Stimulus complexity and prospective timing: Clues for a parallel process model of time perception

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Acta Psychologica 128 (2008) 63–74

Stimulus complexity and prospective timing: Clues for a parallelprocess model of time perception

Florent Aubry a,b,*, Nicolas Guillaume a,b, Giovanni Mogicato a,b,c,Laure Bergeret a,b, Pierre Celsis a,b

a INSERM, U825, ‘Imagerie cerebrale et handicaps neurologiques’, Toulouse F-31000, Franceb Universite Toulouse III Paul Sabatier, Toulouse F-31000, France

c Ecole Nationale Veterinaire de Toulouse, Toulouse F-31000, France

Received 5 March 2007; received in revised form 27 September 2007; accepted 28 September 2007Available online 14 November 2007

Abstract

Whereas many studies have considered the role of attention in prospective timing, fewer have established relations between movementcomplexity and prospective timing. The present study aims at assessing to what extent motion complexity interferes with prospectivetiming and at delineating a neuropsychophysical plausible model. We have thus designed a visual paradigm presenting stimuli in sequen-tial pairs (reference comparison interval). Stimuli are motionless or moving according to different complexities, and stimulus complexitiesare intermixed within each pair. To prevent a possible attention-sharing effect, no concurrent task was required. Our study suggests thatmovement complexity is a key component of duration perception, and that the relative judgement of durations depends on spatio-tem-poral features of stimuli. In particular, it shows that movement complexity can bias subjects’ perception and performance, and that sub-jects detect that comparison intervals are longer than reference before their end. In the discussion, we advocate that the classical internalclock model cannot easily account for our results. Consequently, we propose a model for time perception, based on a parallel processingbetween comparison interval perception and the reconstruction of the reference duration.� 2007 Elsevier B.V. All rights reserved.

PsycINFO classification: 2340

Keywords: Prospective timing; Stimulus complexity; Human subjects; Reaction time; Perceptual discrimination

1. Introduction

Time plays an important part in the everyday life sincethe perception and the estimation of time allow the livingorganisms to adapt themselves to their environment. Ineffect, the temporal dimension of the perceived eventsmakes it possible to coordinate, plan and time theresponses to these events (for example, to escape from apredator, to intercept any target or to carry out a complexmovement). Humans thus have to manage a dynamic envi-

0001-6918/$ - see front matter � 2007 Elsevier B.V. All rights reserved.

doi:10.1016/j.actpsy.2007.09.011

* Corresponding author. Address: INSERM, U825, ‘Imagerie cerebraleet handicaps neurologiques’, Toulouse F-31000, France. Tel.: +33 5 61 7795 47; fax: +33 5 61 49 95 24.

E-mail address: [email protected] (F. Aubry).

ronment, where changes span a large range of rates, struc-tures, complexities and predictabilities. Therefore, to adaptto their environment and anticipate events or actions,humans have to cope with the spatio-temporal dimensionsof perceived events, not only by predicting their durations(absolute judgement), but also by comparing durations oftwo or more events (relative judgement). In this prospect,the ‘subjective present’, which is located in the range of afew hundred milliseconds to a few seconds (Buhusi &Meck, 2005), is of capital importance because it corre-sponds to the time-constants of the conscious behaviourand of the high level cognitive functions, that is, of pro-cesses allowing interactions with the environment by build-ing a representation of the world, and by planning,executing or supervising the intentional actions (Hazeltine,

mailto:[email protected]

64 F. Aubry et al. / Acta Psychologica 128 (2008) 63–74

Helmuth, & Ivry, 1997; Ivry, 1996). It has been shown thathumans use different strategies to evaluate event durationsaccording to whether they complete a retrospective evalua-tion of past events, or whether they perform a prospectiveestimate of the duration of a given event, based on an expli-cit observation of its temporal dimension (Zakay & Block,2004). The retrospective estimate rests on a rebuilding ofthe duration, primarily from non-temporal informationassociated with the event, i.e. information for which neitherdates nor durations are directly assigned. On the contrary,for a prospective estimate, the subject makes use of specificchronometric mechanisms. The present study considers thislast framework and aims at investigating interactionsbetween perception of moving stimuli and chronometricmechanisms, and at assessing to what extent complexityof stimulus movements is able to support prospective dura-tion perception.

Many studies have considered the role of the attentionin prospective timing by the means of dual-task paradigmsinvolving a parallel processing of temporal and non-tempo-ral information. These studies showed a time shortening(Zakay & Block, 2004). Indeed, when subjects are askedto perform non-temporal information processing in paral-lel with the temporal task, attentional resources are sharedbetween temporal and non-temporal tasks. Thus, theamount of attentional resources allocated to the temporaltask decreases, and durations are underestimated. More-over, the accuracy of judgement decreases as a functionof the amount (e.g., quantity or complexity) of non-tempo-ral information actually processed (Macar, 1996; Prede-bon, 1996) and tends to become less accurate (Brown,1995; Macar, 1996; Zakay, 1998).

On the other hand, since the beginning of the 20th cen-tury, several studies have established relations betweendynamic stimuli and timing processes. These studies werecarried out by using moving stimuli (Brown, 1995; Kanai& Watanabe, 2006) or by introducing temporal markersinto stimuli (e.g., visual flicker or auditory clicks) (Droit-Volet & Wearden, 2002; Treisman, Cook, Naish, &MacCrone, 1994), or concentric sinusoidal grating (Kanai,Paffen, Hogendoorn, & Verstraten, 2006), but withoutrequesting from the subjects a specific processing of thesemarkers. Allan (1979) and Fraisse (1984) have shown thatcluttered intervals appeared longer than empty intervals,whatever the interval size and the time estimation para-digm. Predebon (1996) and Brown (1995) showed thatstimulus motion lengthened perceived time, a phenomenoncalled time dilation. To explain such effect, Fraisse (1964,1984) advocated a mechanism based both on the numberof changes perceived during the event, or stimulus consis-tency, and on attention devoted to the temporal task. Orn-stein (1969) developed a storage-size model where judgedduration is assumed to increase with the amount of mem-ory storage space needed to encode the set of consistentepisodes that occurred during the temporal interval. Blockand Reed (1978) hypothesised that the duration judgementis an increasing function of the number of contextual

