Sensation Time

One main finding of Fröhlich was that the size of the mislocalization f increased with movement speed v, and that the ratio f/v proved to be fairly constant (Fröhlich, Reference Fröhlich1923). The fixed ratio f/v turns the spatial error into a temporal error, and Fröhlich interpreted the time constancy as an expression of the sensation time (“Empfindungszeit”). The sensation time was understood as the time between the retinal impact of light and the corresponding visual sensation (see also Kreegipuu & Allik, Reference Kreegipuu and Allik2003). Fröhlich saw the finding that the sensation time varied with the brightness of stimuli as plausible evidence for his explanation. It was, as expected, on the order of 100 msec with faint stimuli and about 50 msec with bright stimuli.

At first glance, the idea of sensation time appeared attractive to explain the localization error. However, the explanation was criticized early by the contemporaries of Fröhlich, both empirically and theoretically. Rubin (Reference Rubin1930), for instance, noted that reducing the size of the window (i.e., reducing the trajectory length) shortened the Fröhlich effect (see also Müsseler & Neumann, Reference Müsseler and Neumann1992) and thereby should also shorten the sensation time. Also, Metzger (Reference Metzger1932) proposed that the sensation time might be longer at motion onset than at positions further along the trajectory (similar the latency differences discussed to explain other spatiotemporal phenomena; e.g., see Bachmann, Reference Bachmann1999; Hubbard, Reference Hubbard and Ruppel2014; Whitney, Reference Whitney2002). However, these variations are not consistent with the basic idea of sensation time and are therefore theoretically problematic. Metzger (Reference Metzger1932) pointed out correctly that the concept of sensation time has to be applied not only to the onset of motion but to the entire motion trajectory. In this case, an observer should perceive the moving stimulus with a corresponding temporal delay, but at all positions of the trajectory.

Thus, the concept of sensation time could not provide a satisfactory answer to the question of why only the first positions were excluded from perception. Furthermore, at the time of Fröhlich it was not clear at all whether the first positions were perceptually missed or whether the first positions were simply displaced in the direction of motion.Footnote ² Only later studies revealed that observers have indeed no access to the first positions: In experiments of Müsseler and coworkers (Müsseler & Aschersleben, Reference Müsseler and Aschersleben1998, Exp. 5; Müsseler & Tiggelbeck, Reference Müsseler and Tiggelbeck2013, Exp. 1), observers failed to detect brief pattern changes at motion onset but were better in detecting the change at positions further along the trajectory (see also Ansorge, Carbone, Becker, & Turatto, Reference Ansorge, Carbone, Becker and Turatto2010 for evidence from reaction time studies). Thus, a mechanism is called for that prevents the very first positions from being perceived.

Metacontrast Masking and Lateral Inhibition

At first sight, accounts of the Fröhlich effect based on metacontrast masking and lateral inhibition seemed to explain the low visibility of the initial part of the trajectory (cf. Carbone & Ansorge, Reference Carbone and Ansorge2008; Geer & Schmidt, Reference Geer and Schmidt2006; Kirschfeld & Kammer, Reference Kirschfeld and Kammer1999; Piéron, Reference Piéron1935). Metacontrast masking was first described by Stigler (Reference Stigler1910) and refers to the observation that the visibility of a stationary, flashed target is reduced when it is followed by a mask in its spatial vicinity (visual backward masking). Backward masking is optimal when target and mask share common stimulus boundaries, for instance, when the target is a disk and the mask is a surrounding ring. Optimal stimulus onset asynchronies (SOAs) between target and mask are between 40 msec and 100 msec and are thus within the range of the temporal error in the Fröhlich effect. Piéron (Reference Piéron1935) was the first to hypothesize the Fröhlich effect to be caused by masking mechanisms.

Lateral inhibition has been used to interpret metacontrast masking (e.g. Bridgeman, Reference 376Bridgeman2006). The basic assumption is that the presentation of a stimulus elicits excitatory and inhibitory neuronal activity in a retinotopic (cortical) map, for instance in the form of a simplified Mexican-hat function (Figure 7.2a). The inhibitory parts could be crucial for the Fröhlich effect, and Geer and Schmidt (Reference Geer and Schmidt2006) proposed that multiple inhibitory connections from neighboring space have a cumulative masking effect on early parts of the target trajectory (Figure 7.2b). The authors interpreted the effect of trajectory length accordingly by assuming that inhibition from adjacent stimulus positions accumulates across the trajectory. Therefore, the Fröhlich effect increases with trajectory length.

Figure 7.2 Simplified assumptions (a) of lateral inhibition with stationary stimuli, (b) cumulative lateral inhibition with moving stimuli with regard to Geer and Schmidt (Reference Geer and Schmidt2006), and (c) metacontrast and visual focal attention with regard to Kirschfeld and Kammer (Reference Kirschfeld and Kammer1999, fig. 6). The latter figure illustrates only the additional excitatory and inhibitory neuronal activity, which is elicited by the motion of the stimulus.

However, if the area of lateral inhibition or any other masking mechanism just moves across a retinotopic map (cf. Figure 7.2b), there is no way to explain why only the first positions are excluded from the perception. This explanatory gap was already encountered by the sensation time account. As a matter of fact, the masking account predicts that most of the trajectory (except for the last position) should become invisible, because each stimulus presentation is masked by the subsequent stimulus presentations. Clearly, that is not the case. Therefore, an additional component is needed, which explains why the target becomes visible at all. In the subsequent accounts, this function was assigned to visual attention.

Visual Attention and Its Neuronal Implementation

At the end of the 1990s, two independently developed accounts refer to attentional mechanisms to explain the Fröhlich effect. Kirschfeld and Kammer’s (Reference Kirschfeld and Kammer1999) masking-plus-focal-attention account assumed that positions on the trajectory behind the target are masked (cf. Figure 7.2c), similar to (Reference Piéron1935) ideas and nowadays postulated by Geer and Schmidt (Reference Geer and Schmidt2006). The new assumption was that positions on the trajectory before the target are pre-activated by the target itself (cf. Figure 7.2c). The authors associated this pre-activation with mechanisms similar to cue-induced visual focal attention. Thus, the approach combines mechanisms of metacontrast masking and visual focal attention.

With regard to Kirschfeld and Kammer (Reference Kirschfeld and Kammer1999), focal attention ensures that masking does not occur along the entire trajectory. However, focal attention must first be shifted to the moving stimulus, and that is why the first positions of the trajectory are excluded from perception (the Fröhlich effect). Once attention has reached the moving stimulus, it becomes visible because masking is counteracted and overcome.

To support their view, Kirschfeld and Kammer (Reference Kirschfeld and Kammer1999) presented a rotating rod that was continuously illuminated and was additionally flashed with far higher energy when it first appeared. The resulting percept was actually of two bars: a flashed bar at the correct initial position, and a moving bar that was displaced in the direction of motion (the Fröhlich effect). The interpretation was that the transient, flashed illumination of the initial orientation was strong enough to overcome masking, while the initial portion of the moving bar’s trajectory was suppressed until the pre-activation (focal attention) was established. Further, Kirschfeld and Kammer concluded that perception of the moving bar had a shorter latency than perception of the stationary flashed bar, because the moving bar appeared ahead of the flashed bar and both bars appeared simultaneously (cf. the flash-lag effect; Metzger, Reference Metzger1932; Nijhawan, Reference Nijhawan1994; Rubin, Reference Rubin1930). The conclusion that moving stimuli have shorter latencies than flashed stimuli has also been confirmed in reaction-time experiments (Aschersleben & Müsseler, Reference Aschersleben and Müsseler1999).

The other attentional account was originally developed without reference to masking mechanisms.Footnote ³ Müsseler and coworkers (Müsseler & Aschersleben, Reference Müsseler and Aschersleben1998; Müsseler & Neumann, Reference Müsseler and Neumann1992, Exp. 6) simply started from three well-accepted attentional mechanisms used to explain effects with stationary stimuli (e.g., spatial cuing effects), but which should be equally applicable to situations in which stimuli are in motion (see also Ansorge et al., Reference Ansorge, Carbone, Becker and Turatto2010; Carbone & Pomplun, Reference Carbone and Pomplun2007; Kerzel & Gegenfurtner, Reference Kerzel and Gegenfurtner2004; Müsseler, Stork, & Kerzel, Reference Müsseler, Stork and Kerzel2002): (1) the presentation of a stimulus in the visual field elicits an attentional shift toward that stimulus; (2) an attention shift takes time; (3) a phenomenal representation of a stimulus is not available before the end of the attention shift. Applied to the Fröhlich-effect situation, this means that with the presentation of a moving stimulus, a visual focus shift is initiated, and while this shift is under way, the stimulus continues to move. The first phenomenal representation of the stimulus is available at the end of the focus shift, and this is what is observed in the Fröhlich effect.

Both attentional accounts were able to explain the main findings observed with the Fröhlich effect, for instance, that the Fröhlich effect increases with increasing target velocity. The effect of stimulus brightness (or stimulus contrast; Fröhlich, Reference Fröhlich1923) can be plausibly addressed by assuming that establishing focal attention or eliciting an attentional shift is more effective with bright than with faint stimuli. Further, both accounts predicted that cuing the onset position with a stationary stimulus reduced the Fröhlich effect. The observed reduction effect was small but reliable (Adamian & Cavanagh, Reference Adamian and Cavanagh2017; Kerzel & Müsseler, Reference Kerzel and Müsseler2002; Müsseler & Aschersleben, Reference Müsseler and Aschersleben1998; Whitney & Cavanagh, Reference Whitney and Cavanagh2000a). Finally, they explain why mislocalizations are more pronounced in the Fröhlich effect than in the flash-lag effect: At the beginning of the movement, attention is far from the moving object and a large mislocalization results. As the motion progresses, attention catches up with the moving object and the mislocalization is reduced (Müsseler et al., Reference Müsseler, Stork and Kerzel2002).

However, the attentional accounts have also serious problems with some findings: for instance, that an increase of trajectory length led to an increase of the Fröhlich effect (Rubin, Reference Rubin1930; Müsseler & Neumann, Reference Müsseler and Neumann1992, Exp. 6). The authors of the masking-plus-focal-attention account (Kirschfeld & Kammer, Reference Kirschfeld and Kammer1999) might integrate Geer and Schmidt’s (Reference Geer and Schmidt2006) assumption that inhibition from adjacent stimulus positions accumulates across the trajectory, which leads to larger Fröhlich effects with longer trajectories. The attention-shifting account of Müsseler and Aschersleben (Reference Müsseler and Aschersleben1998) has more difficulties to accommodate this finding. The solution could be a modification of their third assumption, which claims that a phenomenal representation of a stimulus is not available before the end of the attention shift. This claim may be too strong. Note that shifting attention toward a stimulus implies at least coarse knowledge of the stimulus location prior to the start of the shift. What happens when an attention shift cannot be successfully completed, as would be the case when the moving target has a short trajectory and has already disappeared from the screen? Taking the third assumption literally, no stimulus should be perceived at all. It is more likely that the coarse representation of the stimulus at the beginning of the attention shift together with the incoming position information during the shift establishes what is seen. In any case, the perceived position should be closer to the starting position, i.e., the Fröhlich effect would be decreased.

Another point is that both attentional approaches use different levels of description. While Kirschfeld and Kammer (Reference Kirschfeld and Kammer1999) selected a neuronal level of description to address masking and attentional processes, the attention shifting account of Müsseler and coworkers (Müsseler & Aschersleben, Reference Müsseler and Aschersleben1998; Müsseler & Neumann, Reference Müsseler and Neumann1992) was framed in a functional formal way, which leaves the neuronal processes unspecified. Therefore, Müsseler et al. (Reference Müsseler, Stork and Kerzel2002; see also Müsseler & Tiggelbeck, Reference Müsseler and Tiggelbeck2013) attempted to identify the attention-shifting component in the neuronal models of Kirschfeld and Kammer (Reference Kirschfeld and Kammer1999) and particularly in the dynamic-field account of Jancke and Erlhagen (Jancke et al., Reference Jancke, Erlhagen, Dinse, Akhavan, Giese and Steinhage1999; Jancke & Erlhagen, Reference Jancke, Erlhagen, Nijhawan and Khurana2010). The dynamic-field account, originally developed to explain the activity of neuronal populations in the primary visual cortex of the cat (Jancke et al., Reference Jancke, Erlhagen, Dinse, Akhavan, Giese and Steinhage1999) and then successfully applied to perceptual mislocalizations with moving stimuli (for an overview, see Jancke & Erlhagen, Reference Jancke, Erlhagen, Nijhawan and Khurana2010), assumes that the presentation of a stimulus forms an activation pattern that is not restricted to the area covered by the stimulus (see also Hubbard, Reference Hubbard1994). Rather, it spreads its activation to and integrates contextual information from the adjacent parts of the visual field. Therefore, in response to an afferent input, the activation is assumed to interact with new incoming information and, thus, modifies suprathreshold activity.

When a stimulus moves through the visual field, it can be assumed that the incoming information contributes to and modifies the activation pattern in such a way that a stimulus-driven bow wave of activity occurs, which moves continuously across the visual scene (Müsseler et al., Reference Müsseler, Stork and Kerzel2002). Depending on velocity, it peaks at or even ahead of the leading edge of the stimulus. Since the Fröhlich effect emerges in the buildup phase of the bow wave, activation is accumulated starting from the resting level. The movement resulted in a skew wave that exceeds the perceptual threshold (distance between resting level and supraliminal activation), and the Fröhlich effect is observed. It has been suggested that spreading subthreshold activation constitutes a neuronal correlate of a cue-induced attentional mechanism that alters the processing of spatial information (Bocianski, Müsseler, & Erlhagen, Reference Bocianski, Müsseler and Erlhagen2008, Reference Bocianski, Müsseler and Erlhagen2010; Kirschfeld & Kammer, Reference Kirschfeld and Kammer1999; Müsseler & Tiggelbeck, Reference Müsseler and Tiggelbeck2013; Steinman, Steinman, & Lehmkuhle, Reference Steinman, Steinman and Lehmkuhle1995). We will return to this point later in the chapter.

Mental Extrapolation (Visual Prediction)

Mental extrapolations often occur in everyday life. When, for instance, a tennis ball flies through the visual scene, a spatial lag between the ball’s position in the real world and its perceived position should emerge from neuronal transmission latencies. In order to hit the ball with a racket successfully, there must be some form of compensation, and this compensation might be in the motor system (e.g., Kerzel & Gegenfurtner, Reference Kerzel and Gegenfurtner2004). It overcomes the lag by predicting the position of the moving target forward.

However, in Nijhawan’s view (Reference Nijhawan1994, Reference Nijhawan2008; see also Hubbard, Chapter 9 in this volume), the lag is compensated not only by motor predictions but also by visual predictions. In this view, the flash-lag effect can be understood as the visualized percept of this prediction. The flash lags because the visual system extrapolates the position of the moving target, and this is what is seen. Thus, in the strong version of the extrapolation assumption, stimuli in motion are perceived at their real-time positions and do not lag behind. Alternative accounts assume different perceptual latencies for the flash and the moving target (e.g., Baldo & Klein, Reference Baldo and Klein1995; Whitney & Murakami, Reference Whitney and Murakami1998).

The extrapolation assumption is controversially debated (see, e.g., the discussion in Baldo & Klein, Reference Baldo and Klein2008; Krekelberg, Reference Krekelberg2008; Nijhawan, Reference Nijhawan2008; Whitney, Reference Whitney2008). Although also seen as an explanation for the Fröhlich effect (e.g., Maus, Weigelt, Nijhawan, & Muckli, Reference Maus, Weigelt, Nijhawan and Muckli2010), it is especially difficult to see how an extrapolation mechanism works at the onset position of moving stimuli. Predicting future positions of a target requires some knowledge about the target’s motion direction and velocity. As there is no preceding motion trajectory at motion onset, it is unclear how extrapolation could account for the Fröhlich effect. Here one must probably recruit mechanisms that have been introduced in the previous sections.

As a last remark, it should be noted here that a predictive component also exists in the masking-plus-focal-attention account (Kirschfeld & Kammer, Reference Kirschfeld and Kammer1999) and in the bow-wave account or dynamic field model, respectively (Jancke & Erlhagen, Reference Jancke, Erlhagen, Nijhawan and Khurana2010; Müsseler, et al., Reference Müsseler, Stork and Kerzel2002). The difference is that visual prediction determines the percept while a pre-activation only prepares an area for the target to be seen.

Taking into Account the Mislocalization Opposite to the Direction of Motion: The Onset-Repulsion Effect

As already noted in the Introduction, some studies also found mislocalization opposite to the direction of motion. Note that this error is contrary to the Fröhlich effect: In the onset-repulsion effect (Thornton, Reference Thornton2002), the judged onset position of the target was found to be consistently mislocalized opposite to the direction of motion (Figure 7.1d; see also Actis-Grosso & Stucchi, Reference Actis-Grosso and Stucchi2003; Hubbard & Motes, Reference Hubbard and Motes2002; Hubbard & Ruppel, Reference Hubbard and Ruppel2011; Kerzel, Reference Kerzel2002; Kerzel & Gegenfurtner, Reference Kerzel and Gegenfurtner2004).

Studies concerned with the onset-repulsion effect sometimes revealed contradictory findings. For instance, some studies found that an increment in velocity shifted the judged onset further opposite to motion direction (Kerzel, Reference Kerzel2002; Thornton, Reference Thornton2002), whereas other studies did not find any effect of velocity (Actis-Grosso & Stucchi, Reference Actis-Grosso and Stucchi2003; Hubbard & Motes, Reference Hubbard and Motes2002; Kerzel, Reference Kerzel2002; Müsseler & Kerzel, Reference Müsseler and Kerzel2004). Some authors found the onset-repulsion effect only with a relative judgment task (Kerzel, Reference Kerzel2002), whereas others did so also with an absolute positioning task (Müsseler & Kerzel, Reference Müsseler and Kerzel2004; Thornton, Reference Thornton2002). Further, the onset-repulsion effect seems to depend on motion type and motion direction. It is largest with smooth, continuous motions and decreases with implied motions (Kerzel, Reference Kerzel2004; Thornton, Reference Thornton2002). Finally, upward motion or right-to-left motion resulted in stronger onset-repulsion effects than downward or left-to-right motion (Thornton, Reference Thornton2002).

It is obvious that accounts in terms of sensation time, metacontrast, or attention simply do not apply to these findings, most obviously because perceptual processes could never have been triggered at positions where the target was never presented (opposite to target motion). Instead, explanations of the onset-repulsion effect often refer to non-perceptual mechanisms. For instance, it is possible that the onset position is accurately perceived but is distorted during the delay before the judgment is made. In this case the onset-repulsion effect would originate from a memory failure, similar to the proposed mechanisms underlying representational momentum (Freyd & Finke, Reference 394Freyd and Finke1984; for an overview, see Hubbard, Chapter 8 in this volume). It is also possible that in this case observers have an imprecise percept of the onset position and tend to estimate the origin of the motion post hoc, which is subject to biases (see discussion below).

However, mislocalizations of the type of representational momentum are in the direction of motion, and a mechanism is needed to explain why the onset-repulsion effect is in the opposite direction. Therefore, it has been discussed that estimations of the onset position run backward along the observed trajectory, as this reflects more natural, physical tendencies (Thornton, Reference Thornton2002). In the same vein, Runeson (Reference Runeson1974) reported that observers perceive an illusory deceleration at the onset of a motion even when the physical velocity is constant. This may result in an opposite error if the post hoc estimation of the onset position is calculated on the basis of constant motion along the entire trajectory.

The most critical point, however, is how to explain the contrary findings of the Fröhlich and onset-repulsion effects. It turned out that the experimental procedures used to measure the mislocalizations were quite different. In reports of the Fröhlich effect, observers were able to predict where the moving target would appear. For instance, the moving target always appeared at the fixed edge of a window (Fröhlich, Reference Fröhlich1923) or at two fixed eccentricities to the left or right of fixation (Müsseler & Aschersleben, Reference Müsseler and Aschersleben1998). In reports of the onset-repulsion effect, however, the moving target appeared randomly in a relatively large area (Hubbard & Motes, Reference Hubbard and Motes2002; Thornton, Reference Thornton2002), and observers were unable to predict the onset positions.

