LEARNING TO TIME: A PERSPECTIVE

In the last decades, researchers have proposed a large number of theoretical models of timing. These models make different assumptions concerning how animals learn to time events and how such learning is represented in memory. However, few studies have examined these different assumptions either empirically or conceptually. For knowledge to accumulate, variation in theoretical models must be accompanied by selection of models and model ideas. To that end, we review two timing models, Scalar Expectancy Theory (SET), the dominant model in the field, and the Learning‐to‐Time (LeT) model, one of the few models dealing explicitly with learning. In the first part of this article, we describe how each model works in prototypical concurrent and retrospective timing tasks, identify their structural similarities, and classify their differences concerning temporal learning and memory. In the second part, we review a series of studies that examined these differences and conclude that both the memory structure postulated by SET and the state dynamics postulated by LeT are probably incorrect. In the third part, we propose a hybrid model that may improve on its parents. The hybrid model accounts for the typical findings in fixed‐interval schedules, the peak procedure, mixed fixed interval schedules, simple and double temporal bisection, and temporal generalization tasks. In the fourth and last part, we identify seven challenges that any timing model must meet.     

Double bisection of auditory temporal intervals by humans

Scalar Expectancy Theory (SET) has been the leading theory in timing research, and has also influenced research into human timing. However, other timing theories exist, such as Learning to Time (LeT). The double bisection task was designed to test the SET and LeT theories in pigeons. The purpose of this experiment was to verify whether similar results emerge from a human adaptation of the double bisection task. The results indicated that humans perform the double bisection task in the same way as pigeons do. However, the assumptions inherent in LeT cannot be applied to humans. Two other explanations are also assessed here.     

Repeated measurements of reinforcement effects on gradients of stimulus control

Two experiments studied the effects of reinforcement schedules on generalization gradients. In Exp. 1, after pigeons' responding to a vertical line was reinforced, the pigeons were tested with 10 lines differing in orientation. Reconditioning and the redetermination of generalization gradients were repeated from 8 to 11 times with the schedule of reinforcement varied in the reconditioning phase. Stable gradients could not be observed because the successive reconditionings and tests steepened the gradients and reduced responding. Experiment 2 over-came these effects by first training the birds to respond to all of the stimuli. Then, brief periods of reinforced responding to the stimulus correlated with reinforcement alternated with the presentation of the 10 lines in extinction. The development of stimulus control was studied eight times with each bird, twice with each of four schedules of reinforcement. Gradients were similar each time a schedule was imposed; the degree of control by the stimulus correlated with reinforcement varied with particular schedules. Behavioral contrast occurred when periods of reinforcement and extinction alternated and was more durable with fixed-interval, variable-interval, and variable-ratio schedules than with fixed-ratio or differential-reinforcement-of-low-rate schedules.     

Temporal control by progressive-interval schedules of reinforcement.

Progressive-interval performances are described using measures that have proven to be successful in the analysis of fixed-interval responding. Five rats were trained with schedules in which the durations of consecutive intervals increased arithmetically as each interval was completed (either 6-s or 12-s steps for different subjects). The response patterns that emerged with extended training (90 sessions) indicated that performances had come under temporal control. Postreinforcement pausing increased as a function of the interval duration, the pauses were proportional to the prevailing duration, and the likelihood of the first response within an interval increased as the interval elapsed. To assess the resistance of these patterns to disruption, subjects were trained with a schedule that generated high response rates and short pauses (variable ratio). When the progressive-interval schedule was reinstated, pausing was attenuated and rates were elevated, but performances reverted to earlier patterns with continued exposure. The results indicated that temporal control by progressive-interval schedules, although slow to develop, is similar in many respects to that for fixed-interval schedules.     

Effects of variations in the temporal distribution of reinforcements on interval schedule performance

Pigeons were exposed to variable-interval and fixed-interval schedules and schedules approximating variable-interval and fixed-interval schedules. The probabilities of the variable-interval and fixed-interval components in a mixed fixed-interval variable-interval schedule in Experiment I and the minimum and maximum interreinforcement intervals in Experiment II in a variable-interval schedule were manipulated to create intermediate schedule contingencies and contingencies approximating simple variable-interval or fixed-interval contingencies. Maximal control by time as defined by quantitative indices of the temporal pattern of response occurred as fixed-interval contingencies were approximated and minimal control occurred as variable-interval contingencies were approximated. Changes in the temporal pattern of response were systematically related to changes in the temporal distribution of reinforcements with both procedural definitions for manipulating the temporal distribution of reinforcements.     

