The temporal-relevance temporal-uncertainty model of prospective duration judgment

Consciousness and Cognition xxx (2015) xxx–xxx

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The temporal-relevance temporal-uncertainty model of prospective duration judgment Dan Zakay School of Psychological Sciences, Tel-Aviv University, Ramat-Aviv, Israel

a r t i c l e

i n f o

Article history: Received 16 March 2015 Revised 12 October 2015 Accepted 17 October 2015 Available online xxxx Keywords: Attention Prospective duration judgment Temporal Relevance Temporal uncertainty

a b s t r a c t A model aimed at explaining prospective duration judgments in real life settings (as well as in the laboratory) is presented. The model is based on the assumption that situational meaning is continuously being extracted by humans’ perceptual and cognitive information processing systems. Time is one of the important dimensions of situational meaning. Based on the situational meaning, a value for Temporal Relevance is set. Temporal Relevance reflects the importance of temporal aspects for enabling adaptive behavior in a specific moment in time. When Temporal Relevance is above a certain threshold a prospective duration judgment process is evoked automatically. In addition, a search for relevant temporal information is taking place and its outcomes determine the level of Temporal Uncertainty which reflects the degree of knowledge one has regarding temporal aspects of the task to be performed. The levels of Temporal Relevance and Temporal Uncertainty determine the amount of attentional resources allocated for timing by the executive system. The merit of the model is in connecting timing processes with the ongoing general information processing stream. The model rests on findings in various domains which indicate that cognitive-relevance and self-relevance are powerful determinants of resource allocation policy. The feasibility of the model is demonstrated by analyzing various temporal phenomena. Suggestions for further empirical validation of the model are presented. Ó 2015 Elsevier Inc. All rights reserved.

1. Time and the dynamic environment Both the external and the internal environments are in constant change (Zakay, in press). Humans are faced with the difficult task of acting upon important cues while simultaneously collecting new information from countless sources, all within the constraints of a limited processing capacity. Helpful in this endeavor is the ability to screen the environment and determine which incoming stimuli warrant further attentional resources. Some of this screening is done pre-attentively (Gray, Ambody, Lowenthal, & Deldin, 2004). Psychological time fulfills several vital functions which enable living in these complex environments. Examples are the planning and performing of psychomotor activities and movements (Flanagan & Wing, 1997), or monitoring human communication (Zakay, Fleisig, & David, 2014). The time dimension is already embedded in any human experience or activity and is an inseparable part of it (Flaherty & Meer, 1994). Because of that, no understanding of human behavior can be complete without referring to the notion of time (Zakay, 2014). Of special importance are duration judgments of intervals enduring seconds and minutes. Such intervals set temporal boundaries to the building blocks of behavior. Indeed, humans can sense the flow of time and judge quite accurately durations of seconds and minutes (Merchant, Harrington, & Meck, 2013). E-mail address: [email protected] http://dx.doi.org/10.1016/j.concog.2015.10.006 1053-8100/Ó 2015 Elsevier Inc. All rights reserved.

Please cite this article in press as: Zakay, D. The temporal-relevance temporal-uncertainty model of prospective duration judgment. Consciousness and Cognition (2015), http://dx.doi.org/10.1016/j.concog.2015.10.006

