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
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References
[1] 黄希庭, 郭秀艳, 聂晶. (2003). 认知加工中时间与非时间信息的相互关系. 心理科学, 26(5), 770-774.
[2] 李宝林, 黄希庭. (2019). 时距知觉适应后效的研究进展. 生理学报, 71(1), 95-104.
[3] 张雯, 董亓易如, 龚丽娟, 尚琪, 程琛, 丁雪辰. (2022). 运算动量效应的理论解释及其发展性预测因素. 心理科学进展, 30(12), 2777-2788.
[4] Battacchi M. W., Pelamatti G. M., & Umiltà C. (1990). Is there a modality effect? Evidence for visual recency and suffix effects. Memory and Cognition, 18(6), 651-658.
[5] Berggren, N., & Eimer, M. (2019). The roles of relevance and expectation for the control of attention in visual search. Journal of Experimental Psychology: Human Perception and Performance, 45(9), 1191-1205.
[6] Block R. A., Hancock P. A., & Zakay D. (2010). How cognitive load affects duration judgments: A meta-analytic review. Acta Psychologica, 134(3), 330-343.
[7] Bonato M., D'Ovidio U., Fias W., & Zorzi M. (2021). A momentum effect in temporal arithmetic. Cognition, 206, Article 104488.
[8] Droit-Volet, S., & Meck, W. H. (2007). How emotions colour our perception of time. Trends in Cognitive Sciences, 11(12), 504-513.
[9] Fabbri M., Cancellieri J., & Natale V. (2012). The a theory of magnitude (ATOM) model in temporal perception and reproduction tasks. Acta Psychologica, 139(1), 111-123.
[10] Faul F., Erdfelder E., Lang A. G., & Buchner A. (2007). G*Power 3: A flexible statistical power analysis program for the social, behavioral, and biomedical sciences. Behavior Research Methods, 39(2), 175-191.
[11] Fischer, M. H., & Shaki, S. (2014). Spatial associations in numerical cognition-from single digits to arithmetic. Quarterly Journal of Experimental Psychology, 67(8), 1461-1483.
[12] Gorea, A. (2011). Ticks per thought or thoughts per tick? A selective review of time perception with hints on future research. Journal of Physiology-Paris, 105(4-6), 153-163.
[13] Kanai R., Lloyd H., Bueti D., & Walsh V. (2011). Modality-independent role of the primary auditory cortex in time estimation. Experimental Brain Research, 209(3), 465-471.
[14] Knops A., Dehaene S., Berteletti I., & Zorzi M. (2014). Can approximate mental calculation account for operational momentum in addition and subtraction? Quarterly Journal of Experimental Psychology, 67(8), 1541-1556.
[15] Knops A., Viarouge A., & Dehaene S. (2009). Dynamic representations underlying symbolic and nonsymbolic calculation: Evidence from the operational momentum effect. Attention Perception and Psychophysics, 71(4), 803-821.
[16] LeCompte, D. C. (1992). In search of a strong visual recency effect. Memory and Cognition, 20(5), 563-572.
[17] Mattes, S., & Ulrich, R. (1998). Directed attention prolongs the perceived duration of a brief stimulus. Perception and Psychophysics, 60(8), 1305-1317.
[18] Matthews, W. J. (2013). How does sequence structure affect the judgment of time? Exploring a weighted sum of segments model. Cognitive Psychology, 66(3), 259-282.
[19] Matthews, W. J., & Meck, W. H. (2016). Temporal cognition: Connecting subjective time to perception, attention, and memory. Psychological Bulletin, 142(8), 865-907.
[20] McCrink K., Dehaene S., & Dehaene-Lambertz G. (2007). Moving along the number line: Operational momentum in nonsymbolic arithmetic. Perception and Psychophysics, 69(8), 1324-1333.
[21] Murdock, B. B., Jr. (1962). The serial position effect of free recall. Journal of Experimental Psychology, 64(5), 482-488.
[22] Nairne, J. S. (1988). A framework for interpreting recency effects in immediate serial recall. Memory and Cognition, 16(4), 343-352.
[23] Pinhas, M., & Fischer, M. H. (2008). Mental movements without magnitude? A study of spatial biases in symbolic arithmetic. Cognition, 109(3), 408-415.
[24] Ranganath, C., & Rainer, G. (2003). Neural mechanisms for detecting and remembering novel events. Nature Reviews Neuroscience, 4(3), 193-202.
[25] Roach N. W., Mcgraw P. V., Whitaker D. J., & Heron J. (2017). Generalization of prior information for rapid Bayesian time estimation. Proceedings of the National Academy of Sciences of the United States of America, 114(2), 412-417.
[26] Shaki, S., & Fischer, M. H. (2014). Random walks on the mental number line. Experimental Brain Research, 232(1), 43-49.
[27] Shaki S., Sery N., & Fischer M. H. (2015). 1+2 is more than 2+1: Violations of commutativity and identity axioms in mental arithmetic. Journal of Cognitive Psychology, 27(4), 471-477.
[28] Shi Z. H., Church R. M., & Meck W. H. (2013). Bayesian optimization of time perception. Trends in Cognitive Sciences, 17(11), 556-564.
[29] Sørensen T. A., Vangkilde S., & Bundesen C. (2015). Components of attention modulated by temporal expectation. Journal of Experimental Psychology: Learning, Memory, and Cognition, 41(1), 178-192.
[30] Takahashi, K., & Watanabe, K. (2015). Mental summation of temporal duration within and across senses. PLoS ONE, 10(10), Article e0141466.
[31] Thomas, E. A. C., & Weaver, W. B. (1975). Cognitive processing and time perception. Perception and Psychophysics, 17(4), 363-367.
[32] Walsh, V. (2003). A theory of magnitude: Common cortical metrics of time, space and quantity. Trends in Cognitive Sciences, 7(11), 483-488.
[33] Xuan B., Zhang D. R., He S., & Chen X. C. (2007). Larger stimuli are judged to last longer. Journal of Vision, 7(10), Article 2.
[34] Zakay, D., & Block, R. A. (1997). Temporal cognition. Current Directions in Psychological Science, 6(1), 12-16.
[35] Zhou F., Zhao Q., Chen C. S., & Zhou X. L. (2012). Mental representations of arithmetic facts: Evidence from eye movement recordings supports the preferred operand-order-specific representation hypothesis. Quarterly Journal of Experimental Psychology, 65(4), 661-674.
[36] Zhou X. L., Chen C. H., Zhang H. C., Chen C. S., Zhou R. L., & Dong Q. (2007). The operand-order effect in single-digit multiplication: An ERP study of Chinese adults. Neuroscience Letters, 414(1), 41-44.
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