Practice-induced SNARC: evidence from a null-SNARC sample

The mental representation of numbers inherently involves a spatial organization, often positioning smaller numbers to the left and larger numbers to the right. The SNARC effect, characterized by faster responses to small numbers using the left hand and vice versa for large numbers, is typically attributed to this left-to-right oriented mental number line (MNL). However, the direction of the SNARC effect seems to rely on reading direction, with most research exploring these mechanisms conducted within left-to-right reading cultures where the SNARC effect is prevalent. This study takes advantage of a sample from a left-to-right reading culture that does not exhibit the SNARC effect, allowing us to isolate and elucidate the stand-alone effects of recent experiences on SNARC. Therefore, the current study aims to investigate how MNL-compatible and MNL-incompatible practices induce an effect within a sample lacking the SNARC effect. To accomplish this, we reinvited the individuals from the sample which had previously shown no SNARC, and retested those who agreed to take part in the current study after an MNL-compatible or MNL-incompatible practice manipulation. The findings revealed an absence of the SNARC effect with MNL-compatible practices. Conversely, MNL-incompatible practices yielded a reverse SNARC effect. These results prompt a discussion on SNARC mechanisms within the framework of practice effects.

What makes different number-space mappings interact?

Models of numerical cognition consider a visuo-spatial representation to be at the core of numerical processing, the 'mental number line'. Two main interference effects between number and space have been described: the SNARC effect reflects a small number/left side and large number/right side association (number-location mapping); the size-congruity effect (SCE) reflects a small number/small size and large number/large size association (number-size mapping). Critically, a thorough investigation on the representational source for these two number-space mappings is lacking, leaving open the question of whether the same representation underlies both phenomena. Here, we build on a recent study (Viarouge and de Hevia in Front Hum Neurosci 15:750964, 2021) in order to address this question in three experiments, by systematically manipulating the presence of the two conditions that might elicit an interaction between SNARC and SCE: (i) an implicit task whereby numerical and spatial information are task-irrelevant, (ii) a design in which the number-space congruency relative to both mappings vary at the same level -either both within or between blocks. Experiment 1 replicated the interaction between the two mappings when both factors were present. Experiments 2 and 3 dissociated the two factors by varying the two mappings at the same level but using an explicit comparison task (Experiment 2), or by using an implicit task but with mappings varying at different levels (Experiment 3). We found that both factors, either in combination or used in isolation, drive the interaction between the two number-space mappings. These findings are discussed in terms of the weight given to each mapping, suggesting that a single representation encompassing both number-space mappings is therefore activated whenever both mappings are given equal weight through task requirements.

Understanding the limits to animal cognition

The thriving field of comparative cognition examines the behaviour of diverse animals in cognitive terms. Comparative cognition research has primarily focused on the abilities of animals - what tasks they can do - rather than on the limits of their cognition - tasks that exceed an animal's cognitive abilities. We propose that understanding and identifying cognitive limits is as important as demonstrating the capacities of animal minds. Here, we identify challenges that have deterred the study of cognitive limits related to epistemic, practical and publication problems. The epistemic problem is concerned with how we can confidently infer a cognitive limit from null or negative results. The practical problem is how can we be certain our research has identified a cognitive limit rather than failures in tasks due to methodological or experimental design issues. The publication problem outlines the publication bias toward positive and exciting results over negative or null results in animal cognition. We propose solutions to these three challenges and examples of how to conduct research to confidently identify and confirm cognitive limits in animals. We believe a refocus on the cognitive limits of animals is the next step in the field of comparative cognition. Knowing the limits to the intelligence of different animals will aid us in appreciating the diversity of animal intelligence, and will resolve outstanding questions of how cognition evolves.

Recruitment of the premotor cortex during arithmetic operations by the monkey

Arithmetic operations are complex mental processes rooted in the abstract concept of numerosity. Despite the significance, the neural architecture responsible for these operations has remained largely uncharted. In this study, we explored the presence of specific neuronal activity in the dorsal premotor cortex of the monkey dedicated to numerical addition and subtraction. Our findings reveal that many of these neural activities undergo a transformation, shifting their coding from arithmetic to motor representations. These motor representations include information about which hand to use and the number of steps involved in the action. We consistently observed that cells related to the right-hand encoded addition, while those linked to the left-hand encoded subtraction, suggesting that arithmetic operations and motor commands are intertwining with each other. Furthermore, we used a multivariate decoding technique to predict the monkey's behaviour based on the activity of these arithmetic-related cells. The classifier trained to discern arithmetic operations, including addition and subtraction, not only predicted the arithmetic decisions but also the subsequent motor actions of the right and left-hand. These findings imply a cognitive extension of the motor cortex's function, where inherent neural systems are repurposed to facilitate arithmetic operations.

A number sense as an emergent property of the manipulating brain

The ability to understand and manipulate numbers and quantities emerges during childhood, but the mechanism through which humans acquire and develop this ability is still poorly understood. We explore this question through a model, assuming that the learner is able to pick up and place small objects from, and to, locations of its choosing, and will spontaneously engage in such undirected manipulation. We further assume that the learner's visual system will monitor the changing arrangements of objects in the scene and will learn to predict the effects of each action by comparing perception with a supervisory signal from the motor system. We model perception using standard deep networks for feature extraction and classification. Our main finding is that, from learning the task of action prediction, an unexpected image representation emerges exhibiting regularities that foreshadow the perception and representation of numbers and quantity. These include distinct categories for zero and the first few natural numbers, a strict ordering of the numbers, and a one-dimensional signal that correlates with numerical quantity. As a result, our model acquires the ability to estimate numerosity, i.e. the number of objects in the scene, as well as subitization, i.e. the ability to recognize at a glance the exact number of objects in small scenes. Remarkably, subitization and numerosity estimation extrapolate to scenes containing many objects, far beyond the three objects used during training. We conclude that important aspects of a facility with numbers and quantities may be learned with supervision from a simple pre-training task. Our observations suggest that cross-modal learning is a powerful learning mechanism that may be harnessed in artificial intelligence.