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The experience of time is termed prospective when it is related to the duration of an ongoing interval and the observer is aware of the need to judge its duration. When an observer is not aware of this need until a target interval is terminated, the experience of time is called retrospective (Block, 1989). Robust empirical findings (e.g., Brown, 1985; Predebon, 1996) as well as several comprehensive meta-analyses (Block, Hancock, & Zakay, 2010; Block & Zakay, 1997) indicate that different timing processes underlie the two types of duration judgments. This realization was already acknowledged by James (1890). Retrospective duration judgments are well accounted for by the Contextual Change Model (Block, 1989; Block & Reed, 1978). This model asserts that when retrospective duration judgment is required, one retrieves from his/her memory contextual changes (both external and internal), which were encoded during a target interval. Retrospective judgments are a function of the amount of retrieved contextual changes. The more contextual changes are retrieved, the longer duration judgments are. This reflects a naïve heuristic according to which more contextual changes occurring, perceived and encoded with longer objective durations. The contextual-change model explains why retrospective duration judgments of intervals, during which complex information processing took place, are longer than respective ones of same clock time during which information processing was simple (Block & Zakay, 1997). In contradistinction, prospective duration judgments are activated whenever ongoing temporal judgments are required. Prospective duration judgments are a function of the amount of attentional resources allocated for timing. The more resources are allocated for timing, the longer prospective durations are (e.g., Brown, 1997, 2008). This explains why prospective duration judgments (PDJ) produce a mirror image of retrospective duration judgments (RTJ). PDJ’s of same time periods are longer when non-temporal information processing during an interval is simple than when it is complex (Block & Zakay, 1997; Zakay & Block, 2004). In the present manuscript we focus on prospective duration judgments in relation to ongoing events in the environment. A model which explains how prospective duration judgments are linked with the ongoing stream of information processing is presented. 2. Models of prospective timing Thomas and Weaver (1975) developed a mathematical model in which attentional allocation is proposed to influence duration judgments. The model suggests that the perceived duration of an interval containing certain information is a monotonic function of the weighted average of the amount of information encoded by two processors: a temporal information processor and a non-temporal information processor. The organism divides attention between these two parallel processes. Perceived duration is weighted to optimize the reliability of the information that each processor encodes because as more attention is allocated to one processor, the other becomes more unreliable. When little or no stimulus information occurs during the to-be-judged duration, people tend to allocate more attention to temporal information. In contrast, when a task demands considerable information processing, people tend to allocate more attention to this non-temporal information. This model was tested only with durations of less than 100 ms, but Michon (1985) argued that the model can potentially encompass longer durations and can be considered as a general model of temporal information processing. However, Thomas and Weaver’s model suffers from several drawbacks. The model does not specify the nature of temporal information processing in the temporal information processor and the assumption of averaging the information processed in the temporal and the non-temporal processors was not supported and is quite vague. Zakay’s resource allocation model (1989) is an elaboration of Thomas and Weaver’s model and assumes that prospective duration judgments reflects the amount of attentional resources allocated to the temporal information processor alone. This model is still not specifying what determines the resource allocation policy and the nature of temporal information processing remains unclear. Two more recent models provide better description for the temporal information processing. Zakay and Block (1997) proposed an Attentional Gate model to better conceptualize what temporal information processing is. The model proposes that every time an individual attends to time; a perceptual gate is opened that enables the transmission of a pulse stream produced by a pacemaker to a cognitive counter. The cognitive counter then counts or sums the pulses that have been transmitted in such a way that its momentary total pulse count is transferred to a working memory store, and duration judgment is a function of the overall count of pulses in a certain interval (Zakay, 2000). Accordingly, attending to time can be conceptualized as the wider opening of the gate, allowing for more pulses to pass through the gate in a given time unit. According to the Attentional Gate model, temporal information processing consists of accumulating, counting, storing and comparing the number of pulses, cognitive functions that consume attentional resources. Another model which looks in a similar way on the nature of temporal information processing but suggests a different mechanism to replace the attentional gate is the Dynamic Switch model (Lejeune, 1998). Both models are very effective in providing explanations for temporal experiences which involve prospective duration judgments, but both of them do not explain what determine the allocation of resources for timing. In sum, current attentional models are not complete because they explain the nature of the timing process but do not explain what determines the allocation of attention for timing. As such, the attentional models are detached from the continuous flow of information processing. There is a need to fill this gap.

