Numbers Uniquely Bias Spatial Attention: A Novel Paradigm for UnderstandingSpatial-Numerical Associations

Over the past two-and-a-half decades, numerous empiricalstudies have demonstrated a relationship between numbersand space. A classic interpretation is that these spatial-numerical associations (SNAs) are a product of a stablemental number line (MNL) in the mind, yet others haveargued that SNAs are a product of transient mappings thatoccur in working memory. Importantly, although the latterinterpretation has no implications for the representation ofnumber, the former suggests that the representation ofnumber is inherently spatial. Here, we tease apart questionsof spatial representation (à la an MNL perspective) andspatial strategy (à la alternative accounts). In a novel place-the-number task, we demonstrate that numbersautomatically bias spatial attention whereas other ordinalsequences (i.e., letters) do not. We argue that this isevidence of an inherently spatial representation of numberand explore how this work may help answer futurequestions about the relationship between space andnumber

Visual adaptation reveals multichannel coding for numerosity

Visual numerosity is represented automatically and rapidly, but much remains unknown about the computations underlying this perceptual experience. For example, it is unclear whether numerosity is represented with an opponent channel or multichannel coding system. Within an opponent channel system, all numerical values are represented via the relative activity of two pools of neurons (i.e., one pool with a preference for small numerical values and one pool with a preference for large numerical values). However, within a multichannel coding system, all numerical values are represented directly, with separate pools of neurons for each (discriminable) numerical value. Using an adaptation paradigm, we assessed whether the visual perception of number is better characterized by an opponent channel or multichannel system. Critically, these systems make distinct predictions regarding the pattern of aftereffects exhibited when an observer is adapted to an intermediate numerical value. Opponent channel coding predicts no aftereffects because both pools of neurons adapt equally. By contrast, multichannel coding predicts repulsive aftereffects, wherein numerical values smaller than the adapter are underestimated and those larger than the adapter are overestimated. Consistent with multichannel coding, visual adaptation to an intermediate value (50 dots) yielded repulsive aftereffects, such that participants underestimated stimuli ranging from 10–50 dots, but overestimated stimuli ranging from 50–250 dots. These findings provide novel evidence that the visual perception of number is supported by a multichannel, not opponent channel, coding system, and raise important questions regarding the contributions of different cortical regions, such as the ventral and lateral intraparietal areas, to the representation of number

General magnitude representation in human infants

Behavioral demonstrations of reciprocal interactions among the dimensions of space, number, and time, along with evidence of shared neural mechanisms in posterior parietal cortex, are consistent with a common representational code for general magnitude information. Although much recent speculation has concerned the developmental origins of a system of general magnitude representation, direct evidence in preverbal infants is lacking. Here we show that 9-month-olds transfer associative learning across magnitude dimensions. For example, if shown that larger objects were black and had stripes and that smaller objects were white and had dots, infants expected the same color-pattern mapping to hold for numerosity (i.e., greater numerosity: black with stripes; smaller numerosity: white with dots) and duration (i.e., longer-lasting objects: black with stripes; shorter-lasting objects: white with dots). Cross-dimensional transfer occurred bidirectionally for all combinations of size, numerosity, and duration. These results provide support for the existence of an early-developing and prelinguistic general magnitude system, whereby representations of magnitude information are (at least partially) abstracted from the specific dimensions

An early sex difference in the relation between mental rotation and object preference

Accumulating evidence suggests that males outperform females on mental rotation tasks as early as infancy. Sex differences in object preference have also been shown to emerge early in development and precede sex-typed play in childhood. Although research with adults and older children is suggestive of a relationship between play preferences and visuospatial abilities, including mental rotation, little is known about the developmental origins of this relationship. The present study compared mental rotation ability and object preference in 6- to 13-month-old infants. We used a novel paradigm to examine individual differences in infants’ mental rotation abilities as well as their differential preference for one of two sex-typed objects. A sex difference was found on both tasks, with boys showing an advantage in performance on the mental rotation task and exhibiting greater visual attention to the male-typed object (i.e., a toy truck) than to the female-typed object (i.e., a doll) in comparison to girls. Moreover, we found a relation between mental rotation and object preference that varied by sex. Greater visual interest in the male-typed object was related to greater mental rotation performance in boys, but not in girls. Possible explanations related to perceptual biases, prenatal androgen exposure, and experiential influences for this sex difference are discussed

Approaching stimuli bias attention in numerical space

Increasing evidence suggests that common mechanisms underlie the direction of attention in physical space and numerical space, along the mental number line. The small leftward bias (pseudoneglect) found on paper-and-pencil line bisection is also observed when participants ‘bisect’ number pairs, estimating (without calculating) the number midway between two others. Here we investigated the effect of stimulus motion on attention in numerical space. A two-frame apparent motion paradigm manipulating stimulus size was used to produce the impression that pairs of numbers were approaching (size increase from first to second frame), receding (size decrease), or not moving (no size change). The magnitude of pseudoneglect increased for approaching numbers, even when the final stimulus size was held constant. This result is consistent with previous findings that pseudoneglect in numerical space (as in physical space) increases as stimuli are brought closer to the participant. It also suggests that the perception of stimulus motion modulates attention over the mental number line and provides further support for a connection between the neural representations of physical space and number

Approaching stimuli bias attention in numerical space

Increasing evidence suggests that common mechanisms underlie the direction of attention in physical space and numerical space, along the mental number line. The small leftward bias (pseudoneglect) found on paperand-pencil line bisection is also observed when participants 'bisect' number pairs, estimating (without calculating) the number midway between two others. Here we investigated the effect of stimulus motion on attention in numerical space. A two-frame apparent motion paradigm manipulating stimulus size was used to produce the impression that pairs of numbers were approaching (size increase from first to second frame), receding (size decrease), or not moving (no size change). The magnitude of pseudoneglect increased for approaching numbers, even when the final stimulus size was held constant. This result is consistent with previous findings that pseudoneglect in numerical space (as in physical space) increases as stimuli are brought closer to the participant. It also suggests that the perception of stimulus motion modulates attention over the mental number line and provides further support for a connection between the neural representations of physical space and number

