“One-thousand<Emphasis Type="Italic">one</Emphasis> … one-thousand<Emphasis Type="Italic">two</Emphasis> …”: Chronometric counting violates the scalar property in interval timing

Medical College of Wisconsin, Milwaukee, Wisconsin Weber’s law applied to interval timing is called thescalar property. A hallmark of timing in the secondsto-minutes range, the scalar property is characterized by proportionality between the standard deviation of a response distribution and the duration being timed. In this temporal reproduction study, we assessed whether the scalar property was upheld when participants chronometrically counted three visually presented durations (8, 16, and 24 sec) as compared with explicitly timing durations without counting. Accuracy for timing and accuracy for counting were similar. However, whereas timing variability showed the scalar property, counting variability did not. Counting variability across intervals was accurately modeled by summing a random variable representing an individual count. A second experiment replicated the first and demonstrated that task differences were not due to presentation order or practice effects. The distinct psychophysical properties of counting and timing behaviors argue for greater attention to participant strategies in timing studies.     

Scalar Counters

Poisson processes—random pacemakers driving accurate counters—are common models for timers. Such clocks get relatively more accurate the faster they go. This is not true of real clocks, where the relative error is approximately constant, an example of Weber's law known as scalar timing. This distinction was the core problem motivating Gibbon's Scalar Expectancy Theory. Since worse pacemakers cannot generate scalar timing, the necessary variance must be found elsewhere. This article reviews three failure modes of counters and shows that any one (or all together) provides a mechanism for scalar timing. Unique microdeviations from proportional timing in real data provide signatures of underlying machinery. This paper assays the maps between these signatures and those of stochastic counters, finding family resemblances that range from kissing cousins to clones.     

More consistent,yet less sensitive: Interval timing in autism spectrum disorders

Even though phenomenological observations and anecdotal reports suggest atypical time processing in individuals with an autism spectrum disorder (ASD), very few psychophysical studies have investigated interval timing, and the obtained results are contradictory. The present study aimed to clarify which timing processes function atypically in ASD and whether they are related to the ASD diagnostic profile. Visual, auditory, and cross-modal interval timing was assessed in 18 individuals with ASD using a repeated standards version of the temporal generalization task. The use of two different standard durations (600 and 1,000 ms) allowed for an assessment of the scalar property of interval timing in ASD, a fundamental characteristic of interval timing. The ASD group showed clearer adherence to the scalar property of interval timing than the control group. In addition, both groups showed the normal effect that auditory stimuli had longer subjective durations than visual ones. Yet, signal detection analysis showed that the sensitivity of temporal discrimination was reduced in the ASD group across modalities, in particular for auditory standards. Moreover, response criteria in the ASD group were related to symptom strength in the communication domain. The findings suggest that temporal intervals are fundamentally processed in the same way in ASD and TD, but with reduced sensitivity for temporal interval differences in ASD. Individuals with ASD may show a more conservative response strategy due to generally decreased sensitivity for the perception of time intervals.     

Time and memory: towards a pacemaker-free theory of interval timing

A popular view of interval timing in animals is that it is driven by a discrete pacemaker-accumulator mechanism that yields a linear scale for encoded time. But these mechanisms are fundamentally at odds with the Weber law property of interval timing, and experiments that support linear encoded time can be interpreted in other ways. We argue that the dominant pacemaker-accumulator theory, scalar expectancy theory (SET), fails to explain some basic properties of operant behavior on interval-timing procedures and can only accommodate a number of discrepancies by modifications and elaborations that raise questions about the entire theory. We propose an alternative that is based on principles of memory dynamics derived from the multiple-time-scale (MTS) model of habituation. The MTS timing model can account for data from a wide variety of time-related experiments: proportional and Weber law temporal discrimination, transient as well as persistent effects of reinforcement omission and reinforcement magnitude, bisection, the discrimination of relative as well as absolute duration, and the choose-short effect and its analogue in number-discrimination experiments. Resemblances between timing and counting are an automatic consequence of the model. We also argue that the transient and persistent effects of drugs on time estimates can be interpreted as well within MTS theory as in SET. Recent real-time physiological data conform in surprising detail to the assumptions of the MTS habituation model. Comparisons between the two views suggest a number of novel experiments.     