To examine the hypothesis that the error in motion direction (the Fröhlich effect) and the error opposite to motion direction (the onset-repulsion effect) originated from the predictability of onset positions, Müsseler and Kerzel (Reference Müsseler and Kerzel2004; see also Müsseler et al., Reference Müsseler, Stork and Kerzel2008) conducted experiments in which two different trial contexts were used. In the random context, the target appeared mostly at a random onset position in a large area of the computer screen (similar to Thornton, Reference Thornton2002), but in one-sixth of the trials the target appeared about 6.6° to the left or right of fixation (Figure 7.3). Only these trials of the random-context condition were compared with the trials of the constant-context condition, in which the target always appeared at the onset positions to the left or right of fixation (similar to Müsseler & Aschersleben, Reference Müsseler and Aschersleben1998). The judgments showed a huge difference between context conditions: The onset was localized –0.5° opposite to the direction of motion in the random-context condition (onset-repulsion effect) and 1.5° in the direction of motion in the constant-context condition (the Fröhlich effect). Thus, low predictability of onset positions led to the error opposite to the direction of motion, while high predictability of onset positions led to the error in the direction of motion.Footnote ⁴

Figure 7.3 Trial contexts and findings of Müsseler and Kerzel (Reference Müsseler and Kerzel2004, Exp. 1). In the constant-trial context, the target always appeared at constant onset positions (OP, black dots) to the left or right from fixation. In the random-trial context, the target appeared mostly at random OPs (grey dots) in a 30 x 30° field of the computer screen, but in one-sixth of the trials also at the constant OPs. In the data analysis, only these trials were compared with the trials of the constant context. The results showed that the onset was localized opposite to the direction of motion with the random context (negative localization error of –0.5°; the onset-repulsion effect) and in the direction of motion with the constant context (positive localization error of 1.5°; the Fröhlich effect).

With other authors (Actis-Grosso & Stucchi, Reference Actis-Grosso and Stucchi2003; Kerzel, Reference Kerzel2002; Kerzel & Gegenfurtner, Reference Kerzel and Gegenfurtner2004; Thornton, Reference Thornton2002), we assumed that the difference between context conditions originates from an error in the judgment phase. When positional predictability is low, as is the case in the random-context condition, observers may notice a target relatively late, and with every new trial they might become aware of a possible localization error. To avoid this error, they may overcompensate and point to positions opposite to motion. Consistent with strategic adjustments, differences between the random-context and constant-context conditions were visible after about 15–35 trials (Müsseler & Kerzel, Reference Müsseler and Kerzel2004, Exp. 4).

However, further experiments by Müsseler and Tiggelbeck (Reference Müsseler and Tiggelbeck2013) cast doubts on the overcompensation explanation. With regard to the overcompensation explanation, the error opposite to motion direction is assumed not to be a perceptual one, but to result from the tendency in the judgment phase to correct for the possible spatial error. Consequently, an overcompensation mechanism should mainly affect a localization task, but not a discrimination task. In an experiment of Müsseler and Tiggelbeck (Reference Müsseler and Tiggelbeck2013, Exp. 1), moving targets either started out as squares and changed to circles at different positions on the trajectory, or appeared as circles and did not change (cf. also Ansorge et al., Reference Ansorge, Carbone, Becker and Turatto2010). Observers’ task was to discriminate whether or not they perceived a square during the motion of the target. The overcompensation account expected equal or worse discrimination performance in the random-context condition than in the constant-context condition. This result would point out a response bias, which compensates for a possible localization error in the judgment phase. However, the contrary finding was observed: When the squares appeared in the very first positions of the motion, better discrimination performance was found in the random-context condition than in the constant-context condition. Thereafter, the difference between context conditions vanished.

This finding was somewhat surprising, as it indicated worse perceptual performance in the constant-context condition. And this disadvantage of the constant-context condition was somewhat counterintuitive: When stimuli always appeared at predictable left/right positions, as is the case in the constant-context condition, observers could direct their attention to both positions in advance (parallel allocation of visual attention to two positions; cf. Awh & Pashler, Reference Awh and Pashler2000; Cave, Bush, & Taylor, Reference Cave, Bush and Taylor2010; Franconeri, Alvarez, & Enns, Reference Franconeri, Alvarez and Enns2007; but see also Jans, Peters, & De Weerd, Reference Jans, Peters and DeWeerd2010). Directing attention to a position usually improves spatial localization in this area, as was found in several studies with stationary targets (e.g., Bocianski et al., Reference Bocianski, Müsseler and Erlhagen2008, Reference Bocianski, Müsseler and Erlhagen2010; Tsal & Bareket, Reference Tsal and Bareket1999, Reference Tsal and Bareket2005; Tsal, Meiran, & Lamy, Reference Tsal, Meiran and Lamy1995; Yeshurun & Carrasco, Reference Yeshurun and Carrasco1999). Therefore, observers in the constant-context condition of Müsseler and Tiggelbeck (Reference Müsseler and Tiggelbeck2013) had not directed their attention to the left/right onset positions, or alternatively, directing attention to these positions produced worse localization performance.

To examine the last possibility, Müsseler and Tiggelbeck (Reference Müsseler and Tiggelbeck2013, Exp. 3) used an exogenous cue to direct attention in the random-context condition. The cue was presented at the onset positions, 280 msec before the moving target appeared. If, with moving stimuli, directing attention results in worse localization performance, presenting the cue should result in comparable mislocalizations in both context conditions. And this was what the results actually showed. When the cue preceded the motion onset, the localization error of the random-context condition increased in size relative to the localization error of the constant context.Footnote ⁵ Thus, Müsseler and Tiggelbeck’s experiments delivered consistent results. When observers allocated their attention to the onset position, worse discrimination performance (Exp. 1) went hand in hand with worse localization precision (Exp. 3).

An issue that remains unexplained is why attention improves discrimination and localization performance with stationary stimuli while it seems to impair discrimination and localization precision at the onset position of moving stimuli. We speculated that, contrary to stationary stimuli, moving stimuli require fast spatial disengagement (Petersen & Posner, Reference Petersen and Posner2012) from the previously attended position in order to follow the stimulus, especially at the onset position. It seems plausible that this disengagement could impair processing.

How to implement this idea in the neuronal dynamic field model discussed in the previous section? Bocianski et al. (Reference Bocianski, Müsseler and Erlhagen2008, Reference Bocianski, Müsseler and Erlhagen2010) already applied the model to an illusion with stationary stimuli and extended it by integrating a top–down attentional mechanism. In the empirical part of their paper, observers were confronted with blockwise presentations, similar to the random and constant context used by Müsseler and Kerzel (Reference Müsseler and Kerzel2004). The authors assumed that the blockwise presentation of a target at constant positions modulates the attentional baseline by arousing a peak at attended locations and by suppressing all other locations (for neuronal evidence see, e.g., Bestmann, Ruff, Blakemore, Driver, & Thilo, Reference Bestmann, Ruff, Blakemore, Driver and Thilo2007; Smith, Singh, & Greenlee, Reference Smith, Singh and Greenlee2000). Empirical and modeling data showed that localization precision was improved when the static target was presented in the attended area (Bocianski et al., Reference Bocianski, Müsseler and Erlhagen2010).

When, instead of stationary stimuli, a moving target is presented at the attended area, the only assumption to add is that the target might have left the region of the attentional peak already before a suprathreshold activity is reached. Moreover, the new incoming information of the target may interact within the previous activation pattern, which may additionally impair localization performance. In a sense, the postulated mechanism is similar to that accounting for effects of spatial disengagement from previously attended positions.

Note that this extension of the neuronal dynamic field model can only account for the observed differences between the random and constant context – that is, for the clear mislocalizations in motion direction in the constant-context condition and the more or less precise localizations in the random-context condition. It cannot account for the onset-repulsion effect per se – that is, for the error opposite to motion direction.

Characteristics of the Target

Variables influencing representational momentum that are related to the target include (a) velocity, (b) distance traveled, (c) direction, (d) shape, (e) identity and semantic category, (f) size, (g) eccentricity, (h) visual field, (i) involvement of a human form, and (j) nonvisual stimuli.

Velocity. Faster target velocity generally leads to larger forward displacement (e.g., Freyd & Finke, Reference Freyd and Finke1985; Hubbard & Bharucha, Reference 408Hubbard and Bharucha1988; de sá Teixeira, Hecht, & Oliveira, Reference de sá Teixeira, Hecht and Oliveira2013). If final instantaneous velocity is constant, then a previously accelerating or decelerating target exhibits larger or smaller, respectively, forward displacement (Actis-Grosso, Bastianelli, & Stucchi, Reference Actis-Grosso, Bastianelli and Stucchi2008; Finke, Freyd, & Shyi, Reference Finke, Freyd and Shyi1986). Visual targets or auditory targets with an irregular velocity exhibit less representational momentum, presumably due to decreased predictability of the target (Getzmann & Lewald, Reference Getzmann and Lewald2009). Effects of velocity are diminished (a) with increases in implied friction (Hubbard, Reference Hubbard1995b), (b) if a target is initially stationary and subsequent motion is attributed to contact from another object (Hubbard & Ruppel, Reference Hubbard and Ruppel2002), (c) at very high velocities (Munger & Minchew, Reference Munger and Minchew2002), and (d) for single targets exhibiting continuous motion if observers cannot visually track that target (Kerzel, Jordan, & Musseler, Reference Kerzel, Jordan and Müsseler2001). A velocity effect has been found for changes in auditory pitch (Freyd, Kelly, & DeKay, Reference Freyd, Kelly and DeKay1990; see also Hubbard, Reference Hubbard1995a).

Distance. In most studies of representational momentum, distance traveled by the target is not a factor. Targets travel a fixed distance on every trial (e.g., 34 degrees of rotation, Freyd & Finke, Reference 394Freyd and Finke1984) or different distances of travel are counterbalanced or randomized across trials (e.g., Hubbard & Bharucha, Reference 408Hubbard and Bharucha1988). However, representational momentum decreases with increasing distance traveled by a launched target (Choi & Scholl, Reference Choi and Scholl2006; Hubbard & Ruppel, Reference Hubbard and Ruppel2002).Footnote ¹ Forward displacement decreases with increases in distance traveled by the target for patients with neglect or patients with right hemisphere damage, but not for control participants (McGeorge, Beschin, Colnaghi, Rusconi, & Della Sala, Reference McGeorge, Beschin and Della Sala2006). Relatedly, forward displacement decreases as a target approaches a boundary (Hubbard & Motes, Reference Hubbard and Motes2005) or edge of the display (de sá Teixeira & Oliveira, Reference de sá Teixeira and Oliveira2011); however, this latter finding probably reflects expected change in target motion rather than distance traveled.

Direction. Horizontal motion in the picture plane leads to larger forward displacement than does vertical motion, and downward motion leads to larger forward displacement than does upward motion (Hubbard, Reference Hubbard1990; Hubbard & Bharucha, Reference 408Hubbard and Bharucha1988). Differences between leftward motion and rightward motion are usually not found (e.g., Cooper & Munger, Reference Cooper, Munger, Eilan, McCarthy and Brewer1993; Hubbard, Reference Hubbard1990), but when a difference is found, rightward motion is larger (e.g., Halpern & Kelly, Reference Halpern and Kelly1993). Forward displacement occurs for target motion in depth (e.g., Hayes, Sacher, Thornton, Sereno, & Freyd, Reference Hayes, Sacher, Thornton, Sereno and Freyd1996) and is larger when motion is away from the observer (Hubbard, Reference Hubbard1996a; Nagai, Kazai, & Yagi, Reference Nagai, Kazai and Yagi2002). Forward displacement along the line of sight occurs with motion of an observer’s viewpoint through a scene (Munger, Owens, & Conway, Reference Munger, Owens and Conway2005; Thornton & Hayes, Reference Thornton and Hayes2004). Forward displacement occurs for objects rotating in depth, and displacement is larger when rotation is around an axis that corresponds to observers’ and objects’ coordinate systems (Munger, Solberg, Horrocks, & Preston, Reference Munger, Solberg, Horrocks and Preston1999). Differences in displacement for rotation within the picture plane are usually not reported, although one study found displacement for a target moving along a rectangular clock frame was larger for clockwise motion than for counterclockwise motion (Joordens, Spalek, Razmy, & van Duijn, Reference Bartolomeo, Urbanski, Chokron, Chainay, Moroni and Siéroff2004), and rotation is larger for targets rotating downward than rotating upward (Munger & Minchew, Reference Munger and Minchew2002; Munger & Owens, Reference Munger and Owens2004). Displacement for a target following a circular path is forward along the tangent and inward toward the center (Hubbard, Reference Hubbard1996b).

Shape. The majority of studies of representational momentum presented stimuli consisting of geometric shapes. If each inducing stimulus within a trial is a radically different shape, forward displacement does not occur; however, if inducing stimuli imply a consistent change of shape of a single object (e.g., growing consistently thinner, taller, larger, etc.), then forward displacement in the direction of implied change occurs (Kelly & Freyd, Reference Kelly and Freyd1987; White, Minor, Merrell, & Smith, Reference White, Minor, Merrell and Smith1993). Implied drag does not influence forward displacement of square or rectangular translating targets or rotating pyramid shapes (Cooper & Munger, Reference Cooper, Munger, Eilan, McCarthy and Brewer1993), although in a more extreme case, a line moving parallel to its major axis (i.e., its smaller edge facing the direction of motion) exhibited larger forward displacement than did a line moving parallel to the direction of its minor axis (Hubbard, Reference Hubbard2005a). Displacement is larger if an object moves in the direction it points (Freyd & Pantzer, Reference Freyd, Pantzer, Smith, Ward and Finke1995) or faces (Nagai & Yagi, Reference Nagai and Yagi2001; Vinson & Reed, Reference Vinson and Reed2002).

Identity. If a target is given a verbal label suggesting a specific direction of motion, displacement is larger in that direction. For example, an ambiguous shape exhibited larger forward displacement for upward motion if that shape was labeled “rocket” than if labeled “steeple” (Reed & Vinson, Reference Reed and Vinson1996). This suggests displacement is influenced by object-specific information, and such information is more likely to influence displacement if the target is prototypical of its category and has a typical direction of motion (Nagai & Yagi, Reference Nagai and Yagi2001; Vinson & Reed, Reference Vinson and Reed2002). Forward displacement is increased if an object moves in the direction of its typical (forward) motion (e.g., an airplane moving forward) than if that object moves in an atypical (backward) direction (Nagai & Yagi, Reference Nagai and Yagi2001).

Size. Implied mass of pyramid-shaped objects that rotate in depth does not influence forward displacement (Cooper & Munger, Reference Cooper, Munger, Eilan, McCarthy and Brewer1993). Larger horizontally moving targets exhibit greater downward displacement than do smaller targets, larger downward-moving targets exhibit larger downward displacement than do smaller targets, and larger upward-moving targets exhibit smaller forward displacement than do smaller targets (Hubbard, Reference Hubbard1997, Reference Hubbard1998); this suggests effects of size (mass) are represented by effects of weight, as weight is experienced in the direction of gravitational attraction (i.e., the vertical axis) and not in the direction of motion. More generally, represented location of a target is influenced by implied gravitational attraction (Hubbard, Reference Hubbard1990, Reference Hubbard1997), and this has been referred to as representational gravity (see de sá Teixeira, Reference de sá Teixeira2014; de sá Teixeira & Hecht, Reference Brendel, Hecht, DeLucia and Gamer2014; Hubbard, Reference Hubbard1995c, Reference Hubbard2005b; Motes, Hubbard, Courtney, & Rypma, Reference Dodds, van Belle, Peers, Dove, Cusack and Duncan2008; Zago, Chapter 10 in this volume). If participants estimate how long it would take to stop a moving target, more dense (massive) targets are estimated to take more effort, but not more time, to stop; this has been interpreted as suggesting mass and velocity might interact in representational momentum (de sá Teixeira, Oliveira, & Amorim, Reference 441Peyrin, Michel and Schwartz2010).

Eccentricity. Some studies reported representational momentum for a continuously moving target did not occur if participants maintained central fixation and could not track the target (e.g., de sá Teixeira, Hecht, & Oliveira, Reference de sá Teixeira, Hecht and Oliveira2013; Kerzel, Reference Kerzel2000), and so there was little initial incentive to look for effects of eccentricity on representational momentum. However, one study reported representational momentum for visual targets and auditory targets increased as final target location moved from central to paracentral regions of the visual field and decreased as the final target location moved from paralateral to lateral regions of the visual field (Schmiedchen, Freigang, Rubsamen, & Richter, Reference Rastelli, Tallon-Baudry, Migliaccio, Toba, Ducorps and Pradat-Diehl2013). For visual targets, the initial increase probably reflects decreases in resolution acuity in paracentral and paralateral regions (cf., increase in forward displacement of blurred targets, Fu, Shen, & Dan, Reference Fu, Shen and Dan2001). The reason for the pattern with auditory targets is less clear.

Visual Field. If a stimulus changing in size is presented on the midline of the visual field, and probes are presented to the left or right visual field, representational momentum for size is larger for probes in the left visual field with a retention interval of 500 msec, but this difference vanishes with longer retention intervals (White et al., Reference White, Minor, Merrell and Smith1993). Similarly, representational momentum for location in the picture plane is larger if targets are in the left than in the right visual field (Gottwald, Lawrence, Hayes, & Khan, Reference Gottwald, Lawrence, Hayes and Khan2015; Halpern & Kelly, Reference Halpern and Kelly1993). When targets are lower in the picture plane, representational momentum is larger for vertically moving objects (Hubbard, Reference Hubbard2001) and horizontally moving objects in the left visual field (Gottwald et al., Reference Gottwald, Lawrence, Hayes and Khan2015).

Human Form. Presentation of animated human figures (Verfaillie & Daems, Reference Verfaillie and Daems2002) or point-light walkers (Verfaillie, De Troy, & Van Rensbergen, Reference Verfaillie, De Troy and Van Rensbergen1994) leads to forward displacement for postures of those figures; however, one study found displacement for point-light characters limited to characters presented on a textured surface or from a static viewpoint (Jarraya, Amorim, & Bardy, Reference Jarraya, Amorim and Bardy2005). Representational momentum occurs for faces changing from a neutral to a more extreme expression (Uono, Sato, & Toichi, Reference 441Peyrin, Michel and Schwartz2010, Reference Lewkowicz and Minar2014; Yoshikawa & Sato, Reference Yoshikawa and Sato2006, Reference Yoshikawa and Sato2008; but see Thornton, Reference Thornton2014). Representational momentum occurs for changes in the direction in which a face is oriented, but is reduced when gaze direction of that face differs from the direction in which the face is oriented (Hudson, Liu, & Jellema, Reference Doricchi, Merola, Aiello, Guariglia, Bruschini and Gevers2009) or emotional expression was inconsistent with approach toward the observer (Hudson & Jellema, Reference Hudson and Jellema2011). Representational momentum occurs for hand gestures in sign language; displacement is larger for gestures in the typical direction of motion than in the reversed direction, but this might reflect differences in awkwardness of motion rather than semantic meaningfulness (Wilson, Lancaster, & Emmorey, Reference 441Peyrin, Michel and Schwartz2010). Such an awkwardness effect does not occur with a static stimulus (Munger, Reference Munger2015). Representational momentum for animation of a human hand is influenced by expectations regarding whether that hand would reach toward or withdraw from an object (Hudson, Nicholson, Ellis, & Bach, Reference Hudson, Nicholson, Ellis and Bach2016; Hudson, Nicholson, Simpson, Ellis, & Bach, Reference Hudson, Nicholson, Simpson, Ellis and Bach2016).Footnote ²

Nonvisual Stimuli. Remembered final pitch of a stimulus changing in auditory frequency exhibits forward displacement in pitch (Freyd et al., Reference Freyd, Kelly and DeKay1990; Hubbard, Reference Hubbard1995a; Johnston & Jones, Reference Johnston and Jones2006; Kelly & Freyd, Reference Kelly and Freyd1987). Remembered location in physical space of a sound source translating in the picture plane is displaced in the direction of motion (Getzmann & Lewald, Reference Getzmann and Lewald2007; Getzmann, Lewald, & Guski, Reference Bartolomeo, Urbanski, Chokron, Chainay, Moroni and Siéroff2004). Forward displacement for location of a moving sound source occurs at the beginning and end, but not middle, of the trajectory (Getzmann & Lewald, Reference Getzmann and Lewald2007). Oculomotor behavior does not influence auditory representational momentum for a moving sound source (Getzmann, Reference Getzmann2005). When pitch rises and falls in a predictable manner, displacement in final pitch is backward when listeners expect direction of pitch motion to reverse (Johnston & Jones, Reference Johnston and Jones2006). Representational momentum for a moving sound source increases as vanishing point moves from central to paracentral regions and decreases as vanishing point moves from paralateral to lateral regions (Schmiedchen et al., Reference Rastelli, Tallon-Baudry, Migliaccio, Toba, Ducorps and Pradat-Diehl2013). Changes in grasp aperture consistent with representational momentum occur when participants grasp opening or closing visual pliers (Brouwer, Thornton, & Franz, Reference Brouwer, Thornton and Franz2005) or two visual spheres moving toward or away from each other (Brouwer, Franz, & Thornton Reference Bartolomeo, Urbanski, Chokron, Chainay, Moroni and Siéroff2004).

Characteristics of the Display

Variables influencing representational momentum that are related to the display include (a) surface form, (b) whether the participant controls target motion, (c) retention interval, (d) prior probability a same response to a probe would be correct, (e) response measure, and (f) contrast between target and background.

