Time dilates more with apparent than with physical speed

Abstract

The perceived duration of a moving stimulus correlates positively with its speed. It is not known whether such duration dilation depends on the physical or apparent speed. Here we show the latter to be true. The perceived duration of a shortly presented (500, 900, 1300 ms) Gabor patch whose carrier moved at 1°/s in a direction opposite to a background of random black dots rigidly moving at 3°/s appeared to last 20% longer and to drift 240% faster than the same Gabor carrier moving in the same direction as the random-dot background. Assessment of the perceived speed of each of the two configurations relative to a moving Gabor patch in the absence of the moving background allowed the comparison of the observed duration dilation with that obtained as a function of the corresponding physical speeds, which should have yielded a dilation of only 7%, i.e., three times less. In line with the proposal that perceived duration correlates with the strength of the neural response evoked by the stimuli to be timed, the present data can be accounted for by the increased responsiveness of antagonistic center–surround motion-receptive fields when stimulated with center–surround antagonist motions.

Introduction

Perceived duration is known to depend on a large number of contextual factors both intrinsic to the stimuli whose duration is to be judged (e.g., their size, flicker rate, speed) and extrinsic to them (e.g., attention, expectation or surprise, emotion, task demands; see reviews by Eagleman, 2008; Eagleman & Pariyadath, 2009; Fraisse, 1963, 1967, 1984; Gorea, 2011; Grondin, 2010; James, 1890; van Wassenhove, 2009). Among the former, speed has received meticulous experimental attention (Brown, 1931; Brown, 1995; Kanai, Paffen, Hogendoorn, & Verstraten, 2006; Kaneko & Murakami, 2009; Yamamoto & Miura, 2012). 

The dependency of perceived duration on the speed (as well as on the flicker rate; Vierordt, 1868) of visual stimuli is typically accounted for in terms of the number of processed events (Brown, 1995; Fraisse, 1963; Liverence & Scholl, 2012; Poynter, 1989), presumably correlated with attentional load, which in turn has been shown to correlate with perceived duration (Brown, 1997, 2008, 2010; for a recent review, see Nobre & Coull, 2010). Alternatively, duration dilation could be a consequence of stronger neural responses (Eagleman & Pariyadath, 2009; Mayo & Sommer, 2012) presumably evoked by faster speeds. 

It has been known at least since Duncker (1929) that perceived speed is relative, i.e., it depends on (can be induced by) the speed of adjacent objects in motion (e.g., Baker & Graf, 2008, 2010; van der Smagt, Verstraten, & Paffen, 2010). Baker and Graf (2010) found that a Gabor patch whose carrier moved at 1°/s displayed on the top of a luminance noise background moving at 3°/s in the opposite direction could be perceived to move more than twice as fast as its 1°/s physical speed. Eifuku and Wurtz (1998) have shown that neurons in the lateral ventral region of the medial superior temporal area (MSTl) of the macaque respond much more vigorously to moving stimuli surrounded by an opposite motion than to the same stimuli in the absence of any surround, and even more so relative to stimuli with a surround moving in the same direction. A number of functional magnetic resonance imaging studies have obtained equivalent results in the human MT complex (hMT+; Moutsiana, Field, & Harris, 2011; Takemura, Ashida, Amano, Kitaoka, & Murakami, 2012). Takemura et al. (2012) have shown that the blood-oxygen-level dependent response in this area increases with subjects' perceived speed of the central moving stimulus in the presence of a moving surround rather than with either its physical speed or its speed relative to that of the surround. Inasmuch as the strength of the neural response is a modulator of the perceived duration of the stimulus that evoked it (Eagleman & Pariyadath, 2009; Mayo & Sommer, 2012), perceived duration of such central moving stimuli surrounded by a moving background should also depend on their perceived rather than physical speeds. 

