Composition rule for perceived duration of simultaneous events

Abstract

When a subject is required to monitor the duration of two events that occur simultaneously, the perceived durations of the events are combined in a nonlinear manner. This is in contrast to evaluations of duration of successive events for which the composition rules are close to linear. In each of two experiments, 20 subjects judged the average duration of pairs of temporal intervals varying in duration from .5 to 10.0 sec. For one condition the intervals were presented simultaneously, and for the other they were presented successively. The simultaneous condition differed from that in our previous studies in that the intervals of the pair shared a common offset rather than a common onset, a modification suggested by Eisler, who hypothesized that our previous finding may have been due to an offset asynchrony. Results were consistent with a nonlinear composition rule for describing parallel monitoring of temporal information of simultaneous events and a linear rule for monitoring duration of successive events.The research to be reported follows from research we have conducted previously which deals with the perceived duration of simultaneous events (Curtis & Rule, 1977) and from a modification of those experiments suggested by Eisler (1981). In the Curtis and Rule studies, subjects rated pairs of temporal intervals with respect to their average duration, their total (summed) duration, or their difference ,--'----, tion when the intervals making up the pairs, / sented either simultaneously or successiveiy. 111q uestion of interest concerned the form of the composition rules describing the ways in which the subjective relations were represented in judgments of averages, sums, and differences. For successive presentations, the data were well described by linear expressions consistent with the arithmetic operations set forth in the instructions to subjects. For example, judgments of average duration were consistent with expectations if information concerning the duration of the two intervals was combined according to the rule, (1) where !Pij represents the subjective measure of the I conjoint effect of stimulus i and stimulus j, and !Pi and !Pj denote the subjective magnitudes of the two durations. In contrast, when the durations evaluated were presented simultaneously, the data suggested a This research was supported by Grants AOISI and A9S82 from the Natural Sciences and Engineering Research Council Canada. Requests for reprints should be sent to Stanley J. Rule, Department of Psychology, University of Alberta, Edmonton, Alberta' T6G 2E9, Canada. 569 markedly nonlinear composition rule. For example, judgments of the average duration of two simultaneous events were consistent with the rule:1 C is greater than unity. The data yielded estif c of 1.85 from judgments of averages and 1.94 from judgments of the sums of durations fitted by an analogous expression.On the basis of the nonlinearity of the relation described by Equation 2, we (Curtis & Rule, 1977) questioned a theoretical position advanced by Eisler (1975). A...

Ordinal properties of perceived average duration: Simultaneous and sequential presentations.

“…The product is 1.60. This value compares with previous estimates of 1.85 and 1.94 from judgments of intervals with a common onset (Curtis & Rule, 1977) and 1.50 from judgments of intervals with a common offset (Rule et al, 1983).…”

“…When a subject evaluates the duration of two events that occur sequentially, judgments of the sums or the averages of the two time intervals tend to be proportional to the sums or averages of the perceived durations of each interval (Blankenship & Anderson, 1976; Curtis & Rule, 1977; Rule, Mahon, & Curtis, 1983). For example, judgments of average duration appear to follow the composition rule where ψ ij represents the subjective measure of the conjoint effect of stimulus i and stimulus j , and ψ i and ψ j denote the subjective magnitudes of the two durations.…”

Temporal Decision Making in Simultaneous Timing

“…However, we know from everyday life and from a growing body of research that humans and even non-human animals are able to estimate the durations of more than one stimulus simultaneously (cf. Curtis and Rule, 1977; Rule et al, 1983; Meck and Church, 1984; Rule and Curtis, 1985; Brown and West, 1990; van Rijn and Taatgen, 2008). …”

"Ratio" and "difference" judgments for length, area, and volume: Are there two classes of sensory continua?

“…Another continuum that appears to be readily decomposable is perceived duration. Although duration sums or averages have been studied (Blankenship & Anderson, 1976; Curtis & Rule, 1977; Rule & Curtis, 1985; Rule, Mahon, & Curtis, 1983), we know of no direct comparisons between judgments of duration differences and duration ratios. It would be interesting to determine whether perceived duration behaves like length, area, and volume.…”