A Bayesian Perspective on Accumulation in the Magnitude System

Space-time interference: The asymmetry we get out is the asymmetry we put in

Temporal judgments are more affected by space than vice versa. This asymmetry has often been interpreted as primacy of spatial representations over temporal ones. This interpretation is in line with conceptual metaphor theory that humans conceptualize time by spatial metaphors, but is inconsistent with the assumption of a common neuronal magnitude system. Here we review the accumulating evidence for a genuinely symmetric interference between time and space and discuss potential explanations as to why asymmetric interference can arise, both with respect to the interaction between spatial size and temporal duration, and the interaction between traveled distance and travel time. Contrary to the view of hierarchical representations of time and space, our review suggests that asymmetric interference can be explained on the basis of working memory processes and the aspect of speed inherent in dynamic stimuli. We conclude that the asymmetry we often get out (space affects time more than vice versa) is a consequence of the asymmetry we put in (by using biased paradigms and stimuli facilitating spatial processing).

Measuring temporal bias in sequential numerosity comparison

While several methods have been proposed to assess the influence of continuous visual cues in parallel numerosity estimation, the impact of temporal magnitudes on sequential numerosity judgments has been largely ignored. To overcome this issue, we extend a recently proposed framework that makes it possible to separate the contribution of numerical and non-numerical information in numerosity comparison by introducing a novel stimulus space designed for sequential tasks. Our method systematically varies the temporal magnitudes embedded into event sequences through the orthogonal manipulation of numerosity and two latent factors, which we designate as "duration" and "temporal spacing". This allows us to measure the contribution of finer-grained temporal features on numerosity judgments in several sensory modalities. We validate the proposed method on two different experiments in both visual and auditory modalities: results show that adult participants discriminated sequences primarily by relying on numerosity, with similar acuity in the visual and auditory modality. However, participants were similarly influenced by non-numerical cues, such as the total duration of the stimuli, suggesting that temporal cues can significantly bias numerical processing. Our findings highlight the need to carefully consider the continuous properties of numerical stimuli in a sequential mode of presentation as well, with particular relevance in multimodal and cross-modal investigations. We provide the complete code for creating sequential stimuli and analyzing participants' responses.

Gradient Organization of Space, Time, and Numbers in the Brain: A Meta-analysis of Neuroimaging Studies

In this study, we ran a meta-analysis of neuroimaging studies to pinpoint the neural regions that are commonly activated across space, time, and numerosity, and we tested the existence of gradient transitions among these magnitude representations in the brain. Following PRISMA guidelines, we included in the meta-analysis 112 experiments (for space domain), 114 experiments (time domain), and 115 experiments (numerosity domain), and we used the activation likelihood estimation method. We found a system of brain regions that was commonly recruited in all the three magnitudes, which included bilateral insula, the supplementary motor area (SMA), the right inferior frontal gyrus, and bilateral intraparietal sulci. Gradiental transitions between different magnitudes were found along all these regions but insulae, with space and numbers leading to gradients mainly over parietal regions (and SMA) whereas time and numbers mainly over frontal regions. These findings provide evidence for the GradiATOM theory (Gradient Theory of Magnitude), suggesting that spatial proximity given by overlapping activations and gradients is a key aspect for efficient interactions and integrations among magnitudes.

Memory traces of duration and location in the right intraparietal sulcus

Time and space form an integral part of every human experience, and for the neuronal representation of these perceptual dimensions, previous studies point to the involvement of the right-hemispheric intraparietal sulcus and structures in the medial temporal lobe. Here we used multi-voxel pattern analysis (MVPA) to investigate long-term memory traces for temporal and spatial stimulus features in those areas. Participants were trained on four images associated with short versus long durations and with left versus right locations. Our results demonstrate stable representations of both temporal and spatial information in the right posterior intraparietal sulcus. Building upon previous findings of stable neuronal codes for directly perceived durations and locations, these results show that the reactivation of long-term memory traces for temporal and spatial features can be decoded from neuronal activation patterns in the right parietal cortex.

