Abstract: Duration perception refers to the perception of the interval between two successive events, or the duration of an event, which is a part of time perception. Our perception of the world is closely related to how we perceive the duration information. For example, we need precise timing to perform daily actions, such as perceiving, speaking, playing the piano or video games, or driving a car. However, it has been shown that the perceived durations are distorted by many factors, such as attention, emotion, magnitude, and sensory history. Moreover, the plasticity of duration perception is evident not only in the perception of a single duration, but also in more complex scenarios. For example, when someone asks you how much time you have actually spent studying today, you have to add up the time you spent studying between breaks to answer this question. Typically, we tend to overestimate the duration of time in our mental summation.
The mathematical axioms of commutativity and identity do not seem to hold in mental summation, which could be influenced by the order of the operands, resulting in the order effect. However, we know little about how the order effect arises in mental summation. To answer this question, the present study investigated the order effect and its underlying mechanism of the three-element mental summation of auditory duration. We assumed that if the order effect of mental summation is contingent on the overall increasing or decreasing trend of the operational sequence, it will be weakened or even disappear when the overall trend of the sequence is disrupted. Alternatively, if the order effect depends on the magnitude (i.e., duration) of the operational elements at a specific position (e.g., the last position) in the operational sequence, the order effect will be guaranteed as long as the magnitude at that position is maintained.
To test these hypotheses, two experiments were designed with the auditory sequential presentation paradigm. Twenty-six volunteers participated in Experiment 1 and 24 participated in Experiment 2. Specifically, in Experiment 1, we conducted a 4(sequence type: increasing, decreasing, uniform, random) × 3(sum of durations: 840ms, 1680ms, 2520ms) within-subject design. In Experiment 2, a 2(regularity of the overall trend: regular, irregular) × 2(magnitude of the last position: long, short) within-subject design was employed. In the duration reproduction task, participants were asked to reproduce the total duration of the first, second, and third auditory stimulus by pressing and releasing a button.
The results showed that there were significant operational momentum effects in the mental summation of auditory durations. That is, we found that the sum of the three durations was overestimated in all conditions. Moreover, the order effect of the three-element mental summation of auditory durations was observed. Specifically, the sum of the three durations in the increasing condition was significantly greater than that in the random condition, while the sum was significantly smaller in the decreasing condition than that in the random condition. More importantly, Experiment 2 further found that the main effect of the magnitude of the last position was significant: the sum was significantly larger in the long condition than that in the short condition, while the main effect of regularity of the overall trend and their interaction were not significant. It suggests that the order effect of mental summation of auditory durations is determined by the magnitude of the last position rather than the overall trend of the operational sequence: the greater the magnitude of the last position, the greater the overestimation effect in mental summation.
In summary, this study has uncovered the internal mechanism of the order effect of mental summation of auditory durations. It indicates that when summing several different durations, the latest duration is weighted most heavily. This effect is similar to the recency effect of memory.

Key words: audition, duration perception, mental summation, order effect, operational momentum effect, recency effect

摘要： 时距加法运算会导致个体高估运算时长,且这一效应受到运算序列元素顺序的影响。然而,目前这种顺序效应产生的原因仍不清楚。通过两个实验,结合听觉继时呈现范式和时距复制任务,系统探讨了听觉三元素时距加法运算中的顺序效应及其产生的原因。结果发现,在听觉三元素时距加法运算中出现了显著的顺序效应,即在运算元素时距长度递增条件下的时间偏差指数显著大于递减条件;且这种顺序效应取决于运算序列最后一个元素的时距长度而非运算元素变化的总体趋势。这说明个体在对继时呈现的不同听觉时距段进行累加时,新近的时距信息权重最大,即在听觉时距加法运算中会出现近因效应。

关键词: 听觉, 时距知觉, 加法运算, 顺序效应, 运算动量效应, 三元素