Modal and amodal cognition: an overarching principle in various domains of psychology

Accounting for how the human mind represents the internal and external world is a crucial feature of many theories of human cognition. Central to this question is the distinction between modal as opposed to amodal representational formats. It has often been assumed that one but not both of these two types of representations underlie processing in specific domains of cognition (e.g., perception, mental imagery, and language). However, in this paper, we suggest that both formats play a major role in most cognitive domains. We believe that a comprehensive theory of cognition requires a solid understanding of these representational formats and their functional roles within and across different domains of cognition, the developmental trajectory of these representational formats, and their role in dysfunctional behavior. Here we sketch such an overarching perspective that brings together research from diverse subdisciplines of psychology on modal and amodal representational formats so as to unravel their functional principles and their interactions.

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.

Why birds are smart

Many cognitive neuroscientists believe that both a large brain and an isocortex are crucial for complex cognition. Yet corvids and parrots possess non-cortical brains of just 1-25 g, and these birds exhibit cognitive abilities comparable with those of great apes such as chimpanzees, which have brains of about 400 g. This opinion explores how this cognitive equivalence is possible. We propose four features that may be required for complex cognition: a large number of associative pallial neurons, a prefrontal cortex (PFC)-like area, a dense dopaminergic innervation of association areas, and dynamic neurophysiological fundaments for working memory. These four neural features have convergently evolved and may therefore represent 'hard to replace' mechanisms enabling complex cognition.

Neurobiology of numerical learning

Numerical abilities are complex cognitive skills essential for dealing with requirements of the modern world. Although the brain structures and functions underlying numerical cognition in different species have long been appreciated, genetic and molecular techniques have more recently expanded the knowledge about the mechanisms underlying numerical learning. In this review, we discuss the status of the research related to the neurobiological bases of numerical abilities. We consider how genetic factors have been associated with mathematical capacities and how these link to the current knowledge of brain regions underlying these capacities in human and non-human animals. We further discuss the extent to which significant variations in the levels of specific neurotransmitters may be used as potential markers of individual performance and learning difficulties and take into consideration the therapeutic potential of brain stimulation methods to modulate learning and improve interventional outcomes. The implications of this research for formulating a more comprehensive view of the neural basis of mathematical learning are discussed.

Eye movements reveal that young school children shift attention when solving additions and subtractions

Adults shift their attention to the right or to the left along a spatial continuum when solving additions and subtractions, respectively. Studies suggest that these shifts not only support the exact computation of the results but also anticipatively narrow down the range of plausible answers when processing the operands. However, little is known on when and how these attentional shifts arise in childhood during the acquisition of arithmetic. Here, an eye-tracker with high spatio-temporal resolution was used to measure spontaneous eye movements, used as a proxy for attentional shifts, while children of 2nd (8 y-o; N = 50) and 4th (10 y-o; N = 48) Grade solved simple additions (e.g., 4+3) and subtractions (e.g., 3-2). Gaze patterns revealed horizontal and vertical attentional shifts in both groups. Critically, horizontal eye movements were observed in 4th Graders as soon as the first operand and the operator were presented and thus before the beginning of the exact computation. In 2nd Graders, attentional shifts were only observed after the presentation of the second operand just before the response was made. This demonstrates that spatial attention is recruited when children solve arithmetic problems, even in the early stages of learning mathematics. The time course of these attentional shifts suggests that with practice in arithmetic children start to use spatial attention to anticipatively guide the search for the answer and facilitate the implementation of solving procedures. RESEARCH HIGHLIGHTS: Additions and subtractions are associated to right and left attentional shifts in adults, but it is unknown when these mechanisms arise in childhood. Children of 8-10 years old solved single-digit additions and subtractions while looking at a blank screen. Eye movements showed that children of 8 years old already show spatial biases possibly to represent the response when knowing both operands. Children of 10 years old shift attention before knowing the second operand to anticipatively guide the search for plausible answers.

Magnitude shifts spatial attention from left to right in rhesus monkeys as in the human mental number line

Humans typically represent numbers and quantities along a left-to-right continuum. Early perspectives attributed number-space association to culture; however, recent evidence in newborns and animals challenges this hypothesis. We investigate whether the length of an array of dots influences spatial bias in rhesus macaques. We designed a touch-screen task that required monkeys to remember the location of a target. At test, monkeys maintained high performance with arrays of 2, 4, 6, or 10 dots, regardless of changes in the array's location, spacing, and length. Monkeys remembered better left targets with 2-dot arrays and right targets with 6- or 10-dot arrays. Replacing the 10-dot array with a long bar, yielded more accurate performance with rightward locations, consistent with an underlying left-to-right oriented magnitude code. Our study supports the hypothesis of a spatially oriented mental magnitude line common to humans and animals, countering the idea that this code arises from uniquely human cultural learning.

Quantity misperception by hymenopteran insects observing the solitaire illusion

Visual illusions are errors in signal perception and inform us about the visual and cognitive processes of different animals. Invertebrates are relatively less studied for their illusionary perception, despite the insight that comparative data provides on the evolution of common perceptual mechanisms. The Solitaire Illusion is a numerosity illusion where a viewer typically misperceives the relative quantities of two items of different colors consisting of identical quantity, with more centrally clustered items appearing more numerous. We trained European honeybees (Apis mellifera) and European wasps (Vespula vulgaris) to select stimuli containing a higher quantity of yellow dots in arrays of blue and yellow dots and then presented them with the Solitaire Illusion. Insects learnt to discriminate between dot quantities and showed evidence of perceiving the Solitaire Illusion. Further work should determine whether the illusion is caused by numerical cues only or by both quantity and non-numerical spatial cues.