Please cite this article in press as: Zakay, D. The temporal-relevance temporal-uncertainty model of prospective duration judgment. Consciousness and Cognition (2015), http://dx.doi.org/10.1016/j.concog.2015.10.006

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2.1. Relevance, attention and information processing Before we present a model which can explain the missing link of how attentional allocation for timing is determined, the notion of relevance and its role in the general stream of information processing should be discussed. The more attention is focused on a stimulus the more intensive its processing is. The process of attentional resource allocation is continuous and under the control of executive functions (Gopher, 1996). However, it is still not completely clear how people select information for further processing from the vast amount available in the environment. Robust findings in various domains indicate that stimuli’s relevance and self-relevance are major factors which determine the resource allocation policy and direct behavior. Past work suggests that information related to the self receives preferential access to the limited pool of attentional resources (Gray et al., 2004). A well-known phenomenon which reflects the power of selfrelevance is the cocktail-party effect (Morey, 1959). Already in 1948, Postman, Bruner and McGinnis proposed that what one selects from a near infinitude of potential percepts for further processing is a servant of one’s interests, need and values. Kelly (1955) argued that one’s system of social constructs operates as a scanning pattern that picks up blimps of meaning from the environment. Later on, Bargh (1982) Argues that personal relevance impacts the selection of material from more in-depth processing and information related to personal concerns and values is more likely to receive attentional resources. Henderson (2003) and Henderson, Malcolm, and Schandl (2009) introduced the cognitive relevance hypothesis, which stated that selection of information is based on the needs of the cognitive system in relation to the goal of a current task. These authors validated the hypothesis in the context of real world scene perception and found that cognitive relevance is more powerful than visual salience in gaze control, but, there is no reason to restrict cognitive relevance theory only to this domain. Indeed, Billings and Scherer (1988) found that the importance and relevance one assigns to a certain decision determines the depth of information processing and the amount of resources allocated for making the decision. 3. The case of time and anxiety Macleod and Mathews (1988) demonstrated that anxious subjects consistently deploy attention toward threat-related stimuli, in contradistinctions to non-anxious controls. Bar-Haim, Keren, Lamy, and Zakay (2010) found that anxious individuals perceive time as passing slowly in threatening situations. Similar findings were obtained for people suffering from social anxiety (Mansell, Clarck, Ehlers, & Chen, 1999). Following the same line of thought Effron, Niedenthal, Gil, and Droit-Valet (2006) report that duration of presentation of angry faces is perceived as longer relative to that of neutral faces. Anxiety that is evoked by specific situation affects the perception of time in relation to the specific situations. Individuals with spider phobia have been found to misperceive the time spent observing a spider as longer relative to ‘‘normal” (Watt & Sharrock, 1984). All these findings can serve as a demonstration for our main argument: relevance has an impact on attention allocation, and in cases in which, as a result of temporal-relevance, attention is allocated to time, temporal judgments are augmented as compared with control conditions. For anxious people, threat is of high relevance. They detect threatening stimuli very early in the perceptual process. The relevance directs attention to the threatening stimuli but also to time. Time-relevance is high because the main concern of the anxious person is ‘‘when the threat will disappear”. 4. The Temporal-Relevance Temporal-Uncertainty (TR–TU) model The relevance and importance of time is not constant but varies depending on the meaning assigned to a certain situation. During a course of a day, duration judgments shift in intensity. Sometimes we are highly occupied with time and in other moments we almost pay no attention to it. For example, one can be absorbed by reading an attractive book without noticing the flow of time, and then realizes that he/she is missing an important appointment and immediately can finds him/herself in an intensive duration judgment process. What determines the allocation of attentional resources during these shifts? Zakay (1992) introduced the notions of Temporal Relevance (TR) and of Temporal Uncertainty (TU) and indicates how these notions relate to PDJ. 5. Temporal-Relevance (TR) TR refers to the extent to which temporal judgments are important for the adaptation to a complex dynamic environment in a given moment. The level of TR is dynamic and might change from moment to moment. TR reflects the importance of providing the cognitive and meta-cognitive systems with information which is crucial for adjustment and adaptation in a given setting. The flexibility of attentional allocation for timing was demonstrated by Macar, Grondin, and Casini (1994). In their study they ordered participants to change the amount of resources allocated for timing. In this case it is not clear if TR was changed as well or if participants simply obeyed the experimenter’s instructions. However, the same mechanism can be operated in natural settings when Temporal Relevance is changed due to the dynamic changes in the environment, the task and the conditions. In a former paragraph we have reported evidences about the impact of relevance and selfrelevance in general on attention allocation and on the direction of information processing. Temporal Relevance should be considered another type of relevance which has similar impact on attention and information processing.

