The current goal was to investigate whether a dedicated scalar timing mechanism consistent with scalar expectancy theory (Gibbon et al., 1984
), is ubiquitous across millisecond and second durations for both perceptual and motor tasks. We were particularly interested in the performance of human participants on a number of closely-spaced durations encompassing one second. The overall results cast doubt on the view that a unitary scalar mechanism appropriately describes timing across these tasks and durations. Instead, different timers may operate for perceptual and motor tasks, and there is evidence for departures from scalar variability.
5.1. Timing across tasks
Of the few studies that have directly compared timing performance across motor and perceptual tasks within the same participants, (Ivry & Hazeltine, 1995
; Keele et al., 1985
, Merchant, Zarco, & Prado, 2008
), performance has been assessed within a single timescale (e.g. milliseconds range). Some of these studies found support for a common scalar clock across tasks (Ivry & Hazeltine, 1995
, Keele et al., 1985
). More recent work using a broader range of durations of 1 second or less found overall patterns of scalar variability, but also revealed that differences in modality, encoding context and task type (e.g. perception or production) influenced estimates of duration-dependent variance (Merchant, Zarco, & Prado, 2008
); the authors argued that while some features of timing in different tasks may involve common timing mechanisms, some distributed mechanisms are also differentially engaged, depending on task constraints.
The tasks used in the current set of experiments were designed to equate perceptual and encoding requirements; therefore, we would have expected evidence supporting a common scalar timer. However, we found no significant relationships across tasks in CV measures, and we found task differences in CVs and the Weber slopes from the truncated data and from the non-truncated short duration sets. The absence of significant correlations between CVs for the two timing tasks, despite involvement of the same study participants, is surprising. Though differences in motor preparation and performance may have contributed noise to the CV data, between-task relationships should have emerged if the tasks shared one or more processes for timing. While the small number of participants urges a cautious interpretation of these results we note that our sample size is comparable to that of prior studies using similar analyses (Keele et al., 1985
; Merchant, Zarco, & Prado, 2008
; Robertson et al., 1999
). The significant task effect for short duration set Weber fractions and the absence of cross-task correlations in the milliseconds range are especially noteworthy because they contradict the oft-cited finding of similar timing across tasks for durations in this range (Ivry & Hazeltine, 1995
; Keele et al., 1985
). Interestingly, while timing sensitivity was poorer for temporal discrimination than reproduction, accuracy was similar, suggesting that the mechanisms responsible for timing in the two tasks lead to similar representations of the standard durations.
Reproduction and discrimination are also clearly distinguished by their different patterns of tap latency. Increased latency across durations for reproduction but not discrimination is consistent with the finding by Vidal, Bonnet, and Macar (1991
) that action duration is coded as part of a motor program and can be processed prior to motor execution. This feature of temporal reproduction also fits with Lewis and Miall’s (2003b
) theory that tasks that require replication of a duration via an action may be especially reliant on the motor system; including duration as a dimension of the response may necessitate different encoding and memory processes than those engaged for temporal discrimination. On the other hand, task differences might be due to strategy differences. For example, participants may rehearse the standard duration prior to response or create a latency that is temporally and rhythmically congruous with the standard to support reproduction. Note, however, that latency length did not always match standard duration length in our experiments. Thus, this process of encoding may involve some translation or compression of the duration. Additional work manipulating task encoding, memory, and motor preparation requirements is needed to draw definitive conclusions about the source of task differences on this measure.
We went to great lengths to equate the features of our two timing tasks in experiment 3. Despite our efforts, we acknowledge that the tasks differ in their motor requirements and that contamination from motor processes could have influenced our results. This challenge exists, however, for all studies that compare motor and perceptual timing tasks. Moreover, our efforts to match the features of the reproduction and discrimination tasks in experiment 3 went beyond many prior reports. We also took deliberate steps to prevent participants from using explicit movement-based strategies (e.g. foot tapping), which included monitoring by an experimenter and removal of individuals who reported their use on self-report questionnaires. While we cannot rule out the use of covert or implicit movement-based strategies, our efforts to eliminate their explicit use make our findings of cross-task differences all the more informative.
5.2. Timing across durations
The quadratic, U-shaped pattern of CVs in temporal reproduction from all 3 experiments suggests that timing across millisecond and second durations in this task does not rely on a single scalar clock. This type of pattern has previously been found for both production and categorization timing tasks in pigeons using durations of 500 ms up to 64 s (Bizo et al., 2006
) and rats using durations of several seconds in length (Crystal, 2001
). In the present experiments one minimum reproduction CV occurred at 1000 ms--the point where some researchers argue for a transition between timing mechanisms reliant on the motor system and those that engage executive control processes (Lewis & Miall, 2003a
). The Weber slope data from the first two experiments further implicates different clocks across timescales, with breakpoints from experiment 1 (M
= 956 ms) and the truncated data sets for experiments 2 and 3 (M
= 1021 ms; M
= 1074 ms) occurring near 1000 ms.