changes defined both by changes in the environment, suchas changes in stimulus properties, and in the subject (e.g.,mnemonic activities). Gibson (1979) advocated that theestimation of event duration is directly related to theamount of changes occurring during the event. Morerecently, Johnston, Arnold, and Nishida (2006) and Kanaiet al. (2006) underlined the role of the temporal frequencyin time distortion. In conclusion, these studies confirmedthat perceived duration is an increasing function of thestimulus complexity. However, the notion of complexityneeds to be refined, and relationships between complexity,number or frequency of events and accuracy of durationperception require to be more deeply addressed.

To account for involved cognitive processes, psycholo-gists have developed various computational cognitive mod-els to describe time perception both for animals and forhumans. The prominent psychophysical model is the ScalarExpectancy Theory (SET), developed in the 1970s by Gib-bon, Malapani, Dale, and Gallistel (1997). SET assumesthat the precision of duration judgements is proportionalto the time intervals under consideration, an instance ofWeber’s law (McCormack, Wearden, Smith, & Brown,2005). A task commonly used within the SET frameworkis the temporal generalization (Church & Gibbon, 1982),where subjects are first trained to recognise a standardduration and, then, have to judge whether the durationof a comparison interval equals the standard. The propor-tion of ‘equal’ judgements as a function of comparisoninterval duration produces the generalization gradientcurve. Among healthy subjects, this curve peaks usuallyat the standard duration and decreases apart.

The prototype of the processing levels of the SET mod-els is the ‘internal clock model’, which was developed in the1960s by Treisman (1963) and Church et al. as quoted in(Church & Gibbon, 1982). The model encompasses fourcomponents: a clock, a temporary buffer, a directory ofmeasurements and a comparator (Wearden, 1999). Toaccount for the role of non-temporal characteristics ofstimuli (e.g., movement or complexity), the authors arguedfor a possible modulation of the clock by the environmen-tal conditions (Burle & Bonnet, 1997; Penton-Voak,Edwards, Percival, & Wearden, 1996; Treisman, Faulkner,Naish, & Brogan, 1990). All models, alternative modelsmore biologically plausible than those based on the inter-nal clock (Matell & Meck, 2000) included, usually describehow subjects judge that two stimuli have equal or differentdurations. However, they are not well designed to accountfor how subjects judge stimuli of different types or com-plexities shorter than, equal to or longer than a given refer-ence. Neither do they well account for differences inreaction times according to judgements, stimulus charac-teristics and interval comparison durations.

To study how stimulus complexity interferes with dura-tion comparison and prospective timing, we have designeda visual paradigm where subjects had to perform prospec-tive duration judgements (Guillaume, 2005). To considerthe specific contribution of stimulus complexity and

F. Aubry et al. / Acta Psychologica 128 (2008) 63–74 65

prevent interference with attention sharing, no concurrenttask was required from subjects. To test whether complex-ity is a critical characteristic for time perception and com-parison, the paradigm involved stimuli presenting differentdegrees of movement complexity (i.e., motionless to ran-dom). Firstly, we hypothesised that duration measurementand memorization involve both temporal and non-tempo-ral characteristics of stimuli. We postulated that subjects’performance depends on stimulus complexity, and, espe-cially, that the less predictable the movement was, the lessbiased prospective time comparison was. Moreover, weconjectured that, when comparing two stimuli of differentcomplexities, whatever their position, stimuli with the lesspredictable movement were perceived as the longer. Inother words, the time order effect would depend on com-plexity order. Secondly, we hypothesized that judgements‘comparison interval longer than standard’ are anticipatedbefore the end of the comparison interval.

2. Method

2.1. Subjects

The study included 36 healthy (i.e., free of neurologicaldisorders), right-handed subjects from 18 to 65 years(42 ± 13.5 years), balanced in sex and with normal or cor-rected-to-normal vision. All participants were graduate andwere recruited from the laboratory. Care was taken not torecruit subject skilled in rhythmic activities such as dance,song or music.

Fig. 1. (a) Timing of the paradigm. A first stimulus, the reference, was presente1000 ms, then the comparison interval was displayed for variable durations betwdelay between the end of the comparison interval and the subject’s responseapproximately draw the virtual apices of the cube, which are actually not visiblscreen. Faces of the cubes are filled by random points. Note the fixation crossbetween stimuli also included the cross. We have re-used images provided by P25 Hz.

2.2. Apparatus

Visual stimuli were presented at the centre of a 15 inchLCD computer screen (Toshiba Satellite�, 800 · 600 mon-itor resolution, 60 Hz refresh rate). Subjects sat facing thescreen, at 1 m from the screen. Subjects’ responses andreaction times were acquired on the computer. Subjectsresponded by pressing key arrows of the computer key-board with their right hand. Reaction time was defined asthe delay between the end of the stimulus whose durationhad to be judged, and the subject’s response. The experi-mental control program was written in the SDL language,provided by Presentation� (Neurobehavioral Systems, Inc,Albany, CA).

