Interaction between space and number representations during motor preparation in manual aiming

Unpacking associations among children's spatial skills, mathematics, and arithmetic strategies: decomposition matters

Several studies revealed links between mental rotation and mathematical tasks, but the intervening processes in this connection remain rather unexplored. Here, we aimed to investigate whether children's mental rotation skills relate to their accuracy in solving arithmetic problems via their usage of decomposition strategies, thus probing one potential intervening process. To this end, we examined a sample of 6- to 8-year-olds (N = 183) with a chronometric mental rotation task, and asked children to solve several arithmetic problems while assessing their solution strategies. After each arithmetic problem, children were asked about their strategy to solve the respective arithmetic problem and these were classified as either counting, decomposition, or retrieval strategies. Analyses were controlled for age, sex, fluid and verbal reasoning. Results indicated that children's response times and accuracy in the mental rotation task were best explained by linear functions of rotation angle, suggesting the usage of dynamic mental transformation strategies. A multiple mediation model revealed that children with higher mental rotation skills were more inclined to use higher-level mental strategies such as decomposition which in turn increased their accuracy of solving arithmetic problems. None of the other arithmetic strategies revealed significant indirect effects. These findings suggest that children with higher mental rotation skills may profit from visualizing and flexibly transforming numerical magnitudes, increasing the frequency of decomposition strategies. Overall, decomposition may play a unique role in the connection between children's mental rotation and arithmetic skills, which is an essential information for planning future training and experimental studies.

TAT-HUM: Trajectory analysis toolkit for human movements in Python

Human movement trajectories can reveal useful insights regarding the underlying mechanisms of human behaviors. Extracting information from movement trajectories, however, can be challenging because of their complex and dynamic nature. The current paper presents a Python toolkit developed to help users analyze and extract meaningful information from the trajectories of discrete rapid aiming movements executed by humans. This toolkit uses various open-source Python libraries, such as NumPy and SciPy, and offers a collection of common functionalities to analyze movement trajectory data. To ensure flexibility and ease of use, the toolkit offers two approaches: an automated approach that processes raw data and generates relevant measures automatically, and a manual approach that allows users to selectively use different functions based on their specific needs. A behavioral experiment based on the spatial cueing paradigm was conducted to illustrate how one can use this toolkit in practice. Readers are encouraged to access the publicly available data and relevant analysis scripts as an opportunity to learn about kinematic analysis for human movements.

Scaling up = scaling down? Children's spatial scaling in different perceptual modalities and scaling directions

The present study examined whether scaling direction and perceptual modality affect children's spatial scaling. Children aged 6-8 years (N = 201) were assigned to a visual, visuo-haptic, and haptic condition in which they were presented with colourful, embossed graphics. In the haptic condition, they were asked to wear a blindfold during the test trials. Across several trials, children were asked to learn about the position of a target in a map and to localize a disc at the same location in a referent space. Scaling factor was manipulated systematically, so that children had to either scale up or scale down spatial information. Their absolute deviations from the correct target location, reversal and signed errors, and response times served as dependent variables. Results revealed higher absolute deviations and response times for the haptic modality as opposed to the visual modality. Children's signed errors, however, showed similar response strategies across the perceptual conditions. Therefore, it seems that a functional equivalence between vision and touch seems to emerge slowly across development for spatial scaling. With respect to scaling directions, findings showed that absolute deviations were affected by scaling factors, with symmetric increases in scaling up and scaling down in the haptic condition. Conversely, children showed an unbalanced pattern in the visual conditions, with higher accuracy in scaling down as opposed to scaling up. Overall, our findings suggest that visibility seems to factor into children's scaling process.

Aiming performance during spaceflight: Individual adaptation to microgravity and the benefits of haptic support

Sensorimotor performance is known to deteriorate during spaceflight. Prior research for instance documented that targeted arm motions are performed slower and less precise in microgravity conditions. This article describes an experiment on aiming performance during different stages of a space mission. Moreover, the influence of different haptic settings of the human-machine interface (HMI) was explored. Two separate studies are presented in which the same aiming tasks were performed with a force feedback joystick: 1) A terrestrial study (N = 20) to explore time and haptic setting effects and 2) a space experiment (N = 3) with a pre-mission session, three mission sessions on board the ISS (2, 4, and 6 weeks in space), and a post-mission session. Results showed that sensorimotor performance was mainly affected in the initial phase of exposure to microgravity and this effect was moderated by astronauts' sensorimotor skills. Providing low stiffness at the HMI, however, proved to be an effective measure to maintain aiming precision in microgravity.

