Timing and time perception: A review of recent behavioral and neuroscience findings and theoretical directions

Representing time in language and memory: the role of similarity structure

Every day we read about or watch events in the world and can easily understand or remember how long they last. What aspects of an event are retained in memory? And how do we extract temporal information from our memory representations? These issues are central to human cognition, as they underlie a fundamental aspect of our mental life, namely our representation of time. This paper reviews previous language studies and reports a visual learning study indicating that properties of the events encoded in memory shape the representation of their duration. The evidence indicates that for a given event, the extent to which its associated properties or sub-components differ from one another modulates our representation of its duration. These properties include the similarity between sub-events and the similarity between the situational contexts in which an event occurs. We suggest that the diversity of representations that we associate with events in memory plays an important role in remembering and estimating the duration of experienced or described events.

How are overlapping time intervals perceived? Evidence for a weighted sum of segments model

This study investigated the way in which people time two overlapping intervals. Timing models already proposed in the literature predict different effects of the degree of overlap on each estimate, and empirical findings were compared to these predictions. Two unimodal experiments (in which each to-be-timed interval was a visual stimulus) and one bimodal experiment (in which one to-be-timed interval was auditory and the other visual) were conducted. The estimate of the first interval was either unaffected or decreased, and the estimate of the second interval consistently increased as the intervals were more temporally separated. The only model in the literature that could account for such result patterns is a single pacemaker single accumulator structure with an additional recency weighting (see the weighted sum of segments model). That is, participants appear to segment the two overlapping intervals into three non-overlapping and overlapping segments, time these segments separately, and then combine them to estimate each interval. Importantly, a recency weighting, determined by the time that has passed since the end of that segment, is also applied to each segment in the summation process. Further, in the bimodal experiment the order in which the stimuli of different modalities were presented affected the way in which they were timed, a finding that none of the current models can explain. This highlights that a comprehensive model of interval timing must consider not only the modalities of to-be-timed intervals but also the order in which different modalities must be timed.

Slowing down the clock: a review of experimental studies investigating psychological time dilation

A review of 24 experiments investigated the factors that produce a subjective time dilation. The aim of this review was to investigate the magnitude of the obtained time dilation. The mean time duration judgment ratio of subjective time to objective time for the selected studies was 1.31, SD = .24. The analyses revealed that experimental studies investigating subjective time dilation tend to obtain small to moderate time dilation and that several factors can be manipulated in order to make a specific time interval appear longer than it is. Highlighting the factors that lead to a subjective time dilation has both research implications, by pointing to the underlying cognitive mechanisms of time perception, and practical implications, by indicating the factors that can be manipulated in order to control how we perceive time.

Filling the blanks in temporal intervals: the type of filling influences perceived duration and discrimination performance

In this work we investigate how judgments of perceived duration are influenced by the properties of the signals that define the intervals. Participants compared two auditory intervals that could be any combination of the following four types: intervals filled with continuous tones (filled intervals), intervals filled with regularly-timed short tones (isochronous intervals), intervals filled with irregularly-timed short tones (anisochronous intervals), and intervals demarcated by two short tones (empty intervals). Results indicate that the type of intervals to be compared affects discrimination performance and induces distortions in perceived duration. In particular, we find that duration judgments are most precise when comparing two isochronous and two continuous intervals, while the comparison of two anisochronous intervals leads to the worst performance. Moreover, we determined that the magnitude of the distortions in perceived duration (an effect akin to the filled duration illusion) is higher for tone sequences (no matter whether isochronous or anisochronous) than for continuous tones. Further analysis of how duration distortions depend on the type of filling suggests that distortions are not only due to the perceived duration of the two individual intervals, but they may also be due to the comparison of two different filling types.

Thinking aloud influences perceived time

OBJECTIVE

We investigate whether thinking aloud influences perceived time.

BACKGROUND

Thinking aloud is widely used in usability evaluation, yet it is debated whether thinking aloud influences thought and behavior. If thinking aloud is restricted to the verbalization of information to which a person is already attending, there is evidence that thinking aloud does not influence thought and behavior.

METHOD

In an experiment, 16 thinking-aloud participants and 16 control participants solved a code-breaking task 24 times each. Participants estimated task duration. The 24 trials involved two levels of time constraint (timed, untimed) and resulted in two levels of success (solved, unsolved).

RESULTS

The ratio of perceived time to clock time was lower for thinking-aloud than control participants. Participants overestimated time by an average of 47% (thinking aloud) and 94% (control). The effect of thinking aloud on time perception also held separately for timed, untimed, solved, and unsolved trials.

CONCLUSION

Thinking aloud (verbalization at Levels 1 and 2) influences perceived time. Possible explanations of this effect include that thinking aloud may require attention, cause a processing shift that overshadows the perception of time, or increase mental workload.

APPLICATION

For usability evaluation, this study implies that time estimates made while thinking aloud cannot be compared with time estimates made while not thinking aloud, that ratings of systems experienced while thinking aloud may be inaccurate (because the experience of time influences other experiences), and that it may therefore be considered to replace concurrent thinking aloud with retrospective thinking aloud when evaluations involve time estimation.