Life motion signals bias the perception of apparent motion direction

Walking direction conveyed by biological motion (BM) cues, which humans are highly sensitive to since birth, can elicit involuntary shifts of attention to enhance the detection of static targets. Here, we demonstrated that such intrinsic sensitivity to walking direction could also modulate the direction perception of simultaneously presented dynamic stimuli. We showed that the perceived direction of apparent motion was biased towards the walking direction even though observers had been informed in advance that the walking direction of BM did not predict the apparent motion direction. In particular, rightward BM cues had an advantage over leftward BM cues in altering the perception of motion direction. Intriguingly, this perceptual bias disappeared when BM cues were shown inverted, or when the critical biological characteristics were removed from the cues. Critically, both the perceptual direction bias and the rightward advantage persisted even when only local BM cues were presented without any global configuration. Furthermore, the rightward advantage was found to be specific to social cues (i.e., BM), as it vanished when non-social cues (i.e., arrows) were utilized. Taken together, these findings support the existence of a specific processing mechanism for life motion signals and shed new light on their influences in a dynamic environment.

Intuitive mapping between nonsymbolic quantity and observed action across development

Adults' concurrent processing of numerical and action information yields bidirectional interference effects consistent with a cognitive link between these two systems of representation. This link is in place early in life: infants create expectations of congruency across numerical and action-related stimuli (i.e., a small [large] hand aperture associated with a smaller [larger] numerosity). Although these studies point to a developmental continuity of this mapping, little is known about the later development and thus how experience shapes such relationships. We explored how number-action intuitions develop across early and later childhood using the same methodology as in adults. We asked 3-, 6-, and 8-year-old children, as well as adults, to relate the magnitude of an observed action (a static hand shape, open vs. closed, in Experiment 1; a dynamic hand movement, opening vs. closing, in Experiment 2) to either a small or large nonsymbolic quantity (numerosity in Experiment 1 and numerosity and/or object size in Experiment 2). From 6 years of age, children started performing in a systematic congruent way in some conditions, but only 8-year-olds (added in Experiment 2) and adults performed reliably above chance in this task. We provide initial evidence that early intuitions guiding infants' mapping between magnitude across nonsymbolic number and observed action are used in an explicit way only from late childhood, with a mapping between action and size possibly being the most intuitive. An initial coarse mapping between number and action is likely modulated with extensive experience with grasping and related actions directed to both arrays and individual objects.

Effect of egocentric and allocentric reference frames on spatial-numerical associations

From an embodied view of cognition, sensorimotor mechanisms are strongly involved in abstract processing, such as Arabic number meanings. For example, spatial cognition can influence number processing. These spatial-numerical associations (SNAs) have been deeply explored since the seminal SNAs of response code (SNARC) effect (i.e., faster left/right sided responses to small/large magnitude numbers, respectively). Although these SNAs along the transverse plane (left-to-right axis) have been extensively studied in cognitive sciences, no systematic assessment of other planes of the tridimensional space has been afforded. Moreover, there is no evidence of how SNAs organise themselves throughout the changes in spatial body-reference frames (egocentric and allocentric). Hence, this study aimed to explore how SNAs organise themselves along the transverse and sagittal planes when egocentric and allocentric changes are processed during body displacements in the environment. In the first experiment, the results revealed that, when the participants used an egocentric reference, SNAs were observed only along the sagittal plane. In a second experiment that used an allocentric reference, the reversed pattern of results was observed: SNAs were present only along the transverse plane of the body. Overall, these findings suggest that, depending on the spatial reference frames of the body, SNAs are strongly flexible.

tDCS effects in basic symbolic number magnitude processing are not significantly lateralized

Functional lateralization was previously established for various cognitive domains-but not for number processing. Although numbers are considered to be bilaterally represented in the intraparietal sulcus (IPS), there are some indications of different functional roles of the left vs. right IPS in processing number pairs with small vs. large distance, respectively. This raises the question whether number size plays a distinct role in the lateralization within the IPS. In our preregistered study, we applied anodal transcranial direct current stimulation (tDCS) over the left vs. right IPS to investigate the effect of stimulation as compared to sham on small vs. large distance, in both single-digit and two-digit number comparison. We expected that anodal tDCS over the left IPS facilitates number comparison with small distance, while anodal tDCS over the right IPS facilitates number comparison with large distance. Results indicated no effect of stimulation; however, exploratory analyses revealed that tDCS over the right IPS slowed down single-digit number processing after controlling for the training effect. In conclusion, number magnitude processing might be bilaterally represented in the IPS, however, our exploratory analyses emphasise the need for further investigation on functional lateralization of number processing.

Transfer from continuous to discrete quantities in honeybees

Honeybees can estimate quantities having different dimensions: continuous and uncountable such as the relative size of visual objects in an array, or discrete and countable such as the number of objects of the array. Honeybees can transfer quantity discrimination (i.e., choosing the larger/smaller stimulus) from number to size. Here, we investigated whether honeybees could also generalize from the size (continuous) to the number (discrete) dimension. We trained free-flying foragers to discriminate between large- and small-size elements. At test, bees were presented with a comparison between larger and smaller numerosities controlled for different continuous variables covarying with numerosity such as total area, total perimeter, convex hull, and element size. Results showed that bees generalized from the size to the numerical dimension of the stimuli. This cross-dimensional transfer supports the idea of a universal mechanism for the encoding of abstract magnitudes in invertebrate species comparable to that of vertebrate species.

