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.

Distance in depth: A comparison of explicit and implicit numerical distances in the horizontal and radial dimensions.

Numbers are a constant presence in our daily lives: A brain devoid of the ability to process numbers would not be functional in its external environment. Comparing numerical magnitudes is a fundamental ability that requires the processing of numerical distances. From magnitude comparison tasks, a comparison distance effect (DE) emerges: It describes better performance when comparing numerically distant rather than close numbers. Unlike other signatures of number processing, the comparison DE has been assessed only implicitly, with numerical distance as nonsalient task property. Different assessments permit identification of different cognitive processes underlying a specific effect. To investigate whether explicit and implicit assessment of the comparison DE influences numerical cognition differently, we introduced the distance classification task, involving explicit classification of numbers as close or far from a reference. N = 93 healthy adults classified numbers either by magnitude or by numerical distance. To investigate associations between numerical and physical distance, response buttons were positioned horizontally (Experiment 1) or radially (Experiment 2). In both experiments, there was an advantage for both the closest and farthest numbers with respect to the reference during distance classification, but not during magnitude classification. In Experiment 2, numerically close/far numbers were classified faster with the close/far response button, respectively, suggesting radial correspondence between physical and representational distances. These findings provide new theoretical and methodological insights into the mental representation of numbers. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

How do numbers shift spatial attention? Both processing depth and counting habits matter.

There have been inconsistent reports about whether seeing small versus large numbers (e.g., 1 or 2 vs. 8 or 9) automatically shifts an observer's attention into left versus right hemispace. We report four visual detection experiments (N = 162) where centrally presented uninformative number cues were followed by lateralized targets that required go/no-go responses. Processing depth was manipulated by requiring observers to either distinguish numbers from other symbols (Experiment 1) or to classify numbers by either parity (Experiment 2) or magnitude (Experiments 3 and 4). Attention shifts occurred only after magnitude processing. Importantly, their direction depended on observers' directional preferences for object counting, which was separately assessed in all experiments. These results clarify the mechanism by which abstract concepts activate their inherent spatial associations and lead to spatial attention shifts. They also demonstrate the feasibility of attentional probing to study mechanisms of symbol comprehension in various contexts, ranging from mental arithmetic to language processing. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

Language directs spatial attention differently in explicit and implicit tasks.

How do words with either explicit or implicit spatial meanings (e.g., DOWN, BOOT) shift our attention? Recent studies, presenting prime words followed by probe targets, suggested that, for implicit spatial words, both the spatial meaning of prime words and the target locations must be processed to induce congruency benefits. Here we examined the functional necessity of the latter location component. 91 healthy adults discriminated target letters that followed explicit or implicit spatial words. Words either did or did not have to be semantically processed. Target discrimination speed was used to compute congruency benefits. With explicit prime words, spatial congruency effects emerged without semantic processing instructions. In contrast, with implicit prime words, only instructing their semantic processing ensured a congruency benefit. This shows that, for implicit spatial words, spatial processing of target locations is not necessary; instead, processing the spatial connotation of the prime, together with the identity of the target, can induce congruency benefits. Our results help to understand previous conflicting findings.

Embodied Processing at Six Linguistic Granularity Levels: A Consensus Paper.

Language processing is influenced by sensorimotor experiences. Here, we review behavioral evidence for embodied and grounded influences in language processing across six linguistic levels of granularity. We examine (a) sub-word features, discussing grounded influences on iconicity (systematic associations between word form and meaning); (b) words, discussing boundary conditions and generalizations for the simulation of color, sensory modality, and spatial position; (c) sentences, discussing boundary conditions and applications of action direction simulation; (d) texts, discussing how the teaching of simulation can improve comprehension in beginning readers; (e) conversations, discussing how multi-modal cues improve turn taking and alignment; and (f) text corpora, discussing how distributional semantic models can reveal how grounded and embodied knowledge is encoded in texts. These approaches are converging on a convincing account of the psychology of language, but at the same time, there are important criticisms of the embodied approach and of specific experimental paradigms. The surest way forward requires the adoption of a wide array of scientific methods. By providing complimentary evidence, a combination of multiple methods on various levels of granularity can help us gain a more complete understanding of the role of embodiment and grounding in language processing.

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.

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.

Random walk: Random number generation during backward and forward walking- the role of aging.

Deficits in executive function, visuospatial abilities, and cognitive embodiment may impair gait performance. This study aimed to investigate the effect of age on random number generation (RNG) performance during forward and backward locomotion to assess cognitive flexibility and cognitive embodiment during walking. Another aim was to examine the effect of age on the associations of RNG performance during walking with stride time variability (STV), the percentage of double support (DS%), and visuospatial abilities as measured by a spatial orientation test (SOT). Twenty old (age 68.8 ± 5.3, 65% female) and 20 young (age 25.2 ± 2.2, 45% female) adults generated random numbers during backward walking (BW) and forward walking (FW) over-ground and over a treadmill with an internal focus of attention and visual-attentive distraction; six walking conditions in total. To assess cognitive flexibility, sample entropy was calculated for each RNG sequence. The average of the first 5 numbers in each RNG task was calculated to assess the relationship between small/large numbers and movement direction. STV and DS% were recorded using inertial measurement units, and spatial orientation was measured using a computerized test. The older subjects had less flexibility in generating random numbers in three of the six walking conditions. A negative correlation between RNG flexibility and STV was found in older adults during treadmill BW with visual-attentive distraction and forward over-ground walking, whereas no correlations were demonstrated in the young group. The spatial orientation score (a higher value means a worse outcome) correlated positively with RNG flexibility in the older group under all walking conditions, suggesting that older adults with better visuospatial orientation have lower cognitive flexibility, and vice versa. There was no correlation between small/large numbers and direction of motion in either group. The correlation between RNG flexibility and STV may indicate similar executive control of verbal and gait rhythmicity in old adults. Conversely, our results suggest that cognitive flexibility and visuospatial ability may decline differently.