Models of ADHD: Five ways smaller sooner is better

BACKGROUND

In the delay discounting paradigm choices are made between a good of small utility available soon (SS) vs. a good of greater utility available later (LL). Versions of the task may be used with human and non-human subjects, they generate characteristic data, and are of relevance the topic of this special issue, the imputed impulsivity of organisms categorized as ADHD, and animal models of ADHD.

METHOD

Mathematical models of judgment were formulated. The first model adds the utility of a good to the utility of the delay. It provides distinct information about future perspective, the marginal utility of the goods offered, and the relative weight on delay. It grounds hyperbolic discounting. It predicts slower rates of discount for more preferred goods. It can reduce to an exponential function on future perspective time. When choice is mediated by conditioning, not judgment, a model of conditioned reinforcement strength is written. For studies where only the degree of preference for the LL is reported, a Thurstonian model of discrimination provides a shell that embraces all of the earlier models, providing additional information about the precision and bias of those preferential judgments.

COMPARISON WITH OTHER MODELS

All other prominent models are nested within, or approximations to, the models described here.

RESULTS

The models are fit to exemplary data. They provide some support for theories of delay aversion, and explanations for some inconsistencies in the literature. They involve parameters of general utility and provide connection to economic models.

Subjective expansion of extended time-spans in experienced meditators

Experienced meditators typically report that they experience time slowing down in meditation practice as well as in everyday life. Conceptually this phenomenon may be understood through functional states of mindfulness, i.e., by attention regulation, body awareness, emotion regulation, and enhanced memory. However, hardly any systematic empirical work exists regarding the experience of time in meditators. In the current cross-sectional study, we investigated whether 42 experienced mindfulness meditation practitioners (with on average 10 years of experience) showed differences in the experience of time as compared to 42 controls without any meditation experience matched for age, sex, and education. The perception of time was assessed with a battery of psychophysical tasks assessing the accuracy of prospective time judgments in duration discrimination, duration reproduction, and time estimation in the milliseconds to minutes range as well with several psychometric instruments related to subjective time such as the Zimbardo Time Perspective Inventory, the Barratt Impulsivity Scale and the Freiburg Mindfulness Inventory. In addition, subjective time judgments on the current passage of time and retrospective time ranges were assessed. While subjective judgements of time were found to be significantly different between the two groups on several scales, no differences in duration estimates in the psychophysical tasks were detected. Regarding subjective time, mindfulness meditators experienced less time pressure, more time dilation, and a general slower passage of time. Moreover, they felt that the last week and the last month passed more slowly. Overall, although no intergroup differences in psychophysical tasks were detected, the reported findings demonstrate a close association between mindfulness meditation and the subjective feeling of the passage of time captured by psychometric instruments.

Everywhere and everything: The power and ubiquity of time

Anticipatory timing plays a critical role in many aspects of human and non-human animal behavior. Timing has been consistently observed in the range of milliseconds to hours, and demonstrates a powerful influence on the organization of behavior. Anticipatory timing is acquired early in associative learning and appears to guide association formation in important ways. Importantly, timing participates in regulating goal-directed behaviors in many schedules of reinforcements, and plays a critical role in value-based decision making under concurrent schedules. In addition to playing a key role in fundamental learning processes, timing often dominates when temporal cues are available concurrently with other stimulus dimensions. Such control by the passage of time has even been observed when other cues provide more accurate information and can lead to sub-optimal behaviors. The dominance of temporal cues in governing anticipatory behavior suggests that time may be inherently more salient than many other stimulus dimensions. Discussions of the interface of the timing system with other cognitive processes are provided to demonstrate the powerful and primitive nature of time as a stimulus dimension.

Space-time interdependence: evidence against asymmetric mapping between time and space

Time and space are intimately related, but what is the real nature of this relationship? Is time mapped metaphorically onto space such that effects are always asymmetric (i.e., space affects time more than time affects space)? Or do the two domains share a common representational format and have the ability to influence each other in a flexible manner (i.e., time can sometimes affect space more than vice versa)? In three experiments, we examined whether spatial representations from haptic perception, a modality of relatively low spatial acuity, would lead the effect of time on space to be substantially stronger than the effect of space on time. Participants touched (but could not see) physical sticks while listening to an auditory note, and then reproduced either the length of the stick or the duration of the note. Judgements of length were affected by concurrent stimulus duration, but not vice versa. When participants were allowed to see as well as touch the sticks, however, the higher acuity of visuohaptic perception caused the effects to converge so length and duration influenced each other to a similar extent. These findings run counter to the spatial metaphor account of time, and rather support the spatial representation account in which time and space share a common representational format and the directionality of space-time interaction depends on the perceptual acuity of the modality used to perceive space.

Unpacking a time interval lengthens its perceived temporal distance

In quantity estimation, people often perceive that the whole is less than the sum of its parts. The current study investigated such an unpacking effect in temporal distance judgment. Our results showed that participants in the unpacked condition judged a given time interval longer than those in the packed condition, even the time interval was kept constant between the two conditions. Furthermore, this unpacking effect persists regardless of the unpacking ways we employed. Results suggest that unpacking a time interval may be a good strategy for lengthening its perceived temporal distance.