Please cite this article in press as: Zakay, D. The temporal-relevance temporal-uncertainty model of prospective duration judgment. Consciousness and Cognition (2015), http://dx.doi.org/10.1016/j.concog.2015.10.006

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6. Temporal Uncertainty (TU) Temporal Uncertainty level reflects the amount of knowledge and relevant temporal information an actor has about a temporal task that should be conducted. For example, if one has to perform a mission within a certain time boundaries and accuracy is important, one would like to know how much time it takes to complete the mission. The more information is available, the lower TU is. TU was demonstrated to be an important factor which determines reaction time length. When participants can anticipate the temporal occurrence of a stimulus, the reaction time to this stimulus is short, and this is a robust effect (e.g., Niemi & Naatanen, 1981). The effect is obtained for visual as well as for auditory stimuli and also in cross-modal stimulus situations. It is argued that the reduction of TU improves perceptual analysis. Rolke and Hofmann (2007) claim that Temporal Uncertainty influences stimulus processing at a perceptual level. A strong link between uncertainty and attention in general was found in several studies (e.g., Feldman & Friston, 2010). TU can be manipulated in a reaction time experiment by varying the length of the fore-period and by making its length fixed or random. Highest TU is involved with a random and long fore-period and lowest TU with a fixed and short fore-period. Grondin and Rammsayer (2003) studied the influence of attention on temporal information processing by systematic variations of the period preceding brief empty intervals to be judged. Fore-periods’ durations could be long or short and fixed or random. When foreperiod’s durations varied randomly from trial to trial, perceived duration of the target interval was longer with increasing length of the fore-period. This effect disappeared with fixed fore-period duration. The authors suggest that the manipulation effectively modulate attention mechanisms necessary for temporal information processing. 7. Principles of the TR–TU model The TR–TU model of prospective duration judgments defines the factors which determine the allocation of attentional resources for timing. The model suggests that these factors are mainly Temporal-Relevance and Temporal-Uncertainty, which are rooted in the situational meaning which the information processing system extracts continuously. The TR–TU model fills a gap which exists in current attentional models and enables a consistent explanation of a wide variety of time-dependent experiences and phenomena. The following principles underlie the TR–TU model: 1. Humans’ perceptual and cognitive systems analyze incoming information on a continuous basis and extract the meaning of each momentary situation (Park & Folkman, 1997; Tomaka, Blasovich, Kibler, & Ernst, 1997). TR is one of the dimensions which compose the situational meaning (Kreitler & Kreitler, 1972, 1976). 2. Prospective duration judgments are evoked automatically whenever required by the organism. The need for PDJ is evoked whenever the level of TR is above a certain idiosyncratic threshold. 3. Whenever TR is above a certain threshold, attentional resources are allocated for PDJ. The higher TR is the more attentional resources are allocated for timing. 4. Whenever TR is significant, a process of search for relevant temporal information is evoked. The degree of relevant temporal information found determines the emerging level of TU. For example, when one has to go from A to B the importance of being on time at B determines the level of TR and the existing knowledge about the time it takes to go from A to B determines the level of TU. 5. The overall amount of attentional resources allocated for timing is determined by an interaction between levels of TR and of TU as well as by the amount of resources demanded by concurrent non-temporal tasks (Kahneman, 1973). 6. When TR is not significant (Below a certain threshold) the amount of attentional resources allocated for timing is minimal (we always maintain some track about ongoing time. see Zakay (1993)) regardless of the level of TU. 7. Resources allocated for PDJ ‘‘energizes” a temporal information processing mechanism (like the attentional gate or a dynamic switch). The allocation of resources is dynamic and dependent on the momentary meaning extraction. The intensity of PDJ is changing accordingly. 8. An illustration of the TR–TU model Let us illustrate the TR–TU model with a well known daily example: the watched pot phenomenon. Suppose a person is occupied in reading an interesting book during his/her holiday. Nothing is on the schedule. The reading absorbs almost all of his/her attentional resources. After a while an intense urge for coffee rooted in physiological cues and habits starts to nudge. An electric pot full with water is around. The reader continues his/her reading but devote some portion of his/her resources in order to operate the pot. From time to time he/she shifts her gaze to see if the water is boiling. During this period reading is slower than before and here and there a word is omitted. Suppose that when the pot is operated someone asks the reader to judge how much time it takes for the water to boil. Now the reader will be engaged with a PDJ process, because the level of TR turned to be high, but still not the maximal one. Now suppose that someone commands the reader to give an accurate judgment of the boiling period and state that accuracy is very important. The reader will not continue the reading and instead will keep his/her eyes on the pot in order to observe exactly when the water boils. The level of TR is maximal and if the reader does not know what the duration is, the level of TU is also high. Most probably PDJ process

