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In conclusion, the present study shows, in part, the reliability of the ATOM model using two temporal tasks. This reliability is mainly shown by both individuating the STEARC, SNARC and TiNARC effects, and individuating a triple interaction between time, space and numbers. The STEARC, SNARC and TiNARC effects can arise at a responserelated stage (Ishihara et al., 2008; Keus & Schwarz, 2005; Kiesel & Vierck, 2009). The present data seem to confirm a symmetrical relationship between time, space and quantity, as has been recently observed in experiments involving directional effects on 2010). Further studies should address the reliability of the ATOM rhesus monkeys, which showed large bispatial?temporal judgments (Merritt et al., model using, for instance, numerical or spatial tasks in which time is an irrelevant factor for the performance of the task.ATOM - ert replikeringsexp.
According to Walsh (2003), time, space and numbers are computed by a common metric and they are connected by a common (visuomotor) code for action.ATOM - ert replikeringsexp.
Regarding this point, the ATOM model suggests a role of the right parietal area in processing the three systems (Walsh, 2003), probably explaining the presence of the TiNARC effect for the left space.ATOM - ert replikeringsexp.
In line with previous results, our data show that small magnitudes (1?2orA?B) are associated with short durations, and large magnitudes (8?9orH?I) are associated with long durations (Experiment 1); small magnitudes induce a timing underestimation mainly when short durations are processed and large magnitudes induce timing overestimation with long durations, even if this association fails to reach statistical significance (Experiment 2). Thesefindings indicate the possible presence of a common system processing both quantity and time information. Importantly, the TiNARC effect has been shown for the number condition but it disappears when the letter condition is analyzed. This result could reflect the fact that numerosity is automatically accessed even when it is taskirrelevant (e.g., Roitman, Brannon, Andrews, & Platt, 2007).ATOM - ert replikeringsexp.
The third piece of evidence is linked to the TiNARC effectATOM - ert replikeringsexp.
The second piece of evidence derives from the finding of a SNARC effect (Cappelletti et al., 2009; Dehaene et al., 1993) in both experiments. Our data seem to indicate that the quantity information (i.e. irrelevant for the tasks) is automatically processed and this processing is linked to lateralized response codes (Dehaene & Akhavein, 1995; Dehaene et al., 1993). In Experiment 1, small numbers were responded to faster with the left key while the right key facilitated a faster response to large numbers. In Experiment 2, the ReTs of small numbers were shorter with the left rather than the right key, while those of large numbers were shorter with the right rather than the left key. To our knowledge, this is the first time that a classical SNARC effect has been observed in temporal tasks, extending the work by Kiesel and Vierck (2009) who found a SNARC-like effect using a response duration.ATOM - ert replikeringsexp.
In Experiment 2, the left key determined lower reproduction times when short durations were considered; in a similar way, the right key determined lower ReTs when long durations were considered (see also Vicario et al., 2008). Thesefindings indicate a left-to-right temporal representation which is a useful metaphor in mapping time defined as milliseconds (in the present research), life events (Arzy, Adi-Japha, & Blanke, 2009; Arzy, Collette, Ionta, Fornari, & Blanke, 2009), or past-future categorization (Santiago et al., 2007; Torralbo et al., 2006).ATOM - ert replikeringsexp.
In Experiment 1, the participants performed the task better when short durations were judged by pressing the left key, whereas long durations were judged in a more accurate way when the right key was pressed.ATOM - ert replikeringsexp.
In the present research, the spatial information is provided by two lateralized keys while the numbers or letters providing temporal information are centrally presented. The spatial congruency between time and response facilitates the performance according to the spatial position of temporal information on the MTL. It is worth noting that this time?response congruency is found when presenting either numbers or letters because the time processing is relevant for the task.ATOM - ert replikeringsexp.
The main results obtained in both experiments seem to partially posit that the ATOM model (Bueti & Walsh, 2009; Fabbri & Natale, 2009; Walsh, 2003)reflects a single generalized system dealing with these magnitudes. This assumption seems to derive from three pieces of evidence. The first regards the STEARC effect (Ishihara et al., 2008; Vallesi et al., 2008), reflecting the metaphor of a linear representation of time along a spatially-oriented lineATOM - ert replikeringsexp.
