Random number generation in neglect patients reveals enhanced response stereotypy, but no neglect in number space

It's SNARC o' clock: manipulating the salience of the context in a conceptual replication of Bächtold et al.'s (1998) clockface study

The Spatial-Numerical Association of Response Codes (SNARC) effect consists in faster left-/right-key responses to small/large numbers. (Bächtold et al., Neuropsychologia 36:731-735, 1998) reported the reversal of this effect after eliciting the context of a clockface-where small numbers are represented on the right and large numbers on the left. The present study investigates how the salience of a particular spatial-numerical context, which reflects the level of activation of the context in working memory, can alter Spatial Numerical Associations (SNAs). Four experiments presented the clockface as context and gradually increased its salience using different tasks. In the first two experiments (low salience), the context was presented at the beginning of the experiment and its retrieval was not required to perform the tasks (i.e., random number generation in Experiment 1, magnitude classification and parity judgement in Experiment 2). Results revealed regular left-to-right SNAs, unaffected by the context. In Experiment 3 (medium salience), participants performed magnitude classification and parity judgement (primary task), and a Go/No-go (secondary task) which required the retrieval of the context. Neither the SNARC effect nor a reversed-SNARC emerged, suggesting that performance was affected by the context. Finally, in Experiment 4 (high salience), the primary task required participants to classify numbers based on their position on the clockface. Results revealed a reversed SNARC, as in (Bächtold et al., Neuropsychologia 36:731-735, 1998). In conclusion, SNARC is disrupted when the context is retrieved in a secondary task, but its reversal is observed only when the context is relevant for the primary task.

Counting on random number generation: Uncovering mild executive dysfunction in congenital heart disease

Congenital heart disease (CHD) is associated with various neurocognitive deficits, particularly targeting executive functions (EFs), of which random number generation (RNG) is one indicator. RNG has, however, never been investigated in CHD. We administered the Mental Dice Task (MDT) to 67 young adults with CHD and 55 healthy controls. This 1-minute-task requires the generation of numbers 1 to 6 in a random sequence. RNG performance was correlated with a global EF score. Participants underwent MRI to examine structural-volumetric correlates of RNG. Compared to controls, CHD patients showed increased backward counting, reflecting deficient inhibition of automatized behavior. They also lacked a small-number bias (higher frequency of small relative to large numbers). RNG performance was associated with global EF scores in both groups. In CHD patients, MRI revealed an inverse association of counting bias with most of the volumetric measurements and the amount of small numbers was positively associated with corpus callosum volume, suggesting callosal involvement in the "pseudoneglect in number space". In conclusion, we found an impaired RNG performance in CHD patients, which is associated with brain volumetric measures. RNG, reportedly resistant to learning effects, may be an ideal task for the longitudinal assessment of EFs in patients with CHD.

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.

The right anterior temporal lobe critically contributes to magnitude knowledge

Cognitive estimation is a mental ability applied to solve numerical problems when precise facts are unknown, unavailable or impractical to calculate. It has been associated with several underlying cognitive components, most often with executive functions and semantic memory. Little is known about the neural correlates of cognitive estimation. To address this issue, the present cross-sectional study applied lesion-symptom mapping in a group of 55 patients with left hemineglect due to right-hemisphere stroke. Previous evidence suggests a high prevalence of cognitive estimation impairment in these patients, as they might show a general bias towards large magnitudes. Compared to 55 age- and gender-matched healthy controls, the patient group demonstrated impaired cognitive estimation. However, the expected large magnitude bias was not found. Lesion-symptom mapping related their general estimation impairment predominantly to brain damage in the right anterior temporal lobe. Also critically involved were the right uncinate fasciculus, the anterior commissure and the right inferior frontal gyrus. The main findings of this study emphasize the role of semantic memory in cognitive estimation, with reference to a growing body of neuroscientific literature postulating a transmodal hub for semantic cognition situated in the bilateral anterior temporal lobe. That such semantic hub function may also apply to numerical knowledge is not undisputed. We here propose a critical contribution of the right anterior temporal lobe to at least one aspect of number processing, i.e. the knowledge about real-world numerical magnitudes.

