Vierordt's The Experimental Study of the Time Sense (1868) and its legacy

The paper discusses the results from Vierordt's 1868 book Der Zeitsinn nach Versuchen [The Experimental Study of the Time Sense]. Illustrations of “Vierordt's Law”, the proposition that short durations are judged as longer than they really are, whereas long durations are judged as shorter, with an “indifference point” in between, are provided, mainly from reproduction experiments where Vierordt and his students or colleagues served as experimental participants. Other work from Der Zeitsinn including time discrimination and categorical timing procedures is also presented. Some subsequent research on Vierordt's Law and the “indifference point” is discussed with respect to some issues in contemporary timing theory.     

A probe trial procedure for the study of children's discrimination learning and transfer

A discrimination reversal problem was presented to 192 children varying in age from 3 to 5 years. At the end of both the initial learning and transfer trials, probe trials were introduced to ascertain the response rule describing children's choices. Results were analyzed in terms of a binary division of the children according to their responses to the probe stimuli; children who responded errorlessly (concept responders) were contrasted with children who made errors on the probes (instance responders). Using this criterion, it was found that many children transferred in a way different from the way they learned the initial problem. There was no difference in the proportion of younger and older children responding conceptually to the original problem, but older children were more likely to transfer conceptually when standard geometric blocks were used as stimuli. Future studies must consider the possiblity that learning and transfer may be accomplished by different processes whose application differs with age, the nature of the stimuli, and the stage of training.     

Pigeons group time intervals according to their relative duration

In the present research, we asked whether pigeons tended to judge time intervals not only in terms of their absolute value but also relative to a duration from which they must be discriminated (i.e., longer or shorter). Pigeons were trained on two independent temporal discriminations. In one discrimination, sample durations of 2 and 8 sec were associated with, for example, red and green hue comparisons, respectively, and in the other discrimination, sample durations of 4 and 16 sec were associated with vertical and horizontal line comparisons, respectively. If pigeons are trained on a temporal discrimination and tested with intermediate durations, the subjective midpoint typically occurs close to the geometric mean of the two trained values. The 4- and 8-sec values were selected to be the geometric mean of the two values in the other discrimination. When a 4-sec test sample was presented with the comparisons from the 2- and 8-sec discrimination, the pigeons preferred the comparison associated with the shorter sample. Similarly, when an 8-sec test sample was presented with the comparisons from the 4-and 16-sec discrimination, the pigeons preferred the comparison associated with the longer sample. Thus, a relative grouping effect was found. That is, durations that should have produced indifferent choice were influenced by their relative durations (shorter than or longer than the alternative) during training.     

The effects of setting similarity on children's learning of the transverse patterning problem

A group of 15 fourth-graders were given training on the transverse patterning problem, a task consisting of three different geometric forms presented in pairs. Three other groups of 15 fourth-graders each received training on problems containing the same geometric forms, along with either one (color or size) or two (color and size) additional nonspatial dimensions varying among the settings comprising the different cue-cue patterns. Contrary to a prediction derived from Croll's (1967) extension of Spiker's (1963) theory of discrimination learning, none of the Ss solved the basic transverse patterning problem, nor was there any improvement in performance on this problem after 90 trials. Consistent with predictions derived from Spiker's theory, it was found that the addition of one nonspatial dimersion resulted in solution, and that the greater the number of nonspatial dimensions present, the better the learning.     

Discrimination learning and stimulus generalization by impulsive and reflective children

The proposition that impulsive children inhibit expressive behavior less than reflective children was investigated by providing third grade impulsive and reflective boys with either differential or nondifferential forms or successive discrimination training prior to tests for stimulus generalization. Consistent with specific predictions derived from Spence's theory on the roles of excitation and inhibition, it was found that: (a) Reflectives acquired the discrimination more rapidly, (b) reflectives achieved a higher level of discriminative performance, (c) impulsives exhibited more variable response reates during the nonreinforced stimulus, and (d) the type of training interacted with the child's conceptual tempo to determine the elevation and shape of the post-discrimination generalization gradients. The results provide support for the construct validity of the Matching Familiar Figures Test of reflectivity-impulsivity.     

Asymmetric cross-modal effects in time perception

It is common to judge the duration of an audiovisual event, and yet it remains controversial how the judgment of duration is affected by signals from other modalities. We used an oddball paradigm to examine the effect of sound on the judgment of visual duration and that of a visual object on the judgment of an auditory duration. In a series of standards and oddballs, the participants compared the duration of the oddballs to that of the standards. Results showed asymmetric cross-modal effects, supporting the auditory dominance hypothesis: a sound extends the perceived visual duration, whereas a visual object has no effect on perceived auditory duration. The possible mechanisms (pacemaker or mode switch) proposed in the Scalar Expectancy Theory [Gibbon, J., Church, R. M., & Meck, W. H. (1984). Scalar timing in memory. In J. Gibbon & L. Allan (Eds.), Annals of the New York Academy of Sciences: Vol. 423. Timing and time perception (pp. 52–77). New York: New York Academy of Sciences] were examined using different standard durations. We conclude that sound increases the perceived visual duration by accelerating the pulse rate in the visual pacemaker.     

