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When will the ball rebound? Evidence for the usefulness of mental analogues in appraising the duration of motions.

Yves-Andre Fery [*]

This study explores the way people appraise the duration of motions when these are only seen momentarily. Three possible theoretical accounts of this skill were developed. The first and second held an analogy between the duration of motions and their visuospatial representations. The third account was based on the existence of a pure chronometrical representation. Three copies of a tennis ball trajectory were created to reproduce the characteristics of the trajectory in terms of each account. The participants first memorized the copy and then used it to appraise the duration of the actual hall trajectory seen only momentarily at the beginning of its flight. The performance of a group given the visuospatial copy paralleled those of a referent group who were allowed to see the actual referent trajectory to memorize its duration. Results showed the importance of visuospatial analogous representations. However, a spatial representation seems to allow better memorization of motion duration.

Even though people's knowledge about the behaviour of moving targets may not correspond to the veridical physical laws governing physical motions, people may paradoxically make rather precise appraisals about these motions through time and space (Cooke & Breedin, 1994; Forbus, 1983; Freyd & Jones, 1994). The effectiveness of such appraisals is evidenced by the fact that individuals rarely collide with dynamic entities if the entities have been previously and momentarily seen. This talent may be linked to the particular sensitivity of the perceptual system to change, as well as to the countless everyday life interactions with the natural events one has to process (Freyd, 1993; Hubbard & Bharucha, 1988; Kaiser, Jonides, & Alexander, 1986; Proffitt, Kaiser, & Whelan, 1990; Reed & Vinson, 1996). Yet the fluency of these spatiotemporal appraisals contrasts with the complex problem that the visual system must resolve, which consists of the processing of information through time. Experimental data on spatiotemporal perception are rare (Schill & Zetzsche, 1995) and natural motion has long been considered to be too complex to be studied (Cutting & Proffitt, 1981). This study explores the issue of how the duration of natural motion (a ball thrown into the air) remains accessible even when it is largely masked.

Perception of motion cannot be understood in terms of a compilation of frozen snapshots with dynamic activation as a special case of this capture. Rather, each motion seems to be endowed with its intrinsic dynamic form as an invariant (Johansson, 1950). The resulting phenomenal experience remains continuous. It has been established, for example, that when a moving target vanishes without warning, its final position is typically shifted in the direction of the anticipated motion. The resulting memory representation is always dynamic and, within this representation, forces act on the position of the object. This extrapolation process possesses a momentum referred to as a 'representational momentum' (Freyd & Finke, 1984) which, just like the moving physical object that cannot instantly be halted, must continue for some time on its path. The possibility that representational momentum reflects, in the perceptual system, the internalization of the principles of physical momentum because of inertia [1] has been dem onstrated. Hubbard and Bharucha (1988) reported, for example, that for a round target moving across a video screen--and which participants had to consider as a ball--forward displacement was greater horizontally than vertically. Interestingly, representational momentum is usually considered as a kind of priming or the anticipation of movements (Kosslyn, 1991; Kosslyn & Shin, 1994), reflecting the general apprehension of motions which mentally continue the path of objects that vanish for as much as several seconds. For instance, Schiff and Oldak (1990) asked the participants to guess when a car travelling transversally for 3 s and vanishing when it is a few seconds from a target will reach the said target. The mean appraisal reached 92% of the actual time for a vanishing time of 3 s.

In this context, mental imagery may play a major role and observed similarities between representational momentum and visual imagery have supported a connection between the two phenomena (Freyd, 1987; Kelly & Freyd, 1987). In figuring internal trajectories of objects going through the same intermediate physical and temporal states as the actual (external) trajectories would go through (e.g. Pylyshyn, 1981; Shepard, 1975), imagery is able to preserve the spatiotemporal characteristics of a dynamic event in an analogue form (i.e. independently of beliefs of tacit knowledge). Moreover, neurophysiological studies have suggested that visual imagery involves the use of visual processing areas. For example, Goldenberg et al. (1989), using a regional cerebral blood flow analysis (rCBF) which is impossible for participants to alter voluntarily, found activation of occipital and inferior temporal regions in participants performing visual perceptual tasks as well as tasks requiring the use of visual imagery. It has bee n proposed that an actual rotating object may be imagined as it perceptively rotates (Kosslyn, Pinker, Smith, & Schwartz, 1979; Shepard & Cooper, 1982). Just as people use vision to navigate, or to avoid or to intercept moving objects, they are able to mentally imagine object trajectories in order to anticipate their path (Kosslyn, Seger, Pani, & Hillger, 1990).