Altered time judgements highlight common mechanisms of time and space perception

Space, numbers and time share similar processing mechanisms mediated by parietal cortex. In parallel to the spatial representation of numbers along a horizontal line, temporal information is mapped on a horizontal axis with short intervals (and the past) represented to the left of long intervals (and the future). Little is known about the representation of time in the presence of visuo-spatial deficits. We here report two experiments on the comparative judgment of time. Experiment 1 required patients with left-sided neglect to indicate which of two consecutively presented silent intervals was longer. Their judgments were better if the first interval was longer and they judged the first interval longer on trials in which the two intervals were equally long. These results were not present in right-hemispheric damaged patients without neglect and healthy controls. They are in line with a previously reported finding in a single patient with neglect, but not readily compatible with findings of neglect patients' comparative length judgments. In Experiment 2, healthy participants' performance on an identical task improved for trials with a first-longer interval after caloric vestibular stimulation (CVS) of the right ear with warm water.

Nature and nurture effects on the spatiality of the mental time line

The nature-nurture debate regarding the origin of mental lines is fundamental for cognitive neuroscience. We examined natural-nurture effects on the mental time line, applying three different challenges to the directionality of time representation. We tested (1) patients with left-neglect and healthy participants, who are (2) left-to-right or right-to-left readers/writers, using (3) a lateralized left-right button press or a vocal mode in response to a mental time task, which asks participants to judge whether events have already happened in the past or are still to happen in the future. Using lateralized responses, a spatial-temporal association of response code (STEARC) effect was found, in concordance with the cultural effects. With vocal responses (no lateralization), past and future events showed similar results in both cultures. In patients with neglect, who have a deficit of spatial attention in processing the left side of space, future events were processed more slowly and less accurately than past events in both cultures. Our results indicate the existence of a “natural” disposition to map past and future events along a horizontal mental time line, which is affected by the different ways in which spatial representation of time is introduced.

Reduced Pseudoneglect for Physical Space, but not Mental Representations of Space, for Adults with Autistic Traits

Neurotypical individuals display a leftward attentional bias, called pseudoneglect, for physical space (e.g. landmark task) and mental representations of space (e.g. mental number line bisection). However, leftward bias is reduced in autistic individuals viewing faces, and neurotypical individuals with autistic traits viewing 'greyscale' stimuli, suggestive of atypical lateralization of attention in autism. We investigated whether representational pseudoneglect for individuals with autistic traits is similarly atypically lateralized by comparing biases on a greyscales, landmark, and mental number line task. We found that pseudoneglect was intact only on the representational measure, the mental number line task, suggesting that mechanisms for atypical lateralization of attention in individuals with autistic traits are specific artefacts of processing physically visual stimuli.

Algorithmic complexity for psychology: a user-friendly implementation of the coding theorem method

Kolmogorov-Chaitin complexity has long been believed to be impossible to approximate when it comes to short sequences (e.g. of length 5-50). However, with the newly developed coding theorem method the complexity of strings of length 2-11 can now be numerically estimated. We present the theoretical basis of algorithmic complexity for short strings (ACSS) and describe an R-package providing functions based on ACSS that will cover psychologists' needs and improve upon previous methods in three ways: (1) ACSS is now available not only for binary strings, but for strings based on up to 9 different symbols, (2) ACSS no longer requires time-consuming computing, and (3) a new approach based on ACSS gives access to an estimation of the complexity of strings of any length. Finally, three illustrative examples show how these tools can be applied to psychology.

Acute peripheral vestibular deficit increases redundancy in random number generation

Unilateral peripheral vestibular deficit leads to broad cognitive difficulties and biases in spatial orientation. More specifically, vestibular patients typically show a spatial bias toward their affected ear in the subjective visual vertical, head and trunk orientation, fall tendency, and walking trajectory. By means of a random number generation task, we set out to investigate how an acute peripheral vestibular deficit affects the mental representation of numbers in space. Furthermore, the random number generation task allowed us to test if patients with peripheral vestibular deficit show evidence of impaired executive functions while keeping the head straight and while performing active head turns. Previous research using galvanic vestibular stimulation in healthy people has shown no effects on number space, but revealed increased redundancy of the generated numbers. Other studies reported a spatial bias in number representation during active and passive head turns. In this experiment, we tested 43 patients with acute vestibular neuritis (18 patients with left-sided and 25 with right-sided vestibular deficit) and 28 age-matched healthy controls. We found no bias in number space in patients with peripheral vestibular deficit but showed increased redundancy in patients during active head turns. Patients showed worse performance in generating sequences of random numbers, which indicates a deficit in the updating component of executive functions. We argue that RNG is a promising candidate for a time- and cost-effective assessment of executive functions in patients suffering from a peripheral vestibular deficit.

