigated from a comparative perspective, making use of various animal models. In this review, I discuss evidence showing precocious abilities in nonhuman species to represent (a) objects that move partly or fully out of view and their basic mechanical properties such as solidity, (b) the cardinal and ordinal/sequential aspects of numerical cognition and rudimentary arithmetic with small numerosities, and (c) the geometrical relationships among extended surfaces in the surrounding layout. Controlled rearing studies suggest that the abilities associated with core knowledge systems of objects, number, and geometry are observed in animals in the absence (or with very reduced) experience, supporting a nativistic foundation of such cognitive mechanisms. Animal models also promise a fresh approach to the issue of the neurobiological and genetic mechanisms underlying the expression of core knowledge systems.

Spatial reorientation by geometry with freestanding objects and extended surfaces: a unifying view

The macroscopic, three-dimensional surface layout geometry of an enclosure apparently provides a different contribution for spatial reorientation than the geometric cues associated with freestanding objects arranged in arrays with similar geometric shape. Here, we showed that a unitary spatial representation can account for the capability of animals to reorient both by extended surfaces and discrete objects in a small-scale spatial task. We trained domestic chicks to locate a food-reward from an opening on isolated cylinders arranged either in a geometrically uninformative (square-shaped) or informative (rectangular-shaped) arrays. The arrays were located centrally within a rectangular-shaped enclosure. Chicks trained to access the reward from a fixed position of openings proved able to reorient according to the geometric cues specified by the shape of the enclosure in all conditions. Chicks trained in a fixed position of opening with geometric cues provided both by the arena and the array proved able to reorient according to each shape separately. However, chicks trained to access the reward from a variable position of openings failed to reorient. The results suggest that the physical constrains associated with the presence of obstacles in a scene, rather than their apparent visual extension, are crucial for spatial reorientation.

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.

Impaired representation of geometric relationships in humans with damage to the hippocampal formation

The pivotal role of the hippocampus for spatial memory is well-established. However, while neurophysiological and imaging studies suggest a specialization of the hippocampus for viewpoint-independent or allocentric memory, results from human lesion studies have been less conclusive. It is currently unclear whether disproportionate impairment in allocentric memory tasks reflects impairment of cognitive functions that are not sufficiently supported by regions outside the medial temporal lobe or whether the deficits observed in some studies are due to experimental factors. Here, we have investigated whether hippocampal contributions to spatial memory depend on the spatial references that are available in a certain behavioral context. Patients with medial temporal lobe lesions affecting systematically the right hippocampal formation performed a series of three oculomotor tasks that required memory of a spatial cue either in retinal coordinates or relative to a single environmental reference across a delay of 5000 ms. Stimulus displays varied the availability of spatial references and contained no complex visuo-spatial associations. Patients showed a selective impairment in a condition that critically depended on memory of the geometric relationship between spatial cue and environmental reference. We infer that regions of the medial temporal lobe, most likely the hippocampal formation, contribute to behavior in conditions that exceed the potential of viewpoint-dependent or egocentric representations. Apparently, this already applies to short-term memory of simple geometric relationships and does not necessarily depend on task difficulty or integration of landmarks into more complex representations. Deficient memory of basic geometric relationships may represent a core deficit that contributes to impaired performance in allocentric spatial memory tasks.

Spontaneous discrimination of possible and impossible objects by newly hatched chicks

Four-month-old infants can integrate local cues provided by two-dimensional pictures and interpret global inconsistencies in structural information to discriminate between possible and impossible objects. This leaves unanswered the issue of the relative contribution of maturation of biologically predisposed mechanisms and of experience with real objects, to the development of this capability. Here we show that, after exposure to objects in which junctions providing cues to global structure were occluded, day-old chicks selectively approach the two-dimensional image that depicted the possible rather than the impossible version of a three-dimensional object, after restoration of the junctions. Even more impressively, completely naive newly hatched chicks showed spontaneous preferences towards approaching two-dimensional depictions of structurally possible rather than impossible objects. These findings suggest that the vertebrate brain can be biologically predisposed towards approaching a two-dimensional image representing a view of a structurally possible three-dimensional object.

