Leftward motion restores number space in neglect

Pupil size variations reveal covert shifts of attention induced by numbers

The pupil light response is more than a pure reflexive mechanism that reacts to the amount of light entering the eye. The pupil size may also react to the luminance of objects lying in the visual periphery, revealing the locus of covert attention. In the present study, we took advantage of this response to study the spatial coding of abstract concepts with no physical counterpart: numbers. The participants' gaze was maintained fixed in the middle of a screen whose left and right parts were dark or bright, and variations in pupil size were recorded during an auditory number comparison task. The results showed that small numbers accentuated pupil dilation when the darker part of the screen was on the left, while large numbers accentuated pupil dilation when the darker part of the screen was on the right. This finding provides direct evidence for covert attention shifts on a left-to-right oriented mental spatial representation of numbers. From a more general perspective, it shows that the pupillary response to light is subject to modulation from spatial attention mechanisms operating on mental contents.

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

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

Perceived Motion and Operational Momentum: How Speed, Distance, and Time Influence Two-Digit Arithmetic

Operational momentum was originally defined as a bias toward underestimating outcomes of subtraction and overestimating outcomes of addition. It was suggested that these estimation biases are due to leftward attentional shift along the mental number-line (spatially organized internal representation of number) in subtraction and rightward shift in addition. This assumes the use of “recycled” mechanisms of spatial attention, including “representational momentum” – a tendency to overestimate future position of a moving object, which compensates for the moving object’s shift during preparation of a reaction. We tested a strong version of this assumption directly, priming two-digit addition and subtraction problems with leftward and rightward motion of varied velocity, as velocity of the tracked object was found to be a factor in determining representational momentum effect size. Operands were subsequently moving across the computer screen, and the participants’ task was to validate an outcome proposed at the end of the event, which was either too low, correct, or too high. We found improved accuracy in detecting too-high outcomes of addition, as well as complex patterns of interactions involving arithmetic operation, outcome option, speed, and direction of motion, in the analysis of reaction times. These results significantly extend previous evidence for the involvement of spatial attention in mental arithmetic, showing movement of the external attention focus as a factor directing internal attention in processing numerical information. As a whole, however, the results are incompatible with expectations derived from the strong analogy between operational and representational momenta. We suggest that the full model may be more complex than simply “moving attention along the mental number-line” as a direct counterpart of attention directed at a moving object.

Number space is made by response space: Evidence from left spatial neglect

Whether the semantic representation of numbers is endowed with an intrinsic spatial component, so that smaller numbers are inherently represented to the left of larger ones on a Mental Number Line (MNL), is a central matter of debate in numerical cognition. To gain an insight into this issue, we investigated the performance of right brain damaged patients with left spatial neglect (N+) in a bimanual Magnitude Comparison SNARC task and in a uni-manual Magnitude Comparison Go/No-Go task (i.e. "is the number smaller or larger than 5?"). While the first task requires the use of contrasting left/right spatial codes for response selection, the second task does not require the use of these codes. In line with previous evidence, in the SNARC task N+ patients displayed a significant asymmetry in Reaction Times (RTs), with slower RTs to number "4", that was immediately precedent to the numerical reference "5", with respect to the number "6", that immediately followed the same reference. This RTs asymmetry was correlated with lesion of white matter tracts, i.e. Fronto-Occipital-Fasciculus, that allows prefrontal Ba 8 and 46 to regulate the distribution of attention on sensory and memory traces in posterior occipital, temporal and parietal areas. In contrast, no similar RTs asymmetry was found in the Go/No-Go task. These findings suggest that while in the SNARC task numbers get mentally organised from left-to-right as a function of their increasing magnitude, so that N+ patients display a delay in the processing of number-magnitudes that are immediately smaller than a given numerical reference, in the Go/No-Go task no left-to-right organization is activated. These results support the idea that it is the use of contrasting left/right spatial codes, whether motor or conceptual, that triggers the generation of a spatially left-to-right organised MNL and that the representation of number magnitude is not endowed with an inherent spatial component.

