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).

Ecological Meanings: A Consensus Paper on Individual Differences and Contextual Influences in Embodied Language.

Embodied theories of cognition consider many aspects of language and other cognitive domains as the result of sensory and motor processes. In this view, the appraisal and the use of concepts are based on mechanisms of simulation grounded on prior sensorimotor experiences. Even though these theories continue receiving attention and support, increasing evidence indicates the need to consider the flexible nature of the simulation process, and to accordingly refine embodied accounts. In this consensus paper, we discuss two potential sources of variability in experimental studies on embodiment of language: individual differences and context. Specifically, we show how factors contributing to individual differences may explain inconsistent findings in embodied language phenomena. These factors include sensorimotor or cultural experiences, imagery, context-related factors, and cognitive strategies. We also analyze the different contextual modulations, from single words to sentences and narratives, as well as the top-down and bottom-up influences. Similarly, we review recent efforts to include cultural and language diversity, aging, neurodegenerative diseases, and brain disorders, as well as bilingual evidence into the embodiment framework. We address the importance of considering individual differences and context in clinical studies to drive translational research more efficiently, and we indicate recommendations on how to correctly address these issues in future research. Systematically investigating individual differences and context may contribute to understanding the dynamic nature of simulation in language processes, refining embodied theories of cognition, and ultimately filling the gap between cognition in artificial experimental settings and cognition in the wild (i.e., in everyday life).

White matter tract disconnection in Gerstmann's syndrome: Insights from a single case study.

It has been suggested that Gerstmann's syndrome is the result of subcortical disconnection rather than emerging from damage of a multifunctional brain region within the parietal lobe. However, patterns of white matter tract disconnection following parietal damage have been barely investigated. This single case study allows characterising Gerstmann's syndrome in terms of disconnected networks. We report the case of a left parietal patient affected by Gerstmann's tetrad: agraphia, acalculia, left/right orientation problems, and finger agnosia. Lesion mapping, atlas-based estimation of probability of disconnection, and DTI-based tractography revealed that the lesion was mainly located in the superior parietal lobule, and it caused disruption of both intraparietal tracts passing through the inferior parietal lobule (e.g., tracts connecting the angular, supramarginal, postcentral gyri, and the superior parietal lobule) and fronto-parietal long tracts (e.g., the superior longitudinal fasciculus). The lesion site appears to be located more superiorly as compared to the cerebral regions shown active by other studies during tasks impaired in the syndrome, and it reached the subcortical area potentially critical in the emergence of the syndrome, as hypothesised in previous studies. Importantly, the reconstruction of tracts connecting regions within the parietal lobe indicates that this critical subcortical area is mainly crossed by white matter tracts connecting the angular gyrus and the superior parietal lobule. Taken together, these findings suggest that this case study might be considered as empirical evidence of Gerstmann's tetrad caused by disconnection of intraparietal white matter tracts.

Cortical areas involved in grasping and reaching actions with and without visual information: An ALE meta-analysis of neuroimaging studies.

The functional specialization of the ventral stream in Perception and the dorsal stream in Action is the cornerstone of the leading model proposed by Goodale and Milner in 1992. This model is based on neuropsychological evidence and has been a matter of debate for almost three decades, during which the dual-visual stream hypothesis has received much attention, including support and criticism. The advent of functional magnetic resonance imaging (fMRI) has allowed investigating the brain areas involved in Perception and Action, and provided useful data on the functional specialization of the two streams. Research on this topic has been quite prolific, yet no meta-analysis so far has explored the spatial convergence in the involvement of the two streams in Action. The present meta-analysis (N = 53 fMRI and PET studies) was designed to reveal the specific neural activations associated with Action (i.e., grasping and reaching movements), and the extent to which visual information affects the involvement of the two streams during motor control. Our results provide a comprehensive view of the consistent and spatially convergent neural correlates of Action based on neuroimaging studies conducted over the past two decades. In particular, occipital-temporal areas showed higher activation likelihood in the Vision compared to the No vision condition, but no difference between reach and grasp actions. Frontal-parietal areas were consistently involved in both reach and grasp actions regardless of visual availability. We discuss our results in light of the well-established dual-visual stream model and frame these findings in the context of recent discoveries obtained with advanced fMRI methods, such as multivoxel pattern analysis.

