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.

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.

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.

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.

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.

Does chocolate consumption really boost Nobel Award chances? The peril of over-interpreting correlations in health studies.

A correlation observed between chocolate consumption and the number of Nobel laureates has recently led to the suggestion that consuming more chocolate would increase the number of laureates due to the beneficial effects of cocoa-flavanols on cognitive functioning. We demonstrate that this interpretation is disproved when other flavanol-rich nutriment consumption is considered. We also show the peril of over-interpreting correlations in nutrition and health research by reporting high correlations between the number of Nobel laureates and various other measures, whether cogently related or not. We end by discussing statistical alternatives that may overcome correlation shortcomings.

Numbers reorient visuo-spatial attention during cancellation tasks.

Numbers induce shifts of spatial attention on the left or the right sides of external space as a function of their magnitude. However, whether this number-space association is restricted to the linear horizontal extensions, or extends to the whole visual scene, is still an open question. This study investigates, by means of a cancellation paradigm, the influence of numerical magnitude during scanning tasks in which participants freely explore complex visual scenes unconstrained towards either the horizontal or the vertical unidimensional axes. Five cancellation tasks were adapted in which Arabic digits were used as targets or distracters, in structured (lines and columns) or unstructured visual displays, with a smaller (2 or 3 types of distracters) or larger (10 or more types of distracters) sets of stimuli. Results show that the participants' hits distribution was a function of number magnitude: shifted on the left for small and on the right for large numbers. This effect was maximised when numerical cues were sparse, randomly arranged and, critically, irrelevant to the task. Overall, this study provides novel evidence from visuo-spatial exploratory cancellation tasks for an attentional shift induced by number magnitude.

Common substrate for mental arithmetic and finger representation in the parietal cortex.

The history of mathematics provides several examples of the use of fingers to count or calculate. These observations converge with developmental data showing that fingers play a critical role in the acquisition of arithmetic knowledge. Further studies evidenced specific interference of finger movements with arithmetic problem solving in adults, raising the question of whether or not finger and number manipulations rely on common brain areas. In the present study, functional magnetic resonance imaging (fMRI) was used to investigate the possible overlap between the brain areas involved in mental arithmetic and those involved in finger discrimination. Solving subtraction and multiplication problems was found to increase cerebral activation bilaterally in the horizontal part of the intraparietal sulcus (hIPS) and in the posterior part of the superior parietal lobule (PSPL). Finger discrimination was associated with increased activity in a bilateral occipito-parieto-precentral network extending from the extrastriate body area to the primary somatosensory and motor cortices. A conjunction analysis showed common areas for mental arithmetic and finger representation in the hIPS and PSPL bilaterally. Voxelwise correlations further showed that finger discrimination and mental arithmetic induced a similar pattern of activity within the parietal areas only. Pattern similarity was more important for the left than for the right hIPS and for subtraction than for multiplication. These findings provide the first evidence that the brain circuits involved in finger representation also underlie arithmetic operations in adults.

A common right fronto-parietal network for numerosity and duration processing: an fMRI study.

Numerosity and duration processing have been modeled by a functional mechanism taking the form of an accumulator working under two different operative modes. Separate investigations of their cerebral substrates have revealed partly similar patterns of activation, mainly in parietal and frontal areas. However, the precise cerebral implementation of the accumulator model within these areas has not yet been directly assessed. In this study, we asked participants to categorize the numerosity of flashed dot sequences or the duration of single dot displays, and we used functional magnetic resonance imaging (fMRI) to examine the common neural correlates of these processes. The results reveal a large right-lateralized fronto-parietal network, including the intraparietal sulcus (IPS) and areas in the precentral, middle and superior frontal gyri, which is activated by both numerosity and duration processing. Complementary psychophysiological interaction (PPI) analyses show a functional connectivity between the right IPS and the frontal areas in both tasks, whereas the right IPS was functionally connected to the left IPS and the right precentral area in the numerosity categorization task only. We propose that the right IPS underlies a common magnitude processing system for both numerosity and duration, possibly corresponding to the encoding and accumulation stages of the accumulator model, whereas the frontal areas are involved in subsequent working-memory storage and decision-making processes.

Number generation bias after action observation.

Recent studies have demonstrated that conceptual and abstract knowledge could rely on and could be influenced by sensory-motor processing of usual goal-directed actions. In line with this, interactions have been reported between number magnitude and finger grip with, for example, small-magnitude numbers priming grip closure and large-magnitude numbers priming grip aperture. Here, we assessed whether observing a closing or opening grip was able to influence the magnitude of the numbers produced in a random number generation task, and we tested whether this effect was specific to biological hand actions by using non-biological fake hands with the same closure or aperture amplitude. The participants were asked to produce as randomly as possible numbers between 1 and 10 after they observed a change in posture (i.e. grip closing or grip opening) or in colour (i.e. red or blue hand). The results revealed that the participants produced more often small numbers than large ones after observing a grip closing, whereas they produced equally often small and large numbers after observing a grip opening or colour changes. Importantly, this effect was only present for the biological hands but not for the non-biological fake hands. This finding demonstrates that observing a biological grip closing conveys small-magnitude information, which, in turn, influences the mental selection of a numerical response. We discuss our results in the light of the internal random generator process proposed in the domain of numerical cognition and argue that number semantics is stored with a code governed by sensory-motor mechanisms.