That the perceived passage of time depends on the phenomenal rather than on the physical speed of visual stimuli was first noted by Brown (1931) and then, to our knowledge, never replicated afterward. Brown concluded that “all those structural variations that increase the phenomenal velocity of a movement either increase the phenomenal space or shorten the phenomenal time for equal space correspondingly” (1931, p. 17), contrary to studies finding the inverse relationship between phenomenal time and physical speed (see Brown, 1995). Brown's equipment and experimental setup were of the early 20th century, and his presentation of the results together with their interpretation is practically impossible to follow. As already noted by Kaneko and Murakami (2009), the assessment of perceived duration dependency on perceived rather than on physical speed remains unsettled. The present study clearly shows not only that the modulator of perceived duration is the perceived rather than the physical speed, but also that this modulation is stronger than that exercised by the corresponding physical speed. 

Methods

Stimuli

The stimuli were presented on a 19-in. E96f+SB ViewSonic monitor (1280 × 1024 pixels, 75 Hz) using a Dell Precision T3500 computer. Observers were seated about 80 cm from the monitor. In all the experiments, the test stimuli were achromatic Gabor patches (1 c/°, 50% contrast sinusoidal carrier tilted 45° clockwise or counterclockwise from the vertical, displayed within a 2-D Gaussian envelope with a standard deviation of 0.64°). They were presented by themselves or added without occlusion to circular, 6°-diameter fields filled with black dots (16.7 dots/°², with each dot subtending 0.05° × 0.05°, i.e., 3 × 3 pixels) rigidly translating at a speed of 3°/s. The Gabor patches and the drifting dots were displayed on a 20-cd/m² gray background. 

The centers of the Gabor patches and of the moving-dots area were located 4° to the left and to the right of a red fixation cross (0.3° × 0.3°). The Gabor carriers moved in either of the two directions orthogonal to their orientations with a speed of 1°/s in Experiments 1.1, 1.2, and 3 and with varying speeds in Experiments 2.1, 2.2, and 4 (see later). The black dots moved with a speed of 3°/s in the same direction as the Gabor carriers, in the opposite direction, or in an orthogonal direction. 

Observers

Five observers with normal or corrected-to-normal vision completed five out of six experiments for monetary compensation. Four observers were postdoctoral researchers (two women, two men, ages 29–34) and one was a graduate student (a woman, age 25) at Université Paris Descartes. Participants were naïve as to the purpose of the experiments. Six additional observers—three graduate students (women) and three postdocs (one woman and two men, ages 25–34)—participated at a later stage in a control experiment requested by a reviewer. Only one of these observers had also participated in Experiment 1.1. All 11 observers provided written informed consent before participating in the experiments, and all experimental procedures were reviewed and approved by the institutional review board in accordance with the principles of the Declaration of Helsinki. 

Procedure

Observers completed the six experiments over 3 to 5 days each and over about 1 month altogether. All six experiments were meant to assess the subjective appearance of one of two stimulus features: their perceived duration (Experiments 1.1, 1.2, and 3) and their perceived speed (Experiments 2.1, 2.2, and 4). They all shared a sample-to-match technique but differed in whether the matching procedure used an adaptive (Experiments 1.1, 1.2, 2.1, and 2.2) or a constant stimuli (Experiments 3 and 4) method. They also partly differed in the respective stimulating parameters. 

In Experiments 1.1, 1.2, 2.1, 3, and 4, observers initiated a trial by pressing the space bar on the keyboard (see Figure 1a). The gray background screen (with the fixation cross always present) persisted for 1000 ms after the key press. Then the moving-dots backgrounds appeared simultaneously on the left and right sides of the fixation cross and stayed on the screen until the end of the trial. After 307 ms from the onset of the background fields, two moving Gabor stimuli were presented successively on their respective background fields, with the location (left or right) of the first Gabor randomly chosen across trials. The second Gabor was displayed on the moving-dots background after an interstimulus interval randomized within the range of 400 ± 40 ms. In Experiments 1.1 and 2, irrespective of their order of appearance, one of the two Gabors moved in the same direction as its moving-dots background, while the other Gabor moved in a direction opposite to its moving-dots background. In Experiment 1.2, the probe Gabor moved in a direction orthogonal to its background. Observers reported which Gabor stimulus (the one on the left or on the right) appeared to be longer in duration (Experiments 1.1, 1.2, and 3) or to move faster (Experiments 2 and 4) by pressing one of two arrow keys (left or right) on the keyboard. The motion of the dots was terminated by the observer's key press, with the static random dots remaining on the screen until the observer started the next trial. The motion direction of the background dots and the orientation of the Gabors changed by 90° clockwise from trial to trial to reduce motion aftereffects. Observers confirmed that they did not experience any motion aftereffect during the period when they saw the stationary dots (i.e., after their response and before starting a new trial). 