Influences of hand action on the processing of symbolic numbers: A special role of pointing?

Embodied and grounded cognition theories state that cognitive processing is built upon sensorimotor systems. In the context of numerical cognition, support to this framework comes from the interactions between numerical processing and the hand actions of reaching and grasping documented in skilled adults. Accordingly, mechanisms for the processing of object size and location during reach and grasp actions might scaffold the development of mental representations of numerical magnitude. The present study exploited motor adaptation to test the hypothesis of a functional overlap between neurocognitive mechanisms of hand action and numerical processing. Participants performed repetitive grasping of an object, repetitive pointing, repetitive tapping, or passive viewing. Subsequently, they performed a symbolic number comparison task. Importantly, hand action and number comparison were functionally and temporally dissociated, thereby minimizing context-based effects. Results showed that executing the action of pointing slowed down the responses in number comparison. Moreover, the typical distance effect (faster responses for numbers far from the reference as compared to close ones) was not observed for small numbers after pointing, while it was enhanced by grasping. These findings confirm the functional link between hand action and numerical processing, and suggest new hypotheses on the role of pointing as a meaningful gesture in the development and embodiment of numerical skills.

A common neural substrate for number comparison, hand reaching and grasping: A SDM-PSI meta-analysis of neuroimaging studies.

The reliance of number processing on sensorimotor mechanisms involved in hand action has been extensively documented by behavioural studies. Nonetheless, where and how the computations of number and hand action interact in the brain has received limited attention. In this study we investigated the brain networks underlying symbolic number comparison and the hand action of reaching and grasping, capitalizing on functional imaging studies meta-analyzed with the seed-based d mapping with permutation of subject images meta-analytic method (SDM-PSI). The main objective was to test whether and to what extent symbolic number processing recruits the same sensorimotor network involved in the hand action of reaching and grasping. We included 42 studies (756 participants) adopting symbolic number comparison tasks and 58 studies (867 participants) investigating hand reaching and hand grasping. The conjunction analysis of brain networks common to number processing, reaching, and grasping revealed spatial convergence over frontoparietal areas. Specifically, four clusters were identified, in and around the left and right intraparietal sulci, in the left precentral gyrus, and in the supplementary motor area. The degree of overlap was extensive, since the reach/grasp network mostly included the number areas. A qualitative analysis of functional characterization capitalizing on the Neurosynth database depicted a strong multifunctionality of the regions of overlap between numbers and hand action: these brain areas were also associated to a variety of functions within the domains of memory and imagery, visuospatial attention, and language. Overall, these results characterize the neuroanatomical substrate of the interaction between reaching, grasping, and symbolic number comparison.

Effects of attentional shifts along the vertical axis on number processing: An eye-tracking study with optokinetic stimulation.

Previous studies suggest that associations between numbers and space are mediated by shifts of visuospatial attention along the horizontal axis. In this study, we investigated the effect of vertical shifts of overt attention, induced by optokinetic stimulation (OKS) and monitored through eye-tracking, in two tasks requiring explicit (number comparison) or implicit (parity judgment) processing of number magnitude. Participants were exposed to black-and-white stripes (OKS) that moved vertically (upward or downward) or remained static (control condition). During the OKS, participants were asked to verbally classify auditory one-digit numbers as larger/smaller than 5 (comparison task; Exp. 1) or as odd/even (parity task; Exp. 2). OKS modulated response times in both experiments. In Exp.1, upward attentional displacement decreased the Magnitude effect (slower responses for large numbers) and increased the Distance effect (slower responses for numbers close to the reference). In Exp.2, we observed a complex interaction between parity, magnitude, and OKS, indicating that downward attentional displacement slowed down responses for large odd numbers. Moreover, eye tracking analyses revealed an influence of number processing on eye movements both in Exp. 1, with eye gaze shifting downwards during the processing of small numbers as compared to large ones; and in Exp. 2, with leftward shifts after large even numbers (6,8) and rightward shifts after large odd numbers (7,9). These results provide evidence of bidirectional links between number and space and extend them to the vertical dimension. Moreover, they document the influence of visuo-spatial attention on processing of numerical magnitude, numerical distance, and parity. Together, our findings are in line with grounded and embodied accounts of numerical cognition.