Processing numerosity, length and duration in a three-dimensional Stroop-like task: towards a gradient of processing automaticity?

The existence of a possible continuum of automaticity for numerosity, length and duration processing was tested with a three-dimensional Stroop-like paradigm. Participants had to compare the numerosity, the length or the duration of two successive linear arrays of sequentially flashed dots in which the three dimensions were manipulated independently to create congruent, incongruent or neutral pairs. The results show that numerosity and length both affected duration processing separately and cumulatively, whereas temporal cues did not influence judgements of numerosity or length. Moreover, length and numerosity influenced each other, with numerical cues having a stronger influence on length processing than the reverse. These findings support the idea that, in sequentially presented stimuli, numerosity, length and duration are processed with different levels of automaticity, with numerosity being processed most, and duration least automatically.

Role of distinct parietal areas in arithmetic: an fMRI-guided TMS study.

Although several parietal areas are known to be involved in number processing, their possible role in arithmetic operations remains debated. It has been hypothesized that the horizontal segment of the intraparietal sulcus (hIPS) and the posterior superior parietal lobule (PSPL) contribute to operations solved by calculation procedures, such as subtraction, but whether these areas are also involved in operations solved by memory retrieval, such as multiplication, is controversial. In the present study, we first identified the parietal areas involved in subtraction and multiplication by means of functional magnetic resonance imaging (fMRI) and we found an increased activation, bilaterally, in the hIPS and PSPL during both arithmetic operations. In order to test whether these areas are causally involved in subtraction and multiplication, we used transcranial magnetic stimulation (TMS) to create, in each participant, a virtual lesion of either the hIPS or PSPL, over the sites corresponding to the peaks of activation gathered in fMRI. When compared to a control site, we found an increase in response latencies in both operations after a virtual lesion of either the left or right hIPS, but not of the PSPL. Moreover, TMS over the hIPS increased the error rate in the multiplication task. The present results indicate that even operations solved by memory retrieval, such as multiplication, rely on the hIPS. In contrast, the PSPL seems to underlie processes that are nonessential to solve basic subtraction and multiplication problems.

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.

Mode-dependent and mode-independent representations of numerosity in the right intraparietal sulcus.

In humans, areas around the intraparietal sulcus (IPS) have been found to play a crucial role in coding nonsymbolic numerosities (i.e., number of elements in a collection). In the parietal cortex of monkeys, some populations of neurons were found to respond selectively to sequentially- or simultaneously-presented numerosities, whereas other populations showed similar activation in both modes of presentation. However, whether such mode-dependent and -independent representations of numerosity also exist in humans is still unknown. Here, we used fMRI to identify the areas involved in numerosity processing while participants classified linear arrays of dots (simultaneous stimuli) or flashed dot sequences (sequential stimuli). The processing of simultaneous numerosities induced activations bilaterally in several areas of the IPS, whereas activations during the processing of sequential numerosities were restricted to the right hemisphere. A conjunction analysis showed that only the right IPS and precentral gyrus showed overlapping activations during the judgement of sequential and simultaneous stimuli. Voxelwise correlations confirmed the highly similar pattern of activation found in these regions during both tasks. This pattern was weaker or absent in mode-dependent regions, like the right inferior frontal cortex and the lateral occipital complex. Finally, a close look at the right IPS revealed an anterior-to-posterior gradient of activation with selective activation for sequential and simultaneous stimuli in the anterior and posterior areas, respectively, and overlapping activations in-between. This study provides the first direct evidence that, in humans, the right IPS contains both mode-dependent and mode-independent representations of numerosity.

The neural origin of the priming distance effect: distance-dependent recovery of parietal activation using symbolic magnitudes.

Numerical magnitudes are known to be processed in areas around the intraparietal sulci of the brain. We used an fMRI-adaptation paradigm to investigate how they are actually coded at the neural level. In a number identification task, we manipulated the numerical distance between prime and target numbers (same, close, and far pairs) and their symbolic notation (Arabic and verbal numerals). We show that bilateral parietal activations present a distance-dependent recovery of activation positively correlated with the distance between primes and targets: the larger the prime-target distance, the higher the recovery of activation. Importantly, this effect is only present for trials where an Arabic numeral precedes a verbal numeral and not the reverse. Together, these findings reveal the neural origin of the behavioral priming distance effect and demonstrate that the relative importance of the semantic and nonsemantic pathways in a dual-route model of number processing is modulated by symbolic notation.

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.

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.