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will be most intense (namely, the attentional gate will be very wide). Actually, while waiting for the water to boil the observer might feel as if this will never happen. This phenomenon termed the ‘‘watched pot never boils” was validated empirically (Block, George, & Reed, 1980). The impact of the amount of resources allocated for timing on the length of prospective duration judgments was demonstrated by Grondin & Macar, 1992, and by Macar et al. (1994) who gave participants instructions about how much attention should be allocated for timing. However, in real life no such instructions are given and it is the situational meaning which determines the level of TR and the allocation policy. This illustration emphasizes the need to add the TR–TU notions to current attentional models in order to be able to provide a complete explanation not only of PDJ in isolation but for PDJ as part of the general stream of information processing. Empirical validation of the notion of TR is reported by Zakay (1998). In the first experiment of the study a primary–secondary task manipulation was utilized (e.g., Gopher & Donchin, 1986). Participants were required to simultaneously perform prospective duration judgments and a non-temporal (Stroop-like) task. In one condition the temporal task was defined as the primary task and in another as a secondary task. As expected, prospective duration judgments were significantly longer under the primary than under the secondary task conditions. The results support the notion that PDJ’s are highly influenced by the focusing of attention on temporal information processing and that magnitude of duration judgments reflects the amount of attentional resources allocated for timing. But what determines the allocation policy? The only difference between the experimental conditions was whether or not the temporal task was defined as a primary or as a secondary task. It can be argued with high confidence that when a duration judgment task is the primary task, the level of TR is higher than when it is a secondary one. In Zakay (1998) the experimental conditions were manipulated and this, in turn, determines the allocation policy and the resulting duration judgments length. It should be noted that the validity of the primary-secondary task manipulation was supported by the number of errors performed in the non-temporal task. 9. The feasibility of the TR–TU model In this section we demonstrate the feasibility of the TR–TU model in explaining. Temporal experiences which are common in daily life, without the need to provide a unique model for explaining each one of the phenomena. The first temporal experience to be discussed is duration judgments of stressful events. Loftus, Schooler, Boone, and Kline (1987), tested this issue. In three experiments participants watched a short videotape of a home robbery and later estimated the duration of the tape. Participants were also asked to recall as accurately as possible the details of the robbery. Participants, invariably, overestimated the durations of the robbery. A more stressful version of the event produced a greater overestimates than a less stressful version. Accuracy of time estimation was unrelated to the amount of free recall or accuracy of memory. This contradicts the contextual-change model and hence does not allow a memory-based retrospective duration judgment explanation. However since the paradigm used was a retrospective one the authors suggested a hypothetical latent variable which they call ‘‘internal level of arousal” for explaining the findings. We argue that the TR–TU model can explain the findings with no difficulty. It is clear that a stressful event like a robbery is one which a participant would like to end as soon as possible. Thus, watching stressful events automatically increase the level of TR. This means that despite the experimental paradigm being a retrospective one the meaning of the situation is evoking a prospective duration judgment process. This is causing an intense allocation of resources for timing and according to attentional models of PDJ the resulting duration estimates are long. This also explains why the duration estimates were longer when the robbery was more stressful and threatening. Loftus et al. (1987) report that in real life victims of real crime usually overestimates the durations till the police arrived. Indeed, a victim of a real crime is mostly concern with the question: ‘‘When will the police come to save me”. This means a high level of TR and of TU leading to an intense PDJ process. Another example of overestimation of the duration of a natural disaster is that of earthquakes’ durations. Buckharst, Fox, and Rabinowitz (1989) collected data from 246 people on their retrospective recall of the duration of a moderate earthquake (4.0 on the Richter scale). The duration was overestimated with significantly higher overestimates from people in the area where the most intense quake occurred. The authors explained the findings by proposing that people desired to appear as credible observer of a complex episode. This is a vague explanation outside the framework of timing. The TR–TU model enables to explain the findings within the framework of temporal processes without the need to speculate and invent new models. It is clear that being in an earthquake is stressful and the main wish is for the quake to be over. Thus levels of TR and TU are high, especially in the area where the quake is more intense. The rest of the story is obvious and there is no need to repeat it. A very common phenomenon in daily life is that of waiting for an event, for someone to come or for receiving a service. In many studies (Haynes, 1990; Zakay & Hornik, 1991) it is found that waiting durations are overestimated. This is compatible with an obvious prediction of the TR–TU model since duration is a major factor in the meaning of waiting situations. When one is waiting the major concern is: ‘‘when will the waiting end”, or, ‘‘when will the person arrives”, ‘‘how much time will I have to wait”, etc. The level of TR is very high while waiting, and when the target time is over and the service was not yet received, the level of TU is increasing. All this leads to intense resource allocation, intense PDJ’s process and a large overestimation (Zakay, Fleisig, & Ginzburg, 2009). It is of interest to analyze a field study in which customers were waiting to receive a service (Groth & Gilliland, 2001). The authors found that customers’ reactions to the wait were more positive