Surface Form. The term “surface form” refers to the format in which the target is presented, and three formats have been used. The first is frozen-action photographs, and these are single static images drawn from a larger motion sequence (e.g., a person walking or jumping; e.g., Freyd, Reference Freyd1983; Futterweit & Beilin, Reference Futterweit and Beilin1994).Footnote ³ The second is implied motion (as in Figure 8.1), and this involves a series of separate static stimuli that imply motion in a specific direction (e.g., a series of rectangles at different orientations; Freyd & Finke, Reference 394Freyd and Finke1984). The third is continuous motion, and this involves a target that appears to exhibit smooth and uninterrupted motion (e.g., Hubbard & Bharucha, Reference 408Hubbard and Bharucha1988). No difference between implied motion and continuous motion for displacement in orientation of a rotating rod (Munger & Owens, Reference Munger and Owens2004) or a change in auditory frequency (Hubbard, Reference Hubbard1995a) have been found. Kerzel (Reference Kerzel2003c) reported forward displacement for a target moving along a circular trajectory is less with continuous than with implied motion, and Faust (Reference Faust1990) found displacement for a horizontally moving target is less with implied than with continuous motion. Comparison of displacement across different surface forms is difficult, as direction and other characteristics of motion depicted with each type of surface form are typically different.

Control. If observers control velocity and direction (turning points) of a target, then forward displacement if that target vanishes without warning is less than if observers do not have such control (Jordan & Knoblich, Reference Jordan and Knoblich2004). If observers have control over when the target vanishes, then forward displacement decreases with increases in the latency between when observers indicate the target should vanish and when the target actually vanishes (Jordan, Stork, Knuf, Kerzel, & Musseler Reference Jordan, Stork, Knuf, Kerzel, Müsseler, Prinz and Hommel2002; but see Hubbard, Reference Hubbard2005b). Control over when the target vanishes might interact with oculomotor behavior (Stork & Müsseler, Reference Stork and Müsseler2004). If participants have previous experience controlling a target or observing another person controlling the target, then forward displacement is larger than if participants do not have such experience (Jordan & Hunsinger, Reference Jordan and Hunsinger2008).

Retention Interval. Representational momentum increases during the first few hundred milliseconds after the target vanishes (e.g., Freyd & Johnston, Reference Freyd1987; Halpern & Kelly, Reference Halpern and Kelly1993). This increase occurs with implied motion and continuous motion targets (but has not been examined for frozen-action photographs). Some studies report representational momentum asymptotes (e.g., Finke & Freyd, Reference Finke and Freyd1985; Kerzel, Reference Kerzel2000), and other studies report declines in representational momentum with subsequent increases in retention interval (e.g., Freyd & Johnson, Reference Freyd and Johnson1987; de sá Teixeira, Hecht, & Oliveira, Reference de sá Teixeira, Hecht and Oliveira2013). However, many studies claiming representational momentum asymptotes did not examine representational momentum for extended retention intervals (e.g., Kerzel, Reference Kerzel2000, did not examine retention intervals longer than 500 msec). Studies of retention interval typically use probe response measures (see below), as such measures do not confound time to locate and move a cursor with retention interval per se (although see de sá Teixeira, Hecht, & Oliveira, Reference de sá Teixeira, Hecht and Oliveira2013).

Prior Probabilities. If error feedback suggests prior probability that a same response is correct is relatively small, then overall likelihood of a same response, but not representational momentum, is decreased (Ruppel, Fleming, & Hubbard Reference Doricchi, Merola, Aiello, Guariglia, Bruschini and Gevers2009). If actual or believed prior probability that a same response is correct decreases, the likelihood of a same response, but not the magnitude of representational momentum, decreases (Hubbard & Lange, Reference Hubbard and Lange2010). In other words, decreases in prior probability that a same response is correct on any given trial decreases height of the distribution of same responses but does not influence skew (shift) of that distribution. Decreases in actual or believed prior probability decrease false alarm rates, and decreases in believed prior probability decrease hit rates and beta but not d’ (Hubbard & Lange, Reference Hubbard and Lange2010). Prior probability is most relevant to studies using probe judgment, but it is not clear how prior probability is relevant to studies using cursor positioning or reaching response measures.

Response Measure. Three response measures have been used. The first is probe judgment, in which a stimulus similar or identical to the target is presented after the target vanishes and observers judge whether the probe is the same as or different from the target (e.g., Finke et al., Reference Finke, Freyd and Shyi1986), or, less commonly, whether the probe is to the left or right of final target position (e.g., Kerzel, Reference Kerzel2000). A disadvantage of probe methods is that high numbers of probes and replications of each probe type are required, and this leads to higher numbers of trials (e.g., typically 5–9 probe positions per target position). The second type is cursor positioning (referred to as mouse pointing by Kerzel, Reference Kerzel2003c), in which observers use a computer mouse to position the cursor at the location in a display corresponding to the final location of the target. By clicking a button on the mouse, display coordinates of the cursor are recorded and can be compared with display coordinates of the target (e.g., Hubbard, Reference Hubbard1990; Hubbard & Bharucha, Reference 408Hubbard and Bharucha1988). Cursor positioning typically requires fewer trials than does probe judgment, but some stimulus dimensions are not easily adapted to such a measure (e.g., visual brightness, auditory pitch). The third method is reaching, in which participants touch (with a finger) the location in the display where the target vanished (e.g., Ashida, Reference Ashida2004; Kerzel & Gegenfurtner, Reference Kerzel and Gegenfurtner2003). A disadvantage of reaching is that spatial resolution is typically not as precise as probe judgment or cursor positioning. There haven’t been many comparisons of response measures, but one study found probe judgments resulted in smaller estimates of representational momentum than did reaching (Kerzel, Reference Kerzel2003c).

Contrast. Displacement in remembered luminance of a target changing in luminance is backward (in the direction opposite to representational momentum; Brehaut & Tipper, Reference Brehaut and Tipper1996) and interacts with a bias toward the level of background luminance (Favretto, Reference Favretto2002). If a moving target on a dark background gradually decreases in luminance (decreases in contrast), forward displacement is larger than if a target travels a shorter distance before abruptly vanishing (Maus & Nijhawan, Reference Maus and Nijhawan2006). Weaker motion signals resulting from less contrast between target and background have been suggested to result in smaller displacement (Maus & Nijhawan, Reference Maus and Nijhawan2009), although this does not appear consistent with suggestions that weaker motion signals resulting from less continuous motion result in larger displacement (Kerzel, Reference Kerzel2003c). If a light or dark target is presented on a white or black background, representational momentum for target location is larger if contrast of target and background is high or increasing and lower if contrast of target and background is low or decreasing (Hubbard & Ruppel, Reference Hubbard and Ruppel2014).

Characteristics of the Context

The context includes physical and cognitive elements. Variables influencing representational momentum that are related to the context include (a) physical surroundings, (b) landmarks, (c) shadows and shading, (d) interactions with nontarget stimuli, (e) expectations regarding future target motion, and (f) attributions regarding the source of target motion.

Physical Surroundings. If a rotating target is embedded within a larger surrounding frame, representational momentum for the target is increased if the frame rotates in the same direction or is oriented slightly beyond the final target orientation, and representational momentum for the target is decreased if the frame rotates in the opposite direction or is oriented slightly behind the final target orientation (Hubbard, Reference Hubbard1993). Similarly, if a moving target is near a larger translating grating, representational momentum of the target is increased or decreased if the grating moves in the same or opposite direction, respectively, as the target (e.g., Whitney & Cavanagh, Reference Whitney and Cavanagh2002). If a target moves between stationary distractors (Gray & Thornton, Reference Gray and Thornton2001) or toward a stationary barrier (Hubbard & Motes, Reference Hubbard and Motes2005), forward displacement is decreased. If the target is expected to bounce off a barrier, forward displacement decreases as the target approaches the barrier and reverses at the moment of contact (Hubbard, Reference Hubbard1994; Hubbard & Bharucha, Reference 408Hubbard and Bharucha1988).

If observers view video clips from real-world scenes (e.g., train station, shopping mall), representational momentum for those scenes occurs even if different stimuli in a scene move at different velocities and in different directions (Thornton & Hayes, Reference Thornton and Hayes2004). Forward displacement of an observer’s viewpoint for motion into animated scenes (pyramid landscapes) occurs if probes tested specifically for representational momentum (Munger et al., Reference Munger, Owens and Conway2005). However, if probes were more general, then responses were more consistent with boundary extension (see also DeLucia & Maldia, Reference DeLucia and Maldia2006). Forward displacement of the viewpoint occurs for observers in driving simulations (Thornton & Hayes, Reference Thornton and Hayes2004). If viewpoint of a scene rotates to the left or right, then representational momentum for objects occurs and is larger for objects entering the scene than exiting the scene (Munger et al., Reference Munger, Dellinger, Lloyd, Johnson-Reid, Tonelli, Wolf and Scott2006) even though objects are stationary and it is the viewpoint that moves. Representational momentum for objects in a scene decreases if viewpoint motion involves rotation and translation rather than just rotation (Brown & Munger, Reference Brown and Munger2010).

Landmarks. Examples of context considered above were global in the sense of surrounding a target or occupying a large portion of the surrounding environment. However, context can be local in the sense of an object or landmark providing a single point of reference. If a target moves toward or away from a landmark, forward displacement of that target increases or decreases, respectively (Hubbard & Ruppel, Reference Hubbard and Ruppel1999). This probably reflects a combination of representational momentum with a landmark attraction effect (cf. Bryant & Subbiah, Reference Bryant and Subbiah1994); when representational momentum and landmark attraction operate in the same direction (motion toward the landmark), they sum, and forward displacement is large, whereas when representational momentum and landmark attraction operate in opposite directions (motion away from the landmark), they partially cancel, and forward displacement is small. A target is displaced toward a distractor that is flashed at the moment the target vanishes or during the retention interval, and although consistent with a landmark effect, it has been argued a briefly presented nontarget stimulus should not be considered a landmark (Kerzel, Reference Kerzel2002a).

Shadows and Shading. Information regarding shape or direction of motion provided by shading and shadows influences representational momentum. If the first and third (of three) inducing stimuli are convex, forward displacement is larger if the second inducing stimulus is not concave (cf. coherent motion; Kelly & Freyd, Reference Kelly and Freyd1987), but if inducing stimuli are replaced by luminance-polarized circles (white top-half and black bottom-half for convex; black top-half and white bottom-half for concave), there is no difference in displacement (Hidaka, Kawachi, & Gyoba Reference Doricchi, Merola, Aiello, Guariglia, Bruschini and Gevers2009); thus, effects of shape and shading were due to differences in perceived depth rather than luminance. If the apparent cast shadow of a horizontally moving target diverges from the path of the target, representational momentum is larger than if the cast shadow parallels or converges with the path of the target, and this suggests the diverging shadow is interpreted as suggesting motion toward the observer (Taya & Miura, Reference Taya and Miura2010). If paths of the target and shadow converge, downward displacement of the target is larger, and this was interpreted as suggesting downward motion. Information from shape and shading influences perceived direction of motion, which in turn influences representational momentum.

Interactions with Nontarget Stimuli. A tone that increases or decreases in auditory frequency does not influence forward displacement of a vertically moving visual target, but downward displacement of a horizontally moving visual target is larger if the tone descends than if the tone ascends (Hubbard & Courtney, Reference Hubbard and Courtney2010). If onset of a horizontally moving visual target is accompanied by onset of a tone, representational momentum for the visual target is decreased or increased if the tone terminates slightly before or after, respectively, the visual target vanishes (Teramoto, Hidaka, Gyoba, & Suzuki Reference 441Peyrin, Michel and Schwartz2010). A tone presented just before a visual target vanishes leads to backward displacement of that target (Chien, Ono, & Watanabe Reference Chien, Ono and Watanabe2013; but see Teramoto et al., Reference 441Peyrin, Michel and Schwartz2010). If a tone is presented only to the left or right ear, then backward displacement is larger if the tone is on the same side of space where visual motion originated. If observers are presented with separate visual and auditory targets moving across space, then if the nonjudged modality target vanishes before or after the judged modality target vanishes, displacement of the judged modality target is biased toward the vanishing position of the nonjudged modality target (Schmiedchen et al., Reference Schmiedchen, Freigang, Nitsche and Rübsamen2012). However, if the difference in vanishing times was greater than 2,000 msec, then effects of the nonjudged modality target on the judged modality target only occurred if participants judged auditory targets.

Examples in the preceding paragraph involved target stimuli and nontarget stimuli in different modalities. However, effects of cast shadows, barriers, and landmarks accompanying visual targets suggest nontarget stimuli in the same modality as a target influence representational momentum for that target. In these latter cases, there is no contact between targets and nontarget stimuli (e.g., Hubbard, Reference Hubbard1993), but contact between targets and nontarget stimuli can influence representational momentum for the target. If a target slides along a stationary surface, forward displacement of that target is decreased relative to forward displacement of an otherwise identical target presented in isolation or clearly separated from the larger stationary surface (Hubbard, Reference Hubbard1995b, Reference Hubbard1998). This decrease is referred to as representational friction (Hubbard, Reference Hubbard1995b, Reference Hubbard1995c), and decreases in forward displacement increase as implied friction on the moving target increases (Hubbard, Reference Hubbard1995b, Reference Hubbard1998). Illusory motion of a visual nontarget stimulus might (e.g., Hubbard et al., Reference Hubbard, Piazza, Pinel and Dehaene2005) or might not (e.g., Nagai & Yagi, Reference Nagai and Saiki2005) influence displacement of a visual target. Additional examples of nontarget influences are discussed in the section below on Attributions of the Source of Target Motion (Causality).

Expectations of Future Target Motion. If a target is expected to bounce off a barrier the target is approaching, then forward displacement decreases as the target approaches the barrier, and at the moment of contact, displacement is in the expected (new) direction rather than in the previous direction of motion (Hubbard & Bharucha, Reference 408Hubbard and Bharucha1988). A physical reason for a direction change does not seem to be necessary, as similar patterns occur when visual targets changing in location (Verfaillie & d’Ydewalle, Reference Verfaillie and d’Ydewalle1991), and auditory targets changing in frequency (Johnston & Jones, Reference Johnston and Jones2006), exhibit oscillatory motion in an otherwise blank display. Similarly, forward displacement is larger if a target bounces off rather than crashes through a barrier, as if elastic bouncing off preserved more momentum and rigid crashing-through depleted more momentum (Hubbard, Reference Hubbard1994); interestingly, this difference is stronger if observers received a valid cue (e.g., a cue of “bounce” and the target then “bounced”) than if observers received an invalid cue (e.g., a cue of “bounce” and the target then “crashed”). A similar combination of effects of expected target direction and actual target direction on displacement was reported by Hudson, Nicholson, Ellis et al. (Reference Hudson, Nicholson, Ellis and Bach2016) and Hudson, Nicholson, Simpson et al. (Reference Hudson, Nicholson, Ellis and Bach2016). A spoken mimetic word describing possible target behavior presented during target motion influences displacement (Gobara, Yamada, & Miura Reference Gobara, Yamada and Miura2016).

Attribution of the Source of Target Motion (Causality). If observers attribute motion of an initially stationary target to contact from a moving launcher, forward displacement of the target is less than forward displacement of an otherwise identical target that exhibits autonomous motion (Hubbard & Favretto, Reference Hubbard and Favretto2003; Hubbard & Ruppel, Reference Hubbard and Ruppel2002; Hubbard et al., Reference Hubbard and Blessum2001). The launcher does not need to exhibit physical motion, as illusory gamma motion when a launcher appears adjacent to a target results in a launching effect (Hubbard et al., Reference Hubbard, Piazza, Pinel and Dehaene2005). Choi and Scholl (Reference Choi and Scholl2006) replicated the decreased forward displacement for launched targets found by Hubbard et al. (Reference Hubbard and Blessum2001), but they hypothesized this reflected the presence of two objects and a single motion rather than perception of causality. Hubbard (Reference Hubbard2013c) tested this by comparing displacement of a target in an entraining effect (a launcher continues in motion after contacting the target and appears to carry the target along; Hubbard, Reference Hubbard2013d) with displacement in a launching effect; displacement of entrained targets was larger than displacement of launched targets, and this is inconsistent with Choi and Scholl’s hypothesis. Increases in launcher size and velocity lead to larger representational momentum for the target (de sá Teixeira et al., Reference Dodds, van Belle, Peers, Dove, Cusack and Duncan2008), and forward displacement of a launched target decreases with distance traveled (Hubbard & Ruppel, Reference Hubbard and Ruppel2002).

Characteristics of the Observer

Variables influencing representational momentum that are related to the observer include (a) age, (b) allocation of attention, (c) eye movements and fixation, (d) action plans, (e) expertise, (f) error feedback and knowledge of representational momentum, (g) affective value of the target, (h) presence of psychopathology, and (i) neurophysiological structures involved or implicated in representational momentum.

Age. Children 24–36 months of age viewed a toy car roll down an incline and vanish behind an occluder, and they could open one of four doors in the occluder to retrieve the car (Perry, Smith, & Hockema Reference Dodds, van Belle, Peers, Dove, Cusack and Duncan2008). Children were more likely to open a door beyond where the car would have stopped, and this is consistent with representational momentum. Children 5 to 9 years of age viewed displays similar to those in Finke and Freyd (Reference Finke and Freyd1985), and older children exhibited larger representational momentum than did younger children (Taylor & Jakobson, Reference Taylor and Jakobson2010). Third-grade children, fifth-grade children, and adults shown frozen-action photographs exhibited representational momentum, but there was no effect of age (Futterweit & Beilin, Reference Futterweit and Beilin1994). First-grade children, fourth-grade children, and adults shown horizontally or vertically moving geometric stimuli exhibited representational momentum, and first-grade children exhibited larger representational momentum than did fourth-grade children or adults (Hubbard et al., Reference Hubbard, Matzenbacher and Davis1999). Older adults (more than 65 years of age) exhibited less representational momentum for an implied motion target than did younger adults (Piotrowski & Jakobson, Reference Piotrowski and Jakobson2011); indeed, the oldest participants did not exhibit representational momentum (which might reflect decreased ability to process implied motion). A consistent pattern of developmental changes in representational momentum has not been found, and methodological differences between studies might account for differences in findings.

Allocation of Attention. If an unrelated task (e.g., counting along with a metronome) is concurrent with target presentation, representational momentum for the target is increased (Hayes & Freyd, Reference Hayes and Freyd2002). Similarly, larger forward (smaller backward) displacement is exhibited when participants simultaneously listen to a string of digits and respond each time three odd numbers in a row occur (Joordens et al., Reference Bartolomeo, Urbanski, Chokron, Chainay, Moroni and Siéroff2004). If attention is manipulated by having participants attend to one or two locations on a single trajectory, no effect of allocation of attention occurs (Hubbard & Motes, Reference Hubbard and Motes2002; Kerzel, Reference Kerzel2004). If participants are cued during the target presentation or retention interval regarding final target location, representational momentum decreases but is not eliminated (Hubbard et al., Reference Doricchi, Merola, Aiello, Guariglia, Bruschini and Gevers2009). The inability of a cue to eliminate representational momentum suggests at least some portion of the displacement process is cognitively impenetrable. However, it is possible that cues presented during target presentation or during the retention interval might be displaced in the direction of motion (cf. Hubbard, Reference Hubbard2008) and thus ineffective in cueing actual final location.

An unrelated object flashed (briefly presented) at the moment the target vanished increases representational momentum (Munger & Owens, Reference Munger and Owens2004). When a flashed object is relevant to the task (i.e., participants judged target position at the time of the flash), backward displacement of the target occurs, but if a flashed object is irrelevant (i.e., observers instructed to ignore the flash), forward displacement occurs (Müsseler et al., Reference Müsseler, Stork and Kerzel2002). An unrelated flash during the retention interval results in backward displacement, and this is larger if the distractor is in front of rather than behind the target (Kerzel, Reference Kerzel2003a). These findings suggest tasks or stimuli that draw attention away from the target might influence displacement. The complementary pattern might also occur, that is, forward displacement might influence attention. For example, detection of a gap within a circle is faster and more accurate if the circle is presented slightly in front of the final location of a moving target than if the circle is presented slightly behind the final location of a moving target (Kerzel et al., Reference Kerzel, Jordan and Müsseler2001). Indeed, attention itself might exhibit a form of momentum (e.g., Hubbard, Reference Hubbard2014a, Reference Hubbard2015b; Pratt, Spalek, & Bradshaw Reference Jancke, Erlhagen, Dinse, Akhavan, Giese and Steinhage1999).