Figure 1

 

General spatiotemporal display of the stimuli in Experiments 1, 2.1, 3, and 4 (a) and in Experiment 2.2 (b). See text for more details.

Experiment 1.1: Perceived duration (staircase)

The experiment was meant to assess the perceived duration of a Gabor stimulus moving at 1°/s superimposed on a background of dots rigidly moving in the opposite direction (−3°/s) relative to the perceived duration of an identical Gabor superimposed on a background of dots moving in the same direction (+3°/s). The opposite-direction Gabor stimuli (oppDir), the standards, were presented for one of three durations (507, 907, or 1307 ms) chosen randomly across trials. Two interleaved staircases per standard duration adjusted the duration of the same-direction (sameDir) probe stimuli following a one-up/one-down rule with a step size of 0.2 log units (4 dB) for the first four reversals and 0.1 log units (2 dB) for the remaining trials. The order of the standard–probe sequence was randomized across trials. The starting durations of the probes for each of the two staircases per standard were chosen randomly, one within an interval of −5% to −15% and the other within an interval of +5% to +15% of the standard duration. A staircase was terminated after 18 reversals, and the point of subjective equality (PSE) was computed as the mean of the last four reversals. 

Experiment 1.2 (control): Perceived duration (staircase)

Whatever the expected duration distortion of the oppDir relative to the sameDir configuration, the possibility exists that perceived duration is modulated by the number of displayed directions (two for oppDir and one for sameDir) rather than by their opponency. This control experiment was run a posteriori to answer such a concern expressed by one reviewer. It differed from Experiment 1.1 only in that the sameDir probe was replaced with a configuration where the direction of the Gabor carrier was orthogonal to that of the background dots (orthDir). If the number of directions were the critical perceived duration modulation factor, oppDir and orthDir stimuli should yield identical perceived durations when displayed for identical physical durations. 

Experiment 2.1: Perceived speed (staircase)

This experiment was identical to Experiment 1.1 with the following exceptions: (a) Observers were asked to judge the speed rather than the duration of the standard oppDir stimulus, (b) both standard and probe Gabors were always displayed for 907 ms, and (c) the speed of the sameDir probe Gabor was monitored by the one-up/one-down staircases. In this case the step size was 0.05 log units (as in Baker & Graf, 2010). 

Experiment 2.2: Perceived speed (staircase)

In order to assess the absolute relative-motion effect on the perceived speed, observers were asked to either match the speed of a moving Gabor presented this time without the moving-dots background (noBackgr)—the probe—to the perceived speed of a Gabor displayed with the dotted background (the standards) moving in the same direction as the Gabor (sameDir) and in the opposite direction (oppDir); or to match each of the latter two, used this time as probes, to the perceived speed of the noBackgr stimulus, used this time as the standard (see Figure 1b). Hence, there were four standard–probe configurations (noBackgr–oppDir, noBackgr–sameDir, oppDir–noBackgr, sameDir–noBackgr), with the probe stimulus in each configuration monitored by two staircases. This yielded eight staircases in total. These configurations were randomly interleaved across trials. All other details were as in Experiment 2.1. 