In a series of experiments using tennis ball trajectories (thrown by a compressed air-driven pitcher), Vain Hofe and F[acute{e}]ry (1991, 1993) concluded that visuospatial representations were involved, at least in part, in the appraisal of motion durations. Further support for this hypothesis was provided by F[acute{e}]ry and Vom Hofe (1998) who showed that high imagers--selected on the basis of the Visual Movement Imagery Questionnaire (Issac, Marks, & Russell, 1986)--predicted with greater accuracy than low imagers the duration of a largely masked ball flight. However, two questions remain. First, imagery is a sufficiently general concept that it can encompass several styles of processing (Farah, Hammond, Levine, & Calvanio, 1988). An image may contain both visual and spatial features or it may represent spatial features alone (Anderson, 1985) without visual information (such as form or colour). Thus, the dynamic representation used by high imagers may be based mainly on spatial dimensions rather than on an isomorphic image containing all of these perceptible features. Indeed, an even more refined representation (and certainly one requiring less cognitive effort) may have been used by the imagers. Such an image may have only a minimal (but sufficient) degree of analogy with the represented motion (i.e. distance covered by the tennis ball).

However, a second issue is that the low imagers' errors, which corresponded to less than 20% of the mean duration of the trajectory, suggest the use of other (non-imagined) means to appraise event duration. For example, some authors have proposed the existence of biological clocks which have more arbitrary relations with the perceived event in evaluating its duration (Treisman, 1984; Wing & Kristofferson, 1973). They are based on the activity of cyclic biochemical changes that exist in homeostasis (e.g. neuronal pulses), changes that emit regular signals with constant periods to fill the interval during which the external event is perceived. These biological clocks are made of a store of pulses which act as a metronome and also of a comparator and a counter. The counter may be switched on or off at the onset of specific external stimuli to provide measures of duration elapsing between such stimuli. The number of pulses accumulated during the observation of a motion may be memorized and thus give the duration of this motion event despite its partial vision.

The present study has two purposes: to explore the nature of the mental activity involved in the evaluation of the duration of motion and, in an additional phase, to ascertain the stability through time of this mental activity as it seems to be based on permanent mental structures (Abernethy, 1993; Futterweit & Beilin, 1994; Mandler, 1983).

INTRODUCTION TO THE EXPERIMENT

The task used in the pilot study and main experiment required participants to view a brief portion of a trajectory and estimate its total duration. Participants in the main study were given experience either with the actual trajectory, or with copies of different types. Three copies were constructed [2] of the referent trajectory. Each corresponded to one of the three theoretical accounts developed above. The first copy was visuospatial: the participants were shown the duration of the referent trajectory together with a reproduction of its shape and of the distance covered by the ball. In the second copy (spatial), the duration was presented with the distance alone. In the third copy (temporal), the participants benefited from a purely chronometric presentation of the referent trajectory. A fourth condition was used as a reference in which participants viewed, in its entirety, the actual referent trajectory to memorize its duration. Following exposure to one of these four representations, all the participants were presented with the actual referent trajectory, largely masked, and asked to use the representations they formed to appraise its duration. Performance of each experimental group was compared with the referent group to shed light on the nature of the mental activity involved in the evaluation of the duration of motion.

If a copy condition yielded performance similar to the referent condition, this would suggest that the features provided by the copy capture those of importance extracted and used from the referent. A replication of the experiment was performed one day later to ascertain the stability of the information derived from the copies through time. Prior to the main experiment, a pilot study was conducted to check that estimating the duration of air-driven ball pitches was feasible for lay participants.

