Conflict processing of symbolic and non-symbolic numerosity

Electrophysiological Comparison of Cumulative Area and Non-Symbolic Number Judgments

Despite the importance of representing different magnitudes (i.e., number and cumulative area) for action planning and formal mathematics, there is much debate about the nature of these representations, particularly the extent to which magnitudes interact in the mind and brain. Early interaction views suggest that there are shared perceptual processes that form overlapping magnitude representations. However, late interaction views hold that representations of different magnitudes remain distinct, interacting only when preparing a motor response. The present study sheds light on this debate by examining the temporal onset of ratio and congruity effects as participants made ordinal judgments about number and cumulative area. Event-related potentials (ERPs) were recorded to identify whether the onset of such effects aligned with early versus late views. Ratio effects for both magnitudes were observed starting in the P100. Moreover, a congruity effect emerged within the P100. That interactions were observed early in processing, at the same time that initial ratio effects occurred, suggests that number and cumulative area processes interacted when magnitude representations were being formed, prior to preparing a decision response. Our findings are consistent with an early interaction view of magnitude processing, in which number and cumulative area may rely on shared perceptual mechanisms.

Electrophysiological Correlates of the Interaction of Physical and Numerical Size in Symbolic Number Processing: Insights from a Novel Go/Nogo Numerical Stroop Task

The interaction of physical and numerical size has been investigated and repeatedly demonstrated in the numerical Stroop task, in which participants compare digits of different physical sizes. It is, however, not entirely clear yet what psychological processes contribute to this interaction. The aim of the present study is to investigate the role of inhibition in the interaction of physical and numerical size, by introducing a novel paradigm that is suitable to elicit inhibition-related event-related potential components. To this end, we combined the go/nogo paradigm with the numerical Stroop task while measuring EEG and reaction times. Participants were presented with Arabic number pairs and had to press a button if the number on one side was numerically larger and they had to refrain from responding if the number on the other side was numerically larger. The physical size of the number pairs was also manipulated, in order to create congruent, neutral, and incongruent trials. Behavioural results confirmed the well-established numerical distance and numerical Stroop effects. Analysis of electrophysiological data revealed the classical go/nogo electrophysiological effects with numerical stimuli, and showed that peak amplitudes were larger for nogo than for go trials on the N2, as well as on the P3 component, on frontal and midline electrodes. When analysing the congruency effects, the peak amplitude of N2 was larger in incongruent trials than in neutral and congruent trials, while there was no evidence of a congruency effect on the P3 component peaks. Further analysis of the electrophysiological data revealed an additional facilitatory effect in the go trials, as well as an additional interference effect in the nogo trials. Taken together, it seems that interference effects are probably resolved by inhibitory processes and that facilitatory effects are affected by different cognitive control processes required by go versus nogo trials.

Event-Related Potentials Reveal the Impact of Conflict Strength in a Numerical Stroop Paradigm

Numerical cognition provides an opportunity to study the underlying processes of selective attention to numerical information in the face of conflicting, non-numerical, information of different magnitudes. For instance, in the numerical Stroop paradigm, participants are asked to judge pairs of Arabic digits whose physical size can either be congruent (e.g., 3 vs. 5) or incongruent (e.g., 3 vs. 5) with numerical value. Congruency effects when deciding which of the two digits is numerically larger are thought to reflect the inhibition of the irrelevant physical size. However, few studies have investigated the impact of the salience of the irrelevant non-numerical information on these congruency effects and their neural substrates. EEG was recorded in 32 adults during a numerical Stroop task with two levels of salience (low, high) of the irrelevant size dimension. At the behavioral level, we observed larger congruency effects in the high salience condition (i.e., when the difference in size between the two digits is larger). At the neural level, at centro-parietal electrodes, we replicated previous studies showing a main effect of congruency on event-related potential (ERP) amplitudes between 280 and 370 ms post-stimulus, as well as a main effect of salience around 200 ms post-stimulus. Crucially, congruency and salience interacted both between 230 and 250 ms (P2), and between 290 and 340 ms (P3). These results provide support for separate processes underlying the increase in congruency effect, which can be attributed to higher demands in both the inhibition of the irrelevant dimension, and the attention to the relevant numerical information.

Irregular stimulus distribution increases the negative footprint illusion

As a climate change mitigation strategy, environmentally certified 'green' buildings with low carbon footprints are becoming more prevalent in the world. An interesting psychological question is how people perceive the carbon footprint of these buildings given their spatial distributions in a given community. Here we examine whether regular distribution (i.e., buildings organized in a block) or irregular distribution (i.e., buildings randomly distributed) influences people's perception of the carbon footprint of the communities. We first replicated the negative footprint illusion, the tendency to estimate a lower carbon footprint of a combined group of environmentally certified green buildings and ordinary conventional buildings, than the carbon footprint of the conventional buildings alone. Importantly, we found that irregular distribution of the buildings increased the magnitude of the negative footprint illusion. Potential applied implications for urban planning of green buildings are discussed.