Experiment 3: Perceived duration (method of constant stimuli)

To obtain the whole psychometric function of the relative-motion effect on perceived duration, Experiment 3 was performed using the constant stimuli method. In this experiment, as in Experiment 1, the perceived duration of the sameDir and oppDir Gabor stimuli (the probes) was to be compared with the perceived duration of the sameDir stimulus (the standard). The sameDir–sameDir comparison was meant to reveal any potential acuity (slope of the psychometric function) difference between homogeneous (sameDir–sameDir) and nonhomogeneous (oppDir–sameDir) conditions. There were three standard durations, and four probe durations per standard. Together with the two probe configurations, this yielded 24 different conditions total. Each of the 24 conditions was presented 48 times, yielding 1,152 trials total randomly interleaved within each session. As in Experiment 1.1, the speeds of the Gabor and of the moving dots were fixed at 1°/s and ±3°/s, respectively. The four probe durations (per standard) were chosen to be geometrically centered on the original standard durations, with a ratio of 1.48 between each pair of neighboring durations (i.e., 280, 413, 613, and 907 ms for the 507-ms standard; 493, 733, 1093, and 1627 ms for the 907-ms standard; and 720, 1067, 1587, and 2347 ms for the 1307-ms standard). The three standard durations were set equal to the respective PSEs obtained in Experiment 1.1 for each observer and for each of the three standard durations in that experiment (507, 907, and 1307 ms). It was hence expected that the perceived durations of the oppDir probe stimuli (i.e., their PSEs) in this experiment would equal the physical durations of the sameDir standards used in Experiment 1.1, so that the ratio of PSE_oppDir;Exp3 to Standard_{sameDir;Exp1.1} would equal 1. Equivalently, the ratios between the perceived durations of the sameDir probe stimuli in this experiment should equal the sameDir PSE obtained in Experiment 1.1 for the sameDir–sameDir condition, so that their ratio (PSE_sameDir;Exp3 to PSE_sameDir;Exp1) should also equal 1. 

Experiment 4: Perceived speed (method of constant stimuli)

Experiment 4 was a partial replica of Experiment 3, but bearing this time on observers' perceived speed. In this experiment, the perceived speed of a same-direction (sameDir) standard was to be compared with the perceived speed of both a same-direction (sameDir) and an opposite-direction (oppDir) probe. The presentation duration of all stimuli was fixed at 907 ms. Due to the large difference of the perceived speed between sameDir and oppDir probes (see Results for Experiment 2.1) and to the steepness (high accuracy) of the corresponding psychometric functions (e.g., Johnston, Benton, & Morgan, 1999), the speeds of the standard (sameDir) were set independently when to be compared with those of sameDir and of oppDir: 1°/s for the sameDir–sameDir condition and equal to the individual PSEs measured in Experiment 2.1 for the oppDir–sameDir condition. The four speeds of the probe stimuli were separated by a linear 0.6°/s step, with median centered on the standard speed of 1°/s. Overall, there were eight different conditions, each of which was repeated in 48 times in a random order across trials (2 probe motion directions × 4 probe speeds × 48 trials = 384 trials). 

The five experiments (to the exclusion of Experiment 1.2) were completed in about 5 h per observer, distributed over 4 to 6 days. 

Results

With the exception of Experiments 1.1 and 1.2, where the absolute PSEs are also presented, the results are displayed as ratios of probe to standard (Experiments 1–4) and of standard deviation to mean (i.e., coefficients of variability; Experiments 3 and 4). In the probe/standard ratios, the probe value refers to the observer's PSE and the standard either to the standard used in the specific condition (Experiments 1 and 2) or to the PSE obtained with a different method (Experiments 3 and 4, constant stimuli method; see later). Hence, ratios larger than 1 indicate that observers judged the standard to last longer (Experiments 1.1 and 1.2) or to move faster (Experiments 2.1 and 2.2) than the probe. With one exception in Experiment 4, the displayed data points are averages (arithmetic for PSEs and geometric for ratios) over the five or six (in Experiment 1.2) observers. 