Quantifying auditory temporal stability in a large database of recorded music

“Moving to the beat” is both one of the most basic and one of the most profound means by which humans (and a few other species) interact with music. Computer algorithms that detect the precise temporal location of beats (i.e., pulses of musical “energy”) in recorded music have important practical applications, such as the creation of playlists with a particular tempo for rehabilitation (e.g., rhythmic gait training), exercise (e.g., jogging), or entertainment (e.g., continuous dance mixes). Although several such algorithms return simple point estimates of an audio file’s temporal structure (e.g., “average tempo”, “time signature”), none has sought to quantify the temporal stability of a series of detected beats. Such a method-a “Balanced Evaluation of Auditory Temporal Stability” (BEATS)–is proposed here, and is illustrated using the Million Song Dataset (a collection of audio features and music metadata for nearly one million audio files). A publically accessible web interface is also presented, which combines the thresholdable statistics of BEATS with queryable metadata terms, fostering potential avenues of research and facilitating the creation of highly personalized music playlists for clinical or recreational applications.

Working memory for time intervals in auditory rhythmic sequences

The brain can hold information about multiple objects in working memory. It is not known, however, whether intervals of time can be stored in memory as distinct items. Here, we developed a novel paradigm to examine temporal memory where listeners were required to reproduce the duration of a single probed interval from a sequence of intervals. We demonstrate that memory performance significantly varies as a function of temporal structure (better memory in regular vs. irregular sequences), interval size (better memory for sub- vs. supra-second intervals), and memory load (poor memory for higher load). In contrast memory performance is invariant to attentional cueing. Our data represent the first systematic investigation of temporal memory in sequences that goes beyond previous work based on single intervals. The results support the emerging hypothesis that time intervals are allocated a working memory resource that varies with the amount of other temporal information in a sequence.

Temporal structure of consciousness and minimal self in schizophrenia

The concept of the minimal self refers to the consciousness of oneself as an immediate subject of experience. According to recent studies, disturbances of the minimal self may be a core feature of schizophrenia. They are emphasized in classical psychiatry literature and in phenomenological work. Impaired minimal self-experience may be defined as a distortion of one’s first-person experiential perspective as, for example, an “altered presence” during which the sense of the experienced self (“mineness”) is subtly affected, or “altered sense of demarcation,” i.e., a difficulty discriminating the self from the non-self. Little is known, however, about the cognitive basis of these disturbances. In fact, recent work indicates that disorders of the self are not correlated with cognitive impairments commonly found in schizophrenia such as working-memory and attention disorders. In addition, a major difficulty with exploring the minimal self experimentally lies in its definition as being non-self-reflexive, and distinct from the verbalized, explicit awareness of an “I.” In this paper, we shall discuss the possibility that disturbances of the minimal self observed in patients with schizophrenia are related to alterations in time processing. We shall review the literature on schizophrenia and time processing that lends support to this possibility. In particular we shall discuss the involvement of temporal integration windows on different time scales (implicit time processing) as well as duration perception disturbances (explicit time processing) in disorders of the minimal self. We argue that a better understanding of the relationship between time and the minimal self as well of issues of embodiment require research that looks more specifically at implicit time processing. Some methodological issues will be discussed.

Degradation of cognitive timing mechanisms in behavioural variant frontotemporal dementia

The current study examined motor timing in frontotemporal dementia (FTD), which manifests as progressive deterioration in social, behavioural and cognitive functions. Twenty-patients fulfilling consensus clinical criteria for behavioural variant FTD (bvFTD), 11 patients fulfilling consensus clinical criteria for semantic-variant primary progressive aphasia (svPPA), four patients fulfilling criteria for nonfluent/agrammatic primary progressive aphasia (naPPA), eight patients fulfilling criteria for Alzheimer׳s disease (AD), and 31 controls were assessed on both an externally- and self-paced finger-tapping task requiring maintenance of a regular, 1500 ms beat over 50 taps. Grey and white matter correlates of deficits in motor timing were examined using voxel-based morphometry (VBM) and diffusion tensor imaging (DTI). bvFTD patients exhibited significant deficits in aspects of both externally- and self-paced tapping. Increased mean inter-response interval (faster than target tap time) in the self-paced task was associated with reduced grey matter volume in the cerebellum bilaterally, right middle temporal gyrus, and with increased axial diffusivity in the right superior longitudinal fasciculus, regions and tracts which have been suggested to be involved in a subcortical–cortical network of structures underlying timing abilities. This suggests that such structures can be affected in bvFTD, and that impaired motor timing may underlie some characteristics of the bvFTD phenotype.

•

We examine motor timing in behavioural variant FTD.

•

Patients with behavioural variant FTD showed impaired motor timing.

•

Patients tended to tap faster than target and speed up during the task.

•

Faster tapping was associated with reduced grey matter in the cerebellum.

•

Impaired timing might underlie some other behavioural features of FTD.