Dissociation between line bisection and mental-number-line bisection in healthy adults

Healthy adults bisect visual horizontal lines slightly to the left of their true center. This bias has been termed "pseudoneglect" and is considered to reflect right hemisphere dominance in the orienting of spatial attention. A previous investigation reported a positive correlation between pseudoneglect and a corresponding negative bias towards numbers lower than the true midpoint, i.e. supposedly to the left of the midpoint, during the mental bisection of number intervals that were defined by two visual arabic digits presented one to the left and one to the right of a horizontal line (Longo and Lourenco, 2007, Neuropsychologia, 45, 7, 1400-1407). Here, studying a sample of 60 healthy participants we verified whether this correlation still holds when the endpoints of number intervals are defined verbally, i.e. with no visual-spatial cues suggesting their left-to-right arrangement. Participants bisected horizontal lines (2 cm, 10 cm and 20 cm), short number intervals (3-, 5-, 7- and 9-unit) and large number intervals (16-, 24-, 32-, 40-, 48-, 56-, and 64-unit). Pseudoneglect was observed both in line and number interval bisection, confirming the results of Longo and Lourenco (2007). Nonetheless, the study of correlations between bisection biases averaged across different line and number intervals lengths and between all possible pairings of line and number interval lengths revealed no significant or systematic pattern. During line bisection pseudoneglect increased as a function of line length while with short number intervals pseudoneglect decreased and turned into an opposite positive bias as a function of interval length. With large number intervals no linear relationship was present between bisection bias and interval length and, as in Longo and Lourenco (2007), the higher was the starting point of the number interval the larger was pseudoneglect. These results show that verbally defined number intervals are not mentally inspected with the same mechanisms that are engaged by the bisection of horizontal visual lines. This suggests that number intervals are not inherently arranged along the mental equivalent of a left-to-right oriented horizontal line. This spatial representation seems rather adopted when, as in the case of the SNARC task, "left" vs. "right" codes must be used for the selection of responses associated with numbers or when, as in the case of Longo and Lourenco (2007), the numerical material to be processed is arranged in left-to-right order.

Algorithmic complexity for short binary strings applied to psychology: a primer

As human randomness production has come to be more closely studied and used to assess executive functions (especially inhibition), many normative measures for assessing the degree to which a sequence is randomlike have been suggested. However, each of these measures focuses on one feature of randomness, leading researchers to have to use multiple measures. Although algorithmic complexity has been suggested as a means for overcoming this inconvenience, it has never been used, because standard Kolmogorov complexity is inapplicable to short strings (e.g., of length l ≤ 50), due to both computational and theoretical limitations. Here, we describe a novel technique (the coding theorem method) based on the calculation of a universal distribution, which yields an objective and universal measure of algorithmic complexity for short strings that approximates Kolmogorov-Chaitin complexity.

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.

The Spatial Representation of Numerical and Non-Numerical Ordered Sequences: Insights from a Random Generation Task

It is widely believed that numbers are spatially represented from left to right on the mental number line. Whether this spatial format of representation is specific to numbers or is shared by non-numerical ordered sequences remains controversial. When healthy participants are asked to randomly generate digits they show a systematic small-number bias that has been interpreted in terms of “pseudoneglect in number space”. Here we used a random generation task to compare numerical and non-numerical order. Participants performed the task at three different pacing rates and with three types of stimuli (numbers, letters, and months). In addition to a small-number bias for numbers, we observed a bias towards “early” items for letters and no bias for months. The spatial biases for numbers and letters were rate independent and similar in size, but they did not correlate across participants. Moreover, letter generation was qualified by a systematic forward direction along the sequence, suggesting that the ordinal dimension was more salient for letters than for numbers in a task that did not require its explicit processing. The dissociation between numerical and non-numerical orders is consistent with electrophysiological and neuroimaging studies and suggests that they rely on at least partially different mechanisms.