Sensorimotor impairments during spaceflight: Trigger mechanisms and haptic assistance

In a few years, manned space missions are planned in which the sensorimotor performance of humans will be of outstanding importance. However, research has repeatedly shown that human sensorimotor function can be impaired under conditions of microgravity. One way to compensate for these impairments is haptic feedback provided by the human-machine interface. In the current series of studies, sensorimotor performance was measured in basic aiming and tracking tasks. These tasks had to be performed using a force feedback joystick with different haptic settings (three spring stiffnesses, two dampings, two virtual masses, and no haptics). In two terrestrial studies, we investigated (1) the effects of cognitive load on performance in a dual-task paradigm (N = 10) and (2) which learning effects can be expected in these tasks in a longitudinal study design (N = 20). In the subsequent space study (N = 3 astronauts), the influence of microgravity and haptic settings of the joystick were investigated. For this purpose, three mission sessions after 2, 4, and 6 weeks on board the International Space Station (ISS), as well as terrestrial pre- and post-flight sessions, were conducted. The results of the studies indicated that (1) additional cognitive load led to longer reaction times during aiming and increased tracking error while aiming precision was not affected. (2) Significant learning effects were evident for most measures in the study on time effects. (3) Contrary to the expected learning trend, microgravity impaired the aiming precision performance of all astronauts in the initial phase of adaptation (2 weeks in space). No other significant effects were found. Intriguingly, these performance decrements could be compensated for with low to medium spring stiffness and virtual mass. The general result pattern provides further evidence that distorted proprioception during early adaptation to microgravity conditions is one main mechanism underlying sensorimotor impairment.

The influence of locative expressions on context-dependency of endpoint control in aiming

It has been claimed that increased reliance on context, or allocentric information, develops when aiming movements are more consciously monitored and/or controlled. Since verbalizing target features requires strong conscious monitoring, we expected an increased reliance on allocentric information when verbalizing a target label (i.e. target number) during movement execution. We examined swiping actions towards a global array of targets embedded in different local array configurations on a tablet under no-verbalization and verbalization conditions. The global and local array configurations allowed separation of contextual-effects from any possible numerical magnitude biases triggered from calling out specific target numbers.The patterns of constant errors in the target directionwere used to assess differences between conditions. Variation in the target context configuration systematically biased movement endpoints in both the no-verbalization and verbalization conditions. Ultimately, our results do not support the assertion that calling out target numbers during movement execution increases the context-dependency of targeted actions.

Contrasting left/right codes for response selection must not be necessarily associated with contrasting numerical features to get the SNARC

The SNARC effect consists of faster reaction times to small numerical magnitudes when manual responses are delivered in the left-side of space and to large magnitudes when responses are delivered in the right-side. This spatial compatibility effect points at the interaction between the representations of space and that of numbers. Several studies have highlighted that an important determinant for the production of the SNARC is the use of contrasting left/right spatial codes in the selection of motor responses. In these studies, one spatial code for response selection, e.g. "left", is usually associated with one number feature, e.g. "lower than 5", while the contrasting spatial code, e.g. "right", is associated with the contrasting number feature, e.g. "higher than 5". Using a task with intermixed number and letter targets, here we show that significant and reliable SNARC effects are also produced when: a) one spatial response is associated with the intra-categorical discrimination of a number feature (i.e. magnitude or parity) and the contrasting response with the simple detection of letter targets; b) or when one spatial response is associated with the intra-categorical discrimination of the position of a letter in the alphabet (i.e. before or after "m") and the contrasting spatial response with the simple detection of numerical targets (Experiments 1 and 2). In contrast, no reliable SNARC is found when no intra-categorical number or letter discrimination is required and contrasting left/right spatial response codes are simply associated with the discrimination between numbers and letters, e.g. "push left if the target is a number/push right if it is a letter" (Experiment 3). In a final control test (Experiment 4), we found no SNARC when the magnitude or parity classification of Arabic digits presented at central fixation was made unimanually with a left side or a right side-key and no left/right contrast was present in response selection. These results show that the use of contrasting left/right spatial response codes elicits reliable SNARC effects independently of their assignment to contrasting number features and confirm the important role played by the use of spatial codes in the genesis of the number-space interaction.