The importance of spatial language for early numerical development in preschool: Going beyond verbal number skills

Recent evidence suggests that spatial language in preschool positively affects the development of verbal number skills, as indexed by aggregated performances on counting and number naming tasks. We firstly aimed to specify whether spatial language (the knowledge of locative prepositions) significantly relates to both of these measures. In addition, we assessed whether the predictive value of spatial language extends beyond verbal number skills to numerical subdomains without explicit verbal component, such as number writing, symbolic magnitude classifications, ordinal judgments and numerosity comparisons. To determine the unique contributions of spatial language to these numerical skills, we controlled in our regression analyses for intrinsic and extrinsic spatial abilities, phonological awareness as well as age, socioeconomic status and home language. With respect to verbal number skills, it appeared that spatial language uniquely predicted forward and backward counting but not number naming, which was significantly affected only by phonological awareness. Regarding numerical tasks that do not contain explicit verbal components, spatial language did not relate to number writing or numerosity comparisons. Conversely, it explained unique variance in symbolic magnitude classifications and was the only predictor of ordinal judgments. These findings thus highlight the importance of spatial language for early numerical development beyond verbal number skills and suggest that the knowledge of spatial terms is especially relevant for processing cardinal and ordinal relations between symbolic numbers. Promoting spatial language in preschool might thus be an interesting avenue for fostering the acquisition of these symbolic numerical skills prior to formal schooling.

Associations between physical size and space are strongly asymmetrical

The spatial-size association of response codes (SSARC) effect describes the phenomenon that left responses are faster and more accurate to small stimuli whereas right responses are faster and more accurate to large stimuli, as compared to the opposite mapping. The effect indicates associations between the mental representations of physical size and space. Importantly, the theoretical accounts of SSARC effects make different predictions about the reciprocity and/or symmetry of spatial-size associations. To investigate the reciprocity of SSARC effects, we compared compatibility effects in two verbal choice-response tasks: a size-location (typical SSARC) task and a location-size (reciprocal SSARC) task. In the size-location task, participants responded verbally to a small/large stimulus by saying "left"/"right". In the location-size task, participants responded verbally to a left-/right-side stimulus by saying "small"/"large". Participants completed both tasks with a compatible (small-left, large-right; left-small, right-large) and an incompatible (small-right, large-left; left-large, right-small) mapping. A regular SSARC effect emerged in the size-location task. However, no reciprocal SSARC effect emerged in the location-size task if outliers were excluded. If outliers were not excluded, small reciprocal SSARC effects occurred. Associations underlying the SSARC effect are thus strongly asymmetrical: Physical (stimulus) size can prime spatial responses much more strongly than spatial (stimulus) position can prime size-related responses. The finding of asymmetrical associations between size and space is in line with some theoretical accounts of the SSARC effect but at odds with others.

Larger on the right: Honeybees represent quantities spatially

Giurfa, Marcout, Hilpert, Thevenoy, and Rugani (PNAS, https://doi.org/10.1073/pnas.22035841192022 ) report the first evidence of spatial representation of quantity in invertebrates. In an exciting and well-controlled series of experiments, the authors present evidence that honeybees, like humans, non-human primates, and birds, represent small quantities on one side of space and large quantities on the other side of space.

Investigating the influence of body movements on children's mental arithmetic performance

Several lines of research have demonstrated spatial-numerical associations in both adults and children, which are thought to be based on a spatial representation of numerical information in the form of a mental number line. The acquisition of increasingly precise mental number line representations is assumed to support arithmetic learning in children. It is further suggested that sensorimotor experiences shape the development of number concepts and arithmetic learning, and that mental arithmetic can be characterized as "motion along a path" and might constitute shifts in attention along the mental number line. The present study investigated whether movements in physical space influence mental arithmetic in primary school children, and whether the expected effect depends on concurrency of body movements and mental arithmetic. After turning their body towards the left or right, 48 children aged 8 to 10 years solved simple subtraction and addition problems. Meanwhile, they either walked or stood still and looked towards the respective direction. We report a congruency effect between body orientation and operation type, i.e., higher performance for the combinations leftward orientation and subtraction and rightward orientation and addition. We found no significant difference between walking and looking conditions. The present results suggest that mental arithmetic in children is influenced by preceding sensorimotor cues and not necessarily by concurrent body movements.

Visual number sense for real-world scenes shared by deep neural networks and humans

Recently, visual number sense has been identified from deep neural networks (DNNs). However, whether DNNs have the same capacity for real-world scenes, rather than the simple geometric figures that are often tested, is unclear. In this study, we explore the number perception of scenes using AlexNet and find that numerosity can be represented by the pattern of group activation of the category layer units. The global activation of these units increases with the number of objects in the scene, and the variations in their activation decrease accordingly. By decoding the numerosity from this pattern, we reveal that the embedding coefficient of a scene determines the likelihood of potential objects to contribute to numerical perception. This was demonstrated by the more optimized performance for pictures with relatively high embedding coefficients in both DNNs and humans. This study for the first time shows that a distinct feature in visual environments, revealed by DNNs, can modulate human perception, supported by a group-coding mechanism.

The role of non-numerical information in the perception of temporal numerosity

Numerosity perception refers to the ability to make rapid but approximate estimates of the quantity of elements in a set (spatial numerosity) or presented sequentially (temporal numerosity). Whether numerosity is directly perceived or indirectly recomputed from non-numerical features is a highly debated issue. In the spatial domain, area and density have been suggested as the main parameters through which numerosity would be recomputed. In the temporal domain, stimuli duration and temporal frequency could be similarly exploited to retrieve numerosity. By adapting a psychophysical technique previously exploited in the spatial domain, we investigated whether temporal visual numerosity is directly perceived. Adult participants observed sequences of visual impulses sampled from a stimulus space spanning several levels of temporal frequency and duration (and hence numerosity), and then reproduced the sequence as accurately as possible via a series of keypresses. Crucially, participants were not asked to reproduce any particular property (such as number of impulses) but were free to choose any available cue (such as total duration, or temporal frequency). The results indicate that while the overall sequence duration was barely considered, numerosity and temporal frequency were both spontaneously used as the main cues to reproduce the sequences, with a slight but significant dominance of numerosity. Overall, the results are in line with previous literature suggesting that numerosity is directly encoded, even for temporal sequences, but a non-numerical feature (temporal frequency) is also used in reproducing sequences.