Method

A group of 10 male participants with no experience of fast ball games (mean age = 25.3 years) and a group of 10 male tennis players (more than 10 years of practice, mean age = 24.9 years) volunteered to participate in the pilot study but were not engaged in the experiment. To control individual differences in movement imagery abilities, the Vividness of Movement Imagery Questionnaire (VMIQ; Issac et al., 1986) was used. Participants whose scores were between [pm] 1 SD relative to the mean were considered as normal imagers and recruited. Each participant had to observe a series of six referent trajectories. Each series was followed by a duration appraisal session (described in the 'Materials' and 'Procedure' sections of the main experiment). As studies interested in the memorization of a dynamic copy have found no beneficial effect in asking participants to focus on a particular parameter of the movement (when all its parameters are presented, however; den Brinker, Stiibler, Whiting, & van Wieringen, 1986; Wh iting, Bijlard, & den Brinker, 1987), the participants in the present pilot study were not explicitly asked to pay attention to the duration parameter of the trajectory. They were asked to keep 'clearly in mind the referent trajectory' and they were further instructed to do so 'in order to appraise the duration of the trajectory, later, when it would be largely masked'. After the first series, the performances of the lay group (-274 ms) differed significantly from the performances of the tennis player group (-193 ms; t(18) = 6.22,p [less than] .05). However, after the third series, there was no statistical difference between the two groups (i.e. -187 ms and -158 ms, respectively; t [less than] 1). This result showed that precise estimation of ball-flight duration is not a specific skill and that laypeople may rapidly reach good performances in this exercise. The initial differences can be explained by the lack of familiarity of laypeople with the environment and the material used (compressed air-driven ball p itchers). Indeed, in the third series, they estimated the referent duration with few errors, less than 10% of its duration (2510 ms).

MAIN EXPERIMENT

Participants

Forty-seven male university students at the University Ren[acute{e}] Descartes (mean age = 22.4 years) volunteered to participate. All were novices in fast ball games and reported normal vision. To control individual differences in movement imagery abilities, the participants were selected as in the pilot study using the VMIQ. Forty normal imagers were thus selected and assigned to five groups.

The experimental groups were the visuospatial group, the spatial group and the temporal group, whose performances were compared with the referent group. Finally, a control group was used who were not given any form of training on the trajectories.

The assignment to the five groups was carried out in such a way that the experimental groups were homogenous for mean appraisal scores obtained in a pre-testing session described below. The mean scores (constant error, CE in ms) of the five groups were --608 ms, --614 ms, --614 ms, --622 ms and --617 ms respectively, and expressed their mean appraisal of the referent ball trajectory duration (2510 ms). An analysis of variance on the mean scores showed that there was no significant difference between the five groups (F [less than] 1).

Materials

The experiment took placed in a gymnasium equipped with a large grey wall of uniform appearance. A compressed air-driven ball pitcher was used to throw yellow tennis balls.

Setting for presentation of referent trajectory. The ball was launched for a mean distance of 32.5 m (SD = .90 cm) with an average velocity of 19.4 m/s from the left to the right of each participant, thus describing a constant parabolic flight parallel to the participant's viewing plane. The length was obtained by positioning the cannon at an angle of 42[degrees] relative to the ground. Mean total flight time was 2510 ms. To preserve constant flight duration, each tennis ball was replaced after 200 launches. However, when the ball-flight duration did not reach the referent duration of [pm] 50 ms, the trial was removed and replaced by another one. Thus, during the experiment, 6% of the trials were removed. Each participant was installed 17 m from the trajectory and in front of the apex of the modal trajectory that culminated at 9.7 m. From the participant's point of view, the distance between the server and the rebound represented an angle of 87[degrees]. Participants wore a helmet designed to eliminate outsid e noise and had to lay their chin on a chinrest to reduce additional cues given by head movements.

Setting for duration appraisal of referent trajectory. Two 3 m x 2.7 m moving screens were placed at the participant's right (see Fig. 1) in such a way that he saw the ball launched by the pitcher for only 700 ms before it disappeared definitely behind the screens. A photoelectric cell connected to a microcomputer installed at the end of the cannon of the electric pitcher triggered the trajectory timer and the participant's appraisal timer. The rebound of the ball on the reception plates equipped with shock receptors (piezoelectric captors) stopped the trajectory timer. The other timer stopped when the participant pressed a desk-mounted button with the index finger of his preferred hand. The helmet worn by the participant also served to present auditory signals (100 ms in duration, 800 Hz and 40 dB) generated by the microcomputer.

Specific settings for copies. For the visuospatial copy, the referent trajectory of the tennis ball was reproduced accurately on the wall on its precise shape by a series of 10 strips of orange florescent paper (5 cm wide and 50 cm long). These strips were placed equidistantly 3 m apart (see Fig. 1, top). The referent duration was indicated by the first flash followed by the second flash 2510 ms later. The two flashlights were put in place--one at the beginning of the trajectory and the other at the rebound of the ball. The flashes went from left to right.