2.3. Procedure

In all conditions, each stimulation was composed of twostimuli presented in sequential pairs (Fig. 1a). Stimuli werepresented in central view. They represented a cube of about17 cm in width and height (i.e., ±5 0 of visual angle), filledwith random points (Fig. 1b). Subjects had to judge ifthe duration of the second stimulus, or comparison inter-val, was shorter (S, response key: left-arrow), equal (E,response key: up-arrow) or longer (L, response key: right-arrow) than the first stimulus, or standard, also called here-after reference. This design slightly differed from classicaldesigns, for instance those used in the temporal generaliza-tion gradient, because, firstly, it involved no referencememory, as the reference stimulus was only stored in

d for a standard duration of 1000 ms. It was followed by a black screen ofeen 280 ms and 1720 ms. Subjects’ reaction times (RT) were defined as the. (b) Example of images composing the stimuli. At the left, black lines

e on the computer screen. At the right, an actual image as it appears on theat the centre of the image, visible on the image at the right. Black screenresentation� as examples. Moving images are presented at a frequency of

1 Indeed, for each complexity condition, the complete set (ten repetitionsand seven interval comparison durations) lasted for about 15min.Therefore, if we had presented the nine complete sets, the experimentwould have lasted for more than 2.5 h, trial runs and pauses included.


working memory and, secondly, because it used a ternarydecision choice in the place of the traditional binary forcedchoice (equal vs. non-equal). As argued by Rammsayer andUlrich (2001), such a ternary response provides moredetailed information on the mechanisms underlying tempo-ral judgement than the conventional binary scheme does.Indeed, disclosing the criteria on which subjects based theirjudgements and inferring their judgement strategy requiresthe analysis of the three types of judgements.

2.3.1. Movement complexity and conditions

Since our main purpose was to emphasize the role ofstimuli complexity in time perception, we defined three lev-els of complexity associated with three types of movement.Indeed, movement can be defined by different, but comple-mentary, parameters. One of these parameters concerns themotion complexity. In our work, complexity was defined interms of entropy, which quantifies the consistency of astring, i.e., its predictability (Gray, 1990). One centralresult on time is its scalar property, base of the SET theory,that is, the coefficient of variation (ratio between variabilityand mean) derived from temporal generalization gradientcurves is constant. Would this property only depend onthe temporal characteristics of stimuli, the temporal gener-alization gradient curves (curve for ‘equal’ judgement) forthe different complexities as well as the equivalent curvesfor ‘shorter’ and ‘longer’ judgements must coincide exactlywhen superimposed. Such proposition can be verified byusing homogeneous conditions, that is, conditions wherereference and comparison intervals were of the same com-plexity. To test if perceived temporal magnitudes dependon complexity, i.e., a possible lengthening or shorteningof duration experience, we have defined inhomogeneousconditions where reference and comparison intervals withdifferent complexities are compared.

First complexity, noted MOL, was the lowest. Itinvolved motionless images, as only one perspective ofthe cube was displayed. In this condition only stimulusends were unpredictable because both standard and com-parison interval durations were unknown to subjects. Tosimulate movements, the cube turned around its verticalaxis and the scenario was composed of a sequence of snap-shots lasting for 40 ms each, leading to a scenario with arefresh rate of 25 Hz. This rate was chosen to experienceobject motion, and not simply a succession of discretelydifferent stimuli. The second complexity, noted REG,involved a periodic movement. Whatever the stimulusduration, the cube was rotated regularly, from 0� to 90�then from 90� to 0�, in order to go back to its initial posi-tion at the end of the interval. It was thus impossible forsubjects to use spatial landmarks to estimate durations.REG complexity was moderate because the scenario wasrather predictable in terms of rhythm. The third complex-ity, noted RAN, was the highest. Images were presentedat random, from a randomized initial position, but on aver-age at the same frequency as for the REG. The associatedscenario was thus unpredictable.

Stimulation complexity (hereafter called ‘complexitycondition’) was defined by the combination of referenceand of comparison interval complexities. For example,REG/RAN means that reference complexity was REGand comparison interval complexity RAN, while REGalone stands for REG/REG.

2.3.2. Stimulation timing

To ensure that results can be contrasted between com-plexity conditions, all conditions must present the sametiming. Therefore, the standard stimulus lasted for1000 ms while the comparison one lasted for either thestandard duration (1000 ms) or any of the six non-standarddurations (namely, 280, 520, 760, 1240, 1480 or 1720 ms).This range of short durations below 2 s was chosen to pre-vent as much as possible explicit or implicit counting strat-egies (Fraisse, 1984). Delay between standard andcomparison interval was constant (1000 ms) and delaybetween the end of each pair and the beginning of the fol-lowing one lasted for 5 s.

To prevent subjects’ fatigue, the experiment lasted onlyfor about an hour. Therefore, we were not able to imple-ment all combinations of durations and complexities. Forhomogeneous conditions (i.e., same movement for bothstimuli of the pair), the seven comparison interval dura-tions were presented. For inhomogeneous conditions (i.e.,different movements), comparison intervals and referencesalways lasted for 1000 ms1.

2.3.3. ExperimentAll subjects received a single experimental session com-

posed of an initial trial run to familiarize the subject withthe task, followed by ten test runs. Trial and test runs wereidentical. Each run was composed of 27 presentations,divided into 21 homogeneous conditions (7 durations foreach complexity · 3 homogeneous conditions), and 6 inho-mogeneous conditions. Homogeneous and inhomogeneousconditions were presented at random. Instruction had beengiven to subjects to be exclusively interested in the tempo-ral characteristics of stimuli, not to use any explicit strategyof counting and to respond as quickly as possible. This lastinstruction enabled us to test if judgements ‘longer’ wereanticipated in accordance with our initial assumption.

To prevent subjects for developing strategies that maybias their performance, they were not informed of theexperimental design. Thus, they neither knew the numberof conditions nor that the reference duration was constantacross conditions, nor that there were 7 comparison inter-val durations for homogeneous conditions and only oneduration for inhomogeneous conditions. Neither did theyknow that the delay between stimuli of the pair wasconstant.

Fig. 2. ‘Equal’ judgements: (left) Temporal generalization gradient for a standard duration of 1000 ms (Error bars: 95% centred confidence interval).(right) Reaction times (Error bars: 95% centred confidence interval).