Gazing left, gazing right: exploring a spatial bias in social attention

Faces oriented rightwards are sometimes perceived as more dominant than faces oriented leftwards. In this study, we explored whether faces oriented rightwards can also elicit increased attentional orienting. Participants completed a discrimination task in which they were asked to discriminate, by means of a keypress, a peripheral target. At the same time, a task-irrelevant face oriented leftwards or rightwards appeared at the centre of the screen. The results showed that, while for faces oriented rightwards targets appearing on the right were responded to faster as compared to targets appearing on the left, for faces oriented leftwards no differences emerged between left and right targets. Furthermore, we also found a negative correlation between the magnitude of the orienting response elicited by the faces oriented leftwards and the level of conservatism of the participants. Overall, these findings provide evidence for the existence of a spatial bias reflected in social orienting.

Children grow upwards, and so does the number line: Evidence from a directional number line paradigm

Technological advancements give researchers the opportunity to explore the internal metric that allows to mentally place numbers in a spatial and ordered way to establish relationships between quantities. In this study, we implement the cMNL, an embodied number line paradigm to investigate the configuration of children's number space mappings under multiple conditions. A sample of 185 primary school children aged 8-10years old completed digitally an embodied number line task encompassing directionality and modality as variables. Contrary to the premise of a fixed internal number line moving from left to right in many Western scripts, our results suggest that children's number-space mapping is more robust along a vertical axis. In addition, children's embodied number line estimation differed depending on input modality. The findings provide insight into the variability in children's number line estimation, and the usability of digital assessment in understanding the mechanisms of the developing number-space system.

Spatio-Numerical Mapping in 3D

The close link between number and space is illustrated by the Spatial Numerical Association of Response Codes (SNARC) effect. The current research focuses on the flexibility of the SNARC across three dimensions. Shaki and Fischer (2018) pointed out that spatial attributes of stimuli and response effectors can favor an ad hoc spatial representation. In this paper, we aimed to broaden this perspective using two Go/NoGo experiments with digits being presented at two spatial locations while a central response was required. In Experiment 1, stimuli appeared either to the left or right (horizontal) and below or above fixation (vertical). In Experiment 2, as the monitor was laying down flat on the desk, stimuli appeared either to the left or right (horizontal) and either close or far from the observer (midsagittal). The results of Experiment 1 show significant effects for the two dimensions (horizontal, vertical), while in Experiment 2, we observe only a barely significant effect for the sagittal axis. We interpret these findings as showing (1) the importance of motor response spatialization in eliciting the SNAs and (2) the dominance of the vertical axis over the horizontal when the spatial component of the motor response is removed.

Passive Grouping Enhances Proto-Arithmetic Calculation for Leftward Correct Responses

Baby chicks and other animals including human infants master simple arithmetic. They discriminate 2 vs. 3 (1 + 1 vs. 1 + 1 + 1) but fail with 3 vs. 4 (1 + 1 + 1 vs. 1 + 1 + 1 + 1). Performance is restored when elements are grouped as 2 + 1 vs. 2 + 2. Here, we address whether grouping could lead to asymmetric response bias. We recoded behavioural data from a previous study, in which separate groups of four-day-old domestic chicks underwent an arithmetic task: when the objects were presented one-by-one (1 + 1 + 1 vs. 1 + 1 + 1 + 1), chicks failed in locating the larger group irrespective of its position and did not show any side bias; Experiment 1. When the objects were presented as grouped (2 + 1 vs. 2 + 2), chicks succeeded, performing better when the larger set was on their left; Experiment 2. A similar leftward bias was also observed with harder discriminations (4 vs. 5: 3  +  1 vs. 3  +  2), with baby chicks succeeding in the task only when the larger set was on the left (Experiments 3 and 4). A previous study showed a rightward bias, with tasks enhancing individual processing. Despite a similar effect in boosting proto-arithmetic calculations, individual processing (eliciting a right bias) and grouping (eliciting a left bias) seem to depend on distinct cognitive mechanisms.

Reading/writing direction as a source of directional bias in spatial cognition: Possible mechanisms and scope

Becoming literate has been argued to have a range of social, economic and psychological effects. Less examined is the extent to which repercussions of becoming literate may vary as a function of writing system variation. A salient way in which writing systems differ is in their directionality. Recent studies have claimed that directional biases in a variety of spatial domains are attributable to reading and writing direction. This claim is the focus of the present paper, which considers the scope and possible mechanisms underlying script directionality effects in spatial cognition, with particular attention to domains with real-world relevance. Three questions are addressed: (1) What are possible mediating and moderator variables relevant to script directionality effects in spatial cognition? (2) Does script directionality exert a fixed or a malleable effect? and (3) How can script directionality effects be appropriately tested? After discussing these questions in the context of specific studies, we highlight general methodological issues in this literature and provide recommendations for the design of future research.

Thinking about order: a review of common processing of magnitude and learned orders in animals

Rich behavioral and neurobiological evidence suggests cognitive and neural overlap in how quantitatively comparable dimensions such as quantity, time, and space are processed in humans and animals. While magnitude domains such as physical magnitude, time, and space represent information that can be quantitatively compared (4 "is half of" 8), they also represent information that can be organized ordinally (1→2→3→4). Recent evidence suggests that the common representations seen across physical magnitude, time, and space domains in humans may be due to their common ordinal features rather than their common quantitative features, as these common representations appear to extend beyond magnitude domains to include learned orders. In this review, we bring together separate lines of research on multiple ordinal domains including magnitude-based and learned orders in animals to explore the extent to which there is support for a common cognitive process underlying ordinal processing. Animals show similarities in performance patterns across natural quantitatively comparable ordered domains (physical magnitude, time, space, dominance) and learned orders (acquired through transitive inference or simultaneous chaining). Additionally, they show transfer and interference across tasks within and between ordinal domains that support the theory of a common ordinal representation across domains. This review provides some support for the development of a unified theory of ordinality and suggests areas for future research to better characterize the extent to which there are commonalities in cognitive processing of ordinal information generally.