Scalar properties in animal timing: conformity and violations

The article reviews data from animal subjects on a range of timing tasks (including fixed-interval and temporal differentiation schedules, stimulus timing, aversive conditioning, and Pavlovian methods) with respect to conformity to the two scalar properties of timing behaviour: mean accuracy and scalar (Weberian) variance. Systematic deviations were found in data from temporal differentiation schedules, timing of very short (<100 ms) or very long (>100 s) durations, effects of "task difficulty", and some special cases where circadian and interval timing seemed to interact, or where some specific durations seemed to be timed more precisely than others. Theoretical reconciliation of some of these deviations with underlying scalar timing can be achieved, but a number of problematical cases remain unexplained.     

Scalar properties in animal timing: Conformity and violations

The article reviews data from animal subjects on a range of timing tasks (including fixed-interval and temporal differentiation schedules, stimulus timing, aversive conditioning, and Pavlovian methods) with respect to conformity to the two scalar properties of timing behaviour: mean accuracy and scalar (Weberian) variance. Systematic deviations were found in data from temporal differentiation schedules, timing of very short (<100 ms) or very long (>100 s) durations, effects of “task difficulty”, and some special cases where circadian and interval timing seemed to interact, or where some specific durations seemed to be timed more precisely than others. Theoretical reconciliation of some of these deviations with underlying scalar timing can be achieved, but a number of problematical cases remain unexplained.     

Origines et développement des théories d’horloge interne du temps psychologique

The article describes the origins and development of internal clock theory. The history is traced via body temperature studies in the 1920s and 1930s, with input from 19th. century and early 20th. century psychophysics, through to the model of Treisman (1963). This model derived timed behaviour from an interaction of internal clock, memory store, and comparison processes. A successor to Treisman's model was the scalar expectancy theory (SET) of Gibbon and colleagues (1984). The origins of SET in animal Psychology are described, as is its application to human timing (in the early 1990s), in particular recent work on the operation of the internal clock itself. Finally, a discussion of some recent developmental studies of timing illustrates both how internal clock models have been applied, and how modern research may require a reconceptualization of the operation of classical internal clock models.     

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.     

Good vibrations: Human interval timing in the vibrotactile modality

This article reports a detailed examination of timing in the vibrotactile modality and comparison with that of visual and auditory modalities. Three experiments investigated human timing in the vibrotactile modality. In Experiment 1, a staircase threshold procedure with a standard duration of 1,000 ms revealed a difference threshold of 160.35 ms for vibrotactile stimuli, which was significantly higher than that for auditory stimuli (103.25 ms) but not significantly lower than that obtained for visual stimuli (196.76 ms). In Experiment 2, verbal estimation revealed a significant slope difference between vibrotactile and auditory timing, but not between vibrotactile and visual timing. That is, both vibrations and lights were judged as shorter than sounds, and this comparative difference was greater at longer durations than at shorter ones. In Experiment 3, performance on a temporal generalization task showed characteristics consistent with the predications of scalar expectancy theory (SET: Gibbon, 1977) with both mean accuracy and scalar variance exhibited. The results were modelled using the modified Church and Gibbon model (MCG; derived by Wearden, 1992, from Church & Gibbon 1982). The model was found to give an excellent fit to the data, and the parameter values obtained were compared with those for visual and auditory temporal generalization. The pattern of results suggest that timing in the vibrotactile modality conforms to SET and that the internal clock speed for vibrotactile stimuli is significantly slower than that for auditory stimuli, which is logically consistent with the significant differences in difference threshold that were obtained.     

Alerting attention and time perception in children

This experiment investigated the effect of a signal (i.e., a click) warning of the arrival of a stimulus to be timed on temporal discrimination in children aged 3, 5, and 8 years (N=86), using a bisection task with visual stimuli ranging from 0.5 to 2s or 1 to 4s. In all groups, the psychophysical functions were orderly with the proportion of long responses increasing with the stimulus duration, although the steepness of functions increased with age. Stimulus durations were judged to be longer with than without the click in all age groups. With the click, time sensitivity also improved and more particularly in the younger children. The statistical results suggest, within the framework of the scalar timing theory, that the click reduces the closing latency of the switch that connects the pacemaker to the accumulator in the internal clock and also reduces its trial-by-trial variability.     