Colours + Numbers differs from colours of numbers: cognitive and visual illusions in grapheme-colour synaesthesia.

This study investigates the bi-directionality of synaestesic experience by means of a flanked bisection paradigm in TT, a number-colour synaesthete. Previous studies have shown that bisection is shifted towards the larger digit flanker (e.g., Ranzini & Girelli, 2012). TT and controls performed line bisections with lines flanked by black digits (experiment 1), by TT's photism colours (experiment 2), and by congruently (experiment 3), or incongruently coloured digits (experiment 4). While the results of the control group mainly replicated previous findings, only the colour-digit congruence elicited in TT the larger-digit bias. TT's absence of effects in the other conditions was not due to reduced sensitivity to luminance effects (experiment 5), or to mathematical expertise (experiment 6). We suggest that grapheme-colour synaesthesia might be characterised by a rigid access to semantic representation when the inducer is task-irrelevant.

Hemispatial neglect and serial order in verbal working memory.

Working memory refers to our ability to actively maintain and process a limited amount of information during a brief period of time. Often, not only the information itself but also its serial order is crucial for good task performance. It was recently proposed that serial order is grounded in spatial cognition. Here, we compared performance of a group of right hemisphere-damaged patients with hemispatial neglect to healthy controls in verbal working memory tasks. Participants memorized sequences of consonants at span level and had to judge whether a target consonant belonged to the memorized sequence (item task) or whether a pair of consonants were presented in the same order as in the memorized sequence (order task). In line with this idea that serial order is grounded in spatial cognition, we found that neglect patients made significantly more errors in the order task than in the item task compared to healthy controls. Furthermore, this deficit seemed functionally related to neglect severity and was more frequently observed following right posterior brain damage. Interestingly, this specific impairment for serial order in verbal working memory was not lateralized. We advance the hypotheses of a potential contribution to the deficit of serial order in neglect patients of either or both (1) reduced spatial working memory capacity that enables to keep track of the spatial codes that provide memorized items with a positional context, (2) a spatial compression of these codes in the intact representational space.

The consonant/vowel pattern determines the structure of orthographic representations in the left fusiform gyrus.

Recent findings demonstrated readers' sensitivity to the distinction between consonant and vowel letters. Especially, the way consonants and vowels are organised within written words determines their perceptual structure. The present work attempted to overcome two limitations of previous studies by examining the neurophysiological correlates of this perceptual structure through magnetoencephalography (MEG). One aim was to establish that the extraction of vowel-centred units takes place during early stages of processing. The second objective was to confirm that the vowel-centred structure pertains to the word recognition system and may constitute one level in a hierarchy of neural detectors coding orthographic strings. Participants performed a cross-case matching task in which they had to judge pairs of stimuli as identical or different. The critical manipulation concerned pairs obtained by transposing two letters, so that the vowel-centred structure was either preserved (FOUVERT-fovuert, two vowel letter clusters) or modified (BOUVRET-bovuret). Mismatches were detected faster when the structure was modified. This effect was associated with a significant difference in evoked neuromagnetic fields extending from 129 to 239 msec after the stimulation. Source localization indicated a significant effect in the visual word form area around 200 msec. The results confirm the hypothesis that the vowel-centred structure is extracted during the early phases of letter string processing and that it is encoded in left fusiform regions devoted to visual word recognition.

