On magnitudes in memory: An internal clock account of space–time interaction☆
Introduction
Time is a paradox to the human mind. It is a ubiquitous psychological experience but imperceptible to our senses. That is, there does not seem to be a physical medium for time (like light for vision) or a bodily faculty that tunes into time (like the eye for vision). For instance, we can perceive the empty interval between two clicks and have some memory of its duration, even though none of our bodily senses appear to register the emptiness. Thus, research on time perception has focused on the cognitive processes and memory representations that underlie our capacity to perceive time, and has historically split into two largely parallel but related literatures with separate theoretical emphases and empirical effects: the representational approach and the mechanistic approach.
Since time perception does not appear to rely on any particular bodily sense, the representational approach to time perception concerns the mental or conceptual representational format of temporal durations and investigates how our perception of an event's duration is influenced by other dimensions of the same event (e.g. DeLong, 1981, Piaget, 1969, Xuan et al., 2007). One such dimension that has been heavily investigated in time representation research is spatial distance. It has been repeatedly demonstrated that perceived duration increases as a function of concurrent spatial distance (Cai et al., 2013, Casasanto and Boroditsky, 2008, Merritt et al., 2010). For instance, Casasanto and Boroditsky (2008) displayed a line of a particular length onscreen for a particular duration and then asked participants to reproduce the duration: they showed that participants' reproduced durations increased as a function of concurrent line length. Similarly, Cai et al. (2013) showed that participants reproduced a longer duration for a sung note if the singer in the video made a concurrent long-distance horizontal gesture compared to a short-distance one. Indeed, the ability of space to distort time relies on having a reliable, high-acuity representation of spatial distance. Cai and Connell (2015) showed that when spatial distance is perceived via low-acuity haptics (rather than high-acuity vision), it has no effect on reproduced duration; instead, the relationship flipped so that time distorted space, and reproduced distance increased with duration. These space–time interaction effects suggest a close relationship between the representations of spatial distance and temporal duration. Further work also suggests that time perception is influenced by other dimensions such as digit magnitude (Cai and Wang, 2014, Chang et al., 2011, Oliveri et al., 2008, Xuan et al., 2007), numerosity (Dormal et al., 2006, Javadi and Aichelburg, 2012, Xuan et al., 2007), and spatial size (DeLong, 1981, Rammsayer and Verner, 2014, Xuan et al., 2007).
To account for these non-temporal effects on time, some researchers have proposed that temporal durations are encoded and represented as some kind of nonverbal magnitudes, as are other quantifiable dimensions such as distance, size and numerosity (Bueti and Walsh, 2009, de Hevia et al., 2014, Gallistel and Gelman, 2000, Walsh, 2003, Walsh, 2014). These magnitudes from different dimensions share a common representational format (e.g., Lambrechts, Walsh, & van Wassenhove, 2013) and appear to be processed in the same neural circuits (e.g., Bonato, Zorzi, & Umiltà, 2012; see Bueti & Walsh, 2009, for a review). Due to the noise inherent in these representations (Gallistel and Gelman, 2000, Petzschner et al., 2015), it is possible for concurrently-perceived magnitudes to pull on each other such that a larger magnitude representation of a non-temporal dimension (e.g., a long line versus a short line, or a large number versus a small number) can increase the magnitude representation of a duration. In addition to accounting for the effects of nontemporal dimensions on time perception, the magnitude representation account also helps to explain recent findings that time can also exert influence on the perception of other physical dimensions such as spatial distance and numerosity (Cai and Connell, 2015, Javadi and Aichelburg, 2012, Merritt et al., 2010, Roitman et al., 2007).
The notion of time being represented as mental magnitudes has its root in an earlier mechanistic approach to time perception, which stipulates that temporal durations are perceived and stored as accumulative quantities (e.g. Gibbon et al., 1984, Meck and Church, 1983, Treisman, 1963). The mechanistic approach has focused on how temporal durations are registered, memorized, and retrieved (see Grondin, 2010, for a review). Perhaps the most influential theory of the mechanistic approach to time perception is scalar expectancy theory (Gibbon, 1977). While the theory is incorporated in most current models of time perception (e.g. Gu et al., 2015, Matell and Meck, 2000, Wackermann, 2011), it is probably best known as the internal clock model (Gibbon et al., 1984, Treisman, 1963, Wearden, 1991; see Allman, Teki, Griffiths, & Meck, 2014, for review). The internal clock model stipulates a timing mechanism with an internal clock system (a pacemaker and accumulator), a memory store, and a comparator.1 The pacemaker, a continuously-running timing device, emits signals or pulses at a certain rate. When timing begins, the pacemaker is connected, via a switch, to the accumulator which collects the pulses. The accumulated pulses register the perceived duration, which may be stored and maintained in memory for later reference. When a temporal judgment is to be made, the comparator then compares the perceived duration (i.e., pulses in the accumulator) with a reference duration (i.e., pulses kept in reference memory). For example, a comparison task may require the participant to decide whether a new perceived duration is longer or shorter than a memorized reference duration, while a reproduction task may require the participant to terminate a new, ongoing duration when the accumulated pulses reach a record that is equivalent to the memorized reference duration (for formal formulations of these processes, see Gibbon, 1977, Gibbon et al., 1984).