Oscillatory multiplexing of neural population codes for interval timing and working memory

Interval timing and working memory are critical components of cognition that are supported by neural oscillations in prefrontal-striatal-hippocampal circuits. In this review, the properties of interval timing and working memory are explored in terms of behavioral, anatomical, pharmacological, and neurophysiological findings. We then describe the various neurobiological theories that have been developed to explain these cognitive processes - largely independent of each other. Following this, a coupled excitatory - inhibitory oscillation (EIO) model of temporal processing is proposed to address the shared oscillatory properties of interval timing and working memory. Using this integrative approach, we describe a hybrid model explaining how interval timing and working memory can originate from the same oscillatory processes, but differ in terms of which dimension of the neural oscillation is utilized for the extraction of item, temporal order, and duration information. This extension of the striatal beat-frequency (SBF) model of interval timing (Matell and Meck, 2000, 2004) is based on prefrontal-striatal-hippocampal circuit dynamics and has direct relevance to the pathophysiological distortions observed in time perception and working memory in a variety of psychiatric and neurological conditions.

The effect of visual apparent motion on audiovisual simultaneity

Visual motion information from dynamic environments is important in multisensory temporal perception. However, it is unclear how visual motion information influences the integration of multisensory temporal perceptions. We investigated whether visual apparent motion affects audiovisual temporal perception. Visual apparent motion is a phenomenon in which two flashes presented in sequence in different positions are perceived as continuous motion. Across three experiments, participants performed temporal order judgment (TOJ) tasks. Experiment 1 was a TOJ task conducted in order to assess audiovisual simultaneity during perception of apparent motion. The results showed that the point of subjective simultaneity (PSS) was shifted toward a sound-lead stimulus, and the just noticeable difference (JND) was reduced compared with a normal TOJ task with a single flash. This indicates that visual apparent motion affects audiovisual simultaneity and improves temporal discrimination in audiovisual processing. Experiment 2 was a TOJ task conducted in order to remove the influence of the amount of flash stimulation from Experiment 1. The PSS and JND during perception of apparent motion were almost identical to those in Experiment 1, but differed from those for successive perception when long temporal intervals were included between two flashes without motion. This showed that the result obtained under the apparent motion condition was unaffected by the amount of flash stimulation. Because apparent motion was produced by a constant interval between two flashes, the results may be accounted for by specific prediction. In Experiment 3, we eliminated the influence of prediction by randomizing the intervals between the two flashes. However, the PSS and JND did not differ from those in Experiment 1. It became clear that the results obtained for the perception of visual apparent motion were not attributable to prediction. Our findings suggest that visual apparent motion changes temporal simultaneity perception and improves temporal discrimination in audiovisual processing.

Direction-contingent duration compression is primarily retinotopic

Previous research has shown that prior adaptation to a spatially circumscribed, oscillating grating results in the duration of a subsequent stimulus briefly presented within the adapted region being underestimated. There is an on-going debate about where in the motion processing pathway the adaptation underlying this distortion of sub-second duration perception occurs. One position is that the LGN and, perhaps, early cortical processing areas are likely sites for the adaptation; an alternative suggestion is that visual area MT+ contains the neural mechanisms for sub-second timing; and a third position proposes that the effect is driven by adaptation at multiple levels of the motion processing pathway. A related issue is in what frame of reference - retinotopic or spatiotopic - does adaptation induced duration distortion occur. We addressed these questions by having participants adapt to a unidirectional random dot kinematogram (RDK), and then measuring perceived duration of a 600 ms test RDK positioned in either the same retinotopic or the same spatiotopic location as the adaptor. We found that, when it did occur, duration distortion of the test stimulus was direction contingent; that is it occurred when the adaptor and test stimuli drifted in the same direction, but not when they drifted in opposite directions. Furthermore the duration compression was evident primarily under retinotopic viewing conditions, with little evidence of duration distortion under spatiotopic viewing conditions. Our results support previous research implicating cortical mechanisms in the duration encoding of sub-second visual events, and reveal that these mechanisms encode duration within a retinotopic frame of reference.

Depression does not affect time perception and time-to-contact estimation

Depressed patients frequently report a subjective slowing of the passage of time. However, experimental demonstrations of altered time perception in depressed patients are not conclusive. We added a timed action task (time-to-contact estimation, TTC) and compared this indirect time perception task to the more direct classical methods of verbal time estimation, time production, and time reproduction. In the TTC estimation task, the deviations of the estimates from the veridical values (relative errors) revealed no differences between depressed patients (N= 22) and healthy controls (N= 22). Neither did the relative errors of the TTC estimates differ between groups. There was a weak trend toward higher variability of the estimates in depressed patients but only at the shortest TTC and at the fastest velocities. Time experience (subjective flow of time) as well as time perception in terms of interval timing (verbal estimation, time production, time reproduction) performed on the same subjects likewise failed to produce effects of depression. We conclude that the notion that depression has a sizeable effect on time perception cannot be maintained.