Eye Movements and Eye Fixation. If an observer views a continuously moving target but does not track that target, representational momentum is decreased or eliminated (de sá Teixeira, Hecht, & Oliveira, Reference de sá Teixeira, Hecht and Oliveira2013; Kerzel, Reference Kerzel2000). This initially led to suggestions that forward displacement resulted from pursuit eye movements overshooting final target position and visual persistence (e.g. Kerzel, Reference Kerzel2000; Stork & Müsseler, Reference Stork and Müsseler2004). However, oculomotor behavior does not influence displacement for a target undergoing implied motion (Kerzel, Reference Kerzel2003a); similarly, pursuit movements do not occur with frozen-action photographs, which also result in representational momentum. Nonetheless, the role of eye movements has been debated (e.g., Hubbard, Reference Hubbard2005b, Reference Hubbard2006b; Kerzel, Reference Kerzel2002c, Reference Kerzel2006). Several recent studies challenge the idea that preventing visual tracking of smoothly moving targets eliminates representational momentum (e.g., Getzmann & Lewald, Reference Getzmann and Lewald2009; Schmiedchen et al., Reference Rastelli, Tallon-Baudry, Migliaccio, Toba, Ducorps and Pradat-Diehl2013; Teramoto et al., Reference 441Peyrin, Michel and Schwartz2010). De sá Teixeira, Hecht, and Oliveira (Reference Rastelli, Tallon-Baudry, Migliaccio, Toba, Ducorps and Pradat-Diehl2013) suggested constraining eye movements suppresses or conceals effects of motion representation (cf. Hubbard Reference Hubbard2005b, Reference Hubbard2006b, Reference Hubbard, Nijhawan and Khurana2010, that eye movements might contribute to, but are not causal of, representational momentum). Oculomotor behavior is not related to representational momentum for auditory targets (Getzmann, Reference Getzmann2005) or representational gravity for horizontally moving visual targets (de sá Teixeira, Hecht, & Oliveira, Reference de sá Teixeira, Hecht and Oliveira2013). The presence of representational momentum in patients with schizophrenia (de sá Teixeira, Pimenta, & Raposo, Reference de sá Teixeira, Pimenta and Raposo2013; Jarrett et al., Reference Jarrett, Phillips, Parker and Senior2002), who often exhibit dysfunction of pursuit eye movements, further challenges claims that pursuit eye movements are necessary for generation of representational momentum.

Action Plans. Representational momentum decreases if observers have control over target direction and velocity (Jordan & Knoblich, Reference Jordan and Knoblich2004). Similarly, displacement is influenced by whether participants trigger disappearance of the target or the target vanishes without warning (Jordan et al., Reference Jordan, Stork, Knuf, Kerzel, Müsseler, Prinz and Hommel2002; Stork & Müsseler, Reference Stork and Müsseler2004). This suggests motor plans are coupled to perceptual space, which further suggests sharing or overlap of mechanisms for perception and for action planning. Relatedly, participants with previous experience controlling a target exhibit larger forward displacement than do participants without previous experience controlling that target, and this might reflect activation of action plans (Jordan & Hunsinger, Reference Jordan and Hunsinger2008). Such findings are consistent with effects of expertise on representational momentum (see discussion below), but seem inconsistent with decreases in displacement when participants control the target (Jordan & Knoblich, Reference Jordan and Knoblich2004; Jordan et al., Reference Jordan, Stork, Knuf, Kerzel, Müsseler, Prinz and Hommel2002; Stork & Müsseler, Reference Stork and Müsseler2004); however, it is possible that increased displacement occurs only during passive observation and not during active control.

Expertise. If expert drivers and novice drivers view displays involving roadway scenes filmed on board a moving automobile, all participants exhibited representational momentum, and representational momentum was larger for experts (Blättler, Ferrari, Didierjean, van Elslande, & Marmèche, Reference Blättler, Ferrari, Didierjean, van Elslande and Marmèche2010). If experienced pilots and non-pilots view displays based on aircraft landings, experienced pilots but not non-pilots exhibited representational momentum (Blättler, Ferrari, Didierjean, &Marmèche, Reference Blättler, Ferrari, Didierjean and Marmèche2011). Lack of displacement in non-pilots was attributed to lack of familiarity with the setting and stimuli. Experienced baseball batters exhibit larger representational momentum for a fast-moving object than do inexperienced baseball batters (Nakamoto, Mori, Ikudome, Unenaka, & Imanaka, Reference Nakamoto, Mori, Ikudome, Unenaka and Imanaka2015). These findings are consistent with the notion that representational momentum is related to predictability of the stimulus (cf. Kerzel, Reference Kerzel2002d), as experts are more familiar with the stimuli, and thus more able to predict the near future of those stimuli, than are non-experts. Interestingly, this suggests that attempts to develop training to eliminate representational momentum might be futile, and this is consistent with effects of error feedback on representational momentum.

Error Feedback and Knowledge. Representational momentum was initially claimed to be impervious to error feedback (Freyd, Reference Freyd1987), and this was based on findings that feedback during practice trials did not influence representational momentum on subsequent experimental trials (e.g., Finke & Freyd, Reference Finke and Freyd1985). More recent studies challenged this claim. If participants are instructed regarding representational momentum and asked to guard against it in their responses, forward displacement on subsequent trials is reduced but not eliminated (Courtney & Hubbard, Reference Courtney and Hubbard2008). If participants are given feedback after each trial regarding whether their response was correct or incorrect, such feedback does not reduce representational momentum, although it does reduce overall probability of a same response to any given probe (Ruppel et al., Reference Doricchi, Merola, Aiello, Guariglia, Bruschini and Gevers2009). Furthermore, reduced probability of a same response continues even if feedback is later withdrawn. As most experiments using probe judgment present 5–9 probe positions, the probability that any given probe will reflect the accurate target location is less than 50%, and the relatively low prior probability a same response would be correct might account for decreases in same responses (cf. Hubbard & Lange, Reference Hubbard and Lange2010).

Affective Value. Affective value of an object (e.g., safe, painful) that a hand moved toward or away from influenced representational momentum for location of the hand; more specifically, when affective value of the stimulus matched direction of hand movement (positive affect and motion toward the object, or negative affect and motion away from an object), forward displacement of the hand was larger than when affective value of the stimulus did not match direction of hand motion (Hudson, Nicholson, Ellis et al., Reference Hudson, Nicholson, Ellis and Bach2016; Hudson, Nicholson, Simpson et al., Reference Hudson, Nicholson, Ellis and Bach2016). Analogously, affective value of a target moving toward a stationary object influences displacement of that target. Participants were presented with a neutral stationary object and a moving target, and they read vignettes in which the moving target was described as threatening to the stationary object, neutral, or happy; forward displacement of the moving target was larger when the situation was described as a threatening than when the situation was described as neutral or happy (Greenstein, Franklin, Martins, Sewack, & Meier Reference Greenstein, Franklin, Martins, Sewack and Meier2016). Studies on representational momentum involving changes in facial expression involved different emotions depicted by a facial target, and those studies are discussed in the section on Human Form.

Psychopathology. Patients diagnosed with schizophrenia exhibit larger representational momentum than do control participants (Jarrett, Phillips, Parker, & Senior Reference Jarrett, Phillips, Parker and Senior2002), and target size, but not target velocity, influences representational momentum in such patients (de sá Teixeira, Pimenta, & Raposo, Reference de sá Teixeira, Pimenta and Raposo2013). Patients diagnosed with mental retardation exhibit smaller representational momentum than do control participants (Conners, Wyatt, & Dulaney, Reference Conners, Wyatt and Dulaney1998). Representational momentum is larger in patients with left spatial neglect and patients with right-hemisphere damage but no neglect (McGeorge et al., Reference McGeorge, Beschin and Della Sala2006), and representational momentum decreases with increases in distance traveled by the target for patients but not for control participants. Patients with left hemineglect as a consequence of right-hemisphere damage exhibited larger forward displacement than did patients with right-hemisphere damage without neglect and control participants regardless of direction of target motion (Lenggenhager et al., Reference Schmiedchen, Freigang, Nitsche and Rübsamen2012); furthermore, patients with left hemineglect exhibited larger forward displacement for targets moving toward the left (and a patient with right hemineglect exhibited larger forward displacement for targets moving toward the right). Patients with autism spectrum disorder exhibit decreases representational momentum for changes in facial expression (Uono et al., Reference Lewkowicz and Minar2014).

Neurophysiology. Several studies on neurophysiology of representational momentum involve patients diagnosed with psychopathology, and those studies were discussed in the section on Psychopathology. Retinal ganglion cells of rabbits and salamanders appear to anticipate arrival of a continuously moving stimulus (Berry, Brivanlou, Jordan, & Meister Reference Jancke, Erlhagen, Dinse, Akhavan, Giese and Steinhage1999), but no such patterns have been reported for implied motion or frozen-action stimuli. Representational momentum for changes in size (White et al., Reference White, Minor, Merrell and Smith1993) and location (Gottwald et al., Reference Gottwald, Lawrence, Hayes and Khan2015; Halpern & Kelly, Reference Halpern and Kelly1993) are larger for stimuli in the left visual field (right hemisphere). Consistent with this, increased activity in right parietal cortex occurs when observers exhibit representational momentum (Amorim et al., Reference Amorim, Lang, Lindinger, Mayer, Deecke and Berthoz2000). Frozen-action photographs elicit activation in motion-processing areas of V5/MST (Kourtzi & Kanwisher, Reference Kourtzi and Kanwisher2000; Senior et al., Reference 451Senior, Barnes, Giampietro, Simmons, Bullmore, Brammer and David2000). If a stimulus shown to previously elicit representational momentum is viewed after TMS over area V5/MST, representational momentum does not occur (Senior, Ward, & David Reference Senior, Ward and David2002). Representational momentum has been linked to activity in prefrontal cortex (Rao et al., Reference Bartolomeo, Urbanski, Chokron, Chainay, Moroni and Siéroff2004).

Physical Principles or Naive Physics?

Some researchers suggest representational momentum reflects internalization or incorporation of momentum (e.g., Finke et al., Reference Finke, Freyd and Shyi1986), and other researchers completely reject the notion of such internalization or incorporation (e.g., Kerzel, Reference Kerzel2000, Reference Kerzel2003a). Displacement does not always reflect objective physical principles (e.g., representational momentum does not reflect implied mass and is influenced by expectations regarding future target behavior and by landmark attraction). What is more likely is that displacement reflects subjective consequences of such principles rather than objective principles per se (e.g., displacement is influenced by experienced weight rather than by objective mass), and that such consequences are modulated by expectations regarding the target. Consistent with this, some authors suggest representational momentum might involve naïve physics (e.g., impetus; Hubbard, Reference 407Hubbard, Oliveira, Teixeira, Borges and Ferro2004, Reference Hubbard2013c; Hubbard & Ruppel, Reference Hubbard and Ruppel2002; Kozhevnikov & Hegarty, Reference Kozhevnikov and Hegarty2001). An interpretation emphasizing subjective experience is consistent with contemporary emphases on embodied or grounded cognition (e.g., Barsalou, Reference Barsalou2008; Gibbs, Reference Gibbs2005).

Low-Level Processing or High-Level Processing?

Several strands of evidence suggest representational momentum involves at least some high-level (top-down) processes. Representational momentum is influenced by information regarding source (Hubbard, Reference 407Hubbard, Oliveira, Teixeira, Borges and Ferro2004, Reference Hubbard2013c) and anticipated direction (Hubbard & Bharucha, Reference 408Hubbard and Bharucha1988; Johnston & Jones, Reference Johnston and Jones2006; Verfaillie & d’Ydewalle, Reference Verfaillie and d’Ydewalle1991) of target motion. Representational momentum is influenced by target prototypicality and identity (Nagai & Yagi, Reference Nagai and Yagi2001; Reed & Vinson, Reference Reed and Vinson1996; Vinson & Reed, Reference Vinson and Reed2002). Representational momentum is related to activity in several cortical areas (Amorim et al., Reference Amorim, Lang, Lindinger, Mayer, Deecke and Berthoz2000; Kourtzi & Kanwisher, Reference Kourtzi and Kanwisher2000; Rao et al., Reference Bartolomeo, Urbanski, Chokron, Chainay, Moroni and Siéroff2004; Senior et al., Reference 451Senior, Barnes, Giampietro, Simmons, Bullmore, Brammer and David2000). Representational momentum occurs with different surface forms (cf. Freyd & Finke, Reference 394Freyd and Finke1984; Hubbard & Bharucha, Reference 408Hubbard and Bharucha1988), in different modalities (cf. Johnston & Jones, Reference Johnston and Jones2006; Verfaillie & d’Ydewalle, Reference Verfaillie and d’Ydewalle1991), and is influenced by cross-modal information (e.g., Teramoto et al., Reference 441Peyrin, Michel and Schwartz2010). Rather than a different mechanism for each surface form or modality, it is more parsimonious to suggest a more high-level general-purpose extrapolation mechanism (cf. Hubbard, Reference Hubbard2006b, Reference Hubbard2014a, Reference Hubbard2015a, Reference Hubbard2015b, Reference Hubbard2017). Importantly, allowing for high-level processes and influences does not mean that low-level processes cannot contribute to or modulate displacement (e.g., disrupting information normally provided by eye movements disrupts displacement; de sá Teixeira, Hecht, & Oliveira, 2103).

Relationship to Other Spatial Biases?

Representational momentum is related to other momentum-like effects (e.g., Hubbard, Reference Hubbard2014a, Reference Hubbard2015a, Reference Hubbard2015b, Reference Hubbard2017) and general perceptual or cognitive processes (e.g., mental rotation; Hubbard, Reference Hubbard2006a; Munger, Solberg, & Horrocks, Reference Munger, Solberg and Horrocks1999; perceptual grouping; Hubbard Reference Hubbard, Albertazzi, van Tonder and Vishwanath2011b; aesthetics; Hubbard, Chapter 15 in this volume). These relationships are beyond the scope of this chapter, but a narrower consideration of relationships of representational momentum to other biases in remembered location (Fröhlich effect, flash-lag effect, boundary extension) is presented.

Fröhlich Effect. The perceived onset (initial) location of a moving target is often displaced in the direction of target motion, and this is referred to as the Fröhlich effect (Kerzel, Reference Kerzel, Nijhawan and Khurana2010; Müsseler & Kerzel, Chapter 7 in this volume). Forward displacement of the target in the Fröhlich effect appears similar to forward displacement of the target in representational momentum (cf. Hubbard, Reference Hubbard1990; Müsseler & Aschersleben, 1988). The Fröhlich effect (e.g., Müsseler & Aschersleben, Reference Müsseler and Aschersleben1998) and representational momentum (e.g., Hubbard, Reference Hubbard1990) increase with increases in target velocity. The Fröhlich effect (Whitney & Cavanagh, Reference Whitney and Cavanagh2000a) and representational momentum (Hubbard et al., Reference Doricchi, Merola, Aiello, Guariglia, Bruschini and Gevers2009) are decreased by presentation of a valid cue prior to stimulus presentation. Given such similarities, displacement in the Fröhlich effect might reflect representational momentum and an accurate memory for trajectory length, or displacement in representational momentum might reflect the Fröhlich effect and an accurate memory for trajectory length. However, when the Fröhlich effect and representational momentum are measured for the same trajectory, representational momentum for the vanishing point is found, but memory for initial location is displaced in the direction opposite to target motion (i.e., an onset repulsion effect; Actis-Grosso & Stucchi, Reference Actis-Grosso and Stucchi2003; Hubbard & Motes, Reference Hubbard and Motes2002; Kerzel, Reference Kerzel2004).

Flash-Lag Effect. If a briefly presented (flashed) stationary object is aligned with a moving target, that object appears to lag behind the moving target. This is referred to as the flash-lag effect (Hubbard, Reference Hubbard2014b, Chapter 9 in this volume). Forward displacement in the flash-lag effect appears similar to forward displacement in representational momentum (cf. Munger & Owens, Reference Munger and Owens2004; Shi & de’Sperati, Reference Shi and de’Sperati2008). The flash-lag effect (Wojtach et al., Reference Dodds, van Belle, Peers, Dove, Cusack and Duncan2008) and representational momentum (Hubbard & Bharucha, Reference 408Hubbard and Bharucha1988) increase with increases in target velocity. The flash-lag effect (Namba & Baldo, Reference Namba and Baldo2004; Vreven & Verghese, Reference Vreven and Verghese2005) and representational momentum (Hubbard et al., Reference Doricchi, Merola, Aiello, Guariglia, Bruschini and Gevers2009) are decreased by presentation of a valid cue prior to stimulus presentation. The flash-lag effect (Nagai et al., Reference Nagai, Suganuma, Nijhawan, Freyd, Miller, Watanabe, Nijhawan and Khurana2010; Noguchi & Kakigi, Reference Noguchi and Kakigi2008) and representational momentum (Reed & Vinson, Reference Reed and Vinson1996) are influenced by conceptual knowledge. The flash-lag effect (Ichikawa & Masakura, Reference Ichikawa and Masakura2006, Reference Ichikawa and Masakura2010) and representational momentum (Hubbard, Reference Hubbard2013c; Hubbard et al., Reference Hubbard and Blessum2001) are influenced by attributions regarding the source of target motion. The flash-lag effect (Scocchia, Actis-Grosso, de’Sperati, Stucchi, & Baud-Bovy, Reference Doricchi, Merola, Aiello, Guariglia, Bruschini and Gevers2009) and representational momentum (Jordan & Hunsinger, Reference Jordan and Hunsinger2008) are influenced by whether observers control the stimulus. The flash-lag effect (Sarich, Chappell, & Burgess, Reference Sarich, Chappell and Burgess2007) and representational momentum (Hayes & Freyd, Reference Hayes and Freyd2002) increase with divided attention. The flash-lag effect (Brenner, van Beers, Rotman, & Smeets, Reference Brenner, van Beers, Rotman and Smeets2006; Shi & Nijhawan, Reference Shi and Nijhawan2008) and representational momentum (Hubbard & Ruppel, Reference Hubbard and Ruppel1999) increase with motion toward a landmark or fixation. The main difference is that in the flash-lag effect, displacement of the target is measured relative to the location of a nearby stationary object, whereas in representational momentum, displacement of the target is measured relative to the actual location of the target Hubbard (Reference Hubbard2013b, Reference Hubbard2014b).

Boundary Extension. Memory for a previously viewed scene includes not just information within the initial view but also information that was not viewed but would likely have been present outside the boundaries of the initial view. This has been referred to as boundary extension (Hubbard et al., Reference Hubbard and Courtney2010; Intraub, Reference Intraub2012; Intraub & Gagnier, Chapter 13 in this volume). Boundary extension (Intraub, Daniels, Horowitz, & Wolfe, Reference Dodds, van Belle, Peers, Dove, Cusack and Duncan2008) and representational momentum (Hayes & Freyd, Reference Hayes and Freyd2002) are decreased when more attention is allocated to the target. Boundary extension (Intraub & Dickinson, Reference Intraub and Dickinson2008) and representational momentum (Freyd & Johnson, Reference Freyd and Johnson1987) occur within tens of milliseconds after a target vanishes. Boundary extension (Intraub, Hoffman, Wetherhold, & Stoehs, Reference Intraub, Hoffman, Wetherhold and Stoehs2006) and representational momentum (Jordan et al., Reference Jordan, Stork, Knuf, Kerzel, Müsseler, Prinz and Hommel2002) are influenced by action plans regarding eye movements. Boundary extension (Intraub & Bodamer, Reference Intraub and Bodamer1993) and representational momentum (Courtney & Hubbard, Reference Courtney and Hubbard2008) are decreased but not eliminated if participants receive information regarding the effect and are instructed to counteract the effect. Boundary extension (Hubbard, Reference Hubbard, Algom, Zakay, Chajut, Shaki, Mama and Shakuf2011a) and representational momentum (Hubbard, Reference Hubbard, Albertazzi, van Tonder and Vishwanath2011b) exhibit properties similar to Gestalt principles of perceptual grouping. Munger et al. (Reference Munger, Owens and Conway2005) suggested boundary extension for a scene occurred before representational momentum for objects in that scene.Footnote ⁴

Bridging the Gap?

It takes 100 msec or so for information presented to the retina to be processed in the cortex (e.g., De Valois & De Valois, Reference 386De Valois and De Valois1991); thus, there is a lag between when sensation of a stimulus begins and when information regarding that stimulus enters perceptual awareness. The flash-lag effect has been proposed to compensate for such delays (e.g., Nijhawan, Reference Nijhawan2008), but representational momentum might provide better compensation, as the flash-lag effect is defined in terms of relative position (and so a referent stationary object is necessary), and representational momentum does not require comparison to another stimulus. Indeed, Hubbard (Reference Hubbard2005b) suggested representational momentum bridged the gap between perception and action. When light from a moving stimulus stimulates the retina, a cascade of sensory, perceptual, cognitive, and perhaps motor responses is initiated. However, while this processing is occurring, the stimulus typically does not pause and wait for the observer to finish processing, but instead continues in motion. By the time conscious awareness of the stimulus is achieved, the stimulus has already moved beyond where it was when it first stimulated the retina. If an immediate response from an observer is to be optimal, that response should be calibrated to where the stimulus is in real time and not where the stimulus was when it was initially sensed. What is needed is a bridge between perception (i.e., location at initial sensation) and action (i.e., location when a response would reach the stimulus), and representational momentum might provide such a bridge.