The effect of spatial distance on numerical distance processing

The close relationship between numerical and spatial representation has been widely studied. However, little is known regarding the influence of spatial distance on the processing of numerical distance. The purpose of this study was to examine this relationship by employing a modified numerical Stroop task, in which the spatial distance was either congruent or incongruent with the numerical distance. That is, numerical and spatial distances were either compatible with each other or incompatible. Experiment 1 demonstrated that when participants were directly requested to assess the numerical distance, spatial distance influenced task performance, thereby revealing a novel effect-the spatial-numerical distance congruency effect. Experiment 2 demonstrated that these relations are asymmetrical and revealed that numerical distance did not influence spatial distance when the numerical distance was task-irrelevant. Experiment 3 revealed that the spatial-numerical distance congruency effect can also be obtained automatically by employing a numerical comparison task, which is considered a marker for indirect distance processing. In addition, also tested across the three experiments was whether spatial alignment on the screen (i.e., left, centre, and right) can influence the spatial-numerical distance congruency effect. Results revealed that when numbers were presented more naturally (on the left and centre of the screen), a larger effect was obtained compared with when stimuli were presented on the right side. Together, these findings shed new light regarding the relationship between numerical distance and spatial distance and whether and how these aspects influence each other.

How is visual separation assessed? By counting distance units

How does the human visual system assess the separation between pairs of stimuli in a frontal plane? According to the direct (or subtractive) view the system finds the difference between the positions of the stimuli in a localization system. According to the indirect (or additive) view the system finds the number of instances of a distance unit lying between representations of the stimuli. Critically, position is explicitly represented under the direct view, with separation being derived from position. Position is not explicitly represented under the indirect view; separation is consequently inferred by counting an internal unit of distance. Recent results favor the indirect over the direct view of separation assessment. Dissociations between assessments of separation and position, various context effects in the assessment of separation, and suggestions that position information is not cleanly accessed argue against the direct view. At the same time, various context effects in separation assessment argue for the indirect view. Recent findings regarding the brain bases of vision are consistent with the indirect view. In short, recent results suggest that assessing the separation between two frontal stimuli involves integrating distance units between representations of the stimuli.

Same principle, but different computations in representing time and space

Time and space are two intertwined contexts that frame our cognition of the world and have shared mechanisms. A well-known theory on this case is "A Theory of Magnitude (ATOM)" which states that the perception of these two domains shares common mechanisms. However, evidence regarding shared computations of time and space is intermixed. To investigate this issue, we asked human subjects to reproduce time and distance intervals with saccadic eye movements in similarly designed tasks. We applied an observer model to both modalities and found underlying differences in the processing of time and space. While time and space computations are both probabilistic, adding priors to space perception minimally improved model performance, as opposed to time perception which was consistently better explained by Bayesian computations. We also showed that while both measurement and motor variability were smaller in distance than time reproduction, only the motor variability was correlated between them, as both tasks used saccadic eye movements for response. Our results suggest that time and space perception abide by the same algorithm but have different computational properties.

Separable Representations for Duration and Distance in Virtual Movements

To navigate through the environment, humans must be able to measure both the distance traveled in space, and the interval elapsed in time. Yet, how the brain holds both of these metrics simultaneously is less well known. One possibility is that participants measure how far and how long they have traveled relative to a known reference point. To measure this, we had human participants (n = 24) perform a distance estimation task in a virtual environment in which they were cued to attend to either the spatial or temporal interval traveled while responses were measured with multiband fMRI. We observed that both dimensions evoked similar frontoparietal networks, yet with a striking rostrocaudal dissociation between temporal and spatial estimation. Multivariate classifiers trained on each dimension were further able to predict the temporal or spatial interval traveled, with centers of activation within the SMA and retrosplenial cortex for time and space, respectively. Furthermore, a cross-classification approach revealed the right supramarginal gyrus and occipital place area as regions capable of decoding the general magnitude of the traveled distance. Altogether, our findings suggest the brain uses separate systems for tracking spatial and temporal distances, which are combined together along with dimension-nonspecific estimates.

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.

Distinctive features of experiential time: Duration, speed and event density

William James's use of "time in passing" and "stream of thoughts" may be two sides of the same coin that emerge from the brain segmenting the continuous flow of information into discrete events. Herein, we investigated how the density of events affects two temporal experiences: the felt duration and speed of time. Using a temporal bisection task, participants classified seconds-long videos of naturalistic scenes as short or long (duration), or slow or fast (passage of time). Videos contained a varying number and type of events. We found that a large number of events lengthened subjective duration and accelerated the felt passage of time. Surprisingly, participants were also faster at estimating their felt passage of time compared to duration. The perception of duration scaled with duration and event density, whereas the felt passage of time scaled with the rate of change. Altogether, our results suggest that distinct mechanisms underlie these two experiential times.