Vestibular and Multi-Sensory Influences Upon Self-Motion Perception and the Consequences for Human Behavior

In this manuscript, we comprehensively review both the human and animal literature regarding vestibular and multi-sensory contributions to self-motion perception. This covers the anatomical basis and how and where the signals are processed at all levels from the peripheral vestibular system to the brainstem and cerebellum and finally to the cortex. Further, we consider how and where these vestibular signals are integrated with other sensory cues to facilitate self-motion perception. We conclude by demonstrating the wide-ranging influences of the vestibular system and self-motion perception upon behavior, namely eye movement, postural control, and spatial awareness as well as new discoveries that such perception can impact upon numerical cognition, human affect, and bodily self-consciousness.

Spatial grounding of symbolic arithmetic: an investigation with optokinetic stimulation

Growing evidence suggests that mental calculation might involve movements of attention along a spatial representation of numerical magnitude. Addition and subtraction on nonsymbolic numbers (numerosities) seem to induce a “momentum” effect, and have been linked to distinct patterns of neural activity in cortical regions subserving attention and eye movements. We investigated whether mental arithmetic on symbolic numbers, a cornerstone of abstract mathematical reasoning, can be affected by the manipulation of overt spatial attention induced by optokinetic stimulation (OKS). Participants performed additions or subtractions of auditory two-digit numbers during horizontal (experiment 1) or vertical OKS (experiment 2), and eye movements were concurrently recorded. In both experiments, the results of addition problems were underestimated, whereas results of subtractions were overestimated (a pattern that is opposite to the classic Operational Momentum effect). While this tendency was unaffected by OKS, vertical OKS modulated the occurrence of decade errors during subtractions (i.e., fewer during downward OKS and more frequent during upward OKS). Eye movements, on top of the classic effect induced by OKS, were affected by the type of operation during the calculation phase, with subtraction consistently leading to a downward shift of gaze position and addition leading to an upward shift. These results highlight the pervasive nature of spatial processing in mental arithmetic. Furthermore, the preeminent effect of vertical OKS is in line with the hypothesis that the vertical dimension of space–number associations is grounded in universal (physical) constraints and, thereby, more robust than situated and culture-dependent associations with the horizontal dimension.

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.

Hemispatial Neglect Shows That "Before" Is "Left"

Recent research has led to the hypothesis that events which unfold in time might be spatially represented in a left-to-right fashion, resembling writing direction. Here we studied fourteen right-hemisphere damaged patients, with or without neglect, a disorder of spatial awareness affecting contralesional (here left) space processing and representation. We reasoned that if the processing of time-ordered events is spatial in nature, it should be impaired in the presence of neglect and spared in its absence. Patients categorized events of a story as occurring before or after a central event, which acted as a temporal reference. An asymmetric distance effect emerged in neglect patients, with slower responses to events that took place before the temporal reference. The event occurring immediately before the reference elicited particularly slow responses, closely mirroring the pattern found in neglect patients performing numerical comparison tasks. Moreover, the first item elicited significantly slower responses than the last one, suggesting a preference for a left-to-right scanning/representation of events in time. Patients without neglect showed a regular and symmetric distance effect. These findings further suggest that the representation of events order is spatial in nature and provide compelling evidence that ordinality is similarly represented within temporal and numerical domains.

Extra-powerful on the visuo-perceptual space, but variable on the number space: Different effects of optokinetic stimulation in neglect patients

We studied the effects of optokinetic stimulation (OKS; leftward, rightward, control) on the visuo-perceptual and number space, in the same sample, during line bisection and mental number interval bisection tasks. To this end, we tested six patients with right-hemisphere damage and neglect, six patients with right-hemisphere damage but without neglect, and six neurologically healthy participants. In patients with neglect, we found a strong effect of leftward OKS on line bisection, but not on mental number interval bisection. We suggest that OKS influences the number space only under specific conditions.

When time is space: evidence for a mental time line

Time and space are tightly linked in the physical word. Recently, several lines of evidence have suggested that the mental representation of time might be spatial in nature. For instance, time-space interactions have been described as a strong preference to associate the past with the left space and the future with the right space. Here we review the growing evidence of interactions between time and space processing, systematized according to the type of interaction being investigated. We present the empirical findings supporting the possibility that humans represent the subjective time flow on a spatially oriented "mental time line" that is accessed through spatial attention mechanisms. The heterogeneous time-space interactions are then compared with the number-space interactions described in the numerical cognition literature. An alternative hypothesis, which maintains a common system for magnitude processing, including time, space, and number, is also discussed. Finally, we extend the discussion to the more general issue of how the representation of these concepts might be grounded into the cortical circuits that support spatial attention and sensorimotor transformations.