Contribution of visuospatial attention, short-term memory and executive functions to performance in number interval bisection.

Number interval bisection consists of estimating the mid-number within a pair (1-9=>5). Healthy adults and right-brain damage patients can show biased performance in this task, underestimating and overestimating the mid-number, respectively. The role of visuospatial attention during this task, and its interplay with other cognitive abilities (e.g., working memory) is still object of debate. In this study we explored the relation between visuospatial attention and individual differences in working memory and executive functions during number interval bisection. To manipulate the deployment of visuospatial attention, healthy participants tracked a dot moving to the left or moving to the right while bisecting numerical intervals. We also collected information concerning verbal and visuospatial short-term memory span, and concerning verbal and visuospatial fluency scores. Beside replicating what is typically observed in this task (e.g., underestimation bias), a correlation was observed between verbal short-term memory and bisection bias, and an interesting relation between performance in the number interval bisection, verbal short-term memory, and visuospatial attention. Specifically, performance of those participants with low verbal span was affected by the direction of the moving dot, underestimating at a larger extent when the dot moved leftward than rightward. Finally, it was also observed that participants' verbal fluency ability contributed in the generation of biases in the numerical task. The finding of the involvement of abilities belonging to the verbal domain contributes to unveil the multi-componential nature of number interval bisection. Considering the debate on the nature of number interval bisection and its use in the clinical assessment of deficits following brain damage, this finding may be interesting also from a clinical perspective.

Order information in verbal working memory shifts the subjective midpoint in both the line bisection and the landmark tasks.

A largely substantiated view in the domain of working memory is that the maintenance of serial order is achieved by generating associations of each item with an independent representation of its position, so-called position markers. Recent studies reported that the ordinal position of an item in verbal working memory interacts with spatial processing. This suggests that position markers might be spatial in nature. However, these interactions were so far observed in tasks implying a clear binary categorization of space (i.e., with left and right responses or targets). Such binary categorizations leave room for alternative interpretations, such as congruency between non-spatial categorical codes for ordinal position (e.g., begin and end) and spatial categorical codes for response (e.g., left and right). Here we discard this interpretation by providing evidence that this interaction can also be observed in a task that draws upon a continuous processing of space, the line bisection task. Specifically, bisections are modulated by ordinal position in verbal working memory, with lines bisected more towards the right after retrieving items from the end compared to the beginning of the memorized sequence. This supports the idea that position markers are intrinsically spatial in nature.

Voluntary eye movements direct attention on the mental number space.

Growing evidence suggests that orienting visual attention in space can influence the processing of numerical magnitude, with leftward orienting speeding up the processing of small numbers relative to larger ones and the converse for rightward orienting. The manipulation of eye movements is a convenient way to direct visuospatial attention, but several aspects of the complex relationship between eye movements, attention orienting and number processing remain unexplored. In a previous study, we observed that inducing involuntary, reflexive eye movements by means of optokinetic stimulation affected number processing only when numerical magnitude was task relevant (i.e., during magnitude comparison, but not during parity judgment; Ranzini et al., in J Cogn Psychol 27, 459-470, (2015). Here, we investigated whether processing of task-irrelevant numerical magnitude can be modulated by voluntary eye movements, and whether the type of eye movements (smooth pursuit vs. saccades) would influence this interaction. Participants tracked with their gaze a dot while listening to a digit. The numerical task was to indicate whether the digit was odd or even through non-spatial, verbal responses. The dot could move leftward or rightward either continuously, allowing tracking by smooth pursuit eye movements, or in discrete steps across a series of adjacent locations, triggering a sequence of saccades. Both smooth pursuit and saccadic eye movements similarly affected number processing and modulated response times for large numbers as a function of direction of motion. These findings suggest that voluntary eye movements redirect attention in mental number space and highlight that eye movements should play a key factor in the investigation of number-space interactions.

Perceiving object dangerousness: an escape from pain?