Please cite this article in press as: Zakay, D. The temporal-relevance temporal-uncertainty model of prospective duration judgment. Consciousness and Cognition (2015), http://dx.doi.org/10.1016/j.concog.2015.10.006

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and perceived wait time was short when the waiting procedures were perceived as adequate. A TR–TU explanation for this is that when the procedures are not adequate and people feels unfairness in the queue system, TU is increasing because the level of uncertainty regarding the expected waiting duration increases (Baker & Cameron, 1996; Mann, 1969). This, in turn, increases the allocation of resources for monitoring time. Needless to say that in any waiting condition people is automatically engaged with a prospective duration judgment. Another support for the TR–TU model was obtained by Municher and Rafaeli (2007), who studied the effect different fillers have on perceived durations of telephone waiting. It was found that whereas apologizing for the wait yielded a negative effect, providing information about location in the queue produced the most positive effect. Explanations that were given to the impact of fillers on waiting, suggested that the effect is ‘‘atmospheric” (Bitner, 1990). No need for such a vague explanation. As argued earlier, TR and TU are high during waiting. Information about one’s location in the queue decreases the level of TU and as a result fewer resources are allocated for timing, the intensity of the PDJ process is lowered and the perceived duration of waiting is shorter. This, in turn, reduces stress and increases the feeling of comfort (Antonides, Verhoef, & Aalst, 2002). The next temporal phenomenon to be discussed here is that of the return trip effect, which is manifested when a return trip often seems shorter than an initial trip, even though the distance and time spent traveling are identical in both directions. In three experiments Van de Ven, Bijswijk, and Roy (2011), confirm the existence of the effect. The effect was found on a bus trip and on a bicycle trip. The explanation suggested by the authors was that participants felt that the initial trip took longer than they had expected and in response they lengthened their expectations for the return trip. In comparison with this longer expected duration, the return trip felt shorter. This explanation is out of the context of timing processes. The TR–TU model provides a simple explanation. While going to a target, especially on an unfamiliar route, duration is important and Temporal Uncertainty is high (one usually wants to reach a target and on time). This is activating the whole process of timing processes starting with analyzing the meaning of the situation and setting the levels of TR and of TU. On the way back, duration is less important and TU is low since it is already known how much time will be needed. Thus both TR and TU levels are lower on the way back as compared with the initial trip to the target. The last temporal experience to be analyzed here is the case of expecting a break. Fortin and Massee (2000) conducted experiments in which participants were required to prospectively judge the duration of various intervals. This was done without any concurrent non-temporal task. During target intervals breaks were imposed. Some of them expected and others non-expected. Participants were required to judge the net duration of an interval without the duration of the breaks. The findings indicated that with breaks, intervals’ durations were judged to be longer than without breaks. Furthermore, the longer was the expectation for a break, the more an interval’s duration was judged to be longer. Fortin and Massee (2000) argue that since no concurrent non-temporal task was involved, the findings cannot be explained by models like the AGM (Zakay & Block, 1997), since no competition over resources was inserted. One can assume that expecting a break by itself consumes attentional resources, like in waiting, but then intervals’ durations should be a decreasing function of expecting duration, which was not the case. Fortin and Massee (2000) argue that attentional time-sharing between estimation and expectation of its interruption contributed to the interference effect, independently of any concurrent processing. While it is not quite clear what is attention time-sharing, it still seems that Fortin and Masse’s findings contradict attentional models of prospective timing. Here we suggest a TR–TU based explanation which keeps the breaks phenomena within the boundaries of attentional models. We argue that breaks increases the level of TU like in the case of a variable fore-period. One is expecting a break which should not be considered as part of the interval and the break duration is not known in advance. The same is the case when a break is unexpected. TU regarding the final duration of the target interval increases and as a result more attentional resources (which are available because no concurrent task is in operation) are allocated for timing, and as a result the final judgment is increasing. As for TR, expecting a break create a situation like in a ‘‘watched pot” condition. The main issue now is ‘‘when will the break occur”, and again, TR will increase, more resources will be allocated and prospective judgments will increase. 10. Testing the TR–TU model Like any model, the TR–TU model should be validated empirically and thus a set of predictions which enable its validation should be stated. The TR and the TU notions were already validated separately, as reported earlier (Zakay, 1998). Using a similar manipulation, Zakay and Bibi (2006) manipulated the level of TR by employing the Dual-Task paradigm. In the Dual-Task paradigm two tasks have to be performed concurrently, but one of them is defined as a primary task and the other as a secondary task. Several controls conditions are available: the second task is defined as the primary task and the first task as the secondary task, or no priority is defined at all. Participants are explained that the performance on a primary task is more important than that on a secondary task. It is reasonable to assume that if the two tasks are competing on same resources, more resources will be allocated for a primary than for a secondary task. This indicates that the relevance of the primary task is higher than that of the secondary one. The performance of a task is expected to be better when it is defined as a primary than when it is defined as a secondary or a neutral task. This paradigm is widely used (Brown, 1991). Zakay and Bibi (2006) asked participants to perform a temporal and non-temporal task concurrently under the various conditions of the dual-task paradigm. As

