Does representational momentum reflect a distortion of the length or the endpoint of a trajectory?

Observers viewed a moving target, and after the target vanished, indicated either the initial position or the final position of the target. In Experiment 1, an auditory tone cued observers to indicate either the initial position or the final position; in Experiment 2, different groups of observers indicated the initial position or the final position. Judgments of the initial position were displaced backward in the direction opposite to motion, and judgments of the final position were displaced forward in the direction of motion. The data suggest that the remembered trajectory is longer than the actual trajectory, and the displacement pattern is not consistent with the hypothesis that representational momentum results from a distortion of memory for the location of a trajectory.     

Representational Momentum Beyond Internalized Physics

Abstract— Prediction of future motion is necessary in order to successfully deal with moving objects. Implicit measures have been used to evaluate the sources of information used in this task. For instance, observers may be asked to localize the final position of a moving target. Judgments have been found to be displaced in the direction of motion (forward displacement), suggesting that observers have internalized a mental analogue of physical momentum. However, more recent studies have shown that forward displacement may not be caused by cognitive mechanisms alone. Rather, predictive mechanisms at the perceptual and motor levels may contribute to the forward error. Supporting the notion that mechanisms of anticipation may be embodied, the forward error was found to depend on the execution of eye and pointing movements. Also, forward displacement depended on the motion type that was presented (smooth vs. jerky or implied), which suggests that attention moves to the next expected target position to facilitate responses to this position.     

Environmental invariants in the representation of motion: Implied dynamics and representational momentum,gravity, friction,and centripetal force

Memory for the final position of a moving target is often shifted or displaced from the true final position of that target. Early studies of this memory shift focused on parallels between the momentum of the target and the momentum of the representation of the target and called this displacementrepresentational momentum, but many factors other than momentum contribute to the memory shift. A consideration of the empirical literature on representational momentum and related types of displacement suggests there are at least four different types of factors influencing the direction and magnitude of such memory shifts: stimulus characteristics (e.g., target direction, target velocity), implied dynamics and environmental invariants (e.g., implied momentum, gravity, friction, centripetal force), memory averaging of target and nontarget context (e.g., biases toward previous target locations or nontarget context), and observers’ expectations (both tacit and conscious) regarding future target motion and target/context interactions. Several theories purporting to account for representational momentum and related types of displacement are also considered.     

Centripetal force draws the eyes,not memory of the target,toward the center

Many observers believe that a target will continue on a curved trajectory after exiting a spiral tube. Similarly, when observers were asked to localize the final position of a target moving on a circular orbit, displacement of the judged position in the direction of forward motion ("representational momentum") and toward the center of the orbit was observed (cf. T. L. Hubbard, 1996). The present study shows that memory displacement of targets on a circular orbit is affected by eye movements. Forward displacement was larger with ocular pursuit of the target, whereas inward displacement was larger with motionless eyes. The results challenge an account attributing forward and inward displacement to mental analogues of momentum and centripetal force, respectively.     

Attention maintains mental extrapolation of target position: irrelevant distractors eliminate forward displacement after implied motion

Observers' judgments of the final position of a moving target are typically shifted in the direction of implied motion ("representational momentum"). The role of attention is unclear: visual attention may be necessary to maintain or halt target displacement. When attention was captured by irrelevant distractors presented during the retention interval, forward displacement after implied target motion disappeared, suggesting that attention may be necessary to maintain mental extrapolation of target motion. In a further corroborative experiment, the deployment of attention was measured after a sequence of implied motion, and faster responses were observed to stimuli appearing in the direction of motion. Thus, attention may guide the mental extrapolation of target motion. Additionally, eye movements were measured during stimulus presentation and retention interval. The results showed that forward displacement with implied motion does not depend on eye movements. Differences between implied and smooth motion are discussed with respect to recent neurophysiological findings.     

Illusory motion and representational momentum

When a moving target vanishes abruptly, participants judge its final position as being ahead of its actual final position, in the direction of motion (representational momentum; Freyd & Finke, 1984). In the present study, we presented illusory motion and examined whether or not forward displacement was affected by the perceived direction and speed of the target. Experiments 1A and 1B showed that an illusory direction of movement of a target was perceived, and Experiment 2 showed that an illusory speed of a moving target was observed. However, neither the direction nor the magnitude of forward displacement was affected by these illusions. Therefore, it was suggested that the mechanism underlying forward displacement (or some extrapolation processing) uses different motion signals than does the perceptual mechanism.     