Different methods for reproducing time, different results

One of the most widely used tasks for investigating psychological time, time reproduction, requires from participants the reproduction of the duration of a previously presented stimulus. Although prior studies have investigated the effects of different cognitive processes on time reproduction performance, no studies have looked into the effects of different reproduction methods on these performances. In the present study, participants were randomly assigned to one of three reproduction methods, which included (a) just pressing at the end of the interval, (b) pressing to start and stop the interval, and (c) maintaining continuous pressing during the interval. The study revealed that the three reproduction methods were not equivalent, with the method involving keypresses to start and stop the reproduction showing the highest accuracy, and the method of continuous press generating less variability.

Interval discrimination across different duration ranges with a look at spatial compatibility and context effects

In the present study, a time discrimination task was used to investigate the effect of different contexts for intervals varying from 400 to 1600 ms. A potential time-space interaction was controlled, and participants used both manual responses (Experiments 1 and 2) and vocal responses (Experiment 3). Three ranges of durations were employed (short, middle and long), and within each range condition, three standard values were used (400, 700, and 1000 ms; 700, 1000, and 1300 ms; and 1000, 1300, and 1600 ms). Within each range, standard intervals were randomized (Experiments 1 and 3) or remained constant (Experiment 2) within a block of trials. Our results suggest that context influences time discrimination performances only when the temporal range under investigation is below 1300 ms and the temporal intervals varied within blocks. In the case of temporal intervals longer than 1300 ms, participants presented a tendency to respond “long” independently of the procedure used. Moreover, our results suggested that performances in a discrimination task are mainly influenced by the fact of varying standard durations within blocks, and not much by the time-space compatibility.

Time perception: the bad news and the good

Time perception is fundamental and heavily researched, but the field faces a number of obstacles to theoretical progress. In this advanced review, we focus on three pieces of 'bad news' for time perception research: temporal perception is highly labile across changes in experimental context and task; there are pronounced individual differences not just in overall performance but in the use of different timing strategies and the effect of key variables; and laboratory studies typically bear little relation to timing in the 'real world'. We describe recent examples of these issues and in each case offer some 'good news' by showing how new research is addressing these challenges to provide rich insights into the neural and information-processing bases of timing and time perception. WIREs Cogn Sci 2014, 5:429-446. doi: 10.1002/wcs.1298 This article is categorized under: Psychology > Perception and Psychophysics Neuroscience > Cognition.

Perceived duration decreases with increasing eccentricity

Previous studies examining the influence of stimulus location on temporal perception yield inhomogeneous and contradicting results. Therefore, the aim of the present study is to soundly examine the effect of stimulus eccentricity. In a series of five experiments, subjects compared the duration of foveal disks to disks presented at different retinal eccentricities on the horizontal meridian. The results show that the perceived duration of a visual stimulus declines with increasing eccentricity. The effect was replicated with various stimulus orders (Experiments 1-3), as well as with cortically magnified stimuli (Experiments 4-5), ruling out that the effect was merely caused by different cortical representation sizes. The apparent decreasing duration of stimuli with increasing eccentricity is discussed with respect to current models of time perception, the possible influence of visual attention and respective underlying physiological characteristics of the visual system.

Development of magnitude processing in children with developmental dyscalculia: space, time, and number

Developmental dyscalculia (DD) is a learning disorder associated with impairments in a preverbal non-symbolic approximate number system (ANS) pertaining to areas in and around the intraparietal sulcus (IPS). The current study sought to enhance our understanding of the developmental trajectory of the ANS and symbolic number processing skills, thereby getting insight into whether a deficit in the ANS precedes or is preceded by impaired symbolic and exact number processing. Recent work has also suggested that humans are endowed with a shared magnitude system (beyond the number domain) in the brain. We therefore investigated whether children with DD demonstrated a general magnitude deficit, stemming from the proposed magnitude system, rather than a specific one limited to numerical quantity. Fourth graders with DD were compared to age-matched controls and a group of ability-matched second graders, on a range of magnitude processing tasks pertaining to space, time, and number. Children with DD displayed difficulties across all magnitude dimensions compared to age-matched peers and showed impaired ANS acuity compared to the younger, ability-matched control group, while exhibiting intact symbolic number processing. We conclude that (1) children with DD suffer from a general magnitude-processing deficit, (2) a shared magnitude system likely exists, and (3) a symbolic number-processing deficit in DD tends to be preceded by an ANS deficit.

Visual tracking combined with hand-tracking improves time perception of moving stimuli

A number of studies have shown that performing a secondary task while executing a time-judgment task impairs performance on the latter task. However, this turns out not to be the case for certain motor secondary tasks. We show that concomitant secondary motor tasks involving pointing, when performed during a time-judgment task, can actually improve our time-judgment abilities. We compared adult participants' performance in a time-of-movement paradigm with visual pursuit-only and with visual pursuit plus hand pursuit. Rather than interfering with their estimation of stimulus movement duration, the addition of hand pursuit significantly improved their judgment. In addition, we considered the effect of three different movement profiles and four different movement speeds for the moving stimulus. As predicted by Vierordt's law, time judgments of shorter stimuli are overestimated and longer stimuli underestimated. Finally, timing performances appear to improve when the moving target follows a “biological” velocity profile.