Numerical Affordance Influences Action Execution: A Kinematic Study of Finger Movement

Humans represent symbolic numbers as oriented from left to right: the mental number line (MNL). Up to now, scientific studies have mainly investigated the MNL by means of response times. However, the existing knowledge on the MNL can be advantaged by studies on motor patterns while responding to a number. Cognitive representations, in fact, cannot be fully understood without considering their impact on actions. Here we investigated whether a motor response can be influenced by number processing. Participants seated in front of a little soccer goal. On each trial they were visually presented with a numerical (2, 5, 8) or a non-numerical ($) stimulus. They were instructed to kick a small ball with their right index toward a frontal soccer goal as soon as a stimulus appeared on a screen. However, they had to refrain from kicking when number five was presented (no-go signal). Our main finding is that performing a kicking action after observation of the larger digit proved to be more efficient: the trajectory path was shorter and lower on the surface, velocity peak was anticipated. The smaller number, instead, specifically altered the temporal and spatial aspects of trajectories, leading to more prolonged left deviations. This is the first experimental demonstration that the reaching component of a movement is influenced by number magnitude. Since this paradigm does not require any verbal skill and non-symbolic stimuli (array of dots) can be used, it could be fruitfully adopted to evaluate number abilities in children and even preschoolers. Notably, this is a self-motivating and engaging task, which might help children to get involved and to reduce potential arousal connected to institutional paper-and-pencil examinations.

Numerical value biases sound localization

Speech recognition starts with representations of basic acoustic perceptual features and ends by categorizing the sound based on long-term memory for word meaning. However, little is known about whether the reverse pattern of lexical influences on basic perception can occur. We tested for a lexical influence on auditory spatial perception by having subjects make spatial judgments of number stimuli. Four experiments used pointing or left/right 2-alternative forced choice tasks to examine perceptual judgments of sound location as a function of digit magnitude (1–9). The main finding was that for stimuli presented near the median plane there was a linear left-to-right bias for localizing smaller-to-larger numbers. At lateral locations there was a central-eccentric location bias in the pointing task, and either a bias restricted to the smaller numbers (left side) or no significant number bias (right side). Prior number location also biased subsequent number judgments towards the opposite side. Findings support a lexical influence on auditory spatial perception, with a linear mapping near midline and more complex relations at lateral locations. Results may reflect coding of dedicated spatial channels, with two representing lateral positions in each hemispace, and the midline area represented by either their overlap or a separate third channel.

Reversing the Manual Digit Bias in Two-Digit Number Comparison

Though recent work in numerical cognition has supported a strong tie between numerical and spatial representations (e.g., a mental number line), less is known about such ties in multi-digit number representations. Along this line, Bloechle, Huber, and Moeller (2015) found that pointing positions in two-digit number comparison were biased leftward toward the decade digit. Moreover, this bias was reduced in unit-decade incompatible pairs. In the present study, we tracked computer mouse movements as participants compared two-digit numbers to a fixed standard (55). Similar to Bloechle et al. (2015) , we found that trajectories exhibited a leftward bias that was reduced for unit-decade incompatible comparisons. However, when positions of response labels were reversed, the biases reversed. That is, we found a rightward bias for compatible pairs that was reduced for incompatible pairs. This result calls into question a purely embodied representation of place value structure and instead supports a competition model of two-digit number representation.

Manual actions cover symbolic distances at different speed

A privileged way of representing numbers in the human mind is along an oriented mental number line. Activation of this representation has been proposed to account for the impact of numbers on motor tasks, such as on grasping, pointing, and eye movements. Here we evaluated the impact of numbers on motor control, by exploiting the evidence that the speed reached by the manual connection of two points is correlated with their physical distance. We reasoned that, if irrelevant numbers induce a mis-perception of the distance between two points, this should be reflected in the movement speed. Results showed a speed difference in the manual connection of two numerically close numbers (i.e., connected slower) and two numerically distant numbers (i.e., connected faster), placed at equal physical distance. This representational length effect indicates not only that symbolic distance modulates speed movement as physical distance does, but suggests that the impact of numbers on action planning does not only involve action initiation but it extends to the definition of kinematic parameters. More generally, the reported findings show that the representation of numbers along a mental space affects our behaviour in the physical space.