A variety of studies showed that participants are facilitated when responding to graspable objects, while it has not been fully investigated what happens during interactions with graspable objects that are potentially dangerous. The present study focuses on the mechanisms underlying the processing of dangerous objects. In two experiments, we adopted a paradigm that has never been employed in this context, a bisection task. The line was flanked by objects belonging to different categories. We explored the sensitivity to the distinction between neutral and dangerous objects, by measuring whether the performance was biased toward a specific object category. In Experiment 1 both teenagers and adults bisected lines flanked by dangerous and neutral graspable objects, and they misperceived the line midpoint toward the neutral graspable object or, stated differently, on the opposite side of the dangerous graspable object. In Experiment 2 adults bisected lines flanked by dangerous and neutral objects matched on graspability (both graspable and ungraspable, Experiment 2a), or by graspable and ungraspable objects matched on dangerousness (both neutral and dangerous, Experiment 2b). Results confirmed the finding of Experiment 1, but also indicated that participants misperceived the line midpoint toward the ungraspable object when it was presented, being it dangerous or not. This evidence demonstrated sensitivity to object dangerousness maintained across lifespan. The emergence of aversive affordances evoked by dangerous graspable objects strenghtens the importance to consider graspability in the investigation of dangerous objects. Possible neural mechanisms involved in the processing of dangerous graspable objects are discussed.

Influence of numerical magnitudes on the free choice of an object position.

The link between numerical magnitude and mechanisms of spatial orienting has been underlined in an increasing number of studies. Similarly, the relationship between numerical magnitude and grasping actions has started to be investigated. The present study focuses on the influence of numerical magnitude processing in the free choice of the position of an object. Participants were presented with a digit (1-9 without 5) and were required to decide whether it was smaller or larger than 5. Then, they had to grasp a small cube and change its position before vocally responding "higher" or "lower". Results showed that in the initial phase of the grasp movement, the grip aperture was modulated by the numerical magnitude. Moreover, participants shifted the position of the cube more leftward with smaller digits compared with larger ones, and they tended to position the object closer to themselves with smaller digits compared with larger ones. These results extend the previous findings indicating that the processing of magnitude is tightly related to the mechanisms of spatial orienting that subserve action execution.

Exploiting illusory effects to disclose similarities in numerical and luminance processing.

Recent studies have suggested that numerical and physical magnitudes are similarly processed by a generalized magnitude system. The present study investigates the number-luminance interaction, taking advantage of illusory effects in a cued line bisection task with numerical or nonnumerical flankers and varying levels of luminance. The results showed that both dimensions influenced bisection performance. Whereas numbers (Experiment 1) induced a systematic shift of the subjective midpoint toward the larger digit, luminance (Experiment 2) modulated the bisection performance toward the darker flanker. By combining these two illusions (Experiments 3 and 4), the two dimensions interfered with each other. This pattern of results suggests overlapping representations for physical and numerical magnitudes and highlights the value of illusory effects in cognitive research.

Graspable objects shape number processing.

The field of numerical cognition represents an interesting case for action-based theories of cognition, since number is a special kind of abstract concept. Several studies have shown that within the parietal lobes adjacent neural regions code numerical magnitude and grasping-related information. This anatomical proximity between brain areas involved in number and sensorimotor processes may account for interactions between numerical magnitude and action. In particular, recent studies have demonstrated a causal role of action perception on numerical magnitude processing. If objects are represented in terms of actions (affordances), the causal role of action on number processing should extend to the case of objects affordances. This study investigates the relationship between numbers and objects affordances in two experiments, without (Experiment 1) or with (Experiment 2) the requirement of an action (i.e., participants were asked to hold an object in their hands during the task). The task consisted in repeating aloud the odd or even digit within a pair depending on the type of the preceding or following object. Order of presentation (object-number vs. number-object), Object type (graspable vs. ungraspable), Object size (small vs. large), and Numerical magnitude (small vs. large) were manipulated for each experiment. Experiment 1 showed a facilitation - in terms of quicker responses - for graspable over ungraspable objects preceded by numbers, and an effect of numerical magnitude after the presentation of graspable objects. Experiment 2 demonstrated that the action execution enhanced overall the sensitivity to numerical magnitude, and that at the same time it interfered with the effects of objects affordances on number processing. Overall, these findings demonstrate that numbers and graspable objects are strongly interrelated, supporting the view that abstract concepts may be grounded in the motor experience.