疼痛表情对秒下及秒上时距知觉的影响

采用二分法和泛化法范式,在秒下及秒上呈现时距探究疼痛表情对时距知觉的影响。结果发现,使用二分法,疼痛表情在秒上秒下都显著延长了个体的主观时距,但使用泛化法,疼痛表情仅在秒上产生影响。根据时间分段综合模型和范式特点,该实验结果反映疼痛表情对时距知觉的影响在秒上秒下的作用机制可能不同,在秒下主要是通过唤醒影响,在秒上则可能由唤醒和注意共同调节。     

Developmental changes in time estimation: comparing childhood and old age.

Participants from ages 5 to 99 years completed 2 time estimation tasks: a temporal generalization task and a temporal bisection task. Developmental differences in overall levels of performance were found at both ends of the life span and were more marked on the generalization task than the bisection task. Older adults and children performed at lower levels than young adults, but there were also qualitative differences in the patterns of errors made by the older adults and the children. To capture these findings, the authors propose a new developmental model of temporal generalization and bisection. The model assumes developmental changes across the life span in the noisiness of initial perceptual encoding and across childhood in the extent to which long-term memory of time intervals is distorted.     

Scalar timing without reference memory? Episodic temporal generalization and bisection in humans

Three experiments tested whether the scalar property of timing could occur when humans timed short durations under conditions in which it was unlikely that they developed reference memories of temporal "standards". Experiment 1 used an episodic version of a temporal generalization task where judgements were made of the potential equality of two durations presented on each trial. Unknown to the subject, one of these was always 200, 400, 600, or 800 ms, and the other was of variable duration. Temporal generalization gradients showed the scalar property of superimposition at standard values greater than 200 ms. Experiment 2 used a variant of the "roving bisection" method invented by Rodriguez-Girones and Kacelnik (1998) modified so that the scalar property of timing could be observed empirically. Data from bisection with short/long standard pairs of 100/400, 200/800, and 300/1,200 ms showed nearly perfect scalar-type superimposition. Experiment 3 again used episodic temporal generalization, but durations were never repeated and came from three distinct time ranges. Superimposition was found across these ranges except for the shortest visual stimuli timed. The data suggested that scalar timing could occur in humans in conditions where the formation of reference memories of temporal standards was highly improbable.     

Concurrent fixed-ratio fixed-interval performances in adult human subjects

Two undergraduate males worked for money on a button-pressing task associated with concurrent fixed-ratio fixed-interval schedules of reinforcement. Manipulations of the fixed-ratio requirement produced an interaction between the various fixed-ratio and fixed-interval performances. When the fixed ratio was small, more fixed-interval responding occurred per interval than when the fixed ratio was large. In general, the data were similar to those obtained with lower organisms except that no post-reinforcement pause or ratio strain was seen.     

Effects of reinforcement history on response rate and response pattern in periodic reinforcement

Several researchers have suggested that conditioning history may have long-term effects on fixed-interval performances of rats. To test this idea and to identify possible factors involved in temporal control development, groups of rats initially were exposed to different reinforcement schedules: continuous, fixed-time, and random-interval. Afterwards, half of the rats in each group were studied on a fixed-interval 30-s schedule of reinforcement and the other half on a fixed-interval 90-s schedule of reinforcement. No evidence of long-term effects attributable to conditioning history on either response output or response patterning was found; history effects were transitory. Different tendencies in trajectory across sessions were observed for measures of early and late responding within the interreinforcer interval, suggesting that temporal control is the result of two separate processes: one involved in response output and the other in time allocation of responding and not responding.     

Changing Sensitivity to Duration in Human Scalar Timing: An Experiment, a Review, and Some Possible Explanations

Evidence from a number of studies of human timing, using temporal generalization and bisection tasks, suggests more sensitive behavioural adjustment to presented durations under conditions in which the timing task demands discriminations between more closely spaced stimuli. An experiment using temporal generalization demonstrated this effect, as discrimination between a 600-msec standard duration and non-standard stimuli both shorter and longer than 600 msec was better when non-standard stimuli were more closely spaced around 600 msec. A review showed similar effects in other temporal generalization tasks and in a number of bisection studies, where time discrimination improved as the ratio of the long and short standards on the bisection task decreased. A standard model of human temporal generalization explained the experimental data in terms of a decrease in the response threshold under more difficult conditions, rather than changes in the representation of the standard duration. On the other hand, data from bisection could be modelled by assuming the contrary; that representations of the short and long standards of the task were more precise under the more difficult conditions. Explanations of some of these effects in terms of attention to duration and/or arousal-induced changes in the speed of an internal clock were discussed.     