Because perceived durations are assumed to be the accumulated quantity of pulses that are collected from the pacemaker during the accumulation stage, and stored in working memory during the maintenance stage, the internal clock model predicts that the amount of time perceived can vary as a function of pulse accumulation and memory processes.2 Indeed, external manipulations such as rapid repetitive stimulation (e.g., auditory click train, visual flicker) have been found to increase perceived duration of a stimulus (Droit-Volet and Wearden, 2002, Herbst et al., 2013, Ortega and Lopez, 2008, Penton-Voak et al., 1996, Wearden et al., 1999). Ortega and Lopez (2008), for instance, asked people to decide whether a target duration resembled a short or a long reference duration they had previously learnt and showed that the target duration was more often perceived to be short when the reference duration had been accompanied by a flickering dot, but perceived to be long when the target duration itself was accompanied by a flickering dot. These timecourse-dependent reverse effects support the idea that visual flicker leads to more pulses being accumulated, and hence a larger amount of perceived time for whichever duration it accompanies. Such effects may arise as result of visual flicker accelerating the pacemaker speed (Droit-Volet and Wearden, 2002, Ortega and Lopez, 2008), increasing attentional allocation to duration monitoring and allowing more pulses to be registered (Herbst et al., 2013, Zakay and Block, 1995, Zakay and Block, 1997; see also Lejeune, 1998), or triggering earlier switch-on and/or delayed switch-off of the accumulator (Penney et al., 2000, Wearden et al., 2010). While different, these mechanisms all localize visual flicker effects in the accumulation stage of the internal clock model (we will return to this point in the general discussion).
Time perception can also be affected at the later stage of memory maintenance. Perceived durations may change as a result of reference memory interference or mixing (Grondin, 2005, Gu and Meck, 2011, Jazayeri and Shadlen, 2010, Jones and Wearden, 2004, Penney et al., 1998, Taatgen and van Rijn, 2011). Jazayeri and Shadlen (2010), for example, showed that when multiple durations have to be remembered, reproduced durations show regression towards the mean, with long stimulus durations under-reproduced and short ones over-reproduced. Such inter-duration interference, in the internal clock model, can be attributed to the mixing or blending between different records of accumulated pulses (i.e., different durations) within reference memory (Gu and Meck, 2011, Penney et al., 1998, Taatgen and van Rijn, 2011). Nonetheless, while these studies did examine memory representations of duration, their focus was on interaction within the dimension of time, rather than interactions between time and non-temporal dimensions (i.e., cross-dimensional interference). One exception is Moon, Fincham, Betts, and Anderson (2015), who argued that distance and duration information may cue each other in memory and potentially lead to cross-dimensional interference. However, Moon et al.'s paradigm was unusual in that it required participants to learn and remember mappings between four different colours, response fingers, and reference distances/durations. It is therefore not clear to what extent their effects are purely distance–duration interference, or at what processing stage distance and duration interact with each other.
The above overview illustrates that, despite their shared topic, the representational and mechanistic approaches to time perception each have their own research agenda, theoretical underpinnings, and empirical effects, with little cross-reference to each other's research. The recent comprehensive review of the mechanistic approach by Grondin (2010), for instance, has no reference to theoretical accounts or empirical reports of representational interference between time and non-temporal dimensions (e.g., Casasanto and Boroditsky, 2008, Walsh, 2003, Xuan et al., 2007). The oversight of the representational approach in the mechanistic literature may be attributed to the fact that proponents of the representational approach to time perception have rarely specified a detailed process model whereby time and non-temporal dimensions interact. For instance, the magnitude representation account does not detail when and where in the timecourse of time perception that non-temporal dimensions exert their effects (Walsh, 2003); even very recent reviews of the account fails to touch upon the issue (Walsh, 2014, Winter et al., 2015).
In the present paper, we aim to combine the representational and mechanistic approaches in order to better understand the mechanism of interference between time and non-temporal dimensions. To this end, we focus on identifying a possible locus of space–time interactions within a well-studied mechanistic framework of time perception, the internal clock model. We conducted three experiments using a time reproduction paradigm in which participants perceived a stimulus duration and then reproduced it (e.g. Cai and Connell, 2015, Cai et al., 2013, Casasanto and Boroditsky, 2008, Wearden, 2003). In theoretical terms, participants need to first encode the stimulus duration and maintain it in memory; when they are to reproduce the duration, they first retrieve the stimulus duration, then initiate an unfolding reproduced duration which they terminate when it reaches subjective equality with the retrieved stimulus duration (for theoretical treatment of duration reproduction, see Riemer et al., 2012, Wackermann and Ehm, 2006, Wearden, 2003).