Does time ever fly or slow down? The difficult interpretation of psychophysical data on time perception

Time perception is studied with subjective or semi-objective psychophysical methods. With subjective methods, observers provide quantitative estimates of duration and data depict the psychophysical function relating subjective duration to objective duration. With semi-objective methods, observers provide categorical or comparative judgments of duration and data depict the psychometric function relating the probability of a certain judgment to objective duration. Both approaches are used to study whether subjective and objective time run at the same pace or whether time flies or slows down under certain conditions. We analyze theoretical aspects affecting the interpretation of data gathered with the most widely used semi-objective methods, including single-presentation and paired-comparison methods. For this purpose, a formal model of psychophysical performance is used in which subjective duration is represented via a psychophysical function and the scalar property. This provides the timing component of the model, which is invariant across methods. A decisional component that varies across methods reflects how observers use subjective durations to make judgments and give the responses requested under each method. Application of the model shows that psychometric functions in single-presentation methods are uninterpretable because the various influences on observed performance are inextricably confounded in the data. In contrast, data gathered with paired-comparison methods permit separating out those influences. Prevalent approaches to fitting psychometric functions to data are also discussed and shown to be inconsistent with widely accepted principles of time perception, implicitly assuming instead that subjective time equals objective time and that observed differences across conditions do not reflect differences in perceived duration but criterion shifts. These analyses prompt evidence-based recommendations for best methodological practice in studies on time perception.

Discrimination of two neighboring intra- and intermodal empty time intervals marked by three successive stimuli

We investigated the discrimination of two neighboring intra- or inter-modal empty time intervals marked by three successive stimuli. Each of the three markers was a flash (visual-V) or a sound (auditory-A). The first and last markers were of the same modality, while the second one was either A or V, resulting in four conditions: VVV, VAV, AVA and AAA. Participants judged whether the second interval, whose duration was systematically varied, was shorter or longer than the 500-ms first interval. Compared with VVV and AAA, discrimination was impaired with VAV, but not so much with AVA (in Experiment 1). Whereas VAV and AVA consisted of the same set of single intermodal intervals (VA and AV), discrimination was impaired in the VAV compared to the AVA condition. This difference between VAV and AVA could not be attributed to the participants' strategy to perform the discrimination task, e.g., ignoring the standard interval or replacing the visual stimuli with sounds in their mind (in Experiment 2). These results are discussed in terms of sequential grouping according to sensory similarity.

GABA predicts time perception

Our perception of time constrains our experience of the world and exerts a pivotal influence over a myriad array of cognitive and motor functions. There is emerging evidence that the perceived duration of subsecond intervals is driven by sensory-specific neural activity in human and nonhuman animals, but the mechanisms underlying individual differences in time perception remain elusive. We tested the hypothesis that elevated visual cortex GABA impairs the coding of particular visual stimuli, resulting in a dampening of visual processing and concomitant positive time-order error (relative underestimation) in the perceived duration of subsecond visual intervals. Participants completed psychophysical tasks measuring visual interval discrimination and temporal reproduction and we measured in vivo resting state GABA in visual cortex using magnetic resonance spectroscopy. Time-order error selectively correlated with GABA concentrations in visual cortex, with elevated GABA associated with a rightward horizontal shift in psychometric functions, reflecting a positive time-order error (relative underestimation). These results demonstrate anatomical, neurochemical, and task specificity and suggest that visual cortex GABA contributes to individual differences in time perception.

Temporal dysfunction in traumatic brain injury patients: primary or secondary impairment?

Adequate temporal abilities are required for most daily activities. Traumatic brain injury (TBI) patients often present with cognitive dysfunctions, but few studies have investigated temporal impairments associated with TBI. The aim of the present work is to review the existing literature on temporal abilities in TBI patients. Particular attention is given to the involvement of higher cognitive processes in temporal processing in order to determine if any temporal dysfunction observed in TBI patients is due to the disruption of an internal clock or to the dysfunction of general cognitive processes. The results showed that temporal dysfunctions in TBI patients are related to the deficits in cognitive functions involved in temporal processing rather than to a specific impairment of the internal clock. In fact, temporal dysfunctions are observed when the length of temporal intervals exceeds the working memory span or when the temporal tasks require high cognitive functions to be performed. The consistent higher temporal variability observed in TBI patients is a sign of impaired frontally mediated cognitive functions involved in time perception.

Modulation of isochronous movements in a flexible environment: links between motion and auditory experience

The ability to perform isochronous movements while listening to a rhythmic auditory stimulus requires a flexible process that integrates timing information with movement. Here, we explored how non-temporal and temporal characteristics of an auditory stimulus (presence, interval occupancy, and tempo) affect motor performance. These characteristics were chosen on the basis of their ability to modulate the precision and accuracy of synchronized movements. Subjects have participated in sessions in which they performed sets of repeated isochronous wrist's flexion-extensions under various conditions. The conditions were chosen on the basis of the defined characteristics. Kinematic parameters were evaluated during each session, and temporal parameters were analyzed. In order to study the effects of the auditory stimulus, we have minimized all other sensory information that could interfere with its perception or affect the performance of repeated isochronous movements. The present study shows that the distinct characteristics of an auditory stimulus significantly influence isochronous movements by altering their duration. Results provide evidence for an adaptable control of timing in the audio-motor coupling for isochronous movements. This flexibility would make plausible the use of different encoding strategies to adapt audio-motor coupling for specific tasks.