The link between mental rotation ability and basic numerical representations

Mental rotation and number representation have both been studied widely, but although mental rotation has been linked to higher-level mathematical skills, to date it has not been shown whether mental rotation ability is linked to the most basic mental representation and processing of numbers. To investigate the possible connection between mental rotation abilities and numerical representation, 43 participants completed four tasks: 1) a standard pen-and-paper mental rotation task; 2) a multi-digit number magnitude comparison task assessing the compatibility effect, which indicates separate processing of decade and unit digits; 3) a number-line mapping task, which measures precision of number magnitude representation; and 4) a random number generation task, which yields measures both of executive control and of spatial number representations. Results show that mental rotation ability correlated significantly with both size of the compatibility effect and with number mapping accuracy, but not with any measures from the random number generation task. Together, these results suggest that higher mental rotation abilities are linked to more developed number representation, and also provide further evidence for the connection between spatial and numerical abilities.

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We show a link between mental rotation ability (MRA) and numerical representation.

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MRA correlated with a measure of holding concurrent multiple number representations.

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MRA correlated with a measure of number representation precision (number line task).

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MRA did not correlate with an executive control task (random number generation).

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These findings strengthen the link observed between spatial and numerical abilities.

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.

No inherent left and right side in human 'mental number line': evidence from right brain damage

Spatial reasoning has a relevant role in mathematics and helps daily computational activities. It is widely assumed that in cultures with left-to-right reading, numbers are organized along the mental equivalent of a ruler, the mental number line, with small magnitudes located to the left of larger ones. Patients with right brain damage can disregard smaller numbers while mentally setting the midpoint of number intervals. This has been interpreted as a sign of spatial neglect for numbers on the left side of the mental number line and taken as a strong argument for the intrinsic left-to-right organization of the mental number line. Here, we put forward the understanding of this cognitive disability by discovering that patients with right brain damage disregard smaller numbers both when these are mapped on the left side of the mental number line and on the right side of an imagined clock face. This shows that the right hemisphere supports the representation of small numerical magnitudes independently from their mapping on the left or the right side of a spatial-mental layout. In addition, the study of the anatomical correlates through voxel-based lesion-symptom mapping and the mapping of lesion peaks on the diffusion tensor imaging-based reconstruction of white matter pathways showed that the rightward bias in the imagined clock-face was correlated with lesions of high-level middle temporal visual areas that code stimuli in object-centred spatial coordinates, i.e. stimuli that, like a clock face, have an inherent left and right side. In contrast, bias towards higher numbers on the mental number line was linked to white matter damage in the frontal component of the parietal-frontal number network. These anatomical findings show that the human brain does not represent the mental number line as an object with an inherent left and right side. We conclude that the bias towards higher numbers in the mental bisection of number intervals does not depend on left side spatial, imagery or object-centred neglect and that it rather depends on disruption of an abstract non-spatial representation of small numerical magnitudes.

Functional independence between numerical and visual space: evidence from right brain-damaged patients

What is the relationship between numerical and visual space? Here we tried to shed new light on this debated issue investigating whether and how the two forms of representation are associated or dissociated when co-activated. We carried out a series of visual-numerical bisection experiments on a large group of right brain-damaged patients (N=32) with and without left neglect. We examined (a) the degree of association between the pathological rightward error in the bisection of numerical intervals and left neglect (experiment 1); (b) if the size of the numerical interval modulates spatial errors in bisection tasks in which numerical and visual space representations are co-activated (experiment 2). The results showed that (a) numerical bisection error and left spatial neglect are doubly dissociated and that, when both are present, they are not correlated; (b) the size of the numerical interval did not affect the spatial bisection error but influenced the numerical bisection error. These data suggest that attentional processes involved in the navigation along visual space and numerical internal representations are independent neurocognitive operations. We must emphasize that our findings should be taken with caution because they are based mainly on negative results.

