A functional role for oculomotor preparation in mental arithmetic evidenced by the abducted eye paradigm.

Solving subtraction and addition problems is accompanied by spontaneous leftward and rightward gaze shifts, respectively. These shifts have been related to attentional processes involved in mental arithmetic, but whether these processes induce overt attentional shifts mediated by the activation of the motor programs underlying lateral eye movements or covert shifts only is still unknown. Here, we used the abducted eye paradigm to selectively disrupt activation of the oculomotor system and prevent oculomotor preparation, which affects overt but not covert attentional shifts. Participants had to mentally solve addition and subtraction problems while fixating a screen positioned either in front of them or laterally to their left or right such that they were physically unable to programme and execute saccades further into their temporal field while they still could do so in their nasal field. In comparison to the frontal condition, rightward eye abduction impaired additions (with carrying), and leftward eye abduction impaired subtractions (with borrowing) showing that at least some arithmetic problems rely on processes dedicated to overt attentional shifts. We propose that when solving arithmetic problems requires procedures such as carrying and borrowing, oculomotor mechanisms operating on a mental space transiently built in working memory are recruited to represent one numerical magnitude in relation to another (e.g. the first operand and the result).

Selective interference of hand posture with grasping capability estimation.

Previous studies have shown that judgments about how one would perform an action are affected by the current body posture. Hence, judging one's capability to grasp an object between index and thumb is influenced by their aperture at the time of the judgment. This finding can be explained by a modification of the internal representation of one's hand through the effect of sensorimotor input. Alternatively, the influence of grip aperture might be mediated by a response congruency effect, so that a "less" vs. "more" open grip would bias the judgment toward a "less" vs. "more" capable response. To specify the role of sensorimotor input in prospective action judgments, we asked participants to estimate their capability to grasp circles between index and thumb while performing a secondary task that requires them to squeeze a ball with these two fingers (precision grip) or with a different hand configuration (palm grip). Experiment 1 showed that participants underestimated their grasping capability when the squeezing task involved the same grip as the judged action (precision grip) and their estimates were bound to the relative size of objects as revealed by size-contrast illusions (Ebbinghaus). Experiment 2 showed that the grip reduction caused by the squeezing task also interfered with the discrimination of large numbers in magnitude judgments, but this incongruency effect was only observed for the palm grip. The dissociated effects of the two grips in graspability and numerical judgments indicate that sensorimotor input may affect the perceived ability to grasp objects, independently of response congruency, by modifying the representation of the hand in action.

Shifting attention in visuospatial short-term memory does not require oculomotor planning: Insight from congenital gaze paralysis.

Attention allows pieces of information stored in visuospatial short-term memory (VSSTM) to be selectively processed. Previous studies showed that shifts of attention in VSSTM in response to a retro-cue are accompanied by eye movements in the direction of the position of the memorized item although there is nothing left to look at. This finding raises the possibility that shifts of attention in VSSTM are underpinned by mechanisms originally involved in the planning and control of eye movements. To explore this possibility, we investigated the ability of an individual with congenital horizontal gaze paralysis (HGP2) to shift her attention horizontally or vertically toward a memorized item within VSSTM using a retro-cue paradigm. As efficient oculomotor programming is not innate but requires some trial and error learning and adaptation to develop, congenital paralysis prevents this development. Consequently, if shifts of attention in VSSTM rely on the same mechanisms as those supporting the programming of eye movements, then horizontal congenital gaze paralysis should necessarily prevent typical retro-cueing effect in the paralyzed axis. At odds with this prediction, HGP2 showed a typical retro-cueing effect in her paralyzed axis. This original finding indicates that selecting an item within VSSTM does not depend on the ability to program a saccade.

Role of the fronto-parietal cortex in prospective action judgments.

Prospective judgments about one's capability to perform an action are assumed to involve mental simulation of the action. Previous studies of motor imagery suggest this simulation is supported by a large fronto-parietal network including the motor system. Experiment 1 used fMRI to assess the contribution of this fronto-parietal network to judgments about one's capacity to grasp objects of different sizes between index and thumb. The neural network underlying prospective graspability judgments overlapped the fronto-parietal network involved in explicit motor imagery of grasping. However, shared areas were located in the right hemisphere, outside the motor cortex, and were also activated during perceptual length judgments, suggesting a contribution to object size estimate rather than motor simulation. Experiment 2 used TMS over the motor cortex to probe transient excitability changes undetected with fMRI. Results show that graspability judgments elicited a selective increase of excitability in the thumb and index muscles, which was maximal before the object display and intermediate during the judgment. Together, these findings suggest that prospective action judgments do not rely on the motor system to simulate the action per se but to refresh the memory of one's maximal grip aperture and facilitate its comparison with object size in right fronto-parietal areas.