Perception of acoustically presented time series with varied intervals

Data from three experiments on serial perception of temporal intervals in the supra-second domain are reported. Sequences of short acoustic signals ("pips") separated by periods of silence were presented to the observers. Two types of time series, geometric or alternating, were used, where the modulus 1+δ of the inter-pip series and the base duration Tb (range from 1.1 to 6s) were varied as independent parameters. The observers had to judge whether the series were accelerating, decelerating, or uniform (3 paradigm), or to distinguish regular from irregular sequences (2 paradigm). "Intervals of subjective uniformity" (isus) were obtained by fitting Gaussian psychometric functions to individual subjects' responses. Progression towards longer base durations (Tb=4.4 or 6s) shifts the isus towards negative δs, i.e., accelerating series. This finding is compatible with the phenomenon of "subjective shortening" of past temporal intervals, which is naturally accounted for by the lossy integration model of internal time representation. The opposite effect observed for short durations (Tb=1.1 or 1.5s) remains unexplained by the lossy integration model, and presents a challenge for further research.

In search of the internal structure of the processes underlying interval timing in the sub-second and the second range: a confirmatory factor analysis approach

One of the earliest accounts of duration perception by Karl von Vierordt implied a common process underlying the timing of intervals in the sub-second and the second range. To date, there are two major explanatory approaches for the timing of brief intervals: the Common Timing Hypothesis and the Distinct Timing Hypothesis. While the common timing hypothesis also proceeds from a unitary timing process, the distinct timing hypothesis suggests two dissociable, independent mechanisms for the timing of intervals in the sub-second and the second range, respectively. In the present paper, we introduce confirmatory factor analysis (CFA) to elucidate the internal structure of interval timing in the sub-second and the second range. Our results indicate that the assumption of two mechanisms underlying the processing of intervals in the second and the sub-second range might be more appropriate than the assumption of a unitary timing mechanism. In contrast to the basic assumption of the distinct timing hypothesis, however, these two timing mechanisms are closely associated with each other and share 77% of common variance. This finding suggests either a strong functional relationship between the two timing mechanisms or a hierarchically organized internal structure. Findings are discussed in the light of existing psychophysical and neurophysiological data.

About the time-shrinking illusion in the tactile modality

The aim of this study was to examine the occurrence of a so-called time-shrinking illusion in the tactile modality, while it had been tested so far mainly with auditory and visual stimuli. We examined whether the perception of an empty time interval marked by two brief tactile stimuli, S (240 ms), would be influenced by the presence of a preceding time interval, P (160, 240, or 320 ms). Results showed that S was underestimated when P was shorter than S. This underestimation appeared as a kind of perceptual assimilation between P and S, but S was not overestimated when P was longer. The underestimation was rather interpreted as a manifestation of the time-shrinking illusion.

Duration perception in crossmodally-defined intervals

How humans perform duration judgments with multisensory stimuli is an ongoing debate. Here, we investigated how sub-second duration judgments are achieved by asking participants to compare the duration of a continuous sound to the duration of an empty interval in which onset and offset were marked by signals of different modalities using all combinations of visual, auditory and tactile stimuli. The pattern of perceived durations across five stimulus durations (ranging from 100 ms to 900 ms) follows the Vierordt Law. Furthermore, intervals with a sound as onset (audio-visual, audio-tactile) are perceived longer than intervals with a sound as offset. No modality ordering effect is found for visualtactile intervals. To infer whether a single modality-independent or multiple modality-dependent time-keeping mechanisms exist we tested whether perceived duration follows a summative or a multiplicative distortion pattern by fitting a model to all modality combinations and durations. The results confirm that perceived duration depends on sensory latency (summative distortion). Instead, we did not find evidence for multiplicative distortions. The results of the model and the behavioural data support the concept of a single time-keeping mechanism that allows for judgments of durations marked by multisensory stimuli.

Temporal reproductions are influenced by an internal reference: explaining the Vierordt effect

Several findings from duration perception literature suggest that when making decisions about time, participants rely on an internal reference memory for time rather than merely on the current physical stimuli. According to a recent account, such an internal reference is formed by a continuous dynamic updating process that integrates duration information from previous trials and the current trial. In the present work, we show how such a dynamic mechanism can account for the classical yet unresolved Vierordt effect, which refers to the overestimation of relatively short and the underestimation of relatively long temporal intervals. We conducted an experiment to examine this and related predictions by means of a temporal reproduction task. Specifically, participants were presented with two successive time intervals - a standard s with constant duration and a comparison c with variable duration. Instead of performing a comparison judgment, however, the participants were subsequently cued to reproduce one of the two presented stimuli. Reproductions were affected not only by the temporal position of the to-be-reproduced stimulus, but also by the stimuli presented on earlier trials. These results support the notion of a dynamically updated internal reference underlying our judgments about the time elapsed, which might also be the basis of the Vierordt effect.