Characteristics of the Stimulus

Numerous characteristics of the stimulus influence or reveal properties of the flash-lag effect. These include (a) timing of presentation of the flashed object relative to presentation of the moving target, (b) continuity of the target, (c) distance traveled by the target prior to presentation of the flashed object, (d) distance between the moving target and the flashed object, (e) eccentricity and visual field, (f) velocity of target motion, (g) direction of target motion, (h) binocular disparity, (i) changes in target color and lack of color mixing, (j) luminance of the moving target or of the flashed object, (k) contrast of the moving target and flashed object with the background or each other, (l) spatial frequency of the moving target, (m) identity of the moving target, (n) duration of the flashed object, (o) motion of the flashed object, (p) predictability of the flashed object, and (q) presence of unrelated stimuli.

Relative Timing. The flashed object is typically presented at the onset, midpoint, or offset of target motion, and these displays are referred to as flash-initiated, flash-midpoint, and flash-terminated, respectively. A flash-lag effect typically occurs with flash-initiated and flash-midpoint displays, but not with flash-terminated displays (Eagleman & Sejnowski, Reference Eagleman and Sejnowski2000b; Khurana & Nijhawan, Reference Khurana and Nijhawan1995; Nijhawan, Watanabe, Khurana, & Shimojo, Reference Bartolomeo, Urbanski, Chokron, Chainay, Moroni and Siéroff2004). Many studies that involve flash-initiated, flash-midpoint, and flash-terminated stimuli present the flashed object and moving target as aligned, but a small group of studies varied relative spatial position, and observers adjusted the stimuli so that the flashed object and moving target appear aligned (e.g., Lappe & Krekelberg, Reference Lappe and Krekelberg1998).

Continuity of the Target. A flash-lag effect occurs if the moving target is presented continuously (i.e., target motion appears smooth) or if discrete and clearly separated presentations of the target (i.e., implied motion) are viewed (Rizk, Chappell, & Hine, Reference Doricchi, Merola, Aiello, Guariglia, Bruschini and Gevers2009), although the effect is weaker with discrete presentations. Such a result suggests the flash-lag effect is related more to underlying continuity of the stimulus dimension along which change occurs and from which the target is drawn or sampled (e.g., location, orientation, luminance, hue, etc.) than to characteristics of the target per se. An unexpected change in color or size (Au & Watanabe, Reference Au and Watanabe2013; Moore & Enns, Reference Moore and Enns2004) of the moving target when the flashed object is presented disrupts the flash-lag effect.

Distance Traveled by the Target. Finding a flash-lag effect with flash-initiated and flash-midpoint displays but not flash-terminated displays suggests the flash-lag effect decreases as distance traveled by the target increases. Consistent with this, increases in distance traveled by the target prior to presentation of the flashed object decreases the flash-lag effect (Vreven & Verghese, Reference Vreven and Verghese2005). Maus and Nijhawan (Reference Maus and Nijhawan2006) reported the visible threshold for moving targets was lower if the target traveled farther, and they suggested this involved larger forward displacement of the target; however, larger displacement would presumably result in an increased flash-lag effect with increases in distance traveled by the target (cf., Kanai, Sheth, & Shimojo, Reference Bartolomeo, Urbanski, Chokron, Chainay, Moroni and Siéroff2004).

Distance between Moving Target and Flashed Object. Many studies presented the flashed object embedded within the moving target (e.g., a disk within an annulus; Becker, Ansorge, & Turatto, Reference Becker, Ansorge and Turatto2009; Nijhawan, Reference Nijhawan2001; flashed objects interleaved with different parts of a moving target; Khurana & Nijhawan, Reference Khurana and Nijhawan1995), but other studies varied distance between the moving target and flashed object. In the former studies, a robust flash-lag effect occurred. In the latter studies, increases in distance between the moving target and the flashed object increased the flash-lag effect (Baldo & Klein, Reference Baldo and Klein1995; Baldo et al., Reference Bartolomeo, Urbanski, Chokron, Chainay, Moroni and Siéroff2004). If the flashed object is embedded or interleaved within the moving target, or is spatially separate from the moving target, then there is no partial overlap between the flashed object and the moving target. However, if partial overlap occurs, the portion of the moving target inside the boundaries of the flashed object is veridically perceived, whereas the portion of the moving target outside the boundaries of the flashed object exhibits a flash-lag effect (Kanai & Verstraten, Reference Kanai and Verstraten2006). Thus, whether the moving target encloses, is spatially separated from, or partially overlaps the flashed object influences the flash-lag effect.

Eccentricity and Visual Field. When the flashed object is closer to fixation than is the moving target, the flash-lag effect is increased (Baldo, Kihara, et al. Reference Bartolomeo, Urbanski, Chokron, Chainay, Moroni and Siéroff2004; Baldo & Klein, Reference Baldo and Klein1995), whereas when the flashed object is farther from fixation than is the moving target, the flash-lag effect is decreased (Linares, López-Moliner, & Johnston, Reference Linares and López-Moliner2007) with increases in eccentricity of the flashed object from fixation. The flash-lag effect is more likely to occur with flash-terminated displays as eccentricity increases (Kanai et al., Reference Bartolomeo, Urbanski, Chokron, Chainay, Moroni and Siéroff2004). The flash-lag effect is increased for horizontal target motion in the left visual field relative to the right visual field (Kanai et al., Reference Bartolomeo, Urbanski, Chokron, Chainay, Moroni and Siéroff2004) and is more influenced by target direction if motion is in the right visual field (Shi & Nijhawan, Reference Shi and Nijhawan2008). However, visual field does not influence the flash-lag effect for vertically moving targets (Ishikawa & Masakura, Reference Ichikawa and Masakura2006, Reference Ichikawa and Masakura2010).

Velocity of Target Motion. The flash-lag effect increases with increased target velocity in the picture plane (e.g., Brenner & Smeets, Reference Brenner and Smeets2000; López-Moliner & Linares, Reference López-Moliner and Linares2006; Wojach et al., Reference Dodds, van Belle, Peers, Dove, Cusack and Duncan2008) and in depth (e.g., Lee, Khuu, Li, & Hayes, Reference Dodds, van Belle, Peers, Dove, Cusack and Duncan2008). The effect of target velocity is decreased in multi-target displays relative to single-target displays (Shioiri, Yamamoto, Oshida, Matsubara, & Yaguchi, Reference 441Peyrin, Michel and Schwartz2010). Acceleration or deceleration of the moving target results in an increased or decreased flash-lag effect, respectively (Whitney, Murakami, & Cavanagh, Reference Whitney, Murakami and Cavanagh2000). The effect of velocity is larger if target motion is toward fixation (Blohm et al., 2003). Random changes in velocity decrease the flash-lag effect (Vreven & Verghese, Reference Vreven and Verghese2005). The flash-lag effect is influenced by target velocity after the flashed object is presented (Brenner & Smeets, Reference Brenner and Smeets2000), and this is consistent with an account of the flash-lag effect based on postdiction.

Direction of Target Motion. The flash-lag effect is not influenced by whether targets ascend or descend in the picture plane (Ichikawa & Masakura, Reference Ichikawa and Masakura2006, Reference Ichikawa and Masakura2010). If a target reverses direction at the time of the flash, the flash-lag effect is decreased (Whitney & Murakami, Reference Whitney and Murakami1998). If a vertically moving target turns to the left or right, a flash-lag effect occurs even if the direction of change is unpredictable (Chappell & Hinchy, Reference Chappell and Hinchy2014; Whitney, Cavanagh, & Murakami, Reference Whitney, Cavanagh and Murakami2000). The flash-lag effect is larger if a target moves toward fixation than away from fixation (Brenner, van Beers, Rotman, & Smeets, Reference Brenner, van Beers, Rotman and Smeets2006; Kanai et al., Reference Bartolomeo, Urbanski, Chokron, Chainay, Moroni and Siéroff2004; Mateeff & Hohnsbein, Reference Mateeff and Hohnsbein1988). A flash-lag effect also occurs for targets moving in depth (Harris, Duke, & Kopinska, Reference Harris, Duke and Kopinska2006; Ishii, Seekkuarachchi, Tamura, & Tang, Reference Bartolomeo, Urbanski, Chokron, Chainay, Moroni and Siéroff2004). The flash-lag effect decreases if the target unpredictably changes direction near the time of the flash (Arrighi, Alais, & Burr, Reference Arrighi, Alais and Burr2005; Murakami, Reference Murakami2001b; Vreven & Verghese, Reference Vreven and Verghese2005; Whitney et al., Reference Whitney, Cavanagh and Murakami2000).

Binocular Disparity. A flash-lag effect occurs when the moving target or flashed object is defined solely by binocular disparity. This has been found with random-dot stimuli (Harris et al., Reference Harris, Duke and Kopinska2006; Nieman, Nijhawan, Khurana, & Shimojo, Reference Nieman, Nijhawan, Khurana and Shimojo2006) and stereomotion (Lee et al., Reference Dodds, van Belle, Peers, Dove, Cusack and Duncan2008). As noted by Nieman et al. (Reference Nieman, Nijhawan, Khurana and Shimojo2006), finding a flash-lag effect with random-dot stimuli challenges hypotheses that the flash-lag effect results from retinal or low-level phenomena (e.g., as in Berry, Brivanlou, Jordan, & Meister, Reference Jancke, Erlhagen, Dinse, Akhavan, Giese and Steinhage1999).

Color. If a target gradually changes from red to green and a flashed object is presented during the change, a flash-lag effect for color occurs (Sheth, Nijhawan, & Shimojo, Reference Sheth, Nijhawan and Shimojo2000). If observers view a moving green bar and a briefly flashed red bar is superimposed on the green bar, perception of a yellow bar (based on additive color mixing) might be predicted. However, a flash lag effect in which the red bar lags the green bar occurs (Nijhawan, Reference Nijhawan1997). If observers execute smooth pursuit eye movements past a stationary green bar (that appeared to move across the retina in the direction opposite to the direction of eye movement), and a red bar was briefly superimposed on the green bar, the red bar appeared to be shifted in the opposite direction; this is consistent with a flash-lag effect (Nijhawan, Khurana, Kamitani, Watanabe, & Shimojo, Reference Nijhawan, Khurana, Kamitani, Watanabe and Shimojo1998). A flash-lag effect occurs if the moving object changes color (Kreegipuu & Allik, Reference Kreegipuu and Allik2004), but the perceived color change lags perceived position (Cai & Schlag, Reference Cai and Schlag2001; Gauch & Kerzel, Reference Gauch and Kerzel2008b). If target color is maintained or exhibits multiple changes, a flash-lag effect occurs, but a single unexpected change at the moment of the presentation of the flashed object eliminates the flash-lag effect (Au & Watanabe, Reference Au and Watanabe2013).

Luminance. The flash-lag effect decreases if luminance of the flashed object increases (Öğmen, Patel, Bedell, & Camuz Reference Bartolomeo, Urbanski, Chokron, Chainay, Moroni and Siéroff2004; Purushothaman, Patel, Bedell, & Öğmen, Reference Purushothaman, Patel, Bedell and Öğmen1998); if luminance of the flashed object is very high and luminance of the moving target is very low, the flash-lag effect reverses (i.e., a flash-lead effect occurs). A flash-lag effect is found when the moving target and flashed object are luminance modulated, equiluminant, or equiluminant-in-luminance-noise, except for the specific combination of a luminance modulated flashed object and an equiluminant or equiluminant-in-luminance-noise moving target (Chappell & Mullen, Reference Chappell and Mullen2010). Nieman et al. (Reference Nieman, Nijhawan, Khurana and Shimojo2006) found a flash-lag effect with random-dot stimuli equated in luminance with the background and distinguishable only by binocular disparity. Although for a given velocity targets with low luminance are perceived as moving faster than are targets with high luminance, and that the flash-lag effect is generally larger with faster velocities, differences in velocity related to overall luminance do not influence the flash-lag effect (Vaziri-Pashkam & Cavanagh, Reference Vaziri-Pashkam and Cavanagh2011). A flash-lag effect for luminance occurs for a moving target that is changing in luminance and a flashed object presented at the same luminance as the target (Sheth et al., Reference Sheth, Nijhawan and Shimojo2000).

Contrast. With linearly moving targets, decreases in contrast between the flashed object and moving target increases the flash-lag effect (Kanai et al., Reference Bartolomeo, Urbanski, Chokron, Chainay, Moroni and Siéroff2004), and consistent with this, forward displacement of a moving target is increased if contrast between the target and background gradually fades (Maus & Nijhawan, Reference Maus and Nijhawan2009). However, with rotating targets, decreases in contrast between the flashed object and moving target result in a smaller flash-lag effect or a flash-lead effect (Arnold, Ong, & Roseboom, Reference Arnold, Ong and Roseboom2009). This latter finding is not completely consistent with claims the flash-lag effect results from differential latencies in processing moving targets and flashed objects.

Spatial Frequency. If a square wave grating of a given spatial frequency is briefly presented adjacent to a grating that is increasing or decreasing in spatial frequency, a flash-lag effect for spatial frequency occurs (Sheth et al., Reference Sheth, Nijhawan and Shimojo2000). The flash-lag effect is increased as spatial frequency decreases from 1 to 0.25 cycles per degree (Cantor & Schor, Reference 378Cantor and Schor2007). Forward displacement of a blurry target (high spatial frequencies removed) is larger than forward displacement of a focused target (high spatial frequencies intact; Fu, Shen, & Dan, Reference Fu, Shen and Dan2001). An increase in the flash-lag effect with loss of higher spatial frequency information does not reflect an increase in noise, as noise would be randomly distributed around the actual location and would dilute any consistent shift in a specific direction.

Target Identity. Most studies of the flash-lag effect presented geometric stimuli such as annuli, bars, and disks. If targets are chimeric stimuli comprised of the top half of one (human) face and the bottom half of another (human) face, and the top half is flashed, then observers who judge the identity of the person in the top half perform better when the bottom half is moving than when the bottom half is stationary; this was attributed to a flash-leg effect disrupting normal perceptual alignment effects in facial recognition (Khurana, Carter, Watanabe, & Nijhawan, Reference Khurana, Carter, Watanabe and Nijhawan2006). If a single change in moving target size corresponds with presentation of the flashed object, then the flash-lag effect decreases; this has been attributed to failure to update the original object file of the moving target, and so the suddenly differently sized target is perceived as a different object from the original target (Moore & Enns, Reference Moore and Enns2004). As discussed below, semantic meaningfulness regarding identity or object category attributed to the stimulus influences the flash-lag effect.

Duration of the Flashed Object. Surprisingly, many studies of the flash-lag effect do not report duration of the flashed object. Some studies report use of a single duration ranging from 5 (e.g., Shi & Nijhawan, Reference Shi and Nijhawan2008) to 70 (e.g. Moore & Enns, Reference Moore and Enns2004) msec. Other studies report multiple durations ranging from 1–193 msec (Rotman, Brenner, & Smeets, Reference Rotman, Brenner and Smeets2005) or 24–200 msec (Cantor & Shor, Reference 378Cantor and Schor2007). Eagleman and Sejnowski (Reference Eagleman and Sejnowski2000c) suggested a flash-lag effect would not occur for flash durations longer than 80 msec, but Krekelberg and Lappe (Reference Krekelberg and Lappe1999) reported a flash-lag effect with flash durations of 500 msec.

Motion of the Flashed Object. In most studies of the flash-lag effect, the flashed object is stationary. Indeed, Eagleman and Sejnowski (Reference 389Eagleman and Sejnowski2007) claimed a flash-lag effect would turn into a flash-drag effect if motion were attributed to the flashed object. However, when a flashed object briefly moves along with the moving target, a flash-lag effect can still occur (e.g., Cravo & Baldo, Reference Cravo and Baldo2008), but decreases with increasing motion of the flashed object (Bachmann & Kalev, Reference Bachmann and Kalev1997; Krekelberg & Lappe, Reference Krekelberg and Lappe1999). It is not yet possible to disentangle effects of increased motion of the flashed object from effects of increased duration of the flashed object. A decrease in the flash-lag effect with increased motion of the flashed object might reflect an increase in perceptual processing speed for the flashed object over time (Bachmann, Luiga, Põder, & Kalev, Reference Bachmann, Luiga, Põder and Kalev2003) or an increasing ability to extrapolate position of the flashed object over time. A moving flashed object results in a larger flash-lag effect than does a stationary flashed object for flash-initiated and flash-terminated, but not for flash-midpoint, displays (Gauch & Kerzel, Reference Gauch and Kerzel2008a).

Predictability of the Flashed Object. The validity of a cue presented 100 or 500 msec before the flashed object and indicating whether the flashed object would be on the left or right side of a display does not influence the flash-lag effect (Khurana et al., Reference Khurana, Watanabe and Nijhawan2000). However, a valid cue presented 3,000–5,000 msec before the flashed object appeared results in a smaller flash-lag effect than does an invalid cue (Namba & Baldo, Reference Namba and Baldo2004), and a cue visible from the beginning of a trial until the flashed object appears decreases the flash-lag effect (Brenner & Smeets, Reference Brenner and Smeets2000). The flash-lag effect decreases the second time a stimulus is shown (the first time is analogous to a cue; Rotman et al., Reference Rotman, Brenner and Smeets2005). Cueing which target in a multi-target display would be nearest the flashed object decreases the flash-lag effect (Shioiri et al., Reference 441Peyrin, Michel and Schwartz2010). In general, the flash-lag effect is largest when unpredictability of the flashed object is highest (Baldo, Kihara, et al., Reference Baldo, Kihara, Namba and Klein2002; Baldo & Namba, Reference Baldo and Namba2002; Vreven & Verghese, Reference Vreven and Verghese2005).

Presence of Unrelated Stimuli. If an unrelated stimulus moves toward the location where a flashed object will appear, the flash-lag effect is larger than if an unrelated stimulus moves away from the location where the flashed object will appear (Maiche, Budelli, & Gómez-Sena, Reference Maiche, Budelli and Gómez-Sena2007). Similarly, if an unrelated stimulus moves toward the moving target and is occluded by the target at the time the flashed object is presented, the flash-lag effect increases regardless of whether the unrelated stimulus vanishes after being occluded or emerges from occlusion and continues its original direction of motion (Bachmann, Murd, & Põder, Reference Bachmann, Murd and Põder2012). Bachmann et al. (Reference Bachmann, Murd and Põder2012) suggest this finding is inconsistent with many theories of the flash-lag effect; however, Bachmann et al.’s rejection of attention shift theory in particular might be overstated, as presence of an unrelated object (i.e., divided attention) is linked to increases in other spatial biases such as representational momentum (Hayes & Freyd, Reference Hayes and Freyd2002) and boundary extension (Intraub, Daniels, Horowitz, & Wolfe, Reference Dodds, van Belle, Peers, Dove, Cusack and Duncan2008).

Characteristics of the Observer

Characteristics of the observer that influence the flash-lag effect include (a) allocation of attention, (b) eye movements and eye fixations, (c) body movements of the observer, (d) perceived control of the moving target or flashed object by the observer, and (e) semantic or other meaningfulness the observer attributes to the stimulus.

Allocation of Attention. The flash-lag effect increases as distance between the moving target and flashed object increases, and this has been attributed to the time required to shift attention from the moving target to the flashed object (Baldo & Klein, Reference Baldo and Klein1995). In a multi-target display in which one target is cued, the flash-lag effect increases as distance of the flashed object from the cued target increases (Shioiri et al., Reference 441Peyrin, Michel and Schwartz2010). However, embedding the flashed object within the moving target (thus removing the need for a shift of attention across space) also results in a flash-lag effect (Khurana & Nijhawan, Reference Khurana and Nijhawan1995). The flash-lag effect increases if observers are engaged in a concurrent task (Sarich, Chappell, & Burgess, Reference Sarich, Chappell and Burgess2007; Scocchia, Actis-Grosso, de?Sperati, Stucchi, & Baud-Bovy, Reference Doricchi, Merola, Aiello, Guariglia, Bruschini and Gevers2009). The larger flash-lag effect with random-dot stimuli in Nieman et al. (Reference Nieman, Nijhawan, Khurana and Shimojo2006) supports a role of attention: tracking the target required greater attention, thus leaving less attention for detection of the flashed object, resulting in the flashed object requiring even longer to process and enter into awareness.