Ordinality and Verbal Framing Influence Preschoolers' Memory for Spatial Structure

During the preschool years, children are simultaneously undergoing a reshaping of their mental number line and becoming increasingly sensitive to the social norms expressed by those around them. In the current study, 4- and 5-year-old American and Israeli children were given a task in which an experimenter laid out chips with numbers (1-5), letters (A-E), or colors (Red-Blue, the first colors of the rainbow), and presented them with a specific order (initial through final) and direction (Left-to-right or Right-to-left). The experimenter either did not demonstrate the laying out of the chips (Control), emphasized the process of the left-to-right or right-to-left spatial layout (Process), or used general goal language (Generic). Children were then asked to recreate each sequence after a short delay. Children also completed a short numeracy task. The results indicate that attention to the spatial structuring of the environment was influenced by conventional framing; children exhibited better recall when the manner of layout was emphasized than when it was not. Both American and Israeli children were better able to recall numerical information relative to non-numerical information. Although children did not show an overall benefit for better recall of information related to the culture's dominant spatial direction, American children's tendency to recall numerical direction information predicted their early numeracy ability.

Over-reliance on English hinders cognitive science

English is the dominant language in the study of human cognition and behavior: the individuals studied by cognitive scientists, as well as most of the scientists themselves, are frequently English speakers. However, English differs from other languages in ways that have consequences for the whole of the cognitive sciences, reaching far beyond the study of language itself. Here, we review an emerging body of evidence that highlights how the particular characteristics of English and the linguistic habits of English speakers bias the field by both warping research programs (e.g., overemphasizing features and mechanisms present in English over others) and overgeneralizing observations from English speakers' behaviors, brains, and cognition to our entire species. We propose mitigating strategies that could help avoid some of these pitfalls.

Mice make temporal inferences about novel locations based on previously learned spatiotemporal contingencies

Animals learn multiple spatiotemporal contingencies and organize their anticipatory responses accordingly. The representational/computational capacity that underlies such spatiotemporally guided behaviors is not fully understood. To this end, we investigated whether mice make temporal inferences of novel locations based on previously learned spatiotemporal contingencies. We trained 18 C57BL/6J mice to anticipate reward after three different intervals at three different locations and tested their temporal expectations of a reward at five locations simultaneously, including two locations that were not previously associated with reward delivery but adjacent to the previously trained locations. If mice made spatiotemporal inferences, they were expected to interpolate between duration pairs associated with previously reinforced hoppers surrounding the novel hopper. We found that the maximal response rate at the novel locations indeed fell between the two intervals reinforced at the surrounding hoppers. We argue that this pattern of responding might be underlain by spatially constrained Bayesian computations.

Number selective sensorimotor neurons in the crow translate perceived numerosity into number of actions

Translating a perceived number into a matching number of self-generated actions is a hallmark of numerical reasoning in humans and animals alike. To explore this sensorimotor transformation, we trained crows to judge numerical values in displays and to flexibly plan and perform a matching number of pecks. We report number selective sensorimotor neurons in the crow telencephalon that signaled the impending number of self-generated actions. Neuronal population activity during the sensorimotor transformation period predicted whether the crows mistakenly planned fewer or more pecks than instructed. During sensorimotor transformation, both a static neuronal code characterized by persistently number-selective neurons and a dynamic code originating from neurons carrying rapidly changing numerical information emerged. The findings indicate there are distinct functions of abstract neuronal codes supporting the sensorimotor number system.

An insect brain organizes numbers on a left-to-right mental number line

The ability to judge numbers exists in various vertebrate species but also in honey bees, thus raising the question of the phylogenetic origins of numerosity systems. Here, we studied if bees, like humans, organize numbers spatially from left to right according to their magnitude. As the cultural vs. biological origins of this mental number line (MNL) are a subject of debate, our study provides an important perspective for this discussion. We show that bees order numbers from left to right according to their magnitude and that the location of a number on that line varies with the reference number previously trained. Thus, the MNL is a biological numeric representation that is common to the nervous system with distant evolutionary origins.

The “mental number line” (MNL) is a form of spatial numeric representation that associates small and large numbers with the left and right spaces, respectively. This spatio-numeric organization can be found in adult humans and has been related to cultural factors such as writing and reading habits. Yet, both human newborns and birds order numbers consistently with an MNL, thus raising the question of whether culture is a main explanation for MNL. Here, we explored the numeric sense of honey bees and show that after being trained to associate numbers with a sucrose reward, they order numbers not previously experienced from left to right according to their magnitude. Importantly, the location of a number on that scale varies with the reference number previously trained and does not depend on low-level cues present on numeric stimuli. We provide a series of neural explanations for this effect based on the extensive knowledge accumulated on the neural underpinnings of visual processing in honey bees and conclude that the MNL is a form of numeric representation that is evolutionarily conserved across nervous systems endowed with a sense of number, irrespective of their neural complexity.

Spatial-numerical associations without a motor response? Grip force says 'Yes'

In numerical processing, the functional role of Spatial-Numerical Associations (SNAs, such as the association of smaller numbers with left space and larger numbers with right space, the Mental Number Line hypothesis) is debated. Most studies demonstrate SNAs with lateralized responses, and there is little evidence that SNAs appear when no response is required. We recorded passive holding grip forces in no-go trials during number processing. In Experiment 1, participants performed a surface numerical decision task ("Is it a number or a letter?"). In Experiment 2, we used a deeper semantic task ("Is this number larger or smaller than five?"). Despite instruction to keep their grip force constant, participants' spontaneous grip force changed in both experiments: Smaller numbers led to larger force increase in the left than in the right hand in the numerical decision task (500-700 ms after stimulus onset). In the semantic task, smaller numbers again led to larger force increase in the left hand, and larger numbers increased the right-hand holding force. This effect appeared earlier (180 ms) and lasted longer (until 580 ms after stimulus onset). This is the first demonstration of SNAs with passive holding force. Our result suggests that (1) explicit motor response is not a prerequisite for SNAs to appear, and (2) the timing and strength of SNAs are task-dependent. (216 words).