Neglect impairs explicit processing of the mental number line

Converging evidence suggests that visuospatial attention plays a pivotal role in numerical processing, especially when the task involves the manipulation of numerical magnitudes. Visuospatial neglect impairs contralesional attentional orienting not only in perceptual but also in numerical space. Indeed, patients with left neglect show a bias toward larger numbers when mentally bisecting a numerical interval, as if they were neglecting its leftmost part. In contrast, their performance in parity judgments is unbiased, suggesting a dissociation between explicit and implicit processing of numerical magnitude. Here we further investigate the consequences of these visuospatial attention impairments on numerical processing and their interaction with task demands. Patients with right hemisphere damage, with and without left neglect, were administered both a number comparison and a parity judgment task that had identical stimuli and response requirements. Neglect patients’ performance was normal in the parity task, when processing of numerical magnitude was implicit, whereas they showed characteristic biases in the number comparison task, when access to numerical magnitude was explicit. Compared to patients without neglect, they showed an asymmetric distance effect, with slowing of the number immediately smaller than (i.e., to the left of) the reference and a stronger SNARC effect, particularly for large numbers. The latter might index an exaggerated effect of number-space compatibility after ipsilesional (i.e., rightward) orienting in number space. Thus, the effect of neglect on the explicit processing of numerical magnitude can be understood in terms of both a failure to orient to smaller (i.e., contralesional) magnitudes and a difficulty to disengage from larger (i.e., ipsilesional) magnitudes on the number line, which resembles the disrupted pattern of attention orienting in visual space.

Optokinetic stimulation modulates neglect for the number space: evidence from mental number interval bisection

Behavioral, neuropsychological, and neuroimaging data support the idea that numbers are represented along a mental number line (MNL), an analogical, visuospatial representation of number magnitude. The MNL is left-to-right oriented in Western cultures, with small numbers on the left and larger numbers on the right. Left neglect patients are impaired in the mental bisection of numerical intervals, with a bias toward larger numbers that are relatively to the right on the MNL. In the present study we investigated the effects of optokinetic stimulation (OKS) - a technique inducing visuospatial attention shifts by means of activation of the optokinetic nystagmus - on number interval bisection. One patient with left neglect following right-hemisphere stroke (BG) and four control patients with right-hemisphere damage, but without neglect, performed the number interval bisection task in three conditions of OKS: static, leftward, and rightward. In the static condition, BG misbisected to the right of the true midpoint. BG misbisected to the left following leftward OKS, and again to the right of the midpoint following rightward OKS. Moreover, the variability of BG's performance was smaller following both leftward and rightward OKS, suggesting that the attentional bias induced by OKS reduced the "indifference zone" that is thought to underlie the length effect reported in bisection tasks. We argue that shifts of visuospatial attention, induced by OKS, may affect number interval bisection, thereby revealing an interaction between the processing of the perceptual space and the processing of the number space.

Current tests and trends in single-case neuropsychology

In this issue of Cortex, Crawford, Garthwaite and Ryan publish bayesian statistical tests that will enable researchers to take account of covariates when comparing single patients to control samples. In this article, we provide some context for this development, from an audit of the Cortex archives. We suggest that single-case research is alive and well, and more rigorous than ever, and that current practice has been shaped considerably by Crawford and colleagues' statistical refinements over the past 12 years. However, there is scope for further tightening and standardisation of statistical methods and reporting standards. The advantages offered by the new bayesian tests should promote the even wider use of appropriate statistical methods, with benefits for the validity of individual studies, and for cross-comparability in the single-case literature.

Perceived motion induced by a neglected stimulus

An illusion of motion can be induced by presenting a horizontal line suddenly between two visual markers. If one marker is briefly illuminated (the "cue") prior to the appearance of the line, the line appears to spread from the cue toward the other marker. This is termed the line-motion illusion, and was here reliably demonstrated in a sample of elderly participants. Two patients with left hemineglect reliably reported rightward spread when the cue was on the left, despite being unable to detect the cue when presented without the line. Indeed, rightward motion following a left-sided cue was reported more reliably than leftward motion following a right-sided cue, and one patient effectively failed to report the illusion as a leftward spread at all. These results support the view that low-level mechanisms process motion in the absence of attention, but the attentional bias in neglect then inhibits the reporting of motion into the neglected side.