Figure 2 displays the results of Experiments 1.1 and 1.2: duration PSEs (left-side ordinates and circles) together with linear regressions (straight continuous lines) for the three standard durations used, and ratios of PSE to standard duration (right-hand ordinates and squares) for these same three standard durations. The horizontal dashed-dotted line in Figure 2a represents the predicted ratio of PSE to standard derived from Kaneko and Murakami's (2009) data and from the present Experiment 2.2 (see later). The basic observations are that the perceived duration of a Gabor patch moving at 1°/s in a direction opposite to a 3°/s moving-dots background is about 20% longer than the perceived duration of the same Gabor patch moving in the same direction as (Figure 2a), and 6% longer than the perceived duration of the same Gabor patch moving in a direction orthogonal to (Figure 2b), the moving-dots background for all three standard durations. Hence, perceived duration depends on the apparent rather than the physical speed of a visual object. The number of displayed directions per se does not seem to be a factor, since the duration of the orthDir configuration is substantially contracted relative to that of the oppDir configuration, despite the fact that the two configurations contain two distinct directions. This time dilation due to the perceived speed difference between the two stimulus configurations (sameDir vs. oppDir; see Experiment 2.1 and Figure 3) is significantly larger than the one assessed for the equivalent physical speeds by Kaneko and Murakami (2009). Moreover, the constant Weber ratio observed over the three tested durations (squares) excludes the possibility that the presently measured time dilation with perceived speed is due to a shift of the perceived onset or offset of the Gabor patches induced by the direction opponency. 

Figure 2

 

Experiments 1.1 (a) and 1.2 (b) (staircase): Duration points of subjective equality (PSEs; left-side ordinates and circles) and ratios of PSE to standard duration (right-hand ordinates and squares) as a function of the standard duration. The straight continuous lines are linear regressions through the PSEs (equations given in the inset). The dashed 45° lines show what a perfect judgment would be. The horizontal dashed-and-dotted line in (a) shows the ratio prediction based on Kaneko and Murakami's (2009) data and on the present Experiment 2.2 data (see text). The drawings in each panel specify the experimental condition, with the upper and lower icons representing the probe and standard stimuli, respectively. Vertical bars are ±1 standard error.

Figure 3

 

Experiments 2.1 and 2.2 (staircase): Ratios of speed PSE to standard speed (1°/s; also given as numerical values below or above the bars) in Experiment 2.1 (central gray bar) and in the four conditions of Experiment 2.2. The ordinate axis is logarithmic. The drawings above and below each bar specify the experimental condition, with the upper and lower icons representing the probe and standard stimuli, respectively. Vertical bars are ±1 standard error.

Figure 3 displays the perceived speeds assessed in Experiments 2.1 (gray bar) and 2.2 (remaining bars). The drawings above and below each bar indicate the tested comparisons, with the upper and lower icons referring to the probe and standard stimuli, respectively. The ordinate is in log units. Notice that symmetrical probe–standard configurations (bars with the same hatching orientations) yield close to symmetrical perceived speed enhancement or reduction effects (slightly less than a factor of 2): The use of the noBackgr stimulus as probe or as standard yields very similar, though inverted, ratios of probe to standard. This equivalence testifies in favor of the reliability of the present speed PSE measurements. Also, the similar ratios of probe to standard obtained with a Gabor carrier moving at 1°/s in the opposite (0.51 and 1.68 ratios) and same (0.53 and 1.94 ratios) direction as a 3°/s moving-dots background (oppDir) suggest a close to logarithmic addition or subtraction of the perceived speed effects. This is not, however, sustained by the comparison of the ratio of sameDir to oppDir ratio assessed in Experiment 2.1 (2.44—a ratio similar to the one obtained by Baker & Graf, 2008, 2010) and the equivalent ratio—the average of (noBackgr/oppDir)/(noBackgr/sameDir) and (sameDir/noBackgr)/(oppDir/noBackgr) ratios—of 3.5 in Experiment 3. The apparent discrepancy remains to be explained. 