More linear than log? Non-symbolic number-line estimation in 3- to 5-year-old children

The number-line estimation task has become one of the most important methods in numerical cognition research. Originally applied as a direct measure of spatial number representation, it became also informative regarding various other aspects of number processing and associated strategies. However, most of this work and associated conclusions concerns processing numbers in a symbolic format, by school children and older subjects. Symbolic number system is formally taught and trained at school, and its basic mathematical properties (e.g., equidistance, ordinality) can easily be transferred into a spatial format of an oriented number line. This triggers the question on basic characteristics of number line estimation before children get fully familiar with the symbolic number system, i.e., when they mostly rely on approximate system for non-symbolic quantities. In our three studies, we examine therefore how preschool children (3–5-years old) estimate position of non-symbolic quantities on a line, and how this estimation is related to the developing symbolic number knowledge and cultural (left-to-right) directionality. The children were tested with the Give-a-number task, then they performed a computerized number-line task. In Experiment 1, lines bounded with sets of 1 and 20 elements going left-to-right or right-to-left were used. Even in the least numerically competent group, the linear model better fit the estimates than the logarithmic or cyclic power models. The line direction was irrelevant. In Experiment 2, a 1–9 left-to-right oriented line was used. Advantage of linear model was found at group level, and variance of estimates correlated with tested numerosities. In Experiment 3, a position-to-number procedure again revealed the advantage of the linear model, although the strategy of selecting an option more similar to the closer end of the line was prevalent. The precision of estimation increased with the mastery of counting principles in all three experiments. These results contradict the hypothesis of the log-to-linear shift in development of basic numerical representation, rather supporting the linear model with scalar variance. However, the important question remains whether the number-line task captures the nature of the basic numerical representation, or rather the strategies of mapping that representation to an external space.

Contributions of the psychology of mathematical cognition in early childhood education using apps

Educational interventions are necessary to develop mathematical competence at early ages and prevent widespread mathematics learning failure in the education system as indicated by the results of European reports. Numerous studies agree that domain-specific predictors related to mathematics are symbolic and non-symbolic magnitude comparison, as well as, number line estimation. The goal of this study was to design 4 digital learning app games to train specific cognitive bases of mathematical learning in order to create resources and promote the use of these technologies in the educational community and to promote effective scientific transfer and increase the research visibility. This study involved 193 preschoolers aged 57–79 months. A quasi-experimental design was carried out with 3 groups created after scores were obtained in a standardised mathematical competence assessment test, i.e., low-performance group (N = 49), high-performance group (N = 21), and control group (N = 123). The results show that training with the 4 digital learning app games focusing on magnitude, subitizing, number facts, and estimation tasks improved the numerical skills of the experimental groups, compared to the control group. The implications of the study were, on the one hand, provided verified technological tools for teaching early mathematical competence. On the other hand, this study supports other studies on the importance of cognitive precursors in mathematics performance.

Vertical versus horizontal Spatial-Numerical Associations (SNA): A processing advantage for the vertical dimension

Humans have associations between numbers and physical space on both horizontal and vertical dimensions, called Spatial-Numerical Associations (SNAs). Several studies have considered the hypothesis of there being a dominant orientation by examining on which dimension people are more accurate and efficient at responding during various directional SNA tasks. However, these studies have difficulty differentiating between a person’s efficiency at accessing mental representations of numbers in space, and the efficiency at which they exercise motor control functions, particularly bilateral ones, when manifesting a response during an explicit directional SNA task. In this study we use a conflict test employing combined explicit magnitude and spatial directional processing in which pairs of numbers are placed along the diagonal axes and response accuracy/efficiency are considered across the horizontal and vertical dimensions simultaneously. Participants indicated which number in each pair was largest using a joystick that only required unilateral input. The experiment was run in English using Arabic numerals. Results showed that directional SNAs have a vertical rather than horizontal dominance. A moderating factor was also found during post-hoc analysis, where response efficiency, but not accuracy, is conditional on a person’s native language being oriented the same as the language of the experiment, left to right. The dominance of the vertical orientation suggests adopting more vertical display formats for numbers may provide situational advantages, particularly for explicit magnitude comparisons, with some domains like flight controls and the stock market already using these in some cases.

The role of cognitive control in the SNARC effect: A review

The spatial-numerical association of response codes (SNARC) effect, in which people respond to small numbers faster with the left hand and to large numbers faster with the right hand, is a popular topic in cognitive psychology. Some well-known theoretical accounts explaining this effect include the mental number line model, polarity correspondence principle, dual-route model, and working memory account. However, these fail to explain the finding that the size of the SNARC effect is modulated by cognitive control. Here, we propose a new account-a cognitive control-based view of the SNARC effect. This view argues that the SNARC effect is fundamentally determined by cognitive control in resolving conflicts during stimulus-response mapping. Several subcomponents of cognitive control, such as working memory, mental or task set shifting, inhibition control, and conflict adaptation, can easily modulate the SNARC effect. The cognitive control-based view can account for the flexible SNARC effect observed in diverse task situations while providing new insight into its mechanism.

Number neurons in the nidopallium of young domestic chicks

Numerosity, that is, the number of items in a set, is a significant aspect in the perception of the environment. Behavioral and in silico experiments suggest that number sense belongs to a core knowledge system and can be present already at birth. However, neurons sensitive to the number of visual items have been so far described only in the brain of adult animals. Therefore, it remained unknown to what extent their selectivity would depend on visual learning and experience. We found number neurons in the caudal nidopallium (a higher associative area functionally similar to the mammalian prefrontal cortex) of very young, numerically naïve domestic chicks. This result suggests that numerosity perception is possibly an inborn feature of the vertebrate brain.