Cognitive abilities required in time judgment depending on the temporal tasks used: A comparison of children and adults

The aim of this study was to examine age-related differences in time judgments during childhood as a function of the temporal task used. Children aged 5 and 8 years, as well as adults, were submitted to 3 temporal tasks (bisection, generalization and reproduction) with short (0.4/0.8?s) and long durations (8/16?s). Furthermore, their cognitive capacities in terms of working memory, attentional control, and processing speed were assessed by a wide battery of neuropsychological tests. The results showed that the age-related differences in time judgment were greater in the reproduction task than in the temporal discrimination tasks. This task was indeed more demanding in terms of working memory and information processing speed. In addition, the bisection task appeared to be easier for children than the generalization task, whereas these 2 tasks were similar for the adults, although the generalization task required more attention to be paid to the processing of durations. Our study thus demonstrates that it is important to understand the different cognitive processes involved in time judgment as a function of the temporal tasks used before venturing to draw conclusions about the development of time perception capabilities.     

Context effects in a temporal discrimination task" further tests of the Scalar Expectancy Theory and Learning-to-Time models

Pigeons were trained on two temporal bisection tasks, which alternated every two sessions. In the first task, they learned to choose a red key after a 1-s signal and a green key after a 4-s signal; in the second task, they learned to choose a blue key after a 4-s signal and a yellow key after a 16-s signal. Then the pigeons were exposed to a series of test trials in order to contrast two timing models, Learning-to-Time (LeT) and Scalar Expectancy Theory (SET). The models made substantially different predictions particularly for the test trials in which the sample duration ranged from 1 s to 16 s and the choice keys were Green and Blue, the keys associated with the same 4-s samples: LeT predicted that preference for Green should increase with sample duration, a context effect, but SET predicted that preference for Green should not vary with sample duration. The results were consistent with LeT. The present study adds to the literature the finding that the context effect occurs even when the two basic discriminations are never combined in the same session.     

Conditioned reinforcement versus time to reinforcement in chain schedules.

Pigeons were trained on three-component chain schedules in which the initial component was either a fixed-interval or variable-interval schedule. The middle and terminal components were varied among fixed-interval fixed-interval, variable-interval variable-interval, and an interdependent variable-interval variable-interval schedule in which the sum of the durations of the two variable-interval components was always equal to the sum of the fixed-interval fixed-interval components. At issue was whether the response rate in the initial component was controlled by its time to primary reinforcement or by the temporal parameters of the stimulus correlated with the middle terminal link. The fixed-interval initial-link schedule maintained much lower response rates than the variable-interval initial-link schedule regardless of the schedules in the middle and terminal links. Nevertheless, the intervening schedules played some role: With fixed-interval schedules in the initial links, response rates were consistently highest with independent variable-interval schedules in the middle and terminal links and intermediate with the interdependent variable-interval schedules; these initial-link differences were predicted by the response rates in the middle link of the chain. With variable-interval schedules in the initial links, response rates were lowest with the fixed-interval fixed-interval schedules following the initial link and were not systematically different for the two types of variable-interval variable-interval schedules. The results suggest that time to reinforcement itself accounts for little if any variance in initial-link responding.     

The interaction of temporal generalization gradients predicts the context effect

In a temporal double bisection task, animals learn two discriminations. In the presence of Red and Green keys, responses to Red are reinforced after 1-s samples and responses to Green are reinforced after 4-s samples; in the presence of Blue and Yellow keys, responses to Blue are reinforced after 4-s samples and responses to Yellow are reinforced after 16-s samples. Subsequently, given a choice between Green and Blue, the probability of choosing Green increases with the sample duration-the context effect. In the present study we asked whether this effect could be predicted from the stimulus generalization gradients induced by the two basic discriminations. Six pigeons learned to peck Green following 4-s samples (S(+)) but not following 1-s samples (S(-)) and to peck Red following 4-s samples (S(+)) but not following 16-s samples (S(-)). Temporal generalization gradients for Green and Red were then obtained. Finally, the pigeons were given a choice between Green and Red following sample durations ranging from 1 to 16 s. Results showed that a) the two generalization gradients had the minimum at the S(-) duration, an intermediate value between the S(-) and the S(+) durations, and the maximum at the S(+) as well as more extreme durations; b) on choice trials, preference for Green over Red increased with sample duration, the context effect; and c) the two generalization gradients predicted the average context effect well. The Learning-to-Time model accounts for the major trends in the data.     