The perceived absolute speeds (i.e., PSEs) of sameDir and oppDir stimuli being established (0.52°/s and 1.81°/s, respectively, given that the speed of the standard noBackgr stimulus was 1°/s), one can use Kaneko and Murakami's (2009) equation 3, which best fit their perceived duration dilation data as a function of physical speed (duration dilation = 1.267 + 0.047log₂(speed)), to infer the present apparent speed effects on perceived duration. Accordingly, the predicted dilations relative to a static stimulus should have been a factor of 1.22 and of 1.31 for 0.52°/s and 1.81°/s stimuli, and hence of only a factor of 1.07 between these two speeds (dashed-and-dotted horizontal line in Figure 2). This dilation is well below the 1.2 factor presently found when comparing the relative perceived durations of the sameDir and oppDir stimuli (see Figure 2). 

Experiments 3 (perceived duration) and 4 (perceived speed) were intended as partial replicas of Experiments 1.1 and 2.1, but this time using the constant stimuli method. The constant stimuli method also allowed the assessment of observers' duration and speed discrimination thresholds, expressed here as coefficients of variation, namely the slopes of the respective fitted psychometric functions divided by the respective PSEs. Given the choice of the standard durations in Experiment 3 (see Methods), the respective oppDir and sameDir PSEs should equal, respectively, the standard durations (i.e., 507, 907, and 1307 ms) and the sameDir PSEs from Experiment 1.1. They are hence represented in Figure 4a as such ratios that should be close to 1 if the staircase and constant stimuli methods were to yield equivalent results. This is indeed the case for the sameDir PSEs (squares in Figure 4a) and for the oppDir PSE with the shortest standard duration. The oppDir PSEs for the medium and longest standard durations are respectively 11% and 15% higher than expected. Nonetheless, a repeated-measures 2-way ANOVA (factors: stimulus type and standard duration) shows no significant difference between oppDir/sameDir and sameDir/sameDir ratios. With one exception out of six cases (oppDir/sameDir for the shortest standard duration), the coefficients of variation are independent of the standard duration for both oppDir and sameDir conditions, implying Weber's law. Not surprisingly (e.g., Gorea, Mamassian, & Cardoso-Leite, 2010), these coefficients are high (about 30%), indicating a poor duration discrimination performance. 

Figure 4

 

Experiment 3 (perceived duration, constant stimuli): Duration PSEs for oppDir (circles) and sameDir (squares) over their corresponding references (REF)—i.e., respectively, the standard durations used in Experiment 1 and the sameDir PSE in the sameDir–sameDir condition (also from Experiment 1)—(a) together with the corresponding coefficients of variation (σ/PSE) and (b) as a function of the mean standard durations used. As the standard durations in Experiment 3 were the PSEs obtained in Experiment 1 (see Methods), all the ratios in (a) should have been equal to unity [dashed horizontal line in (a)]. Vertical bars are ±1 standard error.

Figure 5 displays in a format similar to Figure 4 the ratios between the speed PSEs obtained with the method of constant stimuli in Experiment 4 and, given the choice of the standard durations in Experiment 3 (see Methods), a 1°/s standard. The ratios are displayed in Figure 5 at the corresponding standard speeds (1°/s and 2.44°/s for the sameDir–sameDir and oppDir–sameDir conditions). Once again, if the staircase and constant stimuli methods were to yield equivalent results, these ratios should equal unity. This is indeed the case for the oppDir–sameDir condition (circle), but, strangely, not for the sameDir–sameDir condition (solid square). Unfortunately, two of the five observers showed in this condition atypical psychometric functions with very shallow slopes. When those two are excluded, the sameDir–sameDir ratio approaches unity (0.90). The very shallow slopes of these two observers (1.7°/s and 1.8°/s for a 1°/s PSE) also show up in the coefficient of variability averaged over the five observers (solid square in Figure 5b) and its huge standard error. When they are excluded, the coefficient of variability averaged over the remaining three observers (open square) and its standard error drop dramatically. Even so, this coefficient and the one obtained for the oppDir–sameDir condition (circle in Figure 5b) are at the very upper bound of typical Weber fractions for speed discrimination, but compatible with prior results obtained with similar speeds and spatial frequencies (Johnston et al., 1999; McKee, 1981; McKee, Silverman, & Nakayama, 1986). 