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expected it was found that when a temporal task (i.e., prospective reproduction) was declared to be a primary task duration judgments were longer than when the duration judgment of a same interval was declared to be a secondary task. It is most likely to assume that being a primary task, the level of TR increased and more resources were allocated for timing than when the temporal task was a secondary task. This assumption was supported by levels of performance on the concurrent nontemporal task which was worse when matched with a primary temporal task than when matched with a secondary temporal task. The predicted impact of TU on prospective duration judgment was validated by Grondin and Rammsayer (2003), and by Gamache, Grondin, and Zakay (2011). In both cases participants were asked to judge prospectively an interval and before the cue for its beginning was given a fore-period was manipulated to be either of a fixed or of a variable length. Participants were trained several times before judging the duration of the interval. When the fore-period is fixed, one’s level of TU is low. However when a participant is exposed to random fore-period’s lengths, the level of TU is high. In the last case more attentional resources are recruited than in the first case and as a result the same duration should be judged as longer in the high TU than in the low TU case. This predication was empirically supported in both studies. In order to test the complete TR–TU model both levels of TR and of TU should be manipulated concurrently. Schematically, levels of TR can be manipulated by asking participants to perform temporal and non-temporal tasks concurrently while declaring the temporal task to be either a primary or a secondary task. TU can this time be manipulated by a familiarity manipulation. Under a high TU condition, participants will be trained in performing the non-temporal task several times with random durations. Under the low TU condition the training will be conducted while the tasks’ duration is fixed. The hypothesis is that longest prospective duration judgments will be obtained for the condition with high TR and high TU and lowest duration judgment for lowest TR and lowest TU. The conditions of High TR–Low TU and of High TU–low TR, should yield similar intermediate values for the duration judgments. It should be emphasized that the predictions are non-trivial since it entails the whole pattern of results and not only each condition by itself. In any case, the method suggested here (other methods can be invented) is not based on any circularity since in the case of a primary task manipulation it is highly likely that this is the cause of the increase in resources allocated for a temporal task because it was already shown that temporal tasks tend to naturally become secondary tasks, and this is what makes them an ideal measure for workload requirements of a concurrent non-temporal task (Block et al., 2010; Zakay, Block, & Tsal, 1999; Zakay & Schub, 1998). Thus if duration judgment in a temporal task is larger in the presence of a concurrent non-temporal task it is because of the relevance and importance it gains from the manipulation. As for the fore-period manipulation, it is quite clear that it is the cause for the performance on the duration judgment task since the manipulation is taking place even before the to-be-judged interval starts (Grondin & Rammsayer, 2003).