Modality differences in timing and temporal memory throughout the lifespan

The perception of time is heavily influenced by attention and memory, both of which change over the lifespan. In the current study, children (8 yrs), young adults (18–25 yrs), and older adults (60–75 yrs) were tested on a duration bisection procedure using 3 and 6-s auditory and visual signals as anchor durations. During test, participants were exposed to a range of intermediate durations, and the task was to indicate whether test durations were closer to the “short” or “long” anchor. All groups reproduced the classic finding that “sounds are judged longer than lights”. This effect was greater for older adults and children than for young adults, but for different reasons. Replicating previous results, older adults made similar auditory judgments as young adults, but underestimated the duration of visual test stimuli. Children showed the opposite pattern, with similar visual judgments as young adults but overestimation of auditory stimuli. Psychometric functions were analyzed using the Sample Known Exactly-Mixed Memory quantitative model of the Scalar Timing Theory of interval timing. Results indicate that children show an auditory-specific deficit in reference memory for the anchors, rather than a general bias to overestimate time and that aged adults show an exaggerated tendency to judge visual stimuli as “short” due to a reduction in the availability of controlled attention.     

Stimulus factors and listening strategies in auditory memory: A theoretical analysis

A theory for the temporal course of perceptual coding during auditory short-term memory tasks is described. A low-level “sensor” and a high-level “identifier” process item and order information from stimulus word-strings. Both word durations and interword pauses are needed for this processing, and if adequate processing time is unavailable, perceptual delays will lead to degraded recall performance. Stimulus parameters and subject strategies interact to determine the quality and the order in which stimulus items are coded. These hypotheses are supported both by experiments using grammatical sentences and those using lists of unrelated words.     

Nonverbal discrimination of more and fewer elements by children

Fifty-six prekindergarten and 174 kindergarten children learned to choose either the card with more or the card with fewer elements in simultaneous discrimination problems. Learning was faster when the card with more elements was positive, particularly when a zero-element card was involved. This difference appeared to be attributable in part to an initial preference for “more.” On transfer trials involving all possible pairings of the training cards, subjects generally performed as though their choices were governed by the concept “more” or “fewer”. This tendency increased with age and with experience in the situation, even though conditions made verbal mediation appear unlikely.     

A critical analysis of the attention hypothesis of Zeaman and House: problems of parameter interactions in multiparameter models

The attention hypothesis of Zeaman and House [in N. R. Ellis (Ed.), Handbook of mental deficiency. New York: McGraw-Hill, 1963] was examined through a systematic, computer-simulation analysis of the parameter interactions found in the One-Look model. The hypothesis states that mental retardates and normals differ in their initial attention habits but not in their learning rates in the context of discrimination learning. The analysis showed that possible differences in the learning rates cannot be ruled out. The result was used to suggest how shift designs can unconfound the effect of the attention habits from the effect of the learning rates and maximize chances of observing possible differences in the learning rates between retarded and normal children.     

Turning observers into actors: Differential causal attributions as a function of “empathy”

After being instructed either to “empathize with the actor” or to “picture the events clearly,” two groups of observers read a story describing an actor's behavior, and then gave free-response explanations of that behavior, and rated the importance of personal and situational causal factors. The hypothesis that causal attributions of empathizing observers would be less personal and more situational than those of nonempathizing observers received strong support, both from subjects' free responses and from their scale ratings. These findings provide evidence for an information-processing explanation of actor/observer attributional differences. Some practical applications of increasing the situationality of observers' causal attributions are discussed. The results also suggest a novel operational definition of “empathy”; and are interpreted as evidence for the effectiveness of “interpersonal simulations”.     

Instigation of assertive behavior through videotape-mediated assertive models and directed practice

Twenty-eight undergraduate college women received an assertive training procedure in which they observed videotape-mediated assertive models and practiced nine types of assertive responses over a seven-week period. They reported significantly (p< 0.01) more assertive behavior and were rated as significantly (p< 0.01) more assertive than subjects receiving a placebo treatment and subjects receiving no treatment. There were also trends (p's = 0.17, 0.19, 0.29) for Ss receiving assertive training to report lower fear of social conflicts than subjects under the two control conditions.     

Sufficient conditions for an ordered-ring isomorphism onto a positive subinterval: A lemma for polynomial measurement

This paper discusses a sufficient set of conditions for a structure to be ordered-ring isomorphic to a positive subinterval of the real numbers. It extends our previous results concerning bounded versions of Hölder's Theorem (Falmagne, 1971). The main result can serve as a basic lemma for establishing representation theorems in polynomial conjoint measurement when the empirical sets contain neither large elements nor ones close to the natural zero.     

