Adaptation reveals unbalanced interaction between numerosity and time

Auditory time perception impairment in children with developmental dyscalculia

Developmental dyscalculia (DD) is a specific learning disability which prevents children from acquiring adequate numerical and arithmetical competences. We investigated whether difficulties in children with DD spread beyond the numerical domain and impact also their ability to perceive time. A group of 37 children/adolescent with and without DD were tested with an auditory categorization task measuring time perception thresholds in the sub-second (0.25-1 s) and supra-second (0.75-3 s) ranges. Results showed that auditory time perception was strongly impaired in children with DD at both time scales. The impairment remained even when age, non-verbal reasoning, and gender were regressed out. Overall, our results show that the difficulties of DD can affect magnitudes other than numerical and contribute to the increasing evidence that frames dyscalculia as a disorder affecting multiple neurocognitive and perceptual systems.

Cortical quantity representations of visual numerosity and timing overlap increasingly into superior cortices but remain distinct

Many sensory brain areas are organized as topographic maps where neural response preferences change gradually across the cortical surface. Within association cortices, 7-Tesla fMRI and neural model-based analyses have also revealed many topographic maps for quantities like numerosity and event timing, often in similar locations. Numerical and temporal quantity estimations also show behavioral similarities and even interactions. For example, the duration of high-numerosity displays is perceived as longer than that of low-numerosity displays. Such interactions are often ascribed to a generalized magnitude system with shared neural responses across quantities. Anterior quantity responses are more closely linked to behavior. Here, we investigate whether common quantity representations hierarchically emerge by asking whether numerosity and timing maps become increasingly closely related in their overlap, response preferences, and topography. While the earliest quantity maps do not overlap, more superior maps overlap increasingly. In these overlapping areas, some intraparietal maps have consistently correlated numerosity and timing preferences, and some maps have consistent angles between the topographic progressions of numerosity and timing preferences. However, neither of these relationships increases hierarchically like the amount of overlap does. Therefore, responses to different quantities are initially derived separately, then progressively brought together, without generally becoming a common representation. Bringing together distinct responses to different quantities may underlie behavioral interactions and allow shared access to comparison and action planning systems.

Effects of spatial frequency cross-adaptation on the visual number sense

When observing a simple visual scene such as an array of dots, observers can easily and automatically extract their number. How does our visual system accomplish this? We investigate the role of specific spatial frequencies to the encoding of number through cross-adaptation. In two experiments, observers were peripherally adapted to six randomly generated sinusoidal gratings varying from relatively low-spatial frequency (M = 0.44 c/deg) to relatively high-spatial frequency (M = 5.88 c/deg). Subsequently, observers judged which side of the screen had a higher number of dots. We found a strong number-adaptation effect to low-spatial frequency gratings (i.e., participants significantly underestimated the number of dots on the adapted side) but a significantly reduced adaptation effect for high-spatial frequency gratings. Various control conditions demonstrate that these effects are not due to a generic response bias for the adapted side, nor moderated by dot size or spacing effects. In a third experiment, we observed no cross-adaptation for centrally presented gratings. Our results show that observers' peripheral number perception can be adapted even with stimuli lacking any numeric or segmented object information and that low spatial frequencies adapt peripheral number perception more than high ones. Together, our results are consistent with recent number perception models that suggest a key role for spatial frequency in the extraction of number from the visual signal (e.g., Paul, Ackooij, Ten Cate, & Harvey, 2022), but additionally suggest that some spatial frequencies - especially in the low range and in the periphery - may be weighted more by the visual system when estimating number. We argue that the cross-adaptation paradigm is also a useful methodology for discovering the primitives of visual number encoding.

Near-optimal integration of the magnitude information of time and numerosity

Magnitude information is often correlated in the external world, providing complementary information about the environment. As if to reflect this relationship, the perceptions of different magnitudes (e.g. time and numerosity) are known to influence one another. Recent studies suggest that such magnitude interaction is similar to cue integration, such as multisensory integration. Here, we tested whether human observers could integrate the magnitudes of two quantities with distinct physical units (i.e. time and numerosity) as abstract magnitude information. The participants compared the magnitudes of two visual stimuli based on time, numerosity, or both. Consistent with the predictions of the maximum-likelihood estimation model, the participants integrated time and numerosity in a near-optimal manner; the weight of each dimension was proportional to their relative reliability, and the integrated estimate was more reliable than either the time or numerosity estimate. Furthermore, the integration approached a statistical optimum as the temporal discrepancy of the acquisition of each piece of information became smaller. These results suggest that magnitude interaction arises through a similar computational mechanism to cue integration. They are also consistent with the idea that different magnitudes are processed by a generalized magnitude system.