Eye Movements and Eye Fixation. If observers fixate a central point around which a moving target is revolving, a flash-lag effect occurs, whereas if observers track the revolving target, a flash-lag effect does not occur (Nijhawan, Reference Nijhawan1997, Reference Nijhawan2001). A flash-lag effect occurs if the flashed stimulus is presented during smooth anticipatory eye movement (Blohm et al., 2003; cf. Nijhawan, Reference Nijhawan2001). The location of a flashed object is shifted in the direction of eye movement as a moving target is tracked (Rotman, Brenner, & Smeets, Reference Rotman, Brenner and Smeets2002; Rotman et al., Reference Rotman, Brenner and Smeets2005) or in the direction of gaze after the flash (Rotman, Brenner, & Smeets, Reference Bartolomeo, Urbanski, Chokron, Chainay, Moroni and Siéroff2004). A flash-lag effect occurs during pursuit motion if a flashed object is above or below the horizontal trajectory of a moving target (van Beers, Wolpert, & Haggard, Reference van Beers, Wolpert and Haggard2001). If the flash involves an object in a specific location (rather than a background flash), subsequent saccades to the location of the flashed object are not displaced, but subsequent saccades to the location of the moving target at the time of the flashed object are displaced in the direction of motion (Becker et al., Reference Becker, Ansorge and Turatto2009).

Body Movement. If observers in a darkened environment focus on an illuminated stationary line and move their heads back and forth, and another illuminated line aligned with the first line is flashed in mid-movement, then a flash-lag effect occurs (Schlag, Cai, Dorfman, Mohempour, & Schlag-Rey, Reference Schlag, Cai, Dorfman, Mohempour and Schlag-Rey2000). If observers in a darkened environment sit in a rotating chair and a continuously illuminated line rotates with the chair, a flash-lag effect occurs if a stationary line is briefly presented near the continuously illuminated line (Cai, Jacobson, Baloh, Schlag-Rey, & Schlag, Reference Cai, Jacobson, Baloh, Schlag-Rey and Schlag2000). A flash-lag effect occurs if observers in a darkened environment move their (nonvisible) hands and a stationary visual line is flashed near their hand (Nijhawan & Kirschfeld, Reference Nijhawan and Kirschfeld2003), or if a vibration is applied to a finger of a hand moving past a stationary finger on the observer’s other hand (a buzz-lag effect; Cellini, Scocchia, & Drewing, Reference Cellini, Scocchia and Drewing2016). Thus, a flash-lag effect can occur with passive or active motion of one’s own body. A flash-lag effect can also occur for judgments of another person’s movements relevant to a flashed object (Kessler, Gordon, Cessford, & Lages, Reference Kessler, Gordon, Cessford and Lages2010).

Control. If observers believe they control target motion, the flash-lag effect decreases (Ichikawa & Masakura, Reference Ichikawa and Masakura2006, Reference Ichikawa and Masakura2013), but only if mapping between observers’ movements (i.e., body movements controlling a computer mouse, which control target motion) and target movements were familiar (Ichikawa & Masakura, Reference Ichikawa and Masakura2010). However, the flash-lag effect increases if observers actually control target motion, and this might reflect greater attention required for control of the target, leaving less capacity available for processing information related to the flashed object (Scocchia et al., Reference Doricchi, Merola, Aiello, Guariglia, Bruschini and Gevers2009). If observers control presentation of the flashed object, then the flash-lag effect decreases (López-Moliner & Linares, Reference López-Moliner and Linares2006). This is consistent with the possibility that the flash-lag effect results at least in part from high-level attributions regarding the source of target motion.

Meaningfulness. The flash-lag effect is influenced by Gestalt perceptual grouping imposed on a stimulus, and is larger if the flashed object is nearer the leading edge of a moving target than the trailing edge of that moving target (Watanabe, Reference Watanabe2004; Watanabe, Nijhawan, Khurana, & Shimojo, Reference Watanabe, Nijhawan, Khurana and Shimojo2001). The flash-lag effect decreases if moving targets or flashed objects are meaningful (e.g., kanji segments for Japanese speakers; Noguchi & Kakigi, Reference Noguchi and Kakigi2008). Relatedly, if the moving target is an object with a typical facing direction or direction of motion (e.g., a photograph of an automobile) and the flashed object is a dot presented above the target, then the flash-lag effect is larger with backward motion than with forward motion of the target (Nagai, Suganuma, Nijhawan, Freyd, Miller, & Watanabe, Reference Nagai, Suganuma, Nijhawan, Freyd, Miller, Watanabe, Nijhawan and Khurana2010). The complementary pattern can also occur, as the flash-lag effect can influence processing of meaningful stimuli (e.g., faces; Khurana et al., Reference Khurana, Carter, Watanabe and Nijhawan2006).

Spatial or Temporal?

Theories based on motion extrapolation emphasize spatial aspects of the flash-lag effect (e.g., Nijhawan, Reference Nijhawan1994, Reference Nijhawan2008), whereas theories based on differential latencies emphasize temporal aspects of the flash-lag effect (e.g., Whitney & Cavanagh, Reference Whitney, Cavanagh and Murakami2000). Theories based on postdiction emphasize spatial (e.g., Eagleman & Sejnowski, Reference Eagleman and Sejnowski2002) or temporal (e.g., Whitney, Reference Whitney2002) aspects of the flash-lag effect. Temporal judgments (i.e., did a moving target change color prior to presentation of a flashed object?) and spatial judgments (i.e., did a moving target change color after passing a flashed object?) can be dissociated (Kreegipuu & Allik, Reference Kreegipuu and Allik2004; also Gauch & Kerzel, Reference Gauch and Kerzel2008b). Such dissociations probably involve differences in processing latencies for different types of information (e.g., information about color is perceptually available earlier than information about motion; Arnold, Clifford, & Wenderoth, Reference Arnold, Clifford and Wenderoth2001). Other researchers (e.g., Murakami, Reference Murakami2001a) emphasize that the flash-lag effect involves spatiotemporal correlation. As space cannot be traversed without passing through time (and for a moving object, elapsed time relates to traversed space), it seems reasonable to consider the flash-lag effect as spatial and temporal. Indeed, interaction of spatial information and temporal information is found in other illusions (e.g., tau and kappa effects; Collyer, Reference Collyer1977; Jones & Huang, Reference Jones and Huang1982).

Moving Target or Flashed Object?

The flash-lag effect involves bias regarding relative positions of the moving target and flashed object, but it is not initially clear if this involves bias regarding judgment of absolute location of the moving target and/or bias regarding judgment of absolute location of the flashed object. The name “flash-lag” implies veridical perception of the moving target and distortion (i.e., lagging) in perceived location of the flashed object (cf. Nijhawan, Reference Nijhawan2001), but some theories of the flash-lag effect posit veridical perception of the flashed object and distortion (displacement) in perceived location of the moving target. Displacement of absolute locations of the moving target and flashed object have been examined in two studies. In one study, a moving target followed an arc, and the flashed object was a dot in front of or behind the target; judgments of absolute locations of the dot and the target at the time the dot was presented revealed forward displacement for the dot and target, with a larger displacement for the target resulting a flash-lag effect (Shi & de’Sperati, Reference Shi and de’Sperati2008). In another study, a briefly presented stationary object was presented above or below the final location of a horizontally moving target, and the stationary object and moving target were displaced forward (Hubbard, Reference Hubbard2008); lack of a difference in displacement is consistent with lack of a flash-lag effect in flash-terminated displays. Thus, the flash-lag effect might be a derived or second-order illusion resulting from more basic illusions involving perceived absolute positions of the moving target and flashed object (Hubbard, Reference Hubbard2014b).

Multi-Sensory or Crossmodal?

Most research on the flash-lag effect involved visual stimuli, but evidence of auditory, haptic, and crossmodal flash-lag effects have been reported. If the moving target is an auditory frequency sweep or a single auditory frequency moving across space, and the flashed object is a briefly presented tone, an auditory flash-lag effect occurs (Alais & Burr, Reference Alais and Burr2003). If a visual target is moving across space and a localized auditory tone is briefly presented, or if an auditory frequency is moving across space and a localized visual stimulus is briefly presented, then a crossmodal flash-lag effect occurs (Alais & Burr, Reference Alais and Burr2003; but see Hine, White, & Chappell, Reference Hine, White and Chappell2003). If a vibration is applied to a finger of a hand moving past a stationary finger on the observer’s other hand, a haptic flash-lag effect occurs (Cellini et al., Reference Cellini, Scocchia and Drewing2016). If participants in a darkened room move their hand, a brief visual flash aligned with the hand is perceived as lagging behind the hand’s position (Nijhawan & Kirschfeld, Reference Nijhawan and Kirschfeld2003). Crossmodal information can also decrease the flash-lag effect; if observers view a visual moving target, an auditory tone briefly presented before or after a visual flash decreases or increases, respectively, the flash-lag effect (Stekelenburg & Vroomen, Reference Stekelenburg and Vroomen2005; Vroomen & de Gelder, Reference Vroomen and de Gelder2004).

Low Level or High Level?

Several studies suggest high-level processes are involved in the flash-lag effect. The flash-lag effect does not occur prior to perceptual grouping (e.g., Watanabe, Reference Watanabe2004; Watanabe et al., Reference Watanabe, Nijhawan, Khurana and Shimojo2001), pattern recognition (e.g., Linares & López-Moliner, Reference Linares and López-Moliner2007), or tilt illusion (Arnold, Durant, & Johnston, Reference Arnold, Durant and Johnston2003). The flash-lag effect is influenced by conceptual knowledge (e.g., Nagai et al., Reference Nagai, Suganuma, Nijhawan, Freyd, Miller, Watanabe, Nijhawan and Khurana2010; Noguchi & Kakigi, Reference Noguchi and Kakigi2008), beliefs regarding control of the target (Ichikawa & Masakura, Reference Ichikawa and Masakura2006, Reference Ichikawa and Masakura2010), and predictability of the flashed object (Baldo & Namba, Reference Baldo and Namba2002; Vreven & Verghese, Reference Vreven and Verghese2005). A visual flash-lag effect is influenced by presentation of an auditory tone (Vroomen & de Gelder, Reference Vroomen and de Gelder2004), and a flash-lag effect occurs if the moving target and flashed object are in different modalities (Alais & Burr, Reference Alais and Burr2003; Nijhawan & Kirschfeld, Reference Nijhawan and Kirschfeld2003). A flash-lag effect occurs if the moving target and flashed object are presented to different eyes (Whitney & Cavanagh, Reference Whitney and Cavanagh2000b) or in random-dot stereograms (e.g., Harris et al., Reference Harris, Duke and Kopinska2006; Nieman et al., Reference Nieman, Nijhawan, Khurana and Shimojo2006). However, Anstis (Reference Anstis2007, Reference Anstis, Nijhawan and Khurana2010) found a flash-lag effect with stimuli based on a chopsticks illusion and a reversed phi illusion, and he suggested the flash-lag effect reflected physical rather than perceived motion. Also, activation patterns in retinal cells appear to extrapolate a moving target’s trajectory (Gollisch & Meister, Reference Gollisch and Meister2010). It is likely the flash-lag effect involves a combination of low-level and high-level processes or involves top-down influences on low-level processes (e.g., Erlhagen, Reference Erlhagen2003; Gauch & Kerzel, Reference Gauch and Kerzel2009; Jancke & Erlhagen, Reference Jancke, Erlhagen, Nijhawan and Khurana2010).

Continuity of Target Behavior?

A flash-lag effect occurs if the moving target exhibits continuous motion or implied motion involving discrete and distinct presentations of the target (Rizk et al., Reference Doricchi, Merola, Aiello, Guariglia, Bruschini and Gevers2009), although the flash-lag effect is weaker with implied motion. The flash-lag effect decreases if the target unpredictably changes direction near the time of the flash (Arrighi et al., Reference Arrighi, Alais and Burr2005; Murakami, Reference Murakami2001b; Vreven & Verghese, Reference Vreven and Verghese2005; Whitney et al., Reference Whitney, Cavanagh and Murakami2000). Random changes in velocity decrease the flash-lag effect (Vreven & Verghese, Reference Vreven and Verghese2005). If target color is constant or exhibits multiple changes, a flash-lag effect occurs, but a single color change corresponding with presentation of the flashed object eliminates the flash-lag effect (Au & Watanabe, Reference Au and Watanabe2013). A single change in target size corresponding with presentation of the flashed object decreases the flash-lag effect (Moore & Enns, Reference Moore and Enns2004). In general, if disruption in continuity of the target can be bridged by a simple extrapolation that connects the pre-change and post-change target (e.g., implied motion using discrete and separate stimuli), then perception of a single target undergoing motion (or other change) is preserved, and a flash-lag effect occurs. However, if a disruption in continuity cannot be bridged by such an extrapolation (e.g., a single change in size or color at the moment the flashed object is presented), then the moving target is no longer perceived as a single target undergoing motion, and the flash-lag effect does not occur.

Relationship to Other Flash-Related Spatial Biases?

The flash-lag effect is one of several phenomena related to relative positions of a flashed object (or other transient change) and a moving target. Other examples include the flash-lead, flash-drag, flash-grab, and flash-jump effects.

Flash-Lead. In the flash-lead effect, judged location of a briefly flashed object leads rather than lags judged location of a moving target. Increasing luminance of a flashed object (Öğmen et al., Reference Bartolomeo, Urbanski, Chokron, Chainay, Moroni and Siéroff2004; Purushothaman et al., Reference Purushothaman, Patel, Bedell and Öğmen1998) or ratio of luminance of the flashed object to luminance of the moving target (Baldo & Caticha, Reference Baldo and Caticha2005) increases likelihood of a flash-lead effect. Whether absolute intensities or ratio of intensities of the moving target and the flashed object is important for flash-lag and flash-lead effects for stimulus dimensions other than luminance is not known. Additionally, precuing location of the flashed object (Hommuk, Bachmann, & Oja, Reference Dodds, van Belle, Peers, Dove, Cusack and Duncan2008), and decreasing contrast between the moving target and flashed object (Arnold et al., Reference Arnold, Ong and Roseboom2009), can result in a flash-lead effect. If a moving target in a flash-terminated display vanishes at the end of target motion, a flash-lead effect can occur (Roulston, Self, & Zeki, Reference Roulston, Self and Zeki2006; but see Kanai et al. Reference Bartolomeo, Urbanski, Chokron, Chainay, Moroni and Siéroff2004). A flash-lead effect rather than a flash-lag effect can be observed for the first item in a perceptual stream (Bachmann & Põder, Reference Bachmann and Põder2001) and when target motion is away from the fovea (Shi & Nijhawan, Reference Shi and Nijhawan2008). Hine et al. (Reference Hine, White and Chappell2003) reported a flash-lead effect with an auditory flashed object (a click) and a visual moving target.

Flash-Drag. In the flash-drag effect, memory for the position of a briefly flashed object is shifted in the direction of nearby motion (cf. Shi & de’Sperati, Reference Shi and de’Sperati2008). For example, position of a flashed grating is shifted in the direction of motion of a larger inducer grating (Fukiage, Whitney, & Murakami, Reference 375Bourlon, Duret, Pradat-Diehl, Azouvi, Loeper-Jeny and Merat-Blanchard2011). Durant and Johnston (Reference Durant and Johnston2004) reported displacement of stationary flashed stimuli aligned with a rotating bar in the direction of rotation. Hubbard (Reference Hubbard2008) reported displacement of a stationary object aligned with the final location of a horizontally moving target in the direction of motion. Eagleman and Sejnowski (Reference 389Eagleman and Sejnowski2007) suggested the flash-lag and flash-drag effects worked in opposite directions, and increases in the flash-drag effect diluted the flash-lag effect. Curiously, a flash-drag effect (Kosovicheva et al., Reference Kosovicheva, Maus, Anstis, Cavanagh, Tse and Whitney2012), but not a flash-lag effect (Fukiage & Murakami, Reference Fukiage and Murakami2010), influences a tilt aftereffect; however, a flash-drag effect does not influence a position aftereffect (Fukiage & Murakami, Reference Fukiage and Murakami2013). The existence of a flash-drag effect might reflect spreading activation from the target resulting in a shift of the center of activation of the flashed object (in a network representing spatial location) toward the target (cf. Hubbard, Reference Hubbard2008). The flash-drag effect often involves a stationary stimulus (e.g., Whitney & Cavanagh, Reference Whitney and Cavanagh2000b), but a flash-drag effect could be hypothesized to occur with movement of the flashed object.

Flash-Grab. If a target moves back-and-forth, trajectory of that oscillation appears shorter than it actually is (Sinico, Parovel, Casco, & Anstis Reference Doricchi, Merola, Aiello, Guariglia, Bruschini and Gevers2009). In the flash-grab effect, a flashed object at the end of an oscillating trajectory (and which occludes the target) is perceived to be at the endpoint of the perceived trajectory rather than the endpoint of the physical trajectory (Cavanagh & Anstis, Reference Cavanagh and Anstis2013). Although the flash-grab effect seems similar to displacement of a flashed object in the direction of target motion in the flash-drag effect, Cavanagh and Anstis (Reference Cavanagh and Anstis2013) argue the flash-grab effect has a different temporal profile, requires more attention, and is larger than the flash-drag effect. The only reported instances of the flash-grab effect involve oscillating targets, and so whether the flash-grab effect is limited to such stimuli remains an open question. The flash-grab effect contributes to a tilt aftereffect (Ge, Wang, & He, Reference Ge, Wang and He2015), might involve feedback signals from higher visual areas to early retinotopic cortex (Zhou, Ge, Wang, Zhang, & He, Reference Zhou, Ge, Wang, Zhang and He2015), and occurs with visual stimuli and auditory stimuli (Krüger et al., Reference Krüger, Collins, Pressnitzer, Kang, Teki and Patrick2015).

Flash-Jump. In the flash-jump effect, a moving object undergoes a transient change in some feature such as color or size, and that change is judged to have occurred farther along the trajectory (Cai & Schlag, Reference Cai and Schlag2001; Gauch & Kerzel, Reference Gauch and Kerzel2008b). The flash-jump effect has also been referred to as the feature flash-drag effect by Eagleman and Sejnowski (Reference 389Eagleman and Sejnowski2007), as localization of a feature change is displaced (i.e., dragged) in the direction of motion. Cai and Schlag (Reference Cai and Schlag2001) suggest the flash-jump effect results from asynchronous feature binding, and this is related to the idea of object updating in Moore and Enns (Reference Moore and Enns2004); specifically, different features are processed at different rates, and information relevant to different features emerges in perceptual awareness at different times. Alternatively, Eagleman and Sejnowski (Reference 389Eagleman and Sejnowski2007) suggested the flash-jump effect resulted from general motion-biasing effects.

Relationship to Non-Flash Spatial Biases?

The flash-lag effect is consistent with several non-flash phenomena. These include spatial biases studied primarily in the laboratory (Fröhlich effect, representational momentum, backward referral, anisotropic distortions) as well as real-world applications (flag errors in association football).

Fröhlich Effect. The perceived onset (initial) location of a moving target is often displaced in the direction of target motion, and this is referred to as a Fröhlich effect (for review, Kerzel, Reference Kerzel, Nijhawan and Khurana2010; Müsseler & Kerzel, Chapter 7 in this volume). Forward displacement in the Fröhlich effect appears similar to forward displacement of the moving target in the flash-lag effect (cf. Kreegipuu & Allik, Reference Kreegipuu and Allik2003). The Fröhlich effect (e.g., Müsseler & Aschersleben, Reference Müsseler and Aschersleben1998) and flash-lag effect (e.g., Wojtach, Sung, Truong, & Purves, Reference Dodds, van Belle, Peers, Dove, Cusack and Duncan2008) increase with increases in target velocity. The Fröhlich effect (Whitney & Cavanagh, Reference Whitney and Cavanagh2000b) and flash-lag effect (Namba & Baldo, Reference Namba and Baldo2004; Vreven & Verghese, Reference Vreven and Verghese2005) are decreased by presentation of a valid cue. The Fröhlich effect (Müsseler & Aschersleben, Reference Müsseler and Aschersleben1998) and flash-lag effect (Baldo & Klein, Reference Baldo and Klein1995) have been suggested to reflect the time required to shift attention. Given such similarities, displacement of a moving target in a flash-initiated display might appear as nothing more than a Fröhlich effect; indeed, the same mechanisms have been suggested to underlie the Fröhlich effect and flash-lag effect (e.g., Eagleman & Sejnowksi, Reference 389Eagleman and Sejnowski2007; Kirschfeld & Kammer, Reference Kirschfeld and Kammer1999; Müsseler, Stork, & Kerzel, Reference Müsseler, Stork and Kerzel2002). However, the flash-lag effect (Baldo, Kihara, et al., Reference Baldo, Kihara, Namba and Klein2002), but not the Fröhlich effect (Müsseler & Aschersleben, Reference Müsseler and Aschersleben1998), is influenced by eccentricity. When measured on the same set of stimuli, the flash-lag effect is larger than the Fröhlich effect (Chappell, Hine, Acworth, & Hardwick, Reference Chappell, Hine, Acworth and Hardwick2006).