标量计时模型的影响因素及发展

标量计时模型为人类时间知觉的研究提供了理论框架和研究范式, 它采用信息加工的观点, 包含时钟、记忆和决策三个阶段。时间二分任务是在标量计时模型的框架下研究时间知觉和加工的理想范式。它要求被试对时距进行与标量计时模型相对应的多阶段操作, 包含了时间知觉所涉及的各个过程, 能有效测量主观时距和时间敏感性的变化。通过这个范式, 研究者发现, 除了任务参数, 年龄和疾病都会影响人的主观时距和/或时间敏感性。这些时间二分任务的实验结果促进了标量计时模型的发展, 最近提出的两阶段决策模型和差别模型分别以不同的方式对标量计时模型进行了修正, 并解释了参数设置的影响和计时的个体差异。     

Shared timing variability in eye and finger movements increases with interval duration: Support for a distributed timing system below and above one second

The origins of the ability to produce action at will at the hundreds of millisecond to second range remain poorly understood. A central issue is whether such timing is governed by one mechanism or by several different mechanisms, possibly invoked by different effectors used to perform the timing task. If two effectors invoke similar timing mechanisms, then they should both produce similar variability increase with interval duration (interonset interval) and thus adhere to Weber's law (increasing linearly with the duration of the interval to be timed). Additionally, if both effectors invoke the same timing mechanism, the variability of the effectors should be highly correlated across participants. To test these possibilities, we assessed the behavioural characteristics across fingers and eyes as effectors and compared the timing variability between and within them as a function of the interval to be produced (interresponse interval). Sixty participants produced isochronous intervals from 524 to 1431?ms with their fingers and their eyes. High correlations within each effector indicated consistent performance within participants. Consistent with a single mechanism, temporal variability in both fingers and eyes followed Weber's law, and significant correlations between eye and finger variability were found for several intervals. These results can support neither the single clock nor the multiple clock hypotheses but instead suggest a partially overlapping distributed timing system.     

Violation of the scalar property for time perception between 1 and 2 seconds: evidence from interval discrimination, reproduction, and categorization

According to the hypothesis of a scalar property for time, the variability to time ratio should be constant. Three experiments tested the validity of this hypothesis in a restricted range of durations (standard values = 1, 1.3, 1.6, and 1.9 s). In each experiment, time intervals to be discriminated, reproduced, or categorized were presented with 2, 4, or 6 brief successive auditory signals marking 1, 3, or 5 intervals, respectively. In Experiment 1, participants were asked to indicate whether the interval(s) within a second series of sounds were shorter or longer than those of the first. In Experiment 2, the standard interval had to be reproduced. In Experiment 3, after 10 presentations of the standard, participants had to categorize each comparison interval as shorter or longer than the standard. In addition to showing that performance was generally poorer when only 1 interval was presented and remained about the same regardless of whether 3 or 5 intervals were presented (Experiments 1 and 3), the results demonstrated that the variability to time ratio is not constant across the standard interval conditions. Overall, the ratio is higher at 1.9 than at 1 s. This violation of scalar timing occurs whatever the method used and does not interact with the number-of-interval variable.     

Nonverbal Counting in Humans: The Psychophysics of Number Representation

In a nonverbal counting task derived from the animal literature, adult human subjects repeatedly attempted to produce target numbers of key presses at rates that made vocal or subvocal counting difficult or impossible. In a second task, they estimated the number of flashes in a rapid, randomly timed sequence. Congruent with the animal data, mean estimates in both tasks were proportional to target values, as was the variability in the estimates. Converging evidence makes it unlikely that subjects used verbal counting or time durations to perform these tasks. The results support the hypothesis that adult humans share with nonverbal animals a system for representing number by magnitudes that have scalar variability (a constant coefficient of variation). The mapping of numerical symbols to mental magnitudes provides a formal model of the underlying nonverbal meaning of the symbols (a model of numerical semantics).     

Rapidly developed scalar timing in unsignalled shuttlebox avoidance learning

Three groups of rats were given brief inescapable shocks in a shuttlebox with equal shock-shock (S-S) and response-shock (R-S) intervals of 10, 15 or 20 s. Non shock-elicited responses (experimentally defined) postponed the occurrence of the next shock while shock elicited responses had no programmed consequences. Avoidance behaviour was rapidly acquired with all groups avoiding 85% or more of scheduled shocks by the end of the fifth 1 h session. Interresponse times revealed the development of excellent temporal discriminations in all groups. The data provide quantitative support for Gibbon's (1971) scalar timing hypothesis.     