Figure 5

 

Experiment 4 (perceived speed, constant stimuli): Speed PSEs in Experiment 4 (constant stimuli) over a 1°/s speed (see text and Methods) (a) together with the corresponding coefficients of variation (σ/PSE) and (b) for a standard speed of 1°/s in the sameDir–sameDir condition (squares) and equal to the average speed PSE from Experiment 2.1 (2.44°/s) in the oppDir–sameDir condition (circles). Ratios for sameDir–sameDir are shown as averages across all five observers (solid square) and after exclusion of two observers with aberrant psychometric functions (open square). A perfect match between the PSEs measured here and in Experiment 2.1 should have yielded a ratio of 1 [dashed horizontal line in (a)]. Vertical bars are ±1 standard error.

Discussion

The present experiments established that observers' perception of duration (known to correlate positively with the speed of moving visual objects; for reviews, see Gorea, 2011; van Wassenhove, 2009) does not actually depend on their absolute but rather on their apparent (here, “induced”) speed (Duncker, 1929). In the present experiments, the perceived duration of a shortly presented Gabor patch (duration range = 500–1300 ms) whose carrier moved at 1°/s was about 20% longer when the Gabor patch was displayed over a background of dots rigidly moving at 3°/s in the opposite direction compared to the same direction as the Gabor. This relative perceived time dilation is concomitant with observers' overestimating the speed of the opposite-direction Gabor relative to the same-direction one by an average factor of 2.4. When assessed separately relative to a moving Gabor presented in the absence of a moving-dots background, observers over- and underestimated the speed of the Gabor moving in the opposite and in the same direction as the moving-dots background by average factors of 1.8 (i.e., a perceived speed of 1.8°/s) and 1.9 (a perceived speed of 0.52°/s), respectively. According to prior studies by Kanai et al. (2006) and Kaneko and Murakami (2009), and using the analytical fit of the data by the latter, the presently assessed perceived speed of the opposite-direction Gabor should have yielded a 7% duration dilation relative to the same-direction Gabor. The predicted dilation based on the relative physical speeds of the Gabor carrier (i.e., 2°/s and 4°/s) would have been even less (4%). To our best knowledge, within the physical speed range matching the presently assessed perceived speed range, no previous study has reported duration effects induced by physical speed larger than 10% (e.g., Brown, 1931; Brown, 1995; Kanai et al., 2006; Kaneko & Murakami, 2009; Yamamoto & Miura, 2012). It hence appears that the effect of induced speeds on perceived duration is about threefold larger than would be expected had it been induced by physical speeds matched to the presently perceived speeds. An equally enhanced duration effect was observed for objects moving in a 3-D environment, but this enhancement was contributed to by other factors than speed per se (i.e., the moving object's size, perceived trajectory length, foreshortening; Gorea & Hau, 2013). Finally, the characterization of the perceived duration and perceived speed psychometric functions (i.e., their perceived slopes and PSEs; Figures 4b and 5b) pleads in favor of the applicability of Weber's law in these two domains, as the respective coefficients of variation remain more or less constant over the tested durations (600–1600 ms) and speeds (1°/s and 2.44°/s). 

The latter observation excludes two possible confounds of the presently inferred causal link between speed and duration dilation. Opposite- and same-direction configurations might have induced different perceptual onsets or offsets of the respective Gabor patches, thereby accounting for their different perceived durations. Equivalently, the oppDir configuration might have grabbed observers' attention more than the sameDir configuration, hence dilating more the perceived duration of the former (e.g., Tse, 2010). However, these putative modulators of perceived duration should have induced a constant dilation. The presently observed dilation proportionality with the standard duration (Weber law) renders their contribution to the reported effects highly unlikely. Another potential confounding factor (pointed out by a reviewer) is the number of directions per se (two and one for the oppDir and sameDir configurations, respectively) rather than their opponency (hence their induced speed). Experiment 1.2 excluded this possibility, as it showed that the perceived duration of the Gabor patch in the oppDir configuration was also dilated relative to a configuration where the Gabor carrier and the dotted background moved in orthogonal directions. 