Using Key Distance to Clarify a Theory on the SNARC

The most prominent explanation for the spatial numerical association of response codes (SNARC) effect is the direct mapping account (DMA). The DMA assumes that (a) numbers are represented on a mental number line, (b) this mental number line is mapped to external space, and (c) the better the mapping location corresponds to the response location, the faster the response. The DMA leaves open whether a variation of response locations can (ceteris paribus) influence the location to which numbers are mapped in external space. In order to investigate this question, we varied response key distance during a standard parity judgment and a magnitude judgment task. We found that even drastic manipulations of response key distance did not modulate the SNARC effect. Power and meta-analyses show that this null effect is not due to insufficient statistical power or a poor experimental setup. Thus, our results indicate that, in order for the DMA to explain the SNARC effect, it must assume that the mapping from the mental number line to external space is anchored to response location. For future research, our results suggest that it is not necessary to control the horizontal separation of the response keys in basic SNARC experiments.

The Scale Analysis of Number Mapping onto Space: Manual Estimation Study

Previous studies have shown an interference of task-irrelevant numerical information with the spatial parameters of visuomotor behaviour. These findings lend support to the notion that number and space share a common metric with respect to action. Here I argue that the demonstration of the structural similarity between scales for number and space would be a more stringent test for the shared metrics than a mere fact of interference. The present study investigated the scale of number mapping onto space in a manual estimation task. The physical size of target stimuli and the magnitudes of task-irrelevant numbers were parametrically manipulated in the context of the Titchener illusion. The results revealed different scaling schemas for number and space. Whereas estimates in response to changes in stimulus physical size showed a gradual increase, the effect of number was categorical with the largest number (9) showing greater manual estimate than the other numbers (1, 3, and 7). Possible interpretations that are not necessarily incompatible with the hypothesis of shared metrics with respect to action are proposed. However, the present findings suggest that a meticulous scale analysis is required in order to determine the nature of number–space interaction.

Tonal cues modulate line bisection performance: preliminary evidence for a new rehabilitation prospect?

The effect of the presentation of two different auditory pitches (high and low) on manual line-bisection performance was studied to investigate the relationship between space and magnitude representations underlying motor acts. Participants were asked to mark the midpoint of a given line with a pen while they were listening a pitch via headphones. In healthy participants, the effect of the presentation order (blocked or alternative way) of auditory stimuli was tested (Experiment 1). The results showed no biasing effect of pitch in blocked-order presentation, whereas the alternative presentation modulated the line-bisection. Lower pitch produced leftward or downward bisection biases whereas higher pitch produced rightward or upward biases, suggesting that visuomotor processing can be spatially modulated by irrelevant auditory cues. In Experiment 2, the effect of such alternative stimulations in line bisection in right brain damaged patients with a unilateral neglect and without a neglect was tested. Similar biasing effects caused by auditory cues were observed although the white noise presentation also affected the patient's performance. Additionally, the effect of pitch difference was larger for the neglect patient than for the no-neglect patient as well as for healthy participants. The neglect patient's bisection performance gradually improved during the experiment and was maintained even after 1 week. It is therefore, concluded that auditory cues, characterized by both the pitch difference and the dynamic alternation, influence spatial representations. The larger biasing effect seen in the neglect patient compared to the no-neglect patient and healthy participants suggests that auditory cues could modulate the direction of the attentional bias that is characteristic of neglect patients. Thus, the alternative presentation of auditory cues could be used as rehabilitation for neglect patients. The space-pitch associations are discussed in terms of a generalized magnitude system.

Different effects of numerical magnitude on visual and proprioceptive reference frames

This study assessed whether numerical magnitude affects the setting of basic spatial coordinates and reference frames, namely the subjective straight ahead. Three tasks were given to 24 right-handed healthy participants: a proprioceptive and a visuo-proprioceptive task, requiring pointing to the subjective straight ahead, and a visual task, requiring a perceptual judgment about the straight ahead position of a light moving left-to-right, or right-to-left. A control task, requiring the bisection of rods of different lengths, was also given. The four tasks were performed under conditions of passive auditory numerical (i.e., listening to small, “2,” and large, “8,” numbers), and neutral auditory-verbal (“blah”) stimulation. Numerical magnitude modulated the participants’ deviations in the visual straight ahead task, when the movement of the light was from left-to-right, with the small number bringing about a leftward deviation, the large number a rightward deviation. A similar directional modulation was found in the rod bisection task, in line with previous evidence. No effects of numerical magnitude were found on the proprioceptive and visuo-proprioceptive straight ahead tasks. These results suggest that the spatial effects induced by the activation of the mental number line extend to an egocentric frame of reference but only when a portion of horizontal space has to be “actively” explored.