Stimulus timing by people with Parkinson's disease

Previous literature suggests that Parkinson’s disease is marked by deficits in timed behaviour. However, the majority of studies of central timing mechanisms in patients with Parkinson’s disease have used timing tasks with a motor component. Since the motor abnormalities are a defining feature of the condition, the status of timing in Parkinson’s disease remains uncertain. Data are reported from patients with mild to moderate Parkinson’s disease (both on and off medication) and age- and IQ-matched controls on a range of stimulus timing tasks without counting. Tasks used were temporal generalization, bisection, threshold determination, verbal estimation, and a memory for duration task. Performance of patients was generally “normal” on all tasks, but significant differences from performance of controls were found on the memory for duration task. Among the “normal” effects noted were arithmetic mean bisection, asymmetric temporal generalization gradients, and subjective shortening on the memory for duration task. The results suggest (a) that some previous reports of timing “deficits” in Parkinson’s patients were possibly due to the use of tasks requiring a timed manual response and (b) small differences between patients and controls may be found on tasks where two stimuli are presented on each trial, whether patients are on medication or off it.     

Food deliveries during the pause on fixed-interval schedules

Pigeons were trained on fixed-interval schedules of food delivery. In Experiments I and II, the fixed interval was initiated by the previous fixed-interval reinforcer; in Experiment III, the fixed interval was initiated by the first key peck following the preceding fixed-interval reinforcer (a chain fixed-ratio one, fixed-interval schedule). During the postreinforcement pause, variable-time schedules delivered food independent of any specific response. Rate of food delivery during the pause had only small effects on pause duration in Experiments I and II. In Experiment III, however, pause duration increased systematically with the rate of food delivery during the pause. These data suggest that the momentary proximity to reinforcement delivered via the fixed-interval schedule exerts potent control over pause termination. Additional analysis revealed that pause termination was unaffected by the intermittent delivery of food during the pause. Such data suggest that the temporal control by fixed-interval schedules is highly resistant to interference.     

Pure timing in temporal differentiation

Temporal control appears to depend on whether the critical durations are those of stimuli or those of responses. Stimulus timing (temporal discrimination) supports Weber's law, whereas response timing (temporal differentiation) indicates decreasing relative sensitivity with longer time intervals. The two types of procedure also yield different conclusions in scaling experiments designed to study the functional midpoint of two or more durations (temporal bisection procedures). In addition, the fractional-exponent power relation between emitted and required duration usually found with animals in differentiation experiments conflicts with deductions from formal analyses. The experiment reported here derived from considering differentiation arrangements as schedules of reinforcement. When analyzed from this perspective, the procedures are tandem schedules involving a required pause followed by a response, and it is the pause alone that involves temporal control. A choice procedure separated timing from responding, and enabled observations of pause timing in isolation. Pure temporal control in differentiation consisted of linear overestimation of the standard duration, and Weber's law described sensitivity. These results indicate that the two problems, the fractional-exponent power relations and the apparently different nature of sensitivity in differentiation and discrimination, disappear when temporal control is observed alone in differentiation.     

Time flies with music whatever its emotional valence

The present study used a temporal bisection task to investigate whether music affects time estimation differently from a matched auditory neutral stimulus, and whether the emotional valence of the musical stimuli (i.e., sad vs. happy music) modulates this effect. The results showed that, compared to sine wave control music, music presented in a major (happy) or a minor (sad) key shifted the bisection function toward the right, thus increasing the bisection point value (point of subjective equality). This indicates that the duration of a melody is judged shorter than that of a non-melodic control stimulus, thus confirming that “time flies” when we listen to music. Nevertheless, sensitivity to time was similar for all the auditory stimuli. Furthermore, the temporal bisection functions did not differ as a function of musical mode.     

Concurrent-chains schedules as a method to study choice between alcohol-associated conditioned reinforcers

An extensive body of research using concurrent-chains schedules of reinforcement has shown that choice for one of two differentially valued food-associated stimuli is dependent upon the overall temporal context in which those stimuli are embedded. The present experiments examined whether the concurrent chains procedure was useful for the study of behavior maintained by alcohol and alcohol-associated stimuli. In Experiment 1, rats responded on concurrent-chains schedules with equal variable-interval (VI) 10-s schedules in the initial links. Across conditions, fixed-interval schedules in the terminal links were varied to yield 1∶1, 9∶1, and 1∶9 ratios of alcohol delivery. Initial-link response rates reflected changes in terminal-link schedules, with greater relative responding in the rich terminal link. In Experiment 2, terminal-link schedules remained constant with a 9∶1 ratio of alcohol delivery rates while the length of two equal duration initial-link schedules was varied. Preference for the rich terminal link was less extreme when initial links were longer (i.e., the initial-link effect), as has been previously reported with food reinforcers. This result suggests that the conditioned reinforcing value of an alcohol-associated stimulus depends on the temporal context in which it is embedded. The concurrent-chains procedure and quantitative models of concurrent chains performance may provide a useful framework within which to study how contextual variables modulate preference for drug-associated conditioned reinforcers.