The Number Sense Represents (Rational) Numbers

On a now orthodox view, humans and many other animals possess a "number sense," or approximate number system (ANS), that represents number. Recently, this orthodox view has been subject to numerous critiques that question whether the ANS genuinely represents number. We distinguish three lines of critique-the arguments from congruency, confounds, and imprecision-and show that none succeed. We then provide positive reasons to think that the ANS genuinely represents numbers, and not just non-numerical confounds or exotic substitutes for number, such as "numerosities" or "quanticals," as critics propose. In so doing, we raise a neglected question: numbers of what kind? Proponents of the orthodox view have been remarkably coy on this issue. But this is unsatisfactory since the predictions of the orthodox view, including the situations in which the ANS is expected to succeed or fail, turn on the kind(s) of number being represented. In response, we propose that the ANS represents not only natural numbers (e.g. 7), but also non-natural rational numbers (e.g. 3.5). It does not represent irrational numbers (e.g. √2), however, and thereby fails to represent the real numbers more generally. This distances our proposal from existing conjectures, refines our understanding of the ANS, and paves the way for future research.

Frequency-based Dissociation of Symbolic and Nonsymbolic Numerical Processing during Numerical Comparison

Recent evidence suggests that during numerical calculation, symbolic and nonsymbolic processing are functionally distinct operations. Nevertheless, both roughly recruit the same brain areas (spatially overlapping networks in the parietal cortex) and happen at the same time (roughly 250 msec poststimulus onset). We tested the hypothesis that symbolic and nonsymbolic processing are segregated by means of functionally relevant networks in different frequency ranges: high gamma (above 50 Hz) for symbolic processing and lower beta (12–17 Hz) for nonsymbolic processing. EEG signals were quantified as participants compared either symbolic numbers or nonsymbolic quantities. Larger EEG gamma-band power was observed for more difficult symbolic comparisons (ratio of 0.8 between the two numbers) than for easier comparisons (ratio of 0.2) over frontocentral regions. Similarly, beta-band power was larger for more difficult nonsymbolic comparisons than for easier ones over parietal areas. These results confirm the existence of a functional dissociation in EEG oscillatory dynamics during numerical processing that is compatible with the notion of distinct linguistic processing of symbolic numbers and approximation of nonsymbolic numerical information.

The interplay between non-symbolic number and its continuous visual properties revisited: Effects of mixing trials of different types

In the last few years, the existence of a pure number sense has been challenged. Recent studies suggest that numerosity processing is influenced not only by the number of elements in a display but also by continuous magnitudes, such as the size of the elements. The aim of our study was to replicate and extend the findings by Gebuis and Reynvoet, who systematically manipulated different continuous magnitudes either congruently or incongruently with discrete numerosity. We were particularly interested in finding the same pattern of congruency effects and assess its stability and robustness as this pattern indicates a complex influence of continuous magnitudes on numerosity judgements. We did so by showing stimuli of different conditions either in separate blocks or mixed together while participants solved a dot comparison task. Our results are in line with the notion that discrete number and continuous magnitudes are integrated in numerosity judgements by means of a weighing process. Moreover, our findings suggest that this integration is modified by the mode of presentation (blocked vs. mixed).

Grouping effects in numerosity perception under prolonged viewing conditions

Humans can estimate numerosities-such as the number sheep in a flock-without deliberate counting. A number of biases have been identified in these estimates, which seem primarily rooted in the spatial organization of objects (grouping, symmetry, etc). Most previous studies on the number sense used static stimuli with extremely brief exposure times. However, outside the laboratory, visual scenes are often dynamic and freely viewed for prolonged durations (e.g., a flock of moving sheep). The purpose of the present study is to examine grouping-induced numerosity biases in stimuli that more closely mimic these conditions. To this end, we designed two experiments with limited-dot-lifetime displays (LDDs), in which each dot is visible for a brief period of time and replaced by a new dot elsewhere after its disappearance. The dynamic nature of LDDs prevents subjects from counting even when they are free-viewing a stimulus under prolonged presentation. Subjects estimated the number of dots in arrays that were presented either as a single group or were segregated into two groups by spatial clustering, dot size, dot color, or dot motion. Grouping by color and motion reduced perceived numerosity compared to viewing them as a single group. Moreover, the grouping effect sizes between these two features were correlated, which suggests that the effects may share a common, feature-invariant mechanism. Finally, we find that dot size and total stimulus area directly affect perceived numerosity, which makes it difficult to draw reliable conclusions about grouping effects induced by spatial clustering and dot size. Our results provide new insights into biases in numerosity estimation and they demonstrate that the use of LDDs is an effective method to study the human number sense under prolonged viewing.