For the spatial copy, the setting was the same except that the 10 strips were removed. Thus the participants did not benefit from the reproduction of the shape of the trajectory.

For the temporal copy, the visual and spatial references were removed to avoid the participants using visuospatial references. They had to turn around to be presented with the temporal copy, via lights, placed 2 m apart, which produced flashes going from the participants' left to their right (Fig. 1, bottom).

Procedure

Pre-test session. Each participant performed individually. Following an introduction to the general procedure, each participant was given three familiarization duration appraisals. For this, the participant was told: 'Three seconds after the preparatory auditory signal, the ball will be launched. You will only see the beginning of its flight because it will disappear behind the two screens. You will have to appraise the precise duration of the trajectory by pressing the button at the exact moment of the rebound of the ball.' After this short practice phase, the participant had to perform six duration appraisals following the same instructions. No feedback on accuracy was provided. The pre-rest session was followed by the experimental sessions one day later.

Experimental sessions for visuospatial, spatial and temporal groups. There were five experimental sessions, each comprising the following four phases.

(1) Presentation of the referent trajectory. The participants were told: 'The referent trajectory will be presented in its entirety. For this, you are going to observe the tennis ball launched from left to right.' As in the pilot study, the participants were asked to keep clearly in mind the referent trajectory to appraise its duration when it would be largely masked.

(2) Presentation of the copy. Visuospatial copy--'Immediately after, you will be presented with a copy of the referent trajectory. An auditory signal will warn you that 3 s later you will see the first flash. When you see this flash, you have to imagine the trajectory from the launcher, moving in succession over all the anchor points located on the wall and then rebounding at the base of the last strip and the second flashlight, precisely when you see the second flash.'

Spatial copy--The instructions were the same except that participants were told: 'You will have to imagine the trajectory starting from the launcher and then rebounding at the base of the second flashlight, precisely when you see the second flash.'

Temporal copy--The participants turned around to view the copy and were told: 'You will have to imagine the beginning of the trajectory duration when the first flashlight produces the first flash, and its ending when the second flashlight produces the second flash.'

(3) Memorization. The instructions outlining the strategy one must adopt to form a representation of a copy ate of importance (Hall, Buckolz, & Fishburne, 1992; Landers, 1975). This led the experimenters to ask the participants to mentally rehearse only the copy they saw to avoid esoteric visualizations (Driskell, Copper, & Moran, 1994). The participants also had to indicate when they represented mentally the copy in order to ensure better control over their mental activity. Thus, immediately after the presentation of the copy, the participants of the groups were told: 'You will now have to memorize the copy with maximal precision. For this, after a 3-s delay, the warning signal will he presented again. It will inform you that 5 s later, you must mentally generate a reliable representation of the copy without, however, adding additional information. You have to give a vocal signal ('go/stop') at the beginning and at the end of your representation. Five seconds later, an auditory signal will warn you that the copy will be presented again after 3 a.' The copy was presented five times and thus mentally rehearsed five times.

(4) Appraisal of the duration. The participants were asked to appraise the duration of the referent trajectory following the same duration appraisal instructions as in the pre-rest session. They had to perform a block of 10 duration appraisals of trajectories run every 5 s.

Experimental sessions for referent and contra/groups. For the referent group, the experimental settings (strips and flashlights) were removed. The first three phases, which lasted 80 s, were replaced by an observation phase, also lasting 80 s, and during which the participants could see in their entirety six actual referent trajectories run every 10 s.

For the control group, the experimental settings (flashlights and strips) were also removed. After the presentation phase, the participants were told: 'Immediately after the presentation of the referent trajectory, you will have to count backwards from 395 or 532 for 75 s.' This was to prevent the participants from thinking about the trajectory and it replaced the second and third phases for the other groups.

The duration appraisal phase comprising a block of 10 trials terminated each of the five experimental sessions for both the referent and control groups. The instructions were the same but contained no reference to any copy.

Participants of each group were invited to ask about any aspect of the procedure they did not understand.

Results

To indicate the direction of the error, the constant error (CE) scores were calculated. [3] To measure the inconsistency of the appraisals, the variable errors (VE) were also calculated.