Electrophysiological hallmarks for event relations and event roles in working memory

The ability to maintain events (i.e., interactions between/among objects) in working memory is crucial for our everyday cognition, yet the format of this representation is poorly understood. The current ERP study was designed to answer two questions: How is maintaining events (e.g., the tiger hit the lion) neurally different from maintaining item coordinations (e.g., the tiger and the lion)? That is, how is the event relation (present in events but not coordinations) represented? And how is the agent, or initiator of the event encoded differently from the patient, or receiver of the event during maintenance? We used a novel picture-sentence match-across-delay approach in which the working memory representation was "pinged" during the delay, replicated across two ERP experiments with Chinese and English materials. We found that maintenance of events elicited a long-lasting late sustained difference in posterior-occipital electrodes relative to non-events. This effect resembled the negative slow wave reported in previous studies of working memory, suggesting that the maintenance of events in working memory may impose a higher cost compared to coordinations. Although we did not observe significant ERP differences associated with pinging the agent vs. the patient during the delay, we did find that the ping appeared to dampen the ongoing sustained difference, suggesting a shift from sustained activity to activity silent mechanisms. These results suggest a new method by which ERPs can be used to elucidate the format of neural representation for events in working memory.

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.

What came before: Assimilation effects in the categorization of time intervals

Assimilation is the process by which one judgment tends to approach some aspect of another stimulus or judgment. This effect has been known for over half a century in various domains such as the judgment of weight or sound intensity. However, the assimilation of judgments of durations have been relatively unexplored. In the current article, we present the results of five experiments in which participant s were required to judge the duration of a visual stimulus on each trial. In each experiment, we manipulated the pattern of durations they experienced in order to systematically separate the effects of the objective and subjective duration of stimuli on subsequent judgments. We found that duration judgments were primarily driven by prior judgments, with little, if any, effect of the prior objective stimulus duration. This is in contrast to the findings previously reported in regards to non-temporal judgments. We propose two mechanist explanations of this effect; a representational account in which judgments represent the speed of an underlying pacemaker, and an assimilation account in which judgment is based in prior experience. We further discuss results in terms of predictive coding, in which the previous rating is representative of a prior expectation, which is modified by current experience.

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.

A virtual reality time reproduction task for rodents

Estimates of the duration of time intervals and other magnitudes exhibit characteristic biases that likely result from error minimization strategies. To investigate such phenomena, magnitude reproduction tasks are used with humans and other primates. However, such behavioral tasks do not exist for rodents, one of the most important animal orders for neuroscience. We, therefore, developed a time reproduction task that can be used with rodents. It involves an animal reproducing the duration of a timed visual stimulus by walking along a corridor. The task was implemented in virtual reality, which allowed us to ensure that the animals were actually estimating time. The hallway did not contain prominent spatial cues and movement could be de-correlated from optic flow, such that the animals could not learn a mapping between stimulus duration and covered distance. We tested the reproduction of durations of several seconds in three different stimulus ranges. The gerbils reproduced the durations with a precision similar to experiments on humans. Their time reproductions also exhibited the characteristic biases of magnitude estimation experiments. These results demonstrate that our behavioral paradigm provides a means to study time reproduction in rodents.

Conceptually plausible Bayesian inference in interval timing

In a world that is uncertain and noisy, perception makes use of optimization procedures that rely on the statistical properties of previous experiences. A well-known example of this phenomenon is the central tendency effect observed in many psychophysical modalities. For example, in interval timing tasks, previous experiences influence the current percept, pulling behavioural responses towards the mean. In Bayesian observer models, these previous experiences are typically modelled by unimodal statistical distributions, referred to as the prior. Here, we critically assess the validity of the assumptions underlying these models and propose a model that allows for more flexible, yet conceptually more plausible, modelling of empirical distributions. By representing previous experiences as a mixture of lognormal distributions, this model can be parametrized to mimic different unimodal distributions and thus extends previous instantiations of Bayesian observer models. We fit the mixture lognormal model to published interval timing data of healthy young adults and a clinical population of aged mild cognitive impairment patients and age-matched controls, and demonstrate that this model better explains behavioural data and provides new insights into the mechanisms that underlie the behaviour of a memory-affected clinical population.