Numerical cognition is ubiquitous in the animal kingdom. Domestic chicks are a widely used developmental model for studying numerical cognition. Soon after hatching, chicks can perform sophisticated numerical tasks. Nevertheless, the neural basis of their numerical abilities has remained unknown. Here, we describe number neurons in the caudal nidopallium (functionally equivalent to the mammalian prefrontal cortex) of young domestic chicks. Number neurons that we found in young chicks showed remarkable similarities to those in the prefrontal cortex and caudal nidopallium of adult animals. Thus, our results suggest that numerosity perception based on number neurons might be an inborn feature of the vertebrate brain.

Magnitudes for Nervous Systems: Theoretical Issues and Experimental Evidence

Animals’ negotiations with the environment frequently involve quantitative assessments. However, it is largely unknown how different nervous systems can deal with information about magnitude and perform operations on it. Here we review some of the literature on this topic and discuss a few issues worthy of debate that can guide future research directions. First, we present experimental evidence suggesting that, in addition to the cortical (pallial) brain regions that are widely acknowledged to play a role in magnitude estimation, subcortical (more generally, subpallial) brain regions also play an important role. Second, we discuss interactions between different domains of magnitude and put forward a hypothesis to account for the directionality of associations between discrete and continuous magnitude. Finally, we suggest how the distinction between the concepts of number and discrete quantity should foster more attention to the role of sensory areas and circuits in assessing discrete quantities.

The signature-testing approach to mapping biological and artificial intelligences

Making inferences from behaviour to cognition is problematic due to a many-to-one mapping problem, in which any one behaviour can be generated by multiple possible cognitive processes. Attempts to cross this inferential gap when comparing human intelligence to that of animals or machines can generate great debate. Here, we discuss the challenges of making comparisons using 'success-testing' approaches and call attention to an alternate experimental framework, the 'signature-testing' approach. Signature testing places the search for information-processing errors, biases, and other patterns centre stage, rather than focussing predominantly on problem-solving success. We highlight current research on both biological and artificial intelligence that fits within this framework and is creating proactive research programs that make strong inferences about the similarities and differences between the content of human, animal, and machine minds.

Children perform better on left than right targets in an ordinal task

Francis Galton first reported that humans mentally organize numbers from left to right on a mental number line (1880). This spatial-numerical association was long considered to result from writing and reading habits. More recently though, newborns and animals showed a left-to-right oriented spatial numerical association challenging the primary role assigned to culture in determining the link between number and space. Despite growing evidence supporting the intrinsic association between number and space in different species, its adaptive value is still largely unknown. Here we tested for an advantage in identification of left versus right target positions in 3- to 6-year-old children. Children watched as a toy was hidden under one of 10 linearly arranged identical cups and were then asked to help a stuffed animal retrieve the toy. On each trial, the toy was hidden in the 2nd, 3rd, or 4th cup, from the left or right. To prevent children from staring at the target cup, they were asked to pick up the stuffed animal from under their chair after witnessing the hiding of the toy and then to help the stuffed animal find the toy. Older children were more accurate than younger children. Children exhibited a serial position effect, with performance higher for more exterior targets. Remarkably, children also showed a left bias: they remembered the left targets better than the right targets. Only the youngest children were dramatically influenced by the location of the experimenter during search. Additional analyses support the hypothesis that children used a left-to-right oriented searching strategy in this spatial/ordinal task.

Are prime numbers special? Insights from the life sciences

Prime numbers have been attracting the interest of scientists since the first formulation of Euclid’s theorem in 300 B.C. Nowadays, physicists and mathematicians continue to formulate new theorems about prime numbers, trying to comprehensively explain their articulated properties. However, evidence from biology and experimental psychology suggest that prime numbers possess distinctive natural properties that pre-exist human grasping. The present work aims at reviewing the existing literature on prime numbers in the life sciences, including some recent experimental contributions employing newly hatched domestic chicks as animal model to test for spontaneous mechanisms allowing discrimination of primes from non-primes. Our overarching goal is that of discussing some instances of prime numbers in nature, with particular reference to their peculiar, non-mathematical, perceptual properties.

Children gradually construct spatial representations of temporal events

English-speaking adults often recruit a "mental timeline" to represent events from left-to-right (LR), but its developmental origins are debated. Here, we test whether preschoolers prefer ordered linear representations of events and whether they prefer culturally conventional directions. English-speaking adults (n = 85) and 3- to 5-year-olds (n = 513; 50% female; ~47% white, ~35% Latinx, ~18% other; tested 2016-2018) were told three-step stories and asked to choose which of two image sequences best illustrated them. We found that 3- and 4-year-olds chose ordered over unordered sequences, but preferences between directions did not emerge until at least age 5. Together, these results show that children conceptualize time linearly early in development but gradually acquire directional preferences (e.g., for LR).

Pitch–Luminance Crossmodal Correspondence in the Baby Chick: An Investigation on Predisposed and Learned Processes

Our senses are constantly reached by a multitude of stimuli from all different sensory modalities. To create a coherent representation of the environment, we must integrate the various unimodal inputs that refer to the same object into a single multimodal representation. In some cases, however, we tend to bind certain properties of the stimuli without any apparent reason, which is a phenomenon named crossmodal correspondence. For instance, we match a spiky or a rounded shape with the sound “Kiki” or “Bouba”, respectively. Similarly, we associate the left hemispace with low luminance and the right one with high luminance. Instances of crossmodal correspondences were described also in other mammals, and recently, a case of space-luminance crossmodal correspondence was reported in birds (i.e., domestic chicks). Here, we investigate the presence of pitch–luminance crossmodal correspondence in three-day-old chicks, employing experimental methods that exploit either predisposed or learned processes. While failing to report evidence for this phenomenon, we discuss the difference between statistical and structural crossmodal correspondences and the possible role of environmental factors in determining their emergence. Moreover, we discuss the importance of the different experimental methodologies to investigate distinct aspects of this perceptual phenomenon to reach a deeper understanding and unveil the role of innate vs. learned mechanisms.