Exogenous covert shift of attention without the ability to plan eye movements.

The automatic allocation of attention to a salient stimulus in the visual periphery (e.g., a traffic light turning red) while maintaining fixation elsewhere (e.g., on the car ahead) is referred to as exogenous covert shift of attention (ECSA). An influential explanation is that ECSA results from the programming of a saccadic eye movement toward the stimulus of interest [1,2], although the actual movement may be withheld if needed. In this paper, however, we report evidence of ECSA in the paralyzed axis of three individuals with either horizontal or vertical congenital gaze paralysis, including for stimuli appearing at locations that cannot be foveated through head movements. This demonstrates that ECSA does not require programming either eye or head movements and calls for a re-examination of the oculomotor account.

Spatial biases in mental arithmetic are independent of reading/writing habits: Evidence from French and Arabic speakers.

The representation of numbers in human adults is linked to space. In Western cultures, small and large numbers are associated respectively with the left and right sides of space. An influential framework attributes the emergence of these spatial-numerical associations (SNAs) to cultural factors such as the direction of reading and writing, because SNAs were found to be reduced or inverted in right-to-left readers/writers (e.g., Arabic, Farsi, or Hebrew speakers). However, recent cross-cultural and animal studies cast doubt on the determining role of reading and writing directions on SNAs. In this study, we assessed this role in mental arithmetic, which requires explicit number manipulations and has revealed robust leftward or rightward biases in Western participants. We used a temporal order judgement task in French and Arabic speakers, two languages that have opposite reading/writing directions. Participants had to solve subtraction and addition problems presented auditorily while at the same time determining which of a left or right visual target appeared first on a screen. The results showed that the right target was favoured more often when solving additions than when solving subtractions both in the French- (n = 31) and Arabic-speaking (n = 25) groups. This was true even in Arabic-speaking participants whose preference for ordering of various series of numerical and non-numerical stimuli went from right to left (n = 10). These results indicate that SNAs in mental arithmetic cannot be explained by the direction of reading/writing habits and call for a reconsideration of current models to acknowledge the pervasive role of biological factors in SNAs in adults.

Semantic associations between arithmetic and space: Evidence from temporal order judgements.

Spatial biases associated with subtraction or addition problem solving are generally considered as reflecting leftward or rightward attention shifts along a mental numerical continuum, but an alternative hypothesis not implying spatial attention proposes that the operator (plus or minus sign) may favour a response to one side of space (left or right) because of semantic associations. We tested these two accounts in a series of temporal order judgement experiments that consisted in the auditory presentation of addition or subtraction problems followed 200 ms (Experiments 1-2) or 800 ms (Experiment 3) later by the display of two lateralized targets in close temporal succession. To dissociate the side where the operation first brought their attention from the side they had to respond to, we asked participants to report which of the left or right target appeared first or last on screen. Under the attention-orienting account, addition should elicit more rightward responses than subtraction when participants have to focus on the first target, but more leftward responses when they have to focus on the last target, because the latter is opposite to the side where the operation first brought their attention. Under the semantic account, addition should elicit more rightward responses than subtraction, no matter the focus is on the first or last target, because participants should systematically favour the side conceptually linked to the operator. The results of the three experiments converge to indicate that, in lateralized target detection tasks, the spatial biases induced by arithmetic operations stem from semantic associations.

Effect of perceived length on numerosity estimation: Evidence from the Müller-Lyer illusion.

Previous studies showed that the magnitude information conveyed by sensory cues, such as length or surface, influences the ability to compare the numerosity of sets of objects. However, the perceptual nature of this representation and how it interacts with the processes involved in numerical judgements remain unclear. This study aims to address these issues by studying the interference of length on numerosity under different perceptual and response conditions. The first experiment shows that the influence of length does not depend on the actual length but on subjective values reflecting the way length is perceived in a given visual context. The Müller-Lyer illusion was used to manipulate the perceived length of two dot arrays independently of their actual length. When the length of two dot arrays was equal but perceived as different due to the illusion, participants erroneously reported differences in the number of dots contained in each array, evidencing a similar effect of Müller-Lyer illusion on length and numerosity comparison. This finding was replicated in a second experiment where participants had to give a verbal estimate of the number of dots contained in a given array, thereby eliminating the choice between a small or large response. Compared with a neutral condition, estimations were systematically larger than the actual number of dots as the illusory length increased. These results demonstrate that the illusory-induced experience of length influences numerosity estimation over and beyond objective cues and that this influence is not a response selection bias.

Visual illusions modify object size estimates for prospective action judgements.