Intuitive physical reasoning about occluded objects by inexperienced chicks

Questions concerning the role of nature and nurture in higher cognition appear to be intractable if one restricts one's attention to development in humans. However, in other domains, such as sensory development, much information has been gained from controlled rearing studies with animals. Here, we used a similar experimental strategy to investigate intuitive reasoning about occluded objects. Newborn domestic chicks (Gallus gallus) were reared singly with a small object that became their social partner. They were then accustomed to rejoin such an imprinting object when it was made to move and disappear behind either one of two identical opaque screens. After disappearance of the imprinting object, chicks were faced with two screens of different slants, or of different height or different width, which may or may not have been compatible with the presence of the imprinting object hidden beneath/behind them. Chicks consistently chose the screen of slant/height/width compatible with the presence of the object beneath/behind it. Preventing chicks from touching and pecking at the imprinting object before testing did not affect the results, suggesting that intuitive reasoning about physical objects is largely independent of specific experience of interaction with objects and of objects' occluding events.

View-based strategy for reorientation by geometry

Human and non-human animals can use geometric information (metric information and left-right discrimination sense) to reorient themselves in an environment. The hypothesis that in so doing they rely on allocentric (map-like) representations has received wide consensus. However, theoretical models suggest that egocentric representations may represent efficient strategies for visuo-spatial navigation. Here, we provide, for the first time, evidence that a view-based strategy is effectively used by animals to reorient themselves in an array of landmarks. Domestic chicks were trained to locate a food-reward in a rectangular array of either four indistinguishable or distinctive pipes. In the key experimental series, the pipes had four openings, only one of which allowed the chicks to access the reward. The direction of the open access relative to the array was either maintained stable or it was changed throughout training. The relative position of the pipes in the array was maintained stable in both training conditions. Chicks reoriented according to configural geometry as long as the open access pointed in the same direction during training but failed when the positions of the openings was changed throughout training. When the correct pipe was characterized by a distinctive featural cue, chicks learnt to locate the reward irrespective of the stability of the direction to openings, indicating that place-navigation was dissociated from non-spatial learning. These findings provide evidence that view-based strategies to reorient by geometry could be used by animals.

Origins of spatial, temporal and numerical cognition: Insights from comparative psychology

Contemporary comparative cognition has a large repertoire of animal models and methods, with concurrent theoretical advances that are providing initial answers to crucial questions about human cognition. What cognitive traits are uniquely human? What are the species-typical inherited predispositions of the human mind? What is the human mind capable of without certain types of specific experiences with the surrounding environment? Here, we review recent findings from the domains of space, time and number cognition. These findings are produced using different comparative methodologies relying on different animal species, namely birds and non-human great apes. The study of these species not only reveals the range of cognitive abilities across vertebrates, but also increases our understanding of human cognition in crucial ways.

Innate sensitivity for self-propelled causal agency in newly hatched chicks

The idea that sensitivity to self-produced motion could lie at the foundations of the clear-cut divide that the brain operates between the two basic domains of inanimate and animate objects dates back to Aristotle. Sensitivity to self-propelled objects is apparent in human infants from around the fifth month of age, which leaves undetermined whether it is acquired by experience with animate objects or whether it is innately predisposed in the brain. Here, we report that newly hatched, visually naïve domestic chicks presented with objects exhibiting motion either self-produced or caused by physical contact prefer to associate with self-propelled objects. This finding supports the idea of an evolutionarily ancient, predisposed neural mechanism in the vertebrate brain for the detection of animacy.

Encoding geometric and non-geometric information: a study with evolved agents

Vertebrate species use geometric information and non-geometric or featural cues to orient. Under some circumstances, when both geometric and non-geometric information are available, the geometric information overwhelms non-geometric cues (geometric primacy). In other cases, we observe the inverse tendency or the successful integration of both cues. In past years, modular explanations have been proposed for the geometric primacy: geometric and non-geometric information are processed separately, with the geometry module playing a dominant role. The modularity issue is related to the recent debate on the encoding of geometric information: is it innate or does it depend on environmental experience? In order to get insight into the mechanisms that cause the wide variety of behaviors observed in nature, we used Artificial Life experiments. We demonstrated that agents trained mainly with a single class of information oriented efficiently when they were exposed to one class of information (geometric or non-geometric). When they were tested in environments that contained both classes of information, they displayed a primacy for the information that they had experienced more during their training phase. Encoding and processing geometric and non-geometric information was run in a single cognitive neuro-representation. These findings represent a theoretical proof that the exposure frequency to different spatial information during a learning/adaptive history could produce agents with no modular neuro-cognitive systems that are able to process different types of spatial information and display various orientation behaviors (geometric primacy, non-geometric primacy, no primacy at all).