A cross-cultural comparison of finger-based and symbolic number representations.

The current study examined predictions from embodied cognition for effects of finger counting on number processing. Although finger counting is spontaneous and nearly universal, counting habits reflect learning and culture. European cultures use a sub-base-five system, requiring a full hand plus additional fingers to express numbers exceeding 5. Chinese culture requires only one hand to express such numbers. We investigated the differential impact of early-acquired finger-based number representations on adult symbolic number processing. In total, 53 European and 56 Chinese adults performed two versions of the magnitude classification task, where numbers were presented either as Arabic symbols or as finger configurations consistent with respective cultural finger-counting habits. Participants classified numbers as smaller/larger than 5 with horizontally aligned buttons. Finger-based size and distance effects were larger in Chinese compared with Europeans. These differences did not, however, induce reliably different symbol processing signatures. This dissociation challenges the idea that sensory and motor habits shape our conceptual representations and implies notation-specific processing patterns.

Keeping track of time: Horizontal spatial biases for hours, days, and months.

In many Western cultures, the processing of temporal words related to the past and to the future is associated with left and right space, respectively - a phenomenon known as the horizontal Mental Time Line (MTL). While this mapping is apparently quite ubiquitous, its regularity and consistency across different types of temporal concepts remain to be determined. Moreover, it is unclear whether such spatial mappings are an essential and early constituent of concept activation. In the present study, we used words denoting time units at different scales (hours of the day, days of the week, months of the year) associated with either left space (e.g., 9 a.m., Monday, February) or right space (e.g., 8 p.m., Saturday, November) as cues in a line bisection task. Fifty-seven healthy adults listened to temporal words and then moved a mouse cursor to the perceived midpoint of a horizontally presented line. We measured movement trajectories, initial line intersection coordinates, and final bisection response coordinates. We found movement trajectory displacements for left- vs. right-biasing hour and day cues. Initial line intersections were biased specifically by month cues, while final bisection responses were biased specifically by hour cues. Our findings offer general support to the notion of horizontal space-time associations and suggest further investigation of the exact chronometry and strength of this association across individual time units.

How does language affect spatial attention? Deconstructing the prime-target relationship.

It is still unclear how spatially associated concepts (e.g., directional expressions, object names, metaphors) shape our cognitive experience. Here, two experiments (N = 156) investigated the mechanisms by which words with either explicit or implicit spatial meaning induce spatial attention shifts. Participants performed a visual target-discrimination task according to response rules that required different degrees of prime and target processing depth. For explicit prime words, we found spatial congruency effects independent of processing depth, while implicit prime words generated congruency effects only when participants had to compute the congruency relationship. These results were robust across different prime-target intervals and imply that spatial connotations alone do not automatically activate spatial attention shifts. Instead, explicit semantic analysis is a prerequisite for conceptual cueing.

Concrete constraints on abstract concepts-editorial.

This special issue, "Concrete constraints of abstract concepts", addresses the role of concrete determinants, both external and internal to the human body, in acquisition, processing and use of abstract concepts while at the same time presenting to the readers an overview of methods used to assess their representation.

Abstract concepts: external influences, internal constraints, and methodological issues.

There is a longstanding and widely held misconception about the relative remoteness of abstract concepts from concrete experiences. This review examines the current evidence for external influences and internal constraints on the processing, representation, and use of abstract concepts, like truth, friendship, and number. We highlight the theoretical benefit of distinguishing between grounded and embodied cognition and then ask which roles do perception, action, language, and social interaction play in acquiring, representing and using abstract concepts. By reviewing several studies, we show that they are, against the accepted definition, not detached from perception and action. Focussing on magnitude-related concepts, we also discuss evidence for cultural influences on abstract knowledge and explore how internal processes such as inner speech, metacognition, and inner bodily signals (interoception) influence the acquisition and retrieval of abstract knowledge. Finally, we discuss some methodological developments. Specifically, we focus on the importance of studies that investigate the time course of conceptual processing and we argue that, because of the paramount role of sociality for abstract concepts, new methods are necessary to study concepts in interactive situations. We conclude that bodily, linguistic, and social constraints provide important theoretical limitations for our theories of conceptual knowledge.

Grounding (fairly) complex numerical knowledge: an educational example.

In this article, we contextualize and discuss an on-line contribution to this special issue in which a video-recorded lecture demonstrates the teaching of an abstract mathematical concept, namely regression to the mean. We first motivate the pertinence of this example from the perspective of embodied cognition. Then, we identify mechanisms of teaching that reflect embodied cognitive practices, such as the concreteness fading approach. Rather than a comprehensive review of multiple extensive literatures, this article provides the interested reader with several sources or entries into those literatures.