Distressed Mothers and Their Infants Use a Less Efficient Timing Mechanism in Creating Expectancies of Each Other’s Looking Patterns

The prediction of events and the creation of expectancies about their time course is a crucial aspect of an infant's mental life, but temporal mechanisms underlying these predictions are obscure. Scalar timing, in which the ratio of mean durations to their standard deviations is held constant, enables a person to use an estimate of the mean for its standard deviation. It is one efficient mechanism that may facilitate predictability and the creation of expectancies in mother-infant interaction. We illustrate this mechanism with the dyadic gaze rhythm of mother and infant looking at and looking away from each other's faces. Two groups of Hi- and Lo-Distress mothers were created using self-reported depression, anxiety, self-criticism and childhood experiences. Lo-Distress infants (controls) used scalar timing 100% of the time, about double that of Hi-Distress infants. Lo-Distress mothers used scalar timing about nine times as much as Hi-Distress mothers. The diminished use of scalar timing patterns in Hi-Distress mothers and infants may make the anticipation of each other's gaze patterns more difficult for both partners.     

Shifts in the psychometric function and their implications for models of timing

This study examined how two models of timing, scalar expectancy theory (SET) and learning to time (LeT), conceptualize the learning process in temporal tasks, and then reports two experiments to test these conceptualizations. Pigeons responded on a two-alternative free-operant psychophysical procedure in which responses on the left key were reinforceable during the first two, but not the last two, quarters of a 60-s trial, and responses on the right key were reinforceable during the last two, but not the first two, quarters of the trial. In Experiment 1 three groups of birds experienced a difference in reinforcement rates between the two keys only at the end segments of the trial (i.e., between the first and fourth quarters), only around the middle segments of the trial (i.e., between the second and third quarters), or in both end and middle segments. In Condition 1 the difference in reinforcement rate favored the left key; in Condition 2 it favored the right key. When the reinforcement rates differed in the end segments of the trial, the psychometric function--the proportion of right responses across the trial--did not shift across conditions; when it occurred around the middle of the trial or in both end and middle segments, the psychometric function shifted across conditions. Experiment 2 showed that the psychometric function shifts even when the overall reinforcement rate for the two keys is equal, provided the rates differ around the middle of the trial. This pattern of shifts of the psychometric function is inconsistent with SET. In contrast, LeT provided a good quantitative fit to the data.     

时距知觉的动物研究范式及相关神经机制

在探索时距知觉的脑机制的过程中, 相对于人类被试相关研究, 动物研究可以提供较多的药理学、分子生物学、单个神经元电生理学以及光遗传等方面的研究证据。目前较为常用的时距知觉动物研究范式包括时间二分法、峰值间隔法以及低比率差别强化法等。根据不同的研究需求, 动物研究的范式常会进行调整。对时距知觉的动物研究的探讨将基于两方面展开：(1) 常用的时距知觉动物研究范式的介绍及比较; (2) 基于动物研究范式的时距知觉神经机制研究进展, 旨在为深入探索时间知觉的心理学相关研究提供参考。     

Why 'Sounds Are Judged Longer Than Lights': Application of a Model of the Internal Clock in Humans

Three experiments, using temporal generalization and verbal estimation methods, studied judgements of duration of auditory (500-Hz tone) and visual (14-cm blue square) stimuli. With both methods, auditory stimuli were judged longer, and less variable, than visual ones. The verbal estimation experiments used stimuli from 77 to 1183 msec in length, and the slope of the function relating mean estimate to real length differed between modalities (but the intercept did not), consistent with the idea that a pacemaker generating duration representations ran faster for auditory than for visual stimuli. The different variability of auditory and visual stimuli was attributed to differential variability in the operation of a switch of a pacemaker-accumulator clock, and experimental datasuggested that such switch effects were separable from changes in pacemaker speed. Overall, the work showed how a clock model consistent with scalar timing theory, the leading account of animal timing, can address an issue derived from the classical literature on human time perception.     

CAN A DECAY PROCESS EXPLAIN THE TIMING OF CONDITIONED RESPONSES?

To explain time-scale invariant distributions of response latencies, it appears to be necessary to postulate scalar noise in the remembered intervals, against which the subjective measure of the currently elapsing interval is compared. At least in some cases, the observed variability cannot be due to variability in the subjective intervals written to memory; it must come from noise (variability) in the reading of a memory. The Staddon and Higa proposal offers no explanation for the observed variability, and it is unclear what noise assumption would yield the observed variability, given their assumption that intervals are timed by a nonlinear decay process. The decay process cannot plausibly be represented by the logarithmic function, because it begins and ends at infinity. The assumption of any form of nonlinear timing is inconsistent with the most important result of the time-left experiment, which is that the changeover time increases linearly with the comparison-standard difference.