3. Results

Analyses related only to subjects’ answers given in time,i.e., within 2500 ms following the end of the second stimu-lus. Only in less than 1% of the cases did the subjects notanswer or answered out of time. Due to the number of dif-ferent stimulus conditions (7 temporal conditions into 3homogeneous conditions, MOL, RAN and REG, and 6inhomogeneous conditions), we have hypothesised nohabituation with regard to the reference duration. Thedebriefing meeting showed that, on average, the subjectsperceived 5 ± 22 standard durations whereas there wasonly one. Moreover, paired t-tests of both response ratesand reaction times between the first five runs and the lastfive ones showed no significant difference. Consequently,we assumed that no habituation to the reference durationhas occurred.

For both homogeneous and inhomogeneous conditions,we analysed rates of the three possible judgements (shorter,equal and longer) and reaction times. Differences in judge-ment rates according to complexity may indicate possiblebiases and variability of duration comparisons, that is, apossible involvement of non-temporal characteristics induration judgement. The analysis of ‘equal’ judgementsaddresses mainly measurement and memorization pro-cesses, whereas contrasting the conditions underlying thethree judgements discloses mainly the decision-making cri-teria. Moreover, considering reaction times may reveal pos-sible different strategies for completing the task accordingto conditions (i.e., stimulus complexity and comparisoninterval durations) and judgements.

3.1. Homogeneous conditions

First, we have analysed the generalized gradient curves,that is, the percentage of responses ‘equal’ according to the

2 Values rounded to the closest integer.

comparison interval duration (Fig. 2). This analysis wascarried out by using a 2-way ANOVA. Factors were thestimulus complexity: MOL, RAN, and REG, hereafternoted as ‘complexity’; comparison interval duration: 280,520, 760, 1000, 1240, 1480 and 1720 ms, hereafter notedas ‘duration’). ANOVA showed an expected significant‘duration’ effect (F(6, 730) = 246.76; p < 0.001), but also asignificant ‘complexity’ effect (F(2, 730) = 47.27; p <0.001) and an interaction between the two factors (F(12,730) = 12.5; p < 0.001). Comparison between stimuluscomplexities revealed that the interaction is essentiallydue to durations beyond 1000 ms. Globally, for this rangeof durations, the rate of ‘equal’ judgements is the highestfor the REG condition and the lowest for the MOL condi-tion. However, differences between conditions are at thelimit of significance at 1000 ms (p = 0.06) and significantbeyond 1000 ms. The REG and RAN conditions differ sig-nificantly at 1240 ms (t = 7.03, p < 0.001; 1480 ms: t =5.88, p < 0.001) and at 1720 ms (t = 3.90, p < 0.001), anddifference between RAN and MOL conditions is significantat 1240 ms (t = 4.48, p < 0.001) and tends to be significantat 1480 ms (t = 1.91, p = 0.55).

In parallel, we have performed a two-way ANOVA(‘complexity’ · ‘duration’) on reaction times (RTs). Dura-tions of 280 ms and 1720 ms were excluded because of thelow number of responses (i.e., less than 12) for, at least,one movement (Fig. 2). ANOVA showed no ‘complexity’effect, but a significant ‘duration’ effect (F(4, 2187) =12.564, p < 0.001). RTs significantly decreased up to1000 ms (t-tests between 520 and 760 ms: t = 3.96,p < 0.001, between 760 and 1000 ms: t = 4.22, p < 0.001)and they were practically constant beyond 1000 ms.ANOVA also revealed a weak interaction between thetwo factors (F(8, 2187) = 1.83, p = 0.066). Supplementarytests showed that interaction resulted from a differencebetween REG and RAN at 1240 ms (t = 4.99, p < 0.001).

As comparison intervals can be categorized as beingshorter than, equal to or longer than the standard, we havealso analysed ‘shorter’ and ‘longer’ judgements in terms ofrate of answers and reaction times.

Fig. 3. ‘Shorter’ judgements: (left) % of judgements (Error bars: 95% centred confidence interval). (right) Reaction times (Error bars: 95% centredconfidence interval).


For ‘shorter’ judgements (Fig. 3), a two-way ANOVA(‘duration’ · ‘complexity’) showed a significant ‘duration’effect (F(6, 730) = 1521.6; p < 0.001), and a significant‘complexity’ effect (F(2, 730) = 4.36; p = 0.013), but nointeraction between factors. In other words, profiles weremainly shifted along the duration axis, according to the‘complexity’ factor. In fact, points of subjective ‘shortness’(PSS), calculated by using a quadratic interpolation on theANOVA results were 720 ms, 760 ms and 762 ms, respec-tively, for the MOL, RAN and REG conditions. T-testsindicated that profiles of RAN and REG conditions arealmost identical according to duration, but the MOL pro-file was significantly lower than the other two at 520(t = 2.55, p = 0.011) and 760 ms (t = 2.44, p = 0.15).

In parallel, a two-way ANOVA (‘duration’ · ‘complex-ity’) on the rate of ‘longer’ judgements (Fig. 4) showed asignificant ‘duration’ effect (F(6, 730) = 637.95, p <0.001), a ‘complexity’ effect (F(2, 730) = 87.40, p < 0.001)and an interaction between factors (F(12, 730) = 15.53,p < 0.001). Therefore, not only were the profiles shiftedaccording to the duration but also they were more or lessspread out. This means that points of subjective ‘longness’

Fig. 4. ‘Longer’ judgements: (left) % of judgements (Error bars: 95% centrconfidence interval).

(PSL) calculated according to the same procedure as thePSS depended on the stimulus complexity (MOL:1067 ms, RAN: 1238 ms and REG: 1431 ms). In details,tests indicated that there exist no differences between com-plexities for durations below 1000 ms. Beyond 1000 ms, thethree profiles diverged. The RAN profile was between theREG (the lowest) and the MOL (the highest) profiles.RAN value at 1000 ms did not significantly differ fromthe REG value, while RAN value at 1720 ms did not signif-icantly differ from the MOL value. At 1000 ms and1720 ms, the REG and MOL values were significantly dif-ferent. At 1240 and 1480 ms, the three profiles differedsignificantly.