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.

Dissociable neural indices for time and space estimates during virtual distance reproduction

The perception and measurement of spatial and temporal dimensions have been widely studied. Yet, whether these two dimensions are processed independently is still being debated. Additionally, whether EEG components are uniquely associated with time or space, or whether they reflect a more general measure of magnitude quantity remains unknown. While undergoing EEG, subjects performed a virtual distance reproduction task, in which they were required to first walk forward for an unknown distance or time, and then reproduce that distance or time. Walking speed was varied between estimation and reproduction phases, to prevent interference between distance or time in each estimate. Behaviorally, subject performance was more variable when reproducing time than when reproducing distance, but with similar patterns of accuracy. During estimation, EEG data revealed the contingent negative variation (CNV), a measure previously associated with timing and expectation, tracked the probability of the upcoming interval, for both time and distance. However, during reproduction, the CNV exclusively oriented to the upcoming temporal interval at the start of reproduction, with no change across spatial distances. Our findings indicate that time and space are neurally separable dimensions, with the CNV both serving a supramodal role in temporal and spatial expectation, yet an exclusive role in preparing duration reproduction.

Numerical averaging in mice

Rodents can be trained to associate different durations with different stimuli (e.g., light/sound). When the associated stimuli are presented together, maximal responding is observed around the average of individual durations (akin to averaging). The current study investigated whether mice can also average independently trained numerosities. Mice were initially trained to make 10 or 20 lever presses on a single (run) lever to obtain a reward and each fixed-ratio schedule was signaled either with an auditory or visual stimulus. Then, mice were trained to press another lever to obtain the reward after they responded on the run lever for the minimum number of presses [Fixed Consecutive Number (FCN)-10 or -20 trials] signaled by the corresponding discriminative stimulus. Following this training, FCN trials with the compound stimulus were introduced to test the counting behavior of mice when they encountered conflicting information regarding the number of responses required to obtain the reward. Our results showed that the numbers of responses on these compound test trials were around the average of the number of responses in FCN-10 and FCN-20 trials particularly when the auditory stimulus was associated with a fewer number of required responses. The counting strategy explained the behavior of the majority of the mice in the FCN-Compound test trials (as opposed to the timing strategy). The number of responses in FCN-Compound trials was accounted for equally well by the arithmetic, geometric, and Bayesian averages of the number of responses observed in FCN-10 and FCN-20 trials.

Numerosity and cumulative surface area are perceived holistically as integral dimensions

Human and nonhuman animals have a remarkable capacity to rapidly estimate the quantity of objects in the environment. The dominant view of this ability posits an abstract numerosity code, uncontaminated by nonnumerical visual information. The present study provides novel evidence in contradiction to this view by demonstrating that number and cumulative surface area are perceived holistically, classically known as integral dimensions. Whether assessed explicitly (Experiment 1) or implicitly (Experiment 2), perceived similarity for dot arrays that varied parametrically in number and cumulative area was best modeled by Euclidean, as opposed to city-block, distance within the stimulus space, comparable to other integral dimensions (brightness/saturation and radial frequency components) but different from separable dimensions (shape/color and brightness/size). Moreover, Euclidean distance remained the best-performing model, even when compared to models that controlled for other magnitude properties (e.g., density) or image similarity. These findings suggest that numerosity perception entails the obligatory processing of nonnumerical magnitude. (PsycInfo Database Record (c) 2021 APA, all rights reserved).

Number is special: time, space, and number interact in a temporal reproduction task