11. Conclusions In the present manuscript a model of prospective duration judgment is presented. The model is based on the notions of Temporal Relevance and of Temporal Uncertainty and on the assumption that situational meaning is being constantly analyzed. The TR notion is relying on the central role relevance and self-relevance have in determining the direction of information processing. The theoretical framework of TR–TU is compatible not only with the Attentional-Gate model but also with the Dynamic Switch model, which negate the gate notion and suggests a different mechanism. The TR–TU model together with attentional models of prospective duration judgment like the Attentional-Gate or the Dynamic Switch models can provide a complete explanation for prospective duration judgments in connection with the stream of perceptual information processing. The model can provide a unified theoretical umbrella for explaining many temporal phenomena and experiences. This can be considered as an advantage due to scientific parsimony and the principle of Occam’s razor. The complete model should be empirically validated and one way for achieving this goal was portrayed earlier. Of course other methods should be added. In any case, The TR–TU model Yield clear cut predictions and thus can be easily put to the falsification test. References Antonides, G., Verhoef, P. C., & Aalst, M. V. (2002). Consumers’ perception and evaluation of waiting time: A field experiment. Journal of Consumer Psychology, 12(3), 193–202. Baker, J., & Cameron, M. (1996). The effects of service environment on effect, affect and consumer perception of waiting time: An integrated review and research proposition. Academy of Marketing Science Journal, 24(4), 338–349. Bargh, J. A. (1982). Attention and automaticity in the processing of self-relevant information. Journal of Personality and Social Psychology, 43(3), 425–436. Bar-Haim, Y., Keren, A., Lamy, D., & Zakay, D. (2010). When time slows down: The influence of threat on time perception in anxiety. Cognition & Emotion, 24, 255–263. Billings, R. S., & Scherer, L. L. (1988). The effects of response mode and importance on decision-making strategies: Judgment versus choice. Organization Behavior and Decision Processes, 41(1), 1–19. Bitner, M. J. (1990). Evaluating service encounters: The effects of physical surroundings and employer responses. Journal of Marketing, 54(2), 69–82. Block, R. A., George, E. J., & Reed, M. A. (1980). A watched pot sometimes boils: A study of duration experience. Acta Psychologica, 46, 81–94. Block, R. A., Hancock, P. A., & Zakay, D. (2010). How cognitive load affects duration judgments: A meta analytic review. Acta Psychologica, 134, 330–343. Block, R. A. (1989). Experiencing and remembering time: Affordances, context and cognition. In I. Levin & D. Zakay (Eds.), Time and human cognition: A lifespan perspective (pp. 333–361). Amsterdam: Elsevier.

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