Finally, we have derived the equality range of durations,which represent the dispersion of the temporal generaliza-tion gradient curves. This range can be equated with a dif-ference limen. It was estimated as the difference betweenthe PSL and the PSS. We have also estimated a point ofsubjective equality (PSE) as the middle point of the equal-ity range. Therefore, we were able to calculate Weber’sfraction for each complexity condition as the ratio betweenthe equality range and the PSE (Table 1). Within MOL

ed confidence interval). (right) Reaction times (Error bars: 95% centred

Table 1Psychometric indices according to stimulus complexity condition:PSS = point of subjective ‘shortness’; PSL = point of subjective ‘longness’;PSE = point of subjective equality

Complexitycondition

PSS(ms)

PSL(ms)

PSE(ms)

Weber’sfraction

MOL 720 1067 894 0.39RAN 760 1238 999 0.48REG 762 1431 1097 0.61


condition, PSE was shifted towards short durations, mean-ing that comparison intervals were principally consideredas longer than the standard. Within RAN condition, PSEwas close to the standard, so judgements were nearly notbiased. Within REG condition, PSE was shifted towardslong durations, that is, comparison intervals were mainlyperceived as shorter than the standard. Moreover, Weber’sfraction was the largest for REG condition and the smallestfor MOL condition, which may signify that subjectsdetected more easily small variations of duration forMOL condition than for REG condition, and that the dif-ficulty of discrimination between durations for RAN con-dition fell between that of MOL condition and that forREG condition.

For analysing of RTs related to ‘shorter’ judgements, wehave excluded all durations beyond 1000 ms due to the lownumber of ‘shorter’ responses (i.e., less than 12) for at leastone condition. For the same reasons, we have excludeddurations lower than 1000 ms for the analysis of ‘longer’-related RTs. Both analyses were performed by using two-way ANOVAs (‘complexity’ · ‘duration’).

For ‘shorter’ judgements (Fig. 3), the ANOVA showed asignificant ‘duration’ effect (F(3, 2664) = 24.63, p < 0.001),a ‘complexity’ effect (F(2, 2664) = 16.86, p < 0.001) and asignificant interaction (F(6, 2664) = 2.51, p = 0.020). RTswere almost identical for the RAN and MOL conditions.Indeed, RTs were stable up to 520 ms, and then theyincreased according to the comparison interval duration.On the contrary, for the REG condition, RTs were always

Fig. 5. Homogeneous and inhomogeneous conditions when reference and comand accuracy (in black) of judgments, expressed in % of judgments. Accuracy imarked with *, actual TOE is negative. (Error bars: 95% centred confidence in‘shorter’ judgements in grey: ‘equal’ judgements in black: ‘longer’ judgements

lower and first decreasing, reaching their minimum around520 ms (520 ms: t = 5.41, p < 0.001) and 760 ms: t = 5.03,p < 0.001).

For ‘longer’ judgements (Fig. 4), the ANOVA showed asignificant ‘duration’ effect (F(3, 2394) = 45.77, p < 0.001)and a ‘complexity’ effect (F(2, 2394) = 4.85, p = 0.008)but no interaction. If RTs for RAN and REG conditionswere nearly identical, they were significantly shorter forthe MOL condition. For the three conditions, RTs weredecreasing according to the comparison interval duration,following a linear trend (see Appendix A for details). Toquantify this trend, we have performed a supplementaryANCOVA, which showed that the slope of the trend wasaround �0.5.

3.2. Inhomogeneous conditions

First, we analysed subjects’ performance according tocomplexity conditions. Performance was defined by twovariables, subject’s time order error (TOE) and accuracy.This analysis was performed by using a MANOVA onthe nine couples of variables (Fig. 5), each couple (TOE,accuracy) being associated with a complexity condition.

TOE is defined as the difference between percentages of‘shorter’ and of ‘longer’ judgements (Hellstrom, 1985). Itmeasures a tendency in erroneous judgements. Judgementaccuracy was defined as the percentage of ‘equal’, i.e. cor-rect judgements. Therefore, for homogeneous conditions,no presentation order effect will result in a null TOE(judgement errors randomly distributed between ‘shorter’and ‘longer’). For inhomogeneous conditions, performancerelated to pairs of reverse conditions (e.g., RAN/MOL andMOL/RAN) must be compared. No presentation ordereffect and no complexity effect will result in null TOEsand in identical accuracies (i.e., identical numbers of cor-rect judgements). Similarly, a complexity effect withoutpresentation order effect will result in identical not nullTOEs in magnitude, but with opposite sign, and in identi-cal accuracies. Finally, a presentation order effect willresult in any other combination.

parison interval durations are identical. (left) TOE magnitudes (in white)s the percentage of exact (i.e., equal) responses. For complexity conditionsterval). (right) Reaction times according to subjects’ judgements. In white:. (Error bars: 95% centred confidence interval).

Fig. 6. Percentage of ‘longer’ judgements for one type of movementcomplexity, whatever its position (i.e., reference or comparison interval),against another type. For example, REG > RAN (REG longer thanRAN) represents the ratio between the sum of the number of referencesREG considered as longer than comparison intervals RAN and ofcomparison intervals REG considered as longer than references RAN, andthe number of presentations of both reverse conditions REG/RAN andRAN/REG. (error bars: 95% centred confidence interval).


TOEs depended on the complexity condition (Rao(8,25) = 10.69, p < 0.001). To disclose subjects’ behaviour fac-ing with erroneous judgments, we compared TOEs withzero. For homogeneous conditions, TOE behaviour iscoherent with PSE shifting shown in previous analyses.For the RAN/RAN condition, TOE is not significant(t = 0.64; p = 0.527), meaning that subjects expressed‘shorter’ and ‘longer’ judgments at random. For the MOL/MOL condition, TOE is negative (t = 4.77; p < 0.001), thatis, subjects tended to judge comparison intervals longer thanreference more often than shorter. For the REG/REG con-dition, TOE is positive (t = 3.77; p < 0.001), that is, the judg-ment ‘shorter’ prevailed. Furthermore, a Newman–Keulspost-hoc test on significant differences showed that therewas no significant difference between TOE magnitudesbetween REG/MOL and MOL/REG conditions, but thatTOE depended on the RAN position, i.e. reference or com-parison interval. Random stimuli, whatever their position,were erroneously judged longer than motionless or periodicstimuli.