While the quadratic CV data provide consistent evidence of nonlinear timing in temporal reproduction, it is important to note that this may not point to the operation of different timers across timescales. Instead, reproduction may involve a single timer that is simply not a pacemaker-accumulator mechanism adhering to the scalar property. Two possible alternatives include a multiple oscillator clock (Church & Broadbent, 1990
) and the striatal beat frequency (SBF) model (Matell & Meck, 2004
). Both mechanisms could produce scalar variability across most durations along with points of maximal sensitivity at durations that match or are multiplicative values of the component oscillator periods (Church & Broadbent, 1990
; Crystal, 1999
; Matell & Meck, 2004
). Our temporal reproduction CVs could be due to such a mechanism with at least one oscillator period close to 1000 ms. SBF could also account for people's increased sensitivity at 1000 ms via well-tuned coincidence detection due to repeated reinforcement from the observation of timepieces and physiological processes, such as heartbeat. In our experiments, however, there was little indication of significant correlations across timescales in temporal reproduction. If a non-scalar clock were wholly responsible for timing, significant correlations across timescales should still emerge. Moreover, the Weber slope analyses in the first two experiments hint at different mechanisms for timing milliseconds versus seconds-length durations. Thus, the quadratic pattern in CVs may implicate two different timers across timescales.
CV data from experiment 3 suggest that, despite task differences in temporal sensitivity, the manner in which sensitivity changed across timescales did not differ by task. However, the CV correlations within temporal discrimination complicate the picture concerning the mechanism(s) that operates across timescales; correlations emerged between the intermediate standard durations along with many large Pearson correlation coefficients between CVs for shorter durations. Correlations were weak for the longer durations. Additional power could yield a clearer pattern, elucidating whether temporal discrimination in the milliseconds and seconds ranges engages different timers.
Findings from the Weber slope analysis were difficult to interpret. Importantly, fitting independent bilinear regressions to the data assumes two separate scalar timers across a break, but these assumptions may not be correct. Indeed, in experiment 3 nearly half of our participants revealed negative Weber slopes across the long duration set (even for truncated data). These negative slopes may have been due to the durations we used to prevent use of a categorization strategy in experiments 2 and 3 coupled with our bi-linear regression technique. This idea is supported by the fact that we did not find negative slopes in experiment 1. Moreover, prior studies using Weber slope analysis have typically involved durations of one second or less, have investigated a single regression line through all data points, and have no reported negative slopes (Ivry & Hazeltine, 1995
; Merchant, Zarco & Prado, 2008
; Robertson et al., 1999
; Spencer & Zelaznik, 2003
). It is noteworthy that negative slopes were not ubiquitous in our experiments, occurring for some individuals but not others, and more frequently with temporal discrimination. Therefore, they may reflect strategy differences in response to differing task demands associated with timing of longer durations.
Negative slopes for longer durations could result from attempts to subdivide the standard and comparison durations in such a way that variability for longer durations is reduced. One manner of subdivision, counting, is known to cause departures from scalar timing in this way (Grondin, Meilleur-Wells & Lachance, 1999
; Hinton & Rao, 2004
; Killeen & Weiss, 1987
). We eliminated data from individuals who reported counting in our experiments, but some individuals with negative slopes reported trying to associate the standard and comparison durations with the length of a word or words they repeated silently. Negative slopes could also emerge from difficulty maintaining attentional focus when encoding longer durations. Attention is posited to modulate the output of the pacemaker component of SET (see Zakay & Block, 1996
). Difficulty maintaining attention at encoding, therefore, could ultimately lead to duration representations with missed pulses, reducing their discriminability from their shorter neighbors and violating the expected increase in variance with increasing durations. Future studies need to address whether negative Weber slopes are due to individual differences, such as differences in attention, or strategy differences in timing per se.
5.3. Future directions
An important future goal is to determine with greater certainty whether the quadratic pattern of data for temporal reproduction indicates a shift between different timing mechanisms or, instead, points to a single timer which may not adhere to scalar variance. Our current data point to the prior possibility. However, exploration of other models of timing is warranted. Reproduction performance should be systematically investigated with additional durations, including multiples (e.g. 2000 ms, 3000 ms) of the 1000 ms point of maximal sensitivity. Increases in sensitivity at these harmonic values would be consistent with either a multiple oscillator clock or the SBF model of timing. Moreover, exploring additional durations beyond the range of 2 seconds will help clarify whether the quadratic pattern in CV continues with longer durations or whether another transition between timing mechanisms emerges in the 2–3 second range. Given that the evidence of non-scalar timing was much weaker for temporal discrimination in our study, it is similarly important to examine this task in more detail to identify the features of the timing mechanism(s) engaged for the milliseconds and seconds ranges.
Negative Weber slopes were problematic for investigating duration-dependent sources of variance in our studies. Evaluation of truncated data sets solved the problem, to some degree, but these data are not necessarily equivalent to those obtained from duration sets lacking similar end-point pairs. We confirmed in experiments 2 and 3 that the quadratic pattern in the CV data was likely not due to an anchoring strategy, so future research can confidently use Weber slope analysis incorporating bi-linear regression with endpoint durations that are easier to discriminate from their neighbors. Persisting negative slopes will lend further credence to the presence of some difference in the mechanisms or strategies engaged for timing between short and long durations, especially for temporal discrimination.
The present results call attention to the need for further detailed investigations of motor and perceptual timing across an even larger set of durations spanning tens of milliseconds to several seconds in length to clarify where and how many functional breaks in timing exist. Two or more timescale shifts in this range have been suggested (Buhusi & Meck, 2005
; Buonomano & Karmarkar, 2002
), with the current study strongly implicating a shift in the region of one second for temporal reproduction.