The results regarding ReTs from Experiment 2 mirrored those of Experiment 1. That is, general STEARC, SNARC and TiNARC effects were obtained in a reproduction task. This result seems to confirm the idea of one generalized system dealing with all three magnitudes. As before, the three effects were modulated by the type of experimental material presented. These effects were shown when numbers were used as stimuli, even if the TiNARC effect was reliable only when short durations were considered; there was a no significant trend for long durations. The STEARC effect was also found with the presentation of alphabetical materials, as in Experiment 1. These results may be considered to extend the previousfindings of spatial?temporal and temporal?numerical interactions in a time bisection task (Frassinetti et al., 2009; Oliveri et al., 2009; Vicario, 2007), due to the fact that two lateralized response keys were used here. However, Experiment 2 differed from Experiment 1 because the triple interaction between space, duration and magnitude (i.e. Key ×Duration×Magnitude) was not significant. This difference could depend on the nature of the temporal reproduction task compared with the temporal perception task. The difference between them is that the estimation of the whole interval is operationalized by a motor act in the time reproduction task, whereas it is based entirely on a perceptual judgment in the time estimation task (Bueti et al., 2008). Previous studies claim for a sensorimotorial transformation process that mediates stimulus perception and response preparation in STEARC, SNARC and TiNARC effects (Bueti & Walsh, 2009; Walsh, 2003). In line with this assumption, there are studies demonstrating that the three effects arise at response selection stage (Ishihara et al., 2008; Keus & Schwarz, 2005; Kiesel & Vierck, 2009), as was found in Experiment 1. The reproduction task engaging both the response selection and response execution stage could mask or reduce the interaction between the three magnitudes, according to the ATOM model. Recently, Lewis and Miall (2006) stated that tasks requiring replication of a duration via an action may be especially reliant on the motor system. Consequently, including duration as a dimension of the response may necessitate different encoding and memory processes that those engaged for temporal discrimination.ATOM - ert replikeringsexp.
A four-way repeated measures ANOVA was carried out on ReTs with Stimulus (2 levels: numbers vs. letters), Key (2 levels: left vs. right), Duration (2 levels: short and long) and Magnitude (2 levels: small vs. large) as within-subjects factors.ATOM - ert replikeringsexp.
Then, the white reference stimulus (cue) remained centrally on the black screen for one of five different durations: 200, 300, 400, 500 or 600 ms (estimation phase). The durations of 200 and 300 ms were considered as short times while those of 500 and 600 ms were considered as long times. Two reference cues were presented according to the conditions: a number 5 or letter E. After this, five targets could appear according to the conditions (numbers: 1, 2, 5, 8, and 9, vs. letters: A, B, E, H, and I). The participants were then instructed to reproduce the duration of the reference cue after the presentation of a BEEP sound (reproduction phase).ATOM - ert replikeringsexp.
First, the participants were required to reproduce the duration of a presented stimulus. The task was repeated in four separate sessions: numerical condition and right key (in which subjects were instructed to press the ?6? key of a numerical keypad on a normal keyboard with their right hand), numerical condition and left key (the ?4? key was pressed with the left hand), alphabetical condition and right key, alphabetical condition and left key. The response buttons were covered by two green disks in order to avoid any numerical influenceATOM - ert replikeringsexp.
As before, a within-subjects design is applied in order to detect the role of space in modulating the time and number processing. Thus, the participants performed a time reproduction task, pressing a right-hand side button in one condition and a left button in the other, in order to stop an imaginary clock. As before, the participants performed the task both with numerical and alphabetical materials.ATOM - ert replikeringsexp.
In the time estimation task, the motor response is required in order to make an estimation (i.e., shorter-longer), while in the time reproduction task, the motor response is required to reproduce an estimated duration, and thus the response-related stage and response execution are probably involved.ATOM - ert replikeringsexp.
These two tasks are directly comparable as they share common encoding and storing of temporal information, but differ in how participants use time information to make responsesATOM - ert replikeringsexp.