Accuracy depended on the complexity condition (Rao(8,25) = 8.97, p < 0.001). A Newman–Keuls pots-hoc test onsignificant differences showed that accuracy was betterfor homogeneous conditions than for non-homogeneousones. It allowed us to determine five groups of accuracy:the best accuracy (85%) for REG/REG condition; 75% ofaccuracy for RAN/RAN condition; between 60% and70% for MOL/MOL, MOL/REG and REG/MOL condi-tions; 55% for RAN/MOL condition; and worst accuracy(50% or less) for REG/RAN, MOL/RAN and RAN/REG conditions. In conclusion, subjects’ performance isthe worst when inhomogeneous conditions involved ran-dom stimuli. These results suggested that subjects’ perfor-mance depended to a certain extent on presentation orderof complexities, and that random complexity plays a spe-cific role. To assess this role, we analysed the number oftimes that stimuli of a given complexity were consideredas longer than stimuli of another complexity, being refer-ence or comparison interval (Fig. 6). For instance,‘RAN > REG’ is the number of times that RAN stimuliwere judged longer than REG stimuli, that is, the averagebetween shorter judgments for the RAN/REG conditionand longer judgments for the REG/RAN condition. AMANOVA on these six values (RAN > REG, REG >RAN, RAN > MOL, MOL > RAN, REG > MOL andMOL > REG) showed a complexity effect (Rao(5, 31) =15.51, p < 0.001). A Newman–Keuls post-hoc test onsignificant differences confirmed that random stimuli,whatever their position, were perceived without differencesin load, longer than periodic and motionless stimuli, andthat periodic stimuli were judged longer than motionlessstimuli.

These results showed that movement complexity is a keycomponent of time estimation. Consequently, the relativejudgment of durations between stimuli depended on intrin-sic features of stimulus movement and, to a certain extent,on the order of presentation of movement complexities.

Analysis of reaction times was performed by a two-wayANOVA (‘complexity’ · judgments: E, S, L) (Fig. 5). Itshowed a significant judgment effect (F(2, 3177) = 29.67,p < 0.001). A Newman–Keuls post-hoc test on significantdifferences concluded that RTs for longer judgments werethe shortest while RTs for shorter judgments were the lon-gest. Furthermore, the analysis exhibited an interactionbetween complexity condition and judgment (F(16,3177) = 3.20, p < 0.001). A Newman–Keuls post-hoc teston significant differences showed that interaction resultedmainly from the presence of RAN stimuli as reference.Indeed, whatever the complexity condition, post-hoc testconcluded that there exist two groups of RTs. Group ofshortest RTs gathers longer judgments, RAN/REGexcepted, and equal judgments, RAN/MOL and RAN/REG excepted. Group of longest RTs gathers shorterjudgements, RAN/REG longer judgments, and RAN/MOL and RAN/REG equal judgments.

4. Discussion

Our purpose was to assess the role of stimulus complex-ity in prospective timing. For this purpose, we havedesigned an experiment where stimuli varying in durationwere presented in sequential pairs; each stimulus of the pairdisplayed more or less predictable/complex movements.Subjects had to judge if the second stimulus, or comparisoninterval, was shorter than, equal to or longer than the firstone, or standard. As expected, we showed that whereas thesubjects’ judgement principally depends on the temporalfeatures of stimuli, complexity and presentation order alsoparticipated in the judgement. In the following discussion,we first consider the influence of movement complexity onperceptual processes. We examine how movement com-plexity may have induced differences in stimulus segmenta-tion, and differences in the balance between memory traceand attention. Secondly, we discuss the decision-makingprocess, pointing out that subjects anticipated theirresponses when they judged comparison intervals longerthan the standard. As a result, we argue that our results


cannot be completely explained by the ‘internal clock’model and, consequently, we propose an alternative twoparallel-process model.

‘Shorter’ judgements were almost independent frommovement complexity while ‘equal’ and ‘longer’ judge-ments were not. Therefore, PSE and PSL strongly covaryaccording to movement complexity. Such a dependenceof duration measurement on non-temporal informationhas been reported in the literature (Burle & Bonnet, 1997;Jantzen, Steinberg, & Scott Kelso, 2004; Penton-Voaket al., 1996; Treisman et al., 1990). Allan (1979) and Fraisse(1984) have shown that cluttered intervals appeared longerthan empty intervals, whatever the interval size, and thetime estimation paradigm (Predebon, 1996), Brown(1995) showed that stimulus motion lengthened perceivedtime.

As subjects were required not to use any explicit count-ing strategy, our results may be explained by an implicitcounting strategy that should facilitate duration estimationas explicit counting does (Grondin, Ouellet, & Roussel,2004). As actual judgements were strongly dependent onstimulus complexity, we can presume that duration mea-sure is based on subjective time units (STU) dependenton spatio-temporal characteristics like stimulus complexity(Fraisse, 1964; Glicksohn, 2001), which can modify sub-ject’s arousal and attention (Wearden, Pilkington, & Car-ter, 1999). Such a dependence on context is largelydescribed in the literature. For instance, in the frameworkof the internal clock model, it was proposed that contextmay modulate pacemaker frequency (Treisman et al.,1990; Wearden, Philpott, & Win, 1999). More generally,it was shown that stimulus segmentation (Zakay, Tsal,Moses, & Shahar, 1994) or that prior context (e.g., thenumber of preceding intervals or their structure, forinstance empty vs. filled) (Barnes & Jones, 2000; Grondin,2001; Jantzen et al., 2004; Kanai & Watanabe, 2006) influ-enced time perception. Furthermore, our results suggestthat subjects’ performance, described in terms of bias andvariability, is negatively correlated with stimulus predict-ability, supporting the hypothesis that time measure isrelated to the amount of perceived changes. In particular,the REG condition resulted in the best accuracy, but alsoin a positive TOE and the worst precision, pointing outthe difficulty of duration discrimination in this context.Distortions of event times induced by periodic visual stim-uli were underlined by many studies (Burle & Bonnet, 1997;Burle & Bonnet, 1999; Penton-Voak et al., 1996; Treismanet al., 1990; Wearden et al., 1999). As an example, Johnstonet al. (2006) and Kanai et al. (2006) recently supported theidea that temporal frequency may be the most fundamentalfactor in time dilation. However, our study also showedthat, in this context, periodicity or rhythm may also playa counteractive role since subjects were less able in differen-tiating durations when comparison interval is longer thanthe standard compared with other contexts. This may sig-nify that periodicity, or rhythm, competes not only withduration for acceding attentional resources, but also that