Your neighbors define your value: a study of spatial bias in number comparison

Several chronometric biases in numerical cognition have informed our understanding of a mental number line (MNL). Complementing this approach, we investigated spatial performance in a magnitude comparison task. Participants located the larger or smaller number of a pair on a horizontal line representing the interval from 0 to 10. Experiments 1 and 2 used only number pairs one unit apart and found that digits were localized farther to the right with "select larger" instructions than with "select smaller" instructions. However, when numerical distance was varied (Experiment 3), digits were localized away from numerically near neighbors. This repulsion effect reveals context-specific distortions in number representation not previously noticed with chronometric measures.

Rehabilitation of spatial neglect by prism adaptation: a peculiar expansion of sensorimotor after-effects to spatial cognition

Unilateral neglect is a neurological condition responsible for many debilitating effects on everyday life, poor functional recovery, and decreased ability to benefit from treatment. Prism adaptation (PA) to a right lateral displacement of the visual field is classically known to directionally bias visuo-motor and sensory-motor correspondences. One longstanding issue about this visuo-motor plasticity is about its specificity to the exposure condition. In contrast to very poor transfer to unexposed effectors classically described in healthy subjects, therapeutic results obtained in neglect patients suggested that PA can generate unexpected "expansion". Prism adaptation affects numerous levels of neglect symptomatology, suggesting that its effects somehow expand to unexposed sensory, motor and cognitive systems. The available body of evidence in support for this expansion raises important questions about the mechanisms involved in producing unexpected cognitive effects following a simple and moderate visuo-motor adaptation. We further develop here the idea that prism adaptation expansion to spatial cognition involves a cerebello-cortical network and review support for this model. Building on the basic, therapeutical and pathophysiological knowledge accumulated over the last 15 years, we also provide guidelines for the optimal use of prism adaptation in the clinic. Although further research and clinical trials are required to precisely define the ideal regime for routine applications, the current state of the art allows us to outline practical recommendations for therapeutical use of prisms.

Effects of finger counting on numerical development - the opposing views of neurocognition and mathematics education

Children typically learn basic numerical and arithmetic principles using finger-based representations. However, whether or not reliance on finger-based representations is beneficial or detrimental is the subject of an ongoing debate between researchers in neurocognition and mathematics education. From the neurocognitive perspective, finger counting provides multisensory input, which conveys both cardinal and ordinal aspects of numbers. Recent data indicate that children with good finger-based numerical representations show better arithmetic skills and that training finger gnosis, or "finger sense," enhances mathematical skills. Therefore neurocognitive researchers conclude that elaborate finger-based numerical representations are beneficial for later numerical development. However, research in mathematics education recommends fostering mentally based numerical representations so as to induce children to abandon finger counting. More precisely, mathematics education recommends first using finger counting, then concrete structured representations and, finally, mental representations of numbers to perform numerical operations. Taken together, these results reveal an important debate between neurocognitive and mathematics education research concerning the benefits and detriments of finger-based strategies for numerical development. In the present review, the rationale of both lines of evidence will be discussed.

Clues to the foundations of numerical cognitive impairments: evidence from genetic disorders

Several neurodevelopmental disorders of known genetic etiology generate phenotypes that share the characteristic of numerical and mathematical cognitive impairments. This article reviews some of the main findings that suggest a possible key role that spatial and temporal information processing impairments may play in the atypical development of numerical cognitive competence. The question of what neural substrate might underlie these impairments is also addressed, as are the challenges for interpreting neural structure/cognitive function mapping in atypically developing populations.

The amusic brain: lost in music, but not in space

Congenital amusia is a neurogenetic disorder of music processing that is currently ascribed to a deficit in pitch processing. A recent study challenges this view and claims the disorder might arise as a consequence of a general spatial-processing deficit. Here, we assessed spatial processing abilities in two independent samples of individuals with congenital amusia by using line bisection tasks (Experiment 1) and a mental rotation task (Experiment 2). Both amusics and controls showed the classical spatial effects on bisection performance and on mental rotation performance, and amusics and controls did not differ from each other. These results indicate that the neurocognitive impairment of congenital amusia does not affect the processing of space.

Prismatic lenses shift time perception

Previous studies have demonstrated the involvement of spatial codes in the representation of time and numbers. We took advantage of a well-known spatial modulation (prismatic adaptation) to test the hypothesis that the representation of time is spatially oriented from left to right, with smaller time intervals being represented to the left of larger time intervals. Healthy subjects performed a time-reproduction task and a time-bisection task, before and after leftward and rightward prismatic adaptation. Results showed that prismatic adaptation inducing a rightward orientation of spatial attention produced an overestimation of time intervals, whereas prismatic adaptation inducing a leftward shift of spatial attention produced an underestimation of time intervals. These findings not only confirm that temporal intervals are represented as horizontally arranged in space, but also reveal that spatial modulation of time processing most likely occurs via cuing of spatial attention, and that spatial attention can influence the spatial coding of quantity in different dimensions.