How does the eye guide the hand in an ever-changing world? The perception-action model posits that visually-guided actions rely on object size estimates that are computed from an egocentric perspective independently of the visual context. Accordingly, adjusting grip aperture to object size should be resistant to illusions emerging from the contrast between a target and surrounding elements. However, experimental studies gave discrepant results that have remained difficult to explain so far. Visual and proprioceptive information of the acting hand are potential sources of ambiguity in previous studies because the on-line corrections they allow may contribute to masking the illusory effect. To overcome this problem, we investigated the effect on prospective action judgements of the Ebbinghaus illusion, a visual illusion in which the perceived size of a central circle varies according to the size of surrounding circles. Participants had to decide whether they thought they would be able to grasp the central circle of an Ebbinghaus display between their index finger and thumb, without moving their hands. A control group had to judge the size of the central circle relative to a standard. Experiment 1 showed that the illusion affected perceptual and grasping judgements similarly. We further investigated the interaction between visual illusions and grip aperture representation by examining the effect of concurrent motor tasks on grasping judgements. We showed that participants underestimated their ability to grasp the circle when they were squeezing a ball between their index finger and thumb (Experiment 2), whereas they overestimated their ability when their fingers were spread apart (Experiment 3). The illusion also affected the grasping judgement task and modulated the interference of the squeezing movement, with the illusion of largeness enhancing the underestimation of one's grasping ability observed in Experiment 2. We conclude that visual context and body posture both influence action anticipation, and that perception and action support each other.

Time course of overt attentional shifts in mental arithmetic: Evidence from gaze metrics.

Processing numbers induces shifts of spatial attention in probe detection tasks, with small numbers orienting attention to the left and large numbers to the right side of space. This has been interpreted as supporting the concept of a mental number line with number magnitudes ranging from left to right, from small to large numbers. Recently, the investigation of this spatial-numerical link has been extended to mental arithmetic with the hypothesis that solving addition or subtraction problems might induce attentional displacements, rightward or leftward, respectively. At the neurofunctional level, the activations elicited by the solving of additions have been shown to resemble those induced by rightward eye movements. However, the possible behavioural counterpart of these activations has not yet been observed. Here, we investigated overt attentional shifts with a target detection task primed by addition and subtraction problems (2-digit ± 1-digit operands) in participants whose gaze orientation was recorded during the presentation of the problems and while calculating. No evidence of early overt attentional shifts was observed while participants were hearing the first operand, the operator or the second operand, but they shifted their gaze towards the right during the solving step of addition problems. These results show that gaze shifts related to arithmetic problem solving are elicited during the solving procedure and suggest that their functional role is to access, from the first operand, the representation of the result.

Time perception is not for the faint-hearted? Physiological arousal does not influence duration categorisation.

Distortions of duration perception provoked by emotion-induced arousal changes are explained by modifications of an internal clock pace. Yet, uncertainty still abounds regarding whether changes of arousal induced by physical exercise yield such temporal distortions. Here, we report two experiments aiming to test separately the impact of, on the one hand, a physical induction of arousal and, on the other hand, a task delay on duration categorisation. In Experiment 1, participants performed a duration categorisation task before and after heart-rate manipulation (increase, decrease, or no change). Duration overestimation was observed after HR manipulation, irrespective of the condition, implying that changes of physiological arousal alone cannot explain the temporal bias observed. In Experiment 2, participants performed the duration task twice without delay or arousal manipulation, and no overestimation was observed. Together, these results suggest that the overestimation observed in the context of a delayed duration categorisation task is related to a distortion of memorised standard durations caused by time lag rather than by a physiological arousal effect.

Developmental Dyscalculia in Adults: Beyond Numerical Magnitude Impairment.

Numerous studies have tried to identify the core deficit of developmental dyscalculia (DD), mainly by assessing a possible deficit of the mental representation of numerical magnitude. Research in healthy adults has shown that numerosity, duration, and space share a partly common system of magnitude processing and representation. However, in DD, numerosity processing has until now received much more attention than the processing of other non-numerical magnitudes. To assess whether or not the processing of non-numerical magnitudes is impaired in DD, the performance of 15 adults with DD and 15 control participants was compared in four categorization tasks using numerosities, lengths, durations, and faces (as non-magnitude-based control stimuli). Results showed that adults with DD were impaired in processing numerosity and duration, while their performance in length and face categorization did not differ from controls' performance. Our findings support the idea of a nonsymbolic magnitude deficit in DD, affecting numerosity and duration processing but not length processing.

Shifts of spatial attention underlie numerical comparison and mental arithmetic: Evidence from a patient with right unilateral neglect.