In both tasks some motor preparation and/or execution is required and there is a visual presentation of the time durations. The difference between them is that the estimation of the whole duration is operationalized by a motor act in the time reproduction task, whereas it is based entirely on a perceptual judgment in the time estimation task.ATOM - ert replikeringsexp.
Experiment 2 aims to study the interaction between time, space and numbers using a time reproduction task, with a strong motor component. In this way, we should be able to deeply address where the ATOM model takes place. This is prompted by the fact that time estimation and time reproduction tasks seem to be quite similar.ATOM - ert replikeringsexp.
given that even the estimation task requires a response.ATOM - ert replikeringsexp.
All together the ATOM model and alternative views seem to agree with the idea that the STEARC, SNARC and TiNARC effects can arise at a response-related stageATOM - ert replikeringsexp.
Consequently, an influence of non-numerical sequences (letters) on temporal estimation should also be found. This influence was, in part, shown in the general effects and interaction between triple Key × Duration × Magnitude, but the effects tended to disappear when analyzing the temporal performance with letter presentation.ATOM - ert replikeringsexp.
Nevertheless, all these alternative views should predict STEARC-, SNARCand TiNARC-like effects when letters are presented. The letters seem to be spatially ordered from left-to-right just as numbers or time are (Gevers et al., 2003).ATOM - ert replikeringsexp.
According to this view, the STEARC, SNARC and TiNARC effects could be explained taking into account that durations and numbers are ordered sequences.ATOM - ert replikeringsexp.
It is plausible that the position within a sequence of numbers in working memory determines the association between numbers and space: items toward the beginning of the sequence are associated with the left space and those toward the end are linked to the right space. That is to say that the temporary associations between position and space determine the SNARC effect rather than the long-term semantic representations of number.ATOM - ert replikeringsexp.
suggesting the role of working memory resources for the spatial coding of numbers.ATOM - ert replikeringsexp.
the SNARC effect disappears under a working memory loadATOM - ert replikeringsexp.
the SNARC effect reflects a spatial stimulus?response compatibility between the mental number representation and the response position.ATOM - ert replikeringsexp.
Firstly, the SNARC effect seems to reflect a direct mapping between the position of a number on an internal spatial representation and the corresponding response location in the space.ATOM - ert replikeringsexp.
result pattern of NEs. Indeed, the participants committed lower NEs when there was a congruency between temporal and numerical infor mation. This result indicated an association, on one hand, between short duration and small numbers, and on the other hand, between long duration and large numbers (e.g. Cappelletti et al., 2009; Kiesel & Vierck, 2009; Oliveri et al., 2008; Vicario et al., 2008; Xuan et al., 2007). The TiNARC effect could suggest a common cognitive code for time and numerical quantity (Kiesel & Vierck, 2009; Walsh, 2003). That is, the (irrelevant) numerical processing affects the time estima tion, even if this influence has mainly been shown in temporal accuracy. Finally, a triple interaction between space, time and numbers was observed, in agreement with the idea of the ATOM model (Walsh, 2003). This result seems to indicate that there is one generalized sys tem dealing with space, time and magnitude, even if the modulation of STEARC, SNARC and TiNARC effects differed according to the remaining magnitude, temporal or spatial factors respectively. In deed, the STEARC effect remained for both large and small magni tudes. In a similar way, the SNARC effect was shown when long or short durations were analyzed separately. The TiNARC effect was ob served only when the left space was considered, disappearing when the right space was considered. This advantage of left space (i.e. left key or left hand) compared to right space (i.e. right key or right hand) is in line with recent results showing that the left hand is sen sitive to visual context in reaching (Adam, Müskens, Hoonhorst, Pratt, & Fischer, 2010), and in finger lifting and manual aiming (Ishihara & Imanaka, 2007). Given that the role of the right parietal cortex in modulating the interactions among time, space and numbers (Walsh, 2003), this advantage of the left key (hand) for the reliability of the TiNARC effect can be explained by the hemispheric asymmetry in motor domain (Adam et al., 2010; Ishihara & Imanaka, 2007). An other possibility, however, is related to two findings. Firstly, the TiNARC effect remained reliable with the presentation of numerical stimuli but it disappeared with alphabetical stimuli. Secondly, we ob served a magnitude-like effect for letters with increasing RTs from letter A to letter I. As indicated by Gevers et al. (2003), alphabetical material can be ordered from left to right. Even if no SNARC-like effect was found with letters, the association between A and B with the left space probably resulted as more salient than the association between H and I with the right space. Bearing in mind that the triple interaction was significant regardless of experimental stimuli, the TiNARC effect in the left space could be due to additive effects of these two findings.ATOM - ert replikeringsexp.