The more numerous the longer: how the integration between numerosity and time leads to a common neural response

If you are stuck in a traffic jam, the more numerous the queuing cars are, the longer you expect to wait. Time and numerosity are stimulus dimensions often associated in the same percept and whose interaction can lead to misjudgements. At brain level it is unclear to which extent time and numerosity recruit same/different neural populations and how their perceptual integration leads to changes in these populations' responses. Here we used high-spatial-resolution functional magnetic resonance imaging with neural model-based analyses to investigate how the topographic representations of numerosity and time change when these dimensions are varied together on the same visual stimulus in a congruent (the more numerous the items, the longer the display time) or incongruent manner. Compared to baseline conditions, where only one dimension was changed at a time, the variation of both stimulus dimensions led to changes in neural population responses that became more sensitive either to the two features or to one of them. Magnitude integration led also to degradation of topographies and shifts in response preferences. These changes were more pronounced in the comparison between parietal and frontal maps. Our results while pointing to partially distinct representations of time and numerosity show a common neural response to magnitude integration.

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.

Exploring spatiotemporal interactions: On the superiority of time over space

Space and time mutually influence each other such that space affects time estimation (space-on-time effect), and conversely (time-on-space effect). These reciprocal interferences suggest that space and time are intrinsically linked in the human mind. Yet, recent evidence for an asymmetrical advantage for space over time challenges the classical theoretical interpretation. In the present study, we tested whether the superiority of space over time in magnitude interference depends on the cognitive resources engaged in the spatial task. We conducted three experiments in which participants performed judgments on temporal intervals and spatial distances in separate blocks. In each trial, two dots were successively flashed at various locations, and participants were to judge whether the duration or distance between the dots was short or long. To manipulate cognitive demands in the spatial task, distances varied across experiments (highly discriminable for the non-demanding spatial task in Experiment 1 and scarcely discriminable for the demanding spatial task in Experiment 2). Importantly, this manipulation tended to enhance perceptual sensitivity (as indexed by Weber Ratios) but slowed down the decision process (as indexed by response times) in the demanding experiment. Our results provide evidence for robust space-on-time and time-on-space effects (Experiments 1 and 2). More crucially, the involvement of cognitive resources in a demanding spatial task causes a massive time-on-space effect: Spatial judgments are indeed more influenced by irrelevant temporal information than the reverse (Experiments 2 and 3). Overall, the flexibility of spatiotemporal interferences has direct theoretical implications and questions the origins of space-time interaction.

Number-time interaction: Search for a common magnitude system in a cross-modal setting

A theory of magnitude (ATOM) suggests that a generalized magnitude system in the brain processes magnitudes such as space, time, and numbers. Numerous behavioral and neurocognitive studies have provided support to ATOM theory. However, the evidence for common magnitude processing primarily comes from the studies in which numerical and temporal information are presented visually. Our current understanding of such cross-dimensional magnitude interactions is limited to visual modality only. However, it is still unclear whether the ATOM-framework accounts for the integration of cross-modal magnitude information. To examine the cross-modal influence of numerical magnitude on temporal processing of the tone, we conducted three experiments using a temporal bisection task. We presented the numerical magnitude information in the visual domain and the temporal information in the auditory either simultaneously with duration judgment task (Experiment-1), before duration judgment task (Experiment-2), and before duration judgment task but with numerical magnitude also being task-relevant (Experiment-3). The results suggest that the numerical information presented in the visual domain affects temporal processing of the tone only when the numerical magnitudes were task-relevant and available while making a temporal judgment (Experiments-1 and 3). However, numerical information did not interfere with temporal information when presented temporally separated from the duration information (Experiments-2). The findings indicate that the influence of visual numbers on temporal processing in cross-modal settings may not arise from the common magnitude system but instead from general cognitive mechanisms like attention and memory.

The role of neural tuning in quantity perception

Perception of quantities, such as numerosity, timing, and size, is essential for behavior and cognition. Accumulating evidence demonstrates neurons processing quantities are tuned, that is, have a preferred quantity amount, not only for numerosity, but also other quantity dimensions and sensory modalities. We argue that quantity-tuned neurons are fundamental to understanding quantity perception. We illustrate how the properties of quantity-tuned neurons can underlie a range of perceptual phenomena. Furthermore, quantity-tuned neurons are organized in distinct but overlapping topographic maps. We suggest that this overlap in tuning provides the neural basis for perceptual interactions between different quantities, without the need for a common neural representational code.