OBJECTIVES: Recent findings suggest that mental arithmetic involves shifting attention on a mental continuum in which numbers would be ordered from left to right, from small to large numbers, with addition and subtraction causing rightward or leftward shifts, respectively. Neuropsychological data showing that brain-damaged patients with left neglect experience difficulties in solving subtraction but not addition problems support this hypothesis. However, the reverse dissociation is needed to establish the causal role of spatial attention in mental arithmetic. METHOD: R.H., a 65-year-old left-brain-damaged patient exhibiting right unilateral visuospatial and representational neglect, was tested with various numerical tasks including numerical comparison, arithmetic problem-solving, and numerical interval bisection. RESULTS: In numerical comparison, R.H. showed a selective response latency increase when judging numbers larger than the references whereas his performance was normal for numbers smaller than the references. In the arithmetic task, R.H. was impaired in solving addition but not subtraction problems. In contrast, performance in number bisection shows a deviation toward larger numbers. CONCLUSION: These results establish a double dissociation between subtraction and addition solving in patients with left versus right neglect and demonstrate clear evidence that attentional mechanisms are crucial for mental arithmetic. We suggest that attention shifts are involved whenever a number is represented relative to another on a mental continuum, be it during numerical comparison or arithmetic problem-solving. R.H.'s performance in numerical interval bisection indicates that this task involves processes that are distinct from those involved in number comparison and mental arithmetic. (PsycINFO Database Record

Impact of optokinetic stimulation on mental arithmetic.

Solving arithmetic problems has been shown to induce shifts of spatial attention, subtraction problems orienting attention to the left side, and addition problems to the right side of space. At the neurofunctional level, the activations elicited by the solving of arithmetical problems resemble those elicited by horizontal eye movements. Whether overt orientation of attention (i.e., eye movements) can be linked to the solving procedure is, however, still under debate. In the present study, we used optokinetic stimulation (OKS) to trigger automatic eye movements to orient participants' overt attention to the right or to the left of their visual field while they were solving addition or subtraction problems. The results show that, in comparison to leftward OKS and a control condition, rightward OKS facilitates the solving of addition problems that necessitate a carrying procedure. Subtraction solving was unaffected by leftward or rightward OKS. These results converge with previous findings to show that attentional shifts are functionally related to mental arithmetic processing.

Influence of finger and mouth action observation on random number generation: an instance of embodied cognition for abstract concepts.

Numerical magnitude and specific grasping action processing have been shown to interfere with each other because some aspects of numerical meaning may be grounded in sensorimotor transformation mechanisms linked to finger grip control. However, how specific these interactions are to grasping actions is still unknown. The present study tested the specificity of the number-grip relationship by investigating how the observation of different closing-opening stimuli that might or not refer to prehension-releasing actions was able to influence a random number generation task. Participants had to randomly produce numbers after they observed action stimuli representing either closure or aperture of the fingers, the hand or the mouth, or a colour change used as a control condition. Random number generation was influenced by the prior presentation of finger grip actions, whereby observing a closing finger grip led participants to produce small rather than large numbers, whereas observing an opening finger grip led them to produce large rather than small numbers. Hand actions had reduced or no influence on number production; mouth action influence was restricted to opening, with an overproduction of large numbers. Finally, colour changes did not influence number generation. These results show that some characteristics of observed finger, hand and mouth grip actions automatically prime number magnitude, with the strongest effect for finger grasping. The findings are discussed in terms of the functional and neural mechanisms shared between hand actions and number processing, but also between hand and mouth actions. The present study provides converging evidence that part of number semantics is grounded in sensory-motor mechanisms.

Enhancing duration processing with parietal brain stimulation.

Numerosity and duration are thought to share common magnitude-based mechanisms in brain regions including the right parietal and frontal cortices like the supplementary motor area, SMA. Numerosity and duration are, however, also different in several intrinsic features. For instance, in a quantification context, numerosity is known for being more automatically accessed than temporal events, and durations are by definition sequential whereas numerosity can be both sequential and simultaneous. Moreover, numerosity and duration processing diverge in terms of their neuronal correlates. Whether these observed neuronal specificities can be accounted for by differences in automaticity or presentation-mode is however not clear. To address this issue, we used brain stimulation (transcranial random noise stimulation, tRNS) to the right parietal cortex or the SMA combined with experimental stimuli differing in their level of automaticity (numerosity and duration) and presentation mode (sequential or simultaneous). Compared to a no stimulation group, performance changed in duration but not in numerosity categorisation following right parietal but not SMA stimulation. These results indicate that the right parietal cortex is critical for duration processing, and suggest that tRNS has a stronger effect on less automatic processes such as duration.

