Titia Gebuis

The Interplay between Nonsymbolic Number and Its Continuous Visual Properties.

To date, researchers investigating nonsymbolic number processes devoted little attention to the visual properties of their stimuli. This is unexpected, as nonsymbolic number is defined by its visual characteristics. When number changes, its visual properties change accordingly. In this study, we investigated the influence of different visual properties on nonsymbolic number processes and show that the current assumptions about the relation between number and its visual characteristics are incorrect. Similar to previous studies, we controlled the visual cues: Each visual cue was not predictive of number. Nevertheless, participants showed congruency effects induced by the visual properties of the stimuli. These congruency effects scaled with the number of visual cues manipulated, implicating that people do not extract number from a visual scene independent of its visual cues. Instead, number judgments are based on the integration of information from multiple visual cues. Consequently, current ways to control the visual cues of the number stimuli are insufficient, as they control only a single variable at the time. And, more important, the existence of an approximate number system that can extract number independent of the visual cues appears unlikely. We therefore propose that number judgment is the result of the weighing of several distinct visual cues.

The role of visual information in numerosity estimation

Mainstream theory suggests that the approximate number system supports our non-symbolic number abilities (e.g. estimating or comparing different sets of items). It is argued that this system can extract number independently of the visual cues present in the stimulus (diameter, aggregate surface, etc.). However, in a recent report we argue that this might not be the case. We showed that participants combined information from different visual cues to derive their answers. While numerosity comparison requires a rough comparison of two sets of items (smaller versus larger), numerosity estimation requires a more precise mechanism. It could therefore be that numerosity estimation, in contrast to numerosity comparison, might rely on the approximate number system. To test this hypothesis, we conducted a numerosity estimation experiment. We controlled for the visual cues according to current standards: each single visual property was not informative about numerosity. Nevertheless, the results reveal that participants were influenced by the visual properties of the dot arrays. They gave a larger estimate when the dot arrays consisted of dots with, on average, a smaller diameter, aggregate surface or density but a larger convex hull. The reliance on visual cues to estimate numerosity suggests that the existence of an approximate number system that can extract numerosity independently of the visual cues is unlikely. Instead, we propose that humans estimate numerosity by weighing the different visual cues present in the stimuli.

Automatic quantity processing in 5-year olds and adults

In this study adults performed numerical and physical size judgments on a symbolic (Arabic numerals) and non-symbolic (groups of dots) size congruity task. The outcomes would reveal whether a size congruity effect (SCE) can be obtained irrespective of notation. Subsequently, 5-year-old children performed a physical size judgment on both tasks. The outcomes will give a better insight in the ability of 5-year-olds to automatically process symbolic and non-symbolic numerosities. Adult performance on the symbolic and non-symbolic size congruity tasks revealed a SCE for numerical and physical size judgments, indicating that the non-symbolic size congruity task is a valid indicator for automatic processing of non-symbolic numerosities. Physical size judgments on both tasks by children revealed a SCE only for non-symbolic notation, indicating that the lack of a symbolic SCE is not related to the mathematical or cognitive abilities required for the task but instead to an immature association between the number symbol and its meaning.

Continuous visual properties explain neural responses to nonsymbolic number

Nonsymbolic number and its continuous visual properties are confounded in everyday life: When number changes, its continuous visual properties also change. It could therefore be efficient to rely on the visual properties to judge number. The current consensus, however, holds that number is processed independent of its visual properties. In this study, we pitched these two opposing theories against each other. We used electroencephalography to look at the components suggested to process number. The first experiment showed that number and visual cues affect the N1 and/or the P2 component. To disentangle number and visual processes, we controlled the visual cues in the second experiment. Now, no number-related effects were present. When the data were reorganized according to visual cue instead of number size, N1 and P2 effects emerged. These results argue against the idea that number is processed independent of its continuous visual variables.

Numerosities and space; indeed a cognitive illusion! A reply to de Hevia and Spelke (2009).

de Hevia and Spelke (de Hevia and Spelke (2009). Spontaneous mapping of number and space in adults and young children, Cognition, 110, 198-207) investigated the mapping of number onto space. To this end, they introduced a non-symbolic flanker task. Here subjects have to bisect a line that is flanked by a 2-dot and a 9-dot array. Similar to the symbolic line bisection task, a bias towards the larger numerosity was observed. We re-investigated these results both by creating new flanker stimuli that controlled for different (non-numerical) stimulus properties and by developing a new measurement tool. We demonstrate that the bisection bias was caused by the larger area subtended by the 9-dot array compared to the 2-dot array and not numerosity. Our study puts constraints on the results of the study by de Hevia and Spelke. The role of visual cues in numerosity processing in general is discussed.