Temporal enhancement of cross-adaptation between density and size perception based on the theory of magnitude

The ability to estimate spatial extent is an important feature of the visual system. A previous study showed that perceived sizes of stimuli shrank after adaptation to a dense texture and that this density-size aftereffect was modulated by the degree of density. In this study, we found that the aftereffect was also modulated by the temporal density of the adapting texture. The test stimuli were two circles, and the adapting stimulus had a dotted texture. The adapting texture refreshed every 67 to 500 ms, or not at all (static), during the adaptation. The results showed that the aftereffects from a refreshing stimulus were larger than those under the static condition. On the other hand, density adaptation lacked such enhancement. This result indicates that repetitive presentation of an adapting texture enhanced the density-size cross-aftereffect. The fact that density modulation occurs in both the spatial and temporal domains is consistent with the theory of magnitude, which assumes that the processing of the magnitude estimation of space, time, and numbers share a common cortical basis.

Attention mediates the influence of numerical magnitude on temporal processing

The processing of time and numbers has been fundamental to human cognition. One of the prominent theories of magnitude processing, a theory of magnitude (ATOM), suggests that a generalized magnitude system processes space, time, and numbers; thereby, the magnitude dimensions could potentially interact with one another. However, more recent studies have found support for domain-specific magnitude processing and argued that the magnitudes related to time and number are processed through distinct mechanisms. Such mixed findings have raised questions about whether these magnitudes are processed independently or share a common processing mechanism. In the present study, we examine the influence of numerical magnitude on temporal processing. To investigate, we conducted two experiments using a temporal comparison task, wherein we presented positive and negative numerical magnitudes (large and small) in a blocked (Experiment-1) and intermixed manner (Experiment-2). Results from experiment-1 suggest that numerical magnitude affects temporal processing only in positive numbers but not for negative numbers. Further, results from experiment-2 indicate that the polarity (positive and negative) of the numbers influences temporal processing instead of the numerical magnitude itself. Overall, the current study seems to suggest that cross-domain interaction of magnitudes arises from attentional mechanisms and may not need to posit a common magnitude processing system.

Serial dependence in time and numerosity perception is dimension-specific

The perception of a visual event (e.g., a flock of birds) at the present moment can be biased by a previous perceptual experience (e.g., the perception of an earlier flock). Serial dependence is a perceptual bias whereby a current stimulus appears more similar to a previous one than it actually is. Whereas serial dependence emerges within several visual stimulus dimensions, whether it could simultaneously operate across different dimensions of the same stimulus (e.g., the numerosity and the duration of a visual pattern) remains unclear. Here we address this question by assessing the presence of serial dependence across duration and numerosity, two stimulus dimensions that are often associated and can bias each other. Participants performed either a duration or a numerosity discrimination task, in which they compared a constant reference with a variable test stimulus, varying along the task-relevant dimension (either duration or numerosity). Serial dependence was induced by a task-irrelevant inducer, that is, a stimulus presented before the reference and always varying in both duration and numerosity. The results show systematic serial dependencies only within the task-relevant stimulus dimension, that is, stimulus numerosity affects numerosity perception only, and duration affects duration perception only. Additionally, at least in the numerosity condition, the task-irrelevant dimension of the inducer (duration) had an opposite, repulsive effect. These findings thus show that attractive serial dependence operates in a highly specific fashion and does not transfer across different stimulus dimensions. Instead, the repulsive influence, possibly reflecting perceptual adaptation, can transfer from one dimension to another.