rhythm processing may be more automatic than time pro-cessing. Consequently, relationships between time andrhythm perception should be deeply investigated.

The subjective time unit concept is insufficient toaccount for the shift of PSE along durations according tostimulus complexity and TOE differences between reverseinhomogeneous conditions. The literature usually reportsa negative TOE for durations of the same order of magni-tude that those used in our experiment, that is, a tendencyof judging comparison interval duration lasting shorterthan the reference whereas it lasts for the same duration.Fraisse (1984) had pointed out a possible inversion ofTOE sign for durations less than 2 s, and the literaturereports that TOE sign and amplitude depend on the inter-stimulus interval (i.e., delay between comparison intervalsand standard) and on durations (Allan & Gibbon, 1994;Hellstrom, 1985; Hellstrom & Rammsayer, 2004). If judge-ments were exclusively based on comparison between sub-jective time units acquired during standard and comparisoninterval, homogeneous conditions should not present PSEshifting. Moreover, if TOE resulted only from the presen-tation order, subjects should be consistent in the TOE sign(i.e., negative, positive or null) whatever the homogeneouscondition, and if TOE resulted only from complexity, TOEmagnitudes should be identical for each pair of reverse con-ditions. Contrarily, our findings showed that subjects per-ceived differently durations according to complexityconditions and presentation order. For the MOL condition(motionless comparison interval and reference), we showedthat comparison intervals were preferentially judged longerthan the reference, result consistent with the literature.However, for the RAN condition, both stimuli were ratherjudged lasting identically and for the REG condition, com-parison intervals were judged shorter. For inhomogeneousconditions, random stimuli (RAN), whatever their posi-tion, were judged longer than the other stimuli. Besides,for the pairs of reverse conditions involving random stim-uli, TOE magnitude depended on the position of the ran-dom stimulus (higher TOE for RAN/REG than forREG/RAN, and for MOL/RAN than for RAN/MOL).For pairs involving motionless stimuli (MOL) and periodicstimuli (REG), no significant difference in TOEs magnitudewas detected. In parallel, for inhomogeneous conditions,accuracy showed an order effect exclusively for couplescomposed of motionless and random stimulus (MOL andRAN). Consequently, we can infer that relative judgementsof durations depend not only on movement complexity,but also on the presentation order, that is, as stated byJantzen et al. (2004), ‘‘on the method used to establishthe temporal reference’’. Asymmetries in TOE and accu-racy for inhomogeneous conditions and TOE inversionfor homogeneous conditions can be explained within theframework of sensation-weighting model of the subjectivedifference (Hellstrom, 2003). Indeed, this model states thatthe subjective difference between two stimuli is not the dif-ference between their magnitudes, but the differencebetween two compounds, one for each stimulus.


Compounds are weighted averages of sensation magni-tudes of stimuli and subjective magnitudes of their currentreference levels. In our experiment, sensation magnitudesand reference levels could depend on movement complex-ity, and weighting coefficients could depend both on move-ment complexity and on dissipation from memory ofinformation about the first duration (Hellstrom, 1985).So, further experiments are required in order to determinethe actual balance between memory trace decay, or mem-ory dissipation, and attention in the TOE. For instance,varying delay between reference and target could probememory trace decay.

According to our results, reaction times depended bothon the comparison interval durations and on stimulus com-plexity. This means that decision-making stage dependedon spatial and temporal characteristics of stimuli. Indeed,RTs associated with the judgement ‘shorter’ were approxi-mately constant, if not decreasing for condition REG, fordurations lower than the PSS. Beyond this value, theyincreased. This shows that the decision-making for judge-ments ‘shorter’ was of the same order of difficulty whateverthe duration for intervals clearly shorter than the standard.On the other hand, RTs associated with the ‘equal’ judg-ment were similarly decreasing for the three complexitiesup to durations around the PSE. Beyond this value, theytend to become constant. Such a behaviour means thatjudgements were facilitated for durations around the PSEin comparison with shorter durations, and remained ofthe same order of difficulty for longer durations. Finally,for ‘longer’ judgements, RTs decreased monotonouslyaccording to a linear trend whatever the duration and thecomplexity, even far beyond the PSL. Consequently, RTsmeasured as the delay between the end of comparisonintervals and response were shortened proportionally tothe duration. Moreover, inhomogeneous conditionsshowed that reaction times for erroneous ‘shorter’ judge-ments – both stimuli of the pairs having the same duration– were longer than reaction times for erroneous ‘longer’judgements. Considering both results on reaction timesfor ‘longer’ judgements, we may assume that subjectsacknowledged probably that stimuli were longer than thereference before stimuli finished.