Space, time, and number are among fundamental aspects of behavior and reasoning about the environment. Recent studies have shown that these dimensions highly interact with each other. To explain such interaction, two theories have been proposed: A Theory of Magnitude (ATOM), which posits the existence of a common magnitude system, and Conceptual Metaphor Theory (CMT), which proposes abstract domains such as time and number are mapped through more concrete domains such as space. The present study investigates the interaction of number, time and space in a single experimental paradigm using a temporal reproduction task with a visuospatial component. We also investigated whether mathematical education and continuous involvement with calculations and numbers change the processing precision related to number, time, and space. Two groups of students in mathematics (n = 28) and Persian literature (n = 28) participated in a time reproduction task. The stimuli included Arabic numbers 1, 2, 8, and 9, which were presented to the participants over short (300, 400, 500 ms) and long durations (1000, 1100, 1200 ms) on both sides (left and right) of the monitor. The interaction effect of spatialـnumerical and temporal-numerical was found to be significant. There was no overall time-space interaction, but the triple interaction effect between number, time, and space was significant suggesting the existence of a common representational system. This main result was slightly in line with recent proposed theories. Furthermore, the results showed that the main effect of group was not significant. In addition, we found that among the three factors (number, time, and space) the effect of number is more prominent, i.e., when number disappeared the interaction effect was not observed. The results also suggest that the nature of interactions between these factors is not influenced by cognitive and educational factors. The findings of the study are finally discussed in terms of symmetrical or asymmetrical cross-dimensional influences within the frameworks of ATOM and CMT theories.

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.

Monitoring line length reproduction errors

Previous work revealed that humans can keep track of the direction and degree of errors in their temporal and numerical reproductions/estimations. Given the behavioral and psychophysical commonalities to various magnitudes and the implication of an overlapping neuroanatomical locus for their representation, we hypothesized that participants would capture the direction of errors and confidence ratings would track the magnitude of errors in line-length reproductions. In two experiments, participants reproduced various target lengths as accurately as possible, and reported the direction of their errors and provided confidence ratings for their reproductions. The isolated analysis of these two second-order judgments showed that participants can correctly report the direction of errors in their line-length reproductions and subjective confidence decreases as the magnitude of errors increases. These results show that humans can robustly keep track of the direction of errors in their line-length reproductions and their subjective confidence corroborates the magnitude of these errors.

Eliciting contextual temporal calibration: The effect of bottom-up and top-down information in reproduction tasks

Bayesian integration assumes that a current observation is integrated with previous observations. An example in the temporal domain is the central tendency effect: when a range of durations is presented, a regression towards the mean is observed. Furthermore, a context effect emerges if a partially overlapping lower and a higher range of durations is presented in a blocked design, with the overlapping durations pulled towards the mean duration of the block. We determine under which conditions this context effect is observed, and whether explicit cues strengthen the effect. Each block contained either two or three durations, with one duration present in both blocks. We provided either no information at the start of each block about the nature of that block, provided written ("short" / "long" or "A" / "B") categorizations, or operationalized pitch (low vs high) to reflect the temporal context. We demonstrate that (1) the context effect emerges as long as sufficiently distinct durations are presented; (2) the effect is not modulated by explicit instructions or other cues; (3) just a single additional duration is sufficient to produce a context effect. Taken together, these results provide information on the most efficient operationalization to evoke the context effect, allowing for highly economical experimental designs, and highlights the automaticity by which priors are constructed.

Effect of Presentation Format on Judgment of Long-Range Time Intervals

Investigations in the temporal estimation domain are quite vast in the range of milliseconds, seconds, and minutes. This study aimed to determine the psychophysical function that best describes long-range time interval estimation and evaluate the effect of numerals in duration presentation on the form of this function. Participants indicated on a line the magnitude of time intervals presented either as a number + time-unit (e.g., “9 months”; Group I), unitless numerals (e.g., “9”; Group II), or tagged future personal events (e.g., “Wedding”; Group III). The horizontal line was labeled rightward (“Very short” = >“Very long”) or leftward (“Very long” = >“Very short”) for Group I and II, but only rightward for Group III. None of the linear, power, logistic or logarithmic functions provided the best fit to the individual participant data in more than 50% of participants for any group. Individual power exponents were different only between the tagged personal events (Group III) and the other two groups. When the same analysis was repeated for the aggregated data, power functions provided a better fit than other tested functions in all groups with a difference in the power function parameters again between the tagged personal events and the other groups. A non-linear mixed effects analysis indicated a difference in the power function exponent between Group III and the other groups, but not between Group I and II. No effect of scale directionality was found in neither of the experiments in which scale direction was included as independent variable. These results suggest that the judgment of intervals in a number + time-unit presentation invoke, at least in part, processing mechanisms other than those used for time-domain. Consequently, we propose the use of event-tagged assessment for characterizing long-range interval representation. We also recommend that analyses in this field should not be restricted to aggregated data given the qualitative variation between participants.