Representational Momentum. The perceived offset (final) location of a moving target is often displaced in the direction of target motion, and this is referred to as representational momentum (for review, Hubbard, Reference Hubbard2005b, Reference Hubbard2014a, Chapter 8 in this volume). Forward displacement in representational momentum appears similar to forward displacement of the moving target in the flash-lag effect (Munger & Owens, Reference Munger and Owens2004; Shi & de’Sperati, Reference Shi and de’Sperati2008). Representational momentum (Hubbard & Bharucha, Reference 408Hubbard and Bharucha1988) and the flash-lag effect (Wojtach et al., Reference Dodds, van Belle, Peers, Dove, Cusack and Duncan2008) increase with increases in target velocity. Representational momentum (Hubbard, Kumar, & Carp, Reference Doricchi, Merola, Aiello, Guariglia, Bruschini and Gevers2009) and the flash-lag effect (Namba & Baldo, Reference Namba and Baldo2004; Vreven & Verghese, Reference Vreven and Verghese2005) are decreased by presentation of a valid cue. Representational momentum (Reed & Vinson, Reference Reed and Vinson1996) and the flash-lag effect (Nagai et al., Reference Nagai, Suganuma, Nijhawan, Freyd, Miller, Watanabe, Nijhawan and Khurana2010; Noguchi & Kakigi, Reference Noguchi and Kakigi2008) are influenced by conceptual knowledge of the target. Representational momentum (Hubbard, Reference Hubbard2013c; Hubbard, Blessum, & Ruppel, Reference Hubbard and Blessum2001) and the flash-lag effect (Ichikawa & Masakura, Reference Ichikawa and Masakura2006, Reference Ichikawa and Masakura2010) are influenced by attributions regarding the source of target motion. Representational momentum (Jordan & Hunsinger, Reference Jordan and Hunsinger2008) and the flash-lag effect (Scocchia et al., Reference Doricchi, Merola, Aiello, Guariglia, Bruschini and Gevers2009) are influenced by whether the observer controls the stimulus. Representational momentum (Hayes & Freyd, Reference Hayes and Freyd2002) and the flash-lag effect (Sarich et al., Reference Sarich, Chappell and Burgess2007) are increased under divided attention. Representational momentum (Hubbard & Ruppel, Reference Hubbard and Ruppel1999) and the flash-lag effect (Brenner et al., Reference Brenner, van Beers, Rotman and Smeets2006; Shi & Nijhawan, Reference Shi and Nijhawan2008) increase with motion toward a landmark or fixation. Hubbard (Reference Hubbard2013b, Reference Hubbard2014b) suggested forward displacement of the moving target in representational momentum and in the flash-lag effect are similar, but in the former, displacement of the target is measured relative to the actual position of the target, whereas in the latter, displacement of the target is measured relative to a nearby stationary object.

Backward Referral. Libet and his colleagues had experimental participants make a voluntary finger movement, and those participants noted the time on a clock face at which they decided to initiate movement (Libet, Reference Libet1985; Libet, Wright, & Gleason, Reference Libet, Wright and Gleason1982; Libet, Gleason, Wright, & Pearl, Reference Libet, Gleason, Wright and Pearl1983). The average reported time of the conscious decision was 200 msec prior to movement, but a readiness potential appeared in participants’ EEG 500 msec prior to movement. Libet and colleagues interpreted this as suggesting that a decision to move was implemented before a participant became consciously aware of such a decision, and so the timing of the subjective conscious intent was “adjusted” backward in time to reflect the timing of the unconscious decision (cf. the notion of “postdiction” discussed below). This adjustment of the timing of conscious decision was referred to as backward referral. Alternatively, apparent incongruity in conscious and unconscious decision times might result from a flash-lag effect (Klein, Reference Klein2002; van de Grind, Reference van de Grind2002) or representational momentum (Joordens, Spalek, Razmy, & van Duijn, Reference Bartolomeo, Urbanski, Chokron, Chainay, Moroni and Siéroff2004); in these latter cases, represented location of the moving hand on the clock face is displaced forward from its actual position, and so timing of the conscious decision to move appeared more recent than it actually was.

Anisotropic Distortions. In studies of the flash-lag effect with visual stimuli, the flash-lag effect is larger if targets move toward fixation than away from fixation (Shi & Nijhawan, Reference Shi and Nijhawan2008) and if measured at onset of the flashed object than at offset of the flashed object (Bachmann & Kalev, Reference Bachmann and Kalev1997). The flash-lag effect is larger for targets in the left visual field relative to the right visual field and larger for targets in the upper visual field relative to the lower visual field (Kanai et al., Reference Bartolomeo, Urbanski, Chokron, Chainay, Moroni and Siéroff2004). Effects of perceptual grouping on the flash-lag effect (Watanabe, Reference Watanabe2004; Watanabe et al., Reference Watanabe, Nijhawan, Khurana and Shimojo2001) suggest anisotropic distortions associated with the flash-lag effect; indeed, Watanabe and Yokoi (Reference Watanabe and Yokoi2006, Reference Watanabe and Yokoi2007) suggest the flash-lag effect is a special case of two-dimensional anisotropic distortion. However, it is not clear if anisotropic distortions associated with the flash-lag effect occur with nonvisual or crossmodal stimuli or are limited to visual stimuli. More critically, it is not clear whether anisotropic distortions cause the flash-lag effect or if the flash-lag effect causes anisotropic distortions (cf. Rowland & Durant, Reference Rowland and Durant2014). If the former, it might be possible to link other spatial biases to the flash-lag effect through mechanisms or properties of anisotropy; if the later, spatial representation is more flexible and idiosyncratic than often assumed (cf. Tversky, Chapter 16 in this volume).

Judgments of “Offsides”. In association football (known as soccer in North America), judgment of “offsides” occurs when a player is in the opponent’s half of the field, the ball is played to him by a teammate, and he is closer to the goal line at the moment the pass is initiated than both the ball and the second-to-last defender (the last one being the goalkeeper). Referees are more likely to call an offsides penalty when an offsides is not present (referred to as a flag error) than to not call an offsides penalty when an offsides is present (i.e., more likely to false alarm than to miss; although see Wühr, Fasold, & Memmert, Reference Wühr, Fasold and Memmert2015). Baldo, Ranvaud, and Morya (Reference Baldo, Kihara, Namba and Klein2002) suggested flag errors resulted from a flash-lag effect: The player is analogous to the moving target, passing a ball is analogous to a transient flashed object, and position of the player is displaced forward relative to position of the ball (see Catteeuw, Gilis, Wagemans, & Helsen, Reference Catteeuw, Gilis, Wagemans and Helsen2010; Giles et al., Reference Dodds, van Belle, Peers, Dove, Cusack and Duncan2008). Studies of expert referees, amateur referees, and controls suggest that expert referees are more able to compensate (i.e., avoid flag errors) and that compensation involves a shift in decision-making rather than perception (Catteeuw, Helsen, Gilis, van Roie, & Wagemans, Reference 379Catteeuw, Helsen, Gilis, van Roie and Wagemans2009; Put et al., 2012). Simulations and computer animations are useful in training referees to avoid flag errors (Catteeuw, Gilis, Jaspers, Wagemans, & Helsen, Reference Catteeuw, Gilis, Jaspers, Wagemans and Helsen2010).

Motion Extrapolation

The most well-known theory of the flash-lag effect involves motion extrapolation. Nijhawan (Reference Nijhawan1994, Reference Nijhawan2008) suggested the flash-lag effect occurs because the visual system extrapolates the trajectory of a moving target to compensate for delays in perception due to neural processing times. Without such compensation, perceived position of a moving target would lag behind the actual position of that target. Such an account is similar to representational momentum (see Hubbard, Reference Hubbard2005b, Reference Hubbard2013b, Reference Hubbard2014a, Chapter 8 in this volume), but curiously, representational momentum is not mentioned in discussions of motion extrapolation theory. Motion extrapolation has intuitive appeal; however, several findings initially appear inconsistent with motion extrapolation. A flash-lag effect occurs with random motion (Murakami, Reference Murakami2001b) and unpredictable changes in target direction (Chappell & Hinchy, Reference Chappell and Hinchy2014; Eagleman & Sejnowski, Reference Eagleman and Sejnowski2000b; Whitney, Cavanagh, & Murakami, Reference Whitney, Murakami and Cavanagh2000) and target velocity (Brenner & Smeets, Reference Brenner and Smeets2000); random or unpredictable motion would not (by definition) be predictable and able to be extrapolated. Occurrence of a flash-lag effect in flash-initiated displays (when prediction would not be possible) and lack of a flash-lag effect in flash-terminated displays (when prediction should be maximized) are problematic (but see Nijhawan, Reference Nijhawan2008).

Attention Shift

Attention shift theory suggests attention is initially focused on the moving target, and when the flashed object appears, attention shifts from the moving target to the flashed object. This shift takes time, and during this time, the moving target continues to move. By the time information regarding the flashed object reaches conscious awareness, the moving object has already moved some distance beyond where it was located when the flashed object initially appeared, and so the location of the flashed object is perceived as lagging behind the location of the moving target. An attention shift theory is consistent with effects of target velocity (Nijhawan, Reference Nijhawan1994), cueing (Namba & Baldo, Reference Namba and Baldo2004), and predictability of the flashed object (Baldo & Namba, Reference Baldo and Namba2002; Vreven & Verghese, Reference Vreven and Verghese2005). The attention shift notion was initially proposed by Baldo and Klein (Reference Baldo and Klein1995), but Baldo and colleagues have subsequently taken a more conservative view that distribution and allocation of attention modulate but probably do not cause the flash-lag effect (Baldo & Klein, Reference Baldo, Klein, Nijhawan and Khurana2010; Baldo, Kihara et al., Reference Baldo, Kihara, Namba and Klein2002). Findings inconsistent with attention shift theory include occurrence of a flash-lag effect when the flashed object is embedded in (interleaved with) the moving target (e.g., Khurana & Nijhawan Reference Khurana and Nijhawan1995) and occurrence of a flash-lag effect in flash-initiated stimuli.

Differential Latencies

Differential latencies theory suggests a moving target is processed (and reaches conscious awareness) more quickly than does a stationary flashed object. If a moving target and flashed object were aligned, information regarding the moving target would reach perceptual awareness more quickly; therefore, when information regarding the flashed object reached perceptual awareness, the moving target would already be perceived as further along its trajectory (e.g., Kafaligönül, Patel, Öğmen, Bedell, & Purushothaman, Reference Kafaligönül, Patel, Öğmen, Bedell, Purushothaman, Nijhawan and Khurana2010; Öğmen et al., Reference Bartolomeo, Urbanski, Chokron, Chainay, Moroni and Siéroff2004; Purusothaman et al., Reference Purushothaman, Patel, Bedell and Öğmen1998; Whitney & Murakami, Reference Whitney and Murakami1998; Whitney, Murakami, & Cavanagh, Reference Whitney, Murakami and Cavanagh2000). Findings inconsistent with differential latencies theory include temporal order judgments that indicate flashed objects might be processed at the same speed (e.g., Chappell et al., Reference Chappell, Hine, Acworth and Hardwick2006) or more quickly (e.g., Nijhawan et al., Reference Bartolomeo, Urbanski, Chokron, Chainay, Moroni and Siéroff2004; Raiguel, Lagae, Gulyàs, & Orban, Reference Raiguel, Lagae, Gulyàs and Orban1989) than moving targets, effects of perceptual grouping (Watanabe, Reference Watanabe2004; Watanabe et al., Reference Watanabe, Nijhawan, Khurana and Shimojo2001), effects of semantic meaningfulness (Nagai et al., Reference Nagai, Suganuma, Nijhawan, Freyd, Miller, Watanabe, Nijhawan and Khurana2010; Noguchi & Kakiki, Reference Noguchi and Kakigi2008), existence of visual-auditory crossmodal flash-lag (latencies for auditory stimuli are generally faster than latencies for visual stimuli; Alais & Burr, Reference Alais and Burr2003; Arrighi et al., Reference Arrighi, Alais and Burr2005), and occurrence of a flash-lag effect if the flashed object is in motion (Bachmann & Kalev, Reference Bachmann and Kalev1997).

Postdiction

Postdiction theory suggests the flash-lag effect results from information presented after the flashed object vanished (e.g., Eagleman & Sejnowski, Reference Eagleman and Sejnowski2000a, Reference Eagleman and Sejnowski2000b; Rao, Eagleman, & Sejnowski, Reference Rao, Eagleman and Sejnowski2001). Information regarding location is integrated over brief intervals of time for the flashed object and for the moving target,Footnote ¹ and the length of this integration period ranges from 80 msec (Eagleman & Sejnowksi, Reference Eagleman and Sejnowski2000b) to 500 msec (Krekelberg & Lappe, Reference Krekelberg and Lappe1999). For the flashed object, the average location during the integration period is the same as the individual location signals (the object does not move); however, for the moving target, the average location during the integration period beginning with the presentation of the flashed object is shifted forward as the moving target continues in motion throughout the integration period. This averaged information “adjusts” perception of the target forward at the time of the flash (cf. backward referral), and this was initially referred to as postdiction (Eagleman & Sejnowksi, Reference Eagleman and Sejnowski2000b) and subsequently referred to as motion-biasing (Eagleman & Sejnowski, Reference 389Eagleman and Sejnowski2007). Effects of changes in target velocity or direction of motion after presentation of the flashed object (e.g., Brenner & Smeets, Reference Brenner and Smeets2000; Eagleman & Sejnowksi, Reference Eagleman and Sejnowski2000b; Rotman et al., Reference Rotman, Brenner and Smeets2005) and lack of a flash-lag effect in flash-terminated displays (e.g., Eagleman & Sejnowski, Reference Eagleman and Sejnowski2000b; Moore & Enns, Reference Moore and Enns2004; Watanabe, Reference Watanabe2004) are consistent with postdiction. However, postdiction theory suggests information presented prior to the flashed object should not influence the flash-lag effect, and so effects of pre-flash target behavior (Chappell & Hine, Reference Chappell and Hine2004) and pre-flash cues (Baldo, Kihara et al., Reference Baldo, Kihara, Namba and Klein2002; Namba & Baldo, Reference Namba and Baldo2004; Vreven & Verghese, Reference Vreven and Verghese2005) are inconsistent with postdiction theory.

Perceptual Acceleration

Perceptual acceleration theory suggests the moving target and flashed objects are processed in different perceptual streams. When a perceptual stream first appears, the first few items are processed relatively slowly, but processing latency decreases for additional stimuli in that stream; this is referred to as perceptual acceleration (Bachmann et al., Reference Bachmann, Luiga, Põder and Kalev2003). If a flashed object is in a second stream that begins later than the stream involving the moving target, then the flashed object is processed more slowly than the moving target, and this would result in a flash-lag effect. This is similar to differential latencies theory, but differential latencies theory specifies that processing speed is a function of the type or intensity of a stimulus and not a function of the number of preceding stimuli. The perceptual acceleration theory is consistent with findings of a flash-lag effect when a moving target consists of a sequence of discrete stimuli (e.g., letters; Bachmann & Põder, Reference Bachmann and Põder2001). However, although a moving target and a flashed object that were spatially separated might involve separate processing streams, it is less clear whether a flashed object that overlapped or interleaved the moving target (e.g., disk within an annulus) would be considered to involve separate streams. Existence of a flash-lag effect with flash-initiated stimuli, and lack of a flash-lag effect in flash-terminated displays, appears inconsistent with perceptual acceleration (but see Bachmann, Reference Bachmann2007, Reference Bachmann, Nijhawan and Khurana2010).

The Auditory Looming Bias

The auditory looming bias is the strong tendency for listeners to underestimate the arrival time of an approaching sound source. Essentially listeners perceive that the source has arrived when it is still some distance away (Neuhoff, Reference Neuhoff2001). A looming sound source creates several important sources of dynamic acoustic information that listeners can use to make judgments about the arrival time. Perhaps the most studied is the change in intensity that occurs as a source approaches. Simple changes in intensity are sufficient for activating motion-sensitive areas of the brain (Seifritz et al., Reference Seifritz, Neuhoff, Bilecen, Scheffler, Mustovic and Schachinger2002), and the pattern of rising intensity that occurs as a source approaches can physically specify the arrival time, a variable termed acoustic tau (Guski, Reference Guski1992; Shaw, McGowan, & Turvey, Reference Shaw, McGowan and Turvey1991). For a sound source approaching a listener on a close bypass trajectory, the Doppler shift specifies that the frequency observed at the listening point is slightly higher than that emitted by the source and drops gradually as the source draws near. It then drops dramatically as the source passes the listener and continues to drop gradually as the source recedes. Despite this continual drop in frequency, listeners report a rise in pitch as the source approaches, a phenomenon referred to as the Doppler Illusion (Neuhoff & McBeath, Reference Neuhoff and McBeath1996). The illusion is likely due to the rising intensity that occurs as the source approaches and the integral processing of pitch and loudness (McBeath & Neuhoff, Reference McBeath and Neuhoff2002; Neuhoff & McBeath, Reference Neuhoff and McBeath1996; Neuhoff, McBeath, & Wanzie, Reference Neuhoff, McBeath and Wanzie1999).

Rosenblum, Carello, and Pastore (Reference Rosenblum, Carello and Pastore1987) examined the relative effectiveness of Doppler shift, interaural time differences, and overall intensity change in cuing listeners to the arrival time of a looming sound.Footnote ¹ Intensity change was found to be the dominant cue to the point of closest approach for a passing sound source, followed by interaural temporal differences, then the Doppler effect. Performance was best under full cue conditions. However, even under full cue conditions, listeners still exhibited a systematic bias to hear the sound arrive before it actually did. Subsequent work showed that providing explicit feedback on the accuracy of the judgments after each trial diminished but did not eliminate the anticipatory bias (Rosenblum, Gordon, & Wuestefeld, Reference Rosenblum, Gordon and Wuestefeld2000).

There are other potential sources of acoustic information that listeners may use in judging the arrival time of a looming sound, which have yet to be systematically investigated. For example, the ratio of direct to reverberant sound increases as the source draws closer to the listener. The spectral profile of the sound at the listening point also changes due to the decrease in atmospheric damping of high frequencies as the source approaches. Some work has shown greater physiological effects of looming sounds when multiple cues are employed over conditions in which just amplitude changes (Bach, Neuhoff, Perrig, & Seifritz, Reference Bach, Neuhoff, Perrig and Seifritz2009). This implies that listeners are sensitive to these additional cues and may in fact use them in judging arrival time. Other work has shown that the perceived urgency of the sound source can influence judged arrival time, with more urgent sounds being perceived to arrive sooner (Gordon, Russo, & MacDonald, Reference Gordon, Russo and MacDonald2013; Neuhoff, Hamilton, Gittleson, & Mejia, Reference Neuhoff, Hamilton, Gittleson and Mejia2014).

The auditory looming bias is closely linked to the bias to hear rising intensity as changing in loudness more than equivalent falling intensity. If listeners overestimate the approach of a looming sound and loudness change is the dominant cue to approach, then the overestimation of rising loudness may be at the heart of the auditory looming bias. However, if we are to argue that this perceptual bias is an adaptation shaped by evolution, then it should be specific to the conditions under which it would provide the greatest advantage in the natural listening environment over our evolutionary history. To test this prediction, Neuhoff (Reference Neuhoff1998) presented listeners with rising and falling intensity tones and asked them to use a slider to indicate the amount of loudness change they heard in each sound. Rising intensity was consistently heard to change more than equivalent falling intensity, and the louder the range of intensity change presented, the greater the disparity between rising and falling loudness change. In a natural listening environment where closer sounds are louder than equivalent distant sounds, these findings suggest a perceptual priority for looming sounds that are close over those that are more distant. Although the effect occurred with harmonic tones, it did not occur when listeners were presented with broadband noise, a finding that is also consistent with the priorities of localizing moving sound sources in a natural environment. Periodic sounds that have a tonal quality are produced by a wide variety of biological organisms and can act as a reliable marker for the identity of a single source. Although broadband noise can be produced by biological organisms, it can also be produced by widely dispersed nonbiological sources (e.g., wind and rain) for which localization may be less important. Thus, the looming bias is most robust under conditions in which it would be most advantageous to survival (see also McCarthy & Olsen, Reference McCarthy and Olsen2017). Recent magnetoencephalography work supports this hypothesis by showing that strength of sustained magnetic fields over bilateral temporal sensors linearly tracks intensity change in a looming harmonic tone but not in looming broadband noise (Bach, Furl, Barnes, & Dolan, Reference Bach, Furl, Barnes and Dolan2015)

The argument for the looming bias as an adaptation was initially challenged because of the limited number of conditions under which the effect was first demonstrated (Canevet, Scharf, Schlauch, Teghtsoonian, & Teghtsoonian, Reference Canevet, Scharf, Schlauch, Teghtsoonian and Teghtsoonian1999; Neuhoff, Reference Neuhoff1999). However, it has now been replicated under a wide variety of experimental conditions and settings (DiGiovanni & Schlauch, Reference DiGiovanni and Schlauch2007; Grassi, Reference Grassi2010; Grassi & Darwin, Reference Grassi and Darwin2006; Olsen & Stevens, Reference Olsen and Stevens2010; Olsen, Stevens, & Tardieu, Reference 438Olsen, Stevens and Tardieu2010; Ponsot, Meunier, Kacem, Chatron, & Susini, Reference Ponsot, Meunier, Kacem, Chatron and Susini2015; Ponsot, Susini, & Meunier, Reference Ponsot, Susini and Meunier2015; Teghtsoonian, Teghtsoonian, & Canevet, Reference Teghtsoonian, Teghtsoonian and Canevet2005). One of the first studies to replicate the effect used a moving loudspeaker in an outdoor environment (Neuhoff, Reference Neuhoff2001). Blindfolded listeners made terminal egocentric distance estimates of a moving loudspeaker that either approached or receded. The sounding loudspeaker approached from a distance of 12.2 meters and came to rest 6.1 meters from the listener. The receding loudspeaker began directly in front of the listener and stopped at the same distance, 6.1 meters from the listener. Analogous to the rising and falling loudness sounds presented over headphones, the results showed that approaching sounds were perceived to stop closer to the listener than receding sounds, and tones were perceived as stopping closer than noise despite an equal stopping distance from the observation point in all conditions.