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.

Topographic representation of high-level cognition: Numerosity or sensory processing?

A recent study showed that topographic field maps of complex cognitive functions, such as numerosity, exist in the human brain. This is an exciting, novel approach for studying the neural representation of high-level cognition. However, the results can also be explained on the basis of the confounding non-numerical sensory cues of numerosity.

False approximations of the approximate number system

Prior research suggests that the acuity of the approximate number system (ANS) predicts future mathematical abilities. Modelling the development of the ANS might therefore allow monitoring of childrens mathematical skills and instigate educational intervention if necessary. A major problem however, is that our knowledge of the development of the ANS is acquired using fundamentally different paradigms, namely detection in infants versus discrimination in children and adults. Here, we question whether such a comparison is justified, by testing the adult ANS with both a discrimination and a detection task. We show that adults perform markedly better in the discrimination compared to the detection task. Moreover, performance on discrimination but not detection, correlated with performance on mathematics. With a second similar experiment, in which the detection task was replaced by a same-different task, we show that the results of experiment 1 cannot be attributed to differences in chance level. As only task instruction differed, the discrimination and the detection task most likely reflect differences at the decisional level. Future studies intending to model the development of the ANS should therefore rely on data derived from a single paradigm for different age groups. The same-different task appears a viable candidate, due to its applicability across age groups.

The neural mechanisms underlying passive and active processing of numerosity.

To investigate the difference in passive viewing and active processing of numerosity, we presented participants arrays of dots and concurrently measured their EEG. In the first condition, participants naïve to the subject under study passively viewed the dot-arrays. In the second condition, the participants were informed about the changes in numerosity and had to actively process numerosity. The visual properties of the dot-arrays were controlled and could therefore not explain possible numerosity related effects. The results revealed no numerosity related effects in the passive and active conditions. Instead, when the data was reorganised according to visual cue size (surface or diameter, etc.), strong effects of the visual cues were present at lateral occipital and parietal electrode sites. These electrode sites and time windows correspond to the ERP components often suggested to support numerosity processes. Furthermore, a larger central-parietal P3 amplitude effect was present for active versus passive numerosity processing. This result was not influenced by numerosity itself and could not be explained by response processing. It therefore appears to reflect general cognitive processes. Together, our results show that we do not (automatically) extract numerosity from a visual scene during passive or active processing of numerosity. Instead, these results are consistent with the notion that we rely on the continuous sensory properties of numerosity stimuli to make numerosity judgments.

Multiple dimensions in bi-directional synesthesia.

Grapheme‐color synesthetes report seeing a specific color when a number is perceived. The reverse, the synesthetic experience of a specific grapheme after the percept of a color is extremely rare. However, recent studies have revealed these interactions at both behavioral and neurophysiological levels. We investigated whether similar neuronal processes (i.e. perceptual and/or attentional) may underlie this bi‐directional interaction by measuring event‐related potentials (ERPs) during both a number‐color and color‐number priming task. In addition, we investigated the unitarity of synesthesia by comparing two distinct subtypes of synesthetes, projectors and associators, and assessed whether consistencies between measures (i.e. behavioral and electrophysiological) were present across synesthetes. Our results show longer reaction times for incongruent compared with congruent trials in both tasks. This priming effect is also present in the P3b latency (parietal electrode site) and P3a amplitude (frontal electrode site) of the ERP data. Interestingly, projector and associator synesthetes did not reveal distinct behavioral or electrophysiological patterns. Instead, a dissociation was found when synesthetes were divided in two groups on the basis of their behavioral data. Synesthetes with a large behavioral priming effect revealed ERP modulation at the frontal and parietal electrode sites, whereas synesthetes with a small priming effect revealed a frontal effect only. Together, these results show, for the first time, that similar neural mechanisms underlie bi‐directional synesthesia in synesthetes that do not report a synesthetic experience of a grapheme when a color is perceived. In addition, they add support for the notion of the existence of both ‘lower’ and ‘higher’ synesthetes.