With hands I do not centre! Action- and object-related effects of hand-cueing in the line bisection.

A variety of studies have shown action- and object-related visuo-motor priming in behavioural tasks. The peculiarity of this study lies in using a hand-cued line bisection task to explore the main properties of the motor effects evoked by action and object processing. In five experiments it is shown that flanking a line (thin vs. thick line) with images of hands (biological vs. non-biological hand) representing different actions (power vs. precision grip) biases performance towards the action more compatible with the object (power grip - thick line, precision grip - thin line). This effect is larger for the precision grip than for the power grip suggesting a functional rather than manipulative activation. In addition, the effect is larger for the biological than for the non-biological hand. We suggest that this paradigm could be potentially useful for neuropsychological studies as well as for addressing unsolved issues of embodied theories of cognition.

What information is critical to elicit interference in number-form synaesthesia?

Numerous behavioural paradigms have demonstrated a close connection between numbers and space, suggesting that numbers may be represented on an internal mental number line. For example, in the Spatial Numerical Association of Response Codes (SNARC) effect, reaction times are faster for left-sided responses to smaller numbers and for right-sided responses to larger numbers. One valuable tool for exploring such numerical-spatial interactions is the study of number-form synaesthesia, in which participants report vivid, automatic associations of numerical and other ordinal sequences with precise, idiosyncratic, spatial layouts. Recent studies have demonstrated the influence of synaesthetic spatial experiences on behavioural number tasks. The aim of the present study is to further explore these internal spatial representations by presenting a case-study of an unusual synaesthete, DG, who reports highly detailed representations not only of numerical sequences (including representations of negative and Roman numbers), but also different representations for other ordinal sequences, such as time sequences (months, days and hours), the alphabet, financial sequences and different units of measure (e.g., kilograms, kilometres and degrees). Here, we describe DG's synaesthetic experiences and a series of behavioural experiments on numerical tasks concerning the automaticity of this phenomenon. DG's performance on number comparison and cued-detection tasks was modulated by his synaesthetic mental representation for the numerical sequence, such that his reaction times were slower when the spatial layout was incompatible with the orientation of his mental number line. We found that the spatial presentation of stimuli, rather than the implicit or explicit access to numerosity required by tasks, was essential to eliciting DG's number-forms. These results are consistent with previous studies and suggest that numerical-spatial interactions may be most strongly present in synaesthetes when both numerical and spatial information are explicitly task-relevant, consistent with a growing body of literature regarding the SNARC and other related effects.

Neural mechanisms of attentional shifts due to irrelevant spatial and numerical cues.

Studies of endogenous (cue-directed) attention have traditionally assumed that such shifts must be volitional. However, recent behavioural experiments have shown that participants make automatic endogenous shifts of attention when presented with symbolic cues that are systematically associated with particular spatial directions, such as arrows and numerals, even when such cues were not behaviourally relevant. Here we used event-related potentials (ERPs) to test whether these automatic shifts of attention use the same mechanisms as volitional shifts of attention. We presented participants with non-predictive (50% valid) task-irrelevant arrow and numeral cues while measuring cue- and target-locked ERPs. Although the cues were task-irrelevant, they elicited attention-related ERP components previously found in studies that used informative and/or task-relevant cues. These findings further substantiate the dissociation between endogenous and volitional attentional control, and suggest that the same fronto-parietal networks involved in volitional shifts of attention are also involved in reflexive endogenous shifts of attention.