Time dilation with speed is generally accounted for by the debatable notion that motion involves multiple position-change events and that the number of such events increases with speed (e.g., Brown, 1995; Fraisse, 1963; Poynter, 1989; Poynter & Homa, 1983). However, no such discrete events can be isolated either for smoothly moving objects or for random-dot kinematograms with short-lived dots. While any dynamic stimulus can be decomposed into its spatial and temporal frequency components, with the latter putatively used to measure psychological time, Kaneko and Murakami (2009) excluded this possibility and suggested that time dilates with speed per se presumably because the tick rate of the internal clock increases with speed, “an adaptation [that] would provide an ecological advantage in the prevention of accidents, avoidance of predators, and so forth” (p. 11). Nonetheless, they attribute to temporal frequency an equivalent effect, as “the speed-processing stage responds more vigorously with increasing flicker rate” (p. 11)—a claim supported by the literature (Fawcett, Barnes, Hillebrand, & Singh, 2004; Herrmann, 2001; Pastor, Artieda, Arbizu, Valencia, & Masdeu, 2003; Singh, Smith, & Greenlee, 2000). At the same time, the literature also shows that speed-processing mechanisms respond more vigorously to a moving stimulus in the presence of a surround moving in the opposite direction. 

Motion-receptive fields are known to be center–surround antagonistic (e.g., Allman, Miezin, & McGuinness, 1985; Eifuku & Wurtz, 1998; Jones, Grieve, Wang, & Sillito, 2001; Nakayama & Loomis, 1972; Raiguel, van Hulle, Xiao, Marcar, & Orban, 1995; Tadin, Lappin, Gilroy, & Blake, 2003). At least in the motion extrastriate MT+ complex and the equivalent human cortical area hMT+ (Eifuku & Wurtz, 1998; Moutsiana et al., 2011; Takemura et al., 2012)—but also, though not systematically, in V1 (Heeger, Boynton, Demb, Seidemann, & Newsome, 1999; Jones et al., 2001)—neurons' response to their preferred motion direction in the center of their receptive fields increases when the surround motion is in the opposite direction to that in the center and decreases when surround motion is in the same direction as that in the center. Moreover, the hMT+ response to a central moving patch encroached by a moving surround correlates with subjects' perceived speed of the central patch rather than with its physical speed relative to that of the surround (Takemura et al., 2012). Taken together with such findings, the present perceived speed results suggest that the observed perceived duration dependency on perceived speed is mediated by the response strength (or, equivalently, by the amount of energy used to encode a stimulus; Eagleman, 2008; Pariyadath & Eagleman, 2007; Mayo & Sommer, 2012) of neural mechanisms at the hMT+ motion processing stage. The “amount of energy” account of duration perception belongs to the class of “intrinsic” (as opposed to “dedicated”) models of time perception, with some physiological support (see Eagleman, 2008; Ivry & Schlerf, 2008; Mayo & Sommer, 2012). The present findings comply with this view. Nonetheless, as noted by many (e.g., Eagleman, 2008; Gorea, 2011; Grondin, 2010; Ivry & Schlerf, 2008; van Wassenhove, 2009), the amount of energy cannot be the only substrate of our perception of short durations. For example, it cannot account for our capability of timing empty intervals (e.g., Grondin, 1993; Rammsayer, 2010), nor for a number of within- (e.g., Westheimer, 1999) and cross-modal (e.g., Roberts, 1982; van Wassenhove, Buonomano, Shimojo, & Shams, 2008) transfers of learned temporal estimation capabilities. In conjunction with the relevant physiological literature, the present report of duration modulation by perceived rather than by physical speed does, however, emphasize the significant contribution of early sensory mechanisms to our perception of time, at least partly indexed to their response strength. 

Acknowledgments

AG thanks Daniel Linares for helpful discussions and Delphine Rider for helping out with the programming. This work was supported by a grant ANR-12-BSH2-0005-01 to AG. 

Commercial relationships: none. 

Corresponding author: Andrei Gorea. 

Email: [e-mail]. 

Address: Laboratoire Psychologie de la Perception, Université Paris Descartes and CNRS, Paris, France.