Duration and numerical estimation in right brain-damaged patients with and without neglect: Lack of support for a mental time line.

Previous studies have shown that left neglect patients are impaired when they have to orient their attention leftward relative to a standard in numerical comparison tasks. This finding has been accounted for by the idea that numerical magnitudes are represented along a spatial continuum oriented from left to right with small magnitudes on the left and large magnitudes on the right. Similarly, it has been proposed that duration could be represented along a mental time line that shares the properties of the number continuum. By comparing directly duration and numerosity processing, this study investigates whether or not the performance of neglect patients supports the hypothesis of a mental time line. Twenty-two right brain-damaged patients (11 with and 11 without left neglect), as well as 11 age-matched healthy controls, had to judge whether a single dot presented visually lasted shorter or longer than 500 ms and whether a sequence of flashed dots was smaller or larger than 5. Digit spans were also assessed to measure verbal working memory capacities. In duration comparison, no spatial-duration bias was found in neglect patients. Moreover, a significant correlation between verbal working memory and duration performance was observed in right brain-damaged patients, irrespective of the presence or absence of neglect. In numerical comparison, only neglect patients showed an enhanced distance effect for numerical magnitude smaller than the standard. These results do not support the hypothesis of the existence of a mental continuum oriented from left to right for duration. We discuss an alternative account to explain the duration impairment observed in right brain-damaged patients.

Interference of lateralized distractors on arithmetic problem solving: a functional role for attention shifts in mental calculation.

Solving arithmetic problems has been shown to induce shifts of spatial attention in simple probe-detection tasks, subtractions orienting attention to the left side and additions to the right side of space. Whether these attentional shifts constitute epiphenomena or are critically linked to the calculation process is still unknown. In the present study, we investigate participants' performance on addition and subtraction solving while they have to detect central or lateralized targets. The results show that lateralized distractors presented in the hemifield congruent to the operation to be solved interfere with arithmetical solving: participants are slower to solve subtractions or additions when distractors are located on the left or on the right, respectively. These results converge with previous data to show that attentional shifts underlie not only number processing but also mental arithmetic. They extend them as they reveal the reverse effect of the one previously reported by showing that inducing attention shifts interferes with the solving of arithmetic problems. They also demonstrate that spatial attentional shifts are part of the calculation procedure of solving mentally arithmetic problems. Their functional role is to access, from the first operand, the representation of the result in a direction congruent to the operation.

Evidence for the embodiment of space perception: concurrent hand but not arm action moderates reachability and egocentric distance perception.

The perception of reachability (i.e., whether an object is within reach) relies on body representations and action simulation. Similarly, egocentric distance estimation (i.e., the perception of the distance an object is from the self) is thought to be partly derived from embodied action simulation. Although motor simulation is important for both, it is unclear whether the cognitive processes underlying these behaviors rely on the same motor processes. To investigate this, we measured the impact of a motor interference dual-task paradigm on reachability judgment and egocentric distance estimation, while allocentric length estimation (i.e., how distant two stimuli are from each other independent from the self) was used as a control task. Participants were required to make concurrent actions with either hand actions of foam ball grip squeezing or arm actions of weight lifting, or no concurrent actions. Results showed that concurrent squeeze actions significantly slowed response speed in the reachability judgment and egocentric distance estimation tasks, but that there was no impact of the concurrent actions on allocentric length estimation. Together, these results suggest that reachability and distance perception, both egocentric perspective tasks, and in contrast to the allocentric perspective task, involve action simulation cognitive processes. The results are discussed in terms of the implication of action simulation when evaluating the position of a target relative to the observer's body, supporting an embodied view of spatial cognition.

Influence of biological kinematics on abstract concept processing.

During a random number generation task, human beings tend to produce more small numbers than large numbers. However, this small number bias is modulated when motor behaviour, such as a turn of the head, is performed during the random number generation task. This result fits with the finding that number representation is linked to laterally oriented actions, with small- and large-magnitude numbers generally linked to movement towards the left or the right side of space, respectively. To test whether this number-space association is specific to human motor behaviours or extends to any type of laterally oriented movements, we assessed whether the presentation of biological or nonbiological leftward or rightward movement affected a subsequent random number generation task. Biological and nonbiological movements were obtained by varying the kinematic parameters of the movements. Biological kinematics represented the tangential velocity actually observed in a human pointing movement; nonbiological kinematics represented equivalent movements but with an inverse tangential velocity along the path. The results show that only the observation of biological movements induces a space-number bias whereas observing nonbiological movements does not. This finding is the first evidence of a link between a biological marker and the semantic representation of a concept as abstract as number.