We compared the effect of visual flicker and spatial distance on duration reproduction when they were concurrently presented during time encoding (i.e., participants saw spatial distance or visual flicker during perception of a stimulus duration and then reproduced the duration) or time reproduction (i.e., participants perceived a stimulus duration and then saw spatial distance or visual flicker while they were reproducing the duration). As we reviewed above, temporal representations can be biased during the accumulation or memory maintenance stage in the internal clock; thus, either of these stages can be the potential locus of space–time interaction effects.
If space–time interaction occurs during the accumulation stage, spatial distance may operate like visual flicker in biasing time accumulation (i.e., the clock-accumulator account). A visually flickering stimulus (compared to a static, non-flickering stimulus) is believed to increase the number of pulses that are stored in the accumulator (e.g., by altering the speed of the pacemaker, or the timing of the switch operation), resulting in a longer perceived duration (Ortega and Lopez, 2008, Penton-Voak et al., 1996, Wearden et al., 1999). If longer spatial distance likewise biases time accumulation, then we should expect a long-distance line (compared to a short-distance line) to lead to more accumulated pulses and therefore a longer perceived duration. Critically, such a clock-accumulator account means that any effects should reverse when the stimulus is presented during time reproduction instead of time encoding (Droit-Volet and Wearden, 2002, Ortega and Lopez, 2008). Specifically, if more pulses are accumulated while a participant retrieves and reproduces a particular duration from reference memory, it will make time appear to pass more quickly during the reproduction task itself and lead participants to terminate the reproduced duration earlier. Hence, both a visually flickering stimulus and a longer spatial distance should lead to shorter reproduced durations than a static (non-flickering) stimulus or a shorter spatial distance, respectively. In summary, if the locus of space–time interaction lies in the accumulation stage of the internal clock model (as the clock-accumulator account assumes), then a concurrent longer-distance line, compared to a shorter-distance line, should lead to longer reproduced durations when presented during time encoding, but shorter reproduced durations when presented during time reproduction.
Alternatively, if space–time interaction occurs during the memory maintenance stage, spatial distance may bias the magnitude representation of a perceived duration while it is being maintained in memory (i.e., a clock-magnitude account). In this case, we would expect spatial distance to exert a different pattern of effects on time reproduction compared to visual flicker (which will lead to longer reproduced durations if presented at the encoding stage and to shorter reproduction durations if presented at the reproduction stage, as outlined above). When a spatial line is presented for a particular duration during time encoding, the spatial distance information in the line should interfere with the representation of that duration as it resides in reference memory because they share a common magnitude format (Gallistel and Gelman, 2000, Walsh, 2003, Walsh, 2014), such that long-distance lines, compared to short-distance ones, will make the duration seem subjectively longer (Cai and Connell, 2015, Cai et al., 2013, Casasanto and Boroditsky, 2008). Critically, such a clock-magnitude account means that spatial distance presented during time reproduction will not affect reproduced duration as it does not have the opportunity to interfere with its magnitude representation in reference memory. Because the magnitude representation of the duration does not experience any spatial interference as it resides in reference memory, it can be accessed and reproduced regardless of what spatial information might be concurrently perceived during the reproduction task itself. In summary, if the locus of space–time interaction lies in the memory maintenance stage of the internal clock model (as the clock-magnitude account assumes), then a longer-distance line will lead to longer reproduced durations when presented during time encoding, but have no effect when presented during time reproduction.
Section snippets
Participants
Twenty-six volunteers from the University of Manchester community took part in the experiments (13 for Experiment 1a and 13 for Experiment 1b). All had normal or corrected-to-normal vision and were paid £4 for their participation.
Design and materials
Experiments 1a and 1b followed the same basic design (though they differed slightly in the stimulus durations used; see below). The experiments first manipulated the type of stimulus (visual flicker or spatial distance) that was concurrently presented with the stimulus
Experiment 2
Experiments 1a and 1b showed that visual flicker affects time perception by biasing the actual process of duration accumulation while spatial distance does so by biasing the memory of the accumulated duration. However, these conclusions are based on findings from different experiments using different participants. Experiment 2 aimed to replicate these findings using a within-participant design. That is, we compared the effect of visual flicker and spatial distance between the time encoding
General discussion
In the present paper, we examined how temporal information experiences interference from information from other magnitude-based dimensions within a mechanistic framework of time perception, using space–time interaction as the test case. In theory, many current models of time perception (e.g., the internal clock model) allow for cross-dimensional interference at the stage in time processing when pulses from the pacemaker are accumulated as a measure of duration, or the stage when these
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This work was funded in part by a research grant from ESRC (ES/L010224/1) to the first author and a research grant from the Leverhulme Trust (F/00120/CA) to the second author. We thank Ruiming Wang and Wenjuan Liu from South China Normal University for assistance in data collection for Experiment 2.