Musical training generalises across modalities and reveals efficient and adaptive mechanisms for reproducing temporal intervals

Expert musicians are able to time their actions accurately and consistently during a musical performance. We investigated how musical expertise influences the ability to reproduce auditory intervals and how this generalises across different techniques and sensory modalities. We first compared various reproduction strategies and interval length, to examine the effects in general and to optimise experimental conditions for testing the effect of music, and found that the effects were robust and consistent across different paradigms. Focussing on a 'ready-set-go' paradigm subjects reproduced time intervals drawn from distributions varying in total length (176, 352 or 704 ms) or in the number of discrete intervals within the total length (3, 5, 11 or 21 discrete intervals). Overall, Musicians performed more veridical than Non-Musicians, and all subjects reproduced auditory-defined intervals more accurately than visually-defined intervals. However, Non-Musicians, particularly with visual stimuli, consistently exhibited a substantial and systematic regression towards the mean interval. When subjects judged intervals from distributions of longer total length they tended to regress more towards the mean, while the ability to discriminate between discrete intervals within the distribution had little influence on subject error. These results are consistent with a Bayesian model that minimizes reproduction errors by incorporating a central tendency prior weighted by the subject's own temporal precision relative to the current distribution of intervals. Finally a strong correlation was observed between all durations of formal musical training and total reproduction errors in both modalities (accounting for 30% of the variance). Taken together these results demonstrate that formal musical training improves temporal reproduction, and that this improvement transfers from audition to vision. They further demonstrate the flexibility of sensorimotor mechanisms in adapting to different task conditions to minimise temporal estimation errors.

Fast transfer of crossmodal time interval training

Sub-second time perception is essential for many important sensory and perceptual tasks including speech perception, motion perception, motor coordination, and crossmodal interaction. This study investigates to what extent the ability to discriminate sub-second time intervals acquired in one sensory modality can be transferred to another modality. To this end, we used perceptual classification of visual Ternus display (Ternus in Psychol Forsch 7:81-136, 1926) to implicitly measure participants' interval perception in pre- and posttests and implemented an intra- or crossmodal sub-second interval discrimination training protocol in between the tests. The Ternus display elicited either an "element motion" or a "group motion" percept, depending on the inter-stimulus interval between the two visual frames. The training protocol required participants to explicitly compare the interval length between a pair of visual, auditory, or tactile stimuli with a standard interval or to implicitly perceive the length of visual, auditory, or tactile intervals by completing a non-temporal task (discrimination of auditory pitch or tactile intensity). Results showed that after fast explicit training of interval discrimination (about 15 min), participants improved their ability to categorize the visual apparent motion in Ternus displays, although the training benefits were mild for visual timing training. However, the benefits were absent for implicit interval training protocols. This finding suggests that the timing ability in one modality can be rapidly acquired and used to improve timing-related performance in another modality and that there may exist a central clock for sub-second temporal processing, although modality-specific perceptual properties may constrain the functioning of this clock.

Numerical magnitude affects temporal memories but not time encoding

Previous research has suggested that the perception of time is influenced by concurrent magnitude information (e.g., numerical magnitude in digits, spatial distance), but the locus of the effect is unclear, with some findings suggesting that concurrent magnitudes such as space affect temporal memories and others suggesting that numerical magnitudes in digits affect the clock speed during time encoding. The current paper reports 6 experiments in which participants perceived a stimulus duration and then reproduced it. We showed that though a digit of a large magnitude (e.g., 9), relative to a digit of a small magnitude (e.g., 2), led to a longer reproduced duration when the digits were presented during the perception of the stimulus duration, such a magnitude effect disappeared when the digits were presented during the reproduction of the stimulus duration. These findings disconfirm the account that large numerical magnitudes accelerate the speed of an internal clock during time encoding, as such an account incorrectly predicts that a large numerical magnitude should lead to a shorter reproduced duration when presented during reproduction. Instead, the findings suggest that numerical magnitudes, like other magnitudes such as space, affect temporal memories when numerical magnitudes and temporal durations are concurrently held in memory. Under this account, concurrent numerical magnitudes have the chance to influence the memory of the perceived duration when they are presented during perception but not when they are presented at the reproduction stage.

The heart beat does not make us tick: the impacts of heart rate and arousal on time perception

According to popular models of human time perception, variations in prospective timing are caused by two factors: the pulse rate of an internal pacemaker and the amount of attention directed to the passage of time. The results concerning the effect of attention on subjective timing have been conclusive, but the mechanisms that drive the pacemaker are still far from being understood. In two experiments, we examined the impact of two factors that in the existing literature on human time perception have been argued to affect such a pacemaker: arousal and heart rate. Experienced arousal and heart rate were varied independently by means of specific physical exercises: (a) A muscle exercise increased arousal and heart rate; (b) a breath-holding exercise increased arousal but decreased heart rate; and (c) in the control condition, arousal and heart rate were held constant. The results indicate that increased subjective arousal leads to higher time estimates, whereas heart rate itself has no relevant impact on time perception. The results are discussed with respect to the underlying mechanisms of prospective time perception.