The Logic Behind the Adaptation: Error Management Theory

Error Management Theory (EMT) predicts that a wide range of social, cognitive, and perceptual biases have evolved because they increase the likelihood of survival and reproduction. EMT proposes that biases will evolve when judgments are made under conditions of uncertainty, when the decisions have historically had an impact on evolutionary fitness, and when there is an asymmetric cost of making false-positive and false-negative errors (Haselton & Buss, Reference Haselton and Buss2000; Haselton & Nettle, Reference Haselton and Nettle2006; Haselton et al., Reference Doricchi, Merola, Aiello, Guariglia, Bruschini and Gevers2009). All of these conditions are met when a sound source approaches a listener. All perceptual judgments are made under a degree of uncertainty (Mathys et al., Reference Lewkowicz and Minar2014), and predicting the arrival time of a looming sound source may have more uncertainty than many other perceptual judgments. Such decisions could also have life or death consequences and thus undoubtedly have had an impact on evolutionary fitness. Finally, the cost of a false positive (responding too early to a looming sound source by escape or avoidance behaviors) pales in comparison to the potentially deadly cost of a false negative (responding too late). Thus, an organism whose neural architecture represented looming sounds as closer than they actually were would have a selective advantage.

In the context of this discussion, the question is often posed: Wouldn’t it be more advantageous to have veridical perception of a looming sound source and let the listener cognitively decide what appropriate actions should be taken? There are several critical reasons why the answer to this question is “no.” First, let us contrast a hypothetical listener with veridical perception to a listener with a bias to hear looming sounds as closer than they are. Each is tasked with predicting the arrival time of a dangerous looming source. On average, the listener with veridical perception predicts perfectly the arrival time of the source, a point we will call 0 seconds to contact. The listener with the looming bias responds consistently early, for example at an average of 500 msec before contact. However, each listener also has a degree of variability associated with their arrival time judgments, each sometimes responding slightly earlier or later than their respective means. Early judgments are not problematic for either listener, as they provide slightly more time than expected to prepare for the arrival of the source. However, a listener with veridical perception who responds just a half-second late is responding after the source has already arrived. Even if the listener with veridical perception makes the cognitive decision to initiate motor behaviors sooner rather than later in order to prepare for the arrival of the source, their responses are still based on a “veridical” judgment of arrival time that in this instance is a half-second too late and pushes the motor response back by a potentially perilous half-second as well. A late response by the listener with the looming bias still leaves enough time to respond safely.

It is also the case that cognitive resources are limited. If the decision to engage the motor system in the face of a looming sound source were entirely under conscious control, then anyone engaged with a high cognitive load at the time would be disadvantaged in that there would be fewer cognitive resources to devote to the approaching danger. However, a recent study that manipulated cognitive load while participants judged the arrival of a looming sound found just the opposite. McGuire, Gillath, and Vitevitch (2015) asked listeners to judge when a looming sound would reach them while under high cognitive load (memorizing a seven-digit number) or low cognitive load (memorizing a two digit number). They found that the looming bias was significantly larger under high cognitive load. That listeners respond sooner rather than later under high cognitive load suggests that the bias to hear sounds as closer than actual is an automatic process that requires little effortful cognitive processing. Rather than (or at least in addition to) a “decision to respond early,” the looming bias appears to be a perceptual phenomenon that has evolved to keep organisms safe. This finding is consistent with work in representational momentum and boundary extension that also shows an increase in the magnitude of perceptual bias under high cognitive load (Hayes & Freyd, Reference Hayes and Freyd2002; Hubbard, Hutchison, & Courtney, Reference Hubbard, Hutchison and Courtney2010; Intraub, Daniels, Horowitz, & Wolfe, Reference Intraub, Daniels, Horowitz and Wolfe2008).

Converging Evidence for the Looming Bias Adaptation

Behavioral evidence. A wide range of behavioral research has now demonstrated that looming sounds are treated with priority by the auditory system and that listeners demonstrate a consistent underestimation of distance and arrival time when faced with a looming sound (Neuhoff, Reference Neuhoff1998, Reference Neuhoff2001, Reference Neuhoff2016; Neuhoff et al., Reference Lewkowicz and Minar2014; Neuhoff, Long, & Worthington, Reference Neuhoff, Long and Worthington2012; Riskind, Kleiman, Seifritz, & Neuhoff, Reference Riskind, Kleiman, Seifritz and Neuhoff2014; Rosenblum, Wuestefeld, & Saldana, Reference Rosenblum, Wuestefeld and Saldana1993; Rosenblum et al., Reference Rosenblum, Carello and Pastore1987; Rosenblum et al., Reference Rosenblum, Gordon and Wuestefeld2000). The prioritization of looming sounds is present in infancy. Infants as young as four months old show significant differential responding to looming versus receding sounds by exhibiting defensive avoidance responses to looming sounds that do not occur with equivalent receding sounds (Freiberg, Tually, & Crassini, Reference Freiberg, Tually and Crassini2001). By six months, infants have better discrimination abilities for looming versus receding sounds (Morrongiello, Hewitt, & Gotowiec, Reference Morrongiello, Hewitt and Gotowiec1991).

Sex differences have also been demonstrated in the looming bias, with women tending to perceive auditory arrival time as occurring sooner than do men (Neuhoff, Planisek, & Seifritz, Reference Neuhoff, Planisek and Seifritz2009; Schiff & Oldak, Reference Schiff and Oldak1990). In the study of the evolution of behavior, sex differences can be a key piece of evidence for behavioral adaptations. To the extent that men and women have faced different challenges to survival and reproduction over our evolutionary history, we should expect slightly different behavioral adaptations to have evolved to deal with these challenges (Buss, Reference Buss1995; Byrd-Craven & Geary, Reference Byrd-Craven and Geary2007).

Although judging the arrival time of a looming sound is essentially a spatial transformation task, the sex difference in the perception of looming sounds is likely not the product of the well-known male advantage in spatial transformation (Kimura, Reference Kimura1999; Silverman, Choi, & Peters, Reference Silverman, Choi and Peters2007; Voyer, Voyer, & Bryden, Reference Voyer, Voyer and Bryden1995). If it were, we would expect sex differences for the perception of sounds that move both toward and away from the listener. However, Neuhoff et al. (Reference Bach, Neuhoff, Perrig and Seifritz2009) presented male and female listeners with both approaching and receding sounds that stopped equidistant from the listening point. Women perceived the looming sounds to be significantly closer than did men. However, there was no difference between the male and female judgments for the receding sounds. If sex differences in the perception of looming sounds were simply the result of more accurate spatial transformation abilities by men, then we should expect those same differences to occur for receding sounds.

That there were no sex differences in the perceived distance of receding sounds may highlight a particular differential environmental challenge that men and women have faced over our evolutionary history – dealing with an approaching threat. Some of the most reliable differences between males and females are in physical strength, running speed (Nicolay & Walker, Reference Nicolay and Walker2005; Whipp & Ward, Reference Whipp and Ward1992). Both of these characteristics could be crucial in dealing with a dangerous looming sound source. Thus, women would stand to benefit from a larger margin of safety in anticipating the arrival of a looming source. Essentially, those least well prepared to engage a dangerous looming sound source should have the greatest auditory looming bias.

Evidence to support this hypothesis comes from work showing that the magnitude of the looming bias is negatively correlated with strength and physical fitness (Neuhoff et al., Reference Neuhoff, Long and Worthington2012). Individual within-sex correlations were also significant, suggesting that the sex differences in the looming bias may be largely due to differences in strength and fitness rather than biological sex per se. The magnitude of the looming bias is also modulated by factors such as affect, anxiety, depression, and even schizophrenia (Bach, Buxtorf, Strik, Neuhoff, & Seifritz, Reference Bach, Buxtorf, Strik, Neuhoff and Seifritz2011; Ferri, Tajadura-Jimenez, Valjamae, Vastano, & Costantini, Reference Ferri, Tajadura-Jimenez, Valjamae, Vastano and Costantini2015; Neuhoff et al., Reference Lewkowicz and Minar2014; Tajadura-Jimenez, Valjamae, Asutay, & Vastfjall, Reference Tajadura-Jimenez, Valjamae, Asutay and Vastfjall2010)

Comparative Evidence. The argument that a given human behavior is an evolutionary adaptation can be made stronger if the behavior is also found in a closely related species. Thus, if the human bias to perceive looming sounds as closer than actual is an adaptation, then we might expect to observe the bias in related species that have faced similar evolutionary challenges. Ghazanfar, Neuhoff, and Logothetis (Reference Ghazanfar, Neuhoff and Logothetis2002) presented rhesus monkeys with the same simulated looming and receding sounds that were presented to human listeners in the work by Neuhoff (Reference Neuhoff1998). They found a preferential orienting response to looming sounds over receding sounds that matched the pattern of results found in humans. As with humans, the bias occurred for harmonic tones but not for broadband noise. The concomitant neural activity that underlies the perceptual priority for looming sounds shows the same directional asymmetry (Hall & Moore, Reference Hall and Moore2003). Activity in the lateral belt auditory cortex of monkeys is stronger with looming than with receding sounds, and the processing of looming stimuli appears to involve an interaction between the auditory cortex and the superior temporal sulcus that is not apparent with equivalent receding stimuli (Maier, Chandrasekaran, & Ghazanfar, Reference Maier, Chandrasekaran and Ghazanfar2008; Maier & Ghazanfar, Reference Maier and Ghazanfar2007).

Physiological Evidence. Support for the hypothesis that any perceptual trait is an evolutionary adaptation can be strengthened by identifying specific physiological mechanisms that support the trait. Seifritz et al. (Reference Seifritz, Neuhoff, Bilecen, Scheffler, Mustovic and Schachinger2002) used neuroimaging to examine the neural processing of looming sounds in comparison with receding sounds. They found that looming sounds preferentially activate a distributed neural network that is known to subserve auditory motion perception, attention, and motor planning. These findings support an earlier hypothesis by Guski (Reference Guski1992) that suggested that the function of the auditory system in the face of a looming sound is to provide input into a decision about the appropriate motor behaviors in which to engage. Faced with a looming sound, the auditory system provides advanced warning as evidenced by enhanced autonomic responses. Looming sounds when compared with equivalent receding sounds produce stronger amygdala activation, greater skin conductance, more robust pupil dilation, enhanced phasic alertness, and greater emotional arousal (Bach et al., Reference Bach, Schachinger, Neuhoff, Esposito, Di Salle, Lehmann and Seifritz2008; Bach et al., Reference Bach, Neuhoff, Perrig and Seifritz2009; Ferri et al., Reference Ferri, Tajadura-Jimenez, Valjamae, Vastano and Costantini2015; Fletcher et al., Reference Fletcher, Nicholas, Shakespeare, Downey and Golden2015; Tajadura-Jimenez et al., Reference 441Peyrin, Michel and Schwartz2010).

Cues to Visual Looming

As an object approaches an observer,. the image cast on the retina dilates. This optical dilation was one of the first investigated sources of information in judging the arrival time of a looming visual object. The inverse of the rate of dilation (called optical tau) can specify time-to-arrival under some conditions, and observers have been shown to be sensitive to this information (Kaiser & Mowafy, Reference Kaiser and Mowafy1993; Lee, Reference Lee1976; Lee & Reddish, Reference Lee and Reddish1981; Regan & Hamstra, Reference Regan and Hamstra1993; Todd, Reference Todd1981). Tau was initially proposed as a candidate for completely explaining how observers judge visual time-to-arrival (Lee, Reference Lee1976; Savelsbergh, Whiting, & Bootsma, Reference Savelsbergh, Whiting and Bootsma1991; Turvey & Carello, Reference Turvey and Carello1986). However, this version of tau is limited in that it breaks down when looming objects do not have a constant acceleration, are not symmetrical, and are not on a collision course with the observer (Tresilian, Reference Tresilian1999). Optical tau alone also fails to account for how observers can predict the arrival of very small objects or objects that undergo short falls from gravity (Gray & Regan, Reference Gray and Regan1998; Tresilian, Reference Tresilian1993). Subsequent work showed that optical tau is just one of a number of available cues. Several other dynamic tau variables, heuristics, and even pictorial cues such as image size can be used to estimate arrival time (DeLucia, Reference DeLucia1991, Reference DeLucia, Hecht and Savelsbergh2004; Kaiser & Mowafy, Reference Kaiser and Mowafy1993; Tresilian, Reference Tresilian1993, Reference Tresilian1994). For a review, see Tresilian (Reference Tresilian1999).

Bias for Looming Visual Motion

Despite the relatively accurate perception of visual arrival time under full viewing conditions, there are nonetheless well-documented asymmetries in the perceptual processing of looming versus receding motion. For example, it has been known more than 100 years ago that the motion aftereffect for looming motion persists significantly longer than that for equivalent receding motion (Scott, Lavender, McWhirt, & Powell, Reference Scott, Lavender, McWhirt and Powell1966; Wohlgemuth, Reference Wohlgemuth1911). More recent work has shown that the perceptual asymmetry in perceiving looming and receding develops within the first few months of life (Shirai et al., Reference Doricchi, Merola, Aiello, Guariglia, Bruschini and Gevers2009; Shirai, Kanazawa, & Yamaguchi, Reference Shirai, Kanazawa and Yamaguchi2004, Reference Shirai, Kanazawa and Yamaguchi2006). Observers also perceive looming motion as faster than receding motion, detect the onset of looming motion sooner, and show better detection of changes in looming stimuli than in receding ones (K. Ball & Sekuler, Reference Ball and Sekuler1980; Bex & Makous, Reference Bex and Makous1997; Geesaman & Qian, Reference Geesaman and Qian1996; Petersik & Thiel, Reference Petersik and Thiel2010). Under conditions of uncertainty, viewers show a predisposition to perceive objects as looming rather than receding. For example, C. F. Lewis and McBeath (Reference Lewis and McBeath2004) presented viewers with a 3D bistable apparent motion display that could be perceived as either looming or receding. They found that viewers showed a significant bias to perceive the display as looming.

The emotional characteristics of a looming visual stimulus can influence perceived arrival time. Looming threatening stimuli (spiders and snakes) are perceived to arrive more quickly than nonthreatening stimuli (bunnies and butterflies), and the ratings of fear of the stimulus are correlated with perceived arrival time (Vagnoni, Lourenco, & Longo, Reference Vagnoni, Lourenco and Longo2012, Reference Vagnoni, Lourenco and Longo2015). The more fearful the viewer, the sooner the object is perceived to have arrived. Other threatening stimuli (e.g., threatening faces) show similar effects (Brendel, DeLucia, Hecht, Stacy, & Larsen, Reference Brendel, DeLucia, Hecht, Stacy and Larsen2012). However, the notion that “threat” alone is the critical factor at work here is likely an oversimplification. More recent work has also implicated the role of arousal and stimulus complexity. For example, highly arousing positive stimuli (erotica and money) are perceived to arrive as soon as fearful stimuli, and pictorial stimuli, in general, are perceived to arrive sooner that simple colored rectangles (Brendel, Hecht, DeLucia, & Gamer, Reference Brendel, Hecht, DeLucia and Gamer2014).

Looming and receding visual stimuli also have asymmetrical effects on attention. Objects that approach an observer attract attention and are treated with priority. For example, in a visual search task, increasing the number of distractors in a search for a receding target significantly increases search time. However, the same increase in the number of distractors has no effect on search time for looming targets (Takeuchi, Reference Takeuchi1997). This suggests that detecting looming stimuli occurs automatically. Subsequent work has shown that looming, but not receding, objects capture attention even when they are not relevant to the task at hand (Franconeri & Simons, Reference Franconeri and Simons2003). The attentional capture effects of looming stimuli appear to be subserved by covert attentional mechanisms that do not require effortful cognitive processing (Kahan, Colligan, & Wiedman, Reference Kahan, Colligan and Wiedman2011; J. E. Lewis & Neider, Reference Lewis and Neider2015). The evolutionary implications of the priority for looming objects are underscored by the finding that the effects of looming stimuli are magnified when the stimuli are on a collision path with the observer and are not dependent on the sudden onset of motion (Lin, Franconeri, & Enns, Reference Lin, Franconeri and Enns2008; von Muhlenen & Lleras, Reference von Muhlenen and Lleras2007).

Bias for Receding Visual Motion?

Despite the wealth of data demonstrating a perceptual bias for looming visual motion, there are a number of apparently conflicting studies that find a bias for receding motion. For example, observers show better sensitivity as measured by a discrimination task for a contracting pattern of dots than an expanding pattern of dots (Edwards & Badcock, Reference Edwards and Badcock1993; Edwards & Ibbotson, Reference Edwards and Ibbotson2007). Viewers have also demonstrated better sensitivity to acceleration when viewing receding versus looming dot patterns (Mueller & Timney, Reference Mueller and Timney2014). Some researchers have suggested that the better discrimination for these receding optic flow fields is related to postural stability, where falling backward (which creates receding optic flow) is a greater danger than falling forward (Edwards & Ibbotson, Reference Edwards and Ibbotson2007; Mueller & Timney, Reference Mueller and Timney2014; but see Holten, Donker, Stuit, Verstraten, & van der Smagt, Reference Holten, Donker, Stuit, Verstraten and van der Smagt2015). Other work suggests that the direction of asymmetry is also dependent on the speed of the optic flow pattern, which varies across studies (Naito, Sato, & Osaka, Reference Naito, Sato and Osaka2010).

Variability in the nature of the tasks employed may also in part be responsible for the conflicting results. The majority of the studies that find an advantage in the perception of receding stimuli use optic flow fields that are composed of dots. The analogous real-world looming condition would be moving through the world without any indication that a collision is imminent. On the other hand, many of the studies that show a perceptual advantage for looming present a target stimulus that appears to approach the observer on a collision course. Given these differences, both the “postural stability” and the “looming threat” hypotheses may have merit depending on the specific circumstances. Another consideration is that the discrimination tasks typically used in studies that find an advantage for receding stimuli may require more effortful cognitive processing than, for example, visual search or time-to-arrival where attention is captured automatically or where a defensive motor response is appropriate (e.g., Franconeri & Simons, Reference Franconeri and Simons2003; King et al., Reference King, Dykeman, Redgrave and Dean1992; J. E. Lewis & Neider, Reference Lewis and Neider2015; Lin et al., Reference Dodds, van Belle, Peers, Dove, Cusack and Duncan2008). Because the visual features of a looming object are thought to be processed without depleting effortful cognitive resources (Kahan et al., Reference 375Bourlon, Duret, Pradat-Diehl, Azouvi, Loeper-Jeny and Merat-Blanchard2011; J. E. Lewis & Neider, Reference Lewis and Neider2015), looming objects may impact discrimination and visual search differentially. Looming stimuli activate motor defense mechanisms and responses of the autonomic nervous system (King et al., Reference King, Dykeman, Redgrave and Dean1992; Low et al., Reference Dodds, van Belle, Peers, Dove, Cusack and Duncan2008; Skarratt et al., Reference Doricchi, Merola, Aiello, Guariglia, Bruschini and Gevers2009; Skarratt et al., Reference Lewkowicz and Minar2014). This may facilitate the automatic responses to looming objects that do not require effortful processing but interfere with effortful cognitive judgments such as discrimination. Essentially, the different tasks may differentially invoke either visuo-motor or visuo-cognitive systems and account for the conflicting findings (Goodale & Milner, Reference Goodale and Milner1992; Tresilian, Reference Tresilian1995).