Temporal Metacognition as the Decoding of Self-Generated Brain Dynamics

Metacognition, the ability to know about one’s thought process, is self-referential. Here, we combined psychophysics and time-resolved neuroimaging to explore metacognitive inference on the accuracy of a self-generated behavior. Human participants generated a time interval and evaluated the signed magnitude of their temporal production. We show that both self-generation and self-evaluation relied on the power of beta oscillations (β; 15–40 Hz) with increases in early β power predictive of increases in duration. We characterized the dynamics of β power in a low-dimensional space (β state-space trajectories) as a function of timing and found that the more distinct trajectories, the more accurate metacognitive inferences were. These results suggest that β states instantiate an internal variable determining the fate of the timing network’s trajectory, possibly as release from inhibition. Altogether, our study describes oscillatory mechanisms for timing, suggesting that temporal metacognition relies on inferential processes of self-generated dynamics.

Time and distance estimation in children using an egocentric navigation task

Navigation crucially depends on the capability to estimate time elapsed and distance covered during movement. From adults it is known that magnitude estimation is subject to characteristic biases. Most intriguing is the regression effect (central tendency), whose strength depends on the stimulus distribution (i.e. stimulus range), a second characteristic of magnitude estimation known as range effect. We examined regression and range effects for time and distance estimation in eleven-year-olds and young adults, using an egocentric virtual navigation task. Regression effects were stronger for distance compared to time and depended on stimulus range. These effects were more pronounced in children compared to adults due to a more heterogeneous performance among the children. Few children showed veridical estimations similar to adults; most children, however, performed less accurate displaying stronger regression effects. Our findings suggest that children use magnitude processing strategies similar to adults, but it seems that these are not yet fully developed in all eleven-year-olds and are further refined throughout adolescence.

Optimal multisensory integration leads to optimal time estimation

Our brain compensates sensory uncertainty by combining multisensory information derived from an event, and by integrating the current sensory signal with the prior knowledge about the statistical structure of previous events. There is growing evidence that both strategies are statistically optimal; however, how these two stages of information integration interact and shape an optimal percept remains an open question. In the present study, we investigated the perception of time as an amodal perceptual attribute. The central tendency, a phenomenon of biasing the current percept toward previous stimuli, is used to quantify and model how the prior information affects the current timing behavior. We measured the timing sensitivity and the central tendency for unisensory and multisensory stimuli with sensory uncertainty systematically manipulated by adding noise. Psychophysical results demonstrate that the central tendency increases as the uncertainty increases, and that the multisensory timing improves both the timing sensitivity and the central tendency bias compared to the unisensory timing. Computational models indicate that the optimal multisensory integration precedes the optimal integration of prior information causing the central tendency. Our findings suggest that our brain incorporates the multisensory information and prior knowledge in a statistically optimal manner to realize precise and accurate timing behavior.

Robustness of individual differences in temporal interference effects

Magnitudes or quantities of the different dimensions that define a stimulus (e.g., space, speed or numerosity) influence the perceived duration of that stimulus, a phenomenon known as (temporal) interference effects. This complicates studying the neurobiological foundation of the perception of time, as any signatures of temporal processing are tainted by interfering dimensions. In earlier work, in which judgements on either time or numerosity were made while EEG was recorded, we used Maximum Likelihood Estimation (MLE) to estimate, for each participant separately, the influence of temporal and numerical information on making duration or numerosity judgements. We found large individual differences in the estimated magnitudes, but ML-estimates allowed us to partial out interference effects. However, for such analyses, it is essential that estimates are meaningful and stable. Therefore, in the current study, we examined the reliability of the MLE procedure by comparing the interference magnitudes estimated in two sessions, spread a week apart. In addition to the standard paradigm, we also presented task variants in which the interfering dimension was manipulated, to assess which aspects of the numerosity dimension exert the largest influence on temporal processing. The results indicate that individual interference magnitudes are stable, both between sessions and over tasks. Further, the ML-estimates of the time-numerosity judgement tasks were predictive of performance in a standard temporal judgement task. Thus, how much temporal information participants use in time estimations tasks seems to be a stable trait that can be captured with the MLE procedure. ML-estimates are, however, not predictive of performance in other interference-tasks, here operationalized by a numerical Stroop task. Taken together, the MLE procedure is a reliable tool to quantify individual differences in magnitude interference effects and can therefore reliably inform the analysis of neuroimaging data when contrasts are needed between the accumulation of a temporal and an interfering dimension.