Automatic non-symbolic numerosity processing in preschoolers

There has recently been an increasing focus on the development of automatic processing of numerical magnitude. However, little effort has been made to explore automatic access to non-symbolic numerical magnitude in preschool children. In experiment 1, we used a non-symbolic physical size comparison task in 3- to 6-year-olds to examine developmental changes and the effect of ratio and counting principle knowledge. Results showed that the existence of automatic non-symbolic numerical processing began at age 3–4 years and size congruity effects tended to reduce with increasing age from 4 years old. The study also found that non-counting-principle knowers had a larger congruity effect, and in low ratio conditions the size congruity effect was more easily found. In addition, symbolic number comparison ability was negatively related to size congruity effect. In experiment 2, we explored the relationship between inhibition skill and size congruity effects, as well as interference and facilitatory components in children aged 4 years old. Results showed no correlation between inhibition skills and the size congruity effect and only interference effects were found. We also found a larger interference effect in low ratio conditions than in high ratio conditions.

Sensory-integration system rather than approximate number system underlies numerosity processing: A critical review

It is widely accepted that human and nonhuman species possess a specialized system to process large approximate numerosities. The theory of an evolutionarily ancient approximate number system (ANS) has received converging support from developmental studies, comparative experiments, neuroimaging, and computational modelling, and it is one of the most dominant and influential theories in numerical cognition. The existence of an ANS system is significant, as it is believed to be the building block of numerical development in general. The acuity of the ANS is related to future arithmetic achievements, and intervention strategies therefore aim to improve the ANS. Here we critically review current evidence supporting the existence of an ANS. We show that important shortcomings and confounds exist in the empirical studies on human and non-human animals as well as the logic used to build computational models that support the ANS theory. We conclude that rather than taking the ANS theory for granted, a more comprehensive explanation might be provided by a sensory-integration system that compares or estimates large approximate numerosities by integrating the different sensory cues comprising number stimuli.

Learning to integrate versus inhibiting information is modulated by age

Cognitive training aiming at improving learning is often successful, but what exactly underlies the observed improvements and how these differ across the age spectrum are currently unknown. Here we asked whether learning in young and older people may reflect enhanced ability to integrate information required to perform a cognitive task or whether it may instead reflect the ability to inhibit task-irrelevant information for successful task performance. We trained 30 young and 30 aging human participants on a numerosity discrimination task known to engage the parietal cortex and in which cue-integration and inhibitory abilities can be distinguished. We coupled training with parietal, motor, or sham transcranial random noise stimulation, known for modulating neural activity. Numerosity discrimination improved after training and was maintained long term, especially in the training + parietal stimulation group, regardless of age. Despite the quantitatively similar improvement in the two age groups, the content of learning differed remarkably: aging participants improved more in inhibitory abilities, whereas younger subjects improved in cue-integration abilities. Moreover, differences in the content of learning were reflected in different transfer effects to untrained but related abilities: in the younger group, improvements in cue integration paralleled improvements in continuous quantity (time and space), whereas in the elderly group, improvements in numerosity-based inhibitory abilities generalized to other measures of inhibition and corresponded to a decline in space discrimination, possibly because conflicting learning resources are used in numerosity and continuous quantity processing. These results indicate that training can enhance different, age-dependent cognitive processes and highlight the importance of identifying the exact processes underlying learning for effective training programs.

Magnitude representations in Williams syndrome: differential acuity in time, space and number processing

For some authors, the human sensitivity to numerosities would be grounded in our ability to process non-numerical magnitudes. In the present study, the developmental relationships between non numerical and numerical magnitude processing are examined in people with Williams syndrome (WS), a genetic disorder known to associate visuo-spatial and math learning disabilities. Twenty patients with WS and 40 typically developing children matched on verbal or non-verbal abilities were administered three comparison tasks in which they had to compare numerosities, lengths or durations. Participants with WS showed lower acuity (manifested by a higher Weber fraction) than their verbal matched peers when processing numerical and spatial but not temporal magnitudes, indicating that they do not present a domain-general dysfunction of all magnitude processing. Conversely, they do not differ from non-verbal matched participants in any of the three tasks. Finally, correlational analyses revealed that non-numerical and numerical acuity indexes were both related to the first mathematical acquisitions but not with later arithmetical skills.