Comparing mislocalizations with moving stimuli: The Fröhlich effect,the flash-lag,and representational momentum

When observers are asked to localize the onset or the offset position of a moving target, they typically make localization errors in the direction of movement. Similarly, when observers judge a moving target that is presented in alignment with a flash, the target appears to lead the flash. These errors are known as the Fröhlich effect, representational momentum, and flash-lag effect, respectively. This study compared the size of the three mislocalization errors. In Experiment 1, a flash appeared either simultaneously with the onset, the mid-position, or the offset of the moving target. Observers then judged the position where the moving target was located when the flash appeared. Experiments 2 and 3 are exclusively concerned with localizing the onset and the offset of the moving target. When observers localized the position with respect to the point in time when the flash was presented, a clear mislocalization in the direction of movement was observed at the initial position and the mid-position. In contrast, a mislocalization opposite to movement direction occurred at the final position. When observers were asked to ignore the flash (or when no flash was presented at all), a reduced error (or no error) was observed at the initial position and only a minor error in the direction of the movement occurred at the final position. An integrative model is proposed, which suggests a common underlying mechanism, but emphasizes the specific processing components of the Fröhlich effect, flash-lag effect, and representational momentum.     

Larger forward memory displacement in the direction of gravity

An observer's memory for the final position of a moving stimulus is shifted forward in the direction of its motion. Observers in an upright posture typically show a larger forward memory displacement for a physically downward motion than for a physically upward motion of a stimulus (representational gravity; Hubbard & Bharucha, 1988). We examined whether representational gravity occurred along the environmentally vertical axis or the egocentrically vertical axis. In Experiment 1 observers in either upright or prone postures viewed egocentrically upward and downward motions of a stimulus. Egocentrically downward effects were observed only in the upright posture. In Experiment 2 observers in either upright or prone postures viewed approaching and receding motions of a stimulus along the line of sight. Only in the prone posture did the receding motion produce a larger forward memory displacement than the approaching motion. These results indicate that representational gravity depends not on the egocentric axis but on the environmental axis.     

The role of action plans and other cognitive factors in motion extrapolation: A modelling study

When observers are asked to remember the final location of an object undergoing apparent or implied motion, a forward displacement is observed. The magnitude of this form of motion extrapolation is known to depend on various factors including stimulus attributes, action plans, and other cognitive cues. Here we present a modelling approach that aims at bridging different existing theories of displacement within a single theoretical framework. A network model consisting of interacting excitatory and inhibitory cell populations coding for stimulus attributes like position or orientation is used to study the response to motion displays. The intrinsic network dynamics can be modulated by additional information sources representing action plans directed at the moving target or cognitive cues such as prior knowledge about the trajectory. These factors decide the extent to which the dynamic representation overshoots the final position. The model predictions are quantitatively compared with the experimental findings. The results are discussed in relation to theoretical ideas about processing principles underlying motion extrapolation and a comparison with neurophysiological findings linked to movement prediction is made.     

Why eye movements and perceptual factors have to be controlled in studies on "representational momentum"

In order to study memory of the final position of a smoothly moving target, Hubbard (e.g., Hubbard and Bharucha, 1988) presented smooth stimulus motion and used motor responses. In contrast, Freyd (e.g., Freyd and Finke, 1984) presented implied stimulus motion and used the method of constant stimuli. The same forward error was observed in both paradigms. However, the processes underlying the error may be very different. When smooth stimulus motion is followed by smooth pursuit eye movements, the forward error is associated with asynchronous processing of retinal and extraretinal information. In the absence of eye movements, no forward displacement is observed with smooth motion. In contrast, implied motion produces a forward error even without eye movements, suggesting that observers extrapolate the next target step when successive target presentations are far apart. Finally, motor responses produce errors that are not observed with perceptual judgments, indicating that the motor system may compensate for neuronal latencies.     

Comment and Reply Why eye movements and perceptual factors have to be controlled in studies on “representational momentum”

In order to study memory of the final position of a smoothly moving target, Hubbard (e.g., Hubbard & Bharucha, 1988) presented smooth stimulus motion and used motor responses. In contrast, Freyd (e.g., Freyd & Finke, 1984) presented implied stimulus motion and used the method of constant stimuli. The same forward error was observed in both paradigms. However, the processes underlying the error may be very different. When smooth stimulus motion is followed by smooth pursuit eye movements, the forward error is associated with asynchronous processing of retinal and extraretinal information. In the absence of eye movements, no forward displacement is observed with smooth motion. In contrast, implied motion produces a forward error even without eye movements, suggesting that observers extrapolate the next target step when successive target presentations are far apart. Finally, motor responses produce errors that are not observed with perceptual judgments, indicating that the motor system may compensate for neuronal latencies.     