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.

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.

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.

Number to me, space to you: Joint representation of spatial-numerical associations.

Recent work has shown that number concepts activate both spatial and magnitude representations. According to the social co-representation literature which has shown that participants typically represent task components assigned to others together with their own, we asked whether explicit magnitude meaning and explicit spatial coding must be present in a single mind, or can be distributed across two minds, to generate a spatial-numerical congruency effect. In a shared go/no-go task that eliminated peripheral spatial codes, we assigned explicit magnitude processing to participants and spatial processing to either human or non-human co-agents. The spatial-numerical congruency effect emerged only with human co-agents. We demonstrate an inter-personal level of conceptual congruency between space and number that arises from a shared conceptual representation not contaminated by peripheral spatial codes. Theoretical implications of this finding for numerical cognition are discussed.

Turn the beat around: Commentary on "Slow and fast beat sequences are represented differently through space" (De Tommaso & Prpic, 2020, in Attention, Perception, & Psychophysics).

There has been increasing interest in the spatial mapping of various perceptual and cognitive magnitudes, such as expanding the spatial-numerical association of response codes (SNARC) effect into domains outside of numerical cognition. Recently, De Tommaso and Prpic (Attention, Perception, & Psychophysics, 82, 2765-2773, 2020) reported in this journal that only fast tempos over 104 beats per minute have spatial associations, with more right-sided associations and faster responses for faster tempos. After discussing the role of perceived loudness and possible response strategies, we propose and recommend methodological improvements for further research.

Heuristics and biases in the mental manipulation of magnitudes: Evidence from length and time production.

There is a debate about whether and why we overestimate addition and underestimate subtraction results (Operational Momentum or OM effect). Spatial-attentional accounts of OM compete with a model which postulates that OM reflects a weighted combination of multiple arithmetic heuristics and biases (AHAB). This study addressed this debate with the theoretically diagnostic distinction between zero problems (e.g., 3 + 0, 3 - 0) and non-zero problems (e.g., 2 + 1, 4 - 1) because AHAB, in contrast to all other accounts, uniquely predicts reverse OM for the latter problem type. In two tests (line-length production and time production), participants indeed produced shorter lines and under-estimated time intervals in non-zero additions compared with subtractions. This predicted interaction between operation and problem type extends OM to non-spatial magnitudes and highlights the strength of AHAB regarding different problem types and modalities during the mental manipulation of magnitudes. They also suggest that OM reflects methodological details, whereas reverse OM is the more representative behavioural signature of mental arithmetic.

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.

A biological foundation for spatial-numerical associations: the brain's asymmetric frequency tuning.

"Left" and "right" coordinates control our spatial behavior and even influence abstract thoughts. For number concepts, horizontal spatial-numerical associations (SNAs) have been widely documented: we associate few with left and many with right. Importantly, increments are universally coded on the right side even in preverbal humans and nonhuman animals, thus questioning the fundamental role of directional cultural habits, such as reading or finger counting. Here, we propose a biological, nonnumerical mechanism for the origin of SNAs on the basis of asymmetric tuning of animal brains for different spatial frequencies (SFs). The resulting selective visual processing predicts both universal SNAs and their context-dependence. We support our proposal by analyzing the stimuli used to document SNAs in newborns for their SF content. As predicted, the SFs contained in visual patterns with few versus many elements preferentially engage right versus left brain hemispheres, respectively, thus predicting left-versus rightward behavioral biases. Our "brain's asymmetric frequency tuning" hypothesis explains the perceptual origin of horizontal SNAs for nonsymbolic visual numerosities and might be extensible to the auditory domain.

Unstable world: Recent experience affects spatial perception.

An accurate perception of the space surrounding us is central for effective and safe everyday functioning. Understanding the factors influencing spatial perception is therefore vital. Here, we first confirm previous reports that our cultural reading habits shape the perception of space. Twenty-four left-to-right readers (tested in Australia) and 23 right-to-left readers (tested in Israel) over-attend to information presented on the left and right side of space, respectively. We then show that this cultural bias is highly malleable. By employing a simple mirror-reading task prior to the spatial judgments, we demonstrate that the supposed cultural bias can be easily overridden. These findings question hardwired, lateralisation models of spatial-attentional biases and highlight the need for a dynamic model that takes into account hemispheric lateralisation, cultural habits and situational context.