Does the semantic activation of quantity representations influence motor parameters?

In size and parity judgment tasks, we investigated whether the activation of numerical quantity exerts an influence on motor response parameters such as response force. Results showed typically strong effects on reaction time of numerical distance in the size judgment task (Experiments 1 and 2) and SNARC-compatibility (Experiment 1) in both tasks, indicating that semantic quantity representations were activated. Response force, however, varied at most weakly with the numerical magnitudes of the digits. Our results place limits on previously suggested interconnections of the magnitude and response systems. Activations within the magnitude system seem to have a strong influence on the initiation and selection of which action to produce, but only a little influence on the dynamics of response production (i.e., response execution).

Touch perception reveals the dominance of spatial over digital representation of numbers

We learn counting on our fingers, and the digital representation of numbers we develop is still present in adulthood [Andres M, et al. (2007) J Cognit Neurosci 19:563-576]. Such an anatomy-magnitude association establishes tight functional correspondences between fingers and numbers [Di Luca S, et al. (2006) Q J Exp Psychol 59:1648-1663]. However, it has long been known that small-to-large magnitude information is arranged left-to-right along a mental number line [Dehaene S, et al. (1993) J Exp Psychol Genet 122:371-396]. Here, we investigated touch perception to disambiguate whether number representation is embodied on the hand ("1" = thumb; "5" = little finger) or disembodied in the extrapersonal space ("1" = left; "5" = right). We directly contrasted these number representations in two experiments using a single centrally located effector (the foot) and a simple postural manipulation of the hand (palm-up vs. palm-down). We show that visual presentation of a number ("1" or "5") shifts attention cross-modally, modulating the detection of tactile stimuli delivered on the little finger or thumb. With the hand resting palm-down, subjects perform better when reporting tactile stimuli delivered to the little finger after presentation of number "5" than number "1." Crucially, this pattern reverses (better performance after number "1" than "5") when the hand is in a palm-up posture, in which the position of the fingers in external space, but not their relative anatomical position, is reversed. The human brain can thus use either space- or body-based representation of numbers, but in case of competition, the former dominates the latter, showing the stronger role played by the mental number line organization.

An effect of spatial-temporal association of response codes: understanding the cognitive representations of time

The present study addresses the question of how such an abstract concept as time is represented by our cognitive system. Specifically, the aim was to assess whether temporal information is cognitively represented through left-to-right spatial coordinates, as already shown for other ordered sequences (e.g., numbers). In Experiment 1, the task-relevant information was the temporal duration of a cross. RTs were shorter when short and long durations had to be responded to with left and right hands, respectively, than with the opposite stimulus-response mapping. The possible explanation that the foreperiod effect (i.e., shorter RTs for longer durations) is greater with right than with left hand responses is discarded by results of Experiment 2, in which right and left hand responses alternated block-wise in a variable foreperiod paradigm. Other explanations concerning manual or hemispheric asymmetries may be excluded based on the results of control experiments, which show that the compatibility effect between response side and cross duration occurs for accuracy when responses are given with crossed hands (Experiment 3), and for RTs when responses are given within one hand (Experiment 4). This pattern suggests that elapsing time, similarly to other ordered information, is represented in some circumstances through an internal spatial reference frame, in a way that may influence motor performance. Finally, in Experiment 5, the temporal duration was parametrically varied using different values for each response category (i.e., 3 short and 3 long durations). The compatibility effect between hand and duration was replicated, but followed a rectangular function of the duration. The shape of this function is discussed in relation to the specific task demands.

Numeric comparison in a visually-guided manual reaching task

Nearly all studies on perception and cognition have used discrete responses to infer internal cognitive processes. In the current study, we demonstrate that visually-guided manual reaching can provide new opportunities to access internal processes over time. In each trial, participants were required to compare a single digit Arabic number presented on the center square with the standard, 5. Participants were asked to reach and touch one of three squares on the screen with their index finger while their hand movement trajectories were recorded: the left square for 1-4, the center for 5, and the right for 6-9. Direct evidence for an analogue representation of numbers was found in early as well as in later portions of hand trajectories, showing systematic shifts in position for small differences in numerical magnitude.