Time and numerosity estimation in peripersonal and extrapersonal space

The representation of space, time and number is believed to rely on a common encoding system developed to support action guidance. While the ecological advantage of such a shared system is evident when objects are located within the region of space we can act on (known as peri-personal space), it is less obvious in the case of objects located beyond our arms' reach. In the current study we investigated whether and to what extent the distance of the stimuli from the observer affects the perception of duration and numerosity. We first replicated Anelli et al.'s (2015) experiment by asking adult participants to perform a duration reproduction task with stimuli of different sizes displayed in the peri- or extra-personal space, and then applied the same paradigm to a non-symbolic numerosity estimation task. Results show that, independently of size, duration estimates were overestimated when visual stimuli were presented in the extra-personal space, replicating previous findings. A similar effect was also found for numerosity perception, however overestimation for far stimuli was much smaller in magnitude and was accounted by the difference in perceived size between stimuli presented in peripersonal or extrapersonal space. Overall, these results suggest that, while the processing of temporal information is robustly affected by the position of the stimuli in either the peri- or extra-personal space, numerosity perception is independent from stimulus distance. We speculate that, while time and numerosity may be encoded by a shared system in the peri-personal space (to optimize action execution), different and partially independent mechanisms may underlie the representation of time and numerosity in extra-personal space. Furthermore, these results suggest that investigating magnitude perception across spatial planes (where it is or is not possible to act) may unveil processing differences that would otherwise pass unnoticed.

Adaptation to visual numerosity changes neural numerosity selectivity

Perceiving numerosity, i.e. the set size of a group of items, is an evolutionarily preserved ability found in humans and animals. A useful method to infer the neural underpinnings of a given perceptual property is sensory adaptation. Like other primary perceptual attributes, numerosity is susceptible to adaptation. Recently, we have shown numerosity-selective neural populations with a topographic organization in the human brain. Here, we investigated whether numerosity adaptation can affect the numerosity selectivity of these populations using ultra-high field (7 Tesla) functional magnetic resonance imaging (fMRI). Participants viewed stimuli of changing numerosity (1 to 7 dots), which allowed the mapping of numerosity selectivity. We interleaved a low or high numerosity adapter stimulus with these mapping stimuli, repeatedly presenting 1 or 20 dots respectively to adapt the numerosity-selective neural populations. We analyzed the responses using custom-build population receptive field neural models of numerosity encoding and compared estimated numerosity preferences between adaptation conditions. We replicated our previous studies where we found several topographic maps of numerosity-selective responses. We found that overall, numerosity adaptation altered the preferred numerosities within the numerosity maps, resulting in predominantly attractive biases towards the numerosity of the adapter. The differential biases could be explained by the difference between the unadapted preferred numerosity and the numerosity of the adapter, with attractive biases being observed with higher difference. The results could link perceptual numerosity adaptation effects to changes in neural numerosity selectivity.

Adaptation to mean and variance: Interrelationships between mean and variance representations in orientation perception

When there are many visual items, the visual system could represent their summary statistics (e.g., mean, variance) to process them efficiently. Although many previous studies have investigated the mean or variance representation itself, a relationship between these two ensemble representations has not been investigated much. In this study, we tested the potential interaction between mean and variance representations by using a visual adaptation method. We reasoned that if mean and variance representations interact with each other, an adaptation aftereffect to either mean or variance would influence the perception of the other. Participants watched a sequence of orientation arrays containing a specific statistical property during the adaptation period. To produce an adaptation aftereffect specific to variance or mean, one property of the adaptor arrays (variance or mean) had a fixed value while the other property was randomly varied. After the adaptation, participants were asked to discriminate the property of the test array that was randomly varied during the adaptation. We found that the adaptation aftereffect of orientation variance influenced the sensitivity of mean orientation discrimination (Experiment 1), and that the adaptation aftereffect of mean orientation influenced the bias of orientation variance discrimination (Experiment 2). These results suggest that mean and variance representations do closely interact with each other. Considering that mean and variance reflect the representative value and dispersion of multiple items respectively, the interactions between mean and variance representations may reflect their complementary roles to summarize complex visual information effectively.

Can Implicit or Explicit Time Processing Impact Numerical Representation? Evidence From a Dual Task Paradigm

Whether the human brain processes various types of magnitude, such as numbers and time, through a shared representation or whether there are different representations for each type of magnitude is still debated. Here, we investigated two aspects of number-time interaction: the effects of implicit and explicit processing of time on numbers and the bi-directional interaction between time and number processing. Thirty-two participants were randomly assigned into two experimental groups that performed, respectively, a Single task (number comparison, with implicit time processing) and a Dual task (number comparison as a primary task, with explicit time processing as a secondary task). Results showed that participants, only in the Dual task, were faster and more accurate when processing large numbers paired with long rather than short durations, whereas the opposite pattern was not evident for small numbers. Moreover, participants were more accurate when judging long durations after having processed large rather than small numbers, whereas the opposite pattern emerged for short durations. We propose that number processing influences time processing more than vice versa, suggesting that numbers and time might be at least partially independently represented. This finding can pave the way for investigating the hierarchical representation of space, numbers, and time.