Multiple faces elicit augmented neural activity

How do our brains respond when we are being watched by a group of people?Despite the large volume of literature devoted to face processing, this question has received very little attention. Here we measured the effects on the face-sensitive N170 and other ERPs to viewing displays of one, two and three faces in two experiments. In Experiment 1, overall image brightness and contrast were adjusted to be constant, whereas in Experiment 2 local contrast and brightness of individual faces were not manipulated. A robust positive-negative-positive (P100-N170-P250) ERP complex and an additional late positive ERP, the P400, were elicited to all stimulus types. As the number of faces in the display increased, N170 amplitude increased for both stimulus sets, and latency increased in Experiment 2. P100 latency and P250 amplitude were affected by changes in overall brightness and contrast, but not by the number of faces in the display per se. In Experiment 1 when overall brightness and contrast were adjusted to be constant, later ERP (P250 and P400) latencies showed differences as a function of hemisphere. Hence, our data indicate that N170 increases its magnitude when multiple faces are seen, apparently impervious to basic low-level stimulus features including stimulus size. Outstanding questions remain regarding category-sensitive neural activity that is elicited to viewing multiple items of stimulus categories other than faces.

Comparing the neural distance effect derived from the non-symbolic comparison and the same-different task

As a result of the representation of numerosities, more accurate and faster discrimination between two numerosities is observed when the distance between them increases. In previous studies, the comparison and same-different task were most frequently used to investigate this distance effect. Recently, it was questioned whether the non-symbolic distance effects derived from these tasks originate at the same level. In the current study, we examined the behavioral and neural distance effects of the comparison and same-different task to assess potential differences between both tasks. Participants were first year university students. Each participant completed both tasks, while their reaction time, accuracy and brain activity on predefined components was measured. The early N1-P2p transition and the P2p component on temporo-occipital (TO) and inferior parietal (IP) electrode groups were considered, as well as the late P3 component on a central (C) electrode group. The results showed that the behavioral distance effects from both tasks were comparable, although participants' performance was worse on the same-different task. The neural results revealed similar effects of distance on the mean amplitudes for the early components for both tasks (all p′s < 0.02) and an additional effect of task difficulty on the mean amplitudes of these components. Similar as in previous studies, we found a (marginally) significant increase in mean amplitude of the later P3 component with increasing distance for the comparison (p = 0.07), but not for the same-different task. Apparently, the initial stages of number processing are comparable for both tasks, but an additional later stage is only present for the comparison task. The P3 effect would be indicative of this decisional stage, which was previously proposed to underlie the comparison distance effect (CDE).

Automatic and intentional number processing both rely on intact right parietal cortex: a combined FMRI and neuronavigated TMS study

Practice and training usually lead to performance increase in a given task. In addition, a shift from intentional toward more automatic processing mechanisms is often observed. It is currently debated whether automatic and intentional processing is subserved by the same or by different mechanism(s), and whether the same or different regions in the brain are recruited. Previous correlational evidence provided by behavioral, neuroimaging, modeling, and neuropsychological studies addressing this question yielded conflicting results. Here we used transcranial magnetic stimulation (TMS) to compare the causal influence of disrupting either left or right parietal cortex during automatic and intentional numerical processing, as reflected by the size congruity effect and the numerical distance effect, respectively. We found a functional hemispheric asymmetry within parietal cortex with only the TMS-induced right parietal disruption impairing both automatic and intentional numerical processing. In contrast, disrupting the left parietal lobe with TMS, or applying sham stimulation, did not affect performance during automatic or intentional numerical processing. The current results provide causal evidence for the functional relevance of right, but not left, parietal cortex for intentional, and automatic numerical processing, implying that at least within the parietal cortices, automatic, and intentional numerical processing rely on the same underlying hemispheric lateralization.

Incongruence in number-luminance congruency effects

Congruency tasks have provided support for an amodal magnitude system for magnitudes that have a "spatial" character, but conflicting results have been obtained for magnitudes that do not (e.g., luminance). In this study, we extricated the factors that underlie these number-luminance congruency effects and tested alternative explanations: (unsigned) luminance contrast and saliency. When luminance had to be compared under specific task conditions, we revealed, for the first time, a true influence of number on luminance judgments: Darker stimuli were consistently associated with numerically larger stimuli. However, when number had to be compared, luminance contrast, not luminance, influenced number judgments. Apparently, associations exist between number and luminance, as well as luminance contrast, of which the latter is probably stronger. Therefore, similar tasks, comprising exactly the same stimuli, can lead to distinct interference effects.