"BreaThink": breathing affects production and perception of quantities.

Cognition is shaped by signals from outside and within the body. Following recent evidence of interoceptive signals modulating higher-level cognition, we examined whether breathing changes the production and perception of quantities. In Experiment 1, 22 adults verbally produced on average larger random numbers after inhaling than after exhaling. In Experiment 2, 24 further adults estimated the numerosity of dot patterns that were briefly shown after either inhaling or exhaling. Again, we obtained on average larger responses following inhalation than exhalation. These converging results extend models of situated cognition according to which higher-level cognition is sensitive to transient interoceptive states.

Systematic spatial distortion of quantitative estimates.

Magnitude estimation has been studied since the beginnings of scientific psychology and constitutes a fundamental aspect of human behavior. Yet, it has apparently never been noticed that estimates depend on the spatial arrangement used. We tested 167 adults in three experiments to show that the spatial layout of stimuli and responses systematically distorts number estimation, length production, and weight reproduction performance. The direction of distortion depends on the observer's counting habits, but does not seem to reflect the use of spatially associated number concepts. Our results imply that all quantitative estimates are contaminated by a "spell of space" whenever stimuli or responses are spatially distributed.

Separation/connection procedures: From cleansing behavior to numerical cognition.

Lee and Schwarz (L&S) suggest that separation is the grounded procedure underlying cleansing effects in different psychological domains. Here, we interpret L&S's account from a hierarchical view of cognition that considers the influence of physical properties and sensorimotor constraints on mental representations. This approach allows theoretical integration and generalization of L&S's account to the domain of formal quantitative reasoning.

Stimulating numbers: signatures of finger counting in numerosity processing.

Finger counting is one of the first steps in the development of mature number concepts. With a one-to-one correspondence of fingers to numbers in Western finger counting, fingers hold two numerical meanings: one is based on the number of fingers raised and the second is based on their ordinal position within the habitual finger counting sequence. This study investigated how these two numerical meanings of fingers are intertwined with numerical cognition in adults. Participants received tactile stimulation on their fingertips of one hand and named either the number of fingers stimulated (2, 3, or 4 fingers; Experiment 1) or the number of stimulations on one fingertip (2, 3, or 4 stimulations; Experiment 2). Responses were faster and more accurate when the set of stimulated fingers corresponded to finger counting habits (Experiment 1) and when the number of stimulations matched the ordinal position of the stimulated finger (Experiment 2). These results show that tactile numerosity perception is affected by individual finger counting habits and that those habits give numerical meaning to single fingers.

Assessing orienting of attention to understand the time course of mental calculation.

Number processing induces spatial attention shifts to the left or right side for small or large numbers, respectively. This spatial-numerical association (SNA) extends to mental calculation, such that subtractions and additions induce left or right biases, respectively. However, the time course of activating SNAs during mental calculation is unclear. Here, we addressed this issue by measuring visual position discrimination during auditory calculation. Thirty-four healthy adults listened in each trial to five successive elements of arithmetic facts (first operand, operator, second operand, equal and result) and verbally classified their correctness. After each element (except for the result), a fixation dot moved equally often to either the left or right side and participants pressed left or right buttons to discriminate its movement direction (four times per trial). First and second operand magnitude (small/large), operation (addition/subtraction), result correctness (right/wrong) and movement direction (left/right) were balanced across 128 trials. Manual reaction times of dot movement discriminations were considered in relation to previous arithmetic elements. We found no evidence of early attentional shifts after first operand and operator presentation. Discrimination performance was modulated consistent with SNAs after the second operand, suggesting that attentional shifts occur once there is access to all elements necessary to complete an arithmetic operation. Such late-occurring attention shifts may reflect a combination of multiple element-specific biases and confirm their functional role in mental calculation.

On the linear representation of numbers: evidence from a new two-numbers-to-two positions task.

In the number-to-position methodology, a number is presented on each trial and the observer places it on a straight line in a position that corresponds to its felt subjective magnitude. In the novel modification introduced in this study, the two-numbers-to-two-positions method, a pair of numbers rather than a single number is presented on each trial and the observer places them in appropriate positions on the same line. Responses in this method indicate not only the subjective magnitude of each single number but, simultaneously, provide a direct estimation of their subjective numerical distance. The results of four experiments provide strong evidence for a linear representation of numbers and, commensurately, for the linear representation of numerical distances. We attribute earlier results that indicate a logarithmic representation to the ordered nature of numbers and to the task used and not to a truly non-linear underlying representation.