The heterogeneous nature of number-space interactions

It is generally accepted that the mental representation of numerical magnitude consists of a spatial “mental number line” (MNL) with smaller quantities on the left and larger quantities on the right. However, the amount of dissociations between tasks that were believed to tap onto this representational medium is accumulating, questioning the universality of this model. The aim of the present study was to unravel the functional relationship between the different tasks and effects that are typically used as evidence for the MNL. For this purpose, a group of right brain damaged patients (with and without neglect) and healthy controls were subjected to physical line bisection, number interval bisection, parity judgment, and magnitude comparison. Using principal component analysis, different orthogonal components were extracted. We discuss how this component structure captures the dissociations reported in the literature and how it can be considered as a first step toward a new unitary framework for understanding the relation between numbers and space.

Paradoxical extension into the contralesional hemispace in spatial neglect

To explore the idea of a perceptual distortion of space in spatial neglect, neglect patients, age-matched healthy controls and right hemisphere control patients judged the vanishing point of horizontally and vertically-moving stimuli. Hemifield of presentation and movement direction of the stimulus presentation was manipulated. The results suggest that neglect patients show a stronger response bias in the direction of the moving stimuli ("representational momentum") than healthy and right hemisphere controls. Furthermore, neglect patients, but not the control groups, showed a direction-specific response whereby the presence of neglect was associated with a larger representational momentum for leftward-moving stimuli. The one left-hemisphere patient with right-sided neglect showed the opposite effect. Thus, neglect patients showed a relative overextension into their neglected side of space. While these findings are in line with the idea of an extension in the representation of contralesional space, other explanations such as deficient spatial remapping, impairments in smooth pursuit and distortions in memorized visuo-motor movements are considered.

When digits help digits: spatial-numerical associations point to finger counting as prime example of embodied cognition

Spatial-numerical associations (SNAs) are prevalent yet their origin is poorly understood. We first consider the possible prime role of reading habits in shaping SNAs and list three observations that argue against a prominent influence of this role: (1) directional reading habits for numbers may conflict with those for non-numerical symbols, (2) short-term experimental manipulations can overrule the impact of decades of reading experience, (3) SNAs predate the acquisition of reading. As a promising alternative, we discuss behavioral, neuroscientific, and neuropsychological evidence in support of finger counting as the most likely initial determinant of SNAs. Implications of this "manumerical cognition" stance for the distinction between grounded, embodied, and situated cognition are discussed.

Leftward bias in number space is modulated by magical ideation

BACKGROUND

Productive symptoms of schizophrenia and positive-symptom schizotypy have both been related to signs of right-sided hemispatial inattention ("pseudoneglect"). We here set out to explore, in healthy subjects, the relationship between one form of mild schizotypy ("magical ideation"; MI) and asymmetries in number space, which is a bias toward relatively small numbers, reportedly represented to the left of larger numbers.

METHODS

Forty right-handed participants filled in the MI scale and performed a number-line bisection (NLB) task and a randomization task (the Mental Dice Task, MDT, requiring randomization of the digits from 1 to 6).

RESULTS

We found pseudoneglect in number space, that is, more errors toward small numbers in the NLB task and an overproduction of small digits in the MDT. Individual participants' MI scores were correlated to the size of pseudoneglect in both numerical tasks.

CONCLUSIONS

Explicit (NLB) and implicit (MDT) assessments of the exploration of number space may be relevant to studies of the mechanisms underlying the formation of delusional and schizotypal beliefs. We propose that, in healthy subjects, a trait-like imbalance in hemispheric cooperation may not only produce asymmetries in physical and representational space, but also predisposes to develop magical ideas. Specifically, an over-proportional influence of the right hemisphere semantic system (preferentially coding oblique and remote associations) leads to the assumption of connections between randomly associated events.

Strategic Use of Number Representation is Independent of Test Instruction in Random Number Generation

The effects of different instructions on verbal random number generation were examined in 40 healthy students who attempted to generate random sequences of the digits 1 to 6. Two groups of 20 received different instructions with alternative numerical representations. The Symbolic group (Arabic digits) was instructed to randomize while continuously using the analogy of selecting and replacing numbered balls from a hat, whereas the Nonsymbolic group (arrays of dots) was instructed to imagine repeatedly throwing a die. Participants asked for self-reports on their strategies reported spontaneously occurring visuospatial imagination of a mental number line (42%), or imagining throwing a die (23%). Individual number representation was not affected by the initial instruction. There were no differences in randomization performance by group. Comprehensive understanding of the nature of the randomization task requires considering individual differences in construction of mental models.