PAPER Early sex differences in weighting geometric cues

Abstract When geometric and non-geometric information are both available for specifying location, men have been shown to rely more heavily on geometry compared to women. To shed insight on the nature and developmental origins of this sex difference, we examined how 18-to 24-month-olds represented the geometry of a surrounding (rectangular) space when direct non-geometric information (i.e. a beacon) was also available for localizing a hidden object. Children were tested on a disorientation task with multiple phases. Across experiments, boys relied more heavily than girls on geometry to guide localization, as indicated by their errors during the initial phase of the task, and by their search choices following transformations that left only geometry available, or that, under limited conditions, created a conflict between beacon and geometry. Analyses of search times suggested that girls, like boys, had encoded geometry, and testing in a square space ruled out explanations concerned with motivational and methodological variables. Taken together, the findings provide evidence for an early sex difference in the weighting of geometry. This sex difference, we suggest, reflects subtle variation in how boys and girls approach the problem of combining multiple sources of location information

Skeletal representations of shape in human vision: evidence for a pruned medial axis model

A representation of shape that is low dimensional and stable across minor disruptions is critical for object recognition. Computer vision research suggests that such a representation can be supported by the medial axis-a computational model for extracting a shape's internal skeleton. However, few studies have shown evidence of medial axis processing in humans, and even fewer have examined how the medial axis is extracted in the presence of disruptive contours. Here, we tested whether human skeletal representations of shape reflect the medial axis transform (MAT), a computation sensitive to all available contours, or a pruned medial axis, which ignores contours that may be considered ''noise.'' Across three experiments, participants (N = 2062) were shown complete, perturbed, or illusory two-dimensional shapes on a tablet computer and were asked to tap the shapes anywhere once. When directly compared with another viable model of shape perception (based on principal axes), participants' collective responses were better fit by the medial axis, and a direct test of boundary avoidance suggested that this result was not likely because of a task-specific cognitive strategy (Experiment 1). Moreover, participants' responses reflected a pruned computation in shapes with small or large internal or external perturbations (Experiment 2) and under conditions of illusory contours (Experiment 3). These findings extend previous work by suggesting that humans extract a relatively stable medial axis of shapes. A relatively stable skeletal representation, reflected by a pruned model, may be well equipped to support real-world shape perception and object recognition

Bisecting the mental number line in near and far space

Much evidence suggests that common posterior parietal mechanisms underlie the orientation of attention in physical space and along the mental number line. For example, the small leftward bias (pseudoneglect) found in paper-and-pencil line bisection is also found when participants "bisect" number pairs, estimating (without calculating) the number midway between two others. For bisection of physical lines, pseudoneglect has been found to shift rightward as lines are moved from near space (immediately surrounding the body) to far space. We investigated whether the presentation of stimuli in near or far space also modulated spatial attention for the mental number line. Participants bisected physical lines or number pairs presented at four distances (60, 120, 180, 240 cm). Clear rightward shifts in bias were observed for both tasks. Furthermore, the rate at which this shift occurred in the two tasks, as measured by least squares regression slopes, was significantly correlated across participants, suggesting that the transition from near to far distances induced a common modulation of lateral attention in physical and numerical space. These results demonstrate a tight coupling between number and physical space, and show that even such prototypically abstract concepts as number are modulated by our on-line interactions with the world

The clinical impact of MTHFR polymorphism on the vascular complications of sickle cell disease

Sickle cell disease (SCD) is one of the most common inherited diseases in the world and the patients present notorious clinical heterogeneity. It is known that patients with SCD present activation of the blood coagulation and fibrinolytic systems, especially during vaso-occlusive crises, but also during the steady state of the disease. We determined if the presence of the factor V gene G1691A mutation (factor V Leiden), the prothrombin gene G20210A variant, and methylenetetrahydrofolate reductase (MTHFR) C677T polymorphism may be risk factors for vascular complications in individuals with SCD. We studied 53 patients with SCD (60% being women), 29 with SS (sickle cell anemia; 28 years, range: 13-52 years) and 24 with SC (sickle-hemoglobin C disease; 38.5 years, range: 17-72 years) hemoglobinopathy. Factor V Leiden, MTHFR C677T polymorphism, and prothrombin G20210A variant were identified by PCR followed by further digestion of the PCR product with specific endonucleases. The following vascular complications were recorded: stroke, retinopathy, acute thoracic syndrome, and X-ray-documented avascular necrosis. Only one patient was heterozygous for factor V Leiden (1.8%) and there was no prothrombin G20210A variant. MTHFR 677TT polymorphism was detected in 1 patient (1.8%) and the heterozygous form 677TC was observed in 18 patients (34%, 9 with SS and 9 with SC disease), a prevalence similar to that reported by others. No association was detected between the presence of the MTHFR 677T allele and other genetic modulation factors, such as alpha-thalassemia, ß-globin gene haplotype and fetal hemoglobin. The presence of the MTHFR 677T allele was associated with the occurrence of vascular complications in SCD, although this association was not significant when each complication was considered separately. In conclusion, MTHFR C677T polymorphism might be a risk factor for vascular complications in SCD.Universidade Federal de São Paulo (UNIFESP) Paulista de Medicina Disciplina de Hematologia e HemoterapiaUNIFESP, Paulista de Medicina Disciplina de Hematologia e HemoterapiaSciEL