Is the growth of subjective time in humans a linear or nonlinear function of real time?

The difficulties of deciding whether subjective time grows as a linear or nonlinear function of real time are discussed, and two experiments are presented to address this question. In Experiment 1, people received a 10-s standard duration and then had to judge what proportion other durations (ranging from 1 to 10 s) were of the standard. Counting was prevented by a concurrent task. The relation between judged and actual proportions was linear. In Experiment 2, people were required to average together three tone durations (mean duration 600 ms) and to judge whether subsequently presented comparisons were or were not the average. The spacing of the tone durations had no effect on judgements, suggesting a linear underlying time scale.     

Is the growth of subjective time in humans a linear or nonlinear function of real time?

The difficulties of deciding whether subjective time grows as a linear or nonlinear function of real time are discussed, and two experiments are presented to address this question. In Experiment 1, people received a 10-s standard duration and then had to judge what proportion other durations (ranging from 1 to 10 s) were of the standard. Counting was prevented by a concurrent task. The relation between judged and actual proportions was linear. In Experiment 2, people were required to average together three tone durations (mean duration 600 ms) and to judge whether subsequently presented comparisons were or were not the average. The spacing of the tone durations had no effect on judgements, suggesting a linear underlying time scale.     

Differential production of positive and negative discriminative stimuli by normal and retarded children

Using an observing procedure similar to Wyckoff's (1969), two normal and two mentally retarded children were studied. The children were initially trained to earn pennies by pressing a rectangular key according to a multiple variable-interval extinction schedule of reinforcement. After discrimination training, the children were allowed to produce the discriminative stimuli by depressing a second or observing key. The retarded children were different from the normal children in that they produced more of the positive discriminative stimulus (S+) than the negative discriminative stimulus (S?). In the case of the retarded children, S+ observing started high and remained high. In the case of the normal children, S+ observing was initially substantial and then rapidly diminished.     

Scaling relative incentive value in anticipatory behavior

Papini and Pellegrini (Papini, M. R., & Pellegrini, S. Scaling relative incentive value in consummatory behavior. Learning and Motivation, in press) observed that, within limits, the level of consummatory responding of rats exposed to incentive downshifts in the concentration of sucrose solutions was similar when the ratio of test/training solutions was the same. For example, 32 → 4% and 16 → 2% downshifts (1:8 test/training ratios) lead to similar levels of consummatory behavior, despite differences in the absolute concentrations of the solutions involved in the downshift. This suggests the applicability of Weber’s law to spaced-trial, incentive-downshift situations. Experiment 1 extended these results to runway performance using food pellets as reward, and Experiment 2 to lever pressing performance, using an autoshaping procedure and sucrose solutions as rewards. The results conform well to the test/training ratio suggesting that Weber’s law is applicable to anticipatory behavior. A simple mathematical rule that can be easily incorporated into models based on linear operators describes the results of consummatory and anticipatory behavior experiments.     

Measurement scales and scale independence in the analytic hierarchy process

One approach to evaluate the relative performance of decision alternatives with respect to multiple criteria is provided by the analytic hierarchy process. The method is based on pairwise comparisons between attributes, and several numerical measurement scales for the ratio statements have been proposed. The choice of measurement scale is re‐examined, and new arguments supporting the measurement scale of geometric progression are derived. Separately from the measurement scale considerations, the effects of the scale parameter in geometric measurement scale are also studied. By using a regression model for pairwise comparisons data, it is shown that the statistical inference does not depend on the value of the scale parameter in the case of a single pairwise comparison matrix. It is also shown when the scale independence of statistical inference can be achieved in a decision hierarchy. This requires the use of the geometric‐mean aggregation rule instead of the traditional arithmetic‐mean aggregation. The results of the case study demonstrate that the measurement scale and the aggregation rule have potentially large impacts on decision support. Copyright © 2000 John Wiley & Sons, Ltd.     

Stimulus selection with duration as a relevant cue

To date, research has not explicitly examined how duration competes with other stimulus dimensions for control over responding. The present study investigated some familiar selective mechanisms of stimulus control over key pecking in pigeons, with duration and line tilt as discriminative stimuli in successive discrimination procedures. Specifically, pigeon's key pecking was reinforced with food or extinguished following compound stimuli comprising one of two line orientation stimuli presented for one of two different durations. Traditional experimental designs explored stimulus additivity, overshadowing, blocking, and learned irrelevance. Although stimulus additivity was observed, control by duration was masked by line tilt in extinction testing that followed facilitated acquisition with redundant, relevant cues. In addition, although prior training with duration relevant partially blocked subsequent acquisition of control by line tilt when both stimulus dimensions were relevant, there was a tendency for control by duration to decrease with continued compound training. It was suggested that the greater time required to distinguish duration on a trial—compared to more commonly studied stimulus dimensions, which can be distinguished almost immediately—puts duration at a competitive disadvantage in situations where other relevant dimensions are also available.