Analyses of CE

Figure 2 shows the mean CE scores. A 5 x 5 (Group x Block) analysis of variance with repeated measures on the last factor was conducted. There was a significant effect for Group as well as for Block (F(4,35) = 16.59, p [less than] .05; F(4,140) = 7.39, p [less than] .05, respectively). The Group x Block interaction failed to reach significance (F [less than]1). Planned comparisons on the main effect of group revealed that the visuospatial, spatial, temporal and referent groups produced significantly higher performances than the control group (F(l,35) = 28.6, p [less than] .05). Figure 2 suggests that the performances of the referent group and the visuospatial group did not differ from each other but that they did differ from the spatial group performances. Indeed, further analysis of the group source of variance revealed that the referent group s performances were not significantly superior to the visuospatial group's performances (F(1,35) 2.02, p [great than] .05), but that they were superior to the spatial group's performances (F(1,35) = 14.14, p [less than] .05). The visuospatial group outperformed the spatial group (F(1,35) 6.85, p [less than] .05). Finally, only a marginally significant difference was found between the performances of the spatial and the temporal groups (F(1,35) 3.67, p .063).

Analyses of VE

A 5 x 5 (Group x Block) analysis of variance with repeated measures on the last factor showed only a significant effect for Group (F(4,35) = 3.48, p [less than] .05). A planned comparison contrasting the performances of the visuospatial, spatial, temporal and referent groups with the performances of the control group was significant (F(l,35) 10.5, p [less than].05). However, further analysis did not reveal any difference between the experimental groups.

Discussion

The visuospatial group improved throughout the experiment and its performance came very close to that of the referent group whose participants were presented with the actual trajectory. This provided suggestive evidence that visuospatial representations of an external dynamic event may subserve the appraisal of its duration.

This result supports the importance of analogue representations of dynamic forms in the appraisal of their duration, and it underlines the importance of the specification of distance and shape parameters to constitute an effective mental counterpart of these dynamic forms. These results corroborate Poynter's (1989) observation that 'subjects in duration reproduction experiments frequently claim that they mentally replay the visual events (thereby) filling an interval as a strategy for reproducing the interval duration' (p. 327). Even without such a representation of the trajectory, the results showed that a chronometrical copy may provide some consistent and beneficial--though less precise--information. This lends support to the relevance of the chronometrical approach in duration perception. However, when na[ddots[i]}ve people are presented with actual trajectories they rapidly form (as demonstrated in the pilot study) an efficient copy of the trajectory. Comparison of results did not reveal any difference b etween the lay group (-- 187 ms) and the visuospatial group in the main experiment (Fig. 2). In their earlier study, F[acute{e}]ry and Vom Hofe (1998) used the same experimental set-up and the same appraisal groups, but without any recourse to copies. The high imagers (N = 10), with scores of --361 ins, outperformed the low imagers (N = 10) (-- 510 ins) on the last block of appraisals. Comparison of the previous and present results shows that the mean scores of the participants engaged in the visuospatial group (-- 378 ins) were not significantly different from the scores of the high imagers (t(14) [less than] 1). This gives further support to the idea that imagery is engaged in the appraisal of motion duration. The participants engaged in the temporal group (- 500 ins) did not have different scores from those of the low imagers (t(14) [less than] 1). Thus, it seems possible that the low imagers used a purely chronometrical copy.

Even though there is a statistical difference between the appraisals of the spatial and visuospatial groups, inspection of Fig. 2 suggests that a spatial copy alone (Kosslyn, 1991) supports relatively good performance. Moreover, the consistency (VE) of the appraisals did not differ between groups. Interestingly, some of the participants in the visuospatial group spontaneously acknowledged that the isomorphic image was an advantage at the start of the test but that, at the end of the experiment, they only imagined the trajectory 'moving over' the first and the final anchor points and, possibly, over the highest anchor point.

SECOND STAGE OF THE EXPERIMENT

In everyday life, people make precise appraisals about motions through time and space that seem to be based on permanent mental structures (Abernethy, 1993; Futterweit & Beilin, 1994; Mandler, 1983). To investigate this, the experimenters conducted a second stage of the experiment which tested the stability in memory of the representations elaborated during the first stage. A retention session was conducted two days later with the same participants. The underlying assumption was that if a representation endowed with the minimal and essential intrinsic information of the trajectory exists in memory, the retention session scores should, at least, exceed the pre-test scores and, at best, approach the fifth experimental session scores.

Method

The second stage of the experiment took place in a gymnasium with different architectural features to avoid participants using (previous) situational landmarks: otherwise, the experimental set-up was identical to that used previously. The participants were told that they had to appraise the same trajectory. After observing the trajectory once, the participants immediately performed two familiarization appraisals and 10 tested appraisals.

Results

Analyses of CE

A 5 x 3 (Group x Session) analysis of variance with repeated measures on the last factor showed a main effect of Group and Session (F(4,35) = 5.9, p [less than] .05; F(2,70) = 58.33,p [less than] .05, respectively (see Fig. 3)). The Group x Session interaction was also significant (F(8,70) = 2.8, p [less than] .05).

Planned comparisons in the Group effect revealed a significant difference between the performances of the control group and of the visuosparial, spatial, temporal and referent groups (F(1,35) = 11.11, p [less than] .05). Paired comparisons (LSD test) between the referent, visuospatial and spatial groups in the retention test showed a significant difference between the referent group and the visuospatial group only (p = .0074).

Analysis of the session source of variance showed that the retention scores were lower than the fifth session scores (F(1,35) = 71.81, p [less than] .05), but higher than the pre-test scores (F(1,35) = 13.8, p [less than].05). Further comparisons between the scores in the fifth block and in the retention test showed a significant decrease for the visuospatial group (F(1,35) 48.21, p [less than] .05), the spatial group (F(1,35) = 19.39, p [less than] .05), the temporal group (F(1,35) = 10.22, p [less than] .05) and the referent group (F(1,35) 1O.33, p [less than] .05).

Finally, comparisons of the performances of the groups between the retention and pre-test phases showed a significant difference for the spatial and referent groups only (F(1,35) = 4.52, p [greater than] .05; F(1,35) = 11.84, p [greater than] .05, respectively).

Analyses of VE

A 5 x 3 (Group x Session) analysis of variance with repeated measures on the last factor showed a significant effect for Session only (F(2,70) = 8.5, p [less than] .05). Further analysis in the main Session effect showed that the consistency of the performances improved only between the pre-test and the fifth session (F(1,35) = 15.81, p [less than] .05).

Discussion

These results suggest that a spatial copy, which displays only the trajectory extent, allows retention of the duration cures of the trajectory by the spatial group as efficiently as the referent group, whose members benefited from numerous presentations of the actual trajectory. The characteristics of this copy can be considered as revealing the processes used by people to appraise the duration of usual motions.

Interestingly, two of the eight participants engaged in the spatial group declared they were disappointed by the absence of the previous cues (flashes). However, five of the eight participants in the visuospatial group made the same remark about the absence of the previous cues (shape and distance cues, architectural characteristics of the gymnasium). This may be linked to a drop in performances during the retention session relative to the last experimental session, and may reveal a particular lability of the visuospatial copy which may be tied too closely to the external cues.

CONCLUSIONS

The purpose of this study was to explore the way vision may convey information across time. The authors have reason to argue that the visual system is endowed with analogue processing which is sufficiently efficient to appraise the duration of motions. Indeed, the seen trajectory in the experiment may have been coded in a way that preserved its spatiotemporal coherence. This illustrates the 'beautiful' simplicity of the dynamic forms of perception (Cutting & Proffitt, 1981) and the effortless and natural reasoning procured by imagery (Kosslyn et al., 1990). A fruitful way of viewing the encoding of the regularities in the movement of objects may thus reside in the underlying biological medium that instantiates the image and ensures its intrinsic autonomy. Interestingly, Forbus (1983) studied hypothetical mechanisms governing everyday reasoning concerning space and movement. Forbus built programmes that are able to infer resilient ball rebounding behaviours. Although such models are much simpler than the forma l theory of mechanics, their structures reflect people's qualitative experience of the world.

However, the functionality of analogical coding does not necessitate an automatic one-to-one mapping between the actual object or scene and its representation. A clear distinction must indeed exist between the perception of motion and its mental counterparts because, for example, retinal receptive fields do not mirror the visual events that project onto them and also because imagery involves a number of underlying processing components (Kosslyn, 1991). For instance, mental models that underline the spatial formation of images may represent specifically (i.e. nonarbitrarily) a large span of referents which preserve only a minimal degree of analogy with them (Johnson-Laird, 1983). Indeed, according to Denis and De Vega (1993), when interacting with moving objects it is possible to represent only their starting and finishing points, and it is not necessary to carry out a continuous visual exploration of the space between the two points. In the present experimental sessions, the scores in the spatial group impro ved and almost equalled those of the visuospatial group, showing that a reduction of the cues may be likened simply to a refinement. Moreover, this refined spatial model also seemed to have been more stable in time than the more sophisticated visuospatial model. This result may be explained simply by the fact that too much information has to be memorized in an isomorphic model while this is not the case in the simpler spatial model. Interestingly, Profitt and Gilden (1989) and Runeson and Frykholm (1983) proposed that people, in dealing with difficulties when construing dynamic events that are inherently multidimensional, make judgments about the natural motions of objects on the basis of just one parameter of information that is salient in the event. The present results are congruent with the idea that the control of sequences of eye movement in perceptual processes involves actively viewing cognitive models or global scanpaths rather than peripheral vision (Noton & Stark, 1971; Stark & Ellis, 1981; Zangemei ster, Sherman, & Stark, 1995).

Another interpretation may tentatively be proposed. It is motivated by the large decrease in the visuospatial group performances (--361 ms) in the retention session, and also by the remarks of the participants in this group who acknowledged that they were particularly disturbed by the change in the environment in the retention phase. Indeed, it is now well established that the coding and memorization of perceptual targets is determined either in relation to the landmarks surrounding the targets (external model) and/or in relation to the body (corresponding to a sensorial and/or motor mode of processing) (Paillard, 1991; Ventre, Flandrin, & Jeannerod, 1984). The presence of a structured ambient space may have triggered the use of the external model of reference, whereas the sole presence of a visual target within a more homogenous background (in the spatial group) implies the registration of the target location by the egocentric system. The latter system is evidently less sensitive to a change in the environm ent and may explain the more stable spatial appraisals of the trajectory in the retention session. Indeed, the decrease in performances during the retention session relative to the last experimental session was only --229 ms. Interestingly, when Orihara (1980) analysed the relation between mental imagery and time estimation, he indicated that when participants estimate a duration they use tenuous kinesthetic movements (i.e. an egocentric model of reference), and they use them as cues in estimating a given interval. This is--from the present authors' point of view--a good expression of motor theories of motion perception in that it tries to discover the traces of action in the perception of external events. Indeed, as it has recently been argued, event and action codes are commensurate, sharing the same representational domain (Prinz, 1997).

The duration of the ball trajectory may thus have been analogously encoded in the sensorimotor system that transforms the external spatiotemporal coherence of the trajectory into a more internal (bodily) equivalent. The results further support the existence of a permanent framework or schema of movement stored in memory that facilitates the perception of natural motions, a framework which probably fits into a deeper, refined structure which effortlessly guides the fusion of the different views of the motion (Cutting & Proffitt, 1981 ; Johansson, 1950, 1975). In line with this, Schill and Zetzsche (1995) proposed that fluid interactions between humans and their environment have a prerequisite: the existence of a dynamic spatiotemporal memory mapping time in space. Further research is underway to confirm the existence of such permanent structures for dynamic forms--in this case ball trajectories. This study seeks to show that the acquisition of a type of trajectory model may enhance the duration evaluation of m ore or less similar trajectories.

Acknowledgement

The authors thank James McCabe from the Technical Language Centre of the University Rend Descartes for his critical reading of the manuscript.

(*.) Requests for reprints should be addressed to Yves-Andr[acute{e}] F[acute{e}]ry, Laboratoire des Sciences du Sport, UFR STAPS, Universit[acute{e}] Ren[acute{e}] Descartes, 1 rue Lacretelle, 75015 Paris, France (e-mail: fery@staps.univ-paris5.fr).

(1.) Projectiles continue in their rectilinear motions in so far as they are not retarded by the resistance of the air or impelled downwards by the force of gravity (Newton (1687/1962)).

(2.) The term 'copy' has been used to designate the type of representational aid given to the participants. The term 'model' has been reserved for the theoretical approach and the interpretation.

(3.) As the participants always underestimated the actual duration of the trajectory, the CE scores were equivalent to the absolute errors (AE) in representing the amount of the deviation of the scores. Thus, the AE were nor calculated.

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Author:Fery, Yves-Andre; Hofe, Alain Vom
Publication:British Journal of Psychology
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Date:May 1, 2000
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