Performance-informed EEG analysis reveals mixed evidence for EEG signatures unique to the processing of time

Certain EEG components (e.g., the contingent negative variation, CNV, or beta oscillations) have been linked to the perception of temporal magnitudes specifically. However, it is as of yet unclear whether these EEG components are really unique to time perception or reflect the perception of magnitudes in general. In the current study we recorded EEG while participants had to make judgments about duration (time condition) or numerosity (number condition) in a comparison task. This design allowed us to directly compare EEG signals between the processing of time and number. Stimuli consisted of a series of blue dots appearing and disappearing dynamically on a black screen. Each stimulus was characterized by its duration and the total number of dots that it consisted of. Because it is known that tasks like these elicit perceptual interference effects that we used a maximum-likelihood estimation (MLE) procedure to determine, for each participant and dimension separately, to what extent time and numerosity information were taken into account when making a judgement in an extensive post hoc analysis. This approach enabled us to capture individual differences in behavioral performance and, based on the MLE estimates, to select a subset of participants who suppressed task-irrelevant information. Even for this subset of participants, who showed no or only small interference effects and thus were thought to truly process temporal information in the time condition and numerosity information in the number condition, we found CNV patterns in the time-domain EEG signals for both tasks that was more pronounced in the time-task. We found no substantial evidence for differences between the processing of temporal and numerical information in the time–frequency domain.

The effect of attention and working memory on the estimation of elapsed time

Psychological models of time perception involve attention and memory: while attention typically regulates the flow of events, memory maintains timed events or intervals. The precise, and possibly distinct, roles of attention and memory in time perception remain debated. In this behavioral study, we tested 48 participants in a prospective duration estimation task while they fully attended to time or performed a working memory (WM) task. We report that paying attention to time lengthened perceived duration in the range of seconds to minutes, whereas diverting attention away from time shortened perceived duration. The overestimation due to attending to time did not scale with durations. To the contrary, increasing WM load systematically decreased subjective duration and this effect scaled with durations. Herein, we discuss the dissociation between attention and WM in timing and scalar variability from the perspective of Bayesian models of time estimations.

Diminished neural resources allocation to time processing in Autism Spectrum Disorders

Background

Interval timing, the ability to judge the duration of short events, has been shown to be compromised in Autism Spectrum Disorders (ASD). Timing abilities are ubiquitous and underlie behaviours as varied as sensory integration, motor coordination or communication. It has been suggested that atypical temporal processing in ASD could contribute to some of the disorder's symptoms, in particular motor clumsiness and difficulties in social interaction and communication. Recent behavioural investigations have suggested that interval timing in ASD is characterised by intact sensitivity but reduced precision in duration judgements.

Methods

In this study we investigated the processing of duration as compared to pitch in a group of high-functioning individuals with ASD using magnetoencephalography (MEG). 18 adolescents and adults with ASD and 18 age- and IQ-matched typically-developing control (TDC) individuals compared two consecutive tones according to their duration or pitch in separate experimental blocks. The analysis was carried out exclusively on physically identical stimuli (500 Hz tones lasting 600 ms), which served, according to instruction, as standard or probe in a Duration or Pitch task respectively.

Results

Our results suggest that compared to TDC individuals, individuals with ASD are less able to predict the duration of the standard tone accurately, affecting the sensitivity of the comparison process. In addition, contrary to TDC individuals who allocate resources at different times depending on the nature of the task (pitch or duration discrimination), individuals with ASD seem to engage less resources for the Duration task than for the Pitch task regardless of the context. Although individuals with ASD showed top-down adaptation to the context of the task, this neuronal strategy reflects a bias in the readiness to perform different types of tasks, and in particular a diminished allocation of resources to duration processing which could have cascading effect on learning and development of other cognitive functions.

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We investigated MEG response associated with duration or pitch comparison in ASD.

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We found lower sensitivity for duration discrimination behaviourally in ASD.

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ASD adults are less able to predict the offset of a standard tone.

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ASD adults engage less neural resources in duration than pitch discrimination task.