The main results found here reinforced the idea of one generalized system dealing with time, space and numbers. Indeed, general STEARC, SNARC and TiNARC effects were displayed, when both RTs and accuracy were analyzed. However, these effects were linked to experimental materials in different ways. A significant STEARC effect (Ishihara et al., 2008; Vallesi et al., 2008) was found when both numbers and letters were presented: the right space was linked to long durations and the left space was linked to short durations. This spatial congruency between time and response seems to give evidence for a mental representation of time along a spatial line (Casasanto & Boroditsky, 2008). As regards the SNARC effect, the spatial?numerical association was only found when numbers were presented on the screen (Dehaene et al., 1993). This result was in line with the study of Kiesel and Vierck (2009), given that a spatial?numerical association was found even if the numerical processing was irrelevant for the task. When alphabetical material was presented, no SNARC-like effect was obtained (Casarotti et al., 2007; Dehaene et al., 1993; Oliveri et al., 2008; Zorzi et al., 2006). In accordance with Zorzi et al. (2006), we suggest that the association between space and letters might be categorical. Indeed, we found a magnitude-like effect with letters, given that the RTs increased as a function of the increase in letter order. This result could indicate, for instance, that the participants processed the letters in a categorical way. Specifically, the letters A and B were ?lower? than reference E while the letters H and I were greater than reference E. In the present study, when numbers were presented and the resulting pattern of RTs was observed, a TiNARC effect was shown, albeit weakly. In particular, the TiNARC effect was shown in relation to the association between long durations and large numbers, but it disappeared when the association between short durations and small numbers was considered. However, the time?number association was more consistent in theATOM - ert replikeringsexp.
In addition, the ANOVA showed three signi ficant interactions: Stimulus × Key × Magnitude, Key × Duration × Magnitude. Stimulus × Duration × Magnitude, and The evaluation of these significant three-way interactions was explained by a set of two-way ANOVAs as explained below. On the contrary, the lack of statistical significance of the Stimulus×Key×Duration interaction seemed to indicate a similar STEARC effect for numbers and letters.ATOM - ert replikeringsexp.
Within the short durations, the participants obtained higher RTs when a large magnitude (521 ms) was presented compared to a small magnitude (513 ms),ATOM - ert replikeringsexp.
A signi ficant Duration×Magnitude interaction was also found, indicating a TiNARC effect. The post-hoc test showed that a large magnitude was more closely associated with long durations (501 ms) than short durations (521 ms),ATOM - ert replikeringsexp.
indicating a reliable SNARC effectATOM - ert replikeringsexp.
Moreover, the Key factor signi ficantly interacted with Magnitude factor, indicating a general SNARC effect. In the Scheffè post-hoc test, the right key (503 ms) was faster than the left key (520 ms) in responding to large magnitudes while the left key (501 ms) was faster than the right key (516 ms) in responding to small magnitudes (pb.005 for both comparisons).ATOM - ert replikeringsexp.
A negative regression slope was expected, indicating that short durations were associated with the left hand while long durations were associated with the right. The regression weight was ?0.19 ms/duration (SD=0.31 ms/duration), and it deviated significantly from zero, t(35)=?3.63, pb.005, indicating a reliable STEARC effect (Fig. 1A).ATOM - ert replikeringsexp.
The Scheffè post-hoc test revealed that the right key (485 ms) was faster than the left key (520 ms) in detecting long durations while the left key (501 ms) was faster compared to the right key (534 ms) in detecting short durationsATOM - ert replikeringsexp.
According to the aim of the study, the ANOVA showed a significant Key×Duration interaction, indicating a general STEARC effect.ATOM - ert replikeringsexp.
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