Observation of directional storybook reading influences young children's counting direction.

Even before formal schooling, children map numbers onto space in a directional manner. The origin of this preliterate spatial-numerical association is still debated. We investigated the role of enculturation for shaping the directionality of the association between numbers and space, focusing on counting behavior in 3- to 5-year-old preliterate children. Two studies provide evidence that, after observing reading from storybooks (left-to-right or right-to-left reading) children change their counting direction in line with the direction of observed reading. Just observing visuospatial directional movements had no such effect on counting direction. Complementarily, we document that book illustrations, prevalent in children's cultures, exhibit directionality that conforms to the direction of a culture's written language. We propose that shared book reading activates spatiotemporal representations of order in young children, which in turn affect their spatial representation of numbers.

Finger posing primes number comprehension.

Canonical finger postures, as used in counting, activate number knowledge, but the exact mechanism for this priming effect is unclear. Here we dissociated effects of visual versus motor priming of number concepts. In Experiment 1, participants were exposed either to pictures of canonical finger postures (visual priming) or actively produced the same finger postures (motor priming) and then used foot responses to rapidly classify auditory numbers (targets) as smaller or larger than 5. Classification times revealed that manually adopted but not visually perceived postures primed magnitude classifications. Experiment 2 obtained motor priming of number processing through finger postures also with vocal responses. Priming only occurred through canonical and not through non-canonical finger postures. Together, these results provide clear evidence for motor priming of number knowledge. Relative contributions of vision and action for embodied numerical cognition and the importance of canonicity of postures are discussed.

A simple technique to study embodied language processes: the grip force sensor.

Research in cognitive neuroscience has shown that brain structures serving perceptual, emotional, and motor processes are also recruited during the understanding of language when it refers to emotion, perception, and action. However, the exact linguistic and extralinguistic conditions under which such language-induced activity in modality-specific cortex is triggered are not yet well understood. The purpose of this study is to introduce a simple experimental technique that allows for the online measure of language-induced activity in motor structures of the brain. This technique consists in the use of a grip force sensor that captures subtle grip force variations while participants listen to words and sentences. Since grip force reflects activity in motor brain structures, the continuous monitoring of force fluctuations provides a fine-grained estimation of motor activity across time. In other terms, this method allows for both localization of the source of language-induced activity to motor brain structures and high temporal resolution of the recorded data. To facilitate comparison of the data to be collected with this tool, we present two experiments that describe in detail the technical setup, the nature of the recorded data, and the analyses (including justification about the data filtering and artifact rejection) that we applied. We also discuss how the tool could be used in other domains of behavioral research.

Measuring spatial-numerical associations: evidence for a purely conceptual link.

Previous work on spatial-numerical association (SNAs) included either spatially distributed stimuli or responses. This raises the possibility that the inferred spatial nature of number concepts was a methodological artifact. We present results from a novel task that involves two categories (spatially oriented objects and number magnitudes) and dissociates spatial classification from number classification. The results reveal SNAs without inferential limitations of previous work and point to a working memory mechanism that transfers spatial coding across categories.

Ocular drift along the mental number line.

We examined the spontaneous association between numbers and space by documenting attention deployment and the time course of associated spatial-numerical mapping with and without overt oculomotor responses. In Experiment 1, participants maintained central fixation while listening to number names. In Experiment 2, they made horizontal target-direct saccades following auditory number presentation. In both experiments, we continuously measured spontaneous ocular drift in horizontal space during and after number presentation. Experiment 2 also measured visual-probe-directed saccades following number presentation. Reliable ocular drift congruent with a horizontal mental number line emerged during and after number presentation in both experiments. Our results provide new evidence for the implicit and automatic nature of the oculomotor resonance effect associated with the horizontal spatial-numerical mapping mechanism.

Counting is a spatial process: evidence from eye movements.

Spatial-numerical associations (small numbers-left/lower space and large numbers-right/upper space) are regularly found in simple number categorization tasks. These associations were taken as evidence for a spatially oriented mental number line. However, the role of spatial-numerical associations during more complex number processing, such as counting or mental arithmetic is less clear. Here, we investigated whether counting is associated with a movement along the mental number line. Participants counted aloud upward or downward in steps of 3 for 45 s while looking at a blank screen. Gaze position during upward counting shifted rightward and upward, while the pattern for downward counting was less clear. Our results, therefore, confirm the hypothesis of a movement along the mental number line for addition. We conclude that space is not only used to represent number magnitudes but also to actively operate on numbers in more complex tasks such as counting, and that the eyes reflect this spatial mental operation.