In our experiment, Weber’s fraction is the best for MOLand the worst for REG. Within the framework of the clas-sical internal clock model (Church & Gibbon, 1982; Treis-man, 1963), Weber’s fraction, which measures accuracy,may thus reflect higher pacemaker rate for MOL conditionand lower rate for REG condition. Indeed, according tosignal theory, discrimination accuracy should improve assampling base (i.e., pacemaker period) gets shorter. Sucha dependence of pacemaker rate according to stimuli char-acteristics was already reported in the literature (Treismanet al., 1990; Wearden et al., 1999). Notwithstanding, thedependency alone is not able to account for the PSE shift-ing according to conditions. One must suppose that work-ing memory kept trace of spatio-temporal characteristics ofreference, and that, during the comparison interval mea-

surement, a feedback from the working memory towardsthe pacemaker is active. Feedback could modulate pace-maker rate. In accordance with PSE shifts, MOL conditionshould speed up pacemaker, REG condition should slow itdown, and RAN condition not modify its rate. Unfortu-nately, such a scheme led to previsions contradictory withour results. Indeed, for RAN/MOL condition, comparisonintervals should be considered longer than reference,whereas it was actually the opposite. Moreover, internalclock model is sequential by nature, and comparisonbetween the two stimuli can be made only once the secondstimulus duration has been acquired. Therefore, reactiontimes for the three judgements must be identical, or moreprobably, if one considers that the 3-way comparison ismade in two stages (equal vs. different else, if different,shorter vs. longer), RTs for shorter and longer judgementsmust be identical, but longer than those for equal judge-ments. To account for our results concerning inhomoge-neous conditions, it would have then to be supposed thatthe comparator strategy depends on the whole episode,i.e. on the memorising of characteristics and the order ofthe two stimuli. Nonetheless, this is insufficient to explainthe linear decrease of RTs associated with the longer judge-ment, according to comparison interval durations, whendurations are longer than the standard.

Consequently, we advocate a mechanism involving twoparallel processes, as already proposed by Eisler (1981),Gibbons and Rammsayer (2005) or Kristofferson (1977).Such a model should allow us to give a better account ofour results, in terms of judgement frequencies, of adequacyto the Scalar Expectancy Theory, and of reaction time.Furthermore, the model is consistent with the findings ofPfeuty, Ragot, and Pouthas (2003) who detected, fromelectrophysiological data, a central/left activity endingonce the judged duration reaches the standard, while theright activity continues until the end of the comparisoninterval.

Within the proposed model, a pre-emptive and non-interruptible process is devoted to the perception of theexogenous signal (the comparison interval). A second pro-cess replays reference during the comparison interval pre-sentation, reference reproduction being based onmemorized subjective time units. Judgments could resultfrom synchrony mechanisms (Ivry & Spencer, 2004; Meck& Benson, 2002), and phase sign analysis (McAuley &Jones, 2003). When comparison interval duration is shorterthan reference, reference reproduction is imperativelystopped once comparison interval ends, entailing a‘shorter’ judgement. This event is independent of attentionor arousal, so its temporal accuracy is rather good and vir-tually independent of non-temporal characteristics of com-parison intervals. On the contrary, when comparisoninterval is longer than reference, reference reproductionstops while the exogenous signal is still processed, leadingto a ‘longer’ judgement. ‘Equal’ judgements result fromthe simultaneous detection of comparison interval and ref-erence reproduction ends. ‘Longer’ and ‘equal’ judgements


are less reliable because reproduction is less accurate (For-tin & Rousseau, 1998; Grondin, 2005; Harrington et al.,2004; Monfort & Pouthas, 2003; Zakay & Block, 2004).Uncertainty originates, firstly, from reference encoding,and is thus associated with movement predictability, and,secondly, from the reproduction process itself, which cancompete with other processes for the access to attentionalresources (Zakay & Block, 2004). Moreover, limits of brainto detect simultaneous events or to discriminate temporallydistinct stimuli, and the stochastic character of neuronalactivity (Buonomano & Karmarkar, 2002) prevent anaccurate detection of synchrony.

5. Conclusion

Our experiment indicated that, as expected, the tempo-ral dimension is the main dimension supporting relativeduration judgements between stimuli. However, it corrob-orated the interference between movement complexityand time perception, as argued by different authors, suchas Fraisse (1964). Furthermore, it showed that stimulusmovement predictability/complexity is an important fac-tor. Indeed, the more predictable the stimulus, the less itsupports time perception. Moreover, our results suggestedthat ‘longer’ judgements are anticipated before the end ofthe comparison interval.

We have also pointed out that our results cannot be eas-ily accounted for by a serial processing such as the one pro-posed by the internal clock model. Consequently, we havesketched a new model for time perception, based on parallelprocessing between comparison interval perception and ref-erence reconstruction. Our model represents the differentsources of uncertainty in a general framework, based onpsychophysical characteristics assessed in previous studiesand without strong assumptions on measurement/countingmodels (Rammsayer and Ulrich, 2001). Besides, the modelaccounts for differences between reaction times according tosubjects’ judgements. Nevertheless, as mentioned by severalauthors, the internal clock model provides an interestingand useful framework in order to design and analyse exper-iments. Indeed, it provides three evident stages of durationperception: acquiring temporal information, memorisingthe information and comparing the acquired duration witha reference, all stages that have been useful to consider inthe building of our parallel model.

Appendix A. Methodology for testing a linear trend with anANOVA

The linear trend was determined by testing the followingtwo hypotheses for each homogeneous condition (RAN,REG and MOL): (i) differences between the first two mea-surements at 1000 and 1240 ms and between the last two at1480 and 1720 ms are equal i.e., y1 � y0 = y3 � y2; thiscontrast also means that y1 � y3 = y0 � y2 and y2 +y0 = y3 + y1; (ii) difference between extreme values at1000 ms and 1720 ms is 3 times the differences between cen-

tral values at 1240 and 1480 ms, i.e., y0 � y3 = 3(y1 � y2).Let us note that these hypotheses were expressed thanks tosix orthogonal contrasts, which were tested jointly. Thistest resulted in (F(6, 2395) = 0.89, p = 0.5), which meansthat the linear trend can be retained.

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Stimulus complexity and prospective timing: Clues for a parallel process model of time perception