Is direction position? Position- and direction-based correspondence effects in tasks with moving stimuli.

Five experiments were carried out to test whether (task-irrelevant) motion information provided by a stimulus changing its position over time would affect manual left-right responses. So far, some studies reported direction-based Simon effects whereas others did not. In Experiment 1a, a reliable direction-based effect occurred, which was not modulated by the response mode--that is, by whether participants responded by pressing one of two keys or more dynamically by moving a stylus in a certain direction. Experiments 1a, 1b, and 2 lend support to the idea that observers use the starting position of target motion as a reference for spatial coding. That is, observers might process object motion as a shift of position relative to the starting position and not as directional information. The dominance of relative position coding could also be shown in Experiment 3, in which relative position was pitted against motion direction by presenting a static and dynamic stimulus at the same time. Additionally, we explored the role of eye movements in stimulus-response compatibility and showed in Experiments 1b and 3a that the execution or preparation of saccadic eye movements--as proposed by an attention-shifting account--is not necessary for a Simon effect to occur.     

Adaptation to spiral motion in crowding condition

When a single, moving stimulus is presented in the peripheral visual field, its direction of motion can be easily distinguished, but when the same stimulus is flanked by other similar moving stimuli, observers are unable to report its direction of motion. In this condition, known as 'crowding', specific features of visual stimuli do not access conscious perception. The aim of this study was to investigate whether adaptation to spiral motion is preserved in crowding conditions. Logarithmic spirals were used as adapting stimuli. A rotating spiral stimulus (target spiral) was presented, flanked by spirals of the same type, and observers were adapted to its motion. The observers' task was to report the rotational direction of a directionally ambiguous motion (test stimulus) presented afterwards. The directionally ambiguous motion consisted of a pair of spirals flickering in counterphase, which were mirror images of the target spiral. Although observers were not aware of the rotational direction of the target and identified it at chance levels, the direction of rotation reported by the observers during the test phase (motion aftereffect) was contrarotational to the direction of the adapting spiral. Since all contours of the adapting and test stimuli were 90 degrees apart, local motion detectors tuned to the directions of the mirror-image spiral should fail to respond, and therefore not adapt to the adapting spiral. Thus, any motion aftereffect observed should be attributed to adaptation of global motion detectors (ie rotation detectors). Hence, activation of rotation-selective cells is not necessarily correlated with conscious perception.     

Localization of moving sound

The final position of a moving sound source usually appears to be displaced in the direction of motion. We tested the hypothesis that this phenomenon, termed auditory representational momentum, is already emerging during, not merely after, the period of motion. For this purpose, we investigated the localization of a moving sound at different points in time. In a dark anechoic environment, an acoustic target moved along the frontal horizontal plane. In the initial, middle, or final phase of the motion trajectory, subjects received a tactile stimulus and determined the current position of the moving target at the moment of the stimulus by performing either relative-judgment or pointing tasks. Generally, in the initial phase of the auditory motion, the position was perceived to be displaced in the direction of motion, but this forward displacement disappeared in the further course of the motion. When the motion stimulus had ceased, however, its final position was again shifted in the direction of motion. The latter result suggests that representational momentum in spatial hearing is a phenomenon specific to the final point of motion. Mental extrapolation of past trajectory information is discussed as a potential source of this perceptual displacement.     

Localization of moving sound

The final position of a moving sound source usually appears to be displaced in the direction of motion. We tested the hypothesis that this phenomenon, termed auditory representational momentum, is already emerging during, not merely after, the period of motion. For this purpose, we investigated the localization of a moving sound at different points in time. In a dark anechoic environment, an acoustic target moved along the frontal horizontal plane. In the initial, middle, or final phase of the motion trajectory, subjects received a tactile stimulus and determined the current position of the moving target at the moment of the stimulus by performing either relative-judgment or pointing tasks. Generally, in the initial phase of the auditory motion, the position was perceived to be displaced in the direction of motion, but this forward displacement disappeared in the further course of the motion. When the motion stimulus had ceased, however, its final position was again shifted in the direction of motion. The latter result suggests that representational momentum in spatial hearing is a phenomenon specific to the final point of motion. Mental extrapolation of past trajectory information is discussed as a potential source of this perceptual displacement.     

In space, the past can be recast but not the present

We address the relationship between perception and spatial, working memory. Specifically, we argue that perceptual experience following the creation of a representation of target location affects it in a systematic way. We designed a motor task in which observers had to point to the initial or final position of a horizontally drifting target embedded in a vertically drifting background. The target was perceived as having an illusory motion component in a direction opposite that of the inducer dots [Duncker, 1938, Source Book of Gestalt Psychology (London: Kegan Paul, Trench, Trubner and Co)]. For both positions, there was an identical time delay before the observer could respond. Nonetheless, estimates of the initial target position were significantly biased by the illusion in a direction opposite the perceived target motion, and both bias and variability were significantly greater than those of the target's final position. In prior studies on positional accuracy with induced displacement, a delay before a pointing response led to an unbiased position estimate obtained without delay to become biased, leading investigators to argue for a long-lasting, inaccurate cognitive system that overrules an accurate, nonetheless transient, motor one (Bridgeman et al, 1997, Perceptual Psychology 59 456-469). Since the same motor task with identical delay on either position yielded different outcomes, a hypothesis based on distinct motor and cognitive representations of visual space is untenable here. Instead, we argue that an online representation of the target's original position is updated in an ongoing fashion in order to reconcile the perceived illusion with the veridically perceived present (current target location).     

Going the distance: Extra-symbolic contributions to the symbolic control of spatial attention

Over the past 30 years, researchers have used symbolic cues such as spatial words and arrows to direct observers' attention to the location of target objects that appear at a single, fixed distance in simple visual environments; however, they have done so by using symbolic cues that provide only partial—directional—information about the spatial location of target objects. Thus, it remains unclear whether observers can only shift their attention broadly in the cued direction in response to these cues or whether they can shift their attention to the specific location of the target by combining an expectation about direction (derived from apprehension of the directional cue) with an expectation about distance (derived from some extra-symbolic cue). The results of two experiments showed that observers do shift their attention to relatively coarse spatial locations by combining expectancies about direction and distance, and that the extent to which observers do so is modulated by the presence of visible markers and the expected distance of the target. These findings are important because they provide the first evidence that extra-symbolic information about distance contributes to the symbolic control of spatial attention.     

线索呈现的时空特性对表征动量的影响

为揭示注意对表征动量的影响机制,我们结合线索提示和表征动量范式,通过两个实验比较高、低相关线索分别在诱导期间与保持间隔呈现对表征动量的影响,结果发现：(1)高相关线索的时间特性主效应不显著,最终位置均发生边缘性的向前偏移。(2)低相关线索呈现在诱导期间时,表征动量显著;呈现在保持间隔时,发生向后偏移。这些表明,随着注意增大,表征动量减小;高相关线索更有利于定位,而低相关线索易受时间特性的影响。研究结果验证表征动量的双加工理论。     

The role of perception in the mislocalization of the final position of a moving target

The judged final position of a moving stimulus has been suggested to be shifted in the direction of motion because of mental extrapolation (representational momentum). However, a perceptual explanation is possible: The eyes overshoot the final position of the target, and because of a foveal bias, the judged position is shifted in the direction of motion. To test this hypothesis, the authors replicated previous studies, but instead of having participants indicate where the target vanished, the authors probed participants' perceptual focus by presenting probe stimuli close to the vanishing point. Identification of probes in the direction of target motion was more accurate immediately after target offset than it was with a delay. Another experiment demonstrated that judgments of the final position of a moving target are affected by whether the eyes maintain fixation or follow the target. The results are more consistent with a perceptual explanation than with a memory account.     

Representational momentum for rotations in depth: effects of shadings and axis

Representational momentum is a positive memory distortion for an object's final position following the presentation of an implied event (J.J. Freyd, 1987). Positive memory distortions occur when observers accept test positions beyond the final presented position, or forward along the implied trajectory, as the same more readily than positions behind the final position. Four experiments explored implied events depicting rotations about various depth axes in shaded and silhouette conditions. Positive memory distortions were observed for all depth rotations under certain shading conditions, with some differences in the size of the distortion between axes. No directional effects (e.g., right vs. left) were observed. The overall positive memory distortions observed for depth rotations contrasted with the negative distortions previously